Finite Group Databasebeta

← #6819833

Subgroups — #6819833

Order 512.

1484 conjugacy classes of subgroups.

The subgroup lattice has 1233 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#40000C211yesmaximal, characteristic, complemented
2#39377C211yesmaximal, characteristic
3#33316C211yesmaximal, characteristic, complemented
4#32282C211yesmaximal, characteristic, complemented
5#32281C211yesmaximal, characteristic, complemented
6#32280C211yesmaximal, characteristic, complemented
7#32278C211yesmaximal, characteristic, complemented
8#30803C211yesmaximal, characteristic, complemented
9#30801C211yesmaximal, characteristic, complemented
10#30794C211yesmaximal, characteristic, complemented
11#30791C211yesmaximal, characteristic, complemented
12#29987C211yesmaximal, characteristic, complemented
13#29983C211yesmaximal, characteristic, complemented
14#28275C211yesmaximal, characteristic, complemented
15#28236C211yesmaximal, characteristic
16#27944C211yesmaximal, characteristic, complemented
17#27924C211yesmaximal, characteristic, complemented
18#27853C211yesmaximal, characteristic, complemented
19#27839C211yesmaximal, characteristic, complemented
20#27799C211yesmaximal, characteristic, complemented
21#27796C211yesmaximal, characteristic, complemented
22#26078C211yesmaximal, characteristic, complemented
23#26068C211yesmaximal, characteristic, complemented
24#25073C211yesmaximal, characteristic, complemented
25#25070C211yesmaximal, characteristic, complemented
26#25026C211yesmaximal, characteristic
27#25024C211yesmaximal, characteristic, complemented
28#22729C211yesmaximal, characteristic, complemented
29#22659C211yesmaximal, characteristic, complemented
30#21632C211yesmaximal, characteristic, complemented
31#21288C211yesmaximal, characteristic, complemented
32C2×#542—21no—
33C2×#501C2211yescharacteristic
34C2×#501C2211yescharacteristic
35C2×#501C2211yescharacteristic
36C2×#501C2211yescharacteristic
37C2×#484C2211yescharacteristic
38C2×#481C2211yescharacteristic
39C2×#482C2211yescharacteristic
40C2×#483C2211yescharacteristic
41C2×#468C2211yescharacteristic
42C2×#465C2211yescharacteristic
43C2×#446C2211yescharacteristic
44C2×#440C2211yescharacteristic
45C2×#435C2211yescharacteristic
46C2×#428C2211yescharacteristic
47C22×#106C2211yescharacteristic
48#2868C2211yescharacteristic
49#2859C2211yescharacteristic
50#2796—21no—
51#2767—21no—
52#2755—21no—
53#2718—21no—
54#2718—21no—
55#2715—21no—
56#2674—21no—
57#2674—21no—
58#2654—21no—
59#2628—21no—
60#2581C2211yescharacteristic
61#2538C2211yescharacteristic
62#2537C2211yescharacteristic
63#2536C2211yescharacteristic
64#2530—21no—
65#2529—21no—
66#2502C2211yescharacteristic
67#2501C2211yescharacteristic
68#2501C2211yescharacteristic
69#2499C2211yescharacteristic
70#2497C2211yescharacteristic
71#2496C2211yescharacteristic
72#2496C2211yescharacteristic
73#2496C2211yescharacteristic
74#2491C2211yescharacteristic
75#2491C2211yescharacteristic
76#2489C2211yescharacteristic
77#2489C2211yescharacteristic
78#2442C2211yescharacteristic
79#2441C2211yescharacteristic
80#2440C2211yescharacteristic
81#2440C2211yescharacteristic
82#2423—21no—
83#2422—21no—
84#2355C2211yescharacteristic
85#2352C2211yescharacteristic
86Q8×C4⋊C4C2211yescharacteristic
87D4×C4⋊C4C2211yescharacteristic
88#2334—21no—
89C4×#124C2211yescharacteristic
90#2295C2211yescharacteristic
91#2293C2211yescharacteristic
92#2100C2211yescharacteristic
93#2099C2211yescharacteristic
94#2099C2211yescharacteristic
95#2099C2211yescharacteristic
96#2096C2211yescharacteristic
97#2096C2211yescharacteristic
98#2096C2211yescharacteristic
99#2095C2211yescharacteristic
100#2094C2211yescharacteristic
101#2094C2211yescharacteristic
102#2093C2211yescharacteristic
103#2092C2211yescharacteristic
104#2085C2211yescharacteristic
105#2084C2211yescharacteristic
106#2084C2211yescharacteristic
107#2083C2211yescharacteristic
108#2077C2211yescharacteristic
109#2077C2211yescharacteristic
110#2075C2211yescharacteristic
111#2075C2211yescharacteristic
112#2068C2211yescharacteristic
113#2067C2211yescharacteristic
114#2066C2211yescharacteristic
115#2065C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2058C2211yescharacteristic
119#2058C2211yescharacteristic
120#2036C2211yescharacteristic
121#2036C2211yescharacteristic
