Finite Group Databasebeta

← #6772498

Subgroups — #6772498

Order 512.

1527 conjugacy classes of subgroups.

The subgroup lattice has 1268 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38067C211yesmaximal, characteristic, complemented
2#35246C211yesmaximal, characteristic, complemented
3#33005C211yesmaximal, characteristic, complemented
4#32436C211yesmaximal, characteristic, complemented
5#32370C211yesmaximal, characteristic, complemented
6#32370C211yesmaximal, characteristic, complemented
7#32183C211yesmaximal, characteristic, complemented
8#32083C211yesmaximal, characteristic, complemented
9#32083C211yesmaximal, characteristic, complemented
10#31526C211yesmaximal, characteristic, complemented
11#30895C211yesmaximal, characteristic, complemented
12#30139C211yesmaximal, characteristic, complemented
13#30090C211yesmaximal, characteristic, complemented
14#29510C211yesmaximal, characteristic, complemented
15#29378C211yesmaximal, characteristic, complemented
16#29269C211yesmaximal, characteristic, complemented
17#29205C211yesmaximal, characteristic, complemented
18#28336C211yesmaximal, characteristic, complemented
19#27934C211yesmaximal, characteristic
20#27701C211yesmaximal, characteristic, complemented
21#27268C211yesmaximal, characteristic, complemented
22#25500C211yesmaximal, characteristic
23#25202C211yesmaximal, characteristic, complemented
24#25090C211yesmaximal, characteristic
25#24580C211yesmaximal, characteristic, complemented
26#24481C211yesmaximal, characteristic, complemented
27#24066C211yesmaximal, characteristic, complemented
28#22595C211yesmaximal, characteristic, complemented
29#22231C211yesmaximal, characteristic, complemented
30#22161C211yesmaximal, characteristic, complemented
31C2×#1865C211yesmaximal, characteristic, complemented
32C2×#529C2211yescharacteristic
33C22×C4×Q8C2211yescharacteristic
34C2×#491C2211yescharacteristic
35C2×#481C2211yescharacteristic
36C2×#483C2211yescharacteristic
37C2×#480C2211yescharacteristic
38C2×#466C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#463C2211yescharacteristic
41C2×#448C2211yescharacteristic
42C22×#106C2211yescharacteristic
43C22×#103C2211yescharacteristic
44C22×#103C2211yescharacteristic
45#2854C2211yescharacteristic
46#2853—21no—
47#2853—21no—
48#2777—21no—
49#2773—21no—
50#2768—21no—
51#2738—21no—
52#2647C2211yescharacteristic
53#2644C2211yescharacteristic
54#2637—21no—
55#2637—21no—
56#2599—21no—
57#2599—21no—
58#2579—21no—
59#2579—21no—
60#2565C2211yescharacteristic
61#2565C2211yescharacteristic
62#2545C2211yescharacteristic
63#2545C2211yescharacteristic
64#2513C2211yescharacteristic
65#2507C2211yescharacteristic
66#2507C2211yescharacteristic
67#2504C2211yescharacteristic
68#2502C2211yescharacteristic
69#2501C2211yescharacteristic
70#2498—21no—
71#2486—21no—
72#2454C2211yescharacteristic
73#2442C2211yescharacteristic
74#2436C2211yescharacteristic
75#2434C2211yescharacteristic
76#2419—21no—
77#2413—21no—
78#2361C2211yescharacteristic
79#2344C2211yescharacteristic
80#2330C2211yescharacteristic
81#2327C2211yescharacteristic
82#2327C2211yescharacteristic
83#2326C2211yescharacteristic
84#2326C2211yescharacteristic
85#2319C2211yescharacteristic
86C2×#389C2211yescharacteristic
87#2283C2211yescharacteristic
88#2101C2211yescharacteristic
89#2101C2211yescharacteristic
90#2096C2211yescharacteristic
91#2096C2211yescharacteristic
92#2094C2211yescharacteristic
93#2094C2211yescharacteristic
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic
96#2084C2211yescharacteristic
97#2084C2211yescharacteristic
98#2084C2211yescharacteristic
99#2074C2211yescharacteristic
100#2073C2211yescharacteristic
101#2071C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2066C2211yescharacteristic
106#2066C2211yescharacteristic
107#2066C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2059C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2043C2211yescharacteristic
114#2043C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic
121#2026C2211yescharacteristic
122#2025C2211yescharacteristic
123#2025C2211yescharacteristic
124#2013C2211yescharacteristic
125#2013C2211yescharacteristic
126#2012C2211yescharacteristic
127#2012C2211yescharacteristic
128#1991C2211yescharacteristic
129#1983C2211yescharacteristic
