Finite Group Databasebeta

← #6800486

Subgroups — #6800486

Order 512.

1254 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39692C211yesmaximal, characteristic
2#35543C211yesmaximal, characteristic, complemented
3#33157C211yesmaximal, characteristic, complemented
4#32339C211yesmaximal, characteristic, complemented
5#32332C211yesmaximal, characteristic, complemented
6#32331C211yesmaximal, characteristic, complemented
7#32317C211yesmaximal, characteristic, complemented
8#31471C211yesmaximal, characteristic, complemented
9#31471C211yesmaximal, characteristic, complemented
10#31470C211yesmaximal, characteristic, complemented
11#31463C211yesmaximal, characteristic, complemented
12#29979C211yesmaximal, characteristic, complemented
13#29973C211yesmaximal, characteristic, complemented
14#28805C211yesmaximal, characteristic, complemented
15#28798C211yesmaximal, characteristic, complemented
16#27970C211yesmaximal, characteristic, complemented
17#27970C211yesmaximal, characteristic, complemented
18#27967C211yesmaximal, characteristic, complemented
19#27739C211yesmaximal, characteristic, complemented
20#27733C211yesmaximal, characteristic, complemented
21#27655C211yesmaximal, characteristic
22#27655C211yesmaximal, characteristic
23#27650C211yesmaximal, characteristic
24#26523C211yesmaximal, characteristic, complemented
25#26516C211yesmaximal, characteristic, complemented
26#26118C211yesmaximal, characteristic, complemented
27#26107C211yesmaximal, characteristic, complemented
28#22631C211yesmaximal, characteristic, complemented
29#22090C211yesmaximal, characteristic
30#22081C211yesmaximal, characteristic
31#21590C211yesmaximal, characteristic
32C2×#482C2211yescharacteristic
33C2×#482C2211yescharacteristic
34C2×#480C2211yescharacteristic
35#2851C2211yescharacteristic
36#2790—21no—
37#2780—21no—
38#2780—21no—
39#2768—21no—
40#2629C2211yescharacteristic
41#2629C2211yescharacteristic
42#2579—21no—
43#2571C2211yescharacteristic
44#2571C2211yescharacteristic
45#2570C2211yescharacteristic
46#2570C2211yescharacteristic
47#2570C2211yescharacteristic
48#2570C2211yescharacteristic
49#2566—21no—
50#2566C2211yescharacteristic
51#2552C2211yescharacteristic
52#2552C2211yescharacteristic
53#2552C2211yescharacteristic
54#2522—21no—
55#2509—21no—
56#2508—21no—
57#2508C2211yescharacteristic
58#2507—21no—
59#2506—21no—
60#2506C2211yescharacteristic
61#2505—21no—
62#2505—21no—
63#2473—21no—
64#2473—21no—
65#2473—21no—
66#2454C2211yescharacteristic
67#2454C2211yescharacteristic
68#2370C2211yescharacteristic
69D4×C4⋊C4C2211yescharacteristic
70#2324C2211yescharacteristic
71#2324C2211yescharacteristic
72#2317C2211yescharacteristic
73#2317C2211yescharacteristic
74#2317C2211yescharacteristic
75C4×#121C2211yescharacteristic
76#2296C2211yescharacteristic
77C2×#389C2211yescharacteristic
78#2285C2211yescharacteristic
79#2274C2211yescharacteristic
80#2101C2211yescharacteristic
81#2101C2211yescharacteristic
82#2101C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2101C2211yescharacteristic
86#2101C2211yescharacteristic
87#2101C2211yescharacteristic
88#2101C2211yescharacteristic
89#2101C2211yescharacteristic
90#2100C2211yescharacteristic
91#2100C2211yescharacteristic
92#2100C2211yescharacteristic
93#2099C2211yescharacteristic
94#2099C2211yescharacteristic
95#2099C2211yescharacteristic
