Finite Group Databasebeta

← #29648174

Subgroups — #29648174

Order 15616.

878 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459791C211yesmaximal, characteristic
2#21454834C211yesmaximal, characteristic, complemented
3#21454465C211yesmaximal, characteristic, complemented
4#21444455C211yesmaximal, characteristic, complemented
5#21444451C211yesmaximal, characteristic, complemented
6#21444449C211yesmaximal, characteristic, complemented
7#21444446C211yesmaximal, characteristic, complemented
8#21444438C211yesmaximal, characteristic, complemented
9#21444438C211yesmaximal, characteristic, complemented
10#21444432C211yesmaximal, characteristic, complemented
11#21444424C211yesmaximal, characteristic, complemented
12#21444419C211yesmaximal, characteristic, complemented
13#21444406C211yesmaximal, characteristic, complemented
14#330×D61C211yesmaximal, characteristic, complemented
15C61×#1528C211yesmaximal, characteristic, complemented
16#16840489C411yescharacteristic
17#16840468C411yescharacteristic
18#16840467C411yescharacteristic
19#16840465C411yescharacteristic
20#16840460C411yescharacteristic
21#16840450C411yescharacteristic
22#16840447—21no—
23#16840447C411yescharacteristic
24#16840444—21no—
25#16840444—21no—
26#16840413—21no—
27#16840413C411yescharacteristic
28#16840371—21no—
29#16840360—21no—
30#16840359—21no—
31#16840318C2211yescharacteristic
32#16840297C2211yescharacteristic
33#16840297C2211yescharacteristic
34#16840296C2211yescharacteristic
35#125×D61C2211yescharacteristic
36#16840243—21no—
37C4×#11758222C2211yescharacteristic
38#16839892—21no—
39#16839831—21no—
40#16839831—21no—
41C8×D244—21no—
42#16839822—21no—
43#16839820—21no—
44#16839819C2211yescharacteristic
45#16839819C2211yescharacteristic
46#16839817C2211yescharacteristic
47#16839817C2211yescharacteristic
48#16839817C2211yescharacteristic
49#16839817C2211yescharacteristic
50#16839787—21no—
51#16839727—21no—
52#16839714C2211yescharacteristic
53#97×D61C2211yescharacteristic
54#97×D61C2211yescharacteristic
55#97×D61C2211yescharacteristic
56#16839504C2211yescharacteristic
57#16839504C2211yescharacteristic
58#16839504C2211yescharacteristic
59#16839504C2211yescharacteristic
60#16839503C2211yescharacteristic
61#16839503C2211yescharacteristic
62#16839503C2211yescharacteristic
63#16839503C2211yescharacteristic
64#16839501C2211yescharacteristic
65#16839501C2211yescharacteristic
66#16839501C2211yescharacteristic
67#16839501C2211yescharacteristic
68C2×#125×C61C2211yescharacteristic
69C61×#432C2211yescharacteristic
70C4×M16×C61C2211yescharacteristic
71C61×#330C2211yescharacteristic
72C61×#330C2211yescharacteristic
73C61×#330C2211yescharacteristic
74C61×#330C2211yescharacteristic
75C2×#11758222—21no—
76C2×#11758222D411yescharacteristic
77C2×#11758189—21no—
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80C2×C8×D61—21no—
81#14519776—21no—
82#14519776C2×C411yescharacteristic
83#14519776C2×C411yescharacteristic
84#14519772—21no—
85#14519772—21no—
86#14519772—21no—
87#14519772—21no—
88#14519772—21no—
