Finite Group Databasebeta

← #7079976

Subgroups — #7079976

Order 512.

1569 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45187C211yesmaximal, characteristic, complemented
2#42946C211yesmaximal, characteristic, complemented
3#32167C211yesmaximal, characteristic, complemented
4#31988C211yesmaximal, characteristic, complemented
5#31864C211yesmaximal, characteristic, complemented
6#31756C211yesmaximal, characteristic, complemented
7#31643C211yesmaximal, characteristic, complemented
8#31513C211yesmaximal, characteristic, complemented
9#31463C211yesmaximal, characteristic, complemented
10#31003C211yesmaximal, characteristic, complemented
11#29088C211yesmaximal, characteristic, complemented
12#29000C211yesmaximal, characteristic, complemented
13#28569C211yesmaximal, characteristic, complemented
14#27761C211yesmaximal, characteristic, complemented
15#27545C211yesmaximal, characteristic, complemented
16#27278C211yesmaximal, characteristic, complemented
17#27262C211yesmaximal, characteristic, complemented
18#26763C211yesmaximal, characteristic, complemented
19#26429C211yesmaximal, characteristic, complemented
20#26201C211yesmaximal, characteristic, complemented
21#25511C211yesmaximal, characteristic, complemented
22#25335C211yesmaximal, characteristic, complemented
23#25101C211yesmaximal, characteristic, complemented
24#24542C211yesmaximal, characteristic, complemented
25#24512C211yesmaximal, characteristic, complemented
26#24434C211yesmaximal, characteristic
27#23632C211yesmaximal, characteristic, complemented
28#23135C211yesmaximal, characteristic, complemented
29#22907C211yesmaximal, characteristic, complemented
30#22427C211yesmaximal, characteristic, complemented
31#21873C211yesmaximal, characteristic, complemented
32C2×#546C2211yescharacteristic
33C2×#541C2211yescharacteristic
34C2×#489C2211yescharacteristic
35C2×#468C2211yescharacteristic
36C2×#465C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#449C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#436C2211yescharacteristic
41C2×#433C2211yescharacteristic
42C2×#417C2211yescharacteristic
43C2×#418C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2838—21no—
46#2746—21no—
47#2723—21no—
48#2711—21no—
49#2708—21no—
50#2694—21no—
51#2685—21no—
52#2685—21no—
53#2681—21no—
54#2667—21no—
55#2663—21no—
56#2624C2211yescharacteristic
57#2571C2211yescharacteristic, complemented
58#2563C2211yescharacteristic, complemented
59#2558—21no—
60#2553—21no—
61#2545C2211yescharacteristic
62#2512C2211yescharacteristic, complemented
63#2507C2211yescharacteristic, complemented
64#2501C2211yescharacteristic, complemented
65#2494C2211yescharacteristic, complemented
66#2490—21no—
67#2490C2211yescharacteristic
68#2480—21no—
69#2480—21no—
70#2454C2211yescharacteristic
71#2448C2211yescharacteristic
72#2440C2211yescharacteristic
73#2440C2211yescharacteristic, complemented
74#2435C2211yescharacteristic
75#2432C2211yescharacteristic
76#2426C2211yescharacteristic
77#2420C2211yescharacteristic, complemented
78#2416C2211yescharacteristic
79#2415C2211yescharacteristic
80#2395C2211yescharacteristic
81#2367C2211yescharacteristic
82#2363C2211yescharacteristic
83#2362C2211yescharacteristic
84#2352C2211yescharacteristic
85#2341C2211yescharacteristic
86#2317C2211yescharacteristic
87#2309C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2088C2211yescharacteristic, complemented
91#2086C2211yescharacteristic, complemented
92#2076C2211yescharacteristic, complemented
93#2075C2211yescharacteristic, complemented
94#2074C2211yescharacteristic, complemented
95#2073C2211yescharacteristic
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic
98#2073C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2071C2211yescharacteristic
102#2071C2211yescharacteristic
103#2071C2211yescharacteristic
104#2067C2211yescharacteristic
105#2067C2211yescharacteristic
106#2066C2211yescharacteristic, complemented
107#2065C2211yescharacteristic
108#2059C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2054C2211yescharacteristic
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic
113#2043C2211yescharacteristic, complemented
114#2042C2211yescharacteristic
115#2042C2211yescharacteristic