122#2035C2211yescharacteristic
123#2035C2211yescharacteristic
124#2034C2211yescharacteristic
125#2034C2211yescharacteristic
126#2033C2211yescharacteristic
127#2033C2211yescharacteristic
128#2025C2211yescharacteristic
129#2025C2211yescharacteristic
130#2024C2211yescharacteristic
131#2024C2211yescharacteristic
132#1985C2211yescharacteristic
133#1973C2211yescharacteristic
134#1973C2211yescharacteristic
135#1968C2211yescharacteristic
136#1968C2211yescharacteristic
137#1955C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1949C2211yescharacteristic
141#1948C2211yescharacteristic
142#1948C2211yescharacteristic
143#1948C2211yescharacteristic
144#1948C2211yescharacteristic
145#1947C2211yescharacteristic
146#1944C2211yescharacteristic
147#1943C2211yescharacteristic
148#1942C2211yescharacteristic
149#1942C2211yescharacteristic
150#1936C2211yescharacteristic
151#1935C2211yescharacteristic
152#1934C2211yescharacteristic
153#1933C2211yescharacteristic
154#1928C2211yescharacteristic
155#1927C2211yescharacteristic
156#1926C2211yescharacteristic
157#1925C2211yescharacteristic
158#1924C2211yescharacteristic
159#1924C2211yescharacteristic
160#1923C2211yescharacteristic
161#1923C2211yescharacteristic
162#1920C2211yescharacteristic
163#1919C2211yescharacteristic
164#1918C2211yescharacteristic
165#1918C2211yescharacteristic
166#1854C2211yescharacteristic
167#1854C2211yescharacteristic
168#1853C2211yescharacteristic
169#1853C2211yescharacteristic
170#1853C2211yescharacteristic
171#1853C2211yescharacteristic
172#1852C2211yescharacteristic
173#1852C2211yescharacteristic
174#1847C2211yescharacteristic
175#1847C2211yescharacteristic
176#1847C2211yescharacteristic
177#1847C2211yescharacteristic
178#1847C2211yescharacteristic
179#1845C2211yescharacteristic
180#1845C2211yescharacteristic
181#1844C2211yescharacteristic
182#1844C2211yescharacteristic
183#1844C2211yescharacteristic
184#1831C2211yescharacteristic
185#1809C2211yescharacteristic
186#1809C2211yescharacteristic
187#1808C2211yescharacteristic
188#1808C2211yescharacteristic
189#1804C2211yescharacteristic
190#1804C2211yescharacteristic
191#1803C2211yescharacteristic
192#1803C2211yescharacteristic
193#1776C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#107C2211yescharacteristic
196#1763C2211yescharacteristic
197#1762C2211yescharacteristic
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200#1752C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206#542—48no—
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#126—21no—
212C2×#126—21no—
213C2×#126—21no—
214C2×#125C2311yescharacteristic
215C2×#125C2311yescharacteristic
216C2×#124—21no—
217C2×#124—21no—
218C2×#124D411yescharacteristic
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8C2311yescharacteristic
227C2×C22⋊Q8C2311yescharacteristic
228C2×#121—21no—
229C2×#121C2311yescharacteristic
230C2×#121C2311yescharacteristic
231C2×C4×Q8—21no—
232C2×C4×Q8C2311yescharacteristic
233C2×C4×Q8C2311yescharacteristic
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×#117—21no—
238C2×#117C2311yescharacteristic
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242#501—42no—
243#501—42no—
244#501—42no—
245#501—42no—
246#484—42no—
247#483—42no—
248#482—42no—
249#481—42no—
250#468—42no—
251#465—42no—
252#446—24no—
253#440—24no—
254#435—24no—
255#428—42no—
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#106—42no—
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×#106C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×#106C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×#106C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×C22⋊C8C2311yescharacteristic
303C2×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×#97C2311yescharacteristic
309C2×#97C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#399—21no—
325#399—21no—
326#399—21no—
327#399—21no—
328#399—21no—
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398—21no—
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#395—21no—
347#395—21no—
348#395—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#393—21no—
355#393—21no—
356#391—21no—
357#391D411yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#390D411yescharacteristic
363#390C2311yescharacteristic
364#390C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#389—21no—
