Finite Group Databasebeta

← #6632001

Subgroups — #6632001

Order 512.

1246 conjugacy classes of subgroups.

The subgroup lattice has 1165 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35296C211yesmaximal, characteristic
2#35282C211yesmaximal, characteristic, complemented
3#32852C211yesmaximal, characteristic, complemented
4#32851C211yesmaximal, characteristic, complemented
5#32845C211yesmaximal, characteristic, complemented
6#32844C211yesmaximal, characteristic, complemented
7#32844C211yesmaximal, characteristic, complemented
8#32844C211yesmaximal, characteristic, complemented
9#32823C211yesmaximal, characteristic, complemented
10#32819C211yesmaximal, characteristic, complemented
11#32794C211yesmaximal, characteristic, complemented
12#32793C211yesmaximal, characteristic, complemented
13#32782C211yesmaximal, characteristic
14#32779C211yesmaximal, characteristic
15#32747C211yesmaximal, characteristic, complemented
16#32746C211yesmaximal, characteristic, complemented
17#32743C211yesmaximal, characteristic, complemented
18#32742C211yesmaximal, characteristic, complemented
19#23845C211yesmaximal, characteristic, complemented
20#23842C211yesmaximal, characteristic, complemented
21#23830C211yesmaximal, characteristic, complemented
22#23828C211yesmaximal, characteristic, complemented
23#23784C211yesmaximal, characteristic, complemented
24#23781C211yesmaximal, characteristic, complemented
25#23778C211yesmaximal, characteristic, complemented
26#23775C211yesmaximal, characteristic, complemented
27#23771C211yesmaximal, characteristic, complemented
28#23767C211yesmaximal, characteristic, complemented
29#23766C211yesmaximal, characteristic, complemented
30#23766C211yesmaximal, characteristic, complemented
31#20786C211yesmaximal, characteristic, complemented
32#2864C2211yescharacteristic
33#2864C2211yescharacteristic
34#2859C2211yescharacteristic
35#2858C2211yescharacteristic
36#2857C2211yescharacteristic
37#2854C2211yescharacteristic
38#2854C2211yescharacteristic
39#2851C2211yescharacteristic
40#2660C2211yescharacteristic
41#2660C2211yescharacteristic
42#2644C2211yescharacteristic
43#2644C2211yescharacteristic
44#2629C2211yescharacteristic
45#2628C2211yescharacteristic
46#2628C2211yescharacteristic
47#2619C2211yescharacteristic
48#2595—21no—
49#2595—21no—
50#2586—21no—
51#2585—21no—
52#2574—21no—
53#2557—21no—
54#2557—21no—
55#2556—21no—
56#2522—21no—
57#2520—21no—
58#2474—21no—
59#2474—21no—
60#2471—21no—
61#2471—21no—
62#2465—21no—
63#2462—21no—
64#2331C2211yescharacteristic
65#2331C2211yescharacteristic
66#2330C2211yescharacteristic
67#2328C2211yescharacteristic
68#2324C2211yescharacteristic
69#2324C2211yescharacteristic
70#2314C2211yescharacteristic
71#2314C2211yescharacteristic
72C4×C4⋊Q8C2211yescharacteristic
73C4×#125C2211yescharacteristic
74#2293C2211yescharacteristic
75#2293C2211yescharacteristic
76C4×#117C2211yescharacteristic
77#2101C2211yescharacteristic
78#2101C2211yescharacteristic
79#2101C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2099C2211yescharacteristic
89#2094C2211yescharacteristic
90#2094C2211yescharacteristic
91#2094C2211yescharacteristic
92#2093C2211yescharacteristic
93#2092C2211yescharacteristic
94#2092C2211yescharacteristic
