Finite Group Databasebeta

← #6554911

Subgroups — #6554911

Order 512.

1470 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38226C211yesmaximal, characteristic, complemented
2#34487C211yesmaximal, characteristic, complemented
3#30157C211yesmaximal, characteristic, complemented
4#30149C211yesmaximal, characteristic, complemented
5#30003C211yesmaximal, characteristic, complemented
6#29542C211yesmaximal, characteristic, complemented
7#29536C211yesmaximal, characteristic, complemented
8#29437C211yesmaximal, characteristic, complemented
9#29429C211yesmaximal, characteristic, complemented
10#29187C211yesmaximal, characteristic, complemented
11#28290C211yesmaximal, characteristic, complemented
12#27374C211yesmaximal, characteristic, complemented
13#27372C211yesmaximal, characteristic, complemented
14#27199C211yesmaximal, characteristic
15#27190C211yesmaximal, characteristic
16#26863C211yesmaximal, characteristic, complemented
17#26857C211yesmaximal, characteristic, complemented
18#26705C211yesmaximal, characteristic, complemented
19#26692C211yesmaximal, characteristic, complemented
20#25064C211yesmaximal, characteristic, complemented
21#25006C211yesmaximal, characteristic, complemented
22#24338C211yesmaximal, characteristic, complemented
23#24326C211yesmaximal, characteristic, complemented
24#23787C211yesmaximal, characteristic, complemented
25#23774C211yesmaximal, characteristic, complemented
26#23688C211yesmaximal, characteristic
27#23079C211yesmaximal, characteristic, complemented
28#22963C211yesmaximal, characteristic, complemented
29#22826C211yesmaximal, characteristic, complemented
30#22810C211yesmaximal, characteristic, complemented
31#22774C211yesmaximal, characteristic, complemented
32C2×D4×Q8C2211yescharacteristic
33C2×#476C2211yescharacteristic
34C2×#474C2211yescharacteristic
35C2×#442C2211yescharacteristic
36C2×C4×D8C2211yescharacteristic
37#2860C2211yescharacteristic
38#2781—21no—
39#2779—21no—
40#2743—21no—
41#2687—21no—
42#2647C2211yescharacteristic
43#2644C2211yescharacteristic
44#2580C2211yescharacteristic
45#2553—21no—
46#2538C2211yescharacteristic
47#2509C2211yescharacteristic
48#2508C2211yescharacteristic
49#2481—21no—
50#2477—21no—
51#2445C2211yescharacteristic
52#2445C2211yescharacteristic
53#2413—21no—
54#2378—21no—
55#2378—21no—
56#2369C2211yescharacteristic
57#2369C2211yescharacteristic
58#2365C2211yescharacteristic
59#2362—21no—
60#2357C2211yescharacteristic
61#2357C2211yescharacteristic
62#2357C2211yescharacteristic
63#2355C2211yescharacteristic
64#2354C2211yescharacteristic
65D4×C4⋊C4C2211yescharacteristic
66Q8×C22⋊C4—21no—
67#2332—21no—
68#2332—21no—
69#2331C2211yescharacteristic
70#2331C2211yescharacteristic
71#2328C2211yescharacteristic
72#2323—21no—
73#2319C2211yescharacteristic
74#2319C2211yescharacteristic
75#2319C2211yescharacteristic
76#2310—21no—
77C4×C4⋊Q8C2211yescharacteristic
78#2295C2211yescharacteristic
79#2293C2211yescharacteristic
80#2293C2211yescharacteristic
81#2101C2211yescharacteristic
82#2099C2211yescharacteristic
83#2093C2211yescharacteristic
84#2092C2211yescharacteristic
85#2088C2211yescharacteristic
86#2088C2211yescharacteristic
87#2088C2211yescharacteristic
88#2088C2211yescharacteristic
89#2088C2211yescharacteristic
90#2087C2211yescharacteristic
91#2086C2211yescharacteristic
92#2086C2211yescharacteristic
93#2085C2211yescharacteristic
94#2085C2211yescharacteristic
95#2084C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2071C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2065C2211yescharacteristic
108#2065C2211yescharacteristic
109#2058C2211yescharacteristic
110#2058C2211yescharacteristic
111#2057C2211yescharacteristic
112#2057C2211yescharacteristic
113#2054C2211yescharacteristic
114#2054C2211yescharacteristic
115#2041C2211yescharacteristic
116#2023C2211yescharacteristic
117#2023C2211yescharacteristic
118#2023C2211yescharacteristic
119#2023C2211yescharacteristic
120#2011C2211yescharacteristic
