Finite Group Databasebeta

← #29452670

Subgroups — #29452670

Order 15104.

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×#16838169C211yesmaximal, characteristic, complemented
2C22×#14273734C211yesmaximal, characteristic, complemented
3#21432840C213yesmaximal, complemented
4D4×#11745664C213yesmaximal, complemented
5#21432823C213yesmaximal, complemented
6#21432823C213yesmaximal, complemented
7#21432814C213yesmaximal, complemented
8#21432800C213yesmaximal, complemented
9#21432791C213yesmaximal, complemented
10C2×#16837474C213yesmaximal, complemented
11#21432664C211yesmaximal, characteristic, complemented
12#21432545C211yesmaximal, characteristic, complemented
13#21432545C211yesmaximal, characteristic, complemented
14#21432524C211yesmaximal, characteristic, complemented
15D4×#41×C59C211yesmaximal, characteristic
16#16838169—28no—
17C2×#14273734—28no—
18C2×#14273734C2211yescharacteristic
19C2×#14273734C2211yescharacteristic
20C2×#14273734C2211yescharacteristic
21C2×#14273734C2211yescharacteristic
22C2×#14273734C2213yescomplemented
23C2×#14273734C2213yescomplemented
24C2×#14273734C2213yescomplemented
25C2×#14273734C2213yescomplemented
26C22×#11745664C2213yescomplemented
27C22×#11745664C2213yescomplemented
28C22×#11745664C2213yescomplemented
29C23×C59⋊C8C2213yescomplemented
30#16837480C2216yescomplemented
31#16837480C2216yescomplemented
32#16837474C2213yes—
33#16837474C2211yescharacteristic
34#16837474C2216yescomplemented
35#16837474C2213yescomplemented
36#16837474C2213yescomplemented
37#16837474C2213yescomplemented
38#16837474C2213yescomplemented
39#16837474C2213yescomplemented
40#16837474C2213yescomplemented
41#16837474C2216yescomplemented
42#16837474C2216yescomplemented
43D4×C59⋊C8C2216yescomplemented
44D4×C59⋊C8C2216yescomplemented
45#16837429C2213yescomplemented
46#16837429C2213yescomplemented
47#16837426C2213yescomplemented
48C2×C4⋊(C59⋊C8)C2213yescomplemented
49#16837369C2213yescomplemented
50#16837369C2213yescomplemented
51#16837369C2213yescomplemented
52#16837369C2213yescomplemented
53#16837366C2213yescomplemented
54#16837366C2213yescomplemented
55C2×C22⋊(C59⋊C8)C2213yescomplemented
56C2×C22⋊(C59⋊C8)C2213yescomplemented
57#16837358C2213yescomplemented
58#16837358C2213yescomplemented
59C4×#11745664C2213yescomplemented
60C2×#14273638C2213yescomplemented
61C22×#41×C59C2211yescharacteristic
62C22×#41×C59C2211yescharacteristic
63C59×#550C411yescharacteristic
64D4×Q8×C59C411yescharacteristic
65C59×#548C411yescharacteristic
66C59×#548C411yescharacteristic
67C59×#547C413yes—
68C59×#546C413yes—
69C59×#546C413yes—
70D42×C59C413yes—
71C59×#532C2213yes—
72C59×#525C2213yes—
73C59×#525C2213yes—
74C4×#41×C59C2211yescharacteristic
75C2×C4×D4×C59C2213yes—
