Finite Group Databasebeta

← #6592040

Subgroups — #6592040

Order 512.

1795 conjugacy classes of subgroups.

The subgroup lattice has 1328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39493C211yesmaximal, characteristic, complemented
2#34309C211yesmaximal, characteristic
3#33201C211yesmaximal, characteristic, complemented
4#32965C211yesmaximal, characteristic, complemented
5#32962C211yesmaximal, characteristic, complemented
6#29142C211yesmaximal, characteristic, complemented
7#28281C211yesmaximal, characteristic, complemented
8#27689C211yesmaximal, characteristic, complemented
9#27688C211yesmaximal, characteristic, complemented
10#26537C211yesmaximal, characteristic, complemented
11#26534C211yesmaximal, characteristic, complemented
12#26431C211yesmaximal, characteristic, complemented
13#26424C211yesmaximal, characteristic, complemented
14#26413C211yesmaximal, characteristic, complemented
15#26410C211yesmaximal, characteristic, complemented
16#26117C211yesmaximal, characteristic, complemented
17#26115C211yesmaximal, characteristic, complemented
18#25978C211yesmaximal, characteristic, complemented
19#25966C211yesmaximal, characteristic, complemented
20#25958C211yesmaximal, characteristic, complemented
21#25954C211yesmaximal, characteristic, complemented
22#24853C211yesmaximal, characteristic, complemented
23#24847C211yesmaximal, characteristic, complemented
24#22714C211yesmaximal, characteristic, complemented
25#22706C211yesmaximal, characteristic, complemented
26#22651C211yesmaximal, characteristic, complemented
27#22427C211yesmaximal, characteristic
28#22414C211yesmaximal, characteristic
29C4×#476C211yesmaximal, characteristic, complemented
30#20652C211yesmaximal, characteristic, complemented
31#20650C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#520C2211yescharacteristic
34C2×#518C2211yescharacteristic
35C2×#475C2211yescharacteristic, complemented
36C2×#476C2211yescharacteristic
37C2×#476C2211yescharacteristic
38C2×#474C2211yescharacteristic
39C2×#474C2211yescharacteristic
40C2×#436C2211yescharacteristic
41C2×C8×D4C2211yescharacteristic
42C2×#424C2211yescharacteristic
43C2×#424C2211yescharacteristic, complemented
44C2×#417C2211yescharacteristic
45C2×#418C2211yescharacteristic
46C2×#416C2211yescharacteristic
47C22×#102C2211yescharacteristic
48#2862C2211yescharacteristic, complemented
49#2806—21no—
50#2805—21no—
51#2804—21no—
52#2732—21no—
53#2628C2211yescharacteristic
54#2628C2211yescharacteristic, complemented
55#2589—21no—
56#2589—21no—
57#2570C2211yescharacteristic, complemented
58#2570C2211yescharacteristic, complemented
59#2465—21no—
60#2465—21no—
61#2440C2211yescharacteristic
62#2440C2211yescharacteristic, complemented
63#2439C2211yescharacteristic
64#2439C2211yescharacteristic, complemented
65#2367C2211yescharacteristic
66#2364—21no—
67#2362C2211yescharacteristic
68#2361C2211yescharacteristic
69#2359—21no—
70#2358—21no—
71#2352C2211yescharacteristic
72#2352C2211yescharacteristic
73#2352C2211yescharacteristic
74#2349C2211yescharacteristic
75#2342—21no—
76#2339C2211yescharacteristic
77D4×C22⋊C4C2211yescharacteristic
78#2324C2211yescharacteristic
79#2323C2211yescharacteristic
80#2322—21no—
81#2321—21no—
82#2317C2211yescharacteristic
83#2317C2211yescharacteristic, complemented
84C4×C4⋊Q8C2211yescharacteristic, complemented
85C4×#124C2211yescharacteristic
86C4×#121—21no—
87#2293C2211yescharacteristic
88C2×#388—21no—
89C42×D4C2211yescharacteristic
90#2101C2211yescharacteristic, complemented
91#2101C2211yescharacteristic, complemented
92#2100C2211yescharacteristic, complemented
93#2099C2211yescharacteristic, complemented
