Finite Group Databasebeta

← #7053354

Subgroups — #7053354

Order 512.

1388 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45346C211yesmaximal, characteristic, complemented
2#44959C211yesmaximal, characteristic
3#32658C211yesmaximal, characteristic, complemented
4#32627C211yesmaximal, characteristic, complemented
5#32374C211yesmaximal, characteristic, complemented
6#32283C211yesmaximal, characteristic, complemented
7#31948C211yesmaximal, characteristic, complemented
8#31574C211yesmaximal, characteristic, complemented
9#31286C211yesmaximal, characteristic
10#31004C211yesmaximal, characteristic
11#29420C211yesmaximal, characteristic, complemented
12#29019C211yesmaximal, characteristic, complemented
13#28055C211yesmaximal, characteristic, complemented
14#27594C211yesmaximal, characteristic, complemented
15#27559C211yesmaximal, characteristic, complemented
16#27541C211yesmaximal, characteristic, complemented
17#27489C211yesmaximal, characteristic, complemented
18#27478C211yesmaximal, characteristic, complemented
19#27363C211yesmaximal, characteristic, complemented
20#27194C211yesmaximal, characteristic, complemented
21#27168C211yesmaximal, characteristic, complemented
22#26752C211yesmaximal, characteristic, complemented
23#26334C211yesmaximal, characteristic, complemented
24#26159C211yesmaximal, characteristic, complemented
25#25003C211yesmaximal, characteristic, complemented
26#24901C211yesmaximal, characteristic, complemented
27#23767C211yesmaximal, characteristic, complemented
28#23101C211yesmaximal, characteristic, complemented
29#22811C211yesmaximal, characteristic, complemented
30#22328C211yesmaximal, characteristic, complemented
31#22052C211yesmaximal, characteristic, complemented
32C2×#460C2211yescharacteristic
33C2×#450C2211yescharacteristic
34C2×C4×SD16C2211yescharacteristic
35#2772—21no—
36#2767—21no—
37#2754—21no—
38#2753—21no—
39#2719—21no—
40#2706—21no—
41#2685—21no—
42#2684—21no—
43#2610—21no—
44#2603—21no—
45#2590—21no—
46#2582C2211yescharacteristic, complemented
47#2580C2211yescharacteristic
48#2552C2211yescharacteristic, complemented
49#2548C2211yescharacteristic
50#2520—21no—
51#2519—21no—
52#2519—21no—
53#2513C2211yescharacteristic
54#2512C2211yescharacteristic
55#2508C2211yescharacteristic, complemented
56#2506C2211yescharacteristic, complemented
57#2500C2211yescharacteristic
58#2497C2211yescharacteristic
59#2496C2211yescharacteristic
60#2445C2211yescharacteristic
61#2445C2211yescharacteristic
62#2433C2211yescharacteristic
63#2423C2211yescharacteristic
64#2421C2211yescharacteristic
65#2418—21no—
66#2411—21no—
67#2396C2211yescharacteristic
68#2366C2211yescharacteristic
69#2355C2211yescharacteristic, complemented
70#2355C2211yescharacteristic, complemented
71#2355C2211yescharacteristic, complemented
72#2354C2211yescharacteristic
73#2351C2211yescharacteristic, complemented
74#2346C2211yescharacteristic
75D4×C22⋊C4C2211yescharacteristic
76#2324C2211yescharacteristic
77#2323C2211yescharacteristic
78#2314C2211yescharacteristic
79#2309C2211yescharacteristic
80#2101C2211yescharacteristic, complemented
81#2101C2211yescharacteristic, complemented
82#2100C2211yescharacteristic, complemented
83#2097C2211yescharacteristic, complemented
84#2094C2211yescharacteristic
85#2094C2211yescharacteristic
86#2094C2211yescharacteristic, complemented
87#2093C2211yescharacteristic
88#2093C2211yescharacteristic
89#2092C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2085C2211yescharacteristic, complemented
92#2084C2211yescharacteristic, complemented
93#2083C2211yescharacteristic, complemented
94#2083C2211yescharacteristic, complemented
95#2077C2211yescharacteristic
96#2076C2211yescharacteristic
97#2076C2211yescharacteristic
98#2073C2211yescharacteristic
99#2073C2211yescharacteristic
100#2073C2211yescharacteristic
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic, complemented
103#2071C2211yescharacteristic, complemented
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic, complemented
108#2066C2211yescharacteristic, complemented
109#2065C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2035C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2014C2211yescharacteristic
119#2000C2211yescharacteristic
120#1985C2211yescharacteristic, complemented
121#1985C2211yescharacteristic, complemented
122#1982C2211yescharacteristic
123#1973C2211yescharacteristic
124#1973C2211yescharacteristic
125#1973C2211yescharacteristic, complemented
126#1968C2211yescharacteristic
127#1961C2211yescharacteristic
128#1957C2211yescharacteristic
