Finite Group Databasebeta

← #7577297

Subgroups — #7577297

Order 512.

1534 conjugacy classes of subgroups.

The subgroup lattice has 1306 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45171C211yesmaximal, characteristic, complemented
2#35882C211yesmaximal, characteristic, complemented
3#31658C211yesmaximal, characteristic, complemented
4#31610C211yesmaximal, characteristic, complemented
5#31209C211yesmaximal, characteristic, complemented
6#30992C211yesmaximal, characteristic, complemented
7#29510C211yesmaximal, characteristic, complemented
8#29436C211yesmaximal, characteristic, complemented
9#29031C211yesmaximal, characteristic, complemented
10#27788C211yesmaximal, characteristic, complemented
11#27447C211yesmaximal, characteristic, complemented
12#27370C211yesmaximal, characteristic, complemented
13#27240C211yesmaximal, characteristic, complemented
14#27165C211yesmaximal, characteristic, complemented
15#27030C211yesmaximal, characteristic, complemented
16#26978C211yesmaximal, characteristic, complemented
17#26917C211yesmaximal, characteristic, complemented
18#26736C211yesmaximal, characteristic, complemented
19#26713C211yesmaximal, characteristic, complemented
20#26585C211yesmaximal, characteristic, complemented
21#26482C211yesmaximal, characteristic, complemented
22#25457C211yesmaximal, characteristic, complemented
23#25148C211yesmaximal, characteristic
24#25088C211yesmaximal, characteristic, complemented
25#23279C211yesmaximal, characteristic, complemented
26#23108C211yesmaximal, characteristic, complemented
27#23098C211yesmaximal, characteristic, complemented
28#22870C211yesmaximal, characteristic, complemented
29#22562C211yesmaximal, characteristic, complemented
30#21509C211yesmaximal, characteristic, complemented
31#21134C211yesmaximal, characteristic, complemented
32C2×#499C2211yescharacteristic, complemented
33C2×#478C2211yescharacteristic
34C2×#465C2211yescharacteristic
35C2×#463C2211yescharacteristic
36C2×#463C2211yescharacteristic
37C2×#459C2211yescharacteristic
38C2×#447C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#440C2211yescharacteristic, complemented
41C2×C4×D8C2211yescharacteristic
42C2×C4×D8C2211yescharacteristic
43C22×#102C2211yescharacteristic
44#2782—21no—
45#2750—21no—
46#2743—21no—
47#2735—21no—
48#2649—21no—
49#2644C2211yescharacteristic, complemented
50#2597—21no—
51#2576—21no—
52#2576—21no—
53#2566C2211yescharacteristic
54#2508C2211yescharacteristic, complemented
55#2496C2211yescharacteristic
56#2490C2211yescharacteristic
57#2489C2211yescharacteristic
58#2483—21no—
59#2480—21no—
60#2480—21no—
61#2471—21no—
62#2454C2211yescharacteristic
63#2454C2211yescharacteristic, complemented
64#2447C2211yescharacteristic
65#2447C2211yescharacteristic
66#2445C2211yescharacteristic, complemented
67#2444—21no—
68#2435C2211yescharacteristic
69#2428C2211yescharacteristic
70#2421C2211yescharacteristic
71#2420—21no—
72#2420C2211yescharacteristic
73#2419—21no—
74#2401C2211yescharacteristic
75#2392—21no—
76#2370C2211yescharacteristic, complemented
77#2367C2211yescharacteristic
78#2366C2211yescharacteristic, complemented
79#2361C2211yescharacteristic
80#2361C2211yescharacteristic
81#2357C2211yescharacteristic
82#2357C2211yescharacteristic, complemented
83#2344C2211yescharacteristic
84D4×C22⋊C4C2211yescharacteristic
85D4×C22⋊C4C2211yescharacteristic
86#2326C2211yescharacteristic
87#2319C2211yescharacteristic
88#2275C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2101C2211yescharacteristic, complemented
91#2087C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2084C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2073C2211yescharacteristic
96#2071C2211yescharacteristic, complemented
97#2068C2211yescharacteristic, complemented