116#2042C2211yescharacteristic
117#2042C2211yescharacteristic
118#2035C2211yescharacteristic, complemented
119#2034C2211yescharacteristic
120#2025C2211yescharacteristic, complemented
121#2024C2211yescharacteristic, complemented
122#2023C2211yescharacteristic
123#2013C2211yescharacteristic, complemented
124#2012C2211yescharacteristic
125#2012C2211yescharacteristic
126#2000C2211yescharacteristic, complemented
127#1999C2211yescharacteristic
128#1992C2211yescharacteristic, complemented
129#1991C2211yescharacteristic, complemented
130#1988C2211yescharacteristic, complemented
131#1983C2211yescharacteristic
132#1983C2211yescharacteristic
133#1972C2211yescharacteristic
134#1970C2211yescharacteristic
135#1960C2211yescharacteristic, complemented
136#1959C2211yescharacteristic
137#1958C2211yescharacteristic
138#1956C2211yescharacteristic, complemented
139#1940C2211yescharacteristic, complemented
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic, complemented
144#1935C2211yescharacteristic, complemented
145#1934C2211yescharacteristic
146#1934C2211yescharacteristic, complemented
147#1933C2211yescharacteristic, complemented
148#1928C2211yescharacteristic, complemented
149#1925C2211yescharacteristic
150#1924C2211yescharacteristic, complemented
151#1924C2211yescharacteristic, complemented
152#1920C2211yescharacteristic, complemented
153#1920C2211yescharacteristic, complemented
154#1919C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1916C2211yescharacteristic, complemented
157#1916C2211yescharacteristic, complemented
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic, complemented
160#1894C2211yescharacteristic
161#1894C2211yescharacteristic, complemented
162#1892C2211yescharacteristic
163#1880C2211yescharacteristic, complemented
164#1880C2211yescharacteristic, complemented
165#1880C2211yescharacteristic, complemented
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1877C2211yescharacteristic, complemented
169#1875C2211yescharacteristic
170#1874C2211yescharacteristic
171#1873C2211yescharacteristic
172#1873C2211yescharacteristic
173#1872C2211yescharacteristic
174#1872C2211yescharacteristic
175#1872C2211yescharacteristic, complemented
176#1869C2211yescharacteristic
177#1865C2211yescharacteristic, complemented
178#1864C2211yescharacteristic
179#1863C2211yescharacteristic, complemented
180#1863C2211yescharacteristic, complemented
181#1854C2211yescharacteristic
182#1851C2211yescharacteristic
183#1851C2211yescharacteristic, complemented
184#1824C2211yescharacteristic, complemented
185#1805C2211yescharacteristic, complemented
186#1805C2211yescharacteristic, complemented
187#1804C2211yescharacteristic
188#1803C2211yescharacteristic, complemented
189#1803C2211yescharacteristic, complemented
190#1803C2211yescharacteristic, complemented
191#1788C2211yescharacteristic
192#1788C2211yescharacteristic
193#1786C2211yescharacteristic
194#1771C2211yescharacteristic, complemented
195#1763C2211yescharacteristic, complemented
196#1762C2211yescharacteristic, complemented
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic, complemented
199#1752C2211yescharacteristic
200#1736C2211yescharacteristic
201#1735C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×D8C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×M16C2311yescharacteristic
210C22×M16C2311yescharacteristic
211C23×C8C2311yescharacteristic
212#546—24no—
213#546—42no—
214#541—24no—
215#541—42no—
216C2×C4⋊Q8C2311yescharacteristic
217C2×C4⋊Q8C2311yescharacteristic
218C2×#126—21no—
219C2×#126—21no—
220C2×#126—21no—
221C2×#125—21no—
222C2×#125—21no—
223C2×#125C2311yescharacteristic
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#123—21no—
228C2×#123—21no—
229C2×#123—21no—
230C2×C22⋊Q8—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8C2311yescharacteristic
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121—21no—
236C2×#121—21no—
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×#121C2311yescharacteristic
240C2×#120—21no—
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C2×#117C2311yescharacteristic
249C2×#117C2311yescharacteristic
250C22×C4⋊C4C2311yescharacteristic
251C22×C4⋊C4C2311yescharacteristic
