Finite Group Databasebeta

← #30611948

Subgroups — #30611948

Order 15616.

918 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462739C211yesmaximal, characteristic, complemented
2#21462517C211yesmaximal, characteristic, complemented
3#21461356C211yesmaximal, characteristic, complemented
4#21461355C211yesmaximal, characteristic, complemented
5#21461353C211yesmaximal, characteristic, complemented
6#21461350C211yesmaximal, characteristic, complemented
7#21461345C211yesmaximal, characteristic, complemented
8#21461342C211yesmaximal, characteristic, complemented
9#21461338C211yesmaximal, characteristic, complemented
10#21461338C211yesmaximal, characteristic, complemented
11#21461337C211yesmaximal, characteristic, complemented
12#21461333C211yesmaximal, characteristic, complemented
13#21461322C211yesmaximal, characteristic, complemented
14#21461321C211yesmaximal, characteristic, complemented
15#21459729C211yesmaximal, characteristic
16#16840814—21no—
17#16840795—21no—
18#16840793—21no—
19#16840791—21no—
20#16840787—21no—
21#16840786—21no—
22#16840785C2211yescharacteristic
23#16840785C2211yescharacteristic
24#16840782C2211yescharacteristic
25#16840782C2211yescharacteristic
26#16840780C2211yescharacteristic
27#16840779C2211yescharacteristic
28#16840779C2211yescharacteristic
29#16840767C2211yescharacteristic
30#16840765C2211yescharacteristic
31#16840765C2211yescharacteristic
32C2×#14519844C2211yescharacteristic
33C2×#14519844C2211yescharacteristic
34#16840735—21no—
35#16840726—21no—
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#16840486C411yescharacteristic
53#16840482C411yescharacteristic
54#16840476—21no—
55#16840467—21no—
56#16840457—21no—
57#16840457—21no—
58#16840422C411yescharacteristic
59#16840422C411yescharacteristic
60#16840419C411yescharacteristic
61#16840419C411yescharacteristic
62#16840417C411yescharacteristic
63#16840380—21no—
64#16840380—21no—
65#16840341—21no—
66#16840314C2211yescharacteristic
67#16840314C2211yescharacteristic
68#16840309C2211yescharacteristic
69#16840308C2211yescharacteristic
70#16840308C2211yescharacteristic
71C4⋊Q8×D61C2211yescharacteristic
72#16840243—21no—
73C4×#11758224C2211yescharacteristic
74C61×#547C411yescharacteristic
75C2×#11758213—21no—
76C2×#11758217—21no—
77C2×#11758217—21no—
78C22×#92420—21no—
79C22×#92420—21no—
80#14519844—21no—
81#14519844—21no—
82#14519844—21no—
83#14519844C2311yescharacteristic
84#14519844C2311yescharacteristic
85#14519844C2311yescharacteristic
86#14519844C2311yescharacteristic
87#14519844C2311yescharacteristic
88#14519844C2311yescharacteristic
89#14519844C2311yescharacteristic
90#14519844C2311yescharacteristic
91C4⋊#92420—21no—
92C4⋊#92420—21no—
93#14519834—21no—
94#14519834—21no—
95#14519834—21no—
96C22⋊#92420—21no—
97C22⋊#92420—21no—
98C22⋊#92420—21no—
99C22⋊#92420—21no—
100#14519832—21no—
101#14519832—21no—
102#14519832—21no—
103#14519832—21no—
104C4×#92420—21no—
105C4×#92420—21no—
106C4×#92420—21no—
107C2×#11758222—21no—
108C2×#11758222C2×C411yescharacteristic
109C2×#11758222C2×C411yescharacteristic
110C2×#11758224D411yescharacteristic
111C2×Q8×D61C2×C411yescharacteristic
