Finite Group Databasebeta

← #6534795

Subgroups — #6534795

Order 512.

1393 conjugacy classes of subgroups.

The subgroup lattice has 1171 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38927C211yesmaximal, characteristic, complemented
2#34392C211yesmaximal, characteristic
3#30090C211yesmaximal, characteristic, complemented
4#30088C211yesmaximal, characteristic, complemented
5#29693C211yesmaximal, characteristic
6#29405C211yesmaximal, characteristic, complemented
7#29405C211yesmaximal, characteristic, complemented
8#29326C211yesmaximal, characteristic, complemented
9#29324C211yesmaximal, characteristic, complemented
10#27951C211yesmaximal, characteristic, complemented
11#27652C211yesmaximal, characteristic, complemented
12#27060C211yesmaximal, characteristic, complemented
13#27059C211yesmaximal, characteristic, complemented
14#27041C211yesmaximal, characteristic
15#27038C211yesmaximal, characteristic
16#26573C211yesmaximal, characteristic
17#26572C211yesmaximal, characteristic
18#26561C211yesmaximal, characteristic, complemented
19#26560C211yesmaximal, characteristic, complemented
20#26096C211yesmaximal, characteristic, complemented
21#26095C211yesmaximal, characteristic, complemented
22#24687C211yesmaximal, characteristic, complemented
23#24686C211yesmaximal, characteristic, complemented
24#23695C211yesmaximal, characteristic, complemented
25#23695C211yesmaximal, characteristic, complemented
26#23572C211yesmaximal, characteristic
27#22973C211yesmaximal, characteristic, complemented
28#22966C211yesmaximal, characteristic, complemented
29#22685C211yesmaximal, characteristic, complemented
30#22673C211yesmaximal, characteristic, complemented
31#22640C211yesmaximal, characteristic, complemented
32C2×#529C2211yescharacteristic
33C2×#485C2211yescharacteristic
34C2×#485C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#440C2211yescharacteristic
38C2×#440C2211yescharacteristic
39C2×C4×Q16C2211yescharacteristic
40C2×C4×Q16C2211yescharacteristic
41C2×C4×Q16C2211yescharacteristic
42C2×C4×SD16C2211yescharacteristic
43#2851C2211yescharacteristic
44#2770—21no—
45#2769—21no—
46#2768—21no—
47#2767—21no—
48#2647C2211yescharacteristic
49#2647C2211yescharacteristic
50#2575—21no—
51#2570C2211yescharacteristic
52#2565C2211yescharacteristic
53#2524—21no—
54#2524—21no—
55#2515—21no—
56#2497C2211yescharacteristic
57#2495C2211yescharacteristic
58#2423C2211yescharacteristic
59#2421C2211yescharacteristic
60#2376—21no—
61#2376—21no—
62#2370C2211yescharacteristic
63#2363C2211yescharacteristic
64#2363C2211yescharacteristic
65#2362C2211yescharacteristic
66#2362C2211yescharacteristic
67#2357C2211yescharacteristic
68#2356C2211yescharacteristic
69#2351C2211yescharacteristic
70#2351C2211yescharacteristic
71#2349C2211yescharacteristic
72#2347—21no—
73#2343—21no—
74#2334—21no—
75#2334—21no—
76#2330C2211yescharacteristic
77#2330C2211yescharacteristic
78#2326C2211yescharacteristic
79#2326C2211yescharacteristic
80#2320C2211yescharacteristic
81#2320C2211yescharacteristic
82#2319—21no—
83#2318—21no—
84C4×C22⋊Q8C2211yescharacteristic
85#2285C2211yescharacteristic
86#2283C2211yescharacteristic
87#2097C2211yescharacteristic
88#2096C2211yescharacteristic
89#2094C2211yescharacteristic
90#2092C2211yescharacteristic
91#2084C2211yescharacteristic
92#2084C2211yescharacteristic
93#2084C2211yescharacteristic
94#2083C2211yescharacteristic
95#2083C2211yescharacteristic
96#2083C2211yescharacteristic
97#2074C2211yescharacteristic
98#2073C2211yescharacteristic
99#2072C2211yescharacteristic
100#2072C2211yescharacteristic
101#2072C2211yescharacteristic
102#2071C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2056C2211yescharacteristic
111#2056C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2036C2211yescharacteristic
118#2035C2211yescharacteristic
119#2035C2211yescharacteristic
120#2034C2211yescharacteristic
121#2033C2211yescharacteristic
122#2033C2211yescharacteristic
