Finite Group Databasebeta

← #6782884

Subgroups — #6782884

Order 512.

1679 conjugacy classes of subgroups.

The subgroup lattice has 1366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#39042C211yesmaximal, characteristic
2#38081C211yesmaximal, characteristic, complemented
3#33046C211yesmaximal, characteristic, complemented
4#32436C211yesmaximal, characteristic, complemented
5#32182C211yesmaximal, characteristic, complemented
6#32064C211yesmaximal, characteristic, complemented
7#31941C211yesmaximal, characteristic, complemented
8#31546C211yesmaximal, characteristic, complemented
9#31002C211yesmaximal, characteristic, complemented
10#30878C211yesmaximal, characteristic, complemented
11#30522C211yesmaximal, characteristic, complemented
12#30355C211yesmaximal, characteristic, complemented
13#30325C211yesmaximal, characteristic, complemented
14#29568C211yesmaximal, characteristic, complemented
15#29508C211yesmaximal, characteristic, complemented
16#29118C211yesmaximal, characteristic, complemented
17#28320C211yesmaximal, characteristic, complemented
18#24651C211yesmaximal, characteristic, complemented
19#24584C211yesmaximal, characteristic, complemented
20#24538C211yesmaximal, characteristic, complemented
21#24503C211yesmaximal, characteristic, complemented
22#24496C211yesmaximal, characteristic, complemented
23#24358C211yesmaximal, characteristic, complemented
24#24099C211yesmaximal, characteristic, complemented
25#24053C211yesmaximal, characteristic, complemented
26#23982C211yesmaximal, characteristic
27#23855C211yesmaximal, characteristic
28#22162C211yesmaximal, characteristic, complemented
29#22047C211yesmaximal, characteristic, complemented
30#21231C211yesmaximal, characteristic, complemented
31#21109C211yesmaximal, characteristic, complemented
32C23×SD16C2211yescharacteristic
33C2×#552C2211yescharacteristic
34C2×D4×Q8C2211yescharacteristic
35C2×#487C2211yescharacteristic, complemented
36C2×#485C2211yescharacteristic
37C2×#485C2211yescharacteristic
38C2×#461C2211yescharacteristic
39C2×#461C2211yescharacteristic
40C2×#448C2211yescharacteristic
41C2×#448C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#450C2211yescharacteristic
44C2×#431C2211yescharacteristic, complemented
45C2×#427C2211yescharacteristic
46C2×#419C2211yescharacteristic
47C2×#418C2211yescharacteristic
48C2×#405C2211yescharacteristic
49#2857C2211yescharacteristic, complemented
50#2854C2211yescharacteristic
51#2749—21no—
52#2737—21no—
53#2735—21no—
54#2713—21no—
55#2713—21no—
56#2689—21no—
57#2689—21no—
58#2684—21no—
59#2644C2211yescharacteristic
60#2642C2211yescharacteristic, complemented
61#2628C2211yescharacteristic
62#2621C2211yescharacteristic
63#2597—21no—
64#2565C2211yescharacteristic, complemented
65#2561—21no—
66#2546C2211yescharacteristic, complemented
67#2513C2211yescharacteristic
68#2503C2211yescharacteristic, complemented
69#2499C2211yescharacteristic
70#2491C2211yescharacteristic
71#2485C2211yescharacteristic
72#2461—21no—
73#2452C2211yescharacteristic
74#2438—21no—
75#2438—21no—
76#2434C2211yescharacteristic
77#2434C2211yescharacteristic, complemented
78#2420C2211yescharacteristic
79#2419—21no—
80#2419—21no—
81#2418—21no—
82#2408C2211yescharacteristic
83#2347C2211yescharacteristic
84D4×C22⋊C4C2211yescharacteristic
85#2327C2211yescharacteristic, complemented
86#2319C2211yescharacteristic
87#2310C2211yescharacteristic
88#2309C2211yescharacteristic
89C4×#121C2211yescharacteristic
90C2×#391C2211yescharacteristic, complemented
91#2290C2211yescharacteristic