121#1993C2211yescharacteristic
122#1990C2211yescharacteristic
123#1985C2211yescharacteristic
124#1984C2211yescharacteristic
125#1982C2211yescharacteristic
126#1982C2211yescharacteristic
127#1970C2211yescharacteristic
128#1970C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1948C2211yescharacteristic
133#1941C2211yescharacteristic
134#1941C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1926C2211yescharacteristic
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1921C2211yescharacteristic
150#1921C2211yescharacteristic
151#1921C2211yescharacteristic
152#1920C2211yescharacteristic
153#1920C2211yescharacteristic
154#1920C2211yescharacteristic
155#1919C2211yescharacteristic
156#1919C2211yescharacteristic
157#1919C2211yescharacteristic
158#1919C2211yescharacteristic
159#1919C2211yescharacteristic
160#1918C2211yescharacteristic
161#1918C2211yescharacteristic
162#1918C2211yescharacteristic
163#1917C2211yescharacteristic
164#1916C2211yescharacteristic
165#1916C2211yescharacteristic
166#1916C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1846C2211yescharacteristic
180#1843C2211yescharacteristic
181#1836C2211yescharacteristic
182#1832C2211yescharacteristic
183#1831C2211yescharacteristic
184#1804C2211yescharacteristic
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1802C2211yescharacteristic
188#1776C2211yescharacteristic
189C4×#107C2211yescharacteristic
190C4×#107C2211yescharacteristic
191C4×#107C2211yescharacteristic
192#1771C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194#1768C2211yescharacteristic
195#1768C2211yescharacteristic
196C4×C4⋊C8C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#102C2211yescharacteristic
203C23×Q8—21no—
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206D4×Q8—24no—
207D4×Q8—24no—
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#126—21no—
213C2×#123—21no—
214C2×#123—21no—
215C2×C22⋊Q8—21no—
216C2×C22⋊Q8—21no—
217C2×C22⋊Q8—21no—
218C2×C22⋊Q8—21no—
219C2×C4×Q8—21no—
220C2×C4×Q8—21no—
221C2×C4×Q8C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×#117—21no—
230C2×#117—21no—
231C2×#117—21no—
232C22×C4⋊C4—21no—
233#476—24no—
234#474—24no—
235#442—24no—
236C4×D8—24no—
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
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×#102C2311yescharacteristic
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×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#399—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#396—21no—
298#396—21no—
299#396—21no—
300#394—21no—
301#394—21no—
302#394—21no—
303#394—21no—
304#393—21no—
305#391—21no—
306#391—21no—
307#391—21no—
308#391—21no—
309#391—21no—
310#391—21no—
311#391—21no—
312#391—21no—
313#391—21no—
314#391—21no—
315#391—21no—
316#391D411yescharacteristic
317#391D411yescharacteristic
318#390C2311yescharacteristic
319#390C2311yescharacteristic
320#390C2311yescharacteristic
321#390C2311yescharacteristic
322#390C2311yescharacteristic
323#390C2311yescharacteristic
324#390C2311yescharacteristic
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#389—21no—
331#389—21no—
332#389—21no—
333#389—21no—
334#389D411yescharacteristic
335#389D411yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
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#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
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#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387D411yescharacteristic
384#387D411yescharacteristic
385#387D411yescharacteristic
386#387D411yescharacteristic
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#382—21no—
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#382C2311yescharacteristic
403#382C2311yescharacteristic
404#381—21no—
405#381—21no—
406#381—21no—
407#381—21no—
408#381—21no—
409#381—21no—
410#380—21no—
411#380—21no—
412#380—21no—
413#380—21no—
414#380—21no—
415#380—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4C2311yescharacteristic
