Finite Group Databasebeta

← #6837099

Subgroups — #6837099

Order 512.

1477 conjugacy classes of subgroups.

The subgroup lattice has 1206 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39901C211yesmaximal, characteristic, complemented
2#39877C211yesmaximal, characteristic
3#33208C211yesmaximal, characteristic, complemented
4#32208C211yesmaximal, characteristic, complemented
5#32207C211yesmaximal, characteristic, complemented
6#32136C211yesmaximal, characteristic, complemented
7#32135C211yesmaximal, characteristic, complemented
8#31613C211yesmaximal, characteristic, complemented
9#31610C211yesmaximal, characteristic, complemented
10#31573C211yesmaximal, characteristic, complemented
11#31570C211yesmaximal, characteristic, complemented
12#29944C211yesmaximal, characteristic, complemented
13#29694C211yesmaximal, characteristic
14#29011C211yesmaximal, characteristic, complemented
15#29011C211yesmaximal, characteristic, complemented
16#28846C211yesmaximal, characteristic, complemented
17#28841C211yesmaximal, characteristic, complemented
18#28793C211yesmaximal, characteristic, complemented
19#28791C211yesmaximal, characteristic, complemented
20#28067C211yesmaximal, characteristic, complemented
21#28065C211yesmaximal, characteristic, complemented
22#27731C211yesmaximal, characteristic, complemented
23#26094C211yesmaximal, characteristic, complemented
24#25843C211yesmaximal, characteristic, complemented
25#25473C211yesmaximal, characteristic, complemented
26#25458C211yesmaximal, characteristic, complemented
27#25064C211yesmaximal, characteristic, complemented
28#23065C211yesmaximal, characteristic, complemented
29#22519C211yesmaximal, characteristic, complemented
30C8×C22⋊Q8C211yesmaximal, characteristic, complemented
31#21401C211yesmaximal, characteristic
32C2×#554C2211yescharacteristic
33C2×#532C2211yescharacteristic
34C2×#499C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×C8×Q8C2211yescharacteristic
38C22×C4×C8C2211yescharacteristic
39#2851C2211yescharacteristic
40#2851C2211yescharacteristic
41#2766—21no—
42#2755—21no—
43#2722—21no—
44#2700—21no—
45#2690—21no—
46#2681—21no—
47#2674—21no—
48#2672—21no—
49#2655—21no—
50#2638—21no—
51#2584C2211yescharacteristic
52#2580C2211yescharacteristic
53#2570C2211yescharacteristic
54#2570C2211yescharacteristic
55#2566C2211yescharacteristic
56#2552C2211yescharacteristic
57#2551C2211yescharacteristic
58#2550C2211yescharacteristic
59#2507C2211yescharacteristic
60#2507C2211yescharacteristic
61#2496C2211yescharacteristic
62#2496C2211yescharacteristic
63#2495C2211yescharacteristic
64#2494C2211yescharacteristic
65#2491C2211yescharacteristic
66#2490C2211yescharacteristic
67#2478—21no—
68#2478—21no—
69#2445C2211yescharacteristic
70#2445C2211yescharacteristic
71#2432—21no—
72#2422C2211yescharacteristic
73#2420C2211yescharacteristic
74#2406—21no—
75#2370C2211yescharacteristic
76#2357C2211yescharacteristic
77#2355C2211yescharacteristic
78#2336—21no—
79#2322—21no—
80C4×C22⋊Q8C2211yescharacteristic
81#2285C2211yescharacteristic
82#2101C2211yescharacteristic
83#2100C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2093C2211yescharacteristic
87#2093C2211yescharacteristic
88#2092C2211yescharacteristic
89#2092C2211yescharacteristic
90#2088C2211yescharacteristic
91#2087C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2084C2211yescharacteristic
95#2084C2211yescharacteristic
96#2083C2211yescharacteristic
97#2083C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2075C2211yescharacteristic
101#2075C2211yescharacteristic
102#2073C2211yescharacteristic
103#2071C2211yescharacteristic
104#2067C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2065C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2058C2211yescharacteristic
113#2058C2211yescharacteristic
114#2057C2211yescharacteristic
115#2057C2211yescharacteristic
116#2041C2211yescharacteristic
117#2041C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2033C2211yescharacteristic
121#2033C2211yescharacteristic
122#1991C2211yescharacteristic
123#1991C2211yescharacteristic
124#1991C2211yescharacteristic
125#1990C2211yescharacteristic
126#1990C2211yescharacteristic
127#1990C2211yescharacteristic
128#1989C2211yescharacteristic
129#1989C2211yescharacteristic
130#1989C2211yescharacteristic
131#1987C2211yescharacteristic
132#1984C2211yescharacteristic
133#1957C2211yescharacteristic
134#1957C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1948C2211yescharacteristic
140#1948C2211yescharacteristic
141#1942C2211yescharacteristic
142#1942C2211yescharacteristic
143#1942C2211yescharacteristic
144#1941C2211yescharacteristic
145#1941C2211yescharacteristic
146#1941C2211yescharacteristic
147#1939C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1934C2211yescharacteristic
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1921C2211yescharacteristic
