Finite Group Databasebeta

← #30611935

Subgroups — #30611935

Order 15616.

964 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462739C211yesmaximal, characteristic, complemented
2#21462466C211yesmaximal, characteristic, complemented
3#21461357C211yesmaximal, characteristic, complemented
4#21461356C211yesmaximal, characteristic, complemented
5#21461355C211yesmaximal, characteristic, complemented
6#21461354C211yesmaximal, characteristic, complemented
7#21461339C211yesmaximal, characteristic, complemented
8#21461338C211yesmaximal, characteristic, complemented
9#21461337C211yesmaximal, characteristic, complemented
10#21461336C211yesmaximal, characteristic, complemented
11#21461332C211yesmaximal, characteristic, complemented
12#21461331C211yesmaximal, characteristic, complemented
13C2×#16840622C211yesmaximal, characteristic, complemented
14#21461317C211yesmaximal, characteristic, complemented
15#21459725C211yesmaximal, characteristic
16C2×#14519864—21no—
17#16840814—21no—
18#16840795—21no—
19#16840793—21no—
20#16840791—21no—
21#16840785C2211yescharacteristic
22#16840782C2211yescharacteristic
23#16840779C2211yescharacteristic
24#16840769—21no—
25#16840768—21no—
26#16840768—21no—
27#16840767C2211yescharacteristic
28#16840767C2211yescharacteristic
29#16840765C2211yescharacteristic
30#16840765C2211yescharacteristic
31#16840765C2211yescharacteristic
32C2×#14519844C2211yescharacteristic
33C2×#14519844C2211yescharacteristic
34C2×#14519844C2211yescharacteristic
35D61⋊(C4⋊C8)C2211yescharacteristic
36#16840622C2211yescharacteristic
37#16840622C2211yescharacteristic
38#16840622C2211yescharacteristic
39#16840622C2211yescharacteristic
40#16840622C2211yescharacteristic
41#16840622C2211yescharacteristic
42#16840622C2211yescharacteristic
43#16840622C2211yescharacteristic
44#16840621C2211yescharacteristic
45#16840621C2211yescharacteristic
46#16840621C2211yescharacteristic
47#16840621C2211yescharacteristic
48#16840620C2211yescharacteristic
49#16840620C2211yescharacteristic
50#16840620C2211yescharacteristic
51#16840620C2211yescharacteristic
52#16840484C411yescharacteristic
53#16840481C411yescharacteristic
54#16840474—21no—
55#16840466—21no—
56#16840461—21no—
57#16840455—21no—
58#16840423C411yescharacteristic
59#16840421C411yescharacteristic
60#16840418C411yescharacteristic
61#16840414C411yescharacteristic
62#16840411C411yescharacteristic
63#16840382—21no—
64#16840376—21no—
65#16840339—21no—
66#16840316C2211yescharacteristic
67#16840314C2211yescharacteristic
68#16840311C2211yescharacteristic
69#16840308C2211yescharacteristic
70#16840307C2211yescharacteristic
71C2×#14519775C2211yescharacteristic
72#16840241—21no—
73C4×#11758224C2211yescharacteristic
74C61×#548C411yescharacteristic
75#14519864—44no—
76C2×#11758213—21no—
77C2×#11758213—21no—
78C2×#11758217—21no—
79C2×#11758217—21no—
80C2×#11758217—21no—
