Finite Group Databasebeta

← #7091039

Subgroups — #7091039

Order 512.

1788 conjugacy classes of subgroups.

The subgroup lattice has 1429 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#59562C211yesmaximal, characteristic, complemented
2#59411C211yesmaximal, characteristic, complemented
3#32658C211yesmaximal, characteristic, complemented
4#32546C211yesmaximal, characteristic, complemented
5#32025C211yesmaximal, characteristic, complemented
6#31621C211yesmaximal, characteristic, complemented
7#31550C211yesmaximal, characteristic, complemented
8#31301C211yesmaximal, characteristic, complemented
9#31009C211yesmaximal, characteristic, complemented
10#30404C211yesmaximal, characteristic, complemented
11#29369C211yesmaximal, characteristic, complemented
12#29365C211yesmaximal, characteristic, complemented
13#29055C211yesmaximal, characteristic, complemented
14#27533C211yesmaximal, characteristic, complemented
15#26960C211yesmaximal, characteristic, complemented
16#26938C211yesmaximal, characteristic, complemented
17#26564C211yesmaximal, characteristic, complemented
18#25160C211yesmaximal, characteristic, complemented
19#25085C211yesmaximal, characteristic, complemented
20#24895C211yesmaximal, characteristic, complemented
21#24893C211yesmaximal, characteristic, complemented
22#24367C211yesmaximal, characteristic, complemented
23#24204C211yesmaximal, characteristic, complemented
24#24192C211yesmaximal, characteristic, complemented
25#24034C211yesmaximal, characteristic, complemented
26#23869C211yesmaximal, characteristic
27#23676C211yesmaximal, characteristic, complemented
28#22872C211yesmaximal, characteristic, complemented
29#22442C211yesmaximal, characteristic, complemented
30#22389C211yesmaximal, characteristic, complemented
31#22146C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#559C2211yescharacteristic, complemented
34C2×#550C2211yescharacteristic
35C2×#482C2211yescharacteristic, complemented
36C2×#465C2211yescharacteristic
37C2×#463C2211yescharacteristic
38C2×#463C2211yescharacteristic
39C2×#461C2211yescharacteristic
40C2×#449C2211yescharacteristic
41C2×#449C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#447C2211yescharacteristic
44C2×#442C2211yescharacteristic
45C2×C4×D8C2211yescharacteristic
46C2×C4×D8C2211yescharacteristic
47C2×C4×D8C2211yescharacteristic
48C2×#416C2211yescharacteristic, complemented
49#2778—21no—
50#2735—21no—
51#2701—21no—
52#2701—21no—
53#2582C2211yescharacteristic, complemented
54#2580C2211yescharacteristic
55#2576—21no—
56#2544—21no—
57#2538C2211yescharacteristic
58#2538C2211yescharacteristic
59#2497C2211yescharacteristic
60#2494C2211yescharacteristic
61#2485C2211yescharacteristic
62#2477—21no—
63#2472—21no—
64#2471—21no—
65#2447—21no—
66#2445—21no—
67#2432C2211yescharacteristic
68#2432C2211yescharacteristic, complemented
69#2427C2211yescharacteristic
70#2427C2211yescharacteristic, complemented
71#2425—21no—
72#2425—21no—
73#2422C2211yescharacteristic
74#2422C2211yescharacteristic
75#2422C2211yescharacteristic, complemented
76#2420C2211yescharacteristic
77#2411—21no—
78#2408C2211yescharacteristic
79#2363C2211yescharacteristic
80#2363C2211yescharacteristic
81#2349—21no—
82#2342—21no—
83#2339C2211yescharacteristic
84#2339C2211yescharacteristic, complemented
85D4×C22⋊C4C2211yescharacteristic
86D4×C22⋊C4C2211yescharacteristic
87C4×C4⋊Q8C2211yescharacteristic, complemented
88C4×#127C2211yescharacteristic, complemented
89C4×#124C2211yescharacteristic
90#2293C2211yescharacteristic
91#2293C2211yescharacteristic
