Finite Group Databasebeta

← #6609208

Subgroups — #6609208

Order 512.

1491 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#36400C211yesmaximal, characteristic, complemented
2#36293C211yesmaximal, characteristic
3#33282C211yesmaximal, characteristic, complemented
4#33265C211yesmaximal, characteristic, complemented
5#33144C211yesmaximal, characteristic, complemented
6#29574C211yesmaximal, characteristic, complemented
7#29557C211yesmaximal, characteristic, complemented
8#29516C211yesmaximal, characteristic, complemented
9#29496C211yesmaximal, characteristic, complemented
10#29102C211yesmaximal, characteristic, complemented
11#29092C211yesmaximal, characteristic, complemented
12#29035C211yesmaximal, characteristic, complemented
13#29025C211yesmaximal, characteristic, complemented
14#28966C211yesmaximal, characteristic, complemented
15#28895C211yesmaximal, characteristic, complemented
16#28788C211yesmaximal, characteristic, complemented
17#28361C211yesmaximal, characteristic
18#28049C211yesmaximal, characteristic, complemented
19#27708C211yesmaximal, characteristic, complemented
20#27271C211yesmaximal, characteristic
21#26833C211yesmaximal, characteristic, complemented
22#24604C211yesmaximal, characteristic, complemented
23#24501C211yesmaximal, characteristic
24#23144C211yesmaximal, characteristic, complemented
25#22930C211yesmaximal, characteristic, complemented
26#22864C211yesmaximal, characteristic
27#22580C211yesmaximal, characteristic
28C4×#488C211yesmaximal, characteristic, complemented
29#21288C211yesmaximal, characteristic, complemented
30#21095C211yesmaximal, characteristic
31#20472C211yesmaximal, characteristic, complemented
32C2×#488C2211yescharacteristic
33C2×#485C2211yescharacteristic
34C2×#470C2211yescharacteristic
35C2×#450C2211yescharacteristic
36C2×#440C2211yescharacteristic
37C2×#431C2211yescharacteristic
38C2×#418C2211yescharacteristic
39C2×#418C2211yescharacteristic
40C2×C4×M16C2211yescharacteristic
41#2863C2211yescharacteristic, complemented
42#2861C2211yescharacteristic
43#2860C2211yescharacteristic
44#2859C2211yescharacteristic, complemented
45#2855C2211yescharacteristic
46#2855C2211yescharacteristic
47#2611—21no—
48#2597—21no—
49#2575—21no—
50#2573—21no—
51#2533—21no—
52#2531—21no—
53#2526—21no—
54#2524—21no—
55#2513C2211yescharacteristic
56#2511C2211yescharacteristic, complemented
57#2509C2211yescharacteristic, complemented
58#2506C2211yescharacteristic, complemented
59#2499C2211yescharacteristic
60#2482—21no—
61#2480—21no—
62#2479—21no—
63#2475—21no—
64#2454C2211yescharacteristic
65#2453C2211yescharacteristic, complemented
66#2448C2211yescharacteristic
67#2447C2211yescharacteristic
68#2442C2211yescharacteristic
69#2441C2211yescharacteristic
70#2435C2211yescharacteristic
71#2371—21no—
72#2370—21no—
73#2362C2211yescharacteristic
74#2360C2211yescharacteristic
75#2347C2211yescharacteristic
76#2342—21no—
77#2342—21no—
78D4×C22⋊C4C2211yescharacteristic
79C4×#125C2211yescharacteristic, complemented
80C4×#124C2211yescharacteristic
81#2296C2211yescharacteristic
82#2295C2211yescharacteristic, complemented
83#2293C2211yescharacteristic
84C2×#390C2211yescharacteristic
85C4×#117C2211yescharacteristic
86#2101C2211yescharacteristic, complemented
87#2100C2211yescharacteristic, complemented
88#2094C2211yescharacteristic
89#2092C2211yescharacteristic
90#2088C2211yescharacteristic, complemented
91#2086C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2084C2211yescharacteristic, complemented
94#2074C2211yescharacteristic, complemented
95#2071C2211yescharacteristic
96#2068C2211yescharacteristic, complemented
97#2066C2211yescharacteristic, complemented
98#2065C2211yescharacteristic
99#2065C2211yescharacteristic
100#2059C2211yescharacteristic, complemented
101#2059C2211yescharacteristic, complemented
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic
104#2042C2211yescharacteristic
105#2042C2211yescharacteristic
106#2026C2211yescharacteristic, complemented
107#2025C2211yescharacteristic
108#2015C2211yescharacteristic
109#2015C2211yescharacteristic
110#1992C2211yescharacteristic, complemented
