Finite Group Databasebeta

← #35152250

Subgroups — #35152250

Order 20224.

2756 conjugacy classes of subgroups.

The subgroup lattice has 746 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19099330C211yesmaximal, characteristic, complemented
2C22×#14579168C211yesmaximal, characteristic, complemented
3#23772144C213yesmaximal, complemented
4D4×#11929608C213yesmaximal, complemented
5#23772127C213yesmaximal, complemented
6#23772127C213yesmaximal, complemented
7#23772118C213yesmaximal, complemented
8#23772104C213yesmaximal, complemented
9#23772095C213yesmaximal, complemented
10C2×#19098635C213yesmaximal, complemented
11#23771968C211yesmaximal, characteristic, complemented
12#23771849C211yesmaximal, characteristic, complemented
13#23771849C211yesmaximal, characteristic, complemented
14#23771828C211yesmaximal, characteristic, complemented
15D4×#41×C79C211yesmaximal, characteristic
16#19099330—28no—
17C2×#14579168—28no—
18C2×#14579168C2211yescharacteristic
19C2×#14579168C2211yescharacteristic
20C2×#14579168C2211yescharacteristic
21C2×#14579168C2211yescharacteristic
22C2×#14579168C2213yescomplemented
23C2×#14579168C2213yescomplemented
24C2×#14579168C2213yescomplemented
25C2×#14579168C2213yescomplemented
26C22×#11929608C2213yescomplemented
27C22×#11929608C2213yescomplemented
28C22×#11929608C2213yescomplemented
29C23×C79⋊C8C2213yescomplemented
30#19098641C2216yescomplemented
31#19098641C2216yescomplemented
32#19098635C2211yescharacteristic
33#19098635C2213yes—
34#19098635C2213yescomplemented
35#19098635C2213yescomplemented
36#19098635C2213yescomplemented
37#19098635C2213yescomplemented
38#19098635C2213yescomplemented
39#19098635C2213yescomplemented
40#19098635C2216yescomplemented
41#19098635C2216yescomplemented
42#19098635C2216yescomplemented
43D4×C79⋊C8C2216yescomplemented
44D4×C79⋊C8C2216yescomplemented
45#19098590C2213yescomplemented
46#19098590C2213yescomplemented
47#19098587C2213yescomplemented
48C2×C4⋊(C79⋊C8)C2213yescomplemented
49#19098530C2213yescomplemented
50#19098530C2213yescomplemented
51#19098530C2213yescomplemented
52#19098530C2213yescomplemented
53#19098527C2213yescomplemented
54#19098527C2213yescomplemented
55C2×C22⋊(C79⋊C8)C2213yescomplemented
56C2×C22⋊(C79⋊C8)C2213yescomplemented
57#19098519C2213yescomplemented
58#19098519C2213yescomplemented
59C4×#11929608C2213yescomplemented
60C2×#14579072C2213yescomplemented
61C22×#41×C79C2211yescharacteristic
62C22×#41×C79C2211yescharacteristic
63#550×C79C411yescharacteristic
64D4×Q8×C79C411yescharacteristic
65#548×C79C411yescharacteristic
66#548×C79C411yescharacteristic
67#547×C79C413yes—
68#546×C79C413yes—
69#546×C79C413yes—
70D42×C79C413yes—
71#532×C79C2213yes—
72#525×C79C2213yes—
73#525×C79C2213yes—
74C4×#41×C79C2211yescharacteristic
