Finite Group Databasebeta

← #34304566

Subgroups — #34304566

Order 20224.

1194 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099278C211yesmaximal, characteristic
2C2×#19098635C211yesmaximal, characteristic, complemented
3#23764372C211yesmaximal, characteristic, complemented
4#23764352C211yesmaximal, characteristic, complemented
5#23763836C211yesmaximal, characteristic, complemented
6#23763826C211yesmaximal, characteristic, complemented
7#23763722C211yesmaximal, characteristic, complemented
8#23763717C211yesmaximal, characteristic, complemented
9#23763492C211yesmaximal, characteristic, complemented
10#23763492C211yesmaximal, characteristic, complemented
11#23763407C211yesmaximal, characteristic, complemented
12#23763228C211yesmaximal, characteristic, complemented
13#23763119C211yesmaximal, characteristic, complemented
14#23763116C211yesmaximal, characteristic, complemented
15C79×#2352C211yesmaximal, characteristic, complemented
16C22×#11929608C2211yescharacteristic
17C23×C79⋊C8C2211yescharacteristic
18#19099278—24no—
19#19099278C418yescomplemented
20C2×#14579161C2211yescharacteristic
21C2×#14579147—21no—
22C2×#14579147—21no—
23C2×#14579135C2211yescharacteristic
24C2×#14579135C2211yescharacteristic
25C2×#14579132—21no—
26C2×C4×D316C2211yescharacteristic
27C2×#14579120C2211yescharacteristic
28C2×#14579120C2211yescharacteristic
29C2×#14579119—21no—
30#19098635—24no—
31C2×C4⋊(C79⋊C8)C2211yescharacteristic
32C2×#14579081C2211yescharacteristic
33C2×#14579081C2211yescharacteristic
34C2×#14579081C2211yescharacteristic
35C2×#14579081C2211yescharacteristic
36C2×C22⋊(C79⋊C8)C2211yescharacteristic
37C2×C22⋊(C79⋊C8)C2211yescharacteristic
38C2×#14579072C2211yescharacteristic
39#19098325C2211yescharacteristic
40#19098325C2211yescharacteristic
41#19098325C2211yescharacteristic
42#19098325C2211yescharacteristic
43#19098325C2211yescharacteristic
44#19098325C2211yescharacteristic
45#19098325C2211yescharacteristic
46#19098325C2211yescharacteristic
47#19098325C2211yescharacteristic
48#19098325C2211yescharacteristic
49#19098325C2211yescharacteristic
50#19098325C2211yescharacteristic
51C2×C4×D4×C79C2211yescharacteristic
52C2×#117×C79C2211yescharacteristic
53C22×C4⋊C4×C79C2211yescharacteristic
54#388×C79—21no—
55#387×C79—21no—
56#386×C79—21no—
57#382×C79C2211yescharacteristic
58#380×C79C2211yescharacteristic
59#380×C79C2211yescharacteristic
60C4×C4⋊C4×C79C2211yescharacteristic
61C4×C22⋊C4×C79—21no—
62C22×Dic158—21no—
63C22×D316C2311yescharacteristic
64C22×C22⋊D79—21no—
65C22×C22⋊D79—21no—
66C22×C4×D79—21no—
67C2×#11929608—22no—
68C2×#11929608—22no—
69C2×#11929608—41no—
70C22×C79⋊C8—22no—
71C22×C79⋊C8—22no—
72C22×C79⋊C8—41no—
73C22×C79⋊C8C2311yescharacteristic
74C22×C79⋊C8C2311yescharacteristic
75C22×C79⋊C8C2311yescharacteristic
76C22×C79⋊C8C2311yescharacteristic
77#14579161—22no—