111#1992C2211yescharacteristic, complemented
112#1991C2211yescharacteristic, complemented
113#1973C2211yescharacteristic
114#1971C2211yescharacteristic, complemented
115#1969C2211yescharacteristic, complemented
116#1968C2211yescharacteristic
117#1968C2211yescharacteristic
118#1968C2211yescharacteristic
119#1968C2211yescharacteristic
120#1959C2211yescharacteristic
121#1959C2211yescharacteristic
122#1958C2211yescharacteristic
123#1943C2211yescharacteristic, complemented
124#1943C2211yescharacteristic, complemented
125#1942C2211yescharacteristic, complemented
126#1941C2211yescharacteristic, complemented
127#1941C2211yescharacteristic, complemented
128#1941C2211yescharacteristic, complemented
129#1941C2211yescharacteristic, complemented
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1935C2211yescharacteristic, complemented
138#1935C2211yescharacteristic, complemented
139#1935C2211yescharacteristic, complemented
140#1935C2211yescharacteristic, complemented
141#1935C2211yescharacteristic, complemented
142#1934C2211yescharacteristic
143#1934C2211yescharacteristic
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic
149#1934C2211yescharacteristic
150#1933C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1933C2211yescharacteristic, complemented
153#1933C2211yescharacteristic, complemented
154#1933C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1927C2211yescharacteristic, complemented
157#1926C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1921C2211yescharacteristic, complemented
161#1920C2211yescharacteristic, complemented
162#1920C2211yescharacteristic, complemented
163#1920C2211yescharacteristic, complemented
164#1894C2211yescharacteristic
165#1894C2211yescharacteristic
166#1880C2211yescharacteristic
167#1878C2211yescharacteristic, complemented
168#1878C2211yescharacteristic, complemented
169#1877C2211yescharacteristic
170#1873C2211yescharacteristic
171#1872C2211yescharacteristic
172#1865C2211yescharacteristic, complemented
173#1864C2211yescharacteristic
174#1864C2211yescharacteristic
175#1862C2211yescharacteristic
176#1854C2211yescharacteristic
177#1853C2211yescharacteristic
178#1835C2211yescharacteristic, complemented
179#1825C2211yescharacteristic
180#1809C2211yescharacteristic
181#1786C2211yescharacteristic
182#1776C2211yescharacteristic, complemented
183#1771C2211yescharacteristic, complemented
184#1771C2211yescharacteristic, complemented
185#1771C2211yescharacteristic, complemented
186#1771C2211yescharacteristic, complemented
187#1763C2211yescharacteristic, complemented
188#1762C2211yescharacteristic
189C4×#103C2211yescharacteristic, complemented
190C4×#103C2211yescharacteristic, complemented
191C4×#102C2211yescharacteristic
192C4×#102C2211yescharacteristic
193#1753C2211yescharacteristic
194#1753C2211yescharacteristic
195#1753C2211yescharacteristic
196#1753C2211yescharacteristic
197#1744C2211yescharacteristic, complemented
198#1744C2211yescharacteristic, complemented
199#1736C2211yescharacteristic
200#1736C2211yescharacteristic
201C4×#97C2211yescharacteristic, complemented
202C42×C8C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C22×M16C2311yescharacteristic
209C2×#126—21no—
210C2×#125—21no—
211C2×#125—21no—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#124C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×C4×Q8C2311yescharacteristic
219C2×C4×Q8C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×#117—21no—
223C2×#117D411yescharacteristic
224C2×#117D411yescharacteristic
225C2×#117C2311yescharacteristic
226C2×#117C2311yescharacteristic
227C22×C4⋊C4C2311yescharacteristic
228C22×C22⋊C4—21no—
229C22×C22⋊C4—21no—
230C22×C22⋊C4—21no—
231C22×C42C2311yescharacteristic
232#488—24no—
233#485—24no—
234#470—24no—
235#450—24no—
236#440—24no—
237#431—24no—
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×#106C2311yescharacteristic
246C2×#106C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249#418—24no—
250#418—24no—
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#103C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C4×M16—24no—
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287C2×C4×C8C2311yescharacteristic