81C2×D61⋊C8—21no—
82C22×#92420—21no—
83C22×#92420—21no—
84C22×#92420—21no—
85#14519844—21no—
86#14519844—21no—
87#14519844—21no—
88#14519844—21no—
89#14519844—21no—
90#14519844C2311yescharacteristic
91#14519844C2311yescharacteristic
92#14519844C2311yescharacteristic
93#14519844C2311yescharacteristic
94#14519844C2311yescharacteristic
95#14519844C2311yescharacteristic
96#14519844C2311yescharacteristic
97#14519844C2311yescharacteristic
98C4⋊#92420—21no—
99C4⋊#92420—21no—
100C4⋊#92420—21no—
101C4⋊#92420—21no—
102#14519834—21no—
103C22⋊#92420—21no—
104C22⋊#92420—21no—
105#14519832—21no—
106#14519832—21no—
107C4×#92420—21no—
108C2×#11758226C2×C411yescharacteristic
109C2×#11758222C2×C411yescharacteristic
110C2×#11758224—21no—
111C2×#11758224C2×C411yescharacteristic
112C2×#11758224D411yescharacteristic
113C22×Dic122C2×C411yescharacteristic
114#14519776C2311yescharacteristic
115#14519775—21no—
116#14519775—21no—
117#14519775C2×C411yescharacteristic
118#14519775C2×C411yescharacteristic
119#14519775C2311yescharacteristic
120#14519775C2311yescharacteristic
121#14519773C2311yescharacteristic
122#14519772—21no—
123#14519771—21no—
124#14519770—21no—
125#14519770—21no—
126#14519767—21no—
127#14519767—21no—
128#14519766—21no—
129#14519766C2×C411yescharacteristic
130#14519765C2×C411yescharacteristic
131#14519764C2×C411yescharacteristic
132#14519763—21no—
133#14519763—21no—
134#14519763—21no—
135#14519762—21no—
136#14519760—21no—
137#14519759—21no—
138#14519758—21no—
139#14519757C2×C411yescharacteristic
140#14519756C2×C411yescharacteristic
141#14519755—21no—
142#14519755—21no—
143#14519755—21no—
144#14519754—21no—
145#14519754—21no—
146#14519754—21no—
147#14519753—21no—
148#14519753C2×C411yescharacteristic
149#14519751—21no—
150#14519751C2×C411yescharacteristic
151#14519750—21no—
152#14519750—21no—
153#14519750—21no—
154#14519749—21no—
155#14519749—21no—
156#14519749—21no—
157#14519749—21no—
158#14519749—21no—
159#14519749—21no—
160Q8×Dic61C2×C411yescharacteristic
161C4×Dic122—21no—
162C4×Dic122C2×C411yescharacteristic
163C4×Dic122C2×C411yescharacteristic
164#14519742—21no—
165#14519742C2×C411yescharacteristic
166#14519742D411yescharacteristic
167D4×Dic61—21no—
168D4×Dic61C2×C411yescharacteristic
169D4×Dic61D411yescharacteristic
170#14519739C2×C411yescharacteristic
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61C2×C411yescharacteristic
175C4×C22⋊D61C2×C411yescharacteristic
176#14519737—21no—
177#14519737—21no—
178#14519737—21no—
179#14519737—21no—
180#14519737D411yescharacteristic
181#14519737D411yescharacteristic
182#14519735D411yescharacteristic
183#14519734—21no—
184#14519734—21no—
185#14519733—21no—
186#14519733—21no—
187#14519733D411yescharacteristic
188#14519733D411yescharacteristic
189C2×#11758196—21no—
190C2×#11758196—21no—
191C2×#11758196—21no—
192C4⋊C4×D61—21no—
