Finite Group Databasebeta

← #6554041

Subgroups — #6554041

Order 512.

1420 conjugacy classes of subgroups.

The subgroup lattice has 1224 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#38067C211yesmaximal, characteristic, complemented
2#38060C211yesmaximal, characteristic, complemented
3#30391C211yesmaximal, characteristic, complemented
4#30355C211yesmaximal, characteristic, complemented
5#29784C211yesmaximal, characteristic, complemented
6#29456C211yesmaximal, characteristic, complemented
7#29436C211yesmaximal, characteristic, complemented
8#29203C211yesmaximal, characteristic, complemented
9#29020C211yesmaximal, characteristic, complemented
10#29009C211yesmaximal, characteristic, complemented
11#28957C211yesmaximal, characteristic, complemented
12#28878C211yesmaximal, characteristic, complemented
13#28664C211yesmaximal, characteristic, complemented
14#28358C211yesmaximal, characteristic
15#28036C211yesmaximal, characteristic, complemented
16#28027C211yesmaximal, characteristic, complemented
17#27709C211yesmaximal, characteristic, complemented
18#27284C211yesmaximal, characteristic, complemented
19#26845C211yesmaximal, characteristic, complemented
20#26482C211yesmaximal, characteristic, complemented
21#26073C211yesmaximal, characteristic, complemented
22#24602C211yesmaximal, characteristic, complemented
23#24504C211yesmaximal, characteristic
24#23791C211yesmaximal, characteristic, complemented
25#23692C211yesmaximal, characteristic, complemented
26#23617C211yesmaximal, characteristic, complemented
27#23040C211yesmaximal, characteristic, complemented
28#22925C211yesmaximal, characteristic, complemented
29#22878C211yesmaximal, characteristic
30#22582C211yesmaximal, characteristic, complemented
31#20548C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic
33C2×#491C2211yescharacteristic
34C2×#484C2211yescharacteristic
35C2×#468C2211yescharacteristic
36C2×#449C2211yescharacteristic
37C2×#440C2211yescharacteristic
38C2×C4×D8C2211yescharacteristic
39C2×#431C2211yescharacteristic
40C2×#428C2211yescharacteristic
41C2×#423C2211yescharacteristic
42C2×#417C2211yescharacteristic
43C2×#417C2211yescharacteristic
44#2855C2211yescharacteristic
45#2854C2211yescharacteristic
46#2777—21no—
47#2773—21no—
48#2768—21no—
49#2750—21no—
50#2746—21no—
51#2743—21no—
52#2743—21no—
53#2738—21no—
54#2647C2211yescharacteristic
55#2645C2211yescharacteristic
56#2644C2211yescharacteristic
57#2642C2211yescharacteristic
58#2575—21no—
59#2573—21no—
60#2513C2211yescharacteristic
61#2511C2211yescharacteristic
62#2507C2211yescharacteristic
63#2507C2211yescharacteristic
64#2505—21no—
65#2501C2211yescharacteristic
66#2498—21no—
67#2493—21no—
68#2486—21no—
69#2454C2211yescharacteristic
70#2454C2211yescharacteristic
71#2447C2211yescharacteristic
72#2446C2211yescharacteristic
73#2442C2211yescharacteristic
74#2441C2211yescharacteristic
75#2432C2211yescharacteristic
76#2419—21no—
77#2413—21no—
78#2362C2211yescharacteristic
79#2361C2211yescharacteristic
80#2344C2211yescharacteristic
81#2339C2211yescharacteristic
82#2330C2211yescharacteristic
83#2326C2211yescharacteristic
84#2319C2211yescharacteristic
85#2319C2211yescharacteristic
86#2297C2211yescharacteristic
87C2×#389C2211yescharacteristic
88#2283C2211yescharacteristic
89#2100C2211yescharacteristic
90#2099C2211yescharacteristic
91#2095C2211yescharacteristic
92#2093C2211yescharacteristic
93#2087C2211yescharacteristic
94#2087C2211yescharacteristic
95#2087C2211yescharacteristic
96#2086C2211yescharacteristic
97#2085C2211yescharacteristic
98#2083C2211yescharacteristic
99#2074C2211yescharacteristic
100#2071C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2068C2211yescharacteristic
106#2068C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2066C2211yescharacteristic
111#2066C2211yescharacteristic
112#2066C2211yescharacteristic
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#2065C2211yescharacteristic
116#2065C2211yescharacteristic
117#2059C2211yescharacteristic
118#2059C2211yescharacteristic
119#2055C2211yescharacteristic
