Finite Group Databasebeta

← #7039532

Subgroups — #7039532

Order 512.

1420 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#45133C211yesmaximal, characteristic, complemented
2#42586C211yesmaximal, characteristic
3#32252C211yesmaximal, characteristic, complemented
4#32015C211yesmaximal, characteristic, complemented
5#31341C211yesmaximal, characteristic, complemented
6#31325C211yesmaximal, characteristic, complemented
7#31270C211yesmaximal, characteristic, complemented
8#30971C211yesmaximal, characteristic, complemented
9#30568C211yesmaximal, characteristic, complemented
10#30408C211yesmaximal, characteristic, complemented
11#29491C211yesmaximal, characteristic, complemented
12#28715C211yesmaximal, characteristic, complemented
13#28566C211yesmaximal, characteristic, complemented
14#28076C211yesmaximal, characteristic, complemented
15#27868C211yesmaximal, characteristic, complemented
16#27800C211yesmaximal, characteristic, complemented
17#27503C211yesmaximal, characteristic, complemented
18#27478C211yesmaximal, characteristic, complemented
19#27442C211yesmaximal, characteristic, complemented
20#27340C211yesmaximal, characteristic, complemented
21#27238C211yesmaximal, characteristic, complemented
22#26731C211yesmaximal, characteristic, complemented
23#25351C211yesmaximal, characteristic, complemented
24#25120C211yesmaximal, characteristic, complemented
25#24948C211yesmaximal, characteristic, complemented
26#24890C211yesmaximal, characteristic, complemented
27#23767C211yesmaximal, characteristic, complemented
28#23124C211yesmaximal, characteristic, complemented
29#22933C211yesmaximal, characteristic, complemented
30#22584C211yesmaximal, characteristic, complemented
31#22195C211yesmaximal, characteristic, complemented
32C2×#501C2211yescharacteristic, complemented
33C2×#482C2211yescharacteristic
34C2×#478C2211yescharacteristic
35C2×#465C2211yescharacteristic
36C2×#465C2211yescharacteristic
37C2×#450C2211yescharacteristic
38C2×#435C2211yescharacteristic
39C2×#435C2211yescharacteristic, complemented
40C2×#418C2211yescharacteristic
41#2826—21no—
42#2808—21no—
43#2803—21no—
44#2785—21no—
45#2775—21no—
46#2741—21no—
47#2714—21no—
48#2685—21no—
49#2685—21no—
50#2648—21no—
51#2624C2211yescharacteristic
52#2617—21no—
53#2593—21no—
54#2563C2211yescharacteristic
55#2562C2211yescharacteristic
56#2562C2211yescharacteristic, complemented
57#2550C2211yescharacteristic, complemented
58#2537C2211yescharacteristic
59#2536C2211yescharacteristic
60#2532—21no—
61#2529—21no—
62#2512C2211yescharacteristic
63#2508—21no—
64#2496C2211yescharacteristic
65#2492C2211yescharacteristic, complemented
66#2490C2211yescharacteristic
67#2489C2211yescharacteristic
68#2485C2211yescharacteristic
69#2480—21no—
70#2454C2211yescharacteristic
71#2415C2211yescharacteristic
72#2415C2211yescharacteristic, complemented
73#2414C2211yescharacteristic
74#2408C2211yescharacteristic
75#2408C2211yescharacteristic
76#2392C2211yescharacteristic
77#2363C2211yescharacteristic
78#2355C2211yescharacteristic, complemented
79#2354C2211yescharacteristic
80#2347C2211yescharacteristic, complemented
81#2346C2211yescharacteristic
82D4×C22⋊C4C2211yescharacteristic
83#2324C2211yescharacteristic
84#2323C2211yescharacteristic, complemented
85#2314C2211yescharacteristic, complemented
86#2101C2211yescharacteristic, complemented
87#2100C2211yescharacteristic, complemented
88#2095C2211yescharacteristic, complemented
89#2093C2211yescharacteristic
