Finite Group Databasebeta

← #30543994

Subgroups — #30543994

Order 15616.

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×#16840529C211yesmaximal, characteristic, complemented
2C22×#14519784C211yesmaximal, characteristic, complemented
3#21454563C213yesmaximal, complemented
4D4×#11758194C213yesmaximal, complemented
5#21454546C213yesmaximal, complemented
6#21454546C213yesmaximal, complemented
7#21454537C213yesmaximal, complemented
8#21454523C213yesmaximal, complemented
9#21454514C213yesmaximal, complemented
10C2×#16839834C213yesmaximal, complemented
11#21454387C211yesmaximal, characteristic, complemented
12#21454268C211yesmaximal, characteristic, complemented
13#21454268C211yesmaximal, characteristic, complemented
14#21454247C211yesmaximal, characteristic, complemented
15D4×#41×C61C211yesmaximal, characteristic
16#16840529—28no—
17C2×#14519784—28no—
18C2×#14519784C2211yescharacteristic
19C2×#14519784C2211yescharacteristic
20C2×#14519784C2211yescharacteristic
21C2×#14519784C2211yescharacteristic
22C2×#14519784C2213yescomplemented
23C2×#14519784C2213yescomplemented
24C2×#14519784C2213yescomplemented
25C2×#14519784C2213yescomplemented
26C22×#11758194C2213yescomplemented
27C22×#11758194C2213yescomplemented
28C22×#11758194C2213yescomplemented
29C23×#92418C2213yescomplemented
30#16839840C2216yescomplemented
31#16839840C2216yescomplemented
32#16839834C2211yescharacteristic
33#16839834C2213yes—
34#16839834C2213yescomplemented
35#16839834C2213yescomplemented
36#16839834C2213yescomplemented
37#16839834C2213yescomplemented
38#16839834C2213yescomplemented
39#16839834C2213yescomplemented
40#16839834C2216yescomplemented
41#16839834C2216yescomplemented
42#16839834C2216yescomplemented
43D4×#92418C2216yescomplemented
44D4×#92418C2216yescomplemented
45#16839789C2213yescomplemented
46#16839789C2213yescomplemented
47#16839786C2213yescomplemented
48C2×C4⋊#92418C2213yescomplemented
49#16839729C2213yescomplemented
50#16839729C2213yescomplemented
51#16839729C2213yescomplemented
52#16839729C2213yescomplemented
53#16839726C2213yescomplemented
54#16839726C2213yescomplemented
55C2×C22⋊#92418C2213yescomplemented
56C2×C22⋊#92418C2213yescomplemented
57#16839718C2213yescomplemented
58#16839718C2213yescomplemented
59C4×#11758194C2213yescomplemented
60C2×#14519688C2213yescomplemented
61C22×#41×C61C2211yescharacteristic
62C22×#41×C61C2211yescharacteristic
63C61×#550C411yescharacteristic
64D4×Q8×C61C411yescharacteristic
65C61×#548C411yescharacteristic
66C61×#548C411yescharacteristic
67C61×#547C413yes—
68C61×#546C413yes—
69C61×#546C413yes—
70D42×C61C413yes—
71C61×#532C2213yes—
72C61×#525C2213yes—
73C61×#525C2213yes—
74C4×#41×C61C2211yescharacteristic
