Finite Group Databasebeta

← #6879804

Subgroups — #6879804

Order 512.

1395 conjugacy classes of subgroups.

The subgroup lattice has 1247 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39157C211yesmaximal, characteristic, complemented
2#38056C211yesmaximal, characteristic
3#33274C211yesmaximal, characteristic, complemented
4#32442C211yesmaximal, characteristic, complemented
5#32241C211yesmaximal, characteristic, complemented
6#31748C211yesmaximal, characteristic, complemented
7#31716C211yesmaximal, characteristic, complemented
8#31638C211yesmaximal, characteristic, complemented
9#31286C211yesmaximal, characteristic
10#30827C211yesmaximal, characteristic, complemented
11#30547C211yesmaximal, characteristic
12#30356C211yesmaximal, characteristic, complemented
13#30353C211yesmaximal, characteristic, complemented
14#29530C211yesmaximal, characteristic, complemented
15#29504C211yesmaximal, characteristic, complemented
16#29483C211yesmaximal, characteristic, complemented
17#29441C211yesmaximal, characteristic, complemented
18#29360C211yesmaximal, characteristic, complemented
19#29109C211yesmaximal, characteristic, complemented
20#27518C211yesmaximal, characteristic, complemented
21#27423C211yesmaximal, characteristic, complemented
22#27238C211yesmaximal, characteristic, complemented
23#27207C211yesmaximal, characteristic, complemented
24#27047C211yesmaximal, characteristic, complemented
25#27018C211yesmaximal, characteristic, complemented
26#26721C211yesmaximal, characteristic, complemented
27#26692C211yesmaximal, characteristic, complemented
28#22126C211yesmaximal, characteristic, complemented
29#22043C211yesmaximal, characteristic, complemented
30#21652C211yesmaximal, characteristic, complemented
31#21437C211yesmaximal, characteristic, complemented
32C2×#490C2211yescharacteristic
33C2×#478C2211yescharacteristic
34C2×#450C2211yescharacteristic
35#2857C2211yescharacteristic
36#2854C2211yescharacteristic
37#2762—21no—
38#2762—21no—
39#2756—21no—
40#2753—21no—
41#2749—21no—
42#2706—21no—
43#2689—21no—
44#2689—21no—
45#2645C2211yescharacteristic, complemented
46#2645C2211yescharacteristic, complemented
47#2644C2211yescharacteristic
48#2641C2211yescharacteristic
49#2571—21no—
50#2567C2211yescharacteristic, complemented
51#2552C2211yescharacteristic, complemented
52#2534—21no—
53#2513C2211yescharacteristic
54#2509—21no—
55#2496—21no—
56#2496C2211yescharacteristic
57#2496C2211yescharacteristic
58#2494—21no—
59#2489C2211yescharacteristic
60#2489C2211yescharacteristic
61#2454C2211yescharacteristic
62#2445C2211yescharacteristic
63#2445C2211yescharacteristic
64#2442C2211yescharacteristic
65#2433C2211yescharacteristic
66#2418—21no—
67#2412—21no—
68#2412—21no—
69#2369C2211yescharacteristic, complemented
70#2361C2211yescharacteristic
71#2355C2211yescharacteristic, complemented
72D4×C22⋊C4C2211yescharacteristic
73#2330C2211yescharacteristic, complemented
74#2330C2211yescharacteristic, complemented
75#2328C2211yescharacteristic
76#2319C2211yescharacteristic
77C4×C22⋊Q8C2211yescharacteristic
78C2×#390C2211yescharacteristic
79#2283C2211yescharacteristic
80#2100C2211yescharacteristic, complemented
81#2099C2211yescharacteristic, complemented
82#2093C2211yescharacteristic
83#2093C2211yescharacteristic, complemented
84#2088C2211yescharacteristic, complemented