90#2092C2211yescharacteristic
91#2088C2211yescharacteristic, complemented
92#2085C2211yescharacteristic, complemented
93#2084C2211yescharacteristic, complemented
94#2083C2211yescharacteristic, complemented
95#2077C2211yescharacteristic
96#2077C2211yescharacteristic, complemented
97#2077C2211yescharacteristic, complemented
98#2076C2211yescharacteristic
99#2076C2211yescharacteristic
100#2076C2211yescharacteristic, complemented
101#2076C2211yescharacteristic, complemented
102#2075C2211yescharacteristic
103#2073C2211yescharacteristic
104#2071C2211yescharacteristic
105#2065C2211yescharacteristic
106#2059C2211yescharacteristic, complemented
107#2059C2211yescharacteristic, complemented
108#2055C2211yescharacteristic
109#2055C2211yescharacteristic
110#2036C2211yescharacteristic
111#2036C2211yescharacteristic, complemented
112#2035C2211yescharacteristic
113#2035C2211yescharacteristic, complemented
114#2034C2211yescharacteristic
115#2033C2211yescharacteristic
116#2033C2211yescharacteristic
117#2033C2211yescharacteristic
118#2033C2211yescharacteristic
119#2033C2211yescharacteristic
120#2026C2211yescharacteristic, complemented
121#2025C2211yescharacteristic
122#2023C2211yescharacteristic
123#2023C2211yescharacteristic
124#2000C2211yescharacteristic
125#2000C2211yescharacteristic
126#1992C2211yescharacteristic, complemented
127#1989C2211yescharacteristic, complemented
128#1988C2211yescharacteristic, complemented
129#1973C2211yescharacteristic
130#1973C2211yescharacteristic
131#1947C2211yescharacteristic, complemented
132#1944C2211yescharacteristic, complemented
133#1936C2211yescharacteristic
134#1936C2211yescharacteristic
135#1935C2211yescharacteristic, complemented
136#1934C2211yescharacteristic
137#1933C2211yescharacteristic, complemented
138#1928C2211yescharacteristic, complemented
139#1927C2211yescharacteristic, complemented
140#1926C2211yescharacteristic
141#1926C2211yescharacteristic
142#1926C2211yescharacteristic
143#1926C2211yescharacteristic
144#1925C2211yescharacteristic
145#1925C2211yescharacteristic
146#1925C2211yescharacteristic
147#1924C2211yescharacteristic
148#1923C2211yescharacteristic, complemented
149#1921C2211yescharacteristic, complemented
150#1920C2211yescharacteristic, complemented
151#1920C2211yescharacteristic, complemented
152#1919C2211yescharacteristic, complemented
153#1918C2211yescharacteristic, complemented
154#1918C2211yescharacteristic, complemented
155#1918C2211yescharacteristic, complemented
156#1917C2211yescharacteristic, complemented
157#1917C2211yescharacteristic, complemented
158#1895C2211yescharacteristic
159#1895C2211yescharacteristic
160#1894C2211yescharacteristic
161#1894C2211yescharacteristic, complemented
162#1893C2211yescharacteristic
163#1893C2211yescharacteristic
164#1880C2211yescharacteristic
165#1880C2211yescharacteristic
166#1877C2211yescharacteristic
167#1877C2211yescharacteristic
168#1875C2211yescharacteristic
169#1873C2211yescharacteristic, complemented
170#1870C2211yescharacteristic
171#1870C2211yescharacteristic
172#1869C2211yescharacteristic
173#1869C2211yescharacteristic, complemented
174#1865C2211yescharacteristic, complemented
175#1864C2211yescharacteristic
176#1863C2211yescharacteristic, complemented
177#1862C2211yescharacteristic
178#1854C2211yescharacteristic
179#1854C2211yescharacteristic
180#1854C2211yescharacteristic, complemented
181#1854C2211yescharacteristic, complemented
182#1825C2211yescharacteristic
183#1825C2211yescharacteristic, complemented
