Finite Group Databasebeta

← #6880083

Subgroups — #6880083

Order 512.

1297 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#39299C211yesmaximal, characteristic, complemented
2#39070C211yesmaximal, characteristic
3#33268C211yesmaximal, characteristic, complemented
4#32436C211yesmaximal, characteristic, complemented
5#32241C211yesmaximal, characteristic, complemented
6#31749C211yesmaximal, characteristic, complemented
7#31695C211yesmaximal, characteristic, complemented
8#31642C211yesmaximal, characteristic, complemented
9#31294C211yesmaximal, characteristic
10#30811C211yesmaximal, characteristic, complemented
11#30531C211yesmaximal, characteristic
12#30371C211yesmaximal, characteristic, complemented
13#30350C211yesmaximal, characteristic, complemented
14#29516C211yesmaximal, characteristic, complemented
15#29496C211yesmaximal, characteristic, complemented
16#29471C211yesmaximal, characteristic, complemented
17#29441C211yesmaximal, characteristic, complemented
18#29363C211yesmaximal, characteristic, complemented
19#29115C211yesmaximal, characteristic
20#27541C211yesmaximal, characteristic
21#27439C211yesmaximal, characteristic, complemented
22#27238C211yesmaximal, characteristic
23#27212C211yesmaximal, characteristic, complemented
24#27060C211yesmaximal, characteristic, complemented
25#27022C211yesmaximal, characteristic, complemented
26#26749C211yesmaximal, characteristic, complemented
27#26715C211yesmaximal, characteristic, complemented
28#22122C211yesmaximal, characteristic, complemented
29#22052C211yesmaximal, characteristic
30#21648C211yesmaximal, characteristic, complemented
31#21434C211yesmaximal, characteristic, complemented
32C2×#488C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#450C2211yescharacteristic
35#2863C2211yescharacteristic, complemented
36#2860C2211yescharacteristic
37#2793—21no—
38#2783—21no—
39#2776—21no—
40#2767—21no—
41#2751—21no—
42#2740—21no—
43#2736—21no—
44#2735—21no—
45#2645C2211yescharacteristic, complemented
46#2640C2211yescharacteristic
47#2629C2211yescharacteristic
48#2625C2211yescharacteristic
49#2595—21no—
50#2594—21no—
51#2570—21no—
52#2565C2211yescharacteristic, complemented
53#2561—21no—
54#2560—21no—
55#2552C2211yescharacteristic, complemented
56#2525—21no—
57#2524—21no—
58#2513C2211yescharacteristic
59#2497C2211yescharacteristic
60#2495C2211yescharacteristic
61#2489C2211yescharacteristic
62#2489C2211yescharacteristic
63#2480—21no—
64#2452C2211yescharacteristic
65#2448C2211yescharacteristic
66#2447C2211yescharacteristic
67#2439C2211yescharacteristic
68#2435C2211yescharacteristic
69#2370C2211yescharacteristic, complemented
70#2362C2211yescharacteristic
71#2355C2211yescharacteristic, complemented
72D4×C22⋊C4C2211yescharacteristic
73#2330C2211yescharacteristic, complemented
74#2323C2211yescharacteristic
75#2319C2211yescharacteristic
76#2309C2211yescharacteristic
77C4×#125C2211yescharacteristic, complemented
78C4×#124C2211yescharacteristic
79#2298C2211yescharacteristic
80#2101C2211yescharacteristic, complemented
81#2099C2211yescharacteristic, complemented
82#2095C2211yescharacteristic, complemented
83#2092C2211yescharacteristic
84#2088C2211yescharacteristic, complemented
85#2085C2211yescharacteristic, complemented
86#2076C2211yescharacteristic
87#2076C2211yescharacteristic
88#2075C2211yescharacteristic
89#2074C2211yescharacteristic, complemented
90#2072C2211yescharacteristic, complemented
91#2071C2211yescharacteristic
92#2071C2211yescharacteristic
93#2071C2211yescharacteristic
94#2068C2211yescharacteristic, complemented
95#2068C2211yescharacteristic, complemented
96#2067C2211yescharacteristic
97#2067C2211yescharacteristic
98#2059C2211yescharacteristic, complemented
99#2059C2211yescharacteristic, complemented