92#2100C2211yescharacteristic, complemented
93#2099C2211yescharacteristic, complemented
94#2099C2211yescharacteristic, complemented
95#2097C2211yescharacteristic, complemented
96#2094C2211yescharacteristic
97#2093C2211yescharacteristic
98#2088C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2083C2211yescharacteristic, complemented
101#2077C2211yescharacteristic
102#2075C2211yescharacteristic
103#2075C2211yescharacteristic, complemented
104#2072C2211yescharacteristic, complemented
105#2071C2211yescharacteristic
106#2067C2211yescharacteristic
107#2067C2211yescharacteristic, complemented
108#2067C2211yescharacteristic, complemented
109#2066C2211yescharacteristic, complemented
110#2055C2211yescharacteristic
111#2054C2211yescharacteristic
112#2054C2211yescharacteristic
113#2043C2211yescharacteristic, complemented
114#2042C2211yescharacteristic, complemented
115#2042C2211yescharacteristic, complemented
116#2041C2211yescharacteristic, complemented
117#2041C2211yescharacteristic, complemented
118#2036C2211yescharacteristic
119#2036C2211yescharacteristic, complemented
120#2035C2211yescharacteristic
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2033C2211yescharacteristic
124#2013C2211yescharacteristic
125#2012C2211yescharacteristic
126#2012C2211yescharacteristic
127#2011C2211yescharacteristic
128#2011C2211yescharacteristic
129#2000C2211yescharacteristic
130#1999C2211yescharacteristic
131#1999C2211yescharacteristic
132#1985C2211yescharacteristic, complemented
133#1984C2211yescharacteristic, complemented
134#1981C2211yescharacteristic, complemented
135#1973C2211yescharacteristic
136#1968C2211yescharacteristic
137#1968C2211yescharacteristic
138#1959C2211yescharacteristic, complemented
139#1958C2211yescharacteristic, complemented
140#1948C2211yescharacteristic, complemented
141#1944C2211yescharacteristic, complemented
142#1934C2211yescharacteristic
143#1933C2211yescharacteristic, complemented
144#1933C2211yescharacteristic, complemented
145#1933C2211yescharacteristic, complemented
146#1928C2211yescharacteristic, complemented
147#1928C2211yescharacteristic, complemented
148#1926C2211yescharacteristic, complemented
149#1926C2211yescharacteristic, complemented
150#1924C2211yescharacteristic, complemented
151#1923C2211yescharacteristic
152#1923C2211yescharacteristic
153#1923C2211yescharacteristic, complemented
154#1895C2211yescharacteristic
155#1894C2211yescharacteristic
156#1893C2211yescharacteristic
157#1893C2211yescharacteristic, complemented
158#1880C2211yescharacteristic
159#1880C2211yescharacteristic
160#1880C2211yescharacteristic
161#1880C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic
164#1879C2211yescharacteristic
165#1879C2211yescharacteristic
166#1879C2211yescharacteristic
167#1879C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic
172#1873C2211yescharacteristic, complemented
173#1870C2211yescharacteristic
174#1869C2211yescharacteristic
175#1865C2211yescharacteristic, complemented
176#1865C2211yescharacteristic, complemented
177#1864C2211yescharacteristic
178#1864C2211yescharacteristic, complemented
179#1864C2211yescharacteristic, complemented
180#1864C2211yescharacteristic, complemented
181#1863C2211yescharacteristic, complemented
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic, complemented
185#1854C2211yescharacteristic, complemented
186#1851C2211yescharacteristic
187#1850C2211yescharacteristic, complemented
188#1839C2211yescharacteristic, complemented
189#1809C2211yescharacteristic
190#1804C2211yescharacteristic, complemented
191#1802C2211yescharacteristic
