Finite Group Databasebeta

← #34448981

Subgroups — #34448981

Order 20224.

2826 conjugacy classes of subgroups.

The subgroup lattice has 1646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099071C211yesmaximal, characteristic
2#23766419C211yesmaximal, characteristic, complemented
3#23766413C211yesmaximal, characteristic, complemented
4#23766408C211yesmaximal, characteristic, complemented
5#23766402C211yesmaximal, characteristic, complemented
6#23766383C211yesmaximal, characteristic, complemented
7#23766381C211yesmaximal, characteristic, complemented
8#23766378C211yesmaximal, characteristic, complemented
9#23766378C211yesmaximal, characteristic, complemented
10#23766339C211yesmaximal, characteristic, complemented
11#23766335C211yesmaximal, characteristic, complemented
12#23766309C211yesmaximal, characteristic, complemented
13#23766306C211yesmaximal, characteristic, complemented
14#23766290C211yesmaximal, characteristic, complemented
15#23766282C211yesmaximal, characteristic, complemented
16#23766239C211yesmaximal, characteristic, complemented
17#23766226C211yesmaximal, characteristic, complemented
18#23766194C211yesmaximal, characteristic, complemented
19#23766190C211yesmaximal, characteristic, complemented
20#23766186C211yesmaximal, characteristic, complemented
21#23766032C211yesmaximal, characteristic, complemented
22#23766030C211yesmaximal, characteristic, complemented
23#23765934C211yesmaximal, characteristic, complemented
24C4×#14579139C211yesmaximal, characteristic, complemented
25#23765912C211yesmaximal, characteristic, complemented
26C4×#14579134C211yesmaximal, characteristic, complemented
27#380×D79C211yesmaximal, characteristic, complemented
28#23765760C211yesmaximal, characteristic, complemented
29#23765759C211yesmaximal, characteristic, complemented
30C4×C22⋊C4×D79C211yesmaximal, characteristic, complemented
31C79×#2335C211yesmaximal, characteristic, complemented
32C22×#11929623C2211yescharacteristic
33C23×C4×D79C2211yescharacteristic
34#19099071C4116yescomplemented
35C2×#14579144C2211yescharacteristic
36C2×#14579139C2211yescharacteristic
37C2×#14579139C2211yescharacteristic
38C2×#14579134C2211yescharacteristic
39C2×#14579134C2211yescharacteristic
40C2×#14579131C2211yescharacteristic
41C2×#14579129C2211yescharacteristic
42C2×C4×Dic158C2211yescharacteristic, complemented
43C2×#14579126C2211yescharacteristic, complemented
44C2×C4×D316C2211yescharacteristic
45C2×C4×D316C2211yescharacteristic
46C2×#14579123C2211yescharacteristic
47C2×#14579123C2211yescharacteristic
48C2×#14579123C2211yescharacteristic
49C2×#14579123C2211yescharacteristic
50C2×C4×C22⋊D79C2211yescharacteristic
51C2×C4×C22⋊D79C2211yescharacteristic
52C2×C4×C22⋊D79C2211yescharacteristic, complemented
53C2×(C22⋊D79)⋊C4C2211yescharacteristic
54C2×(C22⋊D79)⋊C4C2211yescharacteristic
55C2×(C22⋊D79)⋊C4C2211yescharacteristic
56C2×(C22⋊D79)⋊C4C2211yescharacteristic
57C2×(C22⋊D79)⋊C4C2211yescharacteristic, complemented
58C2×#14579117C2211yescharacteristic
59C2×C4⋊C4×D79C2211yescharacteristic
60C2×C4⋊C4×D79C2211yescharacteristic
61C2×C22⋊C4×D79C2211yescharacteristic
62C2×C22⋊C4×D79C2211yescharacteristic
63C2×C22⋊C4×D79C2211yescharacteristic
64C2×C22⋊C4×D79C2211yescharacteristic
65C2×C42×D79C2211yescharacteristic
66C2×C42×D79C2211yescharacteristic
67#19098467C2211yescharacteristic, complemented
68#19098467C2211yescharacteristic, complemented
69#19098466C2211yescharacteristic
70#19098463C2211yescharacteristic
71#19098463C2211yescharacteristic
72#19098463C2211yescharacteristic, complemented
73#19098463C2211yescharacteristic, complemented
74#19098462C2211yescharacteristic, complemented
75#19098460C2211yescharacteristic, complemented
76#19098460C2211yescharacteristic, complemented
77#19098460C2211yescharacteristic, complemented
78#19098458C2211yescharacteristic, complemented
79#19098458C2211yescharacteristic, complemented
80#19098458C2211yescharacteristic, complemented
81#19098457C2211yescharacteristic
82#19098457C2211yescharacteristic
83#19098456C2211yescharacteristic
84#19098456C2211yescharacteristic
85#19098456C2211yescharacteristic, complemented
86#19098456C2211yescharacteristic, complemented
87#19098455C2211yescharacteristic, complemented
88#19098454C2211yescharacteristic, complemented
89#19098453C2211yescharacteristic, complemented
90#19098452C2211yescharacteristic, complemented
91#19098451C2211yescharacteristic
92#19098451C2211yescharacteristic
93#19098450C2211yescharacteristic, complemented
94#19098449C2211yescharacteristic, complemented
95#19098449C2211yescharacteristic, complemented
96#19098447C2211yescharacteristic, complemented
97#19098445C2211yescharacteristic, complemented
98#19098444C2211yescharacteristic, complemented
99#19098443C2211yescharacteristic
100#19098441C2211yescharacteristic
101#19098441C2211yescharacteristic
102#19098441C2211yescharacteristic
103#19098441C2211yescharacteristic
104#19098439C2211yescharacteristic
105#19098439C2211yescharacteristic
106#19098439C2211yescharacteristic
107#19098439C2211yescharacteristic
108#19098439C2211yescharacteristic
109#19098439C2211yescharacteristic
