Finite Group Databasebeta

← #6456302

Subgroups — #6456302

Order 512.

1668 conjugacy classes of subgroups.

The subgroup lattice has 1308 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#35522C211yesmaximal, characteristic
2#34244C211yesmaximal, characteristic, complemented
3#25072C211yesmaximal, characteristic, complemented
4#25069C211yesmaximal, characteristic, complemented
5#25026C211yesmaximal, characteristic, complemented
6#25023C211yesmaximal, characteristic, complemented
7#24999C211yesmaximal, characteristic, complemented
8#24991C211yesmaximal, characteristic, complemented
9#24974C211yesmaximal, characteristic, complemented
10#24968C211yesmaximal, characteristic, complemented
11#24963C211yesmaximal, characteristic, complemented
12#24961C211yesmaximal, characteristic, complemented
13#24948C211yesmaximal, characteristic, complemented
14#24938C211yesmaximal, characteristic, complemented
15#24890C211yesmaximal, characteristic, complemented
16#24878C211yesmaximal, characteristic, complemented
17#24873C211yesmaximal, characteristic, complemented
18#24869C211yesmaximal, characteristic, complemented
19#23770C211yesmaximal, characteristic, complemented
20#23767C211yesmaximal, characteristic, complemented
21#23764C211yesmaximal, characteristic, complemented
22#23758C211yesmaximal, characteristic, complemented
23#21588C211yesmaximal, characteristic, complemented
24#21584C211yesmaximal, characteristic, complemented
25#21582C211yesmaximal, characteristic, complemented
26C4×#482C211yesmaximal, characteristic, complemented
27#21381C211yesmaximal, characteristic, complemented
28#21367C211yesmaximal, characteristic, complemented
29#20822C211yesmaximal, characteristic, complemented
30#20744C211yesmaximal, characteristic, complemented
31#20416C211yesmaximal, characteristic, complemented
32C2×#529C2211yescharacteristic
33C2×#518C2211yescharacteristic
34C2×#481C2211yescharacteristic
35C2×#482C2211yescharacteristic
36C2×#482C2211yescharacteristic
37C2×#482C2211yescharacteristic
38C2×#433C2211yescharacteristic
39C2×#418C2211yescharacteristic
40C22×#102C2211yescharacteristic
41C2×#405C2211yescharacteristic
42#2580C2211yescharacteristic
43#2538C2211yescharacteristic
44#2537C2211yescharacteristic
45#2535C2211yescharacteristic
46#2485C2211yescharacteristic
47#2485C2211yescharacteristic
48#2480—21no—
49#2472—21no—
50#2467—21no—
51#2463—21no—
52#2460—21no—
53#2456—21no—
54#2424—21no—
55#2418—21no—
56#2408C2211yescharacteristic
57#2408C2211yescharacteristic
58#2374—21no—
59#2374—21no—
60#2372—21no—
61#2371—21no—
62#2355C2211yescharacteristic, complemented
63#2355C2211yescharacteristic, complemented
64#2354C2211yescharacteristic
65#2354C2211yescharacteristic, complemented
66#2352C2211yescharacteristic
67#2352C2211yescharacteristic
68#2352C2211yescharacteristic
69#2352C2211yescharacteristic, complemented
70#2333—21no—
71#2332—21no—
72#2324C2211yescharacteristic
73#2324C2211yescharacteristic
74#2314C2211yescharacteristic
75#2314C2211yescharacteristic
76#2314C2211yescharacteristic, complemented
77C4×#126—21no—
78C4×#126—21no—
79C4×#121C2211yescharacteristic
80C4×#121C2211yescharacteristic
81#2283C2211yescharacteristic, complemented
82#2274C2211yescharacteristic
83#2274C2211yescharacteristic, complemented
84C4×#117C2211yescharacteristic, complemented
85#2101C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2101C2211yescharacteristic, complemented
88#2100C2211yescharacteristic, complemented
89#2093C2211yescharacteristic
90#2092C2211yescharacteristic
91#2092C2211yescharacteristic
92#2092C2211yescharacteristic
93#2085C2211yescharacteristic, complemented
94#2085C2211yescharacteristic, complemented
