Finite Group Databasebeta

← #6594368

Subgroups — #6594368

Order 512.

1454 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37879C211yesmaximal, characteristic
2#37874C211yesmaximal, characteristic
3#33319C211yesmaximal, characteristic, complemented
4#33216C211yesmaximal, characteristic, complemented
5#33211C211yesmaximal, characteristic, complemented
6#29216C211yesmaximal, characteristic, complemented
7#29215C211yesmaximal, characteristic, complemented
8#28839C211yesmaximal, characteristic, complemented
9#28837C211yesmaximal, characteristic, complemented
10#28835C211yesmaximal, characteristic, complemented
11#28834C211yesmaximal, characteristic, complemented
12#27958C211yesmaximal, characteristic, complemented
13#27957C211yesmaximal, characteristic, complemented
14#27954C211yesmaximal, characteristic, complemented
15#27953C211yesmaximal, characteristic, complemented
16#26079C211yesmaximal, characteristic, complemented
17#26078C211yesmaximal, characteristic, complemented
18#26075C211yesmaximal, characteristic, complemented
19#26075C211yesmaximal, characteristic, complemented
20#26074C211yesmaximal, characteristic, complemented
21#26074C211yesmaximal, characteristic, complemented
22#26069C211yesmaximal, characteristic, complemented
23#26068C211yesmaximal, characteristic, complemented
24#22666C211yesmaximal, characteristic
25#22665C211yesmaximal, characteristic
26#22660C211yesmaximal, characteristic
27#22659C211yesmaximal, characteristic
28#21722C211yesmaximal, characteristic, complemented
29#20802C211yesmaximal, characteristic, complemented
30#20800C211yesmaximal, characteristic, complemented
31#20487C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#501C2211yescharacteristic
34C2×#500C2211yescharacteristic
35C2×#499C2211yescharacteristic
36C2×#499C2211yescharacteristic
37C2×#436C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C2×#428C2211yescharacteristic
40C2×#428C2211yescharacteristic
41C2×#428C2211yescharacteristic
42C2×#428C2211yescharacteristic
43C2×#428C2211yescharacteristic
44C2×#428C2211yescharacteristic
45C2×#427C2211yescharacteristic
46C22×#106C2211yescharacteristic
47C2×#405C2211yescharacteristic
48C2×C4×M16C2211yescharacteristic
49#2851C2211yescharacteristic
50#2851C2211yescharacteristic
51#2792—21no—
52#2791—21no—
53#2790—21no—
54#2788—21no—
55#2784—21no—
56#2780—21no—
57#2768—21no—
58#2720—21no—
59#2660C2211yescharacteristic
60#2660C2211yescharacteristic
61#2629C2211yescharacteristic
62#2629C2211yescharacteristic
63#2588—21no—
64#2587—21no—
65#2585—21no—
66#2583—21no—
67#2579—21no—
68#2574—21no—
69#2571C2211yescharacteristic
70#2570C2211yescharacteristic
71#2570C2211yescharacteristic
72#2552C2211yescharacteristic
73#2473—21no—
74#2449—21no—
75#2442C2211yescharacteristic
76#2442C2211yescharacteristic
77#2441C2211yescharacteristic
78#2441C2211yescharacteristic
79#2440C2211yescharacteristic
80#2440C2211yescharacteristic
81#2439C2211yescharacteristic
82#2439C2211yescharacteristic
83#2354C2211yescharacteristic
84#2352C2211yescharacteristic
85#2352C2211yescharacteristic
86D4×C4⋊C4C2211yescharacteristic
87#2330C2211yescharacteristic
88#2330C2211yescharacteristic
89#2317C2211yescharacteristic
90#2317C2211yescharacteristic
91#2290C2211yescharacteristic
92#2285C2211yescharacteristic
93C2×#384C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2084C2211yescharacteristic
103#2084C2211yescharacteristic
104#2084C2211yescharacteristic
105#2084C2211yescharacteristic
106#2083C2211yescharacteristic
107#2083C2211yescharacteristic
108#2083C2211yescharacteristic
109#2083C2211yescharacteristic
110#2059C2211yescharacteristic
111#2059C2211yescharacteristic
112#2059C2211yescharacteristic
113#2059C2211yescharacteristic
114#2058C2211yescharacteristic
115#2058C2211yescharacteristic
116#2057C2211yescharacteristic
117#2057C2211yescharacteristic
118#1992C2211yescharacteristic
119#1992C2211yescharacteristic
120#1992C2211yescharacteristic
121#1992C2211yescharacteristic
122#1991C2211yescharacteristic
123#1991C2211yescharacteristic