95#2092C2211yescharacteristic
96#2092C2211yescharacteristic
97#2088C2211yescharacteristic
98#2088C2211yescharacteristic
99#2088C2211yescharacteristic
100#2088C2211yescharacteristic
101#2087C2211yescharacteristic
102#2087C2211yescharacteristic
103#2087C2211yescharacteristic
104#2086C2211yescharacteristic
105#2085C2211yescharacteristic
106#2085C2211yescharacteristic
107#2085C2211yescharacteristic
108#2085C2211yescharacteristic
109#2085C2211yescharacteristic
110#2085C2211yescharacteristic
111#2085C2211yescharacteristic
112#2085C2211yescharacteristic
113#2084C2211yescharacteristic
114#2084C2211yescharacteristic
115#2084C2211yescharacteristic
116#2083C2211yescharacteristic
117#2077C2211yescharacteristic
118#2077C2211yescharacteristic
119#2077C2211yescharacteristic
120#2077C2211yescharacteristic
121#2077C2211yescharacteristic
122#2077C2211yescharacteristic
123#2076C2211yescharacteristic
124#2075C2211yescharacteristic
125#2073C2211yescharacteristic
126#2073C2211yescharacteristic
127#2073C2211yescharacteristic
128#2073C2211yescharacteristic
129#2071C2211yescharacteristic
130#2071C2211yescharacteristic
131#2071C2211yescharacteristic
132#2071C2211yescharacteristic
133#2067C2211yescharacteristic
134#2067C2211yescharacteristic
135#2065C2211yescharacteristic
136#2065C2211yescharacteristic
137#2065C2211yescharacteristic
138#2065C2211yescharacteristic
139#2065C2211yescharacteristic
140#2065C2211yescharacteristic
141#2059C2211yescharacteristic
142#2059C2211yescharacteristic
143#2059C2211yescharacteristic
144#2059C2211yescharacteristic
145#2058C2211yescharacteristic
146#2058C2211yescharacteristic
147#2058C2211yescharacteristic
148#2058C2211yescharacteristic
149#2058C2211yescharacteristic
150#2058C2211yescharacteristic
151#2057C2211yescharacteristic
152#2057C2211yescharacteristic
153#2041C2211yescharacteristic
154#2041C2211yescharacteristic
155#2041C2211yescharacteristic
156#2041C2211yescharacteristic
157#2034C2211yescharacteristic
158#2034C2211yescharacteristic
159#2034C2211yescharacteristic
160#2034C2211yescharacteristic
161#2033C2211yescharacteristic
162#2033C2211yescharacteristic
163#2033C2211yescharacteristic
164#2033C2211yescharacteristic
165#2025C2211yescharacteristic
166#2025C2211yescharacteristic
167#2025C2211yescharacteristic
168#2025C2211yescharacteristic
169#2023C2211yescharacteristic
170#2023C2211yescharacteristic
171#2023C2211yescharacteristic
172#2023C2211yescharacteristic
173#1840C2211yescharacteristic
174#1840C2211yescharacteristic
175#1831C2211yescharacteristic
176#1831C2211yescharacteristic
177#1818C2211yescharacteristic
178#1818C2211yescharacteristic
179#1797C2211yescharacteristic
180#1797C2211yescharacteristic
181#1776C2211yescharacteristic
182#1776C2211yescharacteristic
183#1776C2211yescharacteristic
184#1776C2211yescharacteristic
185C4×#107C2211yescharacteristic
186C4×#106C2211yescharacteristic
187C4×#106C2211yescharacteristic
188C4×#106C2211yescharacteristic
189#1767C2211yescharacteristic
190C4×C4⋊C8C2211yescharacteristic
191#1762C2211yescharacteristic
192#1762C2211yescharacteristic
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic
199#1750C2211yescharacteristic
200#1750C2211yescharacteristic
201#1746C2211yescharacteristic
202#1746C2211yescharacteristic
