Finite Group Databasebeta

← #7601266

Subgroups — #7601266

Order 512.

1471 conjugacy classes of subgroups.

The subgroup lattice has 1199 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59458C211yesmaximal, characteristic
2#59447C211yesmaximal, characteristic, complemented
3#31636C211yesmaximal, characteristic, complemented
4#31636C211yesmaximal, characteristic, complemented
5#31459C211yesmaximal, characteristic, complemented
6#31454C211yesmaximal, characteristic, complemented
7#29280C211yesmaximal, characteristic, complemented
8#29099C211yesmaximal, characteristic, complemented
9#29083C211yesmaximal, characteristic, complemented
10#28160C211yesmaximal, characteristic
11#27827C211yesmaximal, characteristic, complemented
12#27744C211yesmaximal, characteristic, complemented
13#27741C211yesmaximal, characteristic, complemented
14#27727C211yesmaximal, characteristic, complemented
15#27573C211yesmaximal, characteristic, complemented
16#27566C211yesmaximal, characteristic, complemented
17#27446C211yesmaximal, characteristic, complemented
18#27439C211yesmaximal, characteristic, complemented
19#26836C211yesmaximal, characteristic, complemented
20#26820C211yesmaximal, characteristic, complemented
21#26122C211yesmaximal, characteristic, complemented
22#26038C211yesmaximal, characteristic, complemented
23#25332C211yesmaximal, characteristic
24#25332C211yesmaximal, characteristic
25#23106C211yesmaximal, characteristic
26#23010C211yesmaximal, characteristic
27#22778C211yesmaximal, characteristic, complemented
28#22762C211yesmaximal, characteristic, complemented
29#21674C211yesmaximal, characteristic, complemented
30#21656C211yesmaximal, characteristic
31#21647C211yesmaximal, characteristic, complemented
32C2×#554—21no—
33C2×#490C2211yescharacteristic
34C2×#487C2211yescharacteristic
35C2×#460C2211yescharacteristic
36C2×#460C2211yescharacteristic
37C2×#440C2211yescharacteristic
38C2×C4×SD16C2211yescharacteristic
39#2766—21no—
40#2719—21no—
41#2692—21no—
42#2692—21no—
43#2606—21no—
44#2590—21no—
45#2580—21no—
46#2570C2211yescharacteristic
47#2565C2211yescharacteristic
48#2565C2211yescharacteristic
49#2552C2211yescharacteristic
50#2552C2211yescharacteristic
51#2551C2211yescharacteristic
52#2542C2211yescharacteristic
53#2542C2211yescharacteristic
54#2528—21no—
55#2524—21no—
56#2524—21no—
57#2514C2211yescharacteristic
58#2511C2211yescharacteristic
59#2454—21no—
60#2452—21no—
61#2452C2211yescharacteristic
62#2452C2211yescharacteristic
63#2452C2211yescharacteristic
64#2452C2211yescharacteristic
65#2449—21no—
66#2449—21no—
67#2446C2211yescharacteristic
68#2446C2211yescharacteristic
69#2371—21no—
70#2366C2211yescharacteristic
71#2366C2211yescharacteristic
72#2356C2211yescharacteristic
73#2356C2211yescharacteristic
74#2355C2211yescharacteristic
75#2351C2211yescharacteristic
76D4×C4⋊C4C2211yescharacteristic
77D4×C4⋊C4C2211yescharacteristic
78C4×C4⋊Q8C2211yescharacteristic
79C4×C4⋊Q8C2211yescharacteristic
80C4×#127C2211yescharacteristic
81C4×#125C2211yescharacteristic
82C4×#125C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2100C2211yescharacteristic
86#2099C2211yescharacteristic
87#2099C2211yescharacteristic
88#2099C2211yescharacteristic
89#2099C2211yescharacteristic
90#2099C2211yescharacteristic
91#2088C2211yescharacteristic
92#2086C2211yescharacteristic
