Finite Group Databasebeta

← #34255315

Subgroups — #34255315

Order 20224.

936 conjugacy classes of subgroups.

The subgroup lattice has 880 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23772525C211yesmaximal, characteristic, complemented
2#23772044C211yesmaximal, characteristic, complemented
3#23761873C211yesmaximal, characteristic, complemented
4#23761865C211yesmaximal, characteristic, complemented
5#23761860C211yesmaximal, characteristic, complemented
6#23761847C211yesmaximal, characteristic, complemented
7#23761834C211yesmaximal, characteristic, complemented
8#23761829C211yesmaximal, characteristic, complemented
9#23761813C211yesmaximal, characteristic, complemented
10#23761808C211yesmaximal, characteristic, complemented
11#23761803C211yesmaximal, characteristic, complemented
12#23761795C211yesmaximal, characteristic, complemented
13#23761787C211yesmaximal, characteristic, complemented
14C2×Q8⋊(C79⋊C8)C211yesmaximal, characteristic, complemented
15C79×#3482C211yesmaximal, characteristic
16#19098694—21no—
17#19098635—21no—
18#19098635—21no—
19D4×C79⋊C8—21no—
20#19098624—21no—
21#19098624—21no—
22#19098620C2211yescharacteristic
23#19098620C2211yescharacteristic
24#19098616C2211yescharacteristic
25#19098616C2211yescharacteristic
26#19098616C2211yescharacteristic
27#19098616C2211yescharacteristic
28#19098616C2211yescharacteristic
29#19098590—21no—
30#19098587C2211yescharacteristic
31C2×C4⋊(C79⋊C8)C2211yescharacteristic
32C2×C4⋊(C79⋊C8)C2211yescharacteristic
33#19098530—21no—
34C4×#11929608C2211yescharacteristic
35C2×C4×C79⋊C8C2211yescharacteristic
36Q8⋊(C79⋊C8)C2211yescharacteristic
37Q8⋊(C79⋊C8)C2211yescharacteristic
38Q8⋊(C79⋊C8)C2211yescharacteristic
39Q8⋊(C79⋊C8)C2211yescharacteristic
40Q8⋊(C79⋊C8)C2211yescharacteristic
41Q8⋊(C79⋊C8)C2211yescharacteristic
42Q8⋊(C79⋊C8)C2211yescharacteristic
43Q8⋊(C79⋊C8)C2211yescharacteristic
44Q8⋊(C79⋊C8)C2211yescharacteristic
45Q8⋊(C79⋊C8)C2211yescharacteristic
46Q8⋊(C79⋊C8)C2211yescharacteristic
47Q8⋊(C79⋊C8)C2211yescharacteristic
48D4⋊(C79⋊C8)C2211yescharacteristic
49D4⋊(C79⋊C8)C2211yescharacteristic
50D4⋊(C79⋊C8)C2211yescharacteristic
51D4⋊(C79⋊C8)C2211yescharacteristic
52#557×C79C411yescharacteristic
53#556×C79—21no—
54#556×C79C411yescharacteristic
55#552×C79—21no—
56#552×C79—21no—
57#552×C79C411yescharacteristic
58#552×C79C411yescharacteristic
59D4×Q8×C79C411yescharacteristic
60#548×C79C411yescharacteristic
61#548×C79C411yescharacteristic
62#547×C79—21no—
63#547×C79C411yescharacteristic
64#533×C79—21no—
65#533×C79C2211yescharacteristic
66#529×C79—21no—
67#529×C79—21no—
68#529×C79C2211yescharacteristic
69#529×C79C2211yescharacteristic
70C4×#41×C79—21no—
