Finite Group Databasebeta

← #6883656

Subgroups — #6883656

Order 512.

1315 conjugacy classes of subgroups.

The subgroup lattice has 1172 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39297C211yesmaximal, characteristic, complemented
2#38276C211yesmaximal, characteristic, complemented
3#33213C211yesmaximal, characteristic, complemented
4#32411C211yesmaximal, characteristic, complemented
5#32407C211yesmaximal, characteristic, complemented
6#32225C211yesmaximal, characteristic, complemented
7#32210C211yesmaximal, characteristic, complemented
8#31629C211yesmaximal, characteristic, complemented
9#31625C211yesmaximal, characteristic, complemented
10#30675C211yesmaximal, characteristic
11#30673C211yesmaximal, characteristic
12#30395C211yesmaximal, characteristic, complemented
13#30381C211yesmaximal, characteristic, complemented
14#29452C211yesmaximal, characteristic, complemented
15#29444C211yesmaximal, characteristic, complemented
16#29322C211yesmaximal, characteristic, complemented
17#29318C211yesmaximal, characteristic, complemented
18#26518C211yesmaximal, characteristic, complemented
19#26452C211yesmaximal, characteristic, complemented
20#26096C211yesmaximal, characteristic, complemented
21#26051C211yesmaximal, characteristic, complemented
22#25452C211yesmaximal, characteristic, complemented
23#25452C211yesmaximal, characteristic, complemented
24#24830C211yesmaximal, characteristic, complemented
25#24712C211yesmaximal, characteristic, complemented
26#24712C211yesmaximal, characteristic, complemented
27#24693C211yesmaximal, characteristic, complemented
28#22123C211yesmaximal, characteristic, complemented
29#22114C211yesmaximal, characteristic, complemented
30#21529C211yesmaximal, characteristic
31#21357C211yesmaximal, characteristic, complemented
32C2×#498C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#476C2211yescharacteristic
35C2×#474C2211yescharacteristic
36C2×#474C2211yescharacteristic
37C2×#466C2211yescharacteristic
38C2×#442C2211yescharacteristic
39C2×#433C2211yescharacteristic
40C2×#405C2211yescharacteristic
41#2864C2211yescharacteristic
42#2860C2211yescharacteristic
43#2808—21no—
44#2759—21no—
45#2751—21no—
46#2747—21no—
47#2745—21no—
48#2745—21no—
49#2741—21no—
50#2740—21no—
51#2647C2211yescharacteristic
52#2644C2211yescharacteristic
53#2628C2211yescharacteristic
54#2628C2211yescharacteristic
55#2599—21no—
56#2592—21no—
57#2577—21no—
58#2570C2211yescharacteristic
59#2563C2211yescharacteristic
60#2563C2211yescharacteristic
61#2550C2211yescharacteristic
62#2521—21no—
63#2498—21no—
64#2495C2211yescharacteristic
65#2495C2211yescharacteristic
66#2494C2211yescharacteristic
67#2494C2211yescharacteristic
68#2493—21no—
69#2491C2211yescharacteristic
70#2490C2211yescharacteristic
71#2469—21no—
72#2458—21no—
73#2422C2211yescharacteristic
74#2420C2211yescharacteristic
75#2365C2211yescharacteristic
76#2365C2211yescharacteristic
77#2357C2211yescharacteristic
78#2349C2211yescharacteristic
79#2331C2211yescharacteristic
80#2324C2211yescharacteristic
81#2324C2211yescharacteristic
82#2319C2211yescharacteristic
83C4×#125C2211yescharacteristic
84#2298C2211yescharacteristic
85#2293C2211yescharacteristic
86#2101C2211yescharacteristic
87#2099C2211yescharacteristic
88#2094C2211yescharacteristic
89#2092C2211yescharacteristic
90#2088C2211yescharacteristic
91#2088C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2087C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2076C2211yescharacteristic
103#2076C2211yescharacteristic
104#2075C2211yescharacteristic
105#2075C2211yescharacteristic
106#2073C2211yescharacteristic
107#2073C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#2065C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2057C2211yescharacteristic
119#2057C2211yescharacteristic
120#2054C2211yescharacteristic
121#2054C2211yescharacteristic
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2033C2211yescharacteristic
125#2033C2211yescharacteristic
126#1993C2211yescharacteristic
127#1993C2211yescharacteristic