288C2×C4×C8C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293C2×C4×C8C2311yescharacteristic
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#400—21no—
301#399—21no—
302#399—21no—
303#399—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#396—21no—
315#396—21no—
316#394—21no—
317#394—21no—
318#391C2311yescharacteristic
319#391C2311yescharacteristic
320#391C2311yescharacteristic
321#391C2311yescharacteristic
322#391C2311yescharacteristic
323#391C2311yescharacteristic
324#391C2311yescharacteristic
325#391C2311yescharacteristic
326#390—21no—
327#390—21no—
328#390C2311yescharacteristic
329#390C2311yescharacteristic
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#389—21no—
337#389—21no—
338#389—21no—
339#389—21no—
340#389—21no—
341#389—21no—
342#389C2311yescharacteristic
343#389C2311yescharacteristic
344#389C2311yescharacteristic
345#389C2311yescharacteristic
346#389C2311yescharacteristic
347#389C2311yescharacteristic
348#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
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#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#387—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#387—21no—
394#387—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#386—21no—
399#386—21no—
400#385—21no—
401#385—21no—
402#385—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#383—21no—
411#383—21no—
412#382—21no—
413#382C2311yescharacteristic
414#382C2311yescharacteristic
415#381—21no—
416#381—21no—
417#381—21no—
418#380—21no—
419#380—21no—
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#379—21no—
423#379—21no—
424#379—21no—
425C4×C4⋊C4—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
430C4×C4⋊C4—21no—
431C4×C4⋊C4—21no—
432C4×C4⋊C4D411yescharacteristic
433C4×C4⋊C4D411yescharacteristic
434C4×C4⋊C4C2311yescharacteristic
435C4×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4D411yescharacteristic
445C4×C22⋊C4D411yescharacteristic
446C4×C22⋊C4C2311yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
448#376—21no—
449#376D411yescharacteristic
450#376D411yescharacteristic
451C43C2311yescharacteristic
452C43C2311yescharacteristic
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#340C2311yescharacteristic
478#340C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4—22no—
491C22×D4—21no—
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—41no—
495C22×D4—41no—
496C22×D4—41no—
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2×D411yescharacteristic
503C23×C4C2×D411yescharacteristic
504C23×C4C2411yescharacteristic
505C2×Q16—22no—
506C2×Q16—41no—
507C2×Q16—41no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—41no—
517C2×M16—41no—
518C2×M16—41no—
519C2×M16#4114yes—
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528#126—82no—
529#125—22no—
530#125—41no—
531#125—41no—
532#125—41no—
533#125—44no—
534#125—44no—
535#124—22no—
536#124—41no—
537#124—41no—
538#124—41no—
539C22⋊Q8—22no—
540C22⋊Q8—22no—
541C22⋊Q8—22no—
542C22⋊Q8—22no—
543C4×Q8—22no—
544C4×Q8—41no—
545C4×Q8—41no—
546C4×Q8—41no—
547C4×D4—22no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551#117—22no—
552#117—22no—
553#117—22no—
554#117—42no—
555#117—42no—
556#117—41no—
557#117—82no—
558C2×C4⋊C4—21no—
559C2×C4⋊C4—21no—
560C2×C4⋊C4—21no—
561C2×C4⋊C4—21no—
562C2×C4⋊C4—21no—
563C2×C4⋊C4—21no—
564C2×C4⋊C4—21no—
565C2×C4⋊C4—21no—
566C2×C4⋊C4—21no—
567C2×C4⋊C4—21no—
568C2×C4⋊C4—21no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—41no—
588C2×C4⋊C4—41no—
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
592C2×C4⋊C4C2×D411yescharacteristic
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×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—44no—
634C2×C22⋊C4—44no—
635C2×C22⋊C4—82no—
636C2×C22⋊C4C2×D411yescharacteristic
637C2×C22⋊C4C2×D411yescharacteristic
638C2×C22⋊C4C2×D411yescharacteristic
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C42—22no—
641C2×C42—22no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—21no—
648C2×C42—21no—
649C2×C42—21no—
650C2×C42C2×D411yescharacteristic
651C2×C42C2×D411yescharacteristic