124#1949C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1949C2211yescharacteristic
128#1948C2211yescharacteristic
129#1948C2211yescharacteristic
130#1947C2211yescharacteristic
131#1947C2211yescharacteristic
132#1944C2211yescharacteristic
133#1944C2211yescharacteristic
134#1943C2211yescharacteristic
135#1943C2211yescharacteristic
136#1943C2211yescharacteristic
137#1943C2211yescharacteristic
138#1943C2211yescharacteristic
139#1943C2211yescharacteristic
140#1942C2211yescharacteristic
141#1942C2211yescharacteristic
142#1941C2211yescharacteristic
143#1941C2211yescharacteristic
144#1854C2211yescharacteristic
145#1854C2211yescharacteristic
146#1854C2211yescharacteristic
147#1854C2211yescharacteristic
148#1854C2211yescharacteristic
149#1854C2211yescharacteristic
150#1854C2211yescharacteristic
151#1854C2211yescharacteristic
152#1853C2211yescharacteristic
153#1853C2211yescharacteristic
154#1853C2211yescharacteristic
155#1853C2211yescharacteristic
156#1852C2211yescharacteristic
157#1852C2211yescharacteristic
158#1852C2211yescharacteristic
159#1852C2211yescharacteristic
160#1847C2211yescharacteristic
161#1847C2211yescharacteristic
162#1847C2211yescharacteristic
163#1847C2211yescharacteristic
164#1847C2211yescharacteristic
165#1847C2211yescharacteristic
166#1847C2211yescharacteristic
167#1847C2211yescharacteristic
168#1847C2211yescharacteristic
169#1847C2211yescharacteristic
170#1847C2211yescharacteristic
171#1847C2211yescharacteristic
172#1846C2211yescharacteristic
173#1846C2211yescharacteristic
174#1846C2211yescharacteristic
175#1845C2211yescharacteristic
176#1845C2211yescharacteristic
177#1845C2211yescharacteristic
178#1844C2211yescharacteristic
179#1844C2211yescharacteristic
180#1844C2211yescharacteristic
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic
186#1809C2211yescharacteristic
187#1808C2211yescharacteristic
188#1808C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191C4×#106C2211yescharacteristic
192C4×#106C2211yescharacteristic
193#1771C2211yescharacteristic
194#1770C2211yescharacteristic
195#1768C2211yescharacteristic
196#1753C2211yescharacteristic
197#1753C2211yescharacteristic
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic
200#1750C2211yescharacteristic
201#1749C2211yescharacteristic
202#1726C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#125—21no—
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×C4×D4—21no—
217C2×C4×D4C2311yescharacteristic
218C2×#117C2311yescharacteristic
219C2×#117C2311yescharacteristic
220C2×#117C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C22×C4⋊C4—21no—
224C22×C4⋊C4—21no—
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C42C2311yescharacteristic
230#501—42no—
231#501—42no—
232#500—42no—
233#499—24no—
234#499—42no—
235#436Q818yescomplemented
236#435Q818yescomplemented
237#428—42no—
238#428—42no—
239#428—42no—
240#428—42no—
241#428—42no—
242#428—42no—
243#427—42no—
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#106—42no—
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
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×#106C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×C22⋊C8C2311yescharacteristic
291#405—24no—
292C4×M16—24no—
293C2×#97C2311yescharacteristic
294C2×#97C2311yescharacteristic
295C2×#97C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#399—21no—
312#399—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#396—21no—
337#395—21no—
338#395—21no—
339#395—21no—
340#395—21no—
341#395—21no—
342#395—21no—
343#393—21no—
344#393—21no—
345#391—21no—
346#391—21no—
347#390—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388D411yescharacteristic
378#388D411yescharacteristic
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#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387D411yescharacteristic
398#387D411yescharacteristic
399#386—21no—
400#386—21no—
401#386D411yescharacteristic
402#386D411yescharacteristic
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385D411yescharacteristic
418#385D411yescharacteristic
419#384—21no—
420#384—21no—
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#384C2311yescharacteristic
