Finite Group Databasebeta

← #6795122

Subgroups — #6795122

Order 512.

1465 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37987C211yesmaximal, characteristic, complemented
2#35620C211yesmaximal, characteristic, complemented
3#32968C211yesmaximal, characteristic, complemented
4#32447C211yesmaximal, characteristic, complemented
5#32441C211yesmaximal, characteristic, complemented
6#32440C211yesmaximal, characteristic, complemented
7#32437C211yesmaximal, characteristic, complemented
8#32371C211yesmaximal, characteristic, complemented
9#32356C211yesmaximal, characteristic, complemented
10#32355C211yesmaximal, characteristic, complemented
11#32345C211yesmaximal, characteristic, complemented
12#29916C211yesmaximal, characteristic, complemented
13#29912C211yesmaximal, characteristic, complemented
14#28547C211yesmaximal, characteristic, complemented
15#28534C211yesmaximal, characteristic, complemented
16#27743C211yesmaximal, characteristic, complemented
17#27730C211yesmaximal, characteristic, complemented
18#27597C211yesmaximal, characteristic, complemented
19#27590C211yesmaximal, characteristic, complemented
20#25822C211yesmaximal, characteristic, complemented
21#25466C211yesmaximal, characteristic, complemented
22#25460C211yesmaximal, characteristic, complemented
23#24690C211yesmaximal, characteristic, complemented
24#24677C211yesmaximal, characteristic, complemented
25#24513C211yesmaximal, characteristic
26#24504C211yesmaximal, characteristic
27#24309C211yesmaximal, characteristic, complemented
28#22604C211yesmaximal, characteristic, complemented
29#21991C211yesmaximal, characteristic, complemented
30#21983C211yesmaximal, characteristic, complemented
31#21460C211yesmaximal, characteristic
32C2×#544C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#499C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#478C2211yescharacteristic
38C2×#478C2211yescharacteristic
39C2×#476C2211yescharacteristic
40C2×#449C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×C4×D8C2211yescharacteristic
43C2×#433C2211yescharacteristic
44C2×#431C2211yescharacteristic
45#2854C2211yescharacteristic
46#2777—21no—
47#2770—21no—
48#2761—21no—
49#2750—21no—
50#2629C2211yescharacteristic
51#2624C2211yescharacteristic
52#2611—21no—
53#2571C2211yescharacteristic
54#2568C2211yescharacteristic
55#2568C2211yescharacteristic
56#2566C2211yescharacteristic
57#2566C2211yescharacteristic
58#2566C2211yescharacteristic
59#2565C2211yescharacteristic
60#2565C2211yescharacteristic
61#2563C2211yescharacteristic
62#2563C2211yescharacteristic
63#2558—21no—
64#2529—21no—
65#2513C2211yescharacteristic
66#2513C2211yescharacteristic
67#2509C2211yescharacteristic
68#2506C2211yescharacteristic
69#2470—21no—
70#2450—21no—
71#2450—21no—
72#2450—21no—
73#2450—21no—
74#2442—21no—
75#2442—21no—
76#2439—21no—
77#2439—21no—
78#2370C2211yescharacteristic
79#2354C2211yescharacteristic
80#2324C2211yescharacteristic
81#2317C2211yescharacteristic
82#2314C2211yescharacteristic
83#2311C2211yescharacteristic
84#2297C2211yescharacteristic
85#2296C2211yescharacteristic
86#2283C2211yescharacteristic
87C2×#382C2211yescharacteristic
88#2101C2211yescharacteristic
89#2101C2211yescharacteristic
90#2101C2211yescharacteristic
91#2099C2211yescharacteristic
92#2097C2211yescharacteristic
93#2096C2211yescharacteristic
94#2094C2211yescharacteristic
95#2094C2211yescharacteristic
96#2092C2211yescharacteristic
97#2092C2211yescharacteristic
98#2092C2211yescharacteristic
99#2092C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2084C2211yescharacteristic
104#2074C2211yescharacteristic
105#2074C2211yescharacteristic
106#2073C2211yescharacteristic
107#2073C2211yescharacteristic
108#2073C2211yescharacteristic