110#19098438C2211yescharacteristic, complemented
111#19098437C2211yescharacteristic
112#19098437C2211yescharacteristic
113#19098437C2211yescharacteristic
114#19098437C2211yescharacteristic
115#19098437C2211yescharacteristic, complemented
116#19098434C2211yescharacteristic
117#19098434C2211yescharacteristic
118#19098434C2211yescharacteristic
119#19098434C2211yescharacteristic
120#19098434C2211yescharacteristic, complemented
121#19098430C2211yescharacteristic, complemented
122#19098430C2211yescharacteristic, complemented
123#19098428C2211yescharacteristic, complemented
124#19098427C2211yescharacteristic, complemented
125#19098425C2211yescharacteristic, complemented
126#19098424C2211yescharacteristic, complemented
127#19098423C2211yescharacteristic
128#19098422C2211yescharacteristic
129#19098422C2211yescharacteristic
130#19098421C2211yescharacteristic
131#19098421C2211yescharacteristic
132#19098421C2211yescharacteristic, complemented
133#19098420C2211yescharacteristic
134#19098420C2211yescharacteristic
135#19098420C2211yescharacteristic, complemented
136C4⋊C4×Dic79C2211yescharacteristic, complemented
137C4⋊C4×Dic79C2211yescharacteristic, complemented
138C4×Dic79⋊C4C2211yescharacteristic, complemented
139C4×Dic79⋊C4C2211yescharacteristic, complemented
140C4×Dic79⋊C4C2211yescharacteristic, complemented
141C4×Dic79⋊C4C2211yescharacteristic, complemented
142#19098414C2211yescharacteristic, complemented
143#19098414C2211yescharacteristic, complemented
144#19098414C2211yescharacteristic, complemented
145C22⋊C4×Dic79C2211yescharacteristic
146C22⋊C4×Dic79C2211yescharacteristic
147C22⋊C4×Dic79C2211yescharacteristic, complemented
148C22⋊C4×Dic79C2211yescharacteristic, complemented
149C4×(C2×D79)⋊C4C2211yescharacteristic
150C4×(C2×D79)⋊C4C2211yescharacteristic
151C4×(C2×D79)⋊C4C2211yescharacteristic
152C4×(C2×D79)⋊C4C2211yescharacteristic
153C4×(C2×D79)⋊C4C2211yescharacteristic
154C4×(C2×D79)⋊C4C2211yescharacteristic
155C4×(C2×D79)⋊C4C2211yescharacteristic, complemented
156C4×(C2×D79)⋊C4C2211yescharacteristic, complemented
157C4×C22⋊Dic79C2211yescharacteristic
158#19098410C2211yescharacteristic
159#19098410C2211yescharacteristic
160#19098410C2211yescharacteristic
161#19098410C2211yescharacteristic
162#19098410C2211yescharacteristic
163#19098410C2211yescharacteristic
164#19098410C2211yescharacteristic, complemented
165#19098409C2211yescharacteristic, complemented
166#19098408C2211yescharacteristic, complemented
167C2×C79⋊#95C2211yescharacteristic, complemented
168#95×D79C2211yescharacteristic
169#95×D79C2211yescharacteristic
170#95×D79C2211yescharacteristic
171#95×D79C2211yescharacteristic
172#95×D79C2211yescharacteristic, complemented
173C2×#123×C79C2211yescharacteristic
174#390×C79C2211yescharacteristic
175#389×C79C2211yescharacteristic, complemented
176#388×C79C2211yescharacteristic
177#388×C79C2211yescharacteristic
178#388×C79C2211yescharacteristic, complemented
179#388×C79C2211yescharacteristic, complemented
180#387×C79C2211yescharacteristic, complemented
181#387×C79C2211yescharacteristic, complemented
182#386×C79C2211yescharacteristic
183#385×C79C2211yescharacteristic, complemented
184#380×C79C2211yescharacteristic
185C4×C4⋊C4×C79C2211yescharacteristic, complemented
186C4×C22⋊C4×C79C2211yescharacteristic
187C4×C22⋊C4×C79C2211yescharacteristic, complemented
188C24×D79C2311yescharacteristic
189C2×#11929623—42no—
190C2×#11929623—42no—
191C2×#11929623C2×C418yescomplemented
192C22×Dic158C2311yescharacteristic
193C22×D316C2311yescharacteristic
194C22×D316C2311yescharacteristic
195C22×C22⋊D79C2311yescharacteristic
196C22×C22⋊D79C2311yescharacteristic
197C22×C22⋊D79C2311yescharacteristic
198C22×C22⋊D79C2311yescharacteristic
199C23×Dic79C2311yescharacteristic
200C23×Dic79C2311yescharacteristic
201C23×Dic79C2311yescharacteristic
202C22×C4×D79—42no—
203C22×C4×D79—42no—
204C22×C4×D79C2×C418yescomplemented
205C22×C4×D79C2311yescharacteristic
206C22×C4×D79C2311yescharacteristic
207C22×C4×D79C2311yescharacteristic
208C22×C4×D79C2311yescharacteristic
209C22×C4×D79C2311yescharacteristic
210C22×C4×D79C2311yescharacteristic
211C22×C4×D79C2311yescharacteristic
212C22×C4×D79C2311yescharacteristic
213C22×C4×D79C2311yescharacteristic
214C22×C4×D79C2311yescharacteristic
215C22×C4×D79C2311yescharacteristic
216C22×C4×D79C2311yescharacteristic
217C22×C4×D79C2311yescharacteristic
218C22×C4×D79C2311yescharacteristic
219C22×C4×D79C2311yescharacteristic
220#14579144C2×C418yescomplemented
221#14579139C2×C418yescomplemented
222#14579139C2×C418yescomplemented
223#14579134C2×C418yescomplemented
224#14579134C2×C418yescomplemented
225#14579131C2×C418yescomplemented
226#14579129C2×C418yescomplemented
227C4×Dic158—42no—
228#14579126—42no—
229C4×D316—24no—
230C4×D316—42no—
231#14579123—24no—
232#14579123—42no—
233#14579123C2×C418yescomplemented
234#14579123C2×C418yescomplemented
235C4×C22⋊D79—24no—
236C4×C22⋊D79—42no—
237C4×C22⋊D79—42no—
238(C22⋊D79)⋊C4—24no—
239(C22⋊D79)⋊C4—42no—
240(C22⋊D79)⋊C4—42no—
241(C22⋊D79)⋊C4C2×C418yescomplemented
242(C22⋊D79)⋊C4C2×C418yescomplemented
243#14579117C2×C418yescomplemented