75C2×C4×D4×C61C2213yes—
76#14519784—24no—
77#14519784—24no—
78#14519784—24no—
79#14519784—212no—
80#14519784—212no—
81#14519784—212no—
82#14519784—212no—
83#14519784D418yescomplemented
84C2×#11758194—212no—
85C2×#11758194—212no—
86C2×#11758194—212no—
87C2×#11758194C2313yes—
88C2×#11758194C2313yes—
89C2×#11758194C2313yes—
90C2×#11758194C2311yescharacteristic
91C2×#11758194C2313yes—
92C2×#11758194C2313yes—
93C2×#11758194C2316yes—
94C2×#11758194C2313yes—
95C2×#11758194C2313yes—
96C22×#92418—212no—
97C22×#92418C2313yes—
98C22×#92418C2313yes—
99C22×#92418C2313yes—
100C22×#92418C2311yescharacteristic
101C22×#92418C2313yes—
102C22×#92418C2313yes—
103C22×#92418C2313yes—
104C22×#92418C2316yes—
105C22×#92418C2313yes—
106C4⋊#92418C2311yescharacteristic
107C4⋊#92418C2313yes—
108C4⋊#92418C2313yes—
109C4⋊#92418C2313yes—
110C4⋊#92418C2316yes—
111C22⋊#92418C2311yescharacteristic
112C22⋊#92418C2311yescharacteristic
113C22⋊#92418C2313yes—
114C22⋊#92418C2313yes—
115C22⋊#92418C2313yes—
116C22⋊#92418C2313yes—
117C22⋊#92418C2313yes—
118C22⋊#92418C2313yes—
119C22⋊#92418C2316yes—
120C22⋊#92418C2316yes—
121#14519688C2311yescharacteristic
122#14519688C2313yes—
123#14519688C2313yes—
124#14519688C2313yes—
125C4×#92418C2316yes—
126C2×#41×C61—24no—
127C2×#41×C61—24no—
128C2×#41×C61—24no—
129C2×#41×C61—24no—
130C2×#41×C61C2×C413yes—
131C2×#41×C61C2×C413yes—
132C2×#41×C61C2×C411yescharacteristic
133C2×#41×C61C2×C411yescharacteristic
134C2×#41×C61C2313yes—
135C2×#41×C61C2313yes—
136C2×#41×C61C2311yescharacteristic
137C22×Q8×C61C2×C411yescharacteristic
138C22×Q8×C61C2×C411yescharacteristic
139C22×D4×C61C2×C413yes—
140C22×D4×C61C2×C413yes—
141C22×D4×C61C2×C413yes—
142C23×C4×C61C2313yes—
143C23×C4×C61C2313yes—
144C4⋊Q8×C61C2×C413yes—
145#127×C61C2×C413yes—
146#124×C61C2×C413yes—
147#124×C61C2×C413yes—
148#123×C61C2×C416yes—
149#123×C61C2×C416yes—
150C22⋊Q8×C61C2×C413yes—
151C22⋊Q8×C61C2×C413yes—
152C22⋊Q8×C61C2×C413yes—
153C22⋊Q8×C61C2×C413yes—
154#121×C61C2×C416yes—
155#121×C61C2×C416yes—
156#121×C61C2×C413yes—
157#121×C61C2×C413yes—
158#121×C61C2×C413yes—
159#121×C61C2×C413yes—
160#120×C61C2×C416yes—
161#120×C61C2×C416yes—
162C4×Q8×C61C2×C411yescharacteristic
163C4×Q8×C61C2×C411yescharacteristic
164C4×D4×C61C2×C413yes—
165C4×D4×C61C2×C413yes—
166C4×D4×C61C2×C413yes—
167C4×D4×C61C2×C413yes—
168C4×D4×C61C2×C413yes—
169C4×D4×C61C2×C413yes—
170C4×D4×C61C2313yes—
171C4×D4×C61C2316yes—
172C4×D4×C61C2313yes—
173C4×D4×C61C2311yescharacteristic
174C4×D4×C61C2313yes—
175#117×C61C2313yes—
176C2×C4⋊C4×C61C2×C413yes—
177C2×C22⋊C4×C61C2×C413yes—
178C2×C22⋊C4×C61C2×C413yes—
179C2×C42×C61C2313yes—
180C24×C61C22×C413yes—
181C24×C61C22×C413yes—
182#41×C61—24no—
