Finite Group Databasebeta

← #7592071

Subgroups — #7592071

Order 512.

1362 conjugacy classes of subgroups.

The subgroup lattice has 1186 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59292C211yesmaximal, characteristic, complemented
2#59279C211yesmaximal, characteristic
3#32394C211yesmaximal, characteristic, complemented
4#32370C211yesmaximal, characteristic, complemented
5#32295C211yesmaximal, characteristic, complemented
6#31109C211yesmaximal, characteristic, complemented
7#28852C211yesmaximal, characteristic, complemented
8#28778C211yesmaximal, characteristic, complemented
9#28096C211yesmaximal, characteristic
10#28082C211yesmaximal, characteristic, complemented
11#28052C211yesmaximal, characteristic, complemented
12#28041C211yesmaximal, characteristic, complemented
13#27741C211yesmaximal, characteristic, complemented
14#27718C211yesmaximal, characteristic, complemented
15#27618C211yesmaximal, characteristic, complemented
16#27587C211yesmaximal, characteristic, complemented
17#27375C211yesmaximal, characteristic, complemented
18#27357C211yesmaximal, characteristic, complemented
19#27150C211yesmaximal, characteristic, complemented
20#27118C211yesmaximal, characteristic, complemented
21#26003C211yesmaximal, characteristic, complemented
22#25953C211yesmaximal, characteristic, complemented
23#24944C211yesmaximal, characteristic, complemented
24#24872C211yesmaximal, characteristic
25#23074C211yesmaximal, characteristic, complemented
26#22939C211yesmaximal, characteristic, complemented
27#22708C211yesmaximal, characteristic, complemented
28#22565C211yesmaximal, characteristic, complemented
29#21561C211yesmaximal, characteristic, complemented
30#21086C211yesmaximal, characteristic, complemented
31#20823C211yesmaximal, characteristic, complemented
32C2×#485C2211yescharacteristic
33C2×#479C2211yescharacteristic
34C2×C8×D4C2211yescharacteristic
35C2×#416C2211yescharacteristic
36C2×#416C2211yescharacteristic
37C22×#97C2211yescharacteristic
38#2761—21no—
39#2752—21no—
40#2744—21no—
41#2694—21no—
42#2611—21no—
43#2601—21no—
44#2577—21no—
45#2565C2211yescharacteristic
46#2554—21no—
47#2552C2211yescharacteristic
48#2531—21no—
49#2529—21no—
50#2519—21no—
51#2518—21no—
52#2516—21no—
53#2513C2211yescharacteristic
54#2512C2211yescharacteristic
55#2508—21no—
56#2507C2211yescharacteristic
57#2506C2211yescharacteristic
58#2500C2211yescharacteristic
59#2497C2211yescharacteristic
60#2496C2211yescharacteristic
61#2490C2211yescharacteristic
62#2485C2211yescharacteristic
63#2441C2211yescharacteristic
64#2441C2211yescharacteristic
65#2441C2211yescharacteristic
66#2421C2211yescharacteristic
67#2407C2211yescharacteristic
68#2373—21no—
69#2371—21no—
70#2370C2211yescharacteristic
71#2362C2211yescharacteristic
72#2355C2211yescharacteristic
73#2354C2211yescharacteristic
74#2354C2211yescharacteristic
75#2346C2211yescharacteristic
76#2346C2211yescharacteristic
77#2341C2211yescharacteristic
78C4×#123C2211yescharacteristic
79#2297C2211yescharacteristic
80#2296C2211yescharacteristic
81#2285C2211yescharacteristic
82#2283C2211yescharacteristic
83#2101C2211yescharacteristic
84#2101C2211yescharacteristic
85#2099C2211yescharacteristic
86#2099C2211yescharacteristic
87#2096C2211yescharacteristic
88#2094C2211yescharacteristic
89#2093C2211yescharacteristic
90#2093C2211yescharacteristic
91#2087C2211yescharacteristic
92#2086C2211yescharacteristic
93#2085C2211yescharacteristic
94#2085C2211yescharacteristic
