Finite Group Databasebeta

← #7107524

Subgroups — #7107524

Order 512.

1530 conjugacy classes of subgroups.

The subgroup lattice has 1292 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59208C211yesmaximal, characteristic, complemented
2#39403C211yesmaximal, characteristic, complemented
3#32452C211yesmaximal, characteristic, complemented
4#32242C211yesmaximal, characteristic, complemented
5#32062C211yesmaximal, characteristic, complemented
6#31768C211yesmaximal, characteristic, complemented
7#31444C211yesmaximal, characteristic, complemented
8#31260C211yesmaximal, characteristic, complemented
9#31104C211yesmaximal, characteristic, complemented
10#31016C211yesmaximal, characteristic
11#29109C211yesmaximal, characteristic, complemented
12#29095C211yesmaximal, characteristic, complemented
13#28984C211yesmaximal, characteristic, complemented
14#28983C211yesmaximal, characteristic, complemented
15#28017C211yesmaximal, characteristic, complemented
16#27883C211yesmaximal, characteristic, complemented
17#27825C211yesmaximal, characteristic, complemented
18#27711C211yesmaximal, characteristic, complemented
19#27539C211yesmaximal, characteristic, complemented
20#27450C211yesmaximal, characteristic, complemented
21#27344C211yesmaximal, characteristic, complemented
22#27243C211yesmaximal, characteristic, complemented
23#27143C211yesmaximal, characteristic, complemented
24#26673C211yesmaximal, characteristic, complemented
25#26298C211yesmaximal, characteristic, complemented
26#26202C211yesmaximal, characteristic, complemented
27#23764C211yesmaximal, characteristic, complemented
28#23302C211yesmaximal, characteristic, complemented
29#23075C211yesmaximal, characteristic, complemented
30#22938C211yesmaximal, characteristic, complemented
31#22046C211yesmaximal, characteristic, complemented
32C2×#542—21no—
33C2×#480C2211yescharacteristic
34C2×#476C2211yescharacteristic
35C2×#447C2211yescharacteristic
36#2857C2211yescharacteristic
37#2757—21no—
38#2749—21no—
39#2716—21no—
40#2715—21no—
41#2700—21no—
42#2686—21no—
43#2638—21no—
44#2603—21no—
45#2566C2211yescharacteristic
46#2551C2211yescharacteristic, complemented
47#2547C2211yescharacteristic
48#2534—21no—
49#2526—21no—
50#2513C2211yescharacteristic
51#2512C2211yescharacteristic
52#2512C2211yescharacteristic, complemented
53#2504C2211yescharacteristic
54#2496C2211yescharacteristic
55#2491C2211yescharacteristic
56#2491C2211yescharacteristic, complemented
57#2490C2211yescharacteristic
58#2483—21no—
59#2480—21no—
60#2470—21no—
61#2465—21no—
62#2452C2211yescharacteristic, complemented
63#2442C2211yescharacteristic
64#2440C2211yescharacteristic, complemented
65#2422C2211yescharacteristic, complemented
66#2420C2211yescharacteristic
67#2416C2211yescharacteristic
68#2408C2211yescharacteristic
69#2365C2211yescharacteristic, complemented
70#2361C2211yescharacteristic
71#2358—21no—
72#2357C2211yescharacteristic
73D4×C4⋊C4C2211yescharacteristic
74#2344C2211yescharacteristic, complemented
75D4×C22⋊C4C2211yescharacteristic
76C4×#123C2211yescharacteristic
77C4×#121C2211yescharacteristic
78C2×#390C2211yescharacteristic
79#2283C2211yescharacteristic
80#2101C2211yescharacteristic, complemented
81#2101C2211yescharacteristic, complemented
82#2100C2211yescharacteristic, complemented
83#2100C2211yescharacteristic, complemented
84#2092C2211yescharacteristic, complemented
85#2087C2211yescharacteristic, complemented
86#2085C2211yescharacteristic, complemented
87#2077C2211yescharacteristic
88#2077C2211yescharacteristic
89#2077C2211yescharacteristic
90#2077C2211yescharacteristic, complemented
91#2077C2211yescharacteristic, complemented
92#2075C2211yescharacteristic
93#2075C2211yescharacteristic
94#2075C2211yescharacteristic
95#2073C2211yescharacteristic, complemented
96#2073C2211yescharacteristic, complemented