368#389—21no—
369#389—21no—
370#389—21no—
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389C2311yescharacteristic
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
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#388D411yescharacteristic
395#388D411yescharacteristic
396#388D411yescharacteristic
397#388D411yescharacteristic
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#386—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#384—21no—
421#384—21no—
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#382—21no—
432#382—21no—
433#382D411yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#380—21no—
438#380—21no—
439#380—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448C4×C4⋊C4—21no—
449C4×C4⋊C4—21no—
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4—21no—
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462#376—21no—
463C43C2311yescharacteristic
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#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494C22×Q8—21no—
495C22×Q8—21no—
496C22×Q8C2×D411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C2×D411yescharacteristic
501C22×D4C2411yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C2411yescharacteristic
507C23×C4C2411yescharacteristic
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—22no—
514C22×C8—22no—
515C22×C8—22no—
516C22×C8—22no—
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529C4⋊Q8—44no—
530C4⋊Q8—82no—
531#126—44no—
532#126—44no—
533#126—44no—
534#125—41no—
535#125—41no—
536#125—41no—
537#125—41no—
538#124—24no—
539#124—44no—
540#124—44no—
541#123—44no—
542#123—44no—
543#123—82no—
544#123—82no—
545C22⋊Q8—44no—
546C22⋊Q8—44no—
547C22⋊Q8—44no—
548C22⋊Q8—41no—
549C22⋊Q8—41no—
550C22⋊Q8—41no—
551C22⋊Q8—41no—
552#121—44no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—41no—
557C4×Q8—22no—
558C4×Q8—22no—
559C4×Q8—22no—
560C4×Q8—22no—
561C4×Q8—44no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—44no—
567#117—44no—
568#117—41no—
569#117—41no—
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—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—41no—
609C2×C4⋊C4—41no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4—41no—
612C2×C4⋊C4—41no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C22⋊C4C2×D411yescharacteristic
657C2×C22⋊C4C2×D411yescharacteristic
658C2×C22⋊C4C2×D411yescharacteristic
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—21no—
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42C2×D411yescharacteristic
673C2×C42C2×D411yescharacteristic
674C2×C42C2×D411yescharacteristic
675C2×C42C2×D411yescharacteristic
676C2×C42C2411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681#107—22no—
682#107—22no—
683#107—22no—
684#107—22no—
685#107—22no—
686#107—22no—
687#107—41no—
688#107—41no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#106—22no—
694#106—22no—
695#106—22no—
696#106—22no—
697#106—22no—
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—
707#106—41no—
708C4⋊C8—22no—
709C4⋊C8—22no—
710C4⋊C8—22no—
711C4⋊C8—22no—
712#103—22no—
713#103—22no—
714#103—22no—
715#103—41no—
716#103—41no—
717#103—41no—
718#103—41no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726C22⋊C8—22no—
727C22⋊C8—22no—
728C22⋊C8—22no—
729C22⋊C8—22no—
730C22⋊C8—22no—
731C22⋊C8—22no—
732#97—22no—
733#97—22no—
734#97—22no—
735#97—22no—
736#97#4114yes—
737C4×C8—22no—
738C4×C8—22no—
739C4×C8—22no—
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#95—21no—
775#95—21no—
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
786C24C22×D411yescharacteristic
787C2×Q8—22no—
788C2×Q8—22no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—21no—
795C2×Q8—41no—
796C2×Q8—42no—
797C2×Q8—42no—
798C2×Q8—81no—
799C2×Q8—81no—
800C2×Q8—81no—
801C2×Q8—81no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—41no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—81no—
814C2×D4—81no—
815C2×D4—81no—
816C2×D4—81no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
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—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
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×C4C22×D411yescharacteristic
868C22×C4C2511yescharacteristic
869SD16—44no—
870M16—44no—
871C2×C8—21no—
