Finite Group Databasebeta

← #7339523

Subgroups — #7339523

Order 512.

1618 conjugacy classes of subgroups.

The subgroup lattice has 1412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52969C211yesmaximal, characteristic
2#45238C211yesmaximal, characteristic, complemented
3#32237C211yesmaximal, characteristic, complemented
4#31838C211yesmaximal, characteristic, complemented
5#31838C211yesmaximal, characteristic, complemented
6#31805C211yesmaximal, characteristic, complemented
7#31560C211yesmaximal, characteristic, complemented
8#31361C211yesmaximal, characteristic, complemented
9#31044C211yesmaximal, characteristic, complemented
10#30988C211yesmaximal, characteristic, complemented
11#30892C211yesmaximal, characteristic, complemented
12#30736C211yesmaximal, characteristic, complemented
13#30730C211yesmaximal, characteristic, complemented
14#30456C211yesmaximal, characteristic, complemented
15#29765C211yesmaximal, characteristic, complemented
16#29671C211yesmaximal, characteristic, complemented
17#29343C211yesmaximal, characteristic, complemented
18#28883C211yesmaximal, characteristic, complemented
19#27775C211yesmaximal, characteristic, complemented
20#27572C211yesmaximal, characteristic, complemented
21#27279C211yesmaximal, characteristic, complemented
22#26967C211yesmaximal, characteristic, complemented
23#26935C211yesmaximal, characteristic, complemented
24#26664C211yesmaximal, characteristic, complemented
25#26630C211yesmaximal, characteristic, complemented
26#25607C211yesmaximal, characteristic, complemented
27#25583C211yesmaximal, characteristic, complemented
28#25093C211yesmaximal, characteristic, complemented
29#24728C211yesmaximal, characteristic, complemented
30#23982C211yesmaximal, characteristic, complemented
31#22364C211yesmaximal, characteristic, complemented
32C2×#552C2211yescharacteristic
33C2×#541C2211yescharacteristic, complemented
34C2×#492C2211yescharacteristic
35C2×#490C2211yescharacteristic
36C2×#490C2211yescharacteristic, complemented
37C2×#482C2211yescharacteristic
38C2×#482C2211yescharacteristic, complemented
39C2×#468C2211yescharacteristic
40C2×#460C2211yescharacteristic
41C2×#460C2211yescharacteristic
42C2×#460C2211yescharacteristic
43C2×#460C2211yescharacteristic, complemented
44C2×#450C2211yescharacteristic
45C2×#450C2211yescharacteristic
46C2×C4×SD16C2211yescharacteristic, complemented
47C2×#418C2211yescharacteristic
48#2828—21no—
49#2815—21no—
50#2815—21no—
51#2812—21no—
52#2721—21no—
53#2719—21no—
54#2718—21no—
55#2718—21no—
56#2699—21no—
57#2669—21no—
58#2669—21no—
59#2668—21no—
60#2619C2211yescharacteristic
61#2619C2211yescharacteristic
62#2552—21no—
63#2552C2211yescharacteristic, complemented
64#2541C2211yescharacteristic
65#2541C2211yescharacteristic
66#2541C2211yescharacteristic
67#2519—21no—
68#2513C2211yescharacteristic
69#2513C2211yescharacteristic
70#2502C2211yescharacteristic, complemented
71#2478—21no—
72#2478—21no—
73#2453C2211yescharacteristic, complemented
74#2446C2211yescharacteristic, complemented
75#2441C2211yescharacteristic
76#2433C2211yescharacteristic
77#2433C2211yescharacteristic
78#2429C2211yescharacteristic
79#2428C2211yescharacteristic
80#2428C2211yescharacteristic
81#2423C2211yescharacteristic
82#2420C2211yescharacteristic
83#2420C2211yescharacteristic
84#2415C2211yescharacteristic
85#2408C2211yescharacteristic
86#2395C2211yescharacteristic
87#2362C2211yescharacteristic
88#2362C2211yescharacteristic, complemented
89Q8×C4⋊C4C2211yescharacteristic, complemented
90#2317C2211yescharacteristic, complemented
