Finite Group Databasebeta

← #29648261

Subgroups — #29648261

Order 15616.

876 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459640C211yesmaximal, characteristic
2#21454830C211yesmaximal, characteristic
3#21454828C211yesmaximal, characteristic
4#21444455C211yesmaximal, characteristic, complemented
5#21444445C211yesmaximal, characteristic, complemented
6#21444444C211yesmaximal, characteristic, complemented
7#21444434C211yesmaximal, characteristic, complemented
8#21444432C211yesmaximal, characteristic, complemented
9#21444432C211yesmaximal, characteristic, complemented
10#21444419C211yesmaximal, characteristic, complemented
11#21444419C211yesmaximal, characteristic, complemented
12#21444412C211yesmaximal, characteristic, complemented
13C2×#16839503C211yesmaximal, characteristic, complemented
14#330×D61C211yesmaximal, characteristic, complemented
15C61×#1531C211yesmaximal, characteristic, complemented
16#16840490—21no—
17#16840490—21no—
18#16840472—21no—
19#16840472—21no—
20#16840466—21no—
21#16840466—21no—
22#16840466—21no—
23#16840466—21no—
24#16840390C411yescharacteristic
25#16840390C411yescharacteristic
26#16840389C411yescharacteristic
27#16840389C411yescharacteristic
28#16840389C411yescharacteristic
29#16840389C411yescharacteristic
30#16840318C2211yescharacteristic
31#16840318C2211yescharacteristic
32C2×#14519769C2211yescharacteristic
33#125×D61C2211yescharacteristic
34#125×D61C2211yescharacteristic
35#16840242C411yescharacteristic
36#16840242C411yescharacteristic
37C4×#11758222C2211yescharacteristic
38#16839891—21no—
39#16839890—21no—
40#16839835—21no—
41#16839833—21no—
42#16839832—21no—
43#16839830—21no—
44C8×C22⋊D61—21no—
45#16839825—21no—
46#16839819C2211yescharacteristic
47#16839817C2211yescharacteristic
48#16839817C2211yescharacteristic
49#16839817C2211yescharacteristic
50#16839817C2211yescharacteristic
51#16839714C2211yescharacteristic
52#16839714C2211yescharacteristic
53C2×#14519688C2211yescharacteristic
54#97×D61C2211yescharacteristic
55#97×D61C2211yescharacteristic
56#16839504C2211yescharacteristic
57#16839504C2211yescharacteristic
58#16839504C2211yescharacteristic
59#16839504C2211yescharacteristic
60#16839503C2211yescharacteristic
61#16839503C2211yescharacteristic
62#16839503C2211yescharacteristic
63#16839503C2211yescharacteristic
64#16839503C2211yescharacteristic
65#16839503C2211yescharacteristic
66#16839503C2211yescharacteristic
67#16839503C2211yescharacteristic
68C61×#533C2211yescharacteristic
69C61×#432C2211yescharacteristic
70C2×#97×C61C2211yescharacteristic
71C61×#330C2211yescharacteristic
72C61×#330C2211yescharacteristic
73C61×#330C2211yescharacteristic
74C61×#330C2211yescharacteristic
75C2×#11758222C2×C411yescharacteristic
76C2×#11758189—21no—
77C2×#11758189—21no—
78C22×#92418—21no—
79C2×C8×D61—21no—
80C2×C8×D61—21no—
81#14519777—21no—
82#14519777—21no—
83#14519776C2×C411yescharacteristic
84#14519776C2×C411yescharacteristic
85#14519776C2×C411yescharacteristic
86#14519776C2×C411yescharacteristic
87#14519775—21no—
88#14519775—21no—
89#14519775—21no—
90#14519775—21no—
91#14519769—21no—
92#14519769—21no—
93#14519769—21no—
94#14519769—21no—