76#14273734—24no—
77#14273734—24no—
78#14273734—24no—
79#14273734—212no—
80#14273734—212no—
81#14273734—212no—
82#14273734—212no—
83#14273734D418yescomplemented
84C2×#11745664—212no—
85C2×#11745664—212no—
86C2×#11745664—212no—
87C2×#11745664C2311yescharacteristic
88C2×#11745664C2313yes—
89C2×#11745664C2313yes—
90C2×#11745664C2313yes—
91C2×#11745664C2313yes—
92C2×#11745664C2316yes—
93C2×#11745664C2313yes—
94C2×#11745664C2313yes—
95C2×#11745664C2313yes—
96C22×C59⋊C8—212no—
97C22×C59⋊C8C2311yescharacteristic
98C22×C59⋊C8C2313yes—
99C22×C59⋊C8C2313yes—
100C22×C59⋊C8C2313yes—
101C22×C59⋊C8C2313yes—
102C22×C59⋊C8C2313yes—
103C22×C59⋊C8C2316yes—
104C22×C59⋊C8C2313yes—
105C22×C59⋊C8C2313yes—
106C4⋊(C59⋊C8)C2311yescharacteristic
107C4⋊(C59⋊C8)C2313yes—
108C4⋊(C59⋊C8)C2313yes—
109C4⋊(C59⋊C8)C2313yes—
110C4⋊(C59⋊C8)C2316yes—
111C22⋊(C59⋊C8)C2313yes—
112C22⋊(C59⋊C8)C2313yes—
113C22⋊(C59⋊C8)C2316yes—
114C22⋊(C59⋊C8)C2316yes—
115C22⋊(C59⋊C8)C2311yescharacteristic
116C22⋊(C59⋊C8)C2311yescharacteristic
117C22⋊(C59⋊C8)C2313yes—
118C22⋊(C59⋊C8)C2313yes—
119C22⋊(C59⋊C8)C2313yes—
120C22⋊(C59⋊C8)C2313yes—
121#14273638C2311yescharacteristic
122#14273638C2313yes—
123#14273638C2313yes—
124#14273638C2313yes—
125C4×C59⋊C8C2316yes—
126C2×#41×C59—24no—
127C2×#41×C59—24no—
128C2×#41×C59—24no—
129C2×#41×C59—24no—
130C2×#41×C59C2×C413yes—
131C2×#41×C59C2×C413yes—
132C2×#41×C59C2×C411yescharacteristic
133C2×#41×C59C2×C411yescharacteristic
134C2×#41×C59C2313yes—
135C2×#41×C59C2313yes—
136C2×#41×C59C2311yescharacteristic
137C22×Q8×C59C2×C411yescharacteristic
138C22×Q8×C59C2×C411yescharacteristic
139C22×D4×C59C2×C413yes—
140C22×D4×C59C2×C413yes—
141C22×D4×C59C2×C413yes—
142C23×C4×C59C2313yes—
143C23×C4×C59C2313yes—
144C4⋊Q8×C59C2×C413yes—
145#127×C59C2×C413yes—
146#124×C59C2×C413yes—
147#124×C59C2×C413yes—
148#123×C59C2×C416yes—
149#123×C59C2×C416yes—
150C22⋊Q8×C59C2×C413yes—
151C22⋊Q8×C59C2×C413yes—
152C22⋊Q8×C59C2×C413yes—
153C22⋊Q8×C59C2×C413yes—
154#121×C59C2×C413yes—
155#121×C59C2×C413yes—
156#121×C59C2×C413yes—
157#121×C59C2×C413yes—
158#121×C59C2×C416yes—
159#121×C59C2×C416yes—
160#120×C59C2×C416yes—
161#120×C59C2×C416yes—
162C4×Q8×C59C2×C411yescharacteristic
163C4×Q8×C59C2×C411yescharacteristic
164C4×D4×C59C2×C413yes—
165C4×D4×C59C2×C413yes—
166C4×D4×C59C2×C413yes—
167C4×D4×C59C2×C413yes—
168C4×D4×C59C2×C413yes—
169C4×D4×C59C2×C413yes—
170C4×D4×C59C2313yes—
171C4×D4×C59C2316yes—
172C4×D4×C59C2311yescharacteristic
173C4×D4×C59C2313yes—
174C4×D4×C59C2313yes—
175#117×C59C2313yes—
176C2×C4⋊C4×C59C2×C413yes—
177C2×C22⋊C4×C59C2×C413yes—
178C2×C22⋊C4×C59C2×C413yes—
179C2×C42×C59C2313yes—
180C24×C59C22×C413yes—
181C24×C59C22×C413yes—
182#41×C59—24no—
183#41×C59—24no—
184#41×C59—212no—
185#41×C59—212no—
