Finite Group Databasebeta

← #6695084

Subgroups — #6695084

Order 512.

1666 conjugacy classes of subgroups.

The subgroup lattice has 1341 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#42827C211yesmaximal, characteristic, complemented
2#35713C211yesmaximal, characteristic
3#32966C211yesmaximal, characteristic, complemented
4#32465C211yesmaximal, characteristic, complemented
5#32309C211yesmaximal, characteristic, complemented
6#32001C211yesmaximal, characteristic, complemented
7#31944C211yesmaximal, characteristic, complemented
8#31598C211yesmaximal, characteristic, complemented
9#31552C211yesmaximal, characteristic, complemented
10#31158C211yesmaximal, characteristic, complemented
11#31094C211yesmaximal, characteristic, complemented
12#30369C211yesmaximal, characteristic, complemented
13#30035C211yesmaximal, characteristic, complemented
14#29028C211yesmaximal, characteristic, complemented
15#28842C211yesmaximal, characteristic, complemented
16#27534C211yesmaximal, characteristic, complemented
17#27523C211yesmaximal, characteristic, complemented
18#27312C211yesmaximal, characteristic, complemented
19#26567C211yesmaximal, characteristic, complemented
20#26386C211yesmaximal, characteristic, complemented
21#26175C211yesmaximal, characteristic, complemented
22#26117C211yesmaximal, characteristic, complemented
23#25960C211yesmaximal, characteristic, complemented
24#24921C211yesmaximal, characteristic, complemented
25#24917C211yesmaximal, characteristic, complemented
26#24252C211yesmaximal, characteristic
27#24033C211yesmaximal, characteristic
28#22874C211yesmaximal, characteristic, complemented
29#22677C211yesmaximal, characteristic, complemented
30#22362C211yesmaximal, characteristic, complemented
31#21459C211yesmaximal, characteristic, complemented
32C2×D42C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×#481C2211yescharacteristic
35C2×#478C2211yescharacteristic
36C2×#478C2211yescharacteristic, complemented
37C2×#460C2211yescharacteristic
38C2×#450C2211yescharacteristic
39C2×#450C2211yescharacteristic
40C2×#440C2211yescharacteristic
41C2×#440C2211yescharacteristic
42C2×#440C2211yescharacteristic, complemented
43C2×C4×SD16C2211yescharacteristic
44C22×#102C2211yescharacteristic
45#2839—21no—
46#2807—21no—
47#2781—21no—
48#2777—21no—
49#2769—21no—
50#2654—21no—
51#2649—21no—
52#2629C2211yescharacteristic, complemented
53#2624C2211yescharacteristic
54#2622—21no—
55#2577—21no—
56#2570C2211yescharacteristic, complemented
57#2536C2211yescharacteristic
58#2509C2211yescharacteristic, complemented
59#2500C2211yescharacteristic
60#2495C2211yescharacteristic, complemented
61#2495C2211yescharacteristic, complemented
62#2487C2211yescharacteristic
63#2485C2211yescharacteristic
64#2453C2211yescharacteristic, complemented
65#2445C2211yescharacteristic
66#2445C2211yescharacteristic
67#2444—21no—
68#2443—21no—
69#2442C2211yescharacteristic, complemented
70#2423C2211yescharacteristic, complemented
71#2422C2211yescharacteristic
72#2421C2211yescharacteristic, complemented
73#2420C2211yescharacteristic
74#2418—21no—
75#2418—21no—
76#2412—21no—
77#2405—21no—
78#2395C2211yescharacteristic
79C2×#394—21no—
80#2360C2211yescharacteristic, complemented
81#2351C2211yescharacteristic, complemented
82#2349C2211yescharacteristic
83D4×C4⋊C4C2211yescharacteristic
84D4×C22⋊C4C2211yescharacteristic
85D4×C22⋊C4C2211yescharacteristic
86D4×C22⋊C4C2211yescharacteristic
87#2323C2211yescharacteristic, complemented
88#2101C2211yescharacteristic, complemented
89#2100C2211yescharacteristic, complemented
90#2099C2211yescharacteristic, complemented
91#2097C2211yescharacteristic, complemented
92#2093C2211yescharacteristic, complemented
93#2092C2211yescharacteristic, complemented
94#2092C2211yescharacteristic, complemented
