Finite Group Databasebeta

← #7038011

Subgroups — #7038011

Order 512.

1332 conjugacy classes of subgroups.

The subgroup lattice has 1227 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45128C211yesmaximal, characteristic, complemented
2#42563C211yesmaximal, characteristic
3#32349C211yesmaximal, characteristic, complemented
4#32017C211yesmaximal, characteristic, complemented
5#31756C211yesmaximal, characteristic, complemented
6#31711C211yesmaximal, characteristic, complemented
7#31672C211yesmaximal, characteristic
8#31579C211yesmaximal, characteristic, complemented
9#31302C211yesmaximal, characteristic, complemented
10#30653C211yesmaximal, characteristic, complemented
11#29342C211yesmaximal, characteristic, complemented
12#29025C211yesmaximal, characteristic, complemented
13#28076C211yesmaximal, characteristic, complemented
14#28051C211yesmaximal, characteristic, complemented
15#27898C211yesmaximal, characteristic, complemented
16#27853C211yesmaximal, characteristic, complemented
17#27743C211yesmaximal, characteristic, complemented
18#27539C211yesmaximal, characteristic, complemented
19#27415C211yesmaximal, characteristic, complemented
20#27353C211yesmaximal, characteristic, complemented
21#27351C211yesmaximal, characteristic, complemented
22#27281C211yesmaximal, characteristic, complemented
23#27133C211yesmaximal, characteristic, complemented
24#26760C211yesmaximal, characteristic, complemented
25#24975C211yesmaximal, characteristic, complemented
26#24882C211yesmaximal, characteristic
27#23770C211yesmaximal, characteristic, complemented
28#23303C211yesmaximal, characteristic, complemented
29#23230C211yesmaximal, characteristic, complemented
30#22580C211yesmaximal, characteristic, complemented
31#22093C211yesmaximal, characteristic, complemented
32C2×#489C2211yescharacteristic
33C2×#480C2211yescharacteristic
34C2×#418C2211yescharacteristic
35#2827—21no—
36#2781—21no—
37#2779—21no—
38#2775—21no—
39#2758—21no—
40#2753—21no—
41#2735—21no—
42#2702—21no—
43#2685—21no—
44#2648—21no—
45#2622—21no—
46#2620C2211yescharacteristic
47#2585—21no—
48#2577—21no—
49#2571C2211yescharacteristic, complemented
50#2566C2211yescharacteristic
51#2536C2211yescharacteristic
52#2519—21no—
53#2513C2211yescharacteristic
54#2508C2211yescharacteristic, complemented
55#2506C2211yescharacteristic, complemented
56#2497C2211yescharacteristic
57#2496C2211yescharacteristic
58#2496C2211yescharacteristic
59#2490C2211yescharacteristic
60#2489—21no—
61#2489C2211yescharacteristic
62#2485C2211yescharacteristic
63#2480—21no—
64#2448C2211yescharacteristic
65#2440C2211yescharacteristic, complemented
66#2439C2211yescharacteristic
67#2435C2211yescharacteristic
68#2427C2211yescharacteristic
69#2408C2211yescharacteristic
70#2395C2211yescharacteristic
71#2369C2211yescharacteristic, complemented
72#2367C2211yescharacteristic
73#2352C2211yescharacteristic
74#2347C2211yescharacteristic
75#2347C2211yescharacteristic, complemented
76D4×C22⋊C4C2211yescharacteristic
77#2324C2211yescharacteristic
78#2316C2211yescharacteristic, complemented
79#2314C2211yescharacteristic, complemented
80#2101C2211yescharacteristic, complemented
81#2100C2211yescharacteristic, complemented
82#2100C2211yescharacteristic, complemented
83#2099C2211yescharacteristic, complemented
84#2095C2211yescharacteristic, complemented
85#2093C2211yescharacteristic
86#2092C2211yescharacteristic
87#2088C2211yescharacteristic, complemented
88#2085C2211yescharacteristic, complemented
89#2085C2211yescharacteristic, complemented
90#2077C2211yescharacteristic
91#2077C2211yescharacteristic
92#2077C2211yescharacteristic
93#2076C2211yescharacteristic