94#2097C2211yescharacteristic, complemented
95#2096C2211yescharacteristic, complemented
96#2094C2211yescharacteristic
97#2092C2211yescharacteristic
98#2088C2211yescharacteristic, complemented
99#2088C2211yescharacteristic, complemented
100#2087C2211yescharacteristic, complemented
101#2086C2211yescharacteristic, complemented
102#2068C2211yescharacteristic, complemented
103#2068C2211yescharacteristic, complemented
104#2068C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2066C2211yescharacteristic, complemented
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2024C2211yescharacteristic, complemented
111#2024C2211yescharacteristic, complemented
112#2023C2211yescharacteristic
113#2023C2211yescharacteristic
114#1988C2211yescharacteristic, complemented
115#1987C2211yescharacteristic, complemented
116#1987C2211yescharacteristic, complemented
117#1983C2211yescharacteristic
118#1983C2211yescharacteristic
119#1958C2211yescharacteristic
120#1958C2211yescharacteristic
121#1949C2211yescharacteristic, complemented
122#1949C2211yescharacteristic, complemented
123#1949C2211yescharacteristic, complemented
124#1949C2211yescharacteristic, complemented
125#1949C2211yescharacteristic, complemented
126#1949C2211yescharacteristic, complemented
127#1948C2211yescharacteristic, complemented
128#1939C2211yescharacteristic, complemented
129#1939C2211yescharacteristic, complemented
130#1920C2211yescharacteristic, complemented
131#1920C2211yescharacteristic, complemented
132#1895C2211yescharacteristic
133#1894C2211yescharacteristic
134#1893C2211yescharacteristic
135#1892C2211yescharacteristic
136#1875C2211yescharacteristic
137#1874C2211yescharacteristic
138#1873C2211yescharacteristic
139#1872C2211yescharacteristic
140#1865C2211yescharacteristic, complemented
141#1865C2211yescharacteristic, complemented
142#1864C2211yescharacteristic
143#1864C2211yescharacteristic
144#1864C2211yescharacteristic
145#1864C2211yescharacteristic
146#1864C2211yescharacteristic
147#1864C2211yescharacteristic
148#1862C2211yescharacteristic
149#1862C2211yescharacteristic
150#1854C2211yescharacteristic
151#1854C2211yescharacteristic
152#1854C2211yescharacteristic
153#1854C2211yescharacteristic, complemented
154#1853C2211yescharacteristic
155#1853C2211yescharacteristic, complemented
156#1853C2211yescharacteristic, complemented
157#1853C2211yescharacteristic, complemented
158#1851C2211yescharacteristic
159#1851C2211yescharacteristic, complemented
160#1850C2211yescharacteristic
161#1850C2211yescharacteristic, complemented
162#1842C2211yescharacteristic, complemented
163#1835C2211yescharacteristic, complemented
164#1835C2211yescharacteristic, complemented
165#1809C2211yescharacteristic
166#1809C2211yescharacteristic, complemented
167#1808C2211yescharacteristic, complemented
168#1807C2211yescharacteristic
169#1805C2211yescharacteristic, complemented
170#1805C2211yescharacteristic, complemented
171#1805C2211yescharacteristic, complemented
172#1804C2211yescharacteristic
173#1804C2211yescharacteristic
174#1804C2211yescharacteristic
175#1804C2211yescharacteristic
176#1804C2211yescharacteristic
177#1804C2211yescharacteristic
178#1804C2211yescharacteristic
179#1804C2211yescharacteristic
180#1804C2211yescharacteristic
181#1803C2211yescharacteristic, complemented
182#1803C2211yescharacteristic, complemented
183#1802C2211yescharacteristic
184#1802C2211yescharacteristic
185#1802C2211yescharacteristic
186#1802C2211yescharacteristic
187#1802C2211yescharacteristic
188#1798C2211yescharacteristic
189#1798C2211yescharacteristic, complemented
190#1788C2211yescharacteristic
191#1788C2211yescharacteristic
