Finite Group Databasebeta

← #29648237

Subgroups — #29648237

Order 15616.

902 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459717C211yesmaximal, characteristic
2#21454830C211yesmaximal, characteristic, complemented
3#21454828C211yesmaximal, characteristic, complemented
4#21444449C211yesmaximal, characteristic, complemented
5#21444449C211yesmaximal, characteristic, complemented
6#21444442C211yesmaximal, characteristic, complemented
7#21444438C211yesmaximal, characteristic, complemented
8#21444438C211yesmaximal, characteristic, complemented
9#21444434C211yesmaximal, characteristic, complemented
10#21444425C211yesmaximal, characteristic, complemented
11#21444425C211yesmaximal, characteristic, complemented
12#21444406C211yesmaximal, characteristic, complemented
13#21444406C211yesmaximal, characteristic, complemented
14C2×#16839501C211yesmaximal, characteristic, complemented
15C61×#1531C211yesmaximal, characteristic, complemented
16#16840497—21no—
17#16840497—21no—
18#16840485—21no—
19#16840485—21no—
20#16840439—21no—
21#16840439—21no—
22#16840439—21no—
23#16840439—21no—
24#16840386C411yescharacteristic
25#16840386C411yescharacteristic
26#16840386C411yescharacteristic
27#16840386C411yescharacteristic
28#16840338C411yescharacteristic
29#16840331C411yescharacteristic
30#16840297C2211yescharacteristic
31#16840297C2211yescharacteristic
32#16840297C2211yescharacteristic
33#16840297C2211yescharacteristic
34C2×#14519765C2211yescharacteristic
35#16840239C411yescharacteristic
36#16840236C411yescharacteristic
37C4×#11758222C2211yescharacteristic
38#16839891—21no—
39#16839890—21no—
40#16839835—21no—
41#16839833—21no—
42#16839832—21no—
43#16839830—21no—
44C8×C22⋊D61—21no—
45#16839825—21no—
46#16839819C2211yescharacteristic
47#16839817C2211yescharacteristic, complemented
48#16839817C2211yescharacteristic, complemented
49#16839817C2211yescharacteristic, complemented
50#16839817C2211yescharacteristic, complemented
51#16839714C2211yescharacteristic, complemented
52#16839714C2211yescharacteristic, complemented
53C2×#14519688C2211yescharacteristic
54#97×D61C2211yescharacteristic, complemented
55#97×D61C2211yescharacteristic, complemented
56#16839504C2211yescharacteristic, complemented
57#16839504C2211yescharacteristic, complemented
58#16839504C2211yescharacteristic, complemented
59#16839504C2211yescharacteristic, complemented
60#16839501C2211yescharacteristic
61#16839501C2211yescharacteristic
62#16839501C2211yescharacteristic
63#16839501C2211yescharacteristic
64#16839501C2211yescharacteristic
65#16839501C2211yescharacteristic
66#16839501C2211yescharacteristic
67#16839501C2211yescharacteristic
68C61×#533C2211yescharacteristic
69C61×#432C2211yescharacteristic
70C2×#97×C61C2211yescharacteristic
71C61×#330C2211yescharacteristic, complemented
72C61×#330C2211yescharacteristic, complemented
73C61×#330C2211yescharacteristic, complemented
74C61×#330C2211yescharacteristic, complemented
75C2×#11758222C2×C411yescharacteristic
76C22×Dic122C2×C411yescharacteristic
77C22×D244C2×C411yescharacteristic
78C2×#11758189—21no—
79C2×#11758189—21no—
80C22×#92418—21no—
81C2×C8×D61—21no—
82C2×C8×D61—21no—
83#14519777—21no—
84#14519774—21no—
85#14519772—21no—
86#14519772—21no—
87#14519772—21no—
88#14519772—21no—
89#14519772—21no—
90#14519772—21no—
