Finite Group Databasebeta

← #7043497

Subgroups — #7043497

Order 512.

1344 conjugacy classes of subgroups.

The subgroup lattice has 1196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45358C211yesmaximal, characteristic, complemented
2#44942C211yesmaximal, characteristic, complemented
3#32655C211yesmaximal, characteristic, complemented
4#32581C211yesmaximal, characteristic, complemented
5#32521C211yesmaximal, characteristic, complemented
6#32361C211yesmaximal, characteristic, complemented
7#32155C211yesmaximal, characteristic, complemented
8#31867C211yesmaximal, characteristic, complemented
9#31530C211yesmaximal, characteristic, complemented
10#30951C211yesmaximal, characteristic, complemented
11#29248C211yesmaximal, characteristic, complemented
12#28788C211yesmaximal, characteristic, complemented
13#27688C211yesmaximal, characteristic, complemented
14#27315C211yesmaximal, characteristic, complemented
15#27307C211yesmaximal, characteristic, complemented
16#26868C211yesmaximal, characteristic, complemented
17#26423C211yesmaximal, characteristic, complemented
18#26421C211yesmaximal, characteristic, complemented
19#26394C211yesmaximal, characteristic, complemented
20#26350C211yesmaximal, characteristic, complemented
21#26350C211yesmaximal, characteristic, complemented
22#26286C211yesmaximal, characteristic, complemented
23#26075C211yesmaximal, characteristic, complemented
24#25458C211yesmaximal, characteristic, complemented
25#25069C211yesmaximal, characteristic, complemented
26#24823C211yesmaximal, characteristic, complemented
27#23660C211yesmaximal, characteristic, complemented
28#23140C211yesmaximal, characteristic
29#23039C211yesmaximal, characteristic
30#22294C211yesmaximal, characteristic, complemented
31#22199C211yesmaximal, characteristic
32C2×#499C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#469C2211yescharacteristic
36C2×#442C2211yescharacteristic
37C2×#428C2211yescharacteristic
38C22×#107C2211yescharacteristic
39#2807—21no—
40#2790—21no—
41#2784—21no—
42#2780—21no—
43#2748—21no—
44#2748—21no—
45#2742—21no—
46#2704—21no—
47#2587—21no—
48#2587—21no—
49#2584C2211yescharacteristic
50#2580C2211yescharacteristic
51#2566—21no—
52#2566C2211yescharacteristic
53#2566C2211yescharacteristic
54#2552C2211yescharacteristic
55#2538C2211yescharacteristic
56#2509C2211yescharacteristic
57#2508C2211yescharacteristic
58#2506C2211yescharacteristic
59#2506C2211yescharacteristic
60#2505—21no—
61#2487—21no—
62#2473—21no—
63#2454—21no—
64#2454C2211yescharacteristic
65#2454C2211yescharacteristic
66#2450—21no—
67#2442C2211yescharacteristic
68#2442C2211yescharacteristic
69#2441C2211yescharacteristic
70#2441C2211yescharacteristic
71#2396C2211yescharacteristic
72#2370C2211yescharacteristic
73#2363C2211yescharacteristic
74#2363C2211yescharacteristic
75#2361C2211yescharacteristic
76#2361C2211yescharacteristic
77#2355C2211yescharacteristic
78#2349C2211yescharacteristic
79D4×C4⋊C4C2211yescharacteristic
80#2324C2211yescharacteristic
81#2324C2211yescharacteristic
82#2317C2211yescharacteristic
83#2316C2211yescharacteristic
84#2101C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2094C2211yescharacteristic
89#2092C2211yescharacteristic
90#2092C2211yescharacteristic
91#2092C2211yescharacteristic
92#2088C2211yescharacteristic
93#2088C2211yescharacteristic
94#2087C2211yescharacteristic
95#2087C2211yescharacteristic
96#2087C2211yescharacteristic
97#2086C2211yescharacteristic
98#2085C2211yescharacteristic
99#2085C2211yescharacteristic
100#2085C2211yescharacteristic
101#2085C2211yescharacteristic
102#2085C2211yescharacteristic
103#2085C2211yescharacteristic
104#2084C2211yescharacteristic
105#2084C2211yescharacteristic
106#2083C2211yescharacteristic
