Finite Group Databasebeta

← #6569787

Subgroups — #6569787

Order 512.

2186 conjugacy classes of subgroups.

The subgroup lattice has 1269 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#3344C211yesmaximal, characteristic, complemented
2C2×#3336C211yesmaximal, characteristic, complemented
3C2×#3310C211yesmaximal, characteristic
4C2×#3295C211yesmaximal, characteristic
5#38084C211yesmaximal, characteristic
6#37865C211yesmaximal, characteristic, complemented
7#30287C211yesmaximal, characteristic, complemented
8#30252C211yesmaximal, characteristic, complemented
9#30244C211yesmaximal, characteristic, complemented
10#28547C211yesmaximal, characteristic, complemented
11#28533C211yesmaximal, characteristic, complemented
12#28524C211yesmaximal, characteristic, complemented
13#28431C211yesmaximal, characteristic, complemented
14#28402C211yesmaximal, characteristic, complemented
15#28392C211yesmaximal, characteristic, complemented
16#28361C211yesmaximal, characteristic, complemented
17#28342C211yesmaximal, characteristic, complemented
18#28330C211yesmaximal, characteristic, complemented
19#28330C211yesmaximal, characteristic, complemented
20#28320C211yesmaximal, characteristic, complemented
21#28302C211yesmaximal, characteristic, complemented
22#27946C211yesmaximal, characteristic, complemented
23#27939C211yesmaximal, characteristic, complemented
24#27925C211yesmaximal, characteristic, complemented
25#27924C211yesmaximal, characteristic, complemented
26#27920C211yesmaximal, characteristic, complemented
27#27912C211yesmaximal, characteristic, complemented
28#23809C211yesmaximal, characteristic, complemented
29#23735C211yesmaximal, characteristic, complemented
30C2×#2092C211yesmaximal, characteristic, complemented
31#20557C211yesmaximal, characteristic, complemented
32C2×#554C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×#552C2211yescharacteristic
35C2×D42C2211yescharacteristic
36#3344—28no—
37#3336—28no—
38#3310—28no—
39#3295—28no—
40C2×#501C2211yescharacteristic, complemented
41C2×#499C2211yescharacteristic, complemented
42C2×#490C2211yescharacteristic
43C2×#486C2211yescharacteristic
44C2×#484C2211yescharacteristic, complemented
45C2×#481C2211yescharacteristic
46C2×#481C2211yescharacteristic
47C2×#485C2211yescharacteristic, complemented
48C2×#485C2211yescharacteristic, complemented
49C2×#485C2211yescharacteristic, complemented
50C2×#482C2211yescharacteristic
51C2×#483C2211yescharacteristic, complemented
52C2×#483C2211yescharacteristic, complemented
53C2×#483C2211yescharacteristic, complemented
54C2×#483C2211yescharacteristic, complemented
55C2×#480C2211yescharacteristic
56C2×#479C2211yescharacteristic, complemented
57C2×#479C2211yescharacteristic, complemented
58C2×#479C2211yescharacteristic, complemented
59C2×#475C2211yescharacteristic, complemented
60C2×#478C2211yescharacteristic
61C2×#476C2211yescharacteristic
62C2×#470C2211yescharacteristic, complemented
63C2×#468C2211yescharacteristic
64C2×#467C2211yescharacteristic, complemented
65C2×#467C2211yescharacteristic, complemented
66C2×#467C2211yescharacteristic, complemented
67C2×#465C2211yescharacteristic
68C2×#465C2211yescharacteristic
69C2×#465C2211yescharacteristic
70C2×#460C2211yescharacteristic
71C2×#460C2211yescharacteristic
72C2×#450C2211yescharacteristic
73C2×#450C2211yescharacteristic
74C2×#450C2211yescharacteristic
75C2×#450C2211yescharacteristic
