Finite Group Databasebeta

← #34453613

Subgroups — #34453613

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×#19099207C211yesmaximal, characteristic
2#23766568C211yesmaximal, characteristic, complemented
3#23766552C211yesmaximal, characteristic, complemented
4#23766543C211yesmaximal, characteristic, complemented
5#23766539C211yesmaximal, characteristic, complemented
6#23766509C211yesmaximal, characteristic, complemented
7#23766448C211yesmaximal, characteristic, complemented
8#23766441C211yesmaximal, characteristic, complemented
9#23766398C211yesmaximal, characteristic, complemented
10#23766379C211yesmaximal, characteristic, complemented
11#23766338C211yesmaximal, characteristic, complemented
12#23766337C211yesmaximal, characteristic, complemented
13#23766251C211yesmaximal, characteristic, complemented
14#23766245C211yesmaximal, characteristic, complemented
15#23766226C211yesmaximal, characteristic, complemented
16D4×C22⋊Dic79C211yesmaximal, characteristic, complemented
17#23766209C211yesmaximal, characteristic, complemented
18#23766191C211yesmaximal, characteristic, complemented
19#23766166C211yesmaximal, characteristic, complemented
20#23766153C211yesmaximal, characteristic, complemented
21#23766102C211yesmaximal, characteristic, complemented
22#23766074C211yesmaximal, characteristic, complemented
23#23766058C211yesmaximal, characteristic, complemented
24#23766055C211yesmaximal, characteristic, complemented
25#23766040C211yesmaximal, characteristic, complemented
26#23765996C211yesmaximal, characteristic, complemented
27#23765987C211yesmaximal, characteristic, complemented
28#23765910C211yesmaximal, characteristic, complemented
29#23765840C211yesmaximal, characteristic, complemented
30C2×#19098457C211yesmaximal, characteristic, complemented
31C79×#2308C211yesmaximal, characteristic, complemented
32C22×#11929623C2211yescharacteristic
33#19099207C4116yescomplemented
34C2×#14579148C2211yescharacteristic
35C2×#14579142C2211yescharacteristic
36C2×#14579142C2211yescharacteristic
37C2×#14579140C2211yescharacteristic
38C2×#14579133C2211yescharacteristic
39C2×#14579133C2211yescharacteristic
40C2×#14579132C2211yescharacteristic
41C2×#14579130C2211yescharacteristic
42C2×#14579130C2211yescharacteristic
43C2×D4×Dic79C2211yescharacteristic
44C2×D4×Dic79C2211yescharacteristic
45C2×D4×Dic79C2211yescharacteristic
46C2×C4×C22⋊D79C2211yescharacteristic
47C2×C4×C22⋊D79C2211yescharacteristic, complemented
48C2×C4×C22⋊D79C2211yescharacteristic, complemented
49C2×(C22⋊D79)⋊C4C2211yescharacteristic, complemented
50C2×(C22⋊D79)⋊C4C2211yescharacteristic, complemented
51C2×#14579117C2211yescharacteristic, complemented
52C2×#14579117C2211yescharacteristic, complemented
53C22×Dic79⋊C4C2211yescharacteristic, complemented
54C22×C22⋊Dic79C2211yescharacteristic
55C22×C22⋊Dic79C2211yescharacteristic
56C22×C22⋊Dic79C2211yescharacteristic
57C22×C22⋊Dic79C2211yescharacteristic
58C22×C4×Dic79C2211yescharacteristic, complemented
59#19098467C2211yescharacteristic, complemented
60#19098467C2211yescharacteristic, complemented
61#19098467C2211yescharacteristic, complemented
62#19098467C2211yescharacteristic, complemented
63#19098466C2211yescharacteristic
64#19098466C2211yescharacteristic
65#19098463C2211yescharacteristic
66#19098463C2211yescharacteristic
67#19098463C2211yescharacteristic, complemented
68#19098463C2211yescharacteristic, complemented
69#19098463C2211yescharacteristic, complemented
70#19098463C2211yescharacteristic, complemented
71#19098460C2211yescharacteristic, complemented
72#19098460C2211yescharacteristic, complemented
73#19098460C2211yescharacteristic, complemented
74#19098460C2211yescharacteristic, complemented
75#19098457C2211yescharacteristic
76#19098457C2211yescharacteristic
77#19098457C2211yescharacteristic
78#19098457C2211yescharacteristic
79#19098457C2211yescharacteristic
80#19098457C2211yescharacteristic
81#19098457C2211yescharacteristic
82#19098457C2211yescharacteristic
83#19098457C2211yescharacteristic, complemented
84#19098457C2211yescharacteristic, complemented
