Finite Group Databasebeta

← #34461192

Subgroups — #34461192

Order 20224.

2642 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099150C212yesmaximal, complemented
2#23771752C211yesmaximal, characteristic, complemented
3#23771679C212yesmaximal, complemented
4#23769333C212yesmaximal, complemented
5#23769136C212yesmaximal, complemented
6#23768534C214yesmaximal, complemented
7#23768504C214yesmaximal, complemented
8#23767825C212yesmaximal, complemented
9#23767761C212yesmaximal, complemented
10#23766991C212yesmaximal, complemented
11#23766912C212yesmaximal, complemented
12#23766105C212yesmaximal, complemented
13#121×Dic79C212yesmaximal, complemented
14C2×C4×(C2×D79)⋊C4C211yesmaximal, characteristic, complemented
15C79×#2856C211yesmaximal, characteristic, complemented
16C23×C4×D79C2211yescharacteristic
17#19099150—216no—
18C2×#14579161C2211yescharacteristic, complemented
19C2×#14579156C2214yes—
20C2×#14579147C2214yes—
21C2×#14579145C2214yes—
22C2×#14579140C2212yes—
23C2×#14579133C2214yes—
24C2×#14579132C2212yes—
25C2×#14579132C2212yes—
26C2×#14579129C2214yes—
27C2×D4×Dic79C2214yes—
28C2×D4×Dic79C2212yescomplemented
29C22×(C2×D79)⋊C4C2211yescharacteristic
30C22×(C2×D79)⋊C4C2211yescharacteristic
31C22×C4×Dic79C2211yescharacteristic
32#19098501C2214yescomplemented
33#19098489C2214yes—
34#19098488C2214yescomplemented
35#19098479C2214yes—
36#19098479C2214yes—
37#19098477C2214yescomplemented
38#19098475C2214yescomplemented
39#19098471C2214yes—
40#19098469C2212yescomplemented
41#19098466C2212yescomplemented
42#19098462C2212yescomplemented
43#19098461C2212yescomplemented
44#19098461C2212yescomplemented
45#19098456C2214yescomplemented
46#19098456C2214yescomplemented
47#19098449C2214yescomplemented
48#19098443C2214yes—
49#19098443C2214yes—
50#19098443C2214yescomplemented
51#19098439C2214yes—
52#19098439C2214yes—
53#19098438C2214yescomplemented
54#19098433C2211yescharacteristic, complemented
55#19098423C2212yes—
56#19098423C2212yes—
57#19098420C2212yes—
58#19098420C2212yes—
59C4⋊C4×Dic79C2212yescomplemented
60C22⋊C4×Dic79C2214yescomplemented
61C4×(C2×D79)⋊C4C2212yes—
62C4×(C2×D79)⋊C4C2212yes—
63C4×(C2×D79)⋊C4C2212yes—
64C4×(C2×D79)⋊C4C2212yes—
65C2×C79⋊#95C2211yescharacteristic
66C2×C79⋊#95C2211yescharacteristic
67C2×#127×C79C2211yescharacteristic, complemented
68C2×#121×C79C2212yes—
69C2×#121×C79C2212yes—
70C2×#121×C79C2212yes—
71C22×C42×C79C2211yescharacteristic
72#390×C79C2212yescomplemented
73#390×C79C2212yescomplemented
74#390×C79C2212yescomplemented
75#384×C79C2211yescharacteristic, complemented
76C24×D79C2311yescharacteristic
77C22×Dic158C2312yes—
78C22×C22⋊D79C2314yes—