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—44no—
890C2×C8C2×#4112yes—
891C2×C8C2×#4112yes—
892C2×C8H(5,𝔽2)12yes—
893C2×C8H(5,𝔽2)12yes—
894C2×C82−1+412yes—
895C2×C82−1+412yes—
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—21no—
927C4⋊C4—21no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
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—81no—
946C4⋊C4—81no—
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—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—22no—
970C22⋊C4—22no—
971C22⋊C4—22no—
972C22⋊C4—22no—
973C22⋊C4—41no—
974C22⋊C4—41no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4AGL(1,ℤ/8)14yes—
998C42—22no—
999C42—22no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—21no—
1008C42—41no—
1009C42—41no—
1010C42—42no—
1011C42—42no—
1012C42—42no—
1013C42—42no—
1014C42—42no—
1015C42—81no—
1016C42—81no—
1017C42—81no—
1018C42C2×#4112yes—
1019C422−1+412yes—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—21no—
1031C23—21no—
1032C23—21no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23C2×AGL(1,ℤ/8)12yes—
1041C23C23×D411yescharacteristic
1042Q8—44no—
1043Q8—41no—
1044Q8—41no—
1045Q8—41no—
1046Q8—41no—
1047Q8—162no—
1048Q8—162no—
1049D4—44no—
1050D4—41no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—162no—
1055D4—162no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
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—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
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—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—84no—
1141C2×C4—162no—
1142C2×C4—162no—
1143C2×C4—162no—
1144C2×C4#54712yes—
1145C2×C4#54712yes—
1146C2×C4C2×AGL(1,ℤ/8)12yes—
1147C2×C4C2×AGL(1,ℤ/8)12yes—
1148C2×C4#57712yes—
1149C2×C4C22×#4111yescharacteristic
1150C2×C4C2×H(5,𝔽2)11yescharacteristic
1151C2×C4C2×H(5,𝔽2)11yescharacteristic
1152C2×C4C2×2−1+411yescharacteristic
1153C2×C4C2×2−1+411yescharacteristic
1154C2×C4C2×2−1+411yescharacteristic
1155C8—22no—
1156C8—22no—
1157C8—22no—
1158C8—41no—
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C8#54214yescomplemented
1163C22—22no—
1164C22—22no—
1165C22—22no—
1166C22—41no—
1167C22—41no—
1168C22—41no—
1169C22—41no—
1170C22—41no—
1171C22—41no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—41no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22C2×#54711yescharacteristic
1185C22#349811yescharacteristic
1186C22#349911yescharacteristic
1187C22C22×AGL(1,ℤ/8)11yescharacteristic
1188C22C2×#57711yescharacteristic
1189C22#358611yescharacteristic
1190C22#358611yescharacteristic
1191C4—22no—
1192C4—22no—
1193C4—22no—
1194C4—22no—
1195C4—22no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—41no—
1200C4—41no—
1201C4—41no—
1202C4—41no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4—81no—
1216C4—81no—
1217C4—81no—
1218C4C2×#54211yescharacteristic
1219C4#351111yescharacteristic
1220C4#354411yescharacteristic
1221C4#355211yescharacteristic
1222C2—42no—
1223C2—81no—
1224C2—161no—
1225C2#3937711yescharacteristic
1226C2#6125211yescharacteristic
1227C2#6128111yescharacteristic
1228C2#6242111yescharacteristic
1229C2#6244211yescharacteristic
1230C2#6250311yescharacteristic
1231C2#6251311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2537C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #40000C2semidirect
3. #33316C2semidirect
4. #32282C2semidirect
5. #32281C2semidirect
6. #32280C2semidirect
7. #32278C2semidirect
8. #30803C2semidirect
9. #30801C2semidirect
10. #30794C2semidirect
11. #30791C2semidirect
12. #29987C2semidirect
13. #29983C2semidirect
14. #28275C2semidirect
16. #27944C2semidirect
17. #27924C2semidirect
18. #27853C2semidirect
19. #27839C2semidirect
20. #27799C2semidirect
21. #27796C2semidirect
22. #26078C2semidirect
23. #26068C2semidirect
24. #25073C2semidirect
25. #25070C2semidirect
27. #25024C2semidirect
28. #22729C2semidirect
29. #22659C2semidirect
30. #21632C2semidirect
31. #21288C2semidirect
1162. C8#542semidirect

Maximal subgroups

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

subgroupindex
#400002
#393772
#333162
#322822
#322812
#322802
#322782
#308032
#308012
#307942
#307912
#299872
#299832
#282752
#282362
#279442
#279242
#278532
#278392
#277992
#277962
#260782
#260682
#250732
#250702
#250262
#250242
#227292
#226592
#216322
#212882