85#19098457C2211yescharacteristic, complemented
86#19098457C2211yescharacteristic, complemented
87#19098457C2211yescharacteristic, complemented
88#19098457C2211yescharacteristic, complemented
89#19098457C2211yescharacteristic, complemented
90#19098457C2211yescharacteristic, complemented
91#19098455C2211yescharacteristic, complemented
92#19098455C2211yescharacteristic, complemented
93#19098451C2211yescharacteristic
94#19098451C2211yescharacteristic
95#19098451C2211yescharacteristic
96#19098451C2211yescharacteristic
97#19098451C2211yescharacteristic, complemented
98#19098451C2211yescharacteristic, complemented
99#19098451C2211yescharacteristic, complemented
100#19098451C2211yescharacteristic, complemented
101#19098451C2211yescharacteristic, complemented
102#19098451C2211yescharacteristic, complemented
103#19098451C2211yescharacteristic, complemented
104#19098451C2211yescharacteristic, complemented
105#19098450C2211yescharacteristic, complemented
106#19098450C2211yescharacteristic, complemented
107#19098448C2211yescharacteristic, complemented
108#19098448C2211yescharacteristic, complemented
109#19098446C2211yescharacteristic, complemented
110#19098446C2211yescharacteristic, complemented
111#19098445C2211yescharacteristic, complemented
112#19098445C2211yescharacteristic, complemented
113#19098445C2211yescharacteristic, complemented
114#19098445C2211yescharacteristic, complemented
115#19098443C2211yescharacteristic
116#19098443C2211yescharacteristic
117#19098443C2211yescharacteristic
118#19098443C2211yescharacteristic
119#19098442C2211yescharacteristic, complemented
120#19098442C2211yescharacteristic, complemented
121#19098440C2211yescharacteristic, complemented
122#19098440C2211yescharacteristic, complemented
123#19098439C2211yescharacteristic
124#19098439C2211yescharacteristic
125#19098439C2211yescharacteristic, complemented
126#19098439C2211yescharacteristic, complemented
127#19098439C2211yescharacteristic, complemented
128#19098439C2211yescharacteristic, complemented
129#19098436C2211yescharacteristic, complemented
130#19098436C2211yescharacteristic, complemented
131#19098436C2211yescharacteristic, complemented
132#19098436C2211yescharacteristic, complemented
133#19098435C2211yescharacteristic, complemented
134#19098435C2211yescharacteristic, complemented
135#19098435C2211yescharacteristic, complemented
136#19098435C2211yescharacteristic, complemented
137#19098430C2211yescharacteristic, complemented
138#19098425C2211yescharacteristic, complemented
139#19098424C2211yescharacteristic, complemented
140#19098424C2211yescharacteristic, complemented
141#19098423C2211yescharacteristic
142#19098422C2211yescharacteristic, complemented
143#19098422C2211yescharacteristic, complemented
144#19098421C2211yescharacteristic, complemented
145#19098421C2211yescharacteristic, complemented
146#19098421C2211yescharacteristic, complemented
147#19098421C2211yescharacteristic, complemented
148#19098419C2211yescharacteristic
149#19098419C2211yescharacteristic
150#19098414C2211yescharacteristic, complemented
151#19098414C2211yescharacteristic, complemented
152#19098414C2211yescharacteristic, complemented
153C22⋊C4×Dic79C2211yescharacteristic, complemented
154C22⋊C4×Dic79C2211yescharacteristic, complemented
155C22⋊C4×Dic79C2211yescharacteristic, complemented
156C22⋊C4×Dic79C2211yescharacteristic, complemented
157C22⋊C4×Dic79C2211yescharacteristic, complemented
158C22⋊C4×Dic79C2211yescharacteristic, complemented
159C22⋊C4×Dic79C2211yescharacteristic, complemented
160C22⋊C4×Dic79C2211yescharacteristic, complemented
161C4×C22⋊Dic79C2211yescharacteristic
162C4×C22⋊Dic79C2211yescharacteristic, complemented
163C4×C22⋊Dic79C2211yescharacteristic, complemented
164C4×C22⋊Dic79C2211yescharacteristic, complemented
165C4×C22⋊Dic79C2211yescharacteristic, complemented
166#19098410C2211yescharacteristic, complemented
167#19098410C2211yescharacteristic, complemented
168#19098408C2211yescharacteristic, complemented
169#19098408C2211yescharacteristic, complemented
170C2×C79⋊#95C2211yescharacteristic, complemented