100#2057C2211yescharacteristic, complemented
101#2056C2211yescharacteristic, complemented
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic
104#2042C2211yescharacteristic
105#2042C2211yescharacteristic
106#2036C2211yescharacteristic
107#2035C2211yescharacteristic
108#2035C2211yescharacteristic
109#2035C2211yescharacteristic
110#2026C2211yescharacteristic, complemented
111#2026C2211yescharacteristic, complemented
112#2025C2211yescharacteristic
113#2025C2211yescharacteristic
114#2025C2211yescharacteristic
115#2025C2211yescharacteristic
116#2024C2211yescharacteristic, complemented
117#2015C2211yescharacteristic
118#2015C2211yescharacteristic
119#2001C2211yescharacteristic
120#1991C2211yescharacteristic, complemented
121#1989C2211yescharacteristic, complemented
122#1988C2211yescharacteristic, complemented
123#1987C2211yescharacteristic, complemented
124#1983C2211yescharacteristic
125#1983C2211yescharacteristic
126#1973C2211yescharacteristic
127#1973C2211yescharacteristic
128#1969C2211yescharacteristic, complemented
129#1968C2211yescharacteristic
130#1968C2211yescharacteristic
131#1958C2211yescharacteristic
132#1948C2211yescharacteristic, complemented
133#1944C2211yescharacteristic, complemented
134#1943C2211yescharacteristic, complemented
135#1942C2211yescharacteristic, complemented
136#1942C2211yescharacteristic, complemented
137#1941C2211yescharacteristic, complemented
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1935C2211yescharacteristic, complemented
143#1935C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1927C2211yescharacteristic, complemented
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1924C2211yescharacteristic
161#1924C2211yescharacteristic
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic
164#1921C2211yescharacteristic, complemented
165#1921C2211yescharacteristic, complemented
166#1920C2211yescharacteristic, complemented
167#1920C2211yescharacteristic, complemented
168#1920C2211yescharacteristic, complemented
169#1918C2211yescharacteristic, complemented
170#1917C2211yescharacteristic, complemented
171#1917C2211yescharacteristic, complemented
172#1916C2211yescharacteristic, complemented
173#1916C2211yescharacteristic, complemented
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1878C2211yescharacteristic, complemented
177#1878C2211yescharacteristic, complemented
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic
180#1873C2211yescharacteristic
181#1865C2211yescharacteristic, complemented
182#1865C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1854C2211yescharacteristic
186#1835C2211yescharacteristic, complemented
187#1825C2211yescharacteristic
188#1825C2211yescharacteristic
189#1802C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1768C2211yescharacteristic, complemented
194#1768C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1763C2211yescharacteristic, complemented
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199#1750C2211yescharacteristic
200#1750C2211yescharacteristic
201#1744C2211yescharacteristic, complemented
202C4×#97C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#126—21no—
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×#124C2311yescharacteristic
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C22×C22⋊C4—21no—
224#488—24no—
225#478—24no—
226#450—24no—
227C2×#107C2311yescharacteristic
228C2×#107C2311yescharacteristic
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#106C2311yescharacteristic
233C2×#106C2311yescharacteristic
234C2×#106C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×C4⋊C8C2311yescharacteristic
237C2×C4⋊C8C2311yescharacteristic
238C2×C4⋊C8C2311yescharacteristic
239C2×C4⋊C8C2311yescharacteristic