128#1989C2211yescharacteristic
129#1988C2211yescharacteristic
130#1987C2211yescharacteristic
131#1987C2211yescharacteristic
132#1972C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1949C2211yescharacteristic
136#1949C2211yescharacteristic
137#1949C2211yescharacteristic
138#1949C2211yescharacteristic
139#1949C2211yescharacteristic
140#1949C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1947C2211yescharacteristic
144#1947C2211yescharacteristic
145#1944C2211yescharacteristic
146#1944C2211yescharacteristic
147#1943C2211yescharacteristic
148#1943C2211yescharacteristic
149#1943C2211yescharacteristic
150#1942C2211yescharacteristic
151#1942C2211yescharacteristic
152#1941C2211yescharacteristic
153#1941C2211yescharacteristic
154#1940C2211yescharacteristic
155#1940C2211yescharacteristic
156#1939C2211yescharacteristic
157#1939C2211yescharacteristic
158#1936C2211yescharacteristic
159#1936C2211yescharacteristic
160#1934C2211yescharacteristic
161#1934C2211yescharacteristic
162#1934C2211yescharacteristic
163#1934C2211yescharacteristic
164#1926C2211yescharacteristic
165#1926C2211yescharacteristic
166#1926C2211yescharacteristic
167#1926C2211yescharacteristic
168#1925C2211yescharacteristic
169#1925C2211yescharacteristic
170#1921C2211yescharacteristic
171#1920C2211yescharacteristic
172#1920C2211yescharacteristic
173#1920C2211yescharacteristic
174#1919C2211yescharacteristic
175#1919C2211yescharacteristic
176#1895C2211yescharacteristic
177#1895C2211yescharacteristic
178#1879C2211yescharacteristic
179#1879C2211yescharacteristic
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1851C2211yescharacteristic
183#1851C2211yescharacteristic
184#1850C2211yescharacteristic
185#1850C2211yescharacteristic
186#1846C2211yescharacteristic
187#1809C2211yescharacteristic
188#1809C2211yescharacteristic
189#1807C2211yescharacteristic
190#1807C2211yescharacteristic
191#1807C2211yescharacteristic
192#1804C2211yescharacteristic
193#1804C2211yescharacteristic
194#1804C2211yescharacteristic
195#1804C2211yescharacteristic
196#1776C2211yescharacteristic
197#1768C2211yescharacteristic
198#1768C2211yescharacteristic
199#1767C2211yescharacteristic
200C4×C4⋊C8C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×#126—21no—
210C2×#125C2311yescharacteristic
211C2×#124—21no—
212C2×#123—21no—
213C2×#121C2311yescharacteristic
214C2×#121C2311yescharacteristic
215C2×C4×Q8—21no—
216C2×C4×Q8—21no—
217C2×C4×D4C2311yescharacteristic
218C2×C4×D4C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×#117—21no—
222C2×#117C2311yescharacteristic
223#498—42no—
224#478—24no—
225#476—24no—
226#474—42no—
227#474—42no—
228#466—24no—
229#442—42no—
230#433—42no—
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276#405—42no—
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283#401—21no—
284#401—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#399—21no—
293#399—21no—
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#397—21no—
299#397—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#396—21no—
309#395—21no—
310#395—21no—
311#395—21no—
312#394—21no—
313#394—21no—
314#394—21no—
315#394—21no—
316#393—21no—
317#393—21no—
318#393—21no—
319#393—21no—
320#393—21no—
321#393—21no—
322#393—21no—
323#391—21no—
324#391—21no—
325#391—21no—
326#391—21no—
327#391—21no—
328#390—21no—
329#390—21no—
330#390—21no—
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#389—21no—
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
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#388—21no—
373#388D411yescharacteristic
374#388D411yescharacteristic
375#388D411yescharacteristic
376#388D411yescharacteristic
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387D411yescharacteristic
394#387D411yescharacteristic
395#387D411yescharacteristic
396#387D411yescharacteristic
397#386—21no—
398#386—21no—
399#386—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#384C2311yescharacteristic
406#383—21no—
407#383—21no—
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#381—21no—
416#381—21no—
417#381—21no—
418#380—21no—
