Finite Group Databasebeta

← #6773778

Subgroups — #6773778

Order 512.

1570 conjugacy classes of subgroups.

The subgroup lattice has 1249 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36293C211yesmaximal, characteristic
2#34938C211yesmaximal, characteristic, complemented
3#33099C211yesmaximal, characteristic, complemented
4#32394C211yesmaximal, characteristic, complemented
5#32242C211yesmaximal, characteristic, complemented
6#31592C211yesmaximal, characteristic, complemented
7#31590C211yesmaximal, characteristic, complemented
8#31474C211yesmaximal, characteristic, complemented
9#30962C211yesmaximal, characteristic, complemented
10#30824C211yesmaximal, characteristic, complemented
11#30821C211yesmaximal, characteristic, complemented
12#30150C211yesmaximal, characteristic, complemented
13#30064C211yesmaximal, characteristic, complemented
14#29518C211yesmaximal, characteristic, complemented
15#29389C211yesmaximal, characteristic, complemented
16#28775C211yesmaximal, characteristic, complemented
17#28658C211yesmaximal, characteristic, complemented
18#28203C211yesmaximal, characteristic, complemented
19#27858C211yesmaximal, characteristic, complemented
20#27585C211yesmaximal, characteristic
21#27262C211yesmaximal, characteristic
22#27262C211yesmaximal, characteristic
23#26412C211yesmaximal, characteristic, complemented
24#26340C211yesmaximal, characteristic, complemented
25#26068C211yesmaximal, characteristic, complemented
26#25950C211yesmaximal, characteristic
27#25950C211yesmaximal, characteristic
28#22591C211yesmaximal, characteristic, complemented
29#22223C211yesmaximal, characteristic, complemented
30#22116C211yesmaximal, characteristic, complemented
31C2×#1926C211yesmaximal, characteristic
32C2×#533—21no—
33C2×#501C2211yescharacteristic, complemented
34C2×#489C2211yescharacteristic
35C2×#489C2211yescharacteristic
36C2×#475C2211yescharacteristic, complemented
37C2×#474C2211yescharacteristic
38C2×#474C2211yescharacteristic
39C22×#106C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C22×#102C2211yescharacteristic
42#2861C2211yescharacteristic
43#2860C2211yescharacteristic
44#2855C2211yescharacteristic
45#2597—21no—
46#2552C2211yescharacteristic, complemented
47#2552C2211yescharacteristic, complemented
48#2551C2211yescharacteristic, complemented
49#2551C2211yescharacteristic, complemented
50#2550—21no—
51#2550—21no—
52#2549—21no—
53#2549—21no—
54#2531—21no—
55#2526—21no—
56#2513C2211yescharacteristic
57#2482—21no—
58#2480—21no—
59#2479—21no—
60#2454C2211yescharacteristic
61#2448C2211yescharacteristic
62#2447C2211yescharacteristic
63#2442C2211yescharacteristic
64#2440C2211yescharacteristic
65#2440C2211yescharacteristic
66#2440C2211yescharacteristic
67#2440C2211yescharacteristic
68#2435C2211yescharacteristic
69#2399—21no—
70#2399—21no—
71#2360C2211yescharacteristic
72#2342—21no—
73#2342—21no—
74D4×C22⋊C4C2211yescharacteristic
75C4×C4⋊Q8C2211yescharacteristic, complemented
76C4×C4⋊Q8C2211yescharacteristic, complemented
77C4×C4⋊Q8C2211yescharacteristic, complemented
78C4×C4⋊Q8C2211yescharacteristic, complemented
79C4×#124C2211yescharacteristic
80#2296—21no—
81#2293C2211yescharacteristic
82C2×#390C2211yescharacteristic
83#2285C2211yescharacteristic
84C4×#117C2211yescharacteristic
85C2×C4×C4⋊C4C2211yescharacteristic
86#2100C2211yescharacteristic, complemented
87#2099C2211yescharacteristic, complemented
88#2096C2211yescharacteristic, complemented
89#2095C2211yescharacteristic, complemented
90#2094C2211yescharacteristic
91#2094C2211yescharacteristic
92#2093C2211yescharacteristic
