Finite Group Databasebeta

← #30553059

Subgroups — #30553059

Order 15616.

1822 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459209C211yesmaximal, characteristic, complemented
2#21457284C214yesmaximal, complemented
3#21457275C214yesmaximal, complemented
4#21457245C214yesmaximal, complemented
5#21457230C214yesmaximal, complemented
6#21455628C212yesmaximal, complemented
7#21455624C211yesmaximal, characteristic, complemented
8#21455616C211yesmaximal, characteristic, complemented
9#21455445C212yesmaximal, complemented
10#21455434C212yesmaximal, complemented
11#21455309C212yesmaximal, complemented
12#21455291C211yesmaximal, characteristic, complemented
13#21455283C211yesmaximal, characteristic, complemented
14#21454383C211yesmaximal, characteristic, complemented
15C2×C61×#542C211yesmaximal, characteristic, complemented
16C2×#14519808C2212yes—
17C2×#14519803C2212yes—
18C22×#11758194C2212yes—
19#16840383C2212yescomplemented
20#16840383C2212yescomplemented
21#16840374C2212yescomplemented
22#16840367C2212yescomplemented
23#16840359—21no—
24#16840359—21no—
25#16840350—21no—
26#16840350—21no—
27#16840319C2211yescharacteristic
28#16840312C2211yescharacteristic
29#16840290—22no—
30#16840290—22no—
31#16840273C2212yes—
32C4×#11758222C2212yes—
33#16840069C2214yescomplemented
34#16840062C2214yescomplemented
35#16840057C2212yescomplemented
36#16840054C2214yescomplemented
37#16840052C2212yescomplemented
38#16840049C2214yescomplemented
39#16840047C2212yescomplemented
40#16840044C2214yescomplemented
41#16840042C2212yescomplemented
42#16840039C2214yescomplemented
43#16840018C2214yescomplemented
44#16840013C2214yes—
45#16840010C2214yescomplemented
46#16840006C2214yes—
47#16840001C2214yescomplemented
48#16839996C2214yes—
49#16839993C2214yescomplemented
50#16839989C2214yes—
51#16839984C2214yescomplemented
52#16839981C2214yescomplemented
53#16839981C2214yescomplemented
54#16839977C2214yescomplemented
55#16839974C2214yescomplemented
56#16839974C2214yescomplemented
57#16839972C2212yescomplemented
58#16839967C2212yescomplemented
59#16839962C2212yescomplemented
60#16839957C2212yescomplemented
61#16839802C2212yes—
62#16839802C2212yes—
63#16839789C2214yescomplemented
64#16839789C2214yescomplemented
65#16839786C2211yescharacteristic
66#16839786C2211yescharacteristic
67#16839786C2212yes—
68#16839771C2212yes—
69#16839767C2212yes—
70#16839761C2212yes—
71#16839761C2212yes—
72C61×#542—22no—
73C61×#542—22no—
74C61×#542C2214yes—
75C61×#542C2214yes—
76C2×C4⋊Q8×C61C2211yescharacteristic
77C2×#126×C61—21no—
78C2×#124×C61—21no—
79C2×#124×C61C2211yescharacteristic
80C2×#123×C61—21no—
81C2×C22⋊Q8×C61—21no—
82C2×C22⋊Q8×C61C2211yescharacteristic
83C2×#121×C61C2211yescharacteristic
84C2×C4×Q8×C61C2211yescharacteristic
85C2×C4×D4×C61C2211yescharacteristic
