Finite Group Databasebeta

← #6997285

Subgroups — #6997285

Order 512.

1455 conjugacy classes of subgroups.

The subgroup lattice has 1230 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44941C211yesmaximal, characteristic
2#42818C211yesmaximal, characteristic, complemented
3#32595C211yesmaximal, characteristic, complemented
4#32570C211yesmaximal, characteristic, complemented
5#31546C211yesmaximal, characteristic, complemented
6#31540C211yesmaximal, characteristic, complemented
7#31540C211yesmaximal, characteristic, complemented
8#31526C211yesmaximal, characteristic, complemented
9#30976C211yesmaximal, characteristic, complemented
10#30957C211yesmaximal, characteristic, complemented
11#29175C211yesmaximal, characteristic
12#28781C211yesmaximal, characteristic, complemented
13#28778C211yesmaximal, characteristic, complemented
14#27831C211yesmaximal, characteristic, complemented
15#27827C211yesmaximal, characteristic, complemented
16#27029C211yesmaximal, characteristic, complemented
17#27025C211yesmaximal, characteristic, complemented
18#26495C211yesmaximal, characteristic, complemented
19#26487C211yesmaximal, characteristic, complemented
20#26438C211yesmaximal, characteristic
21#26423C211yesmaximal, characteristic
22#25981C211yesmaximal, characteristic, complemented
23#25963C211yesmaximal, characteristic, complemented
24#25821C211yesmaximal, characteristic, complemented
25#24349C211yesmaximal, characteristic, complemented
26#24331C211yesmaximal, characteristic, complemented
27#23457C211yesmaximal, characteristic, complemented
28#23246C211yesmaximal, characteristic, complemented
29#22885C211yesmaximal, characteristic
30#22855C211yesmaximal, characteristic
31#22058C211yesmaximal, characteristic
32C2×#554C2211yescharacteristic
33C2×#544C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#500C2211yescharacteristic
36C2×#479C2211yescharacteristic
37C2×#477C2211yescharacteristic
38C2×#448C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×C4×SD16C2211yescharacteristic
41C2×#419C2211yescharacteristic
42C22×#103C2211yescharacteristic
43#2841—21no—
44#2809—21no—
45#2806—21no—
46#2806—21no—
47#2799—21no—
48#2720—21no—
49#2692—21no—
50#2683—21no—
51#2677—21no—
52#2667—21no—
53#2667—21no—
54#2628C2211yescharacteristic
55#2607—21no—
56#2582C2211yescharacteristic
57#2582C2211yescharacteristic
58#2567C2211yescharacteristic
59#2565C2211yescharacteristic
60#2565C2211yescharacteristic
61#2556—21no—
62#2552C2211yescharacteristic
63#2551C2211yescharacteristic
64#2542—21no—
65#2542C2211yescharacteristic
66#2454C2211yescharacteristic
67#2453C2211yescharacteristic
68#2453C2211yescharacteristic
69#2452C2211yescharacteristic
70#2451C2211yescharacteristic
71#2451C2211yescharacteristic
72#2449—21no—
73#2441C2211yescharacteristic
74#2441C2211yescharacteristic
75#2441C2211yescharacteristic
76#2440—21no—
77#2440C2211yescharacteristic
78#2396C2211yescharacteristic
79#2370C2211yescharacteristic
80#2363C2211yescharacteristic
81#2361C2211yescharacteristic
82Q8×C22⋊C4C2211yescharacteristic
83Q8×C22⋊C4C2211yescharacteristic
84#2324C2211yescharacteristic
85#2310C2211yescharacteristic
86#2101C2211yescharacteristic
87#2100C2211yescharacteristic
88#2099C2211yescharacteristic
89#2095C2211yescharacteristic
90#2095C2211yescharacteristic
91#2092C2211yescharacteristic
92#2087C2211yescharacteristic
93#2086C2211yescharacteristic
94#2084C2211yescharacteristic
95#2083C2211yescharacteristic
96#2083C2211yescharacteristic
97#2083C2211yescharacteristic
98#2068C2211yescharacteristic
99#2068C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2066C2211yescharacteristic
103#2066C2211yescharacteristic
104#2059C2211yescharacteristic
105#2059C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2057C2211yescharacteristic
110#2057C2211yescharacteristic
111#2057C2211yescharacteristic
112#2057C2211yescharacteristic
113#2026C2211yescharacteristic
114#2026C2211yescharacteristic
115#2026C2211yescharacteristic
116#2026C2211yescharacteristic
117#2026C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic
120#2024C2211yescharacteristic
121#2024C2211yescharacteristic
122#2024C2211yescharacteristic
