Finite Group Databasebeta

← #6728165

Subgroups — #6728165

Order 512.

1341 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42459C211yesmaximal, characteristic, complemented
2#35710C211yesmaximal, characteristic, complemented
3#33121C211yesmaximal, characteristic, complemented
4#32525C211yesmaximal, characteristic, complemented
5#32525C211yesmaximal, characteristic, complemented
6#32431C211yesmaximal, characteristic, complemented
7#32429C211yesmaximal, characteristic, complemented
8#32059C211yesmaximal, characteristic, complemented
9#32057C211yesmaximal, characteristic, complemented
10#31935C211yesmaximal, characteristic, complemented
11#31933C211yesmaximal, characteristic
12#29932C211yesmaximal, characteristic, complemented
13#29813C211yesmaximal, characteristic
14#28790C211yesmaximal, characteristic, complemented
15#28740C211yesmaximal, characteristic, complemented
16#27501C211yesmaximal, characteristic, complemented
17#27495C211yesmaximal, characteristic, complemented
18#26789C211yesmaximal, characteristic, complemented
19#26787C211yesmaximal, characteristic
20#26554C211yesmaximal, characteristic, complemented
21#26551C211yesmaximal, characteristic, complemented
22#26543C211yesmaximal, characteristic, complemented
23#26479C211yesmaximal, characteristic, complemented
24#26328C211yesmaximal, characteristic, complemented
25#26328C211yesmaximal, characteristic, complemented
26#24686C211yesmaximal, characteristic, complemented
27#24685C211yesmaximal, characteristic, complemented
28#23183C211yesmaximal, characteristic, complemented
29#22738C211yesmaximal, characteristic, complemented
30#22099C211yesmaximal, characteristic, complemented
31#21367C211yesmaximal, characteristic, complemented
32C2×#495C2211yescharacteristic
33C2×#481C2211yescharacteristic
34C2×#483C2211yescharacteristic
35C2×#479C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×C8×Q8C2211yescharacteristic
38C2×C4×SD16C2211yescharacteristic
39C2×C4×SD16C2211yescharacteristic
40C2×#433C2211yescharacteristic
41#2837—21no—
42#2800—21no—
43#2790—21no—
44#2772—21no—
45#2718—21no—
46#2652—21no—
47#2649—21no—
48#2637—21no—
49#2620C2211yescharacteristic
50#2620C2211yescharacteristic
51#2592C2211yescharacteristic
52#2592C2211yescharacteristic
53#2587—21no—
54#2573—21no—
55#2571C2211yescharacteristic
56#2566C2211yescharacteristic
57#2565C2211yescharacteristic
58#2552C2211yescharacteristic
59#2529—21no—
60#2518—21no—
61#2512C2211yescharacteristic
62#2512C2211yescharacteristic
63#2511C2211yescharacteristic
64#2511C2211yescharacteristic
65#2500C2211yescharacteristic
66#2499C2211yescharacteristic
67#2490C2211yescharacteristic
68#2489C2211yescharacteristic
69#2469—21no—
70#2466—21no—
71#2458—21no—
72#2423C2211yescharacteristic
73#2422C2211yescharacteristic
74#2398—21no—
75#2396C2211yescharacteristic
76#2367C2211yescharacteristic
77#2367C2211yescharacteristic
78#2361C2211yescharacteristic
79#2360C2211yescharacteristic
80#2357C2211yescharacteristic
81#2356C2211yescharacteristic
82Q8×C4⋊C4C2211yescharacteristic
83Q8×C4⋊C4C2211yescharacteristic
84#2314C2211yescharacteristic
85#2274C2211yescharacteristic
86#2097C2211yescharacteristic
87#2096C2211yescharacteristic
88#2096C2211yescharacteristic
89#2096C2211yescharacteristic
90#2094C2211yescharacteristic
91#2094C2211yescharacteristic
92#2094C2211yescharacteristic
93#2092C2211yescharacteristic
94#2085C2211yescharacteristic
95#2085C2211yescharacteristic
96#2074C2211yescharacteristic
97#2073C2211yescharacteristic
98#2072C2211yescharacteristic
99#2072C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2066C2211yescharacteristic
103#2066C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2059C2211yescharacteristic
107#2059C2211yescharacteristic
108#2056C2211yescharacteristic
109#2055C2211yescharacteristic
110#2055C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2054C2211yescharacteristic
116#2035C2211yescharacteristic
117#2035C2211yescharacteristic
118#2034C2211yescharacteristic
119#2034C2211yescharacteristic
120#2026C2211yescharacteristic
121#2025C2211yescharacteristic
122#2001C2211yescharacteristic
123#2000C2211yescharacteristic
124#2000C2211yescharacteristic