120#2055C2211yescharacteristic
121#2055C2211yescharacteristic
122#2054C2211yescharacteristic
123#2043C2211yescharacteristic
124#2042C2211yescharacteristic
125#2025C2211yescharacteristic
126#2025C2211yescharacteristic
127#2013C2211yescharacteristic
128#2012C2211yescharacteristic
129#1992C2211yescharacteristic
130#1973C2211yescharacteristic
131#1973C2211yescharacteristic
132#1970C2211yescharacteristic
133#1970C2211yescharacteristic
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic
136#1959C2211yescharacteristic
137#1958C2211yescharacteristic
138#1956C2211yescharacteristic
139#1944C2211yescharacteristic
140#1943C2211yescharacteristic
141#1942C2211yescharacteristic
142#1942C2211yescharacteristic
143#1942C2211yescharacteristic
144#1942C2211yescharacteristic
145#1936C2211yescharacteristic
146#1936C2211yescharacteristic
147#1935C2211yescharacteristic
148#1935C2211yescharacteristic
149#1934C2211yescharacteristic
150#1934C2211yescharacteristic
151#1933C2211yescharacteristic
152#1933C2211yescharacteristic
153#1933C2211yescharacteristic
154#1933C2211yescharacteristic
155#1933C2211yescharacteristic
156#1933C2211yescharacteristic
157#1928C2211yescharacteristic
158#1928C2211yescharacteristic
159#1928C2211yescharacteristic
160#1927C2211yescharacteristic
161#1927C2211yescharacteristic
162#1925C2211yescharacteristic
163#1921C2211yescharacteristic
164#1918C2211yescharacteristic
165#1895C2211yescharacteristic
166#1894C2211yescharacteristic
167#1879C2211yescharacteristic
168#1877C2211yescharacteristic
169#1875C2211yescharacteristic
170#1872C2211yescharacteristic
171#1865C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1863C2211yescharacteristic
175#1862C2211yescharacteristic
176#1862C2211yescharacteristic
177#1854C2211yescharacteristic
178#1852C2211yescharacteristic
179#1847C2211yescharacteristic
180#1834C2211yescharacteristic
181#1824C2211yescharacteristic
182#1809C2211yescharacteristic
183#1788C2211yescharacteristic
184#1776C2211yescharacteristic
185C4×#107C2211yescharacteristic
186#1770C2211yescharacteristic
187#1770C2211yescharacteristic
188C8×C4⋊C4C2211yescharacteristic
189C8×C4⋊C4C2211yescharacteristic
190#1768C2211yescharacteristic
191#1768C2211yescharacteristic
192#1768C2211yescharacteristic
193#1768C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1753C2211yescharacteristic
202#1736C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×#123—21no—
214C2×#123—21no—
215C2×#123—21no—
216C2×C22⋊Q8C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×D4—21no—
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×#117—21no—
224C2×#117C2311yescharacteristic
225C22×C4⋊C4—21no—
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C42C2311yescharacteristic
229#499—42no—
230#491—42no—
231#484—24no—
232#468—24no—
233#449—24no—
234#440—42no—
235C4×D8—42no—
236#431—24no—
237#428—42no—
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251#423—24no—
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258#417—24no—
259#417—42no—
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296C2×C4×C8C2311yescharacteristic
297C2×C4×C8C2311yescharacteristic
298#401—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400—21no—
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400—21no—
309#400—21no—
310#400—21no—
311#400—21no—
312#399—21no—
313#399—21no—
314#399—21no—
315#399—21no—
316#399—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#398—21no—
321#398—21no—
322#398—21no—
323#398—21no—
324#398—21no—
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#396—21no—
333#396—21no—
334#396—21no—
335#396—21no—
336#394—21no—
337#394—21no—
338#391C2311yescharacteristic
339#391C2311yescharacteristic
340#391C2311yescharacteristic
341#391C2311yescharacteristic
342#391C2311yescharacteristic
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#389C2311yescharacteristic
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#386—21no—
405#386—21no—
406#386—21no—
407#386—21no—
408#386—21no—
409#386—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#385—21no—
417#385—21no—