85#2085C2211yescharacteristic, complemented
86#2075C2211yescharacteristic
87#2075C2211yescharacteristic
88#2075C2211yescharacteristic
89#2074C2211yescharacteristic, complemented
90#2071C2211yescharacteristic
91#2071C2211yescharacteristic
92#2071C2211yescharacteristic
93#2071C2211yescharacteristic, complemented
94#2068C2211yescharacteristic, complemented
95#2067C2211yescharacteristic
96#2067C2211yescharacteristic
97#2065C2211yescharacteristic, complemented
98#2059C2211yescharacteristic, complemented
99#2059C2211yescharacteristic, complemented
100#2057C2211yescharacteristic, complemented
101#2055C2211yescharacteristic
102#2055C2211yescharacteristic
103#2055C2211yescharacteristic, complemented
104#2041C2211yescharacteristic
105#2041C2211yescharacteristic
106#2035C2211yescharacteristic
107#2033C2211yescharacteristic
108#2033C2211yescharacteristic
109#2033C2211yescharacteristic
110#2026C2211yescharacteristic, complemented
111#2025C2211yescharacteristic
112#2025C2211yescharacteristic
113#2025C2211yescharacteristic, complemented
114#2023C2211yescharacteristic
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic, complemented
117#2014C2211yescharacteristic
118#2014C2211yescharacteristic
119#2000C2211yescharacteristic
120#1991C2211yescharacteristic, complemented
121#1989C2211yescharacteristic, complemented
122#1989C2211yescharacteristic, complemented
123#1989C2211yescharacteristic, complemented
124#1982C2211yescharacteristic
125#1982C2211yescharacteristic
126#1973C2211yescharacteristic
127#1973C2211yescharacteristic
128#1973C2211yescharacteristic, complemented
129#1968C2211yescharacteristic
130#1968C2211yescharacteristic
131#1957C2211yescharacteristic
132#1947C2211yescharacteristic, complemented
133#1944C2211yescharacteristic, complemented
134#1944C2211yescharacteristic, complemented
135#1943C2211yescharacteristic, complemented
136#1942C2211yescharacteristic, complemented
137#1942C2211yescharacteristic, complemented
138#1936C2211yescharacteristic
139#1936C2211yescharacteristic
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic, complemented
143#1935C2211yescharacteristic, complemented
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1934C2211yescharacteristic, complemented
149#1934C2211yescharacteristic, complemented
150#1933C2211yescharacteristic, complemented
151#1933C2211yescharacteristic, complemented
152#1928C2211yescharacteristic, complemented
153#1926C2211yescharacteristic
154#1926C2211yescharacteristic
155#1926C2211yescharacteristic
156#1926C2211yescharacteristic, complemented
157#1925C2211yescharacteristic
158#1925C2211yescharacteristic
159#1925C2211yescharacteristic
160#1924C2211yescharacteristic
161#1924C2211yescharacteristic
162#1923C2211yescharacteristic
163#1923C2211yescharacteristic
164#1921C2211yescharacteristic, complemented
165#1921C2211yescharacteristic, complemented
166#1921C2211yescharacteristic, complemented
167#1920C2211yescharacteristic, complemented
168#1919C2211yescharacteristic, complemented
169#1918C2211yescharacteristic, complemented
170#1917C2211yescharacteristic, complemented
171#1917C2211yescharacteristic, complemented
172#1916C2211yescharacteristic, complemented
173#1916C2211yescharacteristic, complemented
174#1880C2211yescharacteristic
175#1880C2211yescharacteristic