95#14519769C2×C411yescharacteristic
96#14519769C2×C411yescharacteristic
97#14519769C2311yescharacteristic
98#14519769C2311yescharacteristic
99#14519768C2×C411yescharacteristic
100#14519768C2×C411yescharacteristic
101#14519768C2×C411yescharacteristic
102#14519768C2×C411yescharacteristic
103#14519767—21no—
104#14519767—21no—
105#14519767—21no—
106#14519767—21no—
107#14519767—21no—
108#14519767—21no—
109#14519767—21no—
110#14519767—21no—
111#14519755—21no—
112#14519755—21no—
113#14519755—21no—
114#14519755—21no—
115#14519755—21no—
116#14519755—21no—
117#14519755—21no—
118#14519755—21no—
119#14519754—21no—
120#14519754—21no—
121#14519754—21no—
122#14519754—21no—
123#14519753—21no—
124#14519753—21no—
125#14519753—21no—
126#14519753—21no—
127C4×Dic122—21no—
128C4×Dic122—21no—
129C4×Dic122D411yescharacteristic
130C4×Dic122D411yescharacteristic
131#14519742—21no—
132#14519742—21no—
133#14519742—21no—
134#14519742—21no—
135C4×D244—21no—
136C4×D244—21no—
137C4×D244D411yescharacteristic
138C4×D244D411yescharacteristic
139C4×C22⋊D61D411yescharacteristic
140C4×C22⋊D61D411yescharacteristic
141C4×C22⋊D61D411yescharacteristic
142C4×C22⋊D61D411yescharacteristic
143#14519737—21no—
144#14519737—21no—
145#14519737—21no—
146#14519737—21no—
147#14519736C2×C411yescharacteristic
148#14519735C2×C411yescharacteristic
149#14519735C2×C411yescharacteristic
150#14519735C2×C411yescharacteristic
151#14519735C2×C411yescharacteristic
152#14519734C2×C411yescharacteristic
153#14519734C2×C411yescharacteristic
154C2×C4⋊Dic61C2×C411yescharacteristic
155C2×C4⋊Dic61C2×C411yescharacteristic
156C2×#11758196—21no—
157C2×#11758196—21no—
158C4⋊C4×D61—21no—
159C4⋊C4×D61—21no—
160C4⋊C4×D61—21no—
161C4⋊C4×D61—21no—
162C4⋊C4×D61C2×C411yescharacteristic
163C4⋊C4×D61C2×C411yescharacteristic
164C4⋊C4×D61C2×C411yescharacteristic
165C4⋊C4×D61C2×C411yescharacteristic
166C42×D61C2311yescharacteristic
167C42×D61C2311yescharacteristic
168C4⋊#92418—21no—
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418—21no—
174#14519689—21no—
175#14519689—21no—
176#14519689—21no—
177#14519689—21no—
178#14519688—21no—
179#14519688C2311yescharacteristic
180#14519688C2311yescharacteristic
181#14519688C2311yescharacteristic
182#14519688C2311yescharacteristic
183#14519687—21no—
184#14519687—21no—
185C8×Dic61—21no—
186C8×Dic61—21no—
187C22×C8×C61—21no—
188C4⋊Q8×C61C2×C411yescharacteristic
189C4⋊Q8×C61C2×C411yescharacteristic
190#125×C61C2311yescharacteristic
191#125×C61C2311yescharacteristic
192C22⋊Q8×C61—21no—
193C22⋊Q8×C61—21no—
194C4×Q8×C61—21no—
195C4×Q8×C61—21no—
196#117×C61C2×C411yescharacteristic
197#117×C61C2×C411yescharacteristic
198C2×C42×C61C2311yescharacteristic
199C4⋊C8×C61—21no—
200C22⋊C8×C61—21no—
201#97×C61—21no—
202#97×C61C2311yescharacteristic
203#97×C61C2311yescharacteristic
204#97×C61C2311yescharacteristic
205#97×C61C2311yescharacteristic
206C2×Q8×C61—21no—
207C2×Q8×C61—21no—
208C22×C4×C61C22×C411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C2×C22⋊D61C22⋊C411yescharacteristic
212C2×C22⋊D61C22⋊C411yescharacteristic
213C22×Dic61—21no—
214C22×Dic61—21no—
215#11758222—24no—
216C2×D244C22⋊C411yescharacteristic
217C2×C4×D61—21no—
