Finite Group Databasebeta

← #6798147

Subgroups — #6798147

Order 512.

1596 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37878C211yesmaximal, characteristic, complemented
2#37772C211yesmaximal, characteristic
3#33228C211yesmaximal, characteristic, complemented
4#30658C211yesmaximal, characteristic, complemented
5#30653C211yesmaximal, characteristic, complemented
6#30648C211yesmaximal, characteristic, complemented
7#30648C211yesmaximal, characteristic, complemented
8#30644C211yesmaximal, characteristic, complemented
9#30638C211yesmaximal, characteristic, complemented
10#30631C211yesmaximal, characteristic, complemented
11#30630C211yesmaximal, characteristic, complemented
12#29853C211yesmaximal, characteristic, complemented
13#29847C211yesmaximal, characteristic, complemented
14#29217C211yesmaximal, characteristic, complemented
15#28759C211yesmaximal, characteristic, complemented
16#27923C211yesmaximal, characteristic, complemented
17#27911C211yesmaximal, characteristic, complemented
18#26542C211yesmaximal, characteristic, complemented
19#26541C211yesmaximal, characteristic, complemented
20#26537C211yesmaximal, characteristic, complemented
21#26530C211yesmaximal, characteristic, complemented
22#26248C211yesmaximal, characteristic, complemented
23#26245C211yesmaximal, characteristic, complemented
24#26240C211yesmaximal, characteristic, complemented
25#26235C211yesmaximal, characteristic, complemented
26#25680C211yesmaximal, characteristic, complemented
27#25671C211yesmaximal, characteristic, complemented
28#21871C211yesmaximal, characteristic, complemented
29#21869C211yesmaximal, characteristic, complemented
30#21724C211yesmaximal, characteristic, complemented
31#21273C211yesmaximal, characteristic, complemented
32C2×#542C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#498C2211yescharacteristic
35C2×#490C2211yescharacteristic
36C2×#489C2211yescharacteristic
37C2×#489C2211yescharacteristic
38C2×#488C2211yescharacteristic
39C2×#486C2211yescharacteristic
40C2×#486C2211yescharacteristic
41C2×#481C2211yescharacteristic
42C2×#485C2211yescharacteristic
43C2×#485C2211yescharacteristic
44C2×#482C2211yescharacteristic
45C2×#482C2211yescharacteristic
46C2×#482C2211yescharacteristic
47C2×#482C2211yescharacteristic
48C2×#480C2211yescharacteristic
49C2×#433C2211yescharacteristic
50C2×#432C2211yescharacteristic
51#2857C2211yescharacteristic
52#2850C2211yescharacteristic
53#2748—21no—
54#2742—21no—
55#2733—21no—
56#2730—21no—
57#2714—21no—
58#2704—21no—
59#2692—21no—
60#2673—21no—
61#2660C2211yescharacteristic
62#2657C2211yescharacteristic
63#2628C2211yescharacteristic
64#2619C2211yescharacteristic
65#2590—21no—
66#2589—21no—
67#2586—21no—
68#2570C2211yescharacteristic
69#2556—21no—
70#2552C2211yescharacteristic
71#2541C2211yescharacteristic
72#2540C2211yescharacteristic
73#2467—21no—
74#2456—21no—
75#2441C2211yescharacteristic
76#2441C2211yescharacteristic
77#2440C2211yescharacteristic
78#2439C2211yescharacteristic
79#2431—21no—
80#2428C2211yescharacteristic
81#2428C2211yescharacteristic
82#2427C2211yescharacteristic
83#2426C2211yescharacteristic
84#2407—21no—
85#2367C2211yescharacteristic
86#2366C2211yescharacteristic
87#2354C2211yescharacteristic
88#2352C2211yescharacteristic
89#2331C2211yescharacteristic
90#2331C2211yescharacteristic
91#2317C2211yescharacteristic
92#2290C2211yescharacteristic
93#2285C2211yescharacteristic
94#2096C2211yescharacteristic
95#2095C2211yescharacteristic
96#2094C2211yescharacteristic
97#2094C2211yescharacteristic
98#2093C2211yescharacteristic