79C22×C22⋊D79C2314yes—
80C23×Dic79C2311yescharacteristic
81C23×Dic79C2311yescharacteristic
82C23×Dic79C2314yes—
83C23×Dic79C2311yescharacteristic
84C22×C4×D79—24no—
85C22×C4×D79—42no—
86C22×C4×D79—42no—
87C22×C4×D79C2312yes—
88C22×C4×D79C2312yes—
89#14579161—42no—
90#14579156—216no—
91#14579147—216no—
92#14579145—216no—
93#14579140—28no—
94#14579133—216no—
95#14579132—44no—
96#14579132—44no—
97#14579129—216no—
98D4×Dic79—216no—
99D4×Dic79—44no—
100C2×C4⋊Dic79C2312yes—
101C2×C4⋊Dic79C2312yes—
102C2×C4⋊Dic79C2312yes—
103C2×C4⋊Dic79C2314yes—
104C2×C4⋊Dic79C2312yes—
105C2×C4⋊Dic79C2312yes—
106C2×Dic79⋊C4C2314yes—
107C2×C22⋊Dic79C2314yes—
108C2×C22⋊Dic79C2314yes—
109C2×C22⋊Dic79C2314yes—
110C2×C22⋊Dic79C2314yes—
111C2×C22⋊Dic79C2314yes—
112C2×C22⋊Dic79C2314yes—
113C2×(C2×D79)⋊C4—24no—
114C2×(C2×D79)⋊C4D418yescomplemented
115C2×(C2×D79)⋊C4C2312yes—
116C2×(C2×D79)⋊C4C2312yes—
117C2×(C2×D79)⋊C4C2314yes—
118C2×(C2×D79)⋊C4C2314yes—
119C2×(C2×D79)⋊C4C2312yes—
120C2×(C2×D79)⋊C4C2312yes—
121C2×C4×Dic79—42no—
122C2×C4×Dic79C2312yes—
123C2×C4×Dic79C2314yes—
124C2×C4×Dic79C2312yes—
125C79⋊#95C2312yes—
126C79⋊#95C2312yes—
127C79⋊#95C2312yes—
128C79⋊#95C2312yes—
129C79⋊#95C2314yes—
130C79⋊#95C2314yes—
131C79⋊#95C2314yes—
132C79⋊#95C2314yes—
133C79⋊#95C2314yes—
134C79⋊#95C2314yes—
135C22×D4×C79C2314yes—
136C22×D4×C79C2312yes—
137C22×D4×C79C2312yes—
138C22×D4×C79C2312yes—
139C23×C4×C79C2311yescharacteristic
140C23×C4×C79C2311yescharacteristic
141C23×C4×C79C2311yescharacteristic
142#127×C79—42no—
143#121×C79—28no—
144#121×C79—28no—
145#121×C79—28no—
146C2×C4⋊C4×C79C2312yes—
147C2×C4⋊C4×C79C2312yes—
148C2×C4⋊C4×C79C2312yes—
149C2×C22⋊C4×C79C2314yes—
150C2×C22⋊C4×C79C2314yes—
151C2×C22⋊C4×C79C2314yes—
152C2×C42×C79—42no—
153C2×C42×C79C2311yescharacteristic
154C2×C42×C79C2311yescharacteristic
155C2×C42×C79C2311yescharacteristic
156C2×C42×C79C2311yescharacteristic
157C23×D79—22no—
158C23×D79—22no—
159C23×D79—41no—
160C23×D79—41no—
161C23×D79—41no—
162C23×D79—41no—
163C23×D79C2×D414yes—
164C23×D79C2412yes—
165C2×Dic158—24no—
166C2×Dic158—42no—
167C2×Dic158—42no—
168C2×C22⋊D79—28no—
169C2×C22⋊D79—28no—
170C2×C22⋊D79—44no—
171C2×C22⋊D79—44no—
172C2×C22⋊D79—44no—
173C2×C22⋊D79—44no—
174C22×Dic79—28no—
175C22×Dic79—22no—
176C22×Dic79—22no—
177C22×Dic79—41no—
178C22×Dic79—41no—
179C22×Dic79—41no—
180C22×Dic79—41no—
181C22×Dic79—41no—
182C22×Dic79—41no—
183C22×Dic79—44no—
184C22×Dic79—44no—
185C22×Dic79C2×D414yes—
186C22×Dic79C2414yes—
187C22×Dic79C2412yes—
188C22×Dic79C2412yes—
189C22×Dic79C2414yes—
190C22×Dic79C2412yes—
191C2×C4×D79—24no—
192C2×C4×D79—24no—
193C2×C4×D79—24no—
194C2×C4×D79—24no—