93#2073C2211yescharacteristic
94#2073C2211yescharacteristic
95#2072C2211yescharacteristic
96#2072C2211yescharacteristic
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2068C2211yescharacteristic
102#2066C2211yescharacteristic
103#2058C2211yescharacteristic
104#2057C2211yescharacteristic
105#2055C2211yescharacteristic
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2024C2211yescharacteristic
110#2024C2211yescharacteristic
111#2024C2211yescharacteristic
112#2024C2211yescharacteristic
113#2013C2211yescharacteristic
114#2013C2211yescharacteristic
115#1993C2211yescharacteristic
116#1992C2211yescharacteristic
117#1990C2211yescharacteristic
118#1990C2211yescharacteristic
119#1989C2211yescharacteristic
120#1989C2211yescharacteristic
121#1988C2211yescharacteristic
122#1987C2211yescharacteristic
123#1973C2211yescharacteristic
124#1968C2211yescharacteristic
125#1961C2211yescharacteristic
126#1956C2211yescharacteristic
127#1949C2211yescharacteristic
128#1949C2211yescharacteristic
129#1940C2211yescharacteristic
130#1940C2211yescharacteristic
131#1936C2211yescharacteristic
132#1935C2211yescharacteristic
133#1935C2211yescharacteristic
134#1935C2211yescharacteristic
135#1935C2211yescharacteristic
136#1935C2211yescharacteristic
137#1935C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1934C2211yescharacteristic
142#1934C2211yescharacteristic
143#1933C2211yescharacteristic
144#1933C2211yescharacteristic
145#1926C2211yescharacteristic
146#1925C2211yescharacteristic
147#1921C2211yescharacteristic
148#1921C2211yescharacteristic
149#1920C2211yescharacteristic
150#1920C2211yescharacteristic
151#1920C2211yescharacteristic
152#1918C2211yescharacteristic
153#1917C2211yescharacteristic
154#1917C2211yescharacteristic
155#1916C2211yescharacteristic
156#1916C2211yescharacteristic
157#1880C2211yescharacteristic
158#1880C2211yescharacteristic
159#1877C2211yescharacteristic
160#1877C2211yescharacteristic
161#1877C2211yescharacteristic
162#1877C2211yescharacteristic
163#1877C2211yescharacteristic
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1865C2211yescharacteristic
170#1864C2211yescharacteristic
171#1863C2211yescharacteristic
172#1862C2211yescharacteristic
173#1836C2211yescharacteristic
174#1836C2211yescharacteristic
175#1834C2211yescharacteristic
176#1834C2211yescharacteristic
177#1831C2211yescharacteristic
178#1804C2211yescharacteristic
179#1804C2211yescharacteristic
180#1803C2211yescharacteristic
181#1803C2211yescharacteristic
182#1803C2211yescharacteristic
183#1803C2211yescharacteristic
184#1802C2211yescharacteristic
185#1802C2211yescharacteristic
186#1771C2211yescharacteristic
187#1771C2211yescharacteristic
188#1771C2211yescharacteristic
189#1771C2211yescharacteristic
190#1770C2211yescharacteristic
191C8×C4⋊C4C2211yescharacteristic
192#1763C2211yescharacteristic
193#1763C2211yescharacteristic
194#1763C2211yescharacteristic
195#1763C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic
198#1762C2211yescharacteristic
199#1762C2211yescharacteristic
200#1762C2211yescharacteristic
201C4×#102C2211yescharacteristic
202C4×#97C2211yescharacteristic
203C22×SD16C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207#554—48no—
208C2×C4⋊Q8—21no—
209C2×C4⋊Q8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×C4⋊Q8C2311yescharacteristic
