Finite Group Databasebeta

← #7077896

Subgroups — #7077896

Order 512.

1409 conjugacy classes of subgroups.

The subgroup lattice has 1231 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45178C211yesmaximal, characteristic, complemented
2#45019C211yesmaximal, characteristic
3#32487C211yesmaximal, characteristic, complemented
4#32473C211yesmaximal, characteristic, complemented
5#32394C211yesmaximal, characteristic, complemented
6#32368C211yesmaximal, characteristic, complemented
7#32282C211yesmaximal, characteristic, complemented
8#32225C211yesmaximal, characteristic, complemented
9#31618C211yesmaximal, characteristic, complemented
10#30786C211yesmaximal, characteristic, complemented
11#28107C211yesmaximal, characteristic
12#27619C211yesmaximal, characteristic, complemented
13#27594C211yesmaximal, characteristic, complemented
14#27376C211yesmaximal, characteristic, complemented
15#27170C211yesmaximal, characteristic, complemented
16#27157C211yesmaximal, characteristic, complemented
17#27031C211yesmaximal, characteristic, complemented
18#26366C211yesmaximal, characteristic, complemented
19#26090C211yesmaximal, characteristic, complemented
20#26063C211yesmaximal, characteristic, complemented
21#26016C211yesmaximal, characteristic, complemented
22#25976C211yesmaximal, characteristic, complemented
23#25458C211yesmaximal, characteristic, complemented
24#24950C211yesmaximal, characteristic, complemented
25#24886C211yesmaximal, characteristic
26#24592C211yesmaximal, characteristic, complemented
27#23612C211yesmaximal, characteristic, complemented
28#22662C211yesmaximal, characteristic, complemented
29#22574C211yesmaximal, characteristic, complemented
30#22068C211yesmaximal, characteristic, complemented
31#21967C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic, complemented
33C2×#482C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#435C2211yescharacteristic
36C2×#428C2211yescharacteristic, complemented
37C2×#427C2211yescharacteristic
38C2×#424C2211yescharacteristic
39C2×#418C2211yescharacteristic
40C22×#102C2211yescharacteristic
41#2796—21no—
42#2793—21no—
43#2773—21no—
44#2740—21no—
45#2738—21no—
46#2735—21no—
47#2697—21no—
48#2694—21no—
49#2602—21no—
50#2573—21no—
51#2566C2211yescharacteristic
52#2558—21no—
53#2552C2211yescharacteristic, complemented
54#2524—21no—
55#2513C2211yescharacteristic
56#2513C2211yescharacteristic
57#2509C2211yescharacteristic, complemented
58#2506—21no—
59#2506C2211yescharacteristic, complemented
60#2501C2211yescharacteristic
61#2497C2211yescharacteristic, complemented
62#2495C2211yescharacteristic, complemented
63#2490C2211yescharacteristic
64#2486C2211yescharacteristic
65#2482—21no—
66#2471—21no—
67#2441C2211yescharacteristic
68#2441C2211yescharacteristic
69#2441C2211yescharacteristic, complemented
70#2420C2211yescharacteristic
71#2418—21no—
72#2408C2211yescharacteristic
73#2395C2211yescharacteristic
74#2370C2211yescharacteristic, complemented
75#2361C2211yescharacteristic
76#2354C2211yescharacteristic
77#2354C2211yescharacteristic
78#2352C2211yescharacteristic
79#2347C2211yescharacteristic, complemented
80#2345C2211yescharacteristic
81D4×C22⋊C4C2211yescharacteristic
82#2317C2211yescharacteristic
83#2314C2211yescharacteristic
84#2314C2211yescharacteristic
85#2309C2211yescharacteristic
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2099C2211yescharacteristic, complemented
90#2094C2211yescharacteristic
91#2094C2211yescharacteristic
92#2094C2211yescharacteristic
93#2093C2211yescharacteristic
94#2088C2211yescharacteristic, complemented
95#2087C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2083C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2075C2211yescharacteristic, complemented
102#2075C2211yescharacteristic, complemented
103#2073C2211yescharacteristic
104#2073C2211yescharacteristic
105#2071C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2067C2211yescharacteristic
111#2067C2211yescharacteristic
112#2065C2211yescharacteristic
113#2065C2211yescharacteristic
114#2065C2211yescharacteristic
115#2065C2211yescharacteristic
116#2065C2211yescharacteristic
117#2065C2211yescharacteristic
118#2059C2211yescharacteristic, complemented
119#2059C2211yescharacteristic, complemented
120#2059C2211yescharacteristic, complemented
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2034C2211yescharacteristic
124#2033C2211yescharacteristic
125#2025C2211yescharacteristic
126#1989C2211yescharacteristic, complemented
127#1949C2211yescharacteristic, complemented
128#1949C2211yescharacteristic, complemented
129#1949C2211yescharacteristic, complemented
130#1949C2211yescharacteristic, complemented