244C2×C4⋊Dic79C2311yescharacteristic
245C2×C4⋊Dic79C2311yescharacteristic
246C2×C4⋊Dic79C2311yescharacteristic
247C2×C4⋊Dic79C2311yescharacteristic
248C2×C4⋊Dic79C2311yescharacteristic
249C2×Dic79⋊C4C2311yescharacteristic
250C2×Dic79⋊C4C2311yescharacteristic
251C2×Dic79⋊C4C2311yescharacteristic
252C2×Dic79⋊C4C2311yescharacteristic
253C2×Dic79⋊C4C2311yescharacteristic
254C2×Dic79⋊C4C2311yescharacteristic
255C2×Dic79⋊C4C2311yescharacteristic
256C2×Dic79⋊C4C2311yescharacteristic
257C2×Dic79⋊C4C2311yescharacteristic
258C2×Dic79⋊C4C2311yescharacteristic
259C2×Dic79⋊C4C2311yescharacteristic
260C2×Dic79⋊C4C2311yescharacteristic
261C2×Dic79⋊C4C2311yescharacteristic
262C2×Dic79⋊C4C2311yescharacteristic
263C4⋊C4×D79—42no—
264C4⋊C4×D79—42no—
265C2×C22⋊Dic79C2311yescharacteristic
266C2×C22⋊Dic79C2311yescharacteristic
267C2×C22⋊Dic79C2311yescharacteristic
268C2×C22⋊Dic79C2311yescharacteristic
269C2×C22⋊Dic79C2311yescharacteristic
270C2×C22⋊Dic79C2311yescharacteristic
271C2×C22⋊Dic79C2311yescharacteristic
272C2×C22⋊Dic79C2311yescharacteristic
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
290C2×(C2×D79)⋊C4C2311yescharacteristic
291C2×(C2×D79)⋊C4C2311yescharacteristic
292C2×(C2×D79)⋊C4C2311yescharacteristic
293C22⋊C4×D79—24no—
294C22⋊C4×D79—24no—
295C22⋊C4×D79—42no—
296C22⋊C4×D79—42no—
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
308C2×C4×Dic79C2311yescharacteristic
309C2×C4×Dic79C2311yescharacteristic
310C2×C4×Dic79C2311yescharacteristic
311C2×C4×Dic79C2311yescharacteristic
312C2×C4×Dic79C2311yescharacteristic
313C2×C4×Dic79C2311yescharacteristic
314C42×D79—42no—
315C42×D79—42no—
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
336C79⋊#95C2311yescharacteristic
337C79⋊#95C2311yescharacteristic
338C79⋊#95C2311yescharacteristic
339C79⋊#95C2311yescharacteristic
340C79⋊#95C2311yescharacteristic
341C79⋊#95C2311yescharacteristic
342C79⋊#95C2311yescharacteristic
343C79⋊#95C2311yescharacteristic
344C79⋊#95C2311yescharacteristic
345C79⋊#95C2311yescharacteristic
346C22×D4×C79C2311yescharacteristic
347C23×C4×C79C2311yescharacteristic
348C23×C4×C79C2311yescharacteristic
349#123×C79C2×C418yescomplemented
350C2×C4⋊C4×C79C2311yescharacteristic
351C2×C4⋊C4×C79C2311yescharacteristic
352C2×C4⋊C4×C79C2311yescharacteristic
353C2×C4⋊C4×C79C2311yescharacteristic
354C2×C4⋊C4×C79C2311yescharacteristic
355C2×C4⋊C4×C79C2311yescharacteristic
356C2×C4⋊C4×C79C2311yescharacteristic
357C2×C22⋊C4×C79C2311yescharacteristic
358C2×C22⋊C4×C79C2311yescharacteristic
359C2×C22⋊C4×C79C2311yescharacteristic
360C2×C22⋊C4×C79C2311yescharacteristic
361C2×C22⋊C4×C79C2311yescharacteristic
362C2×C22⋊C4×C79C2311yescharacteristic
363C2×C22⋊C4×C79C2311yescharacteristic
364C2×C22⋊C4×C79C2311yescharacteristic
365C2×C22⋊C4×C79C2311yescharacteristic
366C2×C22⋊C4×C79C2311yescharacteristic
367C2×C42×C79C2311yescharacteristic
368C2×C42×C79C2311yescharacteristic
369C2×C42×C79C2311yescharacteristic
370C2×C42×C79C2311yescharacteristic
371C2×C42×C79C2311yescharacteristic
372#95×C79C2311yescharacteristic
373#95×C79C2311yescharacteristic
374#95×C79C2311yescharacteristic
375#95×C79C2311yescharacteristic
376#95×C79C2311yescharacteristic
377#95×C79C2311yescharacteristic
378#95×C79C2311yescharacteristic
379#95×C79C2311yescharacteristic
380#95×C79C2311yescharacteristic
381#95×C79C2311yescharacteristic
382C23×D79—22no—
383C23×D79—22no—
384C23×D79—22no—
385C23×D79—22no—
386C23×D79—41no—
387C23×D79—41no—
388C23×D79C22×C414yes—
389C23×D79C2411yescharacteristic
390C23×D79C2411yescharacteristic
391C23×D79C2411yescharacteristic
392#11929623—416no—
393C2×Dic158—22no—
394C2×Dic158—22no—
395C2×Dic158C22×C414yes—
396C2×D316—22no—
397C2×D316—22no—
398C2×D316—22no—
399C2×D316—22no—
400C2×D316C22×C414yes—
401C2×D316C22×C414yes—
402C2×C22⋊D79—22no—
403C2×C22⋊D79—22no—
404C2×C22⋊D79—22no—
405C2×C22⋊D79—22no—
406C2×C22⋊D79—22no—
407C2×C22⋊D79—22no—
408C2×C22⋊D79—41no—
409C2×C22⋊D79—41no—
410C2×C22⋊D79C22×C414yes—
411C2×C22⋊D79C22×C414yes—
412C2×C22⋊D79C22×C414yes—
413C2×C22⋊D79C22×C414yes—
414C22×Dic79—22no—
415C22×Dic79—22no—
416C22×Dic79—22no—
417C22×Dic79—41no—
418C22×Dic79—41no—
419C22×Dic79—41no—
420C22×Dic79—41no—
421C22×Dic79C22×C414yes—
422C22×Dic79C22×C414yes—
423C22×Dic79C2411yescharacteristic
424C22×Dic79C2411yescharacteristic
425C22×Dic79C2411yescharacteristic
426C22×Dic79C2411yescharacteristic
427C22×Dic79C2411yescharacteristic
428C22×Dic79C2411yescharacteristic
429C22×Dic79C2411yescharacteristic
430C22×Dic79C2411yescharacteristic
431C22×Dic79C2411yescharacteristic
432C22×Dic79C2411yescharacteristic
433C22×Dic79C2411yescharacteristic
434C22×Dic79C2411yescharacteristic
435C22×Dic79C2411yescharacteristic
436C2×C4×D79—22no—
437C2×C4×D79—22no—
438C2×C4×D79—22no—
439C2×C4×D79—22no—
440C2×C4×D79—22no—
441C2×C4×D79—22no—
442C2×C4×D79—22no—
443C2×C4×D79—22no—
444C2×C4×D79—22no—
445C2×C4×D79—22no—
446C2×C4×D79—22no—
447C2×C4×D79—22no—
448C2×C4×D79—22no—
449C2×C4×D79—22no—
450C2×C4×D79—22no—
451C2×C4×D79—22no—
452C2×C4×D79—22no—
453C2×C4×D79—22no—
454C2×C4×D79—41no—
455C2×C4×D79—41no—
456C2×C4×D79—41no—
457C2×C4×D79—41no—
458C2×C4×D79—41no—
459C2×C4×D79—41no—