183#41×C61—24no—
184#41×C61—212no—
185#41×C61—212no—
186#41×C61—26no—
187#41×C61—26no—
188#41×C61—26no—
189#41×C61—26no—
190#41×C61C2×D414yes—
191#41×C61#4114yes—
192C2×Q8×C61—24no—
193C2×Q8×C61—24no—
194C2×Q8×C61C22×C413yes—
195C2×Q8×C61C22×C413yes—
196C2×Q8×C61C22×C411yescharacteristic
197C2×D4×C61—212no—
198C2×D4×C61—212no—
199C2×D4×C61—46no—
200C2×D4×C61C22×C411yescharacteristic
201C2×D4×C61C22×C413yes—
202C2×D4×C61C22×C416yes—
203C2×D4×C61C22×C416yes—
204C2×D4×C61C22×C413yes—
205C2×D4×C61C22×C413yes—
206C2×D4×C61C22×C413yes—
207C2×D4×C61C22×C413yes—
208C2×D4×C61C22×C416yes—
209C2×D4×C61C22×C413yes—
210C22×C4×C61—26no—
211C22×C4×C61—26no—
212C22×C4×C61—26no—
213C22×C4×C61—26no—
214C22×C4×C61C22×C413yes—
215C22×C4×C61C22×C413yes—
216C22×C4×C61C22×C413yes—
217C22×C4×C61C22×C413yes—
218C22×C4×C61C22×C413yes—
219C22×C4×C61C22×C413yes—
220C22×C4×C61C22×C413yes—
221C22×C4×C61C22×C413yes—
222C22×C4×C61C2411yescharacteristic
223C22×C4×C61C2411yescharacteristic
224C22×C4×C61C2413yes—
225C22×C4×C61C2413yes—
226C22×C4×C61C2413yes—
227C4⋊C4×C61C22×C411yescharacteristic
228C4⋊C4×C61C22×C413yes—
229C4⋊C4×C61C22×C413yes—
230C4⋊C4×C61C22×C413yes—
231C4⋊C4×C61C22×C413yes—
232C4⋊C4×C61C22×C413yes—
233C4⋊C4×C61C22×C416yes—
234C22⋊C4×C61C22×C411yescharacteristic
235C22⋊C4×C61C22×C411yescharacteristic
236C22⋊C4×C61C22×C413yes—
237C22⋊C4×C61C22×C413yes—
238C22⋊C4×C61C22×C413yes—
239C22⋊C4×C61C22×C413yes—
240C22⋊C4×C61C22×C413yes—
241C22⋊C4×C61C22×C413yes—
242C22⋊C4×C61C22×C416yes—
243C22⋊C4×C61C22×C416yes—
244C22⋊C4×C61C22×C416yes—
245C42×C61C22×C413yes—
246C42×C61C22×C413yes—
247C42×C61C2411yescharacteristic
248C42×C61C2413yes—
249#11758194—26no—
250#11758194—26no—
251#11758194—26no—
252#11758194—22no—
253#11758194—26no—
254#11758194—26no—
255#11758194—212no—
256#11758194—26no—
257#11758194C2×D4112yescomplemented
258C2×#92418—26no—
259C2×#92418—26no—
260C2×#92418—26no—
261C2×#92418—22no—
262C2×#92418—26no—
263C2×#92418—26no—
264C2×#92418—26no—
265C2×#92418—212no—
266C2×#92418C2×D4112yescomplemented
267C2×#92418C2413yes—
268C2×#92418C2411yescharacteristic
269C2×#92418C2411yescharacteristic
270C2×#92418C2411yescharacteristic
271C2×#92418C2413yes—
272C2×#92418C2413yes—
273C2×#92418C2413yes—
274C2×#92418C2411yescharacteristic
275C23×C61—26no—
276C23×C61—26no—
277C23×C61—26no—
278C23×C61—43no—
279C23×C61—43no—
280C23×C61—43no—
281C23×C61C23×C411yescharacteristic
282C23×C61C23×C413yes—
283C23×C61C23×C413yes—
284C23×C61C23×C413yes—
285C23×C61C23×C411yescharacteristic
286Q8×C61—26no—
287Q8×C61—26no—
288Q8×C61C4×D414yes—
289D4×C61—212no—
290D4×C61—212no—
291D4×C61—22no—
292D4×C61—26no—
293D4×C61—26no—
294D4×C61—26no—
295D4×C61—43no—