89#14519772—21no—
90#14519771—21no—
91#14519769C2311yescharacteristic
92#14519768—21no—
93#14519768C2×C411yescharacteristic
94#14519768C2×C411yescharacteristic
95#14519767—21no—
96#14519767—21no—
97#14519767—21no—
98#14519767—21no—
99#14519767—21no—
100#14519767—21no—
101#14519765C2311yescharacteristic
102#14519762—21no—
103#14519762—21no—
104#14519762—21no—
105#14519762—21no—
106#14519762—21no—
107#14519762—21no—
108#14519760—21no—
109#14519760—21no—
110#14519760—21no—
111#14519757—21no—
112#14519757C2×C411yescharacteristic
113#14519757C2×C411yescharacteristic
114#14519756—21no—
115#14519756C2×C411yescharacteristic
116#14519755—21no—
117#14519755—21no—
118#14519755—21no—
119#14519755—21no—
120#14519755—21no—
121#14519755—21no—
122#14519752—21no—
123#14519752C2×C411yescharacteristic
124#14519752C2×C411yescharacteristic
125#14519751—21no—
126#14519751C2×C411yescharacteristic
127C4×Dic122C2×C411yescharacteristic
128C4×Dic122C2×C411yescharacteristic
129C4×Dic122D411yescharacteristic
130#14519742—21no—
131#14519742—21no—
132#14519742—21no—
133#14519742C2×C411yescharacteristic
134#14519742C2×C411yescharacteristic
135C4×D244C2×C411yescharacteristic
136C4×D244C2×C411yescharacteristic
137C4×D244D411yescharacteristic
138#14519739—21no—
139#14519739—21no—
140#14519739—21no—
141#14519739C2×C411yescharacteristic
142#14519739C2×C411yescharacteristic
143C4×C22⋊D61—21no—
144C4×C22⋊D61—21no—
145C4×C22⋊D61—21no—
146C4×C22⋊D61C2×C411yescharacteristic
147C4×C22⋊D61C2×C411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149C4×C22⋊D61D411yescharacteristic
150#14519736—21no—
151#14519736D411yescharacteristic
152#14519735—21no—
153#14519735—21no—
154#14519735—21no—
155#14519735C2×C411yescharacteristic
156#14519735C2×C411yescharacteristic
157#14519734—21no—
158#14519734D411yescharacteristic
159#14519734D411yescharacteristic
160C4⋊C4×D61—21no—
161C4⋊C4×D61—21no—
162C4⋊C4×D61—21no—
163C4⋊C4×D61C2×C411yescharacteristic
164C4⋊C4×D61C2×C411yescharacteristic
165C42×D61C2311yescharacteristic
166C42×D61C2311yescharacteristic
167C4⋊#92418—21no—
168C4⋊#92418—21no—
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418—21no—
174C22⋊#92418—21no—
175#14519689—21no—
176#14519689—21no—
177#14519689—21no—
178#14519689—21no—
179#14519688C2311yescharacteristic
180#14519688C2311yescharacteristic
181#14519688C2311yescharacteristic
182#14519688C2311yescharacteristic
183#14519687—21no—
184#14519687—21no—
185#14519687—21no—
186C8×Dic61—21no—
187C2×M16×C61—21no—
188#125×C61—21no—
189#125×C61—21no—
190#125×C61C2×C411yescharacteristic
191#125×C61C2×C411yescharacteristic
192#125×C61C2311yescharacteristic
193#125×C61C2311yescharacteristic
194C2×C4⋊C4×C61—21no—
195C2×C4⋊C4×C61—21no—
196C2×C4⋊C4×C61C2×C411yescharacteristic
197C2×C4⋊C4×C61C2×C411yescharacteristic
198C2×C42×C61C2311yescharacteristic
199C4⋊C8×C61—21no—
200C22⋊C8×C61—21no—
201#97×C61C2311yescharacteristic
202#97×C61C2311yescharacteristic
203#97×C61C2311yescharacteristic
204#97×C61C2311yescharacteristic
205C4×C8×C61—21no—