218C2×C4×D61—21no—
219C2×C4×D61—21no—
220C2×C4×D61—21no—
221C2×C4×D61C22×C411yescharacteristic
222C2×C4×D61C22×C411yescharacteristic
223C2×C4×D61C2×D411yescharacteristic
224C2×C4×D61C2×D411yescharacteristic
225C2×C4×D61C2×D411yescharacteristic
226C2×C4×D61C2×D411yescharacteristic
227C2×Dic122—21no—
228C2×Dic122—21no—
229C2×Dic122—21no—
230C2×Dic122—21no—
231C2×Dic122C22⋊C411yescharacteristic
232C2×C8×C61—21no—
233C2×C8×C61—21no—
234C2×C8×C61—21no—
235C2×C8×C61—21no—
236C2×C8×C61—42no—
237C4⋊C4×C61—21no—
238C4⋊C4×C61—21no—
239C4⋊C4×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61C22×C411yescharacteristic
244C4⋊C4×C61C22×C411yescharacteristic
245C4⋊C4×C61C22×C411yescharacteristic
246C4⋊C4×C61C22×C411yescharacteristic
247C22⋊C4×C61—21no—
248C22⋊C4×C61—21no—
249C42×C61—21no—
250C42×C61—21no—
251C42×C61C22×C411yescharacteristic
252C42×C61C2×D411yescharacteristic
253C42×C61C2×D411yescharacteristic
254C42×C61C2411yescharacteristic
255C22⋊Dic61C22⋊C411yescharacteristic
256C22⋊Dic61C22⋊C411yescharacteristic
257#11758198—21no—
258#11758198—21no—
259#11758198—21no—
260#11758198—21no—
261#11758198C22⋊C411yescharacteristic
262#11758198C22⋊C411yescharacteristic
263#11758198C22⋊C411yescharacteristic
264#11758198C22⋊C411yescharacteristic
265C4⋊Dic61—21no—
266C4⋊Dic61—21no—
267C4⋊Dic61—21no—
268C4⋊Dic61—21no—
269C4⋊Dic61—21no—
270C4⋊Dic61—21no—
271C4⋊Dic61C22⋊C411yescharacteristic
272C4⋊Dic61C22⋊C411yescharacteristic
273C4⋊Dic61C22×C411yescharacteristic
274C4⋊Dic61C22×C411yescharacteristic
275C4⋊Dic61C22×C411yescharacteristic
276C4⋊Dic61C22×C411yescharacteristic
277#11758196—21no—
278#11758196—21no—
279#11758196—21no—
280#11758196—21no—
281#11758196—21no—
282#11758196—21no—
283#11758196—21no—
284#11758196—21no—
285#11758196—21no—
286#11758196—21no—
287#11758196—21no—
288#11758196—21no—
289#11758196—21no—
290#11758196—21no—
291#11758196—21no—
292#11758196—21no—
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196C22⋊C411yescharacteristic
298#11758196C22⋊C411yescharacteristic
299#11758196C22⋊C411yescharacteristic
300#11758196C22⋊C411yescharacteristic
301C4×Dic61—21no—
302C4×Dic61—21no—
303C4×Dic61—21no—
304C4×Dic61—21no—
305C4×Dic61C22×C411yescharacteristic
306C4×Dic61C22×C411yescharacteristic
307C4×Dic61C2×D411yescharacteristic
308C4×Dic61C2×D411yescharacteristic
309C4×Dic61C2×D411yescharacteristic
310C4×Dic61C2×D411yescharacteristic
311C2×#92418—21no—
312C2×#92418—21no—
313C2×#92418—21no—
314C2×#92418—21no—
315C2×#92418—42no—
316#11758189—42no—
317#11758189—42no—
318C8×D61—42no—
319C8×D61—42no—
320C23×C61C2×C22⋊C411yescharacteristic
321C22×D61C2×C22⋊C411yescharacteristic
322C22×D61C2×C22⋊C411yescharacteristic
323Q8×C61—81no—
324Q8×C61—81no—
325C2×C4×C61—22no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—21no—
329C2×C4×C61—21no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61C2×C22⋊C411yescharacteristic
333C2×C4×C61C2×C22⋊C411yescharacteristic
334C2×C4×C61C2×C22⋊C411yescharacteristic
335C2×C4×C61C23×C411yescharacteristic
336C2×C4×C61C22×D411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C22⋊D61—22no—
339C22⋊D61#10114yes—
340C2×Dic61—21no—
