Finite Group Databasebeta

← #30575623

Subgroups — #30575623

Order 15616.

1740 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459635C211yesmaximal, characteristic
2#21459397C211yesmaximal, characteristic
3#21458702C212yesmaximal, complemented
4#21458494C212yesmaximal, complemented
5#21458211C212yesmaximal, complemented
6#21458206C214yesmaximal, complemented
7#21457694C212yesmaximal, complemented
8#21457693C214yesmaximal, complemented
9#21457163C212yesmaximal, complemented
10#21457161C211yesmaximal, characteristic, complemented
11#21456969C212yesmaximal, complemented
12#21455860C212yesmaximal, complemented
13#21455859C211yesmaximal, characteristic, complemented
14C2×#16840054C211yesmaximal, characteristic, complemented
15#477×D61C212yesmaximal, complemented
16#21454927C211yesmaximal, characteristic
17C61×#3230C211yesmaximal, characteristic, complemented
18#16840492C2211yescharacteristic
19#16840492C2212yes—
20#16840489—21no—
21#16840487—21no—
22#16840487C2211yescharacteristic
23#16840473C2212yes—
24#16840473C2211yescharacteristic
25#16840470C2212yes—
26#16840468—21no—
27#16840467C2214yes—
28#16840466—22no—
29#16840427—21no—
30#16840427C2211yescharacteristic
31Q8×C22⋊D61—22no—
32#16840425C2212yes—
33#16840393—21no—
34#16840389—22no—
35#16840319C2211yescharacteristic
36#16840317C2212yes—
37#16840316—22no—
38#16840316C2212yes—
39#16840315—21no—
40C4⋊Q8×D61C2212yes—
41#16840243—21no—
42C4×#11758222C2211yescharacteristic
43#16840230—21no—
44C2×C4×Dic122C2211yescharacteristic
45C4×Q8×D61C2212yes—
46#16840166C2214yes—
47#16840111C2214yes—
48#16840099C2214yes—
49#16840099C2214yes—
50#16840098C2212yes—
51#16840096C2214yes—
52#16840058C2211yescharacteristic
53#16840058C2211yescharacteristic
54#16840057C2212yes—
55#16840056C2214yes—
56#16840056C2214yes—
57#16840055C2214yes—
58#16840054C2212yes—
59#16840054C2212yes—
60#16840054C2212yes—
61#16840054C2212yes—
62#16840054C2212yes—
63#16840004C2214yes—
64#16840002C2214yes—
65#16840001C2214yes—
66#16839973C2211yescharacteristic
67#16839973C2211yescharacteristic
68#16839972C2212yes—
69#16839971C2214yes—
70#16839969C2212yes—
71#16839920C2212yes—
72#16839919C2214yes—
73C8×Dic122C2212yes—
74C4×Dic244C2212yes—
75C4×Dic244C2212yes—
76#16839856C2214yes—
77#16839854C2214yes—
78C8×D244C2212yes—
79#16839825C2214yes—
80#16839814C2212yes—
81C2×#14519710C2212yes—
82#107×D61C2214yes—
83C2×C4⋊#92418C2211yescharacteristic
84C4⋊C8×D61C2212yes—
85C2×#14519700C2212yes—
86#103×D61C2214yes—
87C61×#533C2211yescharacteristic
88C2×C4⋊Q8×C61C2211yescharacteristic
89C61×#500C2212yes—
90C61×#487C2212yes—
91C61×#484C2214yes—