296D4×C61—43no—
297D4×C61—46no—
298D4×C61C4×D4112yes—
299C2×C4×C61—26no—
300C2×C4×C61—26no—
301C2×C4×C61—26no—
302C2×C4×C61—26no—
303C2×C4×C61—26no—
304C2×C4×C61—26no—
305C2×C4×C61—21no—
306C2×C4×C61—23no—
307C2×C4×C61—23no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—23no—
312C2×C4×C61—23no—
313C2×C4×C61—43no—
314C2×C4×C61—43no—
315C2×C4×C61C23×C411yescharacteristic
316C2×C4×C61C23×C411yescharacteristic
317C2×C4×C61C23×C413yes—
318C2×C4×C61C23×C413yes—
319C2×C4×C61C23×C411yescharacteristic
320C2×C4×C61C23×C411yescharacteristic
321C2×C4×C61C23×C413yes—
322C2×C4×C61C23×C413yes—
323C2×C4×C61C23×C413yes—
324C2×C4×C61C22×D416yes—
325C2×C4×C61C2×#4116yes—
326C2×C4×C61C2511yescharacteristic
327#92418—21no—
328#92418—23no—
329#92418—21no—
330#92418—23no—
331#92418—21no—
332#92418—23no—
333#92418C22×D412yes—
334#92418C22×D416yes—
335#60146—611nomaximal, Sylow
336C22×C61—21no—
337C22×C61—23no—
338C22×C61—23no—
339C22×C61—21no—
340C22×C61—21no—
341C22×C61—23no—
342C22×C61—23no—
343C22×C61—21no—
344C22×C61—23no—
345C22×C61—23no—
346C22×C61—23no—
347C22×C61—23no—
348C22×C61—21no—
349C22×C61—412no—
350C22×C61—86no—
351C22×C61C2×C4×D416yes—
352C22×C61#56812yescomplemented
353C22×C61C24×C411yescharacteristic
354C4×C61—21no—
355C4×C61—21no—
356C4×C61—23no—
357C4×C61—23no—
358C4×C61—21no—
359C4×C61—23no—
360C4×C61—21no—
361C4×C61—23no—
362C4×C61C2×C4×D416yes—
363C4×C61C23×D411yescharacteristic
364C4×C61C22×#4111yescharacteristic
365C2×#568—611no—
366C22×#131—611no—
367D4×#41D6111yescharacteristic
368#2935—613no—
369D4×M16—613no—
370#2933—613no—
371#2933—613no—
372#2932—613no—
373#2930—613no—
374#2929—613no—
375C2×#435—613no—
376#2906—611no—
377#2880—611no—
378#2880—611no—
379#2875—611no—
380C2×C61—22no—
381C2×C61—26no—
382C2×C61—43no—
383C2×C61—43no—
384C2×C61—41no—
385C2×C61C22×C4×D411yescharacteristic
386C2×C61C2×#56811yescharacteristic
387C2×C61#357311yescharacteristic
388C22×#41C2×D6111yescharacteristic
389C22×#41C2×D6111yescharacteristic
390#568—1228no—
391C2×#131—611no—
392C2×#131—611no—
393C2×#131—611no—
394C2×#131—611no—
395C2×#131—613no—
396C2×#131—613no—
397C2×#131—613no—
398C2×#131—613no—
399C2×#131—1228no—
400C22×M16—613no—
401C22×M16—613no—
402C22×M16—613no—
403C23×C8—613no—
404#550Dic6111yescharacteristic
405D4×Q8Dic6111yescharacteristic
406#548Dic6111yescharacteristic
407#548Dic6111yescharacteristic
408#547Dic6113yes—
409#546Dic6113yes—
410#546Dic6113yes—
411D42Dic6113yes—
412#532C2×D6113yes—
413#525C2×D6113yes—
414#525C2×D6113yes—
415C4×#41C2×D6111yescharacteristic
416C2×C4×D4C2×D6113yes—
417#436—616no—
418#436—616no—
419#435—611no—
420#435—613no—
421#435—613no—
422#435—613no—
423#435—613no—
424#435—613no—