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194C4×#106C2211yescharacteristic, complemented
195C4×#106C2211yescharacteristic, complemented
196C4×C4⋊C8C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic, complemented
201#1735C2211yescharacteristic
202C2×#340C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209#546—24no—
210#546Q818yescomplemented
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×C4⋊Q8C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×#123—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8C2311yescharacteristic
219C2×#121—21no—
220C2×#121C2311yescharacteristic
221C2×#120—21no—
222#520—24no—
223#520—42no—
224#518—24no—
225#518—42no—
226C2×C4×Q8—21no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4—21no—
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×#117—21no—
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4—21no—
249C22×C4⋊C4C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C22⋊C4—21no—
253C22×C22⋊C4—21no—
254C22×C22⋊C4—21no—
255C22×C22⋊C4—21no—
256C22×C42—21no—
257#476—24no—
258#476—42no—
259#475—42no—
260#474—42no—
261#474—42no—
262#436—24no—
263C8×D4—24no—
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276#424—42no—
277#424—42no—
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290#418—42no—
291#417—42no—
292#416—42no—
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#102—42no—
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×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#399—21no—
329#399—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#396—21no—
335#396—21no—
336#395—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#393—21no—
341#393—21no—
342#393—21no—
343#393—21no—
344#391—21no—
345#391—21no—
346#391—21no—
347#391—21no—
348#391—21no—
349#391—21no—
350#391—21no—
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#390—21no—
354#390D411yescharacteristic
355#390D411yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389—21no—
363#389—21no—
364#389D411yescharacteristic
365#389D411yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
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#388—21no—
385#388—21no—
386#388—21no—
387#388D411yescharacteristic
388#388D411yescharacteristic
389#388D411yescharacteristic
390#388D411yescharacteristic
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#381—21no—
433#380—21no—
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437#380C2311yescharacteristic
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#379—21no—
441C4×C4⋊C4—21no—
442C4×C4⋊C4—21no—
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C2×#95—21no—
461C2×#95—21no—
462C43C2311yescharacteristic
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#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#340C2311yescharacteristic
490#340C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497C25—21no—
498C2×#41—22no—
499C2×#41—22no—
500C2×#41—22no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41C2×Q814yes—
504C22×Q8—21no—
505C22×Q8—21no—
506C22×Q8—21no—
507C22×Q8C2411yescharacteristic
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—22no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4C2×D411yescharacteristic
517C22×D4C2×Q814yes—
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4C2411yescharacteristic
532C23×C4C2411yescharacteristic
533C2×M16—22no—
534C2×M16—22no—
535C2×M16—41no—
536C2×M16—41no—
537C2×M16—41no—
538C2×M16—41no—
539C22×C8—22no—
540C22×C8—22no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8—41no—
544C22×C8—41no—
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C4⋊Q8—22no—
554C4⋊Q8—22no—
