Finite Group Databasebeta

← #6771821

Subgroups — #6771821

Order 512.

1704 conjugacy classes of subgroups.

The subgroup lattice has 1389 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39068C211yesmaximal, characteristic, complemented
2#35536C211yesmaximal, characteristic, complemented
3#33018C211yesmaximal, characteristic, complemented
4#32448C211yesmaximal, characteristic, complemented
5#32181C211yesmaximal, characteristic, complemented
6#31663C211yesmaximal, characteristic, complemented
7#31654C211yesmaximal, characteristic, complemented
8#31527C211yesmaximal, characteristic, complemented
9#30891C211yesmaximal, characteristic, complemented
10#30751C211yesmaximal, characteristic, complemented
11#30734C211yesmaximal, characteristic, complemented
12#30128C211yesmaximal, characteristic, complemented
13#30054C211yesmaximal, characteristic, complemented
14#29502C211yesmaximal, characteristic, complemented
15#29376C211yesmaximal, characteristic, complemented
16#28622C211yesmaximal, characteristic, complemented
17#28350C211yesmaximal, characteristic, complemented
18#28163C211yesmaximal, characteristic, complemented
19#27724C211yesmaximal, characteristic, complemented
20#27264C211yesmaximal, characteristic, complemented
21#25791C211yesmaximal, characteristic
22#25514C211yesmaximal, characteristic, complemented
23#25224C211yesmaximal, characteristic, complemented
24#25084C211yesmaximal, characteristic, complemented
25#24537C211yesmaximal, characteristic, complemented
26#24373C211yesmaximal, characteristic, complemented
27#23947C211yesmaximal, characteristic, complemented
28#22594C211yesmaximal, characteristic, complemented
29#22272C211yesmaximal, characteristic, complemented
30#22157C211yesmaximal, characteristic, complemented
31#20929C211yesmaximal, characteristic, complemented
32C22×AGL(1,ℤ/8)C2211yescharacteristic
33C2×#542C2211yescharacteristic
34C2×#518C2211yescharacteristic
35C2×#496C2211yescharacteristic
36C2×#492C2211yescharacteristic
37C2×#490C2211yescharacteristic
38C2×#485C2211yescharacteristic
39C2×#468C2211yescharacteristic
40C2×#467C2211yescharacteristic
41C2×#464C2211yescharacteristic
42C2×#463C2211yescharacteristic
43C2×#463C2211yescharacteristic
44C2×#452C2211yescharacteristic
45C2×#449C2211yescharacteristic
46C2×#450C2211yescharacteristic
47C2×#416C2211yescharacteristic
48C22×#102C2211yescharacteristic
49#2863C2211yescharacteristic, complemented
50#2750—21no—
51#2746—21no—
52#2739—21no—
53#2738—21no—
54#2642C2211yescharacteristic, complemented
55#2625C2211yescharacteristic
56#2578—21no—
57#2578—21no—
58#2569—21no—
59#2563C2211yescharacteristic
60#2544C2211yescharacteristic
61#2544C2211yescharacteristic
62#2542C2211yescharacteristic
63#2514C2211yescharacteristic, complemented
64#2500C2211yescharacteristic
65#2499C2211yescharacteristic
66#2493—21no—
67#2472—21no—
68#2472—21no—
69#2467—21no—
70#2467—21no—
71#2463—21no—
72#2463—21no—
73#2454C2211yescharacteristic, complemented
74#2447C2211yescharacteristic, complemented
75#2446C2211yescharacteristic, complemented
76#2442C2211yescharacteristic
77#2435C2211yescharacteristic
78#2433C2211yescharacteristic
79#2432C2211yescharacteristic
80#2418—21no—
81#2418—21no—
82#2360C2211yescharacteristic
83#2339C2211yescharacteristic
84#2328C2211yescharacteristic
85#2326C2211yescharacteristic
