Finite Group Databasebeta

← #27080259

Subgroups — #27080259

Order 12032.

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×#15689890C211yesmaximal, characteristic, complemented
2C22×#13094031C211yesmaximal, characteristic, complemented
3#20252132C213yesmaximal, complemented
4D4×#10625329C213yesmaximal, complemented
5#20252115C213yesmaximal, complemented
6#20252115C213yesmaximal, complemented
7#20252106C213yesmaximal, complemented
8#20252092C213yesmaximal, complemented
9#20252083C213yesmaximal, complemented
10C2×#15689195C213yesmaximal, complemented
11#20251956C211yesmaximal, characteristic, complemented
12#20251837C211yesmaximal, characteristic, complemented
13#20251837C211yesmaximal, characteristic, complemented
14#20251816C211yesmaximal, characteristic, complemented
15D4×#41×C47C211yesmaximal, characteristic
16#15689890—28no—
17C2×#13094031—28no—
18C2×#13094031C2211yescharacteristic
19C2×#13094031C2211yescharacteristic
20C2×#13094031C2211yescharacteristic
21C2×#13094031C2211yescharacteristic
22C2×#13094031C2213yescomplemented
23C2×#13094031C2213yescomplemented
24C2×#13094031C2213yescomplemented
25C2×#13094031C2213yescomplemented
26C22×#10625329C2213yescomplemented
27C22×#10625329C2213yescomplemented
28C22×#10625329C2213yescomplemented
29C23×C47⋊C8C2213yescomplemented
30#15689201C2216yescomplemented
31#15689201C2216yescomplemented
32#15689195C2211yescharacteristic
33#15689195C2213yes—
34#15689195C2213yescomplemented
35#15689195C2213yescomplemented
36#15689195C2213yescomplemented
37#15689195C2213yescomplemented
38#15689195C2213yescomplemented
39#15689195C2213yescomplemented
40#15689195C2216yescomplemented
41#15689195C2216yescomplemented
42#15689195C2216yescomplemented
43D4×C47⋊C8C2216yescomplemented
44D4×C47⋊C8C2216yescomplemented
45#15689150C2213yescomplemented
46#15689150C2213yescomplemented
47#15689147C2213yescomplemented
48C2×C4⋊(C47⋊C8)C2213yescomplemented
49#15689090C2213yescomplemented
50#15689090C2213yescomplemented
51#15689090C2213yescomplemented
52#15689090C2213yescomplemented
53#15689087C2213yescomplemented
54#15689087C2213yescomplemented
55C2×C22⋊(C47⋊C8)C2213yescomplemented
56C2×C22⋊(C47⋊C8)C2213yescomplemented
57#15689079C2213yescomplemented
58#15689079C2213yescomplemented
59C4×#10625329C2213yescomplemented
60C2×#13093935C2213yescomplemented
61C22×#41×C47C2211yescharacteristic
62C22×#41×C47C2211yescharacteristic
63C47×#550C411yescharacteristic
64D4×Q8×C47C411yescharacteristic
65C47×#548C411yescharacteristic
66C47×#548C411yescharacteristic
67C47×#547C413yes—
68C47×#546C413yes—
69C47×#546C413yes—
70D42×C47C413yes—
71C47×#532C2213yes—
72C47×#525C2213yes—
73C47×#525C2213yes—
74C4×#41×C47C2211yescharacteristic