96#2088C2211yescharacteristic
97#2088C2211yescharacteristic
98#2088C2211yescharacteristic
99#2088C2211yescharacteristic
100#2087C2211yescharacteristic
101#2086C2211yescharacteristic
102#2086C2211yescharacteristic
103#2086C2211yescharacteristic
104#2085C2211yescharacteristic
105#2085C2211yescharacteristic
106#2084C2211yescharacteristic
107#2083C2211yescharacteristic
108#2083C2211yescharacteristic
109#2083C2211yescharacteristic
110#2073C2211yescharacteristic
111#2073C2211yescharacteristic
112#2071C2211yescharacteristic
113#2071C2211yescharacteristic
114#2071C2211yescharacteristic
115#2071C2211yescharacteristic
116#2059C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2059C2211yescharacteristic
120#1992C2211yescharacteristic
121#1992C2211yescharacteristic
122#1992C2211yescharacteristic
123#1992C2211yescharacteristic
124#1991C2211yescharacteristic
125#1991C2211yescharacteristic
126#1989C2211yescharacteristic
127#1989C2211yescharacteristic
128#1949C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1948C2211yescharacteristic
133#1948C2211yescharacteristic
134#1947C2211yescharacteristic
135#1947C2211yescharacteristic
136#1943C2211yescharacteristic
137#1943C2211yescharacteristic
138#1943C2211yescharacteristic
139#1941C2211yescharacteristic
140#1940C2211yescharacteristic
141#1939C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1936C2211yescharacteristic
145#1934C2211yescharacteristic
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic
148#1921C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1920C2211yescharacteristic
152#1920C2211yescharacteristic
153#1919C2211yescharacteristic
154#1919C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1918C2211yescharacteristic
158#1917C2211yescharacteristic
159#1917C2211yescharacteristic
160#1917C2211yescharacteristic
161#1916C2211yescharacteristic
162#1874C2211yescharacteristic
163#1864C2211yescharacteristic
164#1864C2211yescharacteristic
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1853C2211yescharacteristic
168#1853C2211yescharacteristic
169#1852C2211yescharacteristic
170#1836C2211yescharacteristic
171#1836C2211yescharacteristic
172#1836C2211yescharacteristic
173#1836C2211yescharacteristic
174#1834C2211yescharacteristic
175#1834C2211yescharacteristic
176#1825C2211yescharacteristic
177#1825C2211yescharacteristic
178#1825C2211yescharacteristic
179#1825C2211yescharacteristic
180#1825C2211yescharacteristic
181#1825C2211yescharacteristic
182#1824C2211yescharacteristic
183#1824C2211yescharacteristic
184#1823C2211yescharacteristic
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1804C2211yescharacteristic
189#1802C2211yescharacteristic
190#1802C2211yescharacteristic
191#1798C2211yescharacteristic
192#1798C2211yescharacteristic
193#1797C2211yescharacteristic
194#1776C2211yescharacteristic
195C4×#107C2211yescharacteristic
196#1771C2211yescharacteristic
197#1770C2211yescharacteristic
198#1762C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic
202#1749C2211yescharacteristic
203C2×#125—21no—
204C2×#125—21no—
205C2×#125—21no—
206C2×#125C2311yescharacteristic
207C2×#125C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#121C2311yescharacteristic
210C2×C4×D4—21no—
211C2×C4×D4C2311yescharacteristic
212C2×C4×D4C2311yescharacteristic
213C2×C4×D4C2311yescharacteristic
214C2×#117C2311yescharacteristic
215C2×#117C2311yescharacteristic
