Finite Group Databasebeta

← #7037549

Subgroups — #7037549

Order 512.

1389 conjugacy classes of subgroups.

The subgroup lattice has 1260 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#44901C211yesmaximal, characteristic, complemented
2#42630C211yesmaximal, characteristic, complemented
3#32379C211yesmaximal, characteristic, complemented
4#31946C211yesmaximal, characteristic, complemented
5#31691C211yesmaximal, characteristic, complemented
6#31676C211yesmaximal, characteristic, complemented
7#31530C211yesmaximal, characteristic, complemented
8#31369C211yesmaximal, characteristic, complemented
9#31361C211yesmaximal, characteristic, complemented
10#30400C211yesmaximal, characteristic
11#29115C211yesmaximal, characteristic, complemented
12#29080C211yesmaximal, characteristic, complemented
13#28067C211yesmaximal, characteristic, complemented
14#28058C211yesmaximal, characteristic, complemented
15#27885C211yesmaximal, characteristic, complemented
16#27733C211yesmaximal, characteristic, complemented
17#27702C211yesmaximal, characteristic, complemented
18#27550C211yesmaximal, characteristic, complemented
19#27518C211yesmaximal, characteristic, complemented
20#27365C211yesmaximal, characteristic, complemented
21#27123C211yesmaximal, characteristic, complemented
22#26747C211yesmaximal, characteristic, complemented
23#25034C211yesmaximal, characteristic, complemented
24#24978C211yesmaximal, characteristic, complemented
25#24942C211yesmaximal, characteristic, complemented
26#24897C211yesmaximal, characteristic, complemented
27#23771C211yesmaximal, characteristic, complemented
28#23305C211yesmaximal, characteristic, complemented
29#23130C211yesmaximal, characteristic, complemented
30#22758C211yesmaximal, characteristic, complemented
31#22056C211yesmaximal, characteristic, complemented
32C2×#466C2211yescharacteristic
33C2×#447C2211yescharacteristic
34C2×C4×D8C2211yescharacteristic
35#2826—21no—
36#2797—21no—
37#2786—21no—
38#2757—21no—
39#2738—21no—
40#2735—21no—
41#2705—21no—
42#2705—21no—
43#2685—21no—
44#2652—21no—
45#2629C2211yescharacteristic
46#2623—21no—
47#2601—21no—
48#2595—21no—
49#2570C2211yescharacteristic, complemented
50#2566C2211yescharacteristic
51#2535C2211yescharacteristic
52#2512C2211yescharacteristic
53#2512C2211yescharacteristic
54#2509C2211yescharacteristic, complemented
55#2500C2211yescharacteristic
56#2496C2211yescharacteristic
57#2495C2211yescharacteristic, complemented
58#2490C2211yescharacteristic
59#2485C2211yescharacteristic
60#2481—21no—
61#2480—21no—
62#2454C2211yescharacteristic, complemented
63#2441C2211yescharacteristic
64#2441C2211yescharacteristic, complemented
65#2422C2211yescharacteristic
66#2422C2211yescharacteristic, complemented
67#2420C2211yescharacteristic
68#2411—21no—
69#2408C2211yescharacteristic
70#2395C2211yescharacteristic
71#2363C2211yescharacteristic
72#2363C2211yescharacteristic, complemented
73#2354C2211yescharacteristic
74#2354C2211yescharacteristic
75D4×C4⋊C4C2211yescharacteristic, complemented
76D4×C22⋊C4C2211yescharacteristic
77#2324C2211yescharacteristic
78#2314C2211yescharacteristic
79#2309C2211yescharacteristic
80#2101C2211yescharacteristic, complemented
81#2100C2211yescharacteristic, complemented
82#2099C2211yescharacteristic, complemented
83#2099C2211yescharacteristic, complemented
84#2092C2211yescharacteristic