75C2×C4×D4×C47C2213yes—
76#13094031—24no—
77#13094031—24no—
78#13094031—24no—
79#13094031—212no—
80#13094031—212no—
81#13094031—212no—
82#13094031—212no—
83#13094031D418yescomplemented
84C2×#10625329—212no—
85C2×#10625329—212no—
86C2×#10625329—212no—
87C2×#10625329C2313yes—
88C2×#10625329C2313yes—
89C2×#10625329C2313yes—
90C2×#10625329C2311yescharacteristic
91C2×#10625329C2313yes—
92C2×#10625329C2313yes—
93C2×#10625329C2316yes—
94C2×#10625329C2313yes—
95C2×#10625329C2313yes—
96C22×C47⋊C8—212no—
97C22×C47⋊C8C2313yes—
98C22×C47⋊C8C2313yes—
99C22×C47⋊C8C2313yes—
100C22×C47⋊C8C2311yescharacteristic
101C22×C47⋊C8C2313yes—
102C22×C47⋊C8C2313yes—
103C22×C47⋊C8C2313yes—
104C22×C47⋊C8C2316yes—
105C22×C47⋊C8C2313yes—
106C4⋊(C47⋊C8)C2311yescharacteristic
107C4⋊(C47⋊C8)C2313yes—
108C4⋊(C47⋊C8)C2313yes—
109C4⋊(C47⋊C8)C2313yes—
110C4⋊(C47⋊C8)C2316yes—
111C22⋊(C47⋊C8)C2311yescharacteristic
112C22⋊(C47⋊C8)C2311yescharacteristic
113C22⋊(C47⋊C8)C2313yes—
114C22⋊(C47⋊C8)C2313yes—
115C22⋊(C47⋊C8)C2313yes—
116C22⋊(C47⋊C8)C2313yes—
117C22⋊(C47⋊C8)C2313yes—
118C22⋊(C47⋊C8)C2313yes—
119C22⋊(C47⋊C8)C2316yes—
120C22⋊(C47⋊C8)C2316yes—
121#13093935C2311yescharacteristic
122#13093935C2313yes—
123#13093935C2313yes—
124#13093935C2313yes—
125C4×C47⋊C8C2316yes—
126C2×#41×C47—24no—
127C2×#41×C47—24no—
128C2×#41×C47—24no—
129C2×#41×C47—24no—
130C2×#41×C47C2×C413yes—
131C2×#41×C47C2×C413yes—
132C2×#41×C47C2×C411yescharacteristic
133C2×#41×C47C2×C411yescharacteristic
134C2×#41×C47C2313yes—
135C2×#41×C47C2313yes—
136C2×#41×C47C2311yescharacteristic
137C22×Q8×C47C2×C411yescharacteristic
138C22×Q8×C47C2×C411yescharacteristic
139C22×D4×C47C2×C413yes—
140C22×D4×C47C2×C413yes—
141C22×D4×C47C2×C413yes—
142C23×C4×C47C2313yes—
143C23×C4×C47C2313yes—
144C4⋊Q8×C47C2×C413yes—
145#127×C47C2×C413yes—
146#124×C47C2×C413yes—
147#124×C47C2×C413yes—
148#123×C47C2×C416yes—
149#123×C47C2×C416yes—
150C22⋊Q8×C47C2×C413yes—
151C22⋊Q8×C47C2×C413yes—
152C22⋊Q8×C47C2×C413yes—
153C22⋊Q8×C47C2×C413yes—
154#121×C47C2×C413yes—
155#121×C47C2×C413yes—
156#121×C47C2×C413yes—
157#121×C47C2×C413yes—
158#121×C47C2×C416yes—
159#121×C47C2×C416yes—
160#120×C47C2×C416yes—
161#120×C47C2×C416yes—
162C4×Q8×C47C2×C411yescharacteristic
163C4×Q8×C47C2×C411yescharacteristic
164C4×D4×C47C2×C413yes—
165C4×D4×C47C2×C413yes—
166C4×D4×C47C2×C413yes—
167C4×D4×C47C2×C413yes—
168C4×D4×C47C2×C413yes—
169C4×D4×C47C2×C413yes—
170C4×D4×C47C2311yescharacteristic
171C4×D4×C47C2313yes—
172C4×D4×C47C2313yes—
173C4×D4×C47C2313yes—
174C4×D4×C47C2316yes—
175#117×C47C2313yes—
176C2×C4⋊C4×C47C2×C413yes—
177C2×C22⋊C4×C47C2×C413yes—
178C2×C22⋊C4×C47C2×C413yes—
179C2×C42×C47C2313yes—
180C24×C47C22×C413yes—