95#2085C2211yescharacteristic, complemented
96#2083C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2077C2211yescharacteristic, complemented
99#2077C2211yescharacteristic, complemented
100#2076C2211yescharacteristic, complemented
101#2076C2211yescharacteristic, complemented
102#2076C2211yescharacteristic, complemented
103#2075C2211yescharacteristic, complemented
104#2075C2211yescharacteristic, complemented
105#2073C2211yescharacteristic
106#2073C2211yescharacteristic
107#2073C2211yescharacteristic
108#2071C2211yescharacteristic
109#2034C2211yescharacteristic
110#2034C2211yescharacteristic
111#2034C2211yescharacteristic
112#2033C2211yescharacteristic
113#2033C2211yescharacteristic
114#2033C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#1985C2211yescharacteristic, complemented
118#1984C2211yescharacteristic, complemented
119#1955C2211yescharacteristic, complemented
120#1954C2211yescharacteristic, complemented
121#1949C2211yescharacteristic, complemented
122#1949C2211yescharacteristic, complemented
123#1948C2211yescharacteristic, complemented
124#1947C2211yescharacteristic, complemented
125#1926C2211yescharacteristic
126#1926C2211yescharacteristic
127#1926C2211yescharacteristic
128#1926C2211yescharacteristic
129#1926C2211yescharacteristic
130#1925C2211yescharacteristic
131#1925C2211yescharacteristic
132#1925C2211yescharacteristic
133#1921C2211yescharacteristic, complemented
134#1920C2211yescharacteristic, complemented
135#1920C2211yescharacteristic, complemented
136#1920C2211yescharacteristic, complemented
137#1919C2211yescharacteristic, complemented
138#1919C2211yescharacteristic, complemented
139#1918C2211yescharacteristic, complemented
140#1918C2211yescharacteristic, complemented
141#1875C2211yescharacteristic
142#1875C2211yescharacteristic
143#1875C2211yescharacteristic
144#1874C2211yescharacteristic
145#1870C2211yescharacteristic
146#1870C2211yescharacteristic
147#1869C2211yescharacteristic
148#1869C2211yescharacteristic
149#1854C2211yescharacteristic
150#1854C2211yescharacteristic
151#1854C2211yescharacteristic, complemented
152#1854C2211yescharacteristic, complemented
153#1854C2211yescharacteristic, complemented
154#1853C2211yescharacteristic
155#1853C2211yescharacteristic, complemented
156#1852C2211yescharacteristic
157#1847C2211yescharacteristic, complemented
158#1847C2211yescharacteristic, complemented
159#1835C2211yescharacteristic, complemented
160#1834C2211yescharacteristic, complemented
161#1825C2211yescharacteristic
162#1825C2211yescharacteristic
163#1825C2211yescharacteristic, complemented
164#1825C2211yescharacteristic, complemented
165#1825C2211yescharacteristic, complemented
166#1823C2211yescharacteristic, complemented
167#1809C2211yescharacteristic
168#1809C2211yescharacteristic
169#1808C2211yescharacteristic
170#1807C2211yescharacteristic
171#1804C2211yescharacteristic
172#1804C2211yescharacteristic
173#1802C2211yescharacteristic
174#1802C2211yescharacteristic
175#1786C2211yescharacteristic
176#1786C2211yescharacteristic
177#1776C2211yescharacteristic, complemented
178#1776C2211yescharacteristic, complemented
179#1776C2211yescharacteristic, complemented
180#1776C2211yescharacteristic, complemented
181C4×#107C2211yescharacteristic, complemented
182C4×#107C2211yescharacteristic, complemented
183C4×#106C2211yescharacteristic, complemented
184C4×#106C2211yescharacteristic, complemented
185#1762C2211yescharacteristic
186#1762C2211yescharacteristic
187#1762C2211yescharacteristic
188#1762C2211yescharacteristic
189#1762C2211yescharacteristic
190#1762C2211yescharacteristic
191C4×#102C2211yescharacteristic
192C4×#102C2211yescharacteristic
193C4×#102C2211yescharacteristic