76C2×#441C2211yescharacteristic, complemented
77C2×#440C2211yescharacteristic
78C2×C4×Q16C2211yescharacteristic, complemented
79C2×C4×SD16C2211yescharacteristic
80C2×#435C2211yescharacteristic
81C2×C8×D4C2211yescharacteristic
82C2×#428C2211yescharacteristic, complemented
83C2×#427C2211yescharacteristic, complemented
84C22×#107C2211yescharacteristic, complemented
85C22×#106C2211yescharacteristic, complemented
86C2×#418C2211yescharacteristic
87C22×#102C2211yescharacteristic
88C22×#102C2211yescharacteristic
89C22×#102C2211yescharacteristic
90#2857C2211yescharacteristic, complemented
91#2850C2211yescharacteristic
92#2719—22no—
93#2711—22no—
94#2698—22no—
95#2685—22no—
96#2660C2211yescharacteristic, complemented
97#2641C2211yescharacteristic
98#2621C2211yescharacteristic, complemented
99#2620C2211yescharacteristic
100#2568C2211yescharacteristic, complemented
101#2566C2211yescharacteristic
102#2565C2211yescharacteristic, complemented
103#2548C2211yescharacteristic
104#2503C2211yescharacteristic, complemented
105#2503C2211yescharacteristic, complemented
106#2502C2211yescharacteristic, complemented
107#2501C2211yescharacteristic
108#2500C2211yescharacteristic
109#2499C2211yescharacteristic, complemented
110#2438—22no—
111#2435C2211yescharacteristic
112#2435C2211yescharacteristic
113#2419—22no—
114#2411—22no—
115#2405—22no—
116#2327C2211yescharacteristic, complemented
117#2326C2211yescharacteristic
118#2317C2211yescharacteristic, complemented
119#2309C2211yescharacteristic
120C2×#390C2211yescharacteristic
121#2290C2211yescharacteristic
122C2×#382C2211yescharacteristic, complemented
123#2097C2211yescharacteristic, complemented
124#2097C2211yescharacteristic, complemented
125#2097C2211yescharacteristic, complemented
126#2097C2211yescharacteristic, complemented
127#2096C2211yescharacteristic, complemented
128#2096C2211yescharacteristic, complemented
129#2096C2211yescharacteristic, complemented
130#2095C2211yescharacteristic, complemented
131#2095C2211yescharacteristic, complemented
132#2094C2211yescharacteristic
133#2094C2211yescharacteristic, complemented
134#2094C2211yescharacteristic, complemented
135#2094C2211yescharacteristic, complemented
136#2093C2211yescharacteristic
137#2093C2211yescharacteristic, complemented
138#2093C2211yescharacteristic, complemented
139#2092C2211yescharacteristic
140#2092C2211yescharacteristic
141#2092C2211yescharacteristic
142#2092C2211yescharacteristic
143#2092C2211yescharacteristic
144#2092C2211yescharacteristic, complemented
145#2092C2211yescharacteristic, complemented
146#2092C2211yescharacteristic, complemented
147#2092C2211yescharacteristic, complemented
148#2092C2211yescharacteristic, complemented
149#2092C2211yescharacteristic, complemented
150#2092C2211yescharacteristic, complemented
151#2092C2211yescharacteristic, complemented
152#2092C2211yescharacteristic, complemented
153#2016C2211yescharacteristic, complemented
154#2015C2211yescharacteristic
155#2015C2211yescharacteristic
156#2015C2211yescharacteristic, complemented
157#2015C2211yescharacteristic, complemented
158#2015C2211yescharacteristic, complemented
159#2015C2211yescharacteristic, complemented
160#2013C2211yescharacteristic
161#2013C2211yescharacteristic, complemented
162#2013C2211yescharacteristic, complemented
163#1973C2211yescharacteristic
164#1973C2211yescharacteristic, complemented
165#1973C2211yescharacteristic, complemented