71C4×#41×C79C2211yescharacteristic
72C4×#41×C79C2211yescharacteristic
73C2×C4×Q8×C79C2211yescharacteristic
74C2×C4×Q8×C79C2211yescharacteristic
75C2×#11929608—21no—
76C2×#11929608—21no—
77C22×C79⋊C8—21no—
78C22×C79⋊C8—21no—
79C22×C79⋊C8—21no—
80C4⋊(C79⋊C8)—21no—
81C4⋊(C79⋊C8)—21no—
82C4⋊(C79⋊C8)—21no—
83C4⋊(C79⋊C8)—21no—
84C4⋊(C79⋊C8)—21no—
85C4⋊(C79⋊C8)—21no—
86C4⋊(C79⋊C8)—21no—
87C4⋊(C79⋊C8)C2311yescharacteristic
88C4⋊(C79⋊C8)C2311yescharacteristic
89C4⋊(C79⋊C8)C2311yescharacteristic
90C4⋊(C79⋊C8)C2311yescharacteristic
91C22⋊(C79⋊C8)—21no—
92C22⋊(C79⋊C8)—21no—
93C22⋊(C79⋊C8)—21no—
94C22⋊(C79⋊C8)—21no—
95C22⋊(C79⋊C8)—21no—
96C22⋊(C79⋊C8)—21no—
97C22⋊(C79⋊C8)—21no—
98#14579072—21no—
99#14579072—21no—
100#14579072—21no—
101C4×C79⋊C8—21no—
102C4×C79⋊C8—21no—
103C4×C79⋊C8C2311yescharacteristic
104C4×C79⋊C8C2311yescharacteristic
105C4×C79⋊C8C2311yescharacteristic
106C4×C79⋊C8C2311yescharacteristic
107C2×#41×C79—21no—
108C2×#41×C79C2×C411yescharacteristic
109C2×#41×C79D411yescharacteristic
110C22×Q8×C79C2×C411yescharacteristic
111C22×Q8×C79C2×C411yescharacteristic
112C4⋊Q8×C79—21no—
113C4⋊Q8×C79—21no—
114C4⋊Q8×C79C2×C411yescharacteristic
115C4⋊Q8×C79C2×C411yescharacteristic
116#126×C79—21no—
117#126×C79—21no—
118#126×C79—21no—
119#126×C79—21no—
120#126×C79—21no—
121#126×C79—21no—
122#125×C79—21no—
123#125×C79—21no—
124#125×C79—21no—
125#125×C79—21no—
126#125×C79—21no—
127#125×C79C2×C411yescharacteristic
128#125×C79C2×C411yescharacteristic
129#124×C79—21no—
130#124×C79—21no—
131#124×C79C2×C411yescharacteristic
132#124×C79C2×C411yescharacteristic
133#123×C79—21no—
134#123×C79—21no—
135#123×C79—21no—
136#123×C79—21no—
137#123×C79—21no—
138#123×C79—21no—
139C22⋊Q8×C79—21no—
140C22⋊Q8×C79—21no—
141C22⋊Q8×C79—21no—
142C22⋊Q8×C79—21no—
143C22⋊Q8×C79—21no—
144C22⋊Q8×C79—21no—
145C22⋊Q8×C79—21no—
146C22⋊Q8×C79C2×C411yescharacteristic
147C22⋊Q8×C79C2×C411yescharacteristic
148C22⋊Q8×C79C2×C411yescharacteristic
149C22⋊Q8×C79C2×C411yescharacteristic
150#121×C79—21no—
151#121×C79—21no—
152#121×C79C2×C411yescharacteristic
153#121×C79C2×C411yescharacteristic
154C4×Q8×C79—21no—
155C4×Q8×C79—21no—
156C4×Q8×C79—21no—
157C4×Q8×C79—21no—
158C4×Q8×C79—21no—
159C4×Q8×C79—21no—
160C4×Q8×C79C2×C411yescharacteristic
161C4×Q8×C79C2×C411yescharacteristic
162C4×Q8×C79C2×C411yescharacteristic
163C4×Q8×C79C2×C411yescharacteristic
164C4×Q8×C79C2×C411yescharacteristic
165C4×Q8×C79C2×C411yescharacteristic
166C4×Q8×C79D411yescharacteristic
167C4×Q8×C79C2311yescharacteristic
168C4×Q8×C79C2311yescharacteristic
169C4×Q8×C79C2311yescharacteristic
170C4×D4×C79—21no—
171C4×D4×C79—21no—
172C4×D4×C79—21no—
173C4×D4×C79—21no—
174C4×D4×C79—21no—