252C22×C22⋊C4—21no—
253#489—42no—
254#468—42no—
255#465—24no—
256#463—42no—
257#449—42no—
258#447—42no—
259#436—42no—
260#433—42no—
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×C4⋊C8C2311yescharacteristic
266C2×C4⋊C8C2311yescharacteristic
267C2×C4⋊C8C2311yescharacteristic
268C2×C4⋊C8C2311yescharacteristic
269C2×C4⋊C8C2311yescharacteristic
270#418—42no—
271#417—42no—
272C2×#103C2311yescharacteristic
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×#102—42no—
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×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#401—21no—
316#400—21no—
317#400—21no—
318#400D411yescharacteristic
319#399—21no—
320#399—21no—
321#399—21no—
322#399—21no—
323#399—21no—
324#399D411yescharacteristic
325#398—21no—
326#398—21no—
327#398—21no—
328#398—21no—
329#398D411yescharacteristic
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#397D411yescharacteristic
338#397D411yescharacteristic
339#397D411yescharacteristic
340#396—21no—
341#396—21no—
342#396—21no—
343#396—21no—
344#396—21no—
345#396—21no—
346#395—21no—
347#395—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394D411yescharacteristic
360#394D411yescharacteristic
361#393—21no—
362#393—21no—
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#390—21no—
366#390—21no—
367#390—21no—
368#390—21no—
369#390—21no—
370#390—21no—
371#390—21no—
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#389—21no—
383#389—21no—
384#389—21no—
385#389—21no—
386#389—21no—
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#385—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#384C2311yescharacteristic
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#382—21no—
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#382C2311yescharacteristic
433#381—21no—
434#380—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380C2311yescharacteristic
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#380C2311yescharacteristic
442#379—21no—
443#379—21no—
444#379—21no—
445#379—21no—
446C4×C4⋊C4—21no—
447C4×C4⋊C4C2311yescharacteristic
448C4×C4⋊C4C2311yescharacteristic
449C4×C4⋊C4C2311yescharacteristic
450C4×C4⋊C4C2311yescharacteristic
451C4×C4⋊C4C2311yescharacteristic
452C4×C22⋊C4—21no—
453C4×C22⋊C4—21no—
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4C2311yescharacteristic
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#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—22no—
496C2×#41—41no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41—41no—
500C22×Q8—21no—
501C22×Q8C2411yescharacteristic
502C22×Q8C2411yescharacteristic
503C22×D4—22no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—22no—
510C22×D4—22no—
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×C4C2411yescharacteristic
524C23×C4C2411yescharacteristic
525C2×SD16—22no—
526C2×SD16—41no—
527C2×SD16—41no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×D8—22no—
532C2×D8—41no—
533C2×D8—41no—
534C2×D8—41no—
535C2×D8—41no—
536C2×D8—41no—
537C2×M16—22no—
538C2×M16—41no—
539C2×M16—41no—
540C2×M16—41no—
541C2×M16—41no—
542C2×M16—41no—
543C22×C8—22no—
544C22×C8—41no—
545C22×C8—41no—
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C4⋊Q8—22no—
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557C4⋊Q8—41no—
558#126—44no—
559#126—44no—
560#126—82no—
561#125—22no—
562#125—41no—
563#125—44no—
564#125—44no—
565#124—22no—
566#124—22no—
567#124—41no—
568#124—41no—
569#124—41no—
570#124—41no—
571#123—44no—
572#123—82no—
573#123—82no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—41no—
578C22⋊Q8—41no—
579C22⋊Q8—82no—
580C22⋊Q8—82no—
581C22⋊Q8#4114yes—
582#121—22no—
583#121—22no—
584#121—22no—
585#121—44no—
586#121—41no—
587#121—41no—
588#121—41no—
589#121—82no—
590#120—44no—
591C4×Q8—22no—
592C4×Q8—22no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—41no—
601C4×D4—41no—
602C4×D4—41no—
603#117—22no—
604#117—22no—
605#117—41no—
606#117—41no—
607#117—41no—
608#117—41no—
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—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—41no—
637C2×C4⋊C4—41no—
638C2×C4⋊C4—41no—
639C2×C4⋊C4—41no—
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