85#2092C2211yescharacteristic
86#2092C2211yescharacteristic, complemented
87#2088C2211yescharacteristic, complemented
88#2088C2211yescharacteristic, complemented
89#2085C2211yescharacteristic, complemented
90#2084C2211yescharacteristic, complemented
91#2084C2211yescharacteristic, complemented
92#2083C2211yescharacteristic, complemented
93#2077C2211yescharacteristic
94#2077C2211yescharacteristic, complemented
95#2076C2211yescharacteristic
96#2076C2211yescharacteristic
97#2075C2211yescharacteristic
98#2075C2211yescharacteristic
99#2075C2211yescharacteristic
100#2073C2211yescharacteristic
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic
104#2071C2211yescharacteristic, complemented
105#2067C2211yescharacteristic
106#2067C2211yescharacteristic
107#2065C2211yescharacteristic
108#2059C2211yescharacteristic, complemented
109#2054C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2034C2211yescharacteristic
113#2034C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic, complemented
116#2025C2211yescharacteristic
117#2025C2211yescharacteristic
118#2025C2211yescharacteristic, complemented
119#1999C2211yescharacteristic
120#1992C2211yescharacteristic, complemented
121#1991C2211yescharacteristic, complemented
122#1991C2211yescharacteristic, complemented
123#1989C2211yescharacteristic, complemented
124#1972C2211yescharacteristic
125#1970C2211yescharacteristic
126#1955C2211yescharacteristic
127#1949C2211yescharacteristic, complemented
128#1942C2211yescharacteristic, complemented
129#1936C2211yescharacteristic
130#1936C2211yescharacteristic
131#1936C2211yescharacteristic
132#1936C2211yescharacteristic
133#1936C2211yescharacteristic
134#1934C2211yescharacteristic
135#1934C2211yescharacteristic
136#1934C2211yescharacteristic
137#1934C2211yescharacteristic
138#1934C2211yescharacteristic
139#1934C2211yescharacteristic, complemented
140#1926C2211yescharacteristic
141#1925C2211yescharacteristic
142#1925C2211yescharacteristic
143#1924C2211yescharacteristic, complemented
144#1924C2211yescharacteristic, complemented
145#1923C2211yescharacteristic
146#1923C2211yescharacteristic
147#1921C2211yescharacteristic, complemented
148#1921C2211yescharacteristic, complemented
149#1921C2211yescharacteristic, complemented
150#1921C2211yescharacteristic, complemented
151#1919C2211yescharacteristic, complemented
152#1918C2211yescharacteristic, complemented
153#1918C2211yescharacteristic, complemented
154#1916C2211yescharacteristic, complemented
155#1916C2211yescharacteristic, complemented
156#1893C2211yescharacteristic
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1875C2211yescharacteristic
164#1875C2211yescharacteristic
165#1875C2211yescharacteristic
166#1875C2211yescharacteristic, complemented
167#1869C2211yescharacteristic
168#1864C2211yescharacteristic
169#1862C2211yescharacteristic
170#1862C2211yescharacteristic
171#1862C2211yescharacteristic, complemented
172#1854C2211yescharacteristic
173#1854C2211yescharacteristic, complemented
174#1845C2211yescharacteristic, complemented
175#1836C2211yescharacteristic, complemented
176#1836C2211yescharacteristic, complemented
177#1834C2211yescharacteristic, complemented
178#1825C2211yescharacteristic
179#1825C2211yescharacteristic
180#1825C2211yescharacteristic, complemented
181#1825C2211yescharacteristic, complemented
