Finite Group Databasebeta

← #7339458

Subgroups — #7339458

Order 512.

1675 conjugacy classes of subgroups.

The subgroup lattice has 1447 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#52969C211yesmaximal, characteristic, complemented
2#45107C211yesmaximal, characteristic, complemented
3#32243C211yesmaximal, characteristic, complemented
4#31854C211yesmaximal, characteristic, complemented
5#31839C211yesmaximal, characteristic, complemented
6#31805C211yesmaximal, characteristic, complemented
7#31555C211yesmaximal, characteristic, complemented
8#31376C211yesmaximal, characteristic, complemented
9#31040C211yesmaximal, characteristic, complemented
10#31000C211yesmaximal, characteristic, complemented
11#30892C211yesmaximal, characteristic, complemented
12#30749C211yesmaximal, characteristic, complemented
13#30703C211yesmaximal, characteristic, complemented
14#30460C211yesmaximal, characteristic, complemented
15#29763C211yesmaximal, characteristic, complemented
16#29669C211yesmaximal, characteristic, complemented
17#29340C211yesmaximal, characteristic, complemented
18#28897C211yesmaximal, characteristic, complemented
19#27780C211yesmaximal, characteristic, complemented
20#27568C211yesmaximal, characteristic, complemented
21#27254C211yesmaximal, characteristic, complemented
22#26960C211yesmaximal, characteristic, complemented
23#26943C211yesmaximal, characteristic, complemented
24#26676C211yesmaximal, characteristic, complemented
25#26616C211yesmaximal, characteristic, complemented
26#25614C211yesmaximal, characteristic, complemented
27#25581C211yesmaximal, characteristic, complemented
28#25080C211yesmaximal, characteristic, complemented
29#24726C211yesmaximal, characteristic, complemented
30#23963C211yesmaximal, characteristic, complemented
31#22362C211yesmaximal, characteristic, complemented
32C2×#553C2211yescharacteristic
33C2×#542C2211yescharacteristic, complemented
34C2×#496C2211yescharacteristic
35C2×#490C2211yescharacteristic, complemented
36C2×#486C2211yescharacteristic
37C2×#481C2211yescharacteristic, complemented
38C2×#480C2211yescharacteristic
39C2×#465C2211yescharacteristic
40C2×#460C2211yescharacteristic
41C2×#459C2211yescharacteristic
42C2×#459C2211yescharacteristic
43C2×#459C2211yescharacteristic, complemented
44C2×#450C2211yescharacteristic
45C2×#447C2211yescharacteristic
46C2×C4×D8C2211yescharacteristic, complemented
47C22×#102C2211yescharacteristic
48#2828—21no—
49#2815—21no—
50#2815—21no—
51#2812—21no—
52#2722—21no—
53#2717—21no—
54#2708—21no—
55#2699—21no—
56#2689—21no—
57#2669—21no—
58#2669—21no—
59#2668—21no—
60#2619C2211yescharacteristic
61#2619C2211yescharacteristic
62#2550C2211yescharacteristic, complemented
63#2541C2211yescharacteristic
64#2541C2211yescharacteristic
65#2541C2211yescharacteristic
66#2513C2211yescharacteristic
67#2513C2211yescharacteristic
68#2499C2211yescharacteristic, complemented
69#2486—21no—
70#2466—21no—
71#2453C2211yescharacteristic, complemented
72#2449—21no—
73#2447C2211yescharacteristic, complemented
74#2440C2211yescharacteristic
75#2433C2211yescharacteristic
76#2433C2211yescharacteristic
77#2428C2211yescharacteristic
78#2428C2211yescharacteristic
79#2427—21no—
80#2427C2211yescharacteristic
81#2420C2211yescharacteristic