460C2×C4×D79—41no—
461C2×C4×D79—41no—
462C2×C4×D79—41no—
463C2×C4×D79—41no—
464C2×C4×D79—41no—
465C2×C4×D79—41no—
466C2×C4×D79—41no—
467C2×C4×D79—41no—
468C2×C4×D79—41no—
469C2×C4×D79—41no—
470C2×C4×D79—41no—
471C2×C4×D79—41no—
472C2×C4×D79—41no—
473C2×C4×D79—41no—
474C2×C4×D79—41no—
475C2×C4×D79—41no—
476C2×C4×D79—416no—
477C2×C4×D79C22×C414yes—
478C2×C4×D79C22×C414yes—
479C2×C4×D79C22×C414yes—
480C2×C4×D79C22×C414yes—
481C2×C4×D79C22×C414yes—
482C4⋊Dic79—22no—
483C4⋊Dic79—41no—
484C4⋊Dic79—41no—
485C4⋊Dic79—41no—
486C4⋊Dic79—41no—
487Dic79⋊C4—22no—
488Dic79⋊C4—22no—
489Dic79⋊C4—22no—
490Dic79⋊C4—22no—
491Dic79⋊C4—22no—
492Dic79⋊C4—22no—
493Dic79⋊C4—41no—
494Dic79⋊C4—41no—
495Dic79⋊C4—41no—
496Dic79⋊C4—41no—
497Dic79⋊C4C22×C414yes—
498Dic79⋊C4C22×C414yes—
499Dic79⋊C4C22×C414yes—
500Dic79⋊C4C22×C414yes—
501C22⋊Dic79—22no—
502C22⋊Dic79—22no—
503C22⋊Dic79—22no—
504C22⋊Dic79—41no—
505C22⋊Dic79—41no—
506C22⋊Dic79—41no—
507C22⋊Dic79—41no—
508C22⋊Dic79C22×C414yes—
509(C2×D79)⋊C4—22no—
510(C2×D79)⋊C4—22no—
511(C2×D79)⋊C4—22no—
512(C2×D79)⋊C4—22no—
513(C2×D79)⋊C4—22no—
514(C2×D79)⋊C4—22no—
515(C2×D79)⋊C4—22no—
516(C2×D79)⋊C4—22no—
517(C2×D79)⋊C4—41no—
518(C2×D79)⋊C4—41no—
519(C2×D79)⋊C4—41no—
520(C2×D79)⋊C4—41no—
521(C2×D79)⋊C4C22×C414yes—
522(C2×D79)⋊C4C22×C414yes—
523(C2×D79)⋊C4C22×C414yes—
524(C2×D79)⋊C4C22×C414yes—
525(C2×D79)⋊C4C22×C414yes—
526(C2×D79)⋊C4C22×C414yes—
527(C2×D79)⋊C4#4114yescomplemented
528(C2×D79)⋊C4#4114yescomplemented
529C4×Dic79—22no—
530C4×Dic79—22no—
531C4×Dic79—22no—
532C4×Dic79—22no—
533C4×Dic79—22no—
534C4×Dic79—22no—
535C4×Dic79—22no—
536C4×Dic79—41no—
537C4×Dic79—41no—
538C4×Dic79—41no—
539C4×Dic79—41no—
540C4×Dic79—41no—
541C4×Dic79—41no—
542C4×Dic79—41no—
543C4×Dic79—41no—
544C4×Dic79C22×C414yes—
545C4×Dic79C22×C414yes—
546C24×C79C2411yescharacteristic
547C24×C79C2411yescharacteristic
548C2×D4×C79—41no—
549C2×D4×C79—41no—
550C2×D4×C79C22×C414yes—
551C22×C4×C79—22no—
552C22×C4×C79—41no—
553C22×C4×C79—41no—
554C22×C4×C79—41no—
555C22×C4×C79—41no—
556C22×C4×C79C22×C414yes—
557C22×C4×C79C2411yescharacteristic
558C22×C4×C79C2411yescharacteristic
559C22×C4×C79C2411yescharacteristic
560C22×C4×C79C2411yescharacteristic
561C22×C4×C79C2411yescharacteristic
562C22×C4×C79C2411yescharacteristic
563C22×C4×C79C2411yescharacteristic
564C22×C4×C79C2411yescharacteristic
565C22×C4×C79C2411yescharacteristic
566C22×C4×C79C2411yescharacteristic
567C22×C4×C79C2411yescharacteristic
568C22×C4×C79C2411yescharacteristic
569C22×C4×C79C2411yescharacteristic
570C4⋊C4×C79—22no—
571C4⋊C4×C79—41no—
572C4⋊C4×C79—41no—
573C4⋊C4×C79—41no—
574C4⋊C4×C79—41no—
575C4⋊C4×C79C22×C414yes—
576C4⋊C4×C79C22×C414yes—
577C22⋊C4×C79—22no—
578C22⋊C4×C79—22no—
579C22⋊C4×C79—22no—
580C22⋊C4×C79—41no—
581C22⋊C4×C79—41no—
582C22⋊C4×C79—41no—
583C22⋊C4×C79—41no—
584C22⋊C4×C79C22×C414yes—
585C22⋊C4×C79C22×C414yes—
586C22⋊C4×C79C22×C414yes—
587C42×C79—22no—
588C42×C79—41no—
589C42×C79—41no—
590C42×C79—41no—
591C42×C79—41no—
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×C79C2511yescharacteristic
607C22×D79—21no—
608C22×D79—21no—
609C22×D79—21no—
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—28no—
622C22×D79—28no—
623C22×D79—44no—
624C22×D79—44no—
625C22×D79—44no—
626C22×D79—44no—
627C22×D79—44no—
628C22×D79C23×C412yes—
629C22×D79C23×C412yes—
630C22×D79C23×C412yes—
631C22×D79C2×#4112yes—
632C22×D79C2×#4112yes—
633C22×D79H(5,𝔽2)12yes—
634C22×D792−1+412yes—
635D4×C79—44no—
636C2×C4×C79—21no—
637C2×C4×C79—21no—
638C2×C4×C79—21no—
639C2×C4×C79—21no—
640C2×C4×C79—21no—
641C2×C4×C79—21no—
642C2×C4×C79—21no—
643C2×C4×C79—21no—
644C2×C4×C79—21no—
645C2×C4×C79—21no—
646C2×C4×C79—21no—
647C2×C4×C79—21no—
648C2×C4×C79—21no—
649C2×C4×C79—21no—
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—44no—
669C2×C4×C79—82no—
670C2×C4×C79C23×C412yes—
671C2×C4×C79C23×C412yes—
672C2×C4×C79C23×C412yes—
673C2×C4×C79C23×C412yes—
674C2×C4×C79C23×C412yes—
675C2×C4×C79C2×#4112yes—
676C2×C4×C79C2×#4112yes—
677C22⋊D79—28no—
678C22⋊D79—28no—
679C22⋊D79—28no—
680C22⋊D79—44no—
681C2×Dic79—21no—
682C2×Dic79—21no—
683C2×Dic79—21no—
684C2×Dic79—21no—
685C2×Dic79—21no—
686C2×Dic79—21no—
687C2×Dic79—21no—
688C2×Dic79—21no—
689C2×Dic79—21no—
690C2×Dic79—21no—
691C2×Dic79—21no—
692C2×Dic79—21no—
693C2×Dic79—28no—
694C2×Dic79—21no—
695C2×Dic79—21no—
696C2×Dic79—21no—
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—44no—
713C2×Dic79—82no—
714C2×Dic79C23×C412yes—
715C2×Dic79C23×C412yes—
716C2×Dic79C23×C412yes—
717C2×Dic79C23×C412yes—
718C2×Dic79C23×C412yes—
719C2×Dic79C2×#4112yes—
720C2×Dic79C2×#4112yes—
721C2×Dic79H(5,𝔽2)12yes—
722C2×Dic79H(5,𝔽2)12yes—
723D316—28no—
724D316—28no—
725C4×D79—28no—
726C4×D79—28no—
727C4×D79—44no—
728C4×D79—44no—
729C4×D79—44no—
730C4×D79—44no—
731C4×D79—44no—
732C4×D79—44no—
733C4×D79—44no—
734C4×D79—82no—
735C4×D79—82no—
736C4×D79—82no—
737C4×D79—82no—
738C4×D79—82no—
739C4×D79—82no—
740Dic158—28no—
741C22×C79—22no—
742C22×C79—22no—
743C22×C79—22no—
744C22×C79—22no—
745C22×C79—22no—
746C22×C79—22no—
747C22×C79—41no—
748C22×C79—41no—
749C22×C79—41no—
750C22×C79—41no—
751C22×C79—41no—
752C22×C79—41no—