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558C4⋊Q8—41no—
559#124—22no—
560#124C2×Q814yes—
561#123—28no—
562C22⋊Q8—22no—
563C22⋊Q8—82no—
564C22⋊Q8—82no—
565C22⋊Q8C2×Q814yes—
566#121—22no—
567#121—28no—
568#121C2×Q814yes—
569#120—28no—
570C4×Q8—22no—
571C4×Q8—22no—
572C4×Q8—22no—
573C4×Q8—41no—
574C4×Q8—82no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—44no—
588C4×D4—44no—
589C4×D4—44no—
590C4×D4—44no—
591C4×D4—82no—
592C4×D4C2×Q814yes—
593C4×D4C2×Q814yes—
594C4×D4#4114yes—
595C4×D4#4114yes—
596#117—22no—
597#117—22no—
598#117—22no—
599#117—22no—
600#117—22no—
601#117—44no—
602#117—41no—
603#117—41no—
604#117—41no—
605#117—41no—
606#117—41no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—22no—
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—41no—
632C2×C4⋊C4—41no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4—41no—
635C2×C4⋊C4—41no—
636C2×C4⋊C4—44no—
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
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—28no—
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⋊C4—44no—
683C2×C22⋊C4—44no—
684C2×C22⋊C4—82no—
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C42—21no—
696C2×C42—21no—
697C2×C42—21no—
698C2×C42—21no—
699C2×C42—21no—
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42—82no—
706C2×C42C2×D411yescharacteristic
707C2×C42C2×D411yescharacteristic
708C2×C42C2×D411yescharacteristic
709C2×C42C2×D411yescharacteristic
710C2×C42C2411yescharacteristic
711C2×C42C2411yescharacteristic
712C2×C42C2411yescharacteristic
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715#107—41no—
716#107—41no—
717#107—41no—
718#107—41no—
719#106—22no—
720#106—22no—
721#106—41no—
722#106—41no—
723#106—41no—
724#106—41no—
725#106—41no—
726#106—41no—
727C4⋊C8—22no—
728C4⋊C8—22no—
729C4⋊C8—22no—
730C4⋊C8—22no—
731C4⋊C8—22no—
732C4⋊C8—22no—
733C4⋊C8—41no—
734C4⋊C8—41no—
735C4⋊C8—41no—
736C4⋊C8—41no—
737C4⋊C8—41no—
738C4⋊C8—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#103—41no—
746#103—41no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—22no—
754#102—22no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763C22⋊C8—22no—
764C22⋊C8—22no—
765C22⋊C8—22no—
766C22⋊C8—22no—
767C4×C8—22no—
768C4×C8—22no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
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#95—21no—
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812C24—21no—
813C24—21no—
814C24—24no—
815C24—42no—
816C24—42no—
817C24—81no—
818C24—81no—
819C24—81no—
820C24—81no—
821C24C22×D411yescharacteristic
822C24C22×D411yescharacteristic
823#41—28no—
824#41—44no—
825#41—44no—
826#41—44no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—42no—
833C2×Q8—42no—
834C2×Q8—42no—
835C2×Q8—81no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×Q8—81no—
840C2×Q8—81no—
841C2×Q8C22×Q812yes—
842C2×D4—28no—
843C2×D4—24no—
844C2×D4—24no—
845C2×D4—24no—
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—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—41no—
858C2×D4—41no—
859C2×D4—42no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—81no—
864C2×D4—81no—
865C2×D4C22⋊Q814yes—
866C2×D4C22×Q812yes—
867C2×D4C22×Q812yes—
868C2×D4C2×#4112yes—
869C2×D4H(5,𝔽2)12yes—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—21no—
873C22×C4—21no—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—24no—
882C22×C4—24no—
883C22×C4—24no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—42no—
896C22×C4—42no—
897C22×C4—42no—
898C22×C4—42no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—81no—
905C22×C4—81no—
906C22×C4—81no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×Q812yes—