82#2420C2211yescharacteristic
83#2420C2211yescharacteristic
84#2417C2211yescharacteristic
85#2408C2211yescharacteristic
86#2395C2211yescharacteristic
87#2361C2211yescharacteristic, complemented
88#2360C2211yescharacteristic
89D4×C4⋊C4C2211yescharacteristic, complemented
90#2316C2211yescharacteristic, complemented
91#2101C2211yescharacteristic, complemented
92#2101C2211yescharacteristic, complemented
93#2101C2211yescharacteristic, complemented
94#2099C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2085C2211yescharacteristic, complemented
97#2085C2211yescharacteristic, complemented
98#2076C2211yescharacteristic
99#2073C2211yescharacteristic
100#2071C2211yescharacteristic
101#2067C2211yescharacteristic
102#2067C2211yescharacteristic, complemented
103#2067C2211yescharacteristic, complemented
104#2067C2211yescharacteristic, complemented
105#2065C2211yescharacteristic
106#2065C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2041C2211yescharacteristic
111#2041C2211yescharacteristic
112#2041C2211yescharacteristic
113#2041C2211yescharacteristic
114#2041C2211yescharacteristic
115#2041C2211yescharacteristic, complemented
116#2036C2211yescharacteristic
117#2034C2211yescharacteristic
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic
120#2023C2211yescharacteristic
121#2023C2211yescharacteristic, complemented
122#2014C2211yescharacteristic
123#2014C2211yescharacteristic
124#2014C2211yescharacteristic, complemented
125#2012C2211yescharacteristic
126#2012C2211yescharacteristic, complemented
127#2011C2211yescharacteristic
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic, complemented
132#2000C2211yescharacteristic, complemented
133#1999C2211yescharacteristic
134#1999C2211yescharacteristic
135#1999C2211yescharacteristic
136#1999C2211yescharacteristic
137#1999C2211yescharacteristic, complemented
138#1999C2211yescharacteristic, complemented
139#1993C2211yescharacteristic, complemented
140#1989C2211yescharacteristic, complemented
141#1982C2211yescharacteristic
142#1973C2211yescharacteristic
143#1972C2211yescharacteristic
144#1961C2211yescharacteristic
145#1958C2211yescharacteristic, complemented
146#1957C2211yescharacteristic
147#1955C2211yescharacteristic
148#1939C2211yescharacteristic, complemented
149#1936C2211yescharacteristic
150#1936C2211yescharacteristic
151#1936C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1934C2211yescharacteristic
154#1934C2211yescharacteristic
155#1934C2211yescharacteristic, complemented
156#1933C2211yescharacteristic, complemented
157#1927C2211yescharacteristic, complemented
158#1926C2211yescharacteristic
159#1924C2211yescharacteristic
160#1924C2211yescharacteristic
161#1924C2211yescharacteristic, complemented
162#1923C2211yescharacteristic, complemented
163#1920C2211yescharacteristic, complemented
164#1918C2211yescharacteristic, complemented
165#1917C2211yescharacteristic, complemented
166#1917C2211yescharacteristic, complemented
167#1893C2211yescharacteristic
168#1893C2211yescharacteristic
169#1880C2211yescharacteristic
170#1880C2211yescharacteristic, complemented
171#1879C2211yescharacteristic
172#1879C2211yescharacteristic
173#1879C2211yescharacteristic
174#1879C2211yescharacteristic
175#1879C2211yescharacteristic, complemented