95#2088C2211yescharacteristic, complemented
96#2088C2211yescharacteristic, complemented
97#2086C2211yescharacteristic, complemented
98#2085C2211yescharacteristic, complemented
99#2085C2211yescharacteristic, complemented
100#2084C2211yescharacteristic, complemented
101#2077C2211yescharacteristic, complemented
102#2077C2211yescharacteristic, complemented
103#2076C2211yescharacteristic, complemented
104#2076C2211yescharacteristic, complemented
105#2075C2211yescharacteristic, complemented
106#2075C2211yescharacteristic, complemented
107#2073C2211yescharacteristic, complemented
108#2073C2211yescharacteristic, complemented
109#2067C2211yescharacteristic, complemented
110#2067C2211yescharacteristic, complemented
111#2066C2211yescharacteristic, complemented
112#2065C2211yescharacteristic, complemented
113#2065C2211yescharacteristic, complemented
114#2059C2211yescharacteristic, complemented
115#2055C2211yescharacteristic, complemented
116#2055C2211yescharacteristic, complemented
117#2041C2211yescharacteristic
118#2041C2211yescharacteristic
119#2036C2211yescharacteristic, complemented
120#2035C2211yescharacteristic, complemented
121#2034C2211yescharacteristic
122#2034C2211yescharacteristic
123#2033C2211yescharacteristic
124#2033C2211yescharacteristic
125#2025C2211yescharacteristic, complemented
126#2000C2211yescharacteristic
127#2000C2211yescharacteristic
128#1968C2211yescharacteristic, complemented
129#1961C2211yescharacteristic
130#1955C2211yescharacteristic
131#1949C2211yescharacteristic, complemented
132#1944C2211yescharacteristic, complemented
133#1943C2211yescharacteristic, complemented
134#1943C2211yescharacteristic, complemented
135#1942C2211yescharacteristic, complemented
136#1939C2211yescharacteristic, complemented
137#1936C2211yescharacteristic, complemented
138#1936C2211yescharacteristic, complemented
139#1936C2211yescharacteristic, complemented
140#1934C2211yescharacteristic, complemented
141#1934C2211yescharacteristic, complemented
142#1926C2211yescharacteristic, complemented
143#1926C2211yescharacteristic, complemented
144#1925C2211yescharacteristic, complemented
145#1924C2211yescharacteristic, complemented
146#1924C2211yescharacteristic, complemented
147#1924C2211yescharacteristic, complemented
148#1923C2211yescharacteristic, complemented
149#1920C2211yescharacteristic, complemented
150#1917C2211yescharacteristic, complemented
151#1917C2211yescharacteristic, complemented
152#1893C2211yescharacteristic
153#1892C2211yescharacteristic, complemented
154#1880C2211yescharacteristic, complemented
155#1880C2211yescharacteristic, complemented
156#1880C2211yescharacteristic, complemented
157#1877C2211yescharacteristic
158#1877C2211yescharacteristic
159#1877C2211yescharacteristic, complemented
160#1873C2211yescharacteristic, complemented
161#1869C2211yescharacteristic
162#1865C2211yescharacteristic, complemented
163#1865C2211yescharacteristic, complemented
164#1864C2211yescharacteristic
165#1864C2211yescharacteristic
166#1864C2211yescharacteristic
167#1864C2211yescharacteristic
168#1864C2211yescharacteristic
169#1864C2211yescharacteristic, complemented
170#1864C2211yescharacteristic, complemented
171#1863C2211yescharacteristic, complemented
172#1862C2211yescharacteristic
173#1862C2211yescharacteristic
174#1862C2211yescharacteristic
175#1862C2211yescharacteristic, complemented
176#1854C2211yescharacteristic, complemented
177#1854C2211yescharacteristic, complemented
178#1854C2211yescharacteristic, complemented
179#1853C2211yescharacteristic, complemented
180#1852C2211yescharacteristic, complemented
181#1850C2211yescharacteristic, complemented
182#1847C2211yescharacteristic, complemented
183#1835C2211yescharacteristic, complemented
184#1807C2211yescharacteristic, complemented