240C2×#103C2311yescharacteristic
241C2×#103C2311yescharacteristic
242C2×#103C2311yescharacteristic
243C2×#103C2311yescharacteristic
244C2×#103C2311yescharacteristic
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#102C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×C22⋊C8C2311yescharacteristic
267C2×C22⋊C8C2311yescharacteristic
268C2×C22⋊C8C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×#97C2311yescharacteristic
271C2×#97C2311yescharacteristic
272C2×#97C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×C4×C8C2311yescharacteristic
275C2×C4×C8C2311yescharacteristic
276C2×C4×C8C2311yescharacteristic
277C2×C4×C8C2311yescharacteristic
278#401—21no—
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#399—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#398—21no—
294#398—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#396—21no—
308#396—21no—
309#396—21no—
310#396—21no—
311#396—21no—
312#394—21no—
313#394—21no—
314#393—21no—
315#393—21no—
316#393—21no—
317#393—21no—
318#391—21no—
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#391C2311yescharacteristic
327#390—21no—
328#390—21no—
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#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#388D411yescharacteristic
374#388D411yescharacteristic
375#388D411yescharacteristic
376#388D411yescharacteristic
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387D411yescharacteristic
395#387D411yescharacteristic
396#387D411yescharacteristic
397#387D411yescharacteristic
398#386—21no—
399#386—21no—
400#385—21no—
401#385—21no—
402#384—21no—
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#383—21no—
406#383—21no—
407#382—21no—
408#382—21no—
409#382—21no—
410#382C2311yescharacteristic
411#382C2311yescharacteristic
412#381—21no—
413#381—21no—
414#380—21no—
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#379—21no—
420#379—21no—
421#379—21no—
422#379—21no—
423#379—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441#376C2311yescharacteristic
442C43C2311yescharacteristic
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
481C25—21no—
482C22×Q8—21no—
483C22×Q8C2411yescharacteristic
484C22×Q8C2411yescharacteristic
485C22×D4—22no—
486C22×D4—21no—
487C22×D4—41no—
488C22×D4—41no—
489C22×D4—41no—
490C22×D4—41no—
491C22×D4—41no—
492C22×D4C2411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4C2411yescharacteristic
497C2×Q16—41no—
498C2×Q16—41no—
499C2×Q16—41no—
500C2×SD16—22no—
501C2×SD16—22no—
502C2×SD16—41no—
503C2×SD16—41no—
504C2×SD16—41no—
505C2×SD16—41no—
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C4⋊Q8—41no—
515C4⋊Q8—41no—
516#126—82no—
517#125—22no—
518#125—22no—
519#125—41no—
520#125—41no—
521#125—41no—
522#125—41no—
523#124—22no—
524#124—41no—
525#124—41no—
526#124—41no—
527C22⋊Q8—22no—
528C22⋊Q8—41no—
529C22⋊Q8—41no—
530C22⋊Q8—41no—
531C22⋊Q8—82no—
532C4×Q8—41no—
533C4×Q8—41no—
534C4×Q8—41no—
535C4×Q8—41no—
536C4×D4—22no—
537C4×D4—41no—
538C4×D4—41no—
539C4×D4—41no—
540#117—41no—
541#117—41no—
542#117—41no—
543#117—41no—
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—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4C2×D411yescharacteristic
572C2×C4⋊C4C2×D411yescharacteristic
573C2×C4⋊C4C2×D411yescharacteristic
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2411yescharacteristic
578C2×C4⋊C4C2411yescharacteristic
579C2×C4⋊C4C2411yescharacteristic
580C2×C4⋊C4C2411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—82no—
619C2×C22⋊C4C2×D411yescharacteristic
620C2×C22⋊C4C2×D411yescharacteristic
621C2×C22⋊C4C2×D411yescharacteristic
622C2×C22⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C42—21no—
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×C42C2×D411yescharacteristic