206C22×C4×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61C22×C411yescharacteristic
209C22×C4×C61C2×D411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C2×C22⋊D61—21no—
212C2×C22⋊D61C22⋊C411yescharacteristic
213C2×C22⋊D61C22⋊C411yescharacteristic
214#11758222—42no—
215#11758222—44no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244C22⋊C411yescharacteristic
219C2×D244C22×C411yescharacteristic
220C2×C4×D61—21no—
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61C22×C411yescharacteristic
226C2×C4×D61C22×C411yescharacteristic
227C2×C4×D61C2×D411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×Dic122—21no—
232C2×Dic122—21no—
233C2×Dic122C22⋊C411yescharacteristic
234C2×Dic122C22×C411yescharacteristic
235M16×C61—42no—
236C2×C8×C61—21no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C4⋊C4×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61C22×C411yescharacteristic
251C4⋊C4×C61C22×C411yescharacteristic
252C4⋊C4×C61C22×C411yescharacteristic
253C4⋊C4×C61C22×C411yescharacteristic
254C42×C61C22×C411yescharacteristic
255C42×C61C2×D411yescharacteristic
256C42×C61C2×D411yescharacteristic
257C42×C61C2411yescharacteristic
258C22⋊Dic61—21no—
259C22⋊Dic61C22⋊C411yescharacteristic
260C22⋊Dic61C22⋊C411yescharacteristic
261#11758198—21no—
262#11758198—21no—
263#11758198—21no—
264#11758198—21no—
265#11758198—21no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271#11758198—21no—
272#11758198—21no—
273#11758198C22⋊C411yescharacteristic
274#11758198C22⋊C411yescharacteristic
275#11758198C22⋊C411yescharacteristic
276#11758198C22⋊C411yescharacteristic
277C4⋊Dic61—21no—
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61C22⋊C411yescharacteristic
282C4⋊Dic61C22⋊C411yescharacteristic
283C4⋊Dic61C22×C411yescharacteristic
284C4⋊Dic61C22×C411yescharacteristic
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×Dic61—21no—
306C4×Dic61C22×C411yescharacteristic
307C4×Dic61C22×C411yescharacteristic
308C4×Dic61C2×D411yescharacteristic
309C4×Dic61C2×D411yescharacteristic
310C4×Dic61C2×D411yescharacteristic
311C4×Dic61C2×D411yescharacteristic
312C2×#92418—21no—
313C2×#92418—21no—
314C2×#92418—21no—
315C2×#92418—21no—
316#11758189—42no—
317C8×D61—42no—
318C8×D61—42no—
319C8×D61—42no—
320C23×C61C2×C22⋊C411yescharacteristic
321C22×D61—21no—
322C22×D61C2×C22⋊C411yescharacteristic
323C22×D61C2×C22⋊C411yescharacteristic
324C2×C4×C61—21no—
325C2×C4×C61—21no—
326C2×C4×C61—21no—
327C2×C4×C61—21no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—42no—
332C2×C4×C61—81no—
333C2×C4×C61C2×C22⋊C411yescharacteristic
334C2×C4×C61C2×C22⋊C411yescharacteristic
335C2×C4×C61C2×C22⋊C411yescharacteristic
336C2×C4×C61C23×C411yescharacteristic
337C2×C4×C61C22×D411yescharacteristic
338C2×C4×C61C22×D411yescharacteristic
339C22⋊D61—22no—
340C22⋊D61—41no—
341C22⋊D61—42no—
342C2×Dic61—21no—
343C2×Dic61—21no—
344C2×Dic61—21no—
345C2×Dic61C2×C22⋊C411yescharacteristic
346C2×Dic61C2×C22⋊C411yescharacteristic
347C2×Dic61C2×C22⋊C411yescharacteristic
348C2×Dic61C2×C22⋊C411yescharacteristic