341C2×Dic61—21no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—81no—
345C2×Dic61—81no—
346C2×Dic61C2×C22⋊C411yescharacteristic
347C2×Dic61C2×C22⋊C411yescharacteristic
348C2×Dic61C2×C22⋊C411yescharacteristic
349C2×Dic61C2×C22⋊C411yescharacteristic
350C2×Dic61C2×C22⋊C411yescharacteristic
351C2×Dic61C2×C22⋊C411yescharacteristic
352D244—22no—
353C4×D61—22no—
354C4×D61—22no—
355C4×D61—41no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—81no—
360C4×D61—81no—
361C4×D61—81no—
362C4×D61—81no—
363Dic122—22no—
364Dic122—81no—
365Dic122—81no—
366Dic122—81no—
367Dic122—81no—
368C8×C61—22no—
369C8×C61—41no—
370C8×C61—41no—
371C8×C61—41no—
372#92418—22no—
373#92418—41no—
374#92418—41no—
375#92418—41no—
376#17689—611nomaximal, Sylow
377C22×C61—21no—
378C22×C61—21no—
379C22×C61C2×#10112yes—
380C22×C61C22×C22⋊C411yescharacteristic
381C2×D61—21no—
382C2×D61—21no—
383C2×D61—21no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61C2×#10112yes—
387C4×C61—21no—
388C4×C61—21no—
389C4×C61—21no—
390C4×C61—21no—
391C4×C61—21no—
392C4×C61—21no—
393C4×C61—41no—
394C4×C61—41no—
395C4×C61—41no—
396C4×C61—41no—
397Dic61—21no—
398Dic61—21no—
399Dic61—21no—
400Dic61—21no—
401Dic61—21no—
402Dic61—41no—
403Dic61—41no—
404Dic61—41no—
405Dic61—41no—
406Dic61C2×#10112yes—
407#3504—611no—
408#2970—611no—
409#2970—611no—
410#1537—611no—
411#1534—611no—
412#1534—611no—
413#1531—611no—
414#1531—611no—
415#1531—611no—
416#1531D6111yescharacteristic, complemented
417#1528—611no—
418#1528—611no—
419#1526—611no—
420C2×#330—611no—
421C2×#330—611no—
422C2×C61—22no—
423C2×C61C22×#10111yescharacteristic
424C2×C61#290111yescharacteristic
425C2×C61#290111yescharacteristic
426D61—22no—
427D61—41no—
428#557—1221no—
429#557—1221no—
430#554—1221no—
431#554—1221no—
432#554—1221no—
433#554—1221no—
434#554—1221no—
435#554—1221no—
436#544—611no—
437#544—611no—
438#544—611no—
439#544—611no—
440#544—611no—
441#544—611no—
442#533—611no—
443#533—611no—
444#533C2×D6111yescharacteristic
445C2×#125—611no—
446C2×#125—611no—
447C2×#125—611no—
448#520—611no—
449#520—611no—
450C4×#41—611no—
451#446—1221no—
452#446—1221no—
453#435—1221no—
454#435—1221no—
455#435—1221no—
456#435—1221no—
457C8×D4—1221no—
458C8×D4—1221no—
459#432—611no—
460#432—611no—
461#432—611no—
462#432—611no—
463#432—611no—
464#432C2×D6111yescharacteristic
465C4×M16—611no—
466C4×M16—611no—
467C2×#97—611no—
468C2×#97—611no—
469C2×#97—611no—
470C2×#97C2×D6111yescharacteristic
471#330—611no—
472#330—611no—
473#330—611no—
474#330—611no—
475#330—611no—
476#330—611no—
477#330—611no—
478#330—611no—
479#330—611no—
480#330—611no—
481#330—611no—
482#330—611no—
483#330C2×D6111yescharacteristic
484#330C2×D6111yescharacteristic
485#330C2×D6111yescharacteristic
486#330C2×D6111yescharacteristic
487C61#1768911yescharacteristic, complemented, Sylow
488C2×#41—611no—
489C2×M16—1221no—
490C2×M16—1221no—
491C22×C8—21no—
492C22×C8—1221no—
493C22×C8—1221no—
494C22×C8—1221no—
495C4⋊Q8—611no—
496C4⋊Q8—611no—
497C4⋊Q8—611no—
498C4⋊Q8—611no—
499C4⋊Q8—1221no—
500C4⋊Q8—1221no—
501C4⋊Q8—1221no—
502C4⋊Q8—1221no—
503C4⋊Q8—1221no—
504C4⋊Q8—1221no—
505C4⋊Q8C4×D6111yescharacteristic
506C4⋊Q8C4×D6111yescharacteristic
