Finite Group Databasebeta

← #6465324

Subgroups — #6465324

Order 512.

1418 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35656C211yesmaximal, characteristic, complemented
2#35580C211yesmaximal, characteristic
3#29076C211yesmaximal, characteristic
4#29075C211yesmaximal, characteristic
5#29013C211yesmaximal, characteristic, complemented
6#29009C211yesmaximal, characteristic, complemented
7#28793C211yesmaximal, characteristic, complemented
8#28638C211yesmaximal, characteristic, complemented
9#28400C211yesmaximal, characteristic
10#28189C211yesmaximal, characteristic
11#28059C211yesmaximal, characteristic, complemented
12#28050C211yesmaximal, characteristic, complemented
13#27782C211yesmaximal, characteristic, complemented
14#27744C211yesmaximal, characteristic
15#26845C211yesmaximal, characteristic
16#26836C211yesmaximal, characteristic
17#25487C211yesmaximal, characteristic, complemented
18#25308C211yesmaximal, characteristic
19#23793C211yesmaximal, characteristic, complemented
20#23783C211yesmaximal, characteristic, complemented
21#23689C211yesmaximal, characteristic
22#23683C211yesmaximal, characteristic
23#21653C211yesmaximal, characteristic, complemented
24#21645C211yesmaximal, characteristic, complemented
25C4×#487C211yesmaximal, characteristic, complemented
26#21626C211yesmaximal, characteristic, complemented
27#21514C211yesmaximal, characteristic
28#21291C211yesmaximal, characteristic
29#21274C211yesmaximal, characteristic
30#20516C211yesmaximal, characteristic, complemented
31#20504C211yesmaximal, characteristic
32C2×#491C2211yescharacteristic
33C2×#487C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#475C2211yescharacteristic
36C2×#461C2211yescharacteristic
37C2×#446C2211yescharacteristic
38C2×C8×Q8C2211yescharacteristic
39C2×#440C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×C4×SD16C2211yescharacteristic
43C2×C4×SD16C2211yescharacteristic
44#2607—21no—
45#2590—21no—
46#2589—21no—
47#2588—21no—
48#2581C2211yescharacteristic
49#2580C2211yescharacteristic
50#2570C2211yescharacteristic
51#2568C2211yescharacteristic
52#2567C2211yescharacteristic
53#2556—21no—
54#2550C2211yescharacteristic
55#2549—21no—
56#2546C2211yescharacteristic
57#2542C2211yescharacteristic
58#2533—21no—
59#2533—21no—
60#2528—21no—
61#2528—21no—
62#2524—21no—
63#2520—21no—
64#2514C2211yescharacteristic
65#2511C2211yescharacteristic
66#2507C2211yescharacteristic
67#2506C2211yescharacteristic
68#2465—21no—
69#2454C2211yescharacteristic
70#2452C2211yescharacteristic
71#2446C2211yescharacteristic
72#2446C2211yescharacteristic
73#2441—21no—
74#2438—21no—
75#2423—21no—
76#2331C2211yescharacteristic
77#2330C2211yescharacteristic
78#2327C2211yescharacteristic
79#2327C2211yescharacteristic
80#2320C2211yescharacteristic
81#2319C2211yescharacteristic
82C4×C4⋊Q8C2211yescharacteristic
83C4×C4⋊Q8C2211yescharacteristic
84#2295C2211yescharacteristic
85#2295C2211yescharacteristic
86#2293C2211yescharacteristic
87#2276C2211yescharacteristic
88#2275C2211yescharacteristic
89#2100C2211yescharacteristic
90#2099C2211yescharacteristic
91#2096C2211yescharacteristic
92#2096C2211yescharacteristic
93#2088C2211yescharacteristic
94#2088C2211yescharacteristic
95#2088C2211yescharacteristic
96#2088C2211yescharacteristic
97#2085C2211yescharacteristic
98#2083C2211yescharacteristic
99#2073C2211yescharacteristic
100#2071C2211yescharacteristic
101#2068C2211yescharacteristic
102#2068C2211yescharacteristic
103#2068C2211yescharacteristic
104#2068C2211yescharacteristic
105#2068C2211yescharacteristic
106#2068C2211yescharacteristic
107#2066C2211yescharacteristic
108#2066C2211yescharacteristic
109#2059C2211yescharacteristic
110#2057C2211yescharacteristic
111#2055C2211yescharacteristic
112#2055C2211yescharacteristic
113#2055C2211yescharacteristic
114#2055C2211yescharacteristic
115#2043C2211yescharacteristic
116#2043C2211yescharacteristic
117#2026C2211yescharacteristic
118#2024C2211yescharacteristic
119#2013C2211yescharacteristic
120#2013C2211yescharacteristic
121#1993C2211yescharacteristic
122#1991C2211yescharacteristic
123#1990C2211yescharacteristic
124#1987C2211yescharacteristic
125#1981C2211yescharacteristic
126#1973C2211yescharacteristic
