Subgroups — #2103×C₂₁₁ #41009723

Order 27008.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#430×C₂₁₁	C₂	1	1	yes	maximal, characteristic
2	#424×C₂₁₁	C₂	1	1	yes	maximal, characteristic
3	#344×C₂₁₁	C₂	1	2	yes	maximal
4	#341×C₂₁₁	C₂	1	2	yes	maximal
5	#338×C₂₁₁	C₂	1	1	yes	maximal, characteristic
6	C₂×M₁₆×C₂₁₁	C₂²	1	2	yes	—
7	C₂×M₁₆×C₂₁₁	C₂²	1	2	yes	—
8	C₂×M₁₆×C₂₁₁	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₂₁₁	C₂²	1	1	yes	characteristic
10	#117×C₂₁₁	C₂²	1	1	yes	characteristic
11	#108×C₂₁₁	—	2	2	no	—
12	C₄⋊C₈×C₂₁₁	—	2	2	no	—
13	C₂²×C₄×C₂₁₁	C₂³	1	1	yes	characteristic
14	M₁₆×C₂₁₁	—	2	2	no	—
15	M₁₆×C₂₁₁	—	2	2	no	—
16	M₁₆×C₂₁₁	—	2	2	no	—
17	M₁₆×C₂₁₁	—	2	2	no	—
18	M₁₆×C₂₁₁	—	2	2	no	—
19	C₂×C₈×C₂₁₁	—	2	1	no	—
20	C₂×C₈×C₂₁₁	—	2	2	no	—
21	C₂×C₈×C₂₁₁	—	2	2	no	—
22	C₂×C₈×C₂₁₁	—	2	2	no	—
23	C₂×C₈×C₂₁₁	D₄	1	2	yes	—
24	C₄⋊C₄×C₂₁₁	—	2	1	no	—
25	C₂²⋊C₄×C₂₁₁	Q₈	1	2	yes	—
26	C₄²×C₂₁₁	—	2	1	no	—
27	C₂³×C₂₁₁	C₂×Q₈	1	1	yes	characteristic
28	C₂×C₄×C₂₁₁	—	2	2	no	—
29	C₂×C₄×C₂₁₁	C₂×D₄	1	1	yes	characteristic
30	C₂×C₄×C₂₁₁	#41	1	2	yes	—
31	C₂×C₄×C₂₁₁	#41	1	2	yes	—
32	C₂×C₄×C₂₁₁	#41	1	1	yes	characteristic
33	C₈×C₂₁₁	—	2	2	no	—
34	C₈×C₂₁₁	—	4	1	no	—
35	C₈×C₂₁₁	—	4	2	no	—
36	C₈×C₂₁₁	—	4	2	no	—
37	C₂²×C₂₁₁	—	4	1	no	—
38	C₂²×C₂₁₁	C₂²⋊Q₈	1	1	yes	characteristic
39	C₂²×C₂₁₁	#125	1	2	yes	—
40	C₄×C₂₁₁	—	4	2	no	—
41	C₄×C₂₁₁	#123	1	1	yes	characteristic
42	C₄×C₂₁₁	#124	1	1	yes	characteristic
43	C₄×C₂₁₁	#126	1	2	yes	—
44	C₂×C₂₁₁	—	2	1	no	—
45	C₂×C₂₁₁	—	2	2	no	—
46	C₂×C₂₁₁	#400	1	1	yes	characteristic
47	C₂₁₁	#2103	1	1	yes	characteristic, direct product factor, Sylow
48	#2103	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
49	#430	C₂×C₂₁₁	1	1	yes	characteristic
50	#424	C₂×C₂₁₁	1	1	yes	characteristic
51	#344	C₂×C₂₁₁	1	2	yes	—
52	#341	C₂×C₂₁₁	1	2	yes	—
53	#338	C₂×C₂₁₁	1	1	yes	characteristic
54	C₂×M₁₆	C₂²×C₂₁₁	1	2	yes	—
55	C₂×M₁₆	C₂²×C₂₁₁	1	2	yes	—
56	C₂×M₁₆	C₂²×C₂₁₁	1	1	yes	characteristic
57	C₂²×C₈	C₂²×C₂₁₁	1	1	yes	characteristic
58	#117	C₂²×C₂₁₁	1	1	yes	characteristic
59	#108	—	2	2	no	—
60	C₄⋊C₈	—	2	2	no	—
61	C₂²×C₄	C₂³×C₂₁₁	1	1	yes	characteristic
62	M₁₆	—	2	2	no	—
63	M₁₆	—	2	2	no	—
64	M₁₆	—	2	2	no	—
65	M₁₆	—	2	2	no	—
66	M₁₆	—	2	2	no	—
67	C₂×C₈	—	2	1	no	—
68	C₂×C₈	—	2	2	no	—
69	C₂×C₈	—	2	2	no	—
70	C₂×C₈	—	2	2	no	—
71	C₂×C₈	D₄×C₂₁₁	1	2	yes	—
72	C₄⋊C₄	—	2	1	no	—
73	C₂²⋊C₄	Q₈×C₂₁₁	1	2	yes	—
74	C₄²	—	2	1	no	—
75	C₂³	C₂×Q₈×C₂₁₁	1	1	yes	characteristic
76	C₂×C₄	—	2	2	no	—
77	C₂×C₄	C₂×D₄×C₂₁₁	1	1	yes	characteristic
78	C₂×C₄	#41×C₂₁₁	1	2	yes	—
79	C₂×C₄	#41×C₂₁₁	1	2	yes	—
80	C₂×C₄	#41×C₂₁₁	1	1	yes	characteristic
81	C₈	—	2	2	no	—
82	C₈	—	4	1	no	—
83	C₈	—	4	2	no	—
84	C₈	—	4	2	no	—
85	C₂²	—	4	1	no	—
86	C₂²	C₂²⋊Q₈×C₂₁₁	1	1	yes	characteristic
87	C₂²	#125×C₂₁₁	1	2	yes	—
88	C₄	—	4	2	no	—
89	C₄	#123×C₂₁₁	1	1	yes	characteristic
90	C₄	#124×C₂₁₁	1	1	yes	characteristic
91	C₄	#126×C₂₁₁	1	2	yes	—
92	C₂	—	2	1	no	—
93	C₂	—	2	2	no	—
94	C₂	#400×C₂₁₁	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₂₁₁	#124
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₁₁
socle	C₂×C₂₁₁	#400
prime radical	C₂³×C₂₁₁	C₂×Q₈
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₁₁ ◁ C₂²×C₄×C₂₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
47. C₂₁₁	#2103	direct (N × H)
48. #2103	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
#430×C₂₁₁	2
#424×C₂₁₁	2
#344×C₂₁₁	2
#341×C₂₁₁	2
#338×C₂₁₁	2
#2103	211

Subgroups — #2103×C211 #41009723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2103×C₂₁₁ #41009723