Finite Group Databasebeta

← #7589229

Subgroups — #7589229

Order 512.

1730 conjugacy classes of subgroups.

The subgroup lattice has 1370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45225C211yesmaximal, characteristic, complemented
2#35713C211yesmaximal, characteristic
3#32462C211yesmaximal, characteristic, complemented
4#32073C211yesmaximal, characteristic, complemented
5#32063C211yesmaximal, characteristic, complemented
6#32044C211yesmaximal, characteristic, complemented
7#29491C211yesmaximal, characteristic, complemented
8#29490C211yesmaximal, characteristic, complemented
9#28996C211yesmaximal, characteristic, complemented
10#28995C211yesmaximal, characteristic, complemented
11#27245C211yesmaximal, characteristic, complemented
12#27245C211yesmaximal, characteristic, complemented
13#27238C211yesmaximal, characteristic, complemented
14#27238C211yesmaximal, characteristic, complemented
15#26697C211yesmaximal, characteristic, complemented
16#26692C211yesmaximal, characteristic, complemented
17#26569C211yesmaximal, characteristic, complemented
18#26568C211yesmaximal, characteristic, complemented
19#26260C211yesmaximal, characteristic, complemented
20#26260C211yesmaximal, characteristic, complemented
21#26170C211yesmaximal, characteristic, complemented
22#26166C211yesmaximal, characteristic, complemented
23#25753C211yesmaximal, characteristic
24#24044C211yesmaximal, characteristic
25#23303C211yesmaximal, characteristic, complemented
26#22979C211yesmaximal, characteristic, complemented
27#22974C211yesmaximal, characteristic, complemented
28#22884C211yesmaximal, characteristic, complemented
29#22884C211yesmaximal, characteristic, complemented
30#21459C211yesmaximal, characteristic, complemented
31#21459C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×#492C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#478C2211yescharacteristic
37C2×#474C2211yescharacteristic
38C2×#461C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#450C2211yescharacteristic
41C2×#450C2211yescharacteristic
42C2×#450C2211yescharacteristic
43C2×#440C2211yescharacteristic, complemented
44C2×#440C2211yescharacteristic, complemented
45C2×C4×SD16C2211yescharacteristic
46C2×C4×SD16C2211yescharacteristic
47C2×#418C2211yescharacteristic
48#2808—21no—
49#2798—21no—
50#2773—21no—
51#2754—21no—
52#2624C2211yescharacteristic
53#2622—21no—
54#2596—21no—
55#2593—21no—
56#2570—21no—
57#2542C2211yescharacteristic
58#2511—21no—
59#2500C2211yescharacteristic
60#2492C2211yescharacteristic, complemented
61#2492C2211yescharacteristic, complemented
62#2489C2211yescharacteristic, complemented
63#2489C2211yescharacteristic, complemented
64#2485C2211yescharacteristic
65#2485C2211yescharacteristic
66#2446C2211yescharacteristic, complemented
67#2446C2211yescharacteristic, complemented
68#2445C2211yescharacteristic
69#2445C2211yescharacteristic
70#2444—21no—
71#2443—21no—
72#2422C2211yescharacteristic
73#2420C2211yescharacteristic
74#2418—21no—
75#2418—21no—
76#2412—21no—
77#2405—21no—
78#2395C2211yescharacteristic
79C2×#394—21no—
80#2370C2211yescharacteristic, complemented
81#2369C2211yescharacteristic, complemented
82#2362C2211yescharacteristic, complemented
83#2362C2211yescharacteristic, complemented
84#2349C2211yescharacteristic
85D4×C4⋊C4C2211yescharacteristic
86D4×C22⋊C4C2211yescharacteristic
87D4×C22⋊C4C2211yescharacteristic
88D4×C22⋊C4C2211yescharacteristic
89#2323C2211yescharacteristic, complemented
90#2323C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2096C2211yescharacteristic, complemented
93#2088C2211yescharacteristic, complemented
94#2088C2211yescharacteristic, complemented
95#2076C2211yescharacteristic, complemented
96#2076C2211yescharacteristic, complemented