86C2×#117×C61C2211yescharacteristic
87C2×#11758222C2312yes—
88#14519808—44no—
89#14519803—44no—
90C2×#11758202C2314yes—
91C2×#11758200C2314yes—
92C2×#11758201C2314yes—
93C2×#11758199C2314yes—
94C2×#11758194—44no—
95C2×#11758194C2312yes—
96C2×#11758194C2312yes—
97C2×#11758194C2314yes—
98C22×#92418C2314yes—
99#14519777C2311yescharacteristic
100#14519777C2311yescharacteristic
101#14519777C2311yescharacteristic
102#14519774C2311yescharacteristic
103#14519772—22no—
104#14519772—22no—
105#14519770—22no—
106#14519770—22no—
107#14519769C2312yes—
108#14519767—22no—
109#14519767—22no—
110#14519765C2312yes—
111#14519763—22no—
112#14519763—22no—
113#14519762—22no—
114#14519762—22no—
115#14519760—22no—
116#14519759—22no—
117#14519759—22no—
118#14519756—21no—
119#14519756—21no—
120#14519756C2312yes—
121#14519756C2312yes—
122#14519755—22no—
123#14519755—22no—
124#14519751—21no—
125#14519751—21no—
126#14519751C2312yes—
127#14519751C2312yes—
128#14519750—22no—
129#14519750—22no—
130#14519746—22no—
131C4×Dic122—21no—
132C4×Dic122—21no—
133C4×Dic122C2312yes—
134C4×Dic122C2312yes—
135C4×D244—21no—
136C4×D244—21no—
137C4×D244C2312yes—
138C4×D244C2312yes—
139C4×C22⋊D61—22no—
140C4×C22⋊D61—22no—
141C4×C22⋊D61—22no—
142C4×C22⋊D61—22no—
143#14519736C2312yes—
144#14519734—22no—
145C42×D61—22no—
146#14519710C2314yes—
147#14519710C2314yes—
148#14519708C2314yes—
149#14519708C2314yes—
150C4⋊#92418C2312yes—
151C4⋊#92418C2312yes—
152C4⋊#92418C2314yes—
153C4⋊#92418C2314yes—
154C4⋊#92418C2312yes—
155C4⋊#92418C2312yes—
156#14519701C2314yes—
157#14519701C2314yes—
158#14519700C2314yes—
159#14519700C2314yes—
160#14519698C2314yes—
161#14519698C2314yes—
162#14519697C2314yes—
163#14519697C2314yes—
164C22×Q8×C61—21no—
165C22×Q8×C61C2311yescharacteristic
166C22×D4×C61—21no—
167C22×D4×C61C2311yescharacteristic
168C23×C4×C61—21no—
169C23×C4×C61C2311yescharacteristic
170C4⋊Q8×C61—22no—
171C4⋊Q8×C61C2314yes—
172#126×C61—24no—
173#126×C61—24no—
174#124×C61—24no—
175#124×C61—24no—
176#124×C61—22no—
177#124×C61C2314yes—
178#123×C61—24no—
179#123×C61—24no—
180C22⋊Q8×C61—22no—
181C22⋊Q8×C61—24no—
182C22⋊Q8×C61—24no—
183C22⋊Q8×C61C2314yes—
184#121×C61—22no—
185#121×C61C2314yes—
186C4×Q8×C61—21no—
187C4×Q8×C61—21no—
188C4×Q8×C61C2312yes—
189C4×Q8×C61C2312yes—
190C4×D4×C61—21no—
191C4×D4×C61—21no—
192C4×D4×C61C2312yes—
193C4×D4×C61C2312yes—
194#117×C61D412yes—
195#117×C61D412yes—
196#117×C61C2312yes—
197#117×C61C2312yes—
198C2×C4⋊C4×C61—21no—
199C2×C4⋊C4×C61—21no—
200C2×C4⋊C4×C61—21no—
201C2×C4⋊C4×C61D411yescharacteristic
202C2×C4⋊C4×C61D411yescharacteristic
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C4⋊C4×C61C2311yescharacteristic
205C2×C22⋊C4×C61—21no—
206C2×C22⋊C4×C61—21no—
207C2×C22⋊C4×C61—21no—
208C2×C22⋊C4×C61—21no—
209C2×C22⋊C4×C61—21no—
210C2×C22⋊C4×C61D411yescharacteristic