161#1921C2211yescharacteristic
162#1921C2211yescharacteristic
163#1919C2211yescharacteristic
164#1918C2211yescharacteristic
165#1918C2211yescharacteristic
166#1916C2211yescharacteristic
167#1916C2211yescharacteristic
168#1893C2211yescharacteristic
169#1893C2211yescharacteristic
170#1893C2211yescharacteristic
171#1893C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic
176#1850C2211yescharacteristic
177#1850C2211yescharacteristic
178#1846C2211yescharacteristic
179#1835C2211yescharacteristic
180#1834C2211yescharacteristic
181#1808C2211yescharacteristic
182#1808C2211yescharacteristic
183#1807C2211yescharacteristic
184#1807C2211yescharacteristic
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1802C2211yescharacteristic
189#1797C2211yescharacteristic
190C4×#107C2211yescharacteristic
191C4×#106C2211yescharacteristic
192C8×C4⋊C4C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194C8×C4⋊C4C2211yescharacteristic
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic
203C22×#41—21no—
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206#554—24no—
207#554—42no—
208#532—24no—
209#532—42no—
210C2×C4⋊Q8—21no—
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#126—21no—
215C2×#126—21no—
216C2×#125—21no—
217C2×#125C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#125C2311yescharacteristic
220C2×#124—21no—
221C2×#124—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×#123—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8D411yescharacteristic
229C2×#121—21no—
230C2×#121C2311yescharacteristic
231C2×#121C2311yescharacteristic
232C2×C4×Q8C2311yescharacteristic
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117—21no—
239C22×C4⋊C4—21no—
240C22×C42C2311yescharacteristic
241#499—42no—
242#478—24no—
243#478—42no—
244C8×Q8—42no—
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C4×C8—42no—
286C2×C4×C8C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294#401—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#399—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#396—21no—
319#396—21no—
320#395—21no—
321#395—21no—
322#395—21no—
323#395—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#393—21no—
333#393—21no—
334#391—21no—
335#391—21no—
336#391D411yescharacteristic
337#390—21no—
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389D411yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387D411yescharacteristic
391#387D411yescharacteristic
392#386—21no—
393#386—21no—
394#386—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385D411yescharacteristic
405#385D411yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#383—21no—
412#382—21no—
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#381—21no—
419#381—21no—
420#380—21no—
421#380D411yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C22⋊C4—21no—
443C4×C22⋊C4C2311yescharacteristic
444C4×C22⋊C4C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
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
487C2×#41—44no—
488C2×#41—82no—
489C2×#41—82no—
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8C2×D411yescharacteristic
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C2×D411yescharacteristic
504C23×C4C2×D411yescharacteristic
505C23×C4C2411yescharacteristic
506C22×C8—22no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8—41no—
511C22×C8—41no—
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C4⋊Q8—22no—
521C4⋊Q8—22no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524C4⋊Q8—82no—
525#127—22no—
526#127—41no—
527#126—82no—
528#126—82no—
529#125—22no—
530#125—22no—
531#125—22no—
532#125—22no—
533#125—22no—
534#125—41no—
535#125—44no—
536#124—44no—
537#124—82no—
538#123—44no—
539#123—82no—
540#123—82no—
541C22⋊Q8—24no—
542C22⋊Q8—44no—
543C22⋊Q8—44no—
544C22⋊Q8—44no—
545#121—22no—
546#121—22no—
547#121—44no—
548#121—41no—
549#121—41no—
550C4×Q8—22no—
551C4×Q8—22no—
552C4×D4—22no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—41no—
558C4×D4—41no—
559C4×D4—44no—
560C4×D4#4114yes—
561#117—82no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—44no—
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C42—22no—
647C2×C42—22no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42C2×D411yescharacteristic
657C2×C42C2×D411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664#107—22no—
665#107—22no—
666#107—22no—
667#107—41no—
668#107—41no—
669#107—41no—
670#107—41no—
671#107—41no—
672#106—22no—
673#106—41no—
674#106—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679#106—41no—
680C4⋊C8—22no—
681C4⋊C8—22no—
682C4⋊C8—22no—
683C4⋊C8—22no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686#102—22no—
687#102—22no—
688#102—22no—
689#102—22no—
690#102—22no—
691#102—22no—
692#102—22no—
693#102—22no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702C22⋊C8—41no—