185#1804C2211yescharacteristic
186#1804C2211yescharacteristic
187#1804C2211yescharacteristic
188#1803C2211yescharacteristic, complemented
189#1802C2211yescharacteristic
190#1802C2211yescharacteristic, complemented
191#1798C2211yescharacteristic, complemented
192#1786C2211yescharacteristic
193#1786C2211yescharacteristic
194#1786C2211yescharacteristic
195#1786C2211yescharacteristic
196#1786C2211yescharacteristic
197#1771C2211yescharacteristic, complemented
198#1762C2211yescharacteristic
199C4×#102C2211yescharacteristic
200C4×#102C2211yescharacteristic, complemented
201C8×C22⋊C4C2211yescharacteristic, complemented
202#1750C2211yescharacteristic, complemented
203C23×D4—21no—
204C23×D4C2311yescharacteristic
205C23×D4C2311yescharacteristic
206C22×SD16C2311yescharacteristic
207C22×SD16C2311yescharacteristic
208C22×SD16C2311yescharacteristic
209C23×C8C2311yescharacteristic
210D42—42no—
211D42—42no—
212C2×#127C2311yescharacteristic
213C2×#125C2311yescharacteristic
214C2×#123—21no—
215C2×#123—21no—
216C2×#123—21no—
217C2×C22⋊Q8C2311yescharacteristic
218C2×C22⋊Q8C2311yescharacteristic
219C2×#121—21no—
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#120—21no—
223C2×#120—21no—
224#518—42no—
225#518—42no—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×Q8C2311yescharacteristic
228C2×C4×Q8C2311yescharacteristic
229C2×C4×D4—21no—
230C2×C4×D4—21no—
231C2×C4×D4C2311yescharacteristic
232C2×C4×D4C2311yescharacteristic
233C2×C4×D4C2311yescharacteristic
234C2×C4×D4C2311yescharacteristic
235C2×C4×D4C2311yescharacteristic
236C2×C4×D4C2311yescharacteristic
237C2×C4×D4C2311yescharacteristic
238C2×C4×D4C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C22×C4⋊C4—21no—
242C22×C4⋊C4C2311yescharacteristic
243C22×C22⋊C4—21no—
244C22×C22⋊C4—21no—
245C22×C22⋊C4—21no—
246C22×C22⋊C4—21no—
247C22×C22⋊C4—21no—
248#481—42no—
249#478—42no—
250#478—42no—
251#460—42no—
252#450—24no—
253#450—24no—
254#440—24no—
255#440—42no—
256#440—42no—
257C4×SD16—42no—
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#107C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273C2×C4⋊C8C2311yescharacteristic
274C2×C4⋊C8C2311yescharacteristic
275C2×C4⋊C8C2311yescharacteristic
276C2×#103C2311yescharacteristic
277C2×#103C2311yescharacteristic
278C2×#103C2311yescharacteristic
279C2×#103C2311yescharacteristic
280C2×#103C2311yescharacteristic
281C2×#102—42no—
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
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×C22⋊C8C2311yescharacteristic
304C2×C22⋊C8C2311yescharacteristic
305C2×C22⋊C8C2311yescharacteristic
306C2×C22⋊C8C2311yescharacteristic
307C2×C22⋊C8C2311yescharacteristic
308C2×C22⋊C8C2311yescharacteristic
309C2×C22⋊C8C2311yescharacteristic
310C2×#97C2311yescharacteristic
311C2×#97C2311yescharacteristic
312C2×#97C2311yescharacteristic
313C2×C4×C8C2311yescharacteristic
314C2×C4×C8C2311yescharacteristic
315#400—21no—
316#400—21no—
317#400—21no—
318#400—21no—
319#400—21no—
320#400—21no—
321#400—21no—
322#400—21no—
323#400—21no—
324#400D411yescharacteristic
325#399—21no—
326#399—21no—
327#399—21no—
328#399D411yescharacteristic
329#398—21no—
330#398—21no—
331#398—21no—
332#398—21no—
333#398—21no—
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#396—21no—
348#396—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#394—21no—
360#394—21no—
361#394D411yescharacteristic
362#394D411yescharacteristic
363#391C2311yescharacteristic
364#391C2311yescharacteristic
365#390C2311yescharacteristic
366#390C2311yescharacteristic
367#390C2311yescharacteristic
368#390C2311yescharacteristic
369#390C2311yescharacteristic
370#390C2311yescharacteristic
371#389—21no—
372#389—21no—
373#389—21no—
374#389—21no—
375#389—21no—
376#389—21no—
377#389C2311yescharacteristic
378#389C2311yescharacteristic