211C2×C22⋊C4×C61D411yescharacteristic
212C2×C42×C61—21no—
213C2×C42×C61C2311yescharacteristic
214C2×C42×C61C2311yescharacteristic
215C24×C61—21no—
216C24×C61C2×D411yescharacteristic
217C2×Q8×C61—21no—
218C2×Q8×C61—24no—
219C2×Q8×C61—22no—
220C2×Q8×C61—22no—
221C2×Q8×C61—82no—
222C2×Q8×C61C2412yes—
223C2×D4×C61—24no—
224C2×D4×C61—21no—
225C2×D4×C61—22no—
226C2×D4×C61—22no—
227C2×D4×C61—82no—
228C2×D4×C61C2412yes—
229C22×C4×C61—22no—
230C22×C4×C61—22no—
231C22×C4×C61—21no—
232C22×C4×C61—21no—
233C22×C4×C61—21no—
234C22×C4×C61—22no—
235C22×C4×C61—22no—
236C22×C4×C61—82no—
237C22×C4×C61C2×D411yescharacteristic
238C22×C4×C61C2×D412yes—
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2×D411yescharacteristic
241C22×C4×C61C2×D411yescharacteristic
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2412yes—
244C22×C4×C61C2411yescharacteristic
245C2×C22⋊D61—22no—
246C2×C22⋊D61—22no—
247C2×C22⋊D61—22no—
248#11758222—24no—
249#11758222—24no—
250C2×D244—21no—
251C2×D244—21no—
252C2×D244C2412yes—
253C2×C4×D61—22no—
254C2×C4×D61—22no—
255C2×C4×D61—22no—
256C2×Dic122—21no—
257C2×Dic122—21no—
258C2×Dic122C2412yes—
259C4⋊C4×C61—22no—
260C4⋊C4×C61—22no—
261C4⋊C4×C61—24no—
262C4⋊C4×C61—24no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61C2×D412yes—
266C4⋊C4×C61C2×D412yes—
267C4⋊C4×C61C2×D412yes—
268C4⋊C4×C61C2×D412yes—
269C4⋊C4×C61C2412yes—
270C4⋊C4×C61C2412yes—
271C22⋊C4×C61—24no—
272C22⋊C4×C61—22no—
273C22⋊C4×C61—22no—
274C22⋊C4×C61—24no—
275C22⋊C4×C61—24no—
276C22⋊C4×C61—24no—
277C22⋊C4×C61C2×D412yes—
278C22⋊C4×C61C2×D412yes—
279C22⋊C4×C61C2×D412yes—
280C22⋊C4×C61C2×D412yes—
281C42×C61—22no—
282C42×C61—22no—
283C42×C61C2×D411yescharacteristic
284C42×C61C2×D411yescharacteristic
285C42×C61C2×D412yes—
286C42×C61C2411yescharacteristic
287C42×C61C2411yescharacteristic
288C42×C61C2412yes—
289C22⋊Dic61—22no—
290C22⋊Dic61—22no—
291C22⋊Dic61—22no—
292#11758202—44no—
293#11758201—44no—
294#11758200—44no—
295#11758199—44no—
296#11758198—22no—
297#11758198—22no—
298#11758198—22no—
299#11758198—22no—
300#11758198—22no—
301#11758198—22no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61C2412yes—
307C4⋊Dic61C2412yes—
308#11758196—22no—
309#11758196—22no—
310#11758196—22no—
311#11758196—22no—
312#11758196—22no—
313#11758196—22no—
314C4×Dic61—22no—
315C4×Dic61—22no—
316C4×Dic61—22no—
317#11758194—24no—
318#11758194—24no—
319#11758194—44no—
320C2×#92418—44no—
321C2×#92418C2414yes—
322C2×#92418C2414yes—
323C23×C61—22no—
324C23×C61—22no—
325C23×C61—41no—
326C23×C61—41no—
327C23×C61—42no—
328C23×C61—42no—
329C23×C61—42no—
330C23×C61C22×D412yes—
331C23×C61C22×D411yescharacteristic
332C22×D61—22no—
333Q8×C61—22no—
334Q8×C61—22no—
335Q8×C61—42no—
336Q8×C61—84no—
337D4×C61—22no—
338D4×C61—22no—
339D4×C61—42no—
340D4×C61—84no—