86#2319C2211yescharacteristic, complemented
87#2311C2211yescharacteristic
88C4×#127C2211yescharacteristic
89C4×#124C2211yescharacteristic
90C4×#124C2211yescharacteristic, complemented
91#2298C2211yescharacteristic
92#2101C2211yescharacteristic, complemented
93#2100C2211yescharacteristic, complemented
94#2095C2211yescharacteristic, complemented
95#2092C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2074C2211yescharacteristic, complemented
98#2074C2211yescharacteristic, complemented
99#2073C2211yescharacteristic
100#2072C2211yescharacteristic, complemented
101#2072C2211yescharacteristic, complemented
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic, complemented
104#2057C2211yescharacteristic, complemented
105#2055C2211yescharacteristic
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic, complemented
109#2055C2211yescharacteristic, complemented
110#2055C2211yescharacteristic, complemented
111#2042C2211yescharacteristic
112#2042C2211yescharacteristic, complemented
113#2041C2211yescharacteristic
114#2041C2211yescharacteristic
115#2026C2211yescharacteristic, complemented
116#2025C2211yescharacteristic
117#2024C2211yescharacteristic, complemented
118#2024C2211yescharacteristic, complemented
119#2023C2211yescharacteristic, complemented
120#2016C2211yescharacteristic, complemented
121#2015C2211yescharacteristic
122#2015C2211yescharacteristic
123#2015C2211yescharacteristic
124#2015C2211yescharacteristic, complemented
125#2015C2211yescharacteristic, complemented
126#2015C2211yescharacteristic, complemented
127#2014C2211yescharacteristic
128#2013C2211yescharacteristic
129#2012C2211yescharacteristic
130#2012C2211yescharacteristic, complemented
131#2011C2211yescharacteristic
132#1991C2211yescharacteristic, complemented
133#1983C2211yescharacteristic
134#1973C2211yescharacteristic
135#1973C2211yescharacteristic, complemented
136#1971C2211yescharacteristic, complemented
137#1970C2211yescharacteristic
138#1961C2211yescharacteristic
139#1960C2211yescharacteristic, complemented
140#1959C2211yescharacteristic, complemented
141#1947C2211yescharacteristic, complemented
142#1936C2211yescharacteristic
143#1936C2211yescharacteristic
144#1935C2211yescharacteristic, complemented
145#1933C2211yescharacteristic, complemented
146#1926C2211yescharacteristic, complemented
147#1925C2211yescharacteristic
148#1917C2211yescharacteristic, complemented
149#1917C2211yescharacteristic, complemented
150#1917C2211yescharacteristic, complemented
151#1916C2211yescharacteristic, complemented
152#1894C2211yescharacteristic
153#1893C2211yescharacteristic
154#1880C2211yescharacteristic
155#1880C2211yescharacteristic, complemented
156#1880C2211yescharacteristic, complemented
157#1879C2211yescharacteristic
158#1879C2211yescharacteristic
159#1879C2211yescharacteristic
160#1879C2211yescharacteristic
161#1879C2211yescharacteristic
162#1879C2211yescharacteristic
163#1879C2211yescharacteristic, complemented
164#1879C2211yescharacteristic, complemented
165#1879C2211yescharacteristic, complemented
166#1878C2211yescharacteristic, complemented
167#1878C2211yescharacteristic, complemented
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic
171#1877C2211yescharacteristic
172#1877C2211yescharacteristic
173#1877C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic, complemented