176#1880C2211yescharacteristic, complemented
177#1877C2211yescharacteristic
178#1877C2211yescharacteristic
179#1877C2211yescharacteristic, complemented
180#1872C2211yescharacteristic
181#1864C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1853C2211yescharacteristic
186#1836C2211yescharacteristic, complemented
187#1824C2211yescharacteristic
188#1824C2211yescharacteristic
189#1802C2211yescharacteristic
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1768C2211yescharacteristic, complemented
194#1768C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic
198C4×#102C2211yescharacteristic, complemented
199#1749C2211yescharacteristic
200C4×C22⋊C8C2211yescharacteristic
201#1746C2211yescharacteristic, complemented
202#1726C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C2×C4⋊Q8C2311yescharacteristic
208C2×#127C2311yescharacteristic
209C2×#127C2311yescharacteristic
210C2×#126—21no—
211C2×#126—21no—
212C2×#125C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×#123—21no—
216C2×#123—21no—
217C2×#123—21no—
218C2×C22⋊Q8—21no—
219C2×C22⋊Q8C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#120—21no—
222C2×#120—21no—
223C2×C4×Q8C2311yescharacteristic
224C2×C4×D4—21no—
225C2×C4×D4C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C22×C4⋊C4C2311yescharacteristic
229C22×C22⋊C4—21no—
230C22×C22⋊C4—21no—
231C22×C22⋊C4—21no—
232C22×C42C2311yescharacteristic
233#490—24no—
234#478—24no—
235#450—24no—
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#107C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×C4⋊C8C2311yescharacteristic
249C2×#103C2311yescharacteristic
250C2×#103C2311yescharacteristic
251C2×#103C2311yescharacteristic
252C2×#103C2311yescharacteristic
253C2×#103C2311yescharacteristic
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×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×C22⋊C8C2311yescharacteristic
276C2×C22⋊C8C2311yescharacteristic
277C2×C22⋊C8C2311yescharacteristic
278C2×C22⋊C8C2311yescharacteristic
279C2×#97C2311yescharacteristic
280C2×#97C2311yescharacteristic
281C2×#97C2311yescharacteristic
282C2×#97C2311yescharacteristic
283C2×C4×C8C2311yescharacteristic
284C2×C4×C8C2311yescharacteristic
285C2×C4×C8C2311yescharacteristic
286C2×C4×C8C2311yescharacteristic
287#401—21no—
288#401—21no—
289#400—21no—
290#400—21no—
291#400—21no—
292#400—21no—
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#400—21no—
299#400—21no—
300#399—21no—
301#398—21no—
302#398—21no—
303#398—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#397—21no—
313#396—21no—
314#396—21no—
315#395—21no—
316#395—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#392—21no—
326#392—21no—
327#391—21no—
328#391—21no—
329#391—21no—
330#391C2311yescharacteristic
331#391C2311yescharacteristic
332#391C2311yescharacteristic
333#391C2311yescharacteristic
334#391C2311yescharacteristic
335#390—21no—
336#390—21no—
337#390C2311yescharacteristic
338#390C2311yescharacteristic
339#390C2311yescharacteristic
340#390C2311yescharacteristic
341#390C2311yescharacteristic
342#390C2311yescharacteristic
343#390C2311yescharacteristic
344#390C2311yescharacteristic
345#390C2311yescharacteristic
346#390C2311yescharacteristic
347#390C2311yescharacteristic
348#389—21no—
349#389—21no—
350#389—21no—
351#389—21no—
352#389—21no—
353#389—21no—
354#389—21no—
355#389—21no—