175C4×D4×C79—21no—
176C4×D4×C79—21no—
177C4×D4×C79C2×C411yescharacteristic
178C4×D4×C79C2×C411yescharacteristic
179C4×D4×C79C2×C411yescharacteristic
180C4×D4×C79C2×C411yescharacteristic
181C4×D4×C79D411yescharacteristic
182C4×D4×C79D411yescharacteristic
183C4×D4×C79D411yescharacteristic
184C4×D4×C79C2311yescharacteristic
185#117×C79—21no—
186#117×C79—21no—
187#117×C79—21no—
188#117×C79—21no—
189#117×C79—21no—
190#117×C79—21no—
191#117×C79—21no—
192#117×C79C2×C411yescharacteristic
193#117×C79D411yescharacteristic
194#117×C79D411yescharacteristic
195#117×C79D411yescharacteristic
196C2×C4⋊C4×C79—21no—
197C2×C4⋊C4×C79—21no—
198C2×C4⋊C4×C79C2×C411yescharacteristic
199C2×C4⋊C4×C79C2×C411yescharacteristic
200C2×C42×C79—21no—
201C2×C42×C79—21no—
202C2×C42×C79—21no—
203C2×C42×C79C2311yescharacteristic
204C2×C42×C79C2311yescharacteristic
205C2×C42×C79C2311yescharacteristic
206#11929608—42no—
207#11929608—81no—
208C2×C79⋊C8—21no—
209C2×C79⋊C8—21no—
210C2×C79⋊C8—21no—
211C2×C79⋊C8—21no—
212C2×C79⋊C8—21no—
213C2×C79⋊C8—21no—
214C2×C79⋊C8—21no—
215C2×C79⋊C8—21no—
216C2×C79⋊C8—42no—
217C2×C79⋊C8—81no—
218C2×C79⋊C8—81no—
219#41×C79—22no—
220#41×C79—42no—
221#41×C79—41no—
222#41×C79—44no—
223C2×Q8×C79—21no—
224C2×Q8×C79—21no—
225C2×Q8×C79—21no—
226C2×Q8×C79—22no—
227C2×Q8×C79—22no—
228C2×Q8×C79—41no—
229C2×Q8×C79—41no—
230C2×Q8×C79C22⋊C411yescharacteristic
231C2×Q8×C79C22×C411yescharacteristic
232C2×Q8×C79C22×C411yescharacteristic
233C2×Q8×C79C22×C411yescharacteristic
234C2×D4×C79—21no—
235C2×D4×C79—21no—
236C2×D4×C79—21no—
237C2×D4×C79C22⋊C411yescharacteristic
238C2×D4×C79C22⋊C411yescharacteristic
239C2×D4×C79C22⋊C411yescharacteristic
240C2×D4×C79C22×C411yescharacteristic
241C22×C4×C79—21no—
242C22×C4×C79—21no—
243C22×C4×C79—21no—
244C22×C4×C79—21no—
245C22×C4×C79—21no—
246C22×C4×C79—21no—
247C22×C4×C79—21no—
248C22×C4×C79C22×C411yescharacteristic
249C22×C4×C79C22×C411yescharacteristic
250C22×C4×C79C22×C411yescharacteristic
251C22×C4×C79C2×D411yescharacteristic
252C22×C4×C79C2×D411yescharacteristic
253C22×C4×C79C2×D411yescharacteristic
254C22×C4×C79C2×D411yescharacteristic
255C22×C4×C79C2×D411yescharacteristic
256C22×C4×C79C2×D411yescharacteristic
257C4⋊C4×C79—21no—
258C4⋊C4×C79—21no—
259C4⋊C4×C79—21no—
260C4⋊C4×C79—21no—
261C4⋊C4×C79—21no—
262C4⋊C4×C79—21no—
263C4⋊C4×C79—21no—
264C4⋊C4×C79—21no—
265C4⋊C4×C79—21no—
266C4⋊C4×C79—21no—
267C4⋊C4×C79—21no—
268C4⋊C4×C79—21no—
269C4⋊C4×C79—21no—
270C4⋊C4×C79—21no—
271C4⋊C4×C79—21no—
272C4⋊C4×C79—21no—
273C4⋊C4×C79—21no—
274C4⋊C4×C79—21no—
275C4⋊C4×C79—21no—
276C4⋊C4×C79—21no—
277C4⋊C4×C79—21no—
278C4⋊C4×C79C22⋊C411yescharacteristic
279C4⋊C4×C79C22⋊C411yescharacteristic
