Finite Group Databasebeta

← #7592100

Subgroups — #7592100

Order 512.

1425 conjugacy classes of subgroups.

The subgroup lattice has 1225 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45253C211yesmaximal, characteristic, complemented
2#45019C211yesmaximal, characteristic
3#32389C211yesmaximal, characteristic, complemented
4#32349C211yesmaximal, characteristic, complemented
5#32282C211yesmaximal, characteristic, complemented
6#31080C211yesmaximal, characteristic, complemented
7#28854C211yesmaximal, characteristic, complemented
8#28780C211yesmaximal, characteristic, complemented
9#28097C211yesmaximal, characteristic
10#28085C211yesmaximal, characteristic, complemented
11#28049C211yesmaximal, characteristic, complemented
12#28043C211yesmaximal, characteristic, complemented
13#27743C211yesmaximal, characteristic, complemented
14#27717C211yesmaximal, characteristic, complemented
15#27622C211yesmaximal, characteristic, complemented
16#27594C211yesmaximal, characteristic, complemented
17#27365C211yesmaximal, characteristic, complemented
18#27333C211yesmaximal, characteristic, complemented
19#27136C211yesmaximal, characteristic, complemented
20#27096C211yesmaximal, characteristic, complemented
21#26014C211yesmaximal, characteristic, complemented
22#25968C211yesmaximal, characteristic, complemented
23#24956C211yesmaximal, characteristic, complemented
24#24882C211yesmaximal, characteristic
25#23072C211yesmaximal, characteristic, complemented
26#22938C211yesmaximal, characteristic, complemented
27#22706C211yesmaximal, characteristic, complemented
28#22562C211yesmaximal, characteristic, complemented
29#21567C211yesmaximal, characteristic, complemented
30#21091C211yesmaximal, characteristic, complemented
31#20820C211yesmaximal, characteristic, complemented
32C2×#480C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×C8×D4C2211yescharacteristic
35C2×#418C2211yescharacteristic
36C22×#102C2211yescharacteristic
37C2×#405C2211yescharacteristic
38#2796—21no—
39#2794—21no—
40#2771—21no—
41#2767—21no—
42#2743—21no—
43#2740—21no—
44#2735—21no—
45#2697—21no—
46#2609—21no—
47#2602—21no—
48#2575—21no—
49#2571C2211yescharacteristic, complemented
50#2566C2211yescharacteristic
51#2513C2211yescharacteristic
52#2513C2211yescharacteristic
53#2509C2211yescharacteristic, complemented
54#2506C2211yescharacteristic, complemented
55#2501C2211yescharacteristic
56#2497C2211yescharacteristic, complemented
57#2497C2211yescharacteristic, complemented
58#2490C2211yescharacteristic
59#2487C2211yescharacteristic
60#2482—21no—
61#2475—21no—
62#2471—21no—
63#2442C2211yescharacteristic, complemented
64#2441—21no—
65#2441C2211yescharacteristic
66#2441C2211yescharacteristic
67#2420C2211yescharacteristic
68#2418—21no—
69#2408C2211yescharacteristic
70#2395C2211yescharacteristic
71#2370C2211yescharacteristic, complemented
72#2361C2211yescharacteristic
73#2354C2211yescharacteristic
74#2352C2211yescharacteristic
75#2352C2211yescharacteristic
76#2344C2211yescharacteristic
77#2344C2211yescharacteristic, complemented
78D4×C22⋊C4C2211yescharacteristic
79#2317C2211yescharacteristic
80#2314C2211yescharacteristic
81#2314C2211yescharacteristic
82#2309C2211yescharacteristic
83#2101C2211yescharacteristic, complemented
84#2100C2211yescharacteristic, complemented
85#2100C2211yescharacteristic, complemented
86#2099C2211yescharacteristic, complemented
87#2094C2211yescharacteristic
88#2093C2211yescharacteristic
89#2093C2211yescharacteristic
90#2092C2211yescharacteristic
91#2088C2211yescharacteristic, complemented
92#2086C2211yescharacteristic, complemented
93#2085C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2084C2211yescharacteristic, complemented
97#2084C2211yescharacteristic, complemented
98#2076C2211yescharacteristic, complemented
