Finite Group Databasebeta

← #29648011

Subgroups — #29648011

Order 15616.

964 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459785C211yesmaximal, characteristic
2#21454830C211yesmaximal, characteristic, complemented
3#21454248C211yesmaximal, characteristic, complemented
4#21444439C211yesmaximal, characteristic, complemented
5#21444436C211yesmaximal, characteristic, complemented
6#21444432C211yesmaximal, characteristic, complemented
7#21444423C211yesmaximal, characteristic, complemented
8#21444420C211yesmaximal, characteristic, complemented
9#21444419C211yesmaximal, characteristic, complemented
10#21444412C211yesmaximal, characteristic, complemented
11#21444404C211yesmaximal, characteristic, complemented
12#21444404C211yesmaximal, characteristic, complemented
13C2×#16839503C211yesmaximal, characteristic, complemented
14#330×D61C211yesmaximal, characteristic, complemented
15C61×#1524C211yesmaximal, characteristic, complemented
16C2×#14519785—21no—
17#16840488C411yescharacteristic
18#16840471C411yescharacteristic
19#16840470C411yescharacteristic
20#16840464C411yescharacteristic
21#16840462C411yescharacteristic
22#16840454C411yescharacteristic
23#16840453C411yescharacteristic
24#16840451—21no—
25#16840449—21no—
26#16840445—21no—
27#16840412C411yescharacteristic
28#16840410—21no—
29#16840369—21no—
30#16840354—21no—
31#16840353—21no—
32#16840318C2211yescharacteristic
33#16840291C2211yescharacteristic
34#16840291C2211yescharacteristic
35C2×#14519769C2211yescharacteristic
36#125×D61C2211yescharacteristic
37#16840241—21no—
38C4×#11758222C2211yescharacteristic
39#16839890—21no—
40#16839835—21no—
41#16839833—21no—
42C8×C22⋊D61—21no—
43#16839819C2211yescharacteristic
44#16839817C2211yescharacteristic
45#16839817C2211yescharacteristic
46#16839720—21no—
47#16839716—21no—
48#16839716—21no—
49#16839714C2211yescharacteristic
50#16839714C2211yescharacteristic
51#16839714C2211yescharacteristic
52C2×#14519688C2211yescharacteristic
53#97×D61C2211yescharacteristic
54#97×D61C2211yescharacteristic
55#97×D61C2211yescharacteristic
56#16839504C2211yescharacteristic
57#16839504C2211yescharacteristic
58#16839503C2211yescharacteristic
59#16839503C2211yescharacteristic
60#16839503C2211yescharacteristic
61#16839503C2211yescharacteristic
62#16839503C2211yescharacteristic
63#16839503C2211yescharacteristic
64#16839503C2211yescharacteristic
65#16839503C2211yescharacteristic
66#16839502C2211yescharacteristic
67#16839502C2211yescharacteristic
68C61×#529C2211yescharacteristic
69C4×M16×C61C2211yescharacteristic
70C2×#97×C61C2211yescharacteristic
71C61×#330C2211yescharacteristic
72C61×#330C2211yescharacteristic
73C61×#329C2211yescharacteristic
74C61×#329C2211yescharacteristic
75C2×#11758222D411yescharacteristic
76C2×#11758224—21no—
77#14519785—28no—
78C2×#11758189—21no—
79C2×#11758189—21no—
80C2×#11758189—21no—
81C22×#92418—21no—
82C2×C8×D61—21no—
83C2×C8×D61—21no—
84C2×C8×D61—21no—
85#14519776—21no—
86#14519776C2×C411yescharacteristic
87#14519776C2×C411yescharacteristic
88#14519772—21no—
89#14519771—21no—
90#14519770—21no—
91#14519770—21no—
92#14519770—21no—
93#14519770—21no—