112C2×Q8×D61C2×C411yescharacteristic
113#14519777C2×C411yescharacteristic
114#14519776—21no—
115#14519776—21no—
116#14519776C2311yescharacteristic
117#14519775C2311yescharacteristic
118#14519775C2311yescharacteristic
119#14519773C2311yescharacteristic
120#14519772—21no—
121#14519772—21no—
122#14519770—21no—
123#14519770—21no—
124#14519767—21no—
125#14519767—21no—
126#14519766C2×C411yescharacteristic
127#14519766C2×C411yescharacteristic
128#14519764—21no—
129#14519764—21no—
130#14519764C2×C411yescharacteristic
131#14519764C2×C411yescharacteristic
132#14519763—21no—
133#14519763—21no—
134#14519763—21no—
135#14519759—21no—
136#14519759—21no—
137#14519757—21no—
138#14519756—21no—
139#14519756—21no—
140#14519756—21no—
141#14519756C2×C411yescharacteristic
142#14519756C2×C411yescharacteristic
143#14519755—21no—
144#14519755—21no—
145#14519754—21no—
146#14519754—21no—
147#14519752C2×C411yescharacteristic
148#14519750—21no—
149#14519750—21no—
150#14519750—21no—
151#14519749—21no—
152#14519749—21no—
153#14519749—21no—
154#14519749—21no—
155#14519748—21no—
156#14519748—21no—
157#14519748—21no—
158#14519748C2×C411yescharacteristic
159Q8×Dic61C2×C411yescharacteristic
160Q8×Dic61C2×C411yescharacteristic
161C4×Dic122C2×C411yescharacteristic
162#14519742—21no—
163#14519742—21no—
164#14519742C2×C411yescharacteristic
165#14519742C2×C411yescharacteristic
166#14519742D411yescharacteristic
167C4×D244C2×C411yescharacteristic
168D4×Dic61D411yescharacteristic
169#14519739—21no—
170#14519739—21no—
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173C4×C22⋊D61—21no—
174C4×C22⋊D61—21no—
175C4×C22⋊D61—21no—
176C4×C22⋊D61—21no—
177C4×C22⋊D61—21no—
178C4×C22⋊D61C2×C411yescharacteristic
179C4×C22⋊D61C2×C411yescharacteristic
180#14519737D411yescharacteristic
181#14519737D411yescharacteristic
182#14519736—21no—
183#14519735—21no—
184#14519735D411yescharacteristic
185#14519733—21no—
186#14519733—21no—
187#14519733D411yescharacteristic
188#14519733D411yescharacteristic
189C4⋊C4×D61—21no—
190C4⋊C4×D61—21no—
191C4⋊C4×D61—21no—
192C2×C4×Dic61C2311yescharacteristic
193C2×C4×Dic61C2311yescharacteristic
194C42×D61C2311yescharacteristic
195C2×#41×C61C2×C411yescharacteristic
196C2×#41×C61C2×C411yescharacteristic
197C4⋊Q8×C61C2×C411yescharacteristic
198#123×C61—21no—
199#123×C61—21no—
200C22⋊Q8×C61C2×C411yescharacteristic
201C22⋊Q8×C61C2×C411yescharacteristic
202#121×C61—21no—
203C4×D4×C61C2×C411yescharacteristic
204C4×D4×C61C2×C411yescharacteristic
205C2×C4⋊C4×C61—21no—
206#41×C61—81no—
207#41×C61—81no—
208C2×Q8×C61C22×C411yescharacteristic
209C2×Q8×C61C22×C411yescharacteristic
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61C22⋊C411yescharacteristic
213C2×D4×C61C22×C411yescharacteristic
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61C22×C411yescharacteristic
218C22×C4×C61C22×C411yescharacteristic
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61C22⋊C411yescharacteristic
225C2×C22⋊D61C22⋊C411yescharacteristic
226C22×Dic61C2×D411yescharacteristic
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229C22×Dic61C2×D411yescharacteristic
