Finite Group Databasebeta

← #7566186

Subgroups — #7566186

Order 512.

1703 conjugacy classes of subgroups.

The subgroup lattice has 1285 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59820C211yesmaximal, characteristic
2#36133C211yesmaximal, characteristic, complemented
3#32628C211yesmaximal, characteristic, complemented
4#32564C211yesmaximal, characteristic, complemented
5#32226C211yesmaximal, characteristic, complemented
6#30805C211yesmaximal, characteristic, complemented
7#29157C211yesmaximal, characteristic, complemented
8#29103C211yesmaximal, characteristic, complemented
9#29007C211yesmaximal, characteristic, complemented
10#28032C211yesmaximal, characteristic, complemented
11#27695C211yesmaximal, characteristic, complemented
12#27358C211yesmaximal, characteristic, complemented
13#27254C211yesmaximal, characteristic
14#27126C211yesmaximal, characteristic, complemented
15#27126C211yesmaximal, characteristic, complemented
16#26752C211yesmaximal, characteristic, complemented
17#26688C211yesmaximal, characteristic, complemented
18#26688C211yesmaximal, characteristic, complemented
19#26316C211yesmaximal, characteristic, complemented
20#25988C211yesmaximal, characteristic, complemented
21#25950C211yesmaximal, characteristic, complemented
22#24990C211yesmaximal, characteristic, complemented
23#24576C211yesmaximal, characteristic, complemented
24#24476C211yesmaximal, characteristic
25#23237C211yesmaximal, characteristic, complemented
26#23216C211yesmaximal, characteristic, complemented
27#23060C211yesmaximal, characteristic, complemented
28#22611C211yesmaximal, characteristic, complemented
29#22570C211yesmaximal, characteristic, complemented
30C4×#480C211yesmaximal, characteristic, complemented
31C2×#1925C211yesmaximal, characteristic, complemented
32C2×#551—21no—
33C2×#533—21no—
34C2×#486C2211yescharacteristic
35C2×#480C2211yescharacteristic
36C2×#474C2211yescharacteristic
37C22×#107C2211yescharacteristic
38C22×#102C2211yescharacteristic
39C22×#102C2211yescharacteristic
40#2857C2211yescharacteristic
41#2855—21no—
42#2730—21no—
43#2705—21no—
44#2551C2211yescharacteristic, complemented
45#2548C2211yescharacteristic
46#2546C2211yescharacteristic, complemented
47#2538C2211yescharacteristic
48#2534—21no—
49#2512C2211yescharacteristic
50#2512C2211yescharacteristic
51#2506C2211yescharacteristic, complemented
52#2506C2211yescharacteristic, complemented
53#2501C2211yescharacteristic
54#2471—21no—
55#2467—21no—
56#2462—21no—
57#2462—21no—
58#2451—21no—
59#2446—21no—
60#2445C2211yescharacteristic
61#2445C2211yescharacteristic
62#2440C2211yescharacteristic
63#2440C2211yescharacteristic
64#2438—21no—
65#2438—21no—
66#2433C2211yescharacteristic
67#2412—21no—
68#2411—21no—
69#2366C2211yescharacteristic
70#2365C2211yescharacteristic, complemented
71#2365C2211yescharacteristic, complemented
72#2365C2211yescharacteristic, complemented
73#2354C2211yescharacteristic
74Q8×C4⋊C4C2211yescharacteristic, complemented
75#2344C2211yescharacteristic
76#2344C2211yescharacteristic
77#2344C2211yescharacteristic
78D4×C22⋊C4C2211yescharacteristic
79C4×C22⋊Q8C2211yescharacteristic
80C4×#121C2211yescharacteristic
81C2×#390C2211yescharacteristic
82C2×C4×C4⋊C4C2211yescharacteristic
83#2099C2211yescharacteristic, complemented
84#2099C2211yescharacteristic, complemented
85#2099C2211yescharacteristic, complemented
86#2099C2211yescharacteristic, complemented
87#2093C2211yescharacteristic
88#2093C2211yescharacteristic, complemented
89#2086C2211yescharacteristic, complemented
90#2086C2211yescharacteristic, complemented
91#2083C2211yescharacteristic, complemented