92#2092C2211yescharacteristic
93#2092C2211yescharacteristic
94#2085C2211yescharacteristic, complemented
95#2083C2211yescharacteristic, complemented
96#2074C2211yescharacteristic, complemented
97#2074C2211yescharacteristic, complemented
98#2073C2211yescharacteristic
99#2071C2211yescharacteristic
100#2068C2211yescharacteristic, complemented
101#2066C2211yescharacteristic, complemented
102#2066C2211yescharacteristic, complemented
103#2066C2211yescharacteristic, complemented
104#2059C2211yescharacteristic, complemented
105#2059C2211yescharacteristic, complemented
106#2055C2211yescharacteristic
107#2055C2211yescharacteristic
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2043C2211yescharacteristic, complemented
111#2043C2211yescharacteristic, complemented
112#2043C2211yescharacteristic, complemented
113#2043C2211yescharacteristic, complemented
114#2036C2211yescharacteristic, complemented
115#2036C2211yescharacteristic, complemented
116#2035C2211yescharacteristic, complemented
117#2035C2211yescharacteristic, complemented
118#2025C2211yescharacteristic
119#2025C2211yescharacteristic
120#2024C2211yescharacteristic, complemented
121#2024C2211yescharacteristic, complemented
122#2013C2211yescharacteristic
123#2013C2211yescharacteristic
124#2013C2211yescharacteristic
125#2013C2211yescharacteristic
126#2013C2211yescharacteristic
127#2013C2211yescharacteristic
128#2000C2211yescharacteristic
129#2000C2211yescharacteristic
130#2000C2211yescharacteristic
131#2000C2211yescharacteristic
132#1993C2211yescharacteristic, complemented
133#1981C2211yescharacteristic, complemented
134#1981C2211yescharacteristic, complemented
135#1973C2211yescharacteristic
136#1973C2211yescharacteristic
137#1973C2211yescharacteristic
138#1973C2211yescharacteristic
139#1973C2211yescharacteristic
140#1973C2211yescharacteristic
141#1968C2211yescharacteristic
142#1968C2211yescharacteristic
143#1968C2211yescharacteristic
144#1968C2211yescharacteristic
145#1968C2211yescharacteristic
146#1968C2211yescharacteristic
147#1960C2211yescharacteristic, complemented
148#1949C2211yescharacteristic, complemented
149#1948C2211yescharacteristic, complemented
150#1935C2211yescharacteristic, complemented
151#1935C2211yescharacteristic, complemented
152#1935C2211yescharacteristic, complemented
153#1935C2211yescharacteristic, complemented
154#1933C2211yescharacteristic, complemented
155#1933C2211yescharacteristic, complemented
156#1933C2211yescharacteristic, complemented
157#1933C2211yescharacteristic, complemented
158#1928C2211yescharacteristic, complemented
159#1928C2211yescharacteristic, complemented
160#1928C2211yescharacteristic, complemented
161#1927C2211yescharacteristic, complemented
162#1924C2211yescharacteristic, complemented
163#1923C2211yescharacteristic, complemented
164#1917C2211yescharacteristic, complemented
165#1916C2211yescharacteristic, complemented
166#1894C2211yescharacteristic
167#1894C2211yescharacteristic
168#1892C2211yescharacteristic
169#1892C2211yescharacteristic
170#1880C2211yescharacteristic
171#1880C2211yescharacteristic
172#1880C2211yescharacteristic
173#1880C2211yescharacteristic
174#1877C2211yescharacteristic
175#1877C2211yescharacteristic
176#1877C2211yescharacteristic
177#1877C2211yescharacteristic
178#1874C2211yescharacteristic
179#1874C2211yescharacteristic
180#1870C2211yescharacteristic
181#1869C2211yescharacteristic
182#1865C2211yescharacteristic, complemented
183#1865C2211yescharacteristic, complemented
184#1863C2211yescharacteristic, complemented