280C4⋊C4×C79C22⋊C411yescharacteristic
281C4⋊C4×C79C22⋊C411yescharacteristic
282C4⋊C4×C79C22⋊C411yescharacteristic
283C4⋊C4×C79C22⋊C411yescharacteristic
284C4⋊C4×C79C22×C411yescharacteristic
285C4⋊C4×C79C22×C411yescharacteristic
286C4⋊C4×C79C22×C411yescharacteristic
287C4⋊C4×C79C22×C411yescharacteristic
288C22⋊C4×C79—21no—
289C22⋊C4×C79—21no—
290C22⋊C4×C79—21no—
291C22⋊C4×C79—21no—
292C22⋊C4×C79—21no—
293C22⋊C4×C79—21no—
294C22⋊C4×C79—21no—
295C22⋊C4×C79—21no—
296C22⋊C4×C79—21no—
297C22⋊C4×C79—21no—
298C22⋊C4×C79—21no—
299C22⋊C4×C79—21no—
300C22⋊C4×C79—21no—
301C22⋊C4×C79C22⋊C411yescharacteristic
302C22⋊C4×C79C22⋊C411yescharacteristic
303C22⋊C4×C79C22⋊C411yescharacteristic
304C22⋊C4×C79C22⋊C411yescharacteristic
305C22⋊C4×C79C22⋊C411yescharacteristic
306C22⋊C4×C79C22⋊C411yescharacteristic
307C42×C79—21no—
308C42×C79—21no—
309C42×C79—21no—
310C42×C79—21no—
311C42×C79—21no—
312C42×C79—21no—
313C42×C79—21no—
314C42×C79—21no—
315C42×C79—21no—
316C42×C79C22×C411yescharacteristic
317C42×C79C22×C411yescharacteristic
318C42×C79C22×C411yescharacteristic
319C42×C79C2×D411yescharacteristic
320C42×C79C2×D411yescharacteristic
321C42×C79C2×D411yescharacteristic
322C42×C79C2×D411yescharacteristic
323C42×C79C2×D411yescharacteristic
324C42×C79C2×D411yescharacteristic
325C42×C79C2411yescharacteristic
326C23×C79—21no—
327C23×C79C2×C22⋊C411yescharacteristic
328C23×C79C2×C22⋊C411yescharacteristic
329C23×C79C2×C22⋊C411yescharacteristic
330Q8×C79—21no—
331Q8×C79—21no—
332Q8×C79—21no—
333Q8×C79—21no—
334Q8×C79—21no—
335Q8×C79—41no—
336Q8×C79—42no—
337Q8×C79—42no—
338Q8×C79—42no—
339Q8×C79#13112yes—
340D4×C79—22no—
341D4×C79—22no—
342D4×C79—21no—
343D4×C79—21no—
344D4×C79—41no—
345D4×C79—42no—
346D4×C79—42no—
347D4×C79—42no—
348C2×C4×C79—21no—
349C2×C4×C79—22no—
350C2×C4×C79—21no—
351C2×C4×C79—21no—
352C2×C4×C79—21no—
353C2×C4×C79—21no—
354C2×C4×C79—21no—
355C2×C4×C79—21no—
356C2×C4×C79—21no—
357C2×C4×C79—21no—
358C2×C4×C79—21no—
359C2×C4×C79—21no—
360C2×C4×C79—21no—
361C2×C4×C79—21no—
362C2×C4×C79—21no—
363C2×C4×C79—21no—
364C2×C4×C79—21no—
365C2×C4×C79—21no—
366C2×C4×C79—21no—
367C2×C4×C79—21no—
368C2×C4×C79—41no—
369C2×C4×C79—41no—
370C2×C4×C79—42no—
371C2×C4×C79—42no—
372C2×C4×C79—42no—
373C2×C4×C79—42no—
374C2×C4×C79—42no—
375C2×C4×C79—42no—
376C2×C4×C79—41no—
377C2×C4×C79—41no—
378C2×C4×C79C2×C22⋊C411yescharacteristic
379C2×C4×C79C2×C22⋊C411yescharacteristic
380C2×C4×C79C2×C22⋊C411yescharacteristic
381C2×C4×C79C2×C22⋊C411yescharacteristic
382C2×C4×C79C2×C22⋊C411yescharacteristic
383C2×C4×C79C2×C22⋊C411yescharacteristic
384C2×C4×C79C2×C22⋊C411yescharacteristic
385C2×C4×C79C2×C22⋊C411yescharacteristic