129#1949C2211yescharacteristic, complemented
130#1949C2211yescharacteristic, complemented
131#1947C2211yescharacteristic, complemented
132#1944C2211yescharacteristic, complemented
133#1941C2211yescharacteristic, complemented
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1934C2211yescharacteristic
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic, complemented
140#1928C2211yescharacteristic, complemented
141#1928C2211yescharacteristic, complemented
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1926C2211yescharacteristic
145#1926C2211yescharacteristic, complemented
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic, complemented
152#1924C2211yescharacteristic
153#1924C2211yescharacteristic
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic
156#1921C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1918C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1916C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic, complemented
171#1880C2211yescharacteristic, complemented
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic, complemented
174#1873C2211yescharacteristic
175#1864C2211yescharacteristic
176#1863C2211yescharacteristic, complemented
177#1863C2211yescharacteristic, complemented
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic, complemented
181#1854C2211yescharacteristic
182#1854C2211yescharacteristic
183#1854C2211yescharacteristic
184#1845C2211yescharacteristic, complemented
185#1836C2211yescharacteristic, complemented
186#1818C2211yescharacteristic
187#1803C2211yescharacteristic, complemented
188#1802C2211yescharacteristic
189#1802C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1776C2211yescharacteristic, complemented
194#1776C2211yescharacteristic, complemented
195C4×#107C2211yescharacteristic, complemented
196#1770C2211yescharacteristic, complemented
197#1770C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic, complemented
200C4×#103C2211yescharacteristic, complemented
201C4×#102C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C2×#127C2311yescharacteristic
208C2×#127C2311yescharacteristic
209C2×#126—21no—
210C2×#126—21no—
211C2×#125—21no—
212C2×#125—21no—
213C2×#124—21no—
214C2×#123—21no—
215C2×#123—21no—
216C2×C22⋊Q8C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#120—21no—
219C2×#120—21no—
220C2×C4×Q8C2311yescharacteristic
221C2×C4×Q8C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4—21no—
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×#117—21no—
229C2×#117C2311yescharacteristic
230C2×#117C2311yescharacteristic
231C22×C22⋊C4—21no—
232#460—24no—
233#450—24no—
234C4×SD16—24no—
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
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×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×C22⋊C8C2311yescharacteristic
280C2×C22⋊C8C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288#400—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400D411yescharacteristic
294#399—21no—
295#399—21no—
296#399D411yescharacteristic
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398D411yescharacteristic
305#398D411yescharacteristic
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#396—21no—
312#396—21no—
313#396D411yescharacteristic
314#396D411yescharacteristic
315#395D411yescharacteristic
316#394—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#393—21no—
325#393D411yescharacteristic
326#392—21no—
327#392—21no—
328#391—21no—
329#391—21no—
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#390—21no—
334#390—21no—
335#390—21no—
336#390—21no—
337#390—21no—
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
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#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—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#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#382—21no—
412#382—21no—
413#382—21no—
414#382—21no—
415#382—21no—
416#382C2311yescharacteristic
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#380—21no—
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#379—21no—
425#379—21no—
426#379—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C22⋊C4C2311yescharacteristic
443C4×C22⋊C4C2311yescharacteristic
444#376—21no—
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#336C2311yescharacteristic
468#336C2311yescharacteristic
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×Q8C2×D411yescharacteristic
483C22×Q8C2411yescharacteristic
484C22×D4—22no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—41no—
492C22×D4—41no—
493C22×D4—41no—
