Finite Group Databasebeta

← #6484496

Subgroups — #6484496

Order 512.

1310 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35344C211yesmaximal, characteristic
2#34625C211yesmaximal, characteristic
3#33219C211yesmaximal, characteristic
4#33219C211yesmaximal, characteristic
5#33215C211yesmaximal, characteristic
6#33213C211yesmaximal, characteristic
7#30302C211yesmaximal, characteristic
8#30300C211yesmaximal, characteristic
9#30299C211yesmaximal, characteristic
10#30299C211yesmaximal, characteristic
11#29325C211yesmaximal, characteristic, complemented
12#29325C211yesmaximal, characteristic, complemented
13#29323C211yesmaximal, characteristic, complemented
14#29322C211yesmaximal, characteristic, complemented
15#29318C211yesmaximal, characteristic, complemented
16#29317C211yesmaximal, characteristic, complemented
17#29316C211yesmaximal, characteristic, complemented
18#29315C211yesmaximal, characteristic, complemented
19#29217C211yesmaximal, characteristic, complemented
20#29217C211yesmaximal, characteristic, complemented
21#29211C211yesmaximal, characteristic, complemented
22#29209C211yesmaximal, characteristic, complemented
23#28697C211yesmaximal, characteristic, complemented
24#28696C211yesmaximal, characteristic, complemented
25#28695C211yesmaximal, characteristic, complemented
26#28688C211yesmaximal, characteristic, complemented
27#21965C211yesmaximal, characteristic
28#21963C211yesmaximal, characteristic
29#21962C211yesmaximal, characteristic
30#21960C211yesmaximal, characteristic
31#20431C211yesmaximal, characteristic
32C2×#501C2211yescharacteristic
33C2×#501C2211yescharacteristic
34C2×#500C2211yescharacteristic
35C2×#498C2211yescharacteristic
36C2×#423C2211yescharacteristic
37C22×C4⋊C8C2211yescharacteristic
38C2×#405C2211yescharacteristic
39C2×#405C2211yescharacteristic
40#2864C2211yescharacteristic
41#2864C2211yescharacteristic
42#2862C2211yescharacteristic
43#2862C2211yescharacteristic
44#2667—21no—
45#2666—21no—
46#2666—21no—
47#2665—21no—
48#2660C2211yescharacteristic
49#2660C2211yescharacteristic
50#2647C2211yescharacteristic
51#2647C2211yescharacteristic
52#2629C2211yescharacteristic
53#2629C2211yescharacteristic
54#2628C2211yescharacteristic
55#2628C2211yescharacteristic
56#2628C2211yescharacteristic
57#2628C2211yescharacteristic
58#2628C2211yescharacteristic
59#2628C2211yescharacteristic
60#2607—21no—
61#2607—21no—
62#2607—21no—
63#2607—21no—
64#2605—21no—
65#2605—21no—
66#2605—21no—
67#2605—21no—
68#2402—21no—
69#2399—21no—
70#2396—21no—
71#2396—21no—
72#2331C2211yescharacteristic
73#2331C2211yescharacteristic
74#2331C2211yescharacteristic
75#2331C2211yescharacteristic
76C4×C4⋊Q8C2211yescharacteristic
77C4×C4⋊Q8C2211yescharacteristic
78C4×#125C2211yescharacteristic
79C4×#125C2211yescharacteristic
80#2285C2211yescharacteristic
81#2283C2211yescharacteristic
82#2283C2211yescharacteristic
83#2283C2211yescharacteristic
84C4×#117C2211yescharacteristic
85#2085C2211yescharacteristic
86#2085C2211yescharacteristic
87#2085C2211yescharacteristic
88#2085C2211yescharacteristic
89#2085C2211yescharacteristic
90#2085C2211yescharacteristic
91#2085C2211yescharacteristic
92#2085C2211yescharacteristic
93#2085C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2085C2211yescharacteristic
97#2084C2211yescharacteristic
98#2084C2211yescharacteristic
99#2083C2211yescharacteristic
100#2083C2211yescharacteristic
101#2059C2211yescharacteristic
102#2059C2211yescharacteristic
103#2059C2211yescharacteristic
104#2059C2211yescharacteristic
105#2058C2211yescharacteristic
106#2058C2211yescharacteristic