171C2×C79⋊#95C2211yescharacteristic, complemented
172#95×D79C2211yescharacteristic, complemented
173C23×D4×C79C2211yescharacteristic
174C22×C22⋊C4×C79C2211yescharacteristic
175C22×C22⋊C4×C79C2211yescharacteristic
176#386×C79C2211yescharacteristic
177#386×C79C2211yescharacteristic
178#386×C79C2211yescharacteristic
179#386×C79C2211yescharacteristic
180#386×C79C2211yescharacteristic
181#386×C79C2211yescharacteristic
182#386×C79C2211yescharacteristic
183#386×C79C2211yescharacteristic
184#381×C79C2211yescharacteristic
185#381×C79C2211yescharacteristic
186#379×C79C2211yescharacteristic
187#379×C79C2211yescharacteristic
188C2×#11929623—42no—
189C2×#11929623—42no—
190C2×#11929623C2×C418yescomplemented
191C22×Dic158C2311yescharacteristic
192C22×C22⋊D79C2311yescharacteristic
193C22×C22⋊D79C2311yescharacteristic
194C22×C22⋊D79C2311yescharacteristic
195C22×C22⋊D79C2311yescharacteristic
196C22×C22⋊D79C2311yescharacteristic
197C23×Dic79C2311yescharacteristic
198C23×Dic79C2311yescharacteristic
199C23×Dic79C2311yescharacteristic
200C23×Dic79C2311yescharacteristic
201C23×Dic79C2311yescharacteristic
202C23×Dic79C2311yescharacteristic
203C23×Dic79C2311yescharacteristic
204C23×Dic79C2311yescharacteristic
205C22×C4×D79C2311yescharacteristic
206C22×C4×D79C2311yescharacteristic
207C22×C4×D79C2311yescharacteristic
208#14579148C2×C418yescomplemented
209#14579142C2×C418yescomplemented
210#14579142C2×C418yescomplemented
211#14579140C2×C418yescomplemented
212#14579133C2×C418yescomplemented
213#14579133C2×C418yescomplemented
214#14579132C2×C418yescomplemented
215#14579130C2×C418yescomplemented
216#14579130C2×C418yescomplemented
217D4×Dic79—42no—
218D4×Dic79—42no—
219D4×Dic79C2×C418yescomplemented
220C4×C22⋊D79—42no—
221C4×C22⋊D79—42no—
222C4×C22⋊D79C2×C418yescomplemented
223(C22⋊D79)⋊C4—42no—
224(C22⋊D79)⋊C4—42no—
225#14579117—42no—
226#14579117—42no—
227C2×C4⋊Dic79C2311yescharacteristic
228C2×C4⋊Dic79C2311yescharacteristic
229C2×C4⋊Dic79C2311yescharacteristic
230C2×Dic79⋊C4—42no—
231C2×Dic79⋊C4C2311yescharacteristic
232C2×Dic79⋊C4C2311yescharacteristic
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×Dic79⋊C4C2311yescharacteristic
245C2×Dic79⋊C4C2311yescharacteristic
246C2×Dic79⋊C4C2311yescharacteristic
247C2×Dic79⋊C4C2311yescharacteristic
248C2×C22⋊Dic79—42no—
249C2×C22⋊Dic79—42no—
250C2×C22⋊Dic79C2×C418yescomplemented
251C2×C22⋊Dic79C2×C418yescomplemented
252C2×C22⋊Dic79C2311yescharacteristic
253C2×C22⋊Dic79C2311yescharacteristic
254C2×C22⋊Dic79C2311yescharacteristic
255C2×C22⋊Dic79C2311yescharacteristic
256C2×C22⋊Dic79C2311yescharacteristic
257C2×C22⋊Dic79C2311yescharacteristic
258C2×C22⋊Dic79C2311yescharacteristic
259C2×C22⋊Dic79C2311yescharacteristic
260C2×C22⋊Dic79C2311yescharacteristic
261C2×C22⋊Dic79C2311yescharacteristic
262C2×C22⋊Dic79C2311yescharacteristic
263C2×C22⋊Dic79C2311yescharacteristic
264C2×C22⋊Dic79C2311yescharacteristic
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×C22⋊Dic79C2311yescharacteristic
274C2×C22⋊Dic79C2311yescharacteristic
275C2×C22⋊Dic79C2311yescharacteristic
276C2×C22⋊Dic79C2311yescharacteristic
277C2×C22⋊Dic79C2311yescharacteristic
278C2×C22⋊Dic79C2311yescharacteristic
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×C4×Dic79—42no—
287C2×C4×Dic79C2311yescharacteristic
288C2×C4×Dic79C2311yescharacteristic
289C2×C4×Dic79C2311yescharacteristic
290C2×C4×Dic79C2311yescharacteristic
291C2×C4×Dic79C2311yescharacteristic
292C2×C4×Dic79C2311yescharacteristic
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
304C79⋊#95C2311yescharacteristic
305C79⋊#95C2311yescharacteristic
306C79⋊#95C2311yescharacteristic
307C79⋊#95C2311yescharacteristic
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
336C25×C79C2311yescharacteristic
337C25×C79C2311yescharacteristic
338C22×D4×C79—42no—
339C22×D4×C79—42no—
340C22×D4×C79C2×C418yescomplemented
341C22×D4×C79C2311yescharacteristic
342C22×D4×C79C2311yescharacteristic
343C22×D4×C79C2311yescharacteristic
344C22×D4×C79C2311yescharacteristic
345C23×C4×C79C2311yescharacteristic
