Finite Group Databasebeta

← #6998626

Subgroups — #6998626

Order 512.

1575 conjugacy classes of subgroups.

The subgroup lattice has 1345 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45108C211yesmaximal, characteristic, complemented
2#42630C211yesmaximal, characteristic, complemented
3#31778C211yesmaximal, characteristic, complemented
4#31455C211yesmaximal, characteristic, complemented
5#31408C211yesmaximal, characteristic, complemented
6#31309C211yesmaximal, characteristic, complemented
7#31008C211yesmaximal, characteristic, complemented
8#31003C211yesmaximal, characteristic, complemented
9#30883C211yesmaximal, characteristic, complemented
10#30790C211yesmaximal, characteristic, complemented
11#29119C211yesmaximal, characteristic, complemented
12#29062C211yesmaximal, characteristic, complemented
13#29035C211yesmaximal, characteristic, complemented
14#29003C211yesmaximal, characteristic, complemented
15#27764C211yesmaximal, characteristic, complemented
16#27534C211yesmaximal, characteristic, complemented
17#27271C211yesmaximal, characteristic, complemented
18#27047C211yesmaximal, characteristic, complemented
19#26766C211yesmaximal, characteristic, complemented
20#26672C211yesmaximal, characteristic, complemented
21#26642C211yesmaximal, characteristic, complemented
22#26488C211yesmaximal, characteristic, complemented
23#26164C211yesmaximal, characteristic, complemented
24#25684C211yesmaximal, characteristic, complemented
25#24245C211yesmaximal, characteristic
26#24050C211yesmaximal, characteristic, complemented
27#23579C211yesmaximal, characteristic, complemented
28#23303C211yesmaximal, characteristic, complemented
29#23011C211yesmaximal, characteristic, complemented
30#22880C211yesmaximal, characteristic, complemented
31#22053C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#501C2211yescharacteristic, complemented
35C2×#488C2211yescharacteristic
36C2×#485C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#463C2211yescharacteristic
39C2×#449C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#440C2211yescharacteristic, complemented
42C2×C4×D8C2211yescharacteristic
43C2×C4×D8C2211yescharacteristic
44C2×#418C2211yescharacteristic
45#2826—21no—
46#2786—21no—
47#2757—21no—
48#2738—21no—
49#2708—21no—
50#2705—21no—
51#2695—21no—
52#2687—21no—
53#2684—21no—
54#2652—21no—
55#2629C2211yescharacteristic, complemented
56#2623—21no—
57#2570C2211yescharacteristic, complemented
58#2547C2211yescharacteristic
59#2535C2211yescharacteristic
60#2534—21no—
61#2509C2211yescharacteristic, complemented
62#2496C2211yescharacteristic, complemented
63#2495C2211yescharacteristic
64#2492C2211yescharacteristic
65#2485C2211yescharacteristic
66#2481—21no—
67#2480—21no—
68#2454C2211yescharacteristic, complemented
69#2452C2211yescharacteristic
70#2447C2211yescharacteristic
71#2441C2211yescharacteristic
72#2437—21no—
73#2435C2211yescharacteristic
74#2432C2211yescharacteristic
75#2429C2211yescharacteristic
76#2427—21no—
77#2422C2211yescharacteristic
78#2420C2211yescharacteristic, complemented
79#2417C2211yescharacteristic
80#2395C2211yescharacteristic
81#2367C2211yescharacteristic
82#2363C2211yescharacteristic
83#2361C2211yescharacteristic
84D4×C4⋊C4C2211yescharacteristic, complemented
85D4×C22⋊C4C2211yescharacteristic
86#2324C2211yescharacteristic, complemented
87#2311C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2101C2211yescharacteristic, complemented
90#2095C2211yescharacteristic, complemented
91#2087C2211yescharacteristic, complemented
92#2077C2211yescharacteristic
93#2075C2211yescharacteristic
94#2074C2211yescharacteristic, complemented
