Subgroups — #2091×C₂₃₃ #44448123

Order 29824.

222 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#430×C₂₃₃	C₂	1	3	yes	maximal, complemented
2	#407×C₂₃₃	C₂	1	3	yes	maximal
3	#338×C₂₃₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₄×C₂₃₃	C₂²	1	1	yes	characteristic
5	C₂×M₁₆×C₂₃₃	C₂²	1	3	yes	—
6	C₂×M₁₆×C₂₃₃	C₂²	1	3	yes	—
7	#108×C₂₃₃	—	2	6	no	—
8	C₂²⋊C₈×C₂₃₃	—	2	6	no	—
9	C₂⁴×C₂₃₃	Q₈	1	1	yes	characteristic
10	C₂²×C₄×C₂₃₃	—	2	3	no	—
11	C₂²×C₄×C₂₃₃	—	2	3	no	—
12	C₂²×C₄×C₂₃₃	Q₈	1	1	yes	characteristic
13	C₂²×C₄×C₂₃₃	C₂³	1	1	yes	characteristic
14	M₁₆×C₂₃₃	—	2	6	no	—
15	M₁₆×C₂₃₃	—	2	6	no	—
16	C₂×C₈×C₂₃₃	—	2	3	no	—
17	C₂×C₈×C₂₃₃	D₄	1	6	yes	—
18	C₂³×C₂₃₃	—	2	3	no	—
19	C₂³×C₂₃₃	—	4	2	no	—
20	C₂³×C₂₃₃	C₂×Q₈	1	1	yes	characteristic
21	C₂×C₄×C₂₃₃	—	2	3	no	—
22	C₂×C₄×C₂₃₃	—	4	3	no	—
23	C₂×C₄×C₂₃₃	—	4	1	no	—
24	C₂×C₄×C₂₃₃	C₂×D₄	1	3	yes	—
25	C₂×C₄×C₂₃₃	#41	1	3	yes	—
26	C₈×C₂₃₃	—	2	6	no	—
27	C₈×C₂₃₃	—	4	3	no	—
28	C₂²×C₂₃₃	—	2	6	no	—
29	C₂²×C₂₃₃	—	4	1	no	—
30	C₂²×C₂₃₃	—	4	3	no	—
31	C₂²×C₂₃₃	—	4	1	no	—
32	C₂²×C₂₃₃	C₂²⋊Q₈	1	3	yes	—
33	C₄×C₂₃₃	—	4	1	no	—
34	C₄×C₂₃₃	#123	1	3	yes	—
35	C₄×C₂₃₃	#127	1	1	yes	characteristic
36	C₂×C₂₃₃	—	2	3	no	—
37	C₂×C₂₃₃	—	4	2	no	—
38	C₂×C₂₃₃	#399	1	1	yes	characteristic
39	C₂₃₃	#2091	1	1	yes	characteristic, direct product factor, Sylow
40	#2091	C₂₃₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
41	#430	C₂×C₂₃₃	1	3	yes	complemented
42	#407	C₂×C₂₃₃	1	3	yes	—
43	#338	C₂×C₂₃₃	1	1	yes	characteristic, complemented
44	C₂³×C₄	C₂²×C₂₃₃	1	1	yes	characteristic
45	C₂×M₁₆	C₂²×C₂₃₃	1	3	yes	—
46	C₂×M₁₆	C₂²×C₂₃₃	1	3	yes	—
47	#108	—	2	6	no	—
48	C₂²⋊C₈	—	2	6	no	—
49	C₂⁴	Q₈×C₂₃₃	1	1	yes	characteristic
50	C₂²×C₄	—	2	3	no	—
51	C₂²×C₄	—	2	3	no	—
52	C₂²×C₄	Q₈×C₂₃₃	1	1	yes	characteristic
53	C₂²×C₄	C₂³×C₂₃₃	1	1	yes	characteristic
54	M₁₆	—	2	6	no	—
55	M₁₆	—	2	6	no	—
56	C₂×C₈	—	2	3	no	—
57	C₂×C₈	D₄×C₂₃₃	1	6	yes	—
58	C₂³	—	2	3	no	—
59	C₂³	—	4	2	no	—
60	C₂³	C₂×Q₈×C₂₃₃	1	1	yes	characteristic
61	C₂×C₄	—	2	3	no	—
62	C₂×C₄	—	4	3	no	—
63	C₂×C₄	—	4	1	no	—
64	C₂×C₄	C₂×D₄×C₂₃₃	1	3	yes	—
65	C₂×C₄	#41×C₂₃₃	1	3	yes	—
66	C₈	—	2	6	no	—
67	C₈	—	4	3	no	—
68	C₂²	—	2	6	no	—
69	C₂²	—	4	1	no	—
70	C₂²	—	4	3	no	—
71	C₂²	—	4	1	no	—
72	C₂²	C₂²⋊Q₈×C₂₃₃	1	3	yes	—
73	C₄	—	4	1	no	—
74	C₄	#123×C₂₃₃	1	3	yes	—
75	C₄	#127×C₂₃₃	1	1	yes	characteristic
76	C₂	—	2	3	no	—
77	C₂	—	4	2	no	—
78	C₂	#399×C₂₃₃	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₂₃₃	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃₃
socle	C₂×C₂₃₃	#399
prime radical	C₂⁴×C₂₃₃	Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃₃ ◁ C₂²×C₄×C₂₃₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. #430×C₂₃₃	C₂	semidirect
3. #338×C₂₃₃	C₂	semidirect
39. C₂₃₃	#2091	direct (N × H)
40. #2091	C₂₃₃	direct (N × H)
41. #430	C₂×C₂₃₃	semidirect
43. #338	C₂×C₂₃₃	semidirect

Maximal subgroups

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

subgroup	index
#430×C₂₃₃	2
#407×C₂₃₃	2
#338×C₂₃₃	2
#2091	233

Subgroups — #2091×C233 #44448123

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2091×C₂₃₃ #44448123