182#1808C2211yescharacteristic, complemented
183#1804C2211yescharacteristic
184#1802C2211yescharacteristic
185#1802C2211yescharacteristic, complemented
186#1802C2211yescharacteristic, complemented
187#1786C2211yescharacteristic
188#1786C2211yescharacteristic
189#1786C2211yescharacteristic
190#1776C2211yescharacteristic, complemented
191C4×#106C2211yescharacteristic, complemented
192#1770C2211yescharacteristic, complemented
193#1770C2211yescharacteristic, complemented
194#1762C2211yescharacteristic, complemented
195#1762C2211yescharacteristic, complemented
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic, complemented
198C8×C22⋊C4C2211yescharacteristic, complemented
199C8×C22⋊C4C2211yescharacteristic, complemented
200#1750C2211yescharacteristic
201#1750C2211yescharacteristic
202#1735C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×D8C2311yescharacteristic
205C22×D8C2311yescharacteristic
206C23×C8C2311yescharacteristic
207C2×#126—21no—
208C2×#126—21no—
209C2×#126—21no—
210C2×#125C2311yescharacteristic
211C2×#125C2311yescharacteristic
212C2×#123—21no—
213C2×#123—21no—
214C2×#121C2311yescharacteristic
215C2×#121C2311yescharacteristic
216C2×#121C2311yescharacteristic
217C2×#121C2311yescharacteristic
218C2×#120—21no—
219C2×C4×D4C2311yescharacteristic
220C2×C4×D4C2311yescharacteristic
221C2×C4×D4C2311yescharacteristic
222C2×C4×D4C2311yescharacteristic
223C2×C4×D4C2311yescharacteristic
224C2×C4×D4C2311yescharacteristic
225C2×#117—21no—
226C2×#117C2311yescharacteristic
227C2×#117C2311yescharacteristic
228C2×#117C2311yescharacteristic
229C2×#117C2311yescharacteristic
230C22×C4⋊C4—21no—
231C22×C22⋊C4—21no—
232#466—24no—
233#447—24no—
234C4×D8—24no—
235C2×#107C2311yescharacteristic
236C2×#107C2311yescharacteristic
237C2×#107C2311yescharacteristic
238C2×#107C2311yescharacteristic
239C2×#107C2311yescharacteristic
240C2×#107C2311yescharacteristic
241C2×#106C2311yescharacteristic
242C2×#106C2311yescharacteristic
243C2×#106C2311yescharacteristic
244C2×#106C2311yescharacteristic
245C2×C4⋊C8C2311yescharacteristic
246C2×C4⋊C8C2311yescharacteristic
247C2×C4⋊C8C2311yescharacteristic
248C2×#102C2311yescharacteristic
249C2×#102C2311yescharacteristic
250C2×#102C2311yescharacteristic
251C2×#102C2311yescharacteristic
252C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
269C2×C22⋊C8C2311yescharacteristic
270C2×C22⋊C8C2311yescharacteristic
271C2×C22⋊C8C2311yescharacteristic
272C2×C22⋊C8C2311yescharacteristic
273C2×C22⋊C8C2311yescharacteristic
274C2×C22⋊C8C2311yescharacteristic
275C2×#97C2311yescharacteristic
276C2×#97C2311yescharacteristic
277C2×#97C2311yescharacteristic
278C2×C4×C8C2311yescharacteristic
279C2×C4×C8C2311yescharacteristic
280C2×C4×C8C2311yescharacteristic
281C2×C4×C8C2311yescharacteristic
282#400—21no—
283#400—21no—
284#400—21no—
285#400—21no—
286#400—21no—
287#400D411yescharacteristic
288#399—21no—
289#399—21no—
290#399—21no—
291#399D411yescharacteristic
292#398—21no—
293#398—21no—
294#398—21no—
295#398D411yescharacteristic
296#397—21no—
297#397—21no—
298#397—21no—
299#397—21no—
300#397—21no—
301#397—21no—
302#397—21no—
303#397—21no—
304#397—21no—
305#397—21no—
306#397D411yescharacteristic
307#397D411yescharacteristic
308#397D411yescharacteristic
309#396—21no—
310#396—21no—
311#396—21no—
312#396—21no—
313#396—21no—
314#396—21no—
315#396—21no—
316#396—21no—