193C2×C4×Dic61C2311yescharacteristic
194C2×C4×Dic61C2311yescharacteristic
195C42×D61C2311yescharacteristic
196C2×#41×C61C2×C411yescharacteristic
197C22×Q8×C61C2×C411yescharacteristic
198#124×C61—21no—
199#124×C61C2×C411yescharacteristic
200C22⋊Q8×C61—21no—
201C22⋊Q8×C61C2×C411yescharacteristic
202#121×C61—21no—
203#121×C61C2×C411yescharacteristic
204C4×Q8×C61C2×C411yescharacteristic
205C4×D4×C61—21no—
206C4×D4×C61C2×C411yescharacteristic
207#41×C61—81no—
208C2×Q8×C61—21no—
209C2×Q8×C61—81no—
210C2×Q8×C61C22×C411yescharacteristic
211C2×Q8×C61C22×C411yescharacteristic
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61C22⋊C411yescharacteristic
215C2×D4×C61C22×C411yescharacteristic
216C22×C4×C61—21no—
217C22×C4×C61—21no—
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61C22⋊C411yescharacteristic
226C2×C22⋊D61C22⋊C411yescharacteristic
227C22×Dic61—21no—
228C22×Dic61—21no—
229C22×Dic61—21no—
230C22×Dic61C2×D411yescharacteristic
231C22×Dic61C2×D411yescharacteristic
232C22×Dic61C2×D411yescharacteristic
233C22×Dic61C2×D411yescharacteristic
234#11758226—81no—
235#11758224—22no—
236#11758224—22no—
237#11758224—42no—
238#11758224—42no—
239#11758224—81no—
240#11758222—81no—
241C2×D244—21no—
242C2×D244C22×C411yescharacteristic
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61C22×C411yescharacteristic
247C2×C4×D61C2×D411yescharacteristic
248C2×C4×D61C2×D411yescharacteristic
249C2×Dic122—21no—
250C2×Dic122—21no—
251C2×Dic122—81no—
252C2×Dic122C22⋊C411yescharacteristic
253C2×Dic122C22×C411yescharacteristic
254C2×Dic122C22×C411yescharacteristic
255#11758217—42no—
256#11758217—42no—
257#11758217—81no—
258C2×#92420—21no—
259C2×#92420—21no—
260C2×#92420—21no—
261C2×#92420—21no—
262C2×#92420—21no—
263C2×#92420—21no—
264C2×#92420—21no—
265C2×#92420—21no—
266C2×#92420—42no—
267C2×#92420—42no—
268C2×#92420—81no—
269#11758213—42no—
270#11758213—81no—
271D61⋊C8—42no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61C22⋊C411yescharacteristic
275C4⋊C4×C61C22×C411yescharacteristic
276C22⋊C4×C61—21no—
277C22⋊C4×C61—21no—
278C22⋊C4×C61—21no—
279C22⋊C4×C61—21no—
280C22⋊C4×C61C22⋊C411yescharacteristic
281C22⋊C4×C61C22⋊C411yescharacteristic
282C42×C61—21no—
283C42×C61C22×C411yescharacteristic
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61—21no—
287C22⋊Dic61—21no—
288C22⋊Dic61C22⋊C411yescharacteristic
289C22⋊Dic61C22⋊C411yescharacteristic
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198C22⋊C411yescharacteristic
299#11758198C22⋊C411yescharacteristic
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61C22⋊C411yescharacteristic
303C4⋊Dic61C22×C411yescharacteristic
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316#11758196—21no—
317#11758196C22⋊C411yescharacteristic
318#11758196C22⋊C411yescharacteristic
319#11758196C22⋊C411yescharacteristic
320#11758196C22⋊C411yescharacteristic