379#389C2311yescharacteristic
380#389C2311yescharacteristic
381#389C2311yescharacteristic
382#389C2311yescharacteristic
383#389C2311yescharacteristic
384#389C2311yescharacteristic
385#389C2311yescharacteristic
386#389C2311yescharacteristic
387#389C2311yescharacteristic
388#389C2311yescharacteristic
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#388—21no—
396#388—21no—
397#388—21no—
398#388—21no—
399#388—21no—
400#387—21no—
401#387—21no—
402#387—21no—
403#387—21no—
404#387—21no—
405#387—21no—
406#387—21no—
407#387—21no—
408#387—21no—
409#386—21no—
410#386—21no—
411#386—21no—
412#386—21no—
413#386—21no—
414#386—21no—
415#386—21no—
416#386—21no—
417#386—21no—
418#386—21no—
419#385—21no—
420#385—21no—
421#385—21no—
422#385—21no—
423#385—21no—
424#385—21no—
425#385—21no—
426#385—21no—
427#384C2311yescharacteristic
428#384C2311yescharacteristic
429#383—21no—
430#383—21no—
431#382—21no—
432#382C2311yescharacteristic
433#382C2311yescharacteristic
434#382C2311yescharacteristic
435#382C2311yescharacteristic
436#381—21no—
437#380—21no—
438#380—21no—
439#380—21no—
440#380C2311yescharacteristic
441#380C2311yescharacteristic
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⋊C4C2311yescharacteristic
453C4×C4⋊C4C2311yescharacteristic
454C4×C4⋊C4C2311yescharacteristic
455C4×C4⋊C4C2311yescharacteristic
456C4×C22⋊C4—21no—
457C4×C22⋊C4C2311yescharacteristic
458C4×C22⋊C4C2311yescharacteristic
459C4×C22⋊C4C2311yescharacteristic
460C2×#95—21no—
461#340C2311yescharacteristic
462#340C2311yescharacteristic
463#340C2311yescharacteristic
464#340C2311yescharacteristic
465#340C2311yescharacteristic
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#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490#336C2311yescharacteristic
491#336C2311yescharacteristic
492#336C2311yescharacteristic
493C25—21no—
494C25—21no—
495C22×Q8C2411yescharacteristic
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—22no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—22no—
502C22×D4—22no—
503C22×D4—21no—
504C22×D4—21no—
505C22×D4—21no—
506C22×D4—21no—
507C22×D4—21no—
508C22×D4—21no—
509C22×D4—41no—
510C22×D4—41no—
511C22×D4—41no—
512C22×D4—41no—
513C22×D4—41no—
514C22×D4—44no—
515C22×D4—82no—
516C22×D4—82no—
517C22×D4C2×D411yescharacteristic
518C22×D4C2411yescharacteristic
519C22×D4C2411yescharacteristic
520C22×D4C2411yescharacteristic
521C23×C4—21no—
522C23×C4—21no—
523C23×C4—21no—
524C23×C4—21no—
525C23×C4—21no—
526C23×C4—21no—
527C23×C4—21no—
528C23×C4—21no—
529C23×C4C2411yescharacteristic
530C23×C4C2411yescharacteristic
531C2×SD16—22no—
532C2×SD16—22no—
533C2×SD16—22no—
534C2×SD16—22no—
535C2×SD16—22no—
536C2×SD16—41no—
537C2×SD16—41no—
538C2×SD16—41no—
539C2×SD16#4114yes—
540C22×C8—41no—
541C22×C8—41no—
542C22×C8—41no—
543C22×C8C2411yescharacteristic
544C22×C8C2411yescharacteristic
545C22×C8C2411yescharacteristic
546C22×C8C2411yescharacteristic
547C22×C8C2411yescharacteristic
548C22×C8C2411yescharacteristic
549C22×C8C2411yescharacteristic
550C22×C8C2411yescharacteristic
551#127—22no—
552#127—41no—
553#125—41no—
554#125—41no—
555#123—82no—
556#123—82no—
557#123—82no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—41no—
561C22⋊Q8—41no—
562#121—22no—
563#121—41no—
564#121—41no—
565#121—41no—
566#121—44no—
567#120—44no—
568#120—44no—
569C4×Q8—22no—
570C4×Q8—41no—
571C4×Q8—41no—
572C4×Q8—41no—
573C4×Q8—41no—
574C4×Q8—41no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—41no—
583C4×D4—41no—
584C4×D4—41no—
585C4×D4—41no—
586C4×D4—41no—
587C4×D4—41no—
588C4×D4—41no—
589C4×D4—41no—
590C4×D4—41no—
591C4×D4—44no—
592C4×D4—44no—
593#117—41no—
594#117—41no—
595#117—41no—
596#117—41no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—21no—
603C2×C4⋊C4—21no—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—21no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—21no—