341C2×C4×C61—22no—
342C2×C4×C61—24no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—22no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—41no—
352C2×C4×C61—42no—
353C2×C4×C61—42no—
354C2×C4×C61—42no—
355C2×C4×C61—82no—
356C2×C4×C61—82no—
357C2×C4×C61C22×D412yes—
358C2×C4×C61C22×D412yes—
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C22×D411yescharacteristic
361C2×C4×C61C22×D412yes—
362C2×C4×C61C22×D411yescharacteristic
363C2×C4×C61C22×D411yescharacteristic
364C2×C4×C61C22×D411yescharacteristic
365C2×C4×C61H(5,𝔽2)12yes—
366C2×C4×C612−1+412yes—
367C2×C4×C61C2511yescharacteristic
368C22⋊D61—44no—
369C22⋊D61—82no—
370C22⋊D61—82no—
371C2×Dic61—22no—
372C2×Dic61—22no—
373C2×Dic61—22no—
374D244—22no—
375D244—22no—
376D244—81no—
377D244—81no—
378C4×D61—44no—
379C4×D61—82no—
380C4×D61—82no—
381Dic122—22no—
382Dic122—22no—
383Dic122—81no—
384Dic122—81no—
385#92418—24no—
386#92418—24no—
387#60919—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—22no—
393C22×C61—42no—
394C22×C61—42no—
395C22×C61—42no—
396C22×C61—82no—
397C22×C61—84no—
398C22×C61#53712yes—
399C22×C61C23×D411yescharacteristic
400C2×D61—42no—
401C2×D61—42no—
402C2×D61—42no—
403C4×C61—21no—
404C4×C61—22no—
405C4×C61—21no—
406C4×C61—21no—
407C4×C61—22no—
408C4×C61—21no—
409C4×C61—22no—
410C4×C61—42no—
411C4×C61—42no—
412C4×C61—42no—
413C4×C61#53712yes—
414C4×C61C2×H(5,𝔽2)11yescharacteristic
415C4×C61C2×2−1+411yescharacteristic
416Dic61—42no—
417Dic61—42no—
418Dic61—42no—
419#3455—611no—
420C2×#542D6111yescharacteristic, complemented
421#3263—614no—
422#3262—614no—
423#3258—614no—
424#3257—614no—
425#3079—612no—
426#3078—611no—
427#3077—611no—
428#3056—612no—
429#3055—612no—
430#3040—612no—
431#3037—611no—
432#3036—611no—
433#2905—611no—
434C2×C61—22no—
435C2×C61—42no—
436C2×C61—82no—
437C2×C61C2×#53711yescharacteristic
438C2×C61#358511yescharacteristic
439C2×C61#358611yescharacteristic
440D61—82no—
441C2×#137—612no—
442C2×AGL(1,ℤ/8)—612no—
443C22×M16—612no—
444#542—22no—
445#542—22no—
446#542—612no—
447#542—612no—
448#542C2×D6114yes—
449#542C2×D6114yes—
450#541—612no—
451#540—612no—
452#539—1221no—
453#539—1221no—
454#538—1221no—
455#538—1221no—
456#533—611no—
457#532—611no—
458C2×C4⋊Q8C2×D6111yescharacteristic
459#529—1222no—
460#529—1222no—
461C2×#126—21no—
462C2×#124—21no—
463C2×#124C2×D6111yescharacteristic
464#525—612no—
465C2×#123—21no—
466C2×C22⋊Q8—21no—
467C2×C22⋊Q8C2×D6111yescharacteristic
468C2×#121C2×D6111yescharacteristic
469C4×#41—612no—
470C2×C4×Q8C2×D6111yescharacteristic
471C2×C4×D4C2×D6111yescharacteristic
472C2×#117C2×D6111yescharacteristic
473#479—614no—
474#478—614no—
475#477—614no—
476#477—612no—
477#476—614no—
478#476—612no—
479#475—614no—
480#475—612no—
481#474—614no—
482#474—612no—
483#470—614no—
484#469—614no—
485#468—614no—
486#468—614no—