203C2×C4⋊Q8C2311yescharacteristic
204C2×C4⋊Q8C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×#127C2311yescharacteristic
207C2×#125—21no—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#124—21no—
211C2×#124—21no—
212C2×#123—21no—
213C2×#123—21no—
214C2×C22⋊Q8—21no—
215C2×#121C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×C4×Q8—21no—
218C2×C4×D4C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×#117—21no—
221C2×#117—21no—
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C22×C42C2311yescharacteristic
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#106C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×C4⋊C8C2311yescharacteristic
245C2×#102C2311yescharacteristic
246C2×#102C2311yescharacteristic
247C2×#102C2311yescharacteristic
248C2×#102C2311yescharacteristic
249C2×#102C2311yescharacteristic
250C2×#102C2311yescharacteristic
251C2×#102C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×C22⋊C8C2311yescharacteristic
262C2×C22⋊C8C2311yescharacteristic
263C2×C22⋊C8C2311yescharacteristic
264C2×C22⋊C8C2311yescharacteristic
265C2×#97C2311yescharacteristic
266C2×#97C2311yescharacteristic
267C2×C4×C8C2311yescharacteristic
268C2×C4×C8C2311yescharacteristic
269#400—21no—
270#400—21no—
271#399—21no—
272#399—21no—
273#398—21no—
274#398—21no—
275#398—21no—
276#398—21no—
277#398—21no—
278#398—21no—
279#397—21no—
280#397—21no—
281#397—21no—
282#397—21no—
283#397—21no—
284#397—21no—
285#396—21no—
286#396—21no—
287#396—21no—
288#396—21no—
289#395—21no—
290#395—21no—
291#395—21no—
292#395—21no—
293#395—21no—
294#395—21no—
295#394—21no—
296#394—21no—
297#393—21no—
298#393—21no—
299#392—21no—
300#392—21no—
301#391—21no—
302#391—21no—
303#391—21no—
304#391—21no—
305#391—21no—
306#391—21no—
307#390—21no—
308#390—21no—
309#390—21no—
310#390—21no—
311#390C2311yescharacteristic
312#390C2311yescharacteristic
313#390C2311yescharacteristic
314#390C2311yescharacteristic
315#390C2311yescharacteristic
316#390C2311yescharacteristic
317#390C2311yescharacteristic
318#390C2311yescharacteristic
319#389—21no—
320#389—21no—
321#389—21no—
322#389—21no—
323#389—21no—
324#389—21no—
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#388—21no—
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#387—21no—
356#387—21no—
357#387—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#386—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#384C2311yescharacteristic
393#382—21no—
394#382C2311yescharacteristic
395#382C2311yescharacteristic
396#382C2311yescharacteristic
397#382C2311yescharacteristic
398#382C2311yescharacteristic
399#382C2311yescharacteristic
400#380—21no—
401#380C2311yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4D411yescharacteristic
411C4×C4⋊C4D411yescharacteristic
412C4×C4⋊C4D411yescharacteristic
413C4×C4⋊C4D411yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C22⋊C4—21no—
421C4×C22⋊C4—21no—
422C4×C22⋊C4D411yescharacteristic
423C4×C22⋊C4D411yescharacteristic
424C4×C22⋊C4D411yescharacteristic
425C4×C22⋊C4D411yescharacteristic
426#376C2311yescharacteristic
427#376C2311yescharacteristic
428C43C2311yescharacteristic
429C43C2311yescharacteristic
430#340C2311yescharacteristic
431#340C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