346C23×C4×C79C2311yescharacteristic
347C23×C4×C79C2311yescharacteristic
348C23×C4×C79C2311yescharacteristic
349C23×C4×C79C2311yescharacteristic
350C2×C22⋊C4×C79—42no—
351C2×C22⋊C4×C79—42no—
352C2×C22⋊C4×C79C2311yescharacteristic
353C2×C22⋊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×C22⋊C4×C79C2311yescharacteristic
363C2×C22⋊C4×C79C2311yescharacteristic
364C2×C22⋊C4×C79C2311yescharacteristic
365C2×C22⋊C4×C79C2311yescharacteristic
366C2×C22⋊C4×C79C2311yescharacteristic
367C2×C22⋊C4×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×D79C2411yescharacteristic
377#11929623—416no—
378C2×Dic158—41no—
379C2×Dic158—41no—
380C2×Dic158C22×C414yes—
381C2×C22⋊D79—22no—
382C2×C22⋊D79—22no—
383C2×C22⋊D79—41no—
384C2×C22⋊D79—41no—
385C2×C22⋊D79—41no—
386C2×C22⋊D79—41no—
387C2×C22⋊D79—41no—
388C2×C22⋊D79—41no—
389C2×C22⋊D79—41no—
390C2×C22⋊D79—41no—
391C2×C22⋊D79C22×C414yes—
392C2×C22⋊D79C22×C414yes—
393C2×C22⋊D79C22×C414yes—
394C2×C22⋊D79C22×C414yes—
395C2×C22⋊D79C22×C414yes—
396C22×Dic79—22no—
397C22×Dic79—22no—
398C22×Dic79—22no—
399C22×Dic79—22no—
400C22×Dic79—22no—
401C22×Dic79—22no—
402C22×Dic79—41no—
403C22×Dic79—41no—
404C22×Dic79—41no—
405C22×Dic79—41no—
406C22×Dic79—41no—
407C22×Dic79—41no—
408C22×Dic79—41no—
409C22×Dic79—41no—
410C22×Dic79—41no—
411C22×Dic79—41no—
412C22×Dic79—41no—
413C22×Dic79—41no—
414C22×Dic79—41no—
415C22×Dic79—41no—
416C22×Dic79C22×C414yes—
417C22×Dic79C22×C414yes—
418C22×Dic79C22×C414yes—
419C22×Dic79C22×C414yes—
420C22×Dic79C2411yescharacteristic
421C22×Dic79C2411yescharacteristic
422C22×Dic79C2411yescharacteristic
423C22×Dic79C2411yescharacteristic
424C22×Dic79C2411yescharacteristic
425C22×Dic79C2411yescharacteristic
426C22×Dic79C2411yescharacteristic
427C22×Dic79C2411yescharacteristic
428C22×Dic79C2411yescharacteristic
429C22×Dic79C2411yescharacteristic
430C22×Dic79C2411yescharacteristic
431C22×Dic79C2411yescharacteristic
432C22×Dic79C2411yescharacteristic
433C22×Dic79C2411yescharacteristic
434C22×Dic79C2411yescharacteristic
435C2×C4×D79—22no—
436C2×C4×D79—41no—
437C2×C4×D79—41no—
438C2×C4×D79—41no—
439C2×C4×D79—41no—
440C2×C4×D79—41no—
441C2×C4×D79—41no—
442C2×C4×D79—41no—
443C2×C4×D79C22×C414yes—
444C4⋊Dic79—41no—
445C4⋊Dic79—41no—
446C4⋊Dic79C22×C414yes—
447Dic79⋊C4—22no—
448Dic79⋊C4—41no—
449Dic79⋊C4—41no—
450Dic79⋊C4—41no—
451Dic79⋊C4—41no—
452Dic79⋊C4—41no—
453Dic79⋊C4—41no—
454Dic79⋊C4—41no—
455Dic79⋊C4—41no—
456Dic79⋊C4—41no—
457Dic79⋊C4—41no—
458Dic79⋊C4—41no—
459Dic79⋊C4—41no—
460Dic79⋊C4—41no—
461Dic79⋊C4C22×C414yes—
462Dic79⋊C4C22×C414yes—
463Dic79⋊C4C22×C414yes—
464C22⋊Dic79—22no—
465C22⋊Dic79—22no—
466C22⋊Dic79—22no—
467C22⋊Dic79—22no—
468C22⋊Dic79—22no—
469C22⋊Dic79—41no—
470C22⋊Dic79—41no—
471C22⋊Dic79—41no—
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—
483C22⋊Dic79C22×C414yes—
484C22⋊Dic79C22×C414yes—
485C22⋊Dic79C22×C414yes—
486C22⋊Dic79C22×C414yes—
487C22⋊Dic79C22×C414yes—
488C22⋊Dic79C22×C414yes—
489C22⋊Dic79C22×C414yes—
490C22⋊Dic79C22×C414yes—
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)⋊C4C22×C414yes—
498C4×Dic79—22no—
499C4×Dic79—22no—
500C4×Dic79—41no—
501C4×Dic79—41no—
502C4×Dic79—41no—
503C4×Dic79—41no—
504C4×Dic79—41no—
505C4×Dic79—41no—
506C4×Dic79—41no—
507C4×Dic79—41no—
508C4×Dic79—41no—
509C4×Dic79—41no—
510C4×Dic79—41no—
511C4×Dic79—41no—
512C4×Dic79—41no—
513C4×Dic79—41no—
514C4×Dic79C22×C414yes—
515C24×C79—22no—
516C24×C79—22no—
517C24×C79—41no—
518C24×C79—41no—
519C24×C79—41no—
520C24×C79—41no—
521C24×C79—41no—
522C24×C79—41no—
523C24×C79—41no—
524C24×C79—41no—
525C24×C79—41no—
526C24×C79—41no—
527C24×C79C22×C414yes—
528C24×C79C22×C414yes—
529C24×C79C2411yescharacteristic
530C24×C79C2411yescharacteristic
531C24×C79C2411yescharacteristic
532C24×C79C2411yescharacteristic
533C24×C79C2411yescharacteristic
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×C79—41no—
541C2×D4×C79—41no—
542C2×D4×C79—416no—
543C2×D4×C79C22×C414yes—
544C2×D4×C79C22×C414yes—
545C2×D4×C79C22×C414yes—
546C2×D4×C79C22×C414yes—
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×C79C2411yescharacteristic