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic, complemented
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic, complemented
103#2065C2211yescharacteristic
104#2059C2211yescharacteristic, complemented
105#2057C2211yescharacteristic, complemented
106#2054C2211yescharacteristic
107#2054C2211yescharacteristic
108#2034C2211yescharacteristic
109#2033C2211yescharacteristic
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic
112#2025C2211yescharacteristic, complemented
113#2023C2211yescharacteristic
114#2023C2211yescharacteristic
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic
117#2023C2211yescharacteristic
118#1999C2211yescharacteristic
119#1999C2211yescharacteristic
120#1993C2211yescharacteristic, complemented
121#1993C2211yescharacteristic, complemented
122#1993C2211yescharacteristic, complemented
123#1992C2211yescharacteristic, complemented
124#1990C2211yescharacteristic, complemented
125#1989C2211yescharacteristic, complemented
126#1988C2211yescharacteristic, complemented
127#1972C2211yescharacteristic
128#1972C2211yescharacteristic
129#1972C2211yescharacteristic
130#1970C2211yescharacteristic
131#1954C2211yescharacteristic
132#1949C2211yescharacteristic, complemented
133#1948C2211yescharacteristic, complemented
134#1943C2211yescharacteristic, complemented
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic, complemented
143#1934C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic, complemented
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic
153#1924C2211yescharacteristic, complemented
154#1924C2211yescharacteristic, complemented
155#1921C2211yescharacteristic, complemented
156#1921C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1920C2211yescharacteristic, complemented
160#1919C2211yescharacteristic, complemented
161#1919C2211yescharacteristic, complemented
162#1917C2211yescharacteristic, complemented
163#1917C2211yescharacteristic, complemented
164#1893C2211yescharacteristic
165#1893C2211yescharacteristic
166#1893C2211yescharacteristic, complemented
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1874C2211yescharacteristic
172#1874C2211yescharacteristic
173#1874C2211yescharacteristic, complemented
174#1869C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1853C2211yescharacteristic
178#1853C2211yescharacteristic, complemented
179#1853C2211yescharacteristic, complemented
180#1847C2211yescharacteristic, complemented
181#1836C2211yescharacteristic, complemented
182#1824C2211yescharacteristic
183#1824C2211yescharacteristic
184#1824C2211yescharacteristic, complemented
185#1802C2211yescharacteristic
186#1786C2211yescharacteristic
187#1786C2211yescharacteristic
188#1786C2211yescharacteristic
189#1776C2211yescharacteristic, complemented
190#1776C2211yescharacteristic, complemented
191C4×#106C2211yescharacteristic, complemented
192#1771C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic, complemented
197#1762C2211yescharacteristic, complemented
198#1752C2211yescharacteristic, complemented
199#1752C2211yescharacteristic, complemented
200#1749C2211yescharacteristic
201#1749C2211yescharacteristic
202C2×#340C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207#542—48no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×#126—21no—
213C2×#126—21no—
214C2×#126—21no—
215C2×#125C2311yescharacteristic
216C2×#124—21no—
217C2×#124—21no—
218C2×#124—21no—
219C2×#123—21no—
220C2×#123D411yescharacteristic
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×#121—21no—
225C2×#121C2311yescharacteristic
226C2×#121C2311yescharacteristic
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#120—21no—
230C2×C4×Q8—21no—
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×#117—21no—
239C22×C4⋊C4C2311yescharacteristic
240C22×C4⋊C4C2311yescharacteristic