386C2×C4×C79C2×C22⋊C411yescharacteristic
387C2×C4×C79C23×C411yescharacteristic
388C2×C4×C79C22×D411yescharacteristic
389C2×C4×C79C22×D411yescharacteristic
390C79⋊C8—41no—
391C79⋊C8—41no—
392C79⋊C8—41no—
393C79⋊C8—41no—
394C79⋊C8—41no—
395C79⋊C8—41no—
396C79⋊C8—41no—
397C79⋊C8—41no—
398C22×C79—21no—
399C22×C79—21no—
400C22×C79—21no—
401C22×C79—21no—
402C22×C79—21no—
403C22×C79—21no—
404C22×C79—21no—
405C22×C79—21no—
406C22×C79—41no—
407C22×C79—41no—
408C22×C79—41no—
409C22×C79#42112yes—
410C22×C79C22×C22⋊C411yescharacteristic
411C4×C79—21no—
412C4×C79—21no—
413C4×C79—21no—
414C4×C79—22no—
415C4×C79—21no—
416C4×C79—21no—
417C4×C79—21no—
418C4×C79—21no—
419C4×C79—21no—
420C4×C79—21no—
421C4×C79—21no—
422C4×C79—41no—
423C4×C79—41no—
424C4×C79—41no—
425C4×C79—41no—
426C4×C79—41no—
427C4×C79—41no—
428C4×C79C2×#13111yescharacteristic
429C4×C79#56811yescharacteristic
430C4×C79#57711yescharacteristic
431C4×C79#57811yescharacteristic
432#17524—791nomaximal, Sylow
433C2×C79—22no—
434C2×C79—41no—
435C2×C79—41no—
436C2×C79—81no—
437C2×C79#288011yescharacteristic
438C2×C79#289811yescharacteristic
439C2×C79C2×#42111yescharacteristic
440#3482D7911yescharacteristic
441#2990—791no—
442#2922—791no—
443#1497—791no—
444#1495—791no—
445#1494—791no—
446#1491—791no—
447#1488—791no—
448#1487—791no—
449#1483—791no—
450#1482—791no—
451#1481—791no—
452#1479—791no—
453#1477—791no—
454C2×Q8⋊C8—791no—
455C79#1752411yescharacteristic, complemented, Sylow
456#557Dic7911yescharacteristic
457#556—21no—
458#556Dic7911yescharacteristic
459#552—21no—
460#552—21no—
461#552Dic7911yescharacteristic
462#552Dic7911yescharacteristic
463D4×Q8Dic7911yescharacteristic
464#548Dic7911yescharacteristic
465#548Dic7911yescharacteristic
466#547—21no—
467#547Dic7911yescharacteristic
468#533—21no—
469#533C2×D7911yescharacteristic
470#529—21no—
471#529—21no—
472#529C2×D7911yescharacteristic
473#529C2×D7911yescharacteristic
474C4×#41—21no—
475C4×#41C2×D7911yescharacteristic
476C4×#41C2×D7911yescharacteristic
477C2×C4×Q8C2×D7911yescharacteristic
478C2×C4×Q8C2×D7911yescharacteristic
479#446—1581no—
480#435—1581no—
481#435—1581no—
482C8×D4—1581no—
483#433—1581no—
484#433—1581no—
485#432—791no—
486#432—791no—
487#431—791no—
488#431—791no—
489#431—791no—
490#431—791no—
491#431—791no—
492#424—1581no—
493#423—791no—
494C2×C4⋊C8—791no—
495C2×C4⋊C8—791no—
496#408—1581no—
497C4×M16—791no—
498C2×C4×C8—791no—
499Q8⋊C8—791no—
500Q8⋊C8—791no—
501Q8⋊C8—791no—
502Q8⋊C8—791no—
503Q8⋊C8—791no—
504Q8⋊C8—791no—
505Q8⋊C8—791no—
506Q8⋊C8—791no—
507Q8⋊C8—791no—
508Q8⋊C8—791no—
509Q8⋊C8—791no—
510Q8⋊C8—791no—
511D4⋊C8—791no—
512D4⋊C8—791no—
513D4⋊C8—791no—
514D4⋊C8—791no—
515C2×#41—21no—