92C61×#477C2212yes—
93C61×#477C2212yes—
94C61×#431C2211yescharacteristic
95C2×#11758222D411yescharacteristic
96C22×Dic122C2311yescharacteristic
97C2×Q8×D61—22no—
98C2×Q8×D61C2312yes—
99C2×Dic244C2312yes—
100C2×Dic244C2312yes—
101C2×#11758202C2314yes—
102C22×#92418C2312yes—
103C2×C8×D61C2314yes—
104#14519777C2311yescharacteristic
105#14519777C2311yescharacteristic
106#14519776—21no—
107#14519776—21no—
108#14519776—22no—
109#14519776—22no—
110#14519776—22no—
111#14519776C2314yes—
112#14519776C2312yes—
113#14519775—22no—
114#14519775—24no—
115#14519775—22no—
116#14519775C2312yes—
117#14519769—21no—
118#14519768—21no—
119#14519768—22no—
120#14519768—21no—
121#14519768—22no—
122#14519767—22no—
123#14519767—24no—
124#14519767—22no—
125#14519767—22no—
126#14519757—22no—
127#14519757C2314yes—
128#14519757C2312yes—
129#14519756—21no—
130#14519756—24no—
131#14519756C2312yes—
132#14519755—22no—
133#14519755—22no—
134#14519755—24no—
135#14519755—22no—
136#14519754—22no—
137#14519754—22no—
138#14519753—22no—
139#14519753—22no—
140#14519753—24no—
141#14519753C2312yes—
142Q8×Dic61—22no—
143Q8×Dic61C2312yes—
144C4×Dic122—21no—
145C4×Dic122—21no—
146C4×Dic122—21no—
147C4×Dic122—22no—
148C4×Dic122—22no—
149C4×Dic122D411yescharacteristic
150C4×Dic122C2312yes—
151C4×Dic122C2311yescharacteristic
152C4×Dic122C2311yescharacteristic
153C4×Dic122C2311yescharacteristic
154C4×Dic122C2311yescharacteristic
155C4×Dic122C2311yescharacteristic
156#14519742—21no—
157#14519742—21no—
158#14519742—22no—
159#14519742—22no—
160#14519742C2314yes—
161#14519742C2312yes—
162C4×D244D411yescharacteristic
163C4×D244C2311yescharacteristic
164#14519739—21no—
165#14519739—21no—
166#14519739—22no—
167C4×C22⋊D61—24no—
168C4×C22⋊D61D412yes—
169C4×C22⋊D61C2312yes—
170#14519737—22no—
171#14519737—22no—
172#14519736—21no—
173#14519736D411yescharacteristic
174#14519735—22no—
175#14519734—22no—
176#14519734D412yes—
177C2×C4⋊Dic61C2311yescharacteristic
178C2×#11758196—21no—
179C4⋊C4×D61—22no—
180C4⋊C4×D61—22no—
181C4⋊C4×D61C2314yes—
182C4⋊C4×D61C2312yes—
183C2×C4×Dic61—21no—
184C42×D61—22no—
185C42×D61C2312yes—
186#14519711C2312yes—
187#14519711C2312yes—
188#14519710C2314yes—
189#14519710C2314yes—
190#14519710C2314yes—
191C4⋊#92418C2312yes—
192C4⋊#92418C2312yes—
193#14519706C2314yes—
194#14519702C2312yes—
195#14519702C2312yes—
196#14519702C2312yes—
197#14519702C2312yes—
198#14519701C2314yes—
199#14519700C2314yes—
200#14519700C2314yes—
201#14519700C2314yes—
202#14519689C2314yes—
203C8×Dic61C2314yes—
204C22×Q8×C61—21no—
205C4⋊Q8×C61—21no—
206C4⋊Q8×C61—21no—
207C4⋊Q8×C61C2311yescharacteristic
208C4⋊Q8×C61C2312yes—