92#2083C2211yescharacteristic, complemented
93#2071C2211yescharacteristic
94#2071C2211yescharacteristic
95#2071C2211yescharacteristic
96#2071C2211yescharacteristic, complemented
97#2067C2211yescharacteristic
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic, complemented
102#2067C2211yescharacteristic, complemented
103#2057C2211yescharacteristic, complemented
104#2057C2211yescharacteristic, complemented
105#2041C2211yescharacteristic
106#2041C2211yescharacteristic
107#2041C2211yescharacteristic
108#2041C2211yescharacteristic
109#2023C2211yescharacteristic
110#2023C2211yescharacteristic
111#2023C2211yescharacteristic
112#2023C2211yescharacteristic
113#2023C2211yescharacteristic, complemented
114#2023C2211yescharacteristic, complemented
115#1990C2211yescharacteristic, complemented
116#1988C2211yescharacteristic, complemented
117#1984C2211yescharacteristic, complemented
118#1984C2211yescharacteristic, complemented
119#1982C2211yescharacteristic
120#1982C2211yescharacteristic
121#1957C2211yescharacteristic
122#1947C2211yescharacteristic, complemented
123#1947C2211yescharacteristic, complemented
124#1947C2211yescharacteristic, complemented
125#1942C2211yescharacteristic, complemented
126#1942C2211yescharacteristic, complemented
127#1934C2211yescharacteristic
128#1934C2211yescharacteristic
129#1934C2211yescharacteristic
130#1934C2211yescharacteristic
131#1934C2211yescharacteristic
132#1934C2211yescharacteristic
133#1934C2211yescharacteristic
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic, complemented
136#1934C2211yescharacteristic, complemented
137#1925C2211yescharacteristic
138#1925C2211yescharacteristic
139#1925C2211yescharacteristic
140#1925C2211yescharacteristic
141#1925C2211yescharacteristic
142#1925C2211yescharacteristic
143#1925C2211yescharacteristic
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic
147#1925C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic, complemented
150#1925C2211yescharacteristic, complemented
151#1925C2211yescharacteristic, complemented
152#1925C2211yescharacteristic, complemented
153#1918C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1918C2211yescharacteristic, complemented
161#1918C2211yescharacteristic, complemented
162#1918C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1916C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1893C2211yescharacteristic
168#1893C2211yescharacteristic
169#1874C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic, complemented
175#1862C2211yescharacteristic, complemented
176#1852C2211yescharacteristic
177#1850C2211yescharacteristic
178#1850C2211yescharacteristic
179#1834C2211yescharacteristic, complemented
180#1823C2211yescharacteristic
181#1823C2211yescharacteristic
182#1823C2211yescharacteristic
183#1808C2211yescharacteristic
184#1808C2211yescharacteristic
185#1802C2211yescharacteristic
186#1786C2211yescharacteristic
187#1786C2211yescharacteristic
188C4×#107C2211yescharacteristic, complemented
189C4×#107C2211yescharacteristic, complemented
190C4×#107C2211yescharacteristic, complemented
191C4×#107C2211yescharacteristic, complemented
192C8×C4⋊C4C2211yescharacteristic, complemented
193C8×C4⋊C4C2211yescharacteristic, complemented
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic, complemented
198C8×C22⋊C4C2211yescharacteristic
199C8×C22⋊C4C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201C2×#340C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206#551—48no—
207#533—48no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8—21no—
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#127C2311yescharacteristic