230Q8×D61—81no—
231Q8×D61—81no—
232#11758224—41no—
233#11758224—41no—
234#11758222—42no—
235#11758222—42no—
236#11758222—81no—
237#11758222—81no—
238C2×D244—21no—
239C2×D244C22×C411yescharacteristic
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61C22×C411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×C4×D61C2×D411yescharacteristic
248C2×Dic122—21no—
249C2×Dic122—21no—
250C2×Dic122—21no—
251C2×Dic122C22⋊C411yescharacteristic
252C2×Dic122C22×C411yescharacteristic
253C2×Dic122C22×C411yescharacteristic
254#11758217—42no—
255#11758217—81no—
256C2×#92420—21no—
257C2×#92420—21no—
258C2×#92420—21no—
259C2×#92420—21no—
260C2×#92420—21no—
261C2×#92420—21no—
262C2×#92420—21no—
263C2×#92420—21no—
264C2×#92420—42no—
265C2×#92420—81no—
266#11758213—81no—
267C4⋊C4×C61—21no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61C22⋊C411yescharacteristic
272C4⋊C4×C61C22×C411yescharacteristic
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C22⋊C4×C61C22⋊C411yescharacteristic
277C22⋊C4×C61C22⋊C411yescharacteristic
278C42×C61C22×C411yescharacteristic
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283C22⋊Dic61—21no—
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61C22⋊C411yescharacteristic
287C22⋊Dic61C22⋊C411yescharacteristic
288#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198C22⋊C411yescharacteristic
295#11758198C22⋊C411yescharacteristic
296C4⋊Dic61—21no—
297C4⋊Dic61—21no—
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#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196C22⋊C411yescharacteristic
312#11758196C22⋊C411yescharacteristic
313#11758196C22⋊C411yescharacteristic
314#11758196C22⋊C411yescharacteristic
315C4×Dic61—21no—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61—21no—
319C4×Dic61C22×C411yescharacteristic
320C4×Dic61C22×C411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2×D411yescharacteristic
326C4×Dic61C2×D411yescharacteristic
327C4×Dic61C2411yescharacteristic
328C23×C61—21no—
329C23×C61C2×C22⋊C411yescharacteristic
330C23×C61C2×C22⋊C411yescharacteristic
331C22×D61—21no—
332C22×D61C2×C22⋊C411yescharacteristic
333Q8×C61—41no—
334Q8×C61—41no—
335D4×C61—41no—
336D4×C61—41no—
337D4×C61—81no—
338D4×C61—81no—
339C2×C4×C61—21no—
340C2×C4×C61—21no—
341C2×C4×C61—21no—
342C2×C4×C61—41no—
343C2×C4×C61—41no—
344C2×C4×C61—42no—
345C2×C4×C61—81no—
346C2×C4×C61—81no—
347C2×C4×C61C2×C22⋊C411yescharacteristic
348C2×C4×C61C2×C22⋊C411yescharacteristic
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C23×C411yescharacteristic
352C22⋊D61—41no—
353C22⋊D61—41no—
354C22⋊D61—42no—
355C22⋊D61—41no—
356C22⋊D61—41no—
357C22⋊D61—41no—
358C22⋊D61—41no—
359C22⋊D61—81no—
360C22⋊D61—81no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—21no—
370C2×Dic61—21no—
371C2×Dic61—21no—
372C2×Dic61C2×C22⋊C411yescharacteristic
373C2×Dic61C2×C22⋊C411yescharacteristic
374C2×Dic61C2×C22⋊C411yescharacteristic
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61C2×C22⋊C411yescharacteristic
377C2×Dic61C22×D411yescharacteristic
378C2×Dic61C22×D411yescharacteristic
379D244—41no—
380D244—42no—
381C4×D61—21no—
382C4×D61—21no—