99#2093C2211yescharacteristic
100#2092C2211yescharacteristic
101#2092C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2058C2211yescharacteristic
113#2057C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2041C2211yescharacteristic
117#2041C2211yescharacteristic
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#2035C2211yescharacteristic
121#2035C2211yescharacteristic
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2034C2211yescharacteristic
127#2034C2211yescharacteristic
128#2034C2211yescharacteristic
129#2034C2211yescharacteristic
130#2033C2211yescharacteristic
131#2033C2211yescharacteristic
132#2033C2211yescharacteristic
133#2033C2211yescharacteristic
134#1993C2211yescharacteristic
135#1993C2211yescharacteristic
136#1993C2211yescharacteristic
137#1990C2211yescharacteristic
138#1983C2211yescharacteristic
139#1983C2211yescharacteristic
140#1982C2211yescharacteristic
141#1982C2211yescharacteristic
142#1961C2211yescharacteristic
143#1961C2211yescharacteristic
144#1961C2211yescharacteristic
145#1959C2211yescharacteristic
146#1959C2211yescharacteristic
147#1958C2211yescharacteristic
148#1958C2211yescharacteristic
149#1958C2211yescharacteristic
150#1957C2211yescharacteristic
151#1957C2211yescharacteristic
152#1955C2211yescharacteristic
153#1954C2211yescharacteristic
154#1949C2211yescharacteristic
155#1949C2211yescharacteristic
156#1948C2211yescharacteristic
157#1947C2211yescharacteristic
158#1944C2211yescharacteristic
159#1944C2211yescharacteristic
160#1941C2211yescharacteristic
161#1941C2211yescharacteristic
162#1940C2211yescharacteristic
163#1939C2211yescharacteristic
164#1924C2211yescharacteristic
165#1924C2211yescharacteristic
166#1923C2211yescharacteristic
167#1923C2211yescharacteristic
168#1875C2211yescharacteristic
169#1875C2211yescharacteristic
170#1875C2211yescharacteristic
171#1875C2211yescharacteristic
172#1875C2211yescharacteristic
173#1874C2211yescharacteristic
174#1873C2211yescharacteristic
175#1872C2211yescharacteristic
176#1865C2211yescharacteristic
177#1865C2211yescharacteristic
178#1864C2211yescharacteristic
179#1864C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1864C2211yescharacteristic
184#1847C2211yescharacteristic
185#1846C2211yescharacteristic
186#1846C2211yescharacteristic
187#1805C2211yescharacteristic
188#1804C2211yescharacteristic
189#1803C2211yescharacteristic
190#1802C2211yescharacteristic
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1776C2211yescharacteristic
196#1776C2211yescharacteristic
197C4×#106C2211yescharacteristic
198C4×#106C2211yescharacteristic
199#1768C2211yescharacteristic
200#1750C2211yescharacteristic
201C4×C22⋊C8C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×#41—21no—
204#542—24no—
205#542—42no—
206#532—24no—
207#532—42no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127—21no—
212C2×#127C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#126—21no—
216C2×#125—21no—
217C2×#125C2311yescharacteristic
218C2×#124—21no—
219C2×#124—21no—
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×#121—21no—
230C2×#121—21no—
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#121C2311yescharacteristic
236C2×#121C2311yescharacteristic
237C2×#121C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4—21no—
240C2×C4×D4—21no—
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C22×C4⋊C4C2311yescharacteristic
250C22×C42C2311yescharacteristic
251#498—24no—
252#490—42no—
253#489—42no—
254#489—42no—
255#488—42no—
256#486—42no—
257#486—42no—
258#485—42no—
259#485—42no—
260#482—42no—
261#482—42no—
262#482—42no—
263#482—42no—