185#1863C2211yescharacteristic, complemented
186#1853C2211yescharacteristic, complemented
187#1852C2211yescharacteristic, complemented
188#1851C2211yescharacteristic
189#1850C2211yescharacteristic
190#1835C2211yescharacteristic, complemented
191#1825C2211yescharacteristic
192#1825C2211yescharacteristic
193#1804C2211yescharacteristic
194#1802C2211yescharacteristic
195#1787C2211yescharacteristic
196#1787C2211yescharacteristic
197#1787C2211yescharacteristic, complemented
198#1787C2211yescharacteristic, complemented
199#1768C2211yescharacteristic, complemented
200#1750C2211yescharacteristic
201#1749C2211yescharacteristic, complemented
202#1746C2211yescharacteristic, complemented
203C23×Q8C2311yescharacteristic
204C23×Q8C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16—24no—
207C22×SD16—42no—
208C22×SD16—42no—
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×SD16C2311yescharacteristic
213C22×SD16C2311yescharacteristic
214C22×SD16C2311yescharacteristic
215C22×SD16C2311yescharacteristic
216C22×SD16C2311yescharacteristic
217C22×M16C2311yescharacteristic
218C23×C8C2311yescharacteristic
219#552—42no—
220#552—42no—
221D4×Q8—42no—
222D4×Q8—42no—
223C2×C4⋊Q8—21no—
224C2×C4⋊Q8C2311yescharacteristic
225C2×C4⋊Q8C2311yescharacteristic
226C2×C4⋊Q8C2311yescharacteristic
227C2×C4⋊Q8C2311yescharacteristic
228C2×C4⋊Q8C2311yescharacteristic
229C2×#126—21no—
230C2×#125—21no—
231C2×#125C2311yescharacteristic
232C2×#124—21no—
233C2×#123—21no—
234C2×#123—21no—
235C2×C22⋊Q8—21no—
236C2×C22⋊Q8—21no—
237C2×C22⋊Q8—21no—
238C2×C22⋊Q8C2311yescharacteristic
239C2×C22⋊Q8C2311yescharacteristic
240C2×C22⋊Q8C2311yescharacteristic
241C2×C22⋊Q8C2311yescharacteristic
242C2×#121C2311yescharacteristic
243C2×#121C2311yescharacteristic
244C2×#120—21no—
245C2×C4×Q8C2311yescharacteristic
246C2×C4×Q8C2311yescharacteristic
247C2×C4×D4—21no—
248C2×C4×D4—21no—
249C2×C4×D4C2311yescharacteristic
250C2×C4×D4C2311yescharacteristic
251C2×C4×D4C2311yescharacteristic
252C2×#117—21no—
253C2×#117C2311yescharacteristic
254C2×#117C2311yescharacteristic
255C2×#117C2311yescharacteristic
256C22×C4⋊C4C2311yescharacteristic
257C22×C22⋊C4—21no—
258C22×C42C2311yescharacteristic
259#487—42no—
260#485—42no—
261#485—42no—
262#461—24no—
263#461—42no—
264#450—42no—
265#450—42no—
266#448—24no—
267#448—42no—
268#431—42no—
269#427—42no—
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#107C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×#106C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280C2×C4⋊C8C2311yescharacteristic
281C2×C4⋊C8C2311yescharacteristic
282#419—42no—
283#418—42no—
284C2×#103C2311yescharacteristic
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×#103C2311yescharacteristic
299C2×#103C2311yescharacteristic
300C2×#103C2311yescharacteristic
301C2×#103C2311yescharacteristic
302C2×#103C2311yescharacteristic
303C2×#103C2311yescharacteristic
304C2×#103C2311yescharacteristic
305C2×#103C2311yescharacteristic
306C2×#103C2311yescharacteristic
307C2×#103C2311yescharacteristic
308C2×#102C2311yescharacteristic
309C2×#102C2311yescharacteristic
310C2×#102C2311yescharacteristic
311C2×#102C2311yescharacteristic
312C2×#102C2311yescharacteristic
313C2×#102C2311yescharacteristic
314C2×#102C2311yescharacteristic
315C2×#102C2311yescharacteristic
316C2×C22⋊C8C2311yescharacteristic
317C2×C22⋊C8C2311yescharacteristic
318C2×C22⋊C8C2311yescharacteristic
319C2×C22⋊C8C2311yescharacteristic
320C2×C22⋊C8C2311yescharacteristic
321C2×C22⋊C8C2311yescharacteristic
322#405—42no—
323C2×#97C2311yescharacteristic
