Finite Group Databasebeta

← #7030589

Subgroups — #7030589

Order 512.

1564 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45207C211yesmaximal, characteristic, complemented
2#44961C211yesmaximal, characteristic, complemented
3#32639C211yesmaximal, characteristic, complemented
4#32589C211yesmaximal, characteristic, complemented
5#32437C211yesmaximal, characteristic, complemented
6#31938C211yesmaximal, characteristic, complemented
7#31861C211yesmaximal, characteristic, complemented
8#31645C211yesmaximal, characteristic, complemented
9#30996C211yesmaximal, characteristic, complemented
10#30468C211yesmaximal, characteristic
11#29424C211yesmaximal, characteristic, complemented
12#28888C211yesmaximal, characteristic, complemented
13#27563C211yesmaximal, characteristic, complemented
14#27403C211yesmaximal, characteristic, complemented
15#27199C211yesmaximal, characteristic, complemented
16#27189C211yesmaximal, characteristic, complemented
17#27072C211yesmaximal, characteristic, complemented
18#26598C211yesmaximal, characteristic, complemented
19#26596C211yesmaximal, characteristic, complemented
20#26267C211yesmaximal, characteristic, complemented
21#26173C211yesmaximal, characteristic, complemented
22#25639C211yesmaximal, characteristic, complemented
23#25152C211yesmaximal, characteristic, complemented
24#24909C211yesmaximal, characteristic, complemented
25#24204C211yesmaximal, characteristic, complemented
26#23945C211yesmaximal, characteristic, complemented
27#23585C211yesmaximal, characteristic, complemented
28#23005C211yesmaximal, characteristic, complemented
29#22765C211yesmaximal, characteristic, complemented
30#22328C211yesmaximal, characteristic, complemented
31#22056C211yesmaximal, characteristic, complemented
32C2×#559C2211yescharacteristic, complemented
33C2×#542C2211yescharacteristic
34C2×#496C2211yescharacteristic
35C2×#464C2211yescharacteristic
36C2×#463C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#447C2211yescharacteristic
40C2×#447C2211yescharacteristic
41C2×#442C2211yescharacteristic
42C2×#440C2211yescharacteristic, complemented
43C2×C4×Q16C2211yescharacteristic, complemented
44C2×C4×SD16C2211yescharacteristic
45#2761—21no—
46#2735—21no—
47#2735—21no—
48#2723—21no—
49#2710—21no—
50#2706—21no—
51#2695—21no—
52#2674—21no—
53#2592C2211yescharacteristic
54#2563C2211yescharacteristic, complemented
55#2561—21no—
56#2546C2211yescharacteristic, complemented
57#2538C2211yescharacteristic
58#2531—21no—
59#2526—21no—
60#2513C2211yescharacteristic
61#2512C2211yescharacteristic
62#2499C2211yescharacteristic
63#2491—21no—
64#2488—21no—
65#2480—21no—
66#2468—21no—
67#2448C2211yescharacteristic
68#2448C2211yescharacteristic, complemented
69#2447C2211yescharacteristic
70#2445C2211yescharacteristic, complemented
71#2435C2211yescharacteristic
72#2428C2211yescharacteristic
73#2426C2211yescharacteristic
74#2425—21no—
75#2421C2211yescharacteristic
76#2420C2211yescharacteristic
77#2396C2211yescharacteristic
78#2367C2211yescharacteristic
79#2367C2211yescharacteristic, complemented
80#2357C2211yescharacteristic
81#2351C2211yescharacteristic, complemented
82#2349C2211yescharacteristic, complemented
83#2346C2211yescharacteristic
84D4×C22⋊C4C2211yescharacteristic
85#2324C2211yescharacteristic
86#2323C2211yescharacteristic
87#2309C2211yescharacteristic
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2092C2211yescharacteristic
91#2092C2211yescharacteristic, complemented
92#2087C2211yescharacteristic, complemented
93#2084C2211yescharacteristic, complemented
94#2077C2211yescharacteristic
95#2074C2211yescharacteristic, complemented