95#2073C2211yescharacteristic
96#2072C2211yescharacteristic, complemented
97#2071C2211yescharacteristic
98#2071C2211yescharacteristic
99#2067C2211yescharacteristic
100#2066C2211yescharacteristic, complemented
101#2066C2211yescharacteristic, complemented
102#2065C2211yescharacteristic
103#2065C2211yescharacteristic, complemented
104#2057C2211yescharacteristic, complemented
105#2043C2211yescharacteristic, complemented
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic
109#2042C2211yescharacteristic
110#2042C2211yescharacteristic
111#2036C2211yescharacteristic
112#2036C2211yescharacteristic, complemented
113#2036C2211yescharacteristic, complemented
114#2035C2211yescharacteristic
115#2035C2211yescharacteristic, complemented
116#2034C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2026C2211yescharacteristic, complemented
120#2025C2211yescharacteristic
121#2023C2211yescharacteristic, complemented
122#2013C2211yescharacteristic, complemented
123#2012C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#2000C2211yescharacteristic, complemented
127#1999C2211yescharacteristic
128#1990C2211yescharacteristic, complemented
129#1981C2211yescharacteristic, complemented
130#1972C2211yescharacteristic
131#1972C2211yescharacteristic
132#1968C2211yescharacteristic, complemented
133#1960C2211yescharacteristic, complemented
134#1959C2211yescharacteristic
135#1959C2211yescharacteristic
136#1958C2211yescharacteristic
137#1954C2211yescharacteristic
138#1947C2211yescharacteristic, complemented
139#1943C2211yescharacteristic, complemented
140#1941C2211yescharacteristic, complemented
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1935C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1935C2211yescharacteristic, complemented
146#1934C2211yescharacteristic
147#1934C2211yescharacteristic
148#1933C2211yescharacteristic, complemented
149#1933C2211yescharacteristic, complemented
150#1927C2211yescharacteristic, complemented
151#1926C2211yescharacteristic
152#1925C2211yescharacteristic
153#1924C2211yescharacteristic
154#1924C2211yescharacteristic
155#1924C2211yescharacteristic, complemented
156#1924C2211yescharacteristic, complemented
157#1921C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1916C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1895C2211yescharacteristic
163#1894C2211yescharacteristic
164#1894C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1877C2211yescharacteristic, complemented
169#1877C2211yescharacteristic, complemented
170#1877C2211yescharacteristic, complemented
171#1874C2211yescharacteristic, complemented
172#1873C2211yescharacteristic
173#1870C2211yescharacteristic
174#1865C2211yescharacteristic, complemented
175#1864C2211yescharacteristic
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic
178#1863C2211yescharacteristic, complemented
179#1862C2211yescharacteristic
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic, complemented
182#1854C2211yescharacteristic
183#1853C2211yescharacteristic, complemented
184#1824C2211yescharacteristic, complemented
185#1823C2211yescharacteristic, complemented
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1788C2211yescharacteristic
189#1788C2211yescharacteristic
190#1788C2211yescharacteristic
191#1786C2211yescharacteristic
192#1786C2211yescharacteristic
193#1771C2211yescharacteristic, complemented
194#1771C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197#1762C2211yescharacteristic, complemented
198C4×#103C2211yescharacteristic, complemented
199#1753C2211yescharacteristic
200#1753C2211yescharacteristic