563C22×C4×C79C2411yescharacteristic
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×C79—22no—
573C22⋊C4×C79—22no—
574C22⋊C4×C79—41no—
575C22⋊C4×C79—41no—
576C22⋊C4×C79—41no—
577C22⋊C4×C79—41no—
578C22⋊C4×C79—41no—
579C22⋊C4×C79—41no—
580C22⋊C4×C79—41no—
581C22⋊C4×C79—41no—
582C22⋊C4×C79—41no—
583C22⋊C4×C79—41no—
584C22⋊C4×C79—41no—
585C22⋊C4×C79—41no—
586C22⋊C4×C79—41no—
587C22⋊C4×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×C79—21no—
605C23×C79—21no—
606C23×C79—21no—
607C23×C79—21no—
608C23×C79—21no—
609C23×C79—21no—
610C23×C79—21no—
611C23×C79—21no—
612C23×C79—21no—
613C23×C79—21no—
614C23×C79—21no—
615C23×C79—21no—
616C23×C79—28no—
617C23×C79—44no—
618C23×C79—44no—
619C23×C79—44no—
620C23×C79—44no—
621C23×C79—44no—
622C23×C79—82no—
623C23×C79—82no—
624C23×C79—82no—
625C23×C79—82no—
626C23×C79—82no—
627C23×C79—82no—
628C23×C79—82no—
629C23×C79—82no—
630C23×C79C23×C412yes—
631C23×C79C23×C412yes—
632C23×C79C23×C412yes—
633C23×C79C23×C412yes—
634C23×C79C23×C412yes—
635C23×C79H(5,𝔽2)12yes—
636C23×C79H(5,𝔽2)12yes—
637C23×C79C2511yescharacteristic
638C22×D79—21no—
639C22×D79—21no—
640C22×D79—21no—
641C22×D79—21no—
642C22×D79—21no—
643C22×D79—21no—
644C22×D79C23×C412yes—
645D4×C79—28no—
646D4×C79—28no—
647D4×C79—44no—
648D4×C79—44no—
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—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—44no—
678C2×C4×C79—44no—
679C2×C4×C79—82no—
680C2×C4×C79—82no—
681C2×C4×C79—82no—
682C2×C4×C79C23×C412yes—
683C2×C4×C79C23×C412yes—
684C22⋊D79—28no—
685C22⋊D79—44no—
686C22⋊D79—44no—
687C22⋊D79—44no—
688C22⋊D79—44no—
689C2×Dic79—28no—
690C2×Dic79—21no—
691C2×Dic79—21no—
692C2×Dic79—21no—
693C2×Dic79—21no—
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—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—44no—
728C2×Dic79—44no—
729C2×Dic79—44no—
730C2×Dic79—44no—
731C2×Dic79—82no—
732C2×Dic79—82no—
733C2×Dic79—82no—
734C2×Dic79C23×C412yes—
735C2×Dic79C23×C412yes—
736C2×Dic79C23×C412yes—
737C2×Dic79C23×C412yes—
738C2×Dic79C23×C412yes—
739C2×Dic79C23×C412yes—
740C2×Dic79C23×C412yes—
741C2×Dic79H(5,𝔽2)12yes—
742C4×D79—44no—
743C4×D79—82no—
744C4×D79—82no—
745Dic158—44no—
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—22no—
759C22×C79—22no—
760C22×C79—22no—
761C22×C79—22no—
762C22×C79—22no—
763C22×C79—22no—
764C22×C79—41no—
765C22×C79—41no—
766C22×C79—41no—
767C22×C79—41no—
768C22×C79—41no—
769C22×C79—41no—
770C22×C79—41no—
771C22×C79—41no—
772C22×C79—41no—
773C22×C79—41no—
774C22×C79—41no—
775C22×C79—41no—
776C22×C79—41no—
777C22×C79—41no—
778C22×C79—41no—
779C22×C79—41no—
780C22×C79—88no—
781C22×C79—88no—
782C22×C79#51814yes—
783C22×C79C24×C411yescharacteristic
784C22×C79C2×H(5,𝔽2)11yescharacteristic
785C22×C79C2×H(5,𝔽2)11yescharacteristic
786C22×C79C2×H(5,𝔽2)11yescharacteristic
787C22×C79#58511yescharacteristic
788C22×C79#58511yescharacteristic
789C22×C79#58511yescharacteristic
790C2×D79—22no—
791C2×D79—22no—
792C2×D79—22no—
793C2×D79—41no—
794C2×D79—41no—
795C2×D79—41no—
796C2×D79—41no—
797C4×C79—22no—
798C4×C79—22no—
799C4×C79—41no—
800C4×C79—41no—
801C4×C79—41no—
802C4×C79—41no—
803C4×C79—41no—
804C4×C79—41no—
805C4×C79—41no—
806C4×C79—41no—
807Dic79—22no—
808Dic79—22no—
809Dic79—22no—
810Dic79—22no—
811Dic79—22no—
812Dic79—22no—
813Dic79—22no—
814Dic79—22no—
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×C79—42no—
827C2×C79—42no—
828C2×C79C2×#51811yescharacteristic
829C2×C79#342811yescharacteristic
830C2×C79C4×H(5,𝔽2)11yescharacteristic
831C2×C79#353411yescharacteristic
832C2×C79#354211yescharacteristic
833C2×C79#354511yescharacteristic
834C2×C79#356011yescharacteristic
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#2339—791no—
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#2308D7911yescharacteristic, complemented
864C4×#121—791no—
865#2290—791no—
866C2×#388—791no—
867C79#3449211yescharacteristic, complemented, Sylow
868C22×#41—791no—
869C23×D4C2×D7911yescharacteristic
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×D4—791no—
887C2×C4×D4—791no—