166#1973C2211yescharacteristic, complemented
167#1968C2211yescharacteristic
168#1968C2211yescharacteristic
169#1968C2211yescharacteristic
170#1968C2211yescharacteristic, complemented
171#1968C2211yescharacteristic, complemented
172#1968C2211yescharacteristic, complemented
173#1968C2211yescharacteristic, complemented
174#1968C2211yescharacteristic, complemented
175#1959C2211yescharacteristic
176#1959C2211yescharacteristic, complemented
177#1958C2211yescharacteristic
178#1958C2211yescharacteristic, complemented
179#1958C2211yescharacteristic, complemented
180#1958C2211yescharacteristic, complemented
181#1847C2211yescharacteristic, complemented
182#1847C2211yescharacteristic, complemented
183#1846C2211yescharacteristic, complemented
184#1846C2211yescharacteristic, complemented
185#1844C2211yescharacteristic, complemented
186#1844C2211yescharacteristic, complemented
187#1771C2211yescharacteristic, complemented
188C8×C4⋊C4C2211yescharacteristic, complemented
189#1768C2211yescharacteristic, complemented
190#1753C2211yescharacteristic, complemented
191#1752C2211yescharacteristic, complemented
192C8×C22⋊C4C2211yescharacteristic, complemented
193C8×C22⋊C4C2211yescharacteristic, complemented
194#1750C2211yescharacteristic, complemented
195C4×C22⋊C8C2211yescharacteristic, complemented
196#1746C2211yescharacteristic, complemented
197#1729C2211yescharacteristic, complemented
198C2×#336C2211yescharacteristic, complemented
199C23×D4—21no—
200C23×D4C2311yescharacteristic
201C23×D4C2311yescharacteristic
202C22×Q16C2311yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213C23×C8C2311yescharacteristic
214#554—24no—
215#554—24no—
216#552—24no—
217#552—24no—
218#552—24no—
219#552—24no—
220D42—24no—
221D42—24no—
222C2×C4⋊Q8C2311yescharacteristic
223C2×C4⋊Q8C2311yescharacteristic
224C2×#127C2311yescharacteristic
225C2×#126—21no—
226C2×#126—21no—
227C2×#125—21no—
228C2×#125—21no—
229C2×#125—21no—
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#123—21no—
236C2×#123—21no—
237C2×#123—22no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8—21no—
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×C22⋊Q8C2311yescharacteristic
243C2×C22⋊Q8C2311yescharacteristic
244C2×C22⋊Q8C2311yescharacteristic
245C2×C22⋊Q8C2311yescharacteristic
246C2×#121—21no—
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#120—21no—
250C2×#120—21no—
251C2×C4×Q8C2311yescharacteristic
252C2×C4×Q8C2311yescharacteristic
253C2×C4×Q8C2311yescharacteristic
254C2×C4×D4—21no—
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×#117—21no—
258C2×#117—21no—
259C2×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C2×#117C2311yescharacteristic
262C22×C4⋊C4C2311yescharacteristic
263C22×C4⋊C4C2311yescharacteristic
264C22×C4⋊C4C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266C22×C22⋊C4—22no—
267C22×C42C2311yescharacteristic
268#501—24no—
269#499—24no—
270#490—24no—
271#486—24no—
272#485—24no—
273#485—24no—
274#485—24no—
275#484—24no—
276#483—24no—
277#483—24no—
278#483—24no—
279#483—24no—
280#482—24no—
281#481—24no—
282#481—24no—
283#480—24no—
284#479—24no—
285#479—24no—
286#479—24no—
287#478—24no—
288#476—24no—
289#475—24no—
290#470—24no—
291#468—24no—
292#467—24no—
293#467—24no—
294#467—24no—
295#465—24no—
296#465—24no—
297#465—24no—
298#460—24no—
299#460—24no—
300#450—24no—
301#450—24no—
302#450—24no—
303#450—24no—
304#441—24no—
305#440—24no—
306C4×Q16—24no—
307C4×SD16—24no—
308#435D418yes—