131#1949C2211yescharacteristic, complemented
132#1948C2211yescharacteristic, complemented
133#1948C2211yescharacteristic, complemented
134#1948C2211yescharacteristic, complemented
135#1948C2211yescharacteristic, complemented
136#1948C2211yescharacteristic, complemented
137#1948C2211yescharacteristic, complemented
138#1941C2211yescharacteristic, complemented
139#1941C2211yescharacteristic, complemented
140#1939C2211yescharacteristic, complemented
141#1939C2211yescharacteristic, complemented
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic
153#1925C2211yescharacteristic
154#1923C2211yescharacteristic, complemented
155#1923C2211yescharacteristic, complemented
156#1921C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1921C2211yescharacteristic, complemented
159#1920C2211yescharacteristic, complemented
160#1920C2211yescharacteristic, complemented
161#1919C2211yescharacteristic, complemented
162#1918C2211yescharacteristic, complemented
163#1918C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1895C2211yescharacteristic
167#1895C2211yescharacteristic
168#1875C2211yescharacteristic
169#1870C2211yescharacteristic
170#1864C2211yescharacteristic
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1862C2211yescharacteristic
174#1854C2211yescharacteristic
175#1854C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic
178#1854C2211yescharacteristic, complemented
179#1853C2211yescharacteristic, complemented
180#1853C2211yescharacteristic, complemented
181#1851C2211yescharacteristic
182#1851C2211yescharacteristic, complemented
183#1851C2211yescharacteristic, complemented
184#1847C2211yescharacteristic, complemented
185#1844C2211yescharacteristic, complemented
186#1824C2211yescharacteristic
187#1824C2211yescharacteristic, complemented
188#1823C2211yescharacteristic
189#1818C2211yescharacteristic
190#1809C2211yescharacteristic
191#1809C2211yescharacteristic
192#1809C2211yescharacteristic, complemented
193#1807C2211yescharacteristic
194#1807C2211yescharacteristic
195#1802C2211yescharacteristic
196#1786C2211yescharacteristic
197#1786C2211yescharacteristic
198#1776C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202#1736C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C22×M16C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×#125—21no—
208C2×#125—21no—
209C2×#125C2311yescharacteristic
210C2×#125C2311yescharacteristic
211C2×#123—21no—
212C2×#123—21no—
213C2×#123—21no—
214C2×#121C2311yescharacteristic
215C2×#121C2311yescharacteristic
216C2×#120—21no—
217C2×C4×D4—21no—
218C2×C4×D4C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×#117—21no—
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C2×#117C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C22⋊C4—21no—
229#499—42no—
230#482—42no—
231#478—42no—
232#435—24no—
233#428—42no—
234#427—42no—
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×#106C2311yescharacteristic
249C2×#106C2311yescharacteristic
250C2×#106C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255#424—24no—
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263#418—42no—
264C2×#102—24no—
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×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400D411yescharacteristic
295#399—21no—
296#399—21no—
297#399—21no—
298#399—21no—
299#399—21no—
300#399D411yescharacteristic
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398D411yescharacteristic
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397D411yescharacteristic
315#397D411yescharacteristic
316#397D411yescharacteristic
317#396—21no—
318#396—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394D411yescharacteristic
327#394D411yescharacteristic
328#392—21no—
329#390—21no—
330#390—21no—
331#390—21no—
332#390—21no—
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#389—21no—
342#389—21no—
343#389—21no—
344#389—21no—
345#389—21no—
346#389—21no—
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#388—21no—
367#388—21no—
368#388—21no—
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#384—21no—
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#384C2311yescharacteristic
409#383—21no—
410#383—21no—
411#382—21no—
412#382C2311yescharacteristic
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#381—21no—
416#381—21no—
417#380—21no—
418#380—21no—
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#379—21no—
428#379—21no—
429#379—21no—
430#379—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4—21no—
433C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4C2311yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