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—21no—
324C4×Dic61C22×C411yescharacteristic
325C4×Dic61C22×C411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2×D411yescharacteristic
328C4×Dic61C2×D411yescharacteristic
329C4×Dic61C2×D411yescharacteristic
330C4×Dic61C2×D411yescharacteristic
331C4×Dic61C2×D411yescharacteristic
332C4×Dic61C2411yescharacteristic
333C23×C61—21no—
334C23×C61C2×C22⋊C411yescharacteristic
335C23×C61C2×C22⋊C411yescharacteristic
336C22×D61—21no—
337C22×D61C2×C22⋊C411yescharacteristic
338Q8×C61—41no—
339Q8×C61—41no—
340Q8×C61—81no—
341D4×C61—22no—
342D4×C61—41no—
343D4×C61—42no—
344D4×C61—81no—
345C2×C4×C61—21no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—81no—
351C2×C4×C61—81no—
352C2×C4×C61C2×C22⋊C411yescharacteristic
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C23×C411yescharacteristic
357C22⋊D61—22no—
358C22⋊D61—22no—
359C22⋊D61—42no—
360C22⋊D61—41no—
361C22⋊D61—41no—
362C22⋊D61—41no—
363C22⋊D61—41no—
364C22⋊D61—81no—
365C22⋊D61—81no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—21no—
372C2×Dic61—21no—
373C2×Dic61—21no—
374C2×Dic61—21no—
375C2×Dic61—42no—
376C2×Dic61—81no—
377C2×Dic61—81no—
378C2×Dic61C2×C22⋊C411yescharacteristic
379C2×Dic61C2×C22⋊C411yescharacteristic
380C2×Dic61C2×C22⋊C411yescharacteristic
381C2×Dic61C2×C22⋊C411yescharacteristic
382C2×Dic61C2×C22⋊C411yescharacteristic
383C2×Dic61AGL(1,ℤ/8)12yes—
384C2×Dic61#13712yes—
385C2×Dic61C22×D411yescharacteristic
386C2×Dic61C22×D411yescharacteristic
387D244—41no—
388D244—81no—
389C4×D61—21no—
390C4×D61—21no—
391C4×D61—21no—
392C4×D61—21no—
393C4×D61—41no—
394C4×D61—42no—
395C4×D61—81no—
396C4×D61—81no—
397Dic122—22no—
398Dic122—41no—
399Dic122—41no—
400Dic122—41no—
401Dic122—41no—
402Dic122—81no—
403#92420—41no—
404#92420—41no—
405#92420—41no—
406#92420—41no—
407#92420—41no—
408#92420—41no—
409#92420—41no—
410#92420—41no—
411#17764—611nomaximal, Sylow
412C22×C61—21no—
413C22×C61—21no—
414C22×C61—21no—
415C22×C61—21no—
416C22×C61—21no—
417C22×C61—41no—
418C22×C61—41no—
419C22×C61—41no—
420C22×C61#41712yes—
421C22×C61C22×C22⋊C411yescharacteristic
422C2×D61—21no—
423C2×D61—21no—
424C2×D61—21no—
425C2×D61—41no—
426C2×D61—41no—
427C2×D61—41no—
428C4×C61—21no—
429C4×C61—21no—
430C4×C61—21no—
431C4×C61—21no—
432C4×C61—21no—
433C4×C61—41no—
434C4×C61—41no—
435C4×C61—41no—
436Dic61—21no—
437Dic61—21no—
438Dic61—21no—
439Dic61—21no—
440Dic61—41no—
441Dic61—41no—
442Dic61—41no—
443Dic61#41712yes—
444Dic61C2×AGL(1,ℤ/8)11yescharacteristic
445Dic61C2×#13711yescharacteristic
446Dic61#57711yescharacteristic
447Dic61#57811yescharacteristic
448#3511—611no—
449#2989—611no—
450#2906—611no—
451#1560—611no—
452#1560—611no—
453#1559—611no—
454#1559—611no—
455#1551—611no—
456#1551—611no—
457#1550—611no—
458#1550—611no—
459#1548—611no—
460#1547—611no—
461C2×#333—611no—
