Subgroups — #1526×C₂₁₁ #41009146

Order 27008.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#533×C₂₁₁	C₂	1	1	yes	maximal, characteristic
2	C₄×M₁₆×C₂₁₁	C₂	1	2	yes	maximal
3	#330×C₂₁₁	C₂	1	4	yes	maximal, complemented
4	C₂×M₁₆×C₂₁₁	—	2	2	no	—
5	C₄⋊Q₈×C₂₁₁	C₄	1	2	yes	—
6	#125×C₂₁₁	C₂²	1	2	yes	—
7	C₂²⋊Q₈×C₂₁₁	—	2	2	no	—
8	C₄×Q₈×C₂₁₁	—	2	2	no	—
9	#117×C₂₁₁	C₄	1	2	yes	—
10	C₂×C₄²×C₂₁₁	C₂²	1	1	yes	characteristic
11	#97×C₂₁₁	C₂²	1	4	yes	—
12	C₄×C₈×C₂₁₁	—	2	2	no	—
13	C₂×Q₈×C₂₁₁	—	2	2	no	—
14	C₂²×C₄×C₂₁₁	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄×C₂₁₁	D₄	1	2	yes	—
16	M₁₆×C₂₁₁	—	2	8	no	—
17	C₂×C₈×C₂₁₁	—	2	4	no	—
18	C₄⋊C₄×C₂₁₁	—	2	2	no	—
19	C₄⋊C₄×C₂₁₁	—	2	4	no	—
20	C₄⋊C₄×C₂₁₁	C₂×C₄	1	4	yes	—
21	C₂²⋊C₄×C₂₁₁	—	2	2	no	—
22	C₄²×C₂₁₁	—	2	2	no	—
23	C₄²×C₂₁₁	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₂₁₁	D₄	1	2	yes	—
25	C₄²×C₂₁₁	C₂³	1	1	yes	characteristic
26	C₂³×C₂₁₁	C₂²⋊C₄	1	1	yes	characteristic
27	Q₈×C₂₁₁	—	4	4	no	—
28	C₂×C₄×C₂₁₁	—	2	2	no	—
29	C₂×C₄×C₂₁₁	—	2	4	no	—
30	C₂×C₄×C₂₁₁	—	2	4	no	—
31	C₂×C₄×C₂₁₁	C₂²⋊C₄	1	2	yes	—
32	C₂×C₄×C₂₁₁	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₂₁₁	C₂²×C₄	1	1	yes	characteristic
34	C₂×C₄×C₂₁₁	C₂×D₄	1	2	yes	—
35	C₈×C₂₁₁	—	2	8	no	—
36	C₂²×C₂₁₁	—	2	1	no	—
37	C₂²×C₂₁₁	—	2	2	no	—
38	C₂²×C₂₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
39	C₄×C₂₁₁	—	2	1	no	—
40	C₄×C₂₁₁	—	2	2	no	—
41	C₄×C₂₁₁	—	4	4	no	—
42	C₄×C₂₁₁	#101	1	2	yes	—
43	C₄×C₂₁₁	#104	1	4	yes	—
44	C₂×C₂₁₁	—	4	1	no	—
45	C₂×C₂₁₁	C₂×#101	1	1	yes	characteristic
46	C₂×C₂₁₁	C₂×#104	1	2	yes	—
47	C₂₁₁	#1526	1	1	yes	characteristic, direct product factor, Sylow
48	#1526	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	#533	C₂×C₂₁₁	1	1	yes	characteristic
50	C₄×M₁₆	C₂×C₂₁₁	1	2	yes	—
51	#330	C₂×C₂₁₁	1	4	yes	complemented
52	C₂×M₁₆	—	2	2	no	—
53	C₄⋊Q₈	C₄×C₂₁₁	1	2	yes	—
54	#125	C₂²×C₂₁₁	1	2	yes	—
55	C₂²⋊Q₈	—	2	2	no	—
56	C₄×Q₈	—	2	2	no	—
57	#117	C₄×C₂₁₁	1	2	yes	—
58	C₂×C₄²	C₂²×C₂₁₁	1	1	yes	characteristic
59	#97	C₂²×C₂₁₁	1	4	yes	—
60	C₄×C₈	—	2	2	no	—
61	C₂×Q₈	—	2	2	no	—
62	C₂²×C₄	C₂×C₄×C₂₁₁	1	1	yes	characteristic
63	C₂²×C₄	D₄×C₂₁₁	1	2	yes	—
64	M₁₆	—	2	8	no	—
65	C₂×C₈	—	2	4	no	—
66	C₄⋊C₄	—	2	2	no	—
67	C₄⋊C₄	—	2	4	no	—
68	C₄⋊C₄	C₂×C₄×C₂₁₁	1	4	yes	—
69	C₂²⋊C₄	—	2	2	no	—
70	C₄²	—	2	2	no	—
71	C₄²	C₂×C₄×C₂₁₁	1	1	yes	characteristic
72	C₄²	D₄×C₂₁₁	1	2	yes	—
73	C₄²	C₂³×C₂₁₁	1	1	yes	characteristic
74	C₂³	C₂²⋊C₄×C₂₁₁	1	1	yes	characteristic
75	Q₈	—	4	4	no	—
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	—	2	4	no	—
78	C₂×C₄	—	2	4	no	—
79	C₂×C₄	C₂²⋊C₄×C₂₁₁	1	1	yes	characteristic
80	C₂×C₄	C₂²⋊C₄×C₂₁₁	1	2	yes	—
81	C₂×C₄	C₂²×C₄×C₂₁₁	1	1	yes	characteristic
82	C₂×C₄	C₂×D₄×C₂₁₁	1	2	yes	—
83	C₈	—	2	8	no	—
84	C₂²	—	2	1	no	—
85	C₂²	—	2	2	no	—
86	C₂²	C₂×C₂²⋊C₄×C₂₁₁	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	2	2	no	—
89	C₄	—	4	4	no	—
90	C₄	#101×C₂₁₁	1	2	yes	—
91	C₄	#104×C₂₁₁	1	4	yes	—
92	C₂	—	4	1	no	—
93	C₂	C₂×#101×C₂₁₁	1	1	yes	characteristic
94	C₂	C₂×#104×C₂₁₁	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₂₁₁	C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₂₁₁
Frattini, cosocle	C₄²	C₂³×C₂₁₁
socle	C₂²×C₂₁₁	C₂×C₂²⋊C₄
prime radical	C₂³×C₂₁₁	C₂²⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₁₁ ◁ C₂×C₄²×C₂₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. #330×C₂₁₁	C₂	semidirect
47. C₂₁₁	#1526	direct (N × H)
48. #1526	C₂₁₁	direct (N × H)
51. #330	C₂×C₂₁₁	semidirect

Maximal subgroups

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

subgroup	index
#533×C₂₁₁	2
C₄×M₁₆×C₂₁₁	2
#330×C₂₁₁	2
#1526	211

Subgroups — #1526×C211 #41009146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1526×C₂₁₁ #41009146