176#1879C2211yescharacteristic, complemented
177#1877C2211yescharacteristic, complemented
178#1877C2211yescharacteristic, complemented
179#1875C2211yescharacteristic
180#1875C2211yescharacteristic
181#1875C2211yescharacteristic, complemented
182#1875C2211yescharacteristic, complemented
183#1874C2211yescharacteristic
184#1874C2211yescharacteristic
185#1874C2211yescharacteristic
186#1874C2211yescharacteristic, complemented
187#1869C2211yescharacteristic
188#1864C2211yescharacteristic, complemented
189#1862C2211yescharacteristic, complemented
190#1850C2211yescharacteristic
191#1824C2211yescharacteristic
192#1805C2211yescharacteristic, complemented
193#1804C2211yescharacteristic, complemented
194#1804C2211yescharacteristic, complemented
195#1802C2211yescharacteristic, complemented
196#1798C2211yescharacteristic, complemented
197#1786C2211yescharacteristic
198#1771C2211yescharacteristic, complemented
199#1762C2211yescharacteristic, complemented
200#1762C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic
202#1750C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×D8C2311yescharacteristic
209C22×D8C2311yescharacteristic
210C22×D8C2311yescharacteristic
211C22×D8C2311yescharacteristic
212C23×C8C2311yescharacteristic
213#553—42no—
214#553—42no—
215#542—42no—
216#542—42no—
217C2×C4⋊Q8C2311yescharacteristic
218C2×#127—21no—
219C2×#127C2311yescharacteristic
220C2×#127C2311yescharacteristic
221C2×#127C2311yescharacteristic
222C2×#127C2311yescharacteristic
223C2×#127C2311yescharacteristic
224C2×#126—21no—
225C2×#126—21no—
226C2×#125C2311yescharacteristic
227C2×#124—21no—
228C2×#124C2311yescharacteristic
229C2×#123—21no—
230C2×#123—21no—
231C2×C22⋊Q8—21no—
232C2×C22⋊Q8—21no—
233C2×C22⋊Q8C2311yescharacteristic
234C2×C22⋊Q8C2311yescharacteristic
235C2×#121—21no—
236C2×#121—21no—
237C2×#121—21no—
238C2×#121—21no—
239C2×#121—21no—
240C2×#121—21no—
241C2×#121—21no—
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#121C2311yescharacteristic
245C2×#121C2311yescharacteristic
246C2×#121C2311yescharacteristic
247C2×#121C2311yescharacteristic
248C2×#121C2311yescharacteristic
249C2×#121C2311yescharacteristic
250C2×#120—21no—
251C2×#120—21no—
252C2×#120—21no—
253C2×#120—21no—
254C2×#120—21no—
255C2×C4×Q8C2311yescharacteristic
256C2×C4×D4—21no—
257C2×C4×D4—21no—
258C2×C4×D4C2311yescharacteristic
259C2×C4×D4C2311yescharacteristic
260C2×C4×D4C2311yescharacteristic
261C2×C4×D4C2311yescharacteristic
262C2×C4×D4C2311yescharacteristic
263C2×C4×D4C2311yescharacteristic
264C2×#117C2311yescharacteristic
265C2×#117C2311yescharacteristic
266C22×C4⋊C4—21no—
267C22×C4⋊C4C2311yescharacteristic
268C22×C4⋊C4C2311yescharacteristic
269#496—42no—
270#490—42no—
271#486—42no—
272#481—42no—
273#480—42no—
274#465—42no—
275#460—42no—
276#459—42no—
277#459—42no—
278#459—42no—
279#450—42no—
280#447—42no—
281C4×D8—42no—
282C2×#107C2311yescharacteristic
283C2×#107C2311yescharacteristic
284C2×#106C2311yescharacteristic
285C2×#106C2311yescharacteristic
286C2×C4⋊C8C2311yescharacteristic
287C2×C4⋊C8C2311yescharacteristic
288C2×C4⋊C8C2311yescharacteristic
289C2×C4⋊C8C2311yescharacteristic
290C2×C4⋊C8C2311yescharacteristic
291C2×#103C2311yescharacteristic
292C2×#103C2311yescharacteristic
293C2×#103C2311yescharacteristic
