Finite Group Databasebeta

← #30611507

Subgroups — #30611507

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#21462659C211yesmaximal, characteristic, complemented
2#21462390C211yesmaximal, characteristic, complemented
3#21461297C211yesmaximal, characteristic, complemented
4#21461296C211yesmaximal, characteristic, complemented
5#21461291C211yesmaximal, characteristic, complemented
6#21461287C211yesmaximal, characteristic, complemented
7#21461282C211yesmaximal, characteristic, complemented
8#21461281C211yesmaximal, characteristic, complemented
9#21461276C211yesmaximal, characteristic, complemented
10#21461272C211yesmaximal, characteristic, complemented
11#21461272C211yesmaximal, characteristic, complemented
12#21461271C211yesmaximal, characteristic, complemented
13D61⋊#330C211yesmaximal, characteristic, complemented
14C2×#16840619C211yesmaximal, characteristic, complemented
15#21459794C211yesmaximal, characteristic
16C2×#14519864—21no—
17#16840814—21no—
18#16840794—21no—
19#16840793—21no—
20#16840789—21no—
21#16840785C2211yescharacteristic
22#16840783C2211yescharacteristic
23#16840782C2211yescharacteristic
24#16840727—21no—
25#16840726—21no—
26#16840726—21no—
27C4×#11758213C2211yescharacteristic
28C4×#11758217C2211yescharacteristic
29C4×#11758217C2211yescharacteristic
30C4×#11758217C2211yescharacteristic
31#16840721C2211yescharacteristic
32#16840721C2211yescharacteristic
33C2×#14519832C2211yescharacteristic
34C2×#14519832C2211yescharacteristic
35C2×#14519832C2211yescharacteristic
36#16840619C2211yescharacteristic
37#16840619C2211yescharacteristic
38#16840619C2211yescharacteristic
39#16840619C2211yescharacteristic
40#16840619C2211yescharacteristic
41#16840619C2211yescharacteristic
42#16840619C2211yescharacteristic
43#16840619C2211yescharacteristic
44#16840619C2211yescharacteristic
45#16840619C2211yescharacteristic
46#16840619C2211yescharacteristic
47#16840619C2211yescharacteristic
48#16840618C2211yescharacteristic
49#16840618C2211yescharacteristic
50#16840618C2211yescharacteristic
51#16840618C2211yescharacteristic
52#16840488C411yescharacteristic
53#16840470C411yescharacteristic
54#16840468C411yescharacteristic
55#16840458C411yescharacteristic
56#16840456C411yescharacteristic
57#16840450—21no—
58#16840448—21no—
59#16840446C411yescharacteristic
60#16840445—21no—
61#16840413C411yescharacteristic
62#16840410—21no—
63#16840371—21no—
64#16840356—21no—
65#16840353—21no—
66#16840315C2211yescharacteristic
67#16840299C2211yescharacteristic
68#16840298C2211yescharacteristic
69#16840298C2211yescharacteristic
70C2×#14519768C2211yescharacteristic
71#125×D61C2211yescharacteristic
72#16840242—21no—
73C4×#11758224C2211yescharacteristic
74C61×#552C411yescharacteristic
75#14519864—28no—
76C2×#11758213—21no—
77C2×#11758217—21no—
78C2×#11758217—21no—
79C2×#11758217—21no—
80C2×D61⋊C8—21no—
81C2×D61⋊C8—21no—
82C22×#92420—21no—
83C22×#92420—21no—
84C22×#92420—21no—
85#14519844—21no—
86#14519844—21no—
87C4⋊#92420—21no—
88#14519834—21no—
89C22⋊#92420—21no—
90C22⋊#92420—21no—
91#14519832—21no—
92#14519832—21no—
93#14519832—21no—
94#14519832—21no—
95#14519832—21no—
96#14519832C2311yescharacteristic
97#14519832C2311yescharacteristic
98#14519832C2311yescharacteristic
99#14519832C2311yescharacteristic
100#14519832C2311yescharacteristic
101#14519832C2311yescharacteristic
102#14519832C2311yescharacteristic
103#14519832C2311yescharacteristic
104C4×#92420—21no—