212C2×C4⋊Q8C2311yescharacteristic
213C2×#127C2311yescharacteristic
214C2×#125—21no—
215C2×#125—21no—
216C2×#125D411yescharacteristic
217C2×#125C2311yescharacteristic
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8—21no—
220C2×C22⋊Q8—21no—
221C2×C22⋊Q8—21no—
222C2×C22⋊Q8—21no—
223C2×C22⋊Q8—21no—
224C2×C22⋊Q8—21no—
225C2×C22⋊Q8—21no—
226C2×C4×Q8—21no—
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×Q8C2311yescharacteristic
230C2×C4×Q8C2311yescharacteristic
231C2×C4×D4—21no—
232C2×C4×D4—21no—
233C2×C4×D4—21no—
234C2×C4×D4—21no—
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C22×C4⋊C4—21no—
242C22×C4⋊C4—21no—
243#490—24no—
244#487—24no—
245#460—24no—
246#460—24no—
247#440—24no—
248C4×SD16—24no—
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#106C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×C4⋊C8C2311yescharacteristic
254C2×C4⋊C8C2311yescharacteristic
255C2×C4⋊C8C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×#103C2311yescharacteristic
260C2×#103C2311yescharacteristic
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#103C2311yescharacteristic
268C2×#103C2311yescharacteristic
269C2×#103C2311yescharacteristic
270C2×#103C2311yescharacteristic
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×#97C2311yescharacteristic
284C2×#97C2311yescharacteristic
285C2×#97C2311yescharacteristic
286C2×#97C2311yescharacteristic
287C2×#97C2311yescharacteristic
288C2×#97C2311yescharacteristic
289C2×C4×C8C2311yescharacteristic
290C2×C4×C8C2311yescharacteristic
291C2×C4×C8C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293#401—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#399—21no—
301#399—21no—
302#399—21no—
303#399—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#398—21no—
309#398—21no—
310#398—21no—
311#398—21no—
312#398—21no—
313#398—21no—
314#398—21no—
315#396—21no—
316#396—21no—
317#396—21no—
318#396—21no—
319#395—21no—
320#395—21no—
321#393—21no—
322#393—21no—
323#393—21no—
324#393—21no—
325#391—21no—
326#391C2311yescharacteristic
327#391C2311yescharacteristic
328#391C2311yescharacteristic
329#391C2311yescharacteristic
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#390—21no—
335#390—21no—
336#390—21no—
337#390—21no—
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#389—21no—
345#389—21no—
346#389—21no—
347#389—21no—
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389D411yescharacteristic
353#389D411yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#387—21no—
375#387—21no—
376#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387D411yescharacteristic
386#387D411yescharacteristic
387#387D411yescharacteristic
388#387D411yescharacteristic
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#384C2311yescharacteristic
407#384C2311yescharacteristic
408#383—21no—
409#383—21no—
410#383—21no—
411#382—21no—
412#382—21no—
413#382D411yescharacteristic
414#382C2311yescharacteristic
415#382C2311yescharacteristic
416#382C2311yescharacteristic
417#380—21no—
418#380—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4—21no—
423C4×C4⋊C4—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
438#376—21no—
439#376—21no—
440C43C2311yescharacteristic
441#340C2311yescharacteristic
442#340C2311yescharacteristic
443#340C2311yescharacteristic
444#340C2311yescharacteristic
445#340C2311yescharacteristic