94#2076C2211yescharacteristic, complemented
95#2075C2211yescharacteristic, complemented
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2071C2211yescharacteristic
99#2068C2211yescharacteristic, complemented
100#2067C2211yescharacteristic
101#2067C2211yescharacteristic
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic
104#2059C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2057C2211yescharacteristic, complemented
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic
113#2035C2211yescharacteristic, complemented
114#2035C2211yescharacteristic, complemented
115#2034C2211yescharacteristic
116#2034C2211yescharacteristic
117#2034C2211yescharacteristic
118#2033C2211yescharacteristic
119#2023C2211yescharacteristic
120#1992C2211yescharacteristic, complemented
121#1989C2211yescharacteristic, complemented
122#1988C2211yescharacteristic, complemented
123#1983C2211yescharacteristic
124#1959C2211yescharacteristic
125#1958C2211yescharacteristic
126#1954C2211yescharacteristic
127#1949C2211yescharacteristic, complemented
128#1944C2211yescharacteristic, complemented
129#1943C2211yescharacteristic, complemented
130#1942C2211yescharacteristic, complemented
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1935C2211yescharacteristic, complemented
136#1935C2211yescharacteristic, complemented
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic
140#1934C2211yescharacteristic
141#1933C2211yescharacteristic, complemented
142#1927C2211yescharacteristic, complemented
143#1927C2211yescharacteristic, complemented
144#1927C2211yescharacteristic, complemented
145#1926C2211yescharacteristic
146#1926C2211yescharacteristic
147#1926C2211yescharacteristic
148#1925C2211yescharacteristic
149#1925C2211yescharacteristic
150#1925C2211yescharacteristic
151#1924C2211yescharacteristic
152#1924C2211yescharacteristic
153#1924C2211yescharacteristic, complemented
154#1924C2211yescharacteristic, complemented
155#1921C2211yescharacteristic, complemented
156#1920C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1919C2211yescharacteristic, complemented
159#1918C2211yescharacteristic, complemented
160#1916C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1894C2211yescharacteristic
163#1875C2211yescharacteristic
164#1875C2211yescharacteristic
165#1874C2211yescharacteristic
166#1873C2211yescharacteristic
167#1873C2211yescharacteristic, complemented
168#1872C2211yescharacteristic, complemented
169#1870C2211yescharacteristic
170#1865C2211yescharacteristic, complemented
171#1864C2211yescharacteristic
172#1864C2211yescharacteristic
173#1864C2211yescharacteristic
174#1863C2211yescharacteristic, complemented
175#1862C2211yescharacteristic
176#1854C2211yescharacteristic
177#1854C2211yescharacteristic, complemented
178#1844C2211yescharacteristic, complemented
179#1836C2211yescharacteristic, complemented
180#1835C2211yescharacteristic, complemented
181#1825C2211yescharacteristic
182#1824C2211yescharacteristic, complemented
183#1809C2211yescharacteristic
184#1809C2211yescharacteristic
185#1805C2211yescharacteristic, complemented
186#1802C2211yescharacteristic
187#1786C2211yescharacteristic
188#1786C2211yescharacteristic
189#1786C2211yescharacteristic
190#1776C2211yescharacteristic, complemented
191#1776C2211yescharacteristic, complemented
192C4×#107C2211yescharacteristic, complemented
193#1771C2211yescharacteristic, complemented
194#1771C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197C4×#103C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1750C2211yescharacteristic, complemented
202#1750C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C2×C4⋊Q8C2311yescharacteristic