91#14519772—21no—
92#14519772—21no—
93#14519766—21no—
94#14519766—21no—
95#14519766—21no—
96#14519766—21no—
97#14519765—21no—
98#14519765—21no—
99#14519765—21no—
100#14519765—21no—
101#14519765C2×C411yescharacteristic
102#14519765C2×C411yescharacteristic
103#14519765C2311yescharacteristic
104#14519765C2311yescharacteristic
105#14519762—21no—
106#14519762—21no—
107#14519762—21no—
108#14519762—21no—
109#14519762—21no—
110#14519762—21no—
111#14519762—21no—
112#14519762—21no—
113#14519761—21no—
114#14519761—21no—
115#14519757C2×C411yescharacteristic
116#14519757C2×C411yescharacteristic
117#14519757C2×C411yescharacteristic
118#14519757C2×C411yescharacteristic
119#14519753—21no—
120#14519753—21no—
121#14519753—21no—
122#14519753—21no—
123#14519752C2×C411yescharacteristic
124#14519752C2×C411yescharacteristic
125#14519752C2×C411yescharacteristic
126#14519752C2×C411yescharacteristic
127#14519747—21no—
128#14519747—21no—
129C4×Dic122—21no—
130C4×Dic122—21no—
131C4×Dic122D411yescharacteristic
132C4×Dic122D411yescharacteristic
133#14519742C2×C411yescharacteristic
134#14519742C2×C411yescharacteristic
135#14519742C2×C411yescharacteristic
136#14519742C2×C411yescharacteristic
137C4×D244—21no—
138C4×D244—21no—
139C4×D244D411yescharacteristic
140C4×D244D411yescharacteristic
141#14519739—21no—
142#14519739—21no—
143#14519739—21no—
144#14519739—21no—
145#14519739C2×C411yescharacteristic
146#14519739C2×C411yescharacteristic
147#14519739C2×C411yescharacteristic
148#14519739C2×C411yescharacteristic
149C4×C22⋊D61D411yescharacteristic
150C4×C22⋊D61D411yescharacteristic
151C4×C22⋊D61D411yescharacteristic
152C4×C22⋊D61D411yescharacteristic
153#14519736C2×C411yescharacteristic
154#14519735—21no—
155#14519735—21no—
156#14519735—21no—
157#14519735—21no—
158#14519734C2×C411yescharacteristic
159#14519734C2×C411yescharacteristic
160#14519733—21no—
161#14519733—21no—
162C2×#11758198—21no—
163C2×#11758198—21no—
164C22⋊C4×D61—21no—
165C22⋊C4×D61—21no—
166C42×D61C2311yescharacteristic
167C42×D61C2311yescharacteristic
168C4⋊#92418—21no—
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418—21no—
174#14519689—21no—
175#14519689—21no—
176#14519689—21no—
177#14519689—21no—
178#14519688—21no—
179#14519688C2311yescharacteristic
180#14519688C2311yescharacteristic
181#14519688C2311yescharacteristic
182#14519688C2311yescharacteristic
183#14519687—21no—
184#14519687—21no—
185C8×Dic61—21no—
186C8×Dic61—21no—
187C22×C8×C61—21no—
188C4⋊Q8×C61C2×C411yescharacteristic
189C4⋊Q8×C61C2×C411yescharacteristic
190#125×C61C2311yescharacteristic
191#125×C61C2311yescharacteristic
192C22⋊Q8×C61—21no—
193C22⋊Q8×C61—21no—
194C4×Q8×C61—21no—
195C4×Q8×C61—21no—
196#117×C61C2×C411yescharacteristic
197#117×C61C2×C411yescharacteristic
198C2×C42×C61C2311yescharacteristic
199C4⋊C8×C61—21no—
200C22⋊C8×C61—21no—
201#97×C61—21no—
202#97×C61C2311yescharacteristic
203#97×C61C2311yescharacteristic
204#97×C61C2311yescharacteristic
205#97×C61C2311yescharacteristic
206C23×D61—21no—
207C2×Q8×C61—21no—
208C2×Q8×C61—21no—
209C22×C4×C61C22×C411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C2×C22⋊D61C22⋊C411yescharacteristic
213C2×C22⋊D61C22⋊C411yescharacteristic
214C22×Dic61—21no—
215#11758222—42no—
216C2×D244—21no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244—21no—
220C2×D244—21no—