294C2×#103C2311yescharacteristic
295C2×#102—42no—
296C2×#102C2311yescharacteristic
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×#102C2311yescharacteristic
322C2×#102C2311yescharacteristic
323C2×#102C2311yescharacteristic
324C2×C22⋊C8C2311yescharacteristic
325C2×C22⋊C8C2311yescharacteristic
326C2×C22⋊C8C2311yescharacteristic
327C2×C22⋊C8C2311yescharacteristic
328C2×C22⋊C8C2311yescharacteristic
329C2×C22⋊C8C2311yescharacteristic
330C2×C22⋊C8C2311yescharacteristic
331C2×#97C2311yescharacteristic
332C2×#97C2311yescharacteristic
333C2×#97C2311yescharacteristic
334C2×C4×C8C2311yescharacteristic
335C2×C4×C8C2311yescharacteristic
336#400—21no—
337#400D411yescharacteristic
338#399D411yescharacteristic
339#398—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#398D411yescharacteristic
344#397—21no—
345#397—21no—
346#397—21no—
347#397—21no—
348#397—21no—
349#397—21no—
350#397—21no—
351#397—21no—
352#397—21no—
353#397—21no—
354#397—21no—
355#397—21no—
356#397D411yescharacteristic
357#397D411yescharacteristic
358#397D411yescharacteristic
359#396—21no—
360#395—21no—
361#395—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#394—21no—
371#394—21no—
372#394—21no—
373#394D411yescharacteristic
374#394D411yescharacteristic
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#392—21no—
390#392—21no—
391#392—21no—
392#391—21no—
393#391C2311yescharacteristic
394#391C2311yescharacteristic
395#391C2311yescharacteristic
396#390—21no—
397#390C2311yescharacteristic
398#390C2311yescharacteristic
399#390C2311yescharacteristic
400#390C2311yescharacteristic
401#390C2311yescharacteristic
402#390C2311yescharacteristic
403#390C2311yescharacteristic
404#390C2311yescharacteristic
405#390C2311yescharacteristic
406#389—21no—
407#389—21no—
408#389—21no—
409#389—21no—
410#389—21no—
411#389C2311yescharacteristic
412#389C2311yescharacteristic
413#389C2311yescharacteristic
414#389C2311yescharacteristic
415#389C2311yescharacteristic
416#389C2311yescharacteristic
417#389C2311yescharacteristic
418#389C2311yescharacteristic
419#388—21no—
420#388—21no—
421#388—21no—
422#388—21no—
423#388—21no—
424#387—21no—
425#387—21no—
426#387—21no—
427#387—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386—21no—
433#386—21no—
434#386—21no—
435#386—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385—21no—
440#385—21no—
441#385—21no—
442#384C2311yescharacteristic
443#382C2311yescharacteristic
444#382C2311yescharacteristic
445#382C2311yescharacteristic
446#381—21no—
447#381—21no—
448#381—21no—
449#381—21no—
450#380—21no—
451#380—21no—
452#380—21no—
453#380—21no—
454#380—21no—
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#379—21no—
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4—21no—
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×Q8—21no—
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—21no—
517C22×D4—21no—
518C22×D4—41no—
519C22×D4—41no—
520C22×D4—41no—
521C22×D4—41no—
522C22×D4—41no—
523C22×D4—41no—
524C22×D4C2×D411yescharacteristic
525C22×D4C2411yescharacteristic
526C22×D4C2411yescharacteristic
527C22×D4C2411yescharacteristic
528C22×D4C2411yescharacteristic
529C22×D4C2411yescharacteristic
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4C2411yescharacteristic
538C23×C4C2411yescharacteristic