184#1809C2211yescharacteristic
185#1809C2211yescharacteristic
186#1809C2211yescharacteristic, complemented
187#1808C2211yescharacteristic, complemented
188#1808C2211yescharacteristic, complemented
189#1807C2211yescharacteristic, complemented
190#1786C2211yescharacteristic
191#1786C2211yescharacteristic
192#1776C2211yescharacteristic, complemented
193#1776C2211yescharacteristic, complemented
194C4×#107C2211yescharacteristic, complemented
195#1762C2211yescharacteristic
196#1762C2211yescharacteristic
197C4×#102C2211yescharacteristic
198#1753C2211yescharacteristic
199#1752C2211yescharacteristic, complemented
200#1750C2211yescharacteristic, complemented
201#1735C2211yescharacteristic, complemented
202#1729C2211yescharacteristic, complemented
203C23×D4C2311yescharacteristic
204C22×SD16C2311yescharacteristic
205C22×SD16C2311yescharacteristic
206C22×M16C2311yescharacteristic
207C22×M16C2311yescharacteristic
208C23×C8C2311yescharacteristic
209C23×C8C2311yescharacteristic
210C2×C4⋊Q8C2311yescharacteristic
211C2×#126—21no—
212C2×#126—21no—
213C2×#125C2311yescharacteristic
214C2×#125C2311yescharacteristic
215C2×C22⋊Q8C2311yescharacteristic
216C2×C22⋊Q8C2311yescharacteristic
217C2×C22⋊Q8C2311yescharacteristic
218C2×#121—21no—
219C2×#121C2311yescharacteristic
220C2×#121C2311yescharacteristic
221C2×#121C2311yescharacteristic
222C2×#121C2311yescharacteristic
223C2×#120—21no—
224C2×#120—21no—
225C2×C4×Q8C2311yescharacteristic
226C2×C4×D4C2311yescharacteristic
227C2×C4×D4C2311yescharacteristic
228C2×C4×D4C2311yescharacteristic
229C2×C4×D4C2311yescharacteristic
230C2×C4×D4C2311yescharacteristic
231C2×#117C2311yescharacteristic
232C2×#117C2311yescharacteristic
233C2×#117C2311yescharacteristic
234C2×#117C2311yescharacteristic
235C22×C22⋊C4—21no—
236#501—42no—
237#482—24no—
238#478—42no—
239#465—24no—
240#465—42no—
241#450—42no—
242#435—42no—
243#435—42no—
244C2×#107C2311yescharacteristic
245C2×#107C2311yescharacteristic
246C2×#107C2311yescharacteristic
247C2×#107C2311yescharacteristic
248C2×#107C2311yescharacteristic
249C2×#107C2311yescharacteristic
250C2×#107C2311yescharacteristic
251C2×#107C2311yescharacteristic
252C2×#106C2311yescharacteristic
253C2×#106C2311yescharacteristic
254C2×#106C2311yescharacteristic
255C2×#106C2311yescharacteristic
256C2×#106C2311yescharacteristic
257C2×#106C2311yescharacteristic
258C2×C4⋊C8C2311yescharacteristic
259C2×C4⋊C8C2311yescharacteristic
260#418—24no—
261C2×#103C2311yescharacteristic
262C2×#103C2311yescharacteristic
263C2×#103C2311yescharacteristic
264C2×#103C2311yescharacteristic
265C2×#103C2311yescharacteristic
266C2×#103C2311yescharacteristic
267C2×#102C2311yescharacteristic
268C2×#102C2311yescharacteristic
269C2×#102C2311yescharacteristic
270C2×#102C2311yescharacteristic
271C2×#102C2311yescharacteristic
272C2×#102C2311yescharacteristic
273C2×#102C2311yescharacteristic
274C2×#102C2311yescharacteristic
275C2×#102C2311yescharacteristic
276C2×#102C2311yescharacteristic
277C2×#102C2311yescharacteristic
278C2×#102C2311yescharacteristic
279C2×#102C2311yescharacteristic
280C2×#102C2311yescharacteristic
281C2×C22⋊C8C2311yescharacteristic
282C2×C22⋊C8C2311yescharacteristic
283C2×C22⋊C8C2311yescharacteristic
284C2×C22⋊C8C2311yescharacteristic
285C2×C22⋊C8C2311yescharacteristic
286C2×C22⋊C8C2311yescharacteristic
287C2×C22⋊C8C2311yescharacteristic
288C2×C22⋊C8C2311yescharacteristic
289C2×#97C2311yescharacteristic
290C2×#97C2311yescharacteristic
291C2×#97C2311yescharacteristic