215C2×#126—21no—
216C2×#126—21no—
217C2×#125—21no—
218C2×#125—21no—
219C2×#124—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×#123—21no—
223C2×#123—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8D411yescharacteristic
229C2×#121C2311yescharacteristic
230C2×#120—21no—
231C2×#120—21no—
232C2×C4×Q8—21no—
233C2×C4×Q8—21no—
234C2×C4×Q8—21no—
235C2×C4×Q8—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4—21no—
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×#117—21no—
243C2×#117—21no—
244C2×#117—21no—
245C2×#117—21no—
246C22×C4⋊C4C2311yescharacteristic
247C22×C4⋊C4C2311yescharacteristic
248C22×C4⋊C4C2311yescharacteristic
249C22×C22⋊C4—21no—
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252C22×C42—21no—
253C22×C42C2311yescharacteristic
254#486—24no—
255#480—24no—
256#474—24no—
257C2×#107—24no—
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×#102—24no—
275C2×#102—24no—
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301C2×C22⋊C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303C2×C4×C8C2311yescharacteristic
304C2×C4×C8C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308#400—21no—
309#400—21no—
310#399—21no—
311#399—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#398—21no—
316#398—21no—
317#398—21no—
318#397—21no—
319#397—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#395—21no—
325#395—21no—
326#395—21no—
327#395—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#394—21no—
333#394—21no—
334#392—21no—
335#392—21no—
336#391—21no—
337#391—21no—
338#391—21no—
339#391—21no—
340#391—21no—
341#391D411yescharacteristic
342#390—21no—
343#390—21no—
344#390—21no—
345#390—21no—
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#389—21no—
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389D411yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
370#389C2311yescharacteristic
371#389C2311yescharacteristic
372#389C2311yescharacteristic
373#389C2311yescharacteristic
374#389C2311yescharacteristic
375#389C2311yescharacteristic
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#387—21no—
393#387—21no—
394#387—21no—
395#387D411yescharacteristic
396#387D411yescharacteristic
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#386—21no—
404#385—21no—
405#385—21no—
406#385D411yescharacteristic
407#385D411yescharacteristic
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#384C2311yescharacteristic
411#384C2311yescharacteristic
412#384C2311yescharacteristic
413#381—21no—
414#381—21no—
415#381—21no—
416#380—21no—
417#380—21no—
418#380—21no—
419#380D411yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#379—21no—
424C4×C4⋊C4—21no—
425C4×C4⋊C4—21no—
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×C4⋊C4C2311yescharacteristic
436C4×C4⋊C4C2311yescharacteristic
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C22⋊C4—21no—
441C4×C22⋊C4C2311yescharacteristic
442C4×C22⋊C4C2311yescharacteristic
443C2×#95—21no—
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#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
486C25—21no—
487C22×Q8—21no—
488C22×Q8—21no—
489C22×Q8—21no—
490C22×Q8C2×D411yescharacteristic
491C22×D4—22no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4C2×D411yescharacteristic
513C23×C4C2×D411yescharacteristic
514C23×C4C2411yescharacteristic
515C22×C8—22no—
516C22×C8—22no—
517C22×C8—22no—
518C22×C8—41no—
519C22×C8—41no—
520C22×C8—41no—
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524C22×C8C2411yescharacteristic
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C4⋊Q8—22no—
530C4⋊Q8—22no—
531C4⋊Q8—41no—
532C4⋊Q8—41no—
533C4⋊Q8—41no—