98#2067C2211yescharacteristic
99#2067C2211yescharacteristic
100#2067C2211yescharacteristic, complemented
101#2065C2211yescharacteristic
102#2065C2211yescharacteristic, complemented
103#2055C2211yescharacteristic, complemented
104#2054C2211yescharacteristic
105#2054C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2036C2211yescharacteristic
109#2033C2211yescharacteristic
110#2033C2211yescharacteristic
111#2033C2211yescharacteristic
112#2026C2211yescharacteristic, complemented
113#2025C2211yescharacteristic
114#2025C2211yescharacteristic, complemented
115#2025C2211yescharacteristic, complemented
116#2014C2211yescharacteristic, complemented
117#2012C2211yescharacteristic
118#2012C2211yescharacteristic
119#2011C2211yescharacteristic
120#2000C2211yescharacteristic
121#1989C2211yescharacteristic, complemented
122#1983C2211yescharacteristic
123#1972C2211yescharacteristic
124#1970C2211yescharacteristic
125#1970C2211yescharacteristic
126#1970C2211yescharacteristic
127#1968C2211yescharacteristic, complemented
128#1968C2211yescharacteristic, complemented
129#1961C2211yescharacteristic, complemented
130#1958C2211yescharacteristic
131#1949C2211yescharacteristic, complemented
132#1949C2211yescharacteristic, complemented
133#1947C2211yescharacteristic, complemented
134#1942C2211yescharacteristic, complemented
135#1942C2211yescharacteristic, complemented
136#1939C2211yescharacteristic, complemented
137#1936C2211yescharacteristic
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic, complemented
140#1935C2211yescharacteristic, complemented
141#1935C2211yescharacteristic, complemented
142#1934C2211yescharacteristic
143#1928C2211yescharacteristic, complemented
144#1928C2211yescharacteristic, complemented
145#1928C2211yescharacteristic, complemented
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic, complemented
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic
152#1925C2211yescharacteristic, complemented
153#1924C2211yescharacteristic
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic
156#1921C2211yescharacteristic, complemented
157#1918C2211yescharacteristic, complemented
158#1918C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1917C2211yescharacteristic, complemented
161#1917C2211yescharacteristic, complemented
162#1916C2211yescharacteristic, complemented
163#1893C2211yescharacteristic
164#1880C2211yescharacteristic, complemented
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1879C2211yescharacteristic
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1877C2211yescharacteristic, complemented
174#1872C2211yescharacteristic
175#1865C2211yescharacteristic, complemented
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic, complemented
179#1864C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic, complemented
183#1852C2211yescharacteristic
184#1850C2211yescharacteristic
185#1823C2211yescharacteristic
186#1807C2211yescharacteristic
187#1802C2211yescharacteristic, complemented
188#1786C2211yescharacteristic
189C4×#106C2211yescharacteristic, complemented
190#1771C2211yescharacteristic, complemented
191C8×C4⋊C4C2211yescharacteristic, complemented
192#1768C2211yescharacteristic, complemented
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic, complemented
197C4×#103C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199C4×#102C2211yescharacteristic, complemented
200#1752C2211yescharacteristic
201C8×C22⋊C4C2211yescharacteristic
202#1746C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×D8C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C23×C8C2311yescharacteristic
211C2×#127C2311yescharacteristic
212C2×#126—21no—
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#124C2311yescharacteristic