292C2×C4×C8C2311yescharacteristic
293#400—21no—
294#400—21no—
295#400—21no—
296#400—21no—
297#400—21no—
298#399—21no—
299#399—21no—
300#398—21no—
301#398—21no—
302#398D411yescharacteristic
303#397—21no—
304#397—21no—
305#397—21no—
306#397—21no—
307#397—21no—
308#397—21no—
309#397—21no—
310#397—21no—
311#397D411yescharacteristic
312#396—21no—
313#396—21no—
314#396D411yescharacteristic
315#396D411yescharacteristic
316#395—21no—
317#394—21no—
318#394—21no—
319#394—21no—
320#394—21no—
321#394—21no—
322#394—21no—
323#394—21no—
324#394—21no—
325#394—21no—
326#394—21no—
327#394—21no—
328#394—21no—
329#394—21no—
330#394—21no—
331#394D411yescharacteristic
332#394D411yescharacteristic
333#394D411yescharacteristic
334#393—21no—
335#393—21no—
336#393—21no—
337#392—21no—
338#392—21no—
339#392—21no—
340#392D411yescharacteristic
341#391—21no—
342#391—21no—
343#391C2311yescharacteristic
344#391C2311yescharacteristic
345#391C2311yescharacteristic
346#390—21no—
347#390—21no—
348#390—21no—
349#390—21no—
350#390—21no—
351#390—21no—
352#390C2311yescharacteristic
353#390C2311yescharacteristic
354#390C2311yescharacteristic
355#390C2311yescharacteristic
356#390C2311yescharacteristic
357#390C2311yescharacteristic
358#389—21no—
359#389—21no—
360#389—21no—
361#389—21no—
362#389C2311yescharacteristic
363#389C2311yescharacteristic
364#389C2311yescharacteristic
365#389C2311yescharacteristic
366#389C2311yescharacteristic
367#389C2311yescharacteristic
368#389C2311yescharacteristic
369#388—21no—
370#388—21no—
371#388—21no—
372#388—21no—
373#388—21no—
374#388—21no—
375#388—21no—
376#388—21no—
377#388—21no—
378#388—21no—
379#388—21no—
380#388—21no—
381#388—21no—
382#388—21no—
383#388—21no—
384#388—21no—
385#388—21no—
386#388—21no—
387#388—21no—
388#388—21no—
389#388—21no—
390#388—21no—
391#388—21no—
392#388—21no—
393#388—21no—
394#388—21no—
395#387—21no—
396#387—21no—
397#387—21no—
398#387—21no—
399#387—21no—
400#387—21no—
401#387—21no—
402#386—21no—
403#386—21no—
404#386—21no—
405#386—21no—
406#385—21no—
407#385—21no—
408#384C2311yescharacteristic
409#384C2311yescharacteristic
410#383—21no—
411#382—21no—
412#382—21no—
413#382—21no—
414#382—21no—
415#382C2311yescharacteristic
416#380—21no—
417#380—21no—
418#380C2311yescharacteristic
419#380C2311yescharacteristic
420#380C2311yescharacteristic
421#380C2311yescharacteristic
422#380C2311yescharacteristic
423#380C2311yescharacteristic
424#380C2311yescharacteristic
425#380C2311yescharacteristic
426#380C2311yescharacteristic
427#380C2311yescharacteristic
428#380C2311yescharacteristic
429#380C2311yescharacteristic
430#380C2311yescharacteristic
431#379—21no—
432#379—21no—
433#379—21no—
434C4×C4⋊C4—21no—
435C4×C4⋊C4—21no—
436C4×C4⋊C4—21no—
437C4×C4⋊C4C2311yescharacteristic
438C4×C4⋊C4C2311yescharacteristic
439C4×C4⋊C4C2311yescharacteristic
440C4×C4⋊C4C2311yescharacteristic
441C4×C4⋊C4C2311yescharacteristic
442C4×C4⋊C4C2311yescharacteristic
443C4×C4⋊C4C2311yescharacteristic
444C4×C4⋊C4C2311yescharacteristic
445C4×C22⋊C4—21no—
446C4×C22⋊C4C2311yescharacteristic
447C4×C22⋊C4C2311yescharacteristic
448#376—21no—
449#340C2311yescharacteristic
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#336C2311yescharacteristic
478#336C2311yescharacteristic
479#336C2311yescharacteristic
480#336C2311yescharacteristic
481#336C2311yescharacteristic
482#336C2311yescharacteristic
483#336C2311yescharacteristic
484#336C2311yescharacteristic
485#336C2311yescharacteristic
486#336C2311yescharacteristic
