Finite Group Databasebeta

← #6511164

Subgroups — #6511164

Order 512.

1411 conjugacy classes of subgroups.

The subgroup lattice has 1226 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#37502C211yesmaximal, characteristic, complemented
2#35229C211yesmaximal, characteristic, complemented
3#29584C211yesmaximal, characteristic, complemented
4#29530C211yesmaximal, characteristic, complemented
5#29469C211yesmaximal, characteristic, complemented
6#29437C211yesmaximal, characteristic, complemented
7#29186C211yesmaximal, characteristic, complemented
8#29169C211yesmaximal, characteristic, complemented
9#29096C211yesmaximal, characteristic, complemented
10#29000C211yesmaximal, characteristic, complemented
11#28957C211yesmaximal, characteristic, complemented
12#28854C211yesmaximal, characteristic, complemented
13#28770C211yesmaximal, characteristic, complemented
14#28551C211yesmaximal, characteristic
15#28085C211yesmaximal, characteristic, complemented
16#28061C211yesmaximal, characteristic, complemented
17#28004C211yesmaximal, characteristic, complemented
18#27929C211yesmaximal, characteristic, complemented
19#27885C211yesmaximal, characteristic, complemented
20#27868C211yesmaximal, characteristic, complemented
21#27851C211yesmaximal, characteristic, complemented
22#27717C211yesmaximal, characteristic, complemented
23#27717C211yesmaximal, characteristic, complemented
24#27661C211yesmaximal, characteristic, complemented
25#25250C211yesmaximal, characteristic, complemented
26#25250C211yesmaximal, characteristic, complemented
27#22181C211yesmaximal, characteristic, complemented
28#22081C211yesmaximal, characteristic, complemented
29#21578C211yesmaximal, characteristic, complemented
30C2×#1918C211yesmaximal, characteristic, complemented
31#20560C211yesmaximal, characteristic, complemented
32C2×#480C2211yescharacteristic
33C2×#480C2211yescharacteristic
34C2×#466C2211yescharacteristic
35C2×#435C2211yescharacteristic
36C2×C8×D4C2211yescharacteristic
37C22×#107C2211yescharacteristic
38#2854—21no—
39#2853—21no—
40#2837—21no—
41#2836—21no—
42#2667—21no—
43#2654—21no—
44#2651—21no—
45#2649—21no—
46#2647C2211yescharacteristic
47#2644C2211yescharacteristic
48#2629C2211yescharacteristic
49#2624C2211yescharacteristic
50#2623—21no—
51#2618—21no—
52#2522—21no—
53#2516—21no—
54#2513C2211yescharacteristic
55#2507C2211yescharacteristic
56#2507C2211yescharacteristic
57#2501C2211yescharacteristic
58#2501C2211yescharacteristic
59#2497C2211yescharacteristic
60#2497C2211yescharacteristic
61#2490C2211yescharacteristic
62#2486C2211yescharacteristic
63#2486C2211yescharacteristic
64#2454C2211yescharacteristic
65#2442C2211yescharacteristic
66#2442C2211yescharacteristic
67#2425—21no—
68#2425—21no—
69#2420C2211yescharacteristic
70#2419—21no—
71#2419—21no—
72#2416C2211yescharacteristic
73#2416C2211yescharacteristic
74#2330C2211yescharacteristic
75#2324C2211yescharacteristic
76#2319C2211yescharacteristic
77#2314C2211yescharacteristic
78C4×#121C2211yescharacteristic
79C4×#121C2211yescharacteristic
80C2×#389C2211yescharacteristic
81#2290C2211yescharacteristic
82C2×C4×C4⋊C4C2211yescharacteristic
83#2100C2211yescharacteristic
84#2100C2211yescharacteristic
85#2100C2211yescharacteristic
86#2100C2211yescharacteristic
87#2093C2211yescharacteristic
88#2093C2211yescharacteristic
89#2093C2211yescharacteristic
90#2093C2211yescharacteristic
91#2087C2211yescharacteristic
92#2087C2211yescharacteristic
93#2086C2211yescharacteristic
94#2086C2211yescharacteristic
95#2086C2211yescharacteristic
96#2085C2211yescharacteristic
97#2085C2211yescharacteristic
98#2076C2211yescharacteristic
99#2076C2211yescharacteristic
100#2075C2211yescharacteristic
101#2075C2211yescharacteristic
102#2075C2211yescharacteristic
103#2073C2211yescharacteristic
104#2073C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2059C2211yescharacteristic
108#2059C2211yescharacteristic