75C2×C4×D4×C79C2213yes—
76#14579168—24no—
77#14579168—24no—
78#14579168—24no—
79#14579168—212no—
80#14579168—212no—
81#14579168—212no—
82#14579168—212no—
83#14579168D418yescomplemented
84C2×#11929608—212no—
85C2×#11929608—212no—
86C2×#11929608—212no—
87C2×#11929608C2311yescharacteristic
88C2×#11929608C2313yes—
89C2×#11929608C2313yes—
90C2×#11929608C2313yes—
91C2×#11929608C2316yes—
92C2×#11929608C2313yes—
93C2×#11929608C2313yes—
94C2×#11929608C2313yes—
95C2×#11929608C2313yes—
96C22×C79⋊C8—212no—
97C22×C79⋊C8C2313yes—
98C22×C79⋊C8C2313yes—
99C22×C79⋊C8C2316yes—
100C22×C79⋊C8C2311yescharacteristic
101C22×C79⋊C8C2313yes—
102C22×C79⋊C8C2313yes—
103C22×C79⋊C8C2313yes—
104C22×C79⋊C8C2313yes—
105C22×C79⋊C8C2313yes—
106C4⋊(C79⋊C8)C2313yes—
107C4⋊(C79⋊C8)C2316yes—
108C4⋊(C79⋊C8)C2311yescharacteristic
109C4⋊(C79⋊C8)C2313yes—
110C4⋊(C79⋊C8)C2313yes—
111C22⋊(C79⋊C8)C2313yes—
112C22⋊(C79⋊C8)C2313yes—
113C22⋊(C79⋊C8)C2316yes—
114C22⋊(C79⋊C8)C2316yes—
115C22⋊(C79⋊C8)C2311yescharacteristic
116C22⋊(C79⋊C8)C2311yescharacteristic
117C22⋊(C79⋊C8)C2313yes—
118C22⋊(C79⋊C8)C2313yes—
119C22⋊(C79⋊C8)C2313yes—
120C22⋊(C79⋊C8)C2313yes—
121#14579072C2311yescharacteristic
122#14579072C2313yes—
123#14579072C2313yes—
124#14579072C2313yes—
125C4×C79⋊C8C2316yes—
126C2×#41×C79—24no—
127C2×#41×C79—24no—
128C2×#41×C79—24no—
129C2×#41×C79—24no—
130C2×#41×C79C2×C413yes—
131C2×#41×C79C2×C413yes—
132C2×#41×C79C2×C411yescharacteristic
133C2×#41×C79C2×C411yescharacteristic
134C2×#41×C79C2313yes—
135C2×#41×C79C2313yes—
136C2×#41×C79C2311yescharacteristic
137C22×Q8×C79C2×C411yescharacteristic
138C22×Q8×C79C2×C411yescharacteristic
139C22×D4×C79C2×C413yes—
140C22×D4×C79C2×C413yes—
141C22×D4×C79C2×C413yes—
142C23×C4×C79C2313yes—
143C23×C4×C79C2313yes—
144C4⋊Q8×C79C2×C413yes—
145#127×C79C2×C413yes—
146#124×C79C2×C413yes—
147#124×C79C2×C413yes—
148#123×C79C2×C416yes—
149#123×C79C2×C416yes—
150C22⋊Q8×C79C2×C413yes—
151C22⋊Q8×C79C2×C413yes—
152C22⋊Q8×C79C2×C413yes—
153C22⋊Q8×C79C2×C413yes—
154#121×C79C2×C413yes—
155#121×C79C2×C413yes—
156#121×C79C2×C413yes—
157#121×C79C2×C413yes—
158#121×C79C2×C416yes—
159#121×C79C2×C416yes—
160#120×C79C2×C416yes—
161#120×C79C2×C416yes—
162C4×Q8×C79C2×C411yescharacteristic
163C4×Q8×C79C2×C411yescharacteristic
164C4×D4×C79C2×C413yes—
165C4×D4×C79C2×C413yes—
166C4×D4×C79C2×C413yes—
167C4×D4×C79C2×C413yes—
168C4×D4×C79C2×C413yes—
169C4×D4×C79C2×C413yes—
170C4×D4×C79C2313yes—
171C4×D4×C79C2316yes—
172C4×D4×C79C2311yescharacteristic
173C4×D4×C79C2313yes—
174C4×D4×C79C2313yes—
175#117×C79C2313yes—
176C2×C4⋊C4×C79C2×C413yes—
177C2×C22⋊C4×C79C2×C413yes—
178C2×C22⋊C4×C79C2×C413yes—
179C2×C42×C79C2313yes—
180#11929608—22no—
181#11929608—26no—
182#11929608—26no—
183#11929608—212no—
184#11929608—26no—
185#11929608—26no—