507#125—611no—
508#125—611no—
509#125—611no—
510#125—611no—
511#125—611no—
512#125—611no—
513#125—611no—
514#125—611no—
515#125—1221no—
516#125—1221no—
517#125—1221no—
518#125—1221no—
519#125—1221no—
520#125—1221no—
521#125—1221no—
522#125—1221no—
523#125—1221no—
524#125—1221no—
525#125—1221no—
526#125—1221no—
527#125C22×D6111yescharacteristic
528#125C22×D6111yescharacteristic
529C22⋊Q8—21no—
530C22⋊Q8—21no—
531C22⋊Q8—1221no—
532C22⋊Q8—1221no—
533C22⋊Q8—1221no—
534C22⋊Q8—1221no—
535C22⋊Q8—1221no—
536C22⋊Q8—1221no—
537C22⋊Q8—1221no—
538C22⋊Q8—1221no—
539C22⋊Q8—1221no—
540C22⋊Q8—1221no—
541C22⋊Q8—1221no—
542C22⋊Q8—1221no—
543C22⋊Q8—1221no—
544C22⋊Q8—1221no—
545C22⋊Q8—1221no—
546C22⋊Q8—1221no—
547C4×Q8—21no—
548C4×Q8—21no—
549C4×Q8—611no—
550C4×Q8—611no—
551C4×Q8—1221no—
552C4×Q8—1221no—
553C4×Q8—1221no—
554C4×Q8—1221no—
555C4×Q8—1221no—
556C4×Q8—1221no—
557C4×D4—611no—
558C4×D4—611no—
559C4×D4—611no—
560C4×D4—611no—
561C4×D4—611no—
562C4×D4—611no—
563C4×D4—1221no—
564C4×D4—1221no—
565C4×D4—1221no—
566C4×D4—1221no—
567C4×D4—1221no—
568C4×D4—1221no—
569#117—611no—
570#117—611no—
571#117—611no—
572#117—611no—
573#117—611no—
574#117—611no—
575#117—611no—
576#117C4×D6111yescharacteristic
577#117C4×D6111yescharacteristic
578C2×C4⋊C4—611no—
579C2×C4⋊C4—611no—
580C2×C4⋊C4—611no—
581C2×C4⋊C4—611no—
582C2×C4⋊C4—611no—
583C2×C4⋊C4—611no—
584C2×C4⋊C4—1221no—
585C2×C4⋊C4—1221no—
586C2×C4⋊C4—1221no—
587C2×C4⋊C4—1221no—
588C2×C4⋊C4—1221no—
589C2×C4⋊C4—1221no—
590C2×C42—611no—
591C2×C42—611no—
592C2×C42C22×D6111yescharacteristic
593C4⋊C8—21no—
594C4⋊C8—1221no—
595C4⋊C8—1221no—
596C4⋊C8—1221no—
597C4⋊C8—1221no—
598C4⋊C8—1221no—
599C22⋊C8—21no—
600C22⋊C8—1221no—
601C22⋊C8—1221no—
602C22⋊C8—1221no—
603C22⋊C8—1221no—
604C22⋊C8—1221no—
605#97—21no—
606#97—611no—
607#97—611no—
608#97—611no—
609#97—611no—
610#97—1221no—
611#97—1221no—
612#97—1221no—
613#97C22×D6111yescharacteristic
614#97C22×D6111yescharacteristic
615#97C22×D6111yescharacteristic
616#97C22×D6111yescharacteristic
617C4×C8—1221no—
618C4×C8—1221no—
619#41—1224no—
620C2×Q8—21no—
621C2×Q8—21no—
622C2×Q8—611no—
623C2×Q8—1221no—
624C2×Q8—1221no—
625C2×Q8—1221no—
626C2×Q8—1221no—
627C2×D4—611no—
628C2×D4—611no—
629C2×D4—611no—
630C22×C4—611no—
631C22×C4—611no—
632C22×C4—611no—
633C22×C4—611no—
634C22×C4—611no—
635C22×C4—611no—
636C22×C4—1221no—
637C22×C4—1221no—
638C22×C4—1221no—
639C22×C4—1221no—
640C22×C4—1221no—
641C22×C4—1221no—
642C22×C4C2×C4×D6111yescharacteristic
643C22×C4D4×D6111yescharacteristic
644C22×C4D4×D6111yescharacteristic
645M16—2442no—
646M16—2442no—
647C2×C8—21no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—42no—
652C2×C8—1221no—
653C2×C8—1221no—
654C2×C8—1221no—
655C2×C8—1221no—
656C2×C8—2442no—
657C2×C8—2442no—
658C2×C8—2442no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—611no—
666C4⋊C4—611no—
667C4⋊C4—611no—
668C4⋊C4—611no—
669C4⋊C4—611no—
670C4⋊C4—611no—
671C4⋊C4—611no—
672C4⋊C4—611no—
673C4⋊C4—611no—
674C4⋊C4—611no—
675C4⋊C4—1221no—
676C4⋊C4—1221no—
677C4⋊C4—1221no—
678C4⋊C4—1221no—
679C4⋊C4—1221no—
680C4⋊C4—1221no—
681C4⋊C4—1221no—
682C4⋊C4—1221no—
683C4⋊C4—1221no—
684C4⋊C4—1221no—
685C4⋊C4—1221no—