614C2×C4⋊C4—21no—
615C2×C4⋊C4—21no—
616C2×C4⋊C4—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—41no—
622C2×C4⋊C4—41no—
623C2×C4⋊C4—82no—
624C2×C4⋊C4C2×D411yescharacteristic
625C2×C4⋊C4C2×D411yescharacteristic
626C2×C4⋊C4C2×D411yescharacteristic
627C2×C4⋊C4C2×D411yescharacteristic
628C2×C4⋊C4C2×D411yescharacteristic
629C2×C4⋊C4C2×D411yescharacteristic
630C2×C4⋊C4C2×D411yescharacteristic
631C2×C4⋊C4C2411yescharacteristic
632C2×C4⋊C4C2411yescharacteristic
633C2×C4⋊C4C2411yescharacteristic
634C2×C4⋊C4C2411yescharacteristic
635C2×C4⋊C4C2411yescharacteristic
636C2×C4⋊C4C2411yescharacteristic
637C2×C4⋊C4C2411yescharacteristic
638C2×C4⋊C4C2411yescharacteristic
639C2×C4⋊C4C2411yescharacteristic
640C2×C4⋊C4C2411yescharacteristic
641C2×C4⋊C4C2411yescharacteristic
642C2×C4⋊C4C2411yescharacteristic
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4—21no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
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—44no—
676C2×C22⋊C4—44no—
677C2×C22⋊C4—82no—
678C2×C22⋊C4—82no—
679C2×C22⋊C4—82no—
680C2×C22⋊C4C2×D411yescharacteristic
681C2×C22⋊C4C2×D411yescharacteristic
682C2×C22⋊C4C2×D411yescharacteristic
683C2×C22⋊C4C2×D411yescharacteristic
684C2×C22⋊C4C2×D411yescharacteristic
685C2×C22⋊C4C2×D411yescharacteristic
686C2×C22⋊C4C2×D411yescharacteristic
687C2×C22⋊C4C2×D411yescharacteristic
688C2×C22⋊C4C2×D411yescharacteristic
689C2×C22⋊C4C2×D411yescharacteristic
690C2×C42—21no—
691C2×C42—21no—
692C2×C42—21no—
693C2×C42—21no—
694C2×C42—21no—
695C2×C42—21no—
696C2×C42C2411yescharacteristic
697C2×C42C2411yescharacteristic
698C2×C42C2411yescharacteristic
699C2×C42C2411yescharacteristic
700C2×C42C2411yescharacteristic
701#107—22no—
702#107—41no—
703#107—41no—
704#107—41no—
705#107—41no—
706#107—41no—
707#106—41no—
708#106—41no—
709#106—41no—
710#106—41no—
711#106—41no—
712#106—41no—
713#106—41no—
714C4⋊C8—41no—
715C4⋊C8—41no—
716C4⋊C8—41no—
717C4⋊C8—41no—
718C4⋊C8—41no—
719#103—22no—
720#103—41no—
721#103—41no—
722#103—41no—
723#103—41no—
724#102—22no—
725#102—22no—
726#102—22no—
727#102—22no—
728#102—22no—
729#102—22no—
730#102—22no—
731#102—22no—
732#102—22no—
733#102—22no—
734#102—22no—
735#102—22no—
736#102—41no—
737#102—41no—
738#102—41no—
739#102—41no—
740#102—41no—
741#102—41no—
742#102—41no—
743#102—41no—
744#102—41no—
745C22⋊C8—22no—
746C22⋊C8—22no—
747C22⋊C8—41no—
748C22⋊C8—41no—
749C22⋊C8—41no—
750C22⋊C8—41no—
751C22⋊C8—41no—
752#97—22no—
753#97—41no—
754#97—41no—
755C4×C8—41no—
756C4×C8—41no—
757#95—21no—
758#95—21no—
759#95—21no—
760#95—21no—
761#95—21no—
762#95—21no—
763#95—21no—
764#95—21no—
765#95—21no—
766#95—21no—
767#95—21no—
768#95—21no—
769#95—21no—
770#95—21no—
771#95—21no—
772#95—21no—
773#95—21no—
774#95—21no—
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#95C2×D411yescharacteristic
792#95C2×D411yescharacteristic
793#95C2×D411yescharacteristic
794#95C2×D411yescharacteristic
795#95C2×D411yescharacteristic
796#95C2×D411yescharacteristic
797#95C2×D411yescharacteristic
798#95C2×D411yescharacteristic
799#95C2×D411yescharacteristic
800#95C2×D411yescharacteristic
801C24—21no—
802C24—24no—
803C24—21no—
804C24—21no—
805C24—42no—
806C24—42no—
807C24—42no—
808C24—42no—
809C24—42no—
810C24—42no—
811C24—81no—
812C24—81no—
813C24—81no—
814C24—81no—
815C24—81no—
816C24—81no—
817C24—81no—
818C24C22×D411yescharacteristic
819C24C22×D411yescharacteristic
820C2×Q8—21no—
821C2×Q8—21no—
822C2×Q8—21no—
823C2×Q8—21no—
824C2×Q8—21no—
825C2×Q8C2×#4112yes—
826C2×D4—24no—
827C2×D4—22no—
828C2×D4—21no—
829C2×D4—21no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—21no—
841C2×D4—21no—
842C2×D4—41no—
843C2×D4—41no—
844C2×D4—42no—
845C2×D4—42no—
846C2×D4—42no—
847C2×D4—42no—