635C2×C42C2×D411yescharacteristic
636C2×C42C2×D411yescharacteristic
637C2×C42C2×D411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644#107—22no—
645#107—41no—
646#107—41no—
647#107—41no—
648#107—41no—
649#106—22no—
650#106—41no—
651#106—41no—
652#106—41no—
653C4⋊C8—22no—
654C4⋊C8—41no—
655C4⋊C8—41no—
656C4⋊C8—41no—
657#103—22no—
658#103—22no—
659#103—41no—
660#103—41no—
661#103—41no—
662#103—41no—
663#103—41no—
664#103—41no—
665#103—41no—
666#103—41no—
667#103—41no—
668#103—41no—
669#102—22no—
670#102—22no—
671#102—22no—
672#102—41no—
673#102—41no—
674#102—41no—
675#102—41no—
676#102—41no—
677#102—41no—
678#102—41no—
679#102—41no—
680#102—41no—
681#102—41no—
682#102#4114yes—
683C22⋊C8—22no—
684C22⋊C8—41no—
685C22⋊C8—41no—
686C22⋊C8—41no—
687#97—41no—
688#97—41no—
689#97—41no—
690#97—41no—
691C4×C8—22no—
692C4×C8—41no—
693C4×C8—41no—
694C4×C8—41no—
695#95—21no—
696#95—21no—
697#95—21no—
698#95—21no—
699#95—21no—
700#95—21no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
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—42no—
752C24—42no—
753C24—81no—
754C24—81no—
755C24—81no—
756C24—81no—
757C24—81no—
758C24C22×D411yescharacteristic
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—21no—
762C2×Q8—21no—
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—81no—
772C2×Q8—81no—
773C2×Q8—81no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—81no—
788C2×D4—82no—
789C2×D4—82no—
790C2×D4—82no—
791C2×D4—82no—
792C2×D4C2×#4112yes—
793C22×C4—21no—
794C22×C4—21no—
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—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—42no—
814C22×C4—42no—
815C22×C4—81no—
816C22×C4—81no—
817C22×C4—81no—
818C22×C4—81no—
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×D411yescharacteristic
832C22×C4C2511yescharacteristic
833Q16—82no—
834SD16—82no—
835SD16—82no—
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—21no—
859C2×C8C2×#4112yes—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—41no—
884C4⋊C4—41no—
885C4⋊C4—41no—
886C4⋊C4—41no—
887C4⋊C4—41no—
888C4⋊C4—41no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
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⋊C4C2×#4112yes—
917C22⋊C4—41no—
918C22⋊C4—41no—
919C22⋊C4—41no—
920C22⋊C4—41no—
921C22⋊C4—41no—
922C22⋊C4—41no—
923C22⋊C4—42no—
924C22⋊C4—42no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—81no—
930C22⋊C4—81no—
931C22⋊C4—81no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
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—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—21no—
963C42—21no—
964C42—41no—
965C42—41no—
966C42—41no—
967C42—41no—
968C42—42no—
969C42—42no—
970C42—81no—
971C42—81no—
972C42—81no—
973C42—81no—
974C42—81no—
975C42—81no—
976C42—81no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—22no—
983C23—21no—
984C23—21no—
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—84no—
999C23—84no—
1000C23—162no—
1001C23—162no—
1002C23—162no—
1003C23—162no—
1004C23—162no—
1005C23C23×D411yescharacteristic
1006Q8—41no—
1007Q8—41no—
1008Q8—41no—
1009Q8—41no—
1010Q8—41no—
1011Q8—41no—
1012Q8—41no—
1013Q8—41no—
1014Q8—162no—
1015D4—22no—
1016D4—22no—
1017D4—41no—
1018D4—41no—
1019D4—41no—
1020D4—41no—
1021D4—41no—
1022D4—41no—
1023D4—84no—
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—21no—
1045C2×C4—21no—
1046C2×C4—21no—
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—22no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
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—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—162no—
1110C2×C4—162no—
1111C2×C4C22×#4111yescharacteristic
1112C2×C4#58511yescharacteristic
1113C2×C4#58511yescharacteristic
1114C2×C4#58511yescharacteristic