753C22×C79—41no—
754C22×C79—41no—
755C22×C79C24×C411yescharacteristic
756C22×C79C22×#4111yescharacteristic
757C22×C79C22×#4111yescharacteristic
758C22×C79C2×H(5,𝔽2)11yescharacteristic
759C22×C79C2×H(5,𝔽2)11yescharacteristic
760C22×C79C2×H(5,𝔽2)11yescharacteristic
761C22×C79C2×2−1+411yescharacteristic
762C2×D79—22no—
763C2×D79—22no—
764C2×D79—22no—
765C2×D79—22no—
766C2×D79—22no—
767C2×D79—22no—
768C2×D79—22no—
769C2×D79—22no—
770C2×D79—22no—
771C2×D79—22no—
772C2×D79—22no—
773C2×D79—22no—
774C2×D79—22no—
775C2×D79—22no—
776C2×D79—22no—
777C2×D79—416no—
778C2×D79—41no—
779C2×D79—41no—
780C2×D79—41no—
781C2×D79—41no—
782C2×D79C4×#4114yes—
783C2×D79#52014yes—
784C4×C79—22no—
785C4×C79—22no—
786C4×C79—22no—
787C4×C79—22no—
788C4×C79—22no—
789C4×C79—22no—
790C4×C79—22no—
791C4×C79—41no—
792C4×C79—41no—
793C4×C79—41no—
794C4×C79—41no—
795C4×C79—41no—
796C4×C79—41no—
797Dic79—22no—
798Dic79—22no—
799Dic79—22no—
800Dic79—22no—
801Dic79—22no—
802Dic79—22no—
803Dic79—41no—
804Dic79—41no—
805Dic79—41no—
806Dic79—41no—
807Dic79—41no—
808Dic79—41no—
809Dic79#51814yes—
810#34233—791nomaximal, Sylow
811C2×C79—42no—
812C2×C79—42no—
813C2×C79C2×C4×#4111yescharacteristic
814C2×C79C2×#51811yescharacteristic
815C2×C79C2×#52011yescharacteristic
816C2×C79#351911yescharacteristic
817C2×C79#351911yescharacteristic
818C2×C79#352011yescharacteristic
819C2×C79#352011yescharacteristic
820D79—24no—
821D79—24no—
822D79—42no—
823C2×#525—791no—
824#2361—791no—
825#2361—791no—
826#2360—791no—
827#2360—791no—
828#2358—791no—
829#2358—791no—
830#2358—791no—
831#2358—791no—
832#2353—791no—
833#2353—791no—
834#2349—791no—
835#2349—791no—
836#2347—791no—
837#2346—791no—
838#2341—791no—
839#2339—791no—
840#2335—791no—
841#2335—791no—
842#2335—791no—
843#2335D7911yescharacteristic, complemented
844#2318—791no—
845#2318—791no—
846C4×C22⋊Q8—791no—
847C4×C22⋊Q8—791no—
848C4×#121—791no—
849C4×#121—791no—
850C2×#380—791no—
851#2275—791no—
852#2275—791no—
853C2×C4×C22⋊C4—791no—
854C79#3423311yescharacteristic, complemented, Sylow
855C22×#41—791no—
856C24×C4—791no—
857#525—7916no—
858C2×#123—791no—
859C2×#123C2×D7911yescharacteristic
860C2×C22⋊Q8—791no—
861C2×C22⋊Q8—791no—
862C2×#121—791no—
863C2×#121—791no—
864C2×#120—791no—
865C2×#120—791no—
866C2×C4×Q8—791no—
867C2×C4×Q8—791no—
868C2×C4×D4—791no—
869C2×C4×D4—791no—
870C2×C4×D4—791no—
871C2×C4×D4—791no—
872C2×C4×D4—791no—
873C2×C4×D4—791no—
874C2×C4×D4—791no—
875C2×C4×D4—791no—
876C2×C4×D4—791no—
877C2×C4×D4—791no—
878C2×C4×D4—791no—
879C2×C4×D4—791no—
880C2×C4×D4—791no—
881C2×C4×D4—791no—
882C2×#117—791no—
883C22×C4⋊C4—791no—
884C22×C4⋊C4—791no—
885C22×C22⋊C4—791no—
886C22×C22⋊C4—791no—
887C22×C22⋊C4—791no—
888C22×C22⋊C4—791no—
889C22×C42—791no—
890C22×C42—791no—
891#391—791no—
892#391—791no—
893#390—791no—
894#390—791no—
895#390—791no—
896#390—791no—
897#390—791no—
898#390C2×D7911yescharacteristic
899#389—791no—
900#389—791no—
901#389—791no—
902#389—791no—
903#389—791no—
904#389—791no—
905#389—791no—
906#389C2×D7911yescharacteristic, complemented
907#388—791no—
908#388—791no—
909#388—791no—
910#388—791no—
911#388—791no—
912#388—791no—
913#388—791no—
914#388—791no—
915#388—791no—
916#388—791no—
917#388—791no—
918#388—791no—
919#388C2×D7911yescharacteristic
920#388C2×D7911yescharacteristic
921#388C2×D7911yescharacteristic, complemented
922#388C2×D7911yescharacteristic, complemented
923#387—791no—
924#387—791no—
925#387—791no—
926#387—791no—
927#387—791no—
928#387—791no—
929#387C2×D7911yescharacteristic, complemented
930#387C2×D7911yescharacteristic, complemented
931#386—791no—
932#386—791no—
933#386—791no—
934#386—791no—
935#386—791no—
936#386—791no—
937#386—791no—
938#386—791no—
939#386—791no—
940#386—791no—
941#386—791no—
942#386C2×D7911yescharacteristic
943#385—791no—
944#385—791no—
945#385—791no—
946#385—791no—
947#385—791no—
948#385—791no—
949#385—791no—
950#385—791no—
951#385—791no—
952#385—791no—
953#385—791no—
954#385C2×D7911yescharacteristic, complemented
955#383—791no—
956#383—791no—
957#382—791no—
958#382—791no—
959#381—791no—
960#381—791no—
961#380—791no—
962#380—791no—
963#380—791no—
964#380—791no—
965#380—791no—
966#380—791no—
967#380—791no—
968#380—791no—
969#380—791no—
970#380C2×D7911yescharacteristic
971C4×C4⋊C4—791no—
972C4×C4⋊C4—791no—
973C4×C4⋊C4—791no—
974C4×C4⋊C4—791no—
975C4×C4⋊C4—791no—
976C4×C4⋊C4—791no—
977C4×C4⋊C4—791no—
978C4×C4⋊C4—791no—
979C4×C4⋊C4—791no—
980C4×C4⋊C4C2×D7911yescharacteristic, complemented
981C4×C22⋊C4—791no—
982C4×C22⋊C4—791no—
983C4×C22⋊C4—791no—
984C4×C22⋊C4—791no—
985C4×C22⋊C4—791no—
986C4×C22⋊C4—791no—
987C4×C22⋊C4—791no—
988C4×C22⋊C4—791no—
989C4×C22⋊C4—791no—
990C4×C22⋊C4—791no—
991C4×C22⋊C4—791no—
992C4×C22⋊C4—791no—
993C4×C22⋊C4—791no—
994C4×C22⋊C4—791no—
995C4×C22⋊C4—791no—
996C4×C22⋊C4—791no—
997C4×C22⋊C4—791no—
998C4×C22⋊C4—791no—
999C4×C22⋊C4—791no—
1000C4×C22⋊C4—791no—
1001C4×C22⋊C4C2×D7911yescharacteristic
1002C4×C22⋊C4C2×D7911yescharacteristic, complemented
1003#376—791no—
1004#376—791no—
1005C2×#95—791no—
1006C2×#95—791no—
1007C2×#95—791no—
1008C2×#95—791no—
1009C2×#95—791no—
1010C2×#95—791no—