107#2083C2211yescharacteristic
108#2083C2211yescharacteristic
109#2083C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2067C2211yescharacteristic
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#2065C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2059C2211yescharacteristic
120#2059C2211yescharacteristic
121#2059C2211yescharacteristic
122#2025C2211yescharacteristic
123#2025C2211yescharacteristic
124#1992C2211yescharacteristic
125#1991C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1985C2211yescharacteristic
129#1984C2211yescharacteristic
130#1970C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1948C2211yescharacteristic
135#1944C2211yescharacteristic
136#1943C2211yescharacteristic
137#1943C2211yescharacteristic
138#1941C2211yescharacteristic
139#1941C2211yescharacteristic
140#1940C2211yescharacteristic
141#1939C2211yescharacteristic
142#1936C2211yescharacteristic
143#1934C2211yescharacteristic
144#1926C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic
148#1921C2211yescharacteristic
149#1921C2211yescharacteristic
150#1920C2211yescharacteristic
151#1920C2211yescharacteristic
152#1919C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1918C2211yescharacteristic
158#1917C2211yescharacteristic
159#1917C2211yescharacteristic
160#1916C2211yescharacteristic
161#1916C2211yescharacteristic
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1875C2211yescharacteristic
169#1875C2211yescharacteristic
170#1874C2211yescharacteristic
171#1874C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1853C2211yescharacteristic
185#1853C2211yescharacteristic
186#1850C2211yescharacteristic
187#1850C2211yescharacteristic
188#1847C2211yescharacteristic
189#1809C2211yescharacteristic
190#1804C2211yescharacteristic
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic
193#1802C2211yescharacteristic
194#1798C2211yescharacteristic
195C4×#106C2211yescharacteristic
196#1762C2211yescharacteristic
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200#1736C2211yescharacteristic
201#1735C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C2×#125—21no—
207C2×#125—21no—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×C22⋊Q8—21no—
213C2×#121C2311yescharacteristic
214C2×#121C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×D4—21no—
217C2×C4×D4—21no—
218C2×C4×D4C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C22×C4⋊C4—21no—
228C22×C4⋊C4C2311yescharacteristic
229C22×C4⋊C4C2311yescharacteristic
230#499—42no—
231#478—42no—
232#478—42no—
233#469Q818yescomplemented
234#442—42no—
235#428—42no—
236C2×#107—42no—
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400D411yescharacteristic
290#399—21no—
291#399—21no—
292#399—21no—
293#399—21no—
294#399—21no—
295#399D411yescharacteristic
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#398D411yescharacteristic
305#398D411yescharacteristic
306#396—21no—
307#396—21no—
308#396—21no—
309#396—21no—
310#396—21no—
311#396—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#396D411yescharacteristic
317#396D411yescharacteristic
318#395—21no—
319#395D411yescharacteristic
320#393—21no—
321#393D411yescharacteristic
322#391—21no—
323#390—21no—
324#390—21no—
325#390—21no—
326#390—21no—
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389—21no—
343#389—21no—
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#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—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#386—21no—
379#386—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#385—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#384—21no—
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#382—21no—
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#380—21no—
