Finite Group Databasebeta

← #34453623

Subgroups — #34453623

Order 20224.

2636 conjugacy classes of subgroups.

The subgroup lattice has 1672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099201C211yesmaximal, characteristic
2#23766561C211yesmaximal, characteristic, complemented
3#23766559C211yesmaximal, characteristic, complemented
4#23766544C211yesmaximal, characteristic, complemented
5#23766538C211yesmaximal, characteristic, complemented
6#23766511C211yesmaximal, characteristic, complemented
7#23766445C211yesmaximal, characteristic, complemented
8#23766441C211yesmaximal, characteristic, complemented
9#23766388C211yesmaximal, characteristic, complemented
10#23766377C211yesmaximal, characteristic, complemented
11#23766338C211yesmaximal, characteristic, complemented
12#23766336C211yesmaximal, characteristic, complemented
13#23766252C211yesmaximal, characteristic, complemented
14#23766242C211yesmaximal, characteristic, complemented
15#23766218C211yesmaximal, characteristic, complemented
16#23766212C211yesmaximal, characteristic, complemented
17#23766190C211yesmaximal, characteristic, complemented
18#23766166C211yesmaximal, characteristic, complemented
19#23766155C211yesmaximal, characteristic, complemented
20#23766103C211yesmaximal, characteristic, complemented
21#23766066C211yesmaximal, characteristic, complemented
22#23766056C211yesmaximal, characteristic, complemented
23#23766054C211yesmaximal, characteristic, complemented
24#23766040C211yesmaximal, characteristic, complemented
25#23765997C211yesmaximal, characteristic, complemented
26#23765992C211yesmaximal, characteristic, complemented
27#23765974C211yesmaximal, characteristic, complemented
28C4×#14579133C211yesmaximal, characteristic, complemented
29#23765840C211yesmaximal, characteristic, complemented
30C2×#19098455C211yesmaximal, characteristic, complemented
31C79×#2339C211yesmaximal, characteristic, complemented
32C22×D4×D79C2211yescharacteristic
33#19099201C4116yescomplemented
34C2×#14579150C2211yescharacteristic
35C2×#14579144C2211yescharacteristic
36C2×#14579144C2211yescharacteristic
37C2×#14579137C2211yescharacteristic
38C2×#14579135C2211yescharacteristic
39C2×#14579133C2211yescharacteristic
40C2×#14579133C2211yescharacteristic
41C2×#14579129C2211yescharacteristic
42C2×#14579129C2211yescharacteristic
43C2×D4×Dic79C2211yescharacteristic
44C2×C4×C22⋊D79C2211yescharacteristic
45C2×C4×C22⋊D79C2211yescharacteristic
46C2×C4×C22⋊D79C2211yescharacteristic, complemented
47C2×C4×C22⋊D79C2211yescharacteristic, complemented
48C2×(C22⋊D79)⋊C4C2211yescharacteristic
49C2×#14579120C2211yescharacteristic, complemented
50C2×#14579117C2211yescharacteristic, complemented
51C22×C4⋊Dic79C2211yescharacteristic, complemented
52C22×(C2×D79)⋊C4C2211yescharacteristic
53C22×(C2×D79)⋊C4C2211yescharacteristic
54C22×(C2×D79)⋊C4C2211yescharacteristic
55C22×(C2×D79)⋊C4C2211yescharacteristic
56C2×C22⋊C4×D79C2211yescharacteristic
57C2×C22⋊C4×D79C2211yescharacteristic
58C22×C4×Dic79C2211yescharacteristic, complemented
59#19098470C2211yescharacteristic, complemented
60#19098470C2211yescharacteristic, complemented
61#19098466C2211yescharacteristic, complemented
62#19098466C2211yescharacteristic, complemented
63#19098463C2211yescharacteristic
64#19098463C2211yescharacteristic
65#19098463C2211yescharacteristic
66#19098463C2211yescharacteristic
67#19098463C2211yescharacteristic, complemented
68#19098463C2211yescharacteristic, complemented
69#19098460C2211yescharacteristic, complemented
70#19098460C2211yescharacteristic, complemented
71#19098460C2211yescharacteristic, complemented
72#19098458C2211yescharacteristic, complemented
73#19098457C2211yescharacteristic, complemented
74#19098457C2211yescharacteristic, complemented
75#19098457C2211yescharacteristic, complemented
76#19098457C2211yescharacteristic, complemented
77#19098455C2211yescharacteristic
78#19098455C2211yescharacteristic
79#19098455C2211yescharacteristic
80#19098455C2211yescharacteristic
81#19098455C2211yescharacteristic
82#19098455C2211yescharacteristic
83#19098455C2211yescharacteristic, complemented
84#19098455C2211yescharacteristic, complemented
85#19098455C2211yescharacteristic, complemented
86#19098455C2211yescharacteristic, complemented
87#19098455C2211yescharacteristic, complemented
88#19098455C2211yescharacteristic, complemented
89#19098455C2211yescharacteristic, complemented
90#19098454C2211yescharacteristic
91#19098454C2211yescharacteristic
92#19098454C2211yescharacteristic, complemented
93#19098453C2211yescharacteristic
94#19098453C2211yescharacteristic
95#19098453C2211yescharacteristic, complemented
96#19098453C2211yescharacteristic, complemented
97#19098453C2211yescharacteristic, complemented
98#19098452C2211yescharacteristic
99#19098452C2211yescharacteristic
100#19098452C2211yescharacteristic, complemented
101#19098451C2211yescharacteristic, complemented
102#19098451C2211yescharacteristic, complemented
103#19098450C2211yescharacteristic, complemented
104#19098450C2211yescharacteristic, complemented
105#19098450C2211yescharacteristic, complemented
106#19098448C2211yescharacteristic, complemented
107#19098448C2211yescharacteristic, complemented
108#19098447C2211yescharacteristic, complemented
109#19098446C2211yescharacteristic, complemented
110#19098446C2211yescharacteristic, complemented
111#19098445C2211yescharacteristic, complemented
112#19098444C2211yescharacteristic, complemented
113#19098443C2211yescharacteristic
114#19098443C2211yescharacteristic
115#19098443C2211yescharacteristic, complemented
116#19098443C2211yescharacteristic, complemented
117#19098442C2211yescharacteristic
118#19098442C2211yescharacteristic
119#19098442C2211yescharacteristic