177#1877C2211yescharacteristic, complemented
178#1874C2211yescharacteristic
179#1872C2211yescharacteristic
180#1864C2211yescharacteristic
181#1864C2211yescharacteristic
182#1863C2211yescharacteristic, complemented
183#1862C2211yescharacteristic
184#1862C2211yescharacteristic
185#1862C2211yescharacteristic, complemented
186#1851C2211yescharacteristic
187#1850C2211yescharacteristic
188#1840C2211yescharacteristic, complemented
189#1836C2211yescharacteristic, complemented
190#1831C2211yescharacteristic, complemented
191#1825C2211yescharacteristic
192#1818C2211yescharacteristic
193#1805C2211yescharacteristic, complemented
194#1804C2211yescharacteristic, complemented
195#1802C2211yescharacteristic, complemented
196#1786C2211yescharacteristic
197#1768C2211yescharacteristic, complemented
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic
200#1745C2211yescharacteristic, complemented
201#1736C2211yescharacteristic
202#1729C2211yescharacteristic
203C22×#41C2311yescharacteristic
204C23×D4C2311yescharacteristic
205C2×AGL(1,ℤ/8)—24no—
206C2×AGL(1,ℤ/8)—42no—
207C2×AGL(1,ℤ/8)—42no—
208C22×Q16C2311yescharacteristic
209C22×Q16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×D8C2311yescharacteristic
218C22×D8C2311yescharacteristic
219C22×D8C2311yescharacteristic
220C22×M16C2311yescharacteristic
221C23×C8C2311yescharacteristic
222#542—42no—
223#542—42no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×#127C2311yescharacteristic
227C2×#127C2311yescharacteristic
228C2×#126—21no—
229C2×#125C2311yescharacteristic
230C2×#124—21no—
231C2×#124C2311yescharacteristic
232C2×#124C2311yescharacteristic
233C2×#124C2311yescharacteristic
234C2×#124C2311yescharacteristic
235C2×#123—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8—21no—
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×#121C2311yescharacteristic
242C2×#120—21no—
243C2×#120—21no—
244#518—42no—
245#518—42no—
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×#117C2311yescharacteristic
260C2×#117C2311yescharacteristic
261C22×C4⋊C4C2311yescharacteristic
262C22×C22⋊C4—21no—
263C22×C22⋊C4—21no—
264#496—24no—
265#492—42no—
266#490—42no—
267#485—42no—
268#468—42no—
269#467—42no—
270#464—42no—
271#463—24no—
272#463—42no—
273#452—42no—
274#450—42no—
275#449—42no—
276C2×#107C2311yescharacteristic
277C2×#107C2311yescharacteristic
278C2×#107C2311yescharacteristic
279C2×#106C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282C2×C4⋊C8C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284#416—42no—
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#103C2311yescharacteristic
298C2×#102—42no—
299C2×#102C2311yescharacteristic
300C2×#102C2311yescharacteristic
301C2×#102C2311yescharacteristic
302C2×#102C2311yescharacteristic
303C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×#97C2311yescharacteristic
321C2×#97C2311yescharacteristic
322C2×#97C2311yescharacteristic
323C2×C4×C8C2311yescharacteristic
324#401—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#399—21no—
334#399—21no—
335#399—21no—
336#398—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#396—21no—
346#394—21no—
347#394—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#393—21no—
357#393—21no—
358#392—21no—
359#392—21no—
360#391C2311yescharacteristic
361#391C2311yescharacteristic
362#391C2311yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#391C2311yescharacteristic
