Finite Group Databasebeta

← #30552777

Subgroups — #30552777

Order 15616.

1672 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459246C211yesmaximal, characteristic
2#21457102C214yesmaximal, complemented
3#21457087C214yesmaximal, complemented
4#21457040C212yesmaximal, complemented
5#21457033C212yesmaximal, complemented
6#21456998C212yesmaximal, complemented
7#21456970C212yesmaximal, complemented
8#21456353C212yesmaximal, complemented
9#21456189C212yesmaximal, complemented
10#21455797C212yesmaximal
11#21455788C212yesmaximal, complemented
12#21455628C211yesmaximal, characteristic, complemented
13#21455620C211yesmaximal, characteristic, complemented
14#21455601C211yesmaximal, characteristic, complemented
15C2×#16840054C211yesmaximal, characteristic, complemented
16#21454485C211yesmaximal, characteristic, complemented
17C61×#3503C211yesmaximal, characteristic, complemented
18#16840390C2211yescharacteristic
19#16840383C2212yes—
20#16840377—21no—
21#16840374C2212yes—
22#16840370—21no—
23#16840354—22no—
24#16840340C2211yescharacteristic
25#16840338C2211yescharacteristic
26#16840333C2211yescharacteristic
27#16840319C2212yes—
28#16840316—21no—
29#16840296C2212yes—
30#16840294—21no—
31#16840292—22no—
32C4×#11758222C2211yescharacteristic
33C2×C4×Dic122C2211yescharacteristic
34#16840172C2214yes—
35#16840168C2214yes—
36#16840165C2214yes—
37#16840161C2214yes—
38#16840132C2214yes—
39#16840124C2214yes—
40#16840119C2214yes—
41#16840114C2214yes—
42#16840103C2214yes—
43#16840103C2214yes—
44#16840103C2214yes—
45#16840097C2214yes—
46#16840097C2214yes—
47#16840092C2214yes—
48#16840086C2214yes—
49#16840075C2214yes—
50#16840066C2214yes—
51#16840066C2212yes—
52#16840059C2212yes—
53#16840054C2212yes—
54#16840054C2212yes—
55#16840054C2211yescharacteristic
56#16840054C2212yes—
57#16840054C2212yes—
58#16840054C2214yes—
59#16840049C2212yes—
60#16840049C2211yescharacteristic
61#16840044C2212yes—
62#16840044C2212yes—
63#16840044C2211yescharacteristic
64#16840039C2212yes—
65#16840039C2211yescharacteristic
66#16839823C2214yes—
67#16839819C2212yes—
68#16839815C2212yes—
69#16839805C2212yes—
70#16839802C2212yes—
71#16839798C2212yes—
72C2×#14519710C2212yes—
73#16839786C2211yescharacteristic
74C2×C4⋊#92418C2211yescharacteristic
75#16839770C2212yes—
76#16839761C2212yes—
77#16839756C2212yes—
78C2×#14519700C2212yes—
79#16839729C2212yes—
80#16839718C2212yes—
81Q82×C61—21no—
82C61×#557—21no—
83C61×#554—22no—
84C61×#554—21no—
85D4×Q8×C61—22no—
86D4×Q8×C61—21no—
87C61×#544C2212yes—
88C61×#544C2214yes—
89C61×#533C2211yescharacteristic
90C61×#533C2212yes—
91C2×C4⋊Q8×C61C2211yescharacteristic
92C2×C4⋊Q8×C61C2212yes—
93C61×#520C2212yes—