97#2075C2211yescharacteristic, complemented
98#2075C2211yescharacteristic, complemented
99#2074C2211yescharacteristic, complemented
100#2072C2211yescharacteristic, complemented
101#2055C2211yescharacteristic, complemented
102#2055C2211yescharacteristic, complemented
103#2055C2211yescharacteristic, complemented
104#2055C2211yescharacteristic, complemented
105#2043C2211yescharacteristic, complemented
106#2043C2211yescharacteristic, complemented
107#2041C2211yescharacteristic
108#2041C2211yescharacteristic
109#2036C2211yescharacteristic, complemented
110#2036C2211yescharacteristic, complemented
111#2035C2211yescharacteristic, complemented
112#2035C2211yescharacteristic, complemented
113#2034C2211yescharacteristic
114#2033C2211yescharacteristic
115#2025C2211yescharacteristic, complemented
116#2025C2211yescharacteristic, complemented
117#2023C2211yescharacteristic, complemented
118#2023C2211yescharacteristic, complemented
119#2000C2211yescharacteristic
120#2000C2211yescharacteristic
121#2000C2211yescharacteristic
122#2000C2211yescharacteristic
123#1993C2211yescharacteristic, complemented
124#1992C2211yescharacteristic, complemented
125#1982C2211yescharacteristic
126#1973C2211yescharacteristic, complemented
127#1973C2211yescharacteristic, complemented
128#1973C2211yescharacteristic, complemented
129#1973C2211yescharacteristic, complemented
130#1973C2211yescharacteristic, complemented
131#1973C2211yescharacteristic, complemented
132#1954C2211yescharacteristic
133#1949C2211yescharacteristic, complemented
134#1947C2211yescharacteristic, complemented
135#1944C2211yescharacteristic, complemented
136#1943C2211yescharacteristic, complemented
137#1942C2211yescharacteristic, complemented
138#1942C2211yescharacteristic, complemented
139#1934C2211yescharacteristic, complemented
140#1934C2211yescharacteristic, complemented
141#1933C2211yescharacteristic, complemented
142#1933C2211yescharacteristic, complemented
143#1926C2211yescharacteristic, complemented
144#1926C2211yescharacteristic, complemented
145#1926C2211yescharacteristic, complemented
146#1926C2211yescharacteristic, complemented
147#1925C2211yescharacteristic, complemented
148#1925C2211yescharacteristic, complemented
149#1924C2211yescharacteristic, complemented
150#1924C2211yescharacteristic, complemented
151#1924C2211yescharacteristic, complemented
152#1924C2211yescharacteristic, complemented
153#1921C2211yescharacteristic, complemented
154#1921C2211yescharacteristic, complemented
155#1919C2211yescharacteristic, complemented
156#1918C2211yescharacteristic, complemented
157#1916C2211yescharacteristic, complemented
158#1916C2211yescharacteristic, complemented
159#1895C2211yescharacteristic
160#1894C2211yescharacteristic, complemented
161#1894C2211yescharacteristic, complemented
162#1880C2211yescharacteristic, complemented
163#1880C2211yescharacteristic, complemented
164#1877C2211yescharacteristic
165#1877C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1877C2211yescharacteristic
169#1877C2211yescharacteristic
170#1877C2211yescharacteristic, complemented
171#1877C2211yescharacteristic, complemented
172#1873C2211yescharacteristic, complemented
173#1873C2211yescharacteristic, complemented
174#1870C2211yescharacteristic
175#1865C2211yescharacteristic, complemented
176#1864C2211yescharacteristic
177#1864C2211yescharacteristic, complemented
178#1864C2211yescharacteristic, complemented
179#1863C2211yescharacteristic, complemented
180#1862C2211yescharacteristic
181#1862C2211yescharacteristic
182#1862C2211yescharacteristic
183#1854C2211yescharacteristic, complemented
184#1854C2211yescharacteristic, complemented
185#1854C2211yescharacteristic, complemented
186#1854C2211yescharacteristic, complemented
187#1786C2211yescharacteristic
188#1786C2211yescharacteristic