181C24×C47C22×C413yes—
182#41×C47—24no—
183#41×C47—24no—
184#41×C47—212no—
185#41×C47—212no—
186#41×C47—26no—
187#41×C47—26no—
188#41×C47—26no—
189#41×C47—26no—
190#41×C47C2×D414yes—
191#41×C47#4114yes—
192C2×Q8×C47—24no—
193C2×Q8×C47—24no—
194C2×Q8×C47C22×C413yes—
195C2×Q8×C47C22×C413yes—
196C2×Q8×C47C22×C411yescharacteristic
197C2×D4×C47—212no—
198C2×D4×C47—212no—
199C2×D4×C47—46no—
200C2×D4×C47C22×C411yescharacteristic
201C2×D4×C47C22×C413yes—
202C2×D4×C47C22×C416yes—
203C2×D4×C47C22×C416yes—
204C2×D4×C47C22×C413yes—
205C2×D4×C47C22×C413yes—
206C2×D4×C47C22×C413yes—
207C2×D4×C47C22×C413yes—
208C2×D4×C47C22×C416yes—
209C2×D4×C47C22×C413yes—
210C22×C4×C47—26no—
211C22×C4×C47—26no—
212C22×C4×C47—26no—
213C22×C4×C47—26no—
214C22×C4×C47C22×C413yes—
215C22×C4×C47C22×C413yes—
216C22×C4×C47C22×C413yes—
217C22×C4×C47C22×C413yes—
218C22×C4×C47C22×C413yes—
219C22×C4×C47C22×C413yes—
220C22×C4×C47C22×C413yes—
221C22×C4×C47C22×C413yes—
222C22×C4×C47C2411yescharacteristic
223C22×C4×C47C2411yescharacteristic
224C22×C4×C47C2413yes—
225C22×C4×C47C2413yes—
226C22×C4×C47C2413yes—
227C4⋊C4×C47C22×C411yescharacteristic
228C4⋊C4×C47C22×C413yes—
229C4⋊C4×C47C22×C413yes—
230C4⋊C4×C47C22×C413yes—
231C4⋊C4×C47C22×C413yes—
232C4⋊C4×C47C22×C413yes—
233C4⋊C4×C47C22×C416yes—
234C22⋊C4×C47C22×C411yescharacteristic
235C22⋊C4×C47C22×C411yescharacteristic
236C22⋊C4×C47C22×C413yes—
237C22⋊C4×C47C22×C413yes—
238C22⋊C4×C47C22×C413yes—
239C22⋊C4×C47C22×C413yes—
240C22⋊C4×C47C22×C413yes—
241C22⋊C4×C47C22×C413yes—
242C22⋊C4×C47C22×C416yes—
243C22⋊C4×C47C22×C416yes—
244C22⋊C4×C47C22×C416yes—
245C42×C47C22×C413yes—
246C42×C47C22×C413yes—
247C42×C47C2411yescharacteristic
248C42×C47C2413yes—
249#10625329—26no—
250#10625329—26no—
251#10625329—26no—
252#10625329—22no—
253#10625329—26no—
254#10625329—26no—
255#10625329—212no—
256#10625329—26no—
257#10625329C2×D4112yescomplemented
258C2×C47⋊C8—26no—
259C2×C47⋊C8—26no—
260C2×C47⋊C8—26no—
261C2×C47⋊C8—22no—
262C2×C47⋊C8—26no—
263C2×C47⋊C8—26no—
264C2×C47⋊C8—26no—
265C2×C47⋊C8—212no—
266C2×C47⋊C8C2×D4112yescomplemented
267C2×C47⋊C8C2413yes—
268C2×C47⋊C8C2411yescharacteristic
269C2×C47⋊C8C2411yescharacteristic
270C2×C47⋊C8C2411yescharacteristic
271C2×C47⋊C8C2413yes—
272C2×C47⋊C8C2413yes—
273C2×C47⋊C8C2413yes—
274C2×C47⋊C8C2411yescharacteristic
275C23×C47—26no—
276C23×C47—26no—
277C23×C47—26no—
278C23×C47—43no—
279C23×C47—43no—
280C23×C47—43no—
281C23×C47C23×C411yescharacteristic
282C23×C47C23×C413yes—
283C23×C47C23×C413yes—
284C23×C47C23×C413yes—
285C23×C47C23×C411yescharacteristic
286Q8×C47—26no—
287Q8×C47—26no—
288Q8×C47C4×D414yes—
289D4×C47—212no—
290D4×C47—212no—
291D4×C47—22no—
292D4×C47—26no—
293D4×C47—26no—