462#1540—611no—
463C2×C61—22no—
464C2×C61—41no—
465C2×C61—81no—
466C2×C61#288811yescharacteristic
467C2×C61C2×#41711yescharacteristic
468C2×C61#289811yescharacteristic
469D61—41no—
470D61—81no—
471C2×#131—1221no—
472#556—611no—
473#556—611no—
474#555—1221no—
475#554—1221no—
476#553—1221no—
477#553—1221no—
478#548—611no—
479#548—611no—
480#548—611no—
481#548#692311yescharacteristic
482#547—611no—
483#547—611no—
484#542—1221no—
485#542—1221no—
486#537—1221no—
487#533—611no—
488#533—611no—
489#532—611no—
490#532—611no—
491#532—611no—
492C2×C4⋊Q8—611no—
493#520—1221no—
494C4×#41—611no—
495#446—1221no—
496#436—1221no—
497#435—1221no—
498#435—1221no—
499#432—611no—
500#432—611no—
501#431—611no—
502#424—1221no—
503#424—1221no—
504#424—1221no—
505#423—611no—
506#423—611no—
507#423—611no—
508#423—611no—
509#423—611no—
510C2×C4⋊C8—611no—
511C2×C4⋊C8—611no—
512C2×C4⋊C8—611no—
513C2×C4⋊C8—611no—
514#333—611no—
515#333—611no—
516#333—611no—
517#333—611no—
518#333—611no—
519#333—611no—
520#333—611no—
521#333—611no—
522#332—611no—
523#332—611no—
524#332—611no—
525#332—611no—
526#331—611no—
527#331—611no—
528#331—611no—
529#331—611no—
530C61#1776411yescharacteristic, complemented, Sylow
531C2×#41—611no—
532C2×#41—611no—
533C2×#41—611no—
534C2×#41—611no—
535C2×#41—1221no—
536C2×#41C2×#692311yescharacteristic
537C22×Q8—611no—
538C22×Q8C2×#692311yescharacteristic
539#131—2444no—
540C2×M16—1221no—
541C2×M16—1221no—
542C2×M16—1221no—
543C2×M16—1221no—
544C2×M16—1221no—
545C22×C8—1221no—
546C22×C8—1221no—
547C22×C8—1221no—
548C22×C8—1221no—
549C4⋊Q8—611no—
550C4⋊Q8—611no—
551C4⋊Q8—611no—
552C4⋊Q8—611no—
553C4⋊Q8—611no—
554C4⋊Q8—1221no—
555C4⋊Q8—1221no—
556#127—611no—
557#126—1221no—
558#126—1221no—
559#126—1221no—
560#126—1221no—
561#125—1221no—
562#125—1221no—
563#124—21no—
564#124—611no—
565#124—611no—
566#124—611no—
567#124—1221no—
568#124—1221no—
569#124—1221no—
570#124—1221no—
571#124C2×#692311yescharacteristic
572#123—1221no—
573#123—1221no—
574#123—1221no—
575#123—1221no—
576C22⋊Q8—21no—
577C22⋊Q8—611no—
578C22⋊Q8—611no—
579C22⋊Q8—611no—
580C22⋊Q8—1221no—
581C22⋊Q8—1221no—
582C22⋊Q8—1221no—
583C22⋊Q8—1221no—
584C22⋊Q8—1221no—
585C22⋊Q8—1221no—
586C22⋊Q8—1221no—
587C22⋊Q8C2×#692311yescharacteristic
588#121—21no—
589#121—611no—
590#121—1221no—
591#121—1221no—
592#121—1221no—
593#121—1221no—
594#121—1221no—
595#121—1221no—
596#121—1221no—
597#121—1221no—
598#121—1221no—
599#121—1221no—
600#121C2×#692311yescharacteristic
601C4×Q8—611no—
602C4×Q8—611no—
603C4×Q8—611no—
604C4×Q8—611no—
605C4×Q8—611no—
606C4×Q8—1221no—
607C4×Q8—1221no—
608C4×Q8C2×#692311yescharacteristic
609C4×D4—21no—
610C4×D4—611no—
611C4×D4—611no—
612C4×D4—611no—
613C4×D4—611no—
614C4×D4—611no—
615C4×D4—611no—
616C4×D4—611no—
617C4×D4—1221no—
618C4×D4—1221no—
619C4×D4—1221no—
620C4×D4—1221no—
621C4×D4—1221no—
622C4×D4—1221no—