324C2×#97C2311yescharacteristic
325C2×#97C2311yescharacteristic
326C2×C4×C8C2311yescharacteristic
327C2×C4×C8C2311yescharacteristic
328C2×C4×C8C2311yescharacteristic
329#400—21no—
330#400—21no—
331#400—21no—
332#400—21no—
333#400—21no—
334#400—21no—
335#400—21no—
336#399—21no—
337#398—21no—
338#398—21no—
339#398—21no—
340#398—21no—
341#398—21no—
342#398—21no—
343#397—21no—
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#396—21no—
355#396—21no—
356#395—21no—
357#395—21no—
358#395—21no—
359#395—21no—
360#395—21no—
361#394—21no—
362#394—21no—
363#394—21no—
364#394—21no—
365#393—21no—
366#393—21no—
367#393—21no—
368#392—21no—
369#391—21no—
370#391—21no—
371#391—21no—
372#391—21no—
373#391C2311yescharacteristic
374#391C2311yescharacteristic
375#391C2311yescharacteristic
376#391C2311yescharacteristic
377#391C2311yescharacteristic
378#391C2311yescharacteristic
379#391C2311yescharacteristic
380#391C2311yescharacteristic
381#391C2311yescharacteristic
382#391C2311yescharacteristic
383#390—21no—
384#390—21no—
385#390C2311yescharacteristic
386#390C2311yescharacteristic
387#390C2311yescharacteristic
388#390C2311yescharacteristic
389#390C2311yescharacteristic
390#390C2311yescharacteristic
391#390C2311yescharacteristic
392#390C2311yescharacteristic
393#389—21no—
394#389—21no—
395#389—21no—
396#389—21no—
397#389C2311yescharacteristic
398#389C2311yescharacteristic
399#389C2311yescharacteristic
400#389C2311yescharacteristic
401#389C2311yescharacteristic
402#389C2311yescharacteristic
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#388—21no—
409#388—21no—
410#388—21no—
411#388—21no—
412#388—21no—
413#388—21no—
414#388D411yescharacteristic
415#388D411yescharacteristic
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#387—21no—
421#387—21no—
422#387—21no—
423#387—21no—
424#387—21no—
425#387D411yescharacteristic
426#387D411yescharacteristic
427#386—21no—
428#386—21no—
429#386—21no—
430#386—21no—
431#386—21no—
432#386D411yescharacteristic
433#386D411yescharacteristic
434#385—21no—
435#385—21no—
436#385—21no—
437#385—21no—
438#385—21no—
439#385D411yescharacteristic
440#385D411yescharacteristic
441#384C2311yescharacteristic
442#383—21no—
443#382C2311yescharacteristic
444#382C2311yescharacteristic
445#382C2311yescharacteristic
446#381—21no—
447#381—21no—
448#381—21no—
449#381—21no—
450#381—21no—
451#381—21no—
452#380—21no—
453#380—21no—
454#380—21no—
455#380C2311yescharacteristic
456#380C2311yescharacteristic
457#380C2311yescharacteristic
458#380C2311yescharacteristic
459#379—21no—
460#379—21no—
461#379—21no—
462#379—21no—
463C4×C4⋊C4—21no—
464C4×C4⋊C4C2311yescharacteristic
465C4×C4⋊C4C2311yescharacteristic
466C4×C4⋊C4C2311yescharacteristic
467C4×C22⋊C4—21no—
468C4×C22⋊C4C2311yescharacteristic
469C4×C22⋊C4C2311yescharacteristic
470#376C2311yescharacteristic
471C2×#95—21no—
472C2×#95—21no—
473#340C2311yescharacteristic
474#340C2311yescharacteristic
475#340C2311yescharacteristic
476#340C2311yescharacteristic
477#340C2311yescharacteristic
478#340C2311yescharacteristic
479#340C2311yescharacteristic
480#340C2311yescharacteristic
481#340C2311yescharacteristic
482#340C2311yescharacteristic
483#340C2311yescharacteristic
484#340C2311yescharacteristic
485#340C2311yescharacteristic
486#340C2311yescharacteristic
487#340C2311yescharacteristic
488#340C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493#336C2311yescharacteristic
494#336C2311yescharacteristic
495#336C2311yescharacteristic
496#336C2311yescharacteristic
497#336C2311yescharacteristic