241C22×C4⋊C4C2311yescharacteristic
242C22×C22⋊C4—21no—
243C22×C22⋊C4—21no—
244C22×C22⋊C4—21no—
245C22×C42C2311yescharacteristic
246#480—24no—
247#476—24no—
248#447—24no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×#97C2311yescharacteristic
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296#400—21no—
297#400—21no—
298#398—21no—
299#398—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#395—21no—
319#395—21no—
320#395—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#393—21no—
329#393—21no—
330#393—21no—
331#392—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#390—21no—
336#390—21no—
337#390—21no—
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#389—21no—
351#389—21no—
352#389—21no—
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388D411yescharacteristic
373#388D411yescharacteristic
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387D411yescharacteristic
380#387D411yescharacteristic
381#386—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386D411yescharacteristic
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385D411yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#383—21no—
404#382C2311yescharacteristic
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#381—21no—
408#381—21no—
409#381—21no—
410#381—21no—
411#381D411yescharacteristic
412#380—21no—
413#380—21no—
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#379—21no—
423#379—21no—
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4C2311yescharacteristic
437C4×C22⋊C4C2311yescharacteristic
438C4×C22⋊C4C2311yescharacteristic
439#376—21no—
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
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#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482C25—21no—
483C22×Q8—21no—
484C22×Q8—21no—
485C22×Q8—21no—
486C22×D4—22no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—41no—
493C22×D4—41no—
494C22×D4—41no—
495C22×D4—41no—
496C22×D4—41no—
497C22×D4C2×D411yescharacteristic
498C22×D4C2411yescharacteristic
499C22×D4C2411yescharacteristic
500C22×D4C2411yescharacteristic
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4C2×D411yescharacteristic
508C23×C4C2×D411yescharacteristic
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C2×D8—22no—
512C2×D8—22no—
513C2×D8—41no—
514C2×D8—41no—
515C2×D8—41no—
516C2×D8—41no—
517C22×C8—41no—
518C22×C8—41no—
519C22×C8—41no—
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C4⋊Q8—22no—
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534C4⋊Q8—44no—
535#126—44no—
536#126—44no—
537#126—82no—
538#125—41no—
539#125—41no—
540#124—44no—
541#124—44no—
542#124—44no—
543#123—24no—
544#123—44no—
545C22⋊Q8—44no—
546C22⋊Q8—44no—
547C22⋊Q8—44no—
548#121—22no—
549#121—22no—
550#121—41no—
551#121—41no—
552#121—44no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—41no—
557#120—44no—
558C4×Q8—44no—
559C4×D4—22no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—44no—
568C4×D4—82no—
569C4×D4—82no—
570#117—44no—
571C2×C4⋊C4—22no—
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—41no—
595C2×C4⋊C4—41no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—41no—
598C2×C4⋊C4—41no—
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×C22⋊C4—21no—
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⋊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⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—82no—
657C2×C22⋊C4—82no—
658C2×C22⋊C4—82no—
659C2×C22⋊C4C2×D411yescharacteristic
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C42—21no—
668C2×C42—21no—
669C2×C42—21no—
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—41no—
675C2×C42—41no—
676C2×C42C2×D411yescharacteristic
677C2×C42C2×D411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683#107—22no—
684#107—22no—
685#107—41no—
686#107—41no—
687#106—22no—