1011C25—791no—
1012C2×#41—3162no—
1013C2×#41—3162no—
1014C2×#41—798no—
1015C22×Q8—791no—
1016C22×D4—791no—
1017C22×D4—791no—
1018C22×D4—791no—
1019C22×D4—791no—
1020C22×D4—791no—
1021C22×D4—791no—
1022C22×D4C22×D7911yescharacteristic
1023C23×C4—3162no—
1024C23×C4—3162no—
1025C23×C4—791no—
1026C23×C4—798no—
1027C23×C4—791no—
1028C23×C4—791no—
1029C23×C4—791no—
1030C23×C4—791no—
1031C23×C4—791no—
1032C23×C4—791no—
1033C23×C4—791no—
1034C23×C4—791no—
1035C23×C4—791no—
1036C23×C4—791no—
1037C23×C4—791no—
1038C23×C4—791no—
1039C23×C4—791no—
1040C23×C4—791no—
1041C23×C4—791no—
1042C23×C4—791no—
1043C23×C4—791no—
1044C23×C4C22×D7911yescharacteristic
1045C23×C4C22×D7911yescharacteristic
1046#123—798no—
1047#123C4×D7918yescomplemented
1048C22⋊Q8—798no—
1049C22⋊Q8—798no—
1050#121—798no—
1051#121—798no—
1052#120—798no—
1053#120—798no—
1054C4×Q8—3162no—
1055C4×Q8—3162no—
1056C4×D4—3162no—
1057C4×D4—3162no—
1058C4×D4—3162no—
1059C4×D4—3162no—
1060C4×D4—3162no—
1061C4×D4—3162no—
1062C4×D4—798no—
1063C4×D4—798no—
1064C4×D4—798no—
1065C4×D4—798no—
1066C4×D4—1584no—
1067C4×D4—1584no—
1068C4×D4—1584no—
1069C4×D4—1584no—
1070#117—798no—
1071C2×C4⋊C4—3162no—
1072C2×C4⋊C4—3162no—
1073C2×C4⋊C4—791no—
1074C2×C4⋊C4—791no—
1075C2×C4⋊C4—791no—
1076C2×C4⋊C4—791no—
1077C2×C4⋊C4—791no—
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⋊C4C22×D7911yescharacteristic
1093C2×C4⋊C4C22×D7911yescharacteristic
1094C2×C4⋊C4C22×D7911yescharacteristic
1095C2×C4⋊C4C22×D7911yescharacteristic
1096C2×C4⋊C4C22×D7911yescharacteristic
1097C2×C4⋊C4C22×D7911yescharacteristic
1098C2×C4⋊C4C22×D7911yescharacteristic
1099C2×C22⋊C4—3162no—
1100C2×C22⋊C4—3162no—
1101C2×C22⋊C4—791no—
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—1584no—
1130C2×C22⋊C4—1584no—
1131C2×C22⋊C4C22×D7911yescharacteristic
1132C2×C22⋊C4C22×D7911yescharacteristic
1133C2×C22⋊C4C22×D7911yescharacteristic
1134C2×C22⋊C4C22×D7911yescharacteristic
1135C2×C22⋊C4C22×D7911yescharacteristic
1136C2×C22⋊C4C22×D7911yescharacteristic
1137C2×C22⋊C4C22×D7911yescharacteristic
1138C2×C22⋊C4C22×D7911yescharacteristic
1139C2×C22⋊C4C22×D7911yescharacteristic
1140C2×C22⋊C4C22×D7911yescharacteristic
1141C2×C42—3162no—
1142C2×C42—3162no—
1143C2×C42—791no—
1144C2×C42—791no—
1145C2×C42—791no—
1146C2×C42—791no—
1147C2×C42—791no—
1148C2×C42—791no—
1149C2×C42—791no—
1150C2×C42—791no—
1151C2×C42—791no—
1152C2×C42—791no—
1153C2×C42—791no—
1154C2×C42—791no—
1155C2×C42—791no—
1156C2×C42—791no—
1157C2×C42—791no—
1158C2×C42—791no—
1159C2×C42—791no—
1160C2×C42C22×D7911yescharacteristic
1161C2×C42C22×D7911yescharacteristic
1162C2×C42C22×D7911yescharacteristic
1163C2×C42C22×D7911yescharacteristic
1164C2×C42C22×D7911yescharacteristic
1165#95—791no—
1166#95—791no—
1167#95—791no—
1168#95—791no—
1169#95—791no—
1170#95—791no—
1171#95—791no—
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#95C22×D7911yescharacteristic
1196#95C22×D7911yescharacteristic
1197#95C22×D7911yescharacteristic
1198#95C22×D7911yescharacteristic
1199#95C22×D7911yescharacteristic
1200#95C22×D7911yescharacteristic
1201#95C22×D7911yescharacteristic
1202#95C22×D7911yescharacteristic
1203#95C22×D7911yescharacteristic
1204#95C22×D7911yescharacteristic
1205C24—3161no—
1206C24—3161no—
1207C24—794no—
1208C24—791no—
1209C24—791no—
1210C24—791no—
1211C24—1582no—
1212C24—1582no—
1213C24—1582no—
1214C24—1582no—
1215C24C23×D7911yescharacteristic
1216C24C23×D7911yescharacteristic
1217#41—31616no—
1218C2×Q8—794no—
1219C2×Q8—1582no—
1220C2×Q8—1582no—
1221C2×D4—41no—
1222C2×D4—41no—
1223C2×D4—3161no—
1224C2×D4—3161no—
1225C2×D4—794no—
1226C2×D4—794no—
1227C2×D4—794no—
1228C2×D4—794no—
1229C2×D4—794no—
1230C2×D4—794no—
1231C2×D4—1582no—
1232C2×D4—1582no—
1233C2×D4—1582no—
1234C2×D4—1582no—
1235C2×D4—1582no—
1236C2×D4—1582no—
1237C2×D4—1582no—
1238C2×D4—1582no—
1239C2×D4—1582no—
1240C2×D4—1582no—
1241C2×D4C2×C4×D7914yes—
1242C22×C4—22no—
1243C22×C4—41no—
1244C22×C4—41no—
1245C22×C4—41no—
1246C22×C4—41no—
1247C22×C4—3161no—
1248C22×C4—3161no—
1249C22×C4—3161no—
1250C22×C4—3161no—
1251C22×C4—3161no—
1252C22×C4—3161no—
1253C22×C4—3161no—
1254C22×C4—3161no—
1255C22×C4—3161no—
1256C22×C4—3161no—
1257C22×C4—3161no—
1258C22×C4—3161no—
1259C22×C4—3161no—
1260C22×C4—3161no—
1261C22×C4—3161no—
1262C22×C4—3161no—
1263C22×C4—3161no—
1264C22×C4—3161no—
1265C22×C4—3161no—
1266C22×C4—3161no—
1267C22×C4—3161no—
1268C22×C4—3161no—
1269C22×C4—31616no—
1270C22×C4—3161no—
1271C22×C4—3161no—
1272C22×C4—3161no—
1273C22×C4—3161no—
1274C22×C4—794no—
1275C22×C4—794no—
1276C22×C4—794no—
1277C22×C4—794no—
1278C22×C4—791no—
1279C22×C4—791no—
1280C22×C4—791no—
1281C22×C4—791no—
1282C22×C4—791no—
1283C22×C4—791no—
1284C22×C4—791no—
1285C22×C4—794no—
1286C22×C4—794no—
1287C22×C4—794no—
1288C22×C4—791no—
1289C22×C4—791no—
1290C22×C4—791no—
1291C22×C4—791no—
1292C22×C4—791no—
1293C22×C4—791no—
1294C22×C4—1582no—
1295C22×C4—1582no—
1296C22×C4—1582no—
1297C22×C4—1582no—
1298C22×C4—1582no—
1299C22×C4—1582no—
1300C22×C4—1582no—
1301C22×C4—1582no—
1302C22×C4—1582no—
1303C22×C4—1582no—
1304C22×C4—1582no—
1305C22×C4—1582no—
1306C22×C4—1582no—
1307C22×C4—1582no—
1308C22×C4—1582no—