186#41×C59—26no—
187#41×C59—26no—
188#41×C59—26no—
189#41×C59—26no—
190#41×C59C2×D414yes—
191#41×C59#4114yes—
192C2×Q8×C59—24no—
193C2×Q8×C59—24no—
194C2×Q8×C59C22×C413yes—
195C2×Q8×C59C22×C413yes—
196C2×Q8×C59C22×C411yescharacteristic
197C2×D4×C59—212no—
198C2×D4×C59—212no—
199C2×D4×C59—46no—
200C2×D4×C59C22×C411yescharacteristic
201C2×D4×C59C22×C413yes—
202C2×D4×C59C22×C416yes—
203C2×D4×C59C22×C416yes—
204C2×D4×C59C22×C413yes—
205C2×D4×C59C22×C413yes—
206C2×D4×C59C22×C413yes—
207C2×D4×C59C22×C413yes—
208C2×D4×C59C22×C416yes—
209C2×D4×C59C22×C413yes—
210C22×C4×C59—26no—
211C22×C4×C59—26no—
212C22×C4×C59—26no—
213C22×C4×C59—26no—
214C22×C4×C59C22×C413yes—
215C22×C4×C59C22×C413yes—
216C22×C4×C59C22×C413yes—
217C22×C4×C59C22×C413yes—
218C22×C4×C59C22×C413yes—
219C22×C4×C59C22×C413yes—
220C22×C4×C59C22×C413yes—
221C22×C4×C59C22×C413yes—
222C22×C4×C59C2411yescharacteristic
223C22×C4×C59C2411yescharacteristic
224C22×C4×C59C2413yes—
225C22×C4×C59C2413yes—
226C22×C4×C59C2413yes—
227C4⋊C4×C59C22×C411yescharacteristic
228C4⋊C4×C59C22×C413yes—
229C4⋊C4×C59C22×C413yes—
230C4⋊C4×C59C22×C413yes—
231C4⋊C4×C59C22×C413yes—
232C4⋊C4×C59C22×C413yes—
233C4⋊C4×C59C22×C416yes—
234C22⋊C4×C59C22×C411yescharacteristic
235C22⋊C4×C59C22×C411yescharacteristic
236C22⋊C4×C59C22×C413yes—
237C22⋊C4×C59C22×C413yes—
238C22⋊C4×C59C22×C413yes—
239C22⋊C4×C59C22×C413yes—
240C22⋊C4×C59C22×C413yes—
241C22⋊C4×C59C22×C413yes—
242C22⋊C4×C59C22×C416yes—
243C22⋊C4×C59C22×C416yes—
244C22⋊C4×C59C22×C416yes—
245C42×C59C22×C413yes—
246C42×C59C22×C413yes—
247C42×C59C2411yescharacteristic
248C42×C59C2413yes—
249#11745664—26no—
250#11745664—26no—
251#11745664—26no—
252#11745664—22no—
253#11745664—26no—
254#11745664—26no—
255#11745664—212no—
256#11745664—26no—
257#11745664C2×D4112yescomplemented
258C2×C59⋊C8—26no—
259C2×C59⋊C8—26no—
260C2×C59⋊C8—26no—
261C2×C59⋊C8—22no—
262C2×C59⋊C8—26no—
263C2×C59⋊C8—26no—
264C2×C59⋊C8—26no—
265C2×C59⋊C8—212no—
266C2×C59⋊C8C2×D4112yescomplemented
267C2×C59⋊C8C2413yes—
268C2×C59⋊C8C2411yescharacteristic
269C2×C59⋊C8C2411yescharacteristic
270C2×C59⋊C8C2413yes—
271C2×C59⋊C8C2413yes—
272C2×C59⋊C8C2411yescharacteristic
273C2×C59⋊C8C2413yes—
274C2×C59⋊C8C2411yescharacteristic
275C23×C59—26no—
276C23×C59—26no—
277C23×C59—26no—
278C23×C59—43no—
279C23×C59—43no—
280C23×C59—43no—
281C23×C59C23×C411yescharacteristic
282C23×C59C23×C413yes—
283C23×C59C23×C413yes—
284C23×C59C23×C413yes—
285C23×C59C23×C411yescharacteristic
286Q8×C59—26no—
287Q8×C59—26no—
288Q8×C59C4×D414yes—
289D4×C59—212no—
290D4×C59—212no—
291D4×C59—22no—
292D4×C59—26no—
293D4×C59—26no—
294D4×C59—26no—
295D4×C59—43no—
296D4×C59—43no—
297D4×C59—46no—
298D4×C59C4×D4112yes—
299C2×C4×C59—26no—
300C2×C4×C59—26no—
301C2×C4×C59—26no—