94#14519769—21no—
95#14519769—21no—
96#14519769—21no—
97#14519769C2×C411yescharacteristic
98#14519769C2×C411yescharacteristic
99#14519769C2311yescharacteristic
100#14519769C2311yescharacteristic
101#14519768—21no—
102#14519768—21no—
103#14519768C2×C411yescharacteristic
104#14519768C2×C411yescharacteristic
105#14519767—21no—
106#14519767—21no—
107#14519767—21no—
108#14519767—21no—
109#14519762—21no—
110#14519761—21no—
111#14519761—21no—
112#14519760—21no—
113#14519759—21no—
114#14519759—21no—
115#14519759—21no—
116#14519758—21no—
117#14519757—21no—
118#14519756—21no—
119#14519755—21no—
120#14519755—21no—
121#14519754—21no—
122#14519754—21no—
123#14519754—21no—
124#14519754—21no—
125#14519753C2×C411yescharacteristic
126#14519753C2×C411yescharacteristic
127#14519750—21no—
128#14519749—21no—
129#14519748C2×C411yescharacteristic
130#14519748C2×C411yescharacteristic
131Q8×Dic61C2×C411yescharacteristic
132Q8×Dic61C2×C411yescharacteristic
133C4×Dic122—21no—
134C4×Dic122C2×C411yescharacteristic
135C4×Dic122D411yescharacteristic
136#14519742—21no—
137#14519742—21no—
138C4×D244C2×C411yescharacteristic
139C4×D244D411yescharacteristic
140D4×Dic61—21no—
141D4×Dic61C2×C411yescharacteristic
142D4×Dic61C2×C411yescharacteristic
143C4×C22⋊D61—21no—
144C4×C22⋊D61C2×C411yescharacteristic
145C4×C22⋊D61C2×C411yescharacteristic
146C4×C22⋊D61D411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148#14519737—21no—
149#14519737—21no—
150#14519737—21no—
151#14519736D411yescharacteristic
152#14519735C2×C411yescharacteristic
153#14519735C2×C411yescharacteristic
154#14519734—21no—
155#14519734D411yescharacteristic
156#14519734D411yescharacteristic
157#14519733—21no—
158#14519733—21no—
159#14519733—21no—
160C2×C4⋊Dic61C2×C411yescharacteristic
161C2×C4⋊Dic61C2×C411yescharacteristic
162C2×#11758196—21no—
163C2×#11758196—21no—
164C2×#11758196—21no—
165C4⋊C4×D61—21no—
166C4⋊C4×D61—21no—
167C4⋊C4×D61C2×C411yescharacteristic
168C4⋊C4×D61C2×C411yescharacteristic
169C42×D61C2311yescharacteristic
170C42×D61C2311yescharacteristic
171C4⋊#92418—21no—
172#14519706—21no—
173#14519706—21no—
174C22⋊#92418—21no—
175#14519689—21no—
176#14519689—21no—
177#14519688—21no—
178#14519688C2311yescharacteristic
179#14519688C2311yescharacteristic
180#14519688C2311yescharacteristic
181#14519688C2311yescharacteristic
182#14519687—21no—
183#14519687—21no—
184#14519687—21no—
185C8×Dic61—21no—
186C8×Dic61—21no—
187C8×Dic61—21no—
188C2×M16×C61—21no—
189C22×C8×C61—21no—
190#126×C61—21no—
191#125×C61C2311yescharacteristic
192#124×C61C2311yescharacteristic
193#123×C61—21no—
194C22⋊Q8×C61C2×C411yescharacteristic
195#121×C61C2×C411yescharacteristic
196C4×Q8×C61C2×C411yescharacteristic
197C4×D4×C61—21no—
198C4×D4×C61C2×C411yescharacteristic
199#117×C61—21no—
200C2×C42×C61C2311yescharacteristic
201#97×C61—21no—
202#97×C61C2311yescharacteristic
203#97×C61C2311yescharacteristic
204#97×C61C2311yescharacteristic
205#97×C61C2311yescharacteristic
206C4×C8×C61—21no—
207C2×Q8×C61C22×C411yescharacteristic
208C2×D4×C61—21no—
209C2×D4×C61C22×C411yescharacteristic
210C22×C4×C61—21no—
211C22×C4×C61C22×C411yescharacteristic