186#11929608—26no—
187#11929608—26no—
188#11929608C2×D4112yescomplemented
189C2×C79⋊C8—22no—
190C2×C79⋊C8—26no—
191C2×C79⋊C8—26no—
192C2×C79⋊C8—26no—
193C2×C79⋊C8—212no—
194C2×C79⋊C8—26no—
195C2×C79⋊C8—26no—
196C2×C79⋊C8—26no—
197C2×C79⋊C8C2×D4112yescomplemented
198C2×C79⋊C8C2413yes—
199C2×C79⋊C8C2411yescharacteristic
200C2×C79⋊C8C2411yescharacteristic
201C2×C79⋊C8C2413yes—
202C2×C79⋊C8C2413yes—
203C2×C79⋊C8C2411yescharacteristic
204C2×C79⋊C8C2413yes—
205C2×C79⋊C8C2411yescharacteristic
206C24×C79C22×C413yes—
207C24×C79C22×C413yes—
208#41×C79—24no—
209#41×C79—24no—
210#41×C79—212no—
211#41×C79—212no—
212#41×C79—26no—
213#41×C79—26no—
214#41×C79—26no—
215#41×C79—26no—
216#41×C79C2×D414yes—
217#41×C79#4114yes—
218C2×Q8×C79—24no—
219C2×Q8×C79—24no—
220C2×Q8×C79C22×C413yes—
221C2×Q8×C79C22×C413yes—
222C2×Q8×C79C22×C411yescharacteristic
223C2×D4×C79—212no—
224C2×D4×C79—212no—
225C2×D4×C79—46no—
226C2×D4×C79C22×C411yescharacteristic
227C2×D4×C79C22×C413yes—
228C2×D4×C79C22×C416yes—
229C2×D4×C79C22×C416yes—
230C2×D4×C79C22×C413yes—
231C2×D4×C79C22×C413yes—
232C2×D4×C79C22×C413yes—
233C2×D4×C79C22×C413yes—
234C2×D4×C79C22×C416yes—
235C2×D4×C79C22×C413yes—
236C22×C4×C79—26no—
237C22×C4×C79—26no—
238C22×C4×C79—26no—
239C22×C4×C79—26no—
240C22×C4×C79C22×C413yes—
241C22×C4×C79C22×C413yes—
242C22×C4×C79C22×C413yes—
243C22×C4×C79C22×C413yes—
244C22×C4×C79C22×C413yes—
245C22×C4×C79C22×C413yes—
246C22×C4×C79C22×C413yes—
247C22×C4×C79C22×C413yes—
248C22×C4×C79C2411yescharacteristic
249C22×C4×C79C2411yescharacteristic
250C22×C4×C79C2413yes—
251C22×C4×C79C2413yes—
252C22×C4×C79C2413yes—
253C4⋊C4×C79C22×C411yescharacteristic
254C4⋊C4×C79C22×C413yes—
255C4⋊C4×C79C22×C413yes—
256C4⋊C4×C79C22×C413yes—
257C4⋊C4×C79C22×C413yes—
258C4⋊C4×C79C22×C413yes—
259C4⋊C4×C79C22×C416yes—
260C22⋊C4×C79C22×C411yescharacteristic
261C22⋊C4×C79C22×C411yescharacteristic
262C22⋊C4×C79C22×C413yes—
263C22⋊C4×C79C22×C413yes—
264C22⋊C4×C79C22×C413yes—
265C22⋊C4×C79C22×C413yes—
266C22⋊C4×C79C22×C413yes—
267C22⋊C4×C79C22×C413yes—
268C22⋊C4×C79C22×C416yes—
269C22⋊C4×C79C22×C416yes—
270C22⋊C4×C79C22×C416yes—
271C42×C79C22×C413yes—
272C42×C79C22×C413yes—
273C42×C79C2411yescharacteristic
274C42×C79C2413yes—
275C23×C79—26no—
276C23×C79—26no—
277C23×C79—26no—
278C23×C79—43no—
279C23×C79—43no—
280C23×C79—43no—
281C23×C79C23×C411yescharacteristic
282C23×C79C23×C413yes—
283C23×C79C23×C413yes—
284C23×C79C23×C413yes—
285C23×C79C23×C411yescharacteristic
286Q8×C79—26no—
287Q8×C79—26no—
288Q8×C79C4×D414yes—
289D4×C79—212no—
290D4×C79—212no—
291D4×C79—22no—
292D4×C79—26no—
293D4×C79—26no—
294D4×C79—26no—
295D4×C79—43no—
296D4×C79—43no—
297D4×C79—46no—
298D4×C79C4×D4112yes—
299C2×C4×C79—26no—
300C2×C4×C79—26no—
301C2×C4×C79—26no—
302C2×C4×C79—26no—
