Subgroups — C₂×#383×C₂₁₁ #41009902

Order 27008.

624 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²×C₂₁₁	C₂	1	1	yes	maximal, characteristic
2	#383×C₂₁₁	C₂	1	8	yes	maximal, direct product factor
3	C₂×#95×C₂₁₁	C₂	1	6	yes	maximal
4	C₂³×C₄×C₂₁₁	C₂²	1	4	yes	—
5	C₂³×C₄×C₂₁₁	C₂²	1	3	yes	—
6	C₂×C₄²×C₂₁₁	C₄	1	8	yes	complemented
7	C₂×C₄²×C₂₁₁	C₂²	1	4	yes	—
8	#95×C₂₁₁	C₂²	1	24	yes	—
9	C₂⁴×C₂₁₁	C₂³	1	1	yes	characteristic
10	C₂²×C₄×C₂₁₁	—	2	12	no	—
11	C₂²×C₄×C₂₁₁	—	2	24	no	—
12	C₂²×C₄×C₂₁₁	C₂×C₄	1	12	yes	—
13	C₂²×C₄×C₂₁₁	C₂³	1	8	yes	—
14	C₂²×C₄×C₂₁₁	C₂³	1	6	yes	—
15	C₄²×C₂₁₁	C₂×C₄	1	16	yes	complemented
16	C₂³×C₂₁₁	C₂²×C₄	1	2	yes	—
17	C₂³×C₂₁₁	#41	1	12	yes	—
18	C₂³×C₂₁₁	C₂⁴	1	1	yes	characteristic
19	C₂×C₄×C₂₁₁	—	2	24	no	—
20	C₂×C₄×C₂₁₁	—	2	12	no	—
21	C₂×C₄×C₂₁₁	—	2	24	no	—
22	C₂×C₄×C₂₁₁	—	4	16	no	—
23	C₂×C₄×C₂₁₁	C₂²×C₄	1	12	yes	—
24	C₂²×C₂₁₁	#117	1	12	yes	—
25	C₂²×C₂₁₁	#126	1	16	yes	—
26	C₂²×C₂₁₁	C₂³×C₄	1	1	yes	characteristic
27	C₂²×C₂₁₁	C₂×#41	1	6	yes	—
28	C₄×C₂₁₁	—	2	12	no	—
29	C₄×C₂₁₁	—	4	8	no	—
30	C₂×C₂₁₁	#383	1	8	yes	direct product factor
31	C₂×C₂₁₁	C₂×#117	1	3	yes	—
32	C₂×C₂₁₁	C₂×#126	1	4	yes	—
33	C₂₁₁	C₂×#383	1	1	yes	characteristic, direct product factor, Sylow
34	C₂×#383	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
35	C₂²×C₄²	C₂×C₂₁₁	1	1	yes	characteristic
36	#383	C₂×C₂₁₁	1	8	yes	direct product factor
37	C₂×#95	C₂×C₂₁₁	1	6	yes	—
38	C₂³×C₄	C₂²×C₂₁₁	1	4	yes	—
39	C₂³×C₄	C₂²×C₂₁₁	1	3	yes	—
40	C₂×C₄²	C₄×C₂₁₁	1	8	yes	complemented
41	C₂×C₄²	C₂²×C₂₁₁	1	4	yes	—
42	#95	C₂²×C₂₁₁	1	24	yes	—
43	C₂⁴	C₂³×C₂₁₁	1	1	yes	characteristic
44	C₂²×C₄	—	2	12	no	—
45	C₂²×C₄	—	2	24	no	—
46	C₂²×C₄	C₂×C₄×C₂₁₁	1	12	yes	—
47	C₂²×C₄	C₂³×C₂₁₁	1	8	yes	—
48	C₂²×C₄	C₂³×C₂₁₁	1	6	yes	—
49	C₄²	C₂×C₄×C₂₁₁	1	16	yes	complemented
50	C₂³	C₂²×C₄×C₂₁₁	1	2	yes	—
51	C₂³	#41×C₂₁₁	1	12	yes	—
52	C₂³	C₂⁴×C₂₁₁	1	1	yes	characteristic
53	C₂×C₄	—	2	24	no	—
54	C₂×C₄	—	2	12	no	—
55	C₂×C₄	—	2	24	no	—
56	C₂×C₄	—	4	16	no	—
57	C₂×C₄	C₂²×C₄×C₂₁₁	1	12	yes	—
58	C₂²	#117×C₂₁₁	1	12	yes	—
59	C₂²	#126×C₂₁₁	1	16	yes	—
60	C₂²	C₂³×C₄×C₂₁₁	1	1	yes	characteristic
61	C₂²	C₂×#41×C₂₁₁	1	6	yes	—
62	C₄	—	2	12	no	—
63	C₄	—	4	8	no	—
64	C₂	#383×C₂₁₁	1	8	yes	direct product factor
65	C₂	C₂×#117×C₂₁₁	1	3	yes	—
66	C₂	C₂×#126×C₂₁₁	1	4	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₂₁₁	C₂³
commutator	C₂²	C₂³×C₄×C₂₁₁
Frattini, cosocle	C₂³	C₂⁴×C₂₁₁
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. #383×C₂₁₁	C₂	direct (N × H)
6. C₂×C₄²×C₂₁₁	C₄	semidirect
15. C₄²×C₂₁₁	C₂×C₄	semidirect
30. C₂×C₂₁₁	#383	direct (N × H)
33. C₂₁₁	C₂×#383	direct (N × H)
34. C₂×#383	C₂₁₁	direct (N × H)
36. #383	C₂×C₂₁₁	direct (N × H)
40. C₂×C₄²	C₄×C₂₁₁	semidirect
49. C₄²	C₂×C₄×C₂₁₁	semidirect
64. C₂	#383×C₂₁₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄²×C₂₁₁	2
#383×C₂₁₁	2
C₂×#95×C₂₁₁	2
C₂×#383	211

Subgroups — C2×#383×C211 #41009902

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#383×C₂₁₁ #41009902