349C2×Dic61C2×C22⋊C411yescharacteristic
350C2×Dic61C2×C22⋊C411yescharacteristic
351D244—22no—
352D244—41no—
353D244—42no—
354D244—81no—
355C4×D61—22no—
356C4×D61—41no—
357C4×D61—41no—
358C4×D61—41no—
359C4×D61—41no—
360C4×D61—41no—
361C4×D61—42no—
362C4×D61—42no—
363C4×D61—81no—
364C4×D61—81no—
365C4×D61—81no—
366Dic122—41no—
367Dic122—42no—
368Dic122—41no—
369Dic122—81no—
370C8×C61—22no—
371C8×C61—41no—
372C8×C61—41no—
373C8×C61—41no—
374#92418—41no—
375#92418—41no—
376#92418—41no—
377#92418—41no—
378#17680—611nomaximal, Sylow
379C22×C61—21no—
380C22×C61—21no—
381C22×C61—21no—
382C22×C61C22×C22⋊C411yescharacteristic
383C2×D61—21no—
384C2×D61—21no—
385C2×D61—21no—
386C2×D61—21no—
387C2×D61—21no—
388C2×D61—41no—
389C2×D61—41no—
390C2×D61—41no—
391C2×D61#42112yes—
392C4×C61—21no—
393C4×C61—21no—
394C4×C61—21no—
395C4×C61—21no—
396C4×C61—21no—
397C4×C61—21no—
398C4×C61—41no—
399C4×C61—41no—
400C4×C61—41no—
401C4×C61—41no—
402Dic61—21no—
403Dic61—21no—
404Dic61—21no—
405Dic61—21no—
406Dic61—21no—
407Dic61—21no—
408Dic61—41no—
409Dic61—41no—
410Dic61—41no—
411#3515—611no—
412#2970—611no—
413#2923—611no—
414#1537—611no—
415#1535—611no—
416#1535—611no—
417#1534—611no—
418#1532—611no—
419#1532—611no—
420#1531—611no—
421#1529—611no—
422#1528—611no—
423#1528D6111yescharacteristic, complemented
424#1524—611no—
425C2×#330—611no—
426C2×C61—41no—
427C2×C61#288911yescharacteristic
428C2×C61C2×#42111yescharacteristic
429C2×C61#290111yescharacteristic
430D61—22no—
431D61—41no—
432D61—81no—
433#557—611no—
434#554—611no—
435#554—611no—
436#553—611no—
437#553—611no—
438#552—611no—
439#552—611no—
440#552—1221no—
441#552—1221no—
442#552—1221no—
443#547—611no—
444#547—1221no—
445#541—1221no—
446#539—1221no—
447#539—1221no—
448#533—611no—
449#529—611no—
450#529—611no—
451#529—611no—
452C2×#125—611no—
453C2×#125C2×D6111yescharacteristic
454#520—1221no—
455C4×#41—611no—
456#446—1221no—
457#435—1221no—
458#435—1221no—
459C8×D4—1221no—
460#433—1221no—
461#433—1221no—
462#432—611no—
463#432—611no—
464#432—611no—
465#432—611no—
466#432—611no—
467#432—611no—
468#432C2×D6111yescharacteristic
469#424—1221no—
470#408—1221no—
471C4×M16—611no—
472C4×M16C2×D6111yescharacteristic
473C2×#97—611no—
474C2×#97—611no—
475C2×#97—611no—
476#330—611no—
477#330—611no—
478#330—611no—
479#330—611no—
480#330—611no—
481#330—611no—
482#330—611no—
483#330—611no—
484#330C2×D6111yescharacteristic
485#330C2×D6111yescharacteristic
486#330C2×D6111yescharacteristic
487#330C2×D6111yescharacteristic
488#329—611no—
489#329—611no—
490#329—611no—
491#329—611no—
492C61#1768011yescharacteristic, complemented, Sylow
493C2×#41—611no—
494C2×#41—1221no—
495C2×M16—21no—
496C2×M16—1221no—
497C22×C8—1221no—
498C22×C8—1221no—
499C22×C8—1221no—
500C4⋊Q8—611no—
501C4⋊Q8—611no—
502C4⋊Q8—1221no—
503#126—1221no—
504#126—1221no—
505#126—1221no—
506#126—1221no—
507#126—1221no—
508#126—1221no—
509#126—1221no—
510#125—21no—
511#125—21no—
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#125C4×D6111yescharacteristic