209C4⋊Q8×C61C2312yes—
210C4⋊Q8×C61C2311yescharacteristic
211#125×C61—21no—
212C22⋊Q8×C61—21no—
213C22⋊Q8×C61C2312yes—
214C4×Q8×C61—21no—
215C4×Q8×C61C2312yes—
216#117×C61—21no—
217C2×C4⋊C4×C61—21no—
218C2×C4⋊C4×C61C2312yes—
219C2×C42×C61C2311yescharacteristic
220#107×C61C2314yes—
221#107×C61C2314yes—
222C4⋊C8×C61C2311yescharacteristic
223C4⋊C8×C61C2311yescharacteristic
224#103×C61C2314yes—
225#103×C61C2314yes—
226C22⋊C8×C61C2312yes—
227C4×C8×C61C2312yes—
228C2×Q8×C61—22no—
229C2×Q8×C61—21no—
230C2×Q8×C61—22no—
231C2×Q8×C61—82no—
232C2×Q8×C61C2412yes—
233C22×C4×C61—22no—
234C22×C4×C61C2×D411yescharacteristic
235C22×C4×C61C2×D411yescharacteristic
236C22×C4×C61C2411yescharacteristic
237C2×C22⋊D61C2×D412yes—
238C22×Dic61—21no—
239C22×Dic61—21no—
240Q8×D61—24no—
241Q8×D61—42no—
242Q8×D61—84no—
243#11758222Q1618yescomplemented
244C2×D244C2×D411yescharacteristic
245C2×C4×D61—22no—
246C2×C4×D61—24no—
247C2×C4×D61—22no—
248C2×C4×D61C2×D412yes—
249C2×C4×D61C2×D412yes—
250C2×C4×D61C2412yes—
251C2×Dic122—22no—
252C2×Dic122—21no—
253C2×Dic122—21no—
254C2×Dic122—22no—
255C2×Dic122—24no—
256C2×Dic122—22no—
257C2×Dic122—41no—
258C2×Dic122C2×D411yescharacteristic
259C2×Dic122C2411yescharacteristic
260C2×Dic122C2412yes—
261C2×Dic122C2411yescharacteristic
262C2×C8×C61C2412yes—
263C2×C8×C61C2412yes—
264C4⋊C4×C61—22no—
265C4⋊C4×C61—22no—
266C4⋊C4×C61—22no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—22no—
271C4⋊C4×C61—22no—
272C4⋊C4×C61C2414yes—
273C4⋊C4×C61C2412yes—
274C22⋊C4×C61—22no—
275C42×C61—22no—
276C42×C61C2×D411yescharacteristic
277C42×C61C2×D411yescharacteristic
278C42×C61C2411yescharacteristic
279C42×C61C2411yescharacteristic
280C22⋊Dic61—22no—
281C22⋊Dic61C2×D412yes—
282#11758202—44no—
283#11758198—22no—
284#11758198—22no—
285#11758198—24no—
286#11758198C2×D412yes—
287#11758198C2×D412yes—
288C4⋊Dic61—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61—21no—
292C4⋊Dic61—22no—
293C4⋊Dic61—22no—
294C4⋊Dic61—24no—
295C4⋊Dic61C2×D411yescharacteristic
296C4⋊Dic61C2×D411yescharacteristic
297C4⋊Dic61C2412yes—
298C4⋊Dic61C2411yescharacteristic
299C4⋊Dic61C2411yescharacteristic
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—22no—
305#11758196—22no—
306#11758196—24no—
307#11758196—22no—
308#11758196—22no—
309#11758196—24no—
310#11758196—22no—
311#11758196—22no—
312#11758196—24no—
313#11758196—22no—
314#11758196—22no—
315#11758196C2×D412yes—
316#11758196C2×D412yes—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61—21no—
321C4×Dic61—22no—
322C4×Dic61—22no—
323C4×Dic61—22no—
324C4×Dic61—24no—
325C4×Dic61C2×D412yes—
326C4×Dic61C2×D412yes—