356#389—21no—
357#389C2311yescharacteristic
358#389C2311yescharacteristic
359#389C2311yescharacteristic
360#389C2311yescharacteristic
361#389C2311yescharacteristic
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
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#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#387—21no—
386#387—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#386—21no—
394#386—21no—
395#386—21no—
396#386—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#384—21no—
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#383D411yescharacteristic
406#383D411yescharacteristic
407#382—21no—
408#382—21no—
409#382—21no—
410#382D411yescharacteristic
411#382D411yescharacteristic
412#382C2311yescharacteristic
413#381—21no—
414#381D411yescharacteristic
415#381D411yescharacteristic
416#380—21no—
417#380—21no—
418#380—21no—
419#380—21no—
420#380D411yescharacteristic
421#380D411yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#379—21no—
427C4×C4⋊C4—21no—
428C4×C4⋊C4—21no—
429C4×C4⋊C4—21no—
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⋊C4C2311yescharacteristic
440C4×C22⋊C4C2311yescharacteristic
441#376C2311yescharacteristic
442#376C2311yescharacteristic
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#336C2311yescharacteristic
470#336C2311yescharacteristic
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—21no—
489C22×D4—21no—
490C22×D4—21no—
491C22×D4—41no—
492C22×D4—41no—
493C22×D4—41no—
494C22×D4—41no—
495C22×D4—41no—
496C22×D4C2411yescharacteristic
497C22×D4C2411yescharacteristic
498C22×D4C2411yescharacteristic
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4—21no—
503C23×C4C2×D411yescharacteristic
504C23×C4C2×D411yescharacteristic
505C23×C4C2411yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—41no—
509C2×SD16—41no—
510C2×SD16—41no—
511C2×SD16—41no—
512C2×SD16—41no—
513C2×SD16—41no—
514C2×SD16—41no—
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521C22×C8C2411yescharacteristic
522C22×C8C2411yescharacteristic
523C4⋊Q8—41no—
524C4⋊Q8—41no—
525#127—22no—
526#127—41no—
527#127—41no—
528#127—41no—
529#126—82no—
530#126—82no—
531#125—22no—
532#125—22no—
533#125—41no—
534#125—41no—
535#125—41no—
536#125—41no—
537#123—82no—
538#123—82no—
539#123—82no—
540C22⋊Q8—22no—
541C22⋊Q8—41no—
542C22⋊Q8—82no—
543#121—41no—
544#121—41no—
545#120—82no—
546#120—82no—
547C4×Q8—41no—
548C4×Q8—41no—
549C4×D4—22no—
550C4×D4—41no—
551C4×D4—41no—
552C4×D4—41no—
553C4×D4—41no—
554C4×D4—41no—
555C4×D4—82no—
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⋊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—41no—
585C2×C4⋊C4—41no—
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2411yescharacteristic
591C2×C4⋊C4C2411yescharacteristic
592C2×C4⋊C4C2411yescharacteristic
593C2×C4⋊C4C2411yescharacteristic
594C2×C4⋊C4C2411yescharacteristic
595C2×C4⋊C4C2411yescharacteristic
596C2×C4⋊C4C2411yescharacteristic
597C2×C4⋊C4C2411yescharacteristic
598C2×C4⋊C4C2411yescharacteristic
599C2×C4⋊C4C2411yescharacteristic
600C2×C4⋊C4C2411yescharacteristic
601C2×C4⋊C4C2411yescharacteristic
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—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—82no—
634C2×C22⋊C4—82no—
635C2×C22⋊C4—82no—
636C2×C22⋊C4C2×D411yescharacteristic
637C2×C22⋊C4C2×D411yescharacteristic