91#2101C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2100C2211yescharacteristic, complemented
94#2100C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2075C2211yescharacteristic
99#2071C2211yescharacteristic
100#2071C2211yescharacteristic
101#2068C2211yescharacteristic, complemented
102#2067C2211yescharacteristic
103#2067C2211yescharacteristic, complemented
104#2065C2211yescharacteristic
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic, complemented
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2041C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic, complemented
116#2035C2211yescharacteristic
117#2034C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic
120#2025C2211yescharacteristic
121#2025C2211yescharacteristic, complemented
122#2014C2211yescharacteristic
123#2014C2211yescharacteristic
124#2014C2211yescharacteristic
125#2014C2211yescharacteristic, complemented
126#2013C2211yescharacteristic
127#2013C2211yescharacteristic, complemented
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#2000C2211yescharacteristic
133#2000C2211yescharacteristic
134#2000C2211yescharacteristic
135#2000C2211yescharacteristic, complemented
136#2000C2211yescharacteristic, complemented
137#2000C2211yescharacteristic, complemented
138#2000C2211yescharacteristic, complemented
139#1991C2211yescharacteristic, complemented
140#1989C2211yescharacteristic, complemented
141#1982C2211yescharacteristic
142#1973C2211yescharacteristic
143#1968C2211yescharacteristic
144#1960C2211yescharacteristic, complemented
145#1957C2211yescharacteristic
146#1957C2211yescharacteristic
147#1955C2211yescharacteristic
148#1939C2211yescharacteristic, complemented
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic, complemented
152#1934C2211yescharacteristic
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1933C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1925C2211yescharacteristic
159#1923C2211yescharacteristic
160#1923C2211yescharacteristic
161#1923C2211yescharacteristic, complemented
162#1923C2211yescharacteristic, complemented
163#1920C2211yescharacteristic, complemented
164#1918C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1916C2211yescharacteristic, complemented
167#1895C2211yescharacteristic
168#1894C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1880C2211yescharacteristic, complemented
175#1880C2211yescharacteristic, complemented
176#1877C2211yescharacteristic, complemented
177#1877C2211yescharacteristic, complemented
178#1877C2211yescharacteristic, complemented
179#1875C2211yescharacteristic
180#1875C2211yescharacteristic
181#1875C2211yescharacteristic
182#1875C2211yescharacteristic, complemented
183#1874C2211yescharacteristic
184#1874C2211yescharacteristic
185#1874C2211yescharacteristic, complemented
186#1874C2211yescharacteristic, complemented
187#1870C2211yescharacteristic
188#1863C2211yescharacteristic, complemented
189#1862C2211yescharacteristic, complemented
190#1851C2211yescharacteristic
191#1825C2211yescharacteristic
192#1805C2211yescharacteristic, complemented
193#1805C2211yescharacteristic, complemented
194#1802C2211yescharacteristic, complemented
195#1802C2211yescharacteristic, complemented
196#1798C2211yescharacteristic, complemented
197#1786C2211yescharacteristic
198#1770C2211yescharacteristic, complemented
199#1763C2211yescharacteristic, complemented
200C4×#102C2211yescharacteristic, complemented
201#1753C2211yescharacteristic
202#1750C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213#552—42no—
214#552—42no—
215#541—42no—
216#541—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127—21no—