419#380—21no—
420#380—21no—
421#380—21no—
422#380—21no—
423#380—21no—
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4C2311yescharacteristic
445C4×C22⋊C4C2311yescharacteristic
446#376C2311yescharacteristic
447C2×#95—21no—
448C43C2311yescharacteristic
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#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C2411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4C2411yescharacteristic
499C2×D8—22no—
500C2×D8—22no—
501C2×D8—41no—
502C2×M16—22no—
503C2×M16—41no—
504C2×M16—41no—
505C22×C8—22no—
506C22×C8—22no—
507C22×C8—41no—
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C4⋊Q8—22no—
517C4⋊Q8—22no—
518C4⋊Q8—22no—
519C4⋊Q8—22no—
520C4⋊Q8—22no—
521C4⋊Q8—41no—
522#126—82no—
523#125—22no—
524#125—41no—
525#124—82no—
526#123—82no—
527#121—22no—
528#121—22no—
529#121—41no—
530#121—41no—
531C4×Q8—82no—
532C4×Q8—82no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—41no—
540C4×D4—41no—
541#117—22no—
542#117—22no—
543#117—82no—
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⋊C4C2×D411yescharacteristic
568C2×C4⋊C4C2×D411yescharacteristic
569C2×C4⋊C4C2×D411yescharacteristic
570C2×C4⋊C4C2×D411yescharacteristic
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
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⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C22⋊C4C2×D411yescharacteristic
618C2×C22⋊C4C2×D411yescharacteristic
619C2×C22⋊C4C2×D411yescharacteristic
620C2×C22⋊C4C2×D411yescharacteristic
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42C2×D411yescharacteristic
630C2×C42C2×D411yescharacteristic
631C2×C42C2×D411yescharacteristic
632C2×C42C2×D411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639#107—22no—
640#107—22no—
641#107—41no—
642#107—41no—
643#107—41no—
644#107—41no—
645#107—41no—
646#107—41no—
647#107—41no—
648#106—22no—
649#106—22no—
650#106—22no—
651#106—22no—
652#106—41no—
653#106—41no—
654#106—41no—
655#106—41no—
656#106—41no—
657#106—41no—
658C4⋊C8—22no—
659C4⋊C8—22no—
660C4⋊C8—22no—
661C4⋊C8—22no—
662C4⋊C8—22no—
663C4⋊C8—22no—
664C4⋊C8—22no—
665C4⋊C8—22no—
666C4⋊C8—41no—
667C4⋊C8—41no—
668#102—22no—
669#102—22no—
670#102—22no—
671#102—22no—
672#102—22no—
673#102—41no—
674#102—41no—
675#102—41no—
676#102—41no—
677#102—41no—
678#102—41no—
679#102—41no—
680#102—41no—
681#102#4114yes—
682C22⋊C8—41no—
683C22⋊C8—41no—
684#97—22no—
685#97—41no—
686#97—41no—
687C4×C8—22no—
688C4×C8—41no—
689C4×C8—41no—
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
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746C24—21no—
747C24—21no—
748C24C22×D411yescharacteristic
749C2×Q8—42no—
750C2×Q8—42no—
751C2×Q8—42no—
752C2×Q8—81no—
753C2×Q8—81no—
754C2×Q8—81no—
755C2×Q8—81no—
756C2×Q8—81no—
757C2×Q8—81no—
758C2×D4—21no—
759C2×D4—21no—
760C2×D4—21no—
761C2×D4—21no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—42no—
770C2×D4—42no—
771C2×D4—81no—
772C2×D4—81no—
773C2×D4—81no—
774C2×D4—81no—
775C2×D4C2×#4112yes—
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—21no—
786C22×C4—21no—
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—21no—
796C22×C4—42no—
797C22×C4—42no—
798C22×C4—42no—
799C22×C4—42no—
800C22×C4—42no—
801C22×C4—81no—
802C22×C4—81no—
803C22×C4—81no—
804C22×C4—81no—
805C22×C4—81no—
806C22×C4—81no—
807C22×C4—81no—
808C22×C4C22×D411yescharacteristic
809C22×C4C22×D411yescharacteristic
810C22×C4C22×D411yescharacteristic
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C2511yescharacteristic
822D8—44no—
823M16—44no—
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—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—44no—
846C2×C8C2×#4112yes—
847C2×C82−1+412yes—
848C2×C82−1+412yes—
849C4⋊C4—22no—
850C4⋊C4—22no—
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—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—41no—
879C4⋊C4—41no—
880C4⋊C4—41no—
881C4⋊C4—41no—
882C4⋊C4—42no—
883C4⋊C4—42no—
884C4⋊C4—42no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
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—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4C2×#4112yes—