848C2×D4—42no—
849C2×D4—42no—
850C2×D4—42no—
851C2×D4—42no—
852C2×D4—44no—
853C2×D4—44no—
854C2×D4—44no—
855C2×D4—44no—
856C2×D4—44no—
857C2×D4—42no—
858C2×D4—42no—
859C2×D4—42no—
860C2×D4—81no—
861C2×D4—81no—
862C2×D4—81no—
863C2×D4—82no—
864C2×D4—82no—
865C2×D4—82no—
866C2×D4—81no—
867C2×D4—81no—
868C2×D4—81no—
869C2×D4—816no—
870C2×D4C2×#4112yes—
871C2×D4H(5,𝔽2)12yes—
872C2×D4H(5,𝔽2)12yes—
873C2×D42−1+412yes—
874C22×C4—21no—
875C22×C4—21no—
876C22×C4—21no—
877C22×C4—21no—
878C22×C4—21no—
879C22×C4—21no—
880C22×C4—21no—
881C22×C4—21no—
882C22×C4—21no—
883C22×C4—21no—
884C22×C4—21no—
885C22×C4—21no—
886C22×C4—21no—
887C22×C4—21no—
888C22×C4—21no—
889C22×C4—21no—
890C22×C4—21no—
891C22×C4—21no—
892C22×C4—21no—
893C22×C4—21no—
894C22×C4—21no—
895C22×C4—21no—
896C22×C4—21no—
897C22×C4—21no—
898C22×C4—21no—
899C22×C4—42no—
900C22×C4—42no—
901C22×C4—42no—
902C22×C4—42no—
903C22×C4—42no—
904C22×C4—42no—
905C22×C4—42no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—81no—
909C22×C4—81no—
910C22×C4—81no—
911C22×C4—81no—
912C22×C4—81no—
913C22×C4—81no—
914C22×C4—81no—
915C22×C4—81no—
916C22×C4—81no—
917C22×C4—81no—
918C22×C4—81no—
919C22×C4—81no—
920C22×C4—81no—
921C22×C4—81no—
922C22×C4—81no—
923C22×C4C22×D411yescharacteristic
924C22×C4C22×D411yescharacteristic
925C22×C4C22×D411yescharacteristic
926C22×C4C22×D411yescharacteristic
927C22×C4C22×D411yescharacteristic
928C22×C4C22×D411yescharacteristic
929C22×C4C22×D411yescharacteristic
930C22×C4C22×D411yescharacteristic
931C22×C4C22×D411yescharacteristic
932C22×C4C22×D411yescharacteristic
933C22×C4C22×D411yescharacteristic
934C22×C4C22×D411yescharacteristic
935C22×C4C2511yescharacteristic
936SD16—28no—
937SD16—44no—
938SD16—82no—
939C2×C8—21no—
940C2×C8—21no—
941C2×C8—21no—
942C2×C8—21no—
943C2×C8—21no—
944C2×C8—21no—
945C2×C8—21no—
946C2×C8—21no—
947C2×C8—21no—
948C2×C8—21no—
949C2×C8—21no—
950C2×C8—21no—
951C2×C8—21no—
952C2×C8—21no—
953C2×C8—21no—
954C2×C8—21no—
955C2×C8—21no—
956C2×C8—21no—
957C2×C8—21no—
958C2×C8—21no—
959C2×C8—21no—
960C2×C8—21no—
961C2×C8—21no—
962C2×C8—82no—
963C2×C8C2×#4112yes—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—21no—
969C4⋊C4—21no—
970C4⋊C4—21no—
971C4⋊C4—21no—
972C4⋊C4—21no—
973C4⋊C4—21no—
974C4⋊C4—21no—
975C4⋊C4—21no—
976C4⋊C4—21no—
977C4⋊C4—21no—
978C4⋊C4—21no—
979C4⋊C4—21no—
980C4⋊C4—21no—
981C4⋊C4—21no—
982C4⋊C4—21no—
983C4⋊C4—21no—
984C4⋊C4—21no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—21no—
988C4⋊C4—41no—
989C4⋊C4—41no—
990C4⋊C4—41no—
991C4⋊C4—41no—
992C4⋊C4—41no—
993C4⋊C4—41no—
994C4⋊C4—41no—
995C4⋊C4—42no—
996C4⋊C4—42no—
997C4⋊C4—42no—
998C4⋊C4—42no—
999C4⋊C4—81no—
1000C4⋊C4—81no—
1001C4⋊C4—81no—
1002C4⋊C4—81no—
1003C4⋊C4—81no—
1004C4⋊C4—81no—
1005C4⋊C4—81no—
1006C4⋊C4—81no—
1007C4⋊C4—81no—
1008C4⋊C4—81no—
1009C4⋊C4—81no—
1010C4⋊C4—81no—
1011C4⋊C4—81no—
1012C4⋊C4—81no—
1013C4⋊C4—81no—
1014C4⋊C4—81no—
1015C4⋊C4—81no—
1016C4⋊C4—81no—
1017C4⋊C4—81no—
1018C4⋊C4—81no—
1019C22⋊C4—22no—
1020C22⋊C4—22no—
1021C22⋊C4—41no—
1022C22⋊C4—41no—
1023C22⋊C4—41no—
1024C22⋊C4—41no—
1025C22⋊C4—41no—
1026C22⋊C4—41no—
1027C22⋊C4—41no—
1028C22⋊C4—41no—
1029C22⋊C4—42no—
1030C22⋊C4—42no—
1031C22⋊C4—42no—
1032C22⋊C4—42no—
1033C22⋊C4—42no—
1034C22⋊C4—42no—
1035C22⋊C4—42no—
1036C22⋊C4—42no—
1037C22⋊C4—42no—
1038C22⋊C4—42no—
1039C22⋊C4—42no—
1040C22⋊C4—42no—
1041C22⋊C4—42no—
1042C22⋊C4—42no—
1043C22⋊C4—42no—
1044C22⋊C4—42no—
1045C22⋊C4—81no—
1046C22⋊C4—81no—
1047C22⋊C4—81no—
1048C22⋊C4—81no—
1049C22⋊C4—81no—
1050C22⋊C4—81no—
1051C22⋊C4—81no—
1052C22⋊C4—81no—
1053C22⋊C4—81no—
1054C22⋊C4—81no—
1055C22⋊C4—81no—
1056C22⋊C4—81no—
1057C22⋊C4—81no—
1058C22⋊C4—81no—
1059C22⋊C4—81no—
1060C22⋊C4—81no—
1061C42—21no—
1062C42—21no—
1063C42—21no—
1064C42—21no—
1065C42—21no—
1066C42—21no—
1067C42—21no—
1068C42—21no—