201#1750C2211yescharacteristic, complemented
202#1750C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×M16C2311yescharacteristic
210#546—42no—
211#546—42no—
212#542—42no—
213#542—42no—
214C2×C4⋊Q8C2311yescharacteristic
215C2×C4⋊Q8C2311yescharacteristic
216C2×#126—21no—
217C2×#126—21no—
218C2×#125C2311yescharacteristic
219C2×#124—21no—
220C2×#124C2311yescharacteristic
221C2×#124C2311yescharacteristic
222C2×#124C2311yescharacteristic
223C2×#123—21no—
224C2×#123—21no—
225C2×#123—21no—
226C2×C22⋊Q8—21no—
227C2×C22⋊Q8—21no—
228C2×C22⋊Q8C2311yescharacteristic
229C2×C22⋊Q8C2311yescharacteristic
230C2×C22⋊Q8C2311yescharacteristic
231C2×#121—21no—
232C2×#121C2311yescharacteristic
233C2×#121C2311yescharacteristic
234C2×#121C2311yescharacteristic
235C2×#120—21no—
236C2×C4×Q8C2311yescharacteristic
237C2×C4×D4—21no—
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C22×C4⋊C4—21no—
248C22×C4⋊C4C2311yescharacteristic
249C22×C22⋊C4—21no—
250C22×C22⋊C4—21no—
251#501—42no—
252#488—42no—
253#485—42no—
254#463—24no—
255#463—42no—
256#449—24no—
257#447—24no—
258#440—42no—
259C4×D8—42no—
260C4×D8—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#107C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270C2×C4⋊C8C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272#418—42no—
273C2×#103C2311yescharacteristic
274C2×#103C2311yescharacteristic
275C2×#103C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
296C2×#102C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×#97C2311yescharacteristic
314C2×#97C2311yescharacteristic
315C2×#97C2311yescharacteristic
316C2×C4×C8C2311yescharacteristic
317C2×C4×C8C2311yescharacteristic
318C2×C4×C8C2311yescharacteristic
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400—21no—
325#400D411yescharacteristic
326#399—21no—
327#399—21no—
328#399D411yescharacteristic
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
334#398D411yescharacteristic
335#397—21no—
336#397—21no—
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397D411yescharacteristic
346#397D411yescharacteristic
347#397D411yescharacteristic
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#396—21no—
353#396—21no—
354#396—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394D411yescharacteristic
363#394D411yescharacteristic
364#393—21no—
365#393—21no—
366#392—21no—
367#391—21no—
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#390—21no—
373#390—21no—
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#389—21no—
381#389—21no—
382#389—21no—
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#386—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#384C2311yescharacteristic
431#384C2311yescharacteristic
432#383—21no—
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#381—21no—
436#381—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380—21no—
441#380—21no—
442#380—21no—
443#380—21no—
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#379—21no—
451#379—21no—
452#379—21no—
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4C2311yescharacteristic
461C4×C22⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C2×#41—22no—
495C2×#41—41no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×D4—21no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4C2×D411yescharacteristic
515C22×D4C2411yescharacteristic
516C22×D4C2411yescharacteristic
517C22×D4C2411yescharacteristic
518C23×C4—21no—
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4C2411yescharacteristic
527C23×C4C2411yescharacteristic
528C2×SD16—22no—
529C2×SD16—22no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×D8—22no—
535C2×D8—22no—
536C2×D8—41no—