317#396—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#394D411yescharacteristic
327#394D411yescharacteristic
328#392—21no—
329#392—21no—
330#390—21no—
331#390—21no—
332#390—21no—
333#390—21no—
334#390—21no—
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#389—21no—
348#389—21no—
349#389—21no—
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#387—21no—
377#387—21no—
378#387—21no—
379#387—21no—
380#387—21no—
381#387—21no—
382#387—21no—
383#387—21no—
384#387—21no—
385#386—21no—
386#386—21no—
387#386—21no—
388#386—21no—
389#386—21no—
390#386—21no—
391#386—21no—
392#386—21no—
393#385—21no—
394#385—21no—
395#385—21no—
396#385—21no—
397#385—21no—
398#385—21no—
399#385—21no—
400#385—21no—
401#384C2311yescharacteristic
402#384C2311yescharacteristic
403#384C2311yescharacteristic
404#384C2311yescharacteristic
405#384C2311yescharacteristic
406#383—21no—
407#382C2311yescharacteristic
408#382C2311yescharacteristic
409#382C2311yescharacteristic
410#381—21no—
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⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4C2311yescharacteristic
437C4×C22⋊C4C2311yescharacteristic
438C4×C22⋊C4C2311yescharacteristic
439#340C2311yescharacteristic
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#336C2311yescharacteristic
472#336C2311yescharacteristic
473#336C2311yescharacteristic
474#336C2311yescharacteristic
475#336C2311yescharacteristic
476#336C2311yescharacteristic
477#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481C25—21no—
482C22×D4—22no—
483C22×D4—21no—
484C22×D4—21no—
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
496C22×D4C2411yescharacteristic
497C23×C4—21no—
498C23×C4—21no—
499C23×C4—21no—
500C23×C4—21no—
501C23×C4—21no—
502C23×C4C2411yescharacteristic
503C23×C4C2411yescharacteristic
504C2×D8—22no—
505C2×D8—41no—
506C2×D8—41no—
507C2×D8—41no—
508C2×D8—41no—
509C2×D8#4114yes—
510C22×C8—22no—
511C22×C8—41no—
512C22×C8—41no—
513C22×C8C2411yescharacteristic
514C22×C8C2411yescharacteristic
515C22×C8C2411yescharacteristic
516C22×C8C2411yescharacteristic
517C22×C8C2411yescharacteristic
518C22×C8C2411yescharacteristic
519C22×C8C2411yescharacteristic
520C22×C8C2411yescharacteristic
521#126—82no—
522#126—82no—
523#126—82no—
524#125—41no—
525#125—41no—
526#125—41no—
527#125—41no—
528#123—82no—
529#123—82no—
530#121—22no—
531#121—22no—
532#121—22no—
533#121—41no—
534#121—41no—
535#121—41no—
536#121—41no—
537#121—41no—
538#120—82no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—41no—
542C4×D4—41no—
543C4×D4—41no—
544C4×D4—41no—
545C4×D4—41no—
546C4×D4—41no—
547C4×D4—41no—
548C4×D4—41no—
549C4×D4—41no—
550C4×D4—41no—
551#117—41no—
552#117—41no—
553#117—41no—
554#117—41no—
555#117—41no—
556#117—41no—
557#117—41no—
558#117—41no—
559#117—82no—
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—82no—
585C2×C4⋊C4C2×D411yescharacteristic
586C2×C4⋊C4C2×D411yescharacteristic
587C2×C4⋊C4C2×D411yescharacteristic
588C2×C4⋊C4C2×D411yescharacteristic
589C2×C4⋊C4C2×D411yescharacteristic
590C2×C4⋊C4C2×D411yescharacteristic
591C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
603C2×C4⋊C4C2411yescharacteristic
604C2×C4⋊C4C2411yescharacteristic
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—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—82no—
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×C22⋊C4C2×D411yescharacteristic