534C4⋊Q8—41no—
535C4⋊Q8—44no—
536C4⋊Q8—44no—
537#127—22no—
538#127—41no—
539#127—41no—
540#127—41no—
541#126—44no—
542#126—44no—
543#125—44no—
544#125—44no—
545#124—44no—
546#123—44no—
547#123—44no—
548#123—44no—
549#123—82no—
550C22⋊Q8—44no—
551C22⋊Q8—44no—
552C22⋊Q8—44no—
553C22⋊Q8—44no—
554C22⋊Q8D818yes—
555#121—22no—
556#121—22no—
557#120—44no—
558#120—82no—
559C4×Q8—41no—
560C4×Q8—41no—
561C4×Q8—44no—
562C4×Q8—44no—
563C4×Q8—44no—
564C4×Q8—44no—
565C4×D4—22no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—44no—
572C4×D4—44no—
573#117—44no—
574#117—44no—
575#117—44no—
576#117—44no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—22no—
581C2×C4⋊C4—22no—
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—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—41no—
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2×D411yescharacteristic
619C2×C4⋊C4C2×D411yescharacteristic
620C2×C4⋊C4#4114yes—
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C4⋊C4C2411yescharacteristic
628C2×C4⋊C4C2411yescharacteristic
629C2×C4⋊C4C2411yescharacteristic
630C2×C4⋊C4C2411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
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—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—44no—
664C2×C22⋊C4—44no—
665C2×C22⋊C4—82no—
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C42—21no—
671C2×C42—21no—
672C2×C42—21no—
673C2×C42—21no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—41no—
682C2×C42—41no—
683C2×C42—44no—
684C2×C42C2×D411yescharacteristic
685C2×C42C2×D411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688C2×C42C2411yescharacteristic
689C2×C42C2411yescharacteristic
690C2×C42C2411yescharacteristic
691C2×C42C2411yescharacteristic
692#107—22no—
693#107—22no—
694#107—22no—
695#107—22no—
696#107—22no—
697#107—22no—
698#107—22no—
699#107—22no—
700#107—41no—
701#107—41no—
702#107—41no—
703#107—41no—
704C4⋊C8—22no—
705C4⋊C8—41no—
706C4⋊C8—41no—
707C4⋊C8—41no—
708#102—22no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—41no—
722#102—41no—
723#102—41no—
724#102—41no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102—41no—
730#102—41no—
731#102#4114yes—
732C22⋊C8—22no—
733C22⋊C8—22no—
734C4×C8—22no—
735C4×C8—41no—
736C4×C8—41no—
737C4×C8—41no—
738C4×C8—41no—
739C4×C8—41no—
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#95—21no—
765#95—21no—
766#95—21no—
767#95C2×D411yescharacteristic
768#95C2×D411yescharacteristic
769#95C2×D411yescharacteristic
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777C24—21no—
778C24—21no—
779C24—21no—
780C24—42no—
781C24—42no—
782C24—42no—
783C24—42no—
784C24—81no—
785C24—81no—
786C24—81no—
787C24C22×D411yescharacteristic
788C2×Q8—41no—
789C2×Q8—41no—
790C2×Q8—42no—
791C2×Q8—42no—
792C2×Q8—42no—
793C2×Q8—42no—
794C2×Q8—42no—
795C2×Q8—42no—
796C2×Q8—42no—
797C2×Q8—81no—
798C2×Q8—81no—
799C2×Q8C2×D814yes—
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—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—21no—
815C2×D4—21no—
816C2×D4—21no—
817C2×D4—44no—
818C2×D4—44no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—42no—
822C2×D4—42no—
823C2×D4—42no—
824C2×D4—42no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—82no—
829C2×D4—82no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4C2×#4112yes—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—24no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—22no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—41no—
860C22×C4—41no—
861C22×C4—41no—
862C22×C4—41no—
863C22×C4—42no—
864C22×C4—42no—
865C22×C4—42no—
866C22×C4—42no—
867C22×C4—42no—
868C22×C4—42no—