221C2×D244—42no—
222C2×D244C22⋊C411yescharacteristic
223C2×D244C22×C411yescharacteristic
224C2×D244C22×C411yescharacteristic
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61C22×C411yescharacteristic
230C2×C4×D61C22×C411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2×D411yescharacteristic
234C2×C4×D61C2×D411yescharacteristic
235C2×Dic122—21no—
236C2×Dic122—42no—
237C2×Dic122C22⋊C411yescharacteristic
238C2×Dic122C22×C411yescharacteristic
239C2×Dic122C22×C411yescharacteristic
240C2×C8×C61—21no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—42no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61C22×C411yescharacteristic
252C4⋊C4×C61C22×C411yescharacteristic
253C4⋊C4×C61C22×C411yescharacteristic
254C4⋊C4×C61C22×C411yescharacteristic
255C22⋊C4×C61—21no—
256C22⋊C4×C61—21no—
257C42×C61—21no—
258C42×C61—21no—
259C42×C61C22×C411yescharacteristic
260C42×C61C2×D411yescharacteristic
261C42×C61C2×D411yescharacteristic
262C42×C61C2411yescharacteristic
263C22⋊Dic61C22⋊C411yescharacteristic
264C22⋊Dic61C22⋊C411yescharacteristic
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#11758198—21no—
274#11758198—21no—
275#11758198—21no—
276#11758198—21no—
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⋊Dic61—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61C22⋊C411yescharacteristic
294C4⋊Dic61C22⋊C411yescharacteristic
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196C22⋊C411yescharacteristic
300#11758196C22⋊C411yescharacteristic
301#11758196C22⋊C411yescharacteristic
302#11758196C22⋊C411yescharacteristic
303C4×Dic61—21no—
304C4×Dic61—21no—
305C4×Dic61—21no—
306C4×Dic61—21no—
307C4×Dic61C22×C411yescharacteristic
308C4×Dic61C22×C411yescharacteristic
309C4×Dic61C2×D411yescharacteristic
310C4×Dic61C2×D411yescharacteristic
311C4×Dic61C2×D411yescharacteristic
312C4×Dic61C2×D411yescharacteristic
313C2×#92418—21no—
314C2×#92418—21no—
315C2×#92418—21no—
316C2×#92418—21no—
317C2×#92418—42no—
318#11758189—42no—
319#11758189—42no—
320C8×D61—42no—
321C8×D61—42no—
322C23×C61C2×C22⋊C411yescharacteristic
323C22×D61—21no—
324C22×D61—21no—
325C22×D61—42no—
326C22×D61—81no—
327C22×D61—81no—
328C22×D61C2×C22⋊C411yescharacteristic
329C22×D61C2×C22⋊C411yescharacteristic
330Q8×C61—81no—
331Q8×C61—81no—
332C2×C4×C61—22no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—21no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61C2×C22⋊C411yescharacteristic
340C2×C4×C61C2×C22⋊C411yescharacteristic
341C2×C4×C61C2×C22⋊C411yescharacteristic
342C2×C4×C61C23×C411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C2×C4×C61C22×D411yescharacteristic
345C22⋊D61—22no—
346C22⋊D61—22no—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—42no—
350C2×Dic61C2×C22⋊C411yescharacteristic
351C2×Dic61C2×C22⋊C411yescharacteristic
352C2×Dic61C2×C22⋊C411yescharacteristic
353C2×Dic61C2×C22⋊C411yescharacteristic
354C2×Dic61C2×C22⋊C411yescharacteristic
355C2×Dic61C2×C22⋊C411yescharacteristic
356D244—41no—
357D244—41no—
358D244—41no—
359D244—42no—
360D244—81no—
361D244—81no—
362D244—81no—
363D244—81no—
364C4×D61—41no—
365C4×D61—41no—
366C4×D61—41no—
367C4×D61—41no—
368C4×D61—41no—
369C4×D61—41no—
370C4×D61—81no—
371C4×D61—81no—
372C4×D61—81no—
373C4×D61—81no—
374Dic122—41no—
375Dic122—42no—
376Dic122—41no—
377Dic122—41no—
378C8×C61—22no—