194C4×#102C2211yescharacteristic
195C4×#102C2211yescharacteristic
196C4×#102C2211yescharacteristic
197#1750C2211yescharacteristic, complemented
198#1750C2211yescharacteristic, complemented
199#1749C2211yescharacteristic, complemented
200C4×C22⋊C8C2211yescharacteristic, complemented
201#1736C2211yescharacteristic
202#1735C2211yescharacteristic
203C23×D4C2311yescharacteristic
204C22×M16C2311yescharacteristic
205C23×C8C2311yescharacteristic
206#529—24no—
207#529—24no—
208C2×#126D411yescharacteristic
209C2×#126D411yescharacteristic
210C2×#125D411yescharacteristic
211C2×#124D411yescharacteristic
212C2×#123D411yescharacteristic
213C2×#123D411yescharacteristic
214C2×C22⋊Q8—21no—
215C2×C22⋊Q8D411yescharacteristic
216C2×#121—21no—
217C2×#121D411yescharacteristic
218C2×#121C2311yescharacteristic
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#120—21no—
223C2×#120—21no—
224#518—24no—
225#518—24no—
226C2×C4×Q8C2311yescharacteristic
227C2×C4×D4—21no—
228C2×C4×D4—21no—
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×#117C2311yescharacteristic
239C2×#117C2311yescharacteristic
240C2×#117C2311yescharacteristic
241C2×#117C2311yescharacteristic
242C2×#117C2311yescharacteristic
243C2×#117C2311yescharacteristic
244C2×#117C2311yescharacteristic
245C22×C4⋊C4C2311yescharacteristic
246C22×C4⋊C4C2311yescharacteristic
247C22×C22⋊C4—21no—
248C22×C22⋊C4—21no—
249C22×C42C2311yescharacteristic
250#482—24no—
251#482—24no—
252#482—24no—
253#481—24no—
254#433—24no—
255C2×#107C2311yescharacteristic
256C2×#107C2311yescharacteristic
257C2×#107C2311yescharacteristic
258C2×#107C2311yescharacteristic
259C2×#107C2311yescharacteristic
260C2×#107C2311yescharacteristic
261C2×#107C2311yescharacteristic
262C2×#107C2311yescharacteristic
263C2×#106C2311yescharacteristic
264C2×#106C2311yescharacteristic
265C2×#106C2311yescharacteristic
266C2×#106C2311yescharacteristic
267C2×#106C2311yescharacteristic
268C2×#106C2311yescharacteristic
269C2×#106C2311yescharacteristic
270C2×#106C2311yescharacteristic
271C2×C4⋊C8C2311yescharacteristic
272C2×C4⋊C8C2311yescharacteristic
273#418—24no—
274C2×#102—24no—
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×#102C2311yescharacteristic
282C2×#102C2311yescharacteristic
283C2×#102C2311yescharacteristic
284C2×#102C2311yescharacteristic
285C2×#102C2311yescharacteristic
286C2×#102C2311yescharacteristic
287C2×#102C2311yescharacteristic
288C2×#102C2311yescharacteristic
289C2×#102C2311yescharacteristic
290C2×#102C2311yescharacteristic
291C2×C22⋊C8C2311yescharacteristic
292C2×C22⋊C8C2311yescharacteristic
293C2×C22⋊C8C2311yescharacteristic
294C2×C22⋊C8C2311yescharacteristic
295C2×C22⋊C8C2311yescharacteristic
296C2×C22⋊C8C2311yescharacteristic
297C2×C22⋊C8C2311yescharacteristic
298C2×C22⋊C8C2311yescharacteristic
299C2×C22⋊C8C2311yescharacteristic
300C2×C22⋊C8C2311yescharacteristic
301#405—24no—
302C2×#97C2311yescharacteristic
303C2×#97C2311yescharacteristic
304C2×#97C2311yescharacteristic
305C2×C4×C8C2311yescharacteristic
306C2×C4×C8C2311yescharacteristic
307C2×C4×C8C2311yescharacteristic
308#399—21no—
309#397—21no—
310#397—21no—
311#397—21no—
312#396—21no—
313#396—21no—
314#394—21no—
315#394—21no—
316#394—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#393—21no—
321#392—21no—
322#392—21no—
323#392—21no—
324#391—21no—
325#391—21no—
326#390—21no—
327#390—21no—
328#390—21no—
329#390—21no—
330#390C2311yescharacteristic
331#390C2311yescharacteristic
332#390C2311yescharacteristic
333#390C2311yescharacteristic
334#389C2311yescharacteristic
335#389C2311yescharacteristic
336#389C2311yescharacteristic
337#389C2311yescharacteristic
338#388—21no—
339#388—21no—
340#388—21no—
341#388—21no—
342#388—21no—
343#388—21no—