96#2073C2211yescharacteristic
97#2073C2211yescharacteristic, complemented
98#2068C2211yescharacteristic, complemented
99#2066C2211yescharacteristic, complemented
100#2065C2211yescharacteristic
101#2065C2211yescharacteristic
102#2057C2211yescharacteristic, complemented
103#2055C2211yescharacteristic, complemented
104#2054C2211yescharacteristic
105#2054C2211yescharacteristic
106#2042C2211yescharacteristic
107#2042C2211yescharacteristic
108#2042C2211yescharacteristic, complemented
109#2041C2211yescharacteristic, complemented
110#2036C2211yescharacteristic
111#2035C2211yescharacteristic
112#2034C2211yescharacteristic
113#2033C2211yescharacteristic
114#2024C2211yescharacteristic, complemented
115#2023C2211yescharacteristic
116#2023C2211yescharacteristic
117#2015C2211yescharacteristic
118#2015C2211yescharacteristic, complemented
119#2015C2211yescharacteristic, complemented
120#2012C2211yescharacteristic
121#2012C2211yescharacteristic
122#2012C2211yescharacteristic
123#2012C2211yescharacteristic
124#2011C2211yescharacteristic
125#2001C2211yescharacteristic
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#1985C2211yescharacteristic, complemented
129#1985C2211yescharacteristic, complemented
130#1982C2211yescharacteristic, complemented
131#1972C2211yescharacteristic
132#1970C2211yescharacteristic
133#1970C2211yescharacteristic
134#1968C2211yescharacteristic
135#1968C2211yescharacteristic, complemented
136#1959C2211yescharacteristic, complemented
137#1958C2211yescharacteristic
138#1949C2211yescharacteristic, complemented
139#1944C2211yescharacteristic, complemented
140#1936C2211yescharacteristic
141#1936C2211yescharacteristic
142#1936C2211yescharacteristic
143#1935C2211yescharacteristic, complemented
144#1934C2211yescharacteristic
145#1934C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1927C2211yescharacteristic, complemented
148#1926C2211yescharacteristic
149#1926C2211yescharacteristic, complemented
150#1925C2211yescharacteristic
151#1925C2211yescharacteristic, complemented
152#1924C2211yescharacteristic
153#1924C2211yescharacteristic
154#1923C2211yescharacteristic
155#1923C2211yescharacteristic
156#1921C2211yescharacteristic, complemented
157#1920C2211yescharacteristic, complemented
158#1920C2211yescharacteristic, complemented
159#1919C2211yescharacteristic, complemented
160#1916C2211yescharacteristic, complemented
161#1916C2211yescharacteristic, complemented
162#1916C2211yescharacteristic, complemented
163#1916C2211yescharacteristic, complemented
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1880C2211yescharacteristic
167#1880C2211yescharacteristic
168#1880C2211yescharacteristic, complemented
169#1879C2211yescharacteristic
170#1879C2211yescharacteristic
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic
176#1879C2211yescharacteristic
177#1878C2211yescharacteristic, complemented
178#1877C2211yescharacteristic, complemented
179#1877C2211yescharacteristic, complemented
180#1875C2211yescharacteristic
181#1875C2211yescharacteristic
182#1873C2211yescharacteristic
183#1865C2211yescharacteristic, complemented
184#1865C2211yescharacteristic, complemented
185#1864C2211yescharacteristic, complemented
186#1864C2211yescharacteristic, complemented
187#1862C2211yescharacteristic
188#1862C2211yescharacteristic
189#1854C2211yescharacteristic
190#1835C2211yescharacteristic, complemented
191#1818C2211yescharacteristic
192#1805C2211yescharacteristic, complemented
193#1804C2211yescharacteristic
194#1802C2211yescharacteristic, complemented
195#1786C2211yescharacteristic
196#1770C2211yescharacteristic, complemented