418#385—21no—
419#385—21no—
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#383D411yescharacteristic
424#383D411yescharacteristic
425#382D411yescharacteristic
426#382D411yescharacteristic
427#382C2311yescharacteristic
428#381—21no—
429#381—21no—
430#381—21no—
431#381—21no—
432#381—21no—
433#381—21no—
434#381D411yescharacteristic
435#381D411yescharacteristic
436#380—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380D411yescharacteristic
442#380D411yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445C4×C4⋊C4—21no—
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456#376C2311yescharacteristic
457#376C2311yescharacteristic
458C2×#95—21no—
459C2×#95—21no—
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#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C2×#41—22no—
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—41no—
494C2×#41—41no—
495C2×#41—41no—
496C22×Q8C2411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×D4—21no—
499C22×D4—21no—
500C22×D4C2411yescharacteristic
501C22×D4C2411yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C2×D411yescharacteristic
509C23×C4C2×D411yescharacteristic
510C23×C4C2411yescharacteristic
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—41no—
520C2×M16—22no—
521C2×M16—41no—
522C2×M16—41no—
523C2×M16—41no—
524C2×M16—41no—
525C2×M16#4114yes—
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C4⋊Q8—41no—
535C4⋊Q8—41no—
536#125—22no—
537#125—41no—
538#125—41no—
539#125—41no—
540#124—22no—
541#124—41no—
542#123—82no—
543#123—82no—
544#123—82no—
545C22⋊Q8—22no—
546C22⋊Q8—22no—
547#121—22no—
548#121—22no—
549C4×Q8—41no—
550C4×Q8—41no—
551C4×D4—22no—
552C4×D4—22no—
553C4×D4—41no—
554C4×D4—41no—
555C4×D4—41no—
556C4×D4—41no—
557C4×D4—82no—
558#117—41no—
559#117—41no—
560#117—82no—
561C2×C4⋊C4—22no—
562C2×C4⋊C4—22no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—41no—
597C2×C4⋊C4—82no—
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2×D411yescharacteristic
601C2×C4⋊C4C2×D411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×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×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C22⋊C4C2×D411yescharacteristic
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C42—22no—
645C2×C42—22no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42C2×D411yescharacteristic
653C2×C42C2×D411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660#107—22no—
661#107—22no—
662#107—22no—
663#107—22no—
664#107—22no—
665#107—41no—
666#107—41no—
667#107—41no—
668#107—41no—
669#106—22no—
670#106—41no—
671#106—41no—
672#106—41no—
673C4⋊C8—22no—
674C4⋊C8—22no—
675C4⋊C8—22no—
676C4⋊C8—22no—
677C4⋊C8—22no—
678C4⋊C8—22no—
679#103—22no—
680#103—22no—
681#103—22no—
682#103—22no—
683#103—22no—
684#103—22no—
685#103—22no—
686#103—22no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#102—22no—
694#102—22no—
695#102—22no—
696#102—22no—
697#102—22no—
698#102—22no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705C22⋊C8—22no—
706C22⋊C8#4114yes—
707#97—41no—
708#97—41no—
709#97—41no—
710#97—41no—
711C4×C8—22no—
712C4×C8—22no—
713C4×C8—41no—
714C4×C8—41no—
715C4×C8—41no—
716C4×C8—41no—
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#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773C24—21no—
774C24—21no—
775C24C22×D411yescharacteristic
776#41—44no—
777#41—44no—
778#41—82no—
779#41—82no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—42no—
808C2×D4—81no—
809C2×D42−1+412yes—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—22no—
817C22×C4—22no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—41no—
832C22×C4—41no—
833C22×C4—41no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—42no—
840C22×C4—42no—
841C22×C4—42no—
842C22×C4—42no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C2×#4112yes—
866C22×C4C2×#4112yes—
867C22×C4C2511yescharacteristic
868SD16—44no—
869SD16—82no—
870D8—44no—
871M16—44no—
872M16—82no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8C2×#4112yes—
894C2×C8C2×#4112yes—
895C2×C8C2×#4112yes—