869C22×C4—42no—
870C22×C4—42no—
871C22×C4—42no—
872C22×C4—42no—
873C22×C4—42no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4C2×D814yes—
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C22×D411yescharacteristic
887C22×C4C22×D411yescharacteristic
888C22×C4C22×D411yescharacteristic
889C22×C4C22×D411yescharacteristic
890C22×C4C22×D411yescharacteristic
891C22×C4C22×D411yescharacteristic
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C2×#4112yes—
895C22×C42−1+412yes—
896C22×C4C2511yescharacteristic
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—44no—
921C2×C8—82no—
922C2×C8C2×#4112yes—
923C4⋊C4—24no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—41no—
948C4⋊C4—41no—
949C4⋊C4—41no—
950C4⋊C4—41no—
951C4⋊C4—41no—
952C4⋊C4—41no—
953C4⋊C4—42no—
954C4⋊C4—42no—
955C4⋊C4—42no—
956C4⋊C4—42no—
957C4⋊C4—42no—
958C4⋊C4—42no—
959C4⋊C4—42no—
960C4⋊C4—42no—
961C4⋊C4—42no—
962C4⋊C4—42no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—42no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—42no—
972C4⋊C4—42no—
973C4⋊C4—42no—
974C4⋊C4—42no—
975C4⋊C4—42no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4C2×D814yes—
982C4⋊C4C2×D814yes—
983C4⋊C4C2×D814yes—
984C4⋊C4C2×#4112yes—
985C4⋊C4C2×#4112yes—
986C4⋊C4C2×#4112yes—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—42no—
990C22⋊C4—42no—
991C22⋊C4—42no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4C2×D814yes—
1019C22⋊C4C2×D814yes—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—21no—
1028C42—21no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—41no—
1033C42—41no—
1034C42—42no—
1035C42—42no—
1036C42—42no—
1037C42—42no—
1038C42—42no—
1039C42—42no—
1040C42—42no—
1041C42—42no—
1042C42—42no—
1043C42—42no—
1044C42—42no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—22no—
1050C23—41no—
1051C23—41no—
1052C23—41no—
1053C23—41no—
1054C23—41no—
1055C23—41no—
1056C23—41no—
1057C23—41no—
1058C23—41no—
1059C23—41no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—84no—
1071C23—84no—
1072C23—84no—
1073C23—84no—
1074C23—162no—
1075C23—162no—
1076C23—162no—
1077C23#54812yes—
1078C23C22×D812yes—
1079C23#57712yes—
1080C23C23×D411yescharacteristic
1081Q8—44no—
1082Q8—84no—
1083Q8—84no—
1084Q8—84no—
1085D4—22no—
1086D4—22no—
1087D4—41no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—41no—
1095D4—41no—
1096D4—41no—
1097D4—84no—
1098D4—84no—
1099D4—84no—
1100D4—162no—
1101D4—162no—
1102D4—162no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—22no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—22no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—44no—
1143C2×C4—41no—
1144C2×C4—48no—
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—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—84no—
1181C2×C4—82no—
1182C2×C4—84no—
1183C2×C4—84no—
1184C2×C4—162no—
1185C2×C4—162no—
1186C2×C4#54812yes—
1187C2×C4C22×D812yes—
1188C2×C4C22×D812yes—
1189C2×C4C22×D812yes—
1190C2×C4C22×D812yes—
1191C2×C4C22×D812yes—
1192C2×C4C22×D812yes—
1193C2×C4C22×#4111yescharacteristic
1194C2×C4C22×#4111yescharacteristic
1195C2×C4C2×2−1+411yescharacteristic
1196C2×C4#58511yescharacteristic
1197C2×C4#58511yescharacteristic
1198C2×C4#58511yescharacteristic
1199C8—22no—
1200C8—41no—
1201C8—41no—
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C8—41no—
1206C8—41no—
1207C22—22no—
1208C22—22no—
1209C22—22no—
1210C22—22no—
1211C22—22no—
1212C22—22no—
1213C22—42no—
1214C22—42no—
1215C22—42no—
1216C22—81no—
1217C22—81no—
1218C22—81no—
1219C22—81no—
1220C22—81no—
1221C22—81no—
1222C22—81no—
1223C22—81no—
1224C22—81no—
1225C22—81no—
1226C22—81no—
1227C22—81no—