212C22×C4×C61C2×D411yescharacteristic
213C22×C4×C61C2×D411yescharacteristic
214C2×C22⋊D61—21no—
215C2×C22⋊D61—21no—
216C2×C22⋊D61C22⋊C411yescharacteristic
217C2×C22⋊D61C22⋊C411yescharacteristic
218C22×Dic61—21no—
219C22×Dic61—21no—
220C22×Dic61—21no—
221C22×Dic61—21no—
222#11758224—44no—
223#11758222—24no—
224C2×D244C22⋊C411yescharacteristic
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61C22×C411yescharacteristic
228C2×C4×D61C22×C411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122C22⋊C411yescharacteristic
236M16×C61—24no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C2×C8×C61—42no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61C22×C411yescharacteristic
247C4⋊C4×C61C22×C411yescharacteristic
248C22⋊C4×C61—21no—
249C22⋊C4×C61—21no—
250C22⋊C4×C61—21no—
251C22⋊C4×C61—21no—
252C22⋊C4×C61—21no—
253C42×C61—21no—
254C42×C61C22×C411yescharacteristic
255C42×C61C2×D411yescharacteristic
256C42×C61C2×D411yescharacteristic
257C42×C61C2411yescharacteristic
258C22⋊Dic61—21no—
259C22⋊Dic61—21no—
260C22⋊Dic61—21no—
261C22⋊Dic61—21no—
262C22⋊Dic61C22⋊C411yescharacteristic
263C22⋊Dic61C22⋊C411yescharacteristic
264#11758198—21no—
265#11758198—21no—
266#11758198—21no—
267#11758198—21no—
268#11758198C22⋊C411yescharacteristic
269#11758198C22⋊C411yescharacteristic
270#11758198C22⋊C411yescharacteristic
271#11758198C22⋊C411yescharacteristic
272C4⋊Dic61—21no—
273C4⋊Dic61—21no—
274C4⋊Dic61—21no—
275C4⋊Dic61—21no—
276C4⋊Dic61—21no—
277C4⋊Dic61—21no—
278C4⋊Dic61C22⋊C411yescharacteristic
279C4⋊Dic61C22⋊C411yescharacteristic
280C4⋊Dic61C22×C411yescharacteristic
281C4⋊Dic61C22×C411yescharacteristic
282C4⋊Dic61C22×C411yescharacteristic
283C4⋊Dic61C22×C411yescharacteristic
284#11758196—21no—
285#11758196—21no—
286#11758196—21no—
287#11758196—21no—
288#11758196—21no—
289#11758196—21no—
290#11758196—21no—
291#11758196—21no—
292#11758196—21no—
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196C22⋊C411yescharacteristic
301#11758196C22⋊C411yescharacteristic
302#11758196C22⋊C411yescharacteristic
303#11758196C22⋊C411yescharacteristic
304C4×Dic61—21no—
305C4×Dic61—21no—
306C4×Dic61—21no—
307C4×Dic61—21no—
308C4×Dic61C22×C411yescharacteristic
309C4×Dic61C22×C411yescharacteristic
310C4×Dic61C2×D411yescharacteristic
311C4×Dic61C2×D411yescharacteristic
312C4×Dic61C2×D411yescharacteristic
313C4×Dic61C2×D411yescharacteristic
314C2×#92418—24no—
315C2×#92418—21no—
316C2×#92418—21no—
317C2×#92418—21no—
318C2×#92418—21no—
319#11758189—24no—
320#11758189—24no—
321#11758189—42no—
322C8×D61—24no—
323C8×D61—24no—
324C8×D61—42no—
325C23×C61—21no—
326C23×C61C2×C22⋊C411yescharacteristic
327C22×D61C2×C22⋊C411yescharacteristic
328C22×D61C2×C22⋊C411yescharacteristic
329Q8×C61—41no—
330D4×C61—41no—
331D4×C61—42no—
332C2×C4×C61—22no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—21no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—81no—
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—42no—
347C22⋊D61—81no—
348C22⋊D61#10414yes—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—21no—
353C2×Dic61—42no—
354C2×Dic61—42no—
355C2×Dic61—81no—
356C2×Dic61—81no—
357C2×Dic61C2×C22⋊C411yescharacteristic