127#1968C2211yescharacteristic
128#1968C2211yescharacteristic
129#1968C2211yescharacteristic
130#1960C2211yescharacteristic
131#1956C2211yescharacteristic
132#1956C2211yescharacteristic
133#1949C2211yescharacteristic
134#1949C2211yescharacteristic
135#1943C2211yescharacteristic
136#1942C2211yescharacteristic
137#1941C2211yescharacteristic
138#1941C2211yescharacteristic
139#1936C2211yescharacteristic
140#1935C2211yescharacteristic
141#1935C2211yescharacteristic
142#1935C2211yescharacteristic
143#1935C2211yescharacteristic
144#1935C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1933C2211yescharacteristic
149#1933C2211yescharacteristic
150#1933C2211yescharacteristic
151#1933C2211yescharacteristic
152#1933C2211yescharacteristic
153#1933C2211yescharacteristic
154#1933C2211yescharacteristic
155#1933C2211yescharacteristic
156#1933C2211yescharacteristic
157#1933C2211yescharacteristic
158#1933C2211yescharacteristic
159#1928C2211yescharacteristic
160#1927C2211yescharacteristic
161#1920C2211yescharacteristic
162#1919C2211yescharacteristic
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1865C2211yescharacteristic
166#1863C2211yescharacteristic
167#1836C2211yescharacteristic
168#1835C2211yescharacteristic
169#1834C2211yescharacteristic
170#1805C2211yescharacteristic
171#1804C2211yescharacteristic
172#1776C2211yescharacteristic
173#1776C2211yescharacteristic
174#1776C2211yescharacteristic
175C4×#107C2211yescharacteristic
176C4×#106C2211yescharacteristic
177#1771C2211yescharacteristic
178#1771C2211yescharacteristic
179#1770C2211yescharacteristic
180C8×C4⋊C4C2211yescharacteristic
181C8×C4⋊C4C2211yescharacteristic
182C8×C4⋊C4C2211yescharacteristic
183#1768C2211yescharacteristic
184#1768C2211yescharacteristic
185#1767C2211yescharacteristic
186#1763C2211yescharacteristic
187#1763C2211yescharacteristic
188#1763C2211yescharacteristic
189#1763C2211yescharacteristic
190#1763C2211yescharacteristic
191#1762C2211yescharacteristic
192C4×#103C2211yescharacteristic
193C4×#103C2211yescharacteristic
194C4×#103C2211yescharacteristic
195C4×#103C2211yescharacteristic
196C4×#103C2211yescharacteristic
197C4×#103C2211yescharacteristic
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic
200#1726C2211yescharacteristic
201#1726C2211yescharacteristic
202C42×C8C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C2×C4⋊Q8C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×C4⋊Q8C2311yescharacteristic
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×C22⋊Q8—21no—
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8—21no—
216C2×C4×Q8—21no—
217C2×C4×Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×#117—21no—
227#491—24no—
228#487—24no—
229#487—24no—
230#475—24no—
231#461—24no—
232#446—24no—
233C8×Q8—24no—
234#440—24no—
235#440—24no—
236#440—24no—
237C4×SD16—24no—
238C4×SD16—24no—
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251C2×C4⋊C8C2311yescharacteristic
252C2×C4⋊C8C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294C2×C4×C8C2311yescharacteristic
295C2×C4×C8C2311yescharacteristic
296#401—21no—
297#400—21no—
298#400—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#399—21no—
308#399—21no—
309#399—21no—
310#399—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#398—21no—
319#398—21no—
320#396—21no—
321#396—21no—
322#395—21no—
323#395—21no—
324#395—21no—
325#395—21no—
326#393—21no—
327#393—21no—
328#391—21no—
329#391—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391D411yescharacteristic
335#391D411yescharacteristic
336#391C2311yescharacteristic
337#391C2311yescharacteristic
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#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389—21no—
358#389—21no—
359#389D411yescharacteristic
360#389D411yescharacteristic
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#388—21no—
376#388—21no—
377#388—21no—
378#388—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#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#387D411yescharacteristic
409#387D411yescharacteristic
410#387D411yescharacteristic
411#387D411yescharacteristic
412#385—21no—
413#385—21no—
414#385—21no—
415#385—21no—
416#384—21no—
417#384C2311yescharacteristic
418#384C2311yescharacteristic