487C25—21no—
488C22×Q8—21no—
489C22×Q8C2411yescharacteristic
490C22×D4—22no—
491C22×D4—21no—
492C22×D4—21no—
493C22×D4—21no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—41no—
497C22×D4—41no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C2×D411yescharacteristic
502C22×D4C2×D411yescharacteristic
503C22×D4C2×D411yescharacteristic
504C22×D4C2411yescharacteristic
505C22×D4C2411yescharacteristic
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C2411yescharacteristic
509C23×C4C2411yescharacteristic
510C23×C4C2411yescharacteristic
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—41no—
514C2×SD16—41no—
515C2×SD16—41no—
516C2×SD16—41no—
517C2×M16—22no—
518C2×M16—41no—
519C2×M16—41no—
520C2×M16—41no—
521C2×M16—41no—
522C2×M16—41no—
523C22×C8—22no—
524C22×C8—22no—
525C22×C8—41no—
526C22×C8—41no—
527C22×C8—41no—
528C22×C8—41no—
529C22×C8C2411yescharacteristic
530C22×C8C2411yescharacteristic
531C22×C8C2411yescharacteristic
532C22×C8C2411yescharacteristic
533C22×C8C2411yescharacteristic
534C22×C8C2411yescharacteristic
535C22×C8C2411yescharacteristic
536C22×C8C2411yescharacteristic
537C4⋊Q8—41no—
538C4⋊Q8—41no—
539#126—82no—
540#126—82no—
541#125—41no—
542#125—41no—
543#125—41no—
544#125—41no—
545C22⋊Q8—22no—
546C22⋊Q8—41no—
547C22⋊Q8—41no—
548C22⋊Q8—41no—
549C22⋊Q8—41no—
550C22⋊Q8—41no—
551#121—22no—
552#121—22no—
553#121—41no—
554#121—41no—
555#121—41no—
556#121—41no—
557#121—41no—
558#121—41no—
559#121—82no—
560#120—82no—
561#120—82no—
562C4×Q8—41no—
563C4×Q8—41no—
564C4×D4—41no—
565C4×D4—41no—
566C4×D4—41no—
567C4×D4—41no—
568C4×D4—41no—
569C4×D4—41no—
570C4×D4—41no—
571C4×D4—41no—
572C4×D4—41no—
573C4×D4—41no—
574#117—22no—
575#117—22no—
576#117—41no—
577#117—41no—
578#117—41no—
579#117—41no—
580#117—41no—
581#117—41no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
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—21no—
602C2×C4⋊C4C2×D411yescharacteristic
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⋊C4C2411yescharacteristic
610C2×C4⋊C4C2411yescharacteristic
611C2×C4⋊C4C2411yescharacteristic
612C2×C4⋊C4C2411yescharacteristic
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×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—21no—
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—82no—
660C2×C22⋊C4C2×D411yescharacteristic
661C2×C22⋊C4C2×D411yescharacteristic
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—21no—
673C2×C42—21no—
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×C42C2411yescharacteristic
684C2×C42C2411yescharacteristic
685C2×C42C2411yescharacteristic
686C2×C42C2411yescharacteristic
687#107—22no—
688#107—22no—
689#107—41no—
690#107—41no—
691#107—41no—
692#107—41no—
693#107—41no—
694#107—41no—
695#106—22no—
696#106—22no—
697#106—22no—
698#106—41no—
699#106—41no—
700#106—41no—
701C4⋊C8—22no—
702C4⋊C8—41no—
703#103—22no—
704#103—41no—
705#103—41no—
706#103—41no—
707#103—41no—
708#103—41no—
709#102—22no—
710#102—22no—
711#102—22no—
712#102—22no—
713#102—22no—
714#102—41no—
715#102—41no—
716#102—41no—
717#102—41no—
718#102—41no—
719#102—41no—
720#102—41no—
721#102—41no—
722#102#4114yes—
723C22⋊C8—22no—
724C22⋊C8—22no—
725C22⋊C8—22no—
726C22⋊C8—41no—
727C22⋊C8—41no—
728C22⋊C8—41no—
729C22⋊C8—41no—
730C22⋊C8—41no—
731#97—22no—
732#97—41no—
733#97—41no—
734C4×C8—41no—
735#95—21no—
736#95—21no—
737#95—21no—
738#95—21no—
739#95—21no—
740#95—21no—
741#95—21no—
742#95—21no—
743#95—21no—
744#95—21no—
745#95—21no—
746#95—21no—