206C2×#126—21no—
207C2×#126—21no—
208C2×#125—21no—
209C2×#125C2311yescharacteristic
210C2×#124C2311yescharacteristic
211C2×#124C2311yescharacteristic
212C2×C22⋊Q8—21no—
213C2×C22⋊Q8C2311yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×#121C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#120—21no—
218C2×C4×Q8C2311yescharacteristic
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C22×C4⋊C4C2311yescharacteristic
226C22×C22⋊C4—21no—
227#489—24no—
228#480—24no—
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#106C2311yescharacteristic
236C2×#106C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×C4⋊C8C2311yescharacteristic
242C2×C4⋊C8C2311yescharacteristic
243C2×C4⋊C8C2311yescharacteristic
244#418—24no—
245C2×#103C2311yescharacteristic
246C2×#103C2311yescharacteristic
247C2×#103C2311yescharacteristic
248C2×#103C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#102C2311yescharacteristic
254C2×#102C2311yescharacteristic
255C2×#102C2311yescharacteristic
256C2×#102C2311yescharacteristic
257C2×#102C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#400—21no—
291#400D411yescharacteristic
292#399—21no—
293#399D411yescharacteristic
294#398—21no—
295#398—21no—
296#398—21no—
297#398—21no—
298#398D411yescharacteristic
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397D411yescharacteristic
309#397D411yescharacteristic
310#397D411yescharacteristic
311#396—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#396—21no—
317#395—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394D411yescharacteristic
328#394D411yescharacteristic
329#393—21no—
330#392—21no—
331#391—21no—
332#391—21no—
333#391—21no—
334#391C2311yescharacteristic
335#391C2311yescharacteristic
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#389C2311yescharacteristic
349#389C2311yescharacteristic
350#389C2311yescharacteristic
351#389C2311yescharacteristic
352#389C2311yescharacteristic
353#389C2311yescharacteristic
354#389C2311yescharacteristic
355#389C2311yescharacteristic
356#389C2311yescharacteristic
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
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#388—21no—
378#388—21no—
379#388—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#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#384C2311yescharacteristic
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#383—21no—
404#383—21no—
405#382—21no—
406#382—21no—
407#382—21no—
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#382C2311yescharacteristic
411#380—21no—
412#380—21no—
413#380—21no—
414#380C2311yescharacteristic
415#380C2311yescharacteristic
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#379—21no—
423#379—21no—
424#379—21no—
425#379—21no—
426C4×C4⋊C4—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
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×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4C2311yescharacteristic
441C4×C22⋊C4C2311yescharacteristic
442C4×C22⋊C4C2311yescharacteristic
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#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C25—21no—
482C22×Q8—21no—
483C22×Q8C2411yescharacteristic
484C22×D4—22no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4—41no—
489C22×D4—41no—
490C22×D4—41no—
491C22×D4—41no—
492C22×D4—41no—
493C22×D4C2×D411yescharacteristic
494C22×D4C2411yescharacteristic
495C22×D4C2411yescharacteristic
496C23×C4—21no—
497C23×C4—21no—
498C23×C4—21no—
499C23×C4C2411yescharacteristic
500C23×C4C2411yescharacteristic
501C2×M16—22no—
502C2×M16—41no—
503C2×M16—41no—
504C22×C8C2411yescharacteristic
505C22×C8C2411yescharacteristic
506C22×C8C2411yescharacteristic