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×D8—22no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—41no—
556C2×D8—41no—
557C2×D8—41no—
558C2×D8—41no—
559C2×D8—41no—
560C2×D8—41no—
561C2×D8—41no—
562C2×D8—41no—
563C22×C8—41no—
564C22×C8—41no—
565C22×C8—41no—
566C22×C8C2411yescharacteristic
567C22×C8C2411yescharacteristic
568C22×C8C2411yescharacteristic
569C22×C8C2411yescharacteristic
570C22×C8C2411yescharacteristic
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C4⋊Q8—22no—
575C4⋊Q8—41no—
576#127—41no—
577#127—41no—
578#127—41no—
579#127—41no—
580#127—41no—
581#127—41no—
582#127—41no—
583#127—41no—
584#127—41no—
585#127—41no—
586#127—82no—
587#126—44no—
588#126—44no—
589#125—22no—
590#125—41no—
591#124—22no—
592#124—41no—
593#124—44no—
594#123—44no—
595#123—44no—
596C22⋊Q8—22no—
597C22⋊Q8—44no—
598C22⋊Q8—41no—
599C22⋊Q8—41no—
600C22⋊Q8—41no—
601C22⋊Q8—82no—
602#121—22no—
603#121—22no—
604#121—22no—
605#121—41no—
606#121—44no—
607#121—41no—
608#121—41no—
609#121—41no—
610#121—41no—
611#121—41no—
612#121—41no—
613#121—41no—
614#121—41no—
615#121—41no—
616#121—41no—
617#121—41no—
618#121—41no—
619#121—82no—
620#121—82no—
621#121—82no—
622#121—82no—
623#121—82no—
624#121—82no—
625#120—82no—
626#120—82no—
627#120—82no—
628#120—82no—
629#120—82no—
630C4×Q8—22no—
631C4×Q8—41no—
632C4×D4—22no—
633C4×D4—22no—
634C4×D4—22no—
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—41no—
644C4×D4—44no—
645C4×D4—82no—
646#117—41no—
647#117—41no—
648#117—41no—
649#117—41no—
650C2×C4⋊C4—22no—
651C2×C4⋊C4—22no—
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⋊C4—82no—
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⋊C4C2×D411yescharacteristic
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×C4⋊C4C2411yescharacteristic
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—21no—
726C2×C22⋊C4—21no—
727C2×C22⋊C4—21no—
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×C22⋊C4C2×D411yescharacteristic
738C2×C42—21no—
739C2×C42—21no—
740C2×C42—21no—
741C2×C42—21no—
742C2×C42C2411yescharacteristic
743C2×C42C2411yescharacteristic
744C2×C42C2411yescharacteristic
745C2×C42C2411yescharacteristic
746C2×C42C2411yescharacteristic
747#107—22no—
748#107—41no—
749#106—22no—
750#106—41no—
751C4⋊C8—41no—
752C4⋊C8—41no—
753C4⋊C8—41no—
754C4⋊C8—41no—
755C4⋊C8—41no—
756#103—41no—
757#103—41no—
758#103—41no—
759#103—41no—
760#102—22no—
761#102—22no—
762#102—22no—
763#102—22no—
764#102—22no—
765#102—22no—
766#102—22no—
767#102—22no—
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—
782#102—41no—
783#102—41no—
784#102—41no—
785#102—41no—
786#102—41no—
787#102—41no—
788C22⋊C8—41no—
789C22⋊C8—41no—
790C22⋊C8—41no—
791C22⋊C8—41no—
792C22⋊C8—41no—
793C22⋊C8—41no—
794C22⋊C8—41no—
795#97—41no—
796#97—41no—
797#97—41no—
798C4×C8—41no—
799C4×C8—41no—
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#95—21no—
822#95—21no—
823#95—21no—
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
833#95C2×D411yescharacteristic
834C24—21no—
835C24—21no—
836C24—21no—
837C24—21no—
838C24—21no—
839C24—42no—
840C24—81no—
841C24—81no—
842C24—81no—
843C24—81no—
844C24—81no—
845C24—81no—
846C24C22×D411yescharacteristic
847C24C22×D411yescharacteristic
848C2×Q8—21no—
849C2×Q8—21no—
850C2×Q8—21no—