516C2×#41C2×Dic7911yescharacteristic
517C2×#41C22⋊D7911yescharacteristic
518C22×Q8C2×Dic7911yescharacteristic
519C22×Q8C2×Dic7911yescharacteristic
520C2×M16—1581no—
521C2×M16—1581no—
522C22×C8—1581no—
523C22×C8—1581no—
524C22×C8—1581no—
525C4⋊Q8—21no—
526C4⋊Q8—21no—
527C4⋊Q8C2×Dic7911yescharacteristic
528C4⋊Q8C2×Dic7911yescharacteristic
529#126—21no—
530#126—21no—
531#126—21no—
532#126—21no—
533#126—21no—
534#126—21no—
535#125—21no—
536#125—21no—
537#125—21no—
538#125—21no—
539#125—21no—
540#125C2×Dic7911yescharacteristic
541#125C2×Dic7911yescharacteristic
542#124—21no—
543#124—21no—
544#124C2×Dic7911yescharacteristic
545#124C2×Dic7911yescharacteristic
546#123—21no—
547#123—21no—
548#123—21no—
549#123—21no—
550#123—21no—
551#123—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8C2×Dic7911yescharacteristic
560C22⋊Q8C2×Dic7911yescharacteristic
561C22⋊Q8C2×Dic7911yescharacteristic
562C22⋊Q8C2×Dic7911yescharacteristic
563#121—21no—
564#121—21no—
565#121C2×Dic7911yescharacteristic
566#121C2×Dic7911yescharacteristic
567C4×Q8—21no—
568C4×Q8—21no—
569C4×Q8—21no—
570C4×Q8—21no—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8C2×Dic7911yescharacteristic
574C4×Q8C2×Dic7911yescharacteristic
575C4×Q8C2×Dic7911yescharacteristic
576C4×Q8C2×Dic7911yescharacteristic
577C4×Q8C2×Dic7911yescharacteristic
578C4×Q8C2×Dic7911yescharacteristic
579C4×Q8C22⋊D7911yescharacteristic
580C4×Q8C22×D7911yescharacteristic
581C4×Q8C22×D7911yescharacteristic
582C4×Q8C22×D7911yescharacteristic
583C4×D4—21no—
584C4×D4—21no—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—21no—
590C4×D4C2×Dic7911yescharacteristic
591C4×D4C2×Dic7911yescharacteristic
592C4×D4C2×Dic7911yescharacteristic
593C4×D4C2×Dic7911yescharacteristic
594C4×D4C22⋊D7911yescharacteristic
595C4×D4C22⋊D7911yescharacteristic
596C4×D4C22⋊D7911yescharacteristic
597C4×D4C22×D7911yescharacteristic
598#117—21no—
599#117—21no—
600#117—21no—
601#117—21no—
602#117—21no—
603#117—21no—
604#117—21no—
605#117C2×Dic7911yescharacteristic
606#117C22⋊D7911yescharacteristic
607#117C22⋊D7911yescharacteristic
608#117C22⋊D7911yescharacteristic
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4C2×Dic7911yescharacteristic
612C2×C4⋊C4C2×Dic7911yescharacteristic
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42C22×D7911yescharacteristic
617C2×C42C22×D7911yescharacteristic
618C2×C42C22×D7911yescharacteristic
619C4⋊C8—791no—
620C4⋊C8—791no—
621C4⋊C8—791no—
622C4⋊C8—791no—
623C4⋊C8—1581no—
624C4⋊C8—1581no—
625C4⋊C8—1581no—
626C4⋊C8—1581no—
627C4⋊C8—1581no—
628C4⋊C8—1581no—
629C4⋊C8—1581no—
630C22⋊C8—1581no—
631C22⋊C8—1581no—
632C22⋊C8—1581no—
633C22⋊C8—1581no—
634C22⋊C8—1581no—