309C8×D4D418yes—
310#428—24no—
311#427—24no—
312C2×#107—24no—
313C2×#107C2311yescharacteristic
314C2×#107C2311yescharacteristic
315C2×#107C2311yescharacteristic
316C2×#107C2311yescharacteristic
317C2×#107C2311yescharacteristic
318C2×#107C2311yescharacteristic
319C2×#107C2311yescharacteristic
320C2×#107C2311yescharacteristic
321C2×#107C2311yescharacteristic
322C2×#107C2311yescharacteristic
323C2×#106—24no—
324C2×#106C2311yescharacteristic
325C2×#106C2311yescharacteristic
326C2×#106C2311yescharacteristic
327C2×#106C2311yescharacteristic
328C2×#106C2311yescharacteristic
329C2×#106C2311yescharacteristic
330C2×#106C2311yescharacteristic
331C2×#106C2311yescharacteristic
332C2×#106C2311yescharacteristic
333C2×#106C2311yescharacteristic
334C2×#106C2311yescharacteristic
335C2×#106C2311yescharacteristic
336C2×#106C2311yescharacteristic
337C2×#106C2311yescharacteristic
338C2×C4⋊C8C2311yescharacteristic
339C2×C4⋊C8C2311yescharacteristic
340#418—24no—
341C2×#103C2311yescharacteristic
342C2×#103C2311yescharacteristic
343C2×#103C2311yescharacteristic
344C2×#103C2311yescharacteristic
345C2×#103C2311yescharacteristic
346C2×#103C2311yescharacteristic
347C2×#103C2311yescharacteristic
348C2×#103C2311yescharacteristic
349C2×#103C2311yescharacteristic
350C2×#103C2311yescharacteristic
351C2×#103C2311yescharacteristic
352C2×#103C2311yescharacteristic
353C2×#103C2311yescharacteristic
354C2×#103C2311yescharacteristic
355C2×#102—24no—
356C2×#102—24no—
357C2×#102—24no—
358C2×#102C2311yescharacteristic
359C2×#102C2311yescharacteristic
360C2×#102C2311yescharacteristic
361C2×#102C2311yescharacteristic
362C2×#102C2311yescharacteristic
363C2×#102C2311yescharacteristic
364C2×#102C2311yescharacteristic
365C2×#102C2311yescharacteristic
366C2×#102C2311yescharacteristic
367C2×#102C2311yescharacteristic
368C2×#102C2311yescharacteristic
369C2×#102C2311yescharacteristic
370C2×#102C2311yescharacteristic
371C2×#102C2311yescharacteristic
372C2×#102C2311yescharacteristic
373C2×#102C2311yescharacteristic
374C2×#102C2311yescharacteristic
375C2×#102C2311yescharacteristic
376C2×C22⋊C8C2311yescharacteristic
377C2×C22⋊C8C2311yescharacteristic
378C2×C22⋊C8C2311yescharacteristic
379C2×C22⋊C8C2311yescharacteristic
380C2×#97C2311yescharacteristic
381C2×#97C2311yescharacteristic
382C2×#97C2311yescharacteristic
383C2×C4×C8C2311yescharacteristic
384C2×C4×C8C2311yescharacteristic
385C2×C4×C8C2311yescharacteristic
386C2×C4×C8C2311yescharacteristic
387C2×C4×C8C2311yescharacteristic
388#400—22no—
389#400—22no—
390#400—22no—
391#399—22no—
392#398—22no—
393#398—22no—
394#398—22no—
395#398—22no—
396#397—22no—
397#397—22no—
398#396—22no—
399#396—22no—
400#395—22no—
401#394—22no—
402#394—22no—
403#394—22no—
404#394—22no—
405#394—22no—
406#394—22no—
407#394—22no—
408#391—22no—
409#391C2311yescharacteristic
410#391C2311yescharacteristic
411#391C2311yescharacteristic
412#391C2311yescharacteristic
413#391C2311yescharacteristic
414#391C2311yescharacteristic
415#391C2311yescharacteristic
416#390—22no—
417#390—22no—
418#390—22no—
419#390C2311yescharacteristic
420#390C2311yescharacteristic
421#390C2311yescharacteristic
422#390C2311yescharacteristic
423#390C2311yescharacteristic
424#390C2311yescharacteristic
425#390C2311yescharacteristic
426#390C2311yescharacteristic
427#390C2311yescharacteristic
428#389—22no—
429#389—22no—
430#388—22no—
431#388—22no—
432#388—22no—
433#388D412yes—
434#387—22no—