192#1802C2211yescharacteristic, complemented
193#1788C2211yescharacteristic
194#1788C2211yescharacteristic
195#1788C2211yescharacteristic
196#1788C2211yescharacteristic, complemented
197#1786C2211yescharacteristic
198C4×C4⋊C8C2211yescharacteristic, complemented
199C4×#102C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic, complemented
201#1753C2211yescharacteristic
202C8×C22⋊C4C2211yescharacteristic, complemented
203C22×#41C2311yescharacteristic
204C22×#41C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C2×AGL(1,ℤ/8)—24no—
207C2×AGL(1,ℤ/8)—42no—
208C2×AGL(1,ℤ/8)—42no—
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×D8C2311yescharacteristic
214C22×D8C2311yescharacteristic
215C22×D8C2311yescharacteristic
216C22×D8C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#559—42no—
220#559—42no—
221#550—42no—
222#550—42no—
223C2×C4⋊Q8C2311yescharacteristic
224C2×#127—21no—
225C2×#127C2311yescharacteristic
226C2×#124—21no—
227C2×#124D411yescharacteristic
228C2×#124C2311yescharacteristic
229C2×#124C2311yescharacteristic
230C2×#123—21no—
231C2×#123—21no—
232C2×#123—21no—
233C2×#123—21no—
234C2×#123—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8C2311yescharacteristic
237C2×C22⋊Q8C2311yescharacteristic
238C2×#121—21no—
239C2×#121—21no—
240C2×#121C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#120—21no—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×Q8C2311yescharacteristic
248C2×C4×D4—21no—
249C2×C4×D4—21no—
250C2×C4×D4—21no—
251C2×C4×D4—21no—
252C2×C4×D4C2311yescharacteristic
253C2×C4×D4C2311yescharacteristic
254C2×C4×D4C2311yescharacteristic
255C2×C4×D4C2311yescharacteristic
256C2×C4×D4C2311yescharacteristic
257C2×C4×D4C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×#117—21no—
262C2×#117—21no—
263C2×#117C2311yescharacteristic
264C22×C22⋊C4—21no—
265C22×C22⋊C4—21no—
266#482—42no—
267#465—42no—
268#463—42no—
269#463—42no—
270#461—24no—
271#450—42no—
272#449—24no—
273#449—42no—
274#447—42no—
275#442—42no—
276C4×D8—42no—
277C4×D8—42no—
278C4×D8—42no—
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#107C2311yescharacteristic
282C2×#107C2311yescharacteristic
283C2×#106C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×#106C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291#416—42no—
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#102C2311yescharacteristic
305C2×#102C2311yescharacteristic
306C2×#102C2311yescharacteristic
307C2×#102C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×#102C2311yescharacteristic
317C2×#102C2311yescharacteristic
318C2×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×#97C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333C2×C4×C8C2311yescharacteristic
334#401—21no—
335#400—21no—
336#399—21no—
337#398—21no—
338#398—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397—21no—
345#397—21no—
346#397—21no—
347#396—21no—
348#396—21no—
349#396—21no—
350#396—21no—
351#396—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#393—21no—
365#392—21no—
366#391—21no—
367#391D411yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#390—21no—
373#390—21no—
374#390—21no—
375#390—21no—
376#390—21no—
377#390D411yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#390C2311yescharacteristic
381#390C2311yescharacteristic
382#390C2311yescharacteristic
383#390C2311yescharacteristic
384#390C2311yescharacteristic
385#390C2311yescharacteristic
386#389—21no—
387#389—21no—
388#389—21no—
389#389—21no—
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#389C2311yescharacteristic
393#389C2311yescharacteristic
