Subgroups — #1324×C₂₁₁ #41008944

Order 27008.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#382×C₂₁₁	C₂	1	1	yes	maximal, characteristic
2	#324×C₂₁₁	C₂	1	2	yes	maximal
3	C₂×C₄⋊C₄×C₂₁₁	C₄	1	1	yes	characteristic
4	C₂×C₄⋊C₄×C₂₁₁	C₂²	1	1	yes	characteristic
5	C₂×C₄²×C₂₁₁	C₄	1	1	yes	characteristic
6	C₂²⋊C₈×C₂₁₁	—	2	2	no	—
7	#95×C₂₁₁	—	2	2	no	—
8	C₂²×C₄×C₂₁₁	—	2	1	no	—
9	C₂²×C₄×C₂₁₁	—	2	1	no	—
10	C₂²×C₄×C₂₁₁	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₄×C₂₁₁	D₄	1	2	yes	—
12	C₂×C₈×C₂₁₁	—	4	2	no	—
13	C₄⋊C₄×C₂₁₁	—	4	1	no	—
14	C₄⋊C₄×C₂₁₁	—	4	1	no	—
15	C₄²×C₂₁₁	—	2	1	no	—
16	C₄²×C₂₁₁	C₈	1	2	yes	complemented
17	C₂³×C₂₁₁	C₂²⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₂₁₁	—	2	1	no	—
19	C₂×C₄×C₂₁₁	—	2	1	no	—
20	C₂×C₄×C₂₁₁	—	2	2	no	—
21	C₂×C₄×C₂₁₁	—	2	2	no	—
22	C₂×C₄×C₂₁₁	—	4	1	no	—
23	C₂×C₄×C₂₁₁	—	4	1	no	—
24	C₂×C₄×C₂₁₁	—	4	2	no	—
25	C₂×C₄×C₂₁₁	—	4	2	no	—
26	C₂×C₄×C₂₁₁	—	4	1	no	—
27	C₂×C₄×C₂₁₁	C₂×C₈	1	1	yes	characteristic
28	C₂×C₄×C₂₁₁	M₁₆	1	1	yes	characteristic
29	C₈×C₂₁₁	—	8	2	no	—
30	C₂²×C₂₁₁	—	2	1	no	—
31	C₂²×C₂₁₁	—	2	1	no	—
32	C₂²×C₂₁₁	C₂²⋊C₈	1	1	yes	characteristic
33	C₂²×C₂₁₁	#99	1	1	yes	characteristic
34	C₂²×C₂₁₁	#101	1	1	yes	characteristic
35	C₄×C₂₁₁	—	2	1	no	—
36	C₄×C₂₁₁	—	2	1	no	—
37	C₄×C₂₁₁	—	4	2	no	—
38	C₄×C₂₁₁	—	4	2	no	—
39	C₄×C₂₁₁	—	8	1	no	—
40	C₂×C₂₁₁	—	2	1	no	—
41	C₂×C₂₁₁	—	2	1	no	—
42	C₂×C₂₁₁	#324	1	1	yes	characteristic
43	C₂×C₂₁₁	#354	1	1	yes	characteristic
44	C₂×C₂₁₁	#355	1	1	yes	characteristic
45	C₂₁₁	#1324	1	1	yes	characteristic, direct product factor, Sylow
46	#1324	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
47	#382	C₂×C₂₁₁	1	1	yes	characteristic
48	#324	C₂×C₂₁₁	1	2	yes	—
49	C₂×C₄⋊C₄	C₄×C₂₁₁	1	1	yes	characteristic
50	C₂×C₄⋊C₄	C₂²×C₂₁₁	1	1	yes	characteristic
51	C₂×C₄²	C₄×C₂₁₁	1	1	yes	characteristic
52	C₂²⋊C₈	—	2	2	no	—
53	#95	—	2	2	no	—
54	C₂²×C₄	—	2	1	no	—
55	C₂²×C₄	—	2	1	no	—
56	C₂²×C₄	C₂×C₄×C₂₁₁	1	1	yes	characteristic
57	C₂²×C₄	D₄×C₂₁₁	1	2	yes	—
58	C₂×C₈	—	4	2	no	—
59	C₄⋊C₄	—	4	1	no	—
60	C₄⋊C₄	—	4	1	no	—
61	C₄²	—	2	1	no	—
62	C₄²	C₈×C₂₁₁	1	2	yes	complemented
63	C₂³	C₂²⋊C₄×C₂₁₁	1	1	yes	characteristic
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	2	2	no	—
67	C₂×C₄	—	2	2	no	—
68	C₂×C₄	—	4	1	no	—
69	C₂×C₄	—	4	1	no	—
70	C₂×C₄	—	4	2	no	—
71	C₂×C₄	—	4	2	no	—
72	C₂×C₄	—	4	1	no	—
73	C₂×C₄	C₂×C₈×C₂₁₁	1	1	yes	characteristic
74	C₂×C₄	M₁₆×C₂₁₁	1	1	yes	characteristic
75	C₈	—	8	2	no	—
76	C₂²	—	2	1	no	—
77	C₂²	—	2	1	no	—
78	C₂²	C₂²⋊C₈×C₂₁₁	1	1	yes	characteristic
79	C₂²	#99×C₂₁₁	1	1	yes	characteristic
80	C₂²	#101×C₂₁₁	1	1	yes	characteristic
81	C₄	—	2	1	no	—
82	C₄	—	2	1	no	—
83	C₄	—	4	2	no	—
84	C₄	—	4	2	no	—
85	C₄	—	8	1	no	—
86	C₂	—	2	1	no	—
87	C₂	—	2	1	no	—
88	C₂	#324×C₂₁₁	1	1	yes	characteristic
89	C₂	#354×C₂₁₁	1	1	yes	characteristic
90	C₂	#355×C₂₁₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₂₁₁	#99
commutator	C₂×C₄	C₂×C₈×C₂₁₁
Frattini, cosocle	C₂×C₄⋊C₄	C₂²×C₂₁₁
prime radical	C₂³×C₂₁₁	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₁₁ ◁ C₂³×C₂₁₁ ◁ C₂×C₄⋊C₄×C₂₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
16. C₄²×C₂₁₁	C₈	semidirect
45. C₂₁₁	#1324	direct (N × H)
46. #1324	C₂₁₁	direct (N × H)
62. C₄²	C₈×C₂₁₁	semidirect

Maximal subgroups

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

subgroup	index
#382×C₂₁₁	2
#324×C₂₁₁	2
#1324	211

Subgroups — #1324×C211 #41008944

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1324×C₂₁₁ #41008944