487#467—614no—
488#466—614no—
489#465—614no—
490#465—614no—
491#464—614no—
492#464—614no—
493#464—614no—
494#463—614no—
495#463—614no—
496#463—614no—
497#462—612no—
498#461—612no—
499#460—612no—
500#459—612no—
501#428—612no—
502#428—612no—
503#424—614no—
504#424—614no—
505#423—611no—
506#423—611no—
507#423—612no—
508#419—612no—
509#418—612no—
510#417—612no—
511#417—612no—
512C61#6091911yescharacteristic, complemented, Sylow
513C2×#41—612no—
514C22×Q8—21no—
515C22×Q8C22×D6111yescharacteristic
516C22×D4—21no—
517C22×D4C22×D6111yescharacteristic
518C23×C4—21no—
519C23×C4C22×D6111yescharacteristic
520#137—2444no—
521AGL(1,ℤ/8)—2444no—
522C2×Q16—614no—
523C2×SD16—614no—
524C2×SD16—614no—
525C2×D8—614no—
526C2×M16—612no—
527C2×M16—612no—
528C2×M16—614no—
529C2×M16—2444no—
530C22×C8—614no—
531C4⋊Q8—22no—
532C4⋊Q8—611no—
533C4⋊Q8—611no—
534C4⋊Q8—611no—
535C4⋊Q8C22×D6114yes—
536#127—611no—
537#126—24no—
538#126—24no—
539#126—1222no—
540#126—1222no—
541#126—1222no—
542#126—1222no—
543#125—612no—
544#125—1222no—
545#125—1222no—
546#124—24no—
547#124—24no—
548#124—22no—
549#124—612no—
550#124—1222no—
551#124—1222no—
552#124C22×D6114yes—
553#123—24no—
554#123—24no—
555#123—1222no—
556#123—1222no—
557#123—1222no—
558#123—1222no—
559#123—1222no—
560C22⋊Q8—22no—
561C22⋊Q8—24no—
562C22⋊Q8—24no—
563C22⋊Q8—612no—
564C22⋊Q8—612no—
565C22⋊Q8—1221no—
566C22⋊Q8—1221no—
567C22⋊Q8—1222no—
568C22⋊Q8—1222no—
569C22⋊Q8C22×D6114yes—
570#121—22no—
571#121—612no—
572#121—612no—
573#121—1221no—
574#121—1221no—
575#121—1222no—
576#121—1222no—
577#121C22×D6114yes—
578#120—1222no—
579C4×Q8—21no—
580C4×Q8—21no—
581C4×Q8—612no—
582C4×Q8—612no—
583C4×Q8—1221no—
584C4×Q8—1221no—
585C4×Q8C22×D6112yes—
586C4×Q8C22×D6112yes—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—612no—
590C4×D4—612no—
591C4×D4—1222no—
592C4×D4—1222no—
593C4×D4—1222no—
594C4×D4—1222no—
595C4×D4—1221no—
596C4×D4—1221no—
597C4×D4C22×D6112yes—
598C4×D4C22×D6112yes—
599#117—612no—
600#117—1222no—
601#117C22⋊D6112yes—
602#117C22⋊D6112yes—
603#117C22×D6112yes—
604#117C22×D6112yes—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4C22⋊D6111yescharacteristic
609C2×C4⋊C4C22⋊D6111yescharacteristic
610C2×C4⋊C4C22×D6111yescharacteristic
611C2×C4⋊C4C22×D6111yescharacteristic
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4C22⋊D6111yescharacteristic
618C2×C22⋊C4C22⋊D6111yescharacteristic
619C2×C42—21no—
620C2×C42—1222no—
621C2×C42C22×D6111yescharacteristic
622C2×C42C22×D6111yescharacteristic
623#107—614no—
624#107—614no—
625#106—614no—
626#106—614no—
627C4⋊C8—612no—
628C4⋊C8—612no—
629C4⋊C8—612no—
630C4⋊C8—614no—
631C4⋊C8—614no—
632C4⋊C8—612no—
633#103—614no—
634#103—614no—
635#103—614no—
636#103—614no—
637#102—614no—
638#102—614no—
639#102—614no—
640#102—614no—
641C24—21no—