294D4×C47—26no—
295D4×C47—43no—
296D4×C47—43no—
297D4×C47—46no—
298D4×C47C4×D4112yes—
299C2×C4×C47—26no—
300C2×C4×C47—26no—
301C2×C4×C47—26no—
302C2×C4×C47—26no—
303C2×C4×C47—26no—
304C2×C4×C47—26no—
305C2×C4×C47—21no—
306C2×C4×C47—23no—
307C2×C4×C47—23no—
308C2×C4×C47—21no—
309C2×C4×C47—21no—
310C2×C4×C47—21no—
311C2×C4×C47—23no—
312C2×C4×C47—23no—
313C2×C4×C47—43no—
314C2×C4×C47—43no—
315C2×C4×C47C23×C411yescharacteristic
316C2×C4×C47C23×C411yescharacteristic
317C2×C4×C47C23×C413yes—
318C2×C4×C47C23×C413yes—
319C2×C4×C47C23×C411yescharacteristic
320C2×C4×C47C23×C411yescharacteristic
321C2×C4×C47C23×C413yes—
322C2×C4×C47C23×C413yes—
323C2×C4×C47C23×C413yes—
324C2×C4×C47C22×D416yes—
325C2×C4×C47C2×#4116yes—
326C2×C4×C47C2511yescharacteristic
327C47⋊C8—21no—
328C47⋊C8—23no—
329C47⋊C8—21no—
330C47⋊C8—23no—
331C47⋊C8—21no—
332C47⋊C8—23no—
333C47⋊C8C22×D412yes—
334C47⋊C8C22×D416yes—
335#60146—471nomaximal, Sylow
336C22×C47—21no—
337C22×C47—23no—
338C22×C47—23no—
339C22×C47—21no—
340C22×C47—21no—
341C22×C47—23no—
342C22×C47—23no—
343C22×C47—21no—
344C22×C47—23no—
345C22×C47—23no—
346C22×C47—23no—
347C22×C47—23no—
348C22×C47—21no—
349C22×C47—412no—
350C22×C47—86no—
351C22×C47C2×C4×D416yes—
352C22×C47#56812yescomplemented
353C22×C47C24×C411yescharacteristic
354C4×C47—21no—
355C4×C47—21no—
356C4×C47—23no—
357C4×C47—23no—
358C4×C47—21no—
359C4×C47—23no—
360C4×C47—21no—
361C4×C47—23no—
362C4×C47C2×C4×D416yes—
363C4×C47C23×D411yescharacteristic
364C4×C47C22×#4111yescharacteristic
365C2×#568—471no—
366C22×#131—471no—
367D4×#41D4711yescharacteristic
368#2935—473no—
369D4×M16—473no—
370#2933—473no—
371#2933—473no—
372#2932—473no—
373#2930—473no—
374#2929—473no—
375C2×#435—473no—
376#2906—471no—
377#2880—471no—
378#2880—471no—
379#2875—471no—
380C2×C47—22no—
381C2×C47—26no—
382C2×C47—43no—
383C2×C47—43no—
384C2×C47—41no—
385C2×C47C22×C4×D411yescharacteristic
386C2×C47C2×#56811yescharacteristic
387C2×C47#357311yescharacteristic
388C22×#41C2×D4711yescharacteristic
389C22×#41C2×D4711yescharacteristic
390#568—948no—
391C2×#131—471no—
392C2×#131—471no—
393C2×#131—471no—
394C2×#131—471no—
395C2×#131—473no—
396C2×#131—473no—
397C2×#131—473no—
398C2×#131—473no—
399C2×#131—948no—
400C22×M16—473no—
401C22×M16—473no—
402C22×M16—473no—
403C23×C8—473no—
404#550Dic4711yescharacteristic
405D4×Q8Dic4711yescharacteristic
406#548Dic4711yescharacteristic
407#548Dic4711yescharacteristic
408#547Dic4713yes—
409#546Dic4713yes—
410#546Dic4713yes—
411D42Dic4713yes—
412#532C2×D4713yes—
413#525C2×D4713yes—
414#525C2×D4713yes—
415C4×#41C2×D4711yescharacteristic
416C2×C4×D4C2×D4713yes—
417#436—476no—
418#436—476no—
419#435—471no—
420#435—473no—
421#435—473no—
