Finite Group Databasebeta

← #7019550

Subgroups — #7019550

Order 512.

1735 conjugacy classes of subgroups.

The subgroup lattice has 1423 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45125C211yesmaximal, characteristic, complemented
2#45103C211yesmaximal, characteristic
3#32044C211yesmaximal, characteristic, complemented
4#31782C211yesmaximal, characteristic, complemented
5#31676C211yesmaximal, characteristic, complemented
6#31344C211yesmaximal, characteristic, complemented
7#31311C211yesmaximal, characteristic, complemented
8#31297C211yesmaximal, characteristic, complemented
9#31130C211yesmaximal, characteristic, complemented
10#30637C211yesmaximal, characteristic, complemented
11#27398C211yesmaximal, characteristic, complemented
12#27398C211yesmaximal, characteristic, complemented
13#27272C211yesmaximal, characteristic, complemented
14#27110C211yesmaximal, characteristic, complemented
15#27033C211yesmaximal, characteristic, complemented
16#26348C211yesmaximal, characteristic, complemented
17#26249C211yesmaximal, characteristic, complemented
18#26138C211yesmaximal, characteristic, complemented
19#25890C211yesmaximal, characteristic, complemented
20#25261C211yesmaximal, characteristic, complemented
21#24882C211yesmaximal, characteristic, complemented
22#24485C211yesmaximal, characteristic, complemented
23#24050C211yesmaximal, characteristic, complemented
24#24037C211yesmaximal, characteristic, complemented
25#24017C211yesmaximal, characteristic, complemented
26#24011C211yesmaximal, characteristic, complemented
27#23489C211yesmaximal, characteristic, complemented
28#22926C211yesmaximal, characteristic, complemented
29#22427C211yesmaximal, characteristic, complemented
30#22039C211yesmaximal, characteristic, complemented
31#21772C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#546C2211yescharacteristic
34C2×#537C2211yescharacteristic
35C2×#537C2211yescharacteristic
36C2×#488C2211yescharacteristic
37C2×#484C2211yescharacteristic, complemented
38C2×#485C2211yescharacteristic
39C2×#485C2211yescharacteristic, complemented
40C2×#482C2211yescharacteristic
41C2×#480C2211yescharacteristic
42C2×#478C2211yescharacteristic
43C2×#436C2211yescharacteristic
44C22×#106C2211yescharacteristic, complemented
45C2×#417C2211yescharacteristic
46C2×#418C2211yescharacteristic
47C2×#416C2211yescharacteristic
48C2×#408C2211yescharacteristic, complemented
49#2778—21no—
50#2762—21no—
51#2756—21no—
52#2753—21no—
53#2680—21no—
54#2671—21no—
55#2671—21no—
56#2668—21no—
57#2597—21no—
58#2578—21no—
59#2562C2211yescharacteristic
60#2542C2211yescharacteristic
61#2537—21no—
62#2532—21no—
63#2531—21no—
64#2495C2211yescharacteristic, complemented
65#2494C2211yescharacteristic, complemented
66#2485C2211yescharacteristic
67#2485C2211yescharacteristic
68#2485C2211yescharacteristic
69#2442C2211yescharacteristic, complemented
70#2442C2211yescharacteristic, complemented
71#2437—21no—
72#2432C2211yescharacteristic
73#2432C2211yescharacteristic
74#2427C2211yescharacteristic
75#2427C2211yescharacteristic
76#2424—21no—
77#2424—21no—
78#2417C2211yescharacteristic
79#2417C2211yescharacteristic
80#2408C2211yescharacteristic
81#2388C2211yescharacteristic
82#2361C2211yescharacteristic
83#2361C2211yescharacteristic
84#2352C2211yescharacteristic
85#2352C2211yescharacteristic
86#2347C2211yescharacteristic, complemented
87#2346C2211yescharacteristic, complemented
88#2311C2211yescharacteristic, complemented
89#2311C2211yescharacteristic, complemented
90#2097C2211yescharacteristic, complemented
91#2092C2211yescharacteristic
92#2088C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2077C2211yescharacteristic
96#2075C2211yescharacteristic