123#2026C2211yescharacteristic
124#2015C2211yescharacteristic
125#2001C2211yescharacteristic
126#2000C2211yescharacteristic
127#1991C2211yescharacteristic
128#1991C2211yescharacteristic
129#1949C2211yescharacteristic
130#1949C2211yescharacteristic
131#1949C2211yescharacteristic
132#1949C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1948C2211yescharacteristic
136#1947C2211yescharacteristic
137#1947C2211yescharacteristic
138#1947C2211yescharacteristic
139#1944C2211yescharacteristic
140#1944C2211yescharacteristic
141#1944C2211yescharacteristic
142#1943C2211yescharacteristic
143#1942C2211yescharacteristic
144#1942C2211yescharacteristic
145#1942C2211yescharacteristic
146#1941C2211yescharacteristic
147#1939C2211yescharacteristic
148#1939C2211yescharacteristic
149#1928C2211yescharacteristic
150#1928C2211yescharacteristic
151#1927C2211yescharacteristic
152#1927C2211yescharacteristic
153#1924C2211yescharacteristic
154#1924C2211yescharacteristic
155#1923C2211yescharacteristic
156#1923C2211yescharacteristic
157#1921C2211yescharacteristic
158#1921C2211yescharacteristic
159#1920C2211yescharacteristic
160#1920C2211yescharacteristic
161#1920C2211yescharacteristic
162#1920C2211yescharacteristic
163#1919C2211yescharacteristic
164#1919C2211yescharacteristic
165#1865C2211yescharacteristic
166#1865C2211yescharacteristic
167#1865C2211yescharacteristic
168#1865C2211yescharacteristic
169#1865C2211yescharacteristic
170#1865C2211yescharacteristic
171#1865C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1863C2211yescharacteristic
176#1862C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic
181#1846C2211yescharacteristic
182#1846C2211yescharacteristic
183#1840C2211yescharacteristic
184#1840C2211yescharacteristic
185#1825C2211yescharacteristic
186#1825C2211yescharacteristic
187#1805C2211yescharacteristic
188#1805C2211yescharacteristic
189#1805C2211yescharacteristic
190#1804C2211yescharacteristic
191#1797C2211yescharacteristic
192#1770C2211yescharacteristic
193C8×C4⋊C4C2211yescharacteristic
194#1768C2211yescharacteristic
195#1768C2211yescharacteristic
196#1763C2211yescharacteristic
197#1763C2211yescharacteristic
198C4×#103C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×C22⋊C8C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205#529—24no—
206#529—24no—
207C2×#126—21no—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#124C2311yescharacteristic
211C2×#123—21no—
212C2×C22⋊Q8C2311yescharacteristic
213C2×C22⋊Q8C2311yescharacteristic
214C2×#121C2311yescharacteristic
215C2×C4×Q8C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×D4—21no—
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×#117—21no—
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C22×C42C2311yescharacteristic
229#485—42no—
230#485—42no—
231#479—24no—
232#478—24no—
233#440—42no—
234#440—42no—
235C4×Q16—24no—
236C4×Q16—42no—
237C4×Q16—42no—
238C4×SD16—24no—
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#399—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#397—21no—
311#397—21no—
312#396—21no—
313#391C2311yescharacteristic
314#391C2311yescharacteristic
315#391C2311yescharacteristic
316#391C2311yescharacteristic
317#391C2311yescharacteristic
318#390—21no—
319#390—21no—
320#390C2311yescharacteristic
321#390C2311yescharacteristic
322#389—21no—
323#389—21no—
324#389—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389—21no—
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
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#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#386—21no—
385#386—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#384C2311yescharacteristic
396#384C2311yescharacteristic
397#384C2311yescharacteristic
398#384C2311yescharacteristic
399#383—21no—
400#383—21no—
401#383—21no—
402#383—21no—
403#383D411yescharacteristic
404#383D411yescharacteristic
405#382—21no—
406#382—21no—
407#382—21no—
408#382—21no—
409#382D411yescharacteristic