195C2×C4×D79—42no—
196C2×C4×D79—42no—
197C2×C4×D79—416no—
198C4⋊Dic79—28no—
199C4⋊Dic79—24no—
200C4⋊Dic79—24no—
201C4⋊Dic79—24no—
202C4⋊Dic79—42no—
203C4⋊Dic79—42no—
204Dic79⋊C4—28no—
205C22⋊Dic79—28no—
206C22⋊Dic79—28no—
207C22⋊Dic79—44no—
208C22⋊Dic79—44no—
209C22⋊Dic79—44no—
210C22⋊Dic79—44no—
211(C2×D79)⋊C4—28no—
212(C2×D79)⋊C4—28no—
213(C2×D79)⋊C4—24no—
214(C2×D79)⋊C4—24no—
215(C2×D79)⋊C4C2×D418yes—
216(C2×D79)⋊C4C2×D418yes—
217C4×Dic79—28no—
218C4×Dic79—24no—
219C4×Dic79—42no—
220C24×C79C2414yes—
221C24×C79C2411yescharacteristic
222C2×D4×C79—28no—
223C2×D4×C79—28no—
224C2×D4×C79—28no—
225C2×D4×C79—24no—
226C2×D4×C79—24no—
227C2×D4×C79—24no—
228C2×D4×C79—24no—
229C2×D4×C79—24no—
230C2×D4×C79—42no—
231C2×D4×C79—42no—
232C2×D4×C79—42no—
233C2×D4×C79—42no—
234C22×C4×C79—22no—
235C22×C4×C79—22no—
236C22×C4×C79—41no—
237C22×C4×C79—41no—
238C22×C4×C79—41no—
239C22×C4×C79—41no—
240C22×C4×C79C2×D414yes—
241C22×C4×C79#4114yes—
242C22×C4×C79#4114yes—
243C22×C4×C79C2414yes—
244C22×C4×C79C2411yescharacteristic
245C22×C4×C79C2411yescharacteristic
246C22×C4×C79C2411yescharacteristic
247C22×C4×C79C2411yescharacteristic
248C22×C4×C79C2411yescharacteristic
249C22×C4×C79C2411yescharacteristic
250C4⋊C4×C79—24no—
251C4⋊C4×C79—24no—
252C4⋊C4×C79—24no—
253C22⋊C4×C79—28no—
254C22⋊C4×C79—28no—
255C22⋊C4×C79—28no—
256C42×C79—22no—
257C42×C79—22no—
258C42×C79—41no—
259C42×C79—41no—
260C23×C79—21no—
261C23×C79—21no—
262C23×C79—21no—
263C23×C79—21no—
264C23×C79—24no—
265C23×C79—24no—
266C23×C79—24no—
267C23×C79—24no—
268C23×C79—24no—
269C23×C79—24no—
270C23×C79—24no—
271C23×C79C22×D412yes—
272C23×C79C2×#4112yes—
273C23×C79C2×#4112yes—
274C23×C79C2511yescharacteristic
275C22×D79—28no—
276C22×D79—22no—
277C22×D79—22no—
278C22×D79—22no—
279C22×D79—22no—
280C22×D79—22no—
281C22×D79—22no—
282C22×D79—44no—
283C22×D79—44no—
284C22×D79—44no—
285C22×D79—44no—
286C22×D79—44no—
287C22×D79—44no—
288C22×D79C22×D414yes—
289D4×C79—416no—
290D4×C79—48no—
291D4×C79—84no—
292D4×C79—84no—
293C2×C4×C79—21no—
294C2×C4×C79—21no—
295C2×C4×C79—21no—
296C2×C4×C79—21no—
297C2×C4×C79—21no—
298C2×C4×C79—21no—
299C2×C4×C79—21no—
300C2×C4×C79—21no—
301C2×C4×C79—21no—
302C2×C4×C79—21no—
303C2×C4×C79—28no—
304C2×C4×C79—24no—
305C2×C4×C79—24no—
306C2×C4×C79—24no—
307C2×C4×C79—44no—
308C2×C4×C79—44no—
309C2×C4×C79C22×D412yes—
310C2×C4×C79C22×D412yes—
311C2×C4×C79C2×#4112yes—
312C2×C4×C79C2×#4112yes—
313C2×C4×C79C2×#4112yes—
314C2×C4×C79C2×#4112yes—
315C2×C4×C79H(5,𝔽2)12yes—
316C2×C4×C79H(5,𝔽2)12yes—
317C22⋊D79—88no—
318C22⋊D79—88no—
319C2×Dic79—22no—
320C2×Dic79—22no—
321C2×Dic79—24no—
322C2×Dic79—24no—