419#384C2311yescharacteristic
420#383—21no—
421#383—21no—
422#382—21no—
423#382—21no—
424#382C2311yescharacteristic
425#382C2311yescharacteristic
426#382C2311yescharacteristic
427#381—21no—
428#380—21no—
429#380—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
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—
452#376—21no—
453#376—21no—
454#376C2311yescharacteristic
455#376C2311yescharacteristic
456C2×#95—21no—
457C43C2311yescharacteristic
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#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8C2×D411yescharacteristic
493C22×Q8C2411yescharacteristic
494C22×Q8C2411yescharacteristic
495C22×Q8C2411yescharacteristic
496C22×D4C2411yescharacteristic
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C2×SD16—22no—
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—22no—
507C2×SD16—41no—
508C2×SD16—41no—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C4⋊Q8—22no—
518C4⋊Q8—22no—
519C4⋊Q8—22no—
520C4⋊Q8—22no—
521C4⋊Q8—22no—
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527#125—22no—
528#125—41no—
529#125—82no—
530C22⋊Q8—82no—
531C22⋊Q8—82no—
532C22⋊Q8—82no—
533C4×Q8—22no—
534C4×Q8—22no—
535C4×Q8—22no—
536C4×Q8—22no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—22no—
540C4×Q8—22no—
541C4×Q8—22no—
542C4×Q8—22no—
543C4×Q8—22no—
544C4×Q8—41no—
545C4×Q8—82no—
546C4×D4—22no—
547C4×D4—22no—
548C4×D4—22no—
549C4×D4—22no—
550C4×D4—41no—
551C4×D4#4114yes—
552#117—82no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—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⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
593C2×C4⋊C4C2×D411yescharacteristic
594C2×C4⋊C4C2×D411yescharacteristic
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
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×C42—21no—
621C2×C42—21no—
622C2×C42—21no—
623C2×C42—21no—
624C2×C42—21no—
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×C42C2×D411yescharacteristic
634C2×C42C2×D411yescharacteristic
635C2×C42C2×D411yescharacteristic
636C2×C42C2×D411yescharacteristic
637C2×C42C2411yescharacteristic
638C2×C42C2411yescharacteristic
639C2×C42C2411yescharacteristic
640C2×C42C2411yescharacteristic
641C2×C42C2411yescharacteristic
642C2×C42C2411yescharacteristic
643C2×C42C2411yescharacteristic
644#107—22no—
645#107—22no—
646#107—22no—
647#107—41no—
648#106—22no—
649#106—22no—
650#106—22no—
651#106—22no—
652#106—41no—
653C4⋊C8—22no—
654C4⋊C8—22no—
655C4⋊C8—22no—
656C4⋊C8—22no—
657C4⋊C8—22no—
658C4⋊C8#4114yes—
659#103—22no—
660#103—22no—
661#103—22no—
662#103—22no—
663#103—22no—
664#103—22no—
665#103—22no—
666#103—22no—
667#103—22no—
668#103—22no—
669#103—22no—
670#103—22no—
671#103—22no—
672#103—22no—
673#103—22no—
674#103—22no—
675#103—22no—
676#103—22no—
677#103—41no—
678#103—41no—
679#103#4114yes—
680#102—22no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—22no—
685#97—22no—
686#97—22no—
687#97—22no—
688#97—22no—
689#97—22no—
690#97—22no—
691C4×C8—22no—
692C4×C8—22no—
693C4×C8—22no—
694C4×C8—22no—
695C4×C8—22no—
696C4×C8—22no—
697C4×C8—41no—
698C4×C8—41no—
699C4×C8—41no—
700C4×C8#4114yes—
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#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#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
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763C24—21no—
764C2×Q8—22no—
765C2×Q8—22no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
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—41no—
784C2×Q8—42no—
785C2×Q8—42no—
786C2×Q8—42no—
787C2×Q8—81no—
788C2×Q8—81no—
789C2×Q8—81no—
790C2×Q8C2×#4112yes—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4C2×#4112yes—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—24no—
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×C4—81no—
820C22×C4—81no—
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×C4C22×D411yescharacteristic
834C22×C4C22×D411yescharacteristic
835C22×C4C2511yescharacteristic
836SD16—28no—
837SD16—44no—
838SD16—44no—
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×C8C2×#4112yes—
859C2×C8C2×#4112yes—
860C2×C8C2×#4112yes—
861C2×C8C2×#4112yes—
862C2×C8C2×#4112yes—