653C2×C22⋊C4C2×D411yescharacteristic
654C2×C22⋊C4C2×D411yescharacteristic
655C2×C22⋊C4C2×D411yescharacteristic
656C2×C42—21no—
657C2×C42—21no—
658C2×C42—21no—
659C2×C42—21no—
660C2×C42—21no—
661C2×C42—21no—
662C2×C42—21no—
663C2×C42—21no—
664C2×C42C2411yescharacteristic
665C2×C42C2411yescharacteristic
666C2×C42C2411yescharacteristic
667C2×C42C2411yescharacteristic
668C2×C42C2411yescharacteristic
669#107—22no—
670#107—22no—
671#107—41no—
672#107—41no—
673#107—41no—
674#107—41no—
675#106—41no—
676#106—41no—
677#106—41no—
678#106—41no—
679C4⋊C8—41no—
680C4⋊C8—41no—
681C4⋊C8—41no—
682#102—22no—
683#102—22no—
684#102—22no—
685#102—22no—
686#102—22no—
687#102—22no—
688#102—41no—
689#102—41no—
690#102—41no—
691#102—41no—
692#102—41no—
693#102—41no—
694#102—41no—
695#102—41no—
696#102—41no—
697#102—41no—
698#102—41no—
699#102—41no—
700#102—41no—
701#102—41no—
702C22⋊C8—22no—
703C22⋊C8—41no—
704C22⋊C8—41no—
705C22⋊C8—41no—
706C22⋊C8—41no—
707C22⋊C8—41no—
708C22⋊C8—41no—
709#97—41no—
710#97—41no—
711#97—41no—
712C4×C8—22no—
713C4×C8—41no—
714C4×C8—41no—
715C4×C8—41no—
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—
757C24—21no—
758C24—42no—
759C24—42no—
760C24—81no—
761C24—81no—
762C24—81no—
763C24—81no—
764C24—81no—
765C24C22×D411yescharacteristic
766C24C22×D411yescharacteristic
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
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—42no—
788C2×D4—42no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—82no—
793C2×D4—82no—
794C2×D4—82no—
795C2×D4—82no—
796C2×D4—81no—
797C2×D4—81no—
798C2×D4—81no—
799C2×D4—81no—
800C2×D4—81no—
801C2×D4—81no—
802C2×D4—81no—
803C2×D4—81no—
804C2×D4—81no—
805C2×D4C2×#4112yes—
806C2×D4C2×#4112yes—
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—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—42no—
833C22×C4—42no—
834C22×C4—42no—
835C22×C4—42no—
836C22×C4—81no—
837C22×C4—81no—
838C22×C4—81no—
839C22×C4—81no—
840C22×C4—81no—
841C22×C4—81no—
842C22×C4—81no—
843C22×C4—81no—
844C22×C4—81no—
845C22×C4—81no—
846C22×C4—81no—
847C22×C4C22×D411yescharacteristic
848C22×C4C22×D411yescharacteristic
849C22×C4C22×D411yescharacteristic
850C22×C4C22×D411yescharacteristic
851C22×C4C22×D411yescharacteristic
852C22×C4C22×D411yescharacteristic
853C22×C4C22×D411yescharacteristic
854C22×C4C22×D411yescharacteristic
855C22×C4C22×D411yescharacteristic
856C22×C4C22×D411yescharacteristic
857C22×C4C22×D411yescharacteristic
858C22×C4C22×D411yescharacteristic
859C22×C4C2511yescharacteristic
860D8—44no—
861D8—82no—
862C2×C8—21no—
863C2×C8—21no—
864C2×C8—21no—
865C2×C8—21no—
866C2×C8—21no—
867C2×C8—21no—
868C2×C8—21no—
869C2×C8—21no—
870C2×C8—21no—
871C2×C8—21no—
872C2×C8—21no—
873C2×C8—21no—
874C2×C8—21no—
875C2×C8—21no—
876C2×C8—21no—
877C2×C8—21no—
878C2×C8—21no—
879C2×C8—21no—
880C2×C8—21no—
881C2×C8—21no—
882C2×C8—21no—
883C2×C8—21no—
884C2×C8—21no—
885C2×C8—82no—
886C2×C8C2×#4112yes—
887C4⋊C4—22no—
888C4⋊C4—21no—
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—21no—
894C4⋊C4—21no—
895C4⋊C4—21no—
896C4⋊C4—21no—
897C4⋊C4—21no—
898C4⋊C4—21no—
899C4⋊C4—21no—
900C4⋊C4—21no—
901C4⋊C4—21no—
902C4⋊C4—21no—
903C4⋊C4—21no—
904C4⋊C4—21no—
905C4⋊C4—21no—
906C4⋊C4—21no—
907C4⋊C4—21no—
908C4⋊C4—21no—
909C4⋊C4—21no—
910C4⋊C4—21no—
911C4⋊C4—21no—
912C4⋊C4—21no—