125#1999C2211yescharacteristic
126#1991C2211yescharacteristic
127#1991C2211yescharacteristic
128#1985C2211yescharacteristic
129#1983C2211yescharacteristic
130#1983C2211yescharacteristic
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1970C2211yescharacteristic
134#1970C2211yescharacteristic
135#1969C2211yescharacteristic
136#1969C2211yescharacteristic
137#1968C2211yescharacteristic
138#1968C2211yescharacteristic
139#1959C2211yescharacteristic
140#1959C2211yescharacteristic
141#1949C2211yescharacteristic
142#1949C2211yescharacteristic
143#1948C2211yescharacteristic
144#1948C2211yescharacteristic
145#1948C2211yescharacteristic
146#1948C2211yescharacteristic
147#1948C2211yescharacteristic
148#1948C2211yescharacteristic
149#1948C2211yescharacteristic
150#1948C2211yescharacteristic
151#1948C2211yescharacteristic
152#1947C2211yescharacteristic
153#1941C2211yescharacteristic
154#1941C2211yescharacteristic
155#1940C2211yescharacteristic
156#1939C2211yescharacteristic
157#1939C2211yescharacteristic
158#1928C2211yescharacteristic
159#1928C2211yescharacteristic
160#1927C2211yescharacteristic
161#1927C2211yescharacteristic
162#1927C2211yescharacteristic
163#1927C2211yescharacteristic
164#1926C2211yescharacteristic
165#1926C2211yescharacteristic
166#1926C2211yescharacteristic
167#1926C2211yescharacteristic
168#1925C2211yescharacteristic
169#1925C2211yescharacteristic
170#1923C2211yescharacteristic
171#1923C2211yescharacteristic
172#1923C2211yescharacteristic
173#1923C2211yescharacteristic
174#1916C2211yescharacteristic
175#1916C2211yescharacteristic
176#1879C2211yescharacteristic
177#1879C2211yescharacteristic
178#1878C2211yescharacteristic
179#1878C2211yescharacteristic
180#1875C2211yescharacteristic
181#1873C2211yescharacteristic
182#1865C2211yescharacteristic
183#1865C2211yescharacteristic
184#1864C2211yescharacteristic
185#1864C2211yescharacteristic
186#1854C2211yescharacteristic
187#1854C2211yescharacteristic
188#1853C2211yescharacteristic
189#1852C2211yescharacteristic
190#1834C2211yescharacteristic
191#1834C2211yescharacteristic
192#1834C2211yescharacteristic
193#1805C2211yescharacteristic
194#1804C2211yescharacteristic
195#1798C2211yescharacteristic
196#1776C2211yescharacteristic
197#1776C2211yescharacteristic
198C4×#107C2211yescharacteristic
199C4×#106C2211yescharacteristic
200C4×#106C2211yescharacteristic
201C4×#106C2211yescharacteristic
202C8×C4⋊C4C2211yescharacteristic
203C22×Q16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C2×#126—21no—
208C2×#126—21no—
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#124C2311yescharacteristic
212C2×#124C2311yescharacteristic
213C2×#123—21no—
214C2×C22⋊Q8C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×C4×Q8—21no—
219C2×C4×Q8—21no—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4—21no—
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229#495—24no—
230#483—42no—
231#481—42no—
232#479—42no—
233#478—42no—
234C8×Q8—24no—
235C4×SD16—42no—
236C4×SD16—42no—
237#433—24no—
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
289C2×C22⋊C8C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#400—21no—
302#400—21no—
303#400D411yescharacteristic
304#399—21no—
305#399D411yescharacteristic
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398D411yescharacteristic
312#398D411yescharacteristic
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#396—21no—
326#396—21no—
327#396—21no—
328#396—21no—
329#396—21no—
330#396D411yescharacteristic
331#396D411yescharacteristic
332#395D411yescharacteristic
333#394—21no—
334#394—21no—
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#393—21no—
342#393—21no—
343#393D411yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#391C2311yescharacteristic
347#391C2311yescharacteristic
348#391C2311yescharacteristic
349#391C2311yescharacteristic
350#391C2311yescharacteristic
351#391C2311yescharacteristic
352#390—21no—
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#390C2311yescharacteristic
361#389—21no—
362#389—21no—
363#389—21no—
364#389—21no—
365#389—21no—
366#389—21no—
367#389—21no—
368#389—21no—
369#389—21no—