94C4×#41×C61C2211yescharacteristic
95C2×#11758222C2311yescharacteristic
96C22×Dic122C2311yescharacteristic
97C2×#11758194C2312yes—
98C22×#92418C2312yes—
99#14519777C2312yes—
100#14519777C2312yes—
101#14519776—21no—
102#14519775—21no—
103#14519772—22no—
104#14519771—22no—
105#14519770—22no—
106#14519770—22no—
107#14519769—22no—
108#14519769C2312yes—
109#14519768—21no—
110#14519767—22no—
111#14519767—22no—
112#14519765C2312yes—
113#14519764—21no—
114#14519763—22no—
115#14519761—22no—
116#14519760—22no—
117#14519759—22no—
118#14519758—22no—
119#14519757—21no—
120#14519757—21no—
121#14519756—22no—
122#14519756C2312yes—
123#14519756C2312yes—
124#14519756C2312yes—
125#14519755—22no—
126#14519754—22no—
127#14519753—21no—
128#14519751C2312yes—
129#14519749—22no—
130#14519748—21no—
131C4×Dic122—21no—
132C4×Dic122—21no—
133C4×Dic122—22no—
134C4×Dic122C2312yes—
135C4×Dic122C2312yes—
136C4×Dic122C2311yescharacteristic
137C4×Dic122C2311yescharacteristic
138C4×D244C2311yescharacteristic
139C4×D244C2311yescharacteristic
140C4×C22⋊D61—21no—
141C4×C22⋊D61—21no—
142C4×C22⋊D61—22no—
143#14519736—22no—
144#14519736C2311yescharacteristic
145#14519734—21no—
146#14519734—22no—
147C2×C4⋊Dic61C2311yescharacteristic
148C2×#11758196—21no—
149C2×C4×Dic61—21no—
150C42×D61—21no—
151#14519710C2312yes—
152#14519710C2314yes—
153#14519710C2314yes—
154#14519710C2314yes—
155#14519710C2312yes—
156#14519710C2314yes—
157#14519708C2314yes—
158#14519708C2312yes—
159#14519708C2314yes—
160#14519708C2312yes—
161C4⋊#92418C2311yescharacteristic
162C4⋊#92418C2311yescharacteristic
163C4⋊#92418C2312yes—
164C4⋊#92418C2312yes—
165C4⋊#92418C2312yes—
166#14519700C2314yes—
167#14519700C2314yes—
168#14519700C2312yes—
169#14519700C2312yes—
170#14519700C2314yes—
171#14519700C2314yes—
172#14519700C2314yes—
173#14519697C2312yes—
174#14519697C2312yes—
175#14519697C2314yes—
176C22⋊#92418C2314yes—
177C22⋊#92418C2314yes—
178#14519688C2314yes—
179C4×#92418C2314yes—
180C2×#41×C61C2311yescharacteristic
181C22×Q8×C61—21no—
182C22×Q8×C61—22no—
183C4⋊Q8×C61—24no—
184C4⋊Q8×C61—22no—
185C4⋊Q8×C61—21no—
186C4⋊Q8×C61—22no—
187C4⋊Q8×C61—21no—
188C4⋊Q8×C61—22no—
189C4⋊Q8×C61C2312yes—
190C4⋊Q8×C61C2311yescharacteristic
191C4⋊Q8×C61C2312yes—
192C4⋊Q8×C61C2314yes—
193C4⋊Q8×C61C2311yescharacteristic
194#125×C61—22no—
195#125×C61—24no—
196#125×C61C2312yes—
197#125×C61C2314yes—
198C22⋊Q8×C61—21no—
199C22⋊Q8×C61—22no—
200C22⋊Q8×C61—21no—
201C22⋊Q8×C61—22no—
202C22⋊Q8×C61—24no—
203C22⋊Q8×C61—24no—
204C22⋊Q8×C61—24no—
205C4×Q8×C61—22no—
206C4×Q8×C61—21no—
207C4×Q8×C61—22no—
208C4×Q8×C61—21no—
209C4×Q8×C61—22no—
210C4×Q8×C61D411yescharacteristic
211C4×Q8×C61D411yescharacteristic
212C4×D4×C61—22no—