448C4×C22⋊C4C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#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
487C25—21no—
488C22×D4—22no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—21no—
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—41no—
495C22×D4—41no—
496C22×D4—41no—
497C22×D4C2×D411yescharacteristic
498C22×D4C2411yescharacteristic
499C22×D4C2411yescharacteristic
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4—21no—
504C23×C4C2411yescharacteristic
505C23×C4C2411yescharacteristic
506C2×M16—22no—
507C2×M16—22no—
508C2×M16—41no—
509C2×M16—41no—
510C2×M16—41no—
511C2×M16—41no—
512C22×C8—41no—
513C22×C8—41no—
514C22×C8#4114yes—
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523#125—22no—
524#125—41no—
525#125—41no—
526#125—41no—
527#125—82no—
528#125—82no—
529#123—82no—
530#123—82no—
531#123—82no—
532#121—22no—
533#121—41no—
534#121—41no—
535#121—41no—
536#120—82no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—41no—
541C4×D4—41no—
542C4×D4—41no—
543C4×D4—82no—
544#117—22no—
545#117—22no—
546#117—22no—
547#117—22no—
548#117—41no—
549#117—41no—
550#117—41no—
551#117—41no—
552#117—82no—
553C2×C4⋊C4—22no—
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—21no—
583C2×C4⋊C4—41no—
584C2×C4⋊C4—41no—
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×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⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—82no—
638C2×C22⋊C4C2×D411yescharacteristic
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C22⋊C4C2×D411yescharacteristic
641C2×C22⋊C4C2×D411yescharacteristic
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
644C2×C22⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42C2411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664#107—22no—
665#107—22no—
666#107—22no—
667#107—41no—
668#107—41no—
669#107—41no—
670#107—41no—
671#107—41no—
672#106—22no—
673#106—41no—
674#106—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679#106—41no—
680#106—41no—
681#106—41no—
682#106—41no—
683#106—41no—
684C4⋊C8—22no—
685C4⋊C8—22no—
686C4⋊C8—22no—
687C4⋊C8—22no—
688C4⋊C8—22no—
689C4⋊C8—41no—
690C4⋊C8—41no—
691#102—22no—
692#102—22no—
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—
705#102—41no—
706#102—41no—
707C22⋊C8—22no—
708C22⋊C8—22no—
709C22⋊C8—22no—
710C22⋊C8—41no—
711C22⋊C8—41no—
712#97—22no—
713C4×C8—41no—
714C4×C8—41no—
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
759C24—21no—
760C24—21no—
761C24—42no—
762C24—42no—
763C24—81no—
764C24—81no—
765C24—81no—
766C24—81no—
767C24—81no—
768C24C22×D411yescharacteristic
769C24C22×D411yescharacteristic
770C2×D4—22no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—41no—
785C2×D4—41no—
786C2×D4—42no—
787C2×D4—42no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—82no—
792C2×D4—82no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—81no—
797C2×D42−1+412yes—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—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—42no—
825C22×C4—42no—
826C22×C4—81no—
827C22×C4—81no—
828C22×C4—81no—
829C22×C4—81no—
830C22×C4—81no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
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×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C2×#4112yes—
847C22×C42−1+412yes—
848C22×C4C2511yescharacteristic
849M16—44no—
850M16—82no—
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×C8—21no—
872C2×C8—21no—
873C2×C8—44no—
874C2×C8C2×#4112yes—
875C2×C8C2×#4112yes—
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—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—41no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
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⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4H(5,𝔽2)12yes—
939C22⋊C4—22no—
940C22⋊C4—22no—
941C22⋊C4—22no—
942C22⋊C4—22no—
943C22⋊C4—22no—
944C22⋊C4—22no—
945C22⋊C4—41no—
946C22⋊C4—41no—
947C22⋊C4—41no—
948C22⋊C4—41no—
949C22⋊C4—42no—
950C22⋊C4—42no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
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—
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—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—42no—
991C42—42no—
992C42—81no—
993C42—81no—
994C42—81no—
995C42—81no—
996C42—81no—
997C42—81no—
998C42—81no—
999C42—81no—
1000C42—81no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—22no—
1013C23—21no—
1014C23—21no—
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—41no—
1028C23—84no—
1029C23—84no—
1030C23—162no—
1031C23—162no—
1032C23—162no—
1033C23—162no—
1034C23—162no—
1035C23#54712yes—
1036C23C23×D411yescharacteristic
1037D4—22no—
1038D4—22no—