642C24C2×C22⋊D6111yescharacteristic
643#41—1224no—
644#41—1224no—
645C2×Q8—21no—
646C2×Q8—24no—
647C2×Q8—22no—
648C2×Q8—22no—
649C2×Q8—82no—
650C2×Q8—612no—
651C2×Q8—1221no—
652C2×Q8—1221no—
653C2×Q8C23×D6112yes—
654C2×D4—24no—
655C2×D4—21no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—82no—
659C2×D4—612no—
660C2×D4—1222no—
661C2×D4—1222no—
662C2×D4—1222no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4C23×D6112yes—
666C22×C4—22no—
667C22×C4—22no—
668C22×C4—21no—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—82no—
674C22×C4—1222no—
675C22×C4—1222no—
676C22×C4—1222no—
677C22×C4C2×C22⋊D6111yescharacteristic
678C22×C4C2×C22⋊D6112yes—
679C22×C4C2×C22⋊D6111yescharacteristic
680C22×C4C2×C22⋊D6111yescharacteristic
681C22×C4C2×C22⋊D6111yescharacteristic
682C22×C4C2×C22⋊D6111yescharacteristic
683C22×C4C23×D6112yes—
684C22×C4C23×D6111yescharacteristic
685Q16—2444no—
686SD16—2444no—
687SD16—2444no—
688D8—2444no—
689M16—1224no—
690M16—1224no—
691M16—2444no—
692C2×C8—614no—
693C2×C8—614no—
694C2×C8—2444no—
695C4⋊C4—22no—
696C4⋊C4—22no—
697C4⋊C4—24no—
698C4⋊C4—24no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—612no—
702C4⋊C4—612no—
703C4⋊C4—1222no—
704C4⋊C4—1222no—
705C4⋊C4—1222no—
706C4⋊C4—1222no—
707C4⋊C4—1222no—
708C4⋊C4—1222no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4—1221no—
713C4⋊C4C2×C22⋊D6112yes—
714C4⋊C4C2×C22⋊D6112yes—
715C4⋊C4C2×C22⋊D6112yes—
716C4⋊C4C2×C22⋊D6112yes—
717C4⋊C4C23×D6112yes—
718C4⋊C4C23×D6112yes—
719C22⋊C4—24no—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—24no—
723C22⋊C4—24no—
724C22⋊C4—24no—
725C22⋊C4—1222no—
726C22⋊C4—1222no—
727C22⋊C4—1222no—
728C22⋊C4—1222no—
729C22⋊C4—1222no—
730C22⋊C4—1222no—
731C22⋊C4—1222no—
732C22⋊C4—1222no—
733C22⋊C4—1222no—
734C22⋊C4C2×C22⋊D6112yes—
735C22⋊C4C2×C22⋊D6112yes—
736C22⋊C4C2×C22⋊D6112yes—
737C22⋊C4C2×C22⋊D6112yes—
738C42—22no—
739C42—22no—
740C42—1222no—
741C42—1222no—
742C42—1222no—
743C42C2×C22⋊D6112yes—
744C42C2×C22⋊D6111yescharacteristic
745C42C2×C22⋊D6111yescharacteristic
746C42C23×D6112yes—
747C42C23×D6111yescharacteristic
748C42C23×D6111yescharacteristic
749C23—22no—
750C23—22no—
751C23—41no—
752C23—41no—
753C23—42no—
754C23—42no—
755C23—42no—
756C23—1222no—
757C23C22×C22⋊D6112yes—
758C23C22×C22⋊D6111yescharacteristic
759Q8—22no—
760Q8—22no—
761Q8—42no—
762Q8—84no—
763Q8—1222no—
764Q8—1222no—
765Q8—4881no—
766Q8—4881no—
767D4—22no—
768D4—22no—
769D4—42no—
770D4—84no—
771D4—1222no—
772D4—1222no—
773D4—4881no—
774D4—4881no—
775D4—4882no—
776D4—4882no—
777D4—2444no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—22no—
781C2×C4—24no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—82no—
793C2×C4—82no—
794C2×C4—1222no—
795C2×C4—1222no—
796C2×C4—1222no—
797C2×C4—4882no—
798C2×C4—4882no—
799C2×C4—2444no—