107#2058C2211yescharacteristic
108#2058C2211yescharacteristic
109#2058C2211yescharacteristic
110#2058C2211yescharacteristic
111#2057C2211yescharacteristic
112#2057C2211yescharacteristic
113#2057C2211yescharacteristic
114#2057C2211yescharacteristic
115#2057C2211yescharacteristic
116#2057C2211yescharacteristic
117#1993C2211yescharacteristic
118#1993C2211yescharacteristic
119#1993C2211yescharacteristic
120#1993C2211yescharacteristic
121#1991C2211yescharacteristic
122#1991C2211yescharacteristic
123#1990C2211yescharacteristic
124#1990C2211yescharacteristic
125#1949C2211yescharacteristic
126#1949C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1949C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1949C2211yescharacteristic
144#1949C2211yescharacteristic
145#1949C2211yescharacteristic
146#1949C2211yescharacteristic
147#1949C2211yescharacteristic
148#1949C2211yescharacteristic
149#1948C2211yescharacteristic
150#1948C2211yescharacteristic
151#1948C2211yescharacteristic
152#1948C2211yescharacteristic
153#1947C2211yescharacteristic
154#1947C2211yescharacteristic
155#1947C2211yescharacteristic
156#1947C2211yescharacteristic
157#1944C2211yescharacteristic
158#1944C2211yescharacteristic
159#1944C2211yescharacteristic
160#1944C2211yescharacteristic
161#1943C2211yescharacteristic
162#1943C2211yescharacteristic
163#1943C2211yescharacteristic
164#1943C2211yescharacteristic
165#1942C2211yescharacteristic
166#1942C2211yescharacteristic
167#1942C2211yescharacteristic
168#1942C2211yescharacteristic
169#1941C2211yescharacteristic
170#1941C2211yescharacteristic
171#1941C2211yescharacteristic
172#1941C2211yescharacteristic
173#1847C2211yescharacteristic
174#1847C2211yescharacteristic
175#1846C2211yescharacteristic
176#1846C2211yescharacteristic
177#1809C2211yescharacteristic
178#1809C2211yescharacteristic
179#1809C2211yescharacteristic
180#1809C2211yescharacteristic
181#1809C2211yescharacteristic
182#1809C2211yescharacteristic
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1808C2211yescharacteristic
186#1808C2211yescharacteristic
187#1808C2211yescharacteristic
188#1808C2211yescharacteristic
189#1807C2211yescharacteristic
190#1807C2211yescharacteristic
191#1807C2211yescharacteristic
192#1807C2211yescharacteristic
193#1768C2211yescharacteristic
194#1768C2211yescharacteristic
195#1768C2211yescharacteristic
196#1768C2211yescharacteristic
197#1767C2211yescharacteristic
198#1767C2211yescharacteristic
199C4×C4⋊C8C2211yescharacteristic
200C4×C4⋊C8C2211yescharacteristic
201#1729C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×M16C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×C4×Q8—21no—
216C2×C4×Q8—21no—
217C2×#117—21no—
218C2×#117C2311yescharacteristic
219C2×#117C2311yescharacteristic
220C22×C42C2311yescharacteristic
221#501—42no—
222#501—42no—
223#500—42no—
224#498—42no—
225C2×#107C2311yescharacteristic
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257#423Q818yescomplemented
258C2×C4⋊C8Q818yescomplemented
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×C4⋊C8C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267#405—42no—
268#405—42no—
269C2×#97C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×#97C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×C4×C8C2311yescharacteristic
274C2×C4×C8C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277#400—21no—
278#400—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#399—21no—
288#399—21no—
289#399—21no—
290#399—21no—
291#399—21no—
292#399—21no—
293#398—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#396—21no—