78#14579161C2×C414yescomplemented
79#14579147—28no—
80#14579147—28no—
81#14579135—22no—
82#14579135—22no—
83#14579135C2×C414yes—
84#14579135C2×C414yescomplemented
85#14579132—28no—
86C4×D316—22no—
87C4×D316C2×C414yescomplemented
88#14579120—22no—
89#14579120—22no—
90#14579120C2×C414yes—
91#14579120C2×C414yescomplemented
92#14579119—28no—
93C2×C4⋊Dic79—21no—
94C2×C4⋊Dic79C2311yescharacteristic
95C2×C4⋊Dic79C2311yescharacteristic
96C2×C4⋊Dic79C2311yescharacteristic
97C2×C22⋊Dic79—21no—
98C2×C22⋊Dic79—21no—
99C2×(C2×D79)⋊C4—21no—
100C2×(C2×D79)⋊C4—21no—
101C2×(C2×D79)⋊C4—21no—
102C2×C4×Dic79—21no—
103C2×C4×Dic79—21no—
104C4⋊(C79⋊C8)—22no—
105#14579081—22no—
106#14579081—22no—
107#14579081—41no—
108#14579081—41no—
109C22⋊(C79⋊C8)—22no—
110C22⋊(C79⋊C8)—22no—
111#14579072—22no—
112C22×D4×C79D411yescharacteristic
113C23×C4×C79—21no—
114C23×C4×C79C2311yescharacteristic
115C23×C4×C79C2311yescharacteristic
116C4×D4×C79C2×C414yes—
117C4×D4×C79D414yes—
118#117×C79—22no—
119#117×C79—41no—
120C2×C4⋊C4×C79—22no—
121C2×C4⋊C4×C79—21no—
122C2×C4⋊C4×C79—41no—
123C2×C4⋊C4×C79D411yescharacteristic
124C2×C4⋊C4×C79C2311yescharacteristic
125C2×C4⋊C4×C79C2311yescharacteristic
126C2×C4⋊C4×C79C2311yescharacteristic
127C2×C4⋊C4×C79C2311yescharacteristic
128C2×C22⋊C4×C79—21no—
129C2×C22⋊C4×C79—21no—
130C2×C22⋊C4×C79—21no—
131C2×C22⋊C4×C79D411yescharacteristic
132C2×C22⋊C4×C79D411yescharacteristic
133C2×C42×C79—21no—
134C2×C42×C79—21no—
135C2×C42×C79C2311yescharacteristic
136#95×C79—21no—
137#95×C79—21no—
138#95×C79—21no—
139#95×C79—21no—
140#95×C79—21no—
141C23×D79—21no—
142C2×Dic158—24no—
143C2×Dic158—81no—
144C2×Dic158—81no—
145C2×D316—21no—
146C2×D316—21no—
147C2×D316—21no—
148C2×D316—21no—
149C2×D316—21no—
150C2×D316C22×C412yes—
151C2×C22⋊D79—24no—
152C2×C22⋊D79—24no—
153C2×C22⋊D79—81no—
154C2×C22⋊D79—81no—
155C2×C22⋊D79—81no—
156C2×C22⋊D79—81no—
157C22×Dic79—21no—
158C22×Dic79—21no—
159C22×Dic79—21no—
160C2×C4×D79—24no—
161C2×C4×D79—42no—
162C2×C4×D79—42no—
163#11929608—44no—
164C2×C79⋊C8—21no—
165C2×C79⋊C8—21no—
166C2×C79⋊C8—21no—
167C2×C79⋊C8—21no—
168C2×C79⋊C8—21no—
169C2×C79⋊C8—21no—
170C2×C79⋊C8—21no—
171C2×C79⋊C8—21no—
172C2×C79⋊C8—21no—
173C2×C79⋊C8—21no—
174C2×C79⋊C8—21no—
175C2×C79⋊C8—44no—
176C2×C79⋊C8#4112yes—
177C4⋊Dic79—24no—
178C4⋊Dic79—21no—
179C4⋊Dic79—21no—
180C4⋊Dic79—21no—
181C4⋊Dic79C22×C412yes—
182C4⋊Dic79C22×C412yes—
183C4⋊Dic79C22×C412yes—
184C22⋊Dic79—24no—
185C22⋊Dic79—24no—
186(C2×D79)⋊C4—24no—
187(C2×D79)⋊C4—24no—
188(C2×D79)⋊C4—24no—
189C4×Dic79—24no—
190C4×Dic79—24no—
191C24×C79C2×D411yescharacteristic
192C24×C79C2×D411yescharacteristic
193C2×D4×C79—41no—
194C2×D4×C79—41no—
195C2×D4×C79C22⋊C414yes—
196C22×C4×C79—21no—
197C22×C4×C79—21no—
198C22×C4×C79—21no—
199C22×C4×C79—21no—
200C22×C4×C79—21no—
201C22×C4×C79—21no—
202C22×C4×C79—21no—
203C22×C4×C79—21no—