93#2093C2211yescharacteristic
94#2088C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2084C2211yescharacteristic, complemented
99#2083C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2072C2211yescharacteristic, complemented
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic
105#2071C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic
108#2067C2211yescharacteristic
109#2067C2211yescharacteristic
110#2066C2211yescharacteristic, complemented
111#2066C2211yescharacteristic, complemented
112#2059C2211yescharacteristic, complemented
113#2059C2211yescharacteristic, complemented
114#2058C2211yescharacteristic, complemented
115#2058C2211yescharacteristic, complemented
116#2057C2211yescharacteristic, complemented
117#2042C2211yescharacteristic
118#2042C2211yescharacteristic
119#2042C2211yescharacteristic
120#2042C2211yescharacteristic
121#2024C2211yescharacteristic, complemented
122#2023C2211yescharacteristic
123#2023C2211yescharacteristic
124#2023C2211yescharacteristic
125#2023C2211yescharacteristic
126#1993C2211yescharacteristic, complemented
127#1992C2211yescharacteristic, complemented
128#1988C2211yescharacteristic, complemented
129#1959C2211yescharacteristic
130#1959C2211yescharacteristic
131#1948C2211yescharacteristic, complemented
132#1944C2211yescharacteristic, complemented
133#1944C2211yescharacteristic, complemented
134#1943C2211yescharacteristic, complemented
135#1943C2211yescharacteristic, complemented
136#1936C2211yescharacteristic
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1928C2211yescharacteristic, complemented
141#1928C2211yescharacteristic, complemented
142#1928C2211yescharacteristic, complemented
143#1928C2211yescharacteristic, complemented
144#1928C2211yescharacteristic, complemented
145#1928C2211yescharacteristic, complemented
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic
150#1926C2211yescharacteristic
151#1926C2211yescharacteristic
152#1926C2211yescharacteristic
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic
157#1926C2211yescharacteristic
158#1921C2211yescharacteristic, complemented
159#1921C2211yescharacteristic, complemented
160#1921C2211yescharacteristic, complemented
161#1921C2211yescharacteristic, complemented
162#1921C2211yescharacteristic, complemented
163#1921C2211yescharacteristic, complemented
164#1919C2211yescharacteristic, complemented
165#1919C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1917C2211yescharacteristic, complemented
168#1917C2211yescharacteristic, complemented
169#1917C2211yescharacteristic, complemented
170#1892C2211yescharacteristic
171#1892C2211yescharacteristic
172#1872C2211yescharacteristic
173#1872C2211yescharacteristic
174#1865C2211yescharacteristic, complemented
175#1865C2211yescharacteristic, complemented
176#1862C2211yescharacteristic
177#1862C2211yescharacteristic
178#1862C2211yescharacteristic
179#1862C2211yescharacteristic
180#1853C2211yescharacteristic
181#1853C2211yescharacteristic
182#1852C2211yescharacteristic
183#1852C2211yescharacteristic
184#1850C2211yescharacteristic
185#1850C2211yescharacteristic
186#1847C2211yescharacteristic, complemented
187#1839C2211yescharacteristic, complemented
188#1831C2211yescharacteristic, complemented
189#1817C2211yescharacteristic
190#1808C2211yescharacteristic
191#1808C2211yescharacteristic
192#1803C2211yescharacteristic, complemented
193#1802C2211yescharacteristic
194#1802C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1767C2211yescharacteristic, complemented
198#1752C2211yescharacteristic
199#1752C2211yescharacteristic