306#396—21no—
307#396—21no—
308#396—21no—
309#395—21no—
310#395—21no—
311#395—21no—
312#395—21no—
313#395—21no—
314#395—21no—
315#395—21no—
316#395—21no—
317#395—21no—
318#395—21no—
319#393—21no—
320#393—21no—
321#393—21no—
322#393—21no—
323#393—21no—
324#393—21no—
325#391—21no—
326#391—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391—21no—
335#391—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391—21no—
342#391—21no—
343#389—21no—
344#389—21no—
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
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#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#384C2311yescharacteristic
382#384C2311yescharacteristic
383#384C2311yescharacteristic
384#384C2311yescharacteristic
385#383—21no—
386#383—21no—
387#383—21no—
388#382—21no—
389#382C2311yescharacteristic
390#382C2311yescharacteristic
391#382C2311yescharacteristic
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#382C2311yescharacteristic
395#382C2311yescharacteristic
396#382C2311yescharacteristic
397#382C2311yescharacteristic
398#382C2311yescharacteristic
399#382C2311yescharacteristic
400#382C2311yescharacteristic
401#381—21no—
402#381—21no—
403#381—21no—
404#380—21no—
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413C4×C4⋊C4—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4D411yescharacteristic
421C4×C4⋊C4D411yescharacteristic
422C4×C4⋊C4D411yescharacteristic
423C4×C4⋊C4D411yescharacteristic
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×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4D411yescharacteristic
436C4×C22⋊C4D411yescharacteristic
437C4×C22⋊C4D411yescharacteristic
438C4×C22⋊C4D411yescharacteristic
439#376—21no—
440#376—21no—
441#376—21no—
442#376C2311yescharacteristic
443#376C2311yescharacteristic
444C43C2311yescharacteristic
445C43C2311yescharacteristic
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#340C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486C22×Q8—21no—
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8—21no—
491C22×Q8—21no—
492C23×C4C2×D411yescharacteristic
493C23×C4C2×D411yescharacteristic
494C23×C4C2411yescharacteristic
495C2×M16—41no—
496C2×M16—41no—
497C2×M16—41no—
498C2×M16—41no—
499C2×M16C2×Q814yes—
500C2×M16C2×Q814yes—
501C22×C8—41no—
502C22×C8—41no—
503C22×C8—41no—
504C22×C8—41no—
505C22×C8C2×Q814yes—
506C22×C8C2×Q814yes—
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C4⋊Q8—22no—
516C4⋊Q8—22no—
517C4⋊Q8—22no—
518C4⋊Q8—22no—
519C4⋊Q8—22no—
520C4⋊Q8—22no—
521C4⋊Q8—41no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527#125—22no—
528#125—22no—
529#125—41no—
530#125—41no—
531C4×Q8—82no—
532C4×Q8—82no—
533#117—22no—
534#117—22no—
535#117—41no—
536#117—41no—
537#117—82no—
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⋊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⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
601C2×C22⋊C4C2×D411yescharacteristic
602C2×C22⋊C4C2×D411yescharacteristic
603C2×C22⋊C4C2×D411yescharacteristic
604C2×C42—21no—
605C2×C42—21no—
606C2×C42—21no—
607C2×C42—21no—
608C2×C42—21no—
609C2×C42—21no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42C2×D411yescharacteristic
613C2×C42C2×D411yescharacteristic
614C2×C42C2×D411yescharacteristic
615C2×C42C2×D411yescharacteristic
616C2×C42C2×D411yescharacteristic
617C2×C42C2×D411yescharacteristic
618C2×C42C2×D411yescharacteristic
619C2×C42C2×D411yescharacteristic
620C2×C42C2×D411yescharacteristic
621C2×C42C2×D411yescharacteristic
622C2×C42C2×Q814yes—
623C2×C42C2×Q814yes—