189#1786C2211yescharacteristic
190#1771C2211yescharacteristic, complemented
191#1771C2211yescharacteristic, complemented
192#1762C2211yescharacteristic
193#1762C2211yescharacteristic
194#1762C2211yescharacteristic
195#1762C2211yescharacteristic
196C4×#102C2211yescharacteristic
197C4×#102C2211yescharacteristic, complemented
198C4×#102C2211yescharacteristic, complemented
199#1753C2211yescharacteristic, complemented
200#1753C2211yescharacteristic, complemented
201#1750C2211yescharacteristic, complemented
202#1750C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C22×SD16C2311yescharacteristic
210C22×SD16C2311yescharacteristic
211C22×SD16C2311yescharacteristic
212C22×M16C2311yescharacteristic
213D42—42no—
214D42—42no—
215C2×C4⋊Q8C2311yescharacteristic
216C2×C4⋊Q8C2311yescharacteristic
217C2×#127C2311yescharacteristic
218C2×#125C2311yescharacteristic
219C2×#123—21no—
220C2×#123—21no—
221C2×#123—21no—
222C2×C22⋊Q8C2311yescharacteristic
223C2×C22⋊Q8C2311yescharacteristic
224C2×C22⋊Q8C2311yescharacteristic
225C2×C22⋊Q8C2311yescharacteristic
226C2×#121—21no—
227C2×#121C2311yescharacteristic
228C2×#121C2311yescharacteristic
229C2×#120—21no—
230C2×#120—21no—
231#518—42no—
232#518—42no—
233C2×C4×Q8C2311yescharacteristic
234C2×C4×Q8C2311yescharacteristic
235C2×C4×D4—21no—
236C2×C4×D4—21no—
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×C4×D4C2311yescharacteristic
240C2×C4×D4C2311yescharacteristic
241C2×C4×D4C2311yescharacteristic
242C2×C4×D4C2311yescharacteristic
243C2×C4×D4C2311yescharacteristic
244C2×C4×D4C2311yescharacteristic
245C2×#117C2311yescharacteristic
246C2×#117C2311yescharacteristic
247C2×#117C2311yescharacteristic
248C22×C4⋊C4—21no—
249C22×C22⋊C4—21no—
250C22×C22⋊C4—21no—
251C22×C22⋊C4—21no—
252C22×C22⋊C4—21no—
253C22×C22⋊C4—21no—
254#492—42no—
255#482—42no—
256#478—24no—
257#474—24no—
258#461—42no—
259#450—24no—
260#450—24no—
261#450—24no—
262#450—24no—
263#440—42no—
264#440—42no—
265C4×SD16—42no—
266C4×SD16—42no—
267C2×#107C2311yescharacteristic
268C2×#107C2311yescharacteristic
269C2×#107C2311yescharacteristic
270C2×#107C2311yescharacteristic
271C2×#107C2311yescharacteristic
272C2×#107C2311yescharacteristic
273C2×#106C2311yescharacteristic
274C2×#106C2311yescharacteristic
275C2×#106C2311yescharacteristic
276C2×#106C2311yescharacteristic
277C2×C4⋊C8C2311yescharacteristic
278C2×C4⋊C8C2311yescharacteristic
279C2×C4⋊C8C2311yescharacteristic
280#418—42no—
281C2×#103C2311yescharacteristic
282C2×#103C2311yescharacteristic
283C2×#103C2311yescharacteristic
284C2×#103C2311yescharacteristic
285C2×#103C2311yescharacteristic
286C2×#103C2311yescharacteristic
287C2×#103C2311yescharacteristic
288C2×#103C2311yescharacteristic
289C2×#103C2311yescharacteristic
290C2×#103C2311yescharacteristic
291C2×#102C2311yescharacteristic
292C2×#102C2311yescharacteristic
293C2×#102C2311yescharacteristic
294C2×#102C2311yescharacteristic
295C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
310C2×C22⋊C8C2311yescharacteristic
311C2×C22⋊C8C2311yescharacteristic
312C2×C22⋊C8C2311yescharacteristic
313C2×C22⋊C8C2311yescharacteristic
314C2×C22⋊C8C2311yescharacteristic
315C2×C22⋊C8C2311yescharacteristic
316C2×#97C2311yescharacteristic
317C2×#97C2311yescharacteristic
318C2×#97C2311yescharacteristic
319C2×#97C2311yescharacteristic
320C2×C4×C8C2311yescharacteristic
321C2×C4×C8C2311yescharacteristic
322C2×C4×C8C2311yescharacteristic
323#400—21no—
324#400—21no—
325#400—21no—
326#400—21no—
327#400—21no—
328#400—21no—
329#400D411yescharacteristic
330#399—21no—
331#399—21no—
332#399—21no—
333#399D411yescharacteristic
334#398—21no—
335#398—21no—
336#398D411yescharacteristic
337#397—21no—
338#397—21no—
339#397—21no—
340#397—21no—
341#397—21no—
342#397—21no—
343#397—21no—
344#397D411yescharacteristic