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—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—21no—
698C2×C22⋊C4—44no—
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720C2×C42C2411yescharacteristic
721C2×C42C2411yescharacteristic
722#107—41no—
723#107—41no—
724#106—22no—
725#106—41no—
726C4⋊C8—41no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730C4⋊C8—41no—
731#103—22no—
732#103—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#103—41no—
744#103—41no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—41no—
752#102—41no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102—41no—
760#102—41no—
761#102—41no—
762#102—41no—
763C22⋊C8—22no—
764C22⋊C8—22no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768#97—41no—
769#97—41no—
770#97—41no—
771C4×C8—41no—
772C4×C8—41no—
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—81no—
814C24—81no—
815C24—81no—
816C24—81no—
817C24—81no—
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820#41—44no—
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—81no—
836C2×Q8—81no—
837C2×Q8—81no—
838C2×Q8C2×#4112yes—
839C2×D4—22no—
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—21no—
856C2×D4—21no—
857C2×D4—44no—
858C2×D4—44no—
859C2×D4—41no—
860C2×D4—41no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—42no—
868C2×D4—82no—
869C2×D4—82no—
870C2×D4—81no—
871C2×D4—81no—
872C2×D4—81no—
873C2×D4—81no—
874C2×D4—81no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
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—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—81no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4C22×D411yescharacteristic
918C22×C4C22×D411yescharacteristic
919C22×C4C22×D411yescharacteristic
920C22×C4C22×D411yescharacteristic
921C22×C4C22×D411yescharacteristic
922C22×C4C22×D411yescharacteristic
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C2×#4112yes—
930C22×C4H(5,𝔽2)12yes—
931C22×C4C2511yescharacteristic
932SD16—82no—
933SD16—82no—
934D8—82no—
935D8—82no—
936M16—82no—
937M16—82no—
938C2×C8—21no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
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—82no—
963C4⋊C4—24no—
964C4⋊C4—22no—
965C4⋊C4—22no—
966C4⋊C4—22no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
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—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—42no—
993C4⋊C4—42no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
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⋊C4C2×#4112yes—
1019C22⋊C4—24no—
1020C22⋊C4—22no—
1021C22⋊C4—22no—
1022C22⋊C4—22no—
1023C22⋊C4—22no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—41no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—81no—
1041C22⋊C4—81no—
1042C22⋊C4—81no—
1043C22⋊C4—81no—
1044C22⋊C4—81no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
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—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—21no—
1076C42—21no—
1077C42—21no—
1078C42—21no—
1079C42—42no—
1080C42—42no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C42—81no—
1085C42—81no—
1086C42—81no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—21no—
1092C23—21no—
1093C23—21no—
1094C23—21no—
1095C23—21no—
1096C23—21no—
1097C23—21no—
1098C23—22no—
1099C23—21no—
1100C23—21no—
1101C23—41no—
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—41no—
1121C23—84no—
1122C23—84no—
1123C23—162no—
1124C23—162no—
1125C23—162no—
1126C23—162no—
1127C23—162no—
1128C23#54612yes—
1129C23C23×D411yescharacteristic
1130Q8—22no—
1131Q8—22no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—41no—
1136Q8—41no—
1137Q8—41no—
1138Q8—162no—
1139D4—22no—
1140D4—22no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—41no—
1145D4—41no—
1146D4—41no—
1147D4—41no—
1148D4—41no—
1149D4—41no—
1150D4—41no—
1151D4—84no—
1152D4—82no—
1153D4—84no—
1154D4—162no—
1155D4—162no—
1156D4—162no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—22no—
1160C2×C4—22no—
1161C2×C4—22no—
1162C2×C4—22no—
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—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
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—41no—
1239C2×C4—84no—
