Finite Group Databasebeta

← #29646978

Subgroups — #29646978

Order 15616.

948 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459410C211yesmaximal, characteristic
2#21454783C211yesmaximal, characteristic, complemented
3#21454487C211yesmaximal, characteristic, complemented
4#21444286C211yesmaximal, characteristic, complemented
5#21444278C211yesmaximal, characteristic, complemented
6#21444264C211yesmaximal, characteristic, complemented
7#21444256C211yesmaximal, characteristic, complemented
8#21444250C211yesmaximal, characteristic, complemented
9#21444234C211yesmaximal, characteristic, complemented
10#21444232C211yesmaximal, characteristic, complemented
11#21444226C211yesmaximal, characteristic, complemented
12#21444212C211yesmaximal, characteristic, complemented
13#21444207C211yesmaximal, characteristic, complemented
14#21444198C211yesmaximal, characteristic, complemented
15C61×#1495C211yesmaximal, characteristic, complemented
16#16840496—21no—
17#16840494C411yescharacteristic
18#16840489C411yescharacteristic
19#16840483C411yescharacteristic
20#16840479—21no—
21#16840465C411yescharacteristic
22#16840463—21no—
23#16840459C411yescharacteristic
24#16840457—21no—
25#16840430C411yescharacteristic
26#16840422C411yescharacteristic
27#16840420C411yescharacteristic
28#16840309—21no—
29#16840309C2211yescharacteristic
30#16840299C2211yescharacteristic
31#16840292—21no—
32#16840290—21no—
33C4×#11758222C2211yescharacteristic
34C4×#11758222C2211yescharacteristic
35#16840230—21no—
36C4×#11758224C2211yescharacteristic
37C4×Q8×D61C2211yescharacteristic
38#16839891—21no—
39#16839837—21no—
40#16839836—21no—
41#16839832—21no—
42#16839822—21no—
43#16839822—21no—
44#16839818C2211yescharacteristic
45#16839818C2211yescharacteristic
46#16839814C2211yescharacteristic
47#16839814C2211yescharacteristic
48#16839813C2211yescharacteristic
49#16839813C2211yescharacteristic
50C2×C4⋊#92418C2211yescharacteristic
51#16839730—21no—
52#16839720—21no—
53C4×#11758194C2211yescharacteristic
54C4×#11758189C2211yescharacteristic
55C4×C8×D61C2211yescharacteristic
56#16839494C2211yescharacteristic
57#16839494C2211yescharacteristic
58Q8⋊#92418C2211yescharacteristic
59Q8⋊#92418C2211yescharacteristic
60#16839492C2211yescharacteristic
61#16839492C2211yescharacteristic
62#16839491C2211yescharacteristic
63#16839491C2211yescharacteristic
64D4⋊#92418C2211yescharacteristic
65D4⋊#92418C2211yescharacteristic
66#16839489C2211yescharacteristic
67#16839489C2211yescharacteristic
68C61×#529C2211yescharacteristic
69C61×#431C2211yescharacteristic
70C61×#423C2211yescharacteristic
71C61×Q8⋊C8C2211yescharacteristic
72C61×Q8⋊C8C2211yescharacteristic
73C61×D4⋊C8C2211yescharacteristic
74C61×D4⋊C8C2211yescharacteristic
75C2×#11758222—21no—
76C2×#11758222C2×C411yescharacteristic
77C2×#11758222D411yescharacteristic
78C2×#11758224C2×C411yescharacteristic
79C2×Q8×D61C2×C411yescharacteristic
80C2×#11758194—21no—
81C2×#11758189—21no—
82C22×#92418—21no—
83C2×C8×D61—21no—
84#14519776—21no—
85#14519776C2×C411yescharacteristic
86#14519773—21no—
87#14519773C2×C411yescharacteristic
88#14519772—21no—
89#14519772—21no—
90#14519772—21no—
91#14519770—21no—
92#14519770—21no—
93#14519768C2×C411yescharacteristic