204C22×C4×C79—21no—
205C22×C4×C79—21no—
206C22×C4×C79—21no—
207C22×C4×C79—21no—
208C22×C4×C79—42no—
209C22×C4×C79—42no—
210C22×C4×C79—81no—
211C22×C4×C79C22×C412yes—
212C22×C4×C79C22×C412yes—
213C22×C4×C79C2×D411yescharacteristic
214C22×C4×C79C2×D411yescharacteristic
215C22×C4×C79C2×D411yescharacteristic
216C22×C4×C79C2×D411yescharacteristic
217C22×C4×C79C2×D412yes—
218C22×C4×C79C2×D412yes—
219C22×C4×C79C2411yescharacteristic
220C4⋊C4×C79—21no—
221C4⋊C4×C79—21no—
222C4⋊C4×C79—21no—
223C4⋊C4×C79—21no—
224C4⋊C4×C79—21no—
225C4⋊C4×C79—21no—
226C4⋊C4×C79—21no—
227C4⋊C4×C79—42no—
228C4⋊C4×C79C22⋊C414yes—
229C4⋊C4×C79#4112yes—
230C22⋊C4×C79—42no—
231C22⋊C4×C79—42no—
232C22⋊C4×C79—81no—
233C22⋊C4×C79C22⋊C414yes—
234C22⋊C4×C79C22⋊C414yes—
235C42×C79—42no—
236C42×C79—81no—
237C42×C79C22×C412yes—
238C42×C79C2×D412yes—
239C23×C79—21no—
240C23×C79—21no—
241C23×C79—21no—
242C23×C79—21no—
243C23×C79—21no—
244C23×C79—21no—
245C23×C79—21no—
246C23×C79—21no—
247C23×C79—21no—
248C23×C79—21no—
249C23×C79—21no—
250C23×C79—21no—
251C23×C79C2×C22⋊C412yes—
252C23×C79C2×C22⋊C412yes—
253C23×C79C22×D411yescharacteristic
254C22×D79—22no—
255C22×D79—41no—
256C22×D79—41no—
257C22×D79—41no—
258C22×D79—41no—
259C22×D79—41no—
260C22×D79—41no—
261D4×C79—44no—
262C2×C4×C79—21no—
263C2×C4×C79—21no—
264C2×C4×C79—21no—
265C2×C4×C79—21no—
266C2×C4×C79—21no—
267C2×C4×C79—21no—
268C2×C4×C79—21no—
269C2×C4×C79—21no—
270C2×C4×C79—22no—
271C2×C4×C79—22no—
272C2×C4×C79—22no—
273C2×C4×C79—22no—
274C2×C4×C79—22no—
275C2×C4×C79—22no—
276C2×C4×C79—22no—
277C2×C4×C79—22no—
278C2×C4×C79—22no—
279C2×C4×C79—41no—
280C2×C4×C79—41no—
281C2×C4×C79—41no—
282C2×C4×C79—41no—
283C2×C4×C79—41no—
284C2×C4×C79—41no—
285C2×C4×C79—41no—
286C2×C4×C79—41no—
287C2×C4×C79—41no—
288C2×C4×C79—41no—
289C2×C4×C79—41no—
290C2×C4×C79—84no—
291C2×C4×C79C2×C22⋊C412yes—
292C2×C4×C79C2×C22⋊C412yes—
293C2×C4×C79C2×C22⋊C412yes—
294C2×C4×C79C2×C22⋊C412yes—
295C2×C4×C79C23×C411yescharacteristic
296C2×C4×C79C22×D411yescharacteristic
297C2×C4×C79C2×#4111yescharacteristic
298C2×C4×C79C2×#4111yescharacteristic
299C2×C4×C79H(5,𝔽2)11yescharacteristic
300C2×C4×C792−1+411yescharacteristic
301C22⋊D79—84no—
302C22⋊D79—84no—
303C2×Dic79—22no—
304C2×Dic79—22no—
305C2×Dic79—22no—
306C2×Dic79—41no—
307C2×Dic79—41no—
308C2×Dic79—41no—
309C2×Dic79—41no—
310C2×Dic79—41no—
311C2×Dic79—41no—
312D316—22no—
313D316—22no—
314D316—41no—
315D316—41no—
316C4×D79—48no—
317Dic158—84no—
318C79⋊C8—22no—
319C79⋊C8—41no—
320C79⋊C8—41no—
321C79⋊C8—41no—
322C22×C79—22no—
323C22×C79—22no—
324C22×C79—22no—
325C22×C79—22no—
326C22×C79—22no—
327C22×C79—22no—
328C22×C79—41no—
329C22×C79—41no—
330C22×C79—41no—
331C22×C79—41no—
332C22×C79—41no—
333C22×C79—41no—
334C22×C79—41no—
335C22×C79—41no—
336C22×C79C22×C22⋊C411yescharacteristic
337C22×C79#54611yescharacteristic
338C22×C79#54711yescharacteristic