344#388—21no—
345#388—21no—
346#388—21no—
347#388—21no—
348#388—21no—
349#388—21no—
350#388—21no—
351#388—21no—
352#388—21no—
353#388—21no—
354#388—21no—
355#388—21no—
356#388—21no—
357#388—21no—
358#387—21no—
359#387—21no—
360#387—21no—
361#387—21no—
362#387—21no—
363#387—21no—
364#387—21no—
365#387—21no—
366#387—21no—
367#387—21no—
368#387—21no—
369#387—21no—
370#387—21no—
371#387—21no—
372#387—21no—
373#387—21no—
374#386—21no—
375#386—21no—
376#386—21no—
377#386—21no—
378#386—21no—
379#386—21no—
380#386—21no—
381#386—21no—
382#386—21no—
383#386—21no—
384#385—21no—
385#385—21no—
386#385—21no—
387#385—21no—
388#384C2311yescharacteristic
389#384C2311yescharacteristic
390#384C2311yescharacteristic
391#383—21no—
392#382C2311yescharacteristic
393#382C2311yescharacteristic
394#382C2311yescharacteristic
395#382C2311yescharacteristic
396#382C2311yescharacteristic
397#381—21no—
398#380—21no—
399#380—21no—
400#380C2311yescharacteristic
401#380C2311yescharacteristic
402#380C2311yescharacteristic
403#380C2311yescharacteristic
404#380C2311yescharacteristic
405#380C2311yescharacteristic
406#380C2311yescharacteristic
407#380C2311yescharacteristic
408#380C2311yescharacteristic
409#380C2311yescharacteristic
410#380C2311yescharacteristic
411#380C2311yescharacteristic
412#379—21no—
413#379—21no—
414C4×C4⋊C4—21no—
415C4×C4⋊C4—21no—
416C4×C4⋊C4—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4—21no—
419C4×C4⋊C4—21no—
420C4×C4⋊C4—21no—
421C4×C4⋊C4—21no—
422C4×C4⋊C4C2311yescharacteristic
423C4×C4⋊C4C2311yescharacteristic
424C4×C4⋊C4C2311yescharacteristic
425C4×C4⋊C4C2311yescharacteristic
426C4×C4⋊C4C2311yescharacteristic
427C4×C4⋊C4C2311yescharacteristic
428C4×C4⋊C4C2311yescharacteristic
429C4×C4⋊C4C2311yescharacteristic
430C4×C4⋊C4C2311yescharacteristic
431C4×C4⋊C4C2311yescharacteristic
432C4×C4⋊C4C2311yescharacteristic
433C4×C4⋊C4C2311yescharacteristic
434C4×C22⋊C4—21no—
435C4×C22⋊C4—21no—
436C4×C22⋊C4—21no—
437C4×C22⋊C4—21no—
438C4×C22⋊C4—21no—
439C4×C22⋊C4—21no—
440C4×C22⋊C4—21no—
441C4×C22⋊C4—21no—
442C4×C22⋊C4—21no—
443C4×C22⋊C4—21no—
444C4×C22⋊C4—21no—
445C4×C22⋊C4—21no—
446C4×C22⋊C4—21no—
447#376—21no—
448#376—21no—
449C43—21no—
450#340C2311yescharacteristic
451#340C2311yescharacteristic
452#340C2311yescharacteristic
453#340C2311yescharacteristic
454#340C2311yescharacteristic
455#340C2311yescharacteristic
456#340C2311yescharacteristic
457#340C2311yescharacteristic
458#340C2311yescharacteristic
459#340C2311yescharacteristic
460#340C2311yescharacteristic
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#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487#336C2311yescharacteristic
488#336C2311yescharacteristic
489#336C2311yescharacteristic
490C25—21no—
491C22×Q8C2×D411yescharacteristic
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—22no—
500C22×D4—22no—
501C22×D4—41no—
502C22×D4—41no—
503C22×D4C2×D411yescharacteristic
504C22×D4C2×D411yescharacteristic
505C22×D4C2×D411yescharacteristic
506C22×D4C2411yescharacteristic
507C22×D4C2411yescharacteristic
508C23×C4—21no—
509C23×C4—21no—
510C23×C4—21no—
511C23×C4—21no—
512C23×C4—21no—
513C23×C4—21no—
514C23×C4C2×D411yescharacteristic
515C23×C4C2×D411yescharacteristic
516C23×C4C2411yescharacteristic
517C23×C4C2411yescharacteristic
518C23×C4C2411yescharacteristic
519C2×M16—22no—
520C2×M16—22no—
521C2×M16—41no—
522C22×C8—22no—
523C22×C8—22no—
524C22×C8—41no—
525C22×C8C2411yescharacteristic
526C22×C8C2411yescharacteristic
527C22×C8C2411yescharacteristic
528C22×C8C2411yescharacteristic
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533#126—24no—
534#126—24no—
535#125—24no—
536#124—24no—
537#123—24no—
538#123—24no—
539C22⋊Q8—24no—
540C22⋊Q8—82no—