863C4⋊C4—22no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—22no—
867C4⋊C4—22no—
868C4⋊C4—22no—
869C4⋊C4—22no—
870C4⋊C4—22no—
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—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—41no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—42no—
899C4⋊C4—42no—
900C4⋊C4—42no—
901C4⋊C4—42no—
902C4⋊C4—42no—
903C4⋊C4—42no—
904C4⋊C4—42no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
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⋊C4C2×#4112yes—
930C4⋊C4C2×#4112yes—
931C22⋊C4—24no—
932C22⋊C4—42no—
933C22⋊C4—42no—
934C22⋊C4—42no—
935C22⋊C4—42no—
936C22⋊C4—42no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C42—22no—
943C42—22no—
944C42—22no—
945C42—21no—
946C42—21no—
947C42—21no—
948C42—21no—
949C42—21no—
950C42—21no—
951C42—21no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—41no—
956C42—42no—
957C42—42no—
958C42—42no—
959C42—42no—
960C42—42no—
961C42—81no—
962C42—81no—
963C42—81no—
964C42—81no—
965C42—81no—
966C42—81no—
967C42—81no—
968C42—81no—
969C42C2×#4112yes—
970C42C2×#4112yes—
971C42C2×#4112yes—
972C422−1+412yes—
973C23—22no—
974C23—41no—
975C23—41no—
976C23—41no—
977C23—41no—
978C23—41no—
979C23—41no—
980C23C23×D411yescharacteristic
981Q8—22no—
982Q8—22no—
983Q8—44no—
984Q8—41no—
985Q8—41no—
986Q8—41no—
987Q8—41no—
988Q8—41no—
989Q8—41no—
990Q8—41no—
991Q8—41no—
992Q8—41no—
993Q8—41no—
994Q8—84no—
995Q8—162no—
996D4—22no—
997D4—22no—
998D4—41no—
999D4—41no—
1000C2×C4—21no—
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—22no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—22no—
1026C2×C4—22no—
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—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
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—84no—
1081C2×C4—162no—
1082C2×C4—162no—
1083C2×C4#53212yes—
1084C2×C4#53212yes—
1085C2×C4#54812yes—
1086C2×C4#54812yes—
1087C2×C4#57712yes—
1088C2×C4#57712yes—
1089C2×C4#57812yes—
1090C2×C4C22×#4111yescharacteristic
1091C2×C4C22×#4111yescharacteristic
1092C2×C4C22×#4111yescharacteristic
1093C2×C4C22×#4111yescharacteristic
1094C2×C4C2×2−1+411yescharacteristic
1095C2×C4#58511yescharacteristic
1096C8—22no—
1097C8—22no—
1098C8—22no—
1099C8—22no—
1100C8—22no—
1101C8—41no—
1102C8—41no—
1103C8—41no—
1104C22—42no—
1105C22—42no—
1106C22—42no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22—81no—
1111C22C2×#53211yescharacteristic
1112C22C2×#54811yescharacteristic
1113C22D4×#4111yescharacteristic
1114C22C2×#57711yescharacteristic
1115C22C2×#57711yescharacteristic
1116C22C2×#57811yescharacteristic
1117C22#358411yescharacteristic
1118C4—22no—
1119C4—22no—
1120C4—22no—
1121C4—22no—
1122C4—22no—
1123C4—22no—
1124C4—22no—
1125C4—41no—
1126C4—41no—
1127C4—41no—
1128C4—41no—
1129C4—41no—
1130C4—42no—
1131C4—41no—
1132C4—41no—
1133C4—42no—
1134C4—42no—
1135C4—81no—
1136C4—81no—
1137C4—81no—
1138C4—81no—
1139C4—81no—
1140C4—81no—
1141C4—81no—
1142C4—81no—
1143C4—81no—
1144C4—81no—
1145C4—81no—
1146C4—81no—
1147C4#344411yescharacteristic
1148C4#346111yescharacteristic
1149C4#347511yescharacteristic
1150C4#348211yescharacteristic
1151C2—82no—
1152C2#3491911yescharacteristic
1153C2#6070811yescharacteristic
1154C2#6071211yescharacteristic
1155C2#6132611yescharacteristic
1156C2#6133011yescharacteristic
1157C2#6149011yescharacteristic
1158C2#6149911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC22×D4C24
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2295 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #35656C2semidirect
5. #29013C2semidirect
6. #29009C2semidirect
7. #28793C2semidirect
8. #28638C2semidirect
11. #28059C2semidirect
12. #28050C2semidirect
13. #27782C2semidirect
17. #25487C2semidirect
19. #23793C2semidirect
20. #23783C2semidirect
23. #21653C2semidirect
24. #21645C2semidirect
25. C4×#487C2semidirect
26. #21626C2semidirect
30. #20516C2semidirect

Maximal subgroups

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

subgroupindex
#356562
#355802
#290762
#290752
#290132
#290092
#287932
#286382
#284002
#281892
#280592
#280502
#277822
#277442
#268452
#268362
#254872
#253082
#237932
#237832
#236892
#236832
#216532
#216452
C4×#4872
#216262
#215142
#212912
#212742
#205162
#205042