394#389C2311yescharacteristic
395#389C2311yescharacteristic
396#389C2311yescharacteristic
397#389C2311yescharacteristic
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#388D411yescharacteristic
408#388D411yescharacteristic
409#388D411yescharacteristic
410#388D411yescharacteristic
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#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#385—21no—
435#385—21no—
436#384C2311yescharacteristic
437#384C2311yescharacteristic
438#384C2311yescharacteristic
439#382D411yescharacteristic
440#382C2311yescharacteristic
441#381—21no—
442#381—21no—
443#381—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380C2311yescharacteristic
448#380C2311yescharacteristic
449#380C2311yescharacteristic
450#380C2311yescharacteristic
451#380C2311yescharacteristic
452#380C2311yescharacteristic
453#379—21no—
454#379—21no—
455#379—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4—21no—
463C4×C22⋊C4—21no—
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466C4×C22⋊C4C2311yescharacteristic
467C4×C22⋊C4C2311yescharacteristic
468C2×#95—21no—
469C2×#95—21no—
470C43C2311yescharacteristic
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#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C2×#41—22no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—41no—
510C2×#41—41no—
511C2×#41—41no—
512C22×Q8C2×D411yescharacteristic
513C22×Q8C2411yescharacteristic
514C22×Q8C2411yescharacteristic
515C22×D4—22no—
516C22×D4—22no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—21no—
524C22×D4—21no—
525C22×D4—21no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4—41no—
529C22×D4—41no—
530C22×D4C2×D411yescharacteristic
531C22×D4C2411yescharacteristic
532C22×D4C2411yescharacteristic
533C22×D4C2411yescharacteristic
534C22×D4C2411yescharacteristic
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4—21no—
545C23×C4C2411yescharacteristic
546C23×C4C2411yescharacteristic
547AGL(1,ℤ/8)—416no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16#4114yes—
560C2×D8—22no—
561C2×D8—22no—
562C2×D8—22no—
563C2×D8—22no—
564C2×D8—22no—
565C2×D8—22no—
566C2×D8—22no—
567C2×D8—22no—
568C2×D8—22no—
569C2×D8—41no—
570C2×D8—41no—
571C2×D8—41no—
572C2×M16—22no—
573C2×M16—41no—
574C2×M16—41no—
575C22×C8—41no—
576C22×C8—41no—
577C22×C8—41no—
578C22×C8C2411yescharacteristic
579C22×C8C2411yescharacteristic
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C4⋊Q8—22no—
587C4⋊Q8—41no—
588#127—22no—
589#127—22no—
590#127—44no—
591#124—22no—
592#124—22no—
593#124—42no—
594#124—41no—
595#124—41no—
596#124—44no—
597#123—44no—
598#123—44no—
599#123—82no—
600#123—82no—
601#123—82no—
602C22⋊Q8—41no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606C22⋊Q8—82no—
607#121—22no—
608#121—22no—
609#121—22no—
610#121—22no—
611#121—41no—
612#121—41no—
613#121—41no—
614#121—41no—
615#121—44no—
616#121—44no—
617#120—82no—
618C4×Q8—41no—
619C4×Q8—41no—
620C4×Q8—41no—
621C4×Q8—41no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—44no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—41no—
639C4×D4—41no—
640C4×D4—41no—
641C4×D4—41no—
642C4×D4—41no—
643C4×D4—44no—
644C4×D4—44no—
645C4×D4—82no—
646#117—41no—
647#117—41no—
648#117—82no—
649#117—82no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—21no—
655C2×C4⋊C4—21no—
656C2×C4⋊C4—21no—
657C2×C4⋊C4—21no—
658C2×C4⋊C4—21no—
659C2×C4⋊C4—21no—
660C2×C4⋊C4—21no—
661C2×C4⋊C4—21no—
662C2×C4⋊C4—21no—
663C2×C4⋊C4—21no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C4⋊C4C2411yescharacteristic
676C2×C4⋊C4C2411yescharacteristic