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#126—21no—
225C2×#126—21no—
226C2×#126—21no—
227C2×#125—21no—
228C2×#125—21no—
229C2×#125—21no—
230C2×#125C2311yescharacteristic
231C2×#125C2311yescharacteristic
232C2×#123—21no—
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×C22⋊Q8C2311yescharacteristic
236C2×C22⋊Q8C2311yescharacteristic
237C2×#121—21no—
238C2×#121—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121—21no—
242C2×#121—21no—
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#120—21no—
250C2×#120—21no—
251C2×#120—21no—
252C2×#120—21no—
253C2×#120—21no—
254C2×C4×Q8C2311yescharacteristic
255C2×C4×Q8C2311yescharacteristic
256C2×C4×Q8C2311yescharacteristic
257C2×C4×Q8C2311yescharacteristic
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×#117—21no—
262C2×#117C2311yescharacteristic
263C2×#117C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C22×C4⋊C4C2311yescharacteristic
266#492—42no—
267#490—42no—
268#490—42no—
269#482—42no—
270#482—42no—
271#468—42no—
272#460—42no—
273#460—42no—
274#460—42no—
275#460—42no—
276#450—42no—
277#450—42no—
278C4×SD16—42no—
279C2×#107C2311yescharacteristic
280C2×#107C2311yescharacteristic
281C2×#106C2311yescharacteristic
282C2×#106C2311yescharacteristic
283C2×C4⋊C8C2311yescharacteristic
284C2×C4⋊C8C2311yescharacteristic
285C2×C4⋊C8C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288#418—42no—
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#103C2311yescharacteristic
296C2×#103C2311yescharacteristic
297C2×#102C2311yescharacteristic
298C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
319C2×#102C2311yescharacteristic
320C2×#102C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322C2×C22⋊C8C2311yescharacteristic
323C2×C22⋊C8C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×#97C2311yescharacteristic
329C2×#97C2311yescharacteristic
330C2×C4×C8C2311yescharacteristic
331C2×C4×C8C2311yescharacteristic
332C2×C4×C8C2311yescharacteristic
333#400—21no—
334#400—21no—
335#400D411yescharacteristic
336#399—21no—
337#399—21no—
338#399D411yescharacteristic
339#398—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#398—21no—
344#398—21no—
345#398—21no—
346#398—21no—
347#398D411yescharacteristic
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397D411yescharacteristic
356#397D411yescharacteristic
357#397D411yescharacteristic
358#396—21no—
359#396—21no—
360#394—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#394—21no—
366#394—21no—
367#394—21no—
368#394—21no—
369#394—21no—
370#394D411yescharacteristic
371#394D411yescharacteristic
372#392—21no—
373#392—21no—
374#392—21no—
375#392—21no—
376#392—21no—
377#392—21no—
378#392—21no—
379#392—21no—
380#392—21no—
381#392—21no—
382#392—21no—
383#392—21no—
384#392—21no—
385#392—21no—
386#392—21no—
387#392—21no—
388#392—21no—
389#391C2311yescharacteristic
390#391C2311yescharacteristic
391#391C2311yescharacteristic
392#391C2311yescharacteristic
393#390—21no—
394#390C2311yescharacteristic
395#390C2311yescharacteristic
396#390C2311yescharacteristic
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#389—21no—
403#389—21no—
404#389—21no—
405#389—21no—
406#389—21no—
407#389—21no—
408#389—21no—
409#389C2311yescharacteristic
410#389C2311yescharacteristic
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#388—21no—
418#388—21no—
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#388—21no—
425#388—21no—
426#388—21no—
427#388—21no—
428#387—21no—
429#387—21no—
430#387—21no—
431#387—21no—
432#387—21no—
433#387—21no—
434#387—21no—
435#386—21no—
436#386—21no—
437#386—21no—