537C2×D8—41no—
538C2×D8—41no—
539C2×D8#4114yes—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16—41no—
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C4⋊Q8—22no—
552C4⋊Q8—41no—
553C4⋊Q8—41no—
554C4⋊Q8—41no—
555#126—44no—
556#126—82no—
557#125—41no—
558#125—41no—
559#124—22no—
560#124—22no—
561#124—22no—
562#124—41no—
563#124—41no—
564#124—41no—
565#124—44no—
566#123—44no—
567#123—44no—
568#123—82no—
569C22⋊Q8—22no—
570C22⋊Q8—44no—
571C22⋊Q8—41no—
572C22⋊Q8—41no—
573C22⋊Q8—41no—
574C22⋊Q8—41no—
575C22⋊Q8—41no—
576C22⋊Q8—82no—
577#121—22no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—41no—
582#121—41no—
583#121—44no—
584#120—44no—
585C4×Q8—22no—
586C4×Q8—41no—
587C4×D4—22no—
588C4×D4—22no—
589C4×D4—22no—
590C4×D4—41no—
591C4×D4—41no—
592C4×D4—41no—
593C4×D4—41no—
594C4×D4—41no—
595C4×D4—41no—
596C4×D4—41no—
597C4×D4—41no—
598C4×D4—41no—
599C4×D4—41no—
600C4×D4—41no—
601C4×D4—82no—
602#117—41no—
603#117—41no—
604#117—41no—
605#117—41no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—41no—
631C2×C4⋊C4—41no—
632C2×C4⋊C4—82no—
633C2×C4⋊C4C2×D411yescharacteristic
634C2×C4⋊C4C2×D411yescharacteristic
635C2×C4⋊C4C2×D411yescharacteristic
636C2×C4⋊C4C2×D411yescharacteristic
637C2×C4⋊C4C2×D411yescharacteristic
638C2×C4⋊C4C2×D411yescharacteristic
639C2×C4⋊C4C2×D411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C4⋊C4C2411yescharacteristic
644C2×C4⋊C4C2411yescharacteristic
645C2×C4⋊C4C2411yescharacteristic
646C2×C4⋊C4C2411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—44no—
689C2×C22⋊C4—82no—
690C2×C22⋊C4C2×D411yescharacteristic
691C2×C22⋊C4C2×D411yescharacteristic
692C2×C22⋊C4C2×D411yescharacteristic
693C2×C22⋊C4C2×D411yescharacteristic
694C2×C22⋊C4C2×D411yescharacteristic
695C2×C22⋊C4C2×D411yescharacteristic
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C42—21no—
701C2×C42—21no—
702C2×C42—21no—
703C2×C42—21no—
704C2×C42—21no—
705C2×C42C2411yescharacteristic
706C2×C42C2411yescharacteristic
707C2×C42C2411yescharacteristic
708C2×C42C2411yescharacteristic
709C2×C42C2411yescharacteristic
710#107—22no—
711#107—22no—
712#107—41no—
713#107—41no—
714#106—22no—
715#106—41no—
716#106—41no—
717#106—41no—
718C4⋊C8—22no—
719C4⋊C8—41no—
720C4⋊C8—41no—
721#103—22no—
722#103—22no—
723#103—41no—
724#103—41no—
725#103—41no—
726#103—41no—
727#103—41no—
728#103—41no—
729#103—41no—
730#103—41no—
731#103—41no—
732#103—41no—
733#103—41no—
734#103—41no—
735#102—22no—
736#102—22no—
737#102—22no—
738#102—22no—
739#102—22no—
740#102—22no—
741#102—22no—
742#102—22no—
743#102—41no—
744#102—41no—
745#102—41no—
746#102—41no—
747#102—41no—
748#102—41no—
749#102—41no—
750#102—41no—
751#102—41no—
752#102—41no—
753C22⋊C8—22no—
754C22⋊C8—22no—
755C22⋊C8—41no—
756C22⋊C8—41no—
757C22⋊C8—41no—
758C22⋊C8—41no—
759C22⋊C8—41no—
760#97—41no—
761#97—41no—
762#97—41no—
763#97—41no—
764C4×C8—41no—
765C4×C8—41no—
766C4×C8—41no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801#95C2×D411yescharacteristic
802#95C2×D411yescharacteristic
803#95C2×D411yescharacteristic
804#95C2×D411yescharacteristic
805#95C2×D411yescharacteristic
806#95C2×D411yescharacteristic
807#95C2×D411yescharacteristic
808C24—21no—
809C24—21no—
810C24—21no—
811C24—42no—
812C24—42no—
813C24—42no—
814C24—81no—
815C24—81no—
816C24—81no—
817C24—81no—
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820#41—82no—
821#41—82no—
822#41—82no—
823#41—82no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—21no—
832C2×Q8—21no—
833C2×Q8—21no—
834C2×Q8—21no—
835C2×Q8—21no—
836C2×Q8—42no—
837C2×Q8—81no—
838C2×Q8—81no—
839C2×D4—24no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—21no—