623C4×D4—1221no—
624C4×D4—1221no—
625C4×D4C2×#692311yescharacteristic
626#117—611no—
627#117—611no—
628#117—611no—
629#117—1221no—
630#117—1221no—
631#117—1221no—
632#117—1221no—
633C2×C4⋊C4—1221no—
634C2×C4⋊C4—1221no—
635C2×C4⋊C4—1221no—
636C2×C4⋊C4—1221no—
637C2×C42—611no—
638C2×C42—611no—
639C2×C42—611no—
640C4⋊C8—611no—
641C4⋊C8—611no—
642C4⋊C8—611no—
643C4⋊C8—611no—
644C4⋊C8—611no—
645C4⋊C8—611no—
646C4⋊C8—611no—
647C4⋊C8—611no—
648C4⋊C8—1221no—
649C4⋊C8—1221no—
650C4⋊C8—1221no—
651C4⋊C8—1221no—
652C4⋊C8—1221no—
653C4⋊C8—1221no—
654C4⋊C8—1221no—
655C4⋊C8—1221no—
656C4⋊C8—1221no—
657C22⋊C8—1221no—
658C22⋊C8—1221no—
659C22⋊C8—1221no—
660#97—1221no—
661#97—1221no—
662C4×C8—1221no—
663#41—81no—
664#41—1222no—
665#41—1222no—
666#41—4881no—
667#41—4881no—
668#41—4881no—
669#41—2442no—
670#41—2442no—
671C2×Q8—21no—
672C2×Q8—81no—
673C2×Q8—611no—
674C2×Q8—611no—
675C2×Q8—611no—
676C2×Q8—1221no—
677C2×Q8—1221no—
678C2×Q8—4881no—
679C2×Q8C22×#692311yescharacteristic
680C2×Q8C22×#692311yescharacteristic
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—611no—
684C2×D4—611no—
685C2×D4—611no—
686C2×D4—1221no—
687C2×D4—1221no—
688C2×D4—1221no—
689C2×D4—1221no—
690C2×D4—1221no—
691C2×D4—1221no—
692C2×D4C22⋊#692311yescharacteristic
693C2×D4C22×#692311yescharacteristic
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—611no—
699C22×C4—611no—
700C22×C4—611no—
701C22×C4—611no—
702C22×C4—611no—
703C22×C4—1221no—
704C22×C4—1221no—
705C22×C4—1221no—
706C22×C4—1221no—
707C22×C4—1221no—
708C22×C4—1221no—
709C22×C4C22×#692311yescharacteristic
710C22×C4C22×#692311yescharacteristic
711M16—4881no—
712M16—4881no—
713M16—2442no—
714M16—2442no—
715M16—2442no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8—1221no—
721C2×C8—1221no—
722C2×C8—1221no—
723C2×C8—1221no—
724C2×C8—4881no—
725C2×C8—2442no—
726C2×C8—2442no—
727C2×C8—2442no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—611no—
731C4⋊C4—611no—
732C4⋊C4—611no—
733C4⋊C4—611no—
734C4⋊C4—611no—
735C4⋊C4—611no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4—1221no—
742C4⋊C4—1221no—
743C4⋊C4—1221no—
744C4⋊C4—1221no—
745C4⋊C4—1221no—
746C4⋊C4—1221no—
747C4⋊C4—1221no—
748C4⋊C4—1221no—
749C4⋊C4—1221no—
750C4⋊C4—1221no—
751C4⋊C4C22⋊#692311yescharacteristic
752C4⋊C4C22×#692311yescharacteristic
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—611no—
758C22⋊C4—611no—
759C22⋊C4—611no—
760C22⋊C4—611no—
761C22⋊C4—1221no—
762C22⋊C4—1221no—
763C22⋊C4—1221no—
764C22⋊C4—1221no—
765C22⋊C4—1221no—
766C22⋊C4—1221no—
767C22⋊C4—1221no—
768C22⋊C4—1221no—
769C22⋊C4—1221no—
770C22⋊C4—1221no—
771C22⋊C4—1221no—
772C22⋊C4—1221no—
773C22⋊C4C22⋊#692311yescharacteristic
774C22⋊C4C22⋊#692311yescharacteristic
775C42—21no—
776C42—611no—
777C42—611no—
778C42—611no—
779C42—611no—
780C42—611no—
781C42—611no—
782C42—611no—
783C42—611no—
784C42—611no—
785C42—1221no—