120#19098442C2211yescharacteristic, complemented
121#19098442C2211yescharacteristic, complemented
122#19098441C2211yescharacteristic
123#19098441C2211yescharacteristic
124#19098441C2211yescharacteristic
125#19098441C2211yescharacteristic
126#19098440C2211yescharacteristic
127#19098439C2211yescharacteristic
128#19098439C2211yescharacteristic
129#19098439C2211yescharacteristic, complemented
130#19098439C2211yescharacteristic, complemented
131#19098437C2211yescharacteristic, complemented
132#19098437C2211yescharacteristic, complemented
133#19098437C2211yescharacteristic, complemented
134#19098437C2211yescharacteristic, complemented
135#19098437C2211yescharacteristic, complemented
136#19098436C2211yescharacteristic, complemented
137#19098435C2211yescharacteristic, complemented
138#19098434C2211yescharacteristic, complemented
139#19098430C2211yescharacteristic, complemented
140#19098425C2211yescharacteristic
141#19098425C2211yescharacteristic
142#19098424C2211yescharacteristic, complemented
143#19098423C2211yescharacteristic, complemented
144#19098423C2211yescharacteristic, complemented
145#19098423C2211yescharacteristic, complemented
146#19098423C2211yescharacteristic, complemented
147#19098422C2211yescharacteristic
148#19098421C2211yescharacteristic, complemented
149#19098418C2211yescharacteristic
150#19098418C2211yescharacteristic
151#19098418C2211yescharacteristic
152#19098418C2211yescharacteristic
153C4×Dic79⋊C4C2211yescharacteristic, complemented
154#19098414C2211yescharacteristic, complemented
155#19098414C2211yescharacteristic, complemented
156C22⋊C4×Dic79C2211yescharacteristic, complemented
157C22⋊C4×Dic79C2211yescharacteristic, complemented
158C22⋊C4×Dic79C2211yescharacteristic, complemented
159C22⋊C4×Dic79C2211yescharacteristic, complemented
160C4×(C2×D79)⋊C4C2211yescharacteristic, complemented
161C4×(C2×D79)⋊C4C2211yescharacteristic, complemented
162C4×(C2×D79)⋊C4C2211yescharacteristic, complemented
163C4×C22⋊Dic79C2211yescharacteristic, complemented
164C4×C22⋊Dic79C2211yescharacteristic, complemented
165C4×C22⋊Dic79C2211yescharacteristic, complemented
166#19098410C2211yescharacteristic
167#19098410C2211yescharacteristic, complemented
168#19098410C2211yescharacteristic, complemented
169#19098410C2211yescharacteristic, complemented
170#19098408C2211yescharacteristic, complemented
171#19098408C2211yescharacteristic, complemented
172C2×C79⋊#95C2211yescharacteristic, complemented
173C22×#41×C79C2211yescharacteristic
174C2×C4×D4×C79C2211yescharacteristic, complemented
175C2×C4×D4×C79C2211yescharacteristic, complemented
176#391×C79C2211yescharacteristic, complemented
177#391×C79C2211yescharacteristic, complemented
178#386×C79C2211yescharacteristic
179#386×C79C2211yescharacteristic
180#386×C79C2211yescharacteristic, complemented
181#386×C79C2211yescharacteristic, complemented
182#381×C79C2211yescharacteristic, complemented
183#381×C79C2211yescharacteristic, complemented
184#380×C79C2211yescharacteristic, complemented
185C4×C22⋊C4×C79C2211yescharacteristic, complemented
186C2×#95×C79C2211yescharacteristic, complemented
187C2×#95×C79C2211yescharacteristic, complemented
188C24×D79C2311yescharacteristic
189C24×D79C2311yescharacteristic
190C22×D316C2311yescharacteristic
191C22×C22⋊D79C2311yescharacteristic
192C22×C22⋊D79C2311yescharacteristic
193C22×C22⋊D79C2311yescharacteristic
194C22×C22⋊D79C2311yescharacteristic
195C22×C22⋊D79C2311yescharacteristic
196C2×D4×D79—42no—
197C2×D4×D79—42no—
198C2×D4×D79C2×C418yescomplemented
199C23×Dic79C2311yescharacteristic
200C23×Dic79C2311yescharacteristic
201C23×Dic79C2311yescharacteristic
202C23×Dic79C2311yescharacteristic
203C22×C4×D79C2311yescharacteristic
204C22×C4×D79C2311yescharacteristic
205C22×C4×D79C2311yescharacteristic
206C22×C4×D79C2311yescharacteristic
207C22×C4×D79C2311yescharacteristic
208#14579150C2×C418yescomplemented
209#14579144C2×C418yescomplemented
210#14579144C2×C418yescomplemented
211#14579137C2×C418yescomplemented
212#14579135C2×C418yescomplemented
213#14579133C2×C418yescomplemented
214#14579133C2×C418yescomplemented
215#14579129C2×C418yescomplemented
216#14579129C2×C418yescomplemented
217D4×Dic79C2×C418yescomplemented
218C4×C22⋊D79—42no—
219C4×C22⋊D79—42no—
220C4×C22⋊D79—42no—
221C4×C22⋊D79C2×C418yescomplemented
222(C22⋊D79)⋊C4—42no—
223#14579120—42no—
224#14579117—42no—
225C2×C4⋊Dic79—42no—
226C2×C4⋊Dic79C2311yescharacteristic
227C2×C4⋊Dic79C2311yescharacteristic
228C2×C4⋊Dic79C2311yescharacteristic
229C2×C4⋊Dic79C2311yescharacteristic
230C2×C4⋊Dic79C2311yescharacteristic
231C2×C4⋊Dic79C2311yescharacteristic
232C2×C4⋊Dic79C2311yescharacteristic
233C2×Dic79⋊C4C2311yescharacteristic
234C2×Dic79⋊C4C2311yescharacteristic
235C2×Dic79⋊C4C2311yescharacteristic
236C2×Dic79⋊C4C2311yescharacteristic
237C2×Dic79⋊C4C2311yescharacteristic
238C2×Dic79⋊C4C2311yescharacteristic
239C2×Dic79⋊C4C2311yescharacteristic
240C2×Dic79⋊C4C2311yescharacteristic
241C2×Dic79⋊C4C2311yescharacteristic
242C2×Dic79⋊C4C2311yescharacteristic
243C2×Dic79⋊C4C2311yescharacteristic
244C2×C22⋊Dic79C2311yescharacteristic
245C2×C22⋊Dic79C2311yescharacteristic
246C2×C22⋊Dic79C2311yescharacteristic
247C2×C22⋊Dic79C2311yescharacteristic
248C2×C22⋊Dic79C2311yescharacteristic
249C2×C22⋊Dic79C2311yescharacteristic
250C2×C22⋊Dic79C2311yescharacteristic
251C2×C22⋊Dic79C2311yescharacteristic
252C2×C22⋊Dic79C2311yescharacteristic
253C2×C22⋊Dic79C2311yescharacteristic
254C2×C22⋊Dic79C2311yescharacteristic
255C2×C22⋊Dic79C2311yescharacteristic
256C2×C22⋊Dic79C2311yescharacteristic
257C2×(C2×D79)⋊C4—42no—
258C2×(C2×D79)⋊C4—42no—
259C2×(C2×D79)⋊C4C2×C418yescomplemented
260C2×(C2×D79)⋊C4C2×C418yescomplemented
261C2×(C2×D79)⋊C4C2311yescharacteristic