323C2×Dic79—22no—
324C2×Dic79—22no—
325C2×Dic79—22no—
326C2×Dic79—24no—
327C2×Dic79—22no—
328C2×Dic79—22no—
329C2×Dic79—24no—
330C2×Dic79—22no—
331C2×Dic79—24no—
332C2×Dic79—24no—
333C2×Dic79—44no—
334C2×Dic79—44no—
335C2×Dic79—44no—
336C2×Dic79—88no—
337C2×Dic79C22×D414yes—
338C4×D79—48no—
339C4×D79—48no—
340Dic158—84no—
341C22×C79—22no—
342C22×C79—22no—
343C22×C79—22no—
344C22×C79—22no—
345C22×C79—22no—
346C22×C79—22no—
347C22×C79—44no—
348C22×C79—44no—
349C22×C79—44no—
350C22×C79—44no—
351C22×C79—44no—
352C22×C79—44no—
353C22×C79—44no—
354C22×C79#53214yes—
355C22×C79C23×D411yescharacteristic
356C22×C79C22×#4111yescharacteristic
357C22×C79C22×#4111yescharacteristic
358C22×C79C2×H(5,𝔽2)11yescharacteristic
359C22×C79C2×H(5,𝔽2)11yescharacteristic
360C22×C79#58511yescharacteristic
361C22×C79#58511yescharacteristic
362C2×D79—24no—
363C2×D79—24no—
364C2×D79—24no—
365C2×D79—416no—
366C2×D79—42no—
367C2×D79—42no—
368C2×D79—42no—
369C2×D79—42no—
370C4×C79—22no—
371C4×C79—22no—
372C4×C79—22no—
373C4×C79—22no—
374C4×C79—22no—
375C4×C79—44no—
376C4×C79#53814yescomplemented
377Dic79—24no—
378Dic79—42no—
379Dic79—44no—
380Dic79—44no—
381Dic79—42no—
382#35005—791nomaximal, Sylow
383C2×C79—24no—
384C2×C79—84no—
385C2×C79C2×#53211yescharacteristic
386C2×C79C2×#53811yescharacteristic
387C2×C79#345511yescharacteristic
388C2×C79#349611yescharacteristic
389C2×C79#349611yescharacteristic
390C2×C79#350511yescharacteristic
391C2×C79#350611yescharacteristic
392D79—44no—
393C2×#538—792no—
394#2857—791no—
395#2856D7911yescharacteristic, complemented
396#2847—792no—
397#2639—792no—
398#2617—792no—
399#2559—794no—
400#2557—794no—
401#2496—792no—
402#2491—792no—
403#2428—792no—
404#2422—792no—
405#2325—792no—
406C4×#121—792no—
407C2×C4×C22⋊C4—791no—
408C79#3500511yescharacteristic, complemented, Sylow
409C24×C4—791no—
410#538—15816no—
411C2×C4⋊Q8—791no—
412C2×#127C2×D7911yescharacteristic, complemented
413C2×#126—794no—
414C2×#124—794no—
415C2×#123—794no—
416C2×C22⋊Q8—792no—
417C2×#121—792no—
418C2×#121—792no—
419C2×#121—794no—
420C2×#121C2×D7912yes—
421C2×#121C2×D7912yes—
422C2×#121C2×D7912yes—
423C2×#120—794no—
424C2×C4×D4—792no—
425C2×C4×D4—794no—
426C22×C22⋊C4—791no—
427C22×C22⋊C4—791no—
428C22×C42—791no—
429C22×C42C2×D7911yescharacteristic
430#400—794no—
431#397—794no—
432#397—794no—
433#394—794no—
434#394—794no—
435#394—794no—
436#393—794no—
437#392—794no—
438#391—792no—
439#390—792no—
440#390C2×D7912yescomplemented
441#390C2×D7912yescomplemented
442#390C2×D7912yescomplemented
443#389—792no—
444#389—792no—
445#389—792no—
446#388—794no—
447#388—794no—
448#387—794no—
449#386—794no—
450#386—794no—