379C8×C61—41no—
380C8×C61—41no—
381C8×C61—41no—
382#92418—22no—
383#92418—41no—
384#92418—41no—
385#92418—41no—
386#17686—611nomaximal, Sylow
387C22×C61—21no—
388C22×C61—21no—
389C22×C61#41312yes—
390C22×C61C22×C22⋊C411yescharacteristic
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—21no—
394C2×D61—21no—
395C2×D61—21no—
396C2×D61—21no—
397C2×D61—41no—
398C2×D61—41no—
399C2×D61—41no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—162no—
404C4×C61—21no—
405C4×C61—21no—
406C4×C61—21no—
407C4×C61—21no—
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—41no—
411C4×C61—41no—
412C4×C61—41no—
413C4×C61—41no—
414Dic61—21no—
415Dic61—21no—
416Dic61—21no—
417Dic61—21no—
418Dic61—21no—
419Dic61—21no—
420Dic61—41no—
421Dic61—41no—
422#3510—611no—
423#2970—611no—
424#2970—611no—
425#1535—611no—
426#1535—611no—
427#1533—611no—
428#1532—611no—
429#1532—611no—
430#1531—611no—
431#1531D6111yescharacteristic, complemented
432#1529—611no—
433#1529—611no—
434#1524—611no—
435#1524—611no—
436C2×#329—611no—
437C2×C61—22no—
438C2×C61C2×#41311yescharacteristic
439C2×C61#290111yescharacteristic
440C2×C61#290111yescharacteristic
441D61—41no—
442D61—41no—
443D61—81no—
444D61—81no—
445#559—1221no—
446#559—1221no—
447#556—1221no—
448#556—1221no—
449#551—1221no—
450#551—1221no—
451#551—1221no—
452#551—1221no—
453#542—611no—
454#542—611no—
455#542—611no—
456#542—611no—
457#536—611no—
458#535—611no—
459#533C2×D6111yescharacteristic
460#529—611no—
461#529—611no—
462#529—611no—
463#529—611no—
464C2×#124—611no—
465#519—611no—
466#518—611no—
467C4×#41—611no—
468#446—1221no—
469#446—1221no—
470#435—1221no—
471#435—1221no—
472#435—1221no—
473#435—1221no—
474C8×D4—1221no—
475C8×D4—1221no—
476#432—611no—
477#432—611no—
478#432—611no—
479#432—611no—
480#432—611no—
481#432C2×D6111yescharacteristic
482C4×M16—611no—
483C4×M16—611no—
484C2×#97—611no—
485C2×#97—611no—
486C2×#97—611no—
487C2×#97C2×D6111yescharacteristic
488#330—611no—
489#330—611no—
490#330—611no—
491#330—611no—
492#330C2×D6111yescharacteristic, complemented
493#330C2×D6111yescharacteristic, complemented
494#330C2×D6111yescharacteristic, complemented
495#330C2×D6111yescharacteristic, complemented
496#329—611no—
497#329—611no—
498#329—611no—
499#329—611no—
500#329—611no—
501#329—611no—
502#329—611no—
503#329—611no—
504C61#1768611yescharacteristic, complemented, Sylow
505C2×#41—611no—
506C22×Q8—611no—
507C22×D4—611no—
508C2×M16—1221no—
509C2×M16—1221no—
510C22×C8—21no—
511C22×C8—1221no—
512C22×C8—1221no—
513C22×C8—1221no—
514C4⋊Q8—1221no—
515C4⋊Q8C4×D6111yescharacteristic
516C4⋊Q8C4×D6111yescharacteristic
517#127—1221no—
518#126—1221no—
519#126—1221no—
520#126—1221no—
521#126—1221no—
522#126—1221no—
523#126—1221no—
524#126—1221no—
525#126—1221no—
526#125C22×D6111yescharacteristic
527#125C22×D6111yescharacteristic
528#124—611no—
529#124—611no—
530#124—611no—
531#124—611no—
532#124—1221no—
533#124—1221no—
534#124—1221no—
535#124—1221no—
536#124—1221no—
537#124—1221no—
538#124—1221no—
539#124—1221no—
540#123—1221no—
541#123—1221no—
542#123—1221no—
543#123—1221no—
544#123—1221no—
545#123—1221no—
546#123—1221no—
547#123—1221no—
548#123—1221no—
549#123—1221no—
550C22⋊Q8—21no—
551C22⋊Q8—21no—
552C22⋊Q8—611no—
553C22⋊Q8—611no—
554C22⋊Q8—611no—
555C22⋊Q8—611no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560#121—611no—