264#481—42no—
265#480—42no—
266#433—42no—
267#432—42no—
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×#97C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×C4×C8C2311yescharacteristic
335C2×C4×C8C2311yescharacteristic
336C2×C4×C8C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338#400—21no—
339#400—21no—
340#399—21no—
341#399—21no—
342#399—21no—
343#399—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#397—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#395—21no—
356#395—21no—
357#395—21no—
358#395—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#393—21no—
366#393—21no—
367#392—21no—
368#392—21no—
369#392—21no—
370#392—21no—
371#392—21no—
372#392—21no—
373#392—21no—
374#392—21no—
375#392—21no—
376#392—21no—
377#392—21no—
378#391—21no—
379#391—21no—
380#391—21no—
381#391—21no—
382#391—21no—
383#391—21no—
384#391C2311yescharacteristic
385#390—21no—
386#390—21no—
387#390—21no—
388#390—21no—
389#390—21no—
390#390—21no—
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#390C2311yescharacteristic
394#389—21no—
395#389—21no—
396#389—21no—
397#389—21no—
398#389—21no—
399#389—21no—
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#389C2311yescharacteristic
404#389C2311yescharacteristic
405#389C2311yescharacteristic
406#389C2311yescharacteristic
407#389C2311yescharacteristic
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388—21no—
415#388—21no—
416#388D411yescharacteristic
417#388D411yescharacteristic
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#387D411yescharacteristic
429#387D411yescharacteristic
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386D411yescharacteristic
439#386D411yescharacteristic
440#385—21no—
441#385—21no—
442#385—21no—
443#385—21no—
444#385D411yescharacteristic
445#385D411yescharacteristic
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#384C2311yescharacteristic
449#384C2311yescharacteristic
450#384C2311yescharacteristic
451#382C2311yescharacteristic
452#382C2311yescharacteristic
453#382C2311yescharacteristic
454#382C2311yescharacteristic
455#382C2311yescharacteristic
456#380—21no—
457#380—21no—
458#380—21no—
459#380—21no—
460#380C2311yescharacteristic
461#380C2311yescharacteristic
462#380C2311yescharacteristic
463#380C2311yescharacteristic
464C4×C4⋊C4—21no—
465C4×C4⋊C4—21no—
466C4×C4⋊C4—21no—
467C4×C4⋊C4C2311yescharacteristic
468C4×C4⋊C4C2311yescharacteristic
469C4×C4⋊C4C2311yescharacteristic
470C4×C4⋊C4C2311yescharacteristic
471C4×C4⋊C4C2311yescharacteristic
472C4×C22⋊C4—21no—
473C4×C22⋊C4—21no—
474C4×C22⋊C4C2311yescharacteristic
475C4×C22⋊C4C2311yescharacteristic
476#376C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#340C2311yescharacteristic
492#340C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C2×#41—44no—
500C2×#41—82no—
501C2×#41—82no—
502C22×Q8—21no—
503C22×Q8—21no—
504C22×Q8—21no—
505C22×Q8C2411yescharacteristic
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4C2×D411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C22×D4C2411yescharacteristic
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2×D411yescharacteristic
527C23×C4C2×D411yescharacteristic
528C23×C4C2411yescharacteristic
529C23×C4C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C4⋊Q8—22no—
539C4⋊Q8—22no—
540C4⋊Q8—22no—
541C4⋊Q8—41no—
542C4⋊Q8—41no—
543C4⋊Q8#4114yes—
544#127—22no—
545#127—22no—
546#127—22no—
547#127—22no—
548#127—41no—
549#127—41no—
550#127—82no—
551#126—44no—
552#125—41no—
553#125—41no—
554#125—82no—
555#124—22no—
556#124—22no—
557#124—22no—
558#124—22no—
559#124—44no—
560#124—41no—