541#121—24no—
542#121—22no—
543#121—22no—
544#121—22no—
545#121—22no—
546#121—41no—
547#121—41no—
548#121—41no—
549#121—41no—
550#121—82no—
551#120—82no—
552#120—82no—
553C4×Q8—22no—
554C4×Q8—22no—
555C4×D4—22no—
556C4×D4—22no—
557C4×D4—22no—
558C4×D4—22no—
559C4×D4—22no—
560C4×D4—22no—
561C4×D4—22no—
562C4×D4—22no—
563C4×D4—22no—
564C4×D4—22no—
565C4×D4—22no—
566C4×D4—22no—
567C4×D4—22no—
568C4×D4—22no—
569C4×D4—44no—
570C4×D4—44no—
571C4×D4—82no—
572C4×D4—82no—
573#117—22no—
574#117—22no—
575#117—22no—
576#117—22no—
577#117—22no—
578#117—22no—
579#117—22no—
580#117—22no—
581#117—41no—
582#117—41no—
583#117—41no—
584#117—41no—
585#117#4114yes—
586#117#4114yes—
587C2×C4⋊C4—22no—
588C2×C4⋊C4—22no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—21no—
601C2×C4⋊C4—41no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4C2×D411yescharacteristic
604C2×C4⋊C4C2×D411yescharacteristic
605C2×C4⋊C4C2×D411yescharacteristic
606C2×C4⋊C4C2×D411yescharacteristic
607C2×C4⋊C4C2×D411yescharacteristic
608C2×C4⋊C4C2×D411yescharacteristic
609C2×C4⋊C4C2×D411yescharacteristic
610C2×C4⋊C4C2×D411yescharacteristic
611C2×C4⋊C4C2×D411yescharacteristic
612C2×C4⋊C4C2×D411yescharacteristic
613C2×C4⋊C4C2411yescharacteristic
614C2×C4⋊C4C2411yescharacteristic
615C2×C4⋊C4C2411yescharacteristic
616C2×C4⋊C4C2411yescharacteristic
617C2×C4⋊C4C2411yescharacteristic
618C2×C4⋊C4C2411yescharacteristic
619C2×C4⋊C4C2411yescharacteristic
620C2×C4⋊C4C2411yescharacteristic
621C2×C4⋊C4C2411yescharacteristic
622C2×C4⋊C4C2411yescharacteristic
623C2×C4⋊C4C2411yescharacteristic
624C2×C4⋊C4C2411yescharacteristic
625C2×C4⋊C4C2411yescharacteristic
626C2×C4⋊C4C2411yescharacteristic
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4—21no—
631C2×C22⋊C4—21no—
632C2×C22⋊C4—21no—
633C2×C22⋊C4—21no—
634C2×C22⋊C4—21no—
635C2×C22⋊C4—21no—
636C2×C22⋊C4—21no—
637C2×C22⋊C4—21no—
638C2×C22⋊C4—21no—
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
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—44no—
661C2×C22⋊C4—44no—
662C2×C22⋊C4C2×D411yescharacteristic
663C2×C22⋊C4C2×D411yescharacteristic
664C2×C22⋊C4C2×D411yescharacteristic
665C2×C22⋊C4C2×D411yescharacteristic
666C2×C22⋊C4C2×D411yescharacteristic
667C2×C22⋊C4C2×D411yescharacteristic
668C2×C22⋊C4C2×D411yescharacteristic
669C2×C22⋊C4C2×D411yescharacteristic
670C2×C22⋊C4C2×D411yescharacteristic
671C2×C22⋊C4C2×D411yescharacteristic
672C2×C42—22no—
673C2×C42—22no—
674C2×C42—21no—
675C2×C42—21no—
676C2×C42—21no—
677C2×C42—21no—
678C2×C42—21no—
679C2×C42—21no—
680C2×C42—21no—
681C2×C42—21no—
682C2×C42—21no—
683C2×C42—21no—
684C2×C42—21no—
685C2×C42—21no—
686C2×C42—21no—
687C2×C42—21no—
688C2×C42—21no—
689C2×C42—21no—
690C2×C42—21no—
691C2×C42C2×D411yescharacteristic
692C2×C42C2×D411yescharacteristic
693C2×C42C2411yescharacteristic
694C2×C42C2411yescharacteristic
695C2×C42C2411yescharacteristic
696C2×C42C2411yescharacteristic
697#107—22no—
698#107—22no—
699#107—22no—
700#107—41no—
701#107—41no—
702#107—41no—
703#107—41no—
704#107—41no—
705#106—22no—
706#106—22no—
707#106—22no—
708#106—22no—
709#106—22no—
710#106—41no—
711#106—41no—
712#106—41no—
713C4⋊C8—22no—
714C4⋊C8—22no—
715#102—22no—
716#102—22no—
717#102—22no—
718#102—22no—
719#102—22no—
720#102—22no—
721#102—22no—
722#102—22no—
723#102—22no—
724#102—22no—
725#102—41no—
726#102—41no—
727#102—41no—
728#102—41no—
729#102#4114yes—
730#102#4114yes—
731C22⋊C8—22no—
732C22⋊C8—22no—
733C22⋊C8—22no—
734C22⋊C8—22no—
735C22⋊C8—22no—
736C22⋊C8—22no—
737C22⋊C8—41no—
738C22⋊C8—41no—
739C22⋊C8—41no—
740C22⋊C8—41no—
741#97—22no—
742#97—22no—
743#97—22no—
744C4×C8—22no—
745C4×C8—22no—
746C4×C8—22no—
747#95—21no—
748#95—21no—
749#95—21no—
750#95—21no—