435#387—22no—
436#387—22no—
437#387—22no—
438#387D412yes—
439#386—22no—
440#386D412yes—
441#385—22no—
442#385—22no—
443#385—22no—
444#385—22no—
445#385D412yes—
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#384C2311yescharacteristic
451#382—22no—
452#382C2311yescharacteristic
453#382C2311yescharacteristic
454#382C2311yescharacteristic
455#382C2311yescharacteristic
456#382C2311yescharacteristic
457#382C2311yescharacteristic
458#382C2311yescharacteristic
459#381—22no—
460#381—22no—
461#380—22no—
462#379—22no—
463#379—22no—
464#379—22no—
465C4×C4⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468#376C2311yescharacteristic
469C2×#95—22no—
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480C25—21no—
481C25—21no—
482C22×Q8—21no—
483C22×Q8C2411yescharacteristic
484C22×Q8C2411yescharacteristic
485C22×Q8C2411yescharacteristic
486C22×D4—22no—
487C22×D4—22no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—22no—
491C22×D4—22no—
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4—41no—
504C22×D4—44no—
505C22×D4—84no—
506C22×D4C2×D411yescharacteristic
507C22×D4C2411yescharacteristic
508C22×D4C2411yescharacteristic
509C22×D4C2411yescharacteristic
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4C2×D412yes—
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C2×Q16—22no—
519C2×Q16—22no—
520C2×Q16—41no—
521C2×Q16—41no—
522C2×Q16—41no—
523C2×Q16—41no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—22no—
531C2×SD16—22no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×SD16—41no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×M16—41no—
543C2×M16—41no—
544C2×M16C2×D414yes—
545C22×C8—41no—
546C22×C8—41no—
547C22×C8—41no—
548C22×C8—41no—
549C22×C8—41no—
550C22×C8—41no—
551C22×C8C2×D414yes—
552C22×C8C2×D414yes—
553C22×C8C2×D414yes—
554C22×C8C2411yescharacteristic
555C22×C8C2411yescharacteristic
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C4⋊Q8—22no—
563C4⋊Q8—22no—
564C4⋊Q8—41no—
565C4⋊Q8—41no—
566#127—22no—
567#127—22no—
568#126—44no—
569#126—44no—
570#125—22no—
571#125—22no—
572#125—22no—
573#125—22no—
574#125—44no—
575#125—44no—
576#125—44no—
577#124—22no—
578#124—41no—
579#124—41no—
580#124—41no—
581#124—41no—
582#124—41no—
583#123—44no—
584#123—44no—
585#123—84no—
586C22⋊Q8—22no—
587C22⋊Q8—22no—
588C22⋊Q8—22no—
589C22⋊Q8—22no—
590C22⋊Q8—22no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—22no—
596C22⋊Q8—22no—
597C22⋊Q8—22no—
598C22⋊Q8—44no—
599C22⋊Q8—44no—
600#121—22no—
601#121—22no—
602#121—22no—
603#121—22no—
604#121—44no—
605#120—44no—
606#120—44no—
607C4×Q8—22no—
608C4×Q8—22no—
609C4×Q8—22no—
610C4×Q8—22no—
611C4×Q8—22no—
612C4×Q8—22no—
613C4×D4—22no—
614C4×D4—22no—
615C4×D4—44no—
616C4×D4C2×D414yes—
617C4×D4C2×D414yes—
618#117—22no—
619#117—22no—
620#117—22no—
621#117—22no—
622#117—41no—
623#117—41no—
624#117—44no—
625#117—44no—
626C2×C4⋊C4—22no—
627C2×C4⋊C4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—22no—
653C2×C4⋊C4—22no—
654C2×C4⋊C4—22no—
655C2×C4⋊C4—22no—
656C2×C4⋊C4—22no—
657C2×C4⋊C4—22no—
658C2×C4⋊C4C2×D412yes—
659C2×C4⋊C4C2×D412yes—
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2411yescharacteristic
662C2×C4⋊C4C2411yescharacteristic
663C2×C4⋊C4C2411yescharacteristic
664C2×C4⋊C4C2411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—22no—
683C2×C22⋊C4—22no—
684C2×C22⋊C4—22no—
685C2×C22⋊C4—22no—
686C2×C22⋊C4—22no—
687C2×C22⋊C4—22no—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—84no—