494C22×D4—41no—
495C22×D4—41no—
496C22×D4C2411yescharacteristic
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2411yescharacteristic
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—41no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×SD16—41no—
509C2×SD16—41no—
510C2×SD16—41no—
511C2×SD16#4114yes—
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520#127—22no—
521#127—41no—
522#127—41no—
523#127—41no—
524#126—82no—
525#126—82no—
526#125—82no—
527#125—82no—
528#124—82no—
529#123—82no—
530#123—82no—
531C22⋊Q8—22no—
532C22⋊Q8—41no—
533#121—41no—
534#121—41no—
535#120—82no—
536#120—82no—
537C4×Q8—22no—
538C4×Q8—22no—
539C4×Q8—41no—
540C4×Q8—41no—
541C4×Q8—41no—
542C4×Q8—41no—
543C4×Q8—41no—
544C4×Q8—41no—
545C4×D4—22no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551C4×D4—82no—
552#117—41no—
553#117—41no—
554#117—41no—
555#117—41no—
556#117—82no—
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⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊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—82no—
637C2×C22⋊C4C2×D411yescharacteristic
638C2×C22⋊C4C2×D411yescharacteristic
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C22⋊C4C2×D411yescharacteristic
642C2×C22⋊C4C2×D411yescharacteristic
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×C42—21no—
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657C2×C42C2411yescharacteristic
658C2×C42C2411yescharacteristic
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661#107—41no—
662#107—41no—
663#107—41no—
664#107—41no—
665#107—41no—
666#107—41no—
667#107—41no—
668#107—41no—
669#106—22no—
670#106—41no—
671#106—41no—
672#106—41no—
673#106—41no—
674C4⋊C8—22no—
675C4⋊C8—41no—
676C4⋊C8—41no—
677C4⋊C8—41no—
678#103—22no—
679#103—41no—
680#103—41no—
681#103—41no—
682#103—41no—
683#102—22no—
684#102—22no—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—41no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702#102—41no—
703#102—41no—
704C22⋊C8—22no—
705C22⋊C8—41no—
706C22⋊C8—41no—
707C22⋊C8—41no—
708#97—41no—
709#97—41no—
710#97—41no—
711C4×C8—22no—
712C4×C8—41no—
713C4×C8—41no—
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#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758C24—21no—
759C24—21no—
760C24—21no—
761C24—42no—
762C24—42no—
763C24—81no—
764C24—81no—
765C24—81no—
766C24—81no—
767C24—81no—
768C24C22×D411yescharacteristic
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—41no—
775C2×Q8—41no—
776C2×Q8—41no—
777C2×Q8C2×#4112yes—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—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—42no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—81no—
803C2×D4—81no—
804C2×D4—81no—
805C2×D4—81no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4—82no—
812C2×D4—82no—
813C2×D4—82no—
814C2×D4—82no—
815C2×D4—81no—
816C2×D4—81no—
817C2×D4C2×#4112yes—
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—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—42no—
838C22×C4—42no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C2511yescharacteristic
860SD16—44no—
861SD16—82no—
862SD16—82no—
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×C8—21no—
872C2×C8—21no—
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×C8C2×#4112yes—
887C4⋊C4—22no—
888C4⋊C4—22no—
889C4⋊C4—22no—
890C4⋊C4—22no—
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—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—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—41no—
921C4⋊C4—41no—
922C4⋊C4—42no—
923C4⋊C4—42no—
924C4⋊C4—42no—
925C4⋊C4—42no—
926C4⋊C4—42no—
927C4⋊C4—42no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
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—
946C22⋊C4—22no—
947C22⋊C4—22no—
948C22⋊C4—41no—
949C22⋊C4—41no—
950C22⋊C4—41no—
951C22⋊C4—41no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
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—
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—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—42no—
997C42—42no—
998C42—42no—
999C42—42no—
1000C42—42no—
1001C42—42no—
1002C42—81no—
1003C42—81no—
1004C42—81no—
1005C42—81no—
1006C42—81no—
1007C42—81no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—22no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—84no—
1037C23—84no—
1038C23—162no—
1039C23—162no—
1040C23—162no—
1041C23—162no—
1042C23—162no—
1043C23C23×D411yescharacteristic
1044Q8—22no—
1045Q8—22no—
1046Q8—41no—
1047Q8—41no—
1048Q8—82no—
1049D4—22no—
1050D4—22no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—41no—