638C2×C22⋊C4C2×D411yescharacteristic
639C2×C22⋊C4C2×D411yescharacteristic
640C2×C42—21no—
641C2×C42—21no—
642C2×C42—21no—
643C2×C42—21no—
644C2×C42—21no—
645C2×C42—21no—
646C2×C42—21no—
647C2×C42—41no—
648C2×C42—41no—
649C2×C42C2×D411yescharacteristic
650C2×C42C2×D411yescharacteristic
651C2×C42C2411yescharacteristic
652C2×C42C2411yescharacteristic
653C2×C42C2411yescharacteristic
654C2×C42C2411yescharacteristic
655C2×C42C2411yescharacteristic
656C2×C42C2411yescharacteristic
657#107—22no—
658#107—41no—
659#107—41no—
660#107—41no—
661#107—41no—
662#107—41no—
663#106—22no—
664#106—41no—
665#106—41no—
666C4⋊C8—22no—
667C4⋊C8—41no—
668C4⋊C8—41no—
669C4⋊C8—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—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102#4114yes—
696C22⋊C8—22no—
697C22⋊C8—41no—
698C22⋊C8—41no—
699C22⋊C8—41no—
700#97—22no—
701#97—41no—
702#97—41no—
703#97—41no—
704C4×C8—41no—
705C4×C8—41no—
706C4×C8—41no—
707C4×C8—41no—
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
752#95C2×D411yescharacteristic
753#95C2×D411yescharacteristic
754#95C2×D411yescharacteristic
755#95C2×D411yescharacteristic
756#95C2×D411yescharacteristic
757#95C2×D411yescharacteristic
758C24—21no—
759C24—21no—
760C24—21no—
761C24—42no—
762C24—42no—
763C24—42no—
764C24—42no—
765C24—81no—
766C24—81no—
767C24—81no—
768C24C22×D411yescharacteristic
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—21no—
772C2×Q8—21no—
773C2×Q8—21no—
774C2×Q8—21no—
775C2×Q8—42no—
776C2×Q8—81no—
777C2×Q8—81no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—21no—
792C2×D4—21no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—42no—
796C2×D4—42no—
797C2×D4—42no—
798C2×D4—42no—
799C2×D4—42no—
800C2×D4—42no—
801C2×D4—42no—
802C2×D4—81no—
803C2×D4—81no—
804C2×D4—81no—
805C2×D4—81no—
806C2×D4—81no—
807C2×D4—81no—
808C2×D4—81no—
809C2×D4—81no—
810C2×D4—81no—
811C2×D4—81no—
812C2×D4—81no—
813C2×D4—82no—
814C2×D4—82no—
815C2×D4—82no—
816C2×D4—82no—
817C2×D4C2×#4112yes—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—22no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—41no—
840C22×C4—41no—
841C22×C4—41no—
842C22×C4—41no—
843C22×C4—42no—
844C22×C4—42no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4—81no—
848C22×C4—81no—
849C22×C4—81no—
850C22×C4—81no—
851C22×C4—81no—
852C22×C4—81no—
853C22×C4—81no—
854C22×C4—81no—
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C22×D411yescharacteristic
860C22×C4C22×D411yescharacteristic
861C22×C4C22×D411yescharacteristic
862C22×C4C22×D411yescharacteristic
863C22×C4C22×D411yescharacteristic
864C22×C4C22×D411yescharacteristic
865C22×C4C22×D411yescharacteristic
866C22×C4C22×D411yescharacteristic
867C22×C4C22×D411yescharacteristic
868C22×C4C2511yescharacteristic
869SD16—82no—
870SD16—82no—
871SD16—82no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—21no—
886C2×C8—21no—
887C2×C8—21no—
888C2×C8—21no—
889C2×C8—21no—
890C2×C8—21no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8C2×#4112yes—
896C4⋊C4—22no—
897C4⋊C4—22no—
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—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—21no—
915C4⋊C4—21no—
916C4⋊C4—21no—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—41no—
922C4⋊C4—41no—
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—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⋊C4—81no—