366#391C2311yescharacteristic
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
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#389—21no—
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#388—21no—
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#388D411yescharacteristic
398#388D411yescharacteristic
399#388D411yescharacteristic
400#388D411yescharacteristic
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#387—21no—
410#387D411yescharacteristic
411#387D411yescharacteristic
412#387D411yescharacteristic
413#387D411yescharacteristic
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#385—21no—
427#385—21no—
428#385—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#384C2311yescharacteristic
435#384C2311yescharacteristic
436#383—21no—
437#383—21no—
438#382C2311yescharacteristic
439#382C2311yescharacteristic
440#382C2311yescharacteristic
441#381—21no—
442#381—21no—
443#381—21no—
444#380—21no—
445#380—21no—
446#380—21no—
447#380—21no—
448#380—21no—
449#380—21no—
450#380—21no—
451#380C2311yescharacteristic
452#379—21no—
453#379—21no—
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C22⋊C4—21no—
458C4×C22⋊C4—21no—
459C4×C22⋊C4—21no—
460C4×C22⋊C4—21no—
461C4×C22⋊C4—21no—
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464#376C2311yescharacteristic
465C2×#95—21no—
466C43C2311yescharacteristic
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
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—41no—
504C2×#41—41no—
505C2×#41—41no—
506C22×Q8—21no—
507C22×Q8C2411yescharacteristic
508C22×Q8C2411yescharacteristic
509C22×Q8C2411yescharacteristic
510C22×D4—22no—
511C22×D4—22no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—21no—
519C22×D4—22no—
520C22×D4—22no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C2411yescharacteristic
537AGL(1,ℤ/8)—416no—
538C2×Q16—41no—
539C2×Q16—41no—
540C2×Q16—41no—
541C2×Q16—41no—
542C2×Q16—41no—
543C2×Q16—41no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×SD16—41no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16—41no—
560C2×SD16—41no—
561C2×SD16—41no—
562C2×SD16—41no—
563C2×SD16—41no—
564C2×SD16—41no—
565C2×D8—22no—
566C2×D8—22no—
567C2×D8—22no—
568C2×D8—41no—
569C2×D8—41no—
570C2×D8—41no—
571C2×D8—41no—
572C2×D8—41no—
573C2×D8#4114yes—
574C2×M16—22no—
575C2×M16—22no—
576C2×M16—41no—
577C22×C8—22no—
578C22×C8—41no—
579C22×C8—41no—
580C22×C8C2411yescharacteristic
581C22×C8C2411yescharacteristic
582C22×C8C2411yescharacteristic
583C22×C8C2411yescharacteristic
584C22×C8C2411yescharacteristic
585C22×C8C2411yescharacteristic
586C22×C8C2411yescharacteristic
587C22×C8C2411yescharacteristic
588C4⋊Q8—41no—
589C4⋊Q8—41no—
590C4⋊Q8—41no—
591C4⋊Q8—41no—
592#127—22no—
593#127—22no—
594#127—41no—
595#127—41no—
596#126—44no—
597#125—41no—
598#125—41no—
599#124—22no—
600#124—22no—
601#124—22no—
602#124—41no—
603#124—41no—
604#124—41no—
605#124—41no—
606#124—41no—
607#124—44no—
608#123—44no—
609C22⋊Q8—22no—
610C22⋊Q8—22no—
611C22⋊Q8—22no—
612C22⋊Q8—22no—
613C22⋊Q8—44no—
614C22⋊Q8—82no—
615C22⋊Q8—82no—
616#121—22no—
617#121—22no—
618#120—82no—
619#120—82no—
620C4×Q8—41no—
621C4×Q8—41no—
622C4×Q8—41no—
623C4×Q8—41no—
624C4×D4—22no—
625C4×D4—41no—
626C4×D4—41no—
627C4×D4—41no—
628C4×D4—41no—
629C4×D4—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—41no—