216C2×#117C2311yescharacteristic
217C2×#117C2311yescharacteristic
218C22×C4⋊C4—21no—
219C22×C4⋊C4—21no—
220C22×C4⋊C4C2311yescharacteristic
221C22×C4⋊C4C2311yescharacteristic
222C22×C42C2311yescharacteristic
223#482—24no—
224#482—24no—
225#480—24no—
226C2×#107C2311yescharacteristic
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×C4⋊C8C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244C2×#102C2311yescharacteristic
245C2×#102C2311yescharacteristic
246C2×#102C2311yescharacteristic
247C2×#102C2311yescharacteristic
248C2×#102C2311yescharacteristic
249C2×#102C2311yescharacteristic
250C2×#102C2311yescharacteristic
251C2×#102C2311yescharacteristic
252C2×C22⋊C8C2311yescharacteristic
253C2×C22⋊C8C2311yescharacteristic
254C2×C22⋊C8C2311yescharacteristic
255C2×C22⋊C8C2311yescharacteristic
256C2×#97C2311yescharacteristic
257C2×#97C2311yescharacteristic
258C2×#97C2311yescharacteristic
259C2×#97C2311yescharacteristic
260C2×C4×C8C2311yescharacteristic
261C2×C4×C8C2311yescharacteristic
262#400—21no—
263#400—21no—
264#400—21no—
265#400—21no—
266#400—21no—
267#400—21no—
268#400—21no—
269#400—21no—
270#400—21no—
271#400—21no—
272#399—21no—
273#399—21no—
274#398—21no—
275#398—21no—
276#398—21no—
277#398—21no—
278#398—21no—
279#398—21no—
280#398—21no—
281#398—21no—
282#398—21no—
283#398—21no—
284#398—21no—
285#398—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#396—21no—
291#396—21no—
292#396—21no—
293#396—21no—
294#396—21no—
295#396—21no—
296#396—21no—
297#396—21no—
298#390—21no—
299#390—21no—
300#390C2311yescharacteristic
301#390C2311yescharacteristic
302#390C2311yescharacteristic
303#389—21no—
304#389—21no—
305#389—21no—
306#389—21no—
307#389—21no—
308#389—21no—
309#389—21no—
310#389—21no—
311#389—21no—
312#389—21no—
313#389—21no—
314#389—21no—
315#389D411yescharacteristic
316#389D411yescharacteristic
317#389D411yescharacteristic
318#389D411yescharacteristic
319#389C2311yescharacteristic
320#389C2311yescharacteristic
321#389C2311yescharacteristic
322#389C2311yescharacteristic
323#389C2311yescharacteristic
324#389C2311yescharacteristic
325#389C2311yescharacteristic
326#389C2311yescharacteristic
327#389C2311yescharacteristic
328#389C2311yescharacteristic
329#389C2311yescharacteristic
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#388—21no—
337#388—21no—
338#388—21no—
339#387—21no—
340#387—21no—
341#387—21no—
342#387—21no—
343#387—21no—
344#387—21no—
345#387—21no—
346#387—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#387—21no—
351#387—21no—
352#387—21no—
353#386—21no—
354#386—21no—
355#386—21no—
356#385—21no—
357#385—21no—
358#385—21no—
359#385—21no—
360#385—21no—
361#385—21no—
362#385—21no—
363#385—21no—
364#385—21no—
365#385—21no—
366#385—21no—
367#385—21no—
368#385—21no—
369#385—21no—
370#385—21no—
371#385—21no—
372#385D411yescharacteristic
373#385D411yescharacteristic
374#385D411yescharacteristic
375#385D411yescharacteristic
376#384—21no—
377#384—21no—
378#384C2311yescharacteristic
379#384C2311yescharacteristic
380#384C2311yescharacteristic
381#384C2311yescharacteristic
382#384C2311yescharacteristic
383#384C2311yescharacteristic
384#384C2311yescharacteristic
385#384C2311yescharacteristic
386#382—21no—
387#382—21no—
388#382—21no—
389#382—21no—
390#382C2311yescharacteristic
391#382C2311yescharacteristic