415#380—21no—
416#380—21no—
417#380—21no—
418#380—21no—
419#380—21no—
420#380—21no—
421#380—21no—
422#380—21no—
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4C2311yescharacteristic
439C4×C22⋊C4C2311yescharacteristic
440C2×#95—21no—
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485C22×Q8C2×D411yescharacteristic
486C22×D4—21no—
487C22×D4—21no—
488C22×D4C2411yescharacteristic
489C22×D4C2411yescharacteristic
490C23×C4—21no—
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4C2411yescharacteristic
499C2×D8—41no—
500C2×D8—41no—
501C2×D8C2×Q814yes—
502C2×M16—41no—
503C2×M16—41no—
504C2×M16C2×Q814yes—
505C22×C8—22no—
506C22×C8—41no—
507C22×C8—41no—
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516#125—22no—
517#125—41no—
518#125—41no—
519#125—41no—
520#125—41no—
521#125—41no—
522#125—41no—
523#125—41no—
524#125—82no—
525#125—82no—
526C22⋊Q8—82no—
527#121—22no—
528#121—22no—
529#121C2×Q814yes—
530#121C2×Q814yes—
531C4×Q8—41no—
532C4×Q8—41no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C4×D4—41no—
538C4×D4—41no—
539C4×D4—41no—
540C4×D4—41no—
541C4×D4—41no—
542C4×D4—41no—
543C4×D4—41no—
544C4×D4—41no—
545C4×D4—82no—
546C4×D4—82no—
547#117—41no—
548#117—41no—
549#117—41no—
550#117—41no—
551#117—41no—
552#117—41no—
553C2×C4⋊C4—22no—
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—41no—
591C2×C4⋊C4—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—82no—
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2×D411yescharacteristic
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663#107—22no—
664#107—22no—
665#107—22no—
666#107—41no—
667#107—41no—
668#107—41no—
669#107—41no—
670#107—41no—
671#107—41no—
672#106—22no—
673#106—22no—
674#106—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679#106—41no—
680#106—41no—
681#106C2×Q814yes—
682C4⋊C8—41no—
683C4⋊C8—41no—
684C4⋊C8—41no—
685C4⋊C8—41no—
686C4⋊C8—41no—
687C4⋊C8—41no—
688#102—22no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102C2×Q814yes—
701#102C2×Q814yes—
702C22⋊C8—22no—
703C22⋊C8—22no—
704#97—41no—
705#97—41no—
706C4×C8—41no—
707C4×C8—41no—
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#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752C24—21no—
753C24—21no—
754C24C22×D411yescharacteristic
755C2×Q8—41no—
756C2×Q8—41no—
757C2×Q8—41no—
758C2×D4—24no—
759C2×D4—24no—
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—21no—
770C2×D4—81no—
771C2×D4—81no—
772C2×D4—81no—
773C2×D4—81no—
774C2×D4C22×Q812yes—
775C2×D4C22×Q812yes—
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—42no—
795C22×C4—42no—
796C22×C4—42no—
797C22×C4—42no—
798C22×C4—81no—
799C22×C4—81no—
800C22×C4—81no—
801C22×C4—81no—
802C22×C4—81no—
803C22×C4—81no—
804C22×C4—81no—
805C22×C4—81no—
806C22×C4—81no—
807C22×C4—81no—
808C22×C4—81no—
809C22×C4—81no—
810C22×C4—81no—
811C22×C4—81no—
812C22×C4—81no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C22×D411yescharacteristic
824C22×C4C22×D411yescharacteristic
825C22×C4C22×D411yescharacteristic
826C22×C4C22×D411yescharacteristic
827C22×C4C22×D411yescharacteristic
828C22×C4C22×D411yescharacteristic
829C22×C4C22×D411yescharacteristic
830C22×C4C22×D411yescharacteristic
831C22×C4C22×Q812yes—
832C22×C42−1+412yes—
833C22×C4C2511yescharacteristic
834D8—44no—
835M16—44no—
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—21no—
846C2×C8—21no—
847C2×C8—21no—
848C2×C8—21no—
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—44no—
859C2×C8C22×Q812yes—
860C2×C8C22×Q812yes—
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—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
886C4⋊C4—41no—
887C4⋊C4—41no—
888C4⋊C4—41no—
889C4⋊C4—41no—
890C4⋊C4—41no—
891C4⋊C4—41no—
892C4⋊C4—41no—