498#336C2311yescharacteristic
499C25—21no—
500C22×Q8—21no—
501C22×Q8—21no—
502C22×Q8—21no—
503C22×Q8—22no—
504C22×Q8—22no—
505C22×Q8—22no—
506C22×Q8—22no—
507C22×Q8—41no—
508C22×Q8—41no—
509C22×Q8—41no—
510C22×Q8—41no—
511C22×Q8—41no—
512C22×Q8—41no—
513C22×Q8—41no—
514C22×Q8—41no—
515C22×Q8C2411yescharacteristic
516C22×Q8C2411yescharacteristic
517C22×Q8C2411yescharacteristic
518C22×Q8C2411yescharacteristic
519C22×D4—22no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—22no—
524C22×D4—22no—
525C22×D4—41no—
526C22×D4—41no—
527C22×D4—41no—
528C22×D4C2×D411yescharacteristic
529C22×D4C2411yescharacteristic
530C22×D4C2411yescharacteristic
531C23×C4—21no—
532C23×C4—21no—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4C2×D411yescharacteristic
537C23×C4C2×D411yescharacteristic
538C23×C4C2411yescharacteristic
539C23×C4C2411yescharacteristic
540C2×SD16—22no—
541C2×SD16—22no—
542C2×SD16—22no—
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—41no—
548C2×SD16—41no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×SD16—41no—
553C2×SD16—416no—
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#4114yes—
565C2×M16—22no—
566C2×M16—41no—
567C2×M16—41no—
568C22×C8—22no—
569C22×C8—22no—
570C22×C8—22no—
571C22×C8C2411yescharacteristic
572C22×C8C2411yescharacteristic
573C22×C8C2411yescharacteristic
574C22×C8C2411yescharacteristic
575C22×C8C2411yescharacteristic
576C22×C8C2411yescharacteristic
577C22×C8C2411yescharacteristic
578C22×C8C2411yescharacteristic
579C4⋊Q8—22no—
580C4⋊Q8—41no—
581C4⋊Q8—41no—
582C4⋊Q8—41no—
583C4⋊Q8—41no—
584C4⋊Q8—41no—
585C4⋊Q8—41no—
586C4⋊Q8—41no—
587C4⋊Q8—41no—
588C4⋊Q8—41no—
589C4⋊Q8—44no—
590#126—44no—
591#125—41no—
592#125—41no—
593#125—44no—
594#124—82no—
595#123—44no—
596#123—82no—
597C22⋊Q8—22no—
598C22⋊Q8—22no—
599C22⋊Q8—22no—
600C22⋊Q8—22no—
601C22⋊Q8—44no—
602C22⋊Q8—44no—
603C22⋊Q8—41no—
604C22⋊Q8—41no—
605C22⋊Q8—41no—
606C22⋊Q8—41no—
607C22⋊Q8—82no—
608#121—22no—
609#121—41no—
610#121—41no—
611#121—41no—
612#120—82no—
613C4×Q8—41no—
614C4×Q8—41no—
615C4×Q8—41no—
616C4×Q8—41no—
617C4×D4—22no—
618C4×D4—22no—
619C4×D4—22no—
620C4×D4—41no—
621C4×D4—41no—
622C4×D4—41no—
623C4×D4—44no—
624C4×D4—82no—
625#117—22no—
626#117—22no—
627#117—22no—
628#117—22no—
629#117—41no—
630#117—41no—
631#117—44no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—21no—
634C2×C4⋊C4—21no—
635C2×C4⋊C4—21no—
636C2×C4⋊C4—21no—
637C2×C4⋊C4—21no—
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—21no—
642C2×C4⋊C4—21no—
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—41no—
659C2×C4⋊C4—41no—
660C2×C4⋊C4C2×D411yescharacteristic
661C2×C4⋊C4C2×D411yescharacteristic
662C2×C4⋊C4C2×D411yescharacteristic
663C2×C4⋊C4C2×D411yescharacteristic
664C2×C4⋊C4C2×D411yescharacteristic
665C2×C4⋊C4C2411yescharacteristic
666C2×C4⋊C4C2411yescharacteristic
667C2×C4⋊C4C2411yescharacteristic
668C2×C4⋊C4C2411yescharacteristic
669C2×C4⋊C4C2411yescharacteristic
670C2×C4⋊C4C2411yescharacteristic
671C2×C4⋊C4C2411yescharacteristic
672C2×C4⋊C4C2411yescharacteristic
673C2×C4⋊C4C2411yescharacteristic
674C2×C4⋊C4C2411yescharacteristic
675C2×C22⋊C4—21no—
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4—21no—
686C2×C22⋊C4—21no—
687C2×C22⋊C4—21no—
688C2×C22⋊C4—21no—
689C2×C22⋊C4—21no—
690C2×C22⋊C4—21no—
691C2×C22⋊C4—21no—
692C2×C22⋊C4—21no—
693C2×C22⋊C4—21no—
694C2×C22⋊C4—21no—
695C2×C22⋊C4—21no—
696C2×C22⋊C4—21no—
697C2×C22⋊C4—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—82no—
706C2×C22⋊C4C2×D411yescharacteristic
707C2×C22⋊C4C2×D411yescharacteristic