410#382D411yescharacteristic
411#382C2311yescharacteristic
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#381—21no—
417#381D411yescharacteristic
418#381D411yescharacteristic
419#380—21no—
420#380—21no—
421#380—21no—
422#380D411yescharacteristic
423#380D411yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447C4×C22⋊C4—21no—
448C4×C22⋊C4C2311yescharacteristic
449C4×C22⋊C4C2311yescharacteristic
450#376—21no—
451#376C2311yescharacteristic
452#376C2311yescharacteristic
453C2×#95—21no—
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8C2411yescharacteristic
491C22×Q8C2411yescharacteristic
492C22×D4—21no—
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4C2×D411yescharacteristic
498C23×C4C2×D411yescharacteristic
499C23×C4C2411yescharacteristic
500C2×Q16—22no—
501C2×Q16—22no—
502C2×Q16—22no—
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—22no—
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514#126—28no—
515#125—22no—
516#125—22no—
517#125—22no—
518#125—22no—
519#124—22no—
520#124—22no—
521#123—28no—
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8—41no—
526#121—22no—
527#121—22no—
528C4×Q8—22no—
529C4×Q8—22no—
530C4×Q8—22no—
531C4×Q8—22no—
532C4×Q8—22no—
533C4×Q8—41no—
534C4×Q8—41no—
535C4×Q8—41no—
536C4×Q8—41no—
537C4×Q8—41no—
538C4×Q8—41no—
539C4×Q8#4114yes—
540C4×D4—28no—
541C4×D4—22no—
542C4×D4—41no—
543C4×D4—41no—
544C4×D4—41no—
545C4×D4—41no—
546C4×D4#4114yes—
547#117—28no—
548#117—41no—
549#117—41no—
550#117—41no—
551#117—41no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊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⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
620C2×C22⋊C4C2×D411yescharacteristic
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C42—21no—
624C2×C42—22no—
625C2×C42—22no—
626C2×C42—21no—
627C2×C42—21no—
628C2×C42—21no—
629C2×C42—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×C42C2×D411yescharacteristic
641C2×C42C2×D411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644C2×C42C2411yescharacteristic
645C2×C42C2411yescharacteristic
646C2×C42C2411yescharacteristic
647C2×C42C2411yescharacteristic
648#107—22no—
649#107—22no—
650#107—22no—
651#107—41no—
652#107—41no—
653#107—41no—
654#107—41no—
655#107—41no—
656#107—41no—
657#106—22no—
658#106—22no—
659#106—22no—
660#106—41no—
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—22no—
670C4⋊C8—22no—
671C4⋊C8—22no—
672#103—22no—
673#103—22no—
674#103—22no—
675#103—22no—
676#103—22no—
677#103—22no—
678#103—22no—
679#103—22no—
680#103—22no—
681#103—22no—
682#103—41no—
683#103—41no—
684#103—41no—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—22no—
689#102—41no—
690#102—41no—
691#102—41no—
692C22⋊C8—22no—
693C22⋊C8—22no—
694C22⋊C8—41no—
695C22⋊C8—41no—
696#97—41no—
697#97—41no—
698C4×C8—22no—
699C4×C8—22no—
700C4×C8—41no—
701C4×C8—41no—
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#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761C24—21no—
762C24C22×D411yescharacteristic
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8C2×#4112yes—
774C2×Q8H(5,𝔽2)12yes—
775C2×D4—24no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—81no—
782C2×D4—81no—
783C2×D4C2×#4112yes—
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—22no—
795C22×C4—22no—
796C22×C4—24no—
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—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—41no—
809C22×C4—41no—
810C22×C4—41no—
811C22×C4—41no—
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×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×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C2511yescharacteristic
834Q16—28no—
835SD16—28no—
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×C82−1+412yes—
859C2×C82−1+412yes—
860C4⋊C4—24no—
861C4⋊C4—24no—
862C4⋊C4—24no—
863C4⋊C4—24no—
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—21no—
887C4⋊C4—21no—
888C4⋊C4—41no—
889C4⋊C4—41no—
890C4⋊C4—41no—