635C22⋊C8—1581no—
636C22⋊C8—1581no—
637#97—1581no—
638#97—1581no—
639#97—1581no—
640C4×C8—791no—
641C4×C8—791no—
642C4×C8—791no—
643C4×C8—791no—
644C4×C8—1581no—
645C4×C8—1581no—
646#41—22no—
647#41—42no—
648#41—41no—
649#41—44no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—22no—
654C2×Q8—22no—
655C2×Q8—41no—
656C2×Q8—41no—
657C2×Q8C22⋊Dic7911yescharacteristic
658C2×Q8C22×Dic7911yescharacteristic
659C2×Q8C22×Dic7911yescharacteristic
660C2×Q8C22×Dic7911yescharacteristic
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4C22⋊Dic7911yescharacteristic
665C2×D4C22⋊Dic7911yescharacteristic
666C2×D4C22⋊Dic7911yescharacteristic
667C2×D4C22×Dic7911yescharacteristic
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4C22×Dic7911yescharacteristic
676C22×C4C22×Dic7911yescharacteristic
677C22×C4C22×Dic7911yescharacteristic
678C22×C4C2×C22⋊D7911yescharacteristic
679C22×C4C2×C22⋊D7911yescharacteristic
680C22×C4C2×C22⋊D7911yescharacteristic
681C22×C4C2×C22⋊D7911yescharacteristic
682C22×C4C2×C22⋊D7911yescharacteristic
683C22×C4C2×C22⋊D7911yescharacteristic
684M16—3162no—
685M16—6321no—
686C2×C8—3162no—
687C2×C8—6321no—
688C2×C8—6321no—
689C2×C8—1581no—
690C2×C8—1581no—
691C2×C8—1581no—
692C2×C8—1581no—
693C2×C8—1581no—
694C2×C8—1581no—
695C2×C8—1581no—
696C2×C8—1581no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—21no—
709C4⋊C4—21no—
710C4⋊C4—21no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4C22⋊Dic7911yescharacteristic
719C4⋊C4C22⋊Dic7911yescharacteristic
720C4⋊C4C22⋊Dic7911yescharacteristic
721C4⋊C4C22⋊Dic7911yescharacteristic
722C4⋊C4C22⋊Dic7911yescharacteristic
723C4⋊C4C22⋊Dic7911yescharacteristic
724C4⋊C4C22×Dic7911yescharacteristic
725C4⋊C4C22×Dic7911yescharacteristic
726C4⋊C4C22×Dic7911yescharacteristic
727C4⋊C4C22×Dic7911yescharacteristic
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4C22⋊Dic7911yescharacteristic
742C22⋊C4C22⋊Dic7911yescharacteristic
743C22⋊C4C22⋊Dic7911yescharacteristic
744C22⋊C4C22⋊Dic7911yescharacteristic
745C22⋊C4C22⋊Dic7911yescharacteristic
746C22⋊C4C22⋊Dic7911yescharacteristic
747C42—21no—
748C42—21no—
749C42—21no—
750C42—21no—
751C42—21no—
752C42—21no—
753C42—21no—
754C42—21no—
755C42—21no—
756C42C22×Dic7911yescharacteristic
757C42C22×Dic7911yescharacteristic
758C42C22×Dic7911yescharacteristic
759C42C2×C22⋊D7911yescharacteristic
760C42C2×C22⋊D7911yescharacteristic
761C42C2×C22⋊D7911yescharacteristic
762C42C2×C22⋊D7911yescharacteristic
763C42C2×C22⋊D7911yescharacteristic
764C42C2×C22⋊D7911yescharacteristic
765C42C23×D7911yescharacteristic
766C23—21no—
767C23C2×C22⋊Dic7911yescharacteristic
768C23C2×C22⋊Dic7911yescharacteristic
769C23C2×C22⋊Dic7911yescharacteristic
