Finite Group Databasebeta

← #29648155

Subgroups — #29648155

Order 15616.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459768C211yesmaximal, characteristic
2#21454834C211yesmaximal, characteristic, complemented
3#21454465C211yesmaximal, characteristic, complemented
4#21444452C211yesmaximal, characteristic, complemented
5#21444450C211yesmaximal, characteristic, complemented
6#21444449C211yesmaximal, characteristic, complemented
7#21444442C211yesmaximal, characteristic, complemented
8#21444438C211yesmaximal, characteristic, complemented
9#21444438C211yesmaximal, characteristic, complemented
10#21444428C211yesmaximal, characteristic, complemented
11#21444416C211yesmaximal, characteristic, complemented
12#21444415C211yesmaximal, characteristic, complemented
13#21444406C211yesmaximal, characteristic, complemented
14#329×D61C211yesmaximal, characteristic, complemented
15C61×#1529C211yesmaximal, characteristic, complemented
16#16840495C411yescharacteristic
17#16840484C411yescharacteristic
18#16840475—21no—
19#16840436—21no—
20#16840435—21no—
21#16840425C411yescharacteristic
22#16840424C411yescharacteristic
23#16840418C411yescharacteristic
24#16840407C411yescharacteristic
25#16840404—21no—
26#16840403C411yescharacteristic
27#16840396C411yescharacteristic
28#16840378—21no—
29#16840351—21no—
30#16840345—21no—
31#16840311C2211yescharacteristic
32#16840297C2211yescharacteristic
33#16840297C2211yescharacteristic
34C2×#14519765C2211yescharacteristic
35#124×D61C2211yescharacteristic
36#16840234—21no—
37C4×#11758222C2211yescharacteristic
38#16839892—21no—
39#16839831—21no—
40#16839831—21no—
41C8×D244—21no—
42#16839822—21no—
43#16839820—21no—
44#16839819C2211yescharacteristic, complemented
45#16839819C2211yescharacteristic, complemented
46#16839817C2211yescharacteristic, complemented
47#16839817C2211yescharacteristic, complemented
48#16839817C2211yescharacteristic, complemented
49#16839817C2211yescharacteristic, complemented
50#16839787—21no—
51#16839727—21no—
52#16839714C2211yescharacteristic, complemented
53#97×D61C2211yescharacteristic, complemented
54#97×D61C2211yescharacteristic, complemented
55#97×D61C2211yescharacteristic, complemented
56#16839504C2211yescharacteristic, complemented
57#16839504C2211yescharacteristic, complemented
58#16839502C2211yescharacteristic, complemented
59#16839502C2211yescharacteristic, complemented
60#16839501C2211yescharacteristic
61#16839501C2211yescharacteristic
62#16839501C2211yescharacteristic
63#16839501C2211yescharacteristic
64#16839501C2211yescharacteristic, complemented
65#16839501C2211yescharacteristic, complemented
66#16839501C2211yescharacteristic, complemented
67#16839501C2211yescharacteristic, complemented
68C61×#529C2211yescharacteristic
69C61×#432C2211yescharacteristic, complemented
70C4×M16×C61C2211yescharacteristic, complemented
71C61×#330C2211yescharacteristic, complemented
72C61×#330C2211yescharacteristic, complemented
73C61×#329C2211yescharacteristic, complemented
74C61×#329C2211yescharacteristic, complemented
75C2×#11758226C2×C411yescharacteristic
76C2×#11758222D411yescharacteristic
77C2×#11758224C2×C411yescharacteristic
78C22×Dic122C2×C411yescharacteristic
79C2×Q8×D61C2×C411yescharacteristic
80C22×D244C2×C411yescharacteristic
81C2×D4×D61—21no—