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#382C2311yescharacteristic
395#382C2311yescharacteristic
396#382C2311yescharacteristic
397#380—21no—
398#380—21no—
399#380—21no—
400#380—21no—
401#380—21no—
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405C4×C4⋊C4—21no—
406C4×C4⋊C4—21no—
407C4×C4⋊C4—21no—
408C4×C4⋊C4—21no—
409C4×C4⋊C4—21no—
410C4×C4⋊C4C2311yescharacteristic
411C4×C4⋊C4C2311yescharacteristic
412C4×C4⋊C4C2311yescharacteristic
413C4×C4⋊C4C2311yescharacteristic
414C4×C4⋊C4C2311yescharacteristic
415C4×C4⋊C4C2311yescharacteristic
416C4×C4⋊C4C2311yescharacteristic
417C4×C4⋊C4C2311yescharacteristic
418C4×C4⋊C4C2311yescharacteristic
419C4×C4⋊C4C2311yescharacteristic
420C4×C4⋊C4C2311yescharacteristic
421C4×C22⋊C4—21no—
422C4×C22⋊C4—21no—
423C4×C22⋊C4—21no—
424C2×#95—21no—
425#340C2311yescharacteristic
426#340C2311yescharacteristic
427#340C2311yescharacteristic
428#340C2311yescharacteristic
429#340C2311yescharacteristic
430#340C2311yescharacteristic
431#340C2311yescharacteristic
432#340C2311yescharacteristic
433#340C2311yescharacteristic
434#340C2311yescharacteristic
435#340C2311yescharacteristic
436#340C2311yescharacteristic
437#340C2311yescharacteristic
438#340C2311yescharacteristic
439#340C2311yescharacteristic
440#340C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#336C2311yescharacteristic
470#336C2311yescharacteristic
471#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C22×D4—21no—
482C22×D4C2411yescharacteristic
483C23×C4—21no—
484C23×C4—21no—
485C23×C4—21no—
486C23×C4—21no—
487C23×C4—21no—
488C23×C4C2×D411yescharacteristic
489C23×C4C2×D411yescharacteristic
490C23×C4C2411yescharacteristic
491C22×C8C2411yescharacteristic
492C22×C8C2411yescharacteristic
493C22×C8C2411yescharacteristic
494C22×C8C2411yescharacteristic
495C22×C8C2411yescharacteristic
496C22×C8C2411yescharacteristic
497C22×C8C2411yescharacteristic
498C22×C8C2411yescharacteristic
499#125—22no—
500#125—22no—
501#125—41no—
502#125—41no—
503#125—41no—
504#125—41no—
505#125—82no—
506#125—82no—
507#125—82no—
508#121—22no—
509#121#4114yes—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—41no—
513C4×D4—41no—
514C4×D4—41no—
515C4×D4—41no—
516C4×D4—82no—
517#117—22no—
518#117—22no—
519#117—22no—
520#117—22no—
521#117—22no—
522#117—22no—
523#117—41no—
524#117—41no—
525C2×C4⋊C4—22no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—21no—
543C2×C4⋊C4—21no—
544C2×C4⋊C4—21no—
545C2×C4⋊C4—21no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—41no—
569C2×C4⋊C4—41no—
570C2×C4⋊C4—82no—
571C2×C4⋊C4—82no—
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
583C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
615C2×C22⋊C4C2×D411yescharacteristic
616C2×C22⋊C4C2×D411yescharacteristic
617C2×C22⋊C4C2×D411yescharacteristic
618C2×C42—21no—
619C2×C42—21no—
620C2×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
625C2×C42—21no—
626C2×C42—21no—
627C2×C42—41no—
628C2×C42—41no—
629C2×C42C2×D411yescharacteristic
630C2×C42C2×D411yescharacteristic
631C2×C42C2411yescharacteristic
632C2×C42C2411yescharacteristic
633C2×C42C2411yescharacteristic
634C2×C42C2411yescharacteristic
635C2×C42C2411yescharacteristic
636C2×C42C2411yescharacteristic
637#107—22no—
638#107—22no—
639#107—22no—
640#107—22no—
641#107—41no—
642#107—41no—
643#106—22no—
644#106—22no—
645#106—41no—
646#106—41no—
647#106—41no—
648#106—41no—
649C4⋊C8—22no—