345#397D411yescharacteristic
346#397D411yescharacteristic
347#394—21no—
348#394—21no—
349#394—21no—
350#394—21no—
351#394—21no—
352#394—21no—
353#394—21no—
354#394—21no—
355#394—21no—
356#394—21no—
357#394—21no—
358#394—21no—
359#394D411yescharacteristic
360#394D411yescharacteristic
361#393—21no—
362#393—21no—
363#391—21no—
364#391—21no—
365#391—21no—
366#391—21no—
367#391C2311yescharacteristic
368#391C2311yescharacteristic
369#391C2311yescharacteristic
370#391C2311yescharacteristic
371#391C2311yescharacteristic
372#391C2311yescharacteristic
373#390—21no—
374#390C2311yescharacteristic
375#390C2311yescharacteristic
376#390C2311yescharacteristic
377#390C2311yescharacteristic
378#390C2311yescharacteristic
379#390C2311yescharacteristic
380#389—21no—
381#389—21no—
382#389—21no—
383#389—21no—
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#389C2311yescharacteristic
390#389C2311yescharacteristic
391#389C2311yescharacteristic
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#388—21no—
401#388—21no—
402#388—21no—
403#388—21no—
404#388—21no—
405#388—21no—
406#388—21no—
407#388—21no—
408#387—21no—
409#387—21no—
410#387—21no—
411#387—21no—
412#387—21no—
413#387—21no—
414#387—21no—
415#387—21no—
416#387—21no—
417#387—21no—
418#387—21no—
419#387—21no—
420#386—21no—
421#386—21no—
422#386—21no—
423#386—21no—
424#386—21no—
425#386—21no—
426#386—21no—
427#386—21no—
428#386—21no—
429#385—21no—
430#385—21no—
431#385—21no—
432#385—21no—
433#385—21no—
434#384—21no—
435#384C2311yescharacteristic
436#382—21no—
437#382—21no—
438#382C2311yescharacteristic
439#381—21no—
440#380—21no—
441#380—21no—
442#380C2311yescharacteristic
443#380C2311yescharacteristic
444#380C2311yescharacteristic
445#380C2311yescharacteristic
446#380C2311yescharacteristic
447#380C2311yescharacteristic
448#379—21no—
449#379—21no—
450#379—21no—
451C4×C4⋊C4—21no—
452C4×C4⋊C4—21no—
453C4×C4⋊C4—21no—
454C4×C4⋊C4—21no—
455C4×C4⋊C4C2311yescharacteristic
456C4×C4⋊C4C2311yescharacteristic
457C4×C4⋊C4C2311yescharacteristic
458C4×C4⋊C4C2311yescharacteristic
459C4×C4⋊C4C2311yescharacteristic
460C4×C4⋊C4C2311yescharacteristic
461C4×C4⋊C4C2311yescharacteristic
462C4×C22⋊C4C2311yescharacteristic
463C4×C22⋊C4C2311yescharacteristic
464C4×C22⋊C4C2311yescharacteristic
465C2×#95—21no—
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—
497C25—21no—
498C22×Q8—21no—
499C22×Q8C2411yescharacteristic
500C22×Q8C2411yescharacteristic
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—22no—
504C22×D4—22no—
505C22×D4—22no—
506C22×D4—22no—
507C22×D4—22no—
508C22×D4—21no—
509C22×D4—21no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4—41no—
517C22×D4—41no—
518C22×D4—41no—
519C22×D4—44no—
520C22×D4—82no—
521C22×D4—82no—
522C22×D4C2×D411yescharacteristic
523C22×D4C2411yescharacteristic
524C22×D4C2411yescharacteristic
525C22×D4C2411yescharacteristic
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4—21no—
530C23×C4—21no—
531C23×C4—21no—
532C23×C4—21no—
533C23×C4C2411yescharacteristic
534C23×C4C2411yescharacteristic
535C2×SD16—22no—
536C2×SD16—22no—
537C2×SD16—22no—
538C2×SD16—22no—
539C2×SD16—22no—
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×M16—41no—
554C2×M16—41no—
555C2×M16—41no—
556C22×C8C2411yescharacteristic
557C22×C8C2411yescharacteristic
558C22×C8C2411yescharacteristic
559C22×C8C2411yescharacteristic
560C22×C8C2411yescharacteristic
561C22×C8C2411yescharacteristic
562C22×C8C2411yescharacteristic
563C22×C8C2411yescharacteristic
564C4⋊Q8—22no—
565C4⋊Q8—41no—
566C4⋊Q8—41no—
567C4⋊Q8—41no—
568#127—22no—
569#127—41no—
570#125—22no—
571#125—41no—
572#123—82no—
573#123—82no—
574#123—82no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C22⋊Q8—41no—
580C22⋊Q8—41no—
581C22⋊Q8—41no—
582C22⋊Q8—41no—
583#121—22no—