561#121—611no—
562#121—611no—
563#121—611no—
564#120—1221no—
565#120—1221no—
566C4×Q8—21no—
567C4×Q8—21no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—611no—
571C4×Q8—611no—
572C4×Q8—611no—
573C4×Q8—611no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×D4—611no—
577C4×D4—611no—
578C4×D4—611no—
579C4×D4—611no—
580C4×D4—611no—
581C4×D4—611no—
582C4×D4—611no—
583C4×D4—611no—
584C4×D4—611no—
585C4×D4—611no—
586C4×D4—1221no—
587C4×D4—1221no—
588C4×D4—1221no—
589C4×D4—1221no—
590C4×D4—1221no—
591C4×D4—1221no—
592#117—611no—
593#117—611no—
594#117—611no—
595#117—1221no—
596#117—1221no—
597#117—1221no—
598#117—1221no—
599#117—1221no—
600#117—1221no—
601#117C4×D6111yescharacteristic
602#117C4×D6111yescharacteristic
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C22⋊C4—1221no—
607C2×C42—611no—
608C2×C42—611no—
609C2×C42C22×D6111yescharacteristic
610C4⋊C8—21no—
611C4⋊C8—1221no—
612C4⋊C8—1221no—
613C4⋊C8—1221no—
614C4⋊C8—1221no—
615C4⋊C8—1221no—
616C22⋊C8—21no—
617C22⋊C8—1221no—
618C22⋊C8—1221no—
619C22⋊C8—1221no—
620C22⋊C8—1221no—
621C22⋊C8—1221no—
622#97—21no—
623#97—611no—
624#97—611no—
625#97—611no—
626#97—611no—
627#97—1221no—
628#97—1221no—
629#97—1221no—
630#97C22×D6111yescharacteristic
631#97C22×D6111yescharacteristic
632#97C22×D6111yescharacteristic
633#97C22×D6111yescharacteristic
634C4×C8—1221no—
635C4×C8—1221no—
636C24—1221no—
637#41—2442no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—611no—
641C2×Q8—611no—
642C2×Q8—611no—
643C2×Q8—1221no—
644C2×Q8—2442no—
645C2×D4—611no—
646C2×D4—611no—
647C2×D4—611no—
648C2×D4—611no—
649C2×D4—611no—
650C2×D4—1221no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4—1221no—
654C2×D4—1221no—
655C2×D4—2442no—
656C22×C4—611no—
657C22×C4—611no—
658C22×C4—611no—
659C22×C4—611no—
660C22×C4—611no—
661C22×C4—611no—
662C22×C4—1221no—
663C22×C4—1221no—
664C22×C4—1221no—
665C22×C4—1221no—
666C22×C4—1221no—
667C22×C4C2×C4×D6111yescharacteristic
668C22×C4D4×D6111yescharacteristic
669C22×C4D4×D6111yescharacteristic
670M16—2442no—
671M16—2442no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—42no—
677C2×C8—1221no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—2442no—
682C2×C8—2442no—
683C2×C8—2442no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—611no—
691C4⋊C4—611no—
692C4⋊C4—611no—
693C4⋊C4—611no—
694C4⋊C4—611no—
695C4⋊C4—611no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4—1221no—
703C4⋊C4—1221no—
704C4⋊C4C2×C4×D6111yescharacteristic
705C4⋊C4C2×C4×D6111yescharacteristic
706C4⋊C4C2×C4×D6111yescharacteristic
707C4⋊C4C2×C4×D6111yescharacteristic
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—611no—
711C22⋊C4—611no—
712C22⋊C4—611no—
713C22⋊C4—611no—
714C22⋊C4—611no—
715C22⋊C4—611no—
716C22⋊C4—1221no—
717C22⋊C4—1221no—
718C22⋊C4—1221no—
719C22⋊C4—1221no—
720C22⋊C4—1221no—
721C22⋊C4—1221no—
722C22⋊C4—1221no—
723C22⋊C4—1221no—
724C22⋊C4—1221no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4—1221no—
730C22⋊C4—1221no—
731C22⋊C4—1221no—
732C22⋊C4—1221no—
733C22⋊C4—1221no—
734C22⋊C4—1221no—
735C22⋊C4—1221no—
736C42—21no—
737C42—21no—
738C42—611no—
739C42—611no—
740C42—611no—
741C42—611no—
742C42—611no—
743C42—611no—
744C42—1221no—
745C42—1221no—
746C42—1221no—
747C42—1221no—
748C42C2×C4×D6111yescharacteristic