105C4×#92420—21no—
106C4×#92420—21no—
107C4×#92420—21no—
108C2×#11758222—21no—
109C2×#11758224D411yescharacteristic
110#14519776—21no—
111#14519776C2×C411yescharacteristic
112#14519776C2×C411yescharacteristic
113#14519772—21no—
114#14519772—21no—
115#14519772—21no—
116#14519772—21no—
117#14519771—21no—
118#14519770—21no—
119#14519769—21no—
120#14519769C2×C411yescharacteristic
121#14519768—21no—
122#14519768—21no—
123#14519768—21no—
124#14519768C2×C411yescharacteristic
125#14519768C2×C411yescharacteristic
126#14519768C2311yescharacteristic
127#14519768C2311yescharacteristic
128#14519768C2311yescharacteristic
129#14519767—21no—
130#14519767—21no—
131#14519767—21no—
132#14519767—21no—
133#14519766C2311yescharacteristic
134#14519762—21no—
135#14519762—21no—
136#14519761—21no—
137#14519761—21no—
138#14519760—21no—
139#14519759—21no—
140#14519759—21no—
141#14519759—21no—
142#14519757—21no—
143#14519757—21no—
144#14519755—21no—
145#14519755—21no—
146#14519755—21no—
147#14519754—21no—
148#14519754—21no—
149#14519754—21no—
150#14519753C2×C411yescharacteristic
151#14519752C2×C411yescharacteristic
152#14519751C2×C411yescharacteristic
153#14519751C2×C411yescharacteristic
154#14519750—21no—
155#14519749—21no—
156Q8×Dic61C2×C411yescharacteristic
157Q8×Dic61C2×C411yescharacteristic
158C4×Dic122—21no—
159C4×Dic122—21no—
160C4×Dic122—21no—
161C4×Dic122C2×C411yescharacteristic
162#14519742D411yescharacteristic
163C4×D244—21no—
164C4×D244—21no—
165C4×D244C2×C411yescharacteristic
166D4×Dic61D411yescharacteristic
167#14519739C2×C411yescharacteristic
168#14519739C2×C411yescharacteristic
169C4×C22⋊D61C2×C411yescharacteristic
170C4×C22⋊D61C2×C411yescharacteristic
171#14519737—21no—
172#14519737—21no—
173#14519737—21no—
174#14519737—21no—
175#14519737D411yescharacteristic
176#14519737D411yescharacteristic
177#14519736C2×C411yescharacteristic
178#14519735—21no—
179#14519735—21no—
180#14519735—21no—
181#14519735D411yescharacteristic
182#14519734—21no—
183#14519733D411yescharacteristic
184#14519733D411yescharacteristic
185C2×C4⋊Dic61—21no—
186C2×C4⋊Dic61C2×C411yescharacteristic
187C2×#11758196—21no—
188C4⋊C4×D61—21no—
189C4⋊C4×D61—21no—
190C4⋊C4×D61—21no—
191C4⋊C4×D61C2×C411yescharacteristic
192C4⋊C4×D61C2×C411yescharacteristic
193C2×C4×Dic61C2311yescharacteristic
194C2×C4×Dic61C2311yescharacteristic
195C42×D61C2311yescharacteristic
196#126×C61—21no—
197#125×C61—21no—
198#125×C61C2×C411yescharacteristic
199#123×C61—21no—
200C22⋊Q8×C61C2×C411yescharacteristic
201C22⋊Q8×C61C2×C411yescharacteristic
202C4×Q8×C61C2×C411yescharacteristic
203C4×D4×C61C2×C411yescharacteristic
204#117×C61—21no—
205#117×C61C2×C411yescharacteristic
206C2×C4⋊C4×C61C2×C411yescharacteristic
207C2×Q8×C61C22×C411yescharacteristic
208C2×D4×C61C22⋊C411yescharacteristic
209C22×C4×C61—21no—
210C22×C4×C61C22×C411yescharacteristic
211C22×C4×C61C22×C411yescharacteristic
212C2×C22⋊D61—21no—
213C2×C22⋊D61—21no—
214C2×C22⋊D61C22⋊C411yescharacteristic
215C2×C22⋊D61C22⋊C411yescharacteristic
216C22×Dic61—21no—
217C22×Dic61C2×D411yescharacteristic
218C22×Dic61C2×D411yescharacteristic
219C22×Dic61C2×D411yescharacteristic
220C22×Dic61C2×D411yescharacteristic
221#11758224—24no—
222#11758222—44no—
223C2×D244—21no—
224C2×D244C22×C411yescharacteristic
225C2×C4×D61—21no—
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—21no—
230C2×C4×D61C22×C411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×Dic122—21no—