200#1745C2211yescharacteristic, complemented
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206#533—48no—
207C2×C4⋊Q8—21no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#126—21no—
214C2×#125—21no—
215C2×#125—21no—
216C2×#125C2311yescharacteristic
217C2×#124C2311yescharacteristic
218C2×#124C2311yescharacteristic
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8C2311yescharacteristic
224C2×C4×Q8—21no—
225C2×C4×Q8—21no—
226C2×C4×Q8—21no—
227C2×C4×Q8—21no—
228C2×C4×Q8C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117—21no—
232C2×#117—21no—
233C2×#117D411yescharacteristic
234C2×#117D411yescharacteristic
235C22×C4⋊C4C2311yescharacteristic
236C22×C4⋊C4C2311yescharacteristic
237C22×C4⋊C4C2311yescharacteristic
238C22×C22⋊C4—21no—
239C22×C22⋊C4—21no—
240C22×C22⋊C4—21no—
241C22×C42—21no—
242C22×C42C2311yescharacteristic
243#501—42no—
244#489—24no—
245#489—42no—
246#475—42no—
247#474—24no—
248#474—42no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#106—42no—
258C2×#106C2311yescharacteristic
259C2×#106C2311yescharacteristic
260C2×#106C2311yescharacteristic
261C2×#106C2311yescharacteristic
262C2×#106C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×#103C2311yescharacteristic
271C2×#103C2311yescharacteristic
272C2×#103C2311yescharacteristic
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#102—24no—
279C2×#102—42no—
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×#97C2311yescharacteristic
300C2×#97C2311yescharacteristic
301C2×#97C2311yescharacteristic
302#400—21no—
303#399—21no—
304#399—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#396—21no—
320#395—21no—
321#395—21no—
322#395—21no—
323#395—21no—
324#395—21no—
325#395—21no—
326#395—21no—
327#395—21no—
328#394—21no—
329#394—21no—
330#391—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391C2311yescharacteristic
335#391C2311yescharacteristic
336#391C2311yescharacteristic
337#390—21no—
338#390—21no—
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
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#388—21no—
382#388—21no—
383#388—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#386—21no—
388#386—21no—
389#385—21no—
390#385—21no—
391#385—21no—
392#385—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#384C2311yescharacteristic
399#384C2311yescharacteristic
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#382—21no—
405#382C2311yescharacteristic
406#381—21no—
407#381—21no—
408#380—21no—
409#380—21no—
410#380—21no—
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414#379—21no—
415#379—21no—
416#379—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—21no—
424C4×C4⋊C4D411yescharacteristic
425C4×C4⋊C4D411yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
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×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4D411yescharacteristic
440C4×C22⋊C4D411yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442C4×C22⋊C4C2311yescharacteristic
443#376D411yescharacteristic
444#376D411yescharacteristic
445C2×#95—21no—
446C43C2311yescharacteristic
447C43C2311yescharacteristic
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#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488C25—21no—
489C22×Q8—21no—
490C22×Q8—21no—
491C22×Q8—21no—
492C22×Q8—21no—
493C22×Q8C2411yescharacteristic
494C22×D4—22no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C2411yescharacteristic
502C22×D4C2411yescharacteristic
503C23×C4—21no—
504C23×C4—21no—
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C2×D411yescharacteristic