851C2×Q8—21no—
852C2×Q8—21no—
853C2×Q8—21no—
854C2×Q8—42no—
855C2×Q8—81no—
856C2×Q8—81no—
857C2×D4—24no—
858C2×D4—22no—
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—21no—
881C2×D4—21no—
882C2×D4—21no—
883C2×D4—21no—
884C2×D4—21no—
885C2×D4—21no—
886C2×D4—21no—
887C2×D4—21no—
888C2×D4—41no—
889C2×D4—41no—
890C2×D4—42no—
891C2×D4—42no—
892C2×D4—44no—
893C2×D4—42no—
894C2×D4—42no—
895C2×D4—42no—
896C2×D4—42no—
897C2×D4—42no—
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—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—82no—
929C2×D4—82no—
930C2×D4—82no—
931C2×D4—81no—
932C2×D4—81no—
933C2×D4—81no—
934C2×D4—81no—
935C2×D4—81no—
936C2×D4—81no—
937C2×D4—81no—
938C2×D4—81no—
939C2×D4—81no—
940C2×D4—81no—
941C2×D4—81no—
942C2×D4—81no—
943C2×D4—81no—
944C2×D4—81no—
945C2×D4—81no—
946C2×D4—81no—
947C2×D4—81no—
948C2×D4—81no—
949C2×D4—81no—
950C2×D4H(5,𝔽2)12yes—
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—21no—
963C22×C4—21no—
964C22×C4—21no—
965C22×C4—21no—
966C22×C4—21no—
967C22×C4—21no—
968C22×C4—21no—
969C22×C4—21no—
970C22×C4—21no—
971C22×C4—21no—
972C22×C4—21no—
973C22×C4—21no—
974C22×C4—42no—
975C22×C4—42no—
976C22×C4—42no—
977C22×C4—42no—
978C22×C4—42no—
979C22×C4—42no—
980C22×C4—42no—
981C22×C4—42no—
982C22×C4—81no—
983C22×C4—81no—
984C22×C4—81no—
985C22×C4—81no—
986C22×C4—81no—
987C22×C4—81no—
988C22×C4—81no—
989C22×C4—81no—
990C22×C4—81no—
991C22×C4—81no—
992C22×C4—81no—
993C22×C4—81no—
994C22×C4—81no—
995C22×C4C22×D411yescharacteristic
996C22×C4C22×D411yescharacteristic
997C22×C4C22×D411yescharacteristic
998C22×C4C22×D411yescharacteristic
999C22×C4C22×D411yescharacteristic
1000C22×C4C22×D411yescharacteristic
1001C22×C4C22×D411yescharacteristic
1002C22×C4C22×D411yescharacteristic
1003C22×C4C22×D411yescharacteristic
1004C22×C4C22×D411yescharacteristic
1005C22×C4C22×D411yescharacteristic
1006C22×C4C22×D411yescharacteristic
1007C22×C4C2511yescharacteristic
1008SD16—82no—
1009SD16—82no—
1010SD16—82no—
1011SD16—82no—
1012D8—44no—
1013D8—82no—
1014D8—82no—
1015D8—82no—
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—21no—
1033C2×C8—21no—
1034C2×C8—21no—
1035C2×C8—21no—
1036C2×C8—21no—
1037C2×C8—21no—
1038C2×C8—21no—
1039C2×C8—21no—
1040C2×C8—82no—
1041C4⋊C4—22no—
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—21no—
1055C4⋊C4—21no—
1056C4⋊C4—21no—
1057C4⋊C4—21no—
1058C4⋊C4—21no—
1059C4⋊C4—21no—
1060C4⋊C4—41no—
1061C4⋊C4—41no—
1062C4⋊C4—41no—
1063C4⋊C4—41no—
1064C4⋊C4—41no—
1065C4⋊C4—41no—
1066C4⋊C4—42no—
1067C4⋊C4—42no—
1068C4⋊C4—42no—
1069C4⋊C4—42no—
1070C4⋊C4—42no—
1071C4⋊C4—42no—
1072C4⋊C4—42no—
1073C4⋊C4—42no—
1074C4⋊C4—42no—
1075C4⋊C4—42no—
1076C4⋊C4—81no—
1077C4⋊C4—81no—
1078C4⋊C4—81no—
1079C4⋊C4—81no—
1080C4⋊C4—81no—
1081C4⋊C4—81no—
1082C4⋊C4—81no—
1083C4⋊C4—81no—
1084C4⋊C4H(5,𝔽2)12yes—
1085C4⋊C4H(5,𝔽2)12yes—
1086C22⋊C4—24no—
1087C22⋊C4—22no—
1088C22⋊C4—22no—
1089C22⋊C4—22no—
1090C22⋊C4—22no—
1091C22⋊C4—41no—
1092C22⋊C4—41no—
1093C22⋊C4—41no—
1094C22⋊C4—41no—
1095C22⋊C4—41no—
1096C22⋊C4—41no—
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—
1129C22⋊C4—81no—
1130C22⋊C4—81no—
1131C22⋊C4—81no—
1132C22⋊C4—81no—
1133C22⋊C4—81no—
1134C42—21no—
1135C42—21no—
1136C42—21no—
1137C42—21no—
1138C42—21no—
1139C42—21no—
1140C42—21no—