703C22⋊C8—41no—
704C4×C8—22no—
705C4×C8—22no—
706C4×C8—22no—
707C4×C8—22no—
708C4×C8—41no—
709C4×C8—41no—
710C4×C8—41no—
711C4×C8—41no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760C24—21no—
761C24—21no—
762C24C22×D411yescharacteristic
763#41—816no—
764C2×Q8—22no—
765C2×Q8—22no—
766C2×Q8—41no—
767C2×Q8—42no—
768C2×Q8—42no—
769C2×Q8—42no—
770C2×Q8—81no—
771C2×Q8—81no—
772C2×Q8—81no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—42no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4C2×#4112yes—
797C22×C4—22no—
798C22×C4—22no—
799C22×C4—22no—
800C22×C4—21no—
801C22×C4—22no—
802C22×C4—22no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—24no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—41no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—81no—
829C22×C4—81no—
830C22×C4—81no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C2511yescharacteristic
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—44no—
871C2×C8—44no—
872C2×C82−1+412yes—
873C2×C82−1+412yes—
874C2×C82−1+412yes—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
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—41no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4#13514yes—
943C4⋊C4C2×#4112yes—
944C22⋊C4—22no—
945C22⋊C4—22no—
946C22⋊C4—24no—
947C22⋊C4—22no—
948C22⋊C4—22no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C42—22no—
973C42—22no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—42no—
985C42—81no—
986C42—81no—
987C42—81no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42C2×#4112yes—
993C42H(5,𝔽2)12yes—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—22no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23#57612yes—
1015C23C23×D411yescharacteristic
1016Q8—44no—
1017Q8—84no—
1018Q8—162no—
1019D4—22no—
1020D4—22no—
1021D4—41no—
1022D4—41no—
1023D4—41no—
1024D4—41no—
1025D4—41no—
1026D4—41no—
1027D4—84no—
1028D4—84no—
1029D4—84no—
1030D4—84no—
1031C2×C4—28no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
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—44no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
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—84no—
1113C2×C4—84no—
1114C2×C4—84no—
1115C2×C4—162no—
1116C2×C4#54612yes—
1117C2×C4#54612yes—
1118C2×C4C2×#13512yes—
1119C2×C4C2×#13512yes—
1120C2×C4C2×#13512yes—
1121C2×C4#57712yes—
1122C2×C4C22×#4111yescharacteristic
1123C2×C4C2×H(5,𝔽2)11yescharacteristic
1124C2×C4C2×2−1+411yescharacteristic
1125C2×C4C2×2−1+411yescharacteristic
1126C2×C4C2×2−1+411yescharacteristic
1127C2×C4#58511yescharacteristic
1128C8—22no—
1129C8—22no—
1130C8—22no—
1131C8—41no—
1132C8—41no—
1133C8—41no—
1134C8—41no—
1135C8—41no—
1136C22—22no—
1137C22—22no—
1138C22—22no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—42no—
1144C22—42no—
1145C22—42no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22—81no—
1154C22—81no—
1155C22—81no—
1156C22—81no—
1157C22C2×#54611yescharacteristic
1158C22#349711yescharacteristic
1159C22#349911yescharacteristic
1160C22C22×#13511yescharacteristic
1161C22C2×#57611yescharacteristic
1162C22C2×#57711yescharacteristic
1163C22#358411yescharacteristic
1164C4—22no—
1165C4—22no—
1166C4—22no—
1167C4—22no—
1168C4—22no—
1169C4—22no—
1170C4—41no—
1171C4—41no—
1172C4—41no—
1173C4—41no—
1174C4—41no—
1175C4—41no—
1176C4—41no—
1177C4—42no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4#346111yescharacteristic
1192C4#350911yescharacteristic
1193C4#353811yescharacteristic
1194C4#354111yescharacteristic
1195C2—42no—
1196C2—82no—
1197C2—161no—
1198C2#3943511yescharacteristic
1199C2#6112411yescharacteristic
1200C2#6116711yescharacteristic
1201C2#6236311yescharacteristic
1202C2#6238611yescharacteristic
1203C2#6247011yescharacteristic
1204C2#6249211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#532C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39901C2semidirect
3. #33208C2semidirect
4. #32208C2semidirect
5. #32207C2semidirect
6. #32136C2semidirect
7. #32135C2semidirect
8. #31613C2semidirect
9. #31610C2semidirect
10. #31573C2semidirect
11. #31570C2semidirect
12. #29944C2semidirect
14. #29011C2semidirect
15. #29011C2semidirect
16. #28846C2semidirect
17. #28841C2semidirect
18. #28793C2semidirect
19. #28791C2semidirect
20. #28067C2semidirect
21. #28065C2semidirect
22. #27731C2semidirect
23. #26094C2semidirect
24. #25843C2semidirect
25. #25473C2semidirect
26. #25458C2semidirect
27. #25064C2semidirect
28. #23065C2semidirect
29. #22519C2semidirect
30. C8×C22⋊Q8C2semidirect

Maximal subgroups

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

subgroupindex
#399012
#398772
#332082
#322082
#322072
#321362
#321352
#316132
#316102
#315732
#315702
#299442
#296942
#290112
#288462
#288412
#287932
#287912
#280672
#280652
#277312
#260942
#258432
#254732
#254582
#250642
#230652
#225192
C8×C22⋊Q82
#214012