509C23×C4C2×D411yescharacteristic
510C23×C4C2411yescharacteristic
511C22×C8—22no—
512C22×C8—22no—
513C22×C8—22no—
514C22×C8—41no—
515C22×C8—41no—
516C22×C8—41no—
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C4⋊Q8—22no—
526C4⋊Q8—22no—
527C4⋊Q8—22no—
528C4⋊Q8—22no—
529C4⋊Q8—41no—
530C4⋊Q8—41no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533C4⋊Q8—44no—
534C4⋊Q8—44no—
535#126—82no—
536#125—41no—
537#125—41no—
538#125—44no—
539#125—44no—
540#124—22no—
541#124—41no—
542#124—41no—
543#124—41no—
544C22⋊Q8—22no—
545C22⋊Q8—22no—
546C22⋊Q8—44no—
547C22⋊Q8—44no—
548C22⋊Q8—44no—
549C22⋊Q8—44no—
550C4×Q8—44no—
551C4×Q8—44no—
552C4×Q8—44no—
553C4×Q8—44no—
554C4×Q8—41no—
555C4×Q8—41no—
556C4×D4—22no—
557C4×D4—41no—
558C4×D4—41no—
559C4×D4—41no—
560#117—24no—
561#117—24no—
562#117—44no—
563#117—82no—
564C2×C4⋊C4—22no—
565C2×C4⋊C4—22no—
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⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4—41no—
604C2×C4⋊C4—41no—
605C2×C4⋊C4—41no—
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
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—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—44no—
650C2×C22⋊C4—44no—
651C2×C22⋊C4—82no—
652C2×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C42—22no—
657C2×C42—22no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42—21no—
665C2×C42—21no—
666C2×C42—44no—
667C2×C42C2×D411yescharacteristic
668C2×C42C2×D411yescharacteristic
669C2×C42C2×D411yescharacteristic
670C2×C42C2×D411yescharacteristic
671C2×C42C2×D411yescharacteristic
672C2×C42C2×D411yescharacteristic
673C2×C42C2×D411yescharacteristic
674C2×C42C2×D411yescharacteristic
675C2×C42C2×D411yescharacteristic
676C2×C42C2×D411yescharacteristic
677C2×C42C2411yescharacteristic
678C2×C42C2411yescharacteristic
679C2×C42C2411yescharacteristic
680C2×C42C2411yescharacteristic
681C2×C42C2411yescharacteristic
682C2×C42C2411yescharacteristic
683#107—22no—
684#107—22no—
685#107—22no—
686#107—41no—
687#107—41no—
688#107—41no—
689#107—41no—
690#107—41no—
691#106—22no—
692#106—22no—
693#106—41no—
694#106—41no—
695#106—41no—
696#106—41no—
697#106—41no—
698#106—41no—
699C4⋊C8—22no—
700C4⋊C8—41no—
701C4⋊C8—41no—
702C4⋊C8—41no—
703#103—22no—
704#103—22no—
705#103—22no—
706#103—41no—
707#103—41no—
708#103—41no—
709#103—41no—
710#103—41no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102#4114yes—
727C22⋊C8—22no—
728C22⋊C8—22no—
729#97—22no—
730#97—41no—
731#97—41no—
732#97—41no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772C24—21no—
773C24—21no—
774C24—42no—
775C24—42no—
776C24—42no—
777C24—42no—
778C24—81no—
779C24—81no—
780C24—81no—
781C24C22×D411yescharacteristic
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—42no—
789C2×Q8—42no—
790C2×Q8—42no—
791C2×Q8—42no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8—42no—
795C2×Q8—42no—
796C2×Q8—81no—
797C2×Q8—81no—
798C2×Q8—81no—
799C2×Q8—81no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—44no—
812C2×D4—44no—
813C2×D4—42no—
814C2×D4—42no—
815C2×D4—82no—
816C2×D4—82no—
817C2×D4—81no—
818C2×D4C2×#4112yes—
819C22×C4—22no—
820C22×C4—22no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—22no—
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—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—41no—
841C22×C4—41no—
842C22×C4—42no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—42no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—42no—
849C22×C4—42no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4—81no—
856C22×C4—81no—
857C22×C4#13714yes—