1057D4—41no—
1058D4—41no—
1059D4—41no—
1060D4—41no—
1061D4—84no—
1062D4—84no—
1063D4—162no—
1064D4—162no—
1065D4—162no—
1066D4—162no—
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—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—22no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—21no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
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—41no—
1132C2×C4—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—84no—
1148C2×C4—162no—
1149C2×C4—162no—
1150C2×C4#57612yes—
1151C2×C4#57712yes—
1152C2×C4C22×#4111yescharacteristic
1153C2×C4#58511yescharacteristic
1154C2×C4#58511yescharacteristic
1155C2×C4#58511yescharacteristic
1156C2×C4#58511yescharacteristic
1157C2×C4#58511yescharacteristic
1158C8—22no—
1159C8—41no—
1160C8—41no—
1161C8—41no—
1162C8—41no—
1163C8—41no—
1164C8—41no—
1165C8—41no—
1166C22—41no—
1167C22—42no—
1168C22—42no—
1169C22—41no—
1170C22—42no—
1171C22—41no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22—81no—
1192C22—81no—
1193C22—81no—
1194C22—168no—
1195C22D4×#4111yescharacteristic
1196C22#348511yescharacteristic
1197C22#348711yescharacteristic
1198C22C2×#57611yescharacteristic
1199C22C2×#57711yescharacteristic
1200C22#358511yescharacteristic
1201C22#358611yescharacteristic
1202C4—22no—
1203C4—22no—
1204C4—41no—
1205C4—42no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—41no—
1215C4—41no—
1216C4—81no—
1217C4—81no—
1218C4—81no—
1219C4—81no—
1220C4—81no—
1221C4—81no—
1222C4—81no—
1223C4—81no—
1224C4—81no—
1225C4—81no—
1226C4—81no—
1227C4—81no—
1228C4#349111yescharacteristic
1229C4#352111yescharacteristic
1230C4#356611yescharacteristic
1231C4#356611yescharacteristic
1232C2—81no—
1233C2—82no—
1234C2—161no—
1235C2—161no—
1236C2#4354811yescharacteristic
1237C2#6152111yescharacteristic
1238C2#6152311yescharacteristic
1239C2#6178011yescharacteristic
1240C2#6178811yescharacteristic
1241C2#6191111yescharacteristic
1242C2#6192011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2433C22
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. #45346C2semidirect
3. #32658C2semidirect
4. #32627C2semidirect
5. #32374C2semidirect
6. #32283C2semidirect
7. #31948C2semidirect
8. #31574C2semidirect
11. #29420C2semidirect
12. #29019C2semidirect
13. #28055C2semidirect
14. #27594C2semidirect
15. #27559C2semidirect
16. #27541C2semidirect
17. #27489C2semidirect
18. #27478C2semidirect
19. #27363C2semidirect
20. #27194C2semidirect
21. #27168C2semidirect
22. #26752C2semidirect
23. #26334C2semidirect
24. #26159C2semidirect
25. #25003C2semidirect
26. #24901C2semidirect
27. #23767C2semidirect
28. #23101C2semidirect
29. #22811C2semidirect
30. #22328C2semidirect
31. #22052C2semidirect
46. #2582C22semidirect
48. #2552C22semidirect
55. #2508C22semidirect
56. #2506C22semidirect
69. #2355C22semidirect
70. #2355C22semidirect
71. #2355C22semidirect
73. #2351C22semidirect
80. #2101C22semidirect
81. #2101C22semidirect
82. #2100C22semidirect
83. #2097C22semidirect
86. #2094C22semidirect
89. #2092C22semidirect
90. #2088C22semidirect
91. #2085C22semidirect
92. #2084C22semidirect
93. #2083C22semidirect
94. #2083C22semidirect
102. #2071C22semidirect
103. #2071C22semidirect
107. #2067C22semidirect
108. #2066C22semidirect
109. #2065C22semidirect
120. #1985C22semidirect
121. #1985C22semidirect
125. #1973C22semidirect
129. #1949C22semidirect
130. #1949C22semidirect
131. #1947C22semidirect
132. #1944C22semidirect
133. #1941C22semidirect
139. #1934C22semidirect
140. #1928C22semidirect
141. #1928C22semidirect
145. #1926C22semidirect
151. #1925C22semidirect
156. #1921C22semidirect
157. #1920C22semidirect
158. #1919C22semidirect
159. #1918C22semidirect
160. #1918C22semidirect
161. #1918C22semidirect
162. #1916C22semidirect
163. #1916C22semidirect
164. #1916C22semidirect
165. #1916C22semidirect
170. #1880C22semidirect
171. #1880C22semidirect
173. #1877C22semidirect
176. #1863C22semidirect
177. #1863C22semidirect
180. #1862C22semidirect
184. #1845C22semidirect
185. #1836C22semidirect
187. #1803C22semidirect
193. #1776C22semidirect
194. #1776C22semidirect
195. C4×#107C22semidirect
196. #1770C22semidirect
197. #1770C22semidirect
199. #1762C22semidirect
200. C4×#103C22semidirect
201. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#453462
#449592
#326582
#326272
#323742
#322832
#319482
#315742
#312862
#310042
#294202
#290192
#280552
#275942
#275592
#275412
#274892
#274782
#273632
#271942
#271682
#267522
#263342
#261592
#250032
#249012
#237672
#231012
#228112
#223282
#220522