109#2073C2211yescharacteristic
110#2073C2211yescharacteristic
111#2071C2211yescharacteristic
112#2068C2211yescharacteristic
113#2068C2211yescharacteristic
114#2067C2211yescharacteristic
115#2065C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2058C2211yescharacteristic
120#2058C2211yescharacteristic
121#2057C2211yescharacteristic
122#2055C2211yescharacteristic
123#2055C2211yescharacteristic
124#2054C2211yescharacteristic
125#2054C2211yescharacteristic
126#2025C2211yescharacteristic
127#2023C2211yescharacteristic
128#1992C2211yescharacteristic
129#1990C2211yescharacteristic
130#1989C2211yescharacteristic
131#1988C2211yescharacteristic
132#1973C2211yescharacteristic
133#1970C2211yescharacteristic
134#1970C2211yescharacteristic
135#1968C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1949C2211yescharacteristic
141#1949C2211yescharacteristic
142#1947C2211yescharacteristic
143#1947C2211yescharacteristic
144#1940C2211yescharacteristic
145#1939C2211yescharacteristic
146#1936C2211yescharacteristic
147#1934C2211yescharacteristic
148#1933C2211yescharacteristic
149#1933C2211yescharacteristic
150#1928C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1927C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1925C2211yescharacteristic
158#1917C2211yescharacteristic
159#1916C2211yescharacteristic
160#1916C2211yescharacteristic
161#1916C2211yescharacteristic
162#1880C2211yescharacteristic
163#1879C2211yescharacteristic
164#1875C2211yescharacteristic
165#1874C2211yescharacteristic
166#1874C2211yescharacteristic
167#1865C2211yescharacteristic
168#1864C2211yescharacteristic
169#1863C2211yescharacteristic
170#1863C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1854C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1853C2211yescharacteristic
177#1853C2211yescharacteristic
178#1853C2211yescharacteristic
179#1852C2211yescharacteristic
180#1852C2211yescharacteristic
181#1852C2211yescharacteristic
182#1847C2211yescharacteristic
183#1846C2211yescharacteristic
184#1846C2211yescharacteristic
185#1845C2211yescharacteristic
186#1836C2211yescharacteristic
187#1835C2211yescharacteristic
188#1835C2211yescharacteristic
189#1835C2211yescharacteristic
190#1818C2211yescharacteristic
191#1817C2211yescharacteristic
192#1803C2211yescharacteristic
193#1802C2211yescharacteristic
194#1798C2211yescharacteristic
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic
197#1788C2211yescharacteristic
198#1771C2211yescharacteristic
199C8×C4⋊C4C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#103C2211yescharacteristic
202#1750C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×D8C2311yescharacteristic
206#544—42no—
207#544—42no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#125—21no—
212C2×#125—21no—
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#123—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×#121C2311yescharacteristic
220#520—42no—
221#520—42no—
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4—21no—
225C2×C4×D4—21no—
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×#117—21no—
230C2×#117—21no—
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C22×C4⋊C4—21no—
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C42C2311yescharacteristic
238#501—42no—
239#499—42no—
240#479—42no—
241#478—42no—
242#478—42no—
243#476—42no—
244#449—24no—
245#440—42no—
246C4×D8—42no—
247#433—24no—
248#431—24no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#399—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#394—21no—
334#394—21no—
335#393—21no—
336#393—21no—
337#393—21no—
338#393—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#390—21no—
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389D411yescharacteristic