438#386—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#385—21no—
443#384—21no—
444#384—21no—
445#384—21no—
446#384C2311yescharacteristic
447#384C2311yescharacteristic
448#382—21no—
449#382C2311yescharacteristic
450#382C2311yescharacteristic
451#381—21no—
452#381—21no—
453#380C2311yescharacteristic
454#380C2311yescharacteristic
455#379—21no—
456C4×C4⋊C4—21no—
457C4×C4⋊C4—21no—
458C4×C4⋊C4—21no—
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C4⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C4×C22⋊C4C2311yescharacteristic
466#340C2311yescharacteristic
467#340C2311yescharacteristic
468#340C2311yescharacteristic
469#340C2311yescharacteristic
470#340C2311yescharacteristic
471#340C2311yescharacteristic
472#340C2311yescharacteristic
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496C25—21no—
497C22×Q8C2411yescharacteristic
498C22×Q8C2411yescharacteristic
499C22×D4—21no—
500C22×D4—21no—
501C22×D4—21no—
502C22×D4—21no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4—21no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4C2×D411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4C2411yescharacteristic
531C23×C4C2411yescharacteristic
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16—41no—
540C2×SD16—41no—
541C2×SD16—41no—
542C2×SD16—41no—
543C2×SD16—41no—
544C2×SD16—41no—
545C2×SD16—41no—
546C2×SD16—41no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16—41no—
556C2×M16—41no—
557C2×M16—41no—
558C2×M16—41no—
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C22×C8C2411yescharacteristic
565C22×C8C2411yescharacteristic
566C22×C8C2411yescharacteristic
567C4⋊Q8—22no—
568C4⋊Q8—41no—
569#127—41no—
570#127—41no—
571#127—41no—
572#127—41no—
573#127—41no—
574#127—41no—
575#127—41no—
576#127—41no—
577#127—41no—
578#127—41no—
579#127—82no—
580#126—44no—
581#126—44no—
582#126—44no—
583#125—22no—
584#125—22no—
585#125—41no—
586#125—41no—
587#125—44no—
588#125—44no—
589#125—44no—
590#123—44no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593C22⋊Q8—22no—
594C22⋊Q8—22no—
595C22⋊Q8—41no—
596C22⋊Q8—41no—
597C22⋊Q8—41no—
598C22⋊Q8—41no—
599#121—41no—
600#121—41no—
601#121—41no—
602#121—41no—
603#121—41no—
604#121—41no—
605#121—41no—
606#121—41no—
607#121—41no—
608#121—41no—
609#121—41no—
610#121—41no—
611#121—82no—
612#121—82no—
613#121—82no—
614#121—82no—
615#121—82no—
616#121—82no—
617#120—82no—
618#120—82no—
619#120—82no—
620#120—82no—
621#120—82no—
622C4×Q8—22no—
623C4×Q8—22no—
624C4×Q8—22no—
625C4×Q8—22no—
626C4×Q8—41no—
627C4×Q8—41no—
628C4×Q8—41no—
629C4×Q8—41no—
630C4×D4—41no—
631C4×D4—41no—
632C4×D4—41no—
633C4×D4—41no—
634C4×D4—41no—
635C4×D4—41no—
636#117—22no—
637#117—22no—
638#117—41no—
639#117—41no—
640#117—44no—
641#117—41no—
642#117—41no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
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—21no—
666C2×C4⋊C4—21no—
667C2×C4⋊C4—21no—
668C2×C4⋊C4—21no—
669C2×C4⋊C4—21no—
670C2×C4⋊C4—41no—
671C2×C4⋊C4—41no—
672C2×C4⋊C4C2×D411yescharacteristic
673C2×C4⋊C4C2×D411yescharacteristic
674C2×C4⋊C4C2×D411yescharacteristic
675C2×C4⋊C4C2×D411yescharacteristic
676C2×C4⋊C4C2×D411yescharacteristic
677C2×C4⋊C4C2×D411yescharacteristic
678C2×C4⋊C4C2×D411yescharacteristic
679C2×C4⋊C4C2411yescharacteristic
680C2×C4⋊C4C2411yescharacteristic
681C2×C4⋊C4C2411yescharacteristic
682C2×C4⋊C4C2411yescharacteristic
683C2×C4⋊C4C2411yescharacteristic
684C2×C4⋊C4C2411yescharacteristic
685C2×C4⋊C4C2411yescharacteristic
686C2×C4⋊C4C2411yescharacteristic
687C2×C4⋊C4C2411yescharacteristic
688C2×C4⋊C4C2411yescharacteristic