213C4×D4×C61—24no—
214C4×D4×C61D412yes—
215C4×D4×C61D411yescharacteristic
216C4×D4×C61D412yes—
217C4×D4×C61D411yescharacteristic
218#117×C61C2312yes—
219#117×C61C2314yes—
220#117×C61C2311yescharacteristic
221#117×C61C2312yes—
222C2×C4⋊C4×C61—21no—
223C2×C4⋊C4×C61—22no—
224C2×C4⋊C4×C61C2312yes—
225C2×C4⋊C4×C61C2314yes—
226C2×C42×C61C2311yescharacteristic
227C2×C42×C61C2312yes—
228#41×C61—22no—
229#41×C61—22no—
230C2×Q8×C61—21no—
231C2×Q8×C61—21no—
232C2×Q8×C61—22no—
233C2×Q8×C61—22no—
234C2×Q8×C61—24no—
235C2×Q8×C61—84no—
236C2×Q8×C61—82no—
237C2×Q8×C61C2×D411yescharacteristic
238C2×D4×C61C2×D411yescharacteristic
239C2×D4×C61C2×D412yes—
240C22×C4×C61—24no—
241C22×C4×C61—22no—
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2×D412yes—
244C22×C4×C61C2×D411yescharacteristic
245C22×C4×C61C2×D412yes—
246C22×C4×C61C2412yes—
247C22×C4×C61C2411yescharacteristic
248C2×C22⋊D61—21no—
249C2×C22⋊D61—22no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252#11758222—22no—
253#11758222—22no—
254C2×D244C2411yescharacteristic
255C2×C4×D61—21no—
256C2×C4×D61—21no—
257C2×C4×D61—21no—
258C2×Dic122—22no—
259C2×Dic122—22no—
260C2×Dic122—21no—
261C2×Dic122—22no—
262C2×Dic122C2412yes—
263C2×Dic122C2411yescharacteristic
264C4⋊C4×C61—22no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—22no—
267C4⋊C4×C61—24no—
268C4⋊C4×C61—24no—
269C4⋊C4×C61—22no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—22no—
272C4⋊C4×C61—24no—
273C4⋊C4×C61—22no—
274C4⋊C4×C61—24no—
275C4⋊C4×C61C2×D411yescharacteristic
276C4⋊C4×C61C2×D412yes—
277C4⋊C4×C61C2×D412yes—
278C4⋊C4×C61C2×D411yescharacteristic
279C4⋊C4×C61C2414yes—
280C4⋊C4×C61C2412yes—
281C4⋊C4×C61C2412yes—
282C22⋊C4×C61—24no—
283C22⋊C4×C61—22no—
284C22⋊C4×C61C2×D412yes—
285C22⋊C4×C61C2×D412yes—
286C22⋊C4×C61C2×D412yes—
287C42×C61—24no—
288C42×C61—22no—
289C42×C61C2×D411yescharacteristic
290C42×C61C2×D411yescharacteristic
291C42×C61C2×D412yes—
292C42×C61C2×D412yes—
293C42×C61C2411yescharacteristic
294C42×C61C2412yes—
295C42×C61C2411yescharacteristic
296C22⋊Dic61—22no—
297C22⋊Dic61—22no—
298C22⋊Dic61—21no—
299C22⋊Dic61—22no—
300#11758198—21no—
301#11758198—21no—
302#11758198—22no—
303#11758198—22no—
304#11758198—22no—
305C4⋊Dic61—21no—
306C4⋊Dic61—22no—
307C4⋊Dic61—22no—
308C4⋊Dic61—22no—
309C4⋊Dic61C2411yescharacteristic
310C4⋊Dic61C2412yes—
311C4⋊Dic61C2411yescharacteristic
312#11758196—22no—
313#11758196—22no—
314#11758196—21no—
315#11758196—21no—
316#11758196—22no—
317#11758196—22no—
318#11758196—22no—
319#11758196—22no—
320#11758196—22no—
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—21no—
324C4×Dic61—22no—
325C4×Dic61—22no—
326#11758194—24no—
327C2×#92418—24no—