109#2054C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2025C2211yescharacteristic
113#2025C2211yescharacteristic
114#1999C2211yescharacteristic
115#1992C2211yescharacteristic
116#1992C2211yescharacteristic
117#1991C2211yescharacteristic
118#1991C2211yescharacteristic
119#1970C2211yescharacteristic
120#1970C2211yescharacteristic
121#1944C2211yescharacteristic
122#1944C2211yescharacteristic
123#1943C2211yescharacteristic
124#1943C2211yescharacteristic
125#1942C2211yescharacteristic
126#1942C2211yescharacteristic
127#1941C2211yescharacteristic
128#1941C2211yescharacteristic
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1936C2211yescharacteristic
136#1936C2211yescharacteristic
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1926C2211yescharacteristic
140#1926C2211yescharacteristic
141#1925C2211yescharacteristic
142#1925C2211yescharacteristic
143#1921C2211yescharacteristic
144#1921C2211yescharacteristic
145#1921C2211yescharacteristic
146#1921C2211yescharacteristic
147#1918C2211yescharacteristic
148#1918C2211yescharacteristic
149#1918C2211yescharacteristic
150#1918C2211yescharacteristic
151#1918C2211yescharacteristic
152#1918C2211yescharacteristic
153#1918C2211yescharacteristic
154#1918C2211yescharacteristic
155#1918C2211yescharacteristic
156#1918C2211yescharacteristic
157#1895C2211yescharacteristic
158#1895C2211yescharacteristic
159#1893C2211yescharacteristic
160#1893C2211yescharacteristic
161#1893C2211yescharacteristic
162#1893C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1874C2211yescharacteristic
166#1874C2211yescharacteristic
167#1864C2211yescharacteristic
168#1864C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1853C2211yescharacteristic
172#1853C2211yescharacteristic
173#1845C2211yescharacteristic
174#1845C2211yescharacteristic
175#1836C2211yescharacteristic
176#1836C2211yescharacteristic
177#1823C2211yescharacteristic
178#1823C2211yescharacteristic
179#1809C2211yescharacteristic
180#1809C2211yescharacteristic
181#1808C2211yescharacteristic
182#1808C2211yescharacteristic
183#1808C2211yescharacteristic
184#1776C2211yescharacteristic
185#1776C2211yescharacteristic
186#1771C2211yescharacteristic
187#1770C2211yescharacteristic
188#1768C2211yescharacteristic
189#1762C2211yescharacteristic
190#1762C2211yescharacteristic
191#1753C2211yescharacteristic
192#1752C2211yescharacteristic
193#1752C2211yescharacteristic
194C8×C22⋊C4C2211yescharacteristic
195#1750C2211yescharacteristic
196#1749C2211yescharacteristic
197#1746C2211yescharacteristic
198C2×#340C2211yescharacteristic
199C2×#340C2211yescharacteristic
200C2×#340C2211yescharacteristic
201#1729C2211yescharacteristic
202C2×#336C2211yescharacteristic
203C22×D8C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C23×C8C2311yescharacteristic
208C2×#125C2311yescharacteristic
209C2×#125C2311yescharacteristic
210C2×#123—21no—
211C2×#123—21no—
212C2×#123—21no—
213C2×#123—21no—
214C2×#123—21no—
215C2×#123—21no—
216C2×#121—21no—
217C2×#121—21no—
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×C4×D4—21no—
223C2×C4×D4—21no—
224C2×C4×D4C2311yescharacteristic
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C22×C4⋊C4—21no—
229C22×C4⋊C4C2311yescharacteristic
230C22×C4⋊C4C2311yescharacteristic
231C22×C4⋊C4C2311yescharacteristic
232C22×C4⋊C4C2311yescharacteristic
233C22×C42—21no—
234C22×C42C2311yescharacteristic
235#480—24no—
236#480—24no—
237#466—24no—
238#435—24no—
239C8×D4—24no—
240C2×#107—24no—
241C2×#107C2311yescharacteristic
242C2×#107C2311yescharacteristic
243C2×#107C2311yescharacteristic
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×C4⋊C8C2311yescharacteristic
257C2×C4⋊C8C2311yescharacteristic
258C2×#102C2311yescharacteristic
259C2×#102C2311yescharacteristic
260C2×#102C2311yescharacteristic
261C2×#102C2311yescharacteristic
262C2×#102C2311yescharacteristic
263C2×#102C2311yescharacteristic
264C2×#102C2311yescharacteristic