82C2×D4×D61C2×C411yescharacteristic
83C2×#11758189—21no—
84C2×C8×D61—21no—
85C2×C8×D61—21no—
86C2×C8×D61—21no—
87#14519776—21no—
88#14519775C2×C411yescharacteristic
89#14519773C2×C411yescharacteristic
90#14519772—21no—
91#14519772—21no—
92#14519772—21no—
93#14519771—21no—
94#14519766C2×C411yescharacteristic
95#14519765—21no—
96#14519765—21no—
97#14519765—21no—
98#14519765C2×C411yescharacteristic
99#14519765C2×C411yescharacteristic
100#14519765C2311yescharacteristic
101#14519765C2311yescharacteristic
102#14519764C2×C411yescharacteristic
103#14519763—21no—
104#14519763—21no—
105#14519763—21no—
106#14519763—21no—
107#14519762—21no—
108#14519762—21no—
109#14519762—21no—
110#14519761—21no—
111#14519760—21no—
112#14519759—21no—
113#14519757—21no—
114#14519757C2×C411yescharacteristic
115#14519757C2×C411yescharacteristic
116#14519755—21no—
117#14519755—21no—
118#14519754—21no—
119#14519754—21no—
120#14519752—21no—
121#14519752—21no—
122#14519752C2×C411yescharacteristic
123#14519752C2×C411yescharacteristic
124#14519751—21no—
125#14519750—21no—
126#14519750—21no—
127#14519750—21no—
128#14519749—21no—
129#14519747—21no—
130#14519747—21no—
131#14519747—21no—
132#14519745—21no—
133C4×Dic122C2×C411yescharacteristic
134C4×Dic122D411yescharacteristic
135#14519742C2×C411yescharacteristic
136#14519742C2×C411yescharacteristic
137C4×D244—21no—
138C4×D244C2×C411yescharacteristic
139C4×D244D411yescharacteristic
140D4×Dic61—21no—
141#14519739—21no—
142#14519739—21no—
143#14519739C2×C411yescharacteristic
144#14519739C2×C411yescharacteristic
145C4×C22⋊D61—21no—
146C4×C22⋊D61C2×C411yescharacteristic
147C4×C22⋊D61C2×C411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149C4×C22⋊D61D411yescharacteristic
150#14519737—21no—
151#14519737—21no—
152#14519737—21no—
153#14519736D411yescharacteristic
154#14519735—21no—
155#14519735—21no—
156#14519734—21no—
157#14519734D411yescharacteristic
158#14519734D411yescharacteristic
159C2×#11758198—21no—
160C2×#11758198—21no—
161C2×#11758198—21no—
162C22⋊C4×D61—21no—
163C22⋊C4×D61—21no—
164C22⋊C4×D61—21no—
165C42×D61C2311yescharacteristic
166C42×D61C2311yescharacteristic
167C4⋊#92418—21no—
168C4⋊#92418—21no—
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418—21no—
174C22⋊#92418—21no—
175#14519689—21no—
176#14519689—21no—
177#14519689—21no—
178#14519689—21no—
179#14519688C2311yescharacteristic
180#14519688C2311yescharacteristic
181#14519688C2311yescharacteristic
182#14519688C2311yescharacteristic
183#14519687—21no—
184#14519687—21no—
185#14519687—21no—
186C8×Dic61—21no—
187C2×M16×C61—21no—
188#126×C61—21no—
189#125×C61C2311yescharacteristic
190#124×C61C2311yescharacteristic
191#123×C61—21no—
192C22⋊Q8×C61C2×C411yescharacteristic
193#121×C61C2×C411yescharacteristic
194C4×Q8×C61C2×C411yescharacteristic
195C4×D4×C61—21no—
196C4×D4×C61C2×C411yescharacteristic
197#117×C61—21no—
198C2×C42×C61C2311yescharacteristic
199C4⋊C8×C61—21no—
200C22⋊C8×C61—21no—
201#97×C61C2311yescharacteristic
202#97×C61C2311yescharacteristic
203#97×C61C2311yescharacteristic
204#97×C61C2311yescharacteristic
205C4×C8×C61—21no—
206C23×D61—21no—
207C23×D61—21no—
208C2×Q8×C61C22×C411yescharacteristic
209C2×D4×C61—21no—
210C2×D4×C61C22×C411yescharacteristic
211C22×C4×C61—21no—