99#2076C2211yescharacteristic, complemented
100#2073C2211yescharacteristic
101#2073C2211yescharacteristic
102#2073C2211yescharacteristic
103#2065C2211yescharacteristic
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2059C2211yescharacteristic, complemented
108#2059C2211yescharacteristic, complemented
109#2059C2211yescharacteristic, complemented
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2025C2211yescharacteristic
115#1992C2211yescharacteristic, complemented
116#1992C2211yescharacteristic, complemented
117#1989C2211yescharacteristic, complemented
118#1949C2211yescharacteristic, complemented
119#1949C2211yescharacteristic, complemented
120#1948C2211yescharacteristic, complemented
121#1943C2211yescharacteristic, complemented
122#1943C2211yescharacteristic, complemented
123#1936C2211yescharacteristic
124#1936C2211yescharacteristic
125#1936C2211yescharacteristic
126#1936C2211yescharacteristic
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1934C2211yescharacteristic
130#1934C2211yescharacteristic
131#1934C2211yescharacteristic
132#1934C2211yescharacteristic
133#1934C2211yescharacteristic
134#1934C2211yescharacteristic
135#1926C2211yescharacteristic
136#1926C2211yescharacteristic
137#1926C2211yescharacteristic
138#1926C2211yescharacteristic
139#1926C2211yescharacteristic
140#1925C2211yescharacteristic
141#1925C2211yescharacteristic
142#1925C2211yescharacteristic
143#1923C2211yescharacteristic, complemented
144#1923C2211yescharacteristic, complemented
145#1921C2211yescharacteristic, complemented
146#1921C2211yescharacteristic, complemented
147#1920C2211yescharacteristic, complemented
148#1919C2211yescharacteristic, complemented
149#1919C2211yescharacteristic, complemented
150#1918C2211yescharacteristic, complemented
151#1918C2211yescharacteristic, complemented
152#1918C2211yescharacteristic, complemented
153#1916C2211yescharacteristic, complemented
154#1916C2211yescharacteristic, complemented
155#1893C2211yescharacteristic
156#1893C2211yescharacteristic
157#1874C2211yescharacteristic
158#1870C2211yescharacteristic
159#1864C2211yescharacteristic
160#1864C2211yescharacteristic
161#1864C2211yescharacteristic
162#1862C2211yescharacteristic
163#1854C2211yescharacteristic
164#1854C2211yescharacteristic
165#1854C2211yescharacteristic
166#1854C2211yescharacteristic
167#1853C2211yescharacteristic, complemented
168#1853C2211yescharacteristic, complemented
169#1853C2211yescharacteristic, complemented
170#1851C2211yescharacteristic
171#1846C2211yescharacteristic, complemented
172#1844C2211yescharacteristic, complemented
173#1836C2211yescharacteristic, complemented
174#1836C2211yescharacteristic, complemented
175#1835C2211yescharacteristic, complemented
176#1824C2211yescharacteristic
177#1823C2211yescharacteristic
178#1823C2211yescharacteristic, complemented
179#1818C2211yescharacteristic
180#1809C2211yescharacteristic
181#1809C2211yescharacteristic
182#1808C2211yescharacteristic, complemented
183#1807C2211yescharacteristic
184#1807C2211yescharacteristic
185#1802C2211yescharacteristic
186#1786C2211yescharacteristic
187#1786C2211yescharacteristic
188#1776C2211yescharacteristic, complemented
189#1776C2211yescharacteristic, complemented
190C4×#106C2211yescharacteristic, complemented
191C4×#106C2211yescharacteristic, complemented
192C4×#106C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194#1771C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1752C2211yescharacteristic
198#1752C2211yescharacteristic, complemented
199#1752C2211yescharacteristic, complemented
200#1736C2211yescharacteristic
201#1735C2211yescharacteristic
202C2×#340C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×#125—21no—
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#123—21no—
211C2×#123—21no—
212C2×#121C2311yescharacteristic