446#340C2311yescharacteristic
447#340C2311yescharacteristic
448#340C2311yescharacteristic
449#340C2311yescharacteristic
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485C22×Q8—21no—
486C22×Q8—21no—
487C22×Q8—21no—
488C22×Q8C2411yescharacteristic
489C22×Q8C2411yescharacteristic
490C22×D4—21no—
491C22×D4—21no—
492C22×D4C2411yescharacteristic
493C22×D4C2411yescharacteristic
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C2×SD16—22no—
501C2×SD16—22no—
502C2×SD16—22no—
503C2×SD16—22no—
504C2×SD16—22no—
505C2×SD16—22no—
506C2×SD16—41no—
507C2×SD16—41no—
508C2×SD16—41no—
509C2×SD16—41no—
510C2×SD16—41no—
511C2×SD16—41no—
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C4⋊Q8—22no—
521C4⋊Q8—22no—
522C4⋊Q8—41no—
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525C4⋊Q8—41no—
526C4⋊Q8—41no—
527C4⋊Q8—41no—
528C4⋊Q8—44no—
529#127—22no—
530#127#4114yes—
531#125—24no—
532#125—22no—
533#125—22no—
534#125—44no—
535#125—44no—
536C22⋊Q8—44no—
537C22⋊Q8—44no—
538C22⋊Q8—44no—
539C22⋊Q8—44no—
540C22⋊Q8—44no—
541C22⋊Q8—44no—
542C22⋊Q8—82no—
543C22⋊Q8—82no—
544C4×Q8—22no—
545C4×Q8—22no—
546C4×Q8—22no—
547C4×Q8—22no—
548C4×Q8—22no—
549C4×Q8—22no—
550C4×Q8—41no—
551C4×Q8—41no—
552C4×Q8—44no—
553C4×D4—22no—
554C4×D4—22no—
555C4×D4—41no—
556C4×D4—41no—
557C4×D4—44no—
558C4×D4—41no—
559C4×D4—41no—
560C4×D4—41no—
561C4×D4—41no—
562C4×D4—41no—
563C4×D4—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—44no—
567C4×D4—44no—
568C4×D4—82no—
569C2×C4⋊C4—21no—
570C2×C4⋊C4—21no—
571C2×C4⋊C4—21no—
572C2×C4⋊C4—21no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4—21no—
579C2×C4⋊C4—21no—
580C2×C4⋊C4—21no—
581C2×C4⋊C4—21no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—44no—
605C2×C4⋊C4—44no—
606C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2×D411yescharacteristic
614C2×C4⋊C4C2×D411yescharacteristic
615C2×C4⋊C4C2×D411yescharacteristic
616C2×C4⋊C4C2×D411yescharacteristic
617C2×C4⋊C4C2×D411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
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×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×C42—21no—
649C2×C42—21no—
650C2×C42—21no—
651C2×C42—21no—
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42C2×D411yescharacteristic
659C2×C42C2×D411yescharacteristic
660C2×C42C2×D411yescharacteristic
661C2×C42C2×D411yescharacteristic
662C2×C42C2411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669#107—22no—
670#107—41no—
671#106—22no—
672#106—41no—
673C4⋊C8—22no—
674C4⋊C8—22no—
675C4⋊C8—41no—
676C4⋊C8—41no—
677C4⋊C8—41no—
678C4⋊C8—41no—
679#103—22no—
680#103—22no—
681#103—22no—
682#103—41no—
683#103—41no—
684#103—41no—
685#103—41no—
686#103—41no—
687#103—41no—
688#103—41no—
689#103—41no—
690#103#4114yes—
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—22no—
700#102—22no—
701#102—41no—
702#102—41no—
703#97—22no—
704#97—22no—
705#97—22no—
706#97—41no—
707#97—41no—
708#97—41no—
709C4×C8—22no—
710C4×C8—22no—
711C4×C8—41no—
712C4×C8—41no—
713#95—21no—
714#95—21no—
715#95—21no—
716#95—21no—
717#95—21no—
718#95—21no—
719#95—21no—
720#95—21no—
721#95—21no—
722#95—21no—
723#95—21no—
724#95—21no—
725#95—21no—
726#95—21no—
727#95—21no—
728#95—21no—
729#95—21no—
730#95—21no—
731#95—21no—
732#95—21no—
733#95—21no—