302C2×C4×C59—26no—
303C2×C4×C59—26no—
304C2×C4×C59—26no—
305C2×C4×C59—21no—
306C2×C4×C59—23no—
307C2×C4×C59—23no—
308C2×C4×C59—21no—
309C2×C4×C59—21no—
310C2×C4×C59—21no—
311C2×C4×C59—23no—
312C2×C4×C59—23no—
313C2×C4×C59—43no—
314C2×C4×C59—43no—
315C2×C4×C59C23×C411yescharacteristic
316C2×C4×C59C23×C411yescharacteristic
317C2×C4×C59C23×C413yes—
318C2×C4×C59C23×C413yes—
319C2×C4×C59C23×C411yescharacteristic
320C2×C4×C59C23×C411yescharacteristic
321C2×C4×C59C23×C413yes—
322C2×C4×C59C23×C413yes—
323C2×C4×C59C23×C413yes—
324C2×C4×C59C22×D416yes—
325C2×C4×C59C2×#4116yes—
326C2×C4×C59C2511yescharacteristic
327C59⋊C8—21no—
328C59⋊C8—23no—
329C59⋊C8—21no—
330C59⋊C8—23no—
331C59⋊C8—21no—
332C59⋊C8—23no—
333C59⋊C8C22×D412yes—
334C59⋊C8C22×D416yes—
335#60146—591nomaximal, Sylow
336C22×C59—21no—
337C22×C59—23no—
338C22×C59—23no—
339C22×C59—21no—
340C22×C59—21no—
341C22×C59—23no—
342C22×C59—23no—
343C22×C59—21no—
344C22×C59—23no—
345C22×C59—23no—
346C22×C59—23no—
347C22×C59—23no—
348C22×C59—21no—
349C22×C59—412no—
350C22×C59—86no—
351C22×C59C2×C4×D416yes—
352C22×C59#56812yescomplemented
353C22×C59C24×C411yescharacteristic
354C4×C59—21no—
355C4×C59—21no—
356C4×C59—23no—
357C4×C59—23no—
358C4×C59—21no—
359C4×C59—23no—
360C4×C59—21no—
361C4×C59—23no—
362C4×C59C2×C4×D416yes—
363C4×C59C23×D411yescharacteristic
364C4×C59C22×#4111yescharacteristic
365C2×#568—591no—
366C22×#131—591no—
367D4×#41D5911yescharacteristic
368#2935—593no—
369D4×M16—593no—
370#2933—593no—
371#2933—593no—
372#2932—593no—
373#2930—593no—
374#2929—593no—
375C2×#435—593no—
376#2906—591no—
377#2880—591no—
378#2880—591no—
379#2875—591no—
380C2×C59—22no—
381C2×C59—26no—
382C2×C59—43no—
383C2×C59—43no—
384C2×C59—41no—
385C2×C59C22×C4×D411yescharacteristic
386C2×C59C2×#56811yescharacteristic
387C2×C59#357311yescharacteristic
388C22×#41C2×D5911yescharacteristic
389C22×#41C2×D5911yescharacteristic
390#568—1188no—
391C2×#131—591no—
392C2×#131—591no—
393C2×#131—591no—
394C2×#131—591no—
395C2×#131—593no—
396C2×#131—593no—
397C2×#131—593no—
398C2×#131—593no—
399C2×#131—1188no—
400C22×M16—593no—
401C22×M16—593no—
402C22×M16—593no—
403C23×C8—593no—
404#550Dic5911yescharacteristic
405D4×Q8Dic5911yescharacteristic
406#548Dic5911yescharacteristic
407#548Dic5911yescharacteristic
408#547Dic5913yes—
409#546Dic5913yes—
410#546Dic5913yes—
411D42Dic5913yes—
412#532C2×D5913yes—
413#525C2×D5913yes—
414#525C2×D5913yes—
415C4×#41C2×D5911yescharacteristic
416C2×C4×D4C2×D5913yes—
417#436—596no—
418#436—596no—
419#435—591no—
420#435—593no—
421#435—593no—
422#435—593no—
423#435—593no—
424#435—593no—
425#435—593no—
426#435—593no—
427#435—596no—
428#435—596no—
429#435—596no—
430C8×D4—596no—
431C8×D4—596no—
432#424—593no—
433#424—593no—