303C2×C4×C79—26no—
304C2×C4×C79—26no—
305C2×C4×C79—21no—
306C2×C4×C79—23no—
307C2×C4×C79—23no—
308C2×C4×C79—21no—
309C2×C4×C79—21no—
310C2×C4×C79—21no—
311C2×C4×C79—23no—
312C2×C4×C79—23no—
313C2×C4×C79—43no—
314C2×C4×C79—43no—
315C2×C4×C79C23×C411yescharacteristic
316C2×C4×C79C23×C411yescharacteristic
317C2×C4×C79C23×C413yes—
318C2×C4×C79C23×C413yes—
319C2×C4×C79C23×C411yescharacteristic
320C2×C4×C79C23×C411yescharacteristic
321C2×C4×C79C23×C413yes—
322C2×C4×C79C23×C413yes—
323C2×C4×C79C23×C413yes—
324C2×C4×C79C22×D416yes—
325C2×C4×C79C2×#4116yes—
326C2×C4×C79C2511yescharacteristic
327C79⋊C8—21no—
328C79⋊C8—23no—
329C79⋊C8—23no—
330C79⋊C8—21no—
331C79⋊C8—21no—
332C79⋊C8—23no—
333C79⋊C8C22×D412yes—
334C79⋊C8C22×D416yes—
335C22×C79—21no—
336C22×C79—23no—
337C22×C79—23no—
338C22×C79—21no—
339C22×C79—21no—
340C22×C79—23no—
341C22×C79—23no—
342C22×C79—21no—
343C22×C79—23no—
344C22×C79—23no—
345C22×C79—23no—
346C22×C79—23no—
347C22×C79—21no—
348C22×C79—412no—
349C22×C79—86no—
350C22×C79C2×C4×D416yes—
351C22×C79#56812yescomplemented
352C22×C79C24×C411yescharacteristic
353C4×C79—21no—
354C4×C79—21no—
355C4×C79—23no—
356C4×C79—23no—
357C4×C79—21no—
358C4×C79—23no—
359C4×C79—21no—
360C4×C79—23no—
361C4×C79C2×C4×D416yes—
362C4×C79C23×D411yescharacteristic
363C4×C79C22×#4111yescharacteristic
364#60146—791nomaximal, Sylow
365C2×C79—22no—
366C2×C79—26no—
367C2×C79—43no—
368C2×C79—43no—
369C2×C79—41no—
370C2×C79C22×C4×D411yescharacteristic
371C2×C79C2×#56811yescharacteristic
372C2×C79#357311yescharacteristic
373C2×#568—791no—
374C22×#131—791no—
375D4×#41D7911yescharacteristic
376#2935—793no—
377D4×M16—793no—
378#2933—793no—
379#2933—793no—
380#2932—793no—
381#2930—793no—
382#2929—793no—
383C2×#435—793no—
384#2906—791no—
385#2880—791no—
386#2880—791no—
387#2875—791no—
388C79#6014611yescharacteristic, complemented, Sylow
389C22×#41C2×D7911yescharacteristic
390C22×#41C2×D7911yescharacteristic
391#568—1588no—
392C2×#131—791no—
393C2×#131—791no—
394C2×#131—791no—
395C2×#131—791no—
396C2×#131—793no—
397C2×#131—793no—
398C2×#131—793no—
399C2×#131—793no—
400C2×#131—1588no—
401C22×M16—793no—
402C22×M16—793no—
403C22×M16—793no—
404C23×C8—793no—
405#550Dic7911yescharacteristic
406D4×Q8Dic7911yescharacteristic
407#548Dic7911yescharacteristic
408#548Dic7911yescharacteristic
409#547Dic7913yes—
410#546Dic7913yes—
411#546Dic7913yes—
412D42Dic7913yes—
413#532C2×D7913yes—
414#525C2×D7913yes—
415#525C2×D7913yes—
416C4×#41C2×D7911yescharacteristic
417C2×C4×D4C2×D7913yes—
418#436—796no—
419#436—796no—
420#435—791no—
421#435—793no—
422#435—793no—
423#435—793no—
424#435—793no—
425#435—793no—
426#435—793no—
427#435—793no—
428#435—796no—
429#435—796no—
430#435—796no—
431C8×D4—796no—
432C8×D4—796no—
433#424—793no—
434#424—793no—