339C22×C79#57511yescharacteristic
340C22×C79#57511yescharacteristic
341C22×C79#57611yescharacteristic
342C22×C79#57711yescharacteristic
343C2×D79—42no—
344C2×D79—42no—
345C2×D79—42no—
346C2×D79—81no—
347C2×D79—81no—
348C2×D79—81no—
349C2×D79—81no—
350C4×C79—22no—
351C4×C79—22no—
352C4×C79—22no—
353C4×C79—22no—
354C4×C79—42no—
355C4×C79—81no—
356C4×C79—81no—
357C4×C79—81no—
358C4×C79C4×#4111yescharacteristic
359C4×C79#52011yescharacteristic
360C4×C79#54611yescharacteristic
361C4×C79#54711yescharacteristic
362Dic79—42no—
363Dic79—42no—
364Dic79—42no—
365#22492—791nomaximal, Sylow
366C2×C79—42no—
367C2×C79—42no—
368C2×C79#233911yescharacteristic
369C2×C79#289611yescharacteristic
370C2×C79#289711yescharacteristic
371C2×C79#331911yescharacteristic
372C2×C79#332111yescharacteristic
373C2×C79#334711yescharacteristic
374C2×C79#334811yescharacteristic
375D79—82no—
376C2×#555—791no—
377C2×#435—791no—
378#2352D7911yescharacteristic, complemented
379#1993—791no—
380#1988—791no—
381#1895—791no—
382#1893—791no—
383#1875—791no—
384#1874—791no—
385#1825—791no—
386#1825—791no—
387#1804—791no—
388#1762—791no—
389#1736—791no—
390#1735—791no—
391C79#2249211yescharacteristic, complemented, Sylow
392C22×M16—791no—
393C23×C8—791no—
394#555—798no—
395#555—1584no—
396C2×C4⋊Q8—791no—
397C2×#124—1581no—
398C2×#124—1581no—
399C2×#121—791no—
400C2×#121—791no—
401C2×#121—1581no—
402C2×C4×D4—791no—
403C2×C4×D4C2×D7911yescharacteristic
404C2×#117—791no—
405C2×#117—791no—
406C2×#117—1581no—
407C2×#117C2×D7911yescharacteristic
408C22×C4⋊C4C2×D7911yescharacteristic
409#435—1584no—
410C2×C4⋊C8—791no—
411C2×#102—791no—
412C2×#102—791no—
413C2×#102—791no—
414C2×#102—791no—
415C2×C22⋊C8—791no—
416C2×C22⋊C8—791no—
417C2×#97—791no—
418#388—21no—
419#387—21no—
420#386—21no—
421#382C2×D7911yescharacteristic
422#380C2×D7911yescharacteristic
423#380C2×D7911yescharacteristic
424C4×C4⋊C4C2×D7911yescharacteristic
425C4×C22⋊C4—21no—
426#340—791no—
427#340—791no—
428#340—791no—
429#340—791no—
430#340—791no—
431#340—791no—
432#340—791no—
433#340—791no—
434#340—791no—
435#340—791no—
436#340—791no—
437#340—791no—
438C22×Q8—1581no—
439C22×D4—791no—
440C22×D4—1581no—
441C22×D4—1581no—
442C22×D4C22⋊D7911yescharacteristic
443C23×C4—21no—
444C23×C4—1581no—
445C23×C4C22×D7911yescharacteristic
446C23×C4C22×D7911yescharacteristic
447C2×M16—3161no—
448C2×M16—1582no—
449C2×M16—1582no—
450C22×C8—3161no—
451C22×C8—791no—
452C22×C8—791no—
453C22×C8—791no—
454C22×C8—791no—
455C22×C8—1582no—
456C22×C8—1582no—
457C4⋊Q8—794no—
458C4⋊Q8—1582no—
459#124—1588no—
460#124—1588no—
461#121—794no—
462#121—794no—
463#121—1588no—
464#121—1582no—
465#121—1582no—
466C4×D4—794no—
467C4×D4—1582no—
468C4×D4C4×D7914yes—
469C4×D4D31614yes—
470#117—22no—
471#117—41no—
472#117—794no—
473#117—794no—
474#117—1582no—
475#117—1582no—