1141C42—21no—
1142C42—21no—
1143C42—21no—
1144C42—42no—
1145C42—42no—
1146C42—81no—
1147C42—81no—
1148C23—21no—
1149C23—21no—
1150C23—21no—
1151C23—21no—
1152C23—21no—
1153C23—21no—
1154C23—21no—
1155C23—21no—
1156C23—22no—
1157C23—21no—
1158C23—21no—
1159C23—21no—
1160C23—21no—
1161C23—21no—
1162C23—41no—
1163C23—41no—
1164C23—41no—
1165C23—41no—
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—41no—
1191C23—41no—
1192C23—41no—
1193C23—41no—
1194C23—41no—
1195C23—41no—
1196C23—84no—
1197C23—162no—
1198C23—162no—
1199C23—162no—
1200C23—162no—
1201C23—162no—
1202C23—162no—
1203C23#57712yes—
1204C23C23×D411yescharacteristic
1205Q8—41no—
1206Q8—41no—
1207Q8—41no—
1208Q8—41no—
1209Q8—162no—
1210D4—22no—
1211D4—22no—
1212D4—41no—
1213D4—41no—
1214D4—41no—
1215D4—41no—
1216D4—41no—
1217D4—41no—
1218D4—41no—
1219D4—41no—
1220D4—41no—
1221D4—41no—
1222D4—41no—
1223D4—41no—
1224D4—41no—
1225D4—41no—
1226D4—41no—
1227D4—41no—
1228D4—41no—
1229D4—41no—
1230D4—82no—
1231D4—84no—
1232D4—84no—
1233D4—84no—
1234D4—162no—
1235D4—162no—
1236D4—162no—
1237D4—162no—
1238D4—162no—
1239D4—162no—
1240D4—162no—
1241D4—162no—
1242D4—162no—
1243D4—162no—
1244D4—162no—
1245D4—162no—
1246D4—162no—
1247D4—162no—
1248D4—162no—
1249D4—162no—
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—21no—
1268C2×C4—22no—
1269C2×C4—21no—
1270C2×C4—21no—
1271C2×C4—22no—
1272C2×C4—21no—
1273C2×C4—21no—
1274C2×C4—21no—
1275C2×C4—21no—
1276C2×C4—21no—
1277C2×C4—21no—
1278C2×C4—21no—
1279C2×C4—21no—
1280C2×C4—21no—
1281C2×C4—21no—
1282C2×C4—21no—
1283C2×C4—21no—
1284C2×C4—21no—
1285C2×C4—21no—
1286C2×C4—21no—
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—41no—
1311C2×C4—41no—
1312C2×C4—41no—
1313C2×C4—41no—
1314C2×C4—41no—
1315C2×C4—41no—
1316C2×C4—41no—
1317C2×C4—41no—
1318C2×C4—41no—
1319C2×C4—41no—
1320C2×C4—41no—
1321C2×C4—41no—
1322C2×C4—41no—
1323C2×C4—41no—
1324C2×C4—41no—
1325C2×C4—41no—
1326C2×C4—84no—
1327C2×C4—162no—
1328C2×C4—162no—
1329C2×C4—162no—
1330C2×C4—162no—
1331C2×C4—162no—
1332C2×C4—162no—
1333C2×C4#57612yes—
1334C2×C4C2×H(5,𝔽2)11yescharacteristic
1335C2×C4C2×H(5,𝔽2)11yescharacteristic
1336C2×C4C2×H(5,𝔽2)11yescharacteristic
1337C2×C4#58511yescharacteristic
1338C2×C4#58511yescharacteristic
1339C2×C4#58511yescharacteristic
1340C8—41no—
1341C8—41no—
1342C8—41no—
1343C8—41no—
1344C8—41no—
1345C8—41no—
1346C8—41no—
1347C8—41no—
1348C22—22no—
1349C22—22no—
1350C22—22no—
1351C22—41no—
1352C22—41no—
1353C22—41no—
1354C22—41no—
1355C22—41no—
1356C22—41no—
1357C22—41no—
1358C22—42no—
1359C22—41no—
1360C22—41no—
1361C22—41no—
1362C22—42no—
1363C22—42no—
1364C22—41no—
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—81no—
1380C22—81no—
1381C22—81no—
1382C22—81no—
1383C22—81no—
1384C22—81no—
1385C22—81no—
1386C22—81no—
1387C22—81no—
1388C22—81no—
1389C22—81no—
1390C22—81no—
1391C22—81no—
1392C22—81no—
1393C22—81no—
1394C22—81no—
1395C22—81no—
1396C22—81no—
1397C22—168no—
1398C22#348411yescharacteristic
1399C22#348811yescharacteristic
1400C22#350011yescharacteristic
1401C22C2×#57611yescharacteristic
1402C22C2×#57711yescharacteristic
1403C22#358511yescharacteristic
1404C22#358511yescharacteristic
1405C4—22no—
1406C4—42no—
1407C4—41no—
1408C4—41no—
1409C4—41no—
1410C4—41no—
1411C4—41no—
1412C4—41no—