434#423—593no—
435C2×C4⋊C8—593no—
436#408—593no—
437#408—593no—
438#408—593no—
439#408—593no—
440#407—593no—
441#407—593no—
442C2×C22⋊C8—593no—
443C2×C22⋊C8—593no—
444#405—593no—
445#405—593no—
446C4×M16—593no—
447C2×#97—593no—
448C59#6014611yescharacteristic, complemented, Sylow
449C2×#41—24no—
450C2×#41—24no—
451C2×#41—24no—
452C2×#41—24no—
453C2×#41C2×Dic5913yes—
454C2×#41C2×Dic5913yes—
455C2×#41C2×Dic5911yescharacteristic
456C2×#41C2×Dic5911yescharacteristic
457C2×#41C22×D5913yes—
458C2×#41C22×D5913yes—
459C2×#41C22×D5911yescharacteristic
460C22×Q8C2×Dic5911yescharacteristic
461C22×Q8C2×Dic5911yescharacteristic
462C22×D4C2×Dic5913yes—
463C22×D4C2×Dic5913yes—
464C22×D4C2×Dic5913yes—
465C23×C4C22×D5913yes—
466C23×C4C22×D5913yes—
467#131—598no—
468#131—11812no—
469#131—11812no—
470#131—11812no—
471#131—11812no—
472#131—1184no—
473#131—1184no—
474#131—1184no—
475C2×M16—593no—
476C2×M16—591no—
477C2×M16—593no—
478C2×M16—593no—
479C2×M16—593no—
480C2×M16—593no—
481C2×M16—593no—
482C2×M16—596no—
483C2×M16—593no—
484C2×M16—11812no—
485C2×M16—11812no—
486C2×M16—11812no—
487C22×C8—593no—
488C22×C8—591no—
489C22×C8—593no—
490C22×C8—593no—
491C22×C8—593no—
492C22×C8—593no—
493C22×C8—593no—
494C22×C8—596no—
495C22×C8—593no—
496C22×C8—11812no—
497C4⋊Q8C2×Dic5913yes—
498#127C2×Dic5913yes—
499#124C2×Dic5913yes—
500#124C2×Dic5913yes—
501#123C2×Dic5916yes—
502#123C2×Dic5916yes—
503C22⋊Q8C2×Dic5913yes—
504C22⋊Q8C2×Dic5913yes—
505C22⋊Q8C2×Dic5913yes—
506C22⋊Q8C2×Dic5913yes—
507#121C2×Dic5913yes—
508#121C2×Dic5913yes—
509#121C2×Dic5913yes—
510#121C2×Dic5913yes—
511#121C2×Dic5916yes—
512#121C2×Dic5916yes—
513#120C2×Dic5916yes—
514#120C2×Dic5916yes—
515C4×Q8C2×Dic5911yescharacteristic
516C4×Q8C2×Dic5911yescharacteristic
517C4×D4C2×Dic5913yes—
518C4×D4C2×Dic5913yes—
519C4×D4C2×Dic5913yes—
520C4×D4C2×Dic5913yes—
521C4×D4C2×Dic5913yes—
522C4×D4C2×Dic5913yes—
523C4×D4C22×D5911yescharacteristic
524C4×D4C22×D5913yes—
525C4×D4C22×D5913yes—
526C4×D4C22×D5913yes—
527C4×D4C22×D5916yes—
528#117C22×D5913yes—
529C2×C4⋊C4C2×Dic5913yes—
530C2×C22⋊C4C2×Dic5913yes—
531C2×C22⋊C4C2×Dic5913yes—
532C2×C42C22×D5913yes—
533C4⋊C8—591no—
534C4⋊C8—593no—
535C4⋊C8—593no—
536C4⋊C8—593no—
537C4⋊C8—596no—
538C22⋊C8—591no—
539C22⋊C8—591no—
540C22⋊C8—593no—
541C22⋊C8—593no—
542C22⋊C8—593no—
543C22⋊C8—593no—
544C22⋊C8—593no—
545C22⋊C8—593no—
546C22⋊C8—596no—
547C22⋊C8—596no—
548#97—591no—
549#97—593no—
550#97—593no—
551#97—593no—
552C4×C8—596no—
553C24C22×Dic5913yes—
554C24C22×Dic5913yes—
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×D5914yes—
564#41#1174568714yes—
565C2×Q8—24no—
566C2×Q8—24no—
567C2×Q8C22×Dic5913yes—
568C2×Q8C22×Dic5913yes—
569C2×Q8C22×Dic5911yescharacteristic
570C2×D4—212no—