913C4⋊C4—21no—
914C4⋊C4—41no—
915C4⋊C4—41no—
916C4⋊C4—41no—
917C4⋊C4—41no—
918C4⋊C4—41no—
919C4⋊C4—41no—
920C4⋊C4—42no—
921C4⋊C4—42no—
922C4⋊C4—42no—
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⋊C4—81no—
943C4⋊C4—81no—
944C22⋊C4—22no—
945C22⋊C4—22no—
946C22⋊C4—41no—
947C22⋊C4—41no—
948C22⋊C4—41no—
949C22⋊C4—41no—
950C22⋊C4—41no—
951C22⋊C4—41no—
952C22⋊C4—41no—
953C22⋊C4—41no—
954C22⋊C4—42no—
955C22⋊C4—42no—
956C22⋊C4—42no—
957C22⋊C4—42no—
958C22⋊C4—42no—
959C22⋊C4—42no—
960C22⋊C4—42no—
961C22⋊C4—42no—
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—
981C22⋊C4—81no—
982C22⋊C4—81no—
983C22⋊C4—81no—
984C22⋊C4—81no—
985C22⋊C4—81no—
986C22⋊C4—81no—
987C22⋊C4—81no—
988C22⋊C4—81no—
989C22⋊C4—81no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C42—21no—
995C42—21no—
996C42—21no—
997C42—21no—
998C42—21no—
999C42—21no—
1000C42—21no—
1001C42—21no—
1002C42—21no—
1003C42—21no—
1004C42—42no—
1005C42—81no—
1006C42—81no—
1007C42—81no—
1008C42—81no—
1009C42—81no—
1010C42—81no—
1011C42—81no—
1012C23—21no—
1013C23—21no—
1014C23—21no—
1015C23—21no—
1016C23—21no—
1017C23—21no—
1018C23—22no—
1019C23—22no—
1020C23—21no—
1021C23—21no—
1022C23—21no—
1023C23—21no—
1024C23—21no—
1025C23—21no—
1026C23—21no—
1027C23—21no—
1028C23—41no—
1029C23—41no—
1030C23—41no—
1031C23—41no—
1032C23—41no—
1033C23—41no—
1034C23—41no—
1035C23—41no—
1036C23—41no—
1037C23—41no—
1038C23—41no—
1039C23—41no—
1040C23—41no—
1041C23—41no—
1042C23—41no—
1043C23—41no—
1044C23—41no—
1045C23—41no—
1046C23—41no—
1047C23—84no—
1048C23—84no—
1049C23—162no—
1050C23—162no—
1051C23—162no—
1052C23—162no—
1053C23—162no—
1054C23C23×D411yescharacteristic
1055D4—22no—
1056D4—22no—
1057D4—22no—
1058D4—22no—
1059D4—41no—
1060D4—41no—
1061D4—41no—
1062D4—41no—
1063D4—41no—
1064D4—41no—
1065D4—41no—
1066D4—41no—
1067D4—82no—
1068D4—84no—
1069D4—162no—
1070D4—162no—
1071D4—162no—
1072D4—162no—
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—21no—
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—21no—
1107C2×C4—21no—
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—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—84no—
1156C2×C4—84no—
1157C2×C4—162no—
1158C2×C4—162no—
1159C2×C4—162no—
1160C2×C4#57612yes—
1161C2×C4C22×#4111yescharacteristic
1162C2×C4#58511yescharacteristic
1163C2×C4#58511yescharacteristic
1164C2×C4#58511yescharacteristic
1165C2×C4#58511yescharacteristic
1166C2×C4#58511yescharacteristic
1167C8—22no—
1168C8—41no—
1169C8—41no—
1170C8—41no—
1171C8—41no—
1172C8—41no—
1173C8—41no—
1174C8—41no—
1175C22—41no—
1176C22—42no—
1177C22—41no—
1178C22—42no—
1179C22—41no—
1180C22—41no—
1181C22—42no—
1182C22—42no—
1183C22—41no—
1184C22—41no—
1185C22—41no—
1186C22—41no—
1187C22—41no—
1188C22—41no—
1189C22—41no—
1190C22—41no—
1191C22—41no—
1192C22—41no—
1193C22—42no—
1194C22—42no—
1195C22—81no—
1196C22—81no—
1197C22—81no—
1198C22—81no—
1199C22—81no—
1200C22—81no—
1201C22—81no—
1202C22—81no—
1203C22—81no—
1204C22—81no—
1205C22—81no—
1206C22—81no—
1207C22—81no—
1208C22—81no—
1209C22—81no—
1210C22—168no—
1211C22D4×#4111yescharacteristic
1212C22#348511yescharacteristic
1213C22#350011yescharacteristic
1214C22C2×#57611yescharacteristic
1215C22#358411yescharacteristic
1216C22#358411yescharacteristic
1217C22#358511yescharacteristic
1218C4—22no—
1219C4—41no—
1220C4—41no—
1221C4—41no—
1222C4—41no—