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1972C2211yescharacteristic
133#1972C2211yescharacteristic
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1960C2211yescharacteristic
137#1956C2211yescharacteristic
138#1956C2211yescharacteristic
139#1948C2211yescharacteristic
140#1948C2211yescharacteristic
141#1948C2211yescharacteristic
142#1935C2211yescharacteristic
143#1935C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1928C2211yescharacteristic
147#1928C2211yescharacteristic
148#1928C2211yescharacteristic
149#1927C2211yescharacteristic
150#1927C2211yescharacteristic
151#1927C2211yescharacteristic
152#1917C2211yescharacteristic
153#1917C2211yescharacteristic
154#1916C2211yescharacteristic
155#1916C2211yescharacteristic
156#1893C2211yescharacteristic
157#1892C2211yescharacteristic
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1880C2211yescharacteristic
163#1879C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1874C2211yescharacteristic
167#1872C2211yescharacteristic
168#1865C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1865C2211yescharacteristic
173#1865C2211yescharacteristic
174#1865C2211yescharacteristic
175#1865C2211yescharacteristic
176#1865C2211yescharacteristic
177#1865C2211yescharacteristic
178#1865C2211yescharacteristic
179#1865C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1864C2211yescharacteristic
183#1863C2211yescharacteristic
184#1863C2211yescharacteristic
185#1863C2211yescharacteristic
186#1850C2211yescharacteristic
187#1850C2211yescharacteristic
188#1847C2211yescharacteristic
189#1847C2211yescharacteristic
190#1840C2211yescharacteristic
191#1835C2211yescharacteristic
192#1832C2211yescharacteristic
193#1824C2211yescharacteristic
194#1817C2211yescharacteristic
195#1802C2211yescharacteristic
196#1787C2211yescharacteristic
197#1768C2211yescharacteristic
198#1752C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200#1746C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×Q8C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212#529—42no—
213#529—42no—
214C2×#126—21no—
215C2×#125C2311yescharacteristic
216C2×#125C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×#124C2311yescharacteristic
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×C22⋊Q8C2311yescharacteristic
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×C4×Q8—21no—
228C2×C4×Q8—21no—
229C2×C4×Q8—42no—
230C2×C4×Q8—42no—
231C2×C4×Q8C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×Q8C2311yescharacteristic
236C2×C4×D4—21no—
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×#117—21no—
241C2×#117—21no—
242C22×C4⋊C4—21no—
243C22×C4⋊C4—21no—
244C22×C4⋊C4C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C42—21no—
248C22×C42C2311yescharacteristic
249#491—24no—
250#483—42no—
251#481—42no—
252#480—42no—
253#466—42no—
254#465—42no—
255#463—24no—
256#448—42no—
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#106—42no—
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×#103—24no—
275C2×#103—42no—
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×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×C4×C8C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314#400—21no—
315#400—21no—
316#400—21no—
317#399—21no—
318#399—21no—
319#399—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#398—21no—
331#398—21no—
332#398—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#395—21no—
347#395—21no—
348#393—21no—
349#393—21no—
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#391C2311yescharacteristic
353#391C2311yescharacteristic
354#391C2311yescharacteristic
355#391C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#390C2311yescharacteristic
362#390C2311yescharacteristic
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—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#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#384C2311yescharacteristic
433#384C2311yescharacteristic
434#383D411yescharacteristic
435#383D411yescharacteristic
436#382D411yescharacteristic
437#382D411yescharacteristic
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#381—21no—
442#381—21no—
443#381D411yescharacteristic
444#381D411yescharacteristic
445#380—21no—
446#380—21no—
447#380—21no—
448#380D411yescharacteristic
449#380D411yescharacteristic