695C2×C22⋊C4C2×D412yes—
696C2×C22⋊C4C2×D412yes—
697C2×C22⋊C4C2×D412yes—
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—41no—
706C2×C42—41no—
707C2×C42C2×D412yes—
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713#107—22no—
714#107—22no—
715#107—22no—
716#107—22no—
717#107—22no—
718#107—22no—
719#107—22no—
720#107—22no—
721#107—22no—
722#107—22no—
723#106—22no—
724#106—22no—
725#106—22no—
726#106—22no—
727#106—22no—
728#106—22no—
729#106—22no—
730#106—22no—
731#106—22no—
732#106—22no—
733#106—22no—
734#106—22no—
735#106—22no—
736#106—22no—
737C4⋊C8C2×D414yes—
738C4⋊C8C2×D414yes—
739#103—22no—
740#103—22no—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—22no—
748#103—22no—
749#103—22no—
750#103—22no—
751#103—22no—
752#103—22no—
753#102—22no—
754#102—22no—
755#102—22no—
756#102—22no—
757#102—22no—
758#102—22no—
759#102—22no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771C22⋊C8C2×D414yes—
772C22⋊C8C2×D414yes—
773C22⋊C8C2×D414yes—
774C22⋊C8C2×D414yes—
775#97—41no—
776#97—41no—
777#97C2×D414yes—
778C4×C8—41no—
779C4×C8—41no—
780C4×C8—41no—
781C4×C8—41no—
782C4×C8C2×D414yes—
783#95—22no—
784#95—22no—
785#95—22no—
786#95—22no—
787#95—22no—
788#95—22no—
789#95—22no—
790#95—22no—
791#95—22no—
792#95—22no—
793#95—22no—
794#95—22no—
795#95—22no—
796#95—22no—
797#95C2×D412yes—
798#95C2×D412yes—
799#95C2×D412yes—
800#95C2×D412yes—
801#95C2×D412yes—
802C24—21no—
803C24—21no—
804C24—21no—
805C24—42no—
806C24—42no—
807C24—42no—
808C24—42no—
809C24—44no—
810C24—81no—
811C24—81no—
812C24—82no—
813C24—82no—
814C24—82no—
815C24C22×D411yescharacteristic
816C24C22×D411yescharacteristic
817C2×Q8—21no—
818C2×Q8—21no—
819C2×Q8—21no—
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—42no—
836C2×Q8—82no—
837C2×D4—24no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—44no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—82no—
869C2×D4—82no—
870C2×D4—82no—
871C2×D4—82no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—82no—
875C2×D4—82no—
876C2×D4—82no—
877C2×D4—816no—
878C2×D4#12714yes—
879C2×D42−1+412yes—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—24no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—44no—
907C22×C4—44no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—82no—
912C22×C4—82no—
913C22×C4—82no—
914C22×C4C22×D412yes—
915C22×C4C22×D412yes—
916C22×C4C22×D412yes—
917C22×C4C22×D412yes—
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D412yes—
923C22×C4C22×D412yes—
924C22×C4C22×D412yes—
925C22×C4C22×D412yes—
926C22×C4C2511yescharacteristic
927Q16—44no—
928Q16—44no—
929SD16—44no—
930SD16—44no—
931SD16—82no—
932SD16—82no—
933SD16—82no—
934SD16—82no—
935M16—44no—
936C2×C8—21no—
937C2×C8—21no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—44no—
953C2×C8—44no—
954C2×C8—44no—
955C2×C8C22×D412yes—
956C2×C8C22×D412yes—
957C2×C8C22×D412yes—
958C2×C8C22×D412yes—
959C2×C8C22×D412yes—
960C2×C8C22×D412yes—
961C2×C8C22×D412yes—
962C2×C8C22×D412yes—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—42no—
984C4⋊C4—42no—
985C4⋊C4—44no—
986C4⋊C4—42no—
987C4⋊C4—42no—
988C4⋊C4—42no—
989C4⋊C4—42no—
990C4⋊C4—42no—
991C4⋊C4—42no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—82no—
1005C4⋊C4—82no—
1006C4⋊C4—82no—
1007C4⋊C4—82no—
1008C4⋊C4—82no—
1009C4⋊C4#12714yes—
1010C22⋊C4—24no—
1011C22⋊C4—42no—
1012C22⋊C4—42no—
1013C22⋊C4—44no—
1014C22⋊C4—42no—
1015C22⋊C4—42no—