435#423—793no—
436C2×C4⋊C8—793no—
437#408—793no—
438#408—793no—
439#408—793no—
440#408—793no—
441#407—793no—
442#407—793no—
443C2×C22⋊C8—793no—
444C2×C22⋊C8—793no—
445#405—793no—
446#405—793no—
447C4×M16—793no—
448C2×#97—793no—
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—24no—
452C2×#41—24no—
453C2×#41C2×Dic7913yes—
454C2×#41C2×Dic7913yes—
455C2×#41C2×Dic7911yescharacteristic
456C2×#41C2×Dic7911yescharacteristic
457C2×#41C22×D7913yes—
458C2×#41C22×D7913yes—
459C2×#41C22×D7911yescharacteristic
460C22×Q8C2×Dic7911yescharacteristic
461C22×Q8C2×Dic7911yescharacteristic
462C22×D4C2×Dic7913yes—
463C22×D4C2×Dic7913yes—
464C22×D4C2×Dic7913yes—
465C23×C4C22×D7913yes—
466C23×C4C22×D7913yes—
467#131—798no—
468#131—15812no—
469#131—15812no—
470#131—15812no—
471#131—15812no—
472#131—1584no—
473#131—1584no—
474#131—1584no—
475C2×M16—793no—
476C2×M16—791no—
477C2×M16—793no—
478C2×M16—793no—
479C2×M16—793no—
480C2×M16—793no—
481C2×M16—793no—
482C2×M16—796no—
483C2×M16—793no—
484C2×M16—15812no—
485C2×M16—15812no—
486C2×M16—15812no—
487C22×C8—793no—
488C22×C8—791no—
489C22×C8—793no—
490C22×C8—793no—
491C22×C8—793no—
492C22×C8—793no—
493C22×C8—793no—
494C22×C8—796no—
495C22×C8—793no—
496C22×C8—15812no—
497C4⋊Q8C2×Dic7913yes—
498#127C2×Dic7913yes—
499#124C2×Dic7913yes—
500#124C2×Dic7913yes—
501#123C2×Dic7916yes—
502#123C2×Dic7916yes—
503C22⋊Q8C2×Dic7913yes—
504C22⋊Q8C2×Dic7913yes—
505C22⋊Q8C2×Dic7913yes—
506C22⋊Q8C2×Dic7913yes—
507#121C2×Dic7913yes—
508#121C2×Dic7913yes—
509#121C2×Dic7913yes—
510#121C2×Dic7913yes—
511#121C2×Dic7916yes—
512#121C2×Dic7916yes—
513#120C2×Dic7916yes—
514#120C2×Dic7916yes—
515C4×Q8C2×Dic7911yescharacteristic
516C4×Q8C2×Dic7911yescharacteristic
517C4×D4C2×Dic7913yes—
518C4×D4C2×Dic7913yes—
519C4×D4C2×Dic7913yes—
520C4×D4C2×Dic7913yes—
521C4×D4C2×Dic7913yes—
522C4×D4C2×Dic7913yes—
523C4×D4C22×D7911yescharacteristic
524C4×D4C22×D7913yes—
525C4×D4C22×D7913yes—
526C4×D4C22×D7913yes—
527C4×D4C22×D7916yes—
528#117C22×D7913yes—
529C2×C4⋊C4C2×Dic7913yes—
530C2×C22⋊C4C2×Dic7913yes—
531C2×C22⋊C4C2×Dic7913yes—
532C2×C42C22×D7913yes—
533C4⋊C8—791no—
534C4⋊C8—793no—
535C4⋊C8—793no—
536C4⋊C8—793no—
537C4⋊C8—796no—
538C22⋊C8—791no—
539C22⋊C8—791no—
540C22⋊C8—793no—
541C22⋊C8—793no—
542C22⋊C8—793no—
543C22⋊C8—793no—
544C22⋊C8—793no—
545C22⋊C8—793no—
546C22⋊C8—796no—
547C22⋊C8—796no—
548#97—791no—
549#97—793no—
550#97—793no—
551#97—793no—
552C4×C8—796no—
553C24C22×Dic7913yes—
554C24C22×Dic7913yes—
555#41—24no—
556#41—24no—
557#41—212no—
558#41—212no—
559#41—26no—
560#41—26no—
561#41—26no—
562#41—26no—
563#41D4×D7914yes—
564#41#1192962314yes—
565C2×Q8—24no—
566C2×Q8—24no—
567C2×Q8C22×Dic7913yes—
568C2×Q8C22×Dic7913yes—
569C2×Q8C22×Dic7911yescharacteristic
570C2×D4—212no—
571C2×D4—212no—