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⋊C4C2×D7911yescharacteristic
896C22×C22⋊C4C2×D7911yescharacteristic
897C22×C42—791no—
898#391—791no—
899#391—791no—
900#391—791no—
901#391—791no—
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#386C2×D7911yescharacteristic
969#386C2×D7911yescharacteristic
970#386C2×D7911yescharacteristic
971#386C2×D7911yescharacteristic
972#386C2×D7911yescharacteristic
973#386C2×D7911yescharacteristic
974#386C2×D7911yescharacteristic
975#386C2×D7911yescharacteristic
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
989#381C2×D7911yescharacteristic
990#380—791no—
991#380—791no—
992#380—791no—
993#380—791no—
994#380—791no—
995#380—791no—
996#380—791no—
997#379—791no—
998#379—791no—
999#379C2×D7911yescharacteristic
1000#379C2×D7911yescharacteristic
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⋊C4—791no—
1019#376—791no—
1020#376—791no—
1021C2×#95—791no—
1022C2×#95—791no—
1023C2×#95—791no—
1024C25C22×D7911yescharacteristic
1025C25C22×D7911yescharacteristic
1026C2×#41—3162no—
1027C2×#41—3162no—
1028C2×#41—798no—
1029C22×Q8—791no—
1030C22×D4—42no—
1031C22×D4—42no—
1032C22×D4—791no—
1033C22×D4—791no—
1034C22×D4—791no—
1035C22×D4—791no—
1036C22×D4—791no—
1037C22×D4C4×D7918yescomplemented
1038C22×D4C22×D7911yescharacteristic
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×C4—791no—
1052C23×C4—791no—
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—3162no—
1068C4×D4—3162no—
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⋊C4—791no—
1097C2×C4⋊C4—791no—
1098C2×C22⋊C4—42no—
1099C2×C22⋊C4—42no—
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—798no—
1120C2×C22⋊C4—798no—
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—791no—
1132C2×C22⋊C4—791no—
1133C2×C22⋊C4—791no—
1134C2×C22⋊C4—791no—
1135C2×C22⋊C4—791no—
1136C2×C22⋊C4—791no—
1137C2×C22⋊C4—791no—
1138C2×C22⋊C4C22×D7911yescharacteristic
1139C2×C22⋊C4C22×D7911yescharacteristic
1140C2×C22⋊C4C22×D7911yescharacteristic
1141C2×C22⋊C4C22×D7911yescharacteristic
1142C2×C22⋊C4C22×D7911yescharacteristic
1143C2×C22⋊C4C22×D7911yescharacteristic
1144C2×C22⋊C4C22×D7911yescharacteristic
1145C2×C22⋊C4C22×D7911yescharacteristic
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×C42—791no—
1171C2×C42—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#95—791no—
1196#95—791no—
1197#95—791no—
1198#95—791no—
1199#95—791no—
1200#95—791no—
1201#95—791no—
1202#95—791no—
1203#95—791no—
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—22no—
1213C24—22no—
1214C24—41no—
1215C24—41no—
1216C24—41no—
1217C24—41no—
1218C24—41no—
1219C24—41no—
1220C24—41no—
1221C24—41no—
1222C24—41no—
1223C24—41no—
1224C24—791no—
1225C24C2×C4×D7914yes—
1226C24C2×C4×D7914yes—
1227C24C23×D7911yescharacteristic
1228C24C23×D7911yescharacteristic
1229C24C23×D7911yescharacteristic
1230C24C23×D7911yescharacteristic
1231C24C23×D7911yescharacteristic
1232#41—31616no—
1233C2×Q8—3161no—
1234C2×Q8—3161no—
1235C2×Q8—794no—
1236C2×D4—22no—
1237C2×D4—22no—
1238C2×D4—22no—
1239C2×D4—22no—
1240C2×D4—41no—
1241C2×D4—41no—
1242C2×D4—41no—
1243C2×D4—41no—
1244C2×D4—416no—
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—1582no—
1259C2×D4—1582no—
1260C2×D4C2×C4×D7914yes—
1261C2×D4C2×C4×D7914yes—
1262C2×D4C2×C4×D7914yes—
1263C2×D4C2×C4×D7914yes—
1264C22×C4—22no—
1265C22×C4—22no—
1266C22×C4—41no—
1267C22×C4—41no—
1268C22×C4—41no—
1269C22×C4—41no—
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—3161no—
1279C22×C4—3161no—
1280C22×C4—3161no—
1281C22×C4—3161no—
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—794no—
1300C22×C4—794no—
1301C22×C4—794no—
1302C22×C4—794no—
1303C22×C4—791no—
1304C22×C4—791no—
1305C22×C4—791no—
1306C22×C4—791no—
1307C22×C4—791no—
1308C22×C4—791no—
1309C22×C4—791no—
1310C22×C4—791no—
1311C22×C4—794no—
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×C4—1582no—
1323C22×C4—1582no—
1324C22×C4—1582no—
1325C22×C4—1582no—
1326C22×C4C2×C4×D7914yes—
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—3161no—
1338C4⋊C4—3161no—
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—41no—