1016C22⋊C4—42no—
1017C22⋊C4—42no—
1018C22⋊C4—42no—
1019C22⋊C4—42no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—82no—
1026C22⋊C4—82no—
1027C22⋊C4—82no—
1028C22⋊C4—82no—
1029C22⋊C4—82no—
1030C22⋊C4—82no—
1031C22⋊C4—82no—
1032C22⋊C4—82no—
1033C22⋊C4—82no—
1034C22⋊C4—82no—
1035C22⋊C4—82no—
1036C22⋊C4#12714yes—
1037C22⋊C4#12714yes—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—21no—
1044C42—21no—
1045C42—21no—
1046C42—42no—
1047C42—42no—
1048C42—42no—
1049C42—42no—
1050C42—42no—
1051C42—42no—
1052C42C22×D412yes—
1053C42C22×D412yes—
1054C23—22no—
1055C23—21no—
1056C23—21no—
1057C23—22no—
1058C23—21no—
1059C23—21no—
1060C23—22no—
1061C23—22no—
1062C23—42no—
1063C23—41no—
1064C23—41no—
1065C23—42no—
1066C23—42no—
1067C23—42no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—42no—
1075C23—42no—
1076C23—84no—
1077C23—84no—
1078C23—88no—
1079C23—84no—
1080C23—84no—
1081C23—164no—
1082C23—162no—
1083C23—162no—
1084C23—164no—
1085C23—164no—
1086C23C2×#12712yes—
1087C23C2×#12712yes—
1088C23#57714yes—
1089C23C23×D411yescharacteristic
1090Q8—41no—
1091Q8—41no—
1092Q8—41no—
1093Q8—41no—
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—41no—
1098Q8—41no—
1099Q8—41no—
1100Q8—41no—
1101Q8—41no—
1102Q8—162no—
1103D4—28no—
1104D4—22no—
1105D4—22no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—41no—
1115D4—41no—
1116D4—84no—
1117D4—84no—
1118D4—84no—
1119D4—84no—
1120D4—84no—
1121D4—162no—
1122C2×C4—22no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—22no—
1134C2×C4—22no—
1135C2×C4—22no—
1136C2×C4—22no—
1137C2×C4—22no—
1138C2×C4—22no—
1139C2×C4—22no—
1140C2×C4—22no—
1141C2×C4—22no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—22no—
1145C2×C4—22no—
1146C2×C4—22no—
1147C2×C4—22no—
1148C2×C4—42no—
1149C2×C4—42no—
1150C2×C4—42no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—42no—
1173C2×C4—42no—
1174C2×C4—42no—
1175C2×C4—42no—
1176C2×C4—42no—
1177C2×C4—84no—
1178C2×C4—84no—
1179C2×C4—84no—
1180C2×C4—84no—
1181C2×C4—162no—
1182C2×C4—162no—
1183C2×C4C2×#12712yes—
1184C2×C4C2×#12712yes—
1185C2×C4C2×#12712yes—
1186C2×C4C2×#12712yes—
1187C2×C4C23×D411yescharacteristic
1188C2×C4C23×D411yescharacteristic
1189C2×C4C2×2−1+411yescharacteristic
1190C2×C4#58511yescharacteristic
1191C2×C4#58511yescharacteristic
1192C2×C4#58511yescharacteristic
1193C8—22no—
1194C8—22no—
1195C8—22no—
1196C8—22no—
1197C8—22no—
1198C8—22no—
1199C8—22no—
1200C8—22no—
1201C22—24no—
1202C22—24no—
1203C22—22no—
1204C22—22no—
1205C22—22no—
1206C22—22no—
1207C22—22no—
1208C22—42no—
1209C22—42no—
1210C22—44no—
1211C22—42no—
1212C22—82no—
1213C22—81no—
1214C22—81no—
1215C22—82no—
1216C22—82no—
1217C22—82no—
1218C22—82no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—168no—
1226C22—168no—
1227C22#315414yes—
1228C22C22×#12711yescharacteristic
1229C22#348511yescharacteristic
1230C22#348911yescharacteristic
1231C22C2×#57712yes—
1232C22#358412yes—
1233C4—22no—
1234C4—22no—
1235C4—22no—
1236C4—22no—
1237C4—42no—
1238C4—42no—
1239C4—42no—
1240C4—42no—
1241C4—81no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4—81no—
1254C4#348511yescharacteristic
1255C4#348511yescharacteristic
1256C4#348911yescharacteristic
1257C4#348911yescharacteristic
1258C2—24no—
1259C2—42no—
1260C2—82no—
1261C2—161no—
1262C2—161no—
1263C2#3606011yescharacteristic
1264C2C2×#315411yescharacteristic
1265C2#6064911yescharacteristic
1266C2#6177012yes—
1267C2#6221212yes—