770Q8—21no—
771Q8—21no—
772Q8—21no—
773Q8—21no—
774Q8—21no—
775Q8—41no—
776Q8—42no—
777Q8—42no—
778Q8—42no—
779Q8#1457916812yes—
780D4—22no—
781D4—22no—
782D4—21no—
783D4—21no—
784D4—41no—
785D4—42no—
786D4—42no—
787D4—42no—
788C2×C4—21no—
789C2×C4—22no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—21no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—42no—
811C2×C4—42no—
812C2×C4—42no—
813C2×C4—42no—
814C2×C4—42no—
815C2×C4—42no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4C2×C22⋊Dic7911yescharacteristic
819C2×C4C2×C22⋊Dic7911yescharacteristic
820C2×C4C2×C22⋊Dic7911yescharacteristic
821C2×C4C2×C22⋊Dic7911yescharacteristic
822C2×C4C2×C22⋊Dic7911yescharacteristic
823C2×C4C2×C22⋊Dic7911yescharacteristic
824C2×C4C2×C22⋊Dic7911yescharacteristic
825C2×C4C2×C22⋊Dic7911yescharacteristic
826C2×C4C2×C22⋊Dic7911yescharacteristic
827C2×C4C23×Dic7911yescharacteristic
828C2×C4C22×C22⋊D7911yescharacteristic
829C2×C4C22×C22⋊D7911yescharacteristic
830C8—3161no—
831C8—3161no—
832C8—3161no—
833C8—3161no—
834C8—3161no—
835C8—3161no—
836C8—3161no—
837C8—3161no—
838C22—21no—
839C22—21no—
840C22—21no—
841C22—21no—
842C22—21no—
843C22—21no—
844C22—21no—
845C22—21no—
846C22—41no—
847C22—41no—
848C22—41no—
849C22#1909858012yes—
850C22C22×C22⋊Dic7911yescharacteristic
851C4—21no—
852C4—21no—
853C4—21no—
854C4—21no—
855C4—21no—
856C4—21no—
857C4—21no—
858C4—21no—
859C4—21no—
860C4—21no—
861C4—22no—
862C4—41no—
863C4—41no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—41no—
868C4C2×#1457916811yescharacteristic
869C4#1909933011yescharacteristic
870C4#1909937111yescharacteristic
871C4#1909937811yescharacteristic
872C2—22no—
873C2—41no—
874C2—41no—
875C2—81no—
876C2#2377184911yescharacteristic
877C2#2377193311yescharacteristic
878C2C2×#1909858011yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
Fitting, prime radicalC79×#3482C2
socleC22×C79C22×C22⋊C4
cosocleC42×C79C24
hypercenter#3482D79
hypocenterC79#17524
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. #23772525C2semidirect
2. #23772044C2semidirect
3. #23761873C2semidirect
4. #23761865C2semidirect
5. #23761860C2semidirect
6. #23761847C2semidirect
7. #23761834C2semidirect
8. #23761829C2semidirect
9. #23761813C2semidirect
10. #23761808C2semidirect
11. #23761803C2semidirect
12. #23761795C2semidirect
13. #23761787C2semidirect
14. C2×Q8⋊(C79⋊C8)C2semidirect
455. C79#17524semidirect

Maximal subgroups

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

subgroupindex
#237725252
#237720442
#237618732
#237618652
#237618602
#237618472
#237618342
#237618292
#237618132
#237618082
#237618032
#237617952
#237617872
C2×Q8⋊(C79⋊C8)2
C79×#34822
#1752479