677C2×C4⋊C4C2411yescharacteristic
678C2×C4⋊C4C2411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
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—21no—
699C2×C22⋊C4—21no—
700C2×C22⋊C4—21no—
701C2×C22⋊C4—21no—
702C2×C22⋊C4—21no—
703C2×C22⋊C4—21no—
704C2×C22⋊C4—21no—
705C2×C22⋊C4—21no—
706C2×C22⋊C4—21no—
707C2×C22⋊C4—21no—
708C2×C22⋊C4—21no—
709C2×C22⋊C4—21no—
710C2×C22⋊C4—21no—
711C2×C22⋊C4—21no—
712C2×C22⋊C4—21no—
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4—21no—
721C2×C22⋊C4—21no—
722C2×C22⋊C4—21no—
723C2×C22⋊C4—21no—
724C2×C22⋊C4—21no—
725C2×C22⋊C4—44no—
726C2×C22⋊C4—82no—
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C22⋊C4C2×D411yescharacteristic
732C2×C22⋊C4C2×D411yescharacteristic
733C2×C22⋊C4C2×D411yescharacteristic
734C2×C22⋊C4C2×D411yescharacteristic
735C2×C22⋊C4C2×D411yescharacteristic
736C2×C22⋊C4C2×D411yescharacteristic
737C2×C42—21no—
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42C2×D411yescharacteristic
743C2×C42C2×D411yescharacteristic
744C2×C42C2×D411yescharacteristic
745C2×C42C2×D411yescharacteristic
746C2×C42C2411yescharacteristic
747C2×C42C2411yescharacteristic
748C2×C42C2411yescharacteristic
749C2×C42C2411yescharacteristic
750C2×C42C2411yescharacteristic
751#107—41no—
752#107—41no—
753#107—41no—
754#107—41no—
755#106—41no—
756#106—41no—
757#106—41no—
758#106—41no—
759C4⋊C8—22no—
760C4⋊C8—41no—
761C4⋊C8—41no—
762C4⋊C8—41no—
763#103—22no—
764#103—22no—
765#103—22no—
766#103—41no—
767#103—41no—
768#103—41no—
769#103—41no—
770#103—41no—
771#103—41no—
772#103—41no—
773#103—41no—
774#103—41no—
775#102—22no—
776#102—22no—
777#102—22no—
778#102—22no—
779#102—22no—
780#102—22no—
781#102—22no—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788#102—41no—
789#102—41no—
790#102—41no—
791#102—41no—
792#102—41no—
793#102—41no—
794#102—41no—
795C22⋊C8—22no—
796C22⋊C8—41no—
797C22⋊C8—41no—
798C22⋊C8—41no—
799C22⋊C8—41no—
800C22⋊C8—41no—
801#97—41no—
802C4×C8—41no—
803C4×C8—41no—
804C4×C8—41no—
805#95—21no—
806#95—21no—
807#95—21no—
808#95—21no—
809#95—21no—
810#95—21no—
811#95—21no—
812#95—21no—
813#95—21no—
814#95—21no—
815#95—21no—
816#95—21no—
817#95—21no—
818#95—21no—
819#95—21no—
820#95—21no—
821#95—21no—
822#95—21no—
823#95—21no—
824#95—21no—
825#95—21no—
826#95—21no—
827#95—21no—
828#95—21no—
829#95—21no—
830#95—21no—
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833#95C2×D411yescharacteristic
834#95C2×D411yescharacteristic
835#95C2×D411yescharacteristic
836#95C2×D411yescharacteristic
837#95C2×D411yescharacteristic
838#95C2×D411yescharacteristic
839C24—21no—
840C24—21no—
841C24—21no—
842C24—21no—
843C24—42no—
844C24—42no—
845C24—42no—
846C24—81no—
847C24—81no—
848C24—81no—
849C24—81no—
850C24C22×D411yescharacteristic
851C24C22×D411yescharacteristic
852#41—44no—
853#41—44no—
854#41—82no—
855#41—82no—
856#41—82no—
857#41—82no—
858#41—82no—
859#41—82no—
860C2×Q8—22no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—21no—
868C2×Q8—21no—
869C2×Q8—21no—
870C2×Q8—21no—
871C2×Q8—21no—
872C2×Q8—41no—
873C2×Q8—41no—
874C2×Q8C2×#4112yes—
875C2×D4—24no—
876C2×D4—24no—
877C2×D4—22no—
878C2×D4—21no—
879C2×D4—21no—
880C2×D4—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—42no—
899C2×D4—41no—
900C2×D4—41no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—44no—
906C2×D4—42no—
907C2×D4—42no—
908C2×D4—42no—
909C2×D4—42no—
910C2×D4—42no—
911C2×D4—42no—
912C2×D4—42no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4—82no—
917C2×D4—82no—
918C2×D4—82no—
919C2×D4—81no—
920C2×D4—81no—
921C2×D4—81no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4C2×#4112yes—