265C2×#102C2311yescharacteristic
266C2×#102C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×#97C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282C2×C4×C8C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284#400—21no—
285#400—21no—
286#400—21no—
287#400—21no—
288#400—21no—
289#400—21no—
290#399—21no—
291#399—21no—
292#399—21no—
293#399—21no—
294#399—21no—
295#399—21no—
296#398—21no—
297#398—21no—
298#398—21no—
299#398—21no—
300#398—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#398—21no—
305#398—21no—
306#398—21no—
307#398—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#397—21no—
314#397—21no—
315#397—21no—
316#397—21no—
317#397—21no—
318#396—21no—
319#396—21no—
320#396—21no—
321#396—21no—
322#396—21no—
323#396—21no—
324#396—21no—
325#396—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394—21no—
332#390—21no—
333#390—21no—
334#390C2311yescharacteristic
335#390C2311yescharacteristic
336#390C2311yescharacteristic
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#389—21no—
343#389—21no—
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#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
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#388D411yescharacteristic
377#388D411yescharacteristic
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387D411yescharacteristic
387#387D411yescharacteristic
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386D411yescharacteristic
395#386D411yescharacteristic
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385D411yescharacteristic
401#385D411yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#382C2311yescharacteristic
407#382C2311yescharacteristic
408#381—21no—
409#381—21no—
410#381—21no—
411#381—21no—
412#380—21no—
413#380—21no—
414#380—21no—
415#380—21no—
416#380C2311yescharacteristic
417#380C2311yescharacteristic
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
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×C22⋊C4—21no—
434C4×C22⋊C4—21no—
435C4×C22⋊C4C2311yescharacteristic
436C4×C22⋊C4C2311yescharacteristic
437#376C2311yescharacteristic
438C2×#95—21no—
439C2×#95—21no—
440#340C2311yescharacteristic
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#340C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484C22×D4—21no—
485C22×D4—21no—
486C22×D4—21no—
487C22×D4—21no—
488C22×D4C2×D411yescharacteristic
489C22×D4C2411yescharacteristic
490C22×D4C2411yescharacteristic
491C23×C4—21no—
492C23×C4—21no—
493C23×C4—21no—
494C23×C4—21no—
495C23×C4—21no—
496C23×C4—21no—
497C23×C4C2×D411yescharacteristic
498C23×C4C2×D411yescharacteristic
499C23×C4C2411yescharacteristic
500C23×C4C2411yescharacteristic
501C2×D8—22no—
502C2×D8—41no—
503C2×D8—41no—
504C2×M16—22no—
505C2×M16—41no—
506C2×M16—41no—
507C22×C8—22no—
508C22×C8—22no—
509C22×C8—41no—
510C22×C8—41no—
511C22×C8—41no—
512C22×C8—41no—
513C22×C8—41no—
514C22×C8—41no—
515C22×C8#4114yes—
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C22×C8C2411yescharacteristic
524#125—22no—
525#125—41no—
526#125—41no—
527#125—41no—
528#123—82no—
529#123—82no—
530#123—82no—
531#123—82no—
532#123—82no—
533#123—82no—
534#121—22no—
535#121—22no—
536#121—22no—
537#121—22no—
538#121—22no—
539#121—41no—
540#121—41no—
541#121—41no—
542#121—82no—
543#121—82no—
544C4×D4—22no—
545C4×D4—22no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—82no—
551C4×D4—82no—
552#117—41no—
553#117—41no—
554C2×C4⋊C4—22no—
555C2×C4⋊C4—22no—
556C2×C4⋊C4—22no—
557C2×C4⋊C4—22no—
558C2×C4⋊C4—22no—
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⋊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—41no—
592C2×C4⋊C4—41no—
593C2×C4⋊C4—41no—
594C2×C4⋊C4—82no—
595C2×C4⋊C4C2×D411yescharacteristic
596C2×C4⋊C4C2×D411yescharacteristic
597C2×C4⋊C4C2×D411yescharacteristic
598C2×C4⋊C4C2×D411yescharacteristic
599C2×C4⋊C4C2×D411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
602C2×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