94#14519767—21no—
95#14519767—21no—
96#14519766C2×C411yescharacteristic
97#14519763—21no—
98#14519763—21no—
99#14519763—21no—
100#14519763—21no—
101#14519763—21no—
102#14519762—21no—
103#14519762—21no—
104#14519761—21no—
105#14519759—21no—
106#14519758—21no—
107#14519755—21no—
108#14519754—21no—
109#14519753C2×C411yescharacteristic
110#14519752—21no—
111#14519752C2×C411yescharacteristic
112#14519752C2×C411yescharacteristic
113#14519750—21no—
114#14519750—21no—
115#14519750—21no—
116#14519750—21no—
117#14519749—21no—
118#14519748—21no—
119#14519748C2×C411yescharacteristic
120Q8×Dic61C2×C411yescharacteristic
121C4×Dic122—21no—
122C4×Dic122C2×C411yescharacteristic
123C4×Dic122C2×C411yescharacteristic
124C4×Dic122D411yescharacteristic
125C4×Dic122C2311yescharacteristic
126#14519742—21no—
127#14519742—21no—
128#14519742—21no—
129#14519742C2×C411yescharacteristic
130#14519742C2×C411yescharacteristic
131C4×D244—21no—
132C4×D244C2×C411yescharacteristic
133C4×D244C2×C411yescharacteristic
134C4×D244D411yescharacteristic
135C4×D244C2311yescharacteristic
136D4×Dic61C2×C411yescharacteristic
137#14519739—21no—
138#14519739—21no—
139C4×C22⋊D61—21no—
140C4×C22⋊D61—21no—
141C4×C22⋊D61—21no—
142C4×C22⋊D61—21no—
143C4×C22⋊D61C2×C411yescharacteristic
144C4×C22⋊D61C2×C411yescharacteristic
145C4×C22⋊D61D411yescharacteristic
146C4×C22⋊D61D411yescharacteristic
147#14519737—21no—
148#14519737—21no—
149#14519737—21no—
150#14519737—21no—
151#14519737—21no—
152#14519736C2×C411yescharacteristic
153#14519736D411yescharacteristic
154#14519735C2×C411yescharacteristic
155#14519734—21no—
156#14519734—21no—
157#14519734D411yescharacteristic
158#14519734D411yescharacteristic
159#14519733—21no—
160C4⋊C4×D61—21no—
161C4⋊C4×D61C2×C411yescharacteristic
162C2×C4×Dic61—21no—
163C42×D61—21no—
164C42×D61—21no—
165C42×D61C2311yescharacteristic
166C42×D61C2311yescharacteristic
167C4⋊#92418—21no—
168C4⋊#92418C2311yescharacteristic
169C4⋊#92418C2311yescharacteristic
170#14519706—21no—
171#14519706—21no—
172#14519689—21no—
173#14519689—21no—
174#14519689—21no—
175#14519689—21no—
176#14519689—21no—
177#14519689—21no—
178#14519688—21no—
179#14519687—21no—
180#14519687—21no—
181#14519687—21no—
182C4×#92418C2311yescharacteristic
183C4×#92418C2311yescharacteristic
184C8×Dic61—21no—
185C8×Dic61—21no—
186C8×Dic61—21no—
187C2×M16×C61—21no—
188#126×C61—21no—
189#125×C61C2×C411yescharacteristic
190#124×C61C2×C411yescharacteristic
191#123×C61—21no—
192C22⋊Q8×C61C2×C411yescharacteristic
193#121×C61C2×C411yescharacteristic
194C4×Q8×C61C2311yescharacteristic
195C4×D4×C61—21no—
196C4×D4×C61C2311yescharacteristic
197#117×C61—21no—
198C2×C42×C61C2311yescharacteristic
199C4⋊C8×C61—21no—
200C4⋊C8×C61—21no—
201C4⋊C8×C61C2311yescharacteristic
202C4⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61—21no—
204C4×C8×C61C2311yescharacteristic
205C4×C8×C61C2311yescharacteristic
206C2×Q8×C61C22×C411yescharacteristic
207C2×D4×C61—21no—
208C2×D4×C61C22×C411yescharacteristic
209C22×C4×C61—21no—
210C22×C4×C61C22×C411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C2×C22⋊D61—21no—
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61C22⋊C411yescharacteristic
219C2×C22⋊D61C22⋊C411yescharacteristic