1240C2×C4—162no—
1241C2×C4—162no—
1242C2×C4—162no—
1243C2×C4—162no—
1244C2×C4#54612yes—
1245C2×C4C22×#4111yescharacteristic
1246C2×C4C2×H(5,𝔽2)11yescharacteristic
1247C2×C4C2×H(5,𝔽2)11yescharacteristic
1248C2×C4#58511yescharacteristic
1249C2×C4#58511yescharacteristic
1250C2×C4#58511yescharacteristic
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C8—41no—
1258C8—41no—
1259C22—22no—
1260C22—22no—
1261C22—22no—
1262C22—41no—
1263C22—41no—
1264C22—41no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—41no—
1269C22—42no—
1270C22—41no—
1271C22—41no—
1272C22—42no—
1273C22—41no—
1274C22—41no—
1275C22—42no—
1276C22—81no—
1277C22—81no—
1278C22—81no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—81no—
1291C22—81no—
1292C22—81no—
1293C22—81no—
1294C22—168no—
1295C22C2×#54611yescharacteristic
1296C22#348811yescharacteristic
1297C22#350011yescharacteristic
1298C22#358411yescharacteristic
1299C22#358511yescharacteristic
1300C22#358511yescharacteristic
1301C22#358611yescharacteristic
1302C4—22no—
1303C4—41no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—42no—
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#351311yescharacteristic
1328C4#352111yescharacteristic
1329C4#353411yescharacteristic
1330C4#356011yescharacteristic
1331C2—42no—
1332C2—81no—
1333C2—82no—
1334C2—161no—
1335C2—161no—
1336C2#4399811yescharacteristic
1337C2#6118911yescharacteristic
1338C2#6122211yescharacteristic
1339C2#6204811yescharacteristic
1340C2#6207911yescharacteristic
1341C2#6256711yescharacteristic
1342C2#6261311yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#24434C2
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. #45187C2semidirect
2. #42946C2semidirect
3. #32167C2semidirect
4. #31988C2semidirect
5. #31864C2semidirect
6. #31756C2semidirect
7. #31643C2semidirect
8. #31513C2semidirect
9. #31463C2semidirect
10. #31003C2semidirect
11. #29088C2semidirect
12. #29000C2semidirect
13. #28569C2semidirect
14. #27761C2semidirect
15. #27545C2semidirect
16. #27278C2semidirect
17. #27262C2semidirect
18. #26763C2semidirect
19. #26429C2semidirect
20. #26201C2semidirect
21. #25511C2semidirect
22. #25335C2semidirect
23. #25101C2semidirect
24. #24542C2semidirect
25. #24512C2semidirect
27. #23632C2semidirect
28. #23135C2semidirect
29. #22907C2semidirect
30. #22427C2semidirect
31. #21873C2semidirect
57. #2571C22semidirect
58. #2563C22semidirect
62. #2512C22semidirect
63. #2507C22semidirect
64. #2501C22semidirect
65. #2494C22semidirect
73. #2440C22semidirect
77. #2420C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2088C22semidirect
91. #2086C22semidirect
92. #2076C22semidirect
93. #2075C22semidirect
94. #2074C22semidirect
106. #2066C22semidirect
108. #2059C22semidirect
109. #2055C22semidirect
113. #2043C22semidirect
118. #2035C22semidirect
120. #2025C22semidirect
121. #2024C22semidirect
123. #2013C22semidirect
126. #2000C22semidirect
128. #1992C22semidirect
129. #1991C22semidirect
130. #1988C22semidirect
135. #1960C22semidirect
138. #1956C22semidirect
139. #1940C22semidirect
143. #1936C22semidirect
144. #1935C22semidirect
146. #1934C22semidirect
147. #1933C22semidirect
148. #1928C22semidirect
150. #1924C22semidirect
151. #1924C22semidirect
152. #1920C22semidirect
153. #1920C22semidirect
154. #1919C22semidirect
155. #1918C22semidirect
156. #1916C22semidirect
157. #1916C22semidirect
159. #1895C22semidirect
161. #1894C22semidirect
163. #1880C22semidirect
164. #1880C22semidirect
165. #1880C22semidirect
168. #1877C22semidirect
175. #1872C22semidirect
177. #1865C22semidirect
179. #1863C22semidirect
180. #1863C22semidirect
183. #1851C22semidirect
184. #1824C22semidirect
185. #1805C22semidirect
186. #1805C22semidirect
188. #1803C22semidirect
189. #1803C22semidirect
190. #1803C22semidirect
194. #1771C22semidirect
195. #1763C22semidirect
196. #1762C22semidirect
198. #1753C22semidirect

Maximal subgroups

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

subgroupindex
#451872
#429462
#321672
#319882
#318642
#317562
#316432
#315132
#314632
#310032
#290882
#290002
#285692
#277612
#275452
#272782
#272622
#267632
#264292
#262012
#255112
#253352
#251012
#245422
#245122
#244342
#236322
#231352
#229072
#224272
#218732