421C4×C4⋊C4C2311yescharacteristic
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439#376C2311yescharacteristic
440#376C2311yescharacteristic
441C43C2311yescharacteristic
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#336C2311yescharacteristic
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
484C22×Q8—28no—
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8—21no—
488C22×Q8—82no—
489C22×Q8—82no—
490C22×Q8C2×D411yescharacteristic
491C22×D4—21no—
492C22×D4—21no—
493C22×D4C2411yescharacteristic
494C22×D4C2411yescharacteristic
495C22×D4C2411yescharacteristic
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C2×D8—22no—
504C2×D8—22no—
505C2×D8—22no—
506C2×D8—22no—
507C2×D8—41no—
508C2×D8—41no—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C4⋊Q8—22no—
518C4⋊Q8—22no—
519C4⋊Q8—22no—
520C4⋊Q8—22no—
521C4⋊Q8—22no—
522C4⋊Q8#4114yes—
523#127—22no—
524#127—41no—
525#126—82no—
526#123—82no—
527#123—82no—
528C22⋊Q8—28no—
529C22⋊Q8—28no—
530C22⋊Q8—28no—
531C22⋊Q8—82no—
532C4×Q8—22no—
533C4×Q8—22no—
534C4×Q8—82no—
535C4×Q8—82no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544C4×D4—22no—
545C4×D4—22no—
546C4×D4—22no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4#4114yes—
550#117—82no—
551#117—82no—
552#117—82no—
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⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—82no—
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⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
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⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
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×C42—21no—
631C2×C42—21no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42C2×D411yescharacteristic
642C2×C42C2×D411yescharacteristic
643C2×C42C2×D411yescharacteristic
644C2×C42C2×D411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652#107—22no—
653#107—22no—
654#107—22no—
655#107—22no—
656#107—22no—
657#107—41no—
658#106—22no—
659#106—22no—
660#106—22no—
661#106—41no—
662#106—41no—
663#106—41no—
664#106—41no—
665#106—41no—
666C4⋊C8—22no—
667C4⋊C8—22no—
668C4⋊C8—22no—
669C4⋊C8—41no—
670C4⋊C8—41no—
671C4⋊C8—41no—
672C4⋊C8—41no—
673C4⋊C8—41no—
674#102—22no—
675#102—22no—
676#102—22no—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—41no—
685#102—41no—
686#102—41no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#97—22no—
695#97—41no—
696C4×C8—22no—
697C4×C8—41no—
698C4×C8—41no—
699C4×C8—41no—
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#95—21no—
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
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749C24—21no—
750C24—21no—
751C24—21no—
752C2×Q8—24no—
753C2×Q8—24no—
754C2×Q8—22no—
755C2×Q8—24no—
756C2×Q8—22no—
757C2×Q8—41no—
758C2×Q8—42no—
759C2×Q8—42no—
760C2×Q8—81no—
761C2×Q8—81no—
762C2×Q8—81no—
763C2×Q8—81no—
764C2×Q8—816no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—81no—
784C2×D4—81no—
785C2×D4—81no—
786C2×D4—81no—
787C2×D4C2×#4112yes—
788C2×D42−1+412yes—
789C22×C4—24no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—24no—
794C22×C4—24no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—42no—
806C22×C4—42no—
807C22×C4—42no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—81no—
813C22×C4—81no—
814C22×C4—81no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4—81no—
819C22×C4—81no—
820C22×C4—81no—
821C22×C4—81no—
822C22×C4—81no—
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×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C2511yescharacteristic
838D8—44no—
839D8—44no—
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—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C82−1+412yes—
864C4⋊C4—24no—
865C4⋊C4—24no—
866C4⋊C4—24no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—22no—
871C4⋊C4—22no—
872C4⋊C4—22no—
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—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—41no—