450#380C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458#376C2311yescharacteristic
459#376C2311yescharacteristic
460C2×#95—21no—
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
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C22×Q8—21no—
494C22×Q8—22no—
495C22×Q8—22no—
496C22×Q8—22no—
497C22×Q8—22no—
498C22×Q8—41no—
499C22×Q8—41no—
500C22×Q8C2411yescharacteristic
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×D4—21no—
504C22×D4—21no—
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4C2×D411yescharacteristic
514C23×C4C2×D411yescharacteristic
515C23×C4C2411yescharacteristic
516C2×SD16—22no—
517C2×SD16—22no—
518C2×SD16—41no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×SD16—41no—
524C2×SD16—41no—
525C2×D8—22no—
526C2×D8—41no—
527C2×D8—41no—
528C22×C8—22no—
529C22×C8—22no—
530C22×C8—22no—
531C22×C8—41no—
532C22×C8—41no—
533C22×C8—41no—
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C22×C8C2411yescharacteristic
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C4⋊Q8—22no—
543C4⋊Q8—22no—
544C4⋊Q8—41no—
545C4⋊Q8—41no—
546#126—44no—
547#125—22no—
548#125—41no—
549#125—41no—
550#125—41no—
551#124—22no—
552#124—22no—
553#124—41no—
554#124—41no—
555#124—41no—
556#124—41no—
557#123—44no—
558#123—82no—
559#123—82no—
560#123—82no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563#121—22no—
564#121—22no—
565#121—22no—
566#121—22no—
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×Q8—41no—
576C4×Q8—41no—
577C4×Q8—44no—
578C4×Q8—44no—
579C4×D4—22no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—44no—
584C4×D4—82no—
585#117—44no—
586#117—82no—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—22no—
591C2×C4⋊C4—22no—
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—41no—
629C2×C4⋊C4—44no—
630C2×C4⋊C4—82no—
631C2×C4⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C22⋊C4C2×D411yescharacteristic
675C2×C22⋊C4C2×D411yescharacteristic
676C2×C42—22no—
677C2×C42—22no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—44no—
687C2×C42C2×D411yescharacteristic
688C2×C42C2×D411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692C2×C42C2411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695#107—41no—
696#107—41no—
697#107—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705#106—41no—
706#106—41no—
707C4⋊C8—22no—
708C4⋊C8—41no—
709C4⋊C8—41no—
710C4⋊C8—41no—
711#103—22no—
712#103—22no—
713#103—22no—
714#103—22no—
715#103—22no—
716#103—22no—
717#103—22no—
718#103—41no—
719#103—41no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103#4114yes—
732#102—22no—
733#102—41no—
734#102—41no—
735#102—41no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743C22⋊C8—22no—
744C22⋊C8—22no—
745#97—22no—
746#97—41no—
747C4×C8—41no—
748C4×C8—41no—
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#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786#95C2×D411yescharacteristic
787#95C2×D411yescharacteristic
788#95C2×D411yescharacteristic
789#95C2×D411yescharacteristic
790#95C2×D411yescharacteristic
791#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798C24—21no—
799C24—21no—
800C24C22×D411yescharacteristic
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—28no—
804C2×Q8—21no—
805C2×Q8—21no—
806C2×Q8—21no—
807C2×Q8—21no—
808C2×Q8—21no—
809C2×Q8—21no—
810C2×Q8—21no—
811C2×Q8—21no—
812C2×Q8—21no—
813C2×Q8—21no—
814C2×Q8—21no—
815C2×Q8—21no—
816C2×Q8—21no—
817C2×Q8—21no—
818C2×Q8—42no—
819C2×Q8—42no—
820C2×Q8—44no—
821C2×Q8—44no—
822C2×Q8—44no—
823C2×Q8—42no—
824C2×Q8C2×#4112yes—
825C2×Q82−1+412yes—
826C2×D4—21no—
827C2×D4—21no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—42no—
839C2×D4—42no—
840C2×D4—42no—
841C2×D4—42no—
842C2×D4—42no—
843C2×D4—42no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—22no—
849C22×C4—22no—
850C22×C4—22no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—22no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—41no—
867C22×C4—41no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—42no—
875C22×C4—42no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4H(5,𝔽2)12yes—
900C22×C4H(5,𝔽2)12yes—
901C22×C4C2511yescharacteristic
902SD16—82no—
903SD16—82no—
904SD16—82no—
905D8—82no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—44no—
930C2×C8—82no—