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#336C2311yescharacteristic
463#336C2311yescharacteristic
464#336C2311yescharacteristic
465#336C2311yescharacteristic
466#336C2311yescharacteristic
467#336C2311yescharacteristic
468#336C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478C22×Q8—21no—
479C22×Q8—21no—
480C22×Q8—21no—
481C22×D4—21no—
482C22×D4—21no—
483C22×D4—21no—
484C22×D4—21no—
485C22×D4C2411yescharacteristic
486C22×D4C2411yescharacteristic
487C23×C4—21no—
488C23×C4—21no—
489C23×C4C2×D411yescharacteristic
490C23×C4C2×D411yescharacteristic
491C23×C4C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499C22×C8C2411yescharacteristic
500C4⋊Q8—41no—
501C4⋊Q8—41no—
502C4⋊Q8—41no—
503C4⋊Q8—41no—
504C4⋊Q8—41no—
505C4⋊Q8—41no—
506#127—41no—
507#127—41no—
508#125—41no—
509#125—41no—
510#125—41no—
511#125—41no—
512#125—82no—
513#124—82no—
514#124—82no—
515#123—82no—
516#123—82no—
517C22⋊Q8—82no—
518#121—41no—
519#121—41no—
520#121—41no—
521#121—41no—
522C4×Q8—82no—
523C4×D4—22no—
524C4×D4—22no—
525C4×D4—22no—
526C4×D4—22no—
527#117—22no—
528#117—22no—
529#117—41no—
530#117—41no—
531#117—82no—
532#117—82no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4C2×D411yescharacteristic
565C2×C4⋊C4C2×D411yescharacteristic
566C2×C4⋊C4C2×D411yescharacteristic
567C2×C4⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2411yescharacteristic
569C2×C4⋊C4C2411yescharacteristic
570C2×C4⋊C4C2411yescharacteristic
571C2×C4⋊C4C2411yescharacteristic
572C2×C4⋊C4C2411yescharacteristic
573C2×C4⋊C4C2411yescharacteristic
574C2×C4⋊C4C2411yescharacteristic
575C2×C4⋊C4C2411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4C2×D411yescharacteristic
609C2×C22⋊C4C2×D411yescharacteristic
610C2×C22⋊C4C2×D411yescharacteristic
611C2×C22⋊C4C2×D411yescharacteristic
612C2×C42—21no—
613C2×C42—21no—
614C2×C42—21no—
615C2×C42—21no—
616C2×C42—21no—
617C2×C42—21no—
618C2×C42—41no—
619C2×C42—41no—
620C2×C42C2×D411yescharacteristic
621C2×C42C2×D411yescharacteristic
622C2×C42C2×D411yescharacteristic
623C2×C42C2×D411yescharacteristic
624C2×C42C2×D411yescharacteristic
625C2×C42C2×D411yescharacteristic
626C2×C42C2×D411yescharacteristic
627C2×C42C2×D411yescharacteristic
628C2×C42C2×D411yescharacteristic
629C2×C42C2×D411yescharacteristic
630C2×C42C2411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636#107—41no—
637#107—41no—
638#107—41no—
639#107—41no—
640#107—41no—
641#107—41no—
642#106—41no—
643#106—41no—
644#106—41no—
645#106—41no—
646#106—41no—
647#106—41no—
648#106—41no—
649#106—41no—
650#106—41no—
651#106—41no—
652C4⋊C8—41no—
653C4⋊C8—41no—
654C4⋊C8—41no—
655C4⋊C8—41no—
656#102—41no—
657#102—41no—
658#102—41no—
659#102—41no—
660#102—41no—
661#102—41no—
662#102—41no—
663#102—41no—
664#102—41no—
665#102—41no—
666#102—41no—
667#102—41no—
668#102—41no—
669#102—41no—
670#102—41no—
671#102—41no—
672C22⋊C8—41no—
673C22⋊C8—41no—
674C22⋊C8—41no—
675C22⋊C8—41no—
676#97—22no—
677#97—22no—
678C4×C8—22no—
679C4×C8—22no—
680#95—21no—
681#95—21no—
682#95—21no—
683#95—21no—
684#95—21no—
685#95—21no—
686#95—21no—
687#95—21no—
688#95—21no—
689#95—21no—
690#95—21no—
691#95—21no—
692#95—21no—
693#95—21no—
694#95—21no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