123#2024C2211yescharacteristic
124#2024C2211yescharacteristic
125#2023C2211yescharacteristic
126#1993C2211yescharacteristic
127#1992C2211yescharacteristic
128#1992C2211yescharacteristic
129#1992C2211yescharacteristic
130#1991C2211yescharacteristic
131#1990C2211yescharacteristic
132#1989C2211yescharacteristic
133#1989C2211yescharacteristic
134#1985C2211yescharacteristic
135#1984C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic
138#1973C2211yescharacteristic
139#1968C2211yescharacteristic
140#1944C2211yescharacteristic
141#1944C2211yescharacteristic
142#1943C2211yescharacteristic
143#1942C2211yescharacteristic
144#1935C2211yescharacteristic
145#1935C2211yescharacteristic
146#1933C2211yescharacteristic
147#1933C2211yescharacteristic
148#1928C2211yescharacteristic
149#1928C2211yescharacteristic
150#1927C2211yescharacteristic
151#1927C2211yescharacteristic
152#1921C2211yescharacteristic
153#1921C2211yescharacteristic
154#1920C2211yescharacteristic
155#1920C2211yescharacteristic
156#1917C2211yescharacteristic
157#1917C2211yescharacteristic
158#1917C2211yescharacteristic
159#1916C2211yescharacteristic
160#1895C2211yescharacteristic
161#1893C2211yescharacteristic
162#1880C2211yescharacteristic
163#1880C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1875C2211yescharacteristic
169#1865C2211yescharacteristic
170#1864C2211yescharacteristic
171#1863C2211yescharacteristic
172#1863C2211yescharacteristic
173#1863C2211yescharacteristic
174#1863C2211yescharacteristic
175#1863C2211yescharacteristic
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1854C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1851C2211yescharacteristic
185#1850C2211yescharacteristic
186#1809C2211yescharacteristic
187#1808C2211yescharacteristic
188#1803C2211yescharacteristic
189#1803C2211yescharacteristic
190#1802C2211yescharacteristic
191#1802C2211yescharacteristic
192#1787C2211yescharacteristic
193#1771C2211yescharacteristic
194#1771C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197#1753C2211yescharacteristic
198#1752C2211yescharacteristic
199#1750C2211yescharacteristic
200#1736C2211yescharacteristic
201#1735C2211yescharacteristic
202#1729C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C23×C8C2311yescharacteristic
208#554—42no—
209#554—42no—
210#544—42no—
211#544—42no—
212C2×C4⋊Q8—21no—
213C2×C4⋊Q8—21no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#125—21no—
219C2×#125C2311yescharacteristic
220C2×#125C2311yescharacteristic
221C2×#125C2311yescharacteristic
222C2×#125C2311yescharacteristic
223C2×#125C2311yescharacteristic
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8—21no—
229C2×C22⋊Q8—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×#121C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×Q8C2311yescharacteristic
237C2×C4×Q8C2311yescharacteristic
238C2×C4×Q8C2311yescharacteristic
239C2×C4×D4—21no—
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C22×C4⋊C4—21no—
247C22×C4⋊C4C2311yescharacteristic
248#501—42no—
249#500—42no—
250#479—42no—
251#477—42no—
252#448Q818yescomplemented
253#440—42no—
254C4×SD16—42no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273#419—42no—
274C2×#103—42no—
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#400—21no—
304#400—21no—
305#400—21no—
306#400D411yescharacteristic
307#399—21no—
308#399—21no—
309#399—21no—
310#399—21no—
311#399—21no—
312#399—21no—
313#399—21no—
314#399D411yescharacteristic
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398—21no—
330#398D411yescharacteristic
331#398D411yescharacteristic
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#396D411yescharacteristic
338#396D411yescharacteristic
339#395—21no—
340#395—21no—
341#395—21no—
342#395—21no—
343#395—21no—
344#395—21no—
345#395—21no—
346#395—21no—
347#395D411yescharacteristic
348#393—21no—
349#393—21no—
350#393D411yescharacteristic
351#391—21no—
352#391—21no—
353#391—21no—
354#391—21no—
355#391—21no—
356#391—21no—
357#391—21no—
358#391—21no—
359#391—21no—
360#391—21no—
361#391—21no—
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#390—21no—
371#390—21no—
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#389—21no—
376#389—21no—