893C4⋊C4—41no—
894C4⋊C4—41no—
895C4⋊C4—41no—
896C4⋊C4—41no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
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⋊C4C22×Q812yes—
934C4⋊C4C22×Q812yes—
935C4⋊C4H(5,𝔽2)12yes—
936C22⋊C4—24no—
937C22⋊C4—24no—
938C22⋊C4—41no—
939C22⋊C4—41no—
940C22⋊C4—41no—
941C22⋊C4—41no—
942C22⋊C4—41no—
943C22⋊C4—41no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C42—21no—
967C42—21no—
968C42—21no—
969C42—21no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—42no—
979C42—81no—
980C42—81no—
981C42—81no—
982C42—81no—
983C42—81no—
984C42—81no—
985C42—81no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—22no—
993C23—22no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23D4×Q812yes—
1007C23C23×D411yescharacteristic
1008Q8—82no—
1009D4—22no—
1010D4—22no—
1011D4—22no—
1012D4—22no—
1013D4—41no—
1014D4—41no—
1015D4—41no—
1016D4—41no—
1017D4—84no—
1018D4—84no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
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—22no—
1050C2×C4—22no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—21no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—22no—
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—84no—
1104C2×C4—162no—
1105C2×C4—162no—
1106C2×C4—162no—
1107C2×C4—162no—
1108C2×C4—162no—
1109C2×C4—162no—
1110C2×C4—162no—
1111C2×C4D4×Q812yes—
1112C2×C4C23×Q811yescharacteristic
1113C2×C4C2×H(5,𝔽2)11yescharacteristic
1114C2×C4C2×2−1+411yescharacteristic
1115C2×C4#58511yescharacteristic
1116C2×C4#58511yescharacteristic
1117C2×C4#58511yescharacteristic
1118C8—22no—
1119C8—22no—
1120C8—41no—
1121C8—41no—
1122C8—41no—
1123C8—41no—
1124C8—41no—
1125C8—41no—
1126C22—22no—
1127C22—22no—
1128C22—22no—
1129C22—41no—
1130C22—41no—
1131C22—41no—
1132C22—41no—
1133C22—42no—
1134C22—42no—
1135C22—42no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22C2×D4×Q811yescharacteristic
1148C22#348511yescharacteristic
1149C22#348811yescharacteristic
1150C22#358411yescharacteristic
1151C22#358411yescharacteristic
1152C22#358511yescharacteristic
1153C22#358511yescharacteristic
1154C4—22no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—42no—
1168C4—42no—
1169C4—42no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4#350111yescharacteristic
1182C4#350411yescharacteristic
1183C4#354111yescharacteristic
1184C4#355311yescharacteristic
1185C2—42no—
1186C2—82no—
1187C2—82no—
1188C2#4352911yescharacteristic
1189C2#6138511yescharacteristic
1190C2#6138511yescharacteristic
1191C2#6176111yescharacteristic
1192C2#6181311yescharacteristic
1193C2#6206111yescharacteristic
1194C2#6208311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#469C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45358C2semidirect
2. #44942C2semidirect
3. #32655C2semidirect
4. #32581C2semidirect
5. #32521C2semidirect
6. #32361C2semidirect
7. #32155C2semidirect
8. #31867C2semidirect
9. #31530C2semidirect
10. #30951C2semidirect
11. #29248C2semidirect
12. #28788C2semidirect
13. #27688C2semidirect
14. #27315C2semidirect
15. #27307C2semidirect
16. #26868C2semidirect
17. #26423C2semidirect
18. #26421C2semidirect
19. #26394C2semidirect
20. #26350C2semidirect
21. #26350C2semidirect
22. #26286C2semidirect
23. #26075C2semidirect
24. #25458C2semidirect
25. #25069C2semidirect
26. #24823C2semidirect
27. #23660C2semidirect
30. #22294C2semidirect
233. #469Q8semidirect

Maximal subgroups

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

subgroupindex
#453582
#449422
#326552
#325812
#325212
#323612
#321552
#318672
#315302
#309512
#292482
#287882
#276882
#273152
#273072
#268682
#264232
#264212
#263942
#263502
#262862
#260752
#254582
#250692
#248232
#236602
#231402
#230392
#222942
#221992