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#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722#95C2×D411yescharacteristic
723#95C2×D411yescharacteristic
724#95C2×D411yescharacteristic
725#95C2×D411yescharacteristic
726#95C2×D411yescharacteristic
727#95C2×D411yescharacteristic
728C24—21no—
729C24—21no—
730C24C22×D411yescharacteristic
731C2×Q8—42no—
732C2×Q8—42no—
733C2×Q8—42no—
734C2×Q8—81no—
735C2×Q8—81no—
736C2×Q8—81no—
737C2×Q8—81no—
738C2×Q8—81no—
739C2×Q8—81no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—21no—
743C2×D4—21no—
744C2×D4—21no—
745C2×D4—21no—
746C2×D4—21no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—42no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—81no—
757C2×D4—81no—
758C2×D4—81no—
759C2×D4—81no—
760C2×D4—81no—
761C2×D4—81no—
762C2×D4—81no—
763C2×D4—81no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—22no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—41no—
786C22×C4—41no—
787C22×C4—41no—
788C22×C4—41no—
789C22×C4—41no—
790C22×C4—42no—
791C22×C4—42no—
792C22×C4—81no—
793C22×C4—81no—
794C22×C4—81no—
795C22×C4—81no—
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×D411yescharacteristic
801C22×C4C22×D411yescharacteristic
802C22×C4C22×D411yescharacteristic
803C22×C4C22×D411yescharacteristic
804C22×C4C22×D411yescharacteristic
805C22×C4C22×D411yescharacteristic
806C22×C4C22×D411yescharacteristic
807C22×C4C22×D411yescharacteristic
808C22×C4C22×D411yescharacteristic
809C22×C4C2511yescharacteristic
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C2×C8—21no—
814C2×C8—21no—
815C2×C8—21no—
816C2×C8—21no—
817C2×C8—21no—
818C2×C8—21no—
819C2×C8—21no—
820C2×C8—21no—
821C2×C8—21no—
822C2×C8—21no—
823C2×C8—21no—
824C2×C8—21no—
825C2×C8—21no—
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C4⋊C4—22no—
835C4⋊C4—22no—
836C4⋊C4—21no—
837C4⋊C4—21no—
838C4⋊C4—21no—
839C4⋊C4—21no—
840C4⋊C4—21no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—21no—
855C4⋊C4—21no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—41no—
865C4⋊C4—41no—
866C4⋊C4—42no—
867C4⋊C4—42no—
868C4⋊C4—42no—
869C4⋊C4—42no—
870C4⋊C4—42no—
871C4⋊C4—42no—
872C4⋊C4—42no—
873C4⋊C4—42no—
874C4⋊C4—42no—
875C4⋊C4—42no—
876C4⋊C4—42no—
877C4⋊C4—42no—
878C4⋊C4—42no—
879C4⋊C4—81no—
880C4⋊C4—81no—
881C4⋊C4—81no—
882C4⋊C4—81no—
883C4⋊C4—81no—
884C4⋊C4—81no—
885C4⋊C4—81no—
886C4⋊C4—81no—
887C4⋊C4—81no—
888C4⋊C4—81no—
889C4⋊C4—81no—
890C4⋊C4—81no—
891C4⋊C4—81no—
892C4⋊C4—81no—
893C4⋊C4—81no—
894C4⋊C4—81no—
895C4⋊C4—81no—
896C4⋊C4—81no—
897C22⋊C4—22no—
898C22⋊C4—22no—
899C22⋊C4—41no—
900C22⋊C4—41no—
901C22⋊C4—42no—
902C22⋊C4—42no—
903C22⋊C4—42no—
904C22⋊C4—42no—
905C22⋊C4—42no—
906C22⋊C4—42no—
907C22⋊C4—42no—
908C22⋊C4—42no—
909C22⋊C4—81no—
910C22⋊C4—81no—
911C22⋊C4—81no—
912C22⋊C4—81no—
913C22⋊C4—81no—
914C22⋊C4—81no—
915C22⋊C4—81no—
916C22⋊C4—81no—
917C22⋊C4—81no—
918C22⋊C4—81no—
919C22⋊C4—81no—
920C22⋊C4—81no—
921C22⋊C4—81no—
922C22⋊C4—81no—
923C22⋊C4—81no—
924C22⋊C4—81no—
925C22⋊C4—81no—
926C22⋊C4—81no—
927C42—22no—
928C42—22no—
929C42—21no—
930C42—21no—
931C42—21no—
932C42—21no—
933C42—21no—
934C42—21no—
935C42—21no—
936C42—21no—
937C42—21no—
938C42—21no—
939C42—41no—
940C42—41no—
941C42—41no—
942C42—41no—
943C42—41no—
944C42—41no—
945C42—41no—
946C42—41no—
947C42—81no—
948C42—81no—
949C42—81no—
950C42—81no—