584#121—41no—
585#121—41no—
586#121—41no—
587#121—44no—
588#120—44no—
589#120—44no—
590C4×Q8—41no—
591C4×Q8—41no—
592C4×Q8—41no—
593C4×Q8—41no—
594C4×D4—22no—
595C4×D4—22no—
596C4×D4—22no—
597C4×D4—22no—
598C4×D4—22no—
599C4×D4—22no—
600C4×D4—22no—
601C4×D4—41no—
602C4×D4—41no—
603C4×D4—41no—
604C4×D4—41no—
605C4×D4—41no—
606C4×D4—41no—
607C4×D4—41no—
608C4×D4—41no—
609C4×D4—41no—
610C4×D4—44no—
611C4×D4—44no—
612#117—41no—
613#117—41no—
614#117—41no—
615#117—41no—
616#117—41no—
617#117—41no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4—21no—
623C2×C4⋊C4—21no—
624C2×C4⋊C4—21no—
625C2×C4⋊C4—21no—
626C2×C4⋊C4—21no—
627C2×C4⋊C4—21no—
628C2×C4⋊C4—21no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
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—82no—
640C2×C4⋊C4C2×D411yescharacteristic
641C2×C4⋊C4C2×D411yescharacteristic
642C2×C4⋊C4C2×D411yescharacteristic
643C2×C4⋊C4C2×D411yescharacteristic
644C2×C4⋊C4C2×D411yescharacteristic
645C2×C4⋊C4C2×D411yescharacteristic
646C2×C4⋊C4C2×D411yescharacteristic
647C2×C4⋊C4C2411yescharacteristic
648C2×C4⋊C4C2411yescharacteristic
649C2×C4⋊C4C2411yescharacteristic
650C2×C4⋊C4C2411yescharacteristic
651C2×C4⋊C4C2411yescharacteristic
652C2×C4⋊C4C2411yescharacteristic
653C2×C4⋊C4C2411yescharacteristic
654C2×C4⋊C4C2411yescharacteristic
655C2×C4⋊C4C2411yescharacteristic
656C2×C4⋊C4C2411yescharacteristic
657C2×C4⋊C4C2411yescharacteristic
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4—21no—
669C2×C22⋊C4—21no—
670C2×C22⋊C4—21no—
671C2×C22⋊C4—21no—
672C2×C22⋊C4—21no—
673C2×C22⋊C4—21no—
674C2×C22⋊C4—21no—
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—44no—
692C2×C22⋊C4—44no—
693C2×C22⋊C4—82no—
694C2×C22⋊C4—82no—
695C2×C22⋊C4—82no—
696C2×C22⋊C4C2×D411yescharacteristic
697C2×C22⋊C4C2×D411yescharacteristic
698C2×C22⋊C4C2×D411yescharacteristic
699C2×C22⋊C4C2×D411yescharacteristic
700C2×C22⋊C4C2×D411yescharacteristic
701C2×C22⋊C4C2×D411yescharacteristic
702C2×C22⋊C4C2×D411yescharacteristic
703C2×C22⋊C4C2×D411yescharacteristic
704C2×C22⋊C4C2×D411yescharacteristic
705C2×C22⋊C4C2×D411yescharacteristic
706C2×C42—21no—
707C2×C42—21no—
708C2×C42—21no—
709C2×C42—21no—
710C2×C42—21no—
711C2×C42—21no—
712C2×C42—21no—
713C2×C42—21no—
714C2×C42—21no—
715C2×C42C2411yescharacteristic
716C2×C42C2411yescharacteristic
717C2×C42C2411yescharacteristic
718C2×C42C2411yescharacteristic
719C2×C42C2411yescharacteristic
720#107—22no—
721#107—22no—
722#107—22no—
723#107—41no—
724#107—41no—
725#107—41no—
726#106—22no—
727#106—41no—
728#106—41no—
729#106—41no—
730C4⋊C8—22no—
731C4⋊C8—22no—
732C4⋊C8—41no—
733#103—41no—
734#103—41no—
735#103—41no—
736#103—41no—
737#103—41no—
738#103—41no—
739#103—41no—
740#103—41no—
741#103—41no—
742#103—41no—
743#102—22no—
744#102—22no—
745#102—22no—
746#102—22no—
747#102—22no—
748#102—22no—
749#102—22no—
750#102—22no—
751#102—22no—
752#102—22no—
753#102—41no—
754#102—41no—
755#102—41no—
756#102—41no—
757#102—41no—
758#102—41no—
759#102#4114yes—
760#102#4114yes—
761C22⋊C8—22no—
762C22⋊C8—22no—
763C22⋊C8—22no—
764C22⋊C8—22no—
765C22⋊C8—41no—
766C22⋊C8—41no—
767C22⋊C8—41no—
768#97—41no—
769#97—41no—
770#97—41no—
771#97—41no—
772C4×C8—41no—
773C4×C8—41no—
774C4×C8—41no—
775#95—21no—
776#95—21no—
777#95—21no—
778#95—21no—
779#95—21no—
780#95—21no—
781#95—21no—
782#95—21no—
783#95—21no—
784#95—21no—
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#95C2×D411yescharacteristic
809#95C2×D411yescharacteristic
810#95C2×D411yescharacteristic
811#95C2×D411yescharacteristic
812#95C2×D411yescharacteristic
813#95C2×D411yescharacteristic
814#95C2×D411yescharacteristic
815#95C2×D411yescharacteristic
816#95C2×D411yescharacteristic
817#95C2×D411yescharacteristic
818C24—21no—
819C24—24no—
820C24—21no—
821C24—21no—