422#435—473no—
423#435—473no—
424#435—473no—
425#435—473no—
426#435—473no—
427#435—476no—
428#435—476no—
429#435—476no—
430C8×D4—476no—
431C8×D4—476no—
432#424—473no—
433#424—473no—
434#423—473no—
435C2×C4⋊C8—473no—
436#408—473no—
437#408—473no—
438#408—473no—
439#408—473no—
440#407—473no—
441#407—473no—
442C2×C22⋊C8—473no—
443C2×C22⋊C8—473no—
444#405—473no—
445#405—473no—
446C4×M16—473no—
447C2×#97—473no—
448C47#6014611yescharacteristic, complemented, Sylow
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—24no—
452C2×#41—24no—
453C2×#41C2×Dic4713yes—
454C2×#41C2×Dic4713yes—
455C2×#41C2×Dic4711yescharacteristic
456C2×#41C2×Dic4711yescharacteristic
457C2×#41C22×D4713yes—
458C2×#41C22×D4713yes—
459C2×#41C22×D4711yescharacteristic
460C22×Q8C2×Dic4711yescharacteristic
461C22×Q8C2×Dic4711yescharacteristic
462C22×D4C2×Dic4713yes—
463C22×D4C2×Dic4713yes—
464C22×D4C2×Dic4713yes—
465C23×C4C22×D4713yes—
466C23×C4C22×D4713yes—
467#131—478no—
468#131—9412no—
469#131—9412no—
470#131—9412no—
471#131—9412no—
472#131—944no—
473#131—944no—
474#131—944no—
475C2×M16—473no—
476C2×M16—471no—
477C2×M16—473no—
478C2×M16—473no—
479C2×M16—473no—
480C2×M16—473no—
481C2×M16—473no—
482C2×M16—476no—
483C2×M16—473no—
484C2×M16—9412no—
485C2×M16—9412no—
486C2×M16—9412no—
487C22×C8—473no—
488C22×C8—471no—
489C22×C8—473no—
490C22×C8—473no—
491C22×C8—473no—
492C22×C8—473no—
493C22×C8—473no—
494C22×C8—476no—
495C22×C8—473no—
496C22×C8—9412no—
497C4⋊Q8C2×Dic4713yes—
498#127C2×Dic4713yes—
499#124C2×Dic4713yes—
500#124C2×Dic4713yes—
501#123C2×Dic4716yes—
502#123C2×Dic4716yes—
503C22⋊Q8C2×Dic4713yes—
504C22⋊Q8C2×Dic4713yes—
505C22⋊Q8C2×Dic4713yes—
506C22⋊Q8C2×Dic4713yes—
507#121C2×Dic4713yes—
508#121C2×Dic4713yes—
509#121C2×Dic4713yes—
510#121C2×Dic4713yes—
511#121C2×Dic4716yes—
512#121C2×Dic4716yes—
513#120C2×Dic4716yes—
514#120C2×Dic4716yes—
515C4×Q8C2×Dic4711yescharacteristic
516C4×Q8C2×Dic4711yescharacteristic
517C4×D4C2×Dic4713yes—
518C4×D4C2×Dic4713yes—
519C4×D4C2×Dic4713yes—
520C4×D4C2×Dic4713yes—
521C4×D4C2×Dic4713yes—
522C4×D4C2×Dic4713yes—
523C4×D4C22×D4711yescharacteristic
524C4×D4C22×D4713yes—
525C4×D4C22×D4713yes—
526C4×D4C22×D4713yes—
527C4×D4C22×D4716yes—
528#117C22×D4713yes—
529C2×C4⋊C4C2×Dic4713yes—
530C2×C22⋊C4C2×Dic4713yes—
531C2×C22⋊C4C2×Dic4713yes—
532C2×C42C22×D4713yes—
533C4⋊C8—471no—
534C4⋊C8—473no—
535C4⋊C8—473no—
536C4⋊C8—473no—
537C4⋊C8—476no—
538C22⋊C8—471no—
539C22⋊C8—471no—
540C22⋊C8—473no—
541C22⋊C8—473no—
542C22⋊C8—473no—
543C22⋊C8—473no—
544C22⋊C8—473no—
545C22⋊C8—473no—
546C22⋊C8—476no—
547C22⋊C8—476no—
548#97—471no—
549#97—473no—
550#97—473no—
551#97—473no—
552C4×C8—476no—
553C24C22×Dic4713yes—
554C24C22×Dic4713yes—