930C2×D4H(5,𝔽2)12yes—
931C2×D4H(5,𝔽2)12yes—
932C2×D4H(5,𝔽2)12yes—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—21no—
940C22×C4—21no—
941C22×C4—21no—
942C22×C4—21no—
943C22×C4—21no—
944C22×C4—21no—
945C22×C4—21no—
946C22×C4—21no—
947C22×C4—21no—
948C22×C4—21no—
949C22×C4—21no—
950C22×C4—21no—
951C22×C4—21no—
952C22×C4—21no—
953C22×C4—21no—
954C22×C4—21no—
955C22×C4—21no—
956C22×C4—21no—
957C22×C4—42no—
958C22×C4—42no—
959C22×C4—42no—
960C22×C4—42no—
961C22×C4—42no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—42no—
966C22×C4—42no—
967C22×C4—42no—
968C22×C4—42no—
969C22×C4—42no—
970C22×C4—81no—
971C22×C4—81no—
972C22×C4—81no—
973C22×C4—81no—
974C22×C4—81no—
975C22×C4—81no—
976C22×C4—81no—
977C22×C4—81no—
978C22×C4—81no—
979C22×C4—81no—
980C22×C4—81no—
981C22×C4—81no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4C22×D411yescharacteristic
988C22×C4C22×D411yescharacteristic
989C22×C4C22×D411yescharacteristic
990C22×C4C22×D411yescharacteristic
991C22×C4C22×D411yescharacteristic
992C22×C4C22×D411yescharacteristic
993C22×C4C22×D411yescharacteristic
994C22×C4C22×D411yescharacteristic
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C2511yescharacteristic
1000SD16—44no—
1001SD16—44no—
1002SD16—82no—
1003SD16—82no—
1004D8—28no—
1005D8—44no—
1006D8—44no—
1007D8—44no—
1008M16—44no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C2×C8—21no—
1018C2×C8—21no—
1019C2×C8—21no—
1020C2×C8—21no—
1021C2×C8—21no—
1022C2×C8—21no—
1023C2×C8—21no—
1024C2×C8—21no—
1025C2×C8—21no—
1026C2×C8—21no—
1027C2×C8—21no—
1028C2×C8—21no—
1029C2×C8—21no—
1030C2×C8—21no—
1031C2×C8—21no—
1032C2×C8—82no—
1033C2×C8C2×#4112yes—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—21no—
1037C4⋊C4—21no—
1038C4⋊C4—21no—
1039C4⋊C4—21no—
1040C4⋊C4—21no—
1041C4⋊C4—21no—
1042C4⋊C4—21no—
1043C4⋊C4—21no—
1044C4⋊C4—21no—
1045C4⋊C4—21no—
1046C4⋊C4—21no—
1047C4⋊C4—21no—
1048C4⋊C4—21no—
1049C4⋊C4—21no—
1050C4⋊C4—21no—
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—21no—
1054C4⋊C4—41no—
1055C4⋊C4—41no—
1056C4⋊C4—41no—
1057C4⋊C4—41no—
1058C4⋊C4—42no—
1059C4⋊C4—42no—
1060C4⋊C4—42no—
1061C4⋊C4—42no—
1062C4⋊C4—42no—
1063C4⋊C4—42no—
1064C4⋊C4—42no—
1065C4⋊C4—42no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4—81no—
1070C4⋊C4—81no—
1071C4⋊C4—81no—
1072C4⋊C4—81no—
1073C4⋊C4—81no—
1074C4⋊C4—81no—
1075C4⋊C4—81no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C22⋊C4—22no—
1079C22⋊C4—22no—
1080C22⋊C4—22no—
1081C22⋊C4—22no—
1082C22⋊C4—41no—
1083C22⋊C4—41no—
1084C22⋊C4—41no—
1085C22⋊C4—41no—
1086C22⋊C4—41no—
1087C22⋊C4—41no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
1091C22⋊C4—42no—
1092C22⋊C4—42no—
1093C22⋊C4—42no—
1094C22⋊C4—42no—
1095C22⋊C4—42no—
1096C22⋊C4—42no—
1097C22⋊C4—42no—
1098C22⋊C4—42no—
1099C22⋊C4—42no—
1100C22⋊C4—42no—
1101C22⋊C4—42no—
1102C22⋊C4—42no—
1103C22⋊C4—42no—
1104C22⋊C4—42no—
1105C22⋊C4—42no—
1106C22⋊C4—42no—
1107C22⋊C4—42no—
1108C22⋊C4—42no—
1109C22⋊C4—42no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C22⋊C4—81no—
1114C22⋊C4—81no—
1115C22⋊C4—81no—
1116C22⋊C4—81no—
1117C22⋊C4—81no—
1118C22⋊C4—81no—
1119C22⋊C4—81no—
1120C22⋊C4—81no—
1121C22⋊C4—81no—
1122C22⋊C4—81no—
1123C22⋊C4—81no—
1124C22⋊C4—81no—
1125C22⋊C4—81no—
1126C22⋊C4—81no—
1127C22⋊C4—81no—
1128C22⋊C4—81no—
1129C42—22no—
1130C42—22no—
1131C42—22no—
1132C42—21no—
1133C42—21no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—41no—
1143C42—42no—
1144C42—42no—
1145C42—81no—
1146C42—81no—
1147C42—81no—
1148C23—21no—
1149C23—21no—
1150C23—22no—
1151C23—21no—