891C4⋊C4—41no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
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⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4C2×#4112yes—
922C4⋊C4C2×#4112yes—
923C22⋊C4—24no—
924C22⋊C4—24no—
925C22⋊C4—24no—
926C22⋊C4—24no—
927C22⋊C4—24no—
928C22⋊C4—41no—
929C22⋊C4—41no—
930C22⋊C4—41no—
931C22⋊C4—41no—
932C22⋊C4—42no—
933C22⋊C4—42no—
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—
944C42—22no—
945C42—22no—
946C42—24no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—42no—
958C42—42no—
959C42—42no—
960C42—81no—
961C42—81no—
962C42—81no—
963C42—81no—
964C42—81no—
965C42—81no—
966C42—81no—
967C42—81no—
968C42—81no—
969C42—81no—
970C42—81no—
971C42C2×#4112yes—
972C42C2×#4112yes—
973C23—21no—
974C23—21no—
975C23—21no—
976C23—21no—
977C23—22no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—41no—
985C23—41no—
986C23—41no—
987C23C23×D411yescharacteristic
988Q8—22no—
989Q8—22no—
990Q8—22no—
991Q8—22no—
992Q8—41no—
993Q8—41no—
994Q8—41no—
995Q8—41no—
996D4—22no—
997D4—22no—
998D4—41no—
999D4—41no—
1000D4—84no—
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—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—22no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
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—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—82no—
1088C2×C4—82no—
1089C2×C4—84no—
1090C2×C4—162no—
1091C2×C4—162no—
1092C2×C4#52512yes—
1093C2×C4#52512yes—
1094C2×C4C22×#4111yescharacteristic
1095C2×C4C22×#4111yescharacteristic
1096C2×C4C2×H(5,𝔽2)11yescharacteristic
1097C2×C4C2×2−1+411yescharacteristic
1098C2×C4C2×2−1+411yescharacteristic
1099C2×C4#58511yescharacteristic
1100C8—22no—
1101C8—22no—
1102C8—41no—
1103C8—41no—
1104C8—41no—
1105C8—41no—
1106C8—41no—
1107C8—41no—
1108C22—41no—
1109C22—41no—
1110C22—41no—
1111C22—41no—
1112C22—42no—
1113C22—41no—
1114C22—41no—
1115C22—42no—
1116C22—41no—
1117C22—42no—
1118C22—81no—
1119C22—81no—
1120C22—81no—
1121C22—81no—
1122C22C2×#52511yescharacteristic
1123C22#348811yescharacteristic
1124C22#349911yescharacteristic
1125C22#358411yescharacteristic
1126C22#358411yescharacteristic
1127C22#358411yescharacteristic
1128C22#358611yescharacteristic
1129C4—22no—
1130C4—22no—
1131C4—41no—
1132C4—41no—
1133C4—41no—
1134C4—41no—
1135C4—41no—
1136C4—41no—
1137C4—41no—
1138C4—42no—
1139C4—42no—
1140C4—41no—
1141C4—41no—
1142C4—41no—
1143C4—42no—
1144C4—41no—
1145C4—42no—
1146C4—81no—
1147C4—81no—
1148C4—81no—
1149C4—81no—
1150C4—81no—
1151C4—81no—
1152C4—81no—
1153C4—81no—
1154C4—81no—
1155C4—81no—
1156C4—81no—
1157C4#349211yescharacteristic
1158C4#349211yescharacteristic
1159C4#350711yescharacteristic
1160C4#350711yescharacteristic
1161C2—81no—
1162C2—82no—
1163C2#3568611yescharacteristic
1164C2#6055711yescharacteristic
1165C2#6058111yescharacteristic
1166C2#6202911yescharacteristic
1167C2#6206111yescharacteristic
1168C2#6249011yescharacteristic
1169C2#6252311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#121C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #38927C2semidirect
3. #30090C2semidirect
4. #30088C2semidirect
6. #29405C2semidirect
7. #29405C2semidirect
8. #29326C2semidirect
9. #29324C2semidirect
10. #27951C2semidirect
11. #27652C2semidirect
12. #27060C2semidirect
13. #27059C2semidirect
18. #26561C2semidirect
19. #26560C2semidirect
20. #26096C2semidirect
21. #26095C2semidirect
22. #24687C2semidirect
23. #24686C2semidirect
24. #23695C2semidirect
25. #23695C2semidirect
27. #22973C2semidirect
28. #22966C2semidirect
29. #22685C2semidirect
30. #22673C2semidirect
31. #22640C2semidirect

Maximal subgroups

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

subgroupindex
#389272
#343922
#300902
#300882
#296932
#294052
#293262
#293242
#279512
#276522
#270602
#270592
#270412
#270382
#265732
#265722
#265612
#265602
#260962
#260952
#246872
#246862
#236952
#235722
#229732
#229662
#226852
#226732
#226402