197#1770C2211yescharacteristic, complemented
198#1763C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic, complemented
201C4×#102C2211yescharacteristic, complemented
202#1750C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×Q16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C22×D8C2311yescharacteristic
213#559—42no—
214#559—42no—
215#542—42no—
216#542—42no—
217C2×C4⋊Q8—21no—
218C2×C4⋊Q8C2311yescharacteristic
219C2×#127C2311yescharacteristic
220C2×#126—21no—
221C2×#126—21no—
222C2×#124—21no—
223C2×#124—21no—
224C2×#124C2311yescharacteristic
225C2×#124C2311yescharacteristic
226C2×#124C2311yescharacteristic
227C2×#124C2311yescharacteristic
228C2×#123—21no—
229C2×#123—21no—
230C2×#123—21no—
231C2×#123—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8—21no—
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×#121—21no—
237C2×#121C2311yescharacteristic
238C2×#121C2311yescharacteristic
239C2×C4×Q8C2311yescharacteristic
240C2×C4×Q8C2311yescharacteristic
241C2×C4×Q8C2311yescharacteristic
242C2×C4×Q8C2311yescharacteristic
243C2×C4×Q8C2311yescharacteristic
244C2×C4×D4—21no—
245C2×C4×D4C2311yescharacteristic
246C2×C4×D4C2311yescharacteristic
247C2×C4×D4C2311yescharacteristic
248C2×C4×D4C2311yescharacteristic
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×#117C2311yescharacteristic
252C2×#117C2311yescharacteristic
253C22×C22⋊C4—21no—
254#496—42no—
255#464—42no—
256#463—24no—
257#463—42no—
258#450—42no—
259#447—24no—
260#447—42no—
261#442—42no—
262#440—42no—
263C4×Q16—42no—
264C4×SD16—24no—
265C2×#107C2311yescharacteristic
266C2×#107C2311yescharacteristic
267C2×#107C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×#106C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315C2×C4×C8C2311yescharacteristic
316#400—21no—
317#400D411yescharacteristic
318#399—21no—
319#399—21no—
320#399D411yescharacteristic
321#398—21no—
322#398—21no—
323#398D411yescharacteristic
324#398D411yescharacteristic
325#397—21no—
326#397—21no—
327#397—21no—
328#397—21no—
329#397—21no—
330#397—21no—
331#397—21no—
332#397—21no—
333#397—21no—
334#397—21no—
335#397—21no—
336#397—21no—
337#396—21no—
338#396—21no—
339#396—21no—
340#396—21no—
341#396D411yescharacteristic
342#396D411yescharacteristic
343#395D411yescharacteristic
344#394—21no—
345#394—21no—
346#394—21no—
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#393—21no—
352#393—21no—
353#393—21no—
354#393D411yescharacteristic
355#392—21no—
356#391—21no—
357#391C2311yescharacteristic
358#391C2311yescharacteristic
359#391C2311yescharacteristic
360#391C2311yescharacteristic
361#390—21no—
362#390—21no—
363#390—21no—
364#390—21no—
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#390C2311yescharacteristic
372#390C2311yescharacteristic
373#390C2311yescharacteristic
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#389—21no—
378#389—21no—
379#389—21no—
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
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#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#386—21no—
419#386—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#384C2311yescharacteristic
427#382—21no—
428#382—21no—
429#382C2311yescharacteristic
430#382C2311yescharacteristic
431#382C2311yescharacteristic
432#381—21no—
433#381—21no—
434#381—21no—
435#380—21no—
436#380—21no—
437#380—21no—
438#380—21no—
439#380C2311yescharacteristic
440#380C2311yescharacteristic
441#379—21no—
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×C4⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C22⋊C4—21no—
455C4×C22⋊C4—21no—
456C4×C22⋊C4—21no—