425#435—613no—
426#435—613no—
427#435—616no—
428#435—616no—
429#435—616no—
430C8×D4—616no—
431C8×D4—616no—
432#424—613no—
433#424—613no—
434#423—613no—
435C2×C4⋊C8—613no—
436#408—613no—
437#408—613no—
438#408—613no—
439#408—613no—
440#407—613no—
441#407—613no—
442C2×C22⋊C8—613no—
443C2×C22⋊C8—613no—
444#405—613no—
445#405—613no—
446C4×M16—613no—
447C2×#97—613no—
448C61#6014611yescharacteristic, complemented, Sylow
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—24no—
452C2×#41—24no—
453C2×#41C2×Dic6113yes—
454C2×#41C2×Dic6113yes—
455C2×#41C2×Dic6111yescharacteristic
456C2×#41C2×Dic6111yescharacteristic
457C2×#41C22×D6113yes—
458C2×#41C22×D6113yes—
459C2×#41C22×D6111yescharacteristic
460C22×Q8C2×Dic6111yescharacteristic
461C22×Q8C2×Dic6111yescharacteristic
462C22×D4C2×Dic6113yes—
463C22×D4C2×Dic6113yes—
464C22×D4C2×Dic6113yes—
465C23×C4C22×D6113yes—
466C23×C4C22×D6113yes—
467#131—618no—
468#131—12212no—
469#131—12212no—
470#131—12212no—
471#131—12212no—
472#131—1224no—
473#131—1224no—
474#131—1224no—
475C2×M16—613no—
476C2×M16—611no—
477C2×M16—613no—
478C2×M16—613no—
479C2×M16—613no—
480C2×M16—613no—
481C2×M16—613no—
482C2×M16—616no—
483C2×M16—613no—
484C2×M16—12212no—
485C2×M16—12212no—
486C2×M16—12212no—
487C22×C8—613no—
488C22×C8—611no—
489C22×C8—613no—
490C22×C8—613no—
491C22×C8—613no—
492C22×C8—613no—
493C22×C8—613no—
494C22×C8—616no—
495C22×C8—613no—
496C22×C8—12212no—
497C4⋊Q8C2×Dic6113yes—
498#127C2×Dic6113yes—
499#124C2×Dic6113yes—
500#124C2×Dic6113yes—
501#123C2×Dic6116yes—
502#123C2×Dic6116yes—
503C22⋊Q8C2×Dic6113yes—
504C22⋊Q8C2×Dic6113yes—
505C22⋊Q8C2×Dic6113yes—
506C22⋊Q8C2×Dic6113yes—
507#121C2×Dic6113yes—
508#121C2×Dic6113yes—
509#121C2×Dic6113yes—
510#121C2×Dic6113yes—
511#121C2×Dic6116yes—
512#121C2×Dic6116yes—
513#120C2×Dic6116yes—
514#120C2×Dic6116yes—
515C4×Q8C2×Dic6111yescharacteristic
516C4×Q8C2×Dic6111yescharacteristic
517C4×D4C2×Dic6113yes—
518C4×D4C2×Dic6113yes—
519C4×D4C2×Dic6113yes—
520C4×D4C2×Dic6113yes—
521C4×D4C2×Dic6113yes—
522C4×D4C2×Dic6113yes—
523C4×D4C22×D6111yescharacteristic
524C4×D4C22×D6113yes—
525C4×D4C22×D6113yes—
526C4×D4C22×D6113yes—
527C4×D4C22×D6116yes—
528#117C22×D6113yes—
529C2×C4⋊C4C2×Dic6113yes—
530C2×C22⋊C4C2×Dic6113yes—
531C2×C22⋊C4C2×Dic6113yes—
532C2×C42C22×D6113yes—
533C4⋊C8—611no—
534C4⋊C8—613no—
535C4⋊C8—613no—
536C4⋊C8—613no—
537C4⋊C8—616no—
538C22⋊C8—611no—
539C22⋊C8—611no—
540C22⋊C8—613no—
541C22⋊C8—613no—
542C22⋊C8—613no—
543C22⋊C8—613no—
544C22⋊C8—613no—
545C22⋊C8—613no—
546C22⋊C8—616no—
547C22⋊C8—616no—
548#97—611no—
549#97—613no—
550#97—613no—
551#97—613no—
552C4×C8—616no—
553C24C22×Dic6113yes—
554C24C22×Dic6113yes—