220C22×Dic61—21no—
221C22×Dic61—21no—
222Q8×D61—22no—
223Q8×D61—41no—
224#11758224—22no—
225#11758224—41no—
226#11758222—22no—
227#11758222—41no—
228#11758222—41no—
229#11758222—41no—
230#11758222—42no—
231#11758222—42no—
232C2×D244—21no—
233C2×D244—21no—
234C2×D244C22⋊C411yescharacteristic
235C2×D244C22×C411yescharacteristic
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61C22×C411yescharacteristic
242C2×C4×D61C22×C411yescharacteristic
243C2×C4×D61C2×D411yescharacteristic
244C2×C4×D61C2×D411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×Dic122—21no—
248C2×Dic122—21no—
249C2×Dic122C22⋊C411yescharacteristic
250C2×Dic122C22×C411yescharacteristic
251M16×C61—42no—
252C2×C8×C61—21no—
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C2×C8×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61C22×C411yescharacteristic
261C4⋊C4×C61C22×C411yescharacteristic
262C22⋊C4×C61—21no—
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61—21no—
266C22⋊C4×C61—21no—
267C42×C61—21no—
268C42×C61C22×C411yescharacteristic
269C42×C61C2×D411yescharacteristic
270C42×C61C2×D411yescharacteristic
271C42×C61C2411yescharacteristic
272C22⋊Dic61—21no—
273C22⋊Dic61—21no—
274C22⋊Dic61—21no—
275C22⋊Dic61C22⋊C411yescharacteristic
276C22⋊Dic61C22⋊C411yescharacteristic
277#11758198—21no—
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198C22⋊C411yescharacteristic
286#11758198C22⋊C411yescharacteristic
287#11758198C22⋊C411yescharacteristic
288#11758198C22⋊C411yescharacteristic
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61C22⋊C411yescharacteristic
292C4⋊Dic61C22⋊C411yescharacteristic
293C4⋊Dic61C22×C411yescharacteristic
294C4⋊Dic61C22×C411yescharacteristic
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196C22⋊C411yescharacteristic
304#11758196C22⋊C411yescharacteristic
305#11758196C22⋊C411yescharacteristic
306#11758196C22⋊C411yescharacteristic
307C4×Dic61—21no—
308C4×Dic61—21no—
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61C22×C411yescharacteristic
315C4×Dic61C22×C411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320#11758194—42no—
321C2×#92418—21no—
322C2×#92418—21no—
323C2×#92418—21no—
324C2×#92418—21no—
325C2×#92418—42no—
326#11758189—42no—
327C8×D61—42no—
328C23×C61—21no—
329C23×C61C2×C22⋊C411yescharacteristic
330C22×D61—21no—
331C22×D61C2×C22⋊C411yescharacteristic
332C22×D61C2×C22⋊C411yescharacteristic
333Q8×C61—21no—
334Q8×C61—21no—
335D4×C61—21no—
336D4×C61—21no—
337D4×C61—81no—
338C2×C4×C61—21no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—41no—
348C2×C4×C61C2×C22⋊C411yescharacteristic
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C23×C411yescharacteristic
352C2×C4×C61C22×D411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C22⋊D61—41no—
355C22⋊D61—41no—
356C22⋊D61—42no—
357C22⋊D61—42no—
358C22⋊D61—42no—
359C22⋊D61—42no—
360C22⋊D61—81no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—42no—
365C2×Dic61—81no—
366C2×Dic61C2×C22⋊C411yescharacteristic
367C2×Dic61C2×C22⋊C411yescharacteristic
368C2×Dic61C2×C22⋊C411yescharacteristic
369C2×Dic61C2×C22⋊C411yescharacteristic
370C2×Dic61C2×C22⋊C411yescharacteristic
371C2×Dic61C2×C22⋊C411yescharacteristic
372D244—21no—
373D244—21no—