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459#376—21no—
460C2×#95—21no—
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#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C22×Q8—21no—
495C22×Q8C2×D411yescharacteristic
496C22×Q8C2411yescharacteristic
497C22×Q8C2411yescharacteristic
498C22×D4—22no—
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—41no—
505C22×D4—41no—
506C22×D4—41no—
507C22×D4—41no—
508C22×D4—41no—
509C22×D4C2411yescharacteristic
510C22×D4C2411yescharacteristic
511C22×D4C2411yescharacteristic
512C22×D4C2411yescharacteristic
513C23×C4—21no—
514C23×C4—21no—
515C23×C4—21no—
516C23×C4—21no—
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C2411yescharacteristic
520C2×Q16—22no—
521C2×Q16—41no—
522C2×Q16—41no—
523C2×SD16—22no—
524C2×SD16—22no—
525C2×SD16—22no—
526C2×SD16—22no—
527C2×SD16—22no—
528C2×SD16—41no—
529C2×SD16—41no—
530C2×SD16—41no—
531C2×SD16—41no—
532C2×SD16—41no—
533C2×SD16—41no—
534C2×SD16—41no—
535C2×D8—22no—
536C2×D8—22no—
537C2×D8—22no—
538C2×D8—22no—
539C2×D8—22no—
540C2×D8—41no—
541C2×D8—41no—
542C2×D8—41no—
543C2×D8—41no—
544C2×D8—41no—
545C2×D8—41no—
546C2×D8—41no—
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551C22×C8C2411yescharacteristic
552C22×C8C2411yescharacteristic
553C22×C8C2411yescharacteristic
554C22×C8C2411yescharacteristic
555C4⋊Q8—41no—
556C4⋊Q8—41no—
557C4⋊Q8—82no—
558#127—22no—
559#127—41no—
560#126—44no—
561#126—82no—
562#124—22no—
563#124—22no—
564#124—22no—
565#124—22no—
566#124—41no—
567#124—41no—
568#124—41no—
569#124—41no—
570#124—44no—
571#124—44no—
572#123—44no—
573#123—44no—
574#123—44no—
575#123—82no—
576C22⋊Q8—22no—
577C22⋊Q8—44no—
578C22⋊Q8—41no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—82no—
582#121—22no—
583#121—22no—
584#121—41no—
585#121—41no—
586#121—82no—
587C4×Q8—22no—
588C4×Q8—22no—
589C4×Q8—22no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×Q8—41no—
595C4×Q8—41no—
596C4×Q8—41no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—44no—
610#117—41no—
611#117—41no—
612#117—41no—
613#117—41no—
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⋊C4C2×D411yescharacteristic
632C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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—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—82no—
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C42—21no—
705C2×C42—21no—
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42C2411yescharacteristic
714C2×C42C2411yescharacteristic
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719#107—41no—
720#107—41no—
721#107—41no—
722#106—22no—
723#106—41no—
724#106—41no—
725#106—41no—
726C4⋊C8—22no—
727C4⋊C8—41no—
728C4⋊C8—41no—
729C4⋊C8—41no—
730#103—22no—
731#103—22no—
732#103—22no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#102—22no—
741#102—22no—
742#102—41no—
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—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102#4114yes—
760C22⋊C8—22no—
761C22⋊C8—41no—
762C22⋊C8—41no—
763C22⋊C8—41no—
764#97—41no—
765#97—41no—
766#97—41no—
767C4×C8—22no—
768C4×C8—41no—
769C4×C8—41no—
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—21no—
812C24—42no—
813C24—42no—
814C24—81no—
815C24—81no—
816C24—81no—
817C24—81no—
818C24—81no—
819C24C22×D411yescharacteristic
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8—21no—
826C2×Q8—21no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—21no—
830C2×Q8—21no—
831C2×Q8—41no—
832C2×Q8—41no—
833C2×Q8—41no—
834C2×Q8—42no—
835C2×Q8—81no—
836C2×Q8—81no—
837C2×Q8H(5,𝔽2)12yes—
838C2×D4—21no—
839C2×D4—21no—