363#389D411yescharacteristic
364#389D411yescharacteristic
365#389D411yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385D411yescharacteristic
410#385D411yescharacteristic
411#385D411yescharacteristic
412#385D411yescharacteristic
413#384C2311yescharacteristic
414#384C2311yescharacteristic
415#384C2311yescharacteristic
416#384C2311yescharacteristic
417#383—21no—
418#382—21no—
419#382—21no—
420#382—21no—
421#382C2311yescharacteristic
422#382C2311yescharacteristic
423#382C2311yescharacteristic
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#381—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441C4×C4⋊C4—21no—
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454#376—21no—
455C2×#95—21no—
456C2×#95—21no—
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C2×#41—22no—
494C2×#41—22no—
495C2×#41—22no—
496C2×#41—22no—
497C2×#41—41no—
498C2×#41—41no—
499C22×Q8—21no—
500C22×Q8—21no—
501C22×Q8C2411yescharacteristic
502C22×D4—21no—
503C22×D4—21no—
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2411yescharacteristic
515C2×SD16—22no—
516C2×SD16—22no—
517C2×SD16—41no—
518C2×D8—22no—
519C2×D8—22no—
520C2×D8—41no—
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C4⋊Q8—22no—
530C4⋊Q8—22no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533C4⋊Q8—44no—
534#125—22no—
535#125—22no—
536#125—22no—
537#125—22no—
538#125—41no—
539#125—41no—
540#125—44no—
541#125—82no—
542#123—82no—
543C22⋊Q8—44no—
544C22⋊Q8—44no—
545#121—22no—
546#121—22no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—41no—
556C4×D4—41no—
557C4×D4—44no—
558C4×D4—44no—
559#117—22no—
560#117—22no—
561#117—22no—
562#117—22no—
563#117—41no—
564#117—41no—
565#117—44no—
566#117—82no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—44no—
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C42—22no—
655C2×C42—22no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42C2×D411yescharacteristic
665C2×C42C2×D411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669C2×C42C2411yescharacteristic
670C2×C42C2411yescharacteristic
671C2×C42C2411yescharacteristic
672#107—41no—
673#107—41no—
674#107—41no—
675#107—41no—
676#107—41no—
677#107—41no—
678#107—41no—
679#107—41no—
680#107—41no—
681#106—41no—
682#106—41no—
683#106—41no—
684#106—41no—
685#106—41no—
686#106—41no—
687#106—41no—
688#106—41no—
689#106—41no—
690C4⋊C8—22no—
691C4⋊C8—22no—
692C4⋊C8—22no—
693C4⋊C8—22no—
694C4⋊C8—22no—
695C4⋊C8—22no—
696#103—22no—
697#103—22no—
698#103—22no—
699#103—22no—
700#103—41no—
701#103—41no—
702#103—41no—
703#102—22no—
704#102—22no—
705#102—22no—
706#102—22no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102—41no—
716C22⋊C8—22no—
717C22⋊C8—22no—
718C22⋊C8—22no—
719C22⋊C8#4114yes—
720#97—22no—
721#97—22no—
722C4×C8—22no—
723C4×C8—22no—
724C4×C8—22no—
725C4×C8—22no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775C24—21no—
776C24—21no—
777C24C22×D411yescharacteristic
778#41—44no—
779#41—44no—
780#41—44no—
781#41—44no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—42no—
788C2×Q8—42no—
789C2×Q8—81no—
790C2×Q8—81no—
791C2×Q8—81no—
792C2×Q8—81no—
793C2×Q82−1+412yes—
794C2×D4—24no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D42−1+412yes—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—24no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—41no—
834C22×C4—41no—
835C22×C4—41no—
836C22×C4—41no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C2×#4112yes—
868C22×C42−1+412yes—
869C22×C4C2511yescharacteristic
870SD16—44no—
871D8—44no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8C2×#4112yes—
895C2×C8C2×#4112yes—
896C4⋊C4—22no—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—22no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—41no—