708C2×C22⋊C4C2×D411yescharacteristic
709C2×C22⋊C4C2×D411yescharacteristic
710C2×C22⋊C4C2×D411yescharacteristic
711C2×C22⋊C4C2×D411yescharacteristic
712C2×C22⋊C4C2×D411yescharacteristic
713C2×C22⋊C4C2×D411yescharacteristic
714C2×C42—21no—
715C2×C42—21no—
716C2×C42—21no—
717C2×C42—21no—
718C2×C42—21no—
719C2×C42—21no—
720C2×C42—41no—
721C2×C42—41no—
722C2×C42C2×D411yescharacteristic
723C2×C42C2×D411yescharacteristic
724C2×C42C2411yescharacteristic
725C2×C42C2411yescharacteristic
726C2×C42C2411yescharacteristic
727C2×C42C2411yescharacteristic
728C2×C42C2411yescharacteristic
729#107—41no—
730#107—41no—
731#107—41no—
732#107—41no—
733#106—41no—
734#106—41no—
735#106—41no—
736#106—41no—
737C4⋊C8—22no—
738C4⋊C8—22no—
739C4⋊C8—41no—
740C4⋊C8—41no—
741#103—22no—
742#103—22no—
743#103—22no—
744#103—22no—
745#103—22no—
746#103—22no—
747#103—41no—
748#103—41no—
749#103—41no—
750#103—41no—
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#103—41no—
764#103—41no—
765#102—41no—
766#102—41no—
767#102—41no—
768#102—41no—
769#102—41no—
770#102—41no—
771#102—41no—
772#102—41no—
773C22⋊C8—22no—
774C22⋊C8—22no—
775C22⋊C8—22no—
776C22⋊C8—22no—
777C22⋊C8—41no—
778C22⋊C8—41no—
779#97—41no—
780#97—41no—
781#97—41no—
782C4×C8—22no—
783C4×C8—22no—
784C4×C8—41no—
785#95—21no—
786#95—21no—
787#95—21no—
788#95—21no—
789#95—21no—
790#95—21no—
791#95—21no—
792#95—21no—
793#95—21no—
794#95—21no—
795#95—21no—
796#95—21no—
797#95—21no—
798#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#95—21no—
822#95—21no—
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—42no—
836C24—42no—
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×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—42no—
869C2×Q8—42no—
870C2×Q8—44no—
871C2×Q8—44no—
872C2×Q8—42no—
873C2×Q8—81no—
874C2×Q8—81no—
875C2×Q8—81no—
876C2×Q8—81no—
877C2×Q8—81no—
878C2×Q8—82no—
879C2×Q8—82no—
880C2×Q8—82no—
881C2×Q8—82no—
882C2×Q8—82no—
883C2×Q8—82no—
884C2×Q8C2×#4112yes—
885C2×D4—22no—
886C2×D4—22no—
887C2×D4—21no—
888C2×D4—21no—
889C2×D4—21no—
890C2×D4—21no—
891C2×D4—21no—
892C2×D4—21no—
893C2×D4—21no—
894C2×D4—21no—
895C2×D4—21no—
896C2×D4—21no—
897C2×D4—21no—
898C2×D4—44no—
899C2×D4—44no—
900C2×D4—41no—
901C2×D4—42no—
902C2×D4—42no—
903C2×D4—42no—
904C2×D4—42no—
905C2×D4—42no—
906C2×D4—82no—
907C2×D4—82no—
908C2×D4—81no—
909C2×D4—81no—
910C2×D4—81no—
911C2×D4—81no—
912C2×D4C2×#4112yes—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—22no—
918C22×C4—21no—
919C22×C4—22no—
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—21no—
936C22×C4—21no—
937C22×C4—21no—
938C22×C4—21no—
939C22×C4—41no—
940C22×C4—41no—
941C22×C4—41no—
942C22×C4—41no—
943C22×C4—42no—
944C22×C4—42no—
945C22×C4—42no—
946C22×C4—42no—
947C22×C4—42no—
948C22×C4—42no—
949C22×C4—42no—
950C22×C4—42no—
951C22×C4—42no—
952C22×C4—81no—
953C22×C4—81no—
954C22×C4—81no—
955C22×C4—81no—
956C22×C4—81no—
957C22×C4—81no—
958C22×C4C22×D411yescharacteristic
959C22×C4C22×D411yescharacteristic
960C22×C4C22×D411yescharacteristic
961C22×C4C22×D411yescharacteristic
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×C4H(5,𝔽2)12yes—
971C22×C4H(5,𝔽2)12yes—
972C22×C4C2511yescharacteristic
973SD16—44no—
974SD16—44no—
975SD16—44no—
976SD16—44no—
977SD16—82no—
978SD16—82no—
979SD16—82no—
980SD16—82no—
981M16—44no—
982C2×C8—28no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8—21no—
989C2×C8—21no—
990C2×C8—21no—
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×C8C2×#4112yes—
1006C2×C8H(5,𝔽2)12yes—
1007C4⋊C4—22no—