1039D4—41no—
1040D4—41no—
1041D4—41no—
1042D4—41no—
1043D4—41no—
1044D4—41no—
1045D4—84no—
1046D4—82no—
1047D4—84no—
1048D4—162no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—22no—
1054C2×C4—22no—
1055C2×C4—22no—
1056C2×C4—22no—
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—21no—
1080C2×C4—22no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
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—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—84no—
1134C2×C4—162no—
1135C2×C4—162no—
1136C2×C4—162no—
1137C2×C4#54712yes—
1138C2×C4#57712yes—
1139C2×C4C22×#4111yescharacteristic
1140C2×C4C2×H(5,𝔽2)11yescharacteristic
1141C2×C4C2×2−1+411yescharacteristic
1142C2×C4C2×2−1+411yescharacteristic
1143C2×C4#58511yescharacteristic
1144C2×C4#58511yescharacteristic
1145C8—22no—
1146C8—22no—
1147C8—41no—
1148C8—41no—
1149C8—41no—
1150C8—41no—
1151C8—41no—
1152C8—41no—
1153C22—22no—
1154C22—22no—
1155C22—22no—
1156C22—41no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22—41no—
1161C22—41no—
1162C22—41no—
1163C22—41no—
1164C22—41no—
1165C22—42no—
1166C22—42no—
1167C22—41no—
1168C22—41no—
1169C22—42no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—81no—
1179C22—81no—
1180C22—81no—
1181C22—168no—
1182C22C2×#54711yescharacteristic
1183C22#348811yescharacteristic
1184C22#348911yescharacteristic
1185C22C2×#57711yescharacteristic
1186C22#358411yescharacteristic
1187C22#358511yescharacteristic
1188C22#358511yescharacteristic
1189C4—22no—
1190C4—22no—
1191C4—41no—
1192C4—41no—
1193C4—42no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—41no—
1200C4—41no—
1201C4—41no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4—81no—
1214C4—81no—
1215C4#349511yescharacteristic
1216C4#350511yescharacteristic
1217C4#353811yescharacteristic
1218C4#356411yescharacteristic
1219C2—42no—
1220C2—81no—
1221C2—82no—
1222C2—161no—
1223C2#4393511yescharacteristic
1224C2#6126711yescharacteristic
1225C2#6128511yescharacteristic
1226C2#6201411yescharacteristic
1227C2#6203311yescharacteristic
1228C2#6215611yescharacteristic
1229C2#6217611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45178C2semidirect
3. #32487C2semidirect
4. #32473C2semidirect
5. #32394C2semidirect
6. #32368C2semidirect
7. #32282C2semidirect
8. #32225C2semidirect
9. #31618C2semidirect
10. #30786C2semidirect
12. #27619C2semidirect
13. #27594C2semidirect
14. #27376C2semidirect
15. #27170C2semidirect
16. #27157C2semidirect
17. #27031C2semidirect
18. #26366C2semidirect
19. #26090C2semidirect
20. #26063C2semidirect
21. #26016C2semidirect
22. #25976C2semidirect
23. #25458C2semidirect
24. #24950C2semidirect
26. #24592C2semidirect
27. #23612C2semidirect
28. #22662C2semidirect
29. #22574C2semidirect
30. #22068C2semidirect
31. #21967C2semidirect
32. C2×#499C22semidirect
36. C2×#428C22semidirect
53. #2552C22semidirect
57. #2509C22semidirect
59. #2506C22semidirect
61. #2497C22semidirect
62. #2495C22semidirect
69. #2441C22semidirect
74. #2370C22semidirect
79. #2347C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2101C22semidirect
89. #2099C22semidirect
94. #2088C22semidirect
95. #2087C22semidirect
96. #2085C22semidirect
97. #2084C22semidirect
98. #2083C22semidirect
99. #2083C22semidirect
100. #2083C22semidirect
101. #2075C22semidirect
102. #2075C22semidirect
118. #2059C22semidirect
119. #2059C22semidirect
120. #2059C22semidirect
126. #1989C22semidirect
127. #1949C22semidirect
128. #1949C22semidirect
129. #1949C22semidirect
130. #1949C22semidirect
131. #1949C22semidirect
132. #1948C22semidirect
133. #1948C22semidirect
134. #1948C22semidirect
135. #1948C22semidirect
136. #1948C22semidirect
137. #1948C22semidirect
138. #1941C22semidirect
139. #1941C22semidirect
140. #1939C22semidirect
141. #1939C22semidirect
154. #1923C22semidirect
155. #1923C22semidirect
156. #1921C22semidirect
157. #1921C22semidirect
158. #1921C22semidirect
159. #1920C22semidirect
160. #1920C22semidirect
161. #1919C22semidirect
162. #1918C22semidirect
163. #1918C22semidirect
164. #1917C22semidirect
165. #1917C22semidirect
178. #1854C22semidirect
179. #1853C22semidirect
180. #1853C22semidirect
182. #1851C22semidirect
183. #1851C22semidirect
184. #1847C22semidirect
185. #1844C22semidirect
187. #1824C22semidirect
192. #1809C22semidirect
198. #1776C22semidirect

Maximal subgroups

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

subgroupindex
#451782
#450192
#324872
#324732
#323942
#323682
#322822
#322252
#316182
#307862
#281072
#276192
#275942
#273762
#271702
#271572
#270312
#263662
#260902
#260632
#260162
#259762
#254582
#249502
#248862
#245922
#236122
#226622
#225742
#220682
#219672