216C2×#124C2311yescharacteristic
217C2×#123—21no—
218C2×C22⋊Q8C2311yescharacteristic
219C2×#121—21no—
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×C4×Q8C2311yescharacteristic
223C2×C4×D4—21no—
224C2×C4×D4—21no—
225C2×C4×D4—21no—
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×#117—21no—
235C22×C4⋊C4C2311yescharacteristic
236C22×C22⋊C4—21no—
237C22×C22⋊C4—21no—
238#499—42no—
239#478—42no—
240#465—42no—
241#463—24no—
242#463—24no—
243#459—24no—
244#447—24no—
245#447—42no—
246#440—42no—
247C4×D8—24no—
248C4×D8—42no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#107C2311yescharacteristic
253C2×#107C2311yescharacteristic
254C2×#107C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×#106C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260C2×C4⋊C8C2311yescharacteristic
261C2×C4⋊C8C2311yescharacteristic
262C2×C4⋊C8C2311yescharacteristic
263C2×C4⋊C8C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#102—24no—
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×#97C2311yescharacteristic
297C2×#97C2311yescharacteristic
298C2×#97C2311yescharacteristic
299C2×C4×C8C2311yescharacteristic
300C2×C4×C8C2311yescharacteristic
301C2×C4×C8C2311yescharacteristic
302C2×C4×C8C2311yescharacteristic
303#401D411yescharacteristic
304#400—21no—
305#400—21no—
306#400—21no—
307#400—21no—
308#400D411yescharacteristic
309#400D411yescharacteristic
310#400D411yescharacteristic
311#399—21no—
312#399—21no—
313#398—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#397—21no—
319#397—21no—
320#397—21no—
321#397—21no—
322#397—21no—
323#397—21no—
324#397—21no—
325#397—21no—
326#397D411yescharacteristic
327#397D411yescharacteristic
328#397D411yescharacteristic
329#396—21no—
330#396—21no—
331#396—21no—
332#396—21no—
333#396—21no—
334#396D411yescharacteristic
335#394—21no—
336#394—21no—
337#394—21no—
338#394—21no—
339#394—21no—
340#394—21no—
341#394—21no—
342#392—21no—
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#390—21no—
347#390—21no—
348#390C2311yescharacteristic
349#390C2311yescharacteristic
350#390C2311yescharacteristic
351#390C2311yescharacteristic
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#390C2311yescharacteristic
359#390C2311yescharacteristic
360#389—21no—
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#389C2311yescharacteristic
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#388—21no—
385#387—21no—
386#387—21no—
387#387—21no—
388#387—21no—
389#387—21no—
390#387—21no—
391#387—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#386—21no—
398#386—21no—
399#386—21no—
400#386—21no—
401#386—21no—
402#386—21no—
403#385—21no—
404#385—21no—
405#385—21no—
406#385—21no—
407#385—21no—
408#385—21no—
409#385—21no—
410#385—21no—
411#385—21no—
412#385—21no—
413#385—21no—
414#384C2311yescharacteristic
415#382—21no—
416#382—21no—
417#382C2311yescharacteristic
418#382C2311yescharacteristic
419#381—21no—
420#381—21no—
421#381—21no—
422#381—21no—
423#381—21no—
424#381—21no—
425#381—21no—
426#380—21no—
427#380—21no—
428#380—21no—
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#380C2311yescharacteristic
432#379—21no—
433#379—21no—
434#379—21no—
435#379—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C4⋊C4C2311yescharacteristic
446C4×C4⋊C4C2311yescharacteristic
447C4×C22⋊C4—21no—
448C4×C22⋊C4—21no—
449C4×C22⋊C4—21no—
450C4×C22⋊C4—21no—
451C4×C22⋊C4—21no—
452C4×C22⋊C4—21no—
453C4×C22⋊C4C2311yescharacteristic
454C4×C22⋊C4C2311yescharacteristic
455C4×C22⋊C4C2311yescharacteristic
456#376C2311yescharacteristic
457C2×#95—21no—
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#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×Q8C2411yescharacteristic
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4C2411yescharacteristic