97#2073C2211yescharacteristic
98#2068C2211yescharacteristic, complemented
99#2068C2211yescharacteristic, complemented
100#2067C2211yescharacteristic
101#2065C2211yescharacteristic
102#2059C2211yescharacteristic, complemented
103#2043C2211yescharacteristic, complemented
104#2043C2211yescharacteristic, complemented
105#2042C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2036C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic, complemented
112#2036C2211yescharacteristic, complemented
113#2036C2211yescharacteristic, complemented
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic
116#2035C2211yescharacteristic, complemented
117#2035C2211yescharacteristic, complemented
118#2035C2211yescharacteristic, complemented
119#2035C2211yescharacteristic, complemented
120#2035C2211yescharacteristic, complemented
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2033C2211yescharacteristic
129#2026C2211yescharacteristic, complemented
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1981C2211yescharacteristic, complemented
133#1960C2211yescharacteristic, complemented
134#1958C2211yescharacteristic
135#1955C2211yescharacteristic
136#1954C2211yescharacteristic
137#1949C2211yescharacteristic, complemented
138#1942C2211yescharacteristic, complemented
139#1942C2211yescharacteristic, complemented
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1933C2211yescharacteristic, complemented
143#1933C2211yescharacteristic, complemented
144#1927C2211yescharacteristic, complemented
145#1927C2211yescharacteristic, complemented
146#1926C2211yescharacteristic
147#1925C2211yescharacteristic
148#1924C2211yescharacteristic, complemented
149#1923C2211yescharacteristic, complemented
150#1923C2211yescharacteristic, complemented
151#1923C2211yescharacteristic, complemented
152#1921C2211yescharacteristic, complemented
153#1919C2211yescharacteristic, complemented
154#1919C2211yescharacteristic, complemented
155#1919C2211yescharacteristic, complemented
156#1895C2211yescharacteristic
157#1894C2211yescharacteristic
158#1894C2211yescharacteristic
159#1894C2211yescharacteristic, complemented
160#1893C2211yescharacteristic
161#1892C2211yescharacteristic, complemented
162#1875C2211yescharacteristic
163#1875C2211yescharacteristic
164#1874C2211yescharacteristic
165#1874C2211yescharacteristic
166#1873C2211yescharacteristic
167#1873C2211yescharacteristic, complemented
168#1873C2211yescharacteristic, complemented
169#1872C2211yescharacteristic, complemented
170#1872C2211yescharacteristic, complemented
171#1870C2211yescharacteristic
172#1870C2211yescharacteristic
173#1869C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1854C2211yescharacteristic
179#1853C2211yescharacteristic, complemented
180#1852C2211yescharacteristic, complemented
181#1852C2211yescharacteristic, complemented
182#1852C2211yescharacteristic, complemented
183#1850C2211yescharacteristic, complemented
184#1824C2211yescharacteristic, complemented
185#1823C2211yescharacteristic, complemented
186#1809C2211yescharacteristic
187#1804C2211yescharacteristic
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1788C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1780C2211yescharacteristic, complemented
198#1776C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201#1753C2211yescharacteristic, complemented
202#1736C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C22×#41C2311yescharacteristic
206C23×D4C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210#546—24no—
211#546—42no—
212#546—42no—
213#546—42no—
214#537—24no—
215#537—42no—
216#537—42no—
217#537—42no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#123—21no—