213C2×#121C2311yescharacteristic
214C2×#120—21no—
215C2×C4×D4—21no—
216C2×C4×D4C2311yescharacteristic
217C2×C4×D4C2311yescharacteristic
218C2×C4×D4C2311yescharacteristic
219C2×#117—21no—
220C2×#117—21no—
221C2×#117—21no—
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C4⋊C4C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C22⋊C4—21no—
229#480—24no—
230#478—24no—
231C8×D4—24no—
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×#106C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×C4⋊C8C2311yescharacteristic
250C2×C4⋊C8C2311yescharacteristic
251#418—24no—
252C2×#102—24no—
253C2×#102C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274#405—24no—
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400D411yescharacteristic
292#399—21no—
293#399—21no—
294#399—21no—
295#399—21no—
296#399—21no—
297#399D411yescharacteristic
298#398—21no—
299#398—21no—
300#398D411yescharacteristic
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397D411yescharacteristic
308#397D411yescharacteristic
309#397D411yescharacteristic
310#396—21no—
311#396—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#394D411yescharacteristic
320#394D411yescharacteristic
321#392—21no—
322#390—21no—
323#390—21no—
324#390—21no—
325#390C2311yescharacteristic
326#390C2311yescharacteristic
327#390C2311yescharacteristic
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#389—21no—
334#389—21no—
335#389—21no—
336#389—21no—
337#389—21no—
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388—21no—
362#388—21no—
363#388—21no—
364#388—21no—
365#388—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#386—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#384—21no—
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#382—21no—
404#382—21no—
405#382C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#381—21no—
410#381—21no—
411#381—21no—
412#380—21no—
413#380—21no—
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#379—21no—
423#379—21no—
424#379—21no—
425#379—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
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#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C25—21no—
485C22×D4—22no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—21no—
489C22×D4—22no—
490C22×D4—22no—
491C22×D4—41no—
492C22×D4—41no—
493C22×D4—41no—
494C22×D4C2×D411yescharacteristic
495C22×D4C2411yescharacteristic
496C22×D4C2411yescharacteristic
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2411yescharacteristic
503C23×C4C2411yescharacteristic
504C2×M16—22no—
505C2×M16—22no—
506C2×M16—41no—
507C22×C8—22no—
508C22×C8—41no—
509C22×C8—41no—
510C22×C8—41no—
511C22×C8—41no—
512C22×C8#4114yes—
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521#125—22no—
522#125—41no—
523#125—41no—
524#125—41no—
525#125—82no—
526#123—82no—
527#123—82no—
528#121—22no—
529#121—41no—
530#121—41no—
531#121—41no—
532#120—82no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536C4×D4—41no—
537C4×D4—41no—
538C4×D4—41no—
539C4×D4—82no—
540#117—22no—
541#117—22no—
542#117—22no—
543#117—41no—
544#117—41no—
545#117—41no—
546#117—82no—
547#117—82no—
548#117—82no—
549C2×C4⋊C4—22no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—22no—
552C2×C4⋊C4—21no—
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—41no—
580C2×C4⋊C4—41no—
581C2×C4⋊C4—41no—
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⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
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—82no—
634C2×C22⋊C4C2×D411yescharacteristic
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×C22⋊C4C2×D411yescharacteristic
642C2×C22⋊C4C2×D411yescharacteristic
643C2×C22⋊C4C2×D411yescharacteristic
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
659#107—22no—
660#107—22no—
661#107—22no—