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C22×C4×C61C2×D411yescharacteristic
215C2×C22⋊D61—21no—
216C2×C22⋊D61—21no—
217C2×C22⋊D61—21no—
218C2×C22⋊D61—21no—
219C2×C22⋊D61C22⋊C411yescharacteristic
220C2×C22⋊D61C22⋊C411yescharacteristic
221C22×Dic61—21no—
222C22×Dic61—21no—
223#11758226—81no—
224Q8×D61—81no—
225#11758224—81no—
226D4×D61—44no—
227D4×D61—81no—
228#11758222—42no—
229C2×D244—21no—
230C2×D244—21no—
231C2×D244—21no—
232C2×D244—21no—
233C2×D244—81no—
234C2×D244C22⋊C411yescharacteristic
235C2×D244C22×C411yescharacteristic
236C2×D244C22×C411yescharacteristic
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×Dic122—81no—
250C2×Dic122C22⋊C411yescharacteristic
251C2×Dic122C22×C411yescharacteristic
252C2×Dic122C22×C411yescharacteristic
253M16×C61—42no—
254C2×C8×C61—21no—
255C2×C8×C61—21no—
256C2×C8×C61—21no—
257C2×C8×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61—21no—
260C4⋊C4×C61—21no—
261C4⋊C4×C61—21no—
262C4⋊C4×C61C22×C411yescharacteristic
263C4⋊C4×C61C22×C411yescharacteristic
264C22⋊C4×C61—21no—
265C22⋊C4×C61—21no—
266C22⋊C4×C61—21no—
267C22⋊C4×C61—21no—
268C22⋊C4×C61—21no—
269C42×C61—21no—
270C42×C61C22×C411yescharacteristic
271C42×C61C2×D411yescharacteristic
272C42×C61C2×D411yescharacteristic
273C42×C61C2411yescharacteristic
274C22⋊Dic61—21no—
275C22⋊Dic61—21no—
276C22⋊Dic61C22⋊C411yescharacteristic
277C22⋊Dic61C22⋊C411yescharacteristic
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198C22⋊C411yescharacteristic
295#11758198C22⋊C411yescharacteristic
296#11758198C22⋊C411yescharacteristic
297#11758198C22⋊C411yescharacteristic
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61C22⋊C411yescharacteristic
301C4⋊Dic61C22⋊C411yescharacteristic
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308#11758196C22⋊C411yescharacteristic
309#11758196C22⋊C411yescharacteristic
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61C22×C411yescharacteristic
313C4×Dic61C22×C411yescharacteristic
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C4×Dic61C2×D411yescharacteristic
318C2×#92418—21no—
319C2×#92418—21no—
320C2×#92418—21no—
321C2×#92418—21no—
322#11758189—42no—
323C8×D61—42no—
324C8×D61—42no—
325C8×D61—42no—
326C23×C61—21no—
327C23×C61C2×C22⋊C411yescharacteristic
328C22×D61—21no—
329C22×D61—21no—
330C22×D61—42no—
331C22×D61—42no—
332C22×D61—81no—
333C22×D61—81no—
334C22×D61—81no—
335C22×D61—81no—
336C22×D61C2×C22⋊C411yescharacteristic
337C22×D61C2×C22⋊C411yescharacteristic
338Q8×C61—41no—
339D4×C61—41no—
340D4×C61—42no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—41no—
345C2×C4×C61—41no—
346C2×C4×C61—41no—
347C2×C4×C61—81no—
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—22no—
355C22⋊D61—41no—
356C22⋊D61—42no—
357C22⋊D61—81no—
358C22⋊D61—81no—
359C22⋊D61—81no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—81no—
363C2×Dic61—81no—
364C2×Dic61C2×C22⋊C411yescharacteristic
365C2×Dic61C2×C22⋊C411yescharacteristic
366C2×Dic61C2×C22⋊C411yescharacteristic
367C2×Dic61C2×C22⋊C411yescharacteristic
368C2×Dic61C2×C22⋊C411yescharacteristic
369C2×Dic61C2×C22⋊C411yescharacteristic
370D244—22no—
371D244—41no—
372D244—41no—
373D244—42no—
374D244—81no—
375D244—81no—
376D244—81no—
377C4×D61—22no—
378C4×D61—41no—
379C4×D61—41no—
380C4×D61—41no—
381C4×D61—41no—
382C4×D61—41no—
383C4×D61—42no—
384C4×D61—81no—