650C4⋊C8—22no—
651C4⋊C8—41no—
652C4⋊C8—41no—
653C4⋊C8—41no—
654C4⋊C8—41no—
655#102—22no—
656#102—22no—
657#102—22no—
658#102—22no—
659#102—22no—
660#102—22no—
661#102—41no—
662#102—41no—
663C22⋊C8—22no—
664C22⋊C8—22no—
665C22⋊C8—22no—
666C22⋊C8—22no—
667#97—22no—
668#97—41no—
669#97—41no—
670#97—41no—
671C4×C8—22no—
672C4×C8—41no—
673#95—21no—
674#95—21no—
675#95—21no—
676#95—21no—
677#95—21no—
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#95C2×D411yescharacteristic
715#95C2×D411yescharacteristic
716#95C2×D411yescharacteristic
717#95C2×D411yescharacteristic
718#95C2×D411yescharacteristic
719#95C2×D411yescharacteristic
720#95C2×D411yescharacteristic
721#95C2×D411yescharacteristic
722C24—21no—
723C24C22×D411yescharacteristic
724C2×D4—24no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—81no—
731C2×D4—81no—
732C2×D4C2×#4112yes—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—41no—
753C22×C4—41no—
754C22×C4—41no—
755C22×C4—41no—
756C22×C4—41no—
757C22×C4—41no—
758C22×C4—42no—
759C22×C4—42no—
760C22×C4—42no—
761C22×C4—42no—
762C22×C4—81no—
763C22×C4—81no—
764C22×C4—81no—
765C22×C4—81no—
766C22×C4—81no—
767C22×C4—81no—
768C22×C4—81no—
769C22×C4—81no—
770C22×C4—81no—
771C22×C4—81no—
772C22×C4—81no—
773C22×C4C22×D411yescharacteristic
774C22×C4C22×D411yescharacteristic
775C22×C4C22×D411yescharacteristic
776C22×C4C22×D411yescharacteristic
777C22×C4C22×D411yescharacteristic
778C22×C4C22×D411yescharacteristic
779C22×C4C22×D411yescharacteristic
780C22×C4C22×D411yescharacteristic
781C22×C4C22×D411yescharacteristic
782C22×C4C22×D411yescharacteristic
783C22×C4C22×D411yescharacteristic
784C22×C4C22×D411yescharacteristic
785C22×C4C22×D411yescharacteristic
786C22×C4C2×#4112yes—
787C22×C42−1+412yes—
788C22×C4C2511yescharacteristic
789C2×C8—21no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—21no—
809C2×C8—21no—
810C2×C8—21no—
811C2×C8—21no—
812C2×C8—21no—
813C4⋊C4—22no—
814C4⋊C4—22no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—21no—
818C4⋊C4—21no—
819C4⋊C4—21no—
820C4⋊C4—21no—
821C4⋊C4—21no—
822C4⋊C4—21no—
823C4⋊C4—21no—
824C4⋊C4—21no—
825C4⋊C4—21no—
826C4⋊C4—21no—
827C4⋊C4—21no—
828C4⋊C4—21no—
829C4⋊C4—21no—
830C4⋊C4—21no—
831C4⋊C4—21no—
832C4⋊C4—21no—
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—41no—
845C4⋊C4—41no—
846C4⋊C4—41no—
847C4⋊C4—41no—
848C4⋊C4—41no—
849C4⋊C4—41no—
850C4⋊C4—41no—
851C4⋊C4—41no—
852C4⋊C4—41no—
853C4⋊C4—41no—
854C4⋊C4—42no—
855C4⋊C4—42no—
856C4⋊C4—42no—
857C4⋊C4—42no—
858C4⋊C4—42no—
859C4⋊C4—42no—
860C4⋊C4—42no—
861C4⋊C4—42no—
862C4⋊C4—42no—
863C4⋊C4—81no—
864C4⋊C4—81no—
865C4⋊C4—81no—
866C4⋊C4—81no—
867C4⋊C4—81no—
868C4⋊C4—81no—
869C4⋊C4—81no—
870C4⋊C4—81no—
871C4⋊C4—81no—
872C4⋊C4—81no—
873C4⋊C4—81no—
874C4⋊C4—81no—
875C4⋊C4—81no—
876C4⋊C4—81no—
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⋊C4C2×#4112yes—
896C22⋊C4—22no—
897C22⋊C4—22no—
898C22⋊C4—24no—
899C22⋊C4—41no—
900C22⋊C4—41no—
901C22⋊C4—42no—
902C22⋊C4—42no—
903C22⋊C4—42no—
904C22⋊C4—81no—
905C22⋊C4—81no—
906C22⋊C4—81no—
907C22⋊C4—81no—
908C22⋊C4—81no—
909C22⋊C4—81no—
910C22⋊C4—81no—
911C22⋊C4—81no—
912C22⋊C4—81no—
913C22⋊C4—81no—
914C22⋊C4—81no—
915C42—21no—
916C42—21no—
917C42—21no—
918C42—21no—
919C42—21no—
920C42—21no—
921C42—21no—
922C42—21no—
923C42—21no—
924C42—21no—
925C42—41no—
926C42—41no—
927C42—42no—
928C42—42no—
929C42—42no—
930C42—81no—