843C2×D4—21no—
844C2×D4—21no—
845C2×D4—21no—
846C2×D4—21no—
847C2×D4—21no—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—21no—
852C2×D4—21no—
853C2×D4—21no—
854C2×D4—21no—
855C2×D4—41no—
856C2×D4—41no—
857C2×D4—41no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—44no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—81no—
866C2×D4—82no—
867C2×D4—82no—
868C2×D4—82no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4C2×#4112yes—
877C2×D4C2×#4112yes—
878C2×D4H(5,𝔽2)12yes—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—42no—
909C22×C4—42no—
910C22×C4—42no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4—81no—
924C22×C4—81no—
925C22×C4—81no—
926C22×C4—81no—
927C22×C4—81no—
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C22×D411yescharacteristic
936C22×C4C22×D411yescharacteristic
937C22×C4C22×D411yescharacteristic
938C22×C4C22×D411yescharacteristic
939C22×C4C22×D411yescharacteristic
940C22×C4C2511yescharacteristic
941SD16—44no—
942SD16—82no—
943D8—44no—
944D8—44no—
945M16—82no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—21no—
963C2×C8—21no—
964C2×C8—21no—
965C2×C8—21no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8C2×#4112yes—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—21no—
989C4⋊C4—21no—
990C4⋊C4—21no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—41no—
996C4⋊C4—41no—
997C4⋊C4—41no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
1003C4⋊C4—42no—
1004C4⋊C4—42no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C4⋊C4—81no—
1020C4⋊C4—81no—
1021C4⋊C4—81no—
1022C4⋊C4H(5,𝔽2)12yes—
1023C22⋊C4—24no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—41no—
1031C22⋊C4—41no—
1032C22⋊C4—41no—
1033C22⋊C4—41no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—42no—
1046C22⋊C4—42no—
1047C22⋊C4—42no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C22⋊C4—81no—
1062C22⋊C4—81no—
1063C22⋊C4—81no—
1064C22⋊C4—81no—
1065C22⋊C4—81no—
1066C22⋊C4—81no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—21no—
1080C42—42no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C42—81no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—22no—
1094C23—22no—
1095C23—21no—
1096C23—21no—
1097C23—22no—
1098C23—21no—
1099C23—21no—
1100C23—21no—
1101C23—21no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—41no—
1113C23—41no—
1114C23—41no—
1115C23—41no—
1116C23—41no—
1117C23—41no—
1118C23—41no—
1119C23—41no—
1120C23—84no—
1121C23—84no—
1122C23—84no—
1123C23—162no—
1124C23—162no—
1125C23—162no—
1126C23—162no—
1127C23C23×D411yescharacteristic
1128Q8—41no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—162no—
1137D4—22no—
1138D4—22no—
1139D4—22no—
1140D4—22no—
1141D4—22no—
1142D4—22no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—41no—
1149D4—84no—
1150D4—82no—
1151D4—84no—
1152D4—84no—
1153D4—162no—
1154D4—162no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—21no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
1217C2×C4—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—84no—
1239C2×C4—84no—
1240C2×C4—162no—
1241C2×C4—162no—
1242C2×C4—162no—
1243C2×C4—162no—
1244C2×C4—162no—
1245C2×C4—162no—
1246C2×C4C22×#4111yescharacteristic
1247C2×C4C2×H(5,𝔽2)11yescharacteristic
1248C2×C4C2×H(5,𝔽2)11yescharacteristic
1249C2×C4#58511yescharacteristic
1250C2×C4#58511yescharacteristic
1251C2×C4#58511yescharacteristic
1252C8—22no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C8—41no—
1260C22—41no—
1261C22—41no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—41no—
1266C22—42no—
1267C22—41no—
1268C22—42no—
1269C22—42no—
1270C22—41no—
1271C22—41no—