234C2×Dic122—21no—
235C2×Dic122C22⋊C411yescharacteristic
236#11758217—24no—
237#11758217—24no—
238#11758217—42no—
239C2×#92420—24no—
240C2×#92420—24no—
241C2×#92420—21no—
242C2×#92420—21no—
243C2×#92420—21no—
244C2×#92420—21no—
245C2×#92420—21no—
246C2×#92420—21no—
247C2×#92420—21no—
248C2×#92420—21no—
249C2×#92420—42no—
250#11758213—24no—
251D61⋊C8—24no—
252D61⋊C8—42no—
253C4⋊C4×C61—21no—
254C4⋊C4×C61—21no—
255C4⋊C4×C61—21no—
256C4⋊C4×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C4⋊C4×C61C22⋊C411yescharacteristic
260C4⋊C4×C61C22×C411yescharacteristic
261C4⋊C4×C61C22×C411yescharacteristic
262C4⋊C4×C61C22×C411yescharacteristic
263C22⋊C4×C61—21no—
264C22⋊C4×C61—21no—
265C22⋊C4×C61—21no—
266C22⋊C4×C61C22⋊C411yescharacteristic
267C22⋊C4×C61C22⋊C411yescharacteristic
268C42×C61—21no—
269C42×C61—21no—
270C42×C61C22×C411yescharacteristic
271C22⋊Dic61—21no—
272C22⋊Dic61C22⋊C411yescharacteristic
273C22⋊Dic61C22⋊C411yescharacteristic
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#11758198C22⋊C411yescharacteristic
284#11758198C22⋊C411yescharacteristic
285C4⋊Dic61—21no—
286C4⋊Dic61—21no—
287C4⋊Dic61—21no—
288C4⋊Dic61—21no—
289C4⋊Dic61—21no—
290C4⋊Dic61—21no—
291C4⋊Dic61—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61C22⋊C411yescharacteristic
294C4⋊Dic61C22×C411yescharacteristic
295C4⋊Dic61C22×C411yescharacteristic
296C4⋊Dic61C22×C411yescharacteristic
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196C22⋊C411yescharacteristic
310#11758196C22⋊C411yescharacteristic
311#11758196C22⋊C411yescharacteristic
312#11758196C22⋊C411yescharacteristic
313C4×Dic61—21no—
314C4×Dic61—21no—
315C4×Dic61—21no—
316C4×Dic61C22×C411yescharacteristic
317C4×Dic61C22×C411yescharacteristic
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2411yescharacteristic
325C23×C61C2×C22⋊C411yescharacteristic
326C23×C61C2×C22⋊C411yescharacteristic
327C22×D61—21no—
328C22×D61C2×C22⋊C411yescharacteristic
329Q8×C61—41no—
330D4×C61—22no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—21no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—42no—
338C2×C4×C61C2×C22⋊C411yescharacteristic
339C2×C4×C61C2×C22⋊C411yescharacteristic
340C2×C4×C61C2×C22⋊C411yescharacteristic
341C2×C4×C61C2×C22⋊C411yescharacteristic
342C2×C4×C61C23×C411yescharacteristic
343C22⋊D61—22no—
344C22⋊D61—42no—
345C22⋊D61—81no—
346C22⋊D61#10414yes—
347C2×Dic61—22no—
348C2×Dic61—22no—
349C2×Dic61—21no—
350C2×Dic61—21no—
351C2×Dic61—21no—
352C2×Dic61—41no—
353C2×Dic61—41no—
354C2×Dic61—81no—
355C2×Dic61C2×C22⋊C411yescharacteristic
356C2×Dic61C2×C22⋊C411yescharacteristic
357C2×Dic61C2×C22⋊C411yescharacteristic
358C2×Dic61C2×C22⋊C411yescharacteristic
359C2×Dic61C2×C22⋊C411yescharacteristic
360C2×Dic61C22×D411yescharacteristic
361C2×Dic61C22×D411yescharacteristic
362D244—41no—
363D244—42no—
364C4×D61—22no—
365C4×D61—41no—
366C4×D61—41no—
367C4×D61—42no—
368C4×D61—42no—
369C4×D61—81no—
370C4×D61—81no—
371C4×D61—81no—
372Dic122—22no—
373Dic122—42no—
374Dic122—81no—
375#92420—22no—
376#92420—22no—
377#92420—22no—
378#92420—22no—
379#92420—22no—
380#92420—41no—
381#92420—41no—
382#92420—41no—
383#17653—611nomaximal, Sylow
384C22×C61—21no—
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61C2×#10412yes—
390C22×C61C22×C22⋊C411yescharacteristic
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C2×D61C2×#10412yes—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—21no—