751#95—21no—
752#95—21no—
753#95—21no—
754#95—21no—
755#95—21no—
756#95—21no—
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—
785C24—21no—
786C24—21no—
787C24—42no—
788C24—42no—
789C24—42no—
790C24—81no—
791C24—81no—
792C24—81no—
793C24—81no—
794C24C22×D411yescharacteristic
795C24C22×D411yescharacteristic
796C24C22×D411yescharacteristic
797C2×Q8—22no—
798C2×Q8—41no—
799C2×Q8—41no—
800C2×D4—28no—
801C2×D4—22no—
802C2×D4—22no—
803C2×D4—22no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—21no—
809C2×D4—21no—
810C2×D4—21no—
811C2×D4—21no—
812C2×D4—21no—
813C2×D4—21no—
814C2×D4—44no—
815C2×D4—44no—
816C2×D4—42no—
817C2×D4—42no—
818C2×D4—44no—
819C2×D4—41no—
820C2×D4—41no—
821C2×D4—41no—
822C2×D4—41no—
823C2×D4—41no—
824C2×D4—41no—
825C2×D4—42no—
826C2×D4—42no—
827C2×D4—42no—
828C2×D4—42no—
829C2×D4—42no—
830C2×D4—42no—
831C2×D4—42no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4—81no—
837C2×D4—81no—
838C2×D4C2×#4112yes—
839C2×D4C2×#4112yes—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—22no—
859C22×C4—22no—
860C22×C4—21no—
861C22×C4—21no—
862C22×C4—21no—
863C22×C4—21no—
864C22×C4—21no—
865C22×C4—21no—
866C22×C4—21no—
867C22×C4—21no—
868C22×C4—21no—
869C22×C4—21no—
870C22×C4—21no—
871C22×C4—21no—
872C22×C4—41no—
873C22×C4—41no—
874C22×C4—41no—
875C22×C4—41no—
876C22×C4—42no—
877C22×C4—42no—
878C22×C4—42no—
879C22×C4—42no—
880C22×C4—42no—
881C22×C4—42no—
882C22×C4—81no—
883C22×C4—81no—
884C22×C4—81no—
885C22×C4—81no—
886C22×C4—81no—
887C22×C4—81no—
888C22×C4—81no—
889C22×C4—81no—
890C22×C4—81no—
891C22×C4—81no—
892C22×C4—81no—
893C22×C4—81no—
894C22×C4C22×D411yescharacteristic
895C22×C4C22×D411yescharacteristic
896C22×C4C22×D411yescharacteristic
897C22×C4C22×D411yescharacteristic
898C22×C4C22×D411yescharacteristic
899C22×C4C22×D411yescharacteristic
900C22×C4C22×D411yescharacteristic
901C22×C4C22×D411yescharacteristic
902C22×C4C22×D411yescharacteristic
903C22×C4C22×D411yescharacteristic
904C22×C4C22×D411yescharacteristic
905C22×C4C2×#4112yes—
906C22×C4C2×#4112yes—
907C22×C4C2511yescharacteristic
908M16—44no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—21no—
914C2×C8—21no—
915C2×C8—21no—
916C2×C8—21no—
917C2×C8—21no—
918C2×C8—21no—
919C2×C8—21no—
920C2×C8—21no—
921C2×C8—21no—
922C2×C8—21no—
923C2×C8—21no—
924C2×C8—21no—
925C2×C8—21no—
926C2×C8—21no—
927C2×C8—21no—
928C2×C8—21no—
929C2×C8—21no—
930C2×C8—21no—
931C2×C8—44no—
932C2×C8C2×#4112yes—
933C2×C8C2×#4112yes—
934C4⋊C4—22no—
935C4⋊C4—22no—
936C4⋊C4—22no—
937C4⋊C4—22no—
938C4⋊C4—22no—
939C4⋊C4—22no—
940C4⋊C4—22no—
941C4⋊C4—22no—
942C4⋊C4—21no—
943C4⋊C4—21no—
944C4⋊C4—21no—
945C4⋊C4—21no—
946C4⋊C4—21no—
947C4⋊C4—21no—
948C4⋊C4—21no—
949C4⋊C4—21no—
950C4⋊C4—21no—
951C4⋊C4—21no—
952C4⋊C4—21no—
953C4⋊C4—21no—
954C4⋊C4—21no—
955C4⋊C4—21no—
956C4⋊C4—21no—
957C4⋊C4—21no—
958C4⋊C4—21no—
959C4⋊C4—21no—
960C4⋊C4—21no—
961C4⋊C4—21no—
962C4⋊C4—21no—
963C4⋊C4—21no—
964C4⋊C4—21no—
965C4⋊C4—21no—
966C4⋊C4—21no—
967C4⋊C4—21no—
968C4⋊C4—42no—
969C4⋊C4—42no—
970C4⋊C4—42no—
971C4⋊C4—81no—
972C4⋊C4—81no—
973C4⋊C4—81no—
974C4⋊C4—81no—
975C4⋊C4—81no—
976C4⋊C4—81no—
977C4⋊C4—81no—
978C4⋊C4—81no—
979C4⋊C4—81no—
980C4⋊C4#12314yes—
981C4⋊C4#12314yes—
982C4⋊C4C2×#4112yes—
983C4⋊C4C2×#4112yes—
984C22⋊C4—22no—
985C22⋊C4—22no—
986C22⋊C4—22no—
987C22⋊C4—22no—
988C22⋊C4—22no—
989C22⋊C4—22no—
990C22⋊C4—22no—
991C22⋊C4—22no—
992C22⋊C4—42no—
993C22⋊C4—42no—
994C22⋊C4—42no—
995C22⋊C4—42no—
996C22⋊C4—42no—
997C22⋊C4—42no—
998C22⋊C4—42no—
999C22⋊C4—42no—
1000C22⋊C4—42no—
1001C22⋊C4—42no—
1002C22⋊C4—42no—
1003C22⋊C4—42no—
1004C22⋊C4—42no—
1005C22⋊C4—42no—
1006C22⋊C4—42no—
1007C22⋊C4—42no—
1008C22⋊C4—81no—
1009C22⋊C4—81no—
1010C22⋊C4—81no—
1011C22⋊C4—81no—