223C2×#123—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×C22⋊Q8C2311yescharacteristic
232C2×#121—21no—
233C2×#121—21no—
234C2×#121—21no—
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×#121—21no—
239C2×#121—21no—
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#120—21no—
245C2×#120—21no—
246C2×#120—21no—
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C2×#117C2311yescharacteristic
257C22×C4⋊C4C2311yescharacteristic
258C22×C4⋊C4C2311yescharacteristic
259C22×C4⋊C4C2311yescharacteristic
260C22×C4⋊C4C2311yescharacteristic
261C22×C22⋊C4—21no—
262C22×C22⋊C4—21no—
263#488—42no—
264#485—42no—
265#485—42no—
266#484—42no—
267#482—24no—
268#480—42no—
269#478—42no—
270#436—42no—
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#107C2311yescharacteristic
275C2×#107C2311yescharacteristic
276C2×#107C2311yescharacteristic
277C2×#106—42no—
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287#418—42no—
288#417—42no—
289#416—42no—
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
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
322#408—42no—
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×C22⋊C8C2311yescharacteristic
332C2×C22⋊C8C2311yescharacteristic
333C2×C22⋊C8C2311yescharacteristic
334C2×C22⋊C8C2311yescharacteristic
335C2×C22⋊C8C2311yescharacteristic
336C2×#97C2311yescharacteristic
337C2×C4×C8C2311yescharacteristic
338C2×C4×C8C2311yescharacteristic
339#401—21no—
340#400—21no—
341#400—21no—
342#400—21no—
343#400—21no—
344#399—21no—
345#399—21no—
346#398—21no—
347#398—21no—
348#398—21no—
349#398—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#397—21no—
357#396—21no—
358#396—21no—
359#395D411yescharacteristic
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394—21no—
371#394D411yescharacteristic
372#394D411yescharacteristic
373#394D411yescharacteristic
374#393D411yescharacteristic
375#392—21no—
376#392D411yescharacteristic
377#392D411yescharacteristic
378#392D411yescharacteristic
379#391—21no—
380#391—21no—
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#390—21no—
384#390—21no—
385#390—21no—
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#386—21no—
418#386—21no—
419#386—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#385—21no—
437#384—21no—
438#383—21no—
439#383—21no—
440#382—21no—
441#382C2311yescharacteristic
442#382C2311yescharacteristic
443#380—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380—21no—
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#380C2311yescharacteristic
460#380C2311yescharacteristic
461#379—21no—
462C4×C4⋊C4—21no—
463C4×C4⋊C4C2311yescharacteristic
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C22⋊C4—21no—
468C4×C22⋊C4—21no—
469C4×C22⋊C4C2311yescharacteristic
470C4×C22⋊C4C2311yescharacteristic
471C4×C22⋊C4C2311yescharacteristic
472#376—21no—
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
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
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—22no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C2×#41—41no—
513C2×#41—41no—
514C2×#41—41no—
515C2×#41—41no—
516C2×#41—41no—
517C2×#41—41no—
518C22×Q8C2×D411yescharacteristic
519C22×Q8C2411yescharacteristic
520C22×Q8C2411yescharacteristic
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—22no—
525C22×D4—21no—
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—41no—
531C22×D4—41no—
532C22×D4—41no—
533C22×D4—41no—
534C22×D4C2×D411yescharacteristic
535C22×D4C2×D411yescharacteristic
536C22×D4C2×D411yescharacteristic
537C22×D4C2×D411yescharacteristic
538C22×D4C2×D411yescharacteristic
539C22×D4C2×D411yescharacteristic
540C22×D4C2411yescharacteristic
541C22×D4C2411yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4—21no—
547C23×C4—21no—