385C4×D61—81no—
386C4×D61—81no—
387Dic122—41no—
388Dic122—41no—
389Dic122—41no—
390Dic122—81no—
391Dic122—81no—
392C8×C61—22no—
393C8×C61—41no—
394C8×C61—41no—
395C8×C61—41no—
396#92418—41no—
397#92418—41no—
398#92418—41no—
399#92418—41no—
400#17679—611nomaximal, Sylow
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—41no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61C22×C22⋊C411yescharacteristic
408C2×D61—21no—
409C2×D61—21no—
410C2×D61—21no—
411C2×D61—21no—
412C2×D61—21no—
413C2×D61—41no—
414C2×D61—41no—
415C2×D61—41no—
416C2×D61—41no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—162no—
420C2×D61—162no—
421C2×D61#42112yes—
422C4×C61—21no—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—21no—
428C4×C61—41no—
429C4×C61—41no—
430C4×C61—41no—
431Dic61—21no—
432Dic61—21no—
433Dic61—21no—
434Dic61—21no—
435Dic61—21no—
436Dic61—21no—
437Dic61—41no—
438Dic61—41no—
439#3514—611no—
440#2970—611no—
441#2923—611no—
442#1536—611no—
443#1535—611no—
444#1535—611no—
445#1533—611no—
446#1532—611no—
447#1532—611no—
448#1530—611no—
449#1529D6111yescharacteristic, complemented
450#1527—611no—
451#1527—611no—
452#1524—611no—
453C2×#329—611no—
454C2×C61—41no—
455C2×C61—81no—
456C2×C61#288811yescharacteristic
457C2×C61C2×#42111yescharacteristic
458C2×C61#290111yescharacteristic
459D61—22no—
460D61—41no—
461D61—81no—
462D61—81no—
463#559—611no—
464#556—611no—
465#555—1221no—
466#551—1221no—
467#551—1221no—
468D4×Q8—611no—
469#548—611no—
470#548—611no—
471#546—611no—
472#546—611no—
473#546—1221no—
474D42—611no—
475#542—1221no—
476#538—1221no—
477#538—1221no—
478#532—611no—
479#529—611no—
480#529—611no—
481#529C2×D6111yescharacteristic
482C2×#124—611no—
483C2×#124—611no—
484#518—1221no—
485C4×#41—611no—
486#446—1221no—
487#435—1221no—
488#435—1221no—
489C8×D4—1221no—
490#433—1221no—
491#433—1221no—
492#432—611no—
493#432—611no—
494#432—611no—
495#432—611no—
496#432—611no—
497#432—611no—
498#432C2×D6111yescharacteristic, complemented
499#424—1221no—
500#408—1221no—
501C4×M16—611no—
502C4×M16C2×D6111yescharacteristic, complemented
503C2×#97—611no—
504C2×#97—611no—
505C2×#97—611no—
506#330—611no—
507#330—611no—
508#330C2×D6111yescharacteristic, complemented
509#330C2×D6111yescharacteristic, complemented
510#329—611no—
511#329—611no—
512#329—611no—
513#329—611no—
514#329—611no—
515#329—611no—
516#329—611no—
517#329—611no—
518#329—611no—
519#329—611no—
520#329C2×D6111yescharacteristic, complemented
521#329C2×D6111yescharacteristic, complemented
522C61#1767911yescharacteristic, complemented, Sylow
523C2×#41—611no—
524C2×#41—611no—
525C2×#41—611no—
526C22×Q8—611no—
527C22×Q8—611no—
528C22×D4—611no—
529C22×D4—611no—
530C22×D4—1221no—
531C2×M16—21no—
532C2×M16—1221no—
533C22×C8—1221no—
534C22×C8—1221no—
535C22×C8—1221no—
536C4⋊Q8—611no—
537C4⋊Q8—1221no—
538#127—611no—
539#126—21no—
540#126—1221no—
541#126—1221no—
542#126—1221no—
543#126—1221no—
544#125C22×D6111yescharacteristic
545#124—611no—
546#124—611no—
547#124—611no—
548#124—611no—
549#124—611no—
550#124—611no—
551#124—1221no—
552#124—1221no—
553#124—1221no—
554#124—1221no—
555#124—1221no—
556#124—1221no—
557#124—1221no—
558#124C22×D6111yescharacteristic
559#123—21no—
560#123—1221no—
561#123—1221no—
562#123—1221no—
563#123—1221no—
564#123—1221no—