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C22×D4C2411yescharacteristic
507C23×C4—21no—
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4C2411yescharacteristic
517C2×SD16—22no—
518C2×SD16—22no—
519C2×SD16—41no—
520C2×SD16—41no—
521C2×SD16—41no—
522C2×SD16—41no—
523C2×D8—22no—
524C2×D8—22no—
525C2×D8—22no—
526C2×D8—22no—
527C2×D8—41no—
528C2×D8—41no—
529C2×D8—41no—
530C2×D8—41no—
531C2×D8—41no—
532C2×D8—41no—
533C2×D8—41no—
534C2×D8#4114yes—
535C22×C8—22no—
536C22×C8—41no—
537C22×C8—41no—
538C22×C8C2411yescharacteristic
539C22×C8C2411yescharacteristic
540C22×C8C2411yescharacteristic
541C22×C8C2411yescharacteristic
542C22×C8C2411yescharacteristic
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546#127—22no—
547#127—41no—
548#126—82no—
549#125—22no—
550#125—41no—
551#125—41no—
552#125—41no—
553#124—22no—
554#124—22no—
555#124—41no—
556#124—41no—
557#123—82no—
558C22⋊Q8—41no—
559C22⋊Q8—41no—
560#121—22no—
561#121—22no—
562#121—41no—
563#121—41no—
564#121—82no—
565C4×Q8—41no—
566C4×Q8—41no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—22no—
570C4×D4—22no—
571C4×D4—22no—
572C4×D4—22no—
573C4×D4—41no—
574C4×D4—41no—
575C4×D4—41no—
576C4×D4—41no—
577C4×D4—41no—
578C4×D4—41no—
579C4×D4—41no—
580C4×D4—41no—
581C4×D4—41no—
582C4×D4—41no—
583C4×D4—82no—
584C4×D4—82no—
585C4×D4—82no—
586#117—82no—
587C2×C4⋊C4—22no—
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—41no—
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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—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—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—82no—
667C2×C22⋊C4—82no—
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C22⋊C4C2×D411yescharacteristic
673C2×C22⋊C4C2×D411yescharacteristic
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42C2411yescharacteristic
683C2×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687C2×C42C2411yescharacteristic
688#107—22no—
689#107—22no—
690#107—22no—
691#107—41no—
692#107—41no—
693#107—41no—
694#106—22no—
695#106—41no—
696#106—41no—
697#106—41no—
698C4⋊C8—22no—
699C4⋊C8—22no—
700C4⋊C8—22no—
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#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—41no—
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#4114yes—
731C22⋊C8—22no—
732C22⋊C8—41no—
733C22⋊C8—41no—
734#97—41no—
735#97—41no—
736#97—41no—
737C4×C8—22no—
738C4×C8—41no—
739C4×C8—41no—
740C4×C8—41no—
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#95—21no—
768#95—21no—
769#95—21no—
770#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776#95C2×D411yescharacteristic
777#95C2×D411yescharacteristic
778#95C2×D411yescharacteristic
779#95C2×D411yescharacteristic
780#95C2×D411yescharacteristic
781#95C2×D411yescharacteristic
782#95C2×D411yescharacteristic
783#95C2×D411yescharacteristic
784#95C2×D411yescharacteristic
785#95C2×D411yescharacteristic
786C24—21no—
787C24—21no—
788C24—21no—
789C24—21no—
790C24—42no—
791C24—42no—
792C24—42no—
793C24—81no—
794C24—81no—
795C24—81no—
796C24—81no—
797C24C22×D411yescharacteristic
798C2×Q8—21no—
799C2×Q8—21no—
800C2×Q8—21no—
801C2×Q8—21no—
802C2×Q8—21no—
803C2×Q8—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—21no—
818C2×D4—21no—
819C2×D4—21no—
820C2×D4—21no—
821C2×D4—21no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—21no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—44no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4—81no—
839C2×D4—82no—
840C2×D4—82no—
841C2×D4—82no—
842C2×D4—81no—
843C2×D4—81no—
844C2×D4C2×#4112yes—
845C2×D4C2×#4112yes—
846C2×D4C2×#4112yes—
847C22×C4—21no—
848C22×C4—21no—