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—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—42no—
861C2×D4—42no—
862C2×D4—42no—
863C2×D4—42no—
864C2×D4—42no—
865C2×D4—42no—
866C2×D4—42no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—81no—
870C2×D4—81no—
871C2×D4—82no—
872C2×D4—82no—
873C2×D4—82no—
874C2×D4—82no—
875C2×D4—81no—
876C2×D4—81no—
877C2×D4—81no—
878C2×D4—81no—
879C2×D4C2×#4112yes—
880C2×D4H(5,𝔽2)12yes—
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—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—81no—
906C22×C4—81no—
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×C4C22×D411yescharacteristic
930C22×C4C2511yescharacteristic
931Q16—44no—
932SD16—44no—
933SD16—44no—
934SD16—82no—
935SD16—82no—
936D8—44no—
937D8—82no—
938D8—82no—
939D8—82no—
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—21no—
963C2×C8C2×#4112yes—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
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—41no—
984C4⋊C4—41no—
985C4⋊C4—41no—
986C4⋊C4—41no—
987C4⋊C4—41no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—42no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—42no—
1000C4⋊C4—42no—
1001C4⋊C4—42no—
1002C4⋊C4—42no—
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⋊C4C2×#4112yes—
1012C22⋊C4—24no—
1013C22⋊C4—24no—
1014C22⋊C4—41no—
1015C22⋊C4—41no—
1016C22⋊C4—41no—
1017C22⋊C4—41no—
1018C22⋊C4—41no—
1019C22⋊C4—41no—
1020C22⋊C4—42no—
1021C22⋊C4—42no—
1022C22⋊C4—42no—
1023C22⋊C4—42no—
1024C22⋊C4—42no—
1025C22⋊C4—42no—
1026C22⋊C4—42no—
1027C22⋊C4—42no—
1028C22⋊C4—42no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—81no—
1036C22⋊C4—81no—
1037C22⋊C4—81no—
1038C22⋊C4—81no—
1039C22⋊C4—81no—
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—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—21no—
1072C42—21no—
1073C42—21no—
1074C42—21no—
1075C42—42no—
1076C42—42no—
1077C42—42no—
1078C42—42no—
1079C42—81no—
1080C42—81no—
1081C42—81no—
1082C42—81no—
1083C42—81no—
1084C23—21no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—22no—
1089C23—21no—
1090C23—22no—
1091C23—21no—
1092C23—21no—
1093C23—41no—
1094C23—41no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
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—84no—
1120C23—84no—
1121C23—162no—
1122C23—162no—
1123C23—162no—
1124C23—162no—
1125C23—162no—
1126C23C23×D411yescharacteristic
1127Q8—22no—
1128Q8—22no—
1129Q8—41no—
1130Q8—41no—
1131Q8—41no—
1132Q8—41no—
1133Q8—41no—
1134Q8—41no—
1135Q8—82no—
1136Q8—162no—
1137D4—22no—
1138D4—22no—
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—41no—
1152D4—41no—
1153D4—84no—
1154D4—84no—
1155D4—162no—
1156D4—162no—
1157D4—162no—
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—21no—
1186C2×C4—22no—
1187C2×C4—21no—
1188C2×C4—21no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—22no—
1197C2×C4—21no—
1198C2×C4—21no—
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—162no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4—162no—
1241C2×C4—162no—
1242C2×C4—162no—
1243C2×C4C22×#4111yescharacteristic
1244C2×C4C2×H(5,𝔽2)11yescharacteristic
1245C2×C4C2×H(5,𝔽2)11yescharacteristic
1246C2×C4#58511yescharacteristic
1247C2×C4#58511yescharacteristic
1248C2×C4#58511yescharacteristic
1249C8—22no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C8—41no—
1256C8—41no—
1257C22—42no—
1258C22—41no—
1259C22—41no—
1260C22—42no—
1261C22—41no—
1262C22—42no—
1263C22—42no—
1264C22—42no—
1265C22—41no—
1266C22—41no—
1267C22—42no—
1268C22—41no—
1269C22—41no—
1270C22—81no—
1271C22—81no—
1272C22—81no—
1273C22—81no—
1274C22—81no—
1275C22—81no—
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—168no—