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#95C2×D411yescharacteristic
771#95C2×D411yescharacteristic
772#95C2×D411yescharacteristic
773#95C2×D411yescharacteristic
774#95C2×D411yescharacteristic
775#95C2×D411yescharacteristic
776C24—21no—
777C24—21no—
778C24—42no—
779C24—42no—
780C24—81no—
781C24—81no—
782C24—81no—
783C24—81no—
784C24—81no—
785C24C22×D411yescharacteristic
786C24C22×D411yescharacteristic
787C24C22×D411yescharacteristic
788C2×Q8—21no—
789C2×Q8—21no—
790C2×Q8—21no—
791C2×Q8—21no—
792C2×Q8—21no—
793C2×Q8—21no—
794C2×Q8—81no—
795C2×Q8—81no—
796C2×Q8—81no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—21no—
803C2×D4—21no—
804C2×D4—21no—
805C2×D4—21no—
806C2×D4—21no—
807C2×D4—21no—
808C2×D4—41no—
809C2×D4—41no—
810C2×D4—41no—
811C2×D4—41no—
812C2×D4—41no—
813C2×D4—41no—
814C2×D4—41no—
815C2×D4—41no—
816C2×D4—41no—
817C2×D4—42no—
818C2×D4—44no—
819C2×D4—42no—
820C2×D4—42no—
821C2×D4—81no—
822C2×D4—81no—
823C2×D4—82no—
824C2×D4—82no—
825C2×D4—82no—
826C2×D4—81no—
827C2×D4—81no—
828C2×D4—81no—
829C2×D4—81no—
830C2×D4—81no—
831C2×D4—81no—
832C2×D4—81no—
833C2×D4—81no—
834C2×D4—81no—
835C2×D4—81no—
836C2×D4C2×#4112yes—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
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—21no—
859C22×C4—21no—
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—42no—
870C22×C4—81no—
871C22×C4—81no—
872C22×C4—81no—
873C22×C4—81no—
874C22×C4—81no—
875C22×C4C22×D411yescharacteristic
876C22×C4C22×D411yescharacteristic
877C22×C4C22×D411yescharacteristic
878C22×C4C22×D411yescharacteristic
879C22×C4C22×D411yescharacteristic
880C22×C4C22×D411yescharacteristic
881C22×C4C22×D411yescharacteristic
882C22×C4C22×D411yescharacteristic
883C22×C4C22×D411yescharacteristic
884C22×C4C22×D411yescharacteristic
885C22×C4C22×D411yescharacteristic
886C22×C4C2511yescharacteristic
887SD16—82no—
888SD16—82no—
889M16—82no—
890M16—82no—
891C2×C8—21no—
892C2×C8—21no—
893C2×C8—21no—
894C2×C8—21no—
895C2×C8—21no—
896C2×C8—21no—
897C2×C8—21no—
898C2×C8—21no—
899C2×C8—21no—
900C2×C8—21no—
901C2×C8—21no—
902C2×C8—21no—
903C2×C8—21no—
904C2×C8—21no—
905C2×C8—21no—
906C2×C8—21no—
907C2×C8—21no—
908C2×C8—21no—
909C2×C8—21no—
910C2×C8—21no—
911C2×C8—21no—
912C2×C8—21no—
913C2×C8—82no—
914C2×C8—82no—
915C2×C8C2×#4112yes—
916C2×C8H(5,𝔽2)12yes—
917C4⋊C4—21no—
918C4⋊C4—21no—
919C4⋊C4—21no—
920C4⋊C4—21no—
921C4⋊C4—21no—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—21no—
925C4⋊C4—21no—
926C4⋊C4—21no—
927C4⋊C4—21no—
928C4⋊C4—21no—
929C4⋊C4—21no—
930C4⋊C4—21no—
931C4⋊C4—21no—
932C4⋊C4—21no—
933C4⋊C4—21no—
934C4⋊C4—21no—
935C4⋊C4—21no—
936C4⋊C4—21no—
937C4⋊C4—21no—
938C4⋊C4—21no—
939C4⋊C4—21no—
940C4⋊C4—21no—
941C4⋊C4—21no—
942C4⋊C4—41no—
943C4⋊C4—41no—
944C4⋊C4—41no—
945C4⋊C4—41no—
946C4⋊C4—41no—
947C4⋊C4—41no—
948C4⋊C4—41no—
949C4⋊C4—42no—
950C4⋊C4—42no—
951C4⋊C4—42no—
952C4⋊C4—42no—
953C4⋊C4—81no—
954C4⋊C4—81no—
955C4⋊C4—81no—
956C4⋊C4—81no—
957C4⋊C4—81no—
958C4⋊C4—81no—
959C4⋊C4—81no—
960C4⋊C4—81no—
961C4⋊C4—81no—
962C4⋊C4—81no—
963C4⋊C4—81no—
964C4⋊C4—81no—
965C4⋊C4—81no—
966C4⋊C4—81no—
967C4⋊C4—81no—
968C4⋊C4—81no—
969C4⋊C4C2×#4112yes—
970C22⋊C4—41no—
971C22⋊C4—41no—
972C22⋊C4—41no—
973C22⋊C4—41no—
974C22⋊C4—41no—
975C22⋊C4—41no—
976C22⋊C4—41no—
977C22⋊C4—41no—
978C22⋊C4—41no—
979C22⋊C4—41no—
980C22⋊C4—41no—
981C22⋊C4—41no—
982C22⋊C4—42no—
983C22⋊C4—42no—
984C22⋊C4—42no—
985C22⋊C4—42no—
986C22⋊C4—42no—
987C22⋊C4—42no—
988C22⋊C4—42no—
989C22⋊C4—42no—