383C4×D61—21no—
384C4×D61—21no—
385C4×D61—41no—
386C4×D61—42no—
387C4×D61—81no—
388C4×D61—81no—
389C4×D61—81no—
390C4×D61—81no—
391Dic122—41no—
392Dic122—41no—
393Dic122—41no—
394Dic122—41no—
395Dic122—41no—
396Dic122—81no—
397Dic122—81no—
398#92420—41no—
399#92420—41no—
400#92420—41no—
401#92420—41no—
402#92420—41no—
403#92420—41no—
404#92420—41no—
405#92420—41no—
406#17768—611nomaximal, Sylow
407C22×C61—21no—
408C22×C61—21no—
409C22×C61—21no—
410C22×C61—21no—
411C22×C61—21no—
412C22×C61—21no—
413C22×C61—41no—
414C22×C61—41no—
415C22×C61—41no—
416C22×C61C22×C22⋊C411yescharacteristic
417C2×D61—21no—
418C2×D61—21no—
419C2×D61—21no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61—41no—
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—41no—
437Dic61—41no—
438Dic61—41no—
439Dic61#57511yescharacteristic
440Dic61#57511yescharacteristic
441Dic61#57711yescharacteristic
442Dic61#57811yescharacteristic
443#3511—611no—
444#2989—611no—
445#2925—611no—
446#1560—611no—
447#1559—611no—
448#1558—611no—
449#1557—611no—
450#1554—611no—
451#1553—611no—
452#1551—611no—
453#1551—611no—
454#1550—611no—
455#1548—611no—
456#1543—611no—
457#1542—611no—
458C2×C61—41no—
459C2×C61—41no—
460C2×C61—81no—
461C2×C61#288811yescharacteristic
462C2×C61#289611yescharacteristic
463C2×C61#289811yescharacteristic
464D61—41no—
465D61—81no—
466#556—611no—
467#556—611no—
468#555—1221no—
469#554—1221no—
470#553—1221no—
471#553—1221no—
472#548—611no—
473#548—611no—
474#548—611no—
475#548—611no—
476#547—611no—
477#547#692311yescharacteristic
478#542—1221no—
479#542—1221no—
480#537—1221no—
481#533—611no—
482#533—611no—
483#532—611no—
484#532—611no—
485#532—611no—
486C2×C4⋊Q8—611no—
487#520—1221no—
488C4×#41—611no—
489#446—1221no—
490#436—1221no—
491#435—1221no—
492#435—1221no—
493#433—1221no—
494#433—1221no—
495#432—611no—
496#432—611no—
497#432—611no—
498#432—611no—
499#431—611no—
500#431—611no—
501#431—611no—
502#423—611no—
503#423—611no—
504#423—611no—
505C2×C4⋊C8—611no—
506C2×C4⋊C8—611no—
507#408—1221no—
508#405—1221no—
509#333—611no—
510#333—611no—
511#333—611no—
512#333—611no—
513#333—611no—
514#333—611no—
515#333—611no—
516#333—611no—
517#332—611no—
518#332—611no—
519#332—611no—
520#332—611no—
521#331—611no—
522#331—611no—
523#331—611no—
524#331—611no—
525C61#1776811yescharacteristic, complemented, Sylow
526C2×#41—611no—
527C2×#41—611no—
528C2×#41—611no—
529C2×#41—1221no—
530C2×#41C2×#692311yescharacteristic
531C2×#41C2×#692311yescharacteristic
532C22×Q8—611no—
533C22×Q8—611no—
534C2×M16—1221no—
535C2×M16—1221no—
536C2×M16—1221no—
537C22×C8—1221no—
538C22×C8—1221no—
539C4⋊Q8—611no—
540C4⋊Q8—611no—
541C4⋊Q8—611no—
542C4⋊Q8—611no—
543C4⋊Q8—1221no—
544C4⋊Q8—1221no—
545C4⋊Q8C2×#692311yescharacteristic
546#127—611no—
547#126—1221no—
548#126—1221no—
549#126—1221no—
550#126—1221no—
551#125—1221no—
552#125—1221no—
553#124—611no—
554#124—611no—
555#124—611no—
556#124—611no—
557#124—1221no—
558#124—1221no—
559#124—1221no—
560#124—1221no—
561#124—1221no—
562#123—21no—
563#123—21no—
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⋊Q8—1221no—
574C22⋊Q8—1221no—
575C22⋊Q8—1221no—