327C4×Dic61C2412yes—
328C2×#92418—42no—
329C2×#92418C2414yes—
330Dic244—24no—
331Dic244—42no—
332C8×D61—44no—
333C23×C61C22×D411yescharacteristic
334C22×D61C22×D412yes—
335Q8×C61—22no—
336Q8×C61—22no—
337Q8×C61—44no—
338Q8×C61—81no—
339Q8×C61—82no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—24no—
345C2×C4×C61—41no—
346C2×C4×C61—82no—
347C2×C4×C61C2×Q1614yes—
348C2×C4×C61C22×D411yescharacteristic
349C2×C4×C61C22×D411yescharacteristic
350C2×C4×C61C22×D411yescharacteristic
351C2×C4×C61C22×D411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C2511yescharacteristic
354C22⋊D61C2×Q1618yes—
355C2×Dic61—21no—
356C2×Dic61—21no—
357C2×Dic61—22no—
358C2×Dic61—21no—
359C2×Dic61—21no—
360C2×Dic61—22no—
361C2×Dic61—42no—
362C2×Dic61—81no—
363C2×Dic61C22×D412yes—
364C2×Dic61C22×D412yes—
365C2×Dic61C22×D412yes—
366D244C2×Q1614yes—
367C4×D61—22no—
368C4×D61—22no—
369C4×D61—42no—
370C4×D61—44no—
371C4×D61—82no—
372C4×D61—84no—
373C4×D61C2×Q1618yes—
374Dic122—21no—
375Dic122—22no—
376Dic122—21no—
377Dic122—21no—
378Dic122—22no—
379Dic122—44no—
380Dic122—42no—
381Dic122—42no—
382Dic122—82no—
383Dic122—84no—
384Dic122C2×Q1614yes—
385Dic1222−1+412yes—
386C8×C61—22no—
387C8×C61—22no—
388#92418—24no—
389#62100—611nomaximal, Sylow
390C22×C61—21no—
391C22×C61—21no—
392C22×C61C22×Q1612yes—
393C22×C61C23×D411yescharacteristic
394C2×D61—22no—
395C2×D61—22no—
396C2×D61C22×Q1614yes—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—44no—
401C4×C61—42no—
402C4×C61—42no—
403C4×C61C22×Q1612yes—
404C4×C61C22×Q1612yes—
405C4×C61C2×2−1+411yescharacteristic
406C4×C61#58511yescharacteristic
407Dic61—22no—
408Dic61—22no—
409Dic61—22no—
410Dic61—42no—
411Dic61—41no—
412Dic61—41no—
413Dic61—41no—
414Dic61—42no—
415Dic61C22×Q1614yes—
416#3503—611no—
417Q8×#41—611no—
418Q8×Q16—612no—
419#3363—612no—
420#3338—612no—
421#3338—614no—
422#3299—612no—
423#3299—614no—
424#3249—612no—
425#3249—611no—
426#3230—612no—
427#3230D6111yescharacteristic, complemented
428#3104—612no—
429#3104—611no—
430C2×#477—612no—
431C2×#477—611no—
432#2988—611no—
433C2×C61—22no—
434C2×C61#348911yescharacteristic
435C2×C61C23×Q1611yescharacteristic
436C2×C61#358511yescharacteristic
437D61—24no—
438Q82—612no—
439Q82—611no—
440#557—611no—
441#557—1221no—
442#557—1221no—
443#554—611no—
444#554—612no—
445#554—612no—
446#554—614no—
447#554—1222no—
448#554—1221no—
449D4×Q8—611no—
450D4×Q8—612no—
451D4×Q8—1221no—
452D4×Q8—1222no—
453#544—1221no—
454#544—1222no—
455#533—612no—
456#533—612no—
457#533—611no—
458#533—1221no—
459#533—1222no—
460#533C2×D6111yescharacteristic
461C2×C4⋊Q8—612no—