786C42—1221no—
787C42—1221no—
788C42C22×#692311yescharacteristic
789C23—21no—
790C23—611no—
791C23—1221no—
792C23C2×C22⋊#692311yescharacteristic
793C23C2×C22⋊#692311yescharacteristic
794Q8—41no—
795Q8—41no—
796Q8—81no—
797Q8—1222no—
798Q8—4881no—
799Q8—2441no—
800Q8—2441no—
801Q8—2441no—
802Q8—2441no—
803D4—22no—
804D4—41no—
805D4—42no—
806D4—81no—
807D4—1222no—
808D4—1222no—
809D4—4881no—
810D4—4881no—
811D4—4881no—
812D4—2441no—
813D4—2441no—
814D4—2441no—
815D4—2441no—
816D4—2441no—
817D4—2442no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—81no—
824C2×C4—81no—
825C2×C4—612no—
826C2×C4—612no—
827C2×C4—611no—
828C2×C4—611no—
829C2×C4—611no—
830C2×C4—611no—
831C2×C4—611no—
832C2×C4—611no—
833C2×C4—611no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—1221no—
839C2×C4—1221no—
840C2×C4—1221no—
841C2×C4—1221no—
842C2×C4—1221no—
843C2×C4—1221no—
844C2×C4—1221no—
845C2×C4—1221no—
846C2×C4—1221no—
847C2×C4—4881no—
848C2×C4—4881no—
849C2×C4—4881no—
850C2×C4—4881no—
851C2×C4—2441no—
852C2×C4—2442no—
853C2×C4—2442no—
854C2×C4C2×C22⋊#692311yescharacteristic
855C2×C4C2×C22⋊#692311yescharacteristic
856C2×C4C2×C22⋊#692311yescharacteristic
857C2×C4C2×C22⋊#692311yescharacteristic
858C2×C4C23×#692311yescharacteristic
859C8—2441no—
860C8—2441no—
861C8—2441no—
862C8—2441no—
863C8—2441no—
864C8—2441no—
865C8—2441no—
866C8—2441no—
867C22—21no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—1221no—
876C22—1221no—
877C22—1221no—
878C22—2441no—
879C22—2441no—
880C22—2441no—
881C22#1684075312yes—
882C22C22×C22⋊#692311yescharacteristic
883C4—21no—
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—41no—
889C4—41no—
890C4—41no—
891C4—611no—
892C4—611no—
893C4—612no—
894C4—611no—
895C4—611no—
896C4—1221no—
897C4—1221no—
898C4—1221no—
899C4—1221no—
900C4—2441no—
901C4—2441no—
902C4—2441no—
903C2—22no—
904C2—41no—
905C2—81no—
906C2—4881no—
907C2—2441no—
908C2#2146242911yescharacteristic
909C2C2×#1684075311yescharacteristic
910C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#548C4
socleC22×C61C22×C22⋊C4
prime radical#21459725C2
cosocleC4×Dic61C24
hypercenter#548#6923
hypocenterC61#17764
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. #21462739C2semidirect
2. #21462466C2semidirect
3. #21461357C2semidirect
4. #21461356C2semidirect
5. #21461355C2semidirect
6. #21461354C2semidirect
7. #21461339C2semidirect
8. #21461338C2semidirect
9. #21461337C2semidirect
10. #21461336C2semidirect
11. #21461332C2semidirect
12. #21461331C2semidirect
13. C2×#16840622C2semidirect
14. #21461317C2semidirect
530. C61#17764semidirect

Maximal subgroups

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

subgroupindex
#214627392
#214624662
#214613572
#214613562
#214613552
#214613542
#214613392
#214613382
#214613372
#214613362
#214613322
#214613312
C2×#168406222
#214613172
#214597252
#1776461