328C2×#92418C2412yes—
329C2×#92418C2414yes—
330C2×#92418C2412yes—
331C23×C61C22×D412yes—
332C23×C61C22×D411yescharacteristic
333C22×D61—21no—
334Q8×C61—22no—
335Q8×C61—44no—
336Q8×C61—42no—
337Q8×C61—42no—
338Q8×C61—84no—
339Q8×C61—82no—
340D4×C61—24no—
341D4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—24no—
344C2×C4×C61—22no—
345C2×C4×C61—22no—
346C2×C4×C61—22no—
347C2×C4×C61—24no—
348C2×C4×C61—22no—
349C2×C4×C61—42no—
350C2×C4×C61—41no—
351C2×C4×C61—82no—
352C2×C4×C61—84no—
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D412yes—
356C2×C4×C61C22×D411yescharacteristic
357C2×C4×C61C22×D412yes—
358C2×C4×C61C22×D412yes—
359C2×C4×C61C22×D411yescharacteristic
360C2×C4×C61C22×D411yescharacteristic
361C2×C4×C612−1+412yes—
362C2×C4×C612−1+412yes—
363C2×C4×C61C2511yescharacteristic
364C22⋊D61—42no—
365C22⋊D61—82no—
366C2×Dic61—21no—
367C2×Dic61—22no—
368C2×Dic61—21no—
369C2×Dic61—22no—
370C2×Dic61—21no—
371C2×Dic61—42no—
372C2×Dic61—81no—
373D244—21no—
374D244—21no—
375C4×D61—42no—
376C4×D61—42no—
377C4×D61—81no—
378Dic122—22no—
379Dic122—22no—
380Dic122—21no—
381Dic122—21no—
382Dic122—42no—
383Dic122—82no—
384#92418—22no—
385#92418—22no—
386#92418—24no—
387#60893—611nomaximal, Sylow
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—22no—
391C22×C61—22no—
392C22×C61—22no—
393C22×C61#53612yes—
394C22×C61C23×D411yescharacteristic
395C2×D61—41no—
396C2×D61—41no—
397C2×D61—41no—
398C4×C61—22no—
399C4×C61—21no—
400C4×C61—21no—
401C4×C61—22no—
402C4×C61—21no—
403C4×C61—22no—
404C4×C61—44no—
405C4×C61—42no—
406C4×C61—42no—
407C4×C61#53612yes—
408C4×C61#57812yes—
409C4×C61C2×2−1+411yescharacteristic
410C4×C61C2×2−1+411yescharacteristic
411Dic61—41no—
412Dic61—42no—
413Dic61—42no—
414Dic61—41no—
415Dic61—41no—
416#3503D6111yescharacteristic, complemented
417#3461—611no—
418#3243—614no—
419#3242—614no—
420#3238—612no—
421#3237—612no—
422#3233—612no—
423#3230—612no—
424#3164—612no—
425#3137—612no—
426#3098—612no—
427#3097—612no—
428#3079—611no—
429#3078—611no—
430#3076—611no—
431C2×#477—611no—
432#2925—611no—
433C2×C61—22no—
434C2×C61—42no—
435C2×C61C2×#53611yescharacteristic
436C2×C61C2×#57811yescharacteristic
437C2×C61#358511yescharacteristic
438D61—81no—
439Q82—21no—
440#557—21no—
441#554—22no—
442#554—21no—
443D4×Q8—22no—
444D4×Q8—21no—
445#544—611no—
446#544C2×D6112yes—
447#544C2×D6114yes—
448#542—612no—
449#542—1221no—
450#541—612no—
451#541—1221no—
452#539—1222no—
453#537—611no—
454#536—611no—
455#536—611no—
456#533—612no—
457#533—1221no—
458#533C2×D6111yescharacteristic
459#533C2×D6112yes—
460C2×C4⋊Q8C2×D6111yescharacteristic
461C2×C4⋊Q8C2×D6112yes—
462#529—612no—
463#529—1222no—
464#529—1221no—