548C23×C4—21no—
549C23×C4—21no—
550C23×C4C2411yescharacteristic
551C23×C4C2411yescharacteristic
552C23×C4C2411yescharacteristic
553C23×C4C2411yescharacteristic
554C2×M16—22no—
555C2×M16—41no—
556C2×M16—41no—
557C2×M16—41no—
558C2×M16—41no—
559C2×M16—41no—
560C22×C8—22no—
561C22×C8—41no—
562C22×C8—41no—
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C4⋊Q8—41no—
572C4⋊Q8—41no—
573#125—41no—
574#125—41no—
575#124—22no—
576#124—22no—
577#124—41no—
578#124—41no—
579#123—44no—
580#123—44no—
581C22⋊Q8—22no—
582C22⋊Q8—22no—
583C22⋊Q8—22no—
584C22⋊Q8—22no—
585C22⋊Q8—22no—
586C22⋊Q8—22no—
587C22⋊Q8—44no—
588C22⋊Q8—44no—
589C22⋊Q8—41no—
590C22⋊Q8—41no—
591C22⋊Q8—41no—
592C22⋊Q8—41no—
593C22⋊Q8—41no—
594C22⋊Q8—41no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—44no—
601#121—44no—
602#121—44no—
603#121—41no—
604#121—41no—
605#121—44no—
606#121—44no—
607#121—44no—
608#121—44no—
609#121—44no—
610#121#4114yes—
611#120—44no—
612#120—44no—
613#120—82no—
614C4×D4—22no—
615C4×D4—22no—
616C4×D4—22no—
617C4×D4—22no—
618C4×D4—41no—
619C4×D4—41no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—41no—
624C4×D4—82no—
625C4×D4—82no—
626#117—22no—
627#117—22no—
628#117—41no—
629#117—41no—
630#117—41no—
631#117—41no—
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—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—41no—
657C2×C4⋊C4—41no—
658C2×C4⋊C4—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4—41no—
661C2×C4⋊C4—41no—
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—44no—
713C2×C22⋊C4—44no—
714C2×C22⋊C4C2×D411yescharacteristic
715C2×C22⋊C4C2×D411yescharacteristic
716C2×C22⋊C4C2×D411yescharacteristic
717C2×C22⋊C4C2×D411yescharacteristic
718C2×C22⋊C4C2×D411yescharacteristic
719C2×C22⋊C4C2×D411yescharacteristic
720C2×C22⋊C4C2×D411yescharacteristic
721C2×C22⋊C4C2×D411yescharacteristic
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C42—21no—
727C2×C42—21no—
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42—21no—
733C2×C42C2411yescharacteristic
734C2×C42C2411yescharacteristic
735C2×C42C2411yescharacteristic
736#107—22no—
737#107—22no—
738#107—22no—
739#107—41no—
740#107—41no—
741#107—41no—
742#106—22no—
743#106—22no—
744#106—22no—
745#106—41no—
746#106—41no—
747#106—41no—
748C4⋊C8—41no—
749C4⋊C8—41no—
750C4⋊C8—41no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#103—41no—
764#103—41no—
765#103—41no—
766#103—41no—
767#102—22no—
768#102—22no—
769#102—22no—
770#102—22no—
771#102—22no—
772#102—22no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782#102—41no—
783C22⋊C8—22no—
784C22⋊C8—22no—
785C22⋊C8—41no—
786C22⋊C8—41no—
787C22⋊C8—41no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791C22⋊C8—41no—
792C22⋊C8—41no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795C22⋊C8—41no—
796#97—41no—
797C4×C8—41no—
798C4×C8—41no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837C24—21no—
838C24—21no—
839C24—42no—
840C24—42no—
841C24—42no—
842C24—81no—
843C24—81no—
844C24—81no—
845C24—81no—
846C24C22×D411yescharacteristic
847C24C22×D411yescharacteristic
848C24C22×D411yescharacteristic
849C24C22×D411yescharacteristic
850#41—44no—
851#41—44no—
852#41—82no—
853#41—82no—
854#41—82no—
855#41—82no—
856#41—82no—
857#41—82no—
858#41—82no—
859#41—82no—
860#41—82no—
861#41—82no—
862C2×Q8—22no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—21no—
873C2×Q8—21no—
874C2×Q8—21no—
875C2×Q8—41no—
876C2×Q8—41no—
877C2×D4—24no—
878C2×D4—22no—
879C2×D4—24no—
880C2×D4—22no—
881C2×D4—22no—
882C2×D4—22no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—41no—
894C2×D4—41no—
895C2×D4—41no—
896C2×D4—41no—
897C2×D4—41no—
898C2×D4—41no—
899C2×D4—41no—
900C2×D4—41no—
901C2×D4—41no—
902C2×D4—41no—