1228C22—81no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—168no—
1235C22#335814yes—
1236C22C2×#54811yescharacteristic
1237C22D4×#4111yescharacteristic
1238C22#348511yescharacteristic
1239C22C23×D811yescharacteristic
1240C22C2×#57711yescharacteristic
1241C22#358411yescharacteristic
1242C22#358611yescharacteristic
1243C4—22no—
1244C4—22no—
1245C4—22no—
1246C4—22no—
1247C4—22no—
1248C4—22no—
1249C4—22no—
1250C4—41no—
1251C4—41no—
1252C4—41no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—42no—
1257C4—42no—
1258C4—42no—
1259C4—81no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4#347511yescharacteristic
1270C4#349511yescharacteristic
1271C4#351011yescharacteristic
1272C4#356411yescharacteristic
1273C2—24no—
1274C2—82no—
1275C2—161no—
1276C2—161no—
1277C2#5913211yescharacteristic
1278C2C2×#335811yescharacteristic
1279C2#6134411yescharacteristic
1280C2D8×#4111yescharacteristic
1281C2#6152011yescharacteristic
1282C2#6169411yescharacteristic
1283C2#6177011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2433C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×C22⋊Q8 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #36133C2semidirect
3. #32628C2semidirect
4. #32564C2semidirect
5. #32226C2semidirect
6. #30805C2semidirect
7. #29157C2semidirect
8. #29103C2semidirect
9. #29007C2semidirect
10. #28032C2semidirect
11. #27695C2semidirect
12. #27358C2semidirect
14. #27126C2semidirect
15. #27126C2semidirect
16. #26752C2semidirect
17. #26688C2semidirect
18. #26688C2semidirect
19. #26316C2semidirect
20. #25988C2semidirect
21. #25950C2semidirect
22. #24990C2semidirect
23. #24576C2semidirect
25. #23237C2semidirect
26. #23216C2semidirect
27. #23060C2semidirect
28. #22611C2semidirect
29. #22570C2semidirect
30. C4×#480C2semidirect
31. C2×#1925C2semidirect
44. #2551C22semidirect
46. #2546C22semidirect
51. #2506C22semidirect
52. #2506C22semidirect
70. #2365C22semidirect
71. #2365C22semidirect
72. #2365C22semidirect
74. Q8×C4⋊C4C22semidirect
83. #2099C22semidirect
84. #2099C22semidirect
85. #2099C22semidirect
86. #2099C22semidirect
88. #2093C22semidirect
89. #2086C22semidirect
90. #2086C22semidirect
91. #2083C22semidirect
92. #2083C22semidirect
96. #2071C22semidirect
101. #2067C22semidirect
102. #2067C22semidirect
103. #2057C22semidirect
104. #2057C22semidirect
113. #2023C22semidirect
114. #2023C22semidirect
115. #1990C22semidirect
116. #1988C22semidirect
117. #1984C22semidirect
118. #1984C22semidirect
122. #1947C22semidirect
123. #1947C22semidirect
124. #1947C22semidirect
125. #1942C22semidirect
126. #1942C22semidirect
135. #1934C22semidirect
136. #1934C22semidirect
149. #1925C22semidirect
150. #1925C22semidirect
151. #1925C22semidirect
152. #1925C22semidirect
153. #1918C22semidirect
154. #1918C22semidirect
155. #1918C22semidirect
156. #1918C22semidirect
157. #1918C22semidirect
158. #1918C22semidirect
159. #1918C22semidirect
160. #1918C22semidirect
161. #1918C22semidirect
162. #1918C22semidirect
163. #1916C22semidirect
164. #1916C22semidirect
165. #1916C22semidirect
166. #1916C22semidirect
174. #1862C22semidirect
175. #1862C22semidirect
179. #1834C22semidirect
188. C4×#107C22semidirect
189. C4×#107C22semidirect
190. C4×#107C22semidirect
191. C4×#107C22semidirect
192. C8×C4⋊C4C22semidirect
193. C8×C4⋊C4C22semidirect
196. C4×#102C22semidirect
197. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#598202
#361332
#326282
#325642
#322262
#308052
#291572
#291032
#290072
#280322
#276952
#273582
#272542
#271262
#267522
#266882
#263162
#259882
#259502
#249902
#245762
#244762
#232372
#232162
#230602
#226112
#225702
C4×#4802
C2×#19252