822C24—42no—
823C24—42no—
824C24—42no—
825C24—42no—
826C24—42no—
827C24—42no—
828C24—81no—
829C24—81no—
830C24—81no—
831C24—81no—
832C24—81no—
833C24—81no—
834C24—81no—
835C24C22×D411yescharacteristic
836C24C22×D411yescharacteristic
837C2×Q8—21no—
838C2×Q8—21no—
839C2×Q8—21no—
840C2×Q8—21no—
841C2×Q8—21no—
842C2×Q8—21no—
843C2×Q8—21no—
844C2×Q8—21no—
845C2×Q8—21no—
846C2×Q8—21no—
847C2×Q8—21no—
848C2×Q8—21no—
849C2×Q8—42no—
850C2×Q8—81no—
851C2×Q8—81no—
852C2×D4—24no—
853C2×D4—22no—
854C2×D4—21no—
855C2×D4—21no—
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—41no—
869C2×D4—41no—
870C2×D4—42no—
871C2×D4—42no—
872C2×D4—42no—
873C2×D4—42no—
874C2×D4—42no—
875C2×D4—42no—
876C2×D4—42no—
877C2×D4—44no—
878C2×D4—44no—
879C2×D4—44no—
880C2×D4—44no—
881C2×D4—44no—
882C2×D4—42no—
883C2×D4—42no—
884C2×D4—42no—
885C2×D4—42no—
886C2×D4—81no—
887C2×D4—81no—
888C2×D4—81no—
889C2×D4—82no—
890C2×D4—82no—
891C2×D4—82no—
892C2×D4—81no—
893C2×D4—81no—
894C2×D4—81no—
895C2×D4—816no—
896C2×D4C2×#4112yes—
897C2×D4C2×#4112yes—
898C2×D4H(5,𝔽2)12yes—
899C2×D4H(5,𝔽2)12yes—
900C22×C4—21no—
901C22×C4—21no—
902C22×C4—21no—
903C22×C4—21no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—21no—
907C22×C4—21no—
908C22×C4—21no—
909C22×C4—21no—
910C22×C4—21no—
911C22×C4—21no—
912C22×C4—21no—
913C22×C4—21no—
914C22×C4—21no—
915C22×C4—21no—
916C22×C4—21no—
917C22×C4—21no—
918C22×C4—21no—
919C22×C4—21no—
920C22×C4—21no—
921C22×C4—21no—
922C22×C4—21no—
923C22×C4—21no—
924C22×C4—21no—
925C22×C4—42no—
926C22×C4—42no—
927C22×C4—42no—
928C22×C4—42no—
929C22×C4—42no—
930C22×C4—42no—
931C22×C4—42no—
932C22×C4—42no—
933C22×C4—42no—
934C22×C4—81no—
935C22×C4—81no—
936C22×C4—81no—
937C22×C4—81no—
938C22×C4—81no—
939C22×C4—81no—
940C22×C4—81no—
941C22×C4—81no—
942C22×C4—81no—
943C22×C4—81no—
944C22×C4—81no—
945C22×C4—81no—
946C22×C4C22×D411yescharacteristic
947C22×C4C22×D411yescharacteristic
948C22×C4C22×D411yescharacteristic
949C22×C4C22×D411yescharacteristic
950C22×C4C22×D411yescharacteristic
951C22×C4C22×D411yescharacteristic
952C22×C4C22×D411yescharacteristic
953C22×C4C22×D411yescharacteristic
954C22×C4C22×D411yescharacteristic
955C22×C4C22×D411yescharacteristic
956C22×C4C22×D411yescharacteristic
957C22×C4C22×D411yescharacteristic
958C22×C4C2511yescharacteristic
959SD16—44no—
960SD16—44no—
961SD16—44no—
962SD16—44no—
963SD16—82no—
964SD16—82no—
965M16—82no—
966C2×C8—21no—
967C2×C8—21no—
968C2×C8—21no—
969C2×C8—21no—
970C2×C8—21no—
971C2×C8—21no—
972C2×C8—21no—
973C2×C8—21no—
974C2×C8—21no—
975C2×C8—21no—
976C2×C8—21no—
977C2×C8—21no—
978C2×C8—21no—
979C2×C8—21no—
980C2×C8—21no—
981C2×C8—21no—
982C2×C8—21no—
983C2×C8—21no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—21no—
987C2×C8—21no—
988C2×C8C2×#4112yes—
989C2×C8C2×#4112yes—
990C4⋊C4—22no—
991C4⋊C4—22no—
992C4⋊C4—21no—
993C4⋊C4—21no—
994C4⋊C4—21no—
995C4⋊C4—21no—
996C4⋊C4—21no—
997C4⋊C4—21no—
998C4⋊C4—21no—
999C4⋊C4—21no—
1000C4⋊C4—21no—
1001C4⋊C4—21no—
1002C4⋊C4—21no—
1003C4⋊C4—21no—
1004C4⋊C4—21no—
1005C4⋊C4—21no—
1006C4⋊C4—21no—
1007C4⋊C4—21no—
1008C4⋊C4—21no—
1009C4⋊C4—21no—
1010C4⋊C4—21no—
1011C4⋊C4—21no—
1012C4⋊C4—41no—
1013C4⋊C4—41no—
1014C4⋊C4—41no—
1015C4⋊C4—41no—
1016C4⋊C4—41no—
1017C4⋊C4—42no—
1018C4⋊C4—42no—
1019C4⋊C4—42no—
1020C4⋊C4—42no—
1021C4⋊C4—42no—
1022C4⋊C4—42no—
1023C4⋊C4—42no—
1024C4⋊C4—42no—
1025C4⋊C4—42no—
1026C4⋊C4—81no—
1027C4⋊C4—81no—
1028C4⋊C4—81no—
1029C4⋊C4—81no—
1030C4⋊C4—81no—
1031C4⋊C4—81no—
1032C4⋊C4—81no—
1033C4⋊C4—81no—
1034C4⋊C4—81no—
1035C4⋊C4—81no—
1036C4⋊C4—81no—
1037C4⋊C4—81no—
1038C4⋊C4C2×#4112yes—
1039C4⋊C4C2×#4112yes—
1040C22⋊C4—41no—
1041C22⋊C4—41no—
1042C22⋊C4—41no—
1043C22⋊C4—41no—
1044C22⋊C4—41no—
1045C22⋊C4—41no—
1046C22⋊C4—41no—
1047C22⋊C4—41no—
1048C22⋊C4—41no—
1049C22⋊C4—41no—
1050C22⋊C4—42no—