938C22×C4C22×Q812yes—
939C22×C4C2×#4112yes—
940C22×C4C2×#4112yes—
941C22×C4C2511yescharacteristic
942M16—82no—
943M16—82no—
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—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—82no—
969C2×C8—82no—
970C4⋊C4—24no—
971C4⋊C4—22no—
972C4⋊C4—22no—
973C4⋊C4—22no—
974C4⋊C4—22no—
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—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—41no—
1000C4⋊C4—41no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—42no—
1006C4⋊C4—42no—
1007C4⋊C4—81no—
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⋊C4C22⋊Q814yes—
1024C4⋊C4C22×Q812yes—
1025C4⋊C4C2×#4112yes—
1026C22⋊C4—24no—
1027C22⋊C4—24no—
1028C22⋊C4—24no—
1029C22⋊C4—24no—
1030C22⋊C4—24no—
1031C22⋊C4—24no—
1032C22⋊C4—22no—
1033C22⋊C4—22no—
1034C22⋊C4—22no—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—22no—
1038C22⋊C4—41no—
1039C22⋊C4—41no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
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⋊C4C22⋊Q814yes—
1059C22⋊C4C22⋊Q814yes—
1060C42—22no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—41no—
1068C42—41no—
1069C42—41no—
1070C42—42no—
1071C42—42no—
1072C42—42no—
1073C42—42no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C42—81no—
1078C42—81no—
1079C42—81no—
1080C42C22×Q812yes—
1081C42C2×#4112yes—
1082C42C2×#4112yes—
1083C42H(5,𝔽2)12yes—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—22no—
1091C23—21no—
1092C23—21no—
1093C23—22no—
1094C23—22no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—21no—
1099C23—22no—
1100C23—48no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—84no—
1112C23—84no—
1113C23—162no—
1114C23—162no—
1115C23—162no—
1116C23—162no—
1117C23C2×C22⋊Q812yes—
1118C23C2×C22⋊Q812yes—
1119C23C23×D411yescharacteristic
1120Q8—22no—
1121Q8—22no—
1122Q8—41no—
1123Q8—41no—
1124Q8—84no—
1125Q8—162no—
1126Q8—162no—
1127D4—22no—
1128D4—22no—
1129D4—22no—
1130D4—22no—
1131D4—22no—
1132D4—44no—
1133D4—48no—
1134D4—48no—
1135D4—41no—
1136D4—41no—
1137D4—84no—
1138D4#55414yes—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—22no—
1154C2×C4—22no—
1155C2×C4—22no—
1156C2×C4—22no—
1157C2×C4—22no—
1158C2×C4—22no—
1159C2×C4—22no—
1160C2×C4—22no—
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—22no—
1170C2×C4—22no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—22no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—48no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
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—84no—
1220C2×C4—84no—
1221C2×C4—84no—
1222C2×C4—162no—
1223C2×C4—162no—
1224C2×C4—162no—
1225C2×C4—162no—
1226C2×C4—162no—
1227C2×C4—162no—
1228C2×C4—162no—
1229C2×C4C2×C22⋊Q812yes—
1230C2×C4C2×C22⋊Q812yes—
1231C2×C4C2×C22⋊Q812yes—
1232C2×C4C2×C22⋊Q812yes—
1233C2×C4#54612yes—
1234C2×C4#54612yes—
1235C2×C4#57712yes—
1236C2×C4C23×Q811yescharacteristic
1237C2×C4C22×#4111yescharacteristic
1238C2×C4C22×#4111yescharacteristic
1239C2×C4C2×H(5,𝔽2)11yescharacteristic
1240C2×C4C2×H(5,𝔽2)11yescharacteristic
1241C2×C4#58511yescharacteristic
1242C8—41no—
1243C8—41no—
1244C8—41no—
1245C8—41no—
1246C8—41no—
1247C8—41no—
1248C8—41no—
1249C8—41no—
1250C22—22no—
1251C22—22no—
1252C22—24no—
1253C22—22no—
1254C22—22no—
1255C22—22no—
1256C22—22no—
1257C22—42no—
1258C22—41no—
1259C22—41no—
1260C22—42no—
1261C22—41no—
1262C22—41no—
1263C22—42no—
1264C22—42no—
1265C22—41no—
1266C22—41no—
1267C22—42no—
1268C22—42no—
1269C22—41no—
1270C22—41no—
1271C22—42no—
1272C22—42no—
1273C22—42no—
1274C22—81no—
1275C22—81no—
1276C22—81no—
1277C22—81no—
1278C22—168no—
1279C22C22×C22⋊Q811yescharacteristic