927C4⋊C4—41no—
928C4⋊C4—41no—
929C4⋊C4—41no—
930C4⋊C4—41no—
931C4⋊C4—41no—
932C4⋊C4—41no—
933C4⋊C4—41no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C22⋊C4—22no—
962C22⋊C4—22no—
963C22⋊C4—22no—
964C22⋊C4—22no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
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—
991C42—22no—
992C42—22no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—42no—
1004C42—42no—
1005C42—42no—
1006C42—42no—
1007C42—81no—
1008C42—81no—
1009C42—81no—
1010C42—81no—
1011C42H(5,𝔽2)12yes—
1012C42H(5,𝔽2)12yes—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—21no—
1019C23—22no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23#54712yes—
1034C23C23×D411yescharacteristic
1035Q8—22no—
1036Q8—22no—
1037Q8—41no—
1038Q8—41no—
1039Q8—162no—
1040Q8—162no—
1041D4—22no—
1042D4—22no—
1043D4—48no—
1044D4—41no—
1045D4—41no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—162no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—22no—
1058C2×C4—22no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—22no—
1092C2×C4—48no—
1093C2×C4—44no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—84no—
1136C2×C4—82no—
1137C2×C4—162no—
1138C2×C4—162no—
1139C2×C4—162no—
1140C2×C4—162no—
1141C2×C4#53512yes—
1142C2×C4#53512yes—
1143C2×C4#54712yes—
1144C2×C4C22×#4111yescharacteristic
1145C2×C4C2×H(5,𝔽2)11yescharacteristic
1146C2×C4C2×H(5,𝔽2)11yescharacteristic
1147C2×C4C2×2−1+411yescharacteristic
1148C2×C4C2×2−1+411yescharacteristic
1149C2×C4C2×2−1+411yescharacteristic
1150C8—22no—
1151C8—22no—
1152C8—41no—
1153C8—41no—
1154C8—41no—
1155C8—41no—
1156C8—41no—
1157C8—41no—
1158C22—22no—
1159C22—22no—
1160C22—22no—
1161C22—41no—
1162C22—41no—
1163C22—41no—
1164C22—41no—
1165C22—42no—
1166C22—42no—
1167C22—42no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22C2×#53511yescharacteristic
1180C22C2×#54711yescharacteristic
1181C22#348611yescharacteristic
1182C22#358411yescharacteristic
1183C22#358411yescharacteristic
1184C22#358411yescharacteristic
1185C22#358511yescharacteristic
1186C4—22no—
1187C4—22no—
1188C4—22no—
1189C4—42no—
1190C4—41no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—41no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4#352011yescharacteristic
1214C4#352011yescharacteristic
1215C4#353811yescharacteristic
1216C4#353811yescharacteristic
1217C2—42no—
1218C2—82no—
1219C2—161no—
1220C2#3891711yescharacteristic
1221C2#6082311yescharacteristic
1222C2#6083411yescharacteristic
1223C2#6126111yescharacteristic
1224C2#6127611yescharacteristic
1225C2#6186111yescharacteristic
1226C2#6186711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#449C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37987C2semidirect
2. #35620C2semidirect
3. #32968C2semidirect
4. #32447C2semidirect
5. #32441C2semidirect
6. #32440C2semidirect
7. #32437C2semidirect
8. #32371C2semidirect
9. #32356C2semidirect
10. #32355C2semidirect
11. #32345C2semidirect
12. #29916C2semidirect
13. #29912C2semidirect
14. #28547C2semidirect
15. #28534C2semidirect
16. #27743C2semidirect
17. #27730C2semidirect
18. #27597C2semidirect
19. #27590C2semidirect
20. #25822C2semidirect
21. #25466C2semidirect
22. #25460C2semidirect
23. #24690C2semidirect
24. #24677C2semidirect
27. #24309C2semidirect
28. #22604C2semidirect
29. #21991C2semidirect
30. #21983C2semidirect

Maximal subgroups

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

subgroupindex
#379872
#356202
#329682
#324472
#324412
#324402
#324372
#323712
#323562
#323552
#323452
#299162
#299122
#285472
#285342
#277432
#277302
#275972
#275902
#258222
#254662
#254602
#246902
#246772
#245132
#245042
#243092
#226042
#219912
#219832
#214602