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⋊C4C2×D411yescharacteristic
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×C22⋊C4C2×D411yescharacteristic
729C2×C22⋊C4C2×D411yescharacteristic
730C2×C22⋊C4C2×D411yescharacteristic
731C2×C42—21no—
732C2×C42—21no—
733C2×C42—21no—
734C2×C42—21no—
735C2×C42—21no—
736C2×C42—21no—
737C2×C42—21no—
738C2×C42—21no—
739C2×C42C2411yescharacteristic
740C2×C42C2411yescharacteristic
741C2×C42C2411yescharacteristic
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744#107—22no—
745#107—41no—
746#106—22no—
747#106—41no—
748C4⋊C8—41no—
749C4⋊C8—41no—
750C4⋊C8—41no—
751C4⋊C8—41no—
752C4⋊C8—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#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
768#102—22no—
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—
782#102—41no—
783#102—41no—
784#102—41no—
785C22⋊C8—41no—
786C22⋊C8—41no—
787C22⋊C8—41no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791C22⋊C8—41no—
792#97—41no—
793#97—41no—
794C4×C8—41no—
795C4×C8—41no—
796C4×C8—41no—
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
831C24—21no—
832C24—21no—
833C24—21no—
834C24—21no—
835C24—42no—
836C24—81no—
837C24—81no—
838C24—81no—
839C24—81no—
840C24—81no—
841C24—81no—
842C24C22×D411yescharacteristic
843C24C22×D411yescharacteristic
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—21no—
855C2×Q8H(5,𝔽2)12yes—
856C2×D4—21no—
857C2×D4—21no—
858C2×D4—21no—
859C2×D4—21no—
860C2×D4—21no—
861C2×D4—21no—
862C2×D4—21no—
863C2×D4—21no—
864C2×D4—21no—
865C2×D4—21no—
866C2×D4—21no—
867C2×D4—21no—
868C2×D4—21no—
869C2×D4—21no—
870C2×D4—21no—
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—41no—
881C2×D4—41no—
882C2×D4—41no—
883C2×D4—42no—
884C2×D4—44no—
885C2×D4—42no—
886C2×D4—42no—
887C2×D4—42no—
888C2×D4—42no—
889C2×D4—81no—
890C2×D4—81no—
891C2×D4—81no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—81no—
896C2×D4—81no—
897C2×D4—81no—
898C2×D4—81no—
899C2×D4—81no—
900C2×D4—81no—
901C2×D4—81no—
902C2×D4—81no—
903C2×D4—81no—
904C2×D4—81no—
905C2×D4—81no—
906C2×D4—81no—
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×D4—81no—
917C2×D4—81no—
918C2×D4—81no—
919C2×D4—82no—
920C2×D4—82no—
921C2×D4—82no—
922C2×D4—81no—
923C2×D4—81no—
924C2×D4—81no—
925C2×D4—81no—
926C2×D4—81no—
927C2×D4—81no—
928C2×D4—81no—
929C2×D4—81no—
930C2×D4—81no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—81no—
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—21no—
958C22×C4—21no—
959C22×C4—21no—
960C22×C4—21no—
961C22×C4—21no—
962C22×C4—42no—
963C22×C4—42no—
964C22×C4—42no—
965C22×C4—81no—
966C22×C4—81no—
967C22×C4—81no—
968C22×C4—81no—
969C22×C4—81no—
970C22×C4—81no—
971C22×C4C22×D411yescharacteristic
972C22×C4C22×D411yescharacteristic
973C22×C4C22×D411yescharacteristic
974C22×C4C22×D411yescharacteristic
975C22×C4C22×D411yescharacteristic
976C22×C4C22×D411yescharacteristic
977C22×C4C22×D411yescharacteristic
978C22×C4C22×D411yescharacteristic
979C22×C4C22×D411yescharacteristic
980C22×C4C22×D411yescharacteristic
981C22×C4C22×D411yescharacteristic
982C22×C4C22×D411yescharacteristic
983C22×C4C2511yescharacteristic
984SD16—44no—
985SD16—82no—
986SD16—82no—
987SD16—82no—
988SD16—82no—
989SD16—82no—
990SD16—82no—
991SD16—82no—
992M16—82no—
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—21no—
1015C2×C8—21no—
1016C2×C8—21no—
1017C4⋊C4—24no—
1018C4⋊C4—22no—
1019C4⋊C4—22no—
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—21no—
1037C4⋊C4—21no—
1038C4⋊C4—41no—
1039C4⋊C4—41no—
1040C4⋊C4—41no—
1041C4⋊C4—41no—
1042C4⋊C4—41no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