605C2×C4⋊C4C2411yescharacteristic
606C2×C4⋊C4C2411yescharacteristic
607C2×C4⋊C4C2411yescharacteristic
608C2×C4⋊C4C2411yescharacteristic
609C2×C4⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
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—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⋊C4C2×D411yescharacteristic
645C2×C22⋊C4C2×D411yescharacteristic
646C2×C22⋊C4C2×D411yescharacteristic
647C2×C22⋊C4C2×D411yescharacteristic
648C2×C22⋊C4C2×D411yescharacteristic
649C2×C22⋊C4C2×D411yescharacteristic
650C2×C22⋊C4C2×D411yescharacteristic
651C2×C22⋊C4C2×D411yescharacteristic
652C2×C42—21no—
653C2×C42—21no—
654C2×C42—21no—
655C2×C42—21no—
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—41no—
659C2×C42—41no—
660C2×C42—82no—
661C2×C42C2×D411yescharacteristic
662C2×C42C2×D411yescharacteristic
663C2×C42C2411yescharacteristic
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668#107—22no—
669#107—22no—
670#107—22no—
671#107—22no—
672#107—22no—
673#107—22no—
674#107—22no—
675#107—22no—
676#107—22no—
677#107—41no—
678#107—41no—
679#106—22no—
680#106—41no—
681#106—41no—
682#106—41no—
683C4⋊C8—22no—
684C4⋊C8—22no—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—22no—
689#102—22no—
690#102—22no—
691#102—22no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699C22⋊C8—22no—
700C22⋊C8—22no—
701C22⋊C8—22no—
702C22⋊C8#4114yes—
703#97—22no—
704#97—41no—
705#97—41no—
706#97—41no—
707#97—41no—
708C4×C8—22no—
709C4×C8—41no—
710C4×C8—41no—
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#95—21no—
743#95—21no—
744#95—21no—
745#95C2×D411yescharacteristic
746#95C2×D411yescharacteristic
747#95C2×D411yescharacteristic
748#95C2×D411yescharacteristic
749#95C2×D411yescharacteristic
750#95C2×D411yescharacteristic
751#95C2×D411yescharacteristic
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755C24—21no—
756C24—21no—
757C24C22×D411yescharacteristic
758C24C22×D411yescharacteristic
759C2×D4—22no—
760C2×D4—22no—
761C2×D4—22no—
762C2×D4—21no—
763C2×D4—21no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—42no—
775C2×D4—42no—
776C2×D4—42no—
777C2×D4—42no—
778C2×D4—42no—
779C2×D4—42no—
780C2×D4—42no—
781C2×D4—81no—
782C2×D4—81no—
783C2×D4—81no—
784C2×D4—81no—
785C2×D4—81no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—22no—
791C22×C4—21no—
792C22×C4—22no—
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—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—41no—
813C22×C4—41no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—42no—
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—42no—
827C22×C4—81no—
828C22×C4—81no—
829C22×C4—81no—
830C22×C4—81no—
831C22×C4—81no—
832C22×C4—81no—
833C22×C4—81no—
834C22×C4C22×D411yescharacteristic
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×C4C2×#4112yes—
847C22×C4C2×#4112yes—
848C22×C4C2511yescharacteristic
849D8—82no—
850M16—82no—
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—44no—
872C2×C8—82no—
873C2×C8—82no—
874C2×C8C2×#4112yes—
875C2×C8C2×#4112yes—
876C2×C8C2×#4112yes—
877C2×C8C2×#4112yes—
878C4⋊C4—22no—
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—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—41no—
907C4⋊C4—41no—
908C4⋊C4—41no—
909C4⋊C4—41no—
910C4⋊C4—42no—
911C4⋊C4—42no—
912C4⋊C4—42no—
913C4⋊C4—42no—
914C4⋊C4—42no—
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⋊C4—81no—
931C4⋊C4—81no—
932C4⋊C4—81no—
933C4⋊C4—81no—
934C4⋊C4—81no—
935C4⋊C4—81no—
936C4⋊C4—81no—
937C4⋊C4—81no—
938C4⋊C4—81no—
939C4⋊C4—81no—
940C4⋊C4—81no—
941C4⋊C4—81no—
942C4⋊C42−1+412yes—
943C22⋊C4—22no—
944C22⋊C4—22no—
945C22⋊C4—22no—
946C22⋊C4—22no—
947C22⋊C4—41no—
948C22⋊C4—41no—
949C22⋊C4—41no—
950C22⋊C4—41no—
951C22⋊C4—42no—
952C22⋊C4—42no—
953C22⋊C4—42no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
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—
973C22⋊C4—81no—
974C22⋊C4—81no—
975C22⋊C4—81no—