652C2×C42C2×D411yescharacteristic
653C2×C42C2×D411yescharacteristic
654C2×C42C2×D411yescharacteristic
655C2×C42C2×D411yescharacteristic
656C2×C42C2×D411yescharacteristic
657C2×C42C2×D411yescharacteristic
658C2×C42C2×D411yescharacteristic
659C2×C42C2×D411yescharacteristic
660C2×C42C2411yescharacteristic
661C2×C42C2411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666#107—22no—
667#107—22no—
668#107—41no—
669#106—22no—
670#106—22no—
671#106—41no—
672#106—41no—
673#106—41no—
674#106—41no—
675C4⋊C8—22no—
676C4⋊C8—22no—
677#103—22no—
678#103—22no—
679#103—22no—
680#103—22no—
681#103—22no—
682#103—22no—
683#103—22no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#102—22no—
690#102—22no—
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#4114yes—
703C22⋊C8—22no—
704C22⋊C8#4114yes—
705#97—22no—
706#97—22no—
707#97—22no—
708#97—41no—
709#97—41no—
710#97—41no—
711C4×C8—22no—
712C4×C8—22no—
713C4×C8—22no—
714C4×C8—22no—
715C4×C8—22no—
716C4×C8—41no—
717C4×C8—41no—
718C4×C8—41no—
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#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#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763#95C2×D411yescharacteristic
764#95C2×D411yescharacteristic
765#95C2×D411yescharacteristic
766#95C2×D411yescharacteristic
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769C24—21no—
770C24—21no—
771C24—42no—
772C24—42no—
773C24—42no—
774C24—42no—
775C24—81no—
776C24—81no—
777C24—81no—
778C24C22×D411yescharacteristic
779C2×Q8—21no—
780C2×Q8—21no—
781C2×Q8—21no—
782C2×Q8—21no—
783C2×Q8—21no—
784C2×Q8—21no—
785C2×Q8—21no—
786C2×Q8—21no—
787C2×Q8—21no—
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—44no—
803C2×D4—44no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—82no—
807C2×D4—82no—
808C2×D4—81no—
809C2×D4C2×#4112yes—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—22no—
816C22×C4—21no—
817C22×C4—22no—
818C22×C4—22no—
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—41no—
833C22×C4—41no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—42no—
837C22×C4—42no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
857C22×C4C2×#4112yes—
858C22×C4C2511yescharacteristic
859Q16—82no—
860SD16—44no—
861SD16—82no—
862M16—44no—
863M16—44no—
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×C8C2×#4112yes—
884C2×C8C2×#4112yes—
885C2×C8C2×#4112yes—
886C2×C8C2×#4112yes—
887C2×C8C2×#4112yes—
888C4⋊C4—22no—
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—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—41no—
913C4⋊C4—41no—
914C4⋊C4—41no—
915C4⋊C4—42no—
916C4⋊C4—42no—
917C4⋊C4—42no—
918C4⋊C4—42no—
919C4⋊C4—42no—
920C4⋊C4—42no—
921C4⋊C4—42no—
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—42no—
932C4⋊C4—42no—
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⋊C4C2×#4112yes—
945C22⋊C4—22no—
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—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
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—
977C42—22no—
978C42—22no—
979C42—22no—
980C42—22no—
981C42—22no—
982C42—22no—
983C42—22no—
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—41no—
997C42—41no—
998C42—41no—
999C42—42no—
1000C42—42no—
1001C42—42no—
1002C42—42no—
1003C42—81no—
1004C42—81no—
1005C42—81no—
1006C42—81no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—22no—
1014C23—41no—
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—84no—
1028C23—84no—
1029C23—84no—
1030C23—84no—
1031C23—162no—
1032C23—162no—
1033C23—162no—
1034C23#53212yes—
1035C23C23×D411yescharacteristic
1036Q8—41no—
1037Q8—41no—
1038Q8—41no—
1039Q8—41no—
1040Q8—41no—
1041Q8—41no—
1042Q8—41no—
1043Q8—41no—
1044D4—22no—
1045D4—22no—
1046D4—41no—
1047D4—41no—
1048D4—41no—
1049D4—41no—
1050D4—41no—
1051D4—41no—
1052D4—84no—
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—22no—
1062C2×C4—22no—
1063C2×C4—22no—
1064C2×C4—22no—
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—22no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
1083C2×C4—21no—
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—44no—
1094C2×C4—44no—