1280C22C2×#54611yescharacteristic
1281C22#348811yescharacteristic
1282C22C2×#57711yescharacteristic
1283C22#358411yescharacteristic
1284C22#358411yescharacteristic
1285C22#358511yescharacteristic
1286C4—22no—
1287C4—22no—
1288C4—22no—
1289C4—22no—
1290C4—22no—
1291C4—22no—
1292C4—22no—
1293C4—41no—
1294C4—41no—
1295C4—41no—
1296C4—41no—
1297C4—42no—
1298C4—42no—
1299C4—42no—
1300C4—41no—
1301C4—81no—
1302C4—81no—
1303C4—81no—
1304C4—81no—
1305C4—81no—
1306C4—81no—
1307C4—81no—
1308C4—81no—
1309C4—81no—
1310C4—81no—
1311C4—81no—
1312C4C2×#55411yescharacteristic
1313C4#347511yescharacteristic
1314C4#350111yescharacteristic
1315C4#351911yescharacteristic
1316C2—42no—
1317C2—42no—
1318C2—44no—
1319C2—82no—
1320C2#3615411yescharacteristic
1321C2#6048911yescharacteristic
1322C2#6049511yescharacteristic
1323C2#6120811yescharacteristic
1324C2#6121211yescharacteristic
1325C2#6204711yescharacteristic
1326C2#6206311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#546C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2293 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39493C2semidirect
3. #33201C2semidirect
4. #32965C2semidirect
5. #32962C2semidirect
6. #29142C2semidirect
7. #28281C2semidirect
8. #27689C2semidirect
9. #27688C2semidirect
10. #26537C2semidirect
11. #26534C2semidirect
12. #26431C2semidirect
13. #26424C2semidirect
14. #26413C2semidirect
15. #26410C2semidirect
16. #26117C2semidirect
17. #26115C2semidirect
18. #25978C2semidirect
19. #25966C2semidirect
20. #25958C2semidirect
21. #25954C2semidirect
22. #24853C2semidirect
23. #24847C2semidirect
24. #22714C2semidirect
25. #22706C2semidirect
26. #22651C2semidirect
29. C4×#476C2semidirect
30. #20652C2semidirect
31. #20650C2semidirect
35. C2×#475C22semidirect
43. C2×#424C22semidirect
48. #2862C22semidirect
54. #2628C22semidirect
57. #2570C22semidirect
58. #2570C22semidirect
62. #2440C22semidirect
64. #2439C22semidirect
83. #2317C22semidirect
84. C4×C4⋊Q8C22semidirect
90. #2101C22semidirect
91. #2101C22semidirect
92. #2100C22semidirect
93. #2099C22semidirect
94. #2097C22semidirect
95. #2096C22semidirect
98. #2088C22semidirect
99. #2088C22semidirect
100. #2087C22semidirect
101. #2086C22semidirect
102. #2068C22semidirect
103. #2068C22semidirect
104. #2068C22semidirect
106. #2066C22semidirect
110. #2024C22semidirect
111. #2024C22semidirect
114. #1988C22semidirect
115. #1987C22semidirect
116. #1987C22semidirect
121. #1949C22semidirect
122. #1949C22semidirect
123. #1949C22semidirect
124. #1949C22semidirect
125. #1949C22semidirect
126. #1949C22semidirect
127. #1948C22semidirect
128. #1939C22semidirect
129. #1939C22semidirect
130. #1920C22semidirect
131. #1920C22semidirect
140. #1865C22semidirect
141. #1865C22semidirect
153. #1854C22semidirect
155. #1853C22semidirect
156. #1853C22semidirect
157. #1853C22semidirect
159. #1851C22semidirect
161. #1850C22semidirect
162. #1842C22semidirect
163. #1835C22semidirect
164. #1835C22semidirect
166. #1809C22semidirect
167. #1808C22semidirect
169. #1805C22semidirect
170. #1805C22semidirect
171. #1805C22semidirect
181. #1803C22semidirect
182. #1803C22semidirect
189. #1798C22semidirect
194. C4×#106C22semidirect
195. C4×#106C22semidirect
196. C4×C4⋊C8C22semidirect
200. #1736C22semidirect
202. C2×#340C22semidirect
210. #546Q8semidirect

Maximal subgroups

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

subgroupindex
#394932
#343092
#332012
#329652
#329622
#291422
#282812
#276892
#276882
#265372
#265342
#264312
#264242
#264132
#264102
#261172
#261152
#259782
#259662
#259582
#259542
#248532
#248472
#227142
#227062
#226512
#224272
#224142
C4×#4762
#206522
#206502