990C22⋊C4—81no—
991C22⋊C4—81no—
992C22⋊C4—81no—
993C22⋊C4—81no—
994C22⋊C4—81no—
995C22⋊C4—81no—
996C22⋊C4—81no—
997C22⋊C4—81no—
998C22⋊C4—81no—
999C22⋊C4—81no—
1000C22⋊C4—81no—
1001C22⋊C4—81no—
1002C22⋊C4—81no—
1003C22⋊C4—81no—
1004C22⋊C4—81no—
1005C22⋊C4—81no—
1006C22⋊C4—81no—
1007C22⋊C4—81no—
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—
1019C42—21no—
1020C42—21no—
1021C42—21no—
1022C42—21no—
1023C42—21no—
1024C42—21no—
1025C42—21no—
1026C42—21no—
1027C42—42no—
1028C42—42no—
1029C42—42no—
1030C42—81no—
1031C42—81no—
1032C42—81no—
1033C42—81no—
1034C42—81no—
1035C42—81no—
1036C42—81no—
1037C42—81no—
1038C23—21no—
1039C23—21no—
1040C23—21no—
1041C23—21no—
1042C23—21no—
1043C23—21no—
1044C23—21no—
1045C23—21no—
1046C23—21no—
1047C23—21no—
1048C23—21no—
1049C23—21no—
1050C23—21no—
1051C23—21no—
1052C23—21no—
1053C23—22no—
1054C23—21no—
1055C23—21no—
1056C23—21no—
1057C23—21no—
1058C23—21no—
1059C23—21no—
1060C23—41no—
1061C23—41no—
1062C23—41no—
1063C23—41no—
1064C23—41no—
1065C23—41no—
1066C23—41no—
1067C23—41no—
1068C23—41no—
1069C23—41no—
1070C23—41no—
1071C23—41no—
1072C23—41no—
1073C23—84no—
1074C23—84no—
1075C23—162no—
1076C23—162no—
1077C23—162no—
1078C23—162no—
1079C23—162no—
1080C23C23×D411yescharacteristic
1081Q8—41no—
1082Q8—41no—
1083Q8—41no—
1084Q8—41no—
1085Q8—162no—
1086D4—22no—
1087D4—22no—
1088D4—41no—
1089D4—41no—
1090D4—41no—
1091D4—41no—
1092D4—41no—
1093D4—41no—
1094D4—82no—
1095D4—82no—
1096D4—82no—
1097D4—84no—
1098D4—162no—
1099D4—162no—
1100D4—162no—
1101D4—162no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—21no—
1105C2×C4—21no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—21no—
1109C2×C4—21no—
1110C2×C4—21no—
1111C2×C4—21no—
1112C2×C4—21no—
1113C2×C4—21no—
1114C2×C4—21no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—21no—
1118C2×C4—22no—
1119C2×C4—21no—
1120C2×C4—21no—
1121C2×C4—21no—
1122C2×C4—21no—
1123C2×C4—21no—
1124C2×C4—21no—
1125C2×C4—21no—
1126C2×C4—21no—
1127C2×C4—21no—
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—41no—
1137C2×C4—41no—
1138C2×C4—41no—
1139C2×C4—41no—
1140C2×C4—41no—
1141C2×C4—41no—
1142C2×C4—41no—
1143C2×C4—41no—
1144C2×C4—41no—
1145C2×C4—41no—
1146C2×C4—41no—
1147C2×C4—41no—
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—162no—
1190C2×C4—162no—
1191C2×C4C22×#4111yescharacteristic
1192C2×C4C2×H(5,𝔽2)11yescharacteristic
1193C2×C4#58511yescharacteristic
1194C2×C4#58511yescharacteristic
1195C2×C4#58511yescharacteristic
1196C2×C4#58511yescharacteristic
1197C8—22no—
1198C8—22no—
1199C8—41no—
1200C8—41no—
1201C8—41no—
1202C8—41no—
1203C8—41no—
1204C8—41no—
1205C22—41no—
1206C22—41no—
1207C22—41no—
1208C22—41no—
1209C22—41no—
1210C22—42no—
1211C22—41no—
1212C22—41no—
1213C22—41no—
1214C22—41no—
1215C22—41no—
1216C22—41no—
1217C22—41no—
1218C22—42no—
1219C22—41no—
1220C22—41no—
1221C22—41no—
1222C22—41no—
1223C22—41no—
1224C22—41no—
1225C22—41no—
1226C22—41no—
1227C22—41no—
1228C22—42no—
1229C22—81no—
1230C22—81no—
1231C22—81no—
1232C22—81no—
1233C22—81no—
1234C22—81no—
1235C22—81no—
1236C22—81no—
1237C22—81no—
1238C22—81no—
1239C22—81no—
1240C22—168no—
1241C22D4×#4111yescharacteristic
1242C22#348511yescharacteristic
1243C22#349611yescharacteristic
1244C22#358411yescharacteristic
1245C22#358511yescharacteristic
1246C22#358511yescharacteristic
1247C22#358611yescharacteristic
1248C4—41no—
1249C4—41no—
1250C4—41no—
1251C4—41no—
1252C4—42no—
1253C4—41no—
1254C4—41no—
1255C4—41no—
1256C4—41no—
1257C4—41no—