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—21no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
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—81no—
874C22×C4—81no—
875C22×C4—81no—
876C22×C4—81no—
877C22×C4—81no—
878C22×C4—81no—
879C22×C4—81no—
880C22×C4—81no—
881C22×C4—81no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4C22×D411yescharacteristic
893C22×C4C22×D411yescharacteristic
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C2511yescharacteristic
906SD16—44no—
907SD16—82no—
908D8—44no—
909D8—44no—
910D8—82no—
911D8—82no—
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—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—21no—
932C2×C8—21no—
933C2×C8—21no—
934C2×C8—82no—
935C2×C8C2×#4112yes—
936C2×C8C2×#4112yes—
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—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—41no—
958C4⋊C4—41no—
959C4⋊C4—41no—
960C4⋊C4—41no—
961C4⋊C4—41no—
962C4⋊C4—41no—
963C4⋊C4—42no—
964C4⋊C4—42no—
965C4⋊C4—42no—
966C4⋊C4—42no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4—81no—
970C4⋊C4—81no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4—81no—
981C4⋊C4C2×#4112yes—
982C4⋊C4H(5,𝔽2)12yes—
983C22⋊C4—22no—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—41no—
987C22⋊C4—41no—
988C22⋊C4—41no—
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—81no—
1004C22⋊C4—81no—
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⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4—81no—
1026C22⋊C4—81no—
1027C22⋊C4—81no—
1028C22⋊C4—81no—
1029C22⋊C4—81no—
1030C22⋊C4—81no—
1031C42—21no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—21no—
1036C42—21no—
1037C42—21no—
1038C42—21no—
1039C42—21no—
1040C42—21no—
1041C42—21no—
1042C42—21no—
1043C42—42no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C42—81no—
1050C42—81no—
1051C23—21no—
1052C23—21no—
1053C23—21no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—22no—
1058C23—22no—
1059C23—22no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—41no—
1074C23—41no—
1075C23—41no—
1076C23—41no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—84no—
1086C23—84no—
1087C23—84no—
1088C23—162no—
1089C23—162no—
1090C23—162no—
1091C23—162no—
1092C23#57612yes—
1093C23C23×D411yescharacteristic
1094Q8—41no—
1095Q8—41no—
1096Q8—41no—
1097Q8—41no—
1098D4—22no—
1099D4—22no—
1100D4—22no—
1101D4—22no—
1102D4—22no—
1103D4—22no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—41no—
1108D4—41no—
1109D4—41no—
1110D4—41no—
1111D4—41no—
1112D4—41no—
1113D4—41no—
1114D4—84no—
1115D4—84no—
1116D4—84no—
1117D4—84no—
1118D4—162no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
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—21no—
1143C2×C4—21no—
1144C2×C4—21no—
1145C2×C4—22no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—21no—
1149C2×C4—21no—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—22no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
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—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—84no—
1199C2×C4—162no—
1200C2×C4—162no—
1201C2×C4—162no—
1202C2×C4—162no—
1203C2×C4—162no—
1204C2×C4—162no—
1205C2×C4—162no—
1206C2×C4—162no—
1207C2×C4C22×#4111yescharacteristic
1208C2×C4C22×#4111yescharacteristic
1209C2×C4C2×H(5,𝔽2)11yescharacteristic
1210C2×C4#58511yescharacteristic
1211C2×C4#58511yescharacteristic
1212C2×C4#58511yescharacteristic
1213C8—22no—
1214C8—22no—
1215C8—41no—
1216C8—41no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C22—22no—
1222C22—22no—
1223C22—22no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—42no—
1229C22—42no—
1230C22—42no—
1231C22—42no—
1232C22—42no—
1233C22—42no—
1234C22—42no—
1235C22—42no—
1236C22—42no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—81no—