95#2084C2211yescharacteristic
96#2083C2211yescharacteristic
97#2083C2211yescharacteristic
98#2077C2211yescharacteristic
99#2077C2211yescharacteristic
100#2072C2211yescharacteristic
101#2072C2211yescharacteristic
102#2071C2211yescharacteristic
103#2068C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2065C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2059C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic
112#2033C2211yescharacteristic
113#2033C2211yescharacteristic
114#2025C2211yescharacteristic
115#1992C2211yescharacteristic
116#1992C2211yescharacteristic
117#1989C2211yescharacteristic
118#1948C2211yescharacteristic
119#1948C2211yescharacteristic
120#1947C2211yescharacteristic
121#1944C2211yescharacteristic
122#1944C2211yescharacteristic
123#1936C2211yescharacteristic
124#1936C2211yescharacteristic
125#1936C2211yescharacteristic
126#1936C2211yescharacteristic
127#1936C2211yescharacteristic
128#1936C2211yescharacteristic
129#1935C2211yescharacteristic
130#1935C2211yescharacteristic
131#1935C2211yescharacteristic
132#1935C2211yescharacteristic
133#1934C2211yescharacteristic
134#1933C2211yescharacteristic
135#1928C2211yescharacteristic
136#1928C2211yescharacteristic
137#1928C2211yescharacteristic
138#1926C2211yescharacteristic
139#1926C2211yescharacteristic
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1924C2211yescharacteristic
144#1924C2211yescharacteristic
145#1921C2211yescharacteristic
146#1921C2211yescharacteristic
147#1921C2211yescharacteristic
148#1920C2211yescharacteristic
149#1920C2211yescharacteristic
150#1919C2211yescharacteristic
151#1919C2211yescharacteristic
152#1918C2211yescharacteristic
153#1917C2211yescharacteristic
154#1917C2211yescharacteristic
155#1893C2211yescharacteristic
156#1892C2211yescharacteristic
157#1875C2211yescharacteristic
158#1869C2211yescharacteristic
159#1865C2211yescharacteristic
160#1865C2211yescharacteristic
161#1865C2211yescharacteristic
162#1865C2211yescharacteristic
163#1854C2211yescharacteristic
164#1854C2211yescharacteristic
165#1854C2211yescharacteristic
166#1854C2211yescharacteristic
167#1854C2211yescharacteristic
168#1854C2211yescharacteristic
169#1854C2211yescharacteristic
170#1850C2211yescharacteristic
171#1847C2211yescharacteristic
172#1847C2211yescharacteristic
173#1836C2211yescharacteristic
174#1836C2211yescharacteristic
175#1834C2211yescharacteristic
176#1825C2211yescharacteristic
177#1825C2211yescharacteristic
178#1825C2211yescharacteristic
179#1817C2211yescharacteristic
180#1808C2211yescharacteristic
181#1808C2211yescharacteristic
182#1807C2211yescharacteristic
183#1807C2211yescharacteristic
184#1807C2211yescharacteristic
185#1803C2211yescharacteristic
186#1788C2211yescharacteristic
187#1788C2211yescharacteristic
188#1776C2211yescharacteristic
189#1776C2211yescharacteristic
190#1776C2211yescharacteristic
191#1776C2211yescharacteristic
192C4×#107C2211yescharacteristic
193#1771C2211yescharacteristic
194#1771C2211yescharacteristic
195#1763C2211yescharacteristic
196#1763C2211yescharacteristic
197#1752C2211yescharacteristic
198#1752C2211yescharacteristic
199#1752C2211yescharacteristic
200#1735C2211yescharacteristic
201#1735C2211yescharacteristic
202#1735C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×C8C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×#126—21no—
208C2×#126—21no—
209C2×#125—21no—
210C2×#125—21no—
211C2×#125C2311yescharacteristic
212C2×#125C2311yescharacteristic