1258C4—41no—
1259C4—41no—
1260C4—81no—
1261C4—81no—
1262C4—81no—
1263C4—81no—
1264C4—81no—
1265C4—81no—
1266C4—81no—
1267C4—81no—
1268C4—81no—
1269C4—81no—
1270C4—81no—
1271C4—81no—
1272C4—81no—
1273C4#349311yescharacteristic
1274C4#351411yescharacteristic
1275C4#354511yescharacteristic
1276C4#356611yescharacteristic
1277C2—81no—
1278C2—81no—
1279C2—81no—
1280C2—82no—
1281C2—161no—
1282C2#4350411yescharacteristic
1283C2#6150411yescharacteristic
1284C2#6153211yescharacteristic
1285C2#6175111yescharacteristic
1286C2#6179311yescharacteristic
1287C2#6228511yescharacteristic
1288C2#6231011yescharacteristic
subgroupG/H
center, socleC23C23×D4
commutator, Frattini, cosocleC22×C4C25
prime radical#42586C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23 ◁ #2392 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

Complements

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

NH ≅ G/Ntype
1. #45133C2semidirect
3. #32252C2semidirect
4. #32015C2semidirect
5. #31341C2semidirect
6. #31325C2semidirect
7. #31270C2semidirect
8. #30971C2semidirect
9. #30568C2semidirect
10. #30408C2semidirect
11. #29491C2semidirect
12. #28715C2semidirect
13. #28566C2semidirect
14. #28076C2semidirect
15. #27868C2semidirect
16. #27800C2semidirect
17. #27503C2semidirect
18. #27478C2semidirect
19. #27442C2semidirect
20. #27340C2semidirect
21. #27238C2semidirect
22. #26731C2semidirect
23. #25351C2semidirect
24. #25120C2semidirect
25. #24948C2semidirect
26. #24890C2semidirect
27. #23767C2semidirect
28. #23124C2semidirect
29. #22933C2semidirect
30. #22584C2semidirect
31. #22195C2semidirect
32. C2×#501C22semidirect
39. C2×#435C22semidirect
56. #2562C22semidirect
57. #2550C22semidirect
65. #2492C22semidirect
72. #2415C22semidirect
78. #2355C22semidirect
80. #2347C22semidirect
84. #2323C22semidirect
85. #2314C22semidirect
86. #2101C22semidirect
87. #2100C22semidirect
88. #2095C22semidirect
91. #2088C22semidirect
92. #2085C22semidirect
93. #2084C22semidirect
94. #2083C22semidirect
96. #2077C22semidirect
97. #2077C22semidirect
100. #2076C22semidirect
101. #2076C22semidirect
106. #2059C22semidirect
107. #2059C22semidirect
111. #2036C22semidirect
113. #2035C22semidirect
120. #2026C22semidirect
126. #1992C22semidirect
127. #1989C22semidirect
128. #1988C22semidirect
131. #1947C22semidirect
132. #1944C22semidirect
135. #1935C22semidirect
137. #1933C22semidirect
138. #1928C22semidirect
139. #1927C22semidirect
148. #1923C22semidirect
149. #1921C22semidirect
150. #1920C22semidirect
151. #1920C22semidirect
152. #1919C22semidirect
153. #1918C22semidirect
154. #1918C22semidirect
155. #1918C22semidirect
156. #1917C22semidirect
157. #1917C22semidirect
161. #1894C22semidirect
169. #1873C22semidirect
173. #1869C22semidirect
174. #1865C22semidirect
176. #1863C22semidirect
180. #1854C22semidirect
181. #1854C22semidirect
183. #1825C22semidirect
186. #1809C22semidirect
187. #1808C22semidirect
188. #1808C22semidirect
189. #1807C22semidirect
192. #1776C22semidirect
193. #1776C22semidirect
194. C4×#107C22semidirect
199. #1752C22semidirect
200. #1750C22semidirect
201. #1735C22semidirect
202. #1729C22semidirect

Maximal subgroups

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

subgroupindex
#451332
#425862
#322522
#320152
#313412
#313252
#312702
#309712
#305682
#304082
#294912
#287152
#285662
#280762
#278682
#278002
#275032
#274782
#274422
#273402
#272382
#267312
#253512
#251202
#249482
#248902
#237672
#231242
#229332
#225842
#221952