1152C23—21no—
1153C23—22no—
1154C23—22no—
1155C23—21no—
1156C23—21no—
1157C23—22no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—21no—
1163C23—21no—
1164C23—21no—
1165C23—21no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—41no—
1174C23—41no—
1175C23—41no—
1176C23—41no—
1177C23—41no—
1178C23—41no—
1179C23—41no—
1180C23—41no—
1181C23—41no—
1182C23—41no—
1183C23—41no—
1184C23—41no—
1185C23—41no—
1186C23—41no—
1187C23—41no—
1188C23—41no—
1189C23—41no—
1190C23—84no—
1191C23—84no—
1192C23—84no—
1193C23—162no—
1194C23—162no—
1195C23—162no—
1196C23—162no—
1197C23C23×D411yescharacteristic
1198Q8—22no—
1199Q8—22no—
1200Q8—41no—
1201Q8—41no—
1202Q8—41no—
1203Q8—41no—
1204Q8—41no—
1205Q8—41no—
1206Q8—82no—
1207D4—22no—
1208D4—22no—
1209D4—22no—
1210D4—22no—
1211D4—22no—
1212D4—22no—
1213D4—22no—
1214D4—22no—
1215D4—48no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—41no—
1224D4—82no—
1225D4—84no—
1226D4—84no—
1227D4—84no—
1228D4—84no—
1229D4—162no—
1230D4—162no—
1231D4—162no—
1232D4—162no—
1233C2×C4—21no—
1234C2×C4—21no—
1235C2×C4—21no—
1236C2×C4—21no—
1237C2×C4—21no—
1238C2×C4—21no—
1239C2×C4—21no—
1240C2×C4—21no—
1241C2×C4—21no—
1242C2×C4—21no—
1243C2×C4—21no—
1244C2×C4—21no—
1245C2×C4—21no—
1246C2×C4—22no—
1247C2×C4—21no—
1248C2×C4—21no—
1249C2×C4—21no—
1250C2×C4—21no—
1251C2×C4—21no—
1252C2×C4—21no—
1253C2×C4—21no—
1254C2×C4—21no—
1255C2×C4—21no—
1256C2×C4—21no—
1257C2×C4—21no—
1258C2×C4—21no—
1259C2×C4—21no—
1260C2×C4—21no—
1261C2×C4—21no—
1262C2×C4—21no—
1263C2×C4—21no—
1264C2×C4—21no—
1265C2×C4—21no—
1266C2×C4—21no—
1267C2×C4—41no—
1268C2×C4—41no—
1269C2×C4—41no—
1270C2×C4—41no—
1271C2×C4—41no—
1272C2×C4—41no—
1273C2×C4—41no—
1274C2×C4—41no—
1275C2×C4—41no—
1276C2×C4—41no—
1277C2×C4—41no—
1278C2×C4—41no—
1279C2×C4—41no—
1280C2×C4—41no—
1281C2×C4—41no—
1282C2×C4—41no—
1283C2×C4—41no—
1284C2×C4—41no—
1285C2×C4—41no—
1286C2×C4—41no—
1287C2×C4—41no—
1288C2×C4—41no—
1289C2×C4—41no—
1290C2×C4—41no—
1291C2×C4—41no—
1292C2×C4—41no—
1293C2×C4—41no—
1294C2×C4—41no—
1295C2×C4—41no—
1296C2×C4—41no—
1297C2×C4—41no—
1298C2×C4—41no—
1299C2×C4—41no—
1300C2×C4—41no—
1301C2×C4—41no—
1302C2×C4—41no—
1303C2×C4—41no—
1304C2×C4—41no—
1305C2×C4—41no—
1306C2×C4—41no—
1307C2×C4—41no—
1308C2×C4—41no—
1309C2×C4—41no—
1310C2×C4—84no—
1311C2×C4—84no—
1312C2×C4—84no—
1313C2×C4—84no—
1314C2×C4—162no—
1315C2×C4—162no—
1316C2×C4—162no—
1317C2×C4—162no—
1318C2×C4—162no—
1319C2×C4—162no—
1320C2×C4#57512yes—
1321C2×C4#57612yes—
1322C2×C4#57712yes—
1323C2×C4C22×#4111yescharacteristic
1324C2×C4C2×H(5,𝔽2)11yescharacteristic
1325C2×C4C2×H(5,𝔽2)11yescharacteristic
1326C2×C4C2×H(5,𝔽2)11yescharacteristic
1327C2×C4#58511yescharacteristic
1328C2×C4#58511yescharacteristic
1329C8—22no—
1330C8—41no—
1331C8—41no—
1332C8—41no—
1333C8—41no—
1334C8—41no—
1335C8—41no—
1336C8—41no—
1337C22—41no—
1338C22—41no—
1339C22—42no—
1340C22—42no—
1341C22—41no—
1342C22—41no—
1343C22—42no—
1344C22—41no—
1345C22—41no—
1346C22—41no—
1347C22—42no—
1348C22—41no—
1349C22—42no—
1350C22—42no—
1351C22—41no—
1352C22—41no—
1353C22—41no—
1354C22—41no—
1355C22—42no—
1356C22—42no—
1357C22—42no—
1358C22—42no—
1359C22—42no—
1360C22—42no—
1361C22—41no—
1362C22—41no—
1363C22—81no—
1364C22—81no—
1365C22—81no—
1366C22—81no—
1367C22—81no—
1368C22—81no—
1369C22—81no—
1370C22—81no—
1371C22—81no—
1372C22—81no—
1373C22—81no—
1374C22—81no—
1375C22—81no—
1376C22—81no—
1377C22—81no—
1378C22—81no—
1379C22—168no—
1380C22D4×#4111yescharacteristic
1381C22#348411yescharacteristic
1382C22#348811yescharacteristic
1383C22C2×#57511yescharacteristic