451#386—794no—
452#386—794no—
453#386—794no—
454#385—794no—
455#384—791no—
456#384C2×D7911yescharacteristic, complemented
457#380—792no—
458#380—792no—
459#380—792no—
460#380—792no—
461C4×C4⋊C4—792no—
462C4×C22⋊C4—794no—
463C4×C22⋊C4—792no—
464C4×C22⋊C4—792no—
465C4×C22⋊C4—792no—
466C4×C22⋊C4—792no—
467C2×#95—791no—
468C2×#95—791no—
469C25—791no—
470C22×Q8—792no—
471C22×D4—794no—
472C22×D4—794no—
473C22×D4C22×D7914yes—
474C22×D4C22×D7912yes—
475C22×D4C22×D7912yes—
476C22×D4C22×D7912yes—
477C23×C4—3162no—
478C23×C4—3162no—
479C23×C4—791no—
480C23×C4—791no—
481C23×C4—794no—
482C23×C4—791no—
483C23×C4—792no—
484C23×C4—792no—
485C23×C4—1584no—
486C23×C4C22×D7911yescharacteristic
487C23×C4C22×D7911yescharacteristic
488C23×C4C22×D7911yescharacteristic
489C4⋊Q8—3162no—
490#127—42no—
491#126—15816no—
492#124—15816no—
493#123—15816no—
494C22⋊Q8—1588no—
495#121—28no—
496#121—28no—
497#121—28no—
498#121—3164no—
499#121—3164no—
500#121—15816no—
501#120—15816no—
502C4×D4—3164no—
503C4×D4—15816no—
504C2×C4⋊C4—792no—
505C2×C4⋊C4—792no—
506C2×C4⋊C4—792no—
507C2×C4⋊C4—794no—
508C2×C4⋊C4—794no—
509C2×C4⋊C4—792no—
510C2×C4⋊C4—792no—
511C2×C4⋊C4C22×D7912yes—
512C2×C4⋊C4C22×D7912yes—
513C2×C4⋊C4C22×D7912yes—
514C2×C22⋊C4—794no—
515C2×C22⋊C4—794no—
516C2×C22⋊C4—794no—
517C2×C22⋊C4—794no—
518C2×C22⋊C4—798no—
519C2×C22⋊C4—792no—
520C2×C22⋊C4—792no—
521C2×C22⋊C4—794no—
522C2×C22⋊C4—794no—
523C2×C22⋊C4—792no—
524C2×C22⋊C4—792no—
525C2×C22⋊C4—794no—
526C2×C22⋊C4—794no—
527C2×C22⋊C4—1584no—
528C2×C22⋊C4C22×D7914yes—
529C2×C22⋊C4C22×D7914yes—
530C2×C22⋊C4C22×D7914yes—
531C2×C42—42no—
532C2×C42—3162no—
533C2×C42—792no—
534C2×C42—794no—
535C2×C42—792no—
536C2×C42C22×D7911yescharacteristic
537C2×C42C22×D7911yescharacteristic
538C2×C42C22×D7911yescharacteristic
539C2×C42C22×D7911yescharacteristic
540#95—792no—
541#95—792no—
542#95—792no—
543#95—792no—
544#95—794no—
545#95—794no—
546#95—794no—
547#95—794no—
548#95—794no—
549#95—794no—
550C24—3161no—
551C24—3161no—
552C24—3161no—
553C24—3161no—
554C24—794no—
555C24—792no—
556C24—1582no—
557C24—1582no—
558C24C23×D7914yes—
559C24C23×D7911yescharacteristic
560C2×Q8—3162no—
561C2×Q8—3162no—
562C2×Q8—1584no—
563C2×D4—28no—
564C2×D4—28no—
565C2×D4—28no—
566C2×D4—24no—
567C2×D4—24no—
568C2×D4—24no—
569C2×D4—24no—
570C2×D4—24no—
571C2×D4—42no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—3164no—
576C2×D4—3164no—
577C2×D4—3164no—
578C2×D4—3164no—
579C2×D4—1588no—
580C2×D4—1588no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—41no—
584C22×C4—41no—
585C22×C4—41no—
586C22×C4—41no—
587C22×C4—31616no—
588C22×C4—3162no—
589C22×C4—3162no—