662#107—41no—
663#107—41no—
664#107—41no—
665#106—22no—
666#106—41no—
667#106—41no—
668#106—41no—
669#106—41no—
670#106—41no—
671#106—41no—
672#106—41no—
673#106—41no—
674#106—41no—
675C4⋊C8—22no—
676C4⋊C8—22no—
677C4⋊C8—41no—
678#102—22no—
679#102—22no—
680#102—22no—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—22no—
686#102—22no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102#4114yes—
694C22⋊C8—22no—
695C22⋊C8—22no—
696C22⋊C8—22no—
697C22⋊C8—22no—
698C22⋊C8—41no—
699#97—22no—
700#97—22no—
701#97—41no—
702#97—41no—
703C4×C8—22no—
704C4×C8—22no—
705C4×C8—22no—
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#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752C24—21no—
753C24—21no—
754C24—42no—
755C24—42no—
756C24—81no—
757C24—81no—
758C24—81no—
759C24—81no—
760C24—81no—
761C24C22×D411yescharacteristic
762C24C22×D411yescharacteristic
763C2×D4—22no—
764C2×D4—22no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—44no—
777C2×D4—44no—
778C2×D4—41no—
779C2×D4—42no—
780C2×D4—42no—
781C2×D4—42no—
782C2×D4—42no—
783C2×D4—42no—
784C2×D4—82no—
785C2×D4—82no—
786C2×D4—81no—
787C2×D4—81no—
788C2×D4—81no—
789C2×D4—81no—
790C2×D4C2×#4112yes—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
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—42no—
816C22×C4—42no—
817C22×C4—42no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—81no—
822C22×C4—81no—
823C22×C4—81no—
824C22×C4—81no—
825C22×C4—81no—
826C22×C4—81no—
827C22×C4—81no—
828C22×C4—81no—
829C22×C4—81no—
830C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
843C22×C42−1+412yes—
844C22×C4C2511yescharacteristic
845M16—44no—
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×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—44no—
868C2×C8—82no—
869C2×C8C2×#4112yes—
870C2×C8C2×#4112yes—
871C2×C8C2×#4112yes—
872C4⋊C4—22no—
873C4⋊C4—22no—
874C4⋊C4—22no—
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—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—41no—
903C4⋊C4—41no—
904C4⋊C4—41no—
905C4⋊C4—41no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
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⋊C4C2×#4112yes—
934C22⋊C4—22no—
935C22⋊C4—22no—
936C22⋊C4—22no—
937C22⋊C4—22no—
938C22⋊C4—22no—
939C22⋊C4—22no—
940C22⋊C4—41no—
941C22⋊C4—41no—
942C22⋊C4—41no—
943C22⋊C4—41no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
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—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C22⋊C4—81no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—42no—
985C42—42no—
986C42—81no—
987C42—81no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C42—81no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—22no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—84no—
1021C23—84no—
1022C23—162no—
1023C23—162no—
1024C23—162no—
1025C23—162no—
1026C23—162no—
1027C23#54712yes—
1028C23#57712yes—
1029C23C23×D411yescharacteristic
1030D4—22no—
1031D4—22no—
1032D4—44no—
1033D4—41no—
1034D4—41no—
1035D4—41no—
1036D4—41no—
1037D4—41no—
1038D4—41no—
1039D4—84no—
1040D4—84no—
1041D4—162no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
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—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—22no—
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—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—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—84no—
1128C2×C4—84no—
1129C2×C4—84no—
1130C2×C4—162no—
1131C2×C4—162no—
1132C2×C4#54712yes—
1133C2×C4C22×#4111yescharacteristic
1134C2×C4C22×#4111yescharacteristic
1135C2×C4C2×2−1+411yescharacteristic
1136C2×C4#58511yescharacteristic
1137C2×C4#58511yescharacteristic
1138C2×C4#58511yescharacteristic
1139C8—22no—
1140C8—22no—
1141C8—22no—
1142C8—41no—
1143C8—41no—