624C2×C42C2411yescharacteristic
625C2×C42C2411yescharacteristic
626C2×C42C2411yescharacteristic
627C2×C42C2411yescharacteristic
628C2×C42C2411yescharacteristic
629C2×C42C2411yescharacteristic
630#107—41no—
631#107—41no—
632#107—41no—
633#107—41no—
634#107—41no—
635#107—41no—
636#107—41no—
637#107—41no—
638#107—41no—
639#107—41no—
640#107—41no—
641#107—41no—
642#107—41no—
643#107—41no—
644#107—41no—
645#107—41no—
646#106—41no—
647#106—41no—
648#106—41no—
649#106—41no—
650#106—41no—
651#106—41no—
652#106—41no—
653#106—41no—
654#106—41no—
655#106—41no—
656#106—41no—
657#106—41no—
658#106—41no—
659#106—41no—
660#106—41no—
661#106—41no—
662C4⋊C8C2×Q814yes—
663C4⋊C8C2×Q814yes—
664C4⋊C8C2×Q814yes—
665C4⋊C8C2×Q814yes—
666C4⋊C8C2×Q814yes—
667C4⋊C8C2×Q814yes—
668C4⋊C8C2×Q814yes—
669C4⋊C8C2×Q814yes—
670#97—22no—
671#97—22no—
672#97—41no—
673#97—41no—
674C4×C8—22no—
675C4×C8—22no—
676C4×C8—41no—
677C4×C8—41no—
678#95—21no—
679#95—21no—
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#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#95C2×D411yescharacteristic
735#95C2×D411yescharacteristic
736#95C2×D411yescharacteristic
737#95C2×D411yescharacteristic
738#95C2×D411yescharacteristic
739#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742C24C22×D411yescharacteristic
743C2×Q8—42no—
744C2×Q8—42no—
745C2×Q8—42no—
746C2×Q8—42no—
747C2×Q8—42no—
748C2×Q8—42no—
749C2×Q8—81no—
750C2×Q8—81no—
751C2×Q8—81no—
752C2×Q8—81no—
753C2×Q8—81no—
754C2×Q8—81no—
755C2×Q8—81no—
756C2×Q8—81no—
757C2×Q8—81no—
758C2×Q8—81no—
759C2×Q8—81no—
760C2×Q8—81no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
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—41no—
782C22×C4—41no—
783C22×C4—41no—
784C22×C4—41no—
785C22×C4C4⋊Q814yes—
786C22×C4C4⋊Q814yes—
787C22×C4C22×D411yescharacteristic
788C22×C4C22×D411yescharacteristic
789C22×C4C22×D411yescharacteristic
790C22×C4C22×D411yescharacteristic
791C22×C4C22×D411yescharacteristic
792C22×C4C22×D411yescharacteristic
793C22×C4C22×D411yescharacteristic
794C22×C4C22×D411yescharacteristic
795C22×C4C22×D411yescharacteristic
796C22×C4C22×D411yescharacteristic
797C22×C4C22×D411yescharacteristic
798C22×C4C22×D411yescharacteristic
799C22×C4C22×D411yescharacteristic
800C22×C4C22×Q812yes—
801C22×C4C22×Q812yes—
802C22×C4C2511yescharacteristic
803M16—44no—
804M16—44no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
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—44no—
822C2×C8—44no—
823C2×C8C22×Q812yes—
824C2×C8C22×Q812yes—
825C2×C8C22×Q812yes—
826C2×C8C22×Q812yes—
827C2×C8C22×Q812yes—
828C2×C8C22×Q812yes—
829C2×C8C22×Q812yes—
830C2×C8C22×Q812yes—
831C4⋊C4—22no—
832C4⋊C4—22no—
833C4⋊C4—21no—
834C4⋊C4—21no—
835C4⋊C4—21no—
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—21no—
865C4⋊C4—41no—
866C4⋊C4—41no—
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—81no—
878C4⋊C4—81no—
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—
897C4⋊C4—81no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C22⋊C4—22no—
902C22⋊C4—22no—
903C22⋊C4—41no—
904C22⋊C4—41no—
905C22⋊C4—81no—
906C22⋊C4—81no—
907C22⋊C4—81no—
908C22⋊C4—81no—
909C22⋊C4—81no—
910C22⋊C4—81no—
911C22⋊C4—81no—
912C22⋊C4—81no—
913C42—21no—
914C42—21no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—41no—
920C42—41no—
921C42—41no—
922C42—41no—
923C42—41no—
924C42—41no—
925C42—41no—
926C42—41no—
927C42—42no—
928C42—42no—
929C42—42no—
930C42—42no—
931C42—81no—
932C42—81no—
933C42—81no—
934C42—81no—
935C42C4⋊Q814yes—
936C42C4⋊Q814yes—
937C42C22×Q812yes—
938C42C22×Q812yes—
939C42C22×Q812yes—
940C42C22×Q812yes—