262C2×(C2×D79)⋊C4C2311yescharacteristic
263C2×(C2×D79)⋊C4C2311yescharacteristic
264C2×(C2×D79)⋊C4C2311yescharacteristic
265C2×(C2×D79)⋊C4C2311yescharacteristic
266C2×(C2×D79)⋊C4C2311yescharacteristic
267C2×(C2×D79)⋊C4C2311yescharacteristic
268C2×(C2×D79)⋊C4C2311yescharacteristic
269C2×(C2×D79)⋊C4C2311yescharacteristic
270C2×(C2×D79)⋊C4C2311yescharacteristic
271C2×(C2×D79)⋊C4C2311yescharacteristic
272C2×(C2×D79)⋊C4C2311yescharacteristic
273C2×(C2×D79)⋊C4C2311yescharacteristic
274C2×(C2×D79)⋊C4C2311yescharacteristic
275C2×(C2×D79)⋊C4C2311yescharacteristic
276C2×(C2×D79)⋊C4C2311yescharacteristic
277C2×(C2×D79)⋊C4C2311yescharacteristic
278C2×(C2×D79)⋊C4C2311yescharacteristic
279C2×(C2×D79)⋊C4C2311yescharacteristic
280C2×(C2×D79)⋊C4C2311yescharacteristic
281C2×(C2×D79)⋊C4C2311yescharacteristic
282C2×(C2×D79)⋊C4C2311yescharacteristic
283C2×(C2×D79)⋊C4C2311yescharacteristic
284C2×(C2×D79)⋊C4C2311yescharacteristic
285C2×(C2×D79)⋊C4C2311yescharacteristic
286C2×(C2×D79)⋊C4C2311yescharacteristic
287C2×(C2×D79)⋊C4C2311yescharacteristic
288C2×(C2×D79)⋊C4C2311yescharacteristic
289C2×(C2×D79)⋊C4C2311yescharacteristic
290C22⋊C4×D79—42no—
291C22⋊C4×D79—42no—
292C2×C4×Dic79—42no—
293C2×C4×Dic79C2311yescharacteristic
294C2×C4×Dic79C2311yescharacteristic
295C2×C4×Dic79C2311yescharacteristic
296C2×C4×Dic79C2311yescharacteristic
297C2×C4×Dic79C2311yescharacteristic
298C2×C4×Dic79C2311yescharacteristic
299C2×C4×Dic79C2311yescharacteristic
300C2×C4×Dic79C2311yescharacteristic
301C2×C4×Dic79C2311yescharacteristic
302C2×C4×Dic79C2311yescharacteristic
303C2×C4×Dic79C2311yescharacteristic
304C2×C4×Dic79C2311yescharacteristic
305C2×C4×Dic79C2311yescharacteristic
306C2×C4×Dic79C2311yescharacteristic
307C2×C4×Dic79C2311yescharacteristic
308C79⋊#95C2311yescharacteristic
309C79⋊#95C2311yescharacteristic
310C79⋊#95C2311yescharacteristic
311C79⋊#95C2311yescharacteristic
312C79⋊#95C2311yescharacteristic
313C79⋊#95C2311yescharacteristic
314C79⋊#95C2311yescharacteristic
315C79⋊#95C2311yescharacteristic
316C79⋊#95C2311yescharacteristic
317C79⋊#95C2311yescharacteristic
318C79⋊#95C2311yescharacteristic
319C79⋊#95C2311yescharacteristic
320C79⋊#95C2311yescharacteristic
321C79⋊#95C2311yescharacteristic
322C79⋊#95C2311yescharacteristic
323C79⋊#95C2311yescharacteristic
324C79⋊#95C2311yescharacteristic
325C79⋊#95C2311yescharacteristic
326C79⋊#95C2311yescharacteristic
327C79⋊#95C2311yescharacteristic
328C79⋊#95C2311yescharacteristic
329C79⋊#95C2311yescharacteristic
330C79⋊#95C2311yescharacteristic
331C79⋊#95C2311yescharacteristic
332C79⋊#95C2311yescharacteristic
333C79⋊#95C2311yescharacteristic
334C79⋊#95C2311yescharacteristic
335C79⋊#95C2311yescharacteristic
336C2×#41×C79—42no—
337C2×#41×C79—42no—
338C2×#41×C79C2×C418yescomplemented
339C22×Q8×C79C2311yescharacteristic
340C22×D4×C79C2311yescharacteristic
341C22×D4×C79C2311yescharacteristic
342C22×D4×C79C2311yescharacteristic
343C23×C4×C79C2311yescharacteristic
344C23×C4×C79C2311yescharacteristic
345C23×C4×C79C2311yescharacteristic
346C23×C4×C79C2311yescharacteristic
347C23×C4×C79C2311yescharacteristic
348C23×C4×C79C2311yescharacteristic
349C23×C4×C79C2311yescharacteristic
350C4×D4×C79—42no—
351C4×D4×C79—42no—
352C2×C4⋊C4×C79C2311yescharacteristic
353C2×C4⋊C4×C79C2311yescharacteristic
354C2×C22⋊C4×C79C2311yescharacteristic
355C2×C22⋊C4×C79C2311yescharacteristic
356C2×C22⋊C4×C79C2311yescharacteristic
357C2×C22⋊C4×C79C2311yescharacteristic
358C2×C22⋊C4×C79C2311yescharacteristic
359C2×C22⋊C4×C79C2311yescharacteristic
360C2×C22⋊C4×C79C2311yescharacteristic
361C2×C22⋊C4×C79C2311yescharacteristic
362C2×C42×C79C2311yescharacteristic
363C2×C42×C79C2311yescharacteristic
364#95×C79C2311yescharacteristic
365#95×C79C2311yescharacteristic
366#95×C79C2311yescharacteristic
367#95×C79C2311yescharacteristic
368#95×C79C2311yescharacteristic
369#95×C79C2311yescharacteristic
370#95×C79C2311yescharacteristic
371#95×C79C2311yescharacteristic
372#95×C79C2311yescharacteristic
373#95×C79C2311yescharacteristic
374#95×C79C2311yescharacteristic
375#95×C79C2311yescharacteristic
376C23×D79—22no—
377C23×D79—22no—
378C23×D79—41no—
379C23×D79—41no—
380C23×D79—41no—
381C23×D79—41no—
382C23×D79—41no—
383C23×D79—41no—
384C23×D79—41no—
385C23×D79—41no—
386C23×D79—41no—
387C23×D79—41no—
388C23×D79C22×C414yes—
389C23×D79C22×C414yes—
390C23×D79C2411yescharacteristic
391C23×D79C2411yescharacteristic
392C23×D79C2411yescharacteristic
393C2×D316—41no—
394C2×D316—41no—
395C2×D316C22×C414yes—
396C2×C22⋊D79—22no—
397C2×C22⋊D79—22no—
398C2×C22⋊D79—41no—
399C2×C22⋊D79—41no—
400C2×C22⋊D79—41no—
401C2×C22⋊D79—41no—
402C2×C22⋊D79—41no—
403C2×C22⋊D79—41no—
404C2×C22⋊D79—41no—
405C2×C22⋊D79—41no—
406C2×C22⋊D79C22×C414yes—
407C2×C22⋊D79C22×C414yes—
408C2×C22⋊D79C22×C414yes—
409C2×C22⋊D79C22×C414yes—
410C2×C22⋊D79C22×C414yes—
411D4×D79—416no—
412C22×Dic79—22no—
413C22×Dic79—22no—
414C22×Dic79—41no—
415C22×Dic79—41no—
416C22×Dic79—41no—
417C22×Dic79—41no—
418C22×Dic79—41no—
419C22×Dic79—41no—
420C22×Dic79—41no—
421C22×Dic79—41no—
422C22×Dic79C22×C414yes—
423C22×Dic79C22×C414yes—
424C22×Dic79C2411yescharacteristic
425C22×Dic79C2411yescharacteristic
426C22×Dic79C2411yescharacteristic
427C22×Dic79C2411yescharacteristic
428C22×Dic79C2411yescharacteristic
429C22×Dic79C2411yescharacteristic
430C22×Dic79C2411yescharacteristic
431C22×Dic79C2411yescharacteristic
432C22×Dic79C2411yescharacteristic
433C22×Dic79C2411yescharacteristic
434C22×Dic79C2411yescharacteristic
435C22×Dic79C2411yescharacteristic
436C22×Dic79C2411yescharacteristic
437C2×C4×D79—22no—
438C2×C4×D79—41no—
439C2×C4×D79—41no—
440C2×C4×D79—41no—
441C2×C4×D79—41no—
442C2×C4×D79—41no—
443C2×C4×D79—41no—
444C2×C4×D79—41no—
445C2×C4×D79—41no—
446C2×C4×D79—41no—
447C2×C4×D79—41no—