465#520C2×D6112yes—
466C4×#41—611no—
467C4×#41C2×D6111yescharacteristic
468C2×C4×Q8—611no—
469#501—614no—
470#501—614no—
471#500—614no—
472#499—614no—
473#491—614no—
474#489—614no—
475#488—614no—
476#487—614no—
477#485—614no—
478#485—614no—
479#485—614no—
480#484—614no—
481#484—614no—
482#483—614no—
483#482—614no—
484#480—614no—
485#479—612no—
486#479—614no—
487#478—612no—
488#477—612no—
489#477—612no—
490#477—614no—
491#477—611no—
492#477—612no—
493#477—612no—
494#476—611no—
495#476—612no—
496#475—611no—
497#475—612no—
498#475—612no—
499#474—611no—
500#474—612no—
501#433—614no—
502#432—612no—
503#431—612no—
504#428—612no—
505#428—612no—
506#427—612no—
507C2×#107—612no—
508#423—611no—
509C2×C4⋊C8—611no—
510#419—612no—
511#417—612no—
512#416—612no—
513C2×#103—612no—
514#408—612no—
515#405—612no—
516C61#6089311yescharacteristic, complemented, Sylow
517C2×#41—611no—
518C2×#41C22×D6111yescharacteristic
519C22×Q8—21no—
520C22×Q8—22no—
521C22×Q8—611no—
522C2×M16—612no—
523C22×C8—612no—
524C4⋊Q8—24no—
525C4⋊Q8—22no—
526C4⋊Q8—21no—
527C4⋊Q8—22no—
528C4⋊Q8—21no—
529C4⋊Q8—22no—
530C4⋊Q8—612no—
531C4⋊Q8—612no—
532C4⋊Q8—1221no—
533C4⋊Q8—1221no—
534C4⋊Q8C22×D6112yes—
535C4⋊Q8C22×D6111yescharacteristic
536C4⋊Q8C22×D6112yes—
537C4⋊Q8C22×D6114yes—
538C4⋊Q8C22×D6111yescharacteristic
539#126—1222no—
540#126—1222no—
541#126—1222no—
542#126—1222no—
543#125—22no—
544#125—24no—
545#125—612no—
546#125—1222no—
547#125—1221no—
548#125—1222no—
549#125—1222no—
550#125C22×D6112yes—
551#125C22×D6114yes—
552#124—612no—
553#124—1221no—
554#124—1222no—
555#123—1222no—
556#123—1222no—
557#123—1222no—
558#123—1222no—
559C22⋊Q8—21no—
560C22⋊Q8—22no—
561C22⋊Q8—21no—
562C22⋊Q8—22no—
563C22⋊Q8—24no—
564C22⋊Q8—24no—
565C22⋊Q8—24no—
566C22⋊Q8—612no—
567C22⋊Q8—612no—
568C22⋊Q8—612no—
569C22⋊Q8—1221no—
570C22⋊Q8—1222no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573C22⋊Q8—1222no—
574C22⋊Q8—1222no—
575#121—612no—
576#121—1222no—
577#121—1221no—
578C4×Q8—22no—
579C4×Q8—21no—
580C4×Q8—22no—
581C4×Q8—21no—
582C4×Q8—22no—
583C4×Q8—612no—
584C4×Q8—612no—
585C4×Q8—611no—
586C4×Q8—611no—
587C4×Q8—1221no—
588C4×Q8—1221no—
589C4×Q8—1222no—
590C4×Q8C22⋊D6111yescharacteristic
591C4×Q8C22⋊D6111yescharacteristic
592C4×D4—24no—
593C4×D4—22no—
594C4×D4—611no—
595C4×D4—611no—
596C4×D4—1221no—
597C4×D4—1221no—
598C4×D4—1222no—
599C4×D4C22⋊D6111yescharacteristic
600C4×D4C22⋊D6112yes—
601C4×D4C22⋊D6112yes—
602C4×D4C22⋊D6111yescharacteristic
603#117—611no—
604#117—1222no—
605#117—1221no—
606#117—1222no—
607#117C22×D6112yes—
608#117C22×D6114yes—
609#117C22×D6111yescharacteristic
610#117C22×D6112yes—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—22no—