565#123—1221no—
566C22⋊Q8—611no—
567C22⋊Q8—611no—
568C22⋊Q8—1221no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573C22⋊Q8C4×D6111yescharacteristic
574#121—611no—
575#121—611no—
576#121—1221no—
577#121—1221no—
578#121—1221no—
579#121—1221no—
580#121—1221no—
581#121—1221no—
582#121—1221no—
583#121C4×D6111yescharacteristic
584#120—1221no—
585#120—1221no—
586#120—1221no—
587#120—1221no—
588C4×Q8—611no—
589C4×Q8—611no—
590C4×Q8—611no—
591C4×Q8—611no—
592C4×Q8C4×D6111yescharacteristic
593C4×D4—21no—
594C4×D4—611no—
595C4×D4—611no—
596C4×D4—611no—
597C4×D4—611no—
598C4×D4—611no—
599C4×D4—611no—
600C4×D4—611no—
601C4×D4—611no—
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×D4C4×D6111yescharacteristic
611#117—21no—
612#117—611no—
613#117—611no—
614#117—611no—
615#117—1221no—
616#117—1221no—
617#117—1221no—
618C2×C22⋊C4—1221no—
619C2×C22⋊C4—1221no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C42—611no—
625C2×C42—611no—
626C2×C42C22×D6111yescharacteristic
627C4⋊C8—21no—
628C4⋊C8—1221no—
629C4⋊C8—1221no—
630C4⋊C8—1221no—
631C4⋊C8—1221no—
632C4⋊C8—1221no—
633C4⋊C8—1221no—
634C22⋊C8—21no—
635C22⋊C8—1221no—
636C22⋊C8—1221no—
637C22⋊C8—1221no—
638C22⋊C8—1221no—
639C22⋊C8—1221no—
640C22⋊C8—1221no—
641#97—611no—
642#97—611no—
643#97—611no—
644#97—611no—
645#97—1221no—
646#97—1221no—
647#97—1221no—
648#97C22×D6111yescharacteristic
649#97C22×D6111yescharacteristic
650#97C22×D6111yescharacteristic
651#97C22×D6111yescharacteristic
652C4×C8—21no—
653C4×C8—1221no—
654C24—1221no—
655C24—1221no—
656#41—4881no—
657#41—4881no—
658#41—2442no—
659C2×Q8—611no—
660C2×Q8—611no—
661C2×Q8—611no—
662C2×Q8—1221no—
663C2×Q8—1221no—
664C2×Q8—4881no—
665C2×Q8—4881no—
666C2×Q8C2×C4×D6111yescharacteristic
667C2×D4—21no—
668C2×D4—611no—
669C2×D4—611no—
670C2×D4—611no—
671C2×D4—611no—
672C2×D4—611no—
673C2×D4—1221no—
674C2×D4—1221no—
675C2×D4—1221no—
676C2×D4—1221no—
677C2×D4—1221no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—1221no—
681C2×D4—4881no—
682C2×D4—4881no—
683C2×D4—2444no—
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×C4C2×C4×D6111yescharacteristic
699C22×C4D4×D6111yescharacteristic
700C22×C4D4×D6111yescharacteristic
701M16—42no—
702M16—2442no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—2442no—
712C2×C8—2442no—
713C2×C8—2442no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—611no—
719C4⋊C4—611no—
720C4⋊C4—611no—
721C4⋊C4—611no—
722C4⋊C4—611no—
723C4⋊C4—611no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4C2×C4×D6111yescharacteristic
731C4⋊C4C2×C4×D6111yescharacteristic
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—611no—
738C22⋊C4—611no—
739C22⋊C4—611no—
740C22⋊C4—611no—
741C22⋊C4—611no—
742C22⋊C4—611no—
743C22⋊C4—1221no—
744C22⋊C4—1221no—
745C22⋊C4—1221no—
746C22⋊C4—1221no—
747C22⋊C4—1221no—
748C22⋊C4—1221no—
749C22⋊C4—1221no—
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—
770C42C2×C4×D6111yescharacteristic
771C42D4×D6111yescharacteristic
772C42D4×D6111yescharacteristic
773C42C23×D6111yescharacteristic
774C23—21no—
775C23—611no—
776C23—611no—
777C23—1221no—
778C23—1221no—
779C23—4881no—
780C23—4881no—
781C23—4881no—
782C23—4881no—
783C23—2442no—
784C23—2442no—
785C23C22⋊C4×D6111yescharacteristic
786Q8—41no—
787Q8—4881no—
788Q8—4881no—
789Q8—2441no—