1309C22×C4—1582no—
1310C22×C4—1582no—
1311C22×C4—1582no—
1312C22×C4—1582no—
1313C22×C4—1582no—
1314C22×C4—1582no—
1315C22×C4C2×C4×D7914yes—
1316C22×C4C23×D7911yescharacteristic
1317C22×C4C23×D7911yescharacteristic
1318C22×C4C23×D7911yescharacteristic
1319C22×C4C23×D7911yescharacteristic
1320C22×C4C23×D7911yescharacteristic
1321C22×C4C23×D7911yescharacteristic
1322C22×C4C23×D7911yescharacteristic
1323C22×C4C23×D7911yescharacteristic
1324C22×C4C23×D7911yescharacteristic
1325C22×C4C23×D7911yescharacteristic
1326C22×C4C23×D7911yescharacteristic
1327C22×C4C23×D7911yescharacteristic
1328C22×C4C23×D7911yescharacteristic
1329C4⋊C4—22no—
1330C4⋊C4—41no—
1331C4⋊C4—41no—
1332C4⋊C4—41no—
1333C4⋊C4—41no—
1334C4⋊C4—3161no—
1335C4⋊C4—3161no—
1336C4⋊C4—3161no—
1337C4⋊C4—3161no—
1338C4⋊C4—3161no—
1339C4⋊C4—3161no—
1340C4⋊C4—3161no—
1341C4⋊C4—3161no—
1342C4⋊C4—794no—
1343C4⋊C4—794no—
1344C4⋊C4—794no—
1345C4⋊C4—794no—
1346C4⋊C4—1582no—
1347C4⋊C4—1582no—
1348C4⋊C4—1582no—
1349C4⋊C4—1582no—
1350C4⋊C4—1582no—
1351C4⋊C4—1582no—
1352C4⋊C4—1582no—
1353C4⋊C4C2×C4×D7914yes—
1354C4⋊C4C2×C4×D7914yes—
1355C22⋊C4—22no—
1356C22⋊C4—22no—
1357C22⋊C4—22no—
1358C22⋊C4—41no—
1359C22⋊C4—41no—
1360C22⋊C4—41no—
1361C22⋊C4—41no—
1362C22⋊C4—3161no—
1363C22⋊C4—3161no—
1364C22⋊C4—3161no—
1365C22⋊C4—3161no—
1366C22⋊C4—3161no—
1367C22⋊C4—3161no—
1368C22⋊C4—3161no—
1369C22⋊C4—3161no—
1370C22⋊C4—794no—
1371C22⋊C4—794no—
1372C22⋊C4—794no—
1373C22⋊C4—794no—
1374C22⋊C4—794no—
1375C22⋊C4—794no—
1376C22⋊C4—794no—
1377C22⋊C4—794no—
1378C22⋊C4—794no—
1379C22⋊C4—1582no—
1380C22⋊C4—1582no—
1381C22⋊C4—1582no—
1382C22⋊C4—1582no—
1383C22⋊C4—1582no—
1384C22⋊C4—1582no—
1385C22⋊C4—1582no—
1386C22⋊C4—1582no—
1387C22⋊C4—1582no—
1388C22⋊C4—1582no—
1389C22⋊C4—1582no—
1390C22⋊C4C2×C4×D7914yes—
1391C22⋊C4C2×C4×D7914yes—
1392C22⋊C4C2×C4×D7914yes—
1393C42—22no—
1394C42—41no—
1395C42—41no—
1396C42—41no—
1397C42—41no—
1398C42—3161no—
1399C42—3161no—
1400C42—3161no—
1401C42—3161no—
1402C42—3161no—
1403C42—3161no—
1404C42—3161no—
1405C42—3161no—
1406C42—794no—
1407C42—794no—
1408C42—1582no—
1409C42—1582no—
1410C42—1582no—
1411C42—1582no—
1412C42—1582no—
1413C42—1582no—
1414C42—1582no—
1415C23—21no—
1416C23—21no—
1417C23—21no—
1418C23—21no—
1419C23—21no—
1420C23—21no—
1421C23—21no—
1422C23—21no—
1423C23—21no—
1424C23—21no—
1425C23—21no—
1426C23—21no—
1427C23—3164no—
1428C23—3164no—
1429C23—3164no—
1430C23—3164no—
1431C23—3164no—
1432C23—792no—
1433C23—792no—
1434C23—792no—
1435C23—792no—
1436C23—792no—
1437C23—792no—
1438C23—792no—
1439C23—1588no—
1440C23—1588no—
1441C23—1581no—
1442C23—1581no—
1443C23—1581no—
1444C23—1581no—
1445C23—1581no—
1446C23—1581no—
1447C23—1581no—
1448C23—1581no—
1449C23—1581no—
1450C23—1581no—
1451C23—1581no—
1452C23—1581no—
1453C23—1581no—
1454C23—1581no—
1455C23C22×C4×D7912yes—
1456C23C22×C4×D7912yes—
1457C23C24×D7911yescharacteristic
1458Q8—1588no—
1459D4—44no—
1460D4—3164no—
1461D4—1588no—
1462D4—1588no—
1463D4—1588no—
1464D4—1588no—
1465D4—1588no—
1466C2×C4—21no—
1467C2×C4—21no—
1468C2×C4—21no—
1469C2×C4—21no—
1470C2×C4—21no—
1471C2×C4—21no—
1472C2×C4—21no—
1473C2×C4—21no—
1474C2×C4—21no—
1475C2×C4—21no—
1476C2×C4—21no—
1477C2×C4—21no—
1478C2×C4—21no—
1479C2×C4—21no—
1480C2×C4—21no—
1481C2×C4—21no—
1482C2×C4—21no—
1483C2×C4—21no—
1484C2×C4—21no—
1485C2×C4—21no—
1486C2×C4—21no—
1487C2×C4—21no—
1488C2×C4—21no—
1489C2×C4—21no—
1490C2×C4—21no—
1491C2×C4—21no—
1492C2×C4—21no—
1493C2×C4—21no—
1494C2×C4—21no—
1495C2×C4—21no—
1496C2×C4—21no—
1497C2×C4—21no—
1498C2×C4—44no—
1499C2×C4—82no—
1500C2×C4—3164no—
1501C2×C4—3164no—
1502C2×C4—3164no—
1503C2×C4—3164no—
1504C2×C4—3164no—
1505C2×C4—3164no—
1506C2×C4—3164no—
1507C2×C4—3164no—
1508C2×C4—792no—
1509C2×C4—792no—
1510C2×C4—792no—
1511C2×C4—792no—
1512C2×C4—792no—
1513C2×C4—792no—
1514C2×C4—792no—
1515C2×C4—792no—
1516C2×C4—792no—
1517C2×C4—6322no—
1518C2×C4—6322no—
1519C2×C4—6322no—
1520C2×C4—6322no—
1521C2×C4—6322no—
1522C2×C4—6322no—
1523C2×C4—6322no—
1524C2×C4—1588no—
1525C2×C4—1588no—
1526C2×C4—1581no—
1527C2×C4—1581no—
1528C2×C4—1581no—
1529C2×C4—1581no—
1530C2×C4—1581no—
1531C2×C4—1581no—
1532C2×C4—1581no—
1533C2×C4—1581no—
1534C2×C4—1581no—
1535C2×C4—1581no—
1536C2×C4—1581no—
1537C2×C4—1581no—
1538C2×C4—1581no—
1539C2×C4—1581no—
1540C2×C4—1581no—
1541C2×C4—1581no—
1542C2×C4—1581no—
1543C2×C4—1581no—
1544C2×C4—1588no—
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×C4C22×C4×D7912yes—
1558C2×C4C22×C4×D7912yes—
1559C2×C4C22×C4×D7912yes—
1560C2×C4C22×C4×D7912yes—
1561C2×C4C22×C4×D7912yes—
1562C2×C4#41×D7912yes—
1563C2×C4#41×D7912yes—
1564C22—22no—
1565C22—22no—
1566C22—22no—
1567C22—22no—
1568C22—22no—
1569C22—22no—
1570C22—41no—
1571C22—41no—
1572C22—41no—
1573C22—41no—
1574C22—41no—
1575C22—41no—
1576C22—41no—
1577C22—41no—
1578C22—31616no—
1579C22—3161no—
1580C22—3161no—
1581C22—3161no—
1582C22—3161no—
1583C22—794no—
1584C22—794no—
1585C22—1582no—
1586C22—1582no—
1587C22—1582no—
1588C22—1582no—
1589C22—1582no—
1590C22—1582no—
1591C22—1582no—
1592C22—1582no—
1593C22—1582no—
1594C22—1582no—
1595C22—1582no—
1596C22—1582no—
1597C22—1582no—
1598C22—1582no—