1272C22—42no—
1273C22—41no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—41no—
1278C22—41no—
1279C22—42no—
1280C22—42no—
1281C22—41no—
1282C22—41no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—81no—
1295C22—168no—
1296C22D4×#4111yescharacteristic
1297C22#348411yescharacteristic
1298C22#350011yescharacteristic
1299C22#358411yescharacteristic
1300C22#358511yescharacteristic
1301C22#358511yescharacteristic
1302C22#358611yescharacteristic
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—42no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4—81no—
1326C4—81no—
1327C4—81no—
1328C4#350511yescharacteristic
1329C4#351311yescharacteristic
1330C4#356011yescharacteristic
1331C4#356211yescharacteristic
1332C2—81no—
1333C2—81no—
1334C2—82no—
1335C2—82no—
1336C2—82no—
1337C2#4300811yescharacteristic
1338C2#6151011yescharacteristic
1339C2#6153611yescharacteristic
1340C2#6162611yescharacteristic
1341C2#6166911yescharacteristic
1342C2#6256911yescharacteristic
1343C2#6261411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24245C2
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. #45108C2semidirect
2. #42630C2semidirect
3. #31778C2semidirect
4. #31455C2semidirect
5. #31408C2semidirect
6. #31309C2semidirect
7. #31008C2semidirect
8. #31003C2semidirect
9. #30883C2semidirect
10. #30790C2semidirect
11. #29119C2semidirect
12. #29062C2semidirect
13. #29035C2semidirect
14. #29003C2semidirect
15. #27764C2semidirect
16. #27534C2semidirect
17. #27271C2semidirect
18. #27047C2semidirect
19. #26766C2semidirect
20. #26672C2semidirect
21. #26642C2semidirect
22. #26488C2semidirect
23. #26164C2semidirect
24. #25684C2semidirect
26. #24050C2semidirect
27. #23579C2semidirect
28. #23303C2semidirect
29. #23011C2semidirect
30. #22880C2semidirect
31. #22053C2semidirect
34. C2×#501C22semidirect
41. C2×#440C22semidirect
55. #2629C22semidirect
57. #2570C22semidirect
61. #2509C22semidirect
62. #2496C22semidirect
68. #2454C22semidirect
78. #2420C22semidirect
84. D4×C4⋊C4C22semidirect
86. #2324C22semidirect
88. #2101C22semidirect
89. #2101C22semidirect
90. #2095C22semidirect
91. #2087C22semidirect
94. #2074C22semidirect
96. #2072C22semidirect
100. #2066C22semidirect
101. #2066C22semidirect
103. #2065C22semidirect
104. #2057C22semidirect
105. #2043C22semidirect
112. #2036C22semidirect
113. #2036C22semidirect
115. #2035C22semidirect
119. #2026C22semidirect
121. #2023C22semidirect
122. #2013C22semidirect
126. #2000C22semidirect
128. #1990C22semidirect
129. #1981C22semidirect
132. #1968C22semidirect
133. #1960C22semidirect
138. #1947C22semidirect
139. #1943C22semidirect
140. #1941C22semidirect
143. #1935C22semidirect
144. #1935C22semidirect
145. #1935C22semidirect
148. #1933C22semidirect
149. #1933C22semidirect
150. #1927C22semidirect
155. #1924C22semidirect
156. #1924C22semidirect
157. #1921C22semidirect
158. #1920C22semidirect
159. #1919C22semidirect
160. #1916C22semidirect
161. #1916C22semidirect
168. #1877C22semidirect
169. #1877C22semidirect
170. #1877C22semidirect
171. #1874C22semidirect
174. #1865C22semidirect
178. #1863C22semidirect
181. #1862C22semidirect
183. #1853C22semidirect
184. #1824C22semidirect
185. #1823C22semidirect
193. #1771C22semidirect
194. #1771C22semidirect
197. #1762C22semidirect
198. C4×#103C22semidirect
201. #1750C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#451082
#426302
#317782
#314552
#314082
#313092
#310082
#310032
#308832
#307902
#291192
#290622
#290352
#290032
#277642
#275342
#272712
#270472
#267662
#266722
#266422
#264882
#261642
#256842
#242452
#240502
#235792
#233032
#230112
#228802
#220532