571C2×D4—212no—
572C2×D4—46no—
573C2×D4C22×Dic5911yescharacteristic
574C2×D4C22×Dic5913yes—
575C2×D4C22×Dic5916yes—
576C2×D4C22×Dic5916yes—
577C2×D4C22×Dic5913yes—
578C2×D4C22×Dic5913yes—
579C2×D4C22×Dic5913yes—
580C2×D4C22×Dic5913yes—
581C2×D4C22×Dic5916yes—
582C2×D4C22×Dic5913yes—
583C22×C4—26no—
584C22×C4—26no—
585C22×C4—26no—
586C22×C4—26no—
587C22×C4C22×Dic5913yes—
588C22×C4C22×Dic5913yes—
589C22×C4C22×Dic5913yes—
590C22×C4C22×Dic5913yes—
591C22×C4C22×Dic5913yes—
592C22×C4C22×Dic5913yes—
593C22×C4C22×Dic5913yes—
594C22×C4C22×Dic5913yes—
595C22×C4C23×D5911yescharacteristic
596C22×C4C23×D5913yes—
597C22×C4C23×D5913yes—
598C22×C4C23×D5911yescharacteristic
599C22×C4C23×D5913yes—
600M16—5912no—
601M16—1182no—
602M16—1186no—
603M16—1186no—
604M16—1186no—
605M16—11812no—
606M16—1186no—
607M16—1186no—
608M16—1186no—
609C2×C8—5912no—
610C2×C8—593no—
611C2×C8—591no—
612C2×C8—593no—
613C2×C8—591no—
614C2×C8—591no—
615C2×C8—591no—
616C2×C8—593no—
617C2×C8—593no—
618C2×C8—1182no—
619C2×C8—1186no—
620C2×C8—1186no—
621C2×C8—1186no—
622C2×C8—11812no—
623C2×C8—1186no—
624C2×C8—1186no—
625C2×C8—1186no—
626C4⋊C4C22×Dic5911yescharacteristic
627C4⋊C4C22×Dic5913yes—
628C4⋊C4C22×Dic5913yes—
629C4⋊C4C22×Dic5913yes—
630C4⋊C4C22×Dic5913yes—
631C4⋊C4C22×Dic5913yes—
632C4⋊C4C22×Dic5916yes—
633C22⋊C4C22×Dic5911yescharacteristic
634C22⋊C4C22×Dic5911yescharacteristic
635C22⋊C4C22×Dic5913yes—
636C22⋊C4C22×Dic5913yes—
637C22⋊C4C22×Dic5913yes—
638C22⋊C4C22×Dic5913yes—
639C22⋊C4C22×Dic5913yes—
640C22⋊C4C22×Dic5913yes—
641C22⋊C4C22×Dic5916yes—
642C22⋊C4C22×Dic5916yes—
643C22⋊C4C22×Dic5916yes—
644C42C22×Dic5913yes—
645C42C22×Dic5913yes—
646C42C23×D5913yes—
647C42C23×D5911yescharacteristic
648C23—26no—
649C23—26no—
650C23—26no—
651C23—43no—
652C23—43no—
653C23—43no—
654C23C23×Dic5911yescharacteristic
655C23C23×Dic5913yes—
656C23C23×Dic5913yes—
657C23C23×Dic5911yescharacteristic
658C23C23×Dic5913yes—
659Q8—26no—
660Q8—26no—
661Q8D4×Dic5914yes—
662D4—22no—
663D4—26no—
664D4—212no—
665D4—212no—
666D4—26no—
667D4—26no—
668D4—43no—
669D4—43no—
670D4—46no—
671D4D4×Dic59112yes—
672C2×C4—26no—
673C2×C4—26no—
674C2×C4—21no—
675C2×C4—23no—
676C2×C4—23no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—23no—
681C2×C4—23no—
682C2×C4—26no—
683C2×C4—26no—
684C2×C4—26no—
685C2×C4—26no—
686C2×C4—43no—
687C2×C4—43no—
688C2×C4C23×Dic5911yescharacteristic
689C2×C4C23×Dic5911yescharacteristic
690C2×C4C23×Dic5913yes—
691C2×C4C23×Dic5913yes—
692C2×C4C23×Dic5911yescharacteristic
693C2×C4C23×Dic5911yescharacteristic
694C2×C4C23×Dic5913yes—
695C2×C4C23×Dic5913yes—
696C2×C4C23×Dic5913yes—
697C2×C4C2×D4×D5916yes—
698C2×C4C2×#1174568716yes—
699C2×C4C24×D5911yescharacteristic
700C8—592no—
701C8—596no—
702C8—1181no—