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. C2×#3344C2semidirect
2. C2×#3336C2semidirect
6. #37865C2semidirect
7. #30287C2semidirect
8. #30252C2semidirect
9. #30244C2semidirect
10. #28547C2semidirect
11. #28533C2semidirect
12. #28524C2semidirect
13. #28431C2semidirect
14. #28402C2semidirect
15. #28392C2semidirect
16. #28361C2semidirect
17. #28342C2semidirect
18. #28330C2semidirect
19. #28330C2semidirect
20. #28320C2semidirect
21. #28302C2semidirect
22. #27946C2semidirect
23. #27939C2semidirect
24. #27925C2semidirect
25. #27924C2semidirect
26. #27920C2semidirect
27. #27912C2semidirect
28. #23809C2semidirect
29. #23735C2semidirect
30. C2×#2092C2semidirect
31. #20557C2semidirect
40. C2×#501C22semidirect
41. C2×#499C22semidirect
44. C2×#484C22semidirect
47. C2×#485C22semidirect
48. C2×#485C22semidirect
49. C2×#485C22semidirect
51. C2×#483C22semidirect
52. C2×#483C22semidirect
53. C2×#483C22semidirect
54. C2×#483C22semidirect
56. C2×#479C22semidirect
57. C2×#479C22semidirect
58. C2×#479C22semidirect
59. C2×#475C22semidirect
62. C2×#470C22semidirect
64. C2×#467C22semidirect
65. C2×#467C22semidirect
66. C2×#467C22semidirect
76. C2×#441C22semidirect
78. C2×C4×Q16C22semidirect
82. C2×#428C22semidirect
83. C2×#427C22semidirect
84. C22×#107C22semidirect
85. C22×#106C22semidirect
90. #2857C22semidirect
96. #2660C22semidirect
98. #2621C22semidirect
100. #2568C22semidirect
102. #2565C22semidirect
104. #2503C22semidirect
105. #2503C22semidirect
106. #2502C22semidirect
109. #2499C22semidirect
116. #2327C22semidirect
118. #2317C22semidirect
122. C2×#382C22semidirect
123. #2097C22semidirect
124. #2097C22semidirect
125. #2097C22semidirect
126. #2097C22semidirect
127. #2096C22semidirect
128. #2096C22semidirect
129. #2096C22semidirect
130. #2095C22semidirect
131. #2095C22semidirect
133. #2094C22semidirect
134. #2094C22semidirect
135. #2094C22semidirect
137. #2093C22semidirect
138. #2093C22semidirect
144. #2092C22semidirect
145. #2092C22semidirect
146. #2092C22semidirect
147. #2092C22semidirect
148. #2092C22semidirect
149. #2092C22semidirect
150. #2092C22semidirect
151. #2092C22semidirect
152. #2092C22semidirect
153. #2016C22semidirect
156. #2015C22semidirect
157. #2015C22semidirect
158. #2015C22semidirect
159. #2015C22semidirect
161. #2013C22semidirect
162. #2013C22semidirect
164. #1973C22semidirect
165. #1973C22semidirect
166. #1973C22semidirect
170. #1968C22semidirect
171. #1968C22semidirect
172. #1968C22semidirect
173. #1968C22semidirect
174. #1968C22semidirect
176. #1959C22semidirect
178. #1958C22semidirect
179. #1958C22semidirect
180. #1958C22semidirect
181. #1847C22semidirect
182. #1847C22semidirect
183. #1846C22semidirect
184. #1846C22semidirect
185. #1844C22semidirect
186. #1844C22semidirect
187. #1771C22semidirect
188. C8×C4⋊C4C22semidirect
189. #1768C22semidirect
190. #1753C22semidirect
191. #1752C22semidirect
192. C8×C22⋊C4C22semidirect
193. C8×C22⋊C4C22semidirect
194. #1750C22semidirect
195. C4×C22⋊C8C22semidirect
196. #1746C22semidirect
197. #1729C22semidirect
198. C2×#336C22semidirect

Maximal subgroups

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

subgroupindex
C2×#33442
C2×#33362
C2×#33102
C2×#32952
#380842
#378652
#302872
#302522
#302442
#285472
#285332
#285242
#284312
#284022
#283922
#283612
#283422
#283302
#283202
#283022
#279462
#279392
#279252
#279242
#279202
#279122
#238092
#237352
C2×#20922
#205572