448C2×C4×D79—41no—
449C2×C4×D79—41no—
450C2×C4×D79—41no—
451C2×C4×D79C22×C414yes—
452C4⋊Dic79—41no—
453C4⋊Dic79—41no—
454C4⋊Dic79—41no—
455C4⋊Dic79—41no—
456C4⋊Dic79—41no—
457C4⋊Dic79—41no—
458C4⋊Dic79C22×C414yes—
459Dic79⋊C4—22no—
460Dic79⋊C4—41no—
461Dic79⋊C4—41no—
462Dic79⋊C4—41no—
463Dic79⋊C4—41no—
464Dic79⋊C4—41no—
465Dic79⋊C4—41no—
466Dic79⋊C4—41no—
467Dic79⋊C4C22×C414yes—
468Dic79⋊C4C22×C414yes—
469Dic79⋊C4C22×C414yes—
470C22⋊Dic79—22no—
471C22⋊Dic79—22no—
472C22⋊Dic79—41no—
473C22⋊Dic79—41no—
474C22⋊Dic79—41no—
475C22⋊Dic79—41no—
476C22⋊Dic79—41no—
477C22⋊Dic79—41no—
478C22⋊Dic79—41no—
479C22⋊Dic79—41no—
480C22⋊Dic79C22×C414yes—
481C22⋊Dic79C22×C414yes—
482C22⋊Dic79C22×C414yes—
483(C2×D79)⋊C4—22no—
484(C2×D79)⋊C4—22no—
485(C2×D79)⋊C4—41no—
486(C2×D79)⋊C4—41no—
487(C2×D79)⋊C4—41no—
488(C2×D79)⋊C4—41no—
489(C2×D79)⋊C4—41no—
490(C2×D79)⋊C4—41no—
491(C2×D79)⋊C4—41no—
492(C2×D79)⋊C4—41no—
493(C2×D79)⋊C4—41no—
494(C2×D79)⋊C4—41no—
495(C2×D79)⋊C4—41no—
496(C2×D79)⋊C4—41no—
497(C2×D79)⋊C4—41no—
498(C2×D79)⋊C4—41no—
499(C2×D79)⋊C4—41no—
500(C2×D79)⋊C4—41no—
501(C2×D79)⋊C4—41no—
502(C2×D79)⋊C4—41no—
503(C2×D79)⋊C4C22×C414yes—
504(C2×D79)⋊C4C22×C414yes—
505(C2×D79)⋊C4C22×C414yes—
506(C2×D79)⋊C4C22×C414yes—
507(C2×D79)⋊C4C22×C414yes—
508(C2×D79)⋊C4C22×C414yes—
509(C2×D79)⋊C4C22×C414yes—
510(C2×D79)⋊C4C22×C414yes—
511(C2×D79)⋊C4C22×C414yes—
512C4×Dic79—22no—
513C4×Dic79—22no—
514C4×Dic79—41no—
515C4×Dic79—41no—
516C4×Dic79—41no—
517C4×Dic79—41no—
518C4×Dic79—41no—
519C4×Dic79—41no—
520C4×Dic79—41no—
521C4×Dic79—41no—
522C4×Dic79—41no—
523C4×Dic79—41no—
524C4×Dic79—41no—
525C4×Dic79—41no—
526C4×Dic79C22×C414yes—
527C24×C79C2411yescharacteristic
528C24×C79C2411yescharacteristic
529C24×C79C2411yescharacteristic
530#41×C79—416no—
531C2×Q8×C79—41no—
532C2×Q8×C79—41no—
533C2×Q8×C79C22×C414yes—
534C2×D4×C79—22no—
535C2×D4×C79—22no—
536C2×D4×C79—22no—
537C2×D4×C79—22no—
538C2×D4×C79—41no—
539C2×D4×C79—41no—
540C2×D4×C79C22×C414yes—
541C2×D4×C79C22×C414yes—
542C2×D4×C79C22×C414yes—
543C22×C4×C79—22no—
544C22×C4×C79—22no—
545C22×C4×C79—22no—
546C22×C4×C79—22no—
547C22×C4×C79—22no—
548C22×C4×C79—22no—
549C22×C4×C79—41no—
550C22×C4×C79—41no—
551C22×C4×C79—41no—
552C22×C4×C79—41no—
553C22×C4×C79—41no—
554C22×C4×C79—41no—
555C22×C4×C79—41no—
556C22×C4×C79—41no—
557C22×C4×C79—41no—
558C22×C4×C79—41no—
559C22×C4×C79—41no—
560C22×C4×C79—41no—
561C22×C4×C79C22×C414yes—
562C22×C4×C79C22×C414yes—
563C22×C4×C79C22×C414yes—
564C22×C4×C79C2411yescharacteristic
565C22×C4×C79C2411yescharacteristic
566C22×C4×C79C2411yescharacteristic
567C22×C4×C79C2411yescharacteristic
568C22×C4×C79C2411yescharacteristic
569C22×C4×C79C2411yescharacteristic
570C22×C4×C79C2411yescharacteristic
571C22×C4×C79C2411yescharacteristic
572C22×C4×C79C2411yescharacteristic
573C22×C4×C79C2411yescharacteristic
574C22×C4×C79C2411yescharacteristic
575C22×C4×C79C2411yescharacteristic
576C4⋊C4×C79—41no—
577C4⋊C4×C79—41no—
578C22⋊C4×C79—22no—
579C22⋊C4×C79—22no—
580C22⋊C4×C79—22no—
581C22⋊C4×C79—41no—
582C22⋊C4×C79—41no—
583C22⋊C4×C79—41no—
584C22⋊C4×C79—41no—
585C22⋊C4×C79—41no—
586C42×C79—41no—
587C42×C79—41no—
588C23×C79—21no—
589C23×C79—21no—
590C23×C79—21no—
591C23×C79—21no—
592C23×C79—21no—
593C23×C79—21no—
594C23×C79—21no—
595C23×C79—21no—
596C23×C79—21no—
597C23×C79—21no—
598C23×C79—21no—
599C23×C79—21no—
600C23×C79—21no—
601C23×C79—21no—
602C23×C79—21no—
603C23×C79—21no—
604C23×C79C23×C412yes—
605C23×C79C23×C412yes—
606C23×C79C23×C412yes—
607C23×C79H(5,𝔽2)12yes—
608C23×C79H(5,𝔽2)12yes—
609C23×C79C2511yescharacteristic
610C22×D79—21no—
611C22×D79—21no—
612C22×D79—21no—
613C22×D79—21no—
614C22×D79—21no—
615C22×D79—21no—
616C22×D79—21no—
617C22×D79—21no—
618C22×D79—21no—
619C22×D79—21no—
620C22×D79—21no—
621C22×D79—21no—
622C22×D79—21no—
623C22×D79—21no—
624C22×D79—21no—
625C22×D79—21no—
626C22×D79—21no—
627C22×D79—21no—
628C22×D79—28no—
629C22×D79—44no—
630C22×D79—44no—
631C22×D79—44no—
632C22×D79—44no—
633C22×D79—44no—
634C22×D79—82no—
635C22×D79—82no—
636C22×D79—82no—
637C22×D79—82no—
638C22×D79—82no—
639C22×D79—82no—
640C22×D79—82no—
641C22×D79—82no—
642C22×D79C23×C412yes—
643C22×D79C23×C412yes—
644C22×D79C23×C412yes—
645Q8×C79—44no—
646D4×C79—28no—
647D4×C79—28no—
648D4×C79—44no—
649C2×C4×C79—28no—
650C2×C4×C79—21no—
651C2×C4×C79—21no—
652C2×C4×C79—21no—
653C2×C4×C79—21no—
654C2×C4×C79—21no—
655C2×C4×C79—21no—
656C2×C4×C79—21no—
657C2×C4×C79—21no—
658C2×C4×C79—21no—
659C2×C4×C79—21no—
660C2×C4×C79—21no—
661C2×C4×C79—21no—
662C2×C4×C79—21no—
663C2×C4×C79—21no—
664C2×C4×C79—21no—
665C2×C4×C79—21no—
666C2×C4×C79—21no—
667C2×C4×C79—21no—
668C2×C4×C79—21no—
669C2×C4×C79—21no—
670C2×C4×C79—21no—
671C2×C4×C79—21no—
672C2×C4×C79—21no—
673C2×C4×C79—21no—
674C2×C4×C79—21no—
675C2×C4×C79—21no—
676C2×C4×C79—21no—
677C2×C4×C79—21no—
678C2×C4×C79—21no—
679C2×C4×C79—21no—
680C2×C4×C79—21no—
681C2×C4×C79—44no—
682C2×C4×C79—44no—
683C2×C4×C79—44no—
684C2×C4×C79—82no—
685C2×C4×C79—82no—
686C2×C4×C79—82no—
687C2×C4×C79C23×C412yes—
688C2×C4×C79C23×C412yes—
689C2×C4×C79C23×C412yes—
690C2×C4×C79C23×C412yes—
691C2×C4×C79H(5,𝔽2)12yes—
692C22⋊D79—28no—
693C22⋊D79—44no—
694C22⋊D79—44no—
695C22⋊D79—44no—
696C22⋊D79—44no—
697C2×Dic79—21no—
698C2×Dic79—21no—
699C2×Dic79—21no—
700C2×Dic79—21no—
701C2×Dic79—21no—
702C2×Dic79—21no—
703C2×Dic79—21no—
704C2×Dic79—21no—
705C2×Dic79—21no—
706C2×Dic79—21no—
707C2×Dic79—21no—
708C2×Dic79—21no—
709C2×Dic79—21no—
710C2×Dic79—21no—
711C2×Dic79—21no—
712C2×Dic79—21no—
713C2×Dic79—21no—
714C2×Dic79—21no—
715C2×Dic79—21no—
716C2×Dic79—21no—
717C2×Dic79—21no—
718C2×Dic79—21no—
719C2×Dic79—21no—
720C2×Dic79—21no—
721C2×Dic79—21no—
722C2×Dic79—21no—
723C2×Dic79—21no—
724C2×Dic79—21no—
725C2×Dic79—21no—