734#95—21no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#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#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758#95C2×D411yescharacteristic
759#95C2×D411yescharacteristic
760#95C2×D411yescharacteristic
761#95C2×D411yescharacteristic
762#95C2×D411yescharacteristic
763C24—21no—
764C24—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—21no—
776C2×Q8—42no—
777C2×Q8—42no—
778C2×Q8—42no—
779C2×Q8—42no—
780C2×Q8—81no—
781C2×Q8—81no—
782C2×Q8—81no—
783C2×Q8—81no—
784C2×Q8—81no—
785C2×Q8C2×#4112yes—
786C2×D4—24no—
787C2×D4—24no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—81no—
801C2×D4—81no—
802C2×D4C2×#4112yes—
803C2×D4C2×#4112yes—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—42no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—42no—
822C22×C4—42no—
823C22×C4—42no—
824C22×C4—42no—
825C22×C4—42no—
826C22×C4—81no—
827C22×C4—81no—
828C22×C4—81no—
829C22×C4—81no—
830C22×C4—81no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4—81no—
835C22×C4—81no—
836C22×C4C22×D411yescharacteristic
837C22×C4C22×D411yescharacteristic
838C22×C4C22×D411yescharacteristic
839C22×C4C22×D411yescharacteristic
840C22×C4C22×D411yescharacteristic
841C22×C4C22×D411yescharacteristic
842C22×C4C22×D411yescharacteristic
843C22×C4C22×D411yescharacteristic
844C22×C4C22×D411yescharacteristic
845C22×C4C22×D411yescharacteristic
846C22×C4C22×D411yescharacteristic
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C2511yescharacteristic
851SD16—44no—
852SD16—44no—
853SD16—82no—
854SD16—82no—
855C2×C8—21no—
856C2×C8—21no—
857C2×C8—21no—
858C2×C8—21no—
859C2×C8—21no—
860C2×C8—21no—
861C2×C8—21no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—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×C8C2×#4112yes—
879C4⋊C4—22no—
880C4⋊C4—22no—
881C4⋊C4—22no—
882C4⋊C4—22no—
883C4⋊C4—22no—
884C4⋊C4—22no—
885C4⋊C4—22no—
886C4⋊C4—21no—
887C4⋊C4—21no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—41no—
910C4⋊C4—41no—
911C4⋊C4—41no—
912C4⋊C4—41no—
913C4⋊C4—42no—
914C4⋊C4—42no—
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—42no—
934C4⋊C4—42no—
935C4⋊C4—42no—
936C4⋊C4—42no—
937C4⋊C4—42no—
938C4⋊C4—42no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4AGL(1,ℤ/8)14yes—
949C4⋊C4C2×#4112yes—
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—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C42—22no—
969C42—22no—
970C42—21no—
971C42—21no—
972C42—21no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—41no—
983C42—41no—
984C42—42no—
985C42—42no—
986C42—42no—
987C42—42no—
988C42—42no—
989C42—42no—
990C42—42no—
991C42—42no—
992C42—81no—
993C42—81no—
994C42C2×#4112yes—
995C422−1+412yes—
996C23—22no—
997C23—22no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—41no—
1009C23—41no—
1010C23C23×D411yescharacteristic
1011Q8—22no—
1012Q8—22no—
1013Q8—41no—
1014Q8—41no—
1015Q8—41no—
1016Q8—41no—
1017Q8—41no—
1018Q8—41no—
1019Q8—84no—
1020Q8—162no—
1021Q8—162no—
1022D4—22no—
1023D4—22no—
1024D4—22no—
1025D4—22no—
1026D4—48no—
1027D4—41no—
1028D4—41no—
1029D4—41no—
1030D4—41no—
1031D4—84no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—21no—
1052C2×C4—21no—
1053C2×C4—21no—
1054C2×C4—21no—
1055C2×C4—21no—
1056C2×C4—22no—
1057C2×C4—22no—
1058C2×C4—21no—
1059C2×C4—21no—
1060C2×C4—21no—
1061C2×C4—21no—
1062C2×C4—21no—
1063C2×C4—21no—