903C2×D4—41no—
904C2×D4—41no—
905C2×D4—41no—
906C2×D4—41no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—44no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—42no—
914C2×D4—42no—
915C2×D4—42no—
916C2×D4—81no—
917C2×D4—82no—
918C2×D4—82no—
919C2×D4—82no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4C2×#4112yes—
931C2×D4H(5,𝔽2)12yes—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—42no—
971C22×C4—42no—
972C22×C4—42no—
973C22×C4—42no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C22×D411yescharacteristic
1002C22×C4C2×#4112yes—
1003C22×C4H(5,𝔽2)12yes—
1004C22×C4C2511yescharacteristic
1005M16—82no—
1006M16—82no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—44no—
1032C4⋊C4—22no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—21no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—42no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4C2×#4112yes—
1080C4⋊C4H(5,𝔽2)12yes—
1081C22⋊C4—24no—
1082C22⋊C4—22no—
1083C22⋊C4—24no—
1084C22⋊C4—22no—
1085C22⋊C4—41no—
1086C22⋊C4—41no—
1087C22⋊C4—41no—
1088C22⋊C4—41no—
1089C22⋊C4—41no—
1090C22⋊C4—41no—
1091C22⋊C4—41no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—42no—
1111C22⋊C4—42no—
1112C22⋊C4—42no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C42—21no—
1129C42—21no—
1130C42—21no—
1131C42—21no—
1132C42—21no—
1133C42—21no—
1134C42—42no—
1135C42—42no—
1136C42—42no—
1137C42—81no—
1138C42—81no—
1139C42—81no—
1140C42—81no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
1145C23—21no—
1146C23—21no—
1147C23—21no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—21no—
1157C23—21no—
1158C23—21no—
1159C23—22no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—22no—
1164C23—21no—
1165C23—21no—
1166C23—21no—
1167C23—21no—
1168C23—21no—
1169C23—21no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—84no—
1183C23—84no—
1184C23—84no—
1185C23—162no—
1186C23—162no—
1187C23—162no—
1188C23—162no—
1189C23#54612yes—
1190C23C23×D411yescharacteristic
1191Q8—41no—
1192Q8—41no—
1193Q8—41no—
1194Q8—41no—
1195Q8—41no—
1196Q8—41no—
1197Q8—41no—
1198Q8—41no—
1199Q8—82no—
1200D4—22no—
1201D4—22no—
1202D4—22no—
1203D4—22no—
1204D4—41no—
1205D4—41no—
1206D4—41no—
1207D4—41no—
1208D4—82no—
1209D4—82no—
1210D4—82no—
1211D4—82no—
1212D4—84no—
1213D4—84no—
1214D4—82no—
1215D4—82no—
1216D4—84no—
1217D4—84no—
1218D4—84no—
1219D4—162no—
1220D4—162no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—22no—
1224C2×C4—22no—
1225C2×C4—22no—
1226C2×C4—22no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—22no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—21no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—22no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—84no—
1309C2×C4—84no—
1310C2×C4—162no—
1311C2×C4—162no—
1312C2×C4—162no—
1313C2×C4—162no—
1314C2×C4—162no—
1315C2×C4—162no—
1316C2×C4#54612yes—
1317C2×C4C22×#4111yescharacteristic
1318C2×C4C2×H(5,𝔽2)11yescharacteristic
1319C2×C4C2×H(5,𝔽2)11yescharacteristic
1320C2×C4C2×H(5,𝔽2)11yescharacteristic
1321C2×C4#58511yescharacteristic
1322C2×C4#58511yescharacteristic
1323C8—41no—
1324C8—41no—
1325C8—41no—
1326C8—41no—
1327C8—41no—
1328C8—41no—
1329C8—41no—
1330C8—41no—
1331C22—22no—
1332C22—22no—
1333C22—22no—
1334C22—41no—
1335C22—41no—
1336C22—41no—
1337C22—41no—
1338C22—41no—
1339C22—41no—
1340C22—41no—
1341C22—42no—
1342C22—41no—
1343C22—42no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—41no—
1348C22—41no—
1349C22—41no—
1350C22—41no—
1351C22—41no—
1352C22—42no—
1353C22—42no—
1354C22—41no—
1355C22—41no—
1356C22—41no—
1357C22—41no—
1358C22—41no—
1359C22—41no—
1360C22—42no—
1361C22—41no—
1362C22—41no—
1363C22—42no—
1364C22—41no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—168no—