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—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—84no—
1137C2×C4—162no—
1138C2×C4—162no—
1139C2×C4#53212yes—
1140C2×C4#57512yes—
1141C2×C4#57512yes—
1142C2×C4#57712yes—
1143C2×C4C22×#4111yescharacteristic
1144C2×C4C22×#4111yescharacteristic
1145C2×C4C22×#4111yescharacteristic
1146C2×C4#58511yescharacteristic
1147C2×C4#58511yescharacteristic
1148C2×C4#58511yescharacteristic
1149C8—22no—
1150C8—22no—
1151C8—22no—
1152C8—22no—
1153C8—22no—
1154C8—41no—
1155C8—41no—
1156C8—41no—
1157C22—22no—
1158C22—22no—
1159C22—22no—
1160C22—41no—
1161C22—41no—
1162C22—41no—
1163C22—41no—
1164C22—42no—
1165C22—42no—
1166C22—42no—
1167C22—81no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—81no—
1178C22—168no—
1179C22C2×#53211yescharacteristic
1180C22D4×#4111yescharacteristic
1181C22#350011yescharacteristic
1182C22C2×#57511yescharacteristic
1183C22C2×#57511yescharacteristic
1184C22C2×#57711yescharacteristic
1185C22#358411yescharacteristic
1186C4—22no—
1187C4—22no—
1188C4—22no—
1189C4—22no—
1190C4—41no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—42no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—41no—
1199C4—41no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4—81no—
1212C4—81no—
1213C4#347511yescharacteristic
1214C4#347511yescharacteristic
1215C4#349111yescharacteristic
1216C4#352111yescharacteristic
1217C2—42no—
1218C2—82no—
1219C2—161no—
1220C2#3626711yescharacteristic
1221C2#6070211yescharacteristic
1222C2#6070611yescharacteristic
1223C2#6144111yescharacteristic
1224C2#6144811yescharacteristic
1225C2#6254411yescharacteristic
1226C2#6254711yescharacteristic
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
1. #36400C2semidirect
3. #33282C2semidirect
4. #33265C2semidirect
5. #33144C2semidirect
6. #29574C2semidirect
7. #29557C2semidirect
8. #29516C2semidirect
9. #29496C2semidirect
10. #29102C2semidirect
11. #29092C2semidirect
12. #29035C2semidirect
13. #29025C2semidirect
14. #28966C2semidirect
15. #28895C2semidirect
16. #28788C2semidirect
18. #28049C2semidirect
19. #27708C2semidirect
21. #26833C2semidirect
22. #24604C2semidirect
24. #23144C2semidirect
25. #22930C2semidirect
28. C4×#488C2semidirect
29. #21288C2semidirect
31. #20472C2semidirect
41. #2863C22semidirect
44. #2859C22semidirect
56. #2511C22semidirect
57. #2509C22semidirect
58. #2506C22semidirect
65. #2453C22semidirect
79. C4×#125C22semidirect
82. #2295C22semidirect
86. #2101C22semidirect
87. #2100C22semidirect
90. #2088C22semidirect
91. #2086C22semidirect
92. #2085C22semidirect
93. #2084C22semidirect
94. #2074C22semidirect
96. #2068C22semidirect
97. #2066C22semidirect
100. #2059C22semidirect
101. #2059C22semidirect
106. #2026C22semidirect
110. #1992C22semidirect
111. #1992C22semidirect
112. #1991C22semidirect
114. #1971C22semidirect
115. #1969C22semidirect
123. #1943C22semidirect
124. #1943C22semidirect
125. #1942C22semidirect
126. #1941C22semidirect
127. #1941C22semidirect
128. #1941C22semidirect
129. #1941C22semidirect
137. #1935C22semidirect
138. #1935C22semidirect
139. #1935C22semidirect
140. #1935C22semidirect
141. #1935C22semidirect
150. #1933C22semidirect
151. #1933C22semidirect
152. #1933C22semidirect
153. #1933C22semidirect
154. #1933C22semidirect
155. #1933C22semidirect
156. #1927C22semidirect
160. #1921C22semidirect
161. #1920C22semidirect
162. #1920C22semidirect
163. #1920C22semidirect
167. #1878C22semidirect
168. #1878C22semidirect
172. #1865C22semidirect
178. #1835C22semidirect
182. #1776C22semidirect
183. #1771C22semidirect
184. #1771C22semidirect
185. #1771C22semidirect
186. #1771C22semidirect
187. #1763C22semidirect
189. C4×#103C22semidirect
190. C4×#103C22semidirect
197. #1744C22semidirect
198. #1744C22semidirect
201. C4×#97C22semidirect
202. C42×C8C22semidirect

Maximal subgroups

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

subgroupindex
#364002
#362932
#332822
#332652
#331442
#295742
#295572
#295162
#294962
#291022
#290922
#290352
#290252
#289662
#288952
#287882
#283612
#280492
#277082
#272712
#268332
#246042
#245012
#231442
#229302
#228642
#225802
C4×#4882
#212882
#210952
#204722