635C4×D4—41no—
636C4×D4—41no—
637C4×D4—41no—
638C4×D4—44no—
639C4×D4—44no—
640C4×D4—82no—
641C4×D4—82no—
642#117—22no—
643#117—22no—
644#117—22no—
645#117—22no—
646C2×C4⋊C4—21no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4—21no—
649C2×C4⋊C4—21no—
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—41no—
666C2×C4⋊C4—41no—
667C2×C4⋊C4C2×D411yescharacteristic
668C2×C4⋊C4C2×D411yescharacteristic
669C2×C4⋊C4C2×D411yescharacteristic
670C2×C4⋊C4C2×D411yescharacteristic
671C2×C4⋊C4C2×D411yescharacteristic
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
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×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—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—44no—
721C2×C22⋊C4—44no—
722C2×C22⋊C4C2×D411yescharacteristic
723C2×C22⋊C4C2×D411yescharacteristic
724C2×C22⋊C4C2×D411yescharacteristic
725C2×C22⋊C4C2×D411yescharacteristic
726C2×C22⋊C4C2×D411yescharacteristic
727C2×C22⋊C4C2×D411yescharacteristic
728C2×C42—21no—
729C2×C42—21no—
730C2×C42—21no—
731C2×C42—21no—
732C2×C42C2×D411yescharacteristic
733C2×C42C2×D411yescharacteristic
734C2×C42C2×D411yescharacteristic
735C2×C42C2×D411yescharacteristic
736C2×C42C2411yescharacteristic
737C2×C42C2411yescharacteristic
738C2×C42C2411yescharacteristic
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742#107—41no—
743#107—41no—
744#107—41no—
745#106—41no—
746C4⋊C8—22no—
747C4⋊C8—41no—
748C4⋊C8—41no—
749C4⋊C8—41no—
750#103—22no—
751#103—41no—
752#103—41no—
753#103—41no—
754#103—41no—
755#103—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#103—41no—
761#103—41no—
762#103—41no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773#102—41no—
774#102—41no—
775#102—41no—
776#102—41no—
777#102—41no—
778#102—41no—
779#102—41no—
780#102—41no—
781#102—41no—
782C22⋊C8—22no—
783C22⋊C8—22no—
784#97—22no—
785#97—41no—
786#97—41no—
787C4×C8—41no—
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#95—21no—
799#95—21no—
800#95—21no—
801#95—21no—
802#95—21no—
803#95—21no—
804#95—21no—
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#95C2×D411yescharacteristic
822#95C2×D411yescharacteristic
823#95C2×D411yescharacteristic
824#95C2×D411yescharacteristic
825#95C2×D411yescharacteristic
826#95C2×D411yescharacteristic
827#95C2×D411yescharacteristic
828#95C2×D411yescharacteristic
829#95C2×D411yescharacteristic
830#95C2×D411yescharacteristic
831#95C2×D411yescharacteristic
832#95C2×D411yescharacteristic
833C24—21no—
834C24—21no—
835C24—21no—
836C24—21no—
837C24—42no—
838C24—42no—
839C24—42no—
840C24—81no—
841C24—81no—
842C24—81no—
843C24—81no—
844C24C22×D411yescharacteristic
845#41—44no—
846#41—44no—
847#41—82no—
848#41—82no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8—21no—
856C2×Q8—21no—
857C2×Q8—21no—
858C2×Q8—21no—
859C2×Q8—21no—
860C2×Q8—21no—
861C2×Q8—21no—
862C2×Q8—21no—
863C2×Q8—21no—
864C2×Q8—21no—
865C2×Q8—21no—
866C2×Q8—21no—
867C2×Q8—42no—
868C2×Q8—81no—
869C2×Q8—81no—
870C2×D4—28no—
871C2×D4—21no—
872C2×D4—21no—
873C2×D4—21no—
874C2×D4—21no—
875C2×D4—21no—
876C2×D4—21no—
877C2×D4—21no—
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—44no—
893C2×D4—44no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—44no—
897C2×D4—42no—
898C2×D4—42no—
899C2×D4—42no—
900C2×D4—42no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—42no—