896C2×C8C2×#4112yes—
897C4⋊C4—22no—
898C4⋊C4—22no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—41no—
923C4⋊C4—41no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4H(5,𝔽2)12yes—
957C22⋊C4—41no—
958C22⋊C4—41no—
959C22⋊C4—41no—
960C22⋊C4—41no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
966C22⋊C4—42no—
967C22⋊C4—42no—
968C22⋊C4—42no—
969C22⋊C4—42no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C42—22no—
988C42—22no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—81no—
1002C42—81no—
1003C42—81no—
1004C42—81no—
1005C42—81no—
1006C42—81no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—22no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23#53212yes—
1028C23C23×D411yescharacteristic
1029Q8—41no—
1030Q8—41no—
1031Q8—41no—
1032Q8—41no—
1033Q8—41no—
1034Q8—41no—
1035Q8—41no—
1036Q8—41no—
1037D4—22no—
1038D4—22no—
1039D4—41no—
1040D4—41no—
1041D4—41no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—84no—
1046D4—84no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—22no—
1052C2×C4—22no—
1053C2×C4—22no—
1054C2×C4—22no—
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—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—22no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—44no—
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—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—41no—
1121C2×C4—41no—
1122C2×C4—41no—
1123C2×C4—41no—
1124C2×C4—41no—
1125C2×C4—41no—
1126C2×C4—41no—
1127C2×C4—41no—
1128C2×C4—41no—
1129C2×C4—41no—
1130C2×C4—41no—
1131C2×C4—84no—
1132C2×C4—82no—
1133C2×C4—84no—
1134C2×C4—84no—
1135C2×C4—162no—
1136C2×C4—162no—
1137C2×C4—162no—
1138C2×C4#53212yes—
1139C2×C4#57812yes—
1140C2×C4C22×#4111yescharacteristic
1141C2×C4C22×#4111yescharacteristic
1142C2×C4C2×H(5,𝔽2)11yescharacteristic
1143C2×C4C2×2−1+411yescharacteristic
1144C2×C4#58511yescharacteristic
1145C2×C4#58511yescharacteristic
1146C8—22no—
1147C8—22no—
1148C8—22no—
1149C8—22no—
1150C8—41no—
1151C8—41no—
1152C8—41no—
1153C8—41no—
1154C22—22no—
1155C22—22no—
1156C22—22no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22—41no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22—81no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22C2×#53211yescharacteristic
1176C22#348811yescharacteristic
1177C22#348911yescharacteristic
1178C22C2×#57811yescharacteristic
1179C22#358411yescharacteristic
1180C22#358511yescharacteristic
1181C22#358511yescharacteristic
1182C4—22no—
1183C4—22no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—42no—
1190C4—41no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4#349511yescharacteristic
1210C4#350511yescharacteristic
1211C4#352011yescharacteristic
1212C4#352111yescharacteristic
1213C2—42no—
1214C2—82no—
1215C2—161no—
1216C2#3582511yescharacteristic
1217C2#6070411yescharacteristic
1218C2#6070811yescharacteristic
1219C2#6202811yescharacteristic
1220C2#6204611yescharacteristic
1221C2#6218111yescharacteristic
1222C2#6219511yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#449C22
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. #38067C2semidirect
2. #38060C2semidirect
3. #30391C2semidirect
4. #30355C2semidirect
5. #29784C2semidirect
6. #29456C2semidirect
7. #29436C2semidirect
8. #29203C2semidirect
9. #29020C2semidirect
10. #29009C2semidirect
11. #28957C2semidirect
12. #28878C2semidirect
13. #28664C2semidirect
15. #28036C2semidirect
16. #28027C2semidirect
17. #27709C2semidirect
18. #27284C2semidirect
19. #26845C2semidirect
20. #26482C2semidirect
21. #26073C2semidirect
22. #24602C2semidirect
24. #23791C2semidirect
25. #23692C2semidirect
26. #23617C2semidirect
27. #23040C2semidirect
28. #22925C2semidirect
30. #22582C2semidirect
31. #20548C2semidirect

Maximal subgroups

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

subgroupindex
#380672
#380602
#303912
#303552
#297842
#294562
#294362
#292032
#290202
#290092
#289572
#288782
#286642
#283582
#280362
#280272
#277092
#272842
#268452
#264822
#260732
#246022
#245042
#237912
#236922
#236172
#230402
#229252
#228782
#225822
#205482