941C42H(5,𝔽2)12yes—
942C422−1+412yes—
943C23—21no—
944C23—21no—
945C23—21no—
946C23—21no—
947C23—21no—
948C23—21no—
949C23C2×C4⋊Q812yes—
950C23C23×D411yescharacteristic
951Q8—84no—
952Q8—84no—
953Q8—162no—
954Q8—162no—
955Q8—162no—
956Q8—162no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—22no—
973C2×C4—22no—
974C2×C4—22no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—21no—
978C2×C4—21no—
979C2×C4—21no—
980C2×C4—21no—
981C2×C4—21no—
982C2×C4—21no—
983C2×C4—21no—
984C2×C4—21no—
985C2×C4—21no—
986C2×C4—21no—
987C2×C4—21no—
988C2×C4—21no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—44no—
994C2×C4—44no—
995C2×C4—41no—
996C2×C4—41no—
997C2×C4—41no—
998C2×C4—41no—
999C2×C4—41no—
1000C2×C4—41no—
1001C2×C4—41no—
1002C2×C4—41no—
1003C2×C4—41no—
1004C2×C4—41no—
1005C2×C4—41no—
1006C2×C4—41no—
1007C2×C4—41no—
1008C2×C4—41no—
1009C2×C4—41no—
1010C2×C4—41no—
1011C2×C4—41no—
1012C2×C4—41no—
1013C2×C4—41no—
1014C2×C4—41no—
1015C2×C4—41no—
1016C2×C4—41no—
1017C2×C4—41no—
1018C2×C4—41no—
1019C2×C4—41no—
1020C2×C4—41no—
1021C2×C4—41no—
1022C2×C4—41no—
1023C2×C4—41no—
1024C2×C4—41no—
1025C2×C4—41no—
1026C2×C4—41no—
1027C2×C4—41no—
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×C4C2×C4⋊Q812yes—
1044C2×C4C2×C4⋊Q812yes—
1045C2×C4C2×C4⋊Q812yes—
1046C2×C4C2×C4⋊Q812yes—
1047C2×C4C2×C4⋊Q812yes—
1048C2×C4#53712yes—
1049C2×C4#53712yes—
1050C2×C4C23×Q811yescharacteristic
1051C2×C4C23×Q811yescharacteristic
1052C2×C4C2×H(5,𝔽2)11yescharacteristic
1053C2×C4C2×2−1+411yescharacteristic
1054C2×C4#58511yescharacteristic
1055C2×C4#58511yescharacteristic
1056C8—22no—
1057C8—22no—
1058C8—22no—
1059C8—22no—
1060C8—22no—
1061C8—22no—
1062C8—22no—
1063C8—22no—
1064C22—22no—
1065C22—22no—
1066C22—22no—
1067C22—41no—
1068C22—41no—
1069C22—41no—
1070C22—41no—
1071C22C22×C4⋊Q811yescharacteristic
1072C22C2×#53711yescharacteristic
1073C22#344911yescharacteristic
1074C22#358411yescharacteristic
1075C22#358411yescharacteristic
1076C22#358511yescharacteristic
1077C22#358611yescharacteristic
1078C4—22no—
1079C4—22no—
1080C4—22no—
1081C4—22no—
1082C4—22no—
1083C4—22no—
1084C4—22no—
1085C4—41no—
1086C4—41no—
1087C4—41no—
1088C4—41no—
1089C4—41no—
1090C4—41no—
1091C4—81no—
1092C4—81no—
1093C4—81no—
1094C4—81no—
1095C4—81no—
1096C4—81no—
1097C4—81no—
1098C4—81no—
1099C4—81no—
1100C4—81no—
1101C4—81no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4#350111yescharacteristic
1108C4#350111yescharacteristic
1109C4#350211yescharacteristic
1110C4#350211yescharacteristic
1111C2—42no—
1112C2#3517311yescharacteristic
1113C2#6066011yescharacteristic
1114C2#6066411yescharacteristic
1115C2#6092611yescharacteristic
1116C2#6092711yescharacteristic
1117C2#6099611yescharacteristic
1118C2#6099811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC24C22×D4
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
11. #29325C2semidirect
12. #29325C2semidirect
13. #29323C2semidirect
14. #29322C2semidirect
15. #29318C2semidirect
16. #29317C2semidirect
17. #29316C2semidirect
18. #29315C2semidirect
19. #29217C2semidirect
20. #29217C2semidirect
21. #29211C2semidirect
22. #29209C2semidirect
23. #28697C2semidirect
24. #28696C2semidirect
25. #28695C2semidirect
26. #28688C2semidirect
257. #423Q8semidirect
258. C2×C4⋊C8Q8semidirect

Maximal subgroups

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

subgroupindex
#353442
#346252
#332192
#332152
#332132
#303022
#303002
#302992
#293252
#293232
#293222
#293182
#293172
#293162
#293152
#292172
#292112
#292092
#286972
#286962
#286952
#286882
#219652
#219632
#219622
#219602
#204312