507C22×C8C2411yescharacteristic
508C22×C8C2411yescharacteristic
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C4⋊Q8—22no—
513C4⋊Q8—41no—
514#126—82no—
515#126—82no—
516#125—41no—
517#125—41no—
518#125—82no—
519#124—22no—
520#124—41no—
521#124—41no—
522#124—41no—
523C22⋊Q8—41no—
524C22⋊Q8—41no—
525C22⋊Q8—41no—
526C22⋊Q8—41no—
527C22⋊Q8—82no—
528#121—22no—
529#121—41no—
530#121—41no—
531#121—41no—
532#120—82no—
533C4×Q8—41no—
534C4×Q8—41no—
535C4×D4—41no—
536C4×D4—41no—
537C4×D4—41no—
538C4×D4—41no—
539C4×D4—41no—
540C4×D4—41no—
541#117—22no—
542#117—41no—
543#117—41no—
544#117—41no—
545#117—41no—
546#117—41no—
547C2×C4⋊C4—22no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—21no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—21no—
555C2×C4⋊C4—21no—
556C2×C4⋊C4—21no—
557C2×C4⋊C4—21no—
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—41no—
574C2×C4⋊C4C2×D411yescharacteristic
575C2×C4⋊C4C2×D411yescharacteristic
576C2×C4⋊C4C2×D411yescharacteristic
577C2×C4⋊C4C2×D411yescharacteristic
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2411yescharacteristic
582C2×C4⋊C4C2411yescharacteristic
583C2×C4⋊C4C2411yescharacteristic
584C2×C4⋊C4C2411yescharacteristic
585C2×C4⋊C4C2411yescharacteristic
586C2×C4⋊C4C2411yescharacteristic
587C2×C4⋊C4C2411yescharacteristic
588C2×C4⋊C4C2411yescharacteristic
589C2×C4⋊C4C2411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
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—82no—
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C22⋊C4C2×D411yescharacteristic
631C2×C22⋊C4C2×D411yescharacteristic
632C2×C22⋊C4C2×D411yescharacteristic
633C2×C22⋊C4C2×D411yescharacteristic
634C2×C22⋊C4C2×D411yescharacteristic
635C2×C22⋊C4C2×D411yescharacteristic
636C2×C22⋊C4C2×D411yescharacteristic
637C2×C42—21no—
638C2×C42—21no—
639C2×C42—21no—
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42C2411yescharacteristic
648C2×C42C2411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652#107—22no—
653#107—22no—
654#107—41no—
655#107—41no—
656#107—41no—
657#107—41no—
658#106—41no—
659#106—41no—
660#106—41no—
661#106—41no—
662#106—41no—
663#106—41no—
664C4⋊C8—41no—
665C4⋊C8—41no—
666C4⋊C8—41no—
667#103—22no—
668#103—22no—
669#103—41no—
670#103—41no—
671#103—41no—
672#103—41no—
673#103—41no—
674#103—41no—
675#102—22no—
676#102—22no—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—41no—
681#102—41no—
682#102—41no—
683#102—41no—
684#102—41no—
685#102—41no—
686#102—41no—
687#102—41no—
688#102—41no—
689#102—41no—
690#102#4114yes—
691C22⋊C8—22no—
692C22⋊C8—41no—
693C22⋊C8—41no—
694C22⋊C8—41no—
695C22⋊C8—41no—
696C22⋊C8—41no—
697C22⋊C8—41no—
698#97—22no—
699#97—41no—
700#97—41no—
701#97—41no—
702C4×C8—41no—
703C4×C8—41no—
704C4×C8—41no—
705#95—21no—
706#95—21no—
707#95—21no—
708#95—21no—
709#95—21no—
710#95—21no—
711#95—21no—
712#95—21no—
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#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752C24—21no—
753C24—21no—
754C24—42no—
755C24—42no—
756C24—81no—
757C24—81no—
758C24—81no—
759C24—81no—
760C24—81no—
761C24C22×D411yescharacteristic
762C24C22×D411yescharacteristic
763C2×Q8—21no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—42no—
770C2×Q8—81no—
771C2×Q8—81no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—41no—
784C2×D4—41no—
785C2×D4—41no—
786C2×D4—42no—
787C2×D4—44no—
788C2×D4—42no—
789C2×D4—81no—
790C2×D4—81no—
791C2×D4—82no—
792C2×D4—82no—
793C2×D4—82no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—81no—
797C2×D4—81no—
798C2×D4—81no—
799C2×D4C2×#4112yes—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