907C2×D4—81no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4—81no—
913C2×D4—81no—
914C2×D4—81no—
915C2×D4—81no—
916C2×D4C2×#4112yes—
917C2×D4C2×#4112yes—
918C2×D4H(5,𝔽2)12yes—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—21no—
926C22×C4—21no—
927C22×C4—21no—
928C22×C4—21no—
929C22×C4—21no—
930C22×C4—21no—
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—42no—
936C22×C4—42no—
937C22×C4—42no—
938C22×C4—42no—
939C22×C4—42no—
940C22×C4—42no—
941C22×C4—42no—
942C22×C4—42no—
943C22×C4—42no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4—81no—
947C22×C4—81no—
948C22×C4—81no—
949C22×C4—81no—
950C22×C4—81no—
951C22×C4—81no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4—81no—
959C22×C4—81no—
960C22×C4—81no—
961C22×C4—81no—
962C22×C4C22×D411yescharacteristic
963C22×C4C22×D411yescharacteristic
964C22×C4C22×D411yescharacteristic
965C22×C4C22×D411yescharacteristic
966C22×C4C22×D411yescharacteristic
967C22×C4C22×D411yescharacteristic
968C22×C4C22×D411yescharacteristic
969C22×C4C22×D411yescharacteristic
970C22×C4C22×D411yescharacteristic
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4H(5,𝔽2)12yes—
976C22×C4H(5,𝔽2)12yes—
977C22×C4C2511yescharacteristic
978Q16—82no—
979Q16—82no—
980SD16—44no—
981SD16—44no—
982SD16—82no—
983SD16—82no—
984SD16—82no—
985SD16—82no—
986SD16—82no—
987D8—44no—
988D8—44no—
989D8—82no—
990M16—44no—
991C2×C8—21no—
992C2×C8—21no—
993C2×C8—21no—
994C2×C8—21no—
995C2×C8—21no—
996C2×C8—21no—
997C2×C8—21no—
998C2×C8—21no—
999C2×C8—21no—
1000C2×C8—21no—
1001C2×C8—21no—
1002C2×C8—21no—
1003C2×C8—21no—
1004C2×C8—21no—
1005C2×C8—21no—
1006C2×C8—21no—
1007C2×C8—21no—
1008C2×C8—21no—
1009C2×C8—21no—
1010C2×C8—21no—
1011C2×C8—21no—
1012C2×C8—21no—
1013C2×C8—21no—
1014C2×C8—82no—
1015C2×C8C2×#4112yes—
1016C4⋊C4—22no—
1017C4⋊C4—22no—
1018C4⋊C4—21no—
1019C4⋊C4—21no—
1020C4⋊C4—21no—
1021C4⋊C4—21no—
1022C4⋊C4—21no—
1023C4⋊C4—21no—
1024C4⋊C4—21no—
1025C4⋊C4—21no—
1026C4⋊C4—21no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—21no—
1032C4⋊C4—21no—
1033C4⋊C4—21no—
1034C4⋊C4—21no—
1035C4⋊C4—21no—
1036C4⋊C4—41no—
1037C4⋊C4—41no—
1038C4⋊C4—41no—
1039C4⋊C4—41no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—81no—
1047C4⋊C4—81no—
1048C4⋊C4—81no—
1049C4⋊C4—81no—
1050C4⋊C4—81no—
1051C4⋊C4—81no—
1052C4⋊C4—81no—
1053C4⋊C4—81no—
1054C4⋊C4—81no—
1055C4⋊C4—81no—
1056C4⋊C4—81no—
1057C4⋊C4—81no—
1058C4⋊C4—81no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—41no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—42no—
1068C22⋊C4—42no—
1069C22⋊C4—42no—
1070C22⋊C4—42no—
1071C22⋊C4—42no—
1072C22⋊C4—42no—
1073C22⋊C4—42no—
1074C22⋊C4—42no—
1075C22⋊C4—42no—
1076C22⋊C4—42no—
1077C22⋊C4—42no—
1078C22⋊C4—42no—
1079C22⋊C4—42no—
1080C22⋊C4—42no—
1081C22⋊C4—42no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—81no—
1086C22⋊C4—81no—
1087C22⋊C4—81no—
1088C22⋊C4—81no—
1089C22⋊C4—81no—
1090C22⋊C4—81no—
1091C22⋊C4—81no—
1092C22⋊C4—81no—
1093C22⋊C4—81no—
1094C22⋊C4—81no—
1095C22⋊C4—81no—
1096C22⋊C4—81no—
1097C22⋊C4—81no—
1098C22⋊C4—81no—
1099C22⋊C4—81no—
1100C22⋊C4—81no—
1101C22⋊C4—81no—
1102C22⋊C4—81no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—21no—
1107C42—21no—
1108C42—21no—
1109C42—21no—
1110C42—21no—
1111C42—21no—
1112C42—21no—
1113C42—21no—
1114C42—21no—
1115C42—41no—
1116C42—41no—
1117C42—41no—
1118C42—41no—
1119C42—42no—