401C4×C61—21no—
402C4×C61—41no—
403C4×C61—41no—
404C4×C61—41no—
405C4×C61—41no—
406Dic61—21no—
407Dic61—21no—
408Dic61—21no—
409Dic61—21no—
410Dic61—21no—
411Dic61—21no—
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#1524—611no—
429C2×#330—611no—
430C2×#330—611no—
431C2×C61—22no—
432C2×C61—41no—
433C2×C61#288911yescharacteristic
434C2×C61C22×#10411yescharacteristic
435C2×C61#290111yescharacteristic
436D61—22no—
437D61—81no—
438C2×#131—1221no—
439#557—611no—
440#554—611no—
441#554—611no—
442#553—611no—
443#553—611no—
444#552—611no—
445#552—1221no—
446#552—1221no—
447#552—1221no—
448#552#692311yescharacteristic
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#529—611no—
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×M16—611no—
476C2×#97—611no—
477C2×#97—611no—
478C2×#97—611no—
479C2×#97—611no—
480C2×#97—611no—
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#330—611no—
492#330—611no—
493#329—611no—
494#329—611no—
495#329—611no—
496#329—611no—
497C61#1765311yescharacteristic, complemented, Sylow
498C2×#41—611no—
499C2×#41—1221no—
500#131—1228no—
501C2×M16—1221no—
502C2×M16—1221no—
503C2×M16—1221no—
504C2×M16—1221no—
505C22×C8—1221no—
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—21no—
521#125—611no—
522#125—611no—
523#125—611no—
524#125—611no—
525#125—611no—
526#125—611no—
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#125C2×#692311yescharacteristic
536#124—611no—
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—1221no—
548C22⋊Q8—1221no—
549C22⋊Q8—1221no—
550C22⋊Q8—1221no—
551C22⋊Q8—1221no—
552C22⋊Q8—1221no—
553C22⋊Q8—1221no—
554C22⋊Q8—1221no—
555C22⋊Q8C2×#692311yescharacteristic
556C22⋊Q8C2×#692311yescharacteristic
557#121—611no—
558#121—611no—
559#121—611no—
560#121—1221no—
561#121—1221no—
562C4×Q8—611no—
563C4×Q8—611no—
564C4×Q8—611no—
565C4×Q8—611no—
566C4×Q8—1221no—
567C4×Q8—1221no—
568C4×Q8—1221no—
569C4×Q8C2×#692311yescharacteristic
570C4×D4—611no—
571C4×D4—611no—
572C4×D4—611no—
573C4×D4—611no—
574C4×D4—611no—
575C4×D4—611no—
576C4×D4—611no—
577C4×D4—611no—
578C4×D4—1221no—
579C4×D4—1221no—
580C4×D4—1221no—
581C4×D4—1221no—
582C4×D4—1221no—
583C4×D4—1221no—
584C4×D4C2×#692311yescharacteristic
585#117—21no—
586#117—611no—
587#117—611no—
588#117—611no—
589#117—611no—
590#117—1221no—
591#117—1221no—
592#117—1221no—
593#117—1221no—
594#117C2×#692311yescharacteristic
595C2×C4⋊C4—611no—
596C2×C4⋊C4—611no—
597C2×C4⋊C4—611no—
598C2×C4⋊C4—1221no—
599C2×C4⋊C4—1221no—
600C2×C4⋊C4—1221no—
601C2×C4⋊C4—1221no—
602C2×C4⋊C4—1221no—
603C2×C4⋊C4C2×#692311yescharacteristic
604C2×C42—611no—
605C2×C42—611no—
606C2×C42—611no—
607C4⋊C8—1221no—
608C4⋊C8—1221no—
609C4⋊C8—1221no—
610C22⋊C8—1221no—
611C22⋊C8—1221no—
612C22⋊C8—1221no—
613#97—611no—
614#97—611no—
615#97—611no—
616#97—611no—
617#97—611no—
618#97—611no—
619#97—611no—
620#97—611no—
621#97—1221no—
622#97—1221no—
623#97—1221no—
624#97—1221no—
625#97—1221no—
626C4×C8—1221no—
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×Q8C22×#692311yescharacteristic
636C2×D4—611no—
637C2×D4—611no—
638C2×D4—611no—
639C2×D4—1221no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4C22⋊#692311yescharacteristic
643C22×C4—21no—
644C22×C4—611no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4—1221no—
657C22×C4C22×#692311yescharacteristic
658C22×C4C22×#692311yescharacteristic
659M16—1224no—
660M16—1224no—
661M16—1224no—
662M16—2442no—