951C42—81no—
952C42—81no—
953C422−1+412yes—
954C422−1+412yes—
955C23—21no—
956C23—21no—
957C23—21no—
958C23—21no—
959C23—21no—
960C23—21no—
961C23—21no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23—41no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23C23×D411yescharacteristic
977Q8—84no—
978Q8—162no—
979Q8—162no—
980D4—41no—
981D4—41no—
982D4—41no—
983D4—41no—
984D4—41no—
985D4—41no—
986D4—41no—
987D4—41no—
988D4—162no—
989D4—162no—
990D4—162no—
991D4—162no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—21no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—41no—
1029C2×C4—41no—
1030C2×C4—41no—
1031C2×C4—41no—
1032C2×C4—41no—
1033C2×C4—41no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—82no—
1075C2×C4—84no—
1076C2×C4—84no—
1077C2×C4—82no—
1078C2×C4#53612yes—
1079C2×C4#53612yes—
1080C2×C4#57712yes—
1081C2×C4C2×2−1+411yescharacteristic
1082C2×C4C2×2−1+411yescharacteristic
1083C2×C4#58511yescharacteristic
1084C2×C4#58511yescharacteristic
1085C2×C4#58511yescharacteristic
1086C2×C4#58511yescharacteristic
1087C8—41no—
1088C8—41no—
1089C8—41no—
1090C8—41no—
1091C8—41no—
1092C8—41no—
1093C8—41no—
1094C8—41no—
1095C22—41no—
1096C22—41no—
1097C22—41no—
1098C22—41no—
1099C22—41no—
1100C22—41no—
1101C22—41no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22—81no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22C2×#53611yescharacteristic
1117C22#344911yescharacteristic
1118C22#344911yescharacteristic
1119C22C2×#57711yescharacteristic
1120C22#358411yescharacteristic
1121C22#358511yescharacteristic
1122C22#358511yescharacteristic
1123C4—22no—
1124C4—22no—
1125C4—22no—
1126C4—41no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—41no—
1131C4—41no—
1132C4—41no—
1133C4—41no—
1134C4—41no—
1135C4—41no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4#353111yescharacteristic
1151C4#353111yescharacteristic
1152C4#353111yescharacteristic
1153C4#353111yescharacteristic
1154C2—81no—
1155C2—161no—
1156C2—161no—
1157C2#3669911yescharacteristic
1158C2#6089011yescharacteristic
1159C2#6089211yescharacteristic
1160C2#6099411yescharacteristic
1161C2#6099811yescharacteristic
1162C2#6100111yescharacteristic
1163C2#6100311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2619C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35282C2semidirect
3. #32852C2semidirect
4. #32851C2semidirect
5. #32845C2semidirect
6. #32844C2semidirect
7. #32844C2semidirect
8. #32844C2semidirect
9. #32823C2semidirect
10. #32819C2semidirect
11. #32794C2semidirect
12. #32793C2semidirect
15. #32747C2semidirect
16. #32746C2semidirect
17. #32743C2semidirect
18. #32742C2semidirect
19. #23845C2semidirect
20. #23842C2semidirect
21. #23830C2semidirect
22. #23828C2semidirect
23. #23784C2semidirect
24. #23781C2semidirect
25. #23778C2semidirect
26. #23775C2semidirect
27. #23771C2semidirect
28. #23767C2semidirect
29. #23766C2semidirect
30. #23766C2semidirect
31. #20786C2semidirect

Maximal subgroups

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

subgroupindex
#352962
#352822
#328522
#328512
#328452
#328442
#328232
#328192
#327942
#327932
#327822
#327792
#327472
#327462
#327432
#327422
#238452
#238422
#238302
#238282
#237842
#237812
#237782
#237752
#237712
#237672
#237662
#207862