1223C4—41no—
1224C4—41no—
1225C4—41no—
1226C4—41no—
1227C4—41no—
1228C4—41no—
1229C4—41no—
1230C4—81no—
1231C4—81no—
1232C4—81no—
1233C4—81no—
1234C4—81no—
1235C4—81no—
1236C4—81no—
1237C4—81no—
1238C4—81no—
1239C4—81no—
1240C4—81no—
1241C4—81no—
1242C4—81no—
1243C4#349111yescharacteristic
1244C4#352111yescharacteristic
1245C4#356611yescharacteristic
1246C4#356611yescharacteristic
1247C2—81no—
1248C2—81no—
1249C2—82no—
1250C2—82no—
1251C2—161no—
1252C2#4350011yescharacteristic
1253C2#6148711yescharacteristic
1254C2#6151911yescharacteristic
1255C2#6176111yescharacteristic
1256C2#6178411yescharacteristic
1257C2#6256111yescharacteristic
1258C2#6260711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30400C2
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. #44901C2semidirect
2. #42630C2semidirect
3. #32379C2semidirect
4. #31946C2semidirect
5. #31691C2semidirect
6. #31676C2semidirect
7. #31530C2semidirect
8. #31369C2semidirect
9. #31361C2semidirect
11. #29115C2semidirect
12. #29080C2semidirect
13. #28067C2semidirect
14. #28058C2semidirect
15. #27885C2semidirect
16. #27733C2semidirect
17. #27702C2semidirect
18. #27550C2semidirect
19. #27518C2semidirect
20. #27365C2semidirect
21. #27123C2semidirect
22. #26747C2semidirect
23. #25034C2semidirect
24. #24978C2semidirect
25. #24942C2semidirect
26. #24897C2semidirect
27. #23771C2semidirect
28. #23305C2semidirect
29. #23130C2semidirect
30. #22758C2semidirect
31. #22056C2semidirect
49. #2570C22semidirect
54. #2509C22semidirect
57. #2495C22semidirect
62. #2454C22semidirect
64. #2441C22semidirect
66. #2422C22semidirect
72. #2363C22semidirect
75. D4×C4⋊C4C22semidirect
80. #2101C22semidirect
81. #2100C22semidirect
82. #2099C22semidirect
83. #2099C22semidirect
86. #2092C22semidirect
87. #2088C22semidirect
88. #2088C22semidirect
89. #2085C22semidirect
90. #2084C22semidirect
91. #2084C22semidirect
92. #2083C22semidirect
94. #2077C22semidirect
104. #2071C22semidirect
108. #2059C22semidirect
115. #2033C22semidirect
118. #2025C22semidirect
120. #1992C22semidirect
121. #1991C22semidirect
122. #1991C22semidirect
123. #1989C22semidirect
127. #1949C22semidirect
128. #1942C22semidirect
139. #1934C22semidirect
143. #1924C22semidirect
144. #1924C22semidirect
147. #1921C22semidirect
148. #1921C22semidirect
149. #1921C22semidirect
150. #1921C22semidirect
151. #1919C22semidirect
152. #1918C22semidirect
153. #1918C22semidirect
154. #1916C22semidirect
155. #1916C22semidirect
166. #1875C22semidirect
171. #1862C22semidirect
173. #1854C22semidirect
174. #1845C22semidirect
175. #1836C22semidirect
176. #1836C22semidirect
177. #1834C22semidirect
180. #1825C22semidirect
181. #1825C22semidirect
182. #1808C22semidirect
185. #1802C22semidirect
186. #1802C22semidirect
190. #1776C22semidirect
191. C4×#106C22semidirect
192. #1770C22semidirect
193. #1770C22semidirect
194. #1762C22semidirect
195. #1762C22semidirect
197. C4×#102C22semidirect
198. C8×C22⋊C4C22semidirect
199. C8×C22⋊C4C22semidirect
202. #1735C22semidirect

Maximal subgroups

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

subgroupindex
#449012
#426302
#323792
#319462
#316912
#316762
#315302
#313692
#313612
#304002
#291152
#290802
#280672
#280582
#278852
#277332
#277022
#275502
#275182
#273652
#271232
#267472
#250342
#249782
#249422
#248972
#237712
#233052
#231302
#227582
#220562