688#106—22no—
689#106—41no—
690#106—41no—
691#106—41no—
692#106—41no—
693C4⋊C8—22no—
694C4⋊C8—41no—
695C4⋊C8—41no—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708#102—41no—
709#102—41no—
710#102—41no—
711#102—41no—
712#102—41no—
713#102—41no—
714#102—41no—
715#102#4114yes—
716C22⋊C8—22no—
717C22⋊C8—22no—
718C22⋊C8—41no—
719C22⋊C8—41no—
720C22⋊C8—41no—
721C22⋊C8—41no—
722C22⋊C8—41no—
723#97—41no—
724#97—41no—
725#97—41no—
726#97—41no—
727#97—41no—
728#97—41no—
729C4×C8—41no—
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#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#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769C24—21no—
770C24—21no—
771C24—21no—
772C24—42no—
773C24—42no—
774C24—42no—
775C24—42no—
776C24—81no—
777C24—81no—
778C24—81no—
779C24C22×D411yescharacteristic
780C24C22×D411yescharacteristic
781C2×Q8—42no—
782C2×Q8—42no—
783C2×Q8—42no—
784C2×Q8—42no—
785C2×Q8—81no—
786C2×Q8—81no—
787C2×Q8—81no—
788C2×Q8—81no—
789C2×Q8—81no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—41no—
808C2×D4—41no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—42no—
812C2×D4—42no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—42no—
816C2×D4—42no—
817C2×D4—81no—
818C2×D4—82no—
819C2×D4—82no—
820C2×D4—82no—
821C2×D4—82no—
822C2×D4—81no—
823C2×D4—81no—
824C2×D4—81no—
825C2×D4—81no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4AGL(1,ℤ/8)14yes—
829C2×D4C2×#4112yes—
830C22×C4—21no—
831C22×C4—22no—
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—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—41no—
857C22×C4—41no—
858C22×C4—41no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—42no—
862C22×C4—42no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—81no—
867C22×C4—81no—
868C22×C4—81no—
869C22×C4—81no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C2511yescharacteristic
892D8—82no—
893D8—82no—
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—21no—
905C2×C8—21no—
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—82no—
918C2×C8C2×#4112yes—
919C4⋊C4—22no—
920C4⋊C4—22no—
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—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—41no—
947C4⋊C4—41no—
948C4⋊C4—41no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
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⋊C4C2×#4112yes—
972C22⋊C4—22no—
973C22⋊C4—22no—
974C22⋊C4—22no—
975C22⋊C4—41no—
976C22⋊C4—41no—
977C22⋊C4—41no—
978C22⋊C4—41no—
979C22⋊C4—41no—
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—42no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—41no—
1030C42—41no—
1031C42—42no—
1032C42—42no—
1033C42—42no—
1034C42—42no—
1035C42—42no—
1036C42—81no—
1037C42—81no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—22no—
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—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—84no—
1072C23—84no—
1073C23—84no—
1074C23—84no—
1075C23—162no—
1076C23—162no—
1077C23—162no—
1078C23C2×AGL(1,ℤ/8)12yes—
1079C23C2×AGL(1,ℤ/8)12yes—
1080C23C23×D411yescharacteristic
1081Q8—84no—
1082Q8—162no—
1083Q8—162no—
1084D4—22no—
1085D4—22no—
1086D4—44no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—84no—
1098D4—84no—
1099D4—84no—
1100D4—162no—
1101D4—162no—
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—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—22no—
1123C2×C4—21no—
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—21no—
1137C2×C4—21no—
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—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—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—82no—
1185C2×C4—82no—
1186C2×C4—84no—
1187C2×C4—162no—
1188C2×C4—162no—
1189C2×C4—162no—
1190C2×C4—162no—
1191C2×C4—162no—
1192C2×C4C2×AGL(1,ℤ/8)12yes—
1193C2×C4C22×#4111yescharacteristic