476#117—1588no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—41no—
480C2×C4⋊C4—791no—
481C2×C4⋊C4—791no—
482C2×C4⋊C4—791no—
483C2×C4⋊C4—1581no—
484C2×C4⋊C4C22⋊D7911yescharacteristic
485C2×C4⋊C4C22×D7911yescharacteristic
486C2×C4⋊C4C22×D7911yescharacteristic
487C2×C4⋊C4C22×D7911yescharacteristic
488C2×C4⋊C4C22×D7911yescharacteristic
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—1581no—
493C2×C22⋊C4—1581no—
494C2×C22⋊C4—1581no—
495C2×C22⋊C4—1581no—
496C2×C22⋊C4—1581no—
497C2×C22⋊C4C22⋊D7911yescharacteristic
498C2×C22⋊C4C22⋊D7911yescharacteristic
499C2×C42—21no—
500C2×C42—21no—
501C2×C42—1581no—
502C2×C42—1581no—
503C2×C42C22×D7911yescharacteristic
504C4⋊C8—1582no—
505#102—3161no—
506#102—3161no—
507#102—1582no—
508#102—1582no—
509C22⋊C8—1582no—
510C22⋊C8—1582no—
511#97—1582no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95—21no—
516#95—21no—
517C24—1581no—
518C24C2×C22⋊D7911yescharacteristic
519C24C2×C22⋊D7911yescharacteristic
520C2×Q8—6321no—
521C2×Q8—6321no—
522C2×Q8—1584no—
523C2×D4—41no—
524C2×D4—41no—
525C2×D4—792no—
526C2×D4—6321no—
527C2×D4—6321no—
528C2×D4—6321no—
529C2×D4—6321no—
530C2×D4—1584no—
531C2×D4—1584no—
532C2×D4—1581no—
533C2×D4—1581no—
534C2×D4—1581no—
535C2×D4—1581no—
536C2×D4—1581no—
537C2×D4(C2×D79)⋊C414yes—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—42no—
551C22×C4—42no—
552C22×C4—81no—
553C22×C4—3162no—
554C22×C4—3162no—
555C22×C4—1581no—
556C22×C4—1581no—
557C22×C4—1581no—
558C22×C4—1584no—
559C22×C4C2×C4×D7912yes—
560C22×C4C2×C4×D7912yes—
561C22×C4C2×C22⋊D7911yescharacteristic
562C22×C4C2×C22⋊D7911yescharacteristic
563C22×C4C2×C22⋊D7911yescharacteristic
564C22×C4C2×C22⋊D7911yescharacteristic
565C22×C4C2×D31612yes—
566C22×C4C2×D31612yes—
567C22×C4C23×D7911yescharacteristic
568M16—3164no—
569C2×C8—3164no—
570C2×C8—792no—
571C2×C8—1581no—
572C2×C8—1581no—
573C2×C8—1581no—
574C2×C8—1581no—
575C2×C8—1581no—
576C2×C8—1581no—
577C2×C8—1581no—
578C2×C8—1581no—
579C2×C8—1581no—
580C2×C8—1581no—
581C2×C8—1581no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—42no—
590C4⋊C4—792no—
591C4⋊C4—792no—
592C4⋊C4—792no—
593C4⋊C4—1584no—
594C4⋊C4—1581no—
595C4⋊C4—1581no—
596C4⋊C4—1581no—
597C4⋊C4(C2×D79)⋊C414yes—
598C4⋊C4#1192962312yes—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—81no—
602C22⋊C4—1584no—
603C22⋊C4—1584no—
604C22⋊C4—1584no—
605C22⋊C4—1584no—
606C22⋊C4—1584no—
607C22⋊C4(C2×D79)⋊C414yes—
608C22⋊C4(C2×D79)⋊C414yes—
609C42—42no—
610C42—81no—
611C42—1584no—
612C42—1584no—
613C42C2×C4×D7912yes—
614C42C2×D31612yes—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—3161no—
628C23—3161no—
629C23—3161no—
630C23—3161no—
631C23—3161no—
632C23—3161no—
633C23—1582no—
634C23C2×(C2×D79)⋊C412yes—
635C23C2×(C2×D79)⋊C412yes—
636C23C22×C22⋊D7911yescharacteristic
637Q8—6324no—
638D4—44no—
639D4—3161no—
640D4—3161no—
641D4—6324no—