462C2×C4⋊Q8C2×D6111yescharacteristic
463#520—1221no—
464C4×#41—611no—
465C4×#41—1221no—
466C2×C4×Q8—612no—
467C2×C4×Q8—611no—
468#500—614no—
469#500C2×D6112yes—
470#487—614no—
471#487C2×D6112yes—
472#484—614no—
473#484—614no—
474#484—614no—
475#484—612no—
476#484C2×D6114yes—
477#477—612no—
478#477—612no—
479#477—612no—
480#477—612no—
481#477—612no—
482#477—612no—
483#477—614no—
484#477—614no—
485#477—611no—
486#477—611no—
487#477—614no—
488#477C2×D6112yes—
489#477C2×D6112yes—
490#467—614no—
491#467—614no—
492#467—614no—
493#462—612no—
494#462—612no—
495#462—611no—
496#462—611no—
497#462—614no—
498#451—614no—
499#451—612no—
500C8×Q8—612no—
501C4×Q16—614no—
502C4×Q16—614no—
503C4×Q16—612no—
504C4×Q16—612no—
505C8×D4—614no—
506C8×D4—612no—
507#431—612no—
508#431C2×D6111yescharacteristic
509C2×#107—612no—
510C2×#107—614no—
511C2×C4⋊C8—611no—
512C2×C4⋊C8—612no—
513C2×#103—612no—
514C2×#103—614no—
515C61#6210011yescharacteristic, complemented, Sylow
516C2×#41—611no—
517C22×Q8—21no—
518C22×Q8—612no—
519C22×Q8—611no—
520C22×Q8—1222no—
521C2×Q16—614no—
522C2×Q16—612no—
523C2×Q16—612no—
524C22×C8—612no—
525C22×C8—614no—
526C4⋊Q8—21no—
527C4⋊Q8—21no—
528C4⋊Q8—614no—
529C4⋊Q8—612no—
530C4⋊Q8—612no—
531C4⋊Q8—611no—
532C4⋊Q8—611no—
533C4⋊Q8—1222no—
534C4⋊Q8—1222no—
535C4⋊Q8—1222no—
536C4⋊Q8—1221no—
537C4⋊Q8—1221no—
538C4⋊Q8—1222no—
539C4⋊Q8—1222no—
540C4⋊Q8—1224no—
541C4⋊Q8C22×D6111yescharacteristic
542C4⋊Q8C22×D6112yes—
543C4⋊Q8C22×D6112yes—
544C4⋊Q8C22×D6111yescharacteristic
545#125—21no—
546#125—1222no—
547#125—1222no—
548#125—1222no—
549#125—1221no—
550#125—1222no—
551#125—1221no—
552#125—1224no—
553#125—1222no—
554#125—1221no—
555C22⋊Q8—21no—
556C22⋊Q8—612no—
557C22⋊Q8—612no—
558C22⋊Q8—612no—
559C22⋊Q8—614no—
560C22⋊Q8—1222no—
561C22⋊Q8—1222no—
562C22⋊Q8—1222no—
563C22⋊Q8—1222no—
564C22⋊Q8—1222no—
565C22⋊Q8—1224no—
566C22⋊Q8—1224no—
567C22⋊Q8—1222no—
568C22⋊Q8—1224no—
569C22⋊Q8—1222no—
570C22⋊Q8—1222no—
571C22⋊Q8—1221no—
572C22⋊Q8C22×D6112yes—
573C4×Q8—21no—
574C4×Q8—611no—
575C4×Q8—611no—
576C4×Q8—612no—
577C4×Q8—612no—
578C4×Q8—614no—
579C4×Q8—611no—
580C4×Q8—611no—
581C4×Q8—611no—
582C4×Q8—611no—
583C4×Q8—612no—
584C4×Q8—1222no—
585C4×Q8—1222no—
586C4×Q8—1222no—
587C4×Q8—1222no—
588C4×Q8—1221no—
589C4×Q8—1221no—
590C4×Q8—1222no—
591C4×Q8—1221no—
592C4×Q8—1221no—
593C4×Q8—1221no—
594C4×Q8C22×D6112yes—
595C4×D4—612no—
596C4×D4—612no—
597C4×D4—611no—
598C4×D4—611no—
599C4×D4—1222no—
600C4×D4—1222no—
601C4×D4—1221no—
602C4×D4—1221no—
603C4×D4—1222no—
604C4×D4—1224no—
605#117—21no—
606#117—611no—
607#117—612no—
608#117—1222no—
609#117—1222no—