1360C22⋊C4—41no—
1361C22⋊C4—41no—
1362C22⋊C4—41no—
1363C22⋊C4—41no—
1364C22⋊C4—41no—
1365C22⋊C4—41no—
1366C22⋊C4—41no—
1367C22⋊C4—41no—
1368C22⋊C4—41no—
1369C22⋊C4—41no—
1370C22⋊C4—41no—
1371C22⋊C4—41no—
1372C22⋊C4—41no—
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—794no—
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—1582no—
1403C22⋊C4—1582no—
1404C22⋊C4—1582no—
1405C22⋊C4—1582no—
1406C22⋊C4—1582no—
1407C42—3161no—
1408C42—3161no—
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—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—21no—
1447C23—21no—
1448C23—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—28no—
1453C23—44no—
1454C23—44no—
1455C23—44no—
1456C23—44no—
1457C23—44no—
1458C23—82no—
1459C23—82no—
1460C23—82no—
1461C23—82no—
1462C23—82no—
1463C23—82no—
1464C23—82no—
1465C23—82no—
1466C23—792no—
1467C23—1581no—
1468C23—1581no—
1469C23—1581no—
1470C23—1581no—
1471C23—1581no—
1472C23—1581no—
1473C23C22×C4×D7912yes—
1474C23C22×C4×D7912yes—
1475C23C22×C4×D7912yes—
1476C23C22×C4×D7912yes—
1477C23C22×C4×D7912yes—
1478C23#1457920612yes—
1479C23#1457920612yes—
1480C23C24×D7911yescharacteristic
1481Q8—3164no—
1482D4—28no—
1483D4—28no—
1484D4—44no—
1485D4—44no—
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—21no—
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—44no—
1520C2×C4—44no—
1521C2×C4—82no—
1522C2×C4—82no—
1523C2×C4—82no—
1524C2×C4—3164no—
1525C2×C4—3164no—
1526C2×C4—3164no—
1527C2×C4—3164no—
1528C2×C4—3164no—
1529C2×C4—792no—
1530C2×C4—792no—
1531C2×C4—792no—
1532C2×C4—792no—
1533C2×C4—792no—
1534C2×C4—792no—
1535C2×C4—792no—
1536C2×C4—792no—
1537C2×C4—6322no—
1538C2×C4—6322no—
1539C2×C4—6322no—
1540C2×C4—6322no—
1541C2×C4—6322no—
1542C2×C4—1581no—
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×C4—1581no—
1578C2×C4—1581no—
1579C2×C4—1588no—
1580C2×C4C22×C4×D7912yes—
1581C2×C4C22×C4×D7912yes—
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—22no—
1595C22—22no—
1596C22—22no—
1597C22—22no—
1598C22—22no—
1599C22—22no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—41no—
1605C22—41no—
1606C22—41no—
1607C22—41no—
1608C22—41no—
1609C22—41no—
1610C22—41no—
1611C22—41no—
1612C22—41no—
1613C22—41no—
1614C22—41no—
1615C22—41no—
1616C22—88no—
1617C22—88no—
1618C22—3161no—
1619C22—3161no—
1620C22—3161no—
1621C22—3161no—
1622C22—1582no—
1623C22—1582no—
1624C22—1582no—
1625C22#1909903614yes—
1626C22C23×C4×D7911yescharacteristic
1627C22H(5,𝔽2)×D7911yescharacteristic
1628C22C2×#1457920611yescharacteristic
1629C22C2×#1457920611yescharacteristic
1630C22#1909939811yescharacteristic
1631C22#1909939811yescharacteristic
1632C22#1909939811yescharacteristic
1633C4—22no—
1634C4—22no—
1635C4—41no—
1636C4—41no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—3161no—
1644C4—3161no—
1645C4—3161no—
1646C4—3161no—
1647C4—3161no—
1648C4—3161no—
1649C4—3161no—
1650C4—1582no—
1651C4—1582no—
1652C4—1582no—
1653C4—1582no—
1654C4—1582no—
1655C4—1582no—
1656C4—1582no—
1657C4—1582no—
1658C2—24no—
1659C2—42no—
1660C2—42no—
1661C2—42no—
1662C2—42no—
1663C2—3162no—
1664C2C2×#1909903611yescharacteristic
1665C2#2377659811yescharacteristic
1666C2#2377660411yescharacteristic
1667C2#2377758711yescharacteristic
1668C2#2377771111yescharacteristic
1669C2#2377774911yescharacteristic
1670C2#2377794211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D79
commutatorC22×C79C24×C4
FittingC79×#2308C2
socle, cosocleC23×C79C25
prime radicalC2×#19099207C2
hypercenter#2308D79
hypocenterC79#34492
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2308

Complements

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

NH ≅ G/Ntype
2. #23766568C2semidirect
3. #23766552C2semidirect
4. #23766543C2semidirect
5. #23766539C2semidirect
6. #23766509C2semidirect
7. #23766448C2semidirect
8. #23766441C2semidirect
9. #23766398C2semidirect
10. #23766379C2semidirect
11. #23766338C2semidirect
12. #23766337C2semidirect
13. #23766251C2semidirect
14. #23766245C2semidirect
15. #23766226C2semidirect
16. D4×C22⋊Dic79C2semidirect
17. #23766209C2semidirect
18. #23766191C2semidirect