374D244—41no—
375D244—42no—
376D244—81no—
377C4×D61—21no—
378C4×D61—21no—
379C4×D61—21no—
380C4×D61—21no—
381C4×D61—21no—
382C4×D61—21no—
383C4×D61—21no—
384C4×D61—21no—
385C4×D61—41no—
386C4×D61—41no—
387C4×D61—42no—
388C4×D61—42no—
389C4×D61—41no—
390C4×D61—41no—
391C4×D61—81no—
392C4×D61—81no—
393Dic122—21no—
394Dic122—41no—
395Dic122—42no—
396Dic122—42no—
397Dic122#13112yes—
398C8×C61—41no—
399C8×C61—41no—
400C8×C61—41no—
401C8×C61—41no—
402#92418—22no—
403#92418—41no—
404#92418—41no—
405#92418—41no—
406#17516—611nomaximal, Sylow
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—41no—
411C22×C61—41no—
412C22×C61—41no—
413C22×C61C22×C22⋊C411yescharacteristic
414C2×D61—21no—
415C2×D61—21no—
416C2×D61—21no—
417C2×D61—21no—
418C2×D61—21no—
419C2×D61—21no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—41no—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—41no—
428C4×C61—41no—
429C4×C61—41no—
430C4×C61C2×#13111yescharacteristic
431C4×C61#56811yescharacteristic
432C4×C61#57511yescharacteristic
433C4×C61#57511yescharacteristic
434Dic61—22no—
435Dic61—21no—
436Dic61—21no—
437Dic61—21no—
438Dic61—21no—
439Dic61—21no—
440Dic61—21no—
441Dic61—41no—
442Dic61—41no—
443#3480—611no—
444#2965—611no—
445#2925—611no—
446#1496—611no—
447#1495D6111yescharacteristic, complemented
448#1494—611no—
449#1491—611no—
450#1489—611no—
451#1488—611no—
452#1484—611no—
453#1483—611no—
454#1482—611no—
455#1479—611no—
456#1477—611no—
457#1476—611no—
458C2×C61—41no—
459C2×C61—81no—
460C2×C61#288011yescharacteristic
461C2×C61#289611yescharacteristic
462C2×C61#290111yescharacteristic
463D61—41no—
464D61—41no—
465D61—81no—
466#559—611no—
467#559—1221no—
468#557—611no—
469#556—611no—
470#556—1221no—
471#553—611no—
472#553—611no—
473#553—1221no—
474#553—1221no—
475#550—611no—
476#548—611no—
477#548—611no—
478#532—611no—
479#532—1221no—
480#529—611no—
481#529—1221no—
482#529—1221no—
483#529C2×D6111yescharacteristic
484C4×#41—611no—
485C4×#41—611no—
486C4×#41—611no—
487C4×#41—1221no—
488C2×C4×Q8—611no—
489#446—1221no—
490#436—1221no—
491#435—1221no—
492#435—1221no—
493#433—1221no—
494#433—1221no—
495#432—611no—
496#432—611no—
497#431—611no—
498#431—611no—
499#431—611no—
500#431—611no—
501#431C2×D6111yescharacteristic
502#423C2×D6111yescharacteristic
503C2×C4⋊C8—611no—
504#408—1221no—
505#405—1221no—
506C4×M16—611no—
507C4×M16—611no—
508C2×C4×C8—611no—
509Q8⋊C8—611no—
510Q8⋊C8—611no—
511Q8⋊C8—611no—
512Q8⋊C8—611no—
513Q8⋊C8—611no—
514Q8⋊C8—611no—
515Q8⋊C8C2×D6111yescharacteristic
516Q8⋊C8C2×D6111yescharacteristic
517D4⋊C8—611no—
518D4⋊C8—611no—
519D4⋊C8—611no—
520D4⋊C8—611no—
521D4⋊C8—611no—
522D4⋊C8—611no—
523D4⋊C8C2×D6111yescharacteristic
524D4⋊C8C2×D6111yescharacteristic
525C61#1751611yescharacteristic, complemented, Sylow
526C2×#41—611no—
527C2×#41—611no—
528C2×#41—611no—
529C2×#41—1221no—
530C22×Q8—611no—
531C2×M16—21no—
532C2×M16—1221no—
533C2×M16—1221no—
534C22×C8—1221no—
535C22×C8—1221no—
536C4⋊Q8—611no—
537C4⋊Q8—1221no—
538#127—611no—
539#127—1221no—
540#126—21no—
541#126—1221no—
542#126—1221no—
543#126—1221no—
544#126—1221no—
545#126—1221no—
546#125—611no—
547#125—1221no—
548#125—1221no—
549#125C4×D6111yescharacteristic
550#124—611no—