576C22⋊Q8C2×#692311yescharacteristic
577C22⋊Q8C2×#692311yescharacteristic
578#121—21no—
579#121—611no—
580#121—611no—
581#121—1221no—
582#121—1221no—
583#121—1221no—
584#121—1221no—
585#121—1221no—
586#121—1221no—
587#121—1221no—
588#121—1221no—
589#121—1221no—
590#121—1221no—
591C4×Q8—611no—
592C4×Q8—611no—
593C4×Q8—611no—
594C4×Q8—611no—
595C4×Q8—611no—
596C4×Q8—611no—
597C4×Q8—1221no—
598C4×Q8—1221no—
599C4×D4—611no—
600C4×D4—611no—
601C4×D4—611no—
602C4×D4—611no—
603C4×D4—611no—
604C4×D4—611no—
605C4×D4—1221no—
606C4×D4—1221no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4—1221no—
612C4×D4—1221no—
613C4×D4—1221no—
614C4×D4C2×#692311yescharacteristic
615C4×D4C2×#692311yescharacteristic
616#117—611no—
617#117—611no—
618#117—611no—
619#117—1221no—
620#117—1221no—
621#117—1221no—
622#117—1221no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—1221no—
625C2×C4⋊C4—1221no—
626C2×C4⋊C4—1221no—
627C2×C42—611no—
628C2×C42—611no—
629C2×C42—611no—
630C4⋊C8—611no—
631C4⋊C8—611no—
632C4⋊C8—611no—
633C4⋊C8—611no—
634C4⋊C8—611no—
635C4⋊C8—611no—
636C4⋊C8—611no—
637C4⋊C8—611no—
638C4⋊C8—1221no—
639C4⋊C8—1221no—
640C4⋊C8—1221no—
641C4⋊C8—1221no—
642C4⋊C8—1221no—
643C22⋊C8—1221no—
644C22⋊C8—1221no—
645C22⋊C8—1221no—
646C22⋊C8—1221no—
647C22⋊C8—1221no—
648C22⋊C8—1221no—
649C22⋊C8—1221no—
650#97—1221no—
651#97—1221no—
652#97—1221no—
653#97—1221no—
654C4×C8—1221no—
655C4×C8—1221no—
656C4×C8—1221no—
657#41—81no—
658#41—81no—
659#41—4881no—
660#41—4881no—
661#41—2442no—
662#41—2442no—
663#41—2441no—
664#41—2441no—
665C2×Q8—611no—
666C2×Q8—611no—
667C2×Q8—611no—
668C2×Q8—1221no—
669C2×Q8—1221no—
670C2×Q8—1221no—
671C2×Q8—4881no—
672C2×Q8—4881no—
673C2×Q8C22×#692311yescharacteristic
674C2×Q8C22×#692311yescharacteristic
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—611no—
678C2×D4—611no—
679C2×D4—611no—
680C2×D4—1221no—
681C2×D4—1221no—
682C2×D4—1221no—
683C2×D4—1221no—
684C2×D4—1221no—
685C2×D4—1221no—
686C2×D4C22⋊#692311yescharacteristic
687C2×D4C22×#692311yescharacteristic
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—611no—
694C22×C4—611no—
695C22×C4—611no—
696C22×C4—611no—
697C22×C4—611no—
698C22×C4—1221no—
699C22×C4—1221no—
700C22×C4—1221no—
701C22×C4—1221no—
702C22×C4—1221no—
703C22×C4C22×#692311yescharacteristic
704C22×C4C22×#692311yescharacteristic
705M16—4881no—
706M16—4881no—
707M16—2442no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—4881no—
717C2×C8—2442no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—611no—
723C4⋊C4—611no—
724C4⋊C4—611no—
725C4⋊C4—611no—
726C4⋊C4—611no—
727C4⋊C4—611no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4—1221no—
733C4⋊C4—1221no—
734C4⋊C4—1221no—
735C4⋊C4—1221no—
736C4⋊C4—1221no—
737C4⋊C4—1221no—
738C4⋊C4—1221no—
739C4⋊C4—1221no—
740C4⋊C4—1221no—
741C4⋊C4C22⋊#692311yescharacteristic
742C4⋊C4C22×#692311yescharacteristic
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—611no—
747C22⋊C4—611no—
748C22⋊C4—611no—
749C22⋊C4—611no—
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—
761C22⋊C4—1221no—
762C22⋊C4—1221no—
763C22⋊C4C22⋊#692311yescharacteristic
764C22⋊C4C22⋊#692311yescharacteristic