213C2×#123D411yescharacteristic
214C2×C22⋊Q8C2311yescharacteristic
215C2×#121C2311yescharacteristic
216C2×C4×Q8C2311yescharacteristic
217C2×C4×Q8C2311yescharacteristic
218C2×C4×D4C2311yescharacteristic
219C2×#117—21no—
220C2×#117C2311yescharacteristic
221C2×#117C2311yescharacteristic
222C2×#117C2311yescharacteristic
223C2×#117C2311yescharacteristic
224C2×#117C2311yescharacteristic
225C22×C42C2311yescharacteristic
226#485—24no—
227#479—24no—
228C8×D4—24no—
229C2×#107C2311yescharacteristic
230C2×#107C2311yescharacteristic
231C2×#107C2311yescharacteristic
232C2×#107C2311yescharacteristic
233C2×#107C2311yescharacteristic
234C2×#107C2311yescharacteristic
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#106C2311yescharacteristic
238C2×#106C2311yescharacteristic
239C2×#106C2311yescharacteristic
240C2×#106C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248#416—24no—
249#416—24no—
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
254C2×#103C2311yescharacteristic
255C2×#103C2311yescharacteristic
256C2×#103C2311yescharacteristic
257C2×#103C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×C22⋊C8C2311yescharacteristic
267C2×C22⋊C8C2311yescharacteristic
268C2×C22⋊C8C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×#97—24no—
272C2×#97C2311yescharacteristic
273C2×#97C2311yescharacteristic
274C2×#97C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279#400—21no—
280#400—21no—
281#400—21no—
282#400—21no—
283#399—21no—
284#399—21no—
285#399—21no—
286#398—21no—
287#398—21no—
288#398—21no—
289#398—21no—
290#398—21no—
291#398—21no—
292#398—21no—
293#397—21no—
294#397—21no—
295#397—21no—
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#396—21no—
301#396—21no—
302#396—21no—
303#396—21no—
304#396—21no—
305#394—21no—
306#394—21no—
307#394—21no—
308#394—21no—
309#394—21no—
310#392—21no—
311#391C2311yescharacteristic
312#391C2311yescharacteristic
313#391C2311yescharacteristic
314#390—21no—
315#390—21no—
316#390—21no—
317#390—21no—
318#390—21no—
319#390C2311yescharacteristic
320#390C2311yescharacteristic
321#390C2311yescharacteristic
322#390C2311yescharacteristic
323#390C2311yescharacteristic
324#389—21no—
325#389—21no—
326#389—21no—
327#389—21no—
328#389—21no—
329#389—21no—
330#389C2311yescharacteristic
331#389C2311yescharacteristic
332#389C2311yescharacteristic
333#389C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#389C2311yescharacteristic
339#389C2311yescharacteristic
340#389C2311yescharacteristic
341#389C2311yescharacteristic
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#388—21no—
359#388—21no—
360#388—21no—
361#388D411yescharacteristic
362#388D411yescharacteristic
363#387—21no—
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#387D411yescharacteristic
380#387D411yescharacteristic
381#386—21no—
382#386—21no—
383#386—21no—
384#386D411yescharacteristic
385#385—21no—
386#385—21no—
387#385—21no—
388#385D411yescharacteristic
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#384C2311yescharacteristic
392#384C2311yescharacteristic
393#384C2311yescharacteristic
394#384C2311yescharacteristic
395#383—21no—
396#382—21no—
397#382—21no—
398#382—21no—
399#382—21no—
400#382C2311yescharacteristic
401#382C2311yescharacteristic
402#381—21no—
403#381D411yescharacteristic
404#380—21no—
405#380—21no—
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#380C2311yescharacteristic
413#380C2311yescharacteristic