551#124—1221no—
552#124—1221no—
553#124—1221no—
554#124—1221no—
555#124—1221no—
556#124C4×D6111yescharacteristic
557#123—21no—
558#123—1221no—
559#123—1221no—
560#123—1221no—
561#123—1221no—
562#123—1221no—
563C22⋊Q8—611no—
564C22⋊Q8—1221no—
565C22⋊Q8—1221no—
566C22⋊Q8C4×D6111yescharacteristic
567#121—611no—
568#121—611no—
569#121—611no—
570#121—1221no—
571#121—1221no—
572#121—1221no—
573#121—1221no—
574#121—1221no—
575#121—1221no—
576#121—1221no—
577#121C4×D6111yescharacteristic
578C4×Q8—611no—
579C4×Q8—611no—
580C4×Q8—611no—
581C4×Q8—611no—
582C4×Q8—611no—
583C4×Q8—611no—
584C4×Q8—611no—
585C4×Q8—1221no—
586C4×Q8—1221no—
587C4×Q8—1221no—
588C4×Q8—1221no—
589C4×Q8C22×D6111yescharacteristic
590C4×D4—21no—
591C4×D4—611no—
592C4×D4—611no—
593C4×D4—611no—
594C4×D4—611no—
595C4×D4—611no—
596C4×D4—611no—
597C4×D4—611no—
598C4×D4—611no—
599C4×D4—611no—
600C4×D4—1221no—
601C4×D4—1221no—
602C4×D4—1221no—
603C4×D4—1221no—
604C4×D4—1221no—
605C4×D4—1221no—
606C4×D4—1221no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4—1221no—
612C4×D4C22×D6111yescharacteristic
613#117—21no—
614#117—611no—
615#117—611no—
616#117—611no—
617#117—611no—
618#117—611no—
619#117—1221no—
620#117—1221no—
621#117—1221no—
622C2×C4⋊C4—611no—
623C2×C4⋊C4—1221no—
624C2×C42—611no—
625C2×C42—611no—
626C2×C42—1221no—
627C2×C42—1221no—
628C2×C42—1221no—
629C2×C42C22×D6111yescharacteristic
630C4⋊C8—21no—
631C4⋊C8—21no—
632C4⋊C8—611no—
633C4⋊C8—611no—
634C4⋊C8—1221no—
635C4⋊C8—1221no—
636C4⋊C8—1221no—
637C4⋊C8C22×D6111yescharacteristic
638C4⋊C8C22×D6111yescharacteristic
639C22⋊C8—21no—
640C22⋊C8—1221no—
641C22⋊C8—1221no—
642C22⋊C8—1221no—
643C22⋊C8—1221no—
644C22⋊C8—1221no—
645C22⋊C8—1221no—
646#97—1221no—
647#97—1221no—
648#97—1221no—
649#97—1221no—
650C4×C8—611no—
651C4×C8—611no—
652C4×C8—1221no—
653C4×C8—1221no—
654C4×C8—1221no—
655C4×C8C22×D6111yescharacteristic
656C4×C8C22×D6111yescharacteristic
657#41—1222no—
658#41—1222no—
659#41—2441no—
660#41—2441no—
661#41—2441no—
662#41—2442no—
663#41—2442no—
664#41—2441no—
665C2×Q8—611no—
666C2×Q8—611no—
667C2×Q8—1221no—
668C2×Q8—1221no—
669C2×Q8—1222no—
670C2×Q8—2441no—
671C2×Q8C2×C4×D6111yescharacteristic
672C2×D4—21no—
673C2×D4—611no—
674C2×D4—611no—
675C2×D4—611no—
676C2×D4—611no—
677C2×D4—1221no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4C2×C4×D6111yescharacteristic
685C22×C4—21no—
686C22×C4—611no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4—1221no—
699C22×C4C2×C4×D6111yescharacteristic
700C22×C4D4×D6111yescharacteristic
701C22×C4D4×D6111yescharacteristic
702M16—42no—
703M16—2442no—
704M16—2442no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—2442no—
714C2×C8—2442no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—611no—
720C4⋊C4—611no—
721C4⋊C4—611no—
722C4⋊C4—611no—
723C4⋊C4—611no—
724C4⋊C4—611no—
725C4⋊C4—611no—
726C4⋊C4—611no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4C2×C4×D6111yescharacteristic
738C4⋊C4C2×C4×D6111yescharacteristic
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—611no—
745C22⋊C4—611no—
746C22⋊C4—611no—
747C22⋊C4—611no—
748C22⋊C4—611no—
749C22⋊C4—611no—
750C22⋊C4—1221no—
751C22⋊C4—1221no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—1221no—