663C2×C8—1221no—
664C2×C8—1221no—
665C2×C8—1221no—
666C2×C8—1221no—
667C2×C8—1221no—
668C2×C8—1224no—
669C2×C8—1224no—
670C2×C8—1224no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—2442no—
675C2×C8—2442no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
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⋊C4C22⋊#692311yescharacteristic
711C4⋊C4C22×#692311yescharacteristic
712C4⋊C4C22×#692311yescharacteristic
713C4⋊C4C22×#692311yescharacteristic
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—611no—
718C22⋊C4—611no—
719C22⋊C4—611no—
720C22⋊C4—611no—
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⋊C4C22⋊#692311yescharacteristic
732C22⋊C4C22⋊#692311yescharacteristic
733C42—21no—
734C42—21no—
735C42—611no—
736C42—611no—
737C42—611no—
738C42—611no—
739C42—611no—
740C42—611no—
741C42—611no—
742C42—611no—
743C42—611no—
744C42—1221no—
745C42—1221no—
746C42—1221no—
747C42C22×#692311yescharacteristic
748C23—611no—
749C23—1221no—
750C23C2×C22⋊#692311yescharacteristic
751C23C2×C22⋊#692311yescharacteristic
752Q8—41no—
753Q8—1222no—
754Q8—4881no—
755Q8—2442no—
756D4—22no—
757D4—614no—
758D4—1222no—
759D4—4881no—
760D4—2441no—
761D4—2442no—
762D4—2442no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—42no—
770C2×C4—611no—
771C2×C4—611no—
772C2×C4—611no—
773C2×C4—611no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—611no—
777C2×C4—1222no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—4881no—
784C2×C4—4881no—
785C2×C4—4881no—
786C2×C4—4881no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2442no—
790C2×C4—2442no—
791C2×C4—2441no—
792C2×C4—2441no—
793C2×C4C2×C22⋊#692311yescharacteristic
794C2×C4C2×C22⋊#692311yescharacteristic
795C2×C4C2×C22⋊#692311yescharacteristic
796C2×C4C2×C22⋊#692311yescharacteristic
797C2×C4C23×#692311yescharacteristic
798C8—1222no—
799C8—1222no—
800C8—1222no—
801C8—1222no—
802C8—1222no—
803C8—2441no—
804C8—2441no—
805C8—2441no—
806C22—21no—
807C22—21no—
808C22—21no—
809C22—21no—
810C22—21no—
811C22—612no—
812C22—1221no—
813C22—1221no—
814C22—2441no—
815C22—2441no—
816C22—2441no—
817C22D61⋊#10412yes—
818C22C22×C22⋊#692311yescharacteristic
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—612no—
829C4—1221no—
830C4—1221no—
831C4—1221no—
832C4—1221no—
833C4—1221no—
834C4—1221no—
835C4—2441no—
836C4—2441no—
837C4—2441no—
838C2—22no—
839C2—41no—
840C2—1222no—
841C2—4881no—
842C2#2146243111yescharacteristic
843C2C2×D61⋊#10411yescharacteristic
844C2#2146245011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#552C4
socleC22×C61C22×C22⋊C4
prime radical#21459794C2
cosocleC4×Dic61C24
hypercenter#552#6923
hypocenterC61#17653
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #552

Complements

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

NH ≅ G/Ntype
1. #21462659C2semidirect
2. #21462390C2semidirect
3. #21461297C2semidirect
4. #21461296C2semidirect
5. #21461291C2semidirect
6. #21461287C2semidirect
7. #21461282C2semidirect
8. #21461281C2semidirect
9. #21461276C2semidirect
10. #21461272C2semidirect
11. #21461272C2semidirect
12. #21461271C2semidirect
13. D61⋊#330C2semidirect
14. C2×#16840619C2semidirect
497. C61#17653semidirect

Maximal subgroups

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

subgroupindex
#214626592
#214623902
#214612972
#214612962
#214612912
#214612872
#214612822
#214612812
#214612762
#214612722
#214612712
D61⋊#3302
C2×#168406192
#214597942
#1765361