943C4⋊C4—81no—
944C4⋊C4—81no—
945C4⋊C4—81no—
946C4⋊C4—81no—
947C4⋊C4—81no—
948C4⋊C4—81no—
949C4⋊C4—81no—
950C4⋊C4—81no—
951C4⋊C4C2×#4112yes—
952C22⋊C4—22no—
953C22⋊C4—22no—
954C22⋊C4—41no—
955C22⋊C4—41no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
962C22⋊C4—42no—
963C22⋊C4—42no—
964C22⋊C4—42no—
965C22⋊C4—42no—
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—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C42—21no—
988C42—21no—
989C42—21no—
990C42—21no—
991C42—21no—
992C42—21no—
993C42—21no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—41no—
1000C42—41no—
1001C42—42no—
1002C42—42no—
1003C42—81no—
1004C42—81no—
1005C42—81no—
1006C42—81no—
1007C42—81no—
1008C23—21no—
1009C23—21no—
1010C23—21no—
1011C23—21no—
1012C23—21no—
1013C23—21no—
1014C23—22no—
1015C23—41no—
1016C23—41no—
1017C23—41no—
1018C23—41no—
1019C23—41no—
1020C23—41no—
1021C23—41no—
1022C23—41no—
1023C23—41no—
1024C23—41no—
1025C23—41no—
1026C23—41no—
1027C23—41no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—84no—
1036C23—84no—
1037C23—84no—
1038C23—84no—
1039C23—162no—
1040C23—162no—
1041C23—162no—
1042C23#57612yes—
1043C23C23×D411yescharacteristic
1044Q8—41no—
1045Q8—41no—
1046Q8—41no—
1047Q8—41no—
1048Q8—162no—
1049D4—22no—
1050D4—22no—
1051D4—41no—
1052D4—41no—
1053D4—41no—
1054D4—41no—
1055D4—41no—
1056D4—41no—
1057D4—41no—
1058D4—41no—
1059D4—41no—
1060D4—41no—
1061D4—84no—
1062D4—84no—
1063D4—162no—
1064D4—162no—
1065D4—162no—
1066D4—162no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—21no—
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—21no—
1084C2×C4—21no—
1085C2×C4—21no—
1086C2×C4—21no—
1087C2×C4—21no—
1088C2×C4—22no—
1089C2×C4—21no—
1090C2×C4—21no—
1091C2×C4—21no—
1092C2×C4—21no—
1093C2×C4—21no—
1094C2×C4—21no—
1095C2×C4—21no—
1096C2×C4—21no—
1097C2×C4—21no—
1098C2×C4—21no—
1099C2×C4—21no—
1100C2×C4—21no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
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—41no—
1133C2×C4—41no—
1134C2×C4—41no—
1135C2×C4—41no—
1136C2×C4—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
1148C2×C4—82no—
1149C2×C4—82no—
1150C2×C4—162no—
1151C2×C4—162no—
1152C2×C4—162no—
1153C2×C4—162no—
1154C2×C4#57712yes—
1155C2×C4C22×#4111yescharacteristic
1156C2×C4#58511yescharacteristic
1157C2×C4#58511yescharacteristic
1158C2×C4#58511yescharacteristic
1159C2×C4#58511yescharacteristic
1160C2×C4#58511yescharacteristic
1161C8—22no—
1162C8—41no—
1163C8—41no—
1164C8—41no—
1165C8—41no—
1166C8—41no—
1167C8—41no—
1168C8—41no—
1169C22—22no—
1170C22—22no—
1171C22—22no—
1172C22—41no—
1173C22—41no—
1174C22—41no—
1175C22—41no—
1176C22—42no—
1177C22—42no—
1178C22—42no—
1179C22—81no—
1180C22—81no—
1181C22—81no—
1182C22—81no—
1183C22—81no—
1184C22—81no—
1185C22—81no—
1186C22—81no—
1187C22—81no—
1188C22—81no—
1189C22—81no—
1190C22—81no—
1191C22—81no—
1192C22—81no—
1193C22—81no—
1194C22—81no—
1195C22—81no—
1196C22—81no—
1197C22—168no—
1198C22#344911yescharacteristic
1199C22D4×#4111yescharacteristic
1200C22#350011yescharacteristic
1201C22C2×#57611yescharacteristic
1202C22C2×#57711yescharacteristic
1203C22#358511yescharacteristic
1204C22#358611yescharacteristic
1205C4—22no—
1206C4—41no—
1207C4—41no—
1208C4—41no—
1209C4—41no—
1210C4—41no—
1211C4—41no—