1413C4—41no—
1414C4—41no—
1415C4—41no—
1416C4—41no—
1417C4—41no—
1418C4—42no—
1419C4—81no—
1420C4—81no—
1421C4—81no—
1422C4—81no—
1423C4—81no—
1424C4—81no—
1425C4—81no—
1426C4—81no—
1427C4—81no—
1428C4#353911yescharacteristic
1429C4#354211yescharacteristic
1430C4#354611yescharacteristic
1431C4#356011yescharacteristic
1432C2—42no—
1433C2—81no—
1434C2—82no—
1435C2—161no—
1436C2—161no—
1437C2—161no—
1438C2—161no—
1439C2#4795711yescharacteristic
1440C2#6162111yescharacteristic
1441C2#6167911yescharacteristic
1442C2#6200711yescharacteristic
1443C2#6200911yescharacteristic
1444C2#6255011yescharacteristic
1445C2#6256411yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2395 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #52969C2semidirect
2. #45107C2semidirect
3. #32243C2semidirect
4. #31854C2semidirect
5. #31839C2semidirect
6. #31805C2semidirect
7. #31555C2semidirect
8. #31376C2semidirect
9. #31040C2semidirect
10. #31000C2semidirect
11. #30892C2semidirect
12. #30749C2semidirect
13. #30703C2semidirect
14. #30460C2semidirect
15. #29763C2semidirect
16. #29669C2semidirect
17. #29340C2semidirect
18. #28897C2semidirect
19. #27780C2semidirect
20. #27568C2semidirect
21. #27254C2semidirect
22. #26960C2semidirect
23. #26943C2semidirect
24. #26676C2semidirect
25. #26616C2semidirect
26. #25614C2semidirect
27. #25581C2semidirect
28. #25080C2semidirect
29. #24726C2semidirect
30. #23963C2semidirect
31. #22362C2semidirect
33. C2×#542C22semidirect
35. C2×#490C22semidirect
37. C2×#481C22semidirect
43. C2×#459C22semidirect
46. C2×C4×D8C22semidirect
62. #2550C22semidirect
68. #2499C22semidirect
71. #2453C22semidirect
73. #2447C22semidirect
87. #2361C22semidirect
89. D4×C4⋊C4C22semidirect
90. #2316C22semidirect
91. #2101C22semidirect
92. #2101C22semidirect
93. #2101C22semidirect
94. #2099C22semidirect
95. #2088C22semidirect
96. #2085C22semidirect
97. #2085C22semidirect
102. #2067C22semidirect
103. #2067C22semidirect
104. #2067C22semidirect
115. #2041C22semidirect
121. #2023C22semidirect
124. #2014C22semidirect
126. #2012C22semidirect
131. #2000C22semidirect
132. #2000C22semidirect
137. #1999C22semidirect
138. #1999C22semidirect
139. #1993C22semidirect
140. #1989C22semidirect
145. #1958C22semidirect
148. #1939C22semidirect
151. #1936C22semidirect
152. #1935C22semidirect
155. #1934C22semidirect
156. #1933C22semidirect
157. #1927C22semidirect
161. #1924C22semidirect
162. #1923C22semidirect
163. #1920C22semidirect
164. #1918C22semidirect
165. #1917C22semidirect
166. #1917C22semidirect
170. #1880C22semidirect
175. #1879C22semidirect
176. #1879C22semidirect
177. #1877C22semidirect
178. #1877C22semidirect
181. #1875C22semidirect
182. #1875C22semidirect
186. #1874C22semidirect
188. #1864C22semidirect
189. #1862C22semidirect
192. #1805C22semidirect
193. #1804C22semidirect
194. #1804C22semidirect
195. #1802C22semidirect
196. #1798C22semidirect
198. #1771C22semidirect
199. #1762C22semidirect
200. #1762C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#529692
#451072
#322432
#318542
#318392
#318052
#315552
#313762
#310402
#310002
#308922
#307492
#307032
#304602
#297632
#296692
#293402
#288972
#277802
#275682
#272542
#269602
#269432
#266762
#266162
#256142
#255812
#250802
#247262
#239632
#223622