613C2×C4⋊C4—611no—
614C2×C4⋊C4—1221no—
615C2×C4⋊C4C22×D6112yes—
616C2×C4⋊C4C22×D6114yes—
617C2×C42—1221no—
618C2×C42—1221no—
619C2×C42C22×D6111yescharacteristic
620C2×C42C22×D6112yes—
621#107—614no—
622#107—614no—
623#107—612no—
624#107—612no—
625#107—614no—
626#107—614no—
627#106—612no—
628#106—612no—
629#106—614no—
630#106—614no—
631C4⋊C8—611no—
632C4⋊C8—611no—
633C4⋊C8—612no—
634C4⋊C8—612no—
635C4⋊C8—612no—
636#103—614no—
637#103—614no—
638#103—612no—
639#103—612no—
640#103—614no—
641#103—614no—
642#103—614no—
643#102—612no—
644#102—612no—
645#102—614no—
646C22⋊C8—614no—
647C22⋊C8—614no—
648#97—614no—
649C4×C8—614no—
650#41—22no—
651#41—22no—
652#41—1222no—
653#41—1222no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—22no—
657C2×Q8—22no—
658C2×Q8—24no—
659C2×Q8—82no—
660C2×Q8—84no—
661C2×Q8—612no—
662C2×Q8—611no—
663C2×Q8—1222no—
664C2×Q8—1221no—
665C2×Q8—1222no—
666C2×Q8—1222no—
667C2×Q8C2×C22⋊D6111yescharacteristic
668C2×D4—611no—
669C2×D4—1222no—
670C2×D4—1221no—
671C2×D4C2×C22⋊D6112yes—
672C2×D4C2×C22⋊D6111yescharacteristic
673C22×C4—24no—
674C22×C4—22no—
675C22×C4—1221no—
676C22×C4—1221no—
677C22×C4—1221no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4C2×C22⋊D6111yescharacteristic
681C22×C4C2×C22⋊D6112yes—
682C22×C4C2×C22⋊D6111yescharacteristic
683C22×C4C2×C22⋊D6112yes—
684C22×C4C23×D6112yes—
685C22×C4C23×D6111yescharacteristic
686M16—1224no—
687C2×C8—612no—
688C2×C8—614no—
689C2×C8—612no—
690C2×C8—1224no—
691C4⋊C4—22no—
692C4⋊C4—21no—
693C4⋊C4—22no—
694C4⋊C4—24no—
695C4⋊C4—24no—
696C4⋊C4—22no—
697C4⋊C4—21no—
698C4⋊C4—22no—
699C4⋊C4—24no—
700C4⋊C4—22no—
701C4⋊C4—24no—
702C4⋊C4—611no—
703C4⋊C4—612no—
704C4⋊C4—611no—
705C4⋊C4—1221no—
706C4⋊C4—1222no—
707C4⋊C4—1222no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1222no—
711C4⋊C4—1222no—
712C4⋊C4—1222no—
713C4⋊C4—1222no—
714C4⋊C4—1222no—
715C4⋊C4—1222no—
716C4⋊C4—1222no—
717C4⋊C4—1222no—
718C4⋊C4C2×C22⋊D6111yescharacteristic
719C4⋊C4C2×C22⋊D6112yes—
720C4⋊C4C2×C22⋊D6111yescharacteristic
721C4⋊C4C2×C22⋊D6112yes—
722C4⋊C4C23×D6112yes—
723C4⋊C4C23×D6112yes—
724C4⋊C4C23×D6114yes—
725C22⋊C4—24no—
726C22⋊C4—22no—
727C22⋊C4—1221no—
728C22⋊C4—1222no—
729C22⋊C4—1222no—
730C22⋊C4—1222no—
731C22⋊C4—1221no—
732C22⋊C4—1221no—
733C22⋊C4—1222no—
734C22⋊C4—1222no—
735C22⋊C4—1222no—
736C22⋊C4C2×C22⋊D6112yes—
737C22⋊C4C2×C22⋊D6112yes—
738C22⋊C4C2×C22⋊D6112yes—
739C42—24no—
740C42—22no—
741C42—1221no—
742C42—1221no—
743C42—1222no—
744C42—1221no—
745C42—1222no—
746C42C2×C22⋊D6111yescharacteristic
747C42C2×C22⋊D6112yes—
748C42C2×C22⋊D6111yescharacteristic
749C42C2×C22⋊D6112yes—
750C42C23×D6112yes—
751C42C23×D6111yescharacteristic