749C42D4×D6111yescharacteristic
750C42D4×D6111yescharacteristic
751C42C23×D6111yescharacteristic
752C23—611no—
753C23—611no—
754C23—1221no—
755C23—1221no—
756C23—4881no—
757C23—4881no—
758C23—2442no—
759C23C22⋊C4×D6111yescharacteristic
760Q8—81no—
761Q8—81no—
762Q8—2441no—
763Q8—2441no—
764Q8—2441no—
765Q8—2442no—
766D4—1222no—
767D4—1222no—
768D4—4881no—
769D4—4881no—
770D4—4881no—
771D4—4881no—
772D4—2441no—
773D4—2441no—
774D4—2441no—
775D4—2442no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—611no—
784C2×C4—611no—
785C2×C4—611no—
786C2×C4—611no—
787C2×C4—611no—
788C2×C4—611no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—4881no—
792C2×C4—4881no—
793C2×C4—4881no—
794C2×C4—4881no—
795C2×C4—2441no—
796C2×C4—2441no—
797C2×C4—2441no—
798C2×C4—2441no—
799C2×C4—2441no—
800C2×C4—2441no—
801C2×C4—2442no—
802C2×C4C22⋊C4×D6111yescharacteristic
803C2×C4C22⋊C4×D6111yescharacteristic
804C2×C4C22⋊C4×D6111yescharacteristic
805C2×C4C22×C4×D6111yescharacteristic
806C2×C4C2×D4×D6111yescharacteristic
807C2×C4C2×D4×D6111yescharacteristic
808C8—22no—
809C8—41no—
810C8—41no—
811C8—41no—
812C8—1222no—
813C8—2441no—
814C8—2441no—
815C8—2441no—
816C22—21no—
817C22—21no—
818C22—1221no—
819C22—1221no—
820C22—1221no—
821C22—1221no—
822C22—1221no—
823C22—1221no—
824C22—9762no—
825C22—2441no—
826C22—2441no—
827C22—2441no—
828C22—2441no—
829C22—2441no—
830C22—2441no—
831C22#1683974512yes—
832C22C2×C22⋊C4×D6111yescharacteristic
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—41no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—1221no—
844C4—1221no—
845C4—1221no—
846C4—1221no—
847C4—1221no—
848C4—1221no—
849C4—2441no—
850C4—2441no—
851C2—22no—
852C2—4881no—
853C2—4881no—
854C2—2441no—
855C2—2441no—
856C2C2×#1683974511yescharacteristic
857C2#2145436311yescharacteristic
858C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1531C2
socleC22×C61C22×C22⋊C4
prime radical#16840331C4
cosocleC42×C61C24
hypercenter#1531D61
hypocenterC61#17686
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1531

Complements

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

NH ≅ G/Ntype
2. #21454830C2semidirect
3. #21454828C2semidirect
4. #21444449C2semidirect
5. #21444449C2semidirect
6. #21444442C2semidirect
7. #21444438C2semidirect
8. #21444438C2semidirect
9. #21444434C2semidirect
10. #21444425C2semidirect
11. #21444425C2semidirect
12. #21444406C2semidirect
13. #21444406C2semidirect
14. C2×#16839501C2semidirect
15. C61×#1531C2semidirect
47. #16839817C22semidirect
48. #16839817C22semidirect
49. #16839817C22semidirect
50. #16839817C22semidirect
51. #16839714C22semidirect
52. #16839714C22semidirect
54. #97×D61C22semidirect
55. #97×D61C22semidirect
56. #16839504C22semidirect
57. #16839504C22semidirect
58. #16839504C22semidirect
59. #16839504C22semidirect
71. C61×#330C22semidirect
72. C61×#330C22semidirect
73. C61×#330C22semidirect
74. C61×#330C22semidirect
431. #1531D61semidirect
492. #330C2×D61semidirect
493. #330C2×D61semidirect
494. #330C2×D61semidirect
495. #330C2×D61semidirect
504. C61#17686semidirect

Maximal subgroups

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

subgroupindex
#214597172
#214548302
#214548282
#214444492
#214444422
#214444382
#214444342
#214444252
#214444062
C2×#168395012
C61×#15312
#1768661