1008C4⋊C4—22no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—21no—
1014C4⋊C4—21no—
1015C4⋊C4—21no—
1016C4⋊C4—21no—
1017C4⋊C4—21no—
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—41no—
1030C4⋊C4—41no—
1031C4⋊C4—41no—
1032C4⋊C4—42no—
1033C4⋊C4—42no—
1034C4⋊C4—42no—
1035C4⋊C4—42no—
1036C4⋊C4—42no—
1037C4⋊C4—42no—
1038C4⋊C4—42no—
1039C4⋊C4—42no—
1040C4⋊C4—42no—
1041C4⋊C4—42no—
1042C4⋊C4—42no—
1043C4⋊C4—42no—
1044C4⋊C4—42no—
1045C4⋊C4—42no—
1046C4⋊C4—42no—
1047C4⋊C4—42no—
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—
1058C22⋊C4—22no—
1059C22⋊C4—22no—
1060C22⋊C4—22no—
1061C22⋊C4—22no—
1062C22⋊C4—41no—
1063C22⋊C4—41no—
1064C22⋊C4—41no—
1065C22⋊C4—41no—
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—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C22⋊C4—81no—
1084C22⋊C4—81no—
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—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—21no—
1100C42—21no—
1101C42—21no—
1102C42—21no—
1103C42—21no—
1104C42—21no—
1105C42—21no—
1106C42—41no—
1107C42—41no—
1108C42—42no—
1109C42—42no—
1110C42—42no—
1111C42—42no—
1112C42—81no—
1113C42—81no—
1114C23—21no—
1115C23—21no—
1116C23—21no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—21no—
1121C23—21no—
1122C23—21no—
1123C23—21no—
1124C23—21no—
1125C23—21no—
1126C23—22no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—41no—
1139C23—41no—
1140C23—84no—
1141C23—84no—
1142C23—162no—
1143C23—162no—
1144C23—162no—
1145C23—162no—
1146C23—162no—
1147C23#53512yes—
1148C23#57712yes—
1149C23C23×D411yescharacteristic
1150Q8—22no—
1151Q8—22no—
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—41no—
1161Q8—41no—
1162Q8—41no—
1163Q8—41no—
1164Q8—41no—
1165Q8—41no—
1166Q8—84no—
1167Q8—84no—
1168Q8—162no—
1169D4—22no—
1170D4—22no—
1171D4—44no—
1172D4—41no—
1173D4—41no—
1174D4—41no—
1175D4—41no—
1176D4—41no—
1177D4—41no—
1178D4—84no—
1179D4—84no—
1180D4—162no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—22no—
1186C2×C4—22no—
1187C2×C4—22no—
1188C2×C4—22no—
1189C2×C4—21no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—21no—
1196C2×C4—21no—
1197C2×C4—21no—
1198C2×C4—21no—
1199C2×C4—21no—
1200C2×C4—21no—
1201C2×C4—21no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—22no—
1206C2×C4—21no—
1207C2×C4—21no—
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—44no—
1221C2×C4—41no—
1222C2×C4—41no—
1223C2×C4—41no—
1224C2×C4—41no—
1225C2×C4—41no—
1226C2×C4—41no—
1227C2×C4—41no—
1228C2×C4—41no—
1229C2×C4—41no—
1230C2×C4—41no—
1231C2×C4—41no—
1232C2×C4—41no—
1233C2×C4—41no—
1234C2×C4—41no—
1235C2×C4—41no—
1236C2×C4—41no—
1237C2×C4—41no—
1238C2×C4—41no—
1239C2×C4—41no—
1240C2×C4—41no—
1241C2×C4—41no—
1242C2×C4—41no—
1243C2×C4—41no—
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—82no—
1267C2×C4—84no—
1268C2×C4—84no—
1269C2×C4—84no—
1270C2×C4—162no—
1271C2×C4—162no—
1272C2×C4#53512yes—
1273C2×C4#57712yes—
1274C2×C4C22×#4111yescharacteristic
1275C2×C4C2×H(5,𝔽2)11yescharacteristic
1276C2×C4C2×H(5,𝔽2)11yescharacteristic
1277C2×C4C2×H(5,𝔽2)11yescharacteristic
1278C2×C4#58511yescharacteristic
1279C2×C4#58511yescharacteristic
1280C8—22no—
1281C8—22no—
1282C8—41no—
1283C8—41no—
1284C8—41no—
1285C8—41no—
1286C8—41no—
1287C8—41no—
1288C22—22no—
1289C22—22no—
1290C22—22no—
1291C22—22no—
1292C22—22no—
1293C22—22no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—42no—
1303C22—42no—
1304C22—42no—
1305C22—81no—
1306C22—81no—
1307C22—81no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—168no—
1317C22C2×#53511yescharacteristic
1318C22D4×#4111yescharacteristic