19. #23766166C2semidirect
20. #23766153C2semidirect
21. #23766102C2semidirect
22. #23766074C2semidirect
23. #23766058C2semidirect
24. #23766055C2semidirect
25. #23766040C2semidirect
26. #23765996C2semidirect
27. #23765987C2semidirect
28. #23765910C2semidirect
29. #23765840C2semidirect
30. C2×#19098457C2semidirect
31. C79×#2308C2semidirect
33. #19099207C4semidirect
47. C2×C4×C22⋊D79C22semidirect
48. C2×C4×C22⋊D79C22semidirect
49. C2×(C22⋊D79)⋊C4C22semidirect
50. C2×(C22⋊D79)⋊C4C22semidirect
51. C2×#14579117C22semidirect
52. C2×#14579117C22semidirect
53. C22×Dic79⋊C4C22semidirect
58. C22×C4×Dic79C22semidirect
59. #19098467C22semidirect
60. #19098467C22semidirect
61. #19098467C22semidirect
62. #19098467C22semidirect
67. #19098463C22semidirect
68. #19098463C22semidirect
69. #19098463C22semidirect
70. #19098463C22semidirect
71. #19098460C22semidirect
72. #19098460C22semidirect
73. #19098460C22semidirect
74. #19098460C22semidirect
83. #19098457C22semidirect
84. #19098457C22semidirect
85. #19098457C22semidirect
86. #19098457C22semidirect
87. #19098457C22semidirect
88. #19098457C22semidirect
89. #19098457C22semidirect
90. #19098457C22semidirect
91. #19098455C22semidirect
92. #19098455C22semidirect
97. #19098451C22semidirect
98. #19098451C22semidirect
99. #19098451C22semidirect
100. #19098451C22semidirect
101. #19098451C22semidirect
102. #19098451C22semidirect
103. #19098451C22semidirect
104. #19098451C22semidirect
105. #19098450C22semidirect
106. #19098450C22semidirect
107. #19098448C22semidirect
108. #19098448C22semidirect
109. #19098446C22semidirect
110. #19098446C22semidirect
111. #19098445C22semidirect
112. #19098445C22semidirect
113. #19098445C22semidirect
114. #19098445C22semidirect
119. #19098442C22semidirect
120. #19098442C22semidirect
121. #19098440C22semidirect
122. #19098440C22semidirect
125. #19098439C22semidirect
126. #19098439C22semidirect
127. #19098439C22semidirect
128. #19098439C22semidirect
129. #19098436C22semidirect
130. #19098436C22semidirect
131. #19098436C22semidirect
132. #19098436C22semidirect
133. #19098435C22semidirect
134. #19098435C22semidirect
135. #19098435C22semidirect
136. #19098435C22semidirect
137. #19098430C22semidirect
138. #19098425C22semidirect
139. #19098424C22semidirect
140. #19098424C22semidirect
142. #19098422C22semidirect
143. #19098422C22semidirect
144. #19098421C22semidirect
145. #19098421C22semidirect
146. #19098421C22semidirect
147. #19098421C22semidirect
150. #19098414C22semidirect
151. #19098414C22semidirect
152. #19098414C22semidirect
153. C22⋊C4×Dic79C22semidirect
154. C22⋊C4×Dic79C22semidirect
155. C22⋊C4×Dic79C22semidirect
156. C22⋊C4×Dic79C22semidirect
157. C22⋊C4×Dic79C22semidirect
158. C22⋊C4×Dic79C22semidirect
159. C22⋊C4×Dic79C22semidirect
160. C22⋊C4×Dic79C22semidirect
162. C4×C22⋊Dic79C22semidirect
163. C4×C22⋊Dic79C22semidirect
164. C4×C22⋊Dic79C22semidirect
165. C4×C22⋊Dic79C22semidirect
166. #19098410C22semidirect
167. #19098410C22semidirect
168. #19098408C22semidirect
169. #19098408C22semidirect
170. C2×C79⋊#95C22semidirect
171. C2×C79⋊#95C22semidirect
172. #95×D79C22semidirect
190. C2×#11929623C2×C4semidirect
208. #14579148C2×C4semidirect
209. #14579142C2×C4semidirect
210. #14579142C2×C4semidirect
211. #14579140C2×C4semidirect
212. #14579133C2×C4semidirect
213. #14579133C2×C4semidirect
214. #14579132C2×C4semidirect
215. #14579130C2×C4semidirect
216. #14579130C2×C4semidirect
219. D4×Dic79C2×C4semidirect
222. C4×C22⋊D79C2×C4semidirect
250. C2×C22⋊Dic79C2×C4semidirect
251. C2×C22⋊Dic79C2×C4semidirect
340. C22×D4×C79C2×C4semidirect
863. #2308D79semidirect
867. C79#34492semidirect
1037. C22×D4C4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×#190992072
#237665682
#237665522
#237665432
#237665392
#237665092
#237664482
#237664412
#237663982
#237663792
#237663382
#237663372
#237662512
#237662452
#237662262
D4×C22⋊Dic792
#237662092
#237661912
#237661662
#237661532
#237661022
#237660742
#237660582
#237660552
#237660402
#237659962
#237659872
#237659102
#237658402
C2×#190984572
C79×#23082
#3449279