590C22×C4—3161no—
591C22×C4—3161no—
592C22×C4—3161no—
593C22×C4—3161no—
594C22×C4—3161no—
595C22×C4—3161no—
596C22×C4—3164no—
597C22×C4—3164no—
598C22×C4—794no—
599C22×C4—792no—
600C22×C4—792no—
601C22×C4—792no—
602C22×C4—794no—
603C22×C4—794no—
604C22×C4—1582no—
605C22×C4—1582no—
606C22×C4—1584no—
607C22×C4—1584no—
608C22×C4—1584no—
609C22×C4—1584no—
610C22×C4—1588no—
611C22×C4D4×D7914yes—
612C22×C4#1192962314yes—
613C22×C4#1192962314yes—
614C22×C4C23×D7914yes—
615C22×C4C23×D7911yescharacteristic
616C22×C4C23×D7911yescharacteristic
617C22×C4C23×D7911yescharacteristic
618C22×C4C23×D7911yescharacteristic
619C22×C4C23×D7911yescharacteristic
620C22×C4C23×D7911yescharacteristic
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—3162no—
625C4⋊C4—3162no—
626C4⋊C4—1588no—
627C4⋊C4—1584no—
628C4⋊C4—1584no—
629C4⋊C4—1588no—
630C4⋊C4—1584no—
631C22⋊C4—28no—
632C22⋊C4—28no—
633C22⋊C4—28no—
634C22⋊C4—3164no—
635C22⋊C4—3164no—
636C22⋊C4—3164no—
637C22⋊C4—3164no—
638C22⋊C4—798no—
639C22⋊C4—798no—
640C22⋊C4—1588no—
641C22⋊C4—1588no—
642C22⋊C4—1588no—
643C22⋊C4—1588no—
644C22⋊C4—1584no—
645C22⋊C4—1584no—
646C42—22no—
647C42—22no—
648C42—41no—
649C42—41no—
650C42—3162no—
651C42—1588no—
652C42—1584no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—24no—
664C23—3164no—
665C23—3164no—
666C23—3164no—
667C23—3164no—
668C23—3164no—
669C23—3164no—
670C23—794no—
671C23—1582no—
672C23—1582no—
673C23—1582no—
674C23—1582no—
675C23—1588no—
676C23—1582no—
677C23—1582no—
678C23C2×D4×D7912yes—
679C23C2×#1192962312yes—
680C23C2×#1192962312yes—
681C23C24×D7911yescharacteristic
682Q8—6324no—
683D4—416no—
684D4—48no—
685D4—84no—
686D4—84no—
687D4—6328no—
688D4—6328no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—28no—
700C2×C4—24no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—44no—
704C2×C4—44no—
705C2×C4—3168no—
706C2×C4—3164no—
707C2×C4—3164no—
708C2×C4—3168no—
709C2×C4—3164no—
710C2×C4—794no—
711C2×C4—6328no—
712C2×C4—1582no—
713C2×C4—1584no—
714C2×C4—1582no—
715C2×C4—1584no—
716C2×C4—1582no—
717C2×C4—1582no—
718C2×C4—1584no—
719C2×C4—1584no—
720C2×C4—1584no—
721C2×C4—1584no—
722C2×C4—1582no—
723C2×C4—1582no—
724C2×C4—1582no—
725C2×C4—1582no—
726C2×C4C2×D4×D7912yes—
727C2×C4C2×D4×D7912yes—
728C2×C4C2×#1192962312yes—
729C2×C4C2×#1192962312yes—
730C2×C4C2×#1192962312yes—
731C2×C4C2×#1192962312yes—
732C2×C4#1457920612yes—
733C2×C4#1457920712yes—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—44no—
741C22—44no—
742C22—44no—
743C22—44no—
744C22—44no—
745C22—44no—
746C22—44no—
747C22—31616no—
748C22—3162no—
749C22—3162no—
750C22—3162no—
751C22—3162no—
752C22—1584no—
753C22—1584no—