790Q8—2441no—
791Q8—2441no—
792D4—41no—
793D4—42no—
794D4—1222no—
795D4—1222no—
796D4—4881no—
797D4—4881no—
798D4—4881no—
799D4—4881no—
800D4—4881no—
801D4—4881no—
802D4—2441no—
803D4—2441no—
804D4—2442no—
805D4—2441no—
806D4—2442no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—81no—
814C2×C4—611no—
815C2×C4—611no—
816C2×C4—611no—
817C2×C4—611no—
818C2×C4—611no—
819C2×C4—611no—
820C2×C4—1222no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—4881no—
824C2×C4—4881no—
825C2×C4—4881no—
826C2×C4—4881no—
827C2×C4—4881no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4—2442no—
834C2×C4C22⋊C4×D6111yescharacteristic
835C2×C4C22⋊C4×D6111yescharacteristic
836C2×C4C22⋊C4×D6111yescharacteristic
837C2×C4C22×C4×D6111yescharacteristic
838C2×C4C2×D4×D6111yescharacteristic
839C2×C4C2×D4×D6111yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—2441no—
845C8—2441no—
846C8—2441no—
847C8—2441no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—612no—
855C22—1221no—
856C22—1221no—
857C22—1221no—
858C22—1221no—
859C22—1221no—
860C22—9762no—
861C22—9762no—
862C22—2441no—
863C22—2441no—
864C22—2441no—
865C22—2441no—
866C22—2441no—
867C22—2441no—
868C22C2×C22⋊C4×D6111yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—1221no—
879C4—1221no—
880C4—1221no—
881C4—1221no—
882C4—1221no—
883C4—1221no—
884C4—2441no—
885C4—2441no—
886C2—41no—
887C2—81no—
888C2—1222no—
889C2—4881no—
890C2—4881no—
891C2—2441no—
892C2#2145429611yescharacteristic
893C2#421×D6111yescharacteristic
894C2#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1529C2
socleC22×C61C22×C22⋊C4
prime radical#21459768C2
cosocleC42×C61C24
hypercenter#1529D61
hypocenterC61#17679
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1529

Complements

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

NH ≅ G/Ntype
2. #21454834C2semidirect
3. #21454465C2semidirect
4. #21444452C2semidirect
5. #21444450C2semidirect
6. #21444449C2semidirect
7. #21444442C2semidirect
8. #21444438C2semidirect
9. #21444438C2semidirect
10. #21444428C2semidirect
11. #21444416C2semidirect
12. #21444415C2semidirect
13. #21444406C2semidirect
14. #329×D61C2semidirect
15. C61×#1529C2semidirect
44. #16839819C22semidirect
45. #16839819C22semidirect
46. #16839817C22semidirect
47. #16839817C22semidirect
48. #16839817C22semidirect
49. #16839817C22semidirect
52. #16839714C22semidirect
53. #97×D61C22semidirect
54. #97×D61C22semidirect
55. #97×D61C22semidirect
56. #16839504C22semidirect
57. #16839504C22semidirect
58. #16839502C22semidirect
59. #16839502C22semidirect
64. #16839501C22semidirect
65. #16839501C22semidirect
66. #16839501C22semidirect
67. #16839501C22semidirect
69. C61×#432C22semidirect
70. C4×M16×C61C22semidirect
71. C61×#330C22semidirect
72. C61×#330C22semidirect
73. C61×#329C22semidirect
74. C61×#329C22semidirect
449. #1529D61semidirect
498. #432C2×D61semidirect
502. C4×M16C2×D61semidirect
508. #330C2×D61semidirect
509. #330C2×D61semidirect
520. #329C2×D61semidirect
521. #329C2×D61semidirect
522. C61#17679semidirect

Maximal subgroups

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

subgroupindex
#214597682
#214548342
#214544652
#214444522
#214444502
#214444492
#214444422
#214444382
#214444282
#214444162
#214444152
#214444062
#329×D612
C61×#15292
#1767961