Subgroups — C₂×#19149671 #26012013

Order 11072.

226 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19149671	C₂	1	8	yes	maximal, direct product factor
2	C₂×C₄⋊Dic₁₇₃	C₂	1	2	yes	maximal
3	C₂×#14583805	C₂	1	4	yes	maximal
4	C₂×C₄²×C₁₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₇₃	C₂²	1	4	yes	—
6	C₄⋊Dic₁₇₃	C₂²	1	8	yes	—
7	#14583805	C₂²	1	16	yes	—
8	C₂²×C₄×C₁₇₃	C₂²	1	2	yes	—
9	C₂²×C₄×C₁₇₃	C₂²	1	1	yes	characteristic
10	C₄²×C₁₇₃	C₂²	1	4	yes	—
11	C₂×Dic₁₇₃	—	2	8	no	—
12	C₂×Dic₁₇₃	C₂³	1	8	yes	—
13	C₂³×C₁₇₃	C₂³	1	1	yes	characteristic
14	C₂×C₄×C₁₇₃	—	2	4	no	—
15	C₂×C₄×C₁₇₃	Q₈	1	4	yes	—
16	C₂×C₄×C₁₇₃	C₂³	1	4	yes	—
17	C₂×C₄×C₁₇₃	C₂³	1	2	yes	—
18	C₂²×C₁₇₃	C₂×Q₈	1	2	yes	—
19	C₂²×C₁₇₃	#41	1	4	yes	—
20	C₂²×C₁₇₃	C₂⁴	1	1	yes	characteristic
21	C₄×C₁₇₃	—	2	4	no	—
22	C₄×C₁₇₃	C₂×Q₈	1	4	yes	—
23	Dic₁₇₃	—	2	8	no	—
24	C₂×C₁₇₃	#125	1	4	yes	complemented
25	C₂×C₁₇₃	C₂²×Q₈	1	1	yes	characteristic
26	C₂×C₁₇₃	C₂×#41	1	2	yes	—
27	C₁₇₃	C₂×#125	1	1	yes	characteristic, complemented, Sylow
28	C₂×#125	—	173	1	no	maximal, Sylow
29	#125	—	173	8	no	—
30	C₂×C₄⋊C₄	—	173	4	no	—
31	C₂×C₄⋊C₄	—	173	2	no	—
32	C₂×C₄²	D₁₇₃	1	1	yes	characteristic
33	C₂²×C₄	—	173	4	no	—
34	C₂²×C₄	C₂×D₁₇₃	1	2	yes	—
35	C₂²×C₄	C₂×D₁₇₃	1	1	yes	characteristic
36	C₄⋊C₄	—	173	16	no	—
37	C₄⋊C₄	—	173	8	no	—
38	C₄²	C₂×D₁₇₃	1	4	yes	—
39	C₂³	C₂²×D₁₇₃	1	1	yes	characteristic
40	C₂×C₄	—	2	4	no	—
41	C₂×C₄	—	346	8	no	—
42	C₂×C₄	—	173	8	no	—
43	C₂×C₄	Dic₃₄₆	1	4	yes	—
44	C₂×C₄	C₂²×D₁₇₃	1	4	yes	—
45	C₂×C₄	C₂²×D₁₇₃	1	2	yes	—
46	C₂²	C₂×Dic₃₄₆	1	2	yes	—
47	C₂²	#14583826	1	4	yes	—
48	C₂²	C₂³×D₁₇₃	1	1	yes	characteristic
49	C₄	—	2	4	no	—
50	C₄	—	346	8	no	—
51	C₄	C₂×Dic₃₄₆	1	4	yes	—
52	C₂	#19149671	1	4	yes	direct product factor
53	C₂	C₂²×Dic₃₄₆	1	1	yes	characteristic
54	C₂	C₂×#14583826	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂²×D₁₇₃
commutator, cosocle	C₂²×C₁₇₃	C₂⁴
Frattini	C₂²	C₂³×D₁₇₃
Fitting	C₂×C₄²×C₁₇₃	C₂
socle, prime radical	C₂³×C₁₇₃	C₂³
hypercenter	C₂×C₄²	D₁₇₃
hypocenter	C₁₇₃	C₂×#125
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
1. #19149671	C₂	direct (N × H)
24. C₂×C₁₇₃	#125	semidirect
27. C₁₇₃	C₂×#125	semidirect
52. C₂	#19149671	direct (N × H)

Maximal subgroups

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

subgroup	index
#19149671	2
C₂×C₄⋊Dic₁₇₃	2
C₂×#14583805	2
C₂×C₄²×C₁₇₃	2
C₂×#125	173

Subgroups — C2×#19149671 #26012013

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19149671 #26012013