358C2×Dic61C2×C22⋊C411yescharacteristic
359C2×Dic61C2×C22⋊C411yescharacteristic
360C2×Dic61C2×C22⋊C411yescharacteristic
361C2×Dic61C2×C22⋊C411yescharacteristic
362C2×Dic61C2×C22⋊C411yescharacteristic
363D244—22no—
364C4×D61—22no—
365C4×D61—22no—
366C4×D61—41no—
367C4×D61—41no—
368C4×D61—41no—
369C4×D61—41no—
370C4×D61—42no—
371C4×D61—81no—
372Dic122—22no—
373Dic122—42no—
374Dic122—81no—
375C8×C61—22no—
376C8×C61—22no—
377C8×C61—22no—
378C8×C61—41no—
379#92418—22no—
380#92418—22no—
381#92418—41no—
382#92418—41no—
383#17653—611nomaximal, Sylow
384C22×C61—21no—
385C22×C61—21no—
386C22×C61—41no—
387C22×C61—41no—
388C22×C61—41no—
389C22×C61C2×#10412yes—
390C22×C61C22×C22⋊C411yescharacteristic
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—21no—
394C2×D61—21no—
395C2×D61—21no—
396C2×D61C2×#10412yes—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—21no—
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—41no—
404C4×C61—41no—
405C4×C61—41no—
406Dic61—21no—
407Dic61—21no—
408Dic61—21no—
409Dic61—21no—
410Dic61—21no—
411Dic61—41no—
412Dic61—41no—
413Dic61—41no—
414Dic61—41no—
415Dic61C2×#10412yes—
416#3515—611no—
417#2970—611no—
418#2875—611no—
419#1532—611no—
420#1532—611no—
421#1531—611no—
422#1529—611no—
423#1528—611no—
424#1528—611no—
425#1526—611no—
426#1524—611no—
427#1524—611no—
428#1524D6111yescharacteristic, complemented
429C2×#330—611no—
430C2×#330—611no—
431C2×C61—22no—
432C2×C61—81no—
433C2×C61#288911yescharacteristic
434C2×C61C22×#10411yescharacteristic
435C2×C61#290111yescharacteristic
436D61—22no—
437D61—41no—
438C2×#131—1221no—
439#557—611no—
440#554—611no—
441#554—611no—
442#553—611no—
443#553—611no—
444#552—611no—
445#552—611no—
446#552—1221no—
447#552—1221no—
448#552—1221no—
449#547—611no—
450#547—1221no—
451#541—1221no—
452#539—1221no—
453#539—1221no—
454#533—611no—
455#529—611no—
456#529—611no—
457#529C2×D6111yescharacteristic
458C2×#125—611no—
459C2×#125—611no—
460#520—1221no—
461C4×#41—611no—
462#446—1221no—
463#435—1221no—
464#435—1221no—
465C8×D4—1221no—
466#432—611no—
467#432—611no—
468#432—611no—
469#405—1221no—
470#405—1221no—
471#405—1221no—
472C4×M16—611no—
473C4×M16—611no—
474C4×M16—611no—
475C4×M16C2×D6111yescharacteristic
476C2×#97—611no—
477C2×#97—611no—
478C2×#97—611no—
479C2×#97—611no—
480C2×#97C2×D6111yescharacteristic
481#330—611no—
482#330—611no—
483#330—611no—
484#330—611no—
485#330—611no—
486#330—611no—
487#330—611no—
488#330—611no—
489#330—611no—
490#330—611no—
491#330C2×D6111yescharacteristic
492#330C2×D6111yescharacteristic
493#329—611no—
494#329—611no—
495#329C2×D6111yescharacteristic
496#329C2×D6111yescharacteristic
497C61#1765311yescharacteristic, complemented, Sylow
498C2×#41—611no—
499C2×#41—1221no—
500#131—1228no—
501C2×M16—21no—
502C2×M16—1221no—
503C2×M16—1221no—
504C2×M16—1221no—
505C22×C8—21no—
506C22×C8—1221no—
507C22×C8—1221no—
508C22×C8—1221no—
509C22×C8—1221no—
510C4⋊Q8—611no—
511C4⋊Q8—611no—
512C4⋊Q8—1221no—
513#126—21no—
514#126—1221no—
515#126—1221no—
516#126—1221no—
517#126—1221no—
518#126—1221no—
519#126—1221no—
520#125—611no—
521#125—611no—
522#125—611no—
523#125—611no—