425#384C2311yescharacteristic
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#384C2311yescharacteristic
430#384C2311yescharacteristic
431#382—21no—
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#382C2311yescharacteristic
437#382C2311yescharacteristic
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#380—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452C4×C4⋊C4—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4—21no—
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464#376C2311yescharacteristic
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#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495C22×Q8—21no—
496C22×Q8—21no—
497C22×D4C2×D411yescharacteristic
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2×D411yescharacteristic
503C23×C4C2×D411yescharacteristic
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C2×M16—22no—
507C2×M16—22no—
508C2×M16—22no—
509C2×M16—22no—
510C2×M16—22no—
511C2×M16—22no—
512C2×M16C2×Q814yes—
513C2×M16C2×Q814yes—
514C2×M16C2×Q814yes—
515C22×C8—22no—
516C22×C8—22no—
517C22×C8C2×Q814yes—
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—41no—
529C4⋊Q8—41no—
530#125—22no—
531#125—22no—
532#125—22no—
533#125—22no—
534#125—41no—
535#125—41no—
536#125—41no—
537#125—41no—
538#125—82no—
539C22⋊Q8—82no—
540C22⋊Q8—82no—
541C4×D4—82no—
542C4×D4C2×Q814yes—
543C4×D4C2×Q814yes—
544#117—22no—
545#117—22no—
546#117—41no—
547#117—41no—
548#117—41no—
549#117—41no—
550#117—41no—
551#117—41no—
552#117—41no—
553#117—41no—
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⋊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—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—41no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4—41no—
607C2×C4⋊C4—41no—
608C2×C4⋊C4—82no—
609C2×C4⋊C4—82no—
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
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×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⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C42—22no—
652C2×C42—22no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42C2×D411yescharacteristic
662C2×C42C2×D411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668#107—22no—
669#107—22no—
670#107—22no—
671#107—22no—
672#107—22no—
673#107—22no—
674#107—22no—
675#107—22no—
676#107—41no—
677#107—41no—
678#107—41no—
679#107—41no—
680#107—41no—
681#107—41no—
682#107—41no—
683#107—41no—
684#107—41no—
685#107—41no—
686#107—41no—
687#107—41no—
688#106—22no—
689#106—22no—
690#106—22no—
691#106—22no—
692#106—22no—
693#106—22no—
694#106—22no—
695#106—22no—
696#106—41no—
697#106—41no—
698#106—41no—
699#106—41no—
700#106—41no—
701#106—41no—
702#106—41no—
703#106—41no—
704#106—41no—
705#106—41no—
706#106—41no—
707#106—41no—
708C4⋊C8C2×Q814yes—
709C4⋊C8C2×Q814yes—
710C22⋊C8C2×Q814yes—
711C22⋊C8C2×Q814yes—
712C22⋊C8C2×Q814yes—
713C22⋊C8C2×Q814yes—
714#97—22no—
715#97—22no—
716#97—22no—
717#97—22no—
718#97—22no—
719#97—22no—
720#97C2×Q814yes—
721C4×C8—22no—
722C4×C8—22no—
723C4×C8—22no—
724C4×C8C2×Q814yes—
725C4×C8#4114yes—
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#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#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776C24C22×D411yescharacteristic
777C24C22×D411yescharacteristic
778C2×Q8—81no—
779C2×Q8—81no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×Q8—81no—
784C2×D4—41no—
785C2×D4—41no—
786C2×D4C4⋊Q814yes—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—41no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—41no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—81no—
820C22×C4—81no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4—81no—
824C22×C4—81no—
825C22×C4—81no—
826C22×C4—81no—
827C22×C4—81no—
828C22×C4—81no—
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×Q812yes—
842C22×C4C22×Q812yes—
843C22×C4C22×Q812yes—
844C22×C4C22×Q812yes—
845C22×C4C2511yescharacteristic
846M16—28no—
847M16—28no—
848M16—28no—
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—28no—