1051C22⋊C4—42no—
1052C22⋊C4—42no—
1053C22⋊C4—42no—
1054C22⋊C4—42no—
1055C22⋊C4—42no—
1056C22⋊C4—42no—
1057C22⋊C4—42no—
1058C22⋊C4—42no—
1059C22⋊C4—42no—
1060C22⋊C4—42no—
1061C22⋊C4—42no—
1062C22⋊C4—42no—
1063C22⋊C4—42no—
1064C22⋊C4—42no—
1065C22⋊C4—42no—
1066C22⋊C4—42no—
1067C22⋊C4—81no—
1068C22⋊C4—81no—
1069C22⋊C4—81no—
1070C22⋊C4—81no—
1071C22⋊C4—81no—
1072C22⋊C4—81no—
1073C22⋊C4—81no—
1074C22⋊C4—81no—
1075C22⋊C4—81no—
1076C22⋊C4—81no—
1077C22⋊C4—81no—
1078C22⋊C4—81no—
1079C22⋊C4—81no—
1080C22⋊C4—81no—
1081C22⋊C4—81no—
1082C22⋊C4—81no—
1083C42—21no—
1084C42—21no—
1085C42—21no—
1086C42—21no—
1087C42—21no—
1088C42—21no—
1089C42—21no—
1090C42—21no—
1091C42—21no—
1092C42—21no—
1093C42—42no—
1094C42—42no—
1095C42—81no—
1096C42—81no—
1097C42—81no—
1098C42—81no—
1099C42—81no—
1100C42—81no—
1101C42—81no—
1102C23—22no—
1103C23—22no—
1104C23—22no—
1105C23—21no—
1106C23—21no—
1107C23—21no—
1108C23—21no—
1109C23—21no—
1110C23—21no—
1111C23—21no—
1112C23—21no—
1113C23—21no—
1114C23—21no—
1115C23—21no—
1116C23—22no—
1117C23—21no—
1118C23—21no—
1119C23—21no—
1120C23—48no—
1121C23—41no—
1122C23—41no—
1123C23—41no—
1124C23—41no—
1125C23—41no—
1126C23—41no—
1127C23—41no—
1128C23—41no—
1129C23—41no—
1130C23—41no—
1131C23—41no—
1132C23—41no—
1133C23—41no—
1134C23—41no—
1135C23—41no—
1136C23—41no—
1137C23—41no—
1138C23—84no—
1139C23—84no—
1140C23—84no—
1141C23—84no—
1142C23—84no—
1143C23—84no—
1144C23—162no—
1145C23—162no—
1146C23—162no—
1147C23—162no—
1148C23—162no—
1149C23—162no—
1150C23—162no—
1151C23C23×D411yescharacteristic
1152Q8—41no—
1153Q8—41no—
1154Q8—41no—
1155Q8—41no—
1156Q8—41no—
1157Q8—41no—
1158Q8—41no—
1159Q8—41no—
1160Q8—162no—
1161D4—22no—
1162D4—22no—
1163D4—22no—
1164D4—22no—
1165D4—22no—
1166D4—44no—
1167D4—48no—
1168D4—41no—
1169D4—41no—
1170D4—41no—
1171D4—41no—
1172D4—41no—
1173D4—41no—
1174D4—84no—
1175D4—84no—
1176D4—84no—
1177D4—84no—
1178D4—162no—
1179D4#55914yes—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—21no—
1188C2×C4—21no—
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—22no—
1201C2×C4—22no—
1202C2×C4—21no—
1203C2×C4—21no—
1204C2×C4—21no—
1205C2×C4—21no—
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—41no—
1218C2×C4—41no—
1219C2×C4—41no—
1220C2×C4—41no—
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—84no—
1263C2×C4—84no—
1264C2×C4—162no—
1265C2×C4—162no—
1266C2×C4—162no—
1267C2×C4—162no—
1268C2×C4—162no—
1269C2×C4#57712yes—
1270C2×C4C22×#4111yescharacteristic
1271C2×C4C22×#4111yescharacteristic
1272C2×C4C2×H(5,𝔽2)11yescharacteristic
1273C2×C4C2×H(5,𝔽2)11yescharacteristic
1274C2×C4#58511yescharacteristic
1275C2×C4#58511yescharacteristic
1276C8—22no—
1277C8—22no—
1278C8—41no—
1279C8—41no—
1280C8—41no—
1281C8—41no—
1282C8—41no—
1283C8—41no—
1284C22—24no—
1285C22—42no—
1286C22—42no—
1287C22—42no—
1288C22—42no—
1289C22—42no—
1290C22—42no—
1291C22—41no—
1292C22—41no—
1293C22—42no—
1294C22—41no—
1295C22—41no—
1296C22—41no—
1297C22—41no—
1298C22—41no—
1299C22—41no—
1300C22—41no—
1301C22—41no—
1302C22—42no—
1303C22—41no—
1304C22—41no—
1305C22—42no—
1306C22—41no—
1307C22—41no—
1308C22—81no—
1309C22—81no—
1310C22—81no—
1311C22—81no—
1312C22—81no—
1313C22—81no—
1314C22—81no—
1315C22—81no—
1316C22—81no—
1317C22—81no—
1318C22—81no—
1319C22—168no—
1320C22—168no—
1321C22D4×#4111yescharacteristic
1322C22D4×#4111yescharacteristic
1323C22#348411yescharacteristic
1324C22C2×#57711yescharacteristic
1325C22#358511yescharacteristic
1326C22#358511yescharacteristic
1327C22#358611yescharacteristic
1328C4—22no—
1329C4—41no—
1330C4—41no—
1331C4—41no—
1332C4—42no—
1333C4—41no—
1334C4—42no—
1335C4—41no—
1336C4—41no—
1337C4—41no—
1338C4—41no—
1339C4—41no—
1340C4—41no—
1341C4—41no—
1342C4—81no—
1343C4—81no—
1344C4—81no—
1345C4—81no—
1346C4—81no—