726C2×Dic79—21no—
727C2×Dic79—21no—
728C2×Dic79—21no—
729C2×Dic79—21no—
730C2×Dic79—21no—
731C2×Dic79—44no—
732C2×Dic79—44no—
733C2×Dic79—44no—
734C2×Dic79—82no—
735C2×Dic79C23×C412yes—
736C2×Dic79C23×C412yes—
737C2×Dic79C23×C412yes—
738C2×Dic79C23×C412yes—
739C2×Dic79C23×C412yes—
740D316—44no—
741C4×D79—44no—
742C4×D79—82no—
743C4×D79—82no—
744C4×D79—82no—
745C4×D79—82no—
746C22×C79—22no—
747C22×C79—22no—
748C22×C79—22no—
749C22×C79—22no—
750C22×C79—22no—
751C22×C79—22no—
752C22×C79—22no—
753C22×C79—22no—
754C22×C79—22no—
755C22×C79—22no—
756C22×C79—22no—
757C22×C79—22no—
758C22×C79—41no—
759C22×C79—41no—
760C22×C79—41no—
761C22×C79—41no—
762C22×C79—41no—
763C22×C79—41no—
764C22×C79—41no—
765C22×C79—41no—
766C22×C79#51814yes—
767C22×C79C24×C411yescharacteristic
768C22×C79C2×H(5,𝔽2)11yescharacteristic
769C22×C79C2×H(5,𝔽2)11yescharacteristic
770C22×C79C2×H(5,𝔽2)11yescharacteristic
771C22×C79#58511yescharacteristic
772C22×C79#58511yescharacteristic
773C22×C79#58511yescharacteristic
774C2×D79—22no—
775C2×D79—22no—
776C2×D79—22no—
777C2×D79—22no—
778C2×D79—22no—
779C2×D79—22no—
780C2×D79—22no—
781C2×D79—22no—
782C2×D79—22no—
783C2×D79—41no—
784C2×D79—41no—
785C2×D79—41no—
786C2×D79—41no—
787C2×D79—41no—
788C2×D79—41no—
789C2×D79—41no—
790C2×D79—41no—
791C2×D79—41no—
792C2×D79—41no—
793C2×D79—41no—
794C2×D79—41no—
795C2×D79—88no—
796C2×D79—88no—
797C4×C79—22no—
798C4×C79—22no—
799C4×C79—22no—
800C4×C79—22no—
801C4×C79—22no—
802C4×C79—41no—
803C4×C79—41no—
804C4×C79—41no—
805C4×C79—41no—
806C4×C79—41no—
807C4×C79—41no—
808C4×C79—41no—
809Dic79—22no—
810Dic79—22no—
811Dic79—22no—
812Dic79—22no—
813Dic79—22no—
814Dic79—41no—
815Dic79—41no—
816Dic79—41no—
817Dic79—41no—
818Dic79—41no—
819Dic79—41no—
820Dic79—41no—
821Dic79—41no—
822#34492—791nomaximal, Sylow
823C2×C79—24no—
824C2×C79—42no—
825C2×C79—42no—
826C2×C79C2×#51811yescharacteristic
827C2×C79#342811yescharacteristic
828C2×C79C4×H(5,𝔽2)11yescharacteristic
829C2×C79#353411yescharacteristic
830C2×C79#354211yescharacteristic
831C2×C79#354511yescharacteristic
832C2×C79#356011yescharacteristic
833D79—42no—
834D79—42no—
835D79—42no—
836C2×#546—791no—
837#2378—791no—
838#2377—791no—
839#2376—791no—
840#2375—791no—
841#2372—791no—
842#2364—791no—
843#2363—791no—
844#2359—791no—
845#2358—791no—
846#2353—791no—
847#2353—791no—
848#2342—791no—
849#2342—791no—
850#2339D7911yescharacteristic, complemented
851D4×C22⋊C4—791no—
852#2337—791no—
853#2335—791no—
854#2333—791no—
855#2332—791no—
856#2325—791no—
857#2322—791no—
858#2321—791no—
859#2321—791no—
860#2319—791no—
861#2312—791no—
862#2311—791no—
863#2308—791no—
864C4×#121—791no—
865#2290—791no—
866C2×#388—791no—
867C79#3449211yescharacteristic, complemented, Sylow
868C22×#41C2×D7911yescharacteristic
869C23×D4—791no—
870#546—7916no—
871C2×#124—791no—
872C2×#123—791no—
873C2×#123—791no—
874C2×C22⋊Q8—791no—
875C2×#121—791no—
876C2×#121—791no—
877C2×#121—791no—
878C2×#120—791no—
879C2×#120—791no—
880C2×C4×D4—791no—
881C2×C4×D4—791no—
882C2×C4×D4—791no—
883C2×C4×D4—791no—
884C2×C4×D4—791no—
885C2×C4×D4—791no—
886C2×C4×D4C2×D7911yescharacteristic, complemented
887C2×C4×D4C2×D7911yescharacteristic, complemented
888C2×#117—791no—
889C2×#117—791no—
890C22×C4⋊C4—791no—
891C22×C22⋊C4—791no—
892C22×C22⋊C4—791no—
893C22×C22⋊C4—791no—
894C22×C22⋊C4—791no—
895C22×C22⋊C4—791no—
896C22×C22⋊C4—791no—
897C22×C42—791no—
898#391—791no—
899#391—791no—
900#391C2×D7911yescharacteristic, complemented
901#391C2×D7911yescharacteristic, complemented
902#390—791no—
903#390—791no—
904#390—791no—
905#390—791no—
906#390—791no—
907#390—791no—
908#390—791no—
909#390—791no—
910#389—791no—
911#389—791no—
912#389—791no—
913#389—791no—
914#388—791no—
915#388—791no—
916#388—791no—
917#388—791no—
918#388—791no—
919#388—791no—
920#388—791no—
921#388—791no—
922#388—791no—
923#388—791no—
924#388—791no—
925#388—791no—
926#388—791no—
927#388—791no—
928#388—791no—
929#388—791no—
930#388—791no—
931#388—791no—
932#388—791no—
933#388—791no—
934#388—791no—
935#388—791no—
936#388—791no—
937#388—791no—
938#388—791no—
939#388—791no—
940#388—791no—
941#388—791no—
942#388—791no—
943#388—791no—
944#387—791no—
945#387—791no—
946#387—791no—
947#387—791no—
948#387—791no—
949#387—791no—
950#387—791no—
951#387—791no—
952#387—791no—
953#387—791no—
954#386—791no—
955#386—791no—
956#386—791no—
957#386—791no—
958#386—791no—
959#386—791no—
960#386—791no—
961#386—791no—
962#386—791no—
963#386—791no—
964#386—791no—
965#386—791no—
966#386—791no—
967#386—791no—
968#386—791no—
969#386—791no—
970#386—791no—
971#386—791no—
972#386C2×D7911yescharacteristic
973#386C2×D7911yescharacteristic
974#386C2×D7911yescharacteristic, complemented
975#386C2×D7911yescharacteristic, complemented
976#385—791no—
977#385—791no—
978#385—791no—
979#385—791no—
980#385—791no—
981#385—791no—
982#385—791no—
983#385—791no—
984#383—791no—
985#381—791no—
986#381—791no—
987#381—791no—
988#381C2×D7911yescharacteristic, complemented
989#381C2×D7911yescharacteristic, complemented
990#380—791no—
991#380—791no—
992#380—791no—
993#380—791no—
994#380—791no—
995#380—791no—
996#380C2×D7911yescharacteristic, complemented
997#379—791no—
998#379—791no—
999#379—791no—
1000#379—791no—
1001C4×C4⋊C4—791no—
1002C4×C4⋊C4—791no—
1003C4×C4⋊C4—791no—
1004C4×C22⋊C4—791no—
1005C4×C22⋊C4—791no—
1006C4×C22⋊C4—791no—
1007C4×C22⋊C4—791no—
1008C4×C22⋊C4—791no—
1009C4×C22⋊C4—791no—
1010C4×C22⋊C4—791no—
1011C4×C22⋊C4—791no—
1012C4×C22⋊C4—791no—
1013C4×C22⋊C4—791no—
1014C4×C22⋊C4—791no—
1015C4×C22⋊C4—791no—
1016C4×C22⋊C4—791no—
1017C4×C22⋊C4—791no—
1018C4×C22⋊C4C2×D7911yescharacteristic, complemented
1019#376—791no—
1020#376—791no—
1021C2×#95—791no—
1022C2×#95C2×D7911yescharacteristic, complemented