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#388—21no—
375#388—21no—
376#388—21no—
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#388—21no—
391#388—21no—
392#388—21no—
393#388—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#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#386—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#384—21no—
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#384C2311yescharacteristic
421#384C2311yescharacteristic
422#384C2311yescharacteristic
423#384C2311yescharacteristic
424#383—21no—
425#382—21no—
426#382—21no—
427#382C2311yescharacteristic
428#382C2311yescharacteristic
429#382C2311yescharacteristic
430#381—21no—
431#380C2311yescharacteristic
432#380C2311yescharacteristic
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×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C4⋊C4C2311yescharacteristic
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456#376—21no—
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#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C22×Q8C2×D411yescharacteristic
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C2411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4C2411yescharacteristic
498C2×Q16—22no—
499C2×Q16—41no—
500C2×Q16—41no—
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—41no—
504C2×SD16—41no—
505C2×SD16—41no—
506C2×SD16—41no—
507C2×D8—22no—
508C2×D8—41no—
509C2×D8—41no—
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518#126—82no—
519#126—82no—
520#125—41no—
521#125—41no—
522#125—41no—
523#125—41no—
524#124—22no—
525#124—22no—
526#124—22no—
527#124—22no—
528#123—82no—
529C22⋊Q8—41no—
530C22⋊Q8—41no—
531C22⋊Q8—41no—
532C22⋊Q8—41no—
533#121—41no—
534#121—41no—
535#121—41no—
536#121—41no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—82no—
544C4×Q8—82no—
545C4×D4—22no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—82no—
550#117—22no—
551#117—22no—
552#117—41no—
553#117—41no—
554C2×C4⋊C4—22no—
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—41no—
583C2×C4⋊C4C2×D411yescharacteristic
584C2×C4⋊C4C2×D411yescharacteristic
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4C2×D411yescharacteristic
636C2×C22⋊C4C2×D411yescharacteristic
637C2×C22⋊C4C2×D411yescharacteristic
638C2×C22⋊C4C2×D411yescharacteristic
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660#107—22no—
661#107—41no—
662#107—41no—
663#107—41no—
664#106—22no—
665#106—22no—
666#106—22no—
667#106—41no—
668#106—41no—
669#106—41no—
670#106—41no—
671#106—41no—
672#106—41no—
673#106—41no—
674#106—41no—
675#106—41no—
676C4⋊C8—22no—
677C4⋊C8—22no—
678C4⋊C8—22no—
679C4⋊C8—22no—
680C4⋊C8—22no—
681C4⋊C8—22no—
682C4⋊C8—41no—
683C4⋊C8—41no—
684#103—22no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103—41no—
691#103—41no—
692#103—41no—
693#103—41no—
694#103—41no—
695#103—41no—
696#102—22no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704#102—41no—
705#102—41no—
706#102—41no—
707#102—41no—
708C22⋊C8—22no—
709C22⋊C8—22no—
710C22⋊C8—41no—
711C22⋊C8—41no—
712#97—22no—
713C4×C8—22no—
714C4×C8—22no—
715C4×C8—41no—
716C4×C8—41no—
717C4×C8#4114yes—
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#95C2×D411yescharacteristic
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
766C24—21no—
767C24—21no—
768C24C22×D411yescharacteristic
769C2×Q8—22no—
770C2×Q8—22no—
771C2×Q8—22no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—21no—
777C2×Q8—21no—
778C2×Q8—21no—
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—42no—
797C2×D4—81no—
798C2×D4—81no—
799C2×D4—81no—
800C2×D4—81no—
801C2×D4—81no—
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—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—81no—
825C22×C4—81no—
826C22×C4—81no—
827C22×C4—81no—
828C22×C4—81no—
829C22×C4—81no—
830C22×C4—81no—
831C22×C4C22×D411yescharacteristic
832C22×C4C22×D411yescharacteristic
833C22×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C22×D411yescharacteristic
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C2511yescharacteristic
845Q16—82no—
846SD16—44no—
847SD16—44no—
848D8—82no—
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×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8C2×#4112yes—