1347C4—81no—
1348C4—81no—
1349C4—81no—
1350C4—81no—
1351C4—81no—
1352C4—81no—
1353C4C2×#55911yescharacteristic
1354C4#351311yescharacteristic
1355C4#351311yescharacteristic
1356C4#353311yescharacteristic
1357C2—44no—
1358C2—81no—
1359C2—81no—
1360C2—82no—
1361C2—161no—
1362C2#5918911yescharacteristic
1363C2#6150611yescharacteristic
1364C2#6150911yescharacteristic
1365C2#6154011yescharacteristic
1366C2#6154311yescharacteristic
1367C2#6161011yescharacteristic
1368C2#6167011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC2×D42C22
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. #45225C2semidirect
3. #32462C2semidirect
4. #32073C2semidirect
5. #32063C2semidirect
6. #32044C2semidirect
7. #29491C2semidirect
8. #29490C2semidirect
9. #28996C2semidirect
10. #28995C2semidirect
11. #27245C2semidirect
12. #27245C2semidirect
13. #27238C2semidirect
14. #27238C2semidirect
15. #26697C2semidirect
16. #26692C2semidirect
17. #26569C2semidirect
18. #26568C2semidirect
19. #26260C2semidirect
20. #26260C2semidirect
21. #26170C2semidirect
22. #26166C2semidirect
25. #23303C2semidirect
26. #22979C2semidirect
27. #22974C2semidirect
28. #22884C2semidirect
29. #22884C2semidirect
30. #21459C2semidirect
31. #21459C2semidirect
43. C2×#440C22semidirect
44. C2×#440C22semidirect
60. #2492C22semidirect
61. #2492C22semidirect
62. #2489C22semidirect
63. #2489C22semidirect
66. #2446C22semidirect
67. #2446C22semidirect
80. #2370C22semidirect
81. #2369C22semidirect
82. #2362C22semidirect
83. #2362C22semidirect
89. #2323C22semidirect
90. #2323C22semidirect
91. #2097C22semidirect
92. #2096C22semidirect
93. #2088C22semidirect
94. #2088C22semidirect
95. #2076C22semidirect
96. #2076C22semidirect
97. #2075C22semidirect
98. #2075C22semidirect
99. #2074C22semidirect
100. #2072C22semidirect
101. #2055C22semidirect
102. #2055C22semidirect
103. #2055C22semidirect
104. #2055C22semidirect
105. #2043C22semidirect
106. #2043C22semidirect
109. #2036C22semidirect
110. #2036C22semidirect
111. #2035C22semidirect
112. #2035C22semidirect
115. #2025C22semidirect
116. #2025C22semidirect
117. #2023C22semidirect
118. #2023C22semidirect
123. #1993C22semidirect
124. #1992C22semidirect
126. #1973C22semidirect
127. #1973C22semidirect
128. #1973C22semidirect
129. #1973C22semidirect
130. #1973C22semidirect
131. #1973C22semidirect
133. #1949C22semidirect
134. #1947C22semidirect
135. #1944C22semidirect
136. #1943C22semidirect
137. #1942C22semidirect
138. #1942C22semidirect
139. #1934C22semidirect
140. #1934C22semidirect
141. #1933C22semidirect
142. #1933C22semidirect
143. #1926C22semidirect
144. #1926C22semidirect
145. #1926C22semidirect
146. #1926C22semidirect
147. #1925C22semidirect
148. #1925C22semidirect
149. #1924C22semidirect
150. #1924C22semidirect
151. #1924C22semidirect
152. #1924C22semidirect
153. #1921C22semidirect
154. #1921C22semidirect
155. #1919C22semidirect
156. #1918C22semidirect
157. #1916C22semidirect
158. #1916C22semidirect
160. #1894C22semidirect
161. #1894C22semidirect
162. #1880C22semidirect
163. #1880C22semidirect
170. #1877C22semidirect
171. #1877C22semidirect
172. #1873C22semidirect
173. #1873C22semidirect
175. #1865C22semidirect
177. #1864C22semidirect
178. #1864C22semidirect
179. #1863C22semidirect
183. #1854C22semidirect
184. #1854C22semidirect
185. #1854C22semidirect
186. #1854C22semidirect
190. #1771C22semidirect
191. #1771C22semidirect
197. C4×#102C22semidirect
198. C4×#102C22semidirect
199. #1753C22semidirect
200. #1753C22semidirect
201. #1750C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#452252
#357132
#324622
#320732
#320632
#320442
#294912
#294902
#289962
#289952
#272452
#272382
#266972
#266922
#265692
#265682
#262602
#261702
#261662
#257532
#240442
#233032
#229792
#229742
#228842
#214592