642D4—6324no—
643D4—1582no—
644D4—1582no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—84no—
674C2×C4—3168no—
675C2×C4—3161no—
676C2×C4—3161no—
677C2×C4—3161no—
678C2×C4—3161no—
679C2×C4—3161no—
680C2×C4—3161no—
681C2×C4—1582no—
682C2×C4—1582no—
683C2×C4—1582no—
684C2×C4C2×(C2×D79)⋊C412yes—
685C2×C4C2×(C2×D79)⋊C412yes—
686C2×C4C2×(C2×D79)⋊C412yes—
687C2×C4C2×(C2×D79)⋊C412yes—
688C2×C4C22×C4×D7911yescharacteristic
689C2×C4C22×D31611yescharacteristic
690C2×C4#41×D7911yescharacteristic
691C2×C4C2×#1192962311yescharacteristic
692C2×C4#1457920611yescharacteristic
693C2×C4#1457920811yescharacteristic
694C8—3161no—
695C8—3161no—
696C8—3161no—
697C8—1582no—
698C22—22no—
699C22—22no—
700C22—22no—
701C22—22no—
702C22—22no—
703C22—22no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—41no—
711C22—41no—
712C22—3162no—
713C22—3162no—
714C22—3162no—
715C22—6321no—
716C22—6321no—
717C22—6321no—
718C22—6321no—
719C22C22×(C2×D79)⋊C411yescharacteristic
720C22#1909920711yescharacteristic
721C22#1909921211yescharacteristic
722C22#1909936111yescharacteristic
723C22#1909936111yescharacteristic
724C22#1909936611yescharacteristic
725C22#1909937111yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—81no—
732C4—81no—
733C4—81no—
734C4—3162no—
735C4—3162no—
736C4—3162no—
737C4C4×#1192962311yescharacteristic
738C4#1909904211yescharacteristic
739C4#1909920811yescharacteristic
740C4#1909921711yescharacteristic
741C2—42no—
742C2—42no—
743C2—6322no—
744C2#2376622511yescharacteristic
745C2#2377191711yescharacteristic
746C2#2377192311yescharacteristic
747C2#2377555611yescharacteristic
748C2#2377558611yescharacteristic
749C2#2377589411yescharacteristic
750C2#2377590911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC22×C4C23×D79
FittingC79×#2352C2
socleC23×C79C22×D4
prime radicalC2×#19099278C2
cosocleC22×C4×C79C24
hypercenter#2352D79
hypocenterC79#22492
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2352

Complements

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

NH ≅ G/Ntype
2. C2×#19098635C2semidirect
3. #23764372C2semidirect
4. #23764352C2semidirect
5. #23763836C2semidirect
6. #23763826C2semidirect
7. #23763722C2semidirect
8. #23763717C2semidirect
9. #23763492C2semidirect
10. #23763492C2semidirect
11. #23763407C2semidirect
12. #23763228C2semidirect
13. #23763119C2semidirect
14. #23763116C2semidirect
15. C79×#2352C2semidirect
19. #19099278C4semidirect
78. #14579161C2×C4semidirect
84. #14579135C2×C4semidirect
87. C4×D316C2×C4semidirect
91. #14579120C2×C4semidirect
378. #2352D79semidirect
391. C79#22492semidirect

Maximal subgroups

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

subgroupindex
C2×#190992782
C2×#190986352
#237643722
#237643522
#237638362
#237638262
#237637222
#237637172
#237634922
#237634072
#237632282
#237631192
#237631162
C79×#23522
#2249279