1319C22#349611yescharacteristic
1320C22C2×#57711yescharacteristic
1321C22C2×#57711yescharacteristic
1322C22#358611yescharacteristic
1323C22#358611yescharacteristic
1324C4—22no—
1325C4—22no—
1326C4—41no—
1327C4—42no—
1328C4—41no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—41no—
1333C4—41no—
1334C4—41no—
1335C4—41no—
1336C4—41no—
1337C4—81no—
1338C4—81no—
1339C4—81no—
1340C4—81no—
1341C4—81no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4#349011yescharacteristic
1351C4#351311yescharacteristic
1352C4#354211yescharacteristic
1353C4#354511yescharacteristic
1354C2—42no—
1355C2—42no—
1356C2—82no—
1357C2—161no—
1358C2#3842011yescharacteristic
1359C2#6081311yescharacteristic
1360C2#6083611yescharacteristic
1361C2#6152011yescharacteristic
1362C2#6154011yescharacteristic
1363C2#6226811yescharacteristic
1364C2#6228711yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#2408C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2290 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #38081C2semidirect
3. #33046C2semidirect
4. #32436C2semidirect
5. #32182C2semidirect
6. #32064C2semidirect
7. #31941C2semidirect
8. #31546C2semidirect
9. #31002C2semidirect
10. #30878C2semidirect
11. #30522C2semidirect
12. #30355C2semidirect
13. #30325C2semidirect
14. #29568C2semidirect
15. #29508C2semidirect
16. #29118C2semidirect
17. #28320C2semidirect
18. #24651C2semidirect
19. #24584C2semidirect
20. #24538C2semidirect
21. #24503C2semidirect
22. #24496C2semidirect
23. #24358C2semidirect
24. #24099C2semidirect
25. #24053C2semidirect
28. #22162C2semidirect
29. #22047C2semidirect
30. #21231C2semidirect
31. #21109C2semidirect
35. C2×#487C22semidirect
44. C2×#431C22semidirect
49. #2857C22semidirect
60. #2642C22semidirect
64. #2565C22semidirect
66. #2546C22semidirect
68. #2503C22semidirect
77. #2434C22semidirect
85. #2327C22semidirect
90. C2×#391C22semidirect
94. #2085C22semidirect
95. #2083C22semidirect
96. #2074C22semidirect
97. #2074C22semidirect
100. #2068C22semidirect
101. #2066C22semidirect
102. #2066C22semidirect
103. #2066C22semidirect
104. #2059C22semidirect
105. #2059C22semidirect
110. #2043C22semidirect
111. #2043C22semidirect
112. #2043C22semidirect
113. #2043C22semidirect
114. #2036C22semidirect
115. #2036C22semidirect
116. #2035C22semidirect
117. #2035C22semidirect
120. #2024C22semidirect
121. #2024C22semidirect
132. #1993C22semidirect
133. #1981C22semidirect
134. #1981C22semidirect
147. #1960C22semidirect
148. #1949C22semidirect
149. #1948C22semidirect
150. #1935C22semidirect
151. #1935C22semidirect
152. #1935C22semidirect
153. #1935C22semidirect
154. #1933C22semidirect
155. #1933C22semidirect
156. #1933C22semidirect
157. #1933C22semidirect
158. #1928C22semidirect
159. #1928C22semidirect
160. #1928C22semidirect
161. #1927C22semidirect
162. #1924C22semidirect
163. #1923C22semidirect
164. #1917C22semidirect
165. #1916C22semidirect
182. #1865C22semidirect
183. #1865C22semidirect
184. #1863C22semidirect
185. #1863C22semidirect
186. #1853C22semidirect
187. #1852C22semidirect
190. #1835C22semidirect
197. #1787C22semidirect
198. #1787C22semidirect
199. #1768C22semidirect
201. #1749C22semidirect
202. #1746C22semidirect

Maximal subgroups

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

subgroupindex
#390422
#380812
#330462
#324362
#321822
#320642
#319412
#315462
#310022
#308782
#305222
#303552
#303252
#295682
#295082
#291182
#283202
#246512
#245842
#245382
#245032
#244962
#243582
#240992
#240532
#239822
#238552
#221622
#220472
#212312
#211092