610#117—1221no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—611no—
613C2×C4⋊C4—612no—
614C2×C4⋊C4—614no—
615C2×C4⋊C4—1222no—
616C2×C4⋊C4—1222no—
617C2×C4⋊C4—1221no—
618C2×C4⋊C4C22×D6112yes—
619C2×C42—612no—
620C2×C42—1222no—
621C2×C42—1221no—
622C2×C42C22×D6111yescharacteristic
623#107—612no—
624#107—612no—
625#107—614no—
626#107—614no—
627#107—614no—
628#107C22×D6114yes—
629#107C22×D6114yes—
630C4⋊C8—614no—
631C4⋊C8—612no—
632C4⋊C8—612no—
633C4⋊C8C22×D6111yescharacteristic
634C4⋊C8C22×D6111yescharacteristic
635#103—614no—
636#103—612no—
637#103—612no—
638#103—612no—
639#103—612no—
640#103—614no—
641#103—614no—
642#103—614no—
643#103C22×D6114yes—
644#103C22×D6114yes—
645C22⋊C8—614no—
646C22⋊C8C22×D6112yes—
647C4×C8—614no—
648C4×C8C22×D6112yes—
649#41—618no—
650C2×Q8—22no—
651C2×Q8—21no—
652C2×Q8—22no—
653C2×Q8—82no—
654C2×Q8—611no—
655C2×Q8—611no—
656C2×Q8—611no—
657C2×Q8—612no—
658C2×Q8—1222no—
659C2×Q8—1224no—
660C2×Q8—1222no—
661C2×Q8—1222no—
662C2×Q8—1221no—
663C2×Q8—1221no—
664C2×Q8—1224no—
665C2×Q8—4884no—
666C2×Q8—2441no—
667C2×Q8—2442no—
668C2×Q8C23×D6112yes—
669C2×D4—612no—
670C2×D4—611no—
671C22×C4—22no—
672C22×C4—612no—
673C22×C4—612no—
674C22×C4—612no—
675C22×C4—1222no—
676C22×C4—1224no—
677C22×C4—1222no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4D4×D6111yescharacteristic
681C22×C4D4×D6111yescharacteristic
682C22×C4C23×D6111yescharacteristic
683Q16—1224no—
684Q16—2442no—
685Q16—2444no—
686C2×C8—614no—
687C2×C8—2444no—
688C2×C8—2442no—
689C2×C8C23×D6112yes—
690C2×C8C23×D6112yes—
691C4⋊C4—22no—
692C4⋊C4—22no—
693C4⋊C4—22no—
694C4⋊C4—22no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—22no—
699C4⋊C4—612no—
700C4⋊C4—612no—
701C4⋊C4—611no—
702C4⋊C4—611no—
703C4⋊C4—612no—
704C4⋊C4—611no—
705C4⋊C4—611no—
706C4⋊C4—1222no—
707C4⋊C4—1224no—
708C4⋊C4—1224no—
709C4⋊C4—1222no—
710C4⋊C4—1222no—
711C4⋊C4—1222no—
712C4⋊C4—1222no—
713C4⋊C4—1224no—
714C4⋊C4—1222no—
715C4⋊C4—1222no—
716C4⋊C4—1224no—
717C4⋊C4—1222no—
718C4⋊C4—1221no—
719C4⋊C4—1221no—
720C4⋊C4—1221no—
721C4⋊C4—1221no—
722C4⋊C4—1221no—
723C4⋊C4—1221no—
724C4⋊C4—1222no—
725C4⋊C4—1222no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4C23×D6114yes—
729C4⋊C4C23×D6112yes—
730C22⋊C4—22no—
731C22⋊C4—612no—
732C22⋊C4—612no—
733C22⋊C4—612no—
734C22⋊C4—1222no—
735C22⋊C4—1222no—
736C22⋊C4—1224no—
737C22⋊C4—1222no—
738C42—22no—
739C42—612no—
740C42—612no—
741C42—612no—
742C42—1222no—
743C42—1222no—
744C42—1224no—
745C42—1221no—
746C42—1221no—
747C42—1221no—
748C42—1221no—
749C42—1222no—
750C42D4×D6111yescharacteristic
751C42D4×D6111yescharacteristic
752C42C23×D6111yescharacteristic