1384C22C2×#57611yescharacteristic
1385C22C2×#57711yescharacteristic
1386C22#358411yescharacteristic
1387C4—22no—
1388C4—22no—
1389C4—22no—
1390C4—41no—
1391C4—41no—
1392C4—41no—
1393C4—41no—
1394C4—41no—
1395C4—41no—
1396C4—42no—
1397C4—41no—
1398C4—41no—
1399C4—41no—
1400C4—81no—
1401C4—81no—
1402C4—81no—
1403C4—81no—
1404C4—81no—
1405C4—81no—
1406C4—81no—
1407C4—81no—
1408C4—81no—
1409C4—81no—
1410C4—81no—
1411C4#349011yescharacteristic
1412C4#351311yescharacteristic
1413C4#353411yescharacteristic
1414C4#356011yescharacteristic
1415C2—81no—
1416C2—81no—
1417C2—82no—
1418C2—82no—
1419C2—82no—
1420C2—82no—
1421C2#4423111yescharacteristic
1422C2#6144111yescharacteristic
1423C2#6149811yescharacteristic
1424C2#6160411yescharacteristic
1425C2#6165711yescharacteristic
1426C2#6197711yescharacteristic
1427C2#6206811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#23869C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C4×#124 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #59562C2semidirect
2. #59411C2semidirect
3. #32658C2semidirect
4. #32546C2semidirect
5. #32025C2semidirect
6. #31621C2semidirect
7. #31550C2semidirect
8. #31301C2semidirect
9. #31009C2semidirect
10. #30404C2semidirect
11. #29369C2semidirect
12. #29365C2semidirect
13. #29055C2semidirect
14. #27533C2semidirect
15. #26960C2semidirect
16. #26938C2semidirect
17. #26564C2semidirect
18. #25160C2semidirect
19. #25085C2semidirect
20. #24895C2semidirect
21. #24893C2semidirect
22. #24367C2semidirect
23. #24204C2semidirect
24. #24192C2semidirect
25. #24034C2semidirect
27. #23676C2semidirect
28. #22872C2semidirect
29. #22442C2semidirect
30. #22389C2semidirect
31. #22146C2semidirect
33. C2×#559C22semidirect
35. C2×#482C22semidirect
48. C2×#416C22semidirect
53. #2582C22semidirect
68. #2432C22semidirect
70. #2427C22semidirect
75. #2422C22semidirect
84. #2339C22semidirect
87. C4×C4⋊Q8C22semidirect
88. C4×#127C22semidirect
92. #2100C22semidirect
93. #2099C22semidirect
94. #2099C22semidirect
95. #2097C22semidirect
98. #2088C22semidirect
99. #2085C22semidirect
100. #2083C22semidirect
103. #2075C22semidirect
104. #2072C22semidirect
107. #2067C22semidirect
108. #2067C22semidirect
109. #2066C22semidirect
113. #2043C22semidirect
114. #2042C22semidirect
115. #2042C22semidirect
116. #2041C22semidirect
117. #2041C22semidirect
119. #2036C22semidirect
132. #1985C22semidirect
133. #1984C22semidirect
134. #1981C22semidirect
138. #1959C22semidirect
139. #1958C22semidirect
140. #1948C22semidirect
141. #1944C22semidirect
143. #1933C22semidirect
144. #1933C22semidirect
145. #1933C22semidirect
146. #1928C22semidirect
147. #1928C22semidirect
148. #1926C22semidirect
149. #1926C22semidirect
150. #1924C22semidirect
153. #1923C22semidirect
157. #1893C22semidirect
172. #1873C22semidirect
175. #1865C22semidirect
176. #1865C22semidirect
178. #1864C22semidirect
179. #1864C22semidirect
180. #1864C22semidirect
181. #1863C22semidirect
182. #1863C22semidirect
184. #1862C22semidirect
185. #1854C22semidirect
187. #1850C22semidirect
188. #1839C22semidirect
190. #1804C22semidirect
192. #1802C22semidirect
196. #1788C22semidirect
198. C4×C4⋊C8C22semidirect
199. C4×#102C22semidirect
200. C4×#102C22semidirect
202. C8×C22⋊C4C22semidirect

Maximal subgroups

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

subgroupindex
#595622
#594112
#326582
#325462
#320252
#316212
#315502
#313012
#310092
#304042
#293692
#293652
#290552
#275332
#269602
#269382
#265642
#251602
#250852
#248952
#248932
#243672
#242042
#241922
#240342
#238692
#236762
#228722
#224422
#223892
#221462