1120C42—42no—
1121C42—81no—
1122C42—81no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—21no—
1127C23—21no—
1128C23—21no—
1129C23—22no—
1130C23—22no—
1131C23—22no—
1132C23—48no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—41no—
1141C23—41no—
1142C23—41no—
1143C23—41no—
1144C23—41no—
1145C23—41no—
1146C23—41no—
1147C23—41no—
1148C23—41no—
1149C23—41no—
1150C23—41no—
1151C23—41no—
1152C23—41no—
1153C23—41no—
1154C23—41no—
1155C23—41no—
1156C23—41no—
1157C23—41no—
1158C23—162no—
1159C23—162no—
1160C23—162no—
1161C23—162no—
1162C23—162no—
1163C23—162no—
1164C23#53512yes—
1165C23C23×D411yescharacteristic
1166Q8—41no—
1167Q8—41no—
1168Q8—41no—
1169Q8—41no—
1170Q8—41no—
1171Q8—41no—
1172Q8—41no—
1173Q8—41no—
1174Q8—41no—
1175Q8—41no—
1176Q8—41no—
1177Q8—41no—
1178Q8—162no—
1179D4—22no—
1180D4—22no—
1181D4—22no—
1182D4—22no—
1183D4—22no—
1184D4—22no—
1185D4—48no—
1186D4—41no—
1187D4—41no—
1188D4—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—84no—
1197D4—84no—
1198D4—84no—
1199D4—162no—
1200D4—162no—
1201D4—162no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—22no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—21no—
1209C2×C4—21no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—21no—
1214C2×C4—21no—
1215C2×C4—21no—
1216C2×C4—21no—
1217C2×C4—21no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—21no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—21no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—21no—
1229C2×C4—21no—
1230C2×C4—21no—
1231C2×C4—21no—
1232C2×C4—21no—
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—41no—
1245C2×C4—41no—
1246C2×C4—41no—
1247C2×C4—41no—
1248C2×C4—41no—
1249C2×C4—41no—
1250C2×C4—41no—
1251C2×C4—41no—
1252C2×C4—41no—
1253C2×C4—41no—
1254C2×C4—41no—
1255C2×C4—41no—
1256C2×C4—41no—
1257C2×C4—41no—
1258C2×C4—41no—
1259C2×C4—41no—
1260C2×C4—41no—
1261C2×C4—41no—
1262C2×C4—41no—
1263C2×C4—41no—
1264C2×C4—41no—
1265C2×C4—41no—
1266C2×C4—41no—
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—84no—
1281C2×C4—162no—
1282C2×C4—162no—
1283C2×C4—162no—
1284C2×C4—162no—
1285C2×C4—162no—
1286C2×C4—162no—
1287C2×C4—162no—
1288C2×C4—162no—
1289C2×C4#53512yes—
1290C2×C4C22×#4111yescharacteristic
1291C2×C4C2×H(5,𝔽2)11yescharacteristic
1292C2×C4C2×H(5,𝔽2)11yescharacteristic
1293C2×C4C2×H(5,𝔽2)11yescharacteristic
1294C2×C4#58511yescharacteristic
1295C2×C4#58511yescharacteristic
1296C8—22no—
1297C8—41no—
1298C8—41no—
1299C8—41no—
1300C8—41no—
1301C8—41no—
1302C8—41no—
1303C8—41no—
1304C22—22no—
1305C22—22no—
1306C22—22no—
1307C22—41no—
1308C22—41no—
1309C22—41no—
1310C22—41no—
1311C22—42no—
1312C22—42no—
1313C22—42no—
1314C22—42no—
1315C22—42no—
1316C22—42no—
1317C22—42no—
1318C22—42no—
1319C22—42no—
1320C22—81no—
1321C22—81no—
1322C22—81no—
1323C22—81no—
1324C22—81no—
1325C22—81no—
1326C22—81no—
1327C22—81no—
1328C22—81no—
1329C22—81no—
1330C22—81no—
1331C22—81no—
1332C22—81no—
1333C22—81no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—168no—
1340C22C2×#53511yescharacteristic
1341C22D4×#4111yescharacteristic
1342C22#348811yescharacteristic
1343C22#358411yescharacteristic
1344C22#358511yescharacteristic
1345C22#358511yescharacteristic
1346C22#358611yescharacteristic
1347C4—22no—
1348C4—41no—
1349C4—41no—
1350C4—41no—
1351C4—41no—
1352C4—41no—
1353C4—41no—
1354C4—41no—
1355C4—41no—