757C22⋊C4—1221no—
758C22⋊C4—1221no—
759C22⋊C4—1221no—
760C22⋊C4—1221no—
761C42—21no—
762C42—611no—
763C42—611no—
764C42—611no—
765C42—611no—
766C42—611no—
767C42—611no—
768C42—1221no—
769C42—1221no—
770C42—1221no—
771C42—1221no—
772C42—1221no—
773C42—1221no—
774C42—1221no—
775C42C2×C4×D6111yescharacteristic
776C42D4×D6111yescharacteristic
777C42D4×D6111yescharacteristic
778C42C23×D6111yescharacteristic
779C23—21no—
780C23—611no—
781C23—611no—
782C23—1221no—
783C23C22⋊C4×D6111yescharacteristic
784Q8—21no—
785Q8—21no—
786Q8—612no—
787Q8—1221no—
788Q8—2441no—
789Q8—2442no—
790Q8—2442no—
791D4—21no—
792D4—21no—
793D4—81no—
794D4—1221no—
795D4—1221no—
796D4—4881no—
797D4—4881no—
798D4—2441no—
799D4—2442no—
800D4—2441no—
801D4—2441no—
802D4—2442no—
803D4—2442no—
804D4—2442no—
805D4—2442no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—611no—
817C2×C4—611no—
818C2×C4—611no—
819C2×C4—611no—
820C2×C4—611no—
821C2×C4—611no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1221no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—1221no—
833C2×C4—4881no—
834C2×C4—4881no—
835C2×C4—4881no—
836C2×C4—2441no—
837C2×C4—2441no—
838C2×C4—2442no—
839C2×C4—2442no—
840C2×C4—2442no—
841C2×C4—2441no—
842C2×C4—2441no—
843C2×C4C22⋊C4×D6111yescharacteristic
844C2×C4C22⋊C4×D6111yescharacteristic
845C2×C4C22⋊C4×D6111yescharacteristic
846C2×C4C22×C4×D6111yescharacteristic
847C2×C4C2×D4×D6111yescharacteristic
848C2×C4C2×D4×D6111yescharacteristic
849C8—41no—
850C8—41no—
851C8—41no—
852C8—41no—
853C8—1222no—
854C8—2441no—
855C8—2441no—
856C8—2441no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—1221no—
864C22—1221no—
865C22—1221no—
866C22—1221no—
867C22—1221no—
868C22—1221no—
869C22—2441no—
870C22—2441no—
871C22—2441no—
872C22C2×C22⋊C4×D6111yescharacteristic
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—1221no—
881C4—1221no—
882C4—1221no—
883C4—1221no—
884C4—1222no—
885C4—1221no—
886C4—1221no—
887C4—2441no—
888C4—2441no—
889C4#131×D6111yescharacteristic
890C4#1684052711yescharacteristic
891C4#1684055811yescharacteristic
892C4#1684056111yescharacteristic
893C2—41no—
894C2—81no—
895C2—4881no—
896C2—2441no—
897C2—2441no—
898C2#2145426711yescharacteristic
899C2#2145433511yescharacteristic
900C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1495C2
socleC22×C61C22×C22⋊C4
prime radical#21459410C2
cosocleC42×C61C24
hypercenter#1495D61
hypocenterC61#17516
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1495

Complements

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

NH ≅ G/Ntype
2. #21454783C2semidirect
3. #21454487C2semidirect
4. #21444286C2semidirect
5. #21444278C2semidirect
6. #21444264C2semidirect
7. #21444256C2semidirect
8. #21444250C2semidirect
9. #21444234C2semidirect
10. #21444232C2semidirect
11. #21444226C2semidirect
12. #21444212C2semidirect
13. #21444207C2semidirect
14. #21444198C2semidirect
15. C61×#1495C2semidirect
447. #1495D61semidirect
525. C61#17516semidirect

Maximal subgroups

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

subgroupindex
#214594102
#214547832
#214544872
#214442862
#214442782
#214442642
#214442562
#214442502
#214442342
#214442322
#214442262
#214442122
#214442072
#214441982
C61×#14952
#1751661