523#125C4×D6111yescharacteristic
524#125C22×D6111yescharacteristic
525#125C22×D6111yescharacteristic
526#124—611no—
527#123—1221no—
528#123—1221no—
529#123—1221no—
530#123—1221no—
531#123—1221no—
532#123—1221no—
533#123—1221no—
534#123—1221no—
535#123—1221no—
536C22⋊Q8—611no—
537C22⋊Q8—611no—
538C22⋊Q8—611no—
539C22⋊Q8—1221no—
540C22⋊Q8—1221no—
541C22⋊Q8—1221no—
542C22⋊Q8—1221no—
543C22⋊Q8—1221no—
544C22⋊Q8—1221no—
545C22⋊Q8—1221no—
546C22⋊Q8—1221no—
547#121—611no—
548#121—611no—
549#121—611no—
550#121—1221no—
551#121—1221no—
552C4×Q8—611no—
553C4×Q8—611no—
554C4×Q8—611no—
555C4×Q8—611no—
556C4×Q8—611no—
557C4×Q8—1221no—
558C4×Q8—1221no—
559C4×Q8—1221no—
560C4×D4—611no—
561C4×D4—611no—
562C4×D4—611no—
563C4×D4—611no—
564C4×D4—611no—
565C4×D4—611no—
566C4×D4—611no—
567C4×D4—611no—
568C4×D4—611no—
569C4×D4—1221no—
570C4×D4—1221no—
571C4×D4—1221no—
572C4×D4—1221no—
573C4×D4—1221no—
574C4×D4—1221no—
575#117—611no—
576#117—611no—
577#117—611no—
578#117—611no—
579#117—611no—
580#117—1221no—
581#117—1221no—
582#117—1221no—
583#117—1221no—
584#117—1221no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—611no—
588C2×C4⋊C4—611no—
589C2×C4⋊C4—1221no—
590C2×C4⋊C4—1221no—
591C2×C4⋊C4—1221no—
592C2×C4⋊C4C4×D6111yescharacteristic
593C2×C4⋊C4C4×D6111yescharacteristic
594C2×C42—611no—
595C2×C42—611no—
596C2×C42C22×D6111yescharacteristic
597C4⋊C8—21no—
598C4⋊C8—1221no—
599C4⋊C8—1221no—
600C4⋊C8—1221no—
601C4⋊C8—1221no—
602C4⋊C8—1221no—
603C4⋊C8—1221no—
604C22⋊C8—21no—
605C22⋊C8—1221no—
606C22⋊C8—1221no—
607C22⋊C8—1221no—
608C22⋊C8—1221no—
609C22⋊C8—1221no—
610C22⋊C8—1221no—
611#97—611no—
612#97—611no—
613#97—611no—
614#97—611no—
615#97—1221no—
616#97—1221no—
617#97—1221no—
618#97C22×D6111yescharacteristic
619#97C22×D6111yescharacteristic
620#97C22×D6111yescharacteristic
621#97C22×D6111yescharacteristic
622C4×C8—21no—
623C4×C8—1221no—
624#41—2442no—
625#41—2444no—
626C2×Q8—611no—
627C2×Q8—611no—
628C2×Q8—1221no—
629C2×Q8—1221no—
630C2×D4—611no—
631C2×D4—611no—
632C2×D4—611no—
633C2×D4—611no—
634C2×D4—1221no—
635C2×D4—1221no—
636C2×D4—1221no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—611no—
640C22×C4—611no—
641C22×C4—611no—
642C22×C4—611no—
643C22×C4—611no—
644C22×C4—611no—
645C22×C4—1221no—
646C22×C4—1221no—
647C22×C4—1221no—
648C22×C4—1221no—
649C22×C4—1221no—
650C22×C4C2×C4×D6111yescharacteristic
651C22×C4D4×D6111yescharacteristic
652C22×C4D4×D6111yescharacteristic
653M16—42no—
654M16—2442no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—1221no—
660C2×C8—1221no—
661C2×C8—1221no—
662C2×C8—1221no—
663C2×C8—2442no—
664C2×C8—2442no—
665C2×C8—2442no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—611no—
677C4⋊C4—611no—
678C4⋊C4—611no—
679C4⋊C4—611no—
680C4⋊C4—611no—
681C4⋊C4—611no—
682C4⋊C4—611no—
683C4⋊C4—611no—
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⋊C4C2×C4×D6111yescharacteristic
701C4⋊C4C2×C4×D6111yescharacteristic
702C4⋊C4C2×C4×D6111yescharacteristic
703C4⋊C4C2×C4×D6111yescharacteristic
704C22⋊C4—611no—
705C22⋊C4—611no—