906C22⋊C4—22no—
907C22⋊C4—22no—
908C22⋊C4—41no—
909C22⋊C4—41no—
910C22⋊C4—41no—
911C22⋊C4—41no—
912C22⋊C4—42no—
913C22⋊C4—42no—
914C22⋊C4—42no—
915C22⋊C4—42no—
916C22⋊C4—42no—
917C22⋊C4—42no—
918C22⋊C4—42no—
919C22⋊C4—81no—
920C22⋊C4—81no—
921C22⋊C4—81no—
922C22⋊C4—81no—
923C22⋊C4—81no—
924C22⋊C4—81no—
925C22⋊C4—81no—
926C22⋊C4—81no—
927C22⋊C4—81no—
928C22⋊C4—81no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C42—21no—
941C42—21no—
942C42—21no—
943C42—21no—
944C42—21no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—41no—
951C42—41no—
952C42—41no—
953C42—41no—
954C42—42no—
955C42—42no—
956C42—81no—
957C42—81no—
958C42—81no—
959C42—81no—
960C42—81no—
961C42—81no—
962C42H(5,𝔽2)12yes—
963C422−1+412yes—
964C23—21no—
965C23—21no—
966C23—21no—
967C23—21no—
968C23—21no—
969C23—22no—
970C23—21no—
971C23—21no—
972C23—41no—
973C23—41no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23C23×D411yescharacteristic
986Q8—84no—
987Q8—84no—
988Q8—162no—
989D4—22no—
990D4—22no—
991D4—41no—
992D4—41no—
993D4—41no—
994D4—41no—
995D4—41no—
996D4—41no—
997D4—162no—
998D4—162no—
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—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—22no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
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—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—84no—
1083C2×C4—162no—
1084C2×C4—162no—
1085C2×C4—162no—
1086C2×C4#53712yes—
1087C2×C4#53712yes—
1088C2×C4C22×#4111yescharacteristic
1089C2×C4C2×H(5,𝔽2)11yescharacteristic
1090C2×C4C2×2−1+411yescharacteristic
1091C2×C4C2×2−1+411yescharacteristic
1092C2×C4C2×2−1+411yescharacteristic
1093C2×C4#58511yescharacteristic
1094C8—22no—
1095C8—22no—
1096C8—22no—
1097C8—41no—
1098C8—41no—
1099C8—41no—
1100C8—41no—
1101C8—41no—
1102C22—41no—
1103C22—42no—
1104C22—42no—
1105C22—41no—
1106C22—41no—
1107C22—41no—
1108C22—42no—
1109C22—41no—
1110C22—41no—
1111C22—41no—
1112C22—81no—
1113C22—81no—
1114C22—81no—
1115C22—81no—
1116C22—81no—
1117C22—81no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22—81no—
1123C22C2×#53711yescharacteristic
1124C22D4×#4111yescharacteristic
1125C22#349911yescharacteristic
1126C22#358411yescharacteristic
1127C22#358411yescharacteristic
1128C22#358511yescharacteristic
1129C22#358511yescharacteristic
1130C4—22no—
1131C4—22no—
1132C4—41no—
1133C4—41no—
1134C4—41no—
1135C4—41no—
1136C4—41no—
1137C4—41no—
1138C4—41no—
1139C4—41no—
1140C4—41no—
1141C4—42no—
1142C4—41no—
1143C4—41no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4#350911yescharacteristic
1158C4#352011yescharacteristic
1159C4#354111yescharacteristic
1160C4#355511yescharacteristic
1161C2—81no—
1162C2—82no—
1163C2—161no—
1164C2#3995911yescharacteristic
1165C2#6092611yescharacteristic
1166C2#6092611yescharacteristic
1167C2#6148611yescharacteristic
1168C2#6150511yescharacteristic
1169C2#6251811yescharacteristic
1170C2#6252411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#466C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39297C2semidirect
2. #38276C2semidirect
3. #33213C2semidirect
4. #32411C2semidirect
5. #32407C2semidirect
6. #32225C2semidirect
7. #32210C2semidirect
8. #31629C2semidirect
9. #31625C2semidirect
12. #30395C2semidirect
13. #30381C2semidirect
14. #29452C2semidirect
15. #29444C2semidirect
16. #29322C2semidirect
17. #29318C2semidirect
18. #26518C2semidirect
19. #26452C2semidirect
20. #26096C2semidirect
21. #26051C2semidirect
22. #25452C2semidirect
23. #25452C2semidirect
24. #24830C2semidirect
25. #24712C2semidirect
26. #24712C2semidirect
27. #24693C2semidirect
28. #22123C2semidirect
29. #22114C2semidirect
31. #21357C2semidirect

Maximal subgroups

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

subgroupindex
#392972
#382762
#332132
#324112
#324072
#322252
#322102
#316292
#316252
#306752
#306732
#303952
#303812
#294522
#294442
#293222
#293182
#265182
#264522
#260962
#260512
#254522
#248302
#247122
#246932
#221232
#221142
#215292
#213572