377#389—21no—
378#389—21no—
379#389—21no—
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389—21no—
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
398#388—21no—
399#388—21no—
400#388—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#384—21no—
423#384—21no—
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#382C2311yescharacteristic
429#381—21no—
430#381—21no—
431#380—21no—
432#380—21no—
433#380—21no—
434#380C2311yescharacteristic
435#380C2311yescharacteristic
436#380C2311yescharacteristic
437C4×C4⋊C4—21no—
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
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#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8—21no—
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8—22no—
497C22×Q8—41no—
498C22×Q8—41no—
499C22×Q8—41no—
500C22×Q8—41no—
501C22×Q8C2×D411yescharacteristic
502C22×Q8C2×Q814yes—
503C22×Q8C2411yescharacteristic
504C22×Q8C2411yescharacteristic
505C22×D4—21no—
506C22×D4C2411yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C2411yescharacteristic
513C2×SD16—41no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×SD16C2×Q814yes—
518C2×SD16C2×Q814yes—
519C2×M16—22no—
520C2×M16—41no—
521C2×M16—41no—
522C22×C8—22no—
523C22×C8—41no—
524C22×C8—41no—
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C4⋊Q8—22no—
534C4⋊Q8—22no—
535C4⋊Q8—41no—
536C4⋊Q8—41no—
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539C4⋊Q8—41no—
540C4⋊Q8—41no—
541C4⋊Q8—44no—
542C4⋊Q8—82no—
543#125—22no—
544#125—22no—
545#125—22no—
546#125—22no—
547#125—41no—
548#125—41no—
549#125—41no—
550#125—41no—
551#125—41no—
552#125—41no—
553#125—44no—
554C22⋊Q8—44no—
555C22⋊Q8—44no—
556C22⋊Q8—44no—
557C22⋊Q8—44no—
558C22⋊Q8—44no—
559C22⋊Q8—82no—
560C22⋊Q8—82no—
561C22⋊Q8—82no—
562C22⋊Q8—82no—
563#121—22no—
564#121C2×Q814yes—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×Q8—41no—
568C4×Q8—41no—
569C4×Q8—41no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—82no—
582#117—22no—
583#117—41no—
584#117—41no—
585#117—41no—
586#117—41no—
587#117—41no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—41no—
630C2×C4⋊C4—44no—
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691#107—22no—
692#107—22no—
693#107—41no—
694#107—41no—
695#107—41no—
696#107—41no—
697#107—41no—
698#107—41no—
699#107—41no—
700#107—41no—
701#106—22no—
702#106—22no—
703#106—41no—
704#106—41no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708C4⋊C8—41no—
709#103—22no—
710#103—22no—
711#103—22no—
712#103—22no—
713#103—41no—
714#103—41no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103C2×Q814yes—
722#103C2×Q814yes—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729C22⋊C8—22no—
730C22⋊C8C2×Q814yes—
731#97—41no—
732#97—41no—
733#97—41no—
734#97—41no—
735C4×C8—41no—
736C4×C8—41no—
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#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784C24—21no—
785C24C22×D411yescharacteristic
786C2×Q8—24no—
787C2×Q8—22no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—21no—
796C2×Q8—21no—
797C2×Q8—21no—
798C2×Q8—41no—
799C2×Q8—41no—
800C2×Q8—42no—
801C2×Q8—42no—
802C2×Q8—42no—
803C2×Q8—44no—
804C2×Q8—44no—
805C2×Q8—81no—
806C2×Q8—81no—
807C2×Q8—81no—
808C2×Q8—81no—
809C2×Q8—81no—
810C2×Q8—81no—
811C2×Q8—81no—
812C2×Q8—81no—
813C2×Q8—81no—
814C2×Q8—81no—
815C2×Q8—81no—
816C2×Q8—82no—
817C2×Q8—82no—
818C2×Q8C22×Q812yes—
819C2×Q8C22×Q812yes—
820C2×D4—24no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—21no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4C22×Q812yes—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—24no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—42no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4—81no—
858C22×C4—81no—
859C22×C4—81no—
860C22×C4—81no—
861C22×C4—81no—
862C22×C4—81no—
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C4C22×D411yescharacteristic
872C22×C4C22×D411yescharacteristic
873C22×C4C22×D411yescharacteristic
874C22×C4C22×D411yescharacteristic
875C22×C4C22×D411yescharacteristic
876C22×C4C22×Q812yes—
877C22×C42−1+412yes—
878C22×C4C2511yescharacteristic
879SD16—44no—
880SD16—44no—
881M16—82no—