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×D4714yes—
564#41#1062535214yes—
565C2×Q8—24no—
566C2×Q8—24no—
567C2×Q8C22×Dic4713yes—
568C2×Q8C22×Dic4713yes—
569C2×Q8C22×Dic4711yescharacteristic
570C2×D4—212no—
571C2×D4—212no—
572C2×D4—46no—
573C2×D4C22×Dic4711yescharacteristic
574C2×D4C22×Dic4713yes—
575C2×D4C22×Dic4716yes—
576C2×D4C22×Dic4716yes—
577C2×D4C22×Dic4713yes—
578C2×D4C22×Dic4713yes—
579C2×D4C22×Dic4713yes—
580C2×D4C22×Dic4713yes—
581C2×D4C22×Dic4716yes—
582C2×D4C22×Dic4713yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—26no—
586C22×C4—26no—
587C22×C4C22×Dic4713yes—
588C22×C4C22×Dic4713yes—
589C22×C4C22×Dic4713yes—
590C22×C4C22×Dic4713yes—
591C22×C4C22×Dic4713yes—
592C22×C4C22×Dic4713yes—
593C22×C4C22×Dic4713yes—
594C22×C4C22×Dic4713yes—
595C22×C4C23×D4711yescharacteristic
596C22×C4C23×D4713yes—
597C22×C4C23×D4713yes—
598C22×C4C23×D4711yescharacteristic
599C22×C4C23×D4713yes—
600M16—4712no—
601M16—942no—
602M16—946no—
603M16—946no—
604M16—946no—
605M16—9412no—
606M16—946no—
607M16—946no—
608M16—946no—
609C2×C8—4712no—
610C2×C8—473no—
611C2×C8—471no—
612C2×C8—473no—
613C2×C8—471no—
614C2×C8—471no—
615C2×C8—471no—
616C2×C8—473no—
617C2×C8—473no—
618C2×C8—942no—
619C2×C8—946no—
620C2×C8—946no—
621C2×C8—946no—
622C2×C8—9412no—
623C2×C8—946no—
624C2×C8—946no—
625C2×C8—946no—
626C4⋊C4C22×Dic4711yescharacteristic
627C4⋊C4C22×Dic4713yes—
628C4⋊C4C22×Dic4713yes—
629C4⋊C4C22×Dic4713yes—
630C4⋊C4C22×Dic4713yes—
631C4⋊C4C22×Dic4713yes—
632C4⋊C4C22×Dic4716yes—
633C22⋊C4C22×Dic4711yescharacteristic
634C22⋊C4C22×Dic4711yescharacteristic
635C22⋊C4C22×Dic4713yes—
636C22⋊C4C22×Dic4713yes—
637C22⋊C4C22×Dic4713yes—
638C22⋊C4C22×Dic4713yes—
639C22⋊C4C22×Dic4713yes—
640C22⋊C4C22×Dic4713yes—
641C22⋊C4C22×Dic4716yes—
642C22⋊C4C22×Dic4716yes—
643C22⋊C4C22×Dic4716yes—
644C42C22×Dic4713yes—
645C42C22×Dic4713yes—
646C42C23×D4713yes—
647C42C23×D4711yescharacteristic
648C23—26no—
649C23—26no—
650C23—26no—
651C23—43no—
652C23—43no—
653C23—43no—
654C23C23×Dic4711yescharacteristic
655C23C23×Dic4713yes—
656C23C23×Dic4713yes—
657C23C23×Dic4713yes—
658C23C23×Dic4711yescharacteristic
659Q8—26no—
660Q8—26no—
661Q8D4×Dic4714yes—
662D4—212no—
663D4—212no—
664D4—22no—
665D4—26no—
666D4—26no—
667D4—26no—
668D4—43no—
669D4—43no—
670D4—46no—
671D4D4×Dic47112yes—
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×Dic4711yescharacteristic
689C2×C4C23×Dic4711yescharacteristic
690C2×C4C23×Dic4713yes—
691C2×C4C23×Dic4713yes—
692C2×C4C23×Dic4711yescharacteristic
693C2×C4C23×Dic4711yescharacteristic
694C2×C4C23×Dic4713yes—
695C2×C4C23×Dic4713yes—
696C2×C4C23×Dic4713yes—
697C2×C4C2×D4×D4716yes—
698C2×C4C2×#1062535216yes—
699C2×C4C24×D4711yescharacteristic