754C22—1584no—
755C22#1909911114yes—
756C22C22×D4×D7911yescharacteristic
757C22C22×#1192962311yescharacteristic
758C22C22×#1192962311yescharacteristic
759C22C2×#1457920611yescharacteristic
760C22C2×#1457920711yescharacteristic
761C22#1909939911yescharacteristic
762C22#1909939911yescharacteristic
763C4—22no—
764C4—22no—
765C4—22no—
766C4—22no—
767C4—22no—
768C4—44no—
769C4—3164no—
770C4—3164no—
771C4—3162no—
772C4—3162no—
773C4—1584no—
774C4#1909915014yescomplemented
775C2—24no—
776C2—84no—
777C2—3164no—
778C2C2×#1909911111yescharacteristic
779C2C2×#1909915011yescharacteristic
780C2#2377678911yescharacteristic
781C2#2377715711yescharacteristic
782C2#2377716211yescharacteristic
783C2#2377723411yescharacteristic
784C2#2377724911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D79
commutator, socle, cosocleC23×C79C25
FittingC79×#2856C2
hypercenter#2856D79
hypocenterC79#35005
LCSG ▷ C23×C79 ▷ C79
UCSC1 ◁ C23 ◁ #2856

Complements

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

NH ≅ G/Ntype
1. C2×#19099150C2semidirect
2. #23771752C2semidirect
3. #23771679C2semidirect
4. #23769333C2semidirect
5. #23769136C2semidirect
6. #23768534C2semidirect
7. #23768504C2semidirect
8. #23767825C2semidirect
9. #23767761C2semidirect
10. #23766991C2semidirect
11. #23766912C2semidirect
12. #23766105C2semidirect
13. #121×Dic79C2semidirect
14. C2×C4×(C2×D79)⋊C4C2semidirect
15. C79×#2856C2semidirect
18. C2×#14579161C22semidirect
28. C2×D4×Dic79C22semidirect
32. #19098501C22semidirect
34. #19098488C22semidirect
37. #19098477C22semidirect
38. #19098475C22semidirect
40. #19098469C22semidirect
41. #19098466C22semidirect
42. #19098462C22semidirect
43. #19098461C22semidirect
44. #19098461C22semidirect
45. #19098456C22semidirect
46. #19098456C22semidirect
47. #19098449C22semidirect
50. #19098443C22semidirect
53. #19098438C22semidirect
54. #19098433C22semidirect
59. C4⋊C4×Dic79C22semidirect
60. C22⋊C4×Dic79C22semidirect
67. C2×#127×C79C22semidirect
72. #390×C79C22semidirect
73. #390×C79C22semidirect
74. #390×C79C22semidirect
75. #384×C79C22semidirect
114. C2×(C2×D79)⋊C4D4semidirect
376. C4×C79#538semidirect
395. #2856D79semidirect
408. C79#35005semidirect
412. C2×#127C2×D79semidirect
440. #390C2×D79semidirect
441. #390C2×D79semidirect
442. #390C2×D79semidirect
456. #384C2×D79semidirect
774. C4#19099150semidirect

Maximal subgroups

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

subgroupindex
C2×#190991502
#237717522
#237716792
#237693332
#237691362
#237685342
#237685042
#237678252
#237677612
#237669912
#237669122
#237661052
#121×Dic792
C2×C4×(C2×D79)⋊C42
C79×#28562
#3500579