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C22⋊C4—21no—
433C4×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4C2311yescharacteristic
437C4×C22⋊C4C2311yescharacteristic
438C4×C22⋊C4C2311yescharacteristic
439#376—21no—
440#376—21no—
441#376—21no—
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#340C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C2×#41—22no—
485C2×#41—22no—
486C2×#41—22no—
487C2×#41—41no—
488C2×#41—41no—
489C2×#41—41no—
490C22×Q8C2411yescharacteristic
491C22×D4—21no—
492C22×D4—21no—
493C22×D4C2×D411yescharacteristic
494C22×D4C2411yescharacteristic
495C23×C4—21no—
496C23×C4C2×D411yescharacteristic
497C23×C4C2×D411yescharacteristic
498C23×C4C2411yescharacteristic
499C23×C4C2411yescharacteristic
500C22×C8—22no—
501C22×C8—22no—
502C22×C8—22no—
503C22×C8—41no—
504C22×C8—41no—
505C22×C8—41no—
506C22×C8—41no—
507C22×C8—41no—
508C22×C8#4114yes—
509C22×C8C2411yescharacteristic
510C22×C8C2411yescharacteristic
511C22×C8C2411yescharacteristic
512C22×C8C2411yescharacteristic
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517#126—44no—
518#126—82no—
519#125—22no—
520#125—41no—
521#125—41no—
522#125—41no—
523#125—44no—
524#125—82no—
525#123—42no—
526C22⋊Q8—22no—
527C22⋊Q8—41no—
528#121—41no—
529#121—41no—
530C4×Q8—22no—
531C4×Q8—41no—
532C4×Q8—41no—
533C4×Q8—41no—
534C4×D4—22no—
535C4×D4—22no—
536#117—22no—
537#117—22no—
538#117—22no—
539#117—22no—
540#117—41no—
541#117—41no—
542#117—41no—
543#117—41no—
544#117—41no—
545#117—41no—
546#117—82no—
547C2×C4⋊C4—21no—
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—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4—21no—
578C2×C4⋊C4C2×D411yescharacteristic
579C2×C4⋊C4C2×D411yescharacteristic
580C2×C4⋊C4C2×D411yescharacteristic
581C2×C4⋊C4C2×D411yescharacteristic
582C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
623C2×C22⋊C4C2×D411yescharacteristic
624C2×C22⋊C4C2×D411yescharacteristic
625C2×C22⋊C4C2×D411yescharacteristic
626C2×C22⋊C4C2×D411yescharacteristic
627C2×C22⋊C4C2×D411yescharacteristic
628C2×C22⋊C4C2×D411yescharacteristic
629C2×C22⋊C4C2×D411yescharacteristic
630C2×C42—22no—
631C2×C42—22no—
632C2×C42—21no—
633C2×C42—21no—
634C2×C42—21no—
635C2×C42—21no—
636C2×C42—21no—
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×C42C2×D411yescharacteristic
648C2×C42C2×D411yescharacteristic
649C2×C42C2411yescharacteristic
650C2×C42C2411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654#107—22no—
655#107—22no—
656#107—41no—
657#107—41no—
658#107—41no—
659#107—41no—
660#107—41no—
661#107—41no—
662#106—22no—
663#106—22no—
664#106—41no—
665#106—41no—
666#106—41no—
667#106—41no—
668#106—41no—
669#106—41no—
670C4⋊C8—22no—
671C4⋊C8—22no—
672C4⋊C8—41no—
673#103—22no—
674#103—22no—
675#103—22no—
676#103—22no—
677#103—22no—
678#103—41no—
679#103—41no—
680#103#4114yes—
681#102—22no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—41no—
686#102—41no—
687#102—41no—
688#102—41no—
689C22⋊C8—22no—
690C22⋊C8—22no—
691C22⋊C8—22no—
692C22⋊C8—22no—
693C22⋊C8—41no—
694#97—22no—
695#97—22no—
696#97—22no—
697#97—22no—
698#97—41no—
699#97—41no—
700C4×C8—22no—
701#95—21no—
702#95—21no—
703#95—21no—
704#95—21no—
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#95C2×D411yescharacteristic
740#95C2×D411yescharacteristic
741#95C2×D411yescharacteristic
742#95C2×D411yescharacteristic
743#95C2×D411yescharacteristic
744#95C2×D411yescharacteristic
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749C24—21no—