1212C4—41no—
1213C4—41no—
1214C4—42no—
1215C4—41no—
1216C4—41no—
1217C4—41no—
1218C4—41no—
1219C4—81no—
1220C4—81no—
1221C4—81no—
1222C4—81no—
1223C4—81no—
1224C4—81no—
1225C4—81no—
1226C4—81no—
1227C4—81no—
1228C4—81no—
1229C4—81no—
1230C4—81no—
1231C4#351011yescharacteristic
1232C4#352111yescharacteristic
1233C4#356611yescharacteristic
1234C4#356811yescharacteristic
1235C2—42no—
1236C2—82no—
1237C2—161no—
1238C2—161no—
1239C2#3994711yescharacteristic
1240C2#6097811yescharacteristic
1241C2#6098211yescharacteristic
1242C2#6149811yescharacteristic
1243C2#6150911yescharacteristic
1244C2#6260511yescharacteristic
1245C2#6260811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2433C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2283 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39157C2semidirect
3. #33274C2semidirect
4. #32442C2semidirect
5. #32241C2semidirect
6. #31748C2semidirect
7. #31716C2semidirect
8. #31638C2semidirect
10. #30827C2semidirect
12. #30356C2semidirect
13. #30353C2semidirect
14. #29530C2semidirect
15. #29504C2semidirect
16. #29483C2semidirect
17. #29441C2semidirect
18. #29360C2semidirect
19. #29109C2semidirect
20. #27518C2semidirect
21. #27423C2semidirect
22. #27238C2semidirect
23. #27207C2semidirect
24. #27047C2semidirect
25. #27018C2semidirect
26. #26721C2semidirect
27. #26692C2semidirect
28. #22126C2semidirect
29. #22043C2semidirect
30. #21652C2semidirect
31. #21437C2semidirect
45. #2645C22semidirect
46. #2645C22semidirect
50. #2567C22semidirect
51. #2552C22semidirect
69. #2369C22semidirect
71. #2355C22semidirect
73. #2330C22semidirect
74. #2330C22semidirect
80. #2100C22semidirect
81. #2099C22semidirect
83. #2093C22semidirect
84. #2088C22semidirect
85. #2085C22semidirect
89. #2074C22semidirect
93. #2071C22semidirect
94. #2068C22semidirect
97. #2065C22semidirect
98. #2059C22semidirect
99. #2059C22semidirect
100. #2057C22semidirect
103. #2055C22semidirect
110. #2026C22semidirect
113. #2025C22semidirect
116. #2023C22semidirect
120. #1991C22semidirect
121. #1989C22semidirect
122. #1989C22semidirect
123. #1989C22semidirect
128. #1973C22semidirect
132. #1947C22semidirect
133. #1944C22semidirect
134. #1944C22semidirect
135. #1943C22semidirect
136. #1942C22semidirect
137. #1942C22semidirect
142. #1936C22semidirect
143. #1935C22semidirect
148. #1934C22semidirect
149. #1934C22semidirect
150. #1933C22semidirect
151. #1933C22semidirect
152. #1928C22semidirect
156. #1926C22semidirect
164. #1921C22semidirect
165. #1921C22semidirect
166. #1921C22semidirect
167. #1920C22semidirect
168. #1919C22semidirect
169. #1918C22semidirect
170. #1917C22semidirect
171. #1917C22semidirect
172. #1916C22semidirect
173. #1916C22semidirect
176. #1880C22semidirect
179. #1877C22semidirect
181. #1864C22semidirect
182. #1863C22semidirect
186. #1836C22semidirect
193. #1768C22semidirect
194. #1768C22semidirect
196. #1762C22semidirect
198. C4×#102C22semidirect
201. #1746C22semidirect
202. #1726C22semidirect

Maximal subgroups

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

subgroupindex
#391572
#380562
#332742
#324422
#322412
#317482
#317162
#316382
#312862
#308272
#305472
#303562
#303532
#295302
#295042
#294832
#294412
#293602
#291092
#275182
#274232
#272382
#272072
#270472
#270182
#267212
#266922
#221262
#220432
#216522
#214372