1115C2×C4#58511yescharacteristic
1116C2×C4#58511yescharacteristic
1117C8—22no—
1118C8—41no—
1119C8—41no—
1120C8—41no—
1121C8—41no—
1122C8—41no—
1123C8—41no—
1124C8—41no—
1125C22—41no—
1126C22—42no—
1127C22—41no—
1128C22—41no—
1129C22—42no—
1130C22—41no—
1131C22—41no—
1132C22—42no—
1133C22—41no—
1134C22—41no—
1135C22—81no—
1136C22—81no—
1137C22—81no—
1138C22—81no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—168no—
1147C22#344911yescharacteristic
1148C22D4×#4111yescharacteristic
1149C22#350011yescharacteristic
1150C22#358411yescharacteristic
1151C22#358411yescharacteristic
1152C22#358511yescharacteristic
1153C22#358611yescharacteristic
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—41no—
1161C4—41no—
1162C4—41no—
1163C4—42no—
1164C4—41no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4—81no—
1172C4—81no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4#351011yescharacteristic
1182C4#352111yescharacteristic
1183C4#356611yescharacteristic
1184C4#356811yescharacteristic
1185C2—81no—
1186C2—82no—
1187C2—161no—
1188C2#3994711yescharacteristic
1189C2#6097311yescharacteristic
1190C2#6101011yescharacteristic
1191C2#6152711yescharacteristic
1192C2#6153211yescharacteristic
1193C2#6261211yescharacteristic
1194C2#6261411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39299C2semidirect
3. #33268C2semidirect
4. #32436C2semidirect
5. #32241C2semidirect
6. #31749C2semidirect
7. #31695C2semidirect
8. #31642C2semidirect
10. #30811C2semidirect
12. #30371C2semidirect
13. #30350C2semidirect
14. #29516C2semidirect
15. #29496C2semidirect
16. #29471C2semidirect
17. #29441C2semidirect
18. #29363C2semidirect
21. #27439C2semidirect
23. #27212C2semidirect
24. #27060C2semidirect
25. #27022C2semidirect
26. #26749C2semidirect
27. #26715C2semidirect
28. #22122C2semidirect
30. #21648C2semidirect
31. #21434C2semidirect
35. #2863C22semidirect
45. #2645C22semidirect
52. #2565C22semidirect
55. #2552C22semidirect
69. #2370C22semidirect
71. #2355C22semidirect
73. #2330C22semidirect
77. C4×#125C22semidirect
80. #2101C22semidirect
81. #2099C22semidirect
82. #2095C22semidirect
84. #2088C22semidirect
85. #2085C22semidirect
89. #2074C22semidirect
90. #2072C22semidirect
94. #2068C22semidirect
95. #2068C22semidirect
98. #2059C22semidirect
99. #2059C22semidirect
100. #2057C22semidirect
101. #2056C22semidirect
110. #2026C22semidirect
111. #2026C22semidirect
116. #2024C22semidirect
120. #1991C22semidirect
121. #1989C22semidirect
122. #1988C22semidirect
123. #1987C22semidirect
128. #1969C22semidirect
132. #1948C22semidirect
133. #1944C22semidirect
134. #1943C22semidirect
135. #1942C22semidirect
136. #1942C22semidirect
137. #1941C22semidirect
142. #1935C22semidirect
143. #1935C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
150. #1933C22semidirect
151. #1933C22semidirect
152. #1928C22semidirect
153. #1927C22semidirect
164. #1921C22semidirect
165. #1921C22semidirect
166. #1920C22semidirect
167. #1920C22semidirect
168. #1920C22semidirect
169. #1918C22semidirect
170. #1917C22semidirect
171. #1917C22semidirect
172. #1916C22semidirect
173. #1916C22semidirect
176. #1878C22semidirect
177. #1878C22semidirect
181. #1865C22semidirect
182. #1865C22semidirect
186. #1835C22semidirect
193. #1768C22semidirect
194. #1768C22semidirect
195. #1763C22semidirect
196. #1763C22semidirect
201. #1744C22semidirect
202. C4×#97C22semidirect

Maximal subgroups

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

subgroupindex
#392992
#390702
#332682
#324362
#322412
#317492
#316952
#316422
#312942
#308112
#305312
#303712
#303502
#295162
#294962
#294712
#294412
#293632
#291152
#275412
#274392
#272382
#272122
#270602
#270222
#267492
#267152
#221222
#220522
#216482
#214342