1144C8—41no—
1145C8—41no—
1146C8—41no—
1147C22—22no—
1148C22—22no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—41no—
1154C22—41no—
1155C22—41no—
1156C22—41no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22—41no—
1161C22—42no—
1162C22—42no—
1163C22—42no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22—81no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—168no—
1176C22C2×#54711yescharacteristic
1177C22D4×#4111yescharacteristic
1178C22#350011yescharacteristic
1179C22C2×#57711yescharacteristic
1180C22#358411yescharacteristic
1181C22#358511yescharacteristic
1182C22#358511yescharacteristic
1183C4—22no—
1184C4—41no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—42no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—81no—
1197C4—81no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4#347511yescharacteristic
1210C4#349111yescharacteristic
1211C4#349511yescharacteristic
1212C4#356411yescharacteristic
1213C2—42no—
1214C2—42no—
1215C2—82no—
1216C2—161no—
1217C2#5931011yescharacteristic
1218C2#6126311yescharacteristic
1219C2#6129311yescharacteristic
1220C2#6152211yescharacteristic
1221C2#6154711yescharacteristic
1222C2#6259611yescharacteristic
1223C2#6261311yescharacteristic
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. #45253C2semidirect
3. #32389C2semidirect
4. #32349C2semidirect
5. #32282C2semidirect
6. #31080C2semidirect
7. #28854C2semidirect
8. #28780C2semidirect
10. #28085C2semidirect
11. #28049C2semidirect
12. #28043C2semidirect
13. #27743C2semidirect
14. #27717C2semidirect
15. #27622C2semidirect
16. #27594C2semidirect
17. #27365C2semidirect
18. #27333C2semidirect
19. #27136C2semidirect
20. #27096C2semidirect
21. #26014C2semidirect
22. #25968C2semidirect
23. #24956C2semidirect
25. #23072C2semidirect
26. #22938C2semidirect
27. #22706C2semidirect
28. #22562C2semidirect
29. #21567C2semidirect
30. #21091C2semidirect
31. #20820C2semidirect
49. #2571C22semidirect
53. #2509C22semidirect
54. #2506C22semidirect
56. #2497C22semidirect
57. #2497C22semidirect
63. #2442C22semidirect
71. #2370C22semidirect
77. #2344C22semidirect
83. #2101C22semidirect
84. #2100C22semidirect
85. #2100C22semidirect
86. #2099C22semidirect
91. #2088C22semidirect
92. #2086C22semidirect
93. #2085C22semidirect
94. #2085C22semidirect
95. #2085C22semidirect
96. #2084C22semidirect
97. #2084C22semidirect
98. #2076C22semidirect
99. #2076C22semidirect
107. #2059C22semidirect
108. #2059C22semidirect
109. #2059C22semidirect
115. #1992C22semidirect
116. #1992C22semidirect
117. #1989C22semidirect
118. #1949C22semidirect
119. #1949C22semidirect
120. #1948C22semidirect
121. #1943C22semidirect
122. #1943C22semidirect
143. #1923C22semidirect
144. #1923C22semidirect
145. #1921C22semidirect
146. #1921C22semidirect
147. #1920C22semidirect
148. #1919C22semidirect
149. #1919C22semidirect
150. #1918C22semidirect
151. #1918C22semidirect
152. #1918C22semidirect
153. #1916C22semidirect
154. #1916C22semidirect
167. #1853C22semidirect
168. #1853C22semidirect
169. #1853C22semidirect
171. #1846C22semidirect
172. #1844C22semidirect
173. #1836C22semidirect
174. #1836C22semidirect
175. #1835C22semidirect
178. #1823C22semidirect
182. #1808C22semidirect
188. #1776C22semidirect
189. #1776C22semidirect
190. C4×#106C22semidirect
191. C4×#106C22semidirect
192. C4×#106C22semidirect
193. #1771C22semidirect
194. #1771C22semidirect
198. #1752C22semidirect
199. #1752C22semidirect
202. C2×#340C22semidirect

Maximal subgroups

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

subgroupindex
#452532
#450192
#323892
#323492
#322822
#310802
#288542
#287802
#280972
#280852
#280492
#280432
#277432
#277172
#276222
#275942
#273652
#273332
#271362
#270962
#260142
#259682
#249562
#248822
#230722
#229382
#227062
#225622
#215672
#210912
#208202