524#125—611no—
525#125—611no—
526#125—1221no—
527#125—1221no—
528#125—1221no—
529#125—1221no—
530#125—1221no—
531#125—1221no—
532#125—1221no—
533#125—1221no—
534#125—1221no—
535#125C22×D6111yescharacteristic
536#124C22×D6111yescharacteristic
537#123—21no—
538#123—1221no—
539#123—1221no—
540#123—1221no—
541#123—1221no—
542#123—1221no—
543#123—1221no—
544#123—1221no—
545#123—1221no—
546C22⋊Q8—611no—
547C22⋊Q8—611no—
548C22⋊Q8—1221no—
549C22⋊Q8—1221no—
550C22⋊Q8—1221no—
551C22⋊Q8—1221no—
552C22⋊Q8—1221no—
553C22⋊Q8—1221no—
554C22⋊Q8—1221no—
555C22⋊Q8—1221no—
556C22⋊Q8C4×D6111yescharacteristic
557#121—611no—
558#121—611no—
559#121—1221no—
560#121—1221no—
561#121C4×D6111yescharacteristic
562C4×Q8—611no—
563C4×Q8—611no—
564C4×Q8—611no—
565C4×Q8—611no—
566C4×Q8—1221no—
567C4×Q8—1221no—
568C4×Q8—1221no—
569C4×Q8C4×D6111yescharacteristic
570C4×D4—21no—
571C4×D4—611no—
572C4×D4—611no—
573C4×D4—611no—
574C4×D4—611no—
575C4×D4—611no—
576C4×D4—611no—
577C4×D4—611no—
578C4×D4—611no—
579C4×D4—1221no—
580C4×D4—1221no—
581C4×D4—1221no—
582C4×D4—1221no—
583C4×D4—1221no—
584C4×D4C4×D6111yescharacteristic
585#117—21no—
586#117—611no—
587#117—611no—
588#117—611no—
589#117—611no—
590#117—611no—
591#117—1221no—
592#117—1221no—
593#117—1221no—
594#117—1221no—
595C2×C4⋊C4—611no—
596C2×C4⋊C4—611no—
597C2×C4⋊C4—611no—
598C2×C4⋊C4—611no—
599C2×C4⋊C4—1221no—
600C2×C4⋊C4—1221no—
601C2×C4⋊C4—1221no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4—1221no—
604C2×C42—611no—
605C2×C42—611no—
606C2×C42C22×D6111yescharacteristic
607C4⋊C8—1221no—
608C4⋊C8—1221no—
609C4⋊C8—1221no—
610C22⋊C8—1221no—
611C22⋊C8—1221no—
612C22⋊C8—1221no—
613#97—21no—
614#97—611no—
615#97—611no—
616#97—611no—
617#97—611no—
618#97—1221no—
619#97—1221no—
620#97—1221no—
621#97—1221no—
622#97C22×D6111yescharacteristic
623#97C22×D6111yescharacteristic
624#97C22×D6111yescharacteristic
625#97C22×D6111yescharacteristic
626C4×C8—21no—
627C4×C8—1221no—
628C4×C8—1221no—
629C4×C8—1221no—
630#41—1224no—
631#41—2444no—
632C2×Q8—611no—
633C2×Q8—1221no—
634C2×Q8—1221no—
635C2×Q8C2×C4×D6111yescharacteristic
636C2×D4—21no—
637C2×D4—611no—
638C2×D4—611no—
639C2×D4—611no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4C2×C4×D6111yescharacteristic
643C22×C4—21no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—1221no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4C2×C4×D6111yescharacteristic
657C22×C4D4×D6111yescharacteristic
658C22×C4D4×D6111yescharacteristic
659M16—24no—
660M16—1224no—
661M16—1224no—
662M16—2442no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—42no—
668C2×C8—1224no—
669C2×C8—1224no—
670C2×C8—1224no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—1221no—
675C2×C8—2442no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—611no—
681C4⋊C4—611no—
682C4⋊C4—611no—
683C4⋊C4—611no—
684C4⋊C4—611no—
685C4⋊C4—611no—
686C4⋊C4—611no—
687C4⋊C4—611no—
688C4⋊C4—611no—
689C4⋊C4—611no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
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⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4—1221no—
711C4⋊C4—1221no—
712C4⋊C4C2×C4×D6111yescharacteristic