1064C2×C4—21no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4—41no—
1077C2×C4—41no—
1078C2×C4—41no—
1079C2×C4—41no—
1080C2×C4—41no—
1081C2×C4—41no—
1082C2×C4—41no—
1083C2×C4—41no—
1084C2×C4—41no—
1085C2×C4—41no—
1086C2×C4—41no—
1087C2×C4—41no—
1088C2×C4—41no—
1089C2×C4—41no—
1090C2×C4—41no—
1091C2×C4—41no—
1092C2×C4—41no—
1093C2×C4—41no—
1094C2×C4—41no—
1095C2×C4—41no—
1096C2×C4—41no—
1097C2×C4—41no—
1098C2×C4—41no—
1099C2×C4—41no—
1100C2×C4—41no—
1101C2×C4—41no—
1102C2×C4—41no—
1103C2×C4—41no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—41no—
1108C2×C4—41no—
1109C2×C4—41no—
1110C2×C4—84no—
1111C2×C4—84no—
1112C2×C4—162no—
1113C2×C4—162no—
1114C2×C4—162no—
1115C2×C4—162no—
1116C2×C4#54812yes—
1117C2×C4#54812yes—
1118C2×C4C2×AGL(1,ℤ/8)12yes—
1119C2×C4C2×AGL(1,ℤ/8)12yes—
1120C2×C4C2×AGL(1,ℤ/8)12yes—
1121C2×C4#57712yes—
1122C2×C4C22×#4111yescharacteristic
1123C2×C4C22×#4111yescharacteristic
1124C2×C4C2×2−1+411yescharacteristic
1125C2×C4#58511yescharacteristic
1126C2×C4#58511yescharacteristic
1127C2×C4#58511yescharacteristic
1128C8—22no—
1129C8—41no—
1130C8—41no—
1131C8—41no—
1132C8—41no—
1133C8—41no—
1134C8—41no—
1135C8—41no—
1136C22—42no—
1137C22—42no—
1138C22—42no—
1139C22—42no—
1140C22—42no—
1141C22—42no—
1142C22—81no—
1143C22—81no—
1144C22—81no—
1145C22—81no—
1146C22—81no—
1147C22—81no—
1148C22—81no—
1149C22—81no—
1150C22C2×#54811yescharacteristic
1151C22D4×#4111yescharacteristic
1152C22#350011yescharacteristic
1153C22C22×AGL(1,ℤ/8)11yescharacteristic
1154C22C2×#57711yescharacteristic
1155C22#358611yescharacteristic
1156C22#358611yescharacteristic
1157C4—22no—
1158C4—22no—
1159C4—22no—
1160C4—22no—
1161C4—22no—
1162C4—22no—
1163C4—41no—
1164C4—42no—
1165C4—41no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—42no—
1173C4—81no—
1174C4—81no—
1175C4—81no—
1176C4—81no—
1177C4—81no—
1178C4—81no—
1179C4—81no—
1180C4—81no—
1181C4—81no—
1182C4—81no—
1183C4—81no—
1184C4—81no—
1185C4#347511yescharacteristic
1186C4#351511yescharacteristic
1187C4#352111yescharacteristic
1188C4#356511yescharacteristic
1189C2—82no—
1190C2—82no—
1191C2#5958611yescharacteristic
1192C2#6131711yescharacteristic
1193C2#6134011yescharacteristic
1194C2#6145211yescharacteristic
1195C2#6152611yescharacteristic
1196C2#6253911yescharacteristic
1197C2#6257211yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×#127C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#125 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #59447C2semidirect
3. #31636C2semidirect
4. #31636C2semidirect
5. #31459C2semidirect
6. #31454C2semidirect
7. #29280C2semidirect
8. #29099C2semidirect
9. #29083C2semidirect
11. #27827C2semidirect
12. #27744C2semidirect
13. #27741C2semidirect
14. #27727C2semidirect
15. #27573C2semidirect
16. #27566C2semidirect
17. #27446C2semidirect
18. #27439C2semidirect
19. #26836C2semidirect
20. #26820C2semidirect
21. #26122C2semidirect
22. #26038C2semidirect
27. #22778C2semidirect
28. #22762C2semidirect
29. #21674C2semidirect
31. #21647C2semidirect

Maximal subgroups

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

subgroupindex
#594582
#594472
#316362
#314592
#314542
#292802
#290992
#290832
#281602
#278272
#277442
#277412
#277272
#275732
#275662
#274462
#274392
#268362
#268202
#261222
#260382
#253322
#231062
#230102
#227782
#227622
#216742
#216562
#216472