931C2×C8C2×#4112yes—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—41no—
954C4⋊C4—41no—
955C4⋊C4—41no—
956C4⋊C4—41no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4—81no—
982C4⋊C4—81no—
983C4⋊C4—81no—
984C4⋊C4—81no—
985C4⋊C4—81no—
986C4⋊C4—81no—
987C4⋊C4—81no—
988C4⋊C4—81no—
989C4⋊C4—81no—
990C4⋊C4—81no—
991C4⋊C4—81no—
992C4⋊C4—81no—
993C4⋊C4C2×#4112yes—
994C22⋊C4—22no—
995C22⋊C4—22no—
996C22⋊C4—22no—
997C22⋊C4—22no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—42no—
1009C22⋊C4—42no—
1010C22⋊C4—42no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C42—22no—
1025C42—22no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—42no—
1039C42—42no—
1040C42—42no—
1041C42—42no—
1042C42—42no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23#53512yes—
1065C23#57712yes—
1066C23#57712yes—
1067C23C23×D411yescharacteristic
1068Q8—22no—
1069Q8—22no—
1070Q8—22no—
1071Q8—22no—
1072Q8—48no—
1073Q8—41no—
1074Q8—41no—
1075Q8—41no—
1076Q8—41no—
1077Q8—41no—
1078Q8—41no—
1079Q8—41no—
1080Q8—41no—
1081D4—41no—
1082D4—41no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—41no—
1088D4—41no—
1089D4—84no—
1090D4—84no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—22no—
1094C2×C4—22no—
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—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—22no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—48no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—44no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—82no—
1178C2×C4—84no—
1179C2×C4—84no—
1180C2×C4—84no—
1181C2×C4—84no—
1182C2×C4—162no—
1183C2×C4#53512yes—
1184C2×C4C22×#4111yescharacteristic
1185C2×C4C2×H(5,𝔽2)11yescharacteristic
1186C2×C4C2×H(5,𝔽2)11yescharacteristic
1187C2×C4C2×2−1+411yescharacteristic
1188C2×C4#58511yescharacteristic
1189C2×C4#58511yescharacteristic
1190C8—22no—
1191C8—41no—
1192C8—41no—
1193C8—41no—
1194C8—41no—
1195C8—41no—
1196C8—41no—
1197C8—41no—
1198C22—22no—
1199C22—22no—
1200C22—22no—
1201C22—22no—
1202C22—22no—
1203C22—22no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—81no—
1211C22—81no—
1212C22—81no—
1213C22—81no—
1214C22—81no—
1215C22—81no—
1216C22—81no—
1217C22—81no—
1218C22#322114yes—
1219C22C2×#53511yescharacteristic
1220C22D4×#4111yescharacteristic
1221C22#348911yescharacteristic
1222C22C2×#57711yescharacteristic
1223C22C2×#57711yescharacteristic
1224C22#358411yescharacteristic
1225C22#358611yescharacteristic
1226C4—22no—
1227C4—41no—
1228C4—41no—
1229C4—41no—
1230C4—41no—
1231C4—42no—
1232C4—41no—
1233C4—41no—
1234C4—41no—
1235C4—41no—
1236C4—41no—
1237C4—41no—
1238C4—41no—
1239C4—41no—
1240C4—42no—
1241C4—42no—
1242C4—81no—
1243C4—81no—
1244C4—81no—
1245C4—81no—
1246C4—81no—
1247C4—81no—
1248C4—81no—
1249C4—81no—
1250C4—81no—
1251C4—81no—
1252C4—81no—
1253C4#349211yescharacteristic
1254C4#351311yescharacteristic
1255C4#353311yescharacteristic
1256C4#353511yescharacteristic
1257C2—24no—
1258C2—161no—
1259C2—161no—
1260C2#3836711yescharacteristic
1261C2C2×#322111yescharacteristic
1262C2#6081611yescharacteristic
1263C2#6149011yescharacteristic
1264C2#6152611yescharacteristic
1265C2#6215711yescharacteristic
1266C2#6221311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#466C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38067C2semidirect
2. #35246C2semidirect
3. #33005C2semidirect
4. #32436C2semidirect
5. #32370C2semidirect
6. #32370C2semidirect
7. #32183C2semidirect
8. #32083C2semidirect
9. #32083C2semidirect
10. #31526C2semidirect
11. #30895C2semidirect
12. #30139C2semidirect
13. #30090C2semidirect
14. #29510C2semidirect
15. #29378C2semidirect
16. #29269C2semidirect
17. #29205C2semidirect
18. #28336C2semidirect
20. #27701C2semidirect
21. #27268C2semidirect
23. #25202C2semidirect
25. #24580C2semidirect
26. #24481C2semidirect
27. #24066C2semidirect
28. #22595C2semidirect
29. #22231C2semidirect
30. #22161C2semidirect
31. C2×#1865C2semidirect

Maximal subgroups

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

subgroupindex
#380672
#352462
#330052
#324362
#323702
#321832
#320832
#315262
#308952
#301392
#300902
#295102
#293782
#292692
#292052
#283362
#279342
#277012
#272682
#255002
#252022
#250902
#245802
#244812
#240662
#225952
#222312
#221612
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