561#124—41no—
562#124—44no—
563#123—44no—
564C22⋊Q8—22no—
565C22⋊Q8—41no—
566C22⋊Q8—44no—
567C22⋊Q8—41no—
568C22⋊Q8—41no—
569C22⋊Q8—82no—
570C22⋊Q8—82no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—41no—
575#121—41no—
576#121—41no—
577#121—44no—
578#121—41no—
579#121—41no—
580#121—41no—
581#121—41no—
582#121—41no—
583#121—41no—
584#121—82no—
585#121—82no—
586C4×Q8—22no—
587C4×Q8—41no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—22no—
591C4×D4—22no—
592C4×D4—22no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—44no—
597C4×D4—82no—
598#117—22no—
599#117—22no—
600#117—41no—
601#117—41no—
602#117—41no—
603#117—41no—
604#117—41no—
605#117—41no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
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⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C42—22no—
691C2×C42—22no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42C2×D411yescharacteristic
701C2×C42C2×D411yescharacteristic
702C2×C42C2411yescharacteristic
703C2×C42C2411yescharacteristic
704C2×C42C2411yescharacteristic
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707#107—22no—
708#107—22no—
709#107—41no—
710#107—41no—
711#107—41no—
712#107—41no—
713#106—22no—
714#106—22no—
715#106—22no—
716#106—22no—
717#106—22no—
718#106—22no—
719#106—41no—
720#106—41no—
721#106—41no—
722#106—41no—
723C4⋊C8—22no—
724C4⋊C8—22no—
725C4⋊C8—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729#103—22no—
730#103—22no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761C22⋊C8—22no—
762C22⋊C8—22no—
763C22⋊C8—22no—
764C22⋊C8—22no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768C22⋊C8—41no—
769#97—22no—
770#97—22no—
771#97—22no—
772#97—22no—
773C4×C8—22no—
774C4×C8—22no—
775C4×C8—22no—
776C4×C8—22no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815C24—21no—
816C24—21no—
817C24—21no—
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820#41—816no—
821C2×Q8—24no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—42no—
829C2×Q8—81no—
830C2×Q8—81no—
831C2×Q8—81no—
832C2×Q8—81no—
833C2×Q8—81no—
834C2×Q8—81no—
835C2×Q8—81no—
836C2×D4—22no—
837C2×D4—21no—
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—41no—
856C2×D4—41no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4—81no—
880C2×D4—81no—
881C2×D4—81no—
882C2×D4—81no—
883C2×D4—81no—
884C2×D4—81no—
885C2×D4—81no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—22no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—41no—
922C22×C4—41no—
923C22×C4—41no—
924C22×C4—42no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—81no—
930C22×C4—81no—
931C22×C4—81no—
932C22×C4—81no—
933C22×C4—81no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C22×D411yescharacteristic
941C22×C4C22×D411yescharacteristic
942C22×C4C22×D411yescharacteristic
943C22×C4C22×D411yescharacteristic
944C22×C4C22×D411yescharacteristic
945C22×C4C22×D411yescharacteristic
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C2511yescharacteristic
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8H(5,𝔽2)12yes—
972C2×C8H(5,𝔽2)12yes—
973C4⋊C4—22no—
974C4⋊C4—24no—
975C4⋊C4—22no—
976C4⋊C4—22no—
977C4⋊C4—22no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—41no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—42no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4—81no—
1023C4⋊C4—81no—
1024C4⋊C4—81no—
1025C4⋊C4—81no—
1026C4⋊C4—81no—
1027C4⋊C4C2×#4112yes—
1028C4⋊C4C2×#4112yes—
1029C22⋊C4—22no—
1030C22⋊C4—22no—
1031C22⋊C4—22no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—41no—
1035C22⋊C4—41no—