1012C22⋊C4—81no—
1013C22⋊C4—81no—
1014C22⋊C4—81no—
1015C22⋊C4—81no—
1016C22⋊C4—81no—
1017C22⋊C4—81no—
1018C22⋊C4—81no—
1019C22⋊C4—81no—
1020C22⋊C4—81no—
1021C22⋊C4—81no—
1022C22⋊C4—81no—
1023C22⋊C4—81no—
1024C22⋊C4—81no—
1025C22⋊C4#12314yes—
1026C22⋊C4#12314yes—
1027C42—22no—
1028C42—22no—
1029C42—21no—
1030C42—21no—
1031C42—21no—
1032C42—21no—
1033C42—42no—
1034C42—42no—
1035C42—42no—
1036C42—42no—
1037C42—42no—
1038C42—81no—
1039C42—81no—
1040C42—81no—
1041C42—81no—
1042C42—81no—
1043C42—81no—
1044C42—81no—
1045C42—81no—
1046C42—81no—
1047C42—81no—
1048C42—81no—
1049C42—81no—
1050C42C2×#4112yes—
1051C42C2×#4112yes—
1052C42C2×#4112yes—
1053C42C2×#4112yes—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—21no—
1061C23—21no—
1062C23—21no—
1063C23—21no—
1064C23—21no—
1065C23—21no—
1066C23—21no—
1067C23—21no—
1068C23—21no—
1069C23—21no—
1070C23—21no—
1071C23—21no—
1072C23—21no—
1073C23—22no—
1074C23—22no—
1075C23—21no—
1076C23—48no—
1077C23—41no—
1078C23—41no—
1079C23—41no—
1080C23—41no—
1081C23—41no—
1082C23—41no—
1083C23—41no—
1084C23—41no—
1085C23—41no—
1086C23—41no—
1087C23—41no—
1088C23—41no—
1089C23—162no—
1090C23—162no—
1091C23—162no—
1092C23—162no—
1093C23—162no—
1094C23—162no—
1095C23C2×#12312yes—
1096C23C23×D411yescharacteristic
1097Q8—82no—
1098D4—22no—
1099D4—22no—
1100D4—22no—
1101D4—22no—
1102D4—48no—
1103D4—41no—
1104D4—41no—
1105D4—41no—
1106D4—41no—
1107D4—82no—
1108D4—82no—
1109D4—82no—
1110D4—84no—
1111D4—84no—
1112D4—162no—
1113D4—162no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—21no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—21no—
1129C2×C4—21no—
1130C2×C4—21no—
1131C2×C4—21no—
1132C2×C4—21no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—21no—
1137C2×C4—21no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—21no—
1141C2×C4—21no—
1142C2×C4—22no—
1143C2×C4—22no—
1144C2×C4—21no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—21no—
1148C2×C4—41no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—41no—
1152C2×C4—41no—
1153C2×C4—41no—
1154C2×C4—41no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—41no—
1158C2×C4—41no—
1159C2×C4—41no—
1160C2×C4—41no—
1161C2×C4—41no—
1162C2×C4—41no—
1163C2×C4—41no—
1164C2×C4—41no—
1165C2×C4—41no—
1166C2×C4—41no—
1167C2×C4—41no—
1168C2×C4—41no—
1169C2×C4—41no—
1170C2×C4—41no—
1171C2×C4—41no—
1172C2×C4—41no—
1173C2×C4—41no—
1174C2×C4—41no—
1175C2×C4—41no—
1176C2×C4—41no—
1177C2×C4—41no—
1178C2×C4—41no—
1179C2×C4—41no—
1180C2×C4—41no—
1181C2×C4—41no—
1182C2×C4—41no—
1183C2×C4—41no—
1184C2×C4—41no—
1185C2×C4—41no—
1186C2×C4—41no—
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—82no—
1197C2×C4—82no—
1198C2×C4—162no—
1199C2×C4—162no—
1200C2×C4—162no—
1201C2×C4—162no—
1202C2×C4—162no—
1203C2×C4—162no—
1204C2×C4C2×#12312yes—
1205C2×C4C2×#12312yes—
1206C2×C4C2×#12312yes—
1207C2×C4C2×#12312yes—
1208C2×C4C2×#12312yes—
1209C2×C4C22×#4111yescharacteristic
1210C2×C4C22×#4111yescharacteristic
1211C2×C4C22×#4111yescharacteristic
1212C2×C4C22×#4111yescharacteristic
1213C2×C4#58511yescharacteristic
1214C2×C4#58511yescharacteristic
1215C8—22no—
1216C8—22no—
1217C8—41no—
1218C8—41no—
1219C8—41no—
1220C8—41no—
1221C8—41no—
1222C8—41no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—41no—
1230C22—41no—
1231C22—41no—
1232C22—42no—
1233C22—41no—
1234C22—42no—
1235C22—41no—
1236C22—41no—
1237C22—42no—
1238C22—41no—
1239C22—41no—
1240C22—42no—
1241C22—41no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—41no—
1246C22—41no—
1247C22—41no—
1248C22—42no—
1249C22—42no—
1250C22—81no—
1251C22—81no—
1252C22—81no—
1253C22—81no—
1254C22—81no—
1255C22—81no—
1256C22—81no—
1257C22—81no—
1258C22—168no—
1259C22C22×#12311yescharacteristic