706C22⋊C4—611no—
707C22⋊C4—611no—
708C22⋊C4—611no—
709C22⋊C4—611no—
710C22⋊C4—1221no—
711C22⋊C4—1221no—
712C22⋊C4—1221no—
713C22⋊C4—1221no—
714C22⋊C4—1221no—
715C22⋊C4—1221no—
716C22⋊C4—1221no—
717C22⋊C4—1221no—
718C22⋊C4—1221no—
719C22⋊C4—1221no—
720C22⋊C4—1221no—
721C22⋊C4—1221no—
722C22⋊C4—1221no—
723C42—611no—
724C42—611no—
725C42—611no—
726C42—611no—
727C42—611no—
728C42—611no—
729C42—1221no—
730C42—1221no—
731C42—1221no—
732C42—1221no—
733C42—1221no—
734C42C2×C4×D6111yescharacteristic
735C42D4×D6111yescharacteristic
736C42D4×D6111yescharacteristic
737C42C23×D6111yescharacteristic
738C23—611no—
739C23—611no—
740C23—1221no—
741C23C22⋊C4×D6111yescharacteristic
742Q8—4881no—
743Q8—2441no—
744Q8—2441no—
745Q8—2442no—
746D4—1222no—
747D4—1222no—
748D4—4881no—
749D4—2441no—
750D4—2442no—
751D4—2441no—
752D4—2442no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—81no—
762C2×C4—611no—
763C2×C4—611no—
764C2×C4—611no—
765C2×C4—611no—
766C2×C4—611no—
767C2×C4—611no—
768C2×C4—1222no—
769C2×C4—1221no—
770C2×C4—1221no—
771C2×C4—1221no—
772C2×C4—4881no—
773C2×C4—4881no—
774C2×C4—4881no—
775C2×C4—2441no—
776C2×C4—2441no—
777C2×C4—2441no—
778C2×C4—2441no—
779C2×C4—2441no—
780C2×C4—2442no—
781C2×C4—2442no—
782C2×C4C22⋊C4×D6111yescharacteristic
783C2×C4C22⋊C4×D6111yescharacteristic
784C2×C4C22⋊C4×D6111yescharacteristic
785C2×C4C22×C4×D6111yescharacteristic
786C2×C4C2×D4×D6111yescharacteristic
787C2×C4C2×D4×D6111yescharacteristic
788C8—22no—
789C8—41no—
790C8—41no—
791C8—41no—
792C8—2441no—
793C8—2441no—
794C8—2441no—
795C8—2441no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—612no—
800C22—1221no—
801C22—1221no—
802C22—1221no—
803C22—1221no—
804C22—1221no—
805C22—2441no—
806C22—2441no—
807C22—2441no—
808C22C2×C22⋊C4×D6111yescharacteristic
809C4—21no—
810C4—21no—
811C4—21no—
812C4—21no—
813C4—21no—
814C4—21no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—1221no—
820C4—1221no—
821C4—1221no—
822C4—1221no—
823C4—1221no—
824C4—1221no—
825C4—2441no—
826C4—2441no—
827C4—2441no—
828C2—41no—
829C2—1222no—
830C2—4881no—
831C2—2441no—
832C2#2145429911yescharacteristic
833C2#421×D6111yescharacteristic
834C2#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1528C2
socleC22×C61C22×C22⋊C4
prime radical#21459791C2
cosocleC42×C61C24
hypercenter#1528D61
hypocenterC61#17680
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
2. #21454834C2semidirect
3. #21454465C2semidirect
4. #21444455C2semidirect
5. #21444451C2semidirect
6. #21444449C2semidirect
7. #21444446C2semidirect
8. #21444438C2semidirect
9. #21444438C2semidirect
10. #21444432C2semidirect
11. #21444424C2semidirect
12. #21444419C2semidirect
13. #21444406C2semidirect
14. #330×D61C2semidirect
15. C61×#1528C2semidirect
423. #1528D61semidirect
492. C61#17680semidirect

Maximal subgroups

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

subgroupindex
#214597912
#214548342
#214544652
#214444552
#214444512
#214444492
#214444462
#214444382
#214444322
#214444242
#214444192
#214444062
#330×D612
C61×#15282
#1768061