1048C4⋊C4—42no—
1049C4⋊C4—42no—
1050C4⋊C4—42no—
1051C4⋊C4—42no—
1052C4⋊C4—42no—
1053C4⋊C4—42no—
1054C4⋊C4—42no—
1055C4⋊C4—42no—
1056C4⋊C4—42no—
1057C4⋊C4—42no—
1058C4⋊C4—81no—
1059C4⋊C4—81no—
1060C4⋊C4—81no—
1061C4⋊C4—81no—
1062C4⋊C4—81no—
1063C4⋊C4—81no—
1064C4⋊C4—81no—
1065C4⋊C4—81no—
1066C4⋊C4—81no—
1067C4⋊C4—81no—
1068C4⋊C4—81no—
1069C4⋊C4H(5,𝔽2)12yes—
1070C4⋊C4H(5,𝔽2)12yes—
1071C22⋊C4—24no—
1072C22⋊C4—22no—
1073C22⋊C4—22no—
1074C22⋊C4—22no—
1075C22⋊C4—22no—
1076C22⋊C4—41no—
1077C22⋊C4—41no—
1078C22⋊C4—41no—
1079C22⋊C4—41no—
1080C22⋊C4—41no—
1081C22⋊C4—41no—
1082C22⋊C4—42no—
1083C22⋊C4—42no—
1084C22⋊C4—42no—
1085C22⋊C4—42no—
1086C22⋊C4—42no—
1087C22⋊C4—42no—
1088C22⋊C4—42no—
1089C22⋊C4—42no—
1090C22⋊C4—42no—
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—
1103C22⋊C4—81no—
1104C22⋊C4—81no—
1105C22⋊C4—81no—
1106C22⋊C4—81no—
1107C22⋊C4—81no—
1108C22⋊C4—81no—
1109C22⋊C4—81no—
1110C22⋊C4—81no—
1111C22⋊C4—81no—
1112C22⋊C4—81no—
1113C42—21no—
1114C42—21no—
1115C42—21no—
1116C42—21no—
1117C42—21no—
1118C42—21no—
1119C42—21no—
1120C42—21no—
1121C42—21no—
1122C42—21no—
1123C42—42no—
1124C42—42no—
1125C42—42no—
1126C42—42no—
1127C42—42no—
1128C42—42no—
1129C42—42no—
1130C42—81no—
1131C23—21no—
1132C23—21no—
1133C23—21no—
1134C23—21no—
1135C23—21no—
1136C23—21no—
1137C23—21no—
1138C23—21no—
1139C23—21no—
1140C23—21no—
1141C23—21no—
1142C23—21no—
1143C23—21no—
1144C23—21no—
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—41no—
1159C23—41no—
1160C23—41no—
1161C23—41no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
1166C23—41no—
1167C23—41no—
1168C23—41no—
1169C23—41no—
1170C23—41no—
1171C23—41no—
1172C23—41no—
1173C23—84no—
1174C23—162no—
1175C23—162no—
1176C23—162no—
1177C23—162no—
1178C23—162no—
1179C23—162no—
1180C23C23×D411yescharacteristic
1181Q8—22no—
1182Q8—22no—
1183Q8—41no—
1184Q8—41no—
1185Q8—41no—
1186Q8—41no—
1187Q8—41no—
1188Q8—41no—
1189D4—41no—
1190D4—41no—
1191D4—41no—
1192D4—41no—
1193D4—41no—
1194D4—41no—
1195D4—41no—
1196D4—41no—
1197D4—41no—
1198D4—41no—
1199D4—41no—
1200D4—41no—
1201D4—41no—
1202D4—41no—
1203D4—41no—
1204D4—41no—
1205D4—82no—
1206D4—84no—
1207D4—162no—
1208D4—162no—
1209D4—162no—
1210D4—162no—
1211D4—162no—
1212D4—162no—
1213D4—162no—
1214D4—162no—
1215D4—162no—
1216D4—162no—
1217D4—162no—
1218D4—162no—
1219D4—162no—
1220D4—162no—
1221D4—162no—
1222D4—162no—
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—22no—
1242C2×C4—22no—
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—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—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—84no—
1302C2×C4—162no—
1303C2×C4—162no—
1304C2×C4#57712yes—
1305C2×C4#57712yes—
1306C2×C4C2×H(5,𝔽2)11yescharacteristic
1307C2×C4C2×H(5,𝔽2)11yescharacteristic
1308C2×C4C2×H(5,𝔽2)11yescharacteristic
1309C2×C4#58511yescharacteristic
1310C2×C4#58511yescharacteristic
1311C2×C4#58511yescharacteristic
1312C8—41no—
1313C8—41no—
1314C8—41no—
1315C8—41no—
1316C8—41no—
1317C8—41no—
1318C8—41no—
1319C8—41no—
1320C22—41no—
1321C22—41no—
1322C22—41no—
1323C22—41no—
1324C22—41no—
1325C22—41no—
1326C22—41no—
1327C22—41no—
1328C22—41no—
1329C22—41no—
1330C22—41no—
1331C22—41no—
1332C22—41no—
1333C22—41no—
1334C22—81no—
1335C22—81no—
1336C22—81no—
1337C22—81no—
1338C22—81no—
1339C22—81no—
1340C22—81no—
1341C22—81no—
1342C22—81no—
1343C22—81no—
1344C22—81no—
1345C22—81no—
1346C22—81no—
1347C22—81no—
1348C22—81no—
1349C22—81no—
1350C22—81no—
1351C22—81no—
1352C22—81no—
1353C22—81no—
1354C22—81no—
1355C22—81no—
1356C22—81no—
1357C22—81no—
1358C22—81no—
1359C22—81no—
1360C22—81no—