897C4⋊C4—41no—
898C4⋊C4—41no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—81no—
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⋊C4C2×#4112yes—
920C4⋊C4C2×#4112yes—
921C4⋊C4C2×#4112yes—
922C22⋊C4—24no—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—42no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C42—22no—
954C42—22no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—21no—
965C42—21no—
966C42—21no—
967C42—41no—
968C42—41no—
969C42—42no—
970C42—81no—
971C42—81no—
972C42—81no—
973C42—81no—
974C42—81no—
975C42—81no—
976C42—81no—
977C42—81no—
978C42—81no—
979C42—81no—
980C42C2×#4112yes—
981C42C2×#4112yes—
982C23—22no—
983C23—22no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23—41no—
988C23—41no—
989C23—41no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23C23×D411yescharacteristic
1004Q8—44no—
1005Q8—48no—
1006Q8—84no—
1007Q8—84no—
1008D4—22no—
1009D4—22no—
1010D4—22no—
1011D4—22no—
1012D4—41no—
1013D4—41no—
1014D4—41no—
1015D4—41no—
1016D4—41no—
1017D4—41no—
1018D4—41no—
1019D4—41no—
1020D4—162no—
1021D4—162no—
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—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—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
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—48no—
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—84no—
1101C2×C4—84no—
1102C2×C4—84no—
1103C2×C4—84no—
1104C2×C4—162no—
1105C2×C4—162no—
1106C2×C4#52512yes—
1107C2×C4#52512yes—
1108C2×C4#57612yes—
1109C2×C4#57712yes—
1110C2×C4C22×#4111yescharacteristic
1111C2×C4C22×#4111yescharacteristic
1112C2×C4C2×2−1+411yescharacteristic
1113C2×C4C2×2−1+411yescharacteristic
1114C2×C4#58511yescharacteristic
1115C2×C4#58511yescharacteristic
1116C8—22no—
1117C8—41no—
1118C8—41no—
1119C8—41no—
1120C8—41no—
1121C8—41no—
1122C8—41no—
1123C8—41no—
1124C22—42no—
1125C22—42no—
1126C22—42no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22—81no—
1138C22—81no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22C2×#52511yescharacteristic
1146C22#348911yescharacteristic
1147C22#349711yescharacteristic
1148C22C2×#57611yescharacteristic
1149C22C2×#57711yescharacteristic
1150C22#358411yescharacteristic
1151C22#358511yescharacteristic
1152C4—22no—
1153C4—22no—
1154C4—22no—
1155C4—22no—
1156C4—41no—
1157C4—41no—
1158C4—41no—
1159C4—42no—
1160C4—42no—
1161C4—42no—
1162C4—41no—
1163C4—41no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4#349511yescharacteristic
1180C4#349511yescharacteristic
1181C4#352311yescharacteristic
1182C4#352411yescharacteristic
1183C2—82no—
1184C2—82no—
1185C2—161no—
1186C2#3583211yescharacteristic
1187C2#6057211yescharacteristic
1188C2#6057811yescharacteristic
1189C2#6217111yescharacteristic
1190C2#6219911yescharacteristic
1191C2#6237911yescharacteristic
1192C2#6240811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2011C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38226C2semidirect
2. #34487C2semidirect
3. #30157C2semidirect
4. #30149C2semidirect
5. #30003C2semidirect
6. #29542C2semidirect
7. #29536C2semidirect
8. #29437C2semidirect
9. #29429C2semidirect
10. #29187C2semidirect
11. #28290C2semidirect
12. #27374C2semidirect
13. #27372C2semidirect
16. #26863C2semidirect
17. #26857C2semidirect
18. #26705C2semidirect
19. #26692C2semidirect
20. #25064C2semidirect
21. #25006C2semidirect
22. #24338C2semidirect
23. #24326C2semidirect
24. #23787C2semidirect
25. #23774C2semidirect
27. #23079C2semidirect
28. #22963C2semidirect
29. #22826C2semidirect
30. #22810C2semidirect
31. #22774C2semidirect

Maximal subgroups

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

subgroupindex
#382262
#344872
#301572
#301492
#300032
#295422
#295362
#294372
#294292
#291872
#282902
#273742
#273722
#271992
#271902
#268632
#268572
#267052
#266922
#250642
#250062
#243382
#243262
#237872
#237742
#236882
#230792
#229632
#228262
#228102
#227742