931C42—81no—
932C42—81no—
933C42—81no—
934C42—81no—
935C42—81no—
936C422−1+412yes—
937C422−1+412yes—
938C23—21no—
939C23—21no—
940C23—21no—
941C23—21no—
942C23—21no—
943C23—21no—
944C23—22no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23#54812yes—
952C23C23×D411yescharacteristic
953D4—22no—
954D4—22no—
955D4—41no—
956D4—41no—
957D4—84no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—22no—
965C2×C4—22no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—21no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—21no—
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—22no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—21no—
998C2×C4—21no—
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×C4—84no—
1044C2×C4—82no—
1045C2×C4—82no—
1046C2×C4—84no—
1047C2×C4—162no—
1048C2×C4—162no—
1049C2×C4—162no—
1050C2×C4#53612yes—
1051C2×C4#53612yes—
1052C2×C4#54812yes—
1053C2×C4C22×#4111yescharacteristic
1054C2×C4C2×2−1+411yescharacteristic
1055C2×C4C2×2−1+411yescharacteristic
1056C2×C4C2×2−1+411yescharacteristic
1057C2×C4#58511yescharacteristic
1058C2×C4#58511yescharacteristic
1059C8—41no—
1060C8—41no—
1061C8—41no—
1062C8—41no—
1063C8—41no—
1064C8—41no—
1065C8—41no—
1066C8—41no—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—41no—
1071C22—41no—
1072C22—41no—
1073C22—41no—
1074C22—42no—
1075C22—42no—
1076C22—42no—
1077C22—81no—
1078C22—81no—
1079C22—81no—
1080C22—81no—
1081C22C2×#53611yescharacteristic
1082C22C2×#54811yescharacteristic
1083C22#348511yescharacteristic
1084C22#358411yescharacteristic
1085C22#358511yescharacteristic
1086C22#358511yescharacteristic
1087C22#358611yescharacteristic
1088C4—22no—
1089C4—22no—
1090C4—22no—
1091C4—41no—
1092C4—41no—
1093C4—41no—
1094C4—41no—
1095C4—41no—
1096C4—41no—
1097C4—41no—
1098C4—41no—
1099C4—42no—
1100C4—41no—
1101C4—41no—
1102C4—81no—
1103C4—81no—
1104C4—81no—
1105C4—81no—
1106C4—81no—
1107C4—81no—
1108C4—81no—
1109C4—81no—
1110C4—81no—
1111C4—81no—
1112C4—81no—
1113C4—81no—
1114C4—81no—
1115C4—81no—
1116C4#351511yescharacteristic
1117C4#351511yescharacteristic
1118C4#356311yescharacteristic
1119C4#356311yescharacteristic
1120C2—42no—
1121C2—82no—
1122C2#3912211yescharacteristic
1123C2#6088711yescharacteristic
1124C2#6089011yescharacteristic
1125C2#6133211yescharacteristic
1126C2#6135011yescharacteristic
1127C2#6176111yescharacteristic
1128C2#6178011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2296 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #35543C2semidirect
3. #33157C2semidirect
4. #32339C2semidirect
5. #32332C2semidirect
6. #32331C2semidirect
7. #32317C2semidirect
8. #31471C2semidirect
9. #31471C2semidirect
10. #31470C2semidirect
11. #31463C2semidirect
12. #29979C2semidirect
13. #29973C2semidirect
14. #28805C2semidirect
15. #28798C2semidirect
16. #27970C2semidirect
17. #27970C2semidirect
18. #27967C2semidirect
19. #27739C2semidirect
20. #27733C2semidirect
24. #26523C2semidirect
25. #26516C2semidirect
26. #26118C2semidirect
27. #26107C2semidirect
28. #22631C2semidirect

Maximal subgroups

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

subgroupindex
#396922
#355432
#331572
#323392
#323322
#323312
#323172
#314712
#314702
#314632
#299792
#299732
#288052
#287982
#279702
#279672
#277392
#277332
#276552
#276502
#265232
#265162
#261182
#261072
#226312
#220902
#220812
#215902