700C8—472no—
701C8—476no—
702C8—941no—
703C8—943no—
704C8—943no—
705C8—941no—
706C8—941no—
707C8—943no—
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×Dic4716yes—
724C22#1568989012yescomplemented
725C22C24×Dic4711yescharacteristic
726C4—21no—
727C4—21no—
728C4—23no—
729C4—23no—
730C4—21no—
731C4—23no—
732C4—21no—
733C4—23no—
734C4C2×D4×Dic4716yes—
735C4C22×D4×D4711yescharacteristic
736C4C22×#1062535211yescharacteristic
737C2—22no—
738C2—26no—
739C2—43no—
740C2—41no—
741C2—43no—
742C2C22×D4×Dic4711yescharacteristic
743C2C2×#1568989011yescharacteristic
744C2#2025810011yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D47
commutator, socleC22×C47C24×C4
Fitting, prime radicalD4×#41×C47C2
cosocleC2×C4×C47C25
hypercenterD4×#41D47
hypocenterC47#60146
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#15689890C2semidirect
2. C22×#13094031C2semidirect
3. #20252132C2semidirect
4. D4×#10625329C2semidirect
5. #20252115C2semidirect
6. #20252115C2semidirect
7. #20252106C2semidirect
8. #20252092C2semidirect
9. #20252083C2semidirect
10. C2×#15689195C2semidirect
11. #20251956C2semidirect
12. #20251837C2semidirect
13. #20251837C2semidirect
14. #20251816C2semidirect
22. C2×#13094031C22semidirect
23. C2×#13094031C22semidirect
24. C2×#13094031C22semidirect
25. C2×#13094031C22semidirect
26. C22×#10625329C22semidirect
27. C22×#10625329C22semidirect
28. C22×#10625329C22semidirect
29. C23×C47⋊C8C22semidirect
30. #15689201C22semidirect
31. #15689201C22semidirect
34. #15689195C22semidirect
35. #15689195C22semidirect
36. #15689195C22semidirect
37. #15689195C22semidirect
38. #15689195C22semidirect
39. #15689195C22semidirect
40. #15689195C22semidirect
41. #15689195C22semidirect
42. #15689195C22semidirect
43. D4×C47⋊C8C22semidirect
44. D4×C47⋊C8C22semidirect
45. #15689150C22semidirect
46. #15689150C22semidirect
47. #15689147C22semidirect
48. C2×C4⋊(C47⋊C8)C22semidirect
49. #15689090C22semidirect
50. #15689090C22semidirect
51. #15689090C22semidirect
52. #15689090C22semidirect
53. #15689087C22semidirect
54. #15689087C22semidirect
55. C2×C22⋊(C47⋊C8)C22semidirect
56. C2×C22⋊(C47⋊C8)C22semidirect
57. #15689079C22semidirect
58. #15689079C22semidirect
59. C4×#10625329C22semidirect
60. C2×#13093935C22semidirect
83. #13094031D4semidirect
257. #10625329C2×D4semidirect
266. C2×C47⋊C8C2×D4semidirect
352. C22×C47#568semidirect
448. C47#60146semidirect
724. C22#15689890semidirect

Maximal subgroups

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

subgroupindex
C2×#156898902
C22×#130940312
#202521322
D4×#106253292
#202521152
#202521062
#202520922
#202520832
C2×#156891952
#202519562
#202518372
#202518162
D4×#41×C472
#6014647