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×D6114yes—
564#41#1175822414yes—
565C2×Q8—24no—
566C2×Q8—24no—
567C2×Q8C22×Dic6113yes—
568C2×Q8C22×Dic6113yes—
569C2×Q8C22×Dic6111yescharacteristic
570C2×D4—212no—
571C2×D4—212no—
572C2×D4—46no—
573C2×D4C22×Dic6111yescharacteristic
574C2×D4C22×Dic6113yes—
575C2×D4C22×Dic6116yes—
576C2×D4C22×Dic6116yes—
577C2×D4C22×Dic6113yes—
578C2×D4C22×Dic6113yes—
579C2×D4C22×Dic6113yes—
580C2×D4C22×Dic6113yes—
581C2×D4C22×Dic6116yes—
582C2×D4C22×Dic6113yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—26no—
586C22×C4—26no—
587C22×C4C22×Dic6113yes—
588C22×C4C22×Dic6113yes—
589C22×C4C22×Dic6113yes—
590C22×C4C22×Dic6113yes—
591C22×C4C22×Dic6113yes—
592C22×C4C22×Dic6113yes—
593C22×C4C22×Dic6113yes—
594C22×C4C22×Dic6113yes—
595C22×C4C23×D6111yescharacteristic
596C22×C4C23×D6113yes—
597C22×C4C23×D6113yes—
598C22×C4C23×D6111yescharacteristic
599C22×C4C23×D6113yes—
600M16—6112no—
601M16—1222no—
602M16—1226no—
603M16—1226no—
604M16—1226no—
605M16—12212no—
606M16—1226no—
607M16—1226no—
608M16—1226no—
609C2×C8—6112no—
610C2×C8—613no—
611C2×C8—611no—
612C2×C8—613no—
613C2×C8—611no—
614C2×C8—611no—
615C2×C8—611no—
616C2×C8—613no—
617C2×C8—613no—
618C2×C8—1222no—
619C2×C8—1226no—
620C2×C8—1226no—
621C2×C8—1226no—
622C2×C8—12212no—
623C2×C8—1226no—
624C2×C8—1226no—
625C2×C8—1226no—
626C4⋊C4C22×Dic6111yescharacteristic
627C4⋊C4C22×Dic6113yes—
628C4⋊C4C22×Dic6113yes—
629C4⋊C4C22×Dic6113yes—
630C4⋊C4C22×Dic6113yes—
631C4⋊C4C22×Dic6113yes—
632C4⋊C4C22×Dic6116yes—
633C22⋊C4C22×Dic6111yescharacteristic
634C22⋊C4C22×Dic6111yescharacteristic
635C22⋊C4C22×Dic6113yes—
636C22⋊C4C22×Dic6113yes—
637C22⋊C4C22×Dic6113yes—
638C22⋊C4C22×Dic6113yes—
639C22⋊C4C22×Dic6113yes—
640C22⋊C4C22×Dic6113yes—
641C22⋊C4C22×Dic6116yes—
642C22⋊C4C22×Dic6116yes—
643C22⋊C4C22×Dic6116yes—
644C42C22×Dic6113yes—
645C42C22×Dic6113yes—
646C42C23×D6113yes—
647C42C23×D6111yescharacteristic
648C23—26no—
649C23—26no—
650C23—26no—
651C23—43no—
652C23—43no—
653C23—43no—
654C23C23×Dic6111yescharacteristic
655C23C23×Dic6113yes—
656C23C23×Dic6113yes—
657C23C23×Dic6113yes—
658C23C23×Dic6111yescharacteristic
659Q8—26no—
660Q8—26no—
661Q8D4×Dic6114yes—
662D4—212no—
663D4—212no—
664D4—22no—
665D4—26no—
666D4—26no—
667D4—26no—
668D4—43no—
669D4—43no—
670D4—46no—
671D4D4×Dic61112yes—
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×Dic6111yescharacteristic
689C2×C4C23×Dic6111yescharacteristic
690C2×C4C23×Dic6113yes—
691C2×C4C23×Dic6113yes—
692C2×C4C23×Dic6111yescharacteristic
693C2×C4C23×Dic6111yescharacteristic
694C2×C4C23×Dic6113yes—
695C2×C4C23×Dic6113yes—
696C2×C4C23×Dic6113yes—
697C2×C4C2×D4×D6116yes—
698C2×C4C2×#1175822416yes—
699C2×C4C24×D6111yescharacteristic