800C2×C4C22×C22⋊D6111yescharacteristic
801C2×C4C22×C22⋊D6111yescharacteristic
802C2×C4C22×C22⋊D6112yes—
803C2×C4C22×C22⋊D6112yes—
804C2×C4C22×C22⋊D6111yescharacteristic
805C2×C4C22×C22⋊D6111yescharacteristic
806C2×C4C22×C22⋊D6112yes—
807C2×C4C22×C22⋊D6111yescharacteristic
808C2×C4#1451982312yes—
809C2×C4#1451982412yes—
810C2×C4C24×D6111yescharacteristic
811C8—1224no—
812C8—1224no—
813C22—21no—
814C22—21no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—42no—
819C22—42no—
820C22—42no—
821C22—82no—
822C22—84no—
823C22—2442no—
824C22—2442no—
825C22—2442no—
826C22#1684034012yes—
827C22C23×C22⋊D6111yescharacteristic
828C4—21no—
829C4—21no—
830C4—22no—
831C4—22no—
832C4—21no—
833C4—21no—
834C4—22no—
835C4—42no—
836C4—42no—
837C4—42no—
838C4—2442no—
839C4—2442no—
840C4—2442no—
841C4#1684034012yes—
842C4C2×#1451982311yescharacteristic
843C4C2×#1451982411yescharacteristic
844C2—22no—
845C2—42no—
846C2—82no—
847C2—4882no—
848C2C2×#1684034011yescharacteristic
849C2#2146059911yescharacteristic
850C2#2146060611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#542C2
socleC22×C61C23×D4
hypercenterC2×#542D61
hypocenterC61#60919
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#542

Complements

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

NH ≅ G/Ntype
1. #21459209C2semidirect
2. #21457284C2semidirect
3. #21457275C2semidirect
4. #21457245C2semidirect
5. #21457230C2semidirect
6. #21455628C2semidirect
7. #21455624C2semidirect
8. #21455616C2semidirect
9. #21455445C2semidirect
10. #21455434C2semidirect
11. #21455309C2semidirect
12. #21455291C2semidirect
13. #21455283C2semidirect
14. #21454383C2semidirect
15. C2×C61×#542C2semidirect
19. #16840383C22semidirect
20. #16840383C22semidirect
21. #16840374C22semidirect
22. #16840367C22semidirect
33. #16840069C22semidirect
34. #16840062C22semidirect
35. #16840057C22semidirect
36. #16840054C22semidirect
37. #16840052C22semidirect
38. #16840049C22semidirect
39. #16840047C22semidirect
40. #16840044C22semidirect
41. #16840042C22semidirect
42. #16840039C22semidirect
43. #16840018C22semidirect
45. #16840010C22semidirect
47. #16840001C22semidirect
49. #16839993C22semidirect
51. #16839984C22semidirect
52. #16839981C22semidirect
53. #16839981C22semidirect
54. #16839977C22semidirect
55. #16839974C22semidirect
56. #16839974C22semidirect
57. #16839972C22semidirect
58. #16839967C22semidirect
59. #16839962C22semidirect
60. #16839957C22semidirect
63. #16839789C22semidirect
64. #16839789C22semidirect
420. C2×#542D61semidirect
512. C61#60919semidirect

Maximal subgroups

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

subgroupindex
#214592092
#214572842
#214572752
#214572452
#214572302
#214556282
#214556242
#214556162
#214554452
#214554342
#214553092
#214552912
#214552832
#214543832
C2×C61×#5422
#6091961