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×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—82no—
905C2×C8C22×Q812yes—
906C2×C8C22×Q812yes—
907C4⋊C4—24no—
908C4⋊C4—24no—
909C4⋊C4—22no—
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—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—41no—
934C4⋊C4—41no—
935C4⋊C4—41no—
936C4⋊C4—41no—
937C4⋊C4—41no—
938C4⋊C4—41no—
939C4⋊C4—41no—
940C4⋊C4—41no—
941C4⋊C4—41no—
942C4⋊C4—41no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4C22×Q812yes—
982C4⋊C4H(5,𝔽2)12yes—
983C4⋊C4H(5,𝔽2)12yes—
984C22⋊C4—24no—
985C22⋊C4—22no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
989C22⋊C4—41no—
990C22⋊C4—41no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C42—21no—
1006C42—21no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—21no—
1015C42—21no—
1016C42—21no—
1017C42—42no—
1018C42—42no—
1019C42—81no—
1020C42—81no—
1021C42—81no—
1022C42—81no—
1023C42—81no—
1024C42—81no—
1025C42—81no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—22no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23D4×Q812yes—
1040C23C23×D411yescharacteristic
1041Q8—22no—
1042Q8—22no—
1043Q8—22no—
1044Q8—22no—
1045Q8—41no—
1046Q8—41no—
1047Q8—41no—
1048Q8—41no—
1049Q8—82no—
1050Q8—84no—
1051Q8—162no—
1052Q8—162no—
1053Q8—162no—
1054Q8—162no—
1055D4—22no—
1056D4—22no—
1057D4—41no—
1058D4—41no—
1059D4—84no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—22no—
1066C2×C4—22no—
1067C2×C4—22no—
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—22no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—22no—
1096C2×C4—22no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
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—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—84no—
1147C2×C4—84no—
1148C2×C4—162no—
1149C2×C4—162no—
1150C2×C4—162no—
1151C2×C4D4×Q812yes—
1152C2×C4#57812yes—
1153C2×C4C23×Q811yescharacteristic
1154C2×C4C2×H(5,𝔽2)11yescharacteristic
1155C2×C4C2×H(5,𝔽2)11yescharacteristic
1156C2×C4C2×2−1+411yescharacteristic
1157C2×C4#58511yescharacteristic
1158C2×C4#58511yescharacteristic
1159C8—22no—
1160C8—22no—
1161C8—41no—
1162C8—41no—
1163C8—41no—
1164C8—41no—
1165C8—41no—
1166C8—41no—
1167C22—22no—
1168C22—22no—
1169C22—22no—
1170C22—41no—
1171C22—41no—
1172C22—41no—
1173C22—41no—
1174C22—42no—
1175C22—42no—
1176C22—42no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22C2×D4×Q811yescharacteristic
1182C22#348411yescharacteristic
1183C22#350011yescharacteristic
1184C22C2×#57811yescharacteristic
1185C22#358511yescharacteristic
1186C22#358511yescharacteristic
1187C22#358611yescharacteristic
1188C4—22no—
1189C4—22no—
1190C4—41no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—42no—
1198C4—42no—
1199C4—41no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—42no—
1204C4—42no—
1205C4—42no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4#350111yescharacteristic
1217C4#350111yescharacteristic
1218C4#356111yescharacteristic
1219C4#356111yescharacteristic
1220C2—42no—
1221C2—82no—
1222C2#4300311yescharacteristic
1223C2#6137711yescharacteristic
1224C2#6138411yescharacteristic
1225C2#6162211yescharacteristic
1226C2#6167511yescharacteristic
1227C2#6257411yescharacteristic
1228C2#6261911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #42818C2semidirect
3. #32595C2semidirect
4. #32570C2semidirect
5. #31546C2semidirect
6. #31540C2semidirect
7. #31540C2semidirect
8. #31526C2semidirect
9. #30976C2semidirect
10. #30957C2semidirect
12. #28781C2semidirect
13. #28778C2semidirect
14. #27831C2semidirect
15. #27827C2semidirect
16. #27029C2semidirect
17. #27025C2semidirect
18. #26495C2semidirect
19. #26487C2semidirect
22. #25981C2semidirect
23. #25963C2semidirect
24. #25821C2semidirect
25. #24349C2semidirect
26. #24331C2semidirect
27. #23457C2semidirect
28. #23246C2semidirect
252. #448Q8semidirect

Maximal subgroups

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

subgroupindex
#449412
#428182
#325952
#325702
#315462
#315402
#315262
#309762
#309572
#291752
#287812
#287782
#278312
#278272
#270292
#270252
#264952
#264872
#264382
#264232
#259812
#259632
#258212
#243492
#243312
#234572
#232462
#228852
#228552
#220582