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C22×D411yescharacteristic
869C22×C4C22×D411yescharacteristic
870C22×C4C22×D411yescharacteristic
871C22×C42−1+412yes—
872C22×C42−1+412yes—
873C22×C4C2511yescharacteristic
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×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—44no—
898C2×C8—82no—
899C2×C8C2×#4112yes—
900C4⋊C4—22no—
901C4⋊C4—22no—
902C4⋊C4—22no—
903C4⋊C4—22no—
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—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—42no—
929C4⋊C4—42no—
930C4⋊C4—42no—
931C4⋊C4—42no—
932C4⋊C4—42no—
933C4⋊C4—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—42no—
940C4⋊C4—42no—
941C4⋊C4—42no—
942C4⋊C4—42no—
943C4⋊C4—42no—
944C4⋊C4—42no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—42no—
948C4⋊C4—42no—
949C4⋊C4—42no—
950C4⋊C4—81no—
951C4⋊C4—81no—
952C4⋊C4—81no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4C2×#4112yes—
965C4⋊C4H(5,𝔽2)12yes—
966C22⋊C4—22no—
967C22⋊C4—22no—
968C22⋊C4—22no—
969C22⋊C4—42no—
970C22⋊C4—42no—
971C22⋊C4—42no—
972C22⋊C4—42no—
973C22⋊C4—42no—
974C22⋊C4—42no—
975C22⋊C4—42no—
976C22⋊C4—42no—
977C22⋊C4—42no—
978C22⋊C4—42no—
979C22⋊C4—42no—
980C22⋊C4—42no—
981C22⋊C4—42no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4AGL(1,ℤ/8)14yes—
996C42—22no—
997C42—22no—
998C42—22no—
999C42—22no—
1000C42—22no—
1001C42—22no—
1002C42—21no—
1003C42—21no—
1004C42—21no—
1005C42—21no—
1006C42—21no—
1007C42—21no—
1008C42—21no—
1009C42—21no—
1010C42—21no—
1011C42—21no—
1012C42—21no—
1013C42—21no—
1014C42—41no—
1015C42—41no—
1016C42—41no—
1017C42—41no—
1018C42—42no—
1019C42—42no—
1020C42—42no—
1021C42—42no—
1022C42—42no—
1023C42—42no—
1024C42—81no—
1025C42—81no—
1026C23—21no—
1027C23—21no—
1028C23—21no—
1029C23—21no—
1030C23—22no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—84no—
1045C23—84no—
1046C23—84no—
1047C23—84no—
1048C23—162no—
1049C23—162no—
1050C23—162no—
1051C23#53612yes—
1052C23C2×AGL(1,ℤ/8)12yes—
1053C23C2×#13712yes—
1054C23C23×D411yescharacteristic
1055Q8—41no—
1056Q8—41no—
1057Q8—41no—
1058Q8—41no—
1059Q8—84no—
1060Q8—84no—
1061Q8—84no—
1062Q8—84no—
1063D4—22no—
1064D4—22no—
1065D4—41no—
1066D4—41no—
1067D4—41no—
1068D4—41no—
1069D4—41no—
1070D4—41no—
1071D4—84no—
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—28no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—22no—
1084C2×C4—22no—
1085C2×C4—22no—
1086C2×C4—22no—
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—22no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—22no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
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—41no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—84no—
1154C2×C4—82no—
1155C2×C4—84no—
1156C2×C4—84no—
1157C2×C4—162no—
1158C2×C4—162no—
1159C2×C4#53612yes—
1160C2×C4C2×AGL(1,ℤ/8)12yes—
1161C2×C4C2×AGL(1,ℤ/8)12yes—
1162C2×C4C2×#13712yes—
1163C2×C4C2×#13712yes—
1164C2×C4C22×#4111yescharacteristic
1165C2×C4C2×H(5,𝔽2)11yescharacteristic
1166C2×C4C2×2−1+411yescharacteristic
1167C2×C4C2×2−1+411yescharacteristic
1168C2×C4#58511yescharacteristic
1169C2×C4#58511yescharacteristic
1170C8—22no—
1171C8—41no—
1172C8—41no—
1173C8—41no—
1174C8—41no—
1175C8—41no—
1176C8—41no—
1177C8—41no—
1178C22—22no—
1179C22—22no—
1180C22—22no—
1181C22—22no—
1182C22—22no—
1183C22—22no—
1184C22—42no—
1185C22—42no—
1186C22—42no—
1187C22—81no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22—81no—
1192C22—81no—
1193C22—81no—
1194C22—81no—
1195C22—81no—
1196C22—81no—
1197C22—81no—
1198C22—168no—