752C42C23×D6111yescharacteristic
753C23—1221no—
754C23C22×C22⋊D6112yes—
755C23C22×C22⋊D6111yescharacteristic
756Q8—22no—
757Q8—44no—
758Q8—42no—
759Q8—42no—
760Q8—82no—
761Q8—84no—
762Q8—1222no—
763Q8—1222no—
764Q8—1221no—
765Q8—1221no—
766Q8—4882no—
767Q8—2442no—
768D4—24no—
769D4—22no—
770D4—1221no—
771D4—1221no—
772D4—4882no—
773D4—2442no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—24no—
780C2×C4—22no—
781C2×C4—41no—
782C2×C4—42no—
783C2×C4—82no—
784C2×C4—84no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1222no—
788C2×C4—1222no—
789C2×C4—1221no—
790C2×C4—4881no—
791C2×C4—4881no—
792C2×C4—2442no—
793C2×C4—2442no—
794C2×C4—2442no—
795C2×C4C22×C22⋊D6112yes—
796C2×C4C22×C22⋊D6111yescharacteristic
797C2×C4C22×C22⋊D6111yescharacteristic
798C2×C4C22×C22⋊D6111yescharacteristic
799C2×C4C22×C22⋊D6112yes—
800C2×C4C22×C22⋊D6112yes—
801C2×C4C22×C22⋊D6111yescharacteristic
802C2×C4C22×C22⋊D6111yescharacteristic
803C2×C4#1451982512yes—
804C2×C4#1451982512yes—
805C2×C4C24×D6111yescharacteristic
806C8—1222no—
807C8—1222no—
808C8—1224no—
809C22—21no—
810C22—21no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—2441no—
815C22—2441no—
816C22—2441no—
817C22#1684033612yes—
818C22C23×C22⋊D6111yescharacteristic
819C4—21no—
820C4—22no—
821C4—21no—
822C4—21no—
823C4—22no—
824C4—22no—
825C4—42no—
826C4—44no—
827C4—42no—
828C4—2441no—
829C4—2442no—
830C4—2441no—
831C4—2441no—
832C4—2442no—
833C4#1684033612yes—
834C4#1684057712yes—
835C4C2×#1451982511yescharacteristic
836C4C2×#1451982511yescharacteristic
837C2—22no—
838C2—42no—
839C2—4881no—
840C2C2×#1684033611yescharacteristic
841C2C2×#1684057711yescharacteristic
842C2#2146059911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC61×#3503C2
socleC22×C61C23×D4
prime radical#16840340C22
hypercenter#3503D61
hypocenterC61#60893
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3503

Complements

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

NH ≅ G/Ntype
2. #21457102C2semidirect
3. #21457087C2semidirect
4. #21457040C2semidirect
5. #21457033C2semidirect
6. #21456998C2semidirect
7. #21456970C2semidirect
8. #21456353C2semidirect
9. #21456189C2semidirect
11. #21455788C2semidirect
12. #21455628C2semidirect
13. #21455620C2semidirect
14. #21455601C2semidirect
15. C2×#16840054C2semidirect
16. #21454485C2semidirect
17. C61×#3503C2semidirect
416. #3503D61semidirect
516. C61#60893semidirect

Maximal subgroups

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

subgroupindex
#214592462
#214571022
#214570872
#214570402
#214570332
#214569982
#214569702
#214563532
#214561892
#214557972
#214557882
#214556282
#214556202
#214556012
C2×#168400542
#214544852
C61×#35032
#6089361