572C2×D4—46no—
573C2×D4C22×Dic7911yescharacteristic
574C2×D4C22×Dic7913yes—
575C2×D4C22×Dic7916yes—
576C2×D4C22×Dic7916yes—
577C2×D4C22×Dic7913yes—
578C2×D4C22×Dic7913yes—
579C2×D4C22×Dic7913yes—
580C2×D4C22×Dic7913yes—
581C2×D4C22×Dic7916yes—
582C2×D4C22×Dic7913yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—26no—
586C22×C4—26no—
587C22×C4C22×Dic7913yes—
588C22×C4C22×Dic7913yes—
589C22×C4C22×Dic7913yes—
590C22×C4C22×Dic7913yes—
591C22×C4C22×Dic7913yes—
592C22×C4C22×Dic7913yes—
593C22×C4C22×Dic7913yes—
594C22×C4C22×Dic7913yes—
595C22×C4C23×D7911yescharacteristic
596C22×C4C23×D7913yes—
597C22×C4C23×D7913yes—
598C22×C4C23×D7911yescharacteristic
599C22×C4C23×D7913yes—
600M16—7912no—
601M16—1582no—
602M16—1586no—
603M16—1586no—
604M16—1586no—
605M16—15812no—
606M16—1586no—
607M16—1586no—
608M16—1586no—
609C2×C8—793no—
610C2×C8—791no—
611C2×C8—7912no—
612C2×C8—793no—
613C2×C8—791no—
614C2×C8—791no—
615C2×C8—791no—
616C2×C8—793no—
617C2×C8—793no—
618C2×C8—1582no—
619C2×C8—1586no—
620C2×C8—1586no—
621C2×C8—1586no—
622C2×C8—15812no—
623C2×C8—1586no—
624C2×C8—1586no—
625C2×C8—1586no—
626C4⋊C4C22×Dic7911yescharacteristic
627C4⋊C4C22×Dic7913yes—
628C4⋊C4C22×Dic7913yes—
629C4⋊C4C22×Dic7913yes—
630C4⋊C4C22×Dic7913yes—
631C4⋊C4C22×Dic7913yes—
632C4⋊C4C22×Dic7916yes—
633C22⋊C4C22×Dic7911yescharacteristic
634C22⋊C4C22×Dic7911yescharacteristic
635C22⋊C4C22×Dic7913yes—
636C22⋊C4C22×Dic7913yes—
637C22⋊C4C22×Dic7913yes—
638C22⋊C4C22×Dic7913yes—
639C22⋊C4C22×Dic7913yes—
640C22⋊C4C22×Dic7913yes—
641C22⋊C4C22×Dic7916yes—
642C22⋊C4C22×Dic7916yes—
643C22⋊C4C22×Dic7916yes—
644C42C22×Dic7913yes—
645C42C22×Dic7913yes—
646C42C23×D7913yes—
647C42C23×D7911yescharacteristic
648C23—26no—
649C23—26no—
650C23—26no—
651C23—43no—
652C23—43no—
653C23—43no—
654C23C23×Dic7911yescharacteristic
655C23C23×Dic7913yes—
656C23C23×Dic7913yes—
657C23C23×Dic7913yes—
658C23C23×Dic7911yescharacteristic
659Q8—26no—
660Q8—26no—
661Q8D4×Dic7914yes—
662D4—212no—
663D4—212no—
664D4—22no—
665D4—26no—
666D4—26no—
667D4—26no—
668D4—43no—
669D4—43no—
670D4—46no—
671D4D4×Dic79112yes—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—26no—
675C2×C4—26no—
676C2×C4—26no—
677C2×C4—26no—
678C2×C4—21no—
679C2×C4—23no—
680C2×C4—23no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—23no—
685C2×C4—23no—
686C2×C4—43no—
687C2×C4—43no—
688C2×C4C23×Dic7911yescharacteristic
689C2×C4C23×Dic7911yescharacteristic
690C2×C4C23×Dic7913yes—
691C2×C4C23×Dic7913yes—
692C2×C4C23×Dic7911yescharacteristic
693C2×C4C23×Dic7911yescharacteristic
694C2×C4C23×Dic7913yes—
695C2×C4C23×Dic7913yes—
696C2×C4C23×Dic7913yes—
697C2×C4C2×D4×D7916yes—
698C2×C4C2×#1192962316yes—
699C2×C4C24×D7911yescharacteristic
700C8—792no—
701C8—796no—
702C8—1581no—
703C8—1583no—
704C8—1583no—
