Subgroups — #1376×C₂₁₁ #41008996

Order 27008.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×C₂₁₁	C₂	1	2	yes	maximal
2	C₂×C₄×C₈×C₂₁₁	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₈×C₂₁₁	C₄	1	1	yes	characteristic
4	C₂²×C₈×C₂₁₁	C₂²	1	1	yes	characteristic
5	C₂×C₄²×C₂₁₁	C₄	1	1	yes	characteristic
6	M₃₂×C₂₁₁	—	2	2	no	—
7	M₃₂×C₂₁₁	C₄	1	4	yes	complemented
8	C₂×C₁₆×C₂₁₁	—	2	2	no	—
9	C₄×C₈×C₂₁₁	—	2	2	no	—
10	C₂²×C₄×C₂₁₁	—	2	1	no	—
11	C₂²×C₄×C₂₁₁	C₂×C₄	1	1	yes	characteristic
12	C₂×C₈×C₂₁₁	—	2	1	no	—
13	C₂×C₈×C₂₁₁	—	2	1	no	—
14	C₂×C₈×C₂₁₁	C₈	1	2	yes	—
15	C₂×C₈×C₂₁₁	C₂×C₄	1	2	yes	—
16	C₂×C₈×C₂₁₁	D₄	1	2	yes	—
17	C₂×C₈×C₂₁₁	D₄	1	1	yes	characteristic
18	C₂×C₈×C₂₁₁	Q₈	1	1	yes	characteristic
19	C₄²×C₂₁₁	—	2	1	no	—
20	C₄²×C₂₁₁	C₈	1	2	yes	—
21	C₁₆×C₂₁₁	—	2	4	no	—
22	C₂³×C₂₁₁	M₁₆	1	1	yes	characteristic
23	C₂×C₄×C₂₁₁	—	2	4	no	—
24	C₂×C₄×C₂₁₁	—	2	2	no	—
25	C₂×C₄×C₂₁₁	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₂₁₁	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₂₁₁	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₂₁₁	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₂₁₁	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₂₁₁	M₁₆	1	1	yes	characteristic
31	C₈×C₂₁₁	—	2	2	no	—
32	C₈×C₂₁₁	C₂²⋊C₄	1	2	yes	—
33	C₈×C₂₁₁	C₄⋊C₄	1	2	yes	—
34	C₂²×C₂₁₁	—	2	2	no	—
35	C₂²×C₂₁₁	#97	1	1	yes	characteristic
36	C₂²×C₂₁₁	C₂²⋊C₈	1	1	yes	characteristic
37	C₂²×C₂₁₁	C₄⋊C₈	1	1	yes	characteristic
38	C₄×C₂₁₁	—	2	4	no	—
39	C₄×C₂₁₁	#95	1	1	yes	characteristic
40	C₄×C₂₁₁	C₄×C₈	1	1	yes	characteristic
41	C₄×C₂₁₁	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₂₁₁	C₄⋊C₈	1	1	yes	characteristic
43	C₂×C₂₁₁	—	2	1	no	—
44	C₂×C₂₁₁	—	2	1	no	—
45	C₂×C₂₁₁	#336	1	1	yes	characteristic
46	C₂×C₂₁₁	#364	1	2	yes	—
47	C₂₁₁	#1376	1	1	yes	characteristic, direct product factor, Sylow
48	#1376	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	C₂×M₃₂	C₂×C₂₁₁	1	2	yes	—
50	C₂×C₄×C₈	C₂×C₂₁₁	1	1	yes	characteristic
51	C₂²×C₈	C₄×C₂₁₁	1	1	yes	characteristic
52	C₂²×C₈	C₂²×C₂₁₁	1	1	yes	characteristic
53	C₂×C₄²	C₄×C₂₁₁	1	1	yes	characteristic
54	M₃₂	—	2	2	no	—
55	M₃₂	C₄×C₂₁₁	1	4	yes	complemented
56	C₂×C₁₆	—	2	2	no	—
57	C₄×C₈	—	2	2	no	—
58	C₂²×C₄	—	2	1	no	—
59	C₂²×C₄	C₂×C₄×C₂₁₁	1	1	yes	characteristic
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	C₈×C₂₁₁	1	2	yes	—
63	C₂×C₈	C₂×C₄×C₂₁₁	1	2	yes	—
64	C₂×C₈	D₄×C₂₁₁	1	1	yes	characteristic
65	C₂×C₈	D₄×C₂₁₁	1	2	yes	—
66	C₂×C₈	Q₈×C₂₁₁	1	1	yes	characteristic
67	C₄²	—	2	1	no	—
68	C₄²	C₈×C₂₁₁	1	2	yes	—
69	C₁₆	—	2	4	no	—
70	C₂³	M₁₆×C₂₁₁	1	1	yes	characteristic
71	C₂×C₄	—	2	4	no	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	C₄²×C₂₁₁	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊C₄×C₂₁₁	1	1	yes	characteristic
75	C₂×C₄	C₄⋊C₄×C₂₁₁	1	1	yes	characteristic
76	C₂×C₄	C₂×C₈×C₂₁₁	1	1	yes	characteristic
77	C₂×C₄	C₂×C₈×C₂₁₁	1	1	yes	characteristic
78	C₂×C₄	M₁₆×C₂₁₁	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	C₂²⋊C₄×C₂₁₁	1	2	yes	—
81	C₈	C₄⋊C₄×C₂₁₁	1	2	yes	—
82	C₂²	—	2	2	no	—
83	C₂²	#97×C₂₁₁	1	1	yes	characteristic
84	C₂²	C₂²⋊C₈×C₂₁₁	1	1	yes	characteristic
85	C₂²	C₄⋊C₈×C₂₁₁	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	#95×C₂₁₁	1	1	yes	characteristic
88	C₄	C₄×C₈×C₂₁₁	1	1	yes	characteristic
89	C₄	C₂²⋊C₈×C₂₁₁	1	1	yes	characteristic
90	C₄	C₄⋊C₈×C₂₁₁	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#336×C₂₁₁	1	1	yes	characteristic
94	C₂	#364×C₂₁₁	1	2	yes	—

	subgroup	G/H
center	C₂×C₈×C₂₁₁	D₄
commutator	C₄	C₄×C₈×C₂₁₁
Frattini, cosocle	C₂²×C₈	C₂²×C₂₁₁
socle	C₂²×C₂₁₁	C₄⋊C₈
prime radical	C₂³×C₂₁₁	M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₁₁ ◁ C₂²×C₈×C₂₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
7. M₃₂×C₂₁₁	C₄	semidirect
47. C₂₁₁	#1376	direct (N × H)
48. #1376	C₂₁₁	direct (N × H)
55. M₃₂	C₄×C₂₁₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×C₂₁₁	2
C₂×C₄×C₈×C₂₁₁	2
#1376	211

Subgroups — #1376×C211 #41008996

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1376×C₂₁₁ #41008996