686C4⋊C4—1221no—
687C4⋊C4—1221no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4C2×C4×D6111yescharacteristic
702C4⋊C4C2×C4×D6111yescharacteristic
703C4⋊C4C2×C4×D6111yescharacteristic
704C4⋊C4C2×C4×D6111yescharacteristic
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—611no—
708C22⋊C4—611no—
709C22⋊C4—611no—
710C22⋊C4—611no—
711C22⋊C4—611no—
712C22⋊C4—611no—
713C22⋊C4—1221no—
714C22⋊C4—1221no—
715C22⋊C4—1221no—
716C22⋊C4—1221no—
717C42—21no—
718C42—21no—
719C42—611no—
720C42—611no—
721C42—611no—
722C42—611no—
723C42—611no—
724C42—611no—
725C42—1221no—
726C42—1221no—
727C42—1221no—
728C42—1221no—
729C42C2×C4×D6111yescharacteristic
730C42D4×D6111yescharacteristic
731C42D4×D6111yescharacteristic
732C42C23×D6111yescharacteristic
733C23—611no—
734C23—611no—
735C23C22⋊C4×D6111yescharacteristic
736Q8—81no—
737Q8—81no—
738Q8—1222no—
739Q8—4881no—
740Q8—4881no—
741Q8—4881no—
742Q8—4881no—
743D4—614no—
744D4—1222no—
745D4—1222no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—41no—
752C2×C4—41no—
753C2×C4—611no—
754C2×C4—611no—
755C2×C4—611no—
756C2×C4—611no—
757C2×C4—611no—
758C2×C4—611no—
759C2×C4—1222no—
760C2×C4—1222no—
761C2×C4—1221no—
762C2×C4—1221no—
763C2×C4—1221no—
764C2×C4—1221no—
765C2×C4—4881no—
766C2×C4—4881no—
767C2×C4—4881no—
768C2×C4—4881no—
769C2×C4—4881no—
770C2×C4—4881no—
771C2×C4—2441no—
772C2×C4—2441no—
773C2×C4—2441no—
774C2×C4—2441no—
775C2×C4C22⋊C4×D6111yescharacteristic
776C2×C4C22⋊C4×D6111yescharacteristic
777C2×C4C22⋊C4×D6111yescharacteristic
778C2×C4C22×C4×D6111yescharacteristic
779C2×C4C2×D4×D6111yescharacteristic
780C2×C4C2×D4×D6111yescharacteristic
781C8—22no—
782C8—41no—
783C8—41no—
784C8—41no—
785C8—1222no—
786C8—2441no—
787C8—2441no—
788C8—2441no—
789C22—21no—
790C22—21no—
791C22—612no—
792C22—1221no—
793C22—1221no—
794C22—1221no—
795C22—1221no—
796C22—1221no—
797C22#101×D6112yes—
798C22C2×C22⋊C4×D6111yescharacteristic
799C4—21no—
800C4—21no—
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—612no—
810C4—1221no—
811C4—1221no—
812C4—1221no—
813C4—1221no—
814C4—1221no—
815C4—2441no—
816C4—2441no—
817C4—2441no—
818C4—2441no—
819C2—22no—
820C2—1222no—
821C2—2441no—
822C2C2×#101×D6111yescharacteristic
823C2#2145436311yescharacteristic
824C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1531C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#11758222C2×C4
cosocleC42×C61C24
hypercenter#1531D61
hypocenterC61#17689
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1531

Complements

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

NH ≅ G/Ntype
4. #21444455C2semidirect
5. #21444445C2semidirect
6. #21444444C2semidirect
7. #21444434C2semidirect
8. #21444432C2semidirect
9. #21444432C2semidirect
10. #21444419C2semidirect
11. #21444419C2semidirect
12. #21444412C2semidirect
13. C2×#16839503C2semidirect
14. #330×D61C2semidirect
15. C61×#1531C2semidirect
416. #1531D61semidirect
487. C61#17689semidirect

Maximal subgroups

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

subgroupindex
#214596402
#214548302
#214548282
#214444552
#214444452
#214444442
#214444342
#214444322
#214444192
#214444122
C2×#168395032
#330×D612
C61×#15312
#1768961