753C42C23×D6111yescharacteristic
754C23—612no—
755C23C2×D4×D6111yescharacteristic
756Q8—22no—
757Q8—22no—
758Q8—44no—
759Q8—81no—
760Q8—82no—
761Q8—614no—
762Q8—612no—
763Q8—1221no—
764Q8—1222no—
765Q8—1221no—
766Q8—1222no—
767Q8—1221no—
768Q8—4882no—
769Q8—4884no—
770Q8—2442no—
771Q8—2442no—
772Q8—2444no—
773D4—618no—
774D4—614no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—41no—
781C2×C4—82no—
782C2×C4—612no—
783C2×C4—618no—
784C2×C4—612no—
785C2×C4—612no—
786C2×C4—1221no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1221no—
790C2×C4—1222no—
791C2×C4—1221no—
792C2×C4—1221no—
793C2×C4—1222no—
794C2×C4—4882no—
795C2×C4—4884no—
796C2×C4—4881no—
797C2×C4—2442no—
798C2×C4—2444no—
799C2×C4—2442no—
800C2×C4Q16×D6114yes—
801C2×C4C2×D4×D6111yescharacteristic
802C2×C4C2×D4×D6111yescharacteristic
803C2×C4C2×D4×D6111yescharacteristic
804C2×C4C2×D4×D6111yescharacteristic
805C2×C4C2×D4×D6111yescharacteristic
806C2×C4C24×D6111yescharacteristic
807C8—22no—
808C8—22no—
809C8—1224no—
810C22—21no—
811C22—21no—
812C22—614no—
813C22—1222no—
814C22—1222no—
815C22C2×Q16×D6112yes—
816C22C22×D4×D6111yescharacteristic
817C4—21no—
818C4—21no—
819C4—21no—
820C4—42no—
821C4—44no—
822C4—42no—
823C4—614no—
824C4—1222no—
825C4—1222no—
826C4—1222no—
827C4—2441no—
828C4—2442no—
829C4—2441no—
830C4—2442no—
831C4—2441no—
832C4C2×Q16×D6112yes—
833C4C2×Q16×D6112yes—
834C42−1+4×D6111yescharacteristic
835C4#1684059911yescharacteristic
836C2—22no—
837C2—1224no—
838C2#2145949711yescharacteristic
839C2C22×Q16×D6111yescharacteristic
840C2#2146059511yescharacteristic
subgroupG/H
centerC22C22×D4×D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3230C2
socleC22×C61C23×D4
prime radicalC2×#11758222D4
hypercenter#3230D61
hypocenterC61#62100
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3230

Complements

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

NH ≅ G/Ntype
3. #21458702C2semidirect
4. #21458494C2semidirect
5. #21458211C2semidirect
6. #21458206C2semidirect
7. #21457694C2semidirect
8. #21457693C2semidirect
9. #21457163C2semidirect
10. #21457161C2semidirect
11. #21456969C2semidirect
12. #21455860C2semidirect
13. #21455859C2semidirect
14. C2×#16840054C2semidirect
15. #477×D61C2semidirect
17. C61×#3230C2semidirect
243. #11758222Q16semidirect
427. #3230D61semidirect
515. C61#62100semidirect

Maximal subgroups

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

subgroupindex
#214596352
#214593972
#214587022
#214584942
#214582112
#214582062
#214576942
#214576932
#214571632
#214571612
#214569692
#214558602
#214558592
C2×#168400542
#477×D612
#214549272
C61×#32302
#6210061