1374C22C2×#54611yescharacteristic
1375C22#348411yescharacteristic
1376C22#348511yescharacteristic
1377C22#358411yescharacteristic
1378C22#358411yescharacteristic
1379C22#358511yescharacteristic
1380C22#358611yescharacteristic
1381C4—22no—
1382C4—41no—
1383C4—41no—
1384C4—42no—
1385C4—41no—
1386C4—41no—
1387C4—41no—
1388C4—41no—
1389C4—41no—
1390C4—41no—
1391C4—41no—
1392C4—42no—
1393C4—81no—
1394C4—81no—
1395C4—81no—
1396C4—81no—
1397C4—81no—
1398C4—81no—
1399C4—81no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4—81no—
1405C4#351311yescharacteristic
1406C4#351411yescharacteristic
1407C4#353411yescharacteristic
1408C4#354211yescharacteristic
1409C2—42no—
1410C2—81no—
1411C2—81no—
1412C2—81no—
1413C2—82no—
1414C2—82no—
1415C2#4309411yescharacteristic
1416C2#6119811yescharacteristic
1417C2#6120111yescharacteristic
1418C2#6162711yescharacteristic
1419C2#6167811yescharacteristic
1420C2#6177711yescharacteristic
1421C2#6179011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#45103C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2388 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45125C2semidirect
3. #32044C2semidirect
4. #31782C2semidirect
5. #31676C2semidirect
6. #31344C2semidirect
7. #31311C2semidirect
8. #31297C2semidirect
9. #31130C2semidirect
10. #30637C2semidirect
11. #27398C2semidirect
12. #27398C2semidirect
13. #27272C2semidirect
14. #27110C2semidirect
15. #27033C2semidirect
16. #26348C2semidirect
17. #26249C2semidirect
18. #26138C2semidirect
19. #25890C2semidirect
20. #25261C2semidirect
21. #24882C2semidirect
22. #24485C2semidirect
23. #24050C2semidirect
24. #24037C2semidirect
25. #24017C2semidirect
26. #24011C2semidirect
27. #23489C2semidirect
28. #22926C2semidirect
29. #22427C2semidirect
30. #22039C2semidirect
31. #21772C2semidirect
37. C2×#484C22semidirect
39. C2×#485C22semidirect
44. C22×#106C22semidirect
48. C2×#408C22semidirect
64. #2495C22semidirect
65. #2494C22semidirect
69. #2442C22semidirect
70. #2442C22semidirect
86. #2347C22semidirect
87. #2346C22semidirect
88. #2311C22semidirect
89. #2311C22semidirect
90. #2097C22semidirect
92. #2088C22semidirect
93. #2088C22semidirect
94. #2085C22semidirect
98. #2068C22semidirect
99. #2068C22semidirect
102. #2059C22semidirect
103. #2043C22semidirect
104. #2043C22semidirect
111. #2036C22semidirect
112. #2036C22semidirect
113. #2036C22semidirect
116. #2035C22semidirect
117. #2035C22semidirect
118. #2035C22semidirect
119. #2035C22semidirect
120. #2035C22semidirect
129. #2026C22semidirect
132. #1981C22semidirect
133. #1960C22semidirect
137. #1949C22semidirect
138. #1942C22semidirect
139. #1942C22semidirect
142. #1933C22semidirect
143. #1933C22semidirect
144. #1927C22semidirect
145. #1927C22semidirect
148. #1924C22semidirect
149. #1923C22semidirect
150. #1923C22semidirect
151. #1923C22semidirect
152. #1921C22semidirect
153. #1919C22semidirect
154. #1919C22semidirect
155. #1919C22semidirect
159. #1894C22semidirect
161. #1892C22semidirect
167. #1873C22semidirect
168. #1873C22semidirect
169. #1872C22semidirect
170. #1872C22semidirect
179. #1853C22semidirect
180. #1852C22semidirect
181. #1852C22semidirect
182. #1852C22semidirect
183. #1850C22semidirect
184. #1824C22semidirect
185. #1823C22semidirect
197. #1780C22semidirect
198. #1776C22semidirect
201. #1753C22semidirect
202. #1736C22semidirect

Maximal subgroups

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

subgroupindex
#451252
#451032
#320442
#317822
#316762
#313442
#313112
#312972
#311302
#306372
#273982
#272722
#271102
#270332
#263482
#262492
#261382
#258902
#252612
#248822
#244852
#240502
#240372
#240172
#240112
#234892
#229262
#224272
#220392
#217722