700C8—612no—
701C8—616no—
702C8—1221no—
703C8—1223no—
704C8—1223no—
705C8—1221no—
706C8—1221no—
707C8—1223no—
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×Dic6116yes—
724C22#1684052912yescomplemented
725C22C24×Dic6111yescharacteristic
726C4—21no—
727C4—21no—
728C4—23no—
729C4—23no—
730C4—21no—
731C4—23no—
732C4—21no—
733C4—23no—
734C4C2×D4×Dic6116yes—
735C4C22×D4×D6111yescharacteristic
736C4C22×#1175822411yescharacteristic
737C2—22no—
738C2—26no—
739C2—43no—
740C2—41no—
741C2—43no—
742C2C22×D4×Dic6111yescharacteristic
743C2C2×#1684052911yescharacteristic
744C2#2146053111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D61
commutator, socleC22×C61C24×C4
Fitting, prime radicalD4×#41×C61C2
cosocleC2×C4×C61C25
hypercenterD4×#41D61
hypocenterC61#60146
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16840529C2semidirect
2. C22×#14519784C2semidirect
3. #21454563C2semidirect
4. D4×#11758194C2semidirect
5. #21454546C2semidirect
6. #21454546C2semidirect
7. #21454537C2semidirect
8. #21454523C2semidirect
9. #21454514C2semidirect
10. C2×#16839834C2semidirect
11. #21454387C2semidirect
12. #21454268C2semidirect
13. #21454268C2semidirect
14. #21454247C2semidirect
22. C2×#14519784C22semidirect
23. C2×#14519784C22semidirect
24. C2×#14519784C22semidirect
25. C2×#14519784C22semidirect
26. C22×#11758194C22semidirect
27. C22×#11758194C22semidirect
28. C22×#11758194C22semidirect
29. C23×#92418C22semidirect
30. #16839840C22semidirect
31. #16839840C22semidirect
34. #16839834C22semidirect
35. #16839834C22semidirect
36. #16839834C22semidirect
37. #16839834C22semidirect
38. #16839834C22semidirect
39. #16839834C22semidirect
40. #16839834C22semidirect
41. #16839834C22semidirect
42. #16839834C22semidirect
43. D4×#92418C22semidirect
44. D4×#92418C22semidirect
45. #16839789C22semidirect
46. #16839789C22semidirect
47. #16839786C22semidirect
48. C2×C4⋊#92418C22semidirect
49. #16839729C22semidirect
50. #16839729C22semidirect
51. #16839729C22semidirect
52. #16839729C22semidirect
53. #16839726C22semidirect
54. #16839726C22semidirect
55. C2×C22⋊#92418C22semidirect
56. C2×C22⋊#92418C22semidirect
57. #16839718C22semidirect
58. #16839718C22semidirect
59. C4×#11758194C22semidirect
60. C2×#14519688C22semidirect
83. #14519784D4semidirect
257. #11758194C2×D4semidirect
266. C2×#92418C2×D4semidirect
352. C22×C61#568semidirect
448. C61#60146semidirect
724. C22#16840529semidirect

Maximal subgroups

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

subgroupindex
C2×#168405292
C22×#145197842
#214545632
D4×#117581942
#214545462
#214545372
#214545232
#214545142
C2×#168398342
#214543872
#214542682
#214542472
D4×#41×C612
#6014661