750C24C22×D411yescharacteristic
751C24C22×D411yescharacteristic
752#41—44no—
753#41—44no—
754#41—82no—
755#41—82no—
756C2×Q8—21no—
757C2×Q8—21no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8C2×#4112yes—
762C2×D4—22no—
763C2×D4—22no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—41no—
771C2×D4—42no—
772C2×D4—42no—
773C2×D4—81no—
774C2×D4—81no—
775C2×D4—81no—
776C2×D4—81no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—22no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—22no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—41no—
805C22×C4—41no—
806C22×C4—41no—
807C22×C4—41no—
808C22×C4—42no—
809C22×C4—42no—
810C22×C4—81no—
811C22×C4C22×D411yescharacteristic
812C22×C4C22×D411yescharacteristic
813C22×C4C22×D411yescharacteristic
814C22×C4C22×D411yescharacteristic
815C22×C4C22×D411yescharacteristic
816C22×C4C22×D411yescharacteristic
817C22×C4C22×D411yescharacteristic
818C22×C4C22×D411yescharacteristic
819C22×C4C22×D411yescharacteristic
820C22×C4C22×D411yescharacteristic
821C22×C4C22×D411yescharacteristic
822C22×C4C22×D411yescharacteristic
823C22×C4C2×#4112yes—
824C22×C42−1+412yes—
825C22×C4C2511yescharacteristic
826C2×C8—21no—
827C2×C8—21no—
828C2×C8—21no—
829C2×C8—21no—
830C2×C8—21no—
831C2×C8—21no—
832C2×C8—21no—
833C2×C8—21no—
834C2×C8—21no—
835C2×C8—21no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—21no—
842C2×C8—21no—
843C2×C8—21no—
844C2×C8—21no—
845C2×C8—21no—
846C2×C8—21no—
847C2×C8—44no—
848C2×C8—44no—
849C2×C8—82no—
850C2×C8C2×#4112yes—
851C2×C8C2×#4112yes—
852C2×C8C2×#4112yes—
853C4⋊C4—22no—
854C4⋊C4—22no—
855C4⋊C4—22no—
856C4⋊C4—21no—
857C4⋊C4—21no—
858C4⋊C4—21no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—21no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—21no—
871C4⋊C4—21no—
872C4⋊C4—21no—
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—41no—
884C4⋊C4—41no—
885C4⋊C4—42no—
886C4⋊C4—42no—
887C4⋊C4—42no—
888C4⋊C4—42no—
889C4⋊C4—42no—
890C4⋊C4—42no—
891C4⋊C4—42no—
892C4⋊C4—42no—
893C4⋊C4—42no—
894C4⋊C4—42no—
895C4⋊C4—42no—
896C4⋊C4—42no—
897C4⋊C4—42no—
898C4⋊C4—81no—
899C4⋊C4—81no—
900C4⋊C4—81no—
901C4⋊C4—81no—
902C4⋊C4—81no—
903C4⋊C4—81no—
904C4⋊C4—81no—
905C4⋊C4—81no—
906C4⋊C4—81no—
907C4⋊C4—81no—
908C4⋊C4—81no—
909C4⋊C4—81no—
910C4⋊C4—81no—
911C4⋊C4—81no—
912C4⋊C4—81no—
913C4⋊C4—81no—
914C4⋊C4—81no—
915C4⋊C4—81no—
916C4⋊C4C2×#4112yes—
917C22⋊C4—22no—
918C22⋊C4—22no—
919C22⋊C4—41no—
920C22⋊C4—41no—
921C22⋊C4—41no—
922C22⋊C4—41no—
923C22⋊C4—41no—
924C22⋊C4—41no—
925C22⋊C4—42no—
926C22⋊C4—42no—
927C22⋊C4—42no—
928C22⋊C4—42no—
929C22⋊C4—42no—
930C22⋊C4—42no—
931C22⋊C4—42no—
932C22⋊C4—81no—
933C22⋊C4—81no—
934C22⋊C4—81no—
935C22⋊C4—81no—
936C22⋊C4—81no—
937C22⋊C4—81no—
938C22⋊C4—81no—
939C22⋊C4—81no—
940C22⋊C4—81no—
941C22⋊C4—81no—
942C22⋊C4—81no—
943C22⋊C4—81no—
944C22⋊C4—81no—
945C22⋊C4—81no—
946C22⋊C4—81no—
947C22⋊C4—81no—
948C22⋊C4—81no—
949C22⋊C4—81no—
950C42—22no—
951C42—22no—
952C42—21no—
953C42—21no—
954C42—21no—
955C42—21no—
956C42—21no—
957C42—21no—
958C42—21no—
959C42—21no—
960C42—21no—
961C42—21no—
962C42—42no—
963C42—42no—
964C42—42no—
965C42—42no—
966C42—42no—
967C42—42no—
968C42—42no—
969C42—42no—
970C42—81no—
971C42—81no—
972C42—81no—
973C42—81no—
974C42—81no—
975C42—81no—
976C42—81no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—21no—
981C23—21no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—41no—
991C23—41no—
992C23—41no—
993C23—41no—
994C23—41no—
995C23—41no—