1293C22D4×#4111yescharacteristic
1294C22#348411yescharacteristic
1295C22#348711yescharacteristic
1296C22#358411yescharacteristic
1297C22#358411yescharacteristic
1298C22#358511yescharacteristic
1299C22#358511yescharacteristic
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—41no—
1304C4—42no—
1305C4—41no—
1306C4—42no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—41no—
1313C4—41no—
1314C4—41no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4—81no—
1325C4#349411yescharacteristic
1326C4#351311yescharacteristic
1327C4#353311yescharacteristic
1328C4#356011yescharacteristic
1329C2—81no—
1330C2—82no—
1331C2—82no—
1332C2—161no—
1333C2—161no—
1334C2#4311511yescharacteristic
1335C2#6152711yescharacteristic
1336C2#6152911yescharacteristic
1337C2#6165311yescharacteristic
1338C2#6166611yescharacteristic
1339C2#6191911yescharacteristic
1340C2#6192411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#30468C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2396 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45207C2semidirect
2. #44961C2semidirect
3. #32639C2semidirect
4. #32589C2semidirect
5. #32437C2semidirect
6. #31938C2semidirect
7. #31861C2semidirect
8. #31645C2semidirect
9. #30996C2semidirect
11. #29424C2semidirect
12. #28888C2semidirect
13. #27563C2semidirect
14. #27403C2semidirect
15. #27199C2semidirect
16. #27189C2semidirect
17. #27072C2semidirect
18. #26598C2semidirect
19. #26596C2semidirect
20. #26267C2semidirect
21. #26173C2semidirect
22. #25639C2semidirect
23. #25152C2semidirect
24. #24909C2semidirect
25. #24204C2semidirect
26. #23945C2semidirect
27. #23585C2semidirect
28. #23005C2semidirect
29. #22765C2semidirect
30. #22328C2semidirect
31. #22056C2semidirect
32. C2×#559C22semidirect
42. C2×#440C22semidirect
43. C2×C4×Q16C22semidirect
54. #2563C22semidirect
56. #2546C22semidirect
68. #2448C22semidirect
70. #2445C22semidirect
79. #2367C22semidirect
81. #2351C22semidirect
82. #2349C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
91. #2092C22semidirect
92. #2087C22semidirect
93. #2084C22semidirect
95. #2074C22semidirect
97. #2073C22semidirect
98. #2068C22semidirect
99. #2066C22semidirect
102. #2057C22semidirect
103. #2055C22semidirect
108. #2042C22semidirect
109. #2041C22semidirect
114. #2024C22semidirect
118. #2015C22semidirect
119. #2015C22semidirect
128. #1985C22semidirect
129. #1985C22semidirect
130. #1982C22semidirect
135. #1968C22semidirect
136. #1959C22semidirect
138. #1949C22semidirect
139. #1944C22semidirect
143. #1935C22semidirect
145. #1934C22semidirect
146. #1928C22semidirect
147. #1927C22semidirect
149. #1926C22semidirect
151. #1925C22semidirect
156. #1921C22semidirect
157. #1920C22semidirect
158. #1920C22semidirect
159. #1919C22semidirect
160. #1916C22semidirect
161. #1916C22semidirect
162. #1916C22semidirect
163. #1916C22semidirect
168. #1880C22semidirect
177. #1878C22semidirect
178. #1877C22semidirect
179. #1877C22semidirect
183. #1865C22semidirect
184. #1865C22semidirect
185. #1864C22semidirect
186. #1864C22semidirect
190. #1835C22semidirect
192. #1805C22semidirect
194. #1802C22semidirect
196. #1770C22semidirect
197. #1770C22semidirect
198. #1763C22semidirect
199. #1763C22semidirect
200. C4×#102C22semidirect
201. C4×#102C22semidirect

Maximal subgroups

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

subgroupindex
#452072
#449612
#326392
#325892
#324372
#319382
#318612
#316452
#309962
#304682
#294242
#288882
#275632
#274032
#271992
#271892
#270722
#265982
#265962
#262672
#261732
#256392
#251522
#249092
#242042
#239452
#235852
#230052
#227652
#223282
#220562