1023C2×#95C2×D7911yescharacteristic, complemented
1024C25—791no—
1025C25—791no—
1026C2×#41—42no—
1027C2×#41—42no—
1028C2×#41C4×D7918yescomplemented
1029C22×Q8C22×D7911yescharacteristic
1030C22×D4—3162no—
1031C22×D4—3162no—
1032C22×D4—791no—
1033C22×D4—791no—
1034C22×D4—791no—
1035C22×D4—791no—
1036C22×D4—798no—
1037C22×D4—791no—
1038C22×D4—791no—
1039C22×D4C22×D7911yescharacteristic
1040C22×D4C22×D7911yescharacteristic
1041C22×D4C22×D7911yescharacteristic
1042C23×C4—791no—
1043C23×C4—791no—
1044C23×C4—791no—
1045C23×C4—791no—
1046C23×C4—791no—
1047C23×C4—791no—
1048C23×C4—791no—
1049C23×C4—791no—
1050C23×C4—791no—
1051C23×C4C22×D7911yescharacteristic
1052C23×C4C22×D7911yescharacteristic
1053C23×C4C22×D7911yescharacteristic
1054C23×C4C22×D7911yescharacteristic
1055C23×C4C22×D7911yescharacteristic
1056C23×C4C22×D7911yescharacteristic
1057C23×C4C22×D7911yescharacteristic
1058#124—798no—
1059#123—798no—
1060#123—798no—
1061C22⋊Q8—798no—
1062#121—798no—
1063#121—798no—
1064#121—798no—
1065#120—798no—
1066#120—798no—
1067C4×D4—42no—
1068C4×D4—42no—
1069C4×D4—3162no—
1070C4×D4—3162no—
1071C4×D4—3162no—
1072C4×D4—3162no—
1073C4×D4—798no—
1074C4×D4—798no—
1075#117—3162no—
1076#117—3162no—
1077C2×C4⋊C4—3162no—
1078C2×C4⋊C4—791no—
1079C2×C4⋊C4—791no—
1080C2×C4⋊C4—791no—
1081C2×C4⋊C4—791no—
1082C2×C4⋊C4—791no—
1083C2×C4⋊C4—791no—
1084C2×C4⋊C4—791no—
1085C2×C4⋊C4—791no—
1086C2×C4⋊C4—791no—
1087C2×C4⋊C4—791no—
1088C2×C4⋊C4—791no—
1089C2×C4⋊C4—791no—
1090C2×C4⋊C4—791no—
1091C2×C4⋊C4—791no—
1092C2×C4⋊C4—791no—
1093C2×C4⋊C4—791no—
1094C2×C4⋊C4—791no—
1095C2×C4⋊C4—791no—
1096C2×C4⋊C4C22×D7911yescharacteristic
1097C2×C4⋊C4C22×D7911yescharacteristic
1098C2×C22⋊C4—3162no—
1099C2×C22⋊C4—3162no—
1100C2×C22⋊C4—3162no—
1101C2×C22⋊C4—3162no—
1102C2×C22⋊C4—791no—
1103C2×C22⋊C4—791no—
1104C2×C22⋊C4—791no—
1105C2×C22⋊C4—791no—
1106C2×C22⋊C4—791no—
1107C2×C22⋊C4—791no—
1108C2×C22⋊C4—791no—
1109C2×C22⋊C4—791no—
1110C2×C22⋊C4—791no—
1111C2×C22⋊C4—791no—
1112C2×C22⋊C4—791no—
1113C2×C22⋊C4—791no—
1114C2×C22⋊C4—791no—
1115C2×C22⋊C4—791no—
1116C2×C22⋊C4—791no—
1117C2×C22⋊C4—791no—
1118C2×C22⋊C4—791no—
1119C2×C22⋊C4—791no—
1120C2×C22⋊C4—791no—
1121C2×C22⋊C4—791no—
1122C2×C22⋊C4—791no—
1123C2×C22⋊C4—791no—
1124C2×C22⋊C4—791no—
1125C2×C22⋊C4—791no—
1126C2×C22⋊C4—791no—
1127C2×C22⋊C4—791no—
1128C2×C22⋊C4—791no—
1129C2×C22⋊C4—791no—
1130C2×C22⋊C4—791no—
1131C2×C22⋊C4—798no—
1132C2×C22⋊C4—798no—
1133C2×C22⋊C4—791no—
1134C2×C22⋊C4—791no—
1135C2×C22⋊C4—791no—
1136C2×C22⋊C4—791no—
1137C2×C22⋊C4—791no—
1138C2×C22⋊C4—791no—
1139C2×C22⋊C4—791no—
1140C2×C22⋊C4—791no—
1141C2×C22⋊C4—791no—
1142C2×C22⋊C4—791no—
1143C2×C22⋊C4—791no—
1144C2×C22⋊C4—791no—
1145C2×C22⋊C4—791no—
1146C2×C22⋊C4C22×D7911yescharacteristic
1147C2×C22⋊C4C22×D7911yescharacteristic
1148C2×C22⋊C4C22×D7911yescharacteristic
1149C2×C22⋊C4C22×D7911yescharacteristic
1150C2×C22⋊C4C22×D7911yescharacteristic
1151C2×C22⋊C4C22×D7911yescharacteristic
1152C2×C22⋊C4C22×D7911yescharacteristic
1153C2×C22⋊C4C22×D7911yescharacteristic
1154C2×C42—3162no—
1155C2×C42—791no—
1156C2×C42—791no—
1157C2×C42—791no—
1158C2×C42—791no—
1159C2×C42—791no—
1160C2×C42—791no—
1161C2×C42—791no—
1162C2×C42—791no—
1163C2×C42—791no—
1164C2×C42—791no—
1165C2×C42—791no—
1166C2×C42—791no—
1167C2×C42—791no—
1168C2×C42—791no—
1169C2×C42—791no—
1170C2×C42C22×D7911yescharacteristic
1171C2×C42C22×D7911yescharacteristic
1172#95—791no—
1173#95—791no—
1174#95—791no—
1175#95—791no—
1176#95—791no—
1177#95—791no—
1178#95—791no—
1179#95—791no—
1180#95—791no—
1181#95—791no—
1182#95—791no—
1183#95—791no—
1184#95—791no—
1185#95—791no—
1186#95—791no—
1187#95—791no—
1188#95—791no—
1189#95—791no—
1190#95—791no—
1191#95—791no—
1192#95—791no—
1193#95—791no—
1194#95—791no—
1195#95—791no—
1196#95—791no—
1197#95—791no—
1198#95—791no—
1199#95—791no—
1200#95C22×D7911yescharacteristic
1201#95C22×D7911yescharacteristic
1202#95C22×D7911yescharacteristic
1203#95C22×D7911yescharacteristic
1204#95C22×D7911yescharacteristic
1205#95C22×D7911yescharacteristic
1206#95C22×D7911yescharacteristic
1207#95C22×D7911yescharacteristic
1208#95C22×D7911yescharacteristic
1209#95C22×D7911yescharacteristic
1210#95C22×D7911yescharacteristic
1211#95C22×D7911yescharacteristic
1212C24—3161no—
1213C24—3161no—
1214C24—3161no—
1215C24—3161no—
1216C24—3161no—
1217C24—3161no—
1218C24—3161no—
1219C24—3161no—
1220C24—3161no—
1221C24—3161no—
1222C24—794no—
1223C24—794no—
1224C24—791no—
1225C24—791no—
1226C24—791no—
1227C24—1582no—
1228C24—1582no—
1229C24C23×D7911yescharacteristic
1230C24C23×D7911yescharacteristic
1231C24C23×D7911yescharacteristic
1232#41—416no—
1233C2×Q8—41no—
1234C2×Q8—41no—
1235C2×Q8C2×C4×D7914yes—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—22no—
1240C2×D4—41no—
1241C2×D4—41no—
1242C2×D4—3161no—
1243C2×D4—3161no—
1244C2×D4—31616no—
1245C2×D4—3161no—
1246C2×D4—3161no—
1247C2×D4—3161no—
1248C2×D4—3161no—
1249C2×D4—3161no—
1250C2×D4—3161no—
1251C2×D4—3161no—
1252C2×D4—3161no—
1253C2×D4—794no—
1254C2×D4—794no—
1255C2×D4—794no—
1256C2×D4—794no—
1257C2×D4—794no—
1258C2×D4—794no—
1259C2×D4—1582no—
1260C2×D4—1582no—
1261C2×D4C2×C4×D7914yes—
1262C2×D4C2×C4×D7914yes—
1263C2×D4C2×C4×D7914yes—
1264C22×C4—22no—
1265C22×C4—22no—
1266C22×C4—22no—
1267C22×C4—22no—
1268C22×C4—22no—
1269C22×C4—22no—
1270C22×C4—41no—
1271C22×C4—41no—
1272C22×C4—41no—
1273C22×C4—41no—
1274C22×C4—41no—
1275C22×C4—41no—
1276C22×C4—41no—
1277C22×C4—41no—
1278C22×C4—41no—
1279C22×C4—41no—
1280C22×C4—41no—
1281C22×C4—41no—
1282C22×C4—3161no—
1283C22×C4—3161no—
1284C22×C4—3161no—
1285C22×C4—3161no—
1286C22×C4—3161no—
1287C22×C4—3161no—
1288C22×C4—3161no—
1289C22×C4—3161no—
1290C22×C4—3161no—
1291C22×C4—3161no—
1292C22×C4—3161no—
1293C22×C4—3161no—
1294C22×C4—3161no—