996C23—41no—
997C23#54712yes—
998C23C23×D411yescharacteristic
999Q8—22no—
1000Q8—22no—
1001Q8—41no—
1002Q8—41no—
1003D4—44no—
1004D4—41no—
1005D4—41no—
1006D4—41no—
1007D4—41no—
1008D4—84no—
1009D4—162no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—21no—
1013C2×C4—21no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—21no—
1022C2×C4—21no—
1023C2×C4—21no—
1024C2×C4—21no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
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—22no—
1041C2×C4—21no—
1042C2×C4—22no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—44no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
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—84no—
1099C2×C4—82no—
1100C2×C4#54712yes—
1101C2×C4#57512yes—
1102C2×C4C22×#4111yescharacteristic
1103C2×C4C22×#4111yescharacteristic
1104C2×C4C2×2−1+411yescharacteristic
1105C2×C4#58511yescharacteristic
1106C2×C4#58511yescharacteristic
1107C2×C4#58511yescharacteristic
1108C8—22no—
1109C8—22no—
1110C8—22no—
1111C8—41no—
1112C8—41no—
1113C8—41no—
1114C8—41no—
1115C8—41no—
1116C22—22no—
1117C22—22no—
1118C22—22no—
1119C22—41no—
1120C22—41no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—41no—
1128C22—41no—
1129C22—41no—
1130C22—81no—
1131C22—81no—
1132C22—81no—
1133C22—81no—
1134C22—81no—
1135C22—81no—
1136C22—81no—
1137C22C2×#54711yescharacteristic
1138C22D4×#4111yescharacteristic
1139C22#350011yescharacteristic
1140C22C2×#57511yescharacteristic
1141C22#358411yescharacteristic
1142C22#358511yescharacteristic
1143C22#358611yescharacteristic
1144C4—22no—
1145C4—22no—
1146C4—41no—
1147C4—41no—
1148C4—41no—
1149C4—41no—
1150C4—41no—
1151C4—41no—
1152C4—41no—
1153C4—42no—
1154C4—41no—
1155C4—41no—
1156C4—41no—
1157C4—42no—
1158C4—81no—
1159C4—81no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—81no—
1164C4—81no—
1165C4—81no—
1166C4—81no—
1167C4—81no—
1168C4—81no—
1169C4—81no—
1170C4—81no—
1171C4#347511yescharacteristic
1172C4#349111yescharacteristic
1173C4#349511yescharacteristic
1174C4#356411yescharacteristic
1175C2—42no—
1176C2—81no—
1177C2—161no—
1178C2#5931011yescharacteristic
1179C2#6124311yescharacteristic
1180C2#6126511yescharacteristic
1181C2#6146211yescharacteristic
1182C2#6153011yescharacteristic
1183C2#6258711yescharacteristic
1184C2#6260111yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2407C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#123 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59292C2semidirect
3. #32394C2semidirect
4. #32370C2semidirect
5. #32295C2semidirect
6. #31109C2semidirect
7. #28852C2semidirect
8. #28778C2semidirect
10. #28082C2semidirect
11. #28052C2semidirect
12. #28041C2semidirect
13. #27741C2semidirect
14. #27718C2semidirect
15. #27618C2semidirect
16. #27587C2semidirect
17. #27375C2semidirect
18. #27357C2semidirect
19. #27150C2semidirect
20. #27118C2semidirect
21. #26003C2semidirect
22. #25953C2semidirect
23. #24944C2semidirect
25. #23074C2semidirect
26. #22939C2semidirect
27. #22708C2semidirect
28. #22565C2semidirect
29. #21561C2semidirect
30. #21086C2semidirect
31. #20823C2semidirect

Maximal subgroups

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

subgroupindex
#592922
#592792
#323942
#323702
#322952
#311092
#288522
#287782
#280962
#280822
#280522
#280412
#277412
#277182
#276182
#275872
#273752
#273572
#271502
#271182
#260032
#259532
#249442
#248722
#230742
#229392
#227082
#225652
#215612
#210862
#208232