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—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—42no—
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×C4C22×D411yescharacteristic
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×C4C2511yescharacteristic
848M16—82no—
849C2×C8—21no—
850C2×C8—21no—
851C2×C8—21no—
852C2×C8—21no—
853C2×C8—21no—
854C2×C8—21no—
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×C8C2×#4112yes—
873C4⋊C4—21no—
874C4⋊C4—21no—
875C4⋊C4—21no—
876C4⋊C4—21no—
877C4⋊C4—21no—
878C4⋊C4—21no—
879C4⋊C4—21no—
880C4⋊C4—21no—
881C4⋊C4—21no—
882C4⋊C4—21no—
883C4⋊C4—21no—
884C4⋊C4—21no—
885C4⋊C4—21no—
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—41no—
899C4⋊C4—41no—
900C4⋊C4—41no—
901C4⋊C4—41no—
902C4⋊C4—41no—
903C4⋊C4—41no—
904C4⋊C4—41no—
905C4⋊C4—42no—
906C4⋊C4—42no—
907C4⋊C4—42no—
908C4⋊C4—42no—
909C4⋊C4—42no—
910C4⋊C4—42no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4—81no—
917C4⋊C4—81no—
918C4⋊C4—81no—
919C4⋊C4—81no—
920C4⋊C4—81no—
921C4⋊C4—81no—
922C4⋊C4—81no—
923C4⋊C4—81no—
924C4⋊C4—81no—
925C4⋊C4—81no—
926C4⋊C4—81no—
927C4⋊C4—81no—
928C4⋊C4—81no—
929C4⋊C4—81no—
930C4⋊C4C2×#4112yes—
931C22⋊C4—41no—
932C22⋊C4—41no—
933C22⋊C4—41no—
934C22⋊C4—41no—
935C22⋊C4—41no—
936C22⋊C4—41no—
937C22⋊C4—41no—
938C22⋊C4—41no—
939C22⋊C4—41no—
940C22⋊C4—41no—
941C22⋊C4—42no—
942C22⋊C4—42no—
943C22⋊C4—42no—
944C22⋊C4—42no—
945C22⋊C4—42no—
946C22⋊C4—42no—
947C22⋊C4—42no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C22⋊C4—81no—
951C22⋊C4—81no—
952C22⋊C4—81no—
953C22⋊C4—81no—
954C22⋊C4—81no—
955C22⋊C4—81no—
956C22⋊C4—81no—
957C22⋊C4—81no—
958C22⋊C4—81no—
959C22⋊C4—81no—
960C22⋊C4—81no—
961C22⋊C4—81no—
962C22⋊C4—81no—
963C22⋊C4—81no—
964C22⋊C4—81no—
965C22⋊C4—81no—
966C22⋊C4—81no—
967C22⋊C4—81no—
968C22⋊C4—81no—
969C22⋊C4—81no—
970C22⋊C4—81no—
971C22⋊C4—81no—
972C22⋊C4—81no—
973C42—21no—
974C42—21no—
975C42—21no—
976C42—21no—
977C42—21no—
978C42—21no—
979C42—21no—
980C42—21no—
981C42—21no—
982C42—21no—
983C42—42no—
984C42—42no—
985C42—81no—
986C42—81no—
987C42—81no—
988C42—81no—
989C42—81no—
990C42—81no—
991C42—81no—
992C42—81no—
993C23—21no—
994C23—21no—
995C23—21no—
996C23—21no—
997C23—21no—
998C23—21no—
999C23—21no—
1000C23—21no—
1001C23—22no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—41no—
1009C23—41no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—84no—
1022C23—84no—
1023C23—162no—
1024C23—162no—
1025C23—162no—
1026C23—162no—
1027C23—162no—
1028C23C23×D411yescharacteristic
1029Q8—41no—
1030Q8—41no—
1031Q8—41no—
1032Q8—41no—
1033Q8—162no—
1034D4—22no—
1035D4—22no—
1036D4—41no—
1037D4—41no—
1038D4—41no—
1039D4—41no—
1040D4—41no—
1041D4—41no—
1042D4—82no—
1043D4—84no—
1044D4—162no—
1045D4—162no—
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—21no—
1057C2×C4—21no—
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—22no—
1070C2×C4—21no—
1071C2×C4—21no—
1072C2×C4—21no—
1073C2×C4—21no—
1074C2×C4—21no—
1075C2×C4—21no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—21no—
1079C2×C4—21no—
1080C2×C4—21no—
1081C2×C4—21no—
1082C2×C4—21no—
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—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—162no—
1133C2×C4—162no—
1134C2×C4—162no—
1135C2×C4C22×#4111yescharacteristic
1136C2×C4#58511yescharacteristic
1137C2×C4#58511yescharacteristic
1138C2×C4#58511yescharacteristic
1139C2×C4#58511yescharacteristic
1140C2×C4#58511yescharacteristic
1141C8—22no—
1142C8—41no—
1143C8—41no—
1144C8—41no—
1145C8—41no—
1146C8—41no—
1147C8—41no—
1148C8—41no—
1149C22—41no—
1150C22—41no—
1151C22—41no—
1152C22—42no—
1153C22—41no—
1154C22—41no—
1155C22—41no—
1156C22—41no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22—42no—