705C8—1581no—
706C8—1581no—
707C8—1583no—
708C22—21no—
709C22—23no—
710C22—23no—
711C22—21no—
712C22—21no—
713C22—23no—
714C22—23no—
715C22—21no—
716C22—23no—
717C22—23no—
718C22—23no—
719C22—23no—
720C22—21no—
721C22—412no—
722C22—86no—
723C22C2×D4×Dic7916yes—
724C22#1909933012yescomplemented
725C22C24×Dic7911yescharacteristic
726C4—21no—
727C4—21no—
728C4—23no—
729C4—23no—
730C4—21no—
731C4—23no—
732C4—21no—
733C4—23no—
734C4C2×D4×Dic7916yes—
735C4C22×D4×D7911yescharacteristic
736C4C22×#1192962311yescharacteristic
737C2—22no—
738C2—26no—
739C2—43no—
740C2—41no—
741C2—43no—
742C2C22×D4×Dic7911yescharacteristic
743C2C2×#1909933011yescharacteristic
744C2#2377811211yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D79
commutator, socleC22×C79C24×C4
Fitting, prime radicalD4×#41×C79C2
cosocleC2×C4×C79C25
hypercenterD4×#41D79
hypocenterC79#60146
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#19099330C2semidirect
2. C22×#14579168C2semidirect
3. #23772144C2semidirect
4. D4×#11929608C2semidirect
5. #23772127C2semidirect
6. #23772127C2semidirect
7. #23772118C2semidirect
8. #23772104C2semidirect
9. #23772095C2semidirect
10. C2×#19098635C2semidirect
11. #23771968C2semidirect
12. #23771849C2semidirect
13. #23771849C2semidirect
14. #23771828C2semidirect
22. C2×#14579168C22semidirect
23. C2×#14579168C22semidirect
24. C2×#14579168C22semidirect
25. C2×#14579168C22semidirect
26. C22×#11929608C22semidirect
27. C22×#11929608C22semidirect
28. C22×#11929608C22semidirect
29. C23×C79⋊C8C22semidirect
30. #19098641C22semidirect
31. #19098641C22semidirect
34. #19098635C22semidirect
35. #19098635C22semidirect
36. #19098635C22semidirect
37. #19098635C22semidirect
38. #19098635C22semidirect
39. #19098635C22semidirect
40. #19098635C22semidirect
41. #19098635C22semidirect
42. #19098635C22semidirect
43. D4×C79⋊C8C22semidirect
44. D4×C79⋊C8C22semidirect
45. #19098590C22semidirect
46. #19098590C22semidirect
47. #19098587C22semidirect
48. C2×C4⋊(C79⋊C8)C22semidirect
49. #19098530C22semidirect
50. #19098530C22semidirect
51. #19098530C22semidirect
52. #19098530C22semidirect
53. #19098527C22semidirect
54. #19098527C22semidirect
55. C2×C22⋊(C79⋊C8)C22semidirect
56. C2×C22⋊(C79⋊C8)C22semidirect
57. #19098519C22semidirect
58. #19098519C22semidirect
59. C4×#11929608C22semidirect
60. C2×#14579072C22semidirect
83. #14579168D4semidirect
188. #11929608C2×D4semidirect
197. C2×C79⋊C8C2×D4semidirect
351. C22×C79#568semidirect
388. C79#60146semidirect
724. C22#19099330semidirect

Maximal subgroups

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

subgroupindex
C2×#190993302
C22×#145791682
#237721442
D4×#119296082
#237721272
#237721182
#237721042
#237720952
C2×#190986352
#237719682
#237718492
#237718282
D4×#41×C792
#6014679