1356C4—41no—
1357C4—41no—
1358C4—41no—
1359C4—41no—
1360C4—81no—
1361C4—81no—
1362C4—81no—
1363C4—81no—
1364C4—81no—
1365C4—81no—
1366C4—81no—
1367C4—81no—
1368C4—81no—
1369C4—81no—
1370C4—81no—
1371C4—81no—
1372C4#349011yescharacteristic
1373C4#351311yescharacteristic
1374C4#353311yescharacteristic
1375C4#353411yescharacteristic
1376C2—42no—
1377C2—82no—
1378C2—82no—
1379C2—82no—
1380C2—161no—
1381C2#3836611yescharacteristic
1382C2#6083011yescharacteristic
1383C2#6083511yescharacteristic
1384C2#6150911yescharacteristic
1385C2#6154811yescharacteristic
1386C2#6201111yescharacteristic
1387C2#6208711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#25791C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2298 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #39068C2semidirect
2. #35536C2semidirect
3. #33018C2semidirect
4. #32448C2semidirect
5. #32181C2semidirect
6. #31663C2semidirect
7. #31654C2semidirect
8. #31527C2semidirect
9. #30891C2semidirect
10. #30751C2semidirect
11. #30734C2semidirect
12. #30128C2semidirect
13. #30054C2semidirect
14. #29502C2semidirect
15. #29376C2semidirect
16. #28622C2semidirect
17. #28350C2semidirect
18. #28163C2semidirect
19. #27724C2semidirect
20. #27264C2semidirect
22. #25514C2semidirect
23. #25224C2semidirect
24. #25084C2semidirect
25. #24537C2semidirect
26. #24373C2semidirect
27. #23947C2semidirect
28. #22594C2semidirect
29. #22272C2semidirect
30. #22157C2semidirect
31. #20929C2semidirect
49. #2863C22semidirect
54. #2642C22semidirect
63. #2514C22semidirect
73. #2454C22semidirect
74. #2447C22semidirect
75. #2446C22semidirect
86. #2319C22semidirect
90. C4×#124C22semidirect
92. #2101C22semidirect
93. #2100C22semidirect
94. #2095C22semidirect
95. #2092C22semidirect
96. #2085C22semidirect
97. #2074C22semidirect
98. #2074C22semidirect
100. #2072C22semidirect
101. #2072C22semidirect
103. #2067C22semidirect
104. #2057C22semidirect
108. #2055C22semidirect
109. #2055C22semidirect
110. #2055C22semidirect
112. #2042C22semidirect
115. #2026C22semidirect
117. #2024C22semidirect
118. #2024C22semidirect
119. #2023C22semidirect
120. #2016C22semidirect
124. #2015C22semidirect
125. #2015C22semidirect
126. #2015C22semidirect
130. #2012C22semidirect
132. #1991C22semidirect
135. #1973C22semidirect
136. #1971C22semidirect
139. #1960C22semidirect
140. #1959C22semidirect
141. #1947C22semidirect
144. #1935C22semidirect
145. #1933C22semidirect
146. #1926C22semidirect
148. #1917C22semidirect
149. #1917C22semidirect
150. #1917C22semidirect
151. #1916C22semidirect
155. #1880C22semidirect
156. #1880C22semidirect
163. #1879C22semidirect
164. #1879C22semidirect
165. #1879C22semidirect
166. #1878C22semidirect
167. #1878C22semidirect
176. #1877C22semidirect
177. #1877C22semidirect
182. #1863C22semidirect
185. #1862C22semidirect
188. #1840C22semidirect
189. #1836C22semidirect
190. #1831C22semidirect
193. #1805C22semidirect
194. #1804C22semidirect
195. #1802C22semidirect
197. #1768C22semidirect
200. #1745C22semidirect

Maximal subgroups

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

subgroupindex
#390682
#355362
#330182
#324482
#321812
#316632
#316542
#315272
#308912
#307512
#307342
#301282
#300542
#295022
#293762
#286222
#283502
#281632
#277242
#272642
#257912
#255142
#252242
#250842
#245372
#243732
#239472
#225942
#222722
#221572
#209292