1161C22—41no—
1162C22—41no—
1163C22—41no—
1164C22—41no—
1165C22—42no—
1166C22—81no—
1167C22—81no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22—81no—
1177C22—168no—
1178C22D4×#4111yescharacteristic
1179C22#348511yescharacteristic
1180C22#350011yescharacteristic
1181C22#358411yescharacteristic
1182C22#358511yescharacteristic
1183C22#358511yescharacteristic
1184C22#358611yescharacteristic
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—42no—
1190C4—41no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—41no—
1195C4—41no—
1196C4—41no—
1197C4—41no—
1198C4—81no—
1199C4—81no—
1200C4—81no—
1201C4—81no—
1202C4—81no—
1203C4—81no—
1204C4—81no—
1205C4—81no—
1206C4—81no—
1207C4—81no—
1208C4—81no—
1209C4—81no—
1210C4—81no—
1211C4#349311yescharacteristic
1212C4#352111yescharacteristic
1213C4#356611yescharacteristic
1214C4#356611yescharacteristic
1215C2—81no—
1216C2—81no—
1217C2—82no—
1218C2—161no—
1219C2#4350111yescharacteristic
1220C2#6150511yescharacteristic
1221C2#6155011yescharacteristic
1222C2#6174911yescharacteristic
1223C2#6179911yescharacteristic
1224C2#6256811yescharacteristic
1225C2#6261311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45128C2semidirect
3. #32349C2semidirect
4. #32017C2semidirect
5. #31756C2semidirect
6. #31711C2semidirect
8. #31579C2semidirect
9. #31302C2semidirect
10. #30653C2semidirect
11. #29342C2semidirect
12. #29025C2semidirect
13. #28076C2semidirect
14. #28051C2semidirect
15. #27898C2semidirect
16. #27853C2semidirect
17. #27743C2semidirect
18. #27539C2semidirect
19. #27415C2semidirect
20. #27353C2semidirect
21. #27351C2semidirect
22. #27281C2semidirect
23. #27133C2semidirect
24. #26760C2semidirect
25. #24975C2semidirect
27. #23770C2semidirect
28. #23303C2semidirect
29. #23230C2semidirect
30. #22580C2semidirect
31. #22093C2semidirect
49. #2571C22semidirect
54. #2508C22semidirect
55. #2506C22semidirect
65. #2440C22semidirect
71. #2369C22semidirect
75. #2347C22semidirect
78. #2316C22semidirect
79. #2314C22semidirect
80. #2101C22semidirect
81. #2100C22semidirect
82. #2100C22semidirect
83. #2099C22semidirect
84. #2095C22semidirect
87. #2088C22semidirect
88. #2085C22semidirect
89. #2085C22semidirect
94. #2076C22semidirect
95. #2075C22semidirect
99. #2068C22semidirect
104. #2059C22semidirect
105. #2059C22semidirect
106. #2057C22semidirect
113. #2035C22semidirect
114. #2035C22semidirect
120. #1992C22semidirect
121. #1989C22semidirect
122. #1988C22semidirect
127. #1949C22semidirect
128. #1944C22semidirect
129. #1943C22semidirect
130. #1942C22semidirect
135. #1935C22semidirect
136. #1935C22semidirect
141. #1933C22semidirect
142. #1927C22semidirect
143. #1927C22semidirect
144. #1927C22semidirect
153. #1924C22semidirect
154. #1924C22semidirect
155. #1921C22semidirect
156. #1920C22semidirect
157. #1920C22semidirect
158. #1919C22semidirect
159. #1918C22semidirect
160. #1916C22semidirect
161. #1916C22semidirect
167. #1873C22semidirect
168. #1872C22semidirect
170. #1865C22semidirect
174. #1863C22semidirect
177. #1854C22semidirect
178. #1844C22semidirect
179. #1836C22semidirect
180. #1835C22semidirect
182. #1824C22semidirect
185. #1805C22semidirect
190. #1776C22semidirect
191. #1776C22semidirect
192. C4×#107C22semidirect
193. #1771C22semidirect
194. #1771C22semidirect
197. C4×#103C22semidirect
201. #1750C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#451282
#425632
#323492
#320172
#317562
#317112
#316722
#315792
#313022
#306532
#293422
#290252
#280762
#280512
#278982
#278532
#277432
#275392
#274152
#273532
#273512
#272812
#271332
#267602
#249752
#248822
#237702
#233032
#232302
#225802
#220932