1241C22—81no—
1242C22—81no—
1243C22—81no—
1244C22—81no—
1245C22—81no—
1246C22—81no—
1247C22—81no—
1248C22—81no—
1249C22—81no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—168no—
1257C22D4×#4111yescharacteristic
1258C22D4×#4111yescharacteristic
1259C22#348811yescharacteristic
1260C22C2×#57611yescharacteristic
1261C22#358411yescharacteristic
1262C22#358411yescharacteristic
1263C22#358511yescharacteristic
1264C4—41no—
1265C4—41no—
1266C4—41no—
1267C4—41no—
1268C4—41no—
1269C4—41no—
1270C4—41no—
1271C4—41no—
1272C4—41no—
1273C4—42no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—42no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4#347511yescharacteristic
1290C4#350511yescharacteristic
1291C4#351411yescharacteristic
1292C4#356611yescharacteristic
1293C2—42no—
1294C2—82no—
1295C2—82no—
1296C2—82no—
1297C2—161no—
1298C2#5916411yescharacteristic
1299C2#6147111yescharacteristic
1300C2#6148611yescharacteristic
1301C2#6151911yescharacteristic
1302C2#6154811yescharacteristic
1303C2#6201411yescharacteristic
1304C2#6206411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25148C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2401 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45171C2semidirect
2. #35882C2semidirect
3. #31658C2semidirect
4. #31610C2semidirect
5. #31209C2semidirect
6. #30992C2semidirect
7. #29510C2semidirect
8. #29436C2semidirect
9. #29031C2semidirect
10. #27788C2semidirect
11. #27447C2semidirect
12. #27370C2semidirect
13. #27240C2semidirect
14. #27165C2semidirect
15. #27030C2semidirect
16. #26978C2semidirect
17. #26917C2semidirect
18. #26736C2semidirect
19. #26713C2semidirect
20. #26585C2semidirect
21. #26482C2semidirect
22. #25457C2semidirect
24. #25088C2semidirect
25. #23279C2semidirect
26. #23108C2semidirect
27. #23098C2semidirect
28. #22870C2semidirect
29. #22562C2semidirect
30. #21509C2semidirect
31. #21134C2semidirect
32. C2×#499C22semidirect
40. C2×#440C22semidirect
49. #2644C22semidirect
54. #2508C22semidirect
63. #2454C22semidirect
66. #2445C22semidirect
76. #2370C22semidirect
78. #2366C22semidirect
82. #2357C22semidirect
88. #2275C22semidirect
89. #2101C22semidirect
90. #2101C22semidirect
91. #2087C22semidirect
92. #2085C22semidirect
93. #2084C22semidirect
96. #2071C22semidirect
97. #2068C22semidirect
100. #2067C22semidirect
102. #2065C22semidirect
103. #2055C22semidirect
112. #2026C22semidirect
114. #2025C22semidirect
115. #2025C22semidirect
116. #2014C22semidirect
121. #1989C22semidirect
127. #1968C22semidirect
128. #1968C22semidirect
129. #1961C22semidirect
131. #1949C22semidirect
132. #1949C22semidirect
133. #1947C22semidirect
134. #1942C22semidirect
135. #1942C22semidirect
136. #1939C22semidirect
139. #1936C22semidirect
140. #1935C22semidirect
141. #1935C22semidirect
143. #1928C22semidirect
144. #1928C22semidirect
145. #1928C22semidirect
149. #1926C22semidirect
152. #1925C22semidirect
156. #1921C22semidirect
157. #1918C22semidirect
158. #1918C22semidirect
159. #1918C22semidirect
160. #1917C22semidirect
161. #1917C22semidirect
162. #1916C22semidirect
164. #1880C22semidirect
173. #1877C22semidirect
175. #1865C22semidirect
178. #1864C22semidirect
179. #1864C22semidirect
182. #1862C22semidirect
187. #1802C22semidirect
189. C4×#106C22semidirect
190. #1771C22semidirect
191. C8×C4⋊C4C22semidirect
192. #1768C22semidirect
196. #1762C22semidirect
197. C4×#103C22semidirect
199. C4×#102C22semidirect
202. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#451712
#358822
#316582
#316102
#312092
#309922
#295102
#294362
#290312
#277882
#274472
#273702
#272402
#271652
#270302
#269782
#269172
#267362
#267132
#265852
#264822
#254572
#251482
#250882
#232792
#231082
#230982
#228702
#225622
#215092
#211342