862C2×C8C22×Q812yes—
863C2×C8C22×Q812yes—
864C2×C8C22×Q812yes—
865C2×C8C22×Q812yes—
866C2×C8C22×Q812yes—
867C2×C8C22×Q812yes—
868C2×C8C22×Q812yes—
869C2×C8C22×Q812yes—
870C2×C8C2×#4112yes—
871C2×C8C2×#4112yes—
872C2×C8H(5,𝔽2)12yes—
873C2×C8H(5,𝔽2)12yes—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
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—41no—
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—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
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—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
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⋊C4C4⋊Q814yes—
957C22⋊C4—22no—
958C22⋊C4—22no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—41no—
962C22⋊C4—41no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4C4⋊Q814yes—
976C22⋊C4C4⋊Q814yes—
977C42—22no—
978C42—22no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—81no—
986C42—81no—
987C42—81no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C42C22×Q812yes—
994C42C22×Q812yes—
995C42C2×#4112yes—
996C422−1+412yes—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23C2×C4⋊Q812yes—
1010C23C2×C4⋊Q812yes—
1011C23C23×D411yescharacteristic
1012Q8—162no—
1013Q8—162no—
1014D4—44no—
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—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—22no—
1034C2×C4—22no—
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—21no—
1052C2×C4—21no—
1053C2×C4—44no—
1054C2×C4—44no—
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—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—162no—
1104C2×C4—162no—
1105C2×C4—162no—
1106C2×C4—162no—
1107C2×C4C2×C4⋊Q812yes—
1108C2×C4C2×C4⋊Q812yes—
1109C2×C4C2×C4⋊Q812yes—
1110C2×C4C2×C4⋊Q812yes—
1111C2×C4#54712yes—
1112C2×C4#54712yes—
1113C2×C4C23×Q811yescharacteristic
1114C2×C4C23×Q811yescharacteristic
1115C2×C4C22×#4111yescharacteristic
1116C2×C4C2×H(5,𝔽2)11yescharacteristic
1117C2×C4C2×H(5,𝔽2)11yescharacteristic
1118C2×C4C2×2−1+411yescharacteristic
1119C8—22no—
1120C8—22no—
1121C8—22no—
1122C8—22no—
1123C8—22no—
1124C8—22no—
1125C8#55414yes—
1126C8#55414yes—
1127C22—22no—
1128C22—22no—
1129C22—22no—
1130C22—22no—
1131C22—22no—
1132C22—22no—
1133C22—41no—
1134C22—41no—
1135C22—41no—
1136C22—41no—
1137C22—41no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22C22×C4⋊Q811yescharacteristic
1142C22C2×#54711yescharacteristic
1143C22#349811yescharacteristic
1144C22#358511yescharacteristic
1145C22#358511yescharacteristic
1146C22#358611yescharacteristic
1147C22#358611yescharacteristic
1148C4—22no—
1149C4—22no—
1150C4—22no—
1151C4—22no—
1152C4—22no—
1153C4—22no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4C2×#55411yescharacteristic
1177C4C2×#55411yescharacteristic
1178C4#350311yescharacteristic
1179C4#350311yescharacteristic
1180C2—42no—
1181C2—42no—
1182C2#3618011yescharacteristic
1183C2#6066411yescharacteristic
1184C2#6066811yescharacteristic
1185C2#6126511yescharacteristic
1186C2#6126511yescharacteristic
1187C2#6244111yescharacteristic
1188C2#6244211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C2×D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
3. #33319C2semidirect
4. #33216C2semidirect
5. #33211C2semidirect
6. #29216C2semidirect
7. #29215C2semidirect
8. #28839C2semidirect
9. #28837C2semidirect
10. #28835C2semidirect
11. #28834C2semidirect
12. #27958C2semidirect
13. #27957C2semidirect
14. #27954C2semidirect
15. #27953C2semidirect
16. #26079C2semidirect
17. #26078C2semidirect
18. #26075C2semidirect
19. #26075C2semidirect
20. #26074C2semidirect
21. #26074C2semidirect
22. #26069C2semidirect
23. #26068C2semidirect
28. #21722C2semidirect
29. #20802C2semidirect
30. #20800C2semidirect
235. #436Q8semidirect
236. #435Q8semidirect

Maximal subgroups

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

subgroupindex
#378792
#378742
#333192
#332162
#332112
#292162
#292152
#288392
#288372
#288352
#288342
#279582
#279572
#279542
#279532
#260792
#260782
#260752
#260742
#260692
#260682
#226662
#226652
#226602
#226592
#217222
#208022
#208002
#204872