1194C2×C4#58511yescharacteristic
1195C2×C4#58511yescharacteristic
1196C2×C4#58511yescharacteristic
1197C2×C4#58511yescharacteristic
1198C2×C4#58511yescharacteristic
1199C8—22no—
1200C8—41no—
1201C8—41no—
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—41no—
1219C22—41no—
1220C22—41no—
1221C22—42no—
1222C22—42no—
1223C22—42no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—168no—
1243C22D4×#4111yescharacteristic
1244C22#348511yescharacteristic
1245C22#350011yescharacteristic
1246C22C22×AGL(1,ℤ/8)11yescharacteristic
1247C22#358511yescharacteristic
1248C22#358511yescharacteristic
1249C22#358611yescharacteristic
1250C4—22no—
1251C4—41no—
1252C4—42no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—41no—
1261C4—41no—
1262C4—41no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4—81no—
1274C4—81no—
1275C4#351011yescharacteristic
1276C4#352111yescharacteristic
1277C4#356611yescharacteristic
1278C4#356811yescharacteristic
1279C2—42no—
1280C2—42no—
1281C2—82no—
1282C2—161no—
1283C2—161no—
1284C2#4445511yescharacteristic
1285C2#6145111yescharacteristic
1286C2#6150311yescharacteristic
1287C2#6170711yescharacteristic
1288C2#6178211yescharacteristic
1289C2#6256411yescharacteristic
1290C2#6258311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#31016C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59208C2semidirect
2. #39403C2semidirect
3. #32452C2semidirect
4. #32242C2semidirect
5. #32062C2semidirect
6. #31768C2semidirect
7. #31444C2semidirect
8. #31260C2semidirect
9. #31104C2semidirect
11. #29109C2semidirect
12. #29095C2semidirect
13. #28984C2semidirect
14. #28983C2semidirect
15. #28017C2semidirect
16. #27883C2semidirect
17. #27825C2semidirect
18. #27711C2semidirect
19. #27539C2semidirect
20. #27450C2semidirect
21. #27344C2semidirect
22. #27243C2semidirect
23. #27143C2semidirect
24. #26673C2semidirect
25. #26298C2semidirect
26. #26202C2semidirect
27. #23764C2semidirect
28. #23302C2semidirect
29. #23075C2semidirect
30. #22938C2semidirect
31. #22046C2semidirect
46. #2551C22semidirect
52. #2512C22semidirect
56. #2491C22semidirect
62. #2452C22semidirect
64. #2440C22semidirect
65. #2422C22semidirect
69. #2365C22semidirect
74. #2344C22semidirect
80. #2101C22semidirect
81. #2101C22semidirect
82. #2100C22semidirect
83. #2100C22semidirect
84. #2092C22semidirect
85. #2087C22semidirect
86. #2085C22semidirect
90. #2077C22semidirect
91. #2077C22semidirect
95. #2073C22semidirect
96. #2073C22semidirect
100. #2071C22semidirect
102. #2067C22semidirect
104. #2059C22semidirect
105. #2057C22semidirect
112. #2025C22semidirect
120. #1993C22semidirect
121. #1993C22semidirect
122. #1993C22semidirect
123. #1992C22semidirect
124. #1990C22semidirect
125. #1989C22semidirect
126. #1988C22semidirect
132. #1949C22semidirect
133. #1948C22semidirect
134. #1943C22semidirect
142. #1936C22semidirect
148. #1926C22semidirect
153. #1924C22semidirect
154. #1924C22semidirect
155. #1921C22semidirect
156. #1921C22semidirect
157. #1921C22semidirect
158. #1920C22semidirect
159. #1920C22semidirect
160. #1919C22semidirect
161. #1919C22semidirect
162. #1917C22semidirect
163. #1917C22semidirect
166. #1893C22semidirect
173. #1874C22semidirect
178. #1853C22semidirect
179. #1853C22semidirect
180. #1847C22semidirect
181. #1836C22semidirect
184. #1824C22semidirect
189. #1776C22semidirect
190. #1776C22semidirect
191. C4×#106C22semidirect
192. #1771C22semidirect
193. #1771C22semidirect
196. #1762C22semidirect
197. #1762C22semidirect
198. #1752C22semidirect
199. #1752C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#592082
#394032
#324522
#322422
#320622
#317682
#314442
#312602
#311042
#310162
#291092
#290952
#289842
#289832
#280172
#278832
#278252
#277112
#275392
#274502
#273442
#272432
#271432
#266732
#262982
#262022
#237642
#233022
#230752
#229382
#220462