1069C42—21no—
1070C42—21no—
1071C42—42no—
1072C42—42no—
1073C42—81no—
1074C42—81no—
1075C42—81no—
1076C42—81no—
1077C23—21no—
1078C23—21no—
1079C23—21no—
1080C23—21no—
1081C23—22no—
1082C23—22no—
1083C23—21no—
1084C23—22no—
1085C23—21no—
1086C23—21no—
1087C23—21no—
1088C23—21no—
1089C23—21no—
1090C23—21no—
1091C23—22no—
1092C23—21no—
1093C23—21no—
1094C23—48no—
1095C23—41no—
1096C23—41no—
1097C23—41no—
1098C23—41no—
1099C23—41no—
1100C23—41no—
1101C23—41no—
1102C23—41no—
1103C23—41no—
1104C23—41no—
1105C23—41no—
1106C23—41no—
1107C23—41no—
1108C23—41no—
1109C23—41no—
1110C23—41no—
1111C23—41no—
1112C23—84no—
1113C23—84no—
1114C23—84no—
1115C23—84no—
1116C23—84no—
1117C23—84no—
1118C23—162no—
1119C23—162no—
1120C23—162no—
1121C23—162no—
1122C23—162no—
1123C23—162no—
1124C23—162no—
1125C23#57712yes—
1126C23C23×D411yescharacteristic
1127Q8—22no—
1128Q8—22no—
1129Q8—41no—
1130Q8—41no—
1131D4—22no—
1132D4—22no—
1133D4—22no—
1134D4—22no—
1135D4—22no—
1136D4—48no—
1137D4—44no—
1138D4—41no—
1139D4—41no—
1140D4—41no—
1141D4—41no—
1142D4—41no—
1143D4—41no—
1144D4—84no—
1145D4—84no—
1146D4—84no—
1147D4—84no—
1148D4—162no—
1149D4#53914yes—
1150C2×C4—21no—
1151C2×C4—21no—
1152C2×C4—21no—
1153C2×C4—21no—
1154C2×C4—21no—
1155C2×C4—21no—
1156C2×C4—21no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—21no—
1162C2×C4—21no—
1163C2×C4—21no—
1164C2×C4—21no—
1165C2×C4—21no—
1166C2×C4—21no—
1167C2×C4—22no—
1168C2×C4—21no—
1169C2×C4—21no—
1170C2×C4—21no—
1171C2×C4—21no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—21no—
1175C2×C4—21no—
1176C2×C4—21no—
1177C2×C4—21no—
1178C2×C4—21no—
1179C2×C4—21no—
1180C2×C4—21no—
1181C2×C4—21no—
1182C2×C4—21no—
1183C2×C4—21no—
1184C2×C4—21no—
1185C2×C4—21no—
1186C2×C4—21no—
1187C2×C4—41no—
1188C2×C4—41no—
1189C2×C4—41no—
1190C2×C4—41no—
1191C2×C4—41no—
1192C2×C4—41no—
1193C2×C4—41no—
1194C2×C4—41no—
1195C2×C4—41no—
1196C2×C4—41no—
1197C2×C4—41no—
1198C2×C4—41no—
1199C2×C4—41no—
1200C2×C4—41no—
1201C2×C4—41no—
1202C2×C4—41no—
1203C2×C4—41no—
1204C2×C4—41no—
1205C2×C4—41no—
1206C2×C4—41no—
1207C2×C4—41no—
1208C2×C4—41no—
1209C2×C4—41no—
1210C2×C4—41no—
1211C2×C4—41no—
1212C2×C4—41no—
1213C2×C4—41no—
1214C2×C4—41no—
1215C2×C4—41no—
1216C2×C4—41no—
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—84no—
1234C2×C4—84no—
1235C2×C4—162no—
1236C2×C4—162no—
1237C2×C4—162no—
1238C2×C4—162no—
1239C2×C4—162no—
1240C2×C4—162no—
1241C2×C4C22×#4111yescharacteristic
1242C2×C4C2×H(5,𝔽2)11yescharacteristic
1243C2×C4C2×H(5,𝔽2)11yescharacteristic
1244C2×C4C2×2−1+411yescharacteristic
1245C2×C4#58511yescharacteristic
1246C2×C4#58511yescharacteristic
1247C8—22no—
1248C8—41no—
1249C8—41no—
1250C8—41no—
1251C8—41no—
1252C8—41no—
1253C8—41no—
1254C8—41no—
1255C22—22no—
1256C22—24no—
1257C22—22no—
1258C22—22no—
1259C22—42no—
1260C22—42no—
1261C22—41no—
1262C22—41no—
1263C22—42no—
1264C22—41no—
1265C22—42no—
1266C22—42no—
1267C22—41no—
1268C22—42no—
1269C22—41no—
1270C22—41no—
1271C22—41no—
1272C22—42no—
1273C22—42no—
1274C22—41no—
1275C22—41no—
1276C22—41no—
1277C22—42no—
1278C22—41no—
1279C22—81no—
1280C22—81no—
1281C22—81no—
1282C22—81no—
1283C22—81no—
1284C22—81no—
1285C22—81no—
1286C22—81no—
1287C22—81no—
1288C22—81no—
1289C22—81no—
1290C22—168no—
1291C22—168no—
1292C22D4×#4111yescharacteristic
1293C22#348411yescharacteristic
1294C22#348911yescharacteristic
1295C22C2×#57711yescharacteristic
1296C22#358411yescharacteristic
1297C22#358511yescharacteristic
1298C22#358511yescharacteristic
1299C4—41no—
1300C4—41no—
1301C4—41no—
1302C4—41no—
1303C4—42no—
1304C4—41no—
1305C4—41no—
1306C4—41no—
1307C4—41no—
1308C4—41no—
1309C4—41no—
1310C4—41no—
1311C4—41no—
1312C4—81no—
1313C4—81no—
1314C4—81no—
1315C4—81no—
1316C4—81no—
1317C4—81no—
1318C4—81no—
1319C4—81no—
1320C4—81no—
1321C4—81no—