1260C22D4×#4111yescharacteristic
1261C22D4×#4111yescharacteristic
1262C22#358411yescharacteristic
1263C22#358411yescharacteristic
1264C22#358511yescharacteristic
1265C22#358511yescharacteristic
1266C4—22no—
1267C4—22no—
1268C4—22no—
1269C4—22no—
1270C4—22no—
1271C4—42no—
1272C4—42no—
1273C4—41no—
1274C4—41no—
1275C4—41no—
1276C4—41no—
1277C4—41no—
1278C4—41no—
1279C4—81no—
1280C4—81no—
1281C4—81no—
1282C4—81no—
1283C4—81no—
1284C4—81no—
1285C4—81no—
1286C4—81no—
1287C4—81no—
1288C4—81no—
1289C4—81no—
1290C4—81no—
1291C4#344411yescharacteristic
1292C4#345511yescharacteristic
1293C4#347511yescharacteristic
1294C4#347511yescharacteristic
1295C2—42no—
1296C2—81no—
1297C2—81no—
1298C2—82no—
1299C2—82no—
1300C2#3474211yescharacteristic
1301C2#6052311yescharacteristic
1302C2#6052311yescharacteristic
1303C2#6150111yescharacteristic
1304C2#6150411yescharacteristic
1305C2#6152711yescharacteristic
1306C2#6153611yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#35522C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ C2×#529 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
2. #34244C2semidirect
3. #25072C2semidirect
4. #25069C2semidirect
5. #25026C2semidirect
6. #25023C2semidirect
7. #24999C2semidirect
8. #24991C2semidirect
9. #24974C2semidirect
10. #24968C2semidirect
11. #24963C2semidirect
12. #24961C2semidirect
13. #24948C2semidirect
14. #24938C2semidirect
15. #24890C2semidirect
16. #24878C2semidirect
17. #24873C2semidirect
18. #24869C2semidirect
19. #23770C2semidirect
20. #23767C2semidirect
21. #23764C2semidirect
22. #23758C2semidirect
23. #21588C2semidirect
24. #21584C2semidirect
25. #21582C2semidirect
26. C4×#482C2semidirect
27. #21381C2semidirect
28. #21367C2semidirect
29. #20822C2semidirect
30. #20744C2semidirect
31. #20416C2semidirect
62. #2355C22semidirect
63. #2355C22semidirect
65. #2354C22semidirect
69. #2352C22semidirect
76. #2314C22semidirect
81. #2283C22semidirect
83. #2274C22semidirect
84. C4×#117C22semidirect
85. #2101C22semidirect
86. #2101C22semidirect
87. #2101C22semidirect
88. #2100C22semidirect
93. #2085C22semidirect
94. #2085C22semidirect
95. #2085C22semidirect
96. #2083C22semidirect
97. #2077C22semidirect
98. #2077C22semidirect
99. #2077C22semidirect
100. #2076C22semidirect
101. #2076C22semidirect
102. #2076C22semidirect
103. #2075C22semidirect
104. #2075C22semidirect
117. #1985C22semidirect
118. #1984C22semidirect
119. #1955C22semidirect
120. #1954C22semidirect
121. #1949C22semidirect
122. #1949C22semidirect
123. #1948C22semidirect
124. #1947C22semidirect
133. #1921C22semidirect
134. #1920C22semidirect
135. #1920C22semidirect
136. #1920C22semidirect
137. #1919C22semidirect
138. #1919C22semidirect
139. #1918C22semidirect
140. #1918C22semidirect
151. #1854C22semidirect
152. #1854C22semidirect
153. #1854C22semidirect
155. #1853C22semidirect
157. #1847C22semidirect
158. #1847C22semidirect
159. #1835C22semidirect
160. #1834C22semidirect
163. #1825C22semidirect
164. #1825C22semidirect
165. #1825C22semidirect
166. #1823C22semidirect
177. #1776C22semidirect
178. #1776C22semidirect
179. #1776C22semidirect
180. #1776C22semidirect
181. C4×#107C22semidirect
182. C4×#107C22semidirect
183. C4×#106C22semidirect
184. C4×#106C22semidirect
197. #1750C22semidirect
198. #1750C22semidirect
199. #1749C22semidirect
200. C4×C22⋊C8C22semidirect

Maximal subgroups

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

subgroupindex
#355222
#342442
#250722
#250692
#250262
#250232
#249992
#249912
#249742
#249682
#249632
#249612
#249482
#249382
#248902
#248782
#248732
#248692
#237702
#237672
#237642
#237582
#215882
#215842
#215822
C4×#4822
#213812
#213672
#208222
#207442
#204162