872C2×C8C2×#4112yes—
873C4⋊C4—22no—
874C4⋊C4—22no—
875C4⋊C4—22no—
876C4⋊C4—22no—
877C4⋊C4—22no—
878C4⋊C4—22no—
879C4⋊C4—22no—
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—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—41no—
904C4⋊C4—41no—
905C4⋊C4—41no—
906C4⋊C4—41no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
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⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4H(5,𝔽2)12yes—
935C22⋊C4—22no—
936C22⋊C4—22no—
937C22⋊C4—22no—
938C22⋊C4—22no—
939C22⋊C4—41no—
940C22⋊C4—41no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—42no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—42no—
981C42—42no—
982C42—42no—
983C42—42no—
984C42—81no—
985C42—81no—
986C42—81no—
987C42—81no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C42C2×#4112yes—
994C422−1+412yes—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23C23×D411yescharacteristic
1017Q8—28no—
1018Q8—41no—
1019Q8—41no—
1020Q8—41no—
1021Q8—41no—
1022Q8—41no—
1023Q8—41no—
1024Q8—41no—
1025Q8—41no—
1026D4—41no—
1027D4—41no—
1028D4—41no—
1029D4—41no—
1030D4—41no—
1031D4—41no—
1032D4—41no—
1033D4—41no—
1034D4—84no—
1035D4—162no—
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—21no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
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—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—162no—
1118C2×C4—162no—
1119C2×C4—162no—
1120C2×C4#54712yes—
1121C2×C4#54712yes—
1122C2×C4#57712yes—
1123C2×C4#57712yes—
1124C2×C4C22×#4111yescharacteristic
1125C2×C4C2×H(5,𝔽2)11yescharacteristic
1126C2×C4C2×2−1+411yescharacteristic
1127C2×C4#58511yescharacteristic
1128C2×C4#58511yescharacteristic
1129C2×C4#58511yescharacteristic
1130C8—22no—
1131C8—22no—
1132C8—41no—
1133C8—41no—
1134C8—41no—
1135C8—41no—
1136C8—41no—
1137C8—41no—
1138C22—41no—
1139C22—41no—
1140C22—41no—
1141C22—41no—
1142C22—41no—
1143C22—41no—
1144C22—41no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22—81no—
1151C22—81no—
1152C22—81no—
1153C22—81no—
1154C22—81no—
1155C22—81no—
1156C22—81no—
1157C22—81no—
1158C22—81no—
1159C22C2×#54711yescharacteristic
1160C22#348711yescharacteristic
1161C22#348811yescharacteristic
1162C22C2×#57711yescharacteristic
1163C22C2×#57711yescharacteristic
1164C22#358411yescharacteristic
1165C22#358411yescharacteristic
1166C4—22no—
1167C4—22no—
1168C4—22no—
1169C4—22no—
1170C4—41no—
1171C4—41no—
1172C4—41no—
1173C4—41no—
1174C4—41no—
1175C4—41no—
1176C4—42no—
1177C4—41no—
1178C4—41no—
1179C4—41no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4—81no—
1186C4—81no—
1187C4—81no—
1188C4—81no—
1189C4—81no—
1190C4—81no—
1191C4—81no—
1192C4—81no—
1193C4#346011yescharacteristic
1194C4#351011yescharacteristic
1195C4#355411yescharacteristic
1196C4#355711yescharacteristic
1197C2—81no—
1198C2—161no—
1199C2—161no—
1200C2#3779711yescharacteristic
1201C2#6125911yescharacteristic
1202C2#6128911yescharacteristic
1203C2#6192711yescharacteristic
1204C2#6192811yescharacteristic
1205C2#6206811yescharacteristic
1206C2#6207111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#1999C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #42459C2semidirect
2. #35710C2semidirect
3. #33121C2semidirect
4. #32525C2semidirect
5. #32525C2semidirect
6. #32431C2semidirect
7. #32429C2semidirect
8. #32059C2semidirect
9. #32057C2semidirect
10. #31935C2semidirect
12. #29932C2semidirect
14. #28790C2semidirect
15. #28740C2semidirect
16. #27501C2semidirect
17. #27495C2semidirect
18. #26789C2semidirect
20. #26554C2semidirect
21. #26551C2semidirect
22. #26543C2semidirect
23. #26479C2semidirect
24. #26328C2semidirect
25. #26328C2semidirect
26. #24686C2semidirect
27. #24685C2semidirect
28. #23183C2semidirect
29. #22738C2semidirect
30. #22099C2semidirect
31. #21367C2semidirect

Maximal subgroups

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

subgroupindex
#424592
#357102
#331212
#325252
#324312
#324292
#320592
#320572
#319352
#319332
#299322
#298132
#287902
#287402
#275012
#274952
#267892
#267872
#265542
#265512
#265432
#264792
#263282
#246862
#246852
#231832
#227382
#220992
#213672