1199C22#323914yes—
1200C22C2×#53611yescharacteristic
1201C22D4×#4111yescharacteristic
1202C22#348811yescharacteristic
1203C22C22×AGL(1,ℤ/8)11yescharacteristic
1204C22C22×#13711yescharacteristic
1205C22#358411yescharacteristic
1206C22#358511yescharacteristic
1207C4—22no—
1208C4—22no—
1209C4—22no—
1210C4—22no—
1211C4—22no—
1212C4—41no—
1213C4—42no—
1214C4—41no—
1215C4—41no—
1216C4—41no—
1217C4—42no—
1218C4—41no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—81no—
1223C4—81no—
1224C4—81no—
1225C4—81no—
1226C4—81no—
1227C4—81no—
1228C4—81no—
1229C4—81no—
1230C4—81no—
1231C4—81no—
1232C4—81no—
1233C4—81no—
1234C4#349511yescharacteristic
1235C4#352011yescharacteristic
1236C4#356111yescharacteristic
1237C4#356411yescharacteristic
1238C2—24no—
1239C2—82no—
1240C2—161no—
1241C2#3837011yescharacteristic
1242C2C2×#323911yescharacteristic
1243C2#6087511yescharacteristic
1244C2#6143811yescharacteristic
1245C2#6145111yescharacteristic
1246C2#6196511yescharacteristic
1247C2#6198911yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D4C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#117 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34938C2semidirect
3. #33099C2semidirect
4. #32394C2semidirect
5. #32242C2semidirect
6. #31592C2semidirect
7. #31590C2semidirect
8. #31474C2semidirect
9. #30962C2semidirect
10. #30824C2semidirect
11. #30821C2semidirect
12. #30150C2semidirect
13. #30064C2semidirect
14. #29518C2semidirect
15. #29389C2semidirect
16. #28775C2semidirect
17. #28658C2semidirect
18. #28203C2semidirect
19. #27858C2semidirect
23. #26412C2semidirect
24. #26340C2semidirect
25. #26068C2semidirect
28. #22591C2semidirect
29. #22223C2semidirect
30. #22116C2semidirect
33. C2×#501C22semidirect
36. C2×#475C22semidirect
46. #2552C22semidirect
47. #2552C22semidirect
48. #2551C22semidirect
49. #2551C22semidirect
75. C4×C4⋊Q8C22semidirect
76. C4×C4⋊Q8C22semidirect
77. C4×C4⋊Q8C22semidirect
78. C4×C4⋊Q8C22semidirect
86. #2100C22semidirect
87. #2099C22semidirect
88. #2096C22semidirect
89. #2095C22semidirect
94. #2088C22semidirect
95. #2088C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
98. #2084C22semidirect
99. #2083C22semidirect
100. #2083C22semidirect
101. #2072C22semidirect
110. #2066C22semidirect
111. #2066C22semidirect
112. #2059C22semidirect
113. #2059C22semidirect
114. #2058C22semidirect
115. #2058C22semidirect
116. #2057C22semidirect
121. #2024C22semidirect
126. #1993C22semidirect
127. #1992C22semidirect
128. #1988C22semidirect
131. #1948C22semidirect
132. #1944C22semidirect
133. #1944C22semidirect
134. #1943C22semidirect
135. #1943C22semidirect
140. #1928C22semidirect
141. #1928C22semidirect
142. #1928C22semidirect
143. #1928C22semidirect
144. #1928C22semidirect
145. #1928C22semidirect
158. #1921C22semidirect
159. #1921C22semidirect
160. #1921C22semidirect
161. #1921C22semidirect
162. #1921C22semidirect
163. #1921C22semidirect
164. #1919C22semidirect
165. #1919C22semidirect
166. #1917C22semidirect
167. #1917C22semidirect
168. #1917C22semidirect
169. #1917C22semidirect
174. #1865C22semidirect
175. #1865C22semidirect
186. #1847C22semidirect
187. #1839C22semidirect
188. #1831C22semidirect
192. #1803C22semidirect
197. #1767C22semidirect
200. #1745C22semidirect

Maximal subgroups

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

subgroupindex
#362932
#349382
#330992
#323942
#322422
#315922
#315902
#314742
#309622
#308242
#308212
#301502
#300642
#295182
#293892
#287752
#286582
#282032
#278582
#275852
#272622
#264122
#263402
#260682
#259502
#225912
#222232
#221162
C2×#19262