976C22⋊C4—81no—
977C22⋊C4—81no—
978C22⋊C4—81no—
979C22⋊C4—81no—
980C22⋊C4—81no—
981C42—21no—
982C42—21no—
983C42—21no—
984C42—21no—
985C42—21no—
986C42—21no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—41no—
992C42—41no—
993C42—81no—
994C42—81no—
995C42—81no—
996C42—81no—
997C42—81no—
998C42—81no—
999C23—21no—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—21no—
1007C23—21no—
1008C23—21no—
1009C23—21no—
1010C23—41no—
1011C23—41no—
1012C23—41no—
1013C23—41no—
1014C23—41no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23#53212yes—
1025C23#57612yes—
1026C23#57612yes—
1027C23C23×D411yescharacteristic
1028D4—44no—
1029D4—41no—
1030D4—41no—
1031D4—41no—
1032D4—41no—
1033D4—41no—
1034D4—41no—
1035D4—41no—
1036D4—41no—
1037D4—84no—
1038D4—84no—
1039D4—162no—
1040D4—162no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
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—21no—
1070C2×C4—22no—
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—44no—
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—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—82no—
1128C2×C4—84no—
1129C2×C4—84no—
1130C2×C4—84no—
1131C2×C4—162no—
1132C2×C4—162no—
1133C2×C4—162no—
1134C2×C4#53212yes—
1135C2×C4C22×#4111yescharacteristic
1136C2×C4C22×#4111yescharacteristic
1137C2×C4C2×2−1+411yescharacteristic
1138C2×C4#58511yescharacteristic
1139C2×C4#58511yescharacteristic
1140C2×C4#58511yescharacteristic
1141C8—22no—
1142C8—22no—
1143C8—22no—
1144C8—22no—
1145C8—41no—
1146C8—41no—
1147C8—41no—
1148C8—41no—
1149C22—22no—
1150C22—22no—
1151C22—22no—
1152C22—22no—
1153C22—22no—
1154C22—22no—
1155C22—41no—
1156C22—41no—
1157C22—41no—
1158C22—41no—
1159C22—41no—
1160C22—41no—
1161C22—41no—
1162C22—81no—
1163C22—81no—
1164C22—81no—
1165C22—81no—
1166C22—81no—
1167C22—81no—
1168C22—81no—
1169C22—81no—
1170C22—81no—
1171C22—81no—
1172C22—81no—
1173C22—81no—
1174C22—81no—
1175C22—81no—
1176C22#317614yes—
1177C22C2×#53211yescharacteristic
1178C22#348511yescharacteristic
1179C22#348911yescharacteristic
1180C22C2×#57611yescharacteristic
1181C22C2×#57611yescharacteristic
1182C22#358611yescharacteristic
1183C22#358611yescharacteristic
1184C4—22no—
1185C4—41no—
1186C4—41no—
1187C4—41no—
1188C4—41no—
1189C4—41no—
1190C4—41no—
1191C4—41no—
1192C4—41no—
1193C4—41no—
1194C4—41no—
1195C4—42no—
1196C4—41no—
1197C4—81no—
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#349111yescharacteristic
1211C4#350711yescharacteristic
1212C4#351511yescharacteristic
1213C4#352111yescharacteristic
1214C2—24no—
1215C2—81no—
1216C2—161no—
1217C2—161no—
1218C2#3546411yescharacteristic
1219C2C2×#317611yescharacteristic
1220C2#6069911yescharacteristic
1221C2#6174411yescharacteristic
1222C2#6175911yescharacteristic
1223C2#6215511yescharacteristic
1224C2#6217011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#28551C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #37502C2semidirect
2. #35229C2semidirect
3. #29584C2semidirect
4. #29530C2semidirect
5. #29469C2semidirect
6. #29437C2semidirect
7. #29186C2semidirect
8. #29169C2semidirect
9. #29096C2semidirect
10. #29000C2semidirect
11. #28957C2semidirect
12. #28854C2semidirect
13. #28770C2semidirect
15. #28085C2semidirect
16. #28061C2semidirect
17. #28004C2semidirect
18. #27929C2semidirect
19. #27885C2semidirect
20. #27868C2semidirect
21. #27851C2semidirect
22. #27717C2semidirect
23. #27717C2semidirect
24. #27661C2semidirect
25. #25250C2semidirect
26. #25250C2semidirect
27. #22181C2semidirect
28. #22081C2semidirect
29. #21578C2semidirect
30. C2×#1918C2semidirect
31. #20560C2semidirect

Maximal subgroups

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

subgroupindex
#375022
#352292
#295842
#295302
#294692
#294372
#291862
#291692
#290962
#290002
#289572
#288542
#287702
#285512
#280852
#280612
#280042
#279292
#278852
#278682
#278512
#277172
#276612
#252502
#221812
#220812
#215782
C2×#19182
#205602