765C42—611no—
766C42—611no—
767C42—611no—
768C42—611no—
769C42—611no—
770C42—611no—
771C42—611no—
772C42—611no—
773C42—611no—
774C42—1221no—
775C42—1221no—
776C42—1221no—
777C42—1221no—
778C42C22×#692311yescharacteristic
779C23—21no—
780C23—611no—
781C23—1221no—
782C23C2×C22⋊#692311yescharacteristic
783C23C2×C22⋊#692311yescharacteristic
784Q8—41no—
785Q8—41no—
786Q8—4881no—
787Q8—4881no—
788Q8—2441no—
789Q8—2441no—
790Q8—2441no—
791Q8—2441no—
792Q8—2441no—
793D4—41no—
794D4—41no—
795D4—81no—
796D4—81no—
797D4—4881no—
798D4—4881no—
799D4—2441no—
800D4—2442no—
801D4—2441no—
802D4—2441no—
803D4—2441no—
804D4—2441no—
805D4—2441no—
806D4—2441no—
807D4—2442no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—42no—
814C2×C4—81no—
815C2×C4—81no—
816C2×C4—611no—
817C2×C4—611no—
818C2×C4—611no—
819C2×C4—611no—
820C2×C4—611no—
821C2×C4—611no—
822C2×C4—611no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1221no—
830C2×C4—1221no—
831C2×C4—1221no—
832C2×C4—1221no—
833C2×C4—1221no—
834C2×C4—1221no—
835C2×C4—1221no—
836C2×C4—1221no—
837C2×C4—1221no—
838C2×C4—4881no—
839C2×C4—4881no—
840C2×C4—4881no—
841C2×C4—4881no—
842C2×C4—2441no—
843C2×C4—2442no—
844C2×C4C2×C22⋊#692311yescharacteristic
845C2×C4C2×C22⋊#692311yescharacteristic
846C2×C4C2×C22⋊#692311yescharacteristic
847C2×C4C2×C22⋊#692311yescharacteristic
848C2×C4C23×#692311yescharacteristic
849C8—2441no—
850C8—2441no—
851C8—2441no—
852C8—2441no—
853C8—2441no—
854C8—2441no—
855C8—2441no—
856C8—2441no—
857C22—21no—
858C22—21no—
859C22—21no—
860C22—21no—
861C22—21no—
862C22—21no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—1221no—
867C22—1221no—
868C22—1221no—
869C22—2441no—
870C22—2441no—
871C22—2441no—
872C22C22×C22⋊#692311yescharacteristic
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—611no—
882C4—611no—
883C4—611no—
884C4—611no—
885C4—1221no—
886C4—1221no—
887C4—1221no—
888C4—1221no—
889C4—1221no—
890C4—2441no—
891C4—2441no—
892C4—2441no—
893C2—41no—
894C2—41no—
895C2—81no—
896C2—4881no—
897C2—2441no—
898C2#2146242911yescharacteristic
899C2#2146243911yescharacteristic
900C2#2146244111yescharacteristic
subgroupG/H
centerC22C22×C22⋊#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#547C4
socleC22×C61C22×C22⋊C4
prime radical#21459729C2
cosocleC4×Dic61C24
hypercenter#547#6923
hypocenterC61#17768
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×D4 ◁ #547

Complements

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

NH ≅ G/Ntype
1. #21462739C2semidirect
2. #21462517C2semidirect
3. #21461356C2semidirect
4. #21461355C2semidirect
5. #21461353C2semidirect
6. #21461350C2semidirect
7. #21461345C2semidirect
8. #21461342C2semidirect
9. #21461338C2semidirect
10. #21461338C2semidirect
11. #21461337C2semidirect
12. #21461333C2semidirect
13. #21461322C2semidirect
14. #21461321C2semidirect
525. C61#17768semidirect

Maximal subgroups

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

subgroupindex
#214627392
#214625172
#214613562
#214613552
#214613532
#214613502
#214613452
#214613422
#214613382
#214613372
#214613332
#214613222
#214613212
#214597292
#1776861