1036C22⋊C4—41no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—42no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C42—22no—
1068C42—22no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—42no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42—81no—
1081C42—81no—
1082C42—81no—
1083C42C2×#4112yes—
1084C42H(5,𝔽2)12yes—
1085C422−1+412yes—
1086C422−1+412yes—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—41no—
1121C23—41no—
1122C23C23×D411yescharacteristic
1123Q8—41no—
1124Q8—41no—
1125Q8—41no—
1126Q8—41no—
1127Q8—84no—
1128Q8—162no—
1129Q8—162no—
1130D4—41no—
1131D4—41no—
1132D4—41no—
1133D4—41no—
1134D4—41no—
1135D4—41no—
1136D4—41no—
1137D4—41no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—82no—
1143D4—84no—
1144D4—84no—
1145D4—84no—
1146D4—84no—
1147D4—84no—
1148D4—162no—
1149D4—162no—
1150D4—162no—
1151D4—162no—
1152D4—162no—
1153D4—162no—
1154D4—162no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—22no—
1180C2×C4—22no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—44no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—82no—
1235C2×C4—84no—
1236C2×C4—84no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4#53612yes—
1240C2×C4#53612yes—
1241C2×C4#54612yes—
1242C2×C4#54612yes—
1243C2×C4#57712yes—
1244C2×C4C22×#4111yescharacteristic
1245C2×C4C2×H(5,𝔽2)11yescharacteristic
1246C2×C4C2×H(5,𝔽2)11yescharacteristic
1247C2×C4C2×H(5,𝔽2)11yescharacteristic
1248C2×C4C2×2−1+411yescharacteristic
1249C2×C4C2×2−1+411yescharacteristic
1250C8—22no—
1251C8—22no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C22—41no—
1259C22—41no—
1260C22—41no—
1261C22—41no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22C2×#53611yescharacteristic
1294C22C2×#54611yescharacteristic
1295C22#349811yescharacteristic
1296C22C2×#57711yescharacteristic
1297C22#358411yescharacteristic
1298C22#358511yescharacteristic
1299C22#358511yescharacteristic
1300C4—22no—
1301C4—22no—
1302C4—22no—
1303C4—22no—
1304C4—22no—
1305C4—41no—
1306C4—42no—
1307C4—42no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4#352211yescharacteristic
1326C4#352211yescharacteristic
1327C4#354811yescharacteristic
1328C4#354811yescharacteristic
1329C2—81no—
1330C2—81no—
1331C2—161no—
1332C2—161no—
1333C2—161no—
1334C2#3895211yescharacteristic
1335C2#6087511yescharacteristic
1336C2#6089211yescharacteristic
1337C2#6118411yescharacteristic
1338C2#6118911yescharacteristic
1339C2#6243811yescharacteristic
1340C2#6244311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#37772C2
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. #37878C2semidirect
3. #33228C2semidirect
4. #30658C2semidirect
5. #30653C2semidirect
6. #30648C2semidirect
7. #30648C2semidirect
8. #30644C2semidirect
9. #30638C2semidirect
10. #30631C2semidirect
11. #30630C2semidirect
12. #29853C2semidirect
13. #29847C2semidirect
14. #29217C2semidirect
15. #28759C2semidirect
16. #27923C2semidirect
17. #27911C2semidirect
18. #26542C2semidirect
19. #26541C2semidirect
20. #26537C2semidirect
21. #26530C2semidirect
22. #26248C2semidirect
23. #26245C2semidirect
24. #26240C2semidirect
25. #26235C2semidirect
26. #25680C2semidirect
27. #25671C2semidirect
28. #21871C2semidirect
29. #21869C2semidirect
30. #21724C2semidirect
31. #21273C2semidirect

Maximal subgroups

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

subgroupindex
#378782
#377722
#332282
#306582
#306532
#306482
#306442
#306382
#306312
#306302
#298532
#298472
#292172
#287592
#279232
#279112
#265422
#265412
#265372
#265302
#262482
#262452
#262402
#262352
#256802
#256712
#218712
#218692
#217242
#212732