1295C22×C4—3161no—
1296C22×C4—3161no—
1297C22×C4—3161no—
1298C22×C4—3161no—
1299C22×C4—3161no—
1300C22×C4—3161no—
1301C22×C4—3161no—
1302C22×C4—3161no—
1303C22×C4—794no—
1304C22×C4—794no—
1305C22×C4—794no—
1306C22×C4—791no—
1307C22×C4—791no—
1308C22×C4—791no—
1309C22×C4—791no—
1310C22×C4—791no—
1311C22×C4—791no—
1312C22×C4—791no—
1313C22×C4—791no—
1314C22×C4—791no—
1315C22×C4—791no—
1316C22×C4—791no—
1317C22×C4—791no—
1318C22×C4—791no—
1319C22×C4—1582no—
1320C22×C4—1582no—
1321C22×C4—1582no—
1322C22×C4C2×C4×D7914yes—
1323C22×C4C2×C4×D7914yes—
1324C22×C4C2×C4×D7914yes—
1325C22×C4C23×D7911yescharacteristic
1326C22×C4C23×D7911yescharacteristic
1327C22×C4C23×D7911yescharacteristic
1328C22×C4C23×D7911yescharacteristic
1329C22×C4C23×D7911yescharacteristic
1330C22×C4C23×D7911yescharacteristic
1331C22×C4C23×D7911yescharacteristic
1332C22×C4C23×D7911yescharacteristic
1333C22×C4C23×D7911yescharacteristic
1334C22×C4C23×D7911yescharacteristic
1335C22×C4C23×D7911yescharacteristic
1336C22×C4C23×D7911yescharacteristic
1337C4⋊C4—41no—
1338C4⋊C4—41no—
1339C4⋊C4—3161no—
1340C4⋊C4—3161no—
1341C4⋊C4—3161no—
1342C4⋊C4—3161no—
1343C4⋊C4—3161no—
1344C4⋊C4—3161no—
1345C4⋊C4—3161no—
1346C4⋊C4—3161no—
1347C4⋊C4—3161no—
1348C4⋊C4—3161no—
1349C4⋊C4—3161no—
1350C4⋊C4—3161no—
1351C4⋊C4—3161no—
1352C4⋊C4—794no—
1353C4⋊C4—794no—
1354C4⋊C4—794no—
1355C4⋊C4—794no—
1356C4⋊C4—1582no—
1357C22⋊C4—22no—
1358C22⋊C4—22no—
1359C22⋊C4—22no—
1360C22⋊C4—41no—
1361C22⋊C4—41no—
1362C22⋊C4—41no—
1363C22⋊C4—41no—
1364C22⋊C4—41no—
1365C22⋊C4—3161no—
1366C22⋊C4—3161no—
1367C22⋊C4—3161no—
1368C22⋊C4—3161no—
1369C22⋊C4—3161no—
1370C22⋊C4—3161no—
1371C22⋊C4—3161no—
1372C22⋊C4—3161no—
1373C22⋊C4—3161no—
1374C22⋊C4—3161no—
1375C22⋊C4—3161no—
1376C22⋊C4—3161no—
1377C22⋊C4—3161no—
1378C22⋊C4—3161no—
1379C22⋊C4—3161no—
1380C22⋊C4—3161no—
1381C22⋊C4—3161no—
1382C22⋊C4—3161no—
1383C22⋊C4—3161no—
1384C22⋊C4—3161no—
1385C22⋊C4—3161no—
1386C22⋊C4—3161no—
1387C22⋊C4—3161no—
1388C22⋊C4—3161no—
1389C22⋊C4—3161no—
1390C22⋊C4—3161no—
1391C22⋊C4—794no—
1392C22⋊C4—794no—
1393C22⋊C4—794no—
1394C22⋊C4—794no—
1395C22⋊C4—794no—
1396C22⋊C4—794no—
1397C22⋊C4—794no—
1398C22⋊C4—794no—
1399C22⋊C4—794no—
1400C22⋊C4—794no—
1401C22⋊C4—794no—
1402C22⋊C4—794no—
1403C22⋊C4—1582no—
1404C22⋊C4—1582no—
1405C22⋊C4—1582no—
1406C22⋊C4—1582no—
1407C42—41no—
1408C42—41no—
1409C42—3161no—
1410C42—3161no—
1411C42—3161no—
1412C42—3161no—
1413C42—3161no—
1414C42—3161no—
1415C42—3161no—
1416C42—3161no—
1417C42—3161no—
1418C42—3161no—
1419C42—3161no—
1420C42—3161no—
1421C42—794no—
1422C42—1582no—
1423C42—1582no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—21no—
1428C23—21no—
1429C23—21no—
1430C23—21no—
1431C23—21no—
1432C23—21no—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—3164no—
1441C23—3164no—
1442C23—3164no—
1443C23—3164no—
1444C23—3164no—
1445C23—792no—
1446C23—792no—
1447C23—792no—
1448C23—6322no—
1449C23—6322no—
1450C23—6322no—
1451C23—6322no—
1452C23—6322no—
1453C23—6322no—
1454C23—6322no—
1455C23—6322no—
1456C23—1581no—
1457C23—1581no—
1458C23—1581no—
1459C23—1581no—
1460C23—1581no—
1461C23—1581no—
1462C23—1581no—
1463C23—1581no—
1464C23—1581no—
1465C23—1581no—
1466C23—1581no—
1467C23—1581no—
1468C23—1581no—
1469C23—1581no—
1470C23—1581no—
1471C23—1581no—
1472C23—1581no—
1473C23—1581no—
1474C23—1588no—
1475C23C22×C4×D7912yes—
1476C23C22×C4×D7912yes—
1477C23C22×C4×D7912yes—
1478C23#1457920612yes—
1479C23#1457920612yes—
1480C23C24×D7911yescharacteristic
1481Q8—44no—
1482D4—28no—
1483D4—28no—
1484D4—44no—
1485D4—3164no—
1486D4—3164no—
1487D4—3164no—
1488D4—3164no—
1489D4—3164no—
1490D4—1588no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—28no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—44no—
1524C2×C4—44no—
1525C2×C4—44no—
1526C2×C4—82no—
1527C2×C4—82no—
1528C2×C4—82no—
1529C2×C4—3164no—
1530C2×C4—3164no—
1531C2×C4—3164no—
1532C2×C4—3164no—
1533C2×C4—792no—
1534C2×C4—792no—
1535C2×C4—792no—
1536C2×C4—792no—
1537C2×C4—792no—
1538C2×C4—6322no—
1539C2×C4—6322no—
1540C2×C4—6322no—
1541C2×C4—6322no—
1542C2×C4—6322no—
1543C2×C4—1581no—
1544C2×C4—1581no—
1545C2×C4—1581no—
1546C2×C4—1581no—
1547C2×C4—1581no—
1548C2×C4—1581no—
1549C2×C4—1581no—
1550C2×C4—1581no—
1551C2×C4—1581no—
1552C2×C4—1581no—
1553C2×C4—1581no—
1554C2×C4—1581no—
1555C2×C4—1581no—
1556C2×C4—1581no—
1557C2×C4—1581no—
1558C2×C4—1581no—
1559C2×C4—1581no—
1560C2×C4—1581no—
1561C2×C4—1581no—
1562C2×C4—1581no—
1563C2×C4—1581no—
1564C2×C4—1581no—
1565C2×C4—1581no—
1566C2×C4—1581no—
1567C2×C4—1581no—
1568C2×C4—1581no—
1569C2×C4—1581no—
1570C2×C4—1581no—
1571C2×C4—1581no—
1572C2×C4—1581no—
1573C2×C4—1581no—
1574C2×C4—1581no—
1575C2×C4—1581no—
1576C2×C4—1581no—
1577C2×C4C22×C4×D7912yes—
1578C2×C4C22×C4×D7912yes—
1579C2×C4C22×C4×D7912yes—
1580C2×C4C22×C4×D7912yes—
1581C2×C4#1457920712yes—
1582C22—22no—
1583C22—22no—
1584C22—22no—
1585C22—22no—
1586C22—22no—
1587C22—22no—
1588C22—22no—
1589C22—22no—
1590C22—22no—
1591C22—22no—
1592C22—22no—
1593C22—22no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—3161no—
1603C22—3161no—
1604C22—3161no—
1605C22—3161no—
1606C22—3161no—
1607C22—3161no—
1608C22—3161no—
1609C22—3161no—
1610C22—3161no—
1611C22—3161no—
1612C22—3161no—
1613C22—3161no—
1614C22—6328no—
1615C22—6328no—
1616C22—1582no—
1617C22—1582no—
1618C22—1582no—
1619C22—1582no—
1620C22—1582no—
1621C22—1582no—
1622C22—1582no—
1623C22—1582no—
1624C22—1582no—
1625C22#1909903614yes—
1626C22C23×C4×D7911yescharacteristic
1627C22C2×#1457920611yescharacteristic
1628C22C2×#1457920611yescharacteristic
1629C22C2×#1457920711yescharacteristic
1630C22#1909939811yescharacteristic
1631C22#1909939911yescharacteristic
1632C22#1909940011yescharacteristic
1633C4—22no—
1634C4—22no—
