Subgroups — #1356×C₂₁₁ #41008976

Order 27008.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#491×C₂₁₁	C₂	1	1	yes	maximal, characteristic
2	#347×C₂₁₁	C₂	1	2	yes	maximal
3	C₄⋊Q₈×C₂₁₁	C₄	1	1	yes	characteristic
4	#125×C₂₁₁	C₄	1	1	yes	characteristic
5	M₃₂×C₂₁₁	—	2	2	no	—
6	#103×C₂₁₁	—	2	2	no	—
7	#97×C₂₁₁	C₂²	1	1	yes	characteristic
8	C₂×Q₈×C₂₁₁	—	2	1	no	—
9	C₂×C₈×C₂₁₁	D₄	1	2	yes	—
10	C₄⋊C₄×C₂₁₁	—	2	1	no	—
11	C₄⋊C₄×C₂₁₁	—	4	1	no	—
12	C₄⋊C₄×C₂₁₁	—	4	1	no	—
13	C₄²×C₂₁₁	C₂×C₄	1	1	yes	characteristic
14	C₁₆×C₂₁₁	—	2	4	no	—
15	Q₈×C₂₁₁	—	4	2	no	—
16	C₂×C₄×C₂₁₁	—	2	1	no	—
17	C₂×C₄×C₂₁₁	—	4	1	no	—
18	C₂×C₄×C₂₁₁	—	4	1	no	—
19	C₂×C₄×C₂₁₁	C₂²⋊C₄	1	1	yes	characteristic
20	C₈×C₂₁₁	—	2	2	no	—
21	C₂²×C₂₁₁	#100	1	1	yes	characteristic
22	C₄×C₂₁₁	—	4	1	no	—
23	C₄×C₂₁₁	—	8	1	no	—
24	C₄×C₂₁₁	—	8	1	no	—
25	C₄×C₂₁₁	#104	1	2	yes	—
26	C₂×C₂₁₁	—	2	1	no	—
27	C₂×C₂₁₁	#329	1	1	yes	characteristic
28	C₂₁₁	#1356	1	1	yes	characteristic, direct product factor, Sylow
29	#1356	C₂₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
30	#491	C₂×C₂₁₁	1	1	yes	characteristic
31	#347	C₂×C₂₁₁	1	2	yes	—
32	C₄⋊Q₈	C₄×C₂₁₁	1	1	yes	characteristic
33	#125	C₄×C₂₁₁	1	1	yes	characteristic
34	M₃₂	—	2	2	no	—
35	#103	—	2	2	no	—
36	#97	C₂²×C₂₁₁	1	1	yes	characteristic
37	C₂×Q₈	—	2	1	no	—
38	C₂×C₈	D₄×C₂₁₁	1	2	yes	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	4	1	no	—
41	C₄⋊C₄	—	4	1	no	—
42	C₄²	C₂×C₄×C₂₁₁	1	1	yes	characteristic
43	C₁₆	—	2	4	no	—
44	Q₈	—	4	2	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	4	1	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	C₂²⋊C₄×C₂₁₁	1	1	yes	characteristic
49	C₈	—	2	2	no	—
50	C₂²	#100×C₂₁₁	1	1	yes	characteristic
51	C₄	—	4	1	no	—
52	C₄	—	8	1	no	—
53	C₄	—	8	1	no	—
54	C₄	#104×C₂₁₁	1	2	yes	—
55	C₂	—	2	1	no	—
56	C₂	#329×C₂₁₁	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₂₁₁	#329
commutator	C₄²	C₂×C₄×C₂₁₁
Frattini, cosocle	#97	C₂²×C₂₁₁
prime radical	C₂²×C₂₁₁	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₁₁ ◁ C₂×C₄×C₂₁₁ ◁ #97×C₂₁₁ ◁ G

Complements

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

N	H ≅ G/N	type
28. C₂₁₁	#1356	direct (N × H)
29. #1356	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
#491×C₂₁₁	2
#347×C₂₁₁	2
#1356	211

Subgroups — #1356×C211 #41008976

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #1356×C₂₁₁ #41008976