703C8—1183no—
704C8—1183no—
705C8—1181no—
706C8—1181no—
707C8—1183no—
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×Dic5916yes—
724C22#1683816912yescomplemented
725C22C24×Dic5911yescharacteristic
726C4—21no—
727C4—21no—
728C4—23no—
729C4—23no—
730C4—21no—
731C4—23no—
732C4—21no—
733C4—23no—
734C4C2×D4×Dic5916yes—
735C4C22×D4×D5911yescharacteristic
736C4C22×#1174568711yescharacteristic
737C2—22no—
738C2—26no—
739C2—43no—
740C2—41no—
741C2—43no—
742C2C22×D4×Dic5911yescharacteristic
743C2C2×#1683816911yescharacteristic
744C2#2143880811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D59
commutator, socleC22×C59C24×C4
Fitting, prime radicalD4×#41×C59C2
cosocleC2×C4×C59C25
hypercenterD4×#41D59
hypocenterC59#60146
LCSG ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ D4×#41

Complements

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

NH ≅ G/Ntype
1. C2×#16838169C2semidirect
2. C22×#14273734C2semidirect
3. #21432840C2semidirect
4. D4×#11745664C2semidirect
5. #21432823C2semidirect
6. #21432823C2semidirect
7. #21432814C2semidirect
8. #21432800C2semidirect
9. #21432791C2semidirect
10. C2×#16837474C2semidirect
11. #21432664C2semidirect
12. #21432545C2semidirect
13. #21432545C2semidirect
14. #21432524C2semidirect
22. C2×#14273734C22semidirect
23. C2×#14273734C22semidirect
24. C2×#14273734C22semidirect
25. C2×#14273734C22semidirect
26. C22×#11745664C22semidirect
27. C22×#11745664C22semidirect
28. C22×#11745664C22semidirect
29. C23×C59⋊C8C22semidirect
30. #16837480C22semidirect
31. #16837480C22semidirect
34. #16837474C22semidirect
35. #16837474C22semidirect
36. #16837474C22semidirect
37. #16837474C22semidirect
38. #16837474C22semidirect
39. #16837474C22semidirect
40. #16837474C22semidirect
41. #16837474C22semidirect
42. #16837474C22semidirect
43. D4×C59⋊C8C22semidirect
44. D4×C59⋊C8C22semidirect
45. #16837429C22semidirect
46. #16837429C22semidirect
47. #16837426C22semidirect
48. C2×C4⋊(C59⋊C8)C22semidirect
49. #16837369C22semidirect
50. #16837369C22semidirect
51. #16837369C22semidirect
52. #16837369C22semidirect
53. #16837366C22semidirect
54. #16837366C22semidirect
55. C2×C22⋊(C59⋊C8)C22semidirect
56. C2×C22⋊(C59⋊C8)C22semidirect
57. #16837358C22semidirect
58. #16837358C22semidirect
59. C4×#11745664C22semidirect
60. C2×#14273638C22semidirect
83. #14273734D4semidirect
257. #11745664C2×D4semidirect
266. C2×C59⋊C8C2×D4semidirect
352. C22×C59#568semidirect
448. C59#60146semidirect
724. C22#16838169semidirect

Maximal subgroups

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

subgroupindex
C2×#168381692
C22×#142737342
#214328402
D4×#117456642
#214328232
#214328142
#214328002
#214327912
C2×#168374742
#214326642
#214325452
#214325242
D4×#41×C592
#6014659