1635C4—22no—
1636C4—22no—
1637C4—22no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—3161no—
1646C4—3161no—
1647C4—3161no—
1648C4—3161no—
1649C4—3161no—
1650C4—3161no—
1651C4—3161no—
1652C4—3161no—
1653C4—1582no—
1654C4—1582no—
1655C4—1582no—
1656C4—1582no—
1657C4—1582no—
1658C2—24no—
1659C2—42no—
1660C2—42no—
1661C2—3162no—
1662C2—3162no—
1663C2—3162no—
1664C2C2×#1909903611yescharacteristic
1665C2#2377660011yescharacteristic
1666C2C4×#1457920711yescharacteristic
1667C2#2377758611yescharacteristic
1668C2#2377771711yescharacteristic
1669C2#2377774711yescharacteristic
1670C2#2377794811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
FittingC79×#2339C2
socle, cosocleC23×C79C25
prime radicalC2×#19099201C2
hypercenter#2339D79
hypocenterC79#34492
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2339

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #23766561C2semidirect
3. #23766559C2semidirect
4. #23766544C2semidirect
5. #23766538C2semidirect
6. #23766511C2semidirect
7. #23766445C2semidirect
8. #23766441C2semidirect
9. #23766388C2semidirect
10. #23766377C2semidirect
11. #23766338C2semidirect
12. #23766336C2semidirect
13. #23766252C2semidirect
14. #23766242C2semidirect
15. #23766218C2semidirect
16. #23766212C2semidirect
17. #23766190C2semidirect
18. #23766166C2semidirect
19. #23766155C2semidirect
20. #23766103C2semidirect
21. #23766066C2semidirect
22. #23766056C2semidirect
23. #23766054C2semidirect
24. #23766040C2semidirect
25. #23765997C2semidirect
26. #23765992C2semidirect
27. #23765974C2semidirect
28. C4×#14579133C2semidirect
29. #23765840C2semidirect
30. C2×#19098455C2semidirect
31. C79×#2339C2semidirect
33. #19099201C4semidirect
46. C2×C4×C22⋊D79C22semidirect
47. C2×C4×C22⋊D79C22semidirect
49. C2×#14579120C22semidirect
50. C2×#14579117C22semidirect
51. C22×C4⋊Dic79C22semidirect
58. C22×C4×Dic79C22semidirect
59. #19098470C22semidirect
60. #19098470C22semidirect
61. #19098466C22semidirect
62. #19098466C22semidirect
67. #19098463C22semidirect
68. #19098463C22semidirect
69. #19098460C22semidirect
70. #19098460C22semidirect
71. #19098460C22semidirect
72. #19098458C22semidirect
73. #19098457C22semidirect
74. #19098457C22semidirect
75. #19098457C22semidirect
76. #19098457C22semidirect
83. #19098455C22semidirect
84. #19098455C22semidirect
85. #19098455C22semidirect
86. #19098455C22semidirect
87. #19098455C22semidirect
88. #19098455C22semidirect
89. #19098455C22semidirect
92. #19098454C22semidirect
95. #19098453C22semidirect
96. #19098453C22semidirect
97. #19098453C22semidirect
100. #19098452C22semidirect
101. #19098451C22semidirect
102. #19098451C22semidirect
103. #19098450C22semidirect
104. #19098450C22semidirect
105. #19098450C22semidirect
106. #19098448C22semidirect
107. #19098448C22semidirect
108. #19098447C22semidirect
109. #19098446C22semidirect
110. #19098446C22semidirect
111. #19098445C22semidirect
112. #19098444C22semidirect
115. #19098443C22semidirect
116. #19098443C22semidirect
120. #19098442C22semidirect
121. #19098442C22semidirect
129. #19098439C22semidirect
130. #19098439C22semidirect
131. #19098437C22semidirect
132. #19098437C22semidirect
133. #19098437C22semidirect
134. #19098437C22semidirect
135. #19098437C22semidirect
136. #19098436C22semidirect
137. #19098435C22semidirect
138. #19098434C22semidirect
139. #19098430C22semidirect
142. #19098424C22semidirect
143. #19098423C22semidirect
144. #19098423C22semidirect
145. #19098423C22semidirect
146. #19098423C22semidirect
148. #19098421C22semidirect
153. C4×Dic79⋊C4C22semidirect
154. #19098414C22semidirect
155. #19098414C22semidirect
156. C22⋊C4×Dic79C22semidirect
157. C22⋊C4×Dic79C22semidirect
158. C22⋊C4×Dic79C22semidirect
159. C22⋊C4×Dic79C22semidirect
160. C4×(C2×D79)⋊C4C22semidirect
161. C4×(C2×D79)⋊C4C22semidirect
162. C4×(C2×D79)⋊C4C22semidirect
163. C4×C22⋊Dic79C22semidirect
164. C4×C22⋊Dic79C22semidirect
165. C4×C22⋊Dic79C22semidirect
167. #19098410C22semidirect
168. #19098410C22semidirect
169. #19098410C22semidirect
170. #19098408C22semidirect
171. #19098408C22semidirect
172. C2×C79⋊#95C22semidirect
174. C2×C4×D4×C79C22semidirect
175. C2×C4×D4×C79C22semidirect
176. #391×C79C22semidirect
177. #391×C79C22semidirect
180. #386×C79C22semidirect
181. #386×C79C22semidirect
182. #381×C79C22semidirect
183. #381×C79C22semidirect
184. #380×C79C22semidirect
185. C4×C22⋊C4×C79C22semidirect
186. C2×#95×C79C22semidirect
187. C2×#95×C79C22semidirect
198. C2×D4×D79C2×C4semidirect
208. #14579150C2×C4semidirect
209. #14579144C2×C4semidirect
210. #14579144C2×C4semidirect
211. #14579137C2×C4semidirect
212. #14579135C2×C4semidirect
213. #14579133C2×C4semidirect
214. #14579133C2×C4semidirect
215. #14579129C2×C4semidirect
216. #14579129C2×C4semidirect
217. D4×Dic79C2×C4semidirect
221. C4×C22⋊D79C2×C4semidirect
259. C2×(C2×D79)⋊C4C2×C4semidirect
260. C2×(C2×D79)⋊C4C2×C4semidirect
338. C2×#41×C79C2×C4semidirect
850. #2339D79semidirect
867. C79#34492semidirect
886. C2×C4×D4C2×D79semidirect
887. C2×C4×D4C2×D79semidirect
900. #391C2×D79semidirect
901. #391C2×D79semidirect
974. #386C2×D79semidirect
975. #386C2×D79semidirect
988. #381C2×D79semidirect
989. #381C2×D79semidirect
996. #380C2×D79semidirect
1018. C4×C22⋊C4C2×D79semidirect
1022. C2×#95C2×D79semidirect
1023. C2×#95C2×D79semidirect
1028. C2×#41C4×D79semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#190992012
#237665612
#237665592
#237665442
#237665382
#237665112
#237664452
#237664412
#237663882
#237663772
#237663382
#237663362
#237662522
#237662422
#237662182
#237662122
#237661902
#237661662
#237661552
#237661032
#237660662
#237660562
#237660542
#237660402
#237659972
#237659922
#237659742
C4×#145791332
#237658402
C2×#190984552
C79×#23392
#3449279