1361C22—81no—
1362C22—168no—
1363C22#348411yescharacteristic
1364C22#348811yescharacteristic
1365C22#350011yescharacteristic
1366C22C2×#57711yescharacteristic
1367C22C2×#57711yescharacteristic
1368C22#358511yescharacteristic
1369C22#358511yescharacteristic
1370C4—22no—
1371C4—22no—
1372C4—41no—
1373C4—42no—
1374C4—41no—
1375C4—41no—
1376C4—42no—
1377C4—41no—
1378C4—41no—
1379C4—41no—
1380C4—41no—
1381C4—41no—
1382C4—41no—
1383C4—41no—
1384C4—42no—
1385C4—81no—
1386C4—81no—
1387C4—81no—
1388C4—81no—
1389C4—81no—
1390C4—81no—
1391C4—81no—
1392C4—81no—
1393C4—81no—
1394C4#353911yescharacteristic
1395C4#354211yescharacteristic
1396C4#354611yescharacteristic
1397C4#356011yescharacteristic
1398C2—81no—
1399C2—81no—
1400C2—161no—
1401C2—161no—
1402C2—161no—
1403C2—161no—
1404C2#4795711yescharacteristic
1405C2#6165111yescharacteristic
1406C2#6166411yescharacteristic
1407C2#6200911yescharacteristic
1408C2#6203311yescharacteristic
1409C2#6259611yescharacteristic
1410C2#6260811yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#52969C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #45238C2semidirect
3. #32237C2semidirect
4. #31838C2semidirect
5. #31838C2semidirect
6. #31805C2semidirect
7. #31560C2semidirect
8. #31361C2semidirect
9. #31044C2semidirect
10. #30988C2semidirect
11. #30892C2semidirect
12. #30736C2semidirect
13. #30730C2semidirect
14. #30456C2semidirect
15. #29765C2semidirect
16. #29671C2semidirect
17. #29343C2semidirect
18. #28883C2semidirect
19. #27775C2semidirect
20. #27572C2semidirect
21. #27279C2semidirect
22. #26967C2semidirect
23. #26935C2semidirect
24. #26664C2semidirect
25. #26630C2semidirect
26. #25607C2semidirect
27. #25583C2semidirect
28. #25093C2semidirect
29. #24728C2semidirect
30. #23982C2semidirect
31. #22364C2semidirect
33. C2×#541C22semidirect
36. C2×#490C22semidirect
38. C2×#482C22semidirect
43. C2×#460C22semidirect
46. C2×C4×SD16C22semidirect
63. #2552C22semidirect
70. #2502C22semidirect
73. #2453C22semidirect
74. #2446C22semidirect
88. #2362C22semidirect
89. Q8×C4⋊C4C22semidirect
90. #2317C22semidirect
91. #2101C22semidirect
92. #2101C22semidirect
93. #2100C22semidirect
94. #2100C22semidirect
95. #2088C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
101. #2068C22semidirect
103. #2067C22semidirect
106. #2065C22semidirect
115. #2041C22semidirect
121. #2025C22semidirect
125. #2014C22semidirect
127. #2013C22semidirect
135. #2000C22semidirect
136. #2000C22semidirect
137. #2000C22semidirect
138. #2000C22semidirect
139. #1991C22semidirect
140. #1989C22semidirect
144. #1960C22semidirect
148. #1939C22semidirect
151. #1936C22semidirect
154. #1934C22semidirect
155. #1933C22semidirect
156. #1933C22semidirect
157. #1927C22semidirect
161. #1923C22semidirect
162. #1923C22semidirect
163. #1920C22semidirect
164. #1918C22semidirect
165. #1917C22semidirect
166. #1916C22semidirect
174. #1880C22semidirect
175. #1880C22semidirect
176. #1877C22semidirect
177. #1877C22semidirect
178. #1877C22semidirect
182. #1875C22semidirect
185. #1874C22semidirect
186. #1874C22semidirect
188. #1863C22semidirect
189. #1862C22semidirect
192. #1805C22semidirect
193. #1805C22semidirect
194. #1802C22semidirect
195. #1802C22semidirect
196. #1798C22semidirect
198. #1770C22semidirect
199. #1763C22semidirect
200. C4×#102C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#529692
#452382
#322372
#318382
#318052
#315602
#313612
#310442
#309882
#308922
#307362
#307302
#304562
#297652
#296712
#293432
#288832
#277752
#275722
#272792
#269672
#269352
#266642
#266302
#256072
#255832
#250932
#247282
#239822
#223642