1599C22—1582no—
1600C22C23×C4×D7911yescharacteristic
1601C22C2×#41×D7911yescharacteristic
1602C22C2×#41×D7911yescharacteristic
1603C22H(5,𝔽2)×D7911yescharacteristic
1604C22H(5,𝔽2)×D7911yescharacteristic
1605C22H(5,𝔽2)×D7911yescharacteristic
1606C222−1+4×D7911yescharacteristic
1607C4—22no—
1608C4—22no—
1609C4—22no—
1610C4—22no—
1611C4—22no—
1612C4—22no—
1613C4—22no—
1614C4—41no—
1615C4—41no—
1616C4—41no—
1617C4—41no—
1618C4—41no—
1619C4—41no—
1620C4—3161no—
1621C4—3161no—
1622C4—3161no—
1623C4—3161no—
1624C4—3161no—
1625C4—3161no—
1626C4—794no—
1627C4—1582no—
1628C4—1582no—
1629C4—1582no—
1630C4—1582no—
1631C4—1582no—
1632C4—1582no—
1633C2—42no—
1634C2—42no—
1635C2—3162no—
1636C2—1584no—
1637C2—1584no—
1638C2C4×#41×D7911yescharacteristic
1639C2#518×D7911yescharacteristic
1640C2#520×D7911yescharacteristic
1641C2#2377742411yescharacteristic
1642C2#2377743011yescharacteristic
1643C2#2377744111yescharacteristic
1644C2#2377744711yescharacteristic
subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
FittingC79×#2335C2
socle, cosocleC23×C79C25
prime radicalC2×#19099071C2
hypercenter#2335D79
hypocenterC79#34233
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2335

Complements

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

NH ≅ G/Ntype
2. #23766419C2semidirect
3. #23766413C2semidirect
4. #23766408C2semidirect
5. #23766402C2semidirect
6. #23766383C2semidirect
7. #23766381C2semidirect
8. #23766378C2semidirect
9. #23766378C2semidirect
10. #23766339C2semidirect
11. #23766335C2semidirect
12. #23766309C2semidirect
13. #23766306C2semidirect
14. #23766290C2semidirect
15. #23766282C2semidirect
16. #23766239C2semidirect
17. #23766226C2semidirect
18. #23766194C2semidirect
19. #23766190C2semidirect
20. #23766186C2semidirect
21. #23766032C2semidirect
22. #23766030C2semidirect
23. #23765934C2semidirect
24. C4×#14579139C2semidirect
25. #23765912C2semidirect
26. C4×#14579134C2semidirect
27. #380×D79C2semidirect
28. #23765760C2semidirect
29. #23765759C2semidirect
30. C4×C22⋊C4×D79C2semidirect
31. C79×#2335C2semidirect
34. #19099071C4semidirect
42. C2×C4×Dic158C22semidirect
43. C2×#14579126C22semidirect
52. C2×C4×C22⋊D79C22semidirect
57. C2×(C22⋊D79)⋊C4C22semidirect
67. #19098467C22semidirect
68. #19098467C22semidirect
72. #19098463C22semidirect
73. #19098463C22semidirect
74. #19098462C22semidirect
75. #19098460C22semidirect
76. #19098460C22semidirect
77. #19098460C22semidirect
78. #19098458C22semidirect
79. #19098458C22semidirect
80. #19098458C22semidirect
85. #19098456C22semidirect
86. #19098456C22semidirect
87. #19098455C22semidirect
88. #19098454C22semidirect
89. #19098453C22semidirect
90. #19098452C22semidirect
93. #19098450C22semidirect
94. #19098449C22semidirect
95. #19098449C22semidirect
96. #19098447C22semidirect
97. #19098445C22semidirect
98. #19098444C22semidirect
110. #19098438C22semidirect
115. #19098437C22semidirect
120. #19098434C22semidirect
121. #19098430C22semidirect
122. #19098430C22semidirect
123. #19098428C22semidirect
124. #19098427C22semidirect
125. #19098425C22semidirect
126. #19098424C22semidirect
132. #19098421C22semidirect
135. #19098420C22semidirect
136. C4⋊C4×Dic79C22semidirect
137. C4⋊C4×Dic79C22semidirect
138. C4×Dic79⋊C4C22semidirect
139. C4×Dic79⋊C4C22semidirect
140. C4×Dic79⋊C4C22semidirect
141. C4×Dic79⋊C4C22semidirect
142. #19098414C22semidirect
143. #19098414C22semidirect
144. #19098414C22semidirect
147. C22⋊C4×Dic79C22semidirect
148. C22⋊C4×Dic79C22semidirect
155. C4×(C2×D79)⋊C4C22semidirect
156. C4×(C2×D79)⋊C4C22semidirect
164. #19098410C22semidirect
165. #19098409C22semidirect
166. #19098408C22semidirect
167. C2×C79⋊#95C22semidirect
172. #95×D79C22semidirect
175. #389×C79C22semidirect
178. #388×C79C22semidirect
179. #388×C79C22semidirect
180. #387×C79C22semidirect
181. #387×C79C22semidirect
183. #385×C79C22semidirect
185. C4×C4⋊C4×C79C22semidirect
187. C4×C22⋊C4×C79C22semidirect
191. C2×#11929623C2×C4semidirect
204. C22×C4×D79C2×C4semidirect
220. #14579144C2×C4semidirect
221. #14579139C2×C4semidirect
222. #14579139C2×C4semidirect
223. #14579134C2×C4semidirect
224. #14579134C2×C4semidirect
225. #14579131C2×C4semidirect
226. #14579129C2×C4semidirect
233. #14579123C2×C4semidirect
234. #14579123C2×C4semidirect
241. (C22⋊D79)⋊C4C2×C4semidirect
242. (C22⋊D79)⋊C4C2×C4semidirect
243. #14579117C2×C4semidirect
349. #123×C79C2×C4semidirect
527. (C2×D79)⋊C4#41semidirect
528. (C2×D79)⋊C4#41semidirect
843. #2335D79semidirect
854. C79#34233semidirect
906. #389C2×D79semidirect
921. #388C2×D79semidirect
922. #388C2×D79semidirect
929. #387C2×D79semidirect
930. #387C2×D79semidirect
954. #385C2×D79semidirect
980. C4×C4⋊C4C2×D79semidirect
1002. C4×C22⋊C4C2×D79semidirect
1047. #123C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190990712
#237664192
#237664132
#237664082
#237664022
#237663832
#237663812
#237663782
#237663392
#237663352
#237663092
#237663062
#237662902
#237662822
#237662392
#237662262
#237661942
#237661902
#237661862
#237660322
#237660302
#237659342
C4×#145791392
#237659122
C4×#145791342
#380×D792
#237657602
#237657592
C4×C22⋊C4×D792
C79×#23352
#3423379