1322C4—81no—
1323C4—81no—
1324C4C2×#53911yescharacteristic
1325C4#351311yescharacteristic
1326C4#353311yescharacteristic
1327C4#353511yescharacteristic
1328C2—42no—
1329C2—44no—
1330C2—81no—
1331C2—82no—
1332C2—161no—
1333C2#3771211yescharacteristic
1334C2#6149011yescharacteristic
1335C2#6150411yescharacteristic
1336C2#6161011yescharacteristic
1337C2#6167811yescharacteristic
1338C2#6215911yescharacteristic
1339C2#6216411yescharacteristic
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. #42827C2semidirect
3. #32966C2semidirect
4. #32465C2semidirect
5. #32309C2semidirect
6. #32001C2semidirect
7. #31944C2semidirect
8. #31598C2semidirect
9. #31552C2semidirect
10. #31158C2semidirect
11. #31094C2semidirect
12. #30369C2semidirect
13. #30035C2semidirect
14. #29028C2semidirect
15. #28842C2semidirect
16. #27534C2semidirect
17. #27523C2semidirect
18. #27312C2semidirect
19. #26567C2semidirect
20. #26386C2semidirect
21. #26175C2semidirect
22. #26117C2semidirect
23. #25960C2semidirect
24. #24921C2semidirect
25. #24917C2semidirect
28. #22874C2semidirect
29. #22677C2semidirect
30. #22362C2semidirect
31. #21459C2semidirect
36. C2×#478C22semidirect
42. C2×#440C22semidirect
52. #2629C22semidirect
56. #2570C22semidirect
58. #2509C22semidirect
60. #2495C22semidirect
61. #2495C22semidirect
64. #2453C22semidirect
69. #2442C22semidirect
70. #2423C22semidirect
72. #2421C22semidirect
80. #2360C22semidirect
81. #2351C22semidirect
87. #2323C22semidirect
88. #2101C22semidirect
89. #2100C22semidirect
90. #2099C22semidirect
91. #2097C22semidirect
92. #2093C22semidirect
93. #2092C22semidirect
94. #2092C22semidirect
95. #2088C22semidirect
96. #2088C22semidirect
97. #2086C22semidirect
98. #2085C22semidirect
99. #2085C22semidirect
100. #2084C22semidirect
101. #2077C22semidirect
102. #2077C22semidirect
103. #2076C22semidirect
104. #2076C22semidirect
105. #2075C22semidirect
106. #2075C22semidirect
107. #2073C22semidirect
108. #2073C22semidirect
109. #2067C22semidirect
110. #2067C22semidirect
111. #2066C22semidirect
112. #2065C22semidirect
113. #2065C22semidirect
114. #2059C22semidirect
115. #2055C22semidirect
116. #2055C22semidirect
119. #2036C22semidirect
120. #2035C22semidirect
125. #2025C22semidirect
128. #1968C22semidirect
131. #1949C22semidirect
132. #1944C22semidirect
133. #1943C22semidirect
134. #1943C22semidirect
135. #1942C22semidirect
136. #1939C22semidirect
137. #1936C22semidirect
138. #1936C22semidirect
139. #1936C22semidirect
140. #1934C22semidirect
141. #1934C22semidirect
142. #1926C22semidirect
143. #1926C22semidirect
144. #1925C22semidirect
145. #1924C22semidirect
146. #1924C22semidirect
147. #1924C22semidirect
148. #1923C22semidirect
149. #1920C22semidirect
150. #1917C22semidirect
151. #1917C22semidirect
153. #1892C22semidirect
154. #1880C22semidirect
155. #1880C22semidirect
156. #1880C22semidirect
159. #1877C22semidirect
160. #1873C22semidirect
162. #1865C22semidirect
163. #1865C22semidirect
169. #1864C22semidirect
170. #1864C22semidirect
171. #1863C22semidirect
175. #1862C22semidirect
176. #1854C22semidirect
177. #1854C22semidirect
178. #1854C22semidirect
179. #1853C22semidirect
180. #1852C22semidirect
181. #1850C22semidirect
182. #1847C22semidirect
183. #1835C22semidirect
184. #1807C22semidirect
188. #1803C22semidirect
190. #1802C22semidirect
191. #1798C22semidirect
197. #1771C22semidirect
200. C4×#102C22semidirect
201. C8×C22⋊C4C22semidirect
202. #1750C22semidirect

Maximal subgroups

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

subgroupindex
#428272
#357132
#329662
#324652
#323092
#320012
#319442
#315982
#315522
#311582
#310942
#303692
#300352
#290282
#288422
#275342
#275232
#273122
#265672
#263862
#261752
#261172
#259602
#249212
#249172
#242522
#240332
#228742
#226772
#223622
#214592