713C4⋊C4C2×C4×D6111yescharacteristic
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—611no—
720C22⋊C4—611no—
721C22⋊C4—611no—
722C22⋊C4—611no—
723C22⋊C4—611no—
724C22⋊C4—611no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4—1221no—
730C22⋊C4—1221no—
731C22⋊C4—1221no—
732C22⋊C4—1221no—
733C42—21no—
734C42—611no—
735C42—611no—
736C42—611no—
737C42—611no—
738C42—611no—
739C42—611no—
740C42—1221no—
741C42—1221no—
742C42—1221no—
743C42—1221no—
744C42C2×C4×D6111yescharacteristic
745C42D4×D6111yescharacteristic
746C42D4×D6111yescharacteristic
747C42C23×D6111yescharacteristic
748C23—21no—
749C23—611no—
750C23—611no—
751C23C22⋊C4×D6111yescharacteristic
752Q8—41no—
753Q8—1222no—
754Q8—4881no—
755Q8—2442no—
756D4—41no—
757D4—42no—
758D4—614no—
759D4—1222no—
760D4—1222no—
761D4—4881no—
762D4—2442no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—81no—
770C2×C4—611no—
771C2×C4—611no—
772C2×C4—611no—
773C2×C4—611no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—1222no—
777C2×C4—1222no—
778C2×C4—1221no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—4881no—
783C2×C4—4881no—
784C2×C4—4881no—
785C2×C4—2441no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2442no—
790C2×C4—2442no—
791C2×C4—2442no—
792C2×C4C22⋊C4×D6111yescharacteristic
793C2×C4C22⋊C4×D6111yescharacteristic
794C2×C4C22⋊C4×D6111yescharacteristic
795C2×C4C22×C4×D6111yescharacteristic
796C2×C4C2×D4×D6111yescharacteristic
797C2×C4C2×D4×D6111yescharacteristic
798C8—22no—
799C8—22no—
800C8—22no—
801C8—41no—
802C8—1222no—
803C8—1222no—
804C8—2441no—
805C8—2441no—
806C22—21no—
807C22—21no—
808C22—41no—
809C22—41no—
810C22—41no—
811C22—612no—
812C22—1221no—
813C22—1221no—
814C22—1221no—
815C22—1221no—
816C22—1221no—
817C22#104×D6112yes—
818C22C2×C22⋊C4×D6111yescharacteristic
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—21no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—612no—
829C4—1221no—
830C4—1221no—
831C4—1221no—
832C4—1221no—
833C4—1221no—
834C4—2441no—
835C4—2441no—
836C4—2441no—
837C4—2441no—
838C2—22no—
839C2—81no—
840C2—1222no—
841C2—2441no—
842C2#2145430011yescharacteristic
843C2C2×#104×D6111yescharacteristic
844C2#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1524C2
socleC22×C61C22×C22⋊C4
prime radical#21459785C2
cosocleC42×C61C24
hypercenter#1524D61
hypocenterC61#17653
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1524

Complements

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

NH ≅ G/Ntype
2. #21454830C2semidirect
3. #21454248C2semidirect
4. #21444439C2semidirect
5. #21444436C2semidirect
6. #21444432C2semidirect
7. #21444423C2semidirect
8. #21444420C2semidirect
9. #21444419C2semidirect
10. #21444412C2semidirect
11. #21444404C2semidirect
12. #21444404C2semidirect
13. C2×#16839503C2semidirect
14. #330×D61C2semidirect
15. C61×#1524C2semidirect
428. #1524D61semidirect
497. C61#17653semidirect

Maximal subgroups

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

subgroupindex
#214597852
#214548302
#214542482
#214444392
#214444362
#214444322
#214444232
#214444202
#214444192
#214444122
#214444042
C2×#168395032
#330×D612
C61×#15242
#1765361