Subgroups — C₂×#26012332 #36368756

Order 22144.

248 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#13063443	C₂	1	2	yes	maximal
2	#26012332	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×Dic₁₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂²×#13063443	C₄	1	4	yes	—
5	C₄×#13063443	C₄	1	4	yes	—
6	C₄×#13063443	C₂²	1	4	yes	—
7	C₂²×#13063436	C₄	1	1	yes	characteristic
8	C₂×C₄×Dic₁₇₃	C₂²	1	1	yes	characteristic
9	C₈×Dic₁₇₃	C₄	1	2	yes	—
10	C₈×Dic₁₇₃	C₂²	1	2	yes	—
11	C₂²×C₈×C₁₇₃	C₄	1	1	yes	characteristic
12	C₂×#13063443	—	2	8	no	—
13	C₂×#13063443	C₂×C₄	1	8	yes	—
14	C₂²×Dic₁₇₃	C₂×C₄	1	2	yes	—
15	C₂×#13063436	C₈	1	4	yes	complemented
16	C₂×#13063436	C₂×C₄	1	2	yes	—
17	C₄×Dic₁₇₃	C₂×C₄	1	2	yes	—
18	C₄×Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
19	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
20	C₂²×C₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₁₇₃	C₈	1	4	yes	complemented
22	C₂×C₈×C₁₇₃	C₂×C₄	1	2	yes	—
23	#13063443	—	2	8	no	—
24	C₂×Dic₁₇₃	C₄²	1	2	yes	—
25	C₂×Dic₁₇₃	M₁₆	1	8	yes	—
26	C₂×Dic₁₇₃	C₂²×C₄	1	2	yes	—
27	#13063436	C₂×C₈	1	4	yes	complemented
28	C₂³×C₁₇₃	C₄²	1	1	yes	characteristic
29	C₂×C₄×C₁₇₃	C₄²	1	1	yes	characteristic
30	C₂×C₄×C₁₇₃	C₂×C₈	1	2	yes	—
31	C₂×C₄×C₁₇₃	C₂×C₈	1	2	yes	—
32	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
33	C₈×C₁₇₃	C₂×C₈	1	4	yes	complemented
34	C₂²×C₁₇₃	C₄×C₈	1	2	yes	—
35	C₂²×C₁₇₃	#97	1	4	yes	—
36	C₂²×C₁₇₃	C₂×C₄²	1	1	yes	characteristic
37	C₄×C₁₇₃	C₄×C₈	1	2	yes	—
38	C₄×C₁₇₃	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₁₇₃	C₂²×C₈	1	1	yes	characteristic
40	Dic₁₇₃	#97	1	4	yes	—
41	Dic₁₇₃	C₂×M₁₆	1	4	yes	—
42	C₂×C₁₇₃	#322	1	4	yes	complemented
43	C₂×C₁₇₃	C₂×C₄×C₈	1	1	yes	characteristic
44	C₂×C₁₇₃	C₂×#97	1	2	yes	—
45	C₁₇₃	C₂×#322	1	1	yes	characteristic, complemented, Sylow
46	C₂×#322	—	173	1	no	maximal, Sylow
47	C₂×C₄×C₈	—	173	2	no	—
48	C₂×C₄×C₈	—	173	1	no	—
49	#322	—	173	4	no	—
50	C₂²×C₈	—	173	4	no	—
51	C₂²×C₈	—	173	1	no	—
52	C₂²×C₈	#10621924	1	1	yes	characteristic
53	C₂×C₄²	—	173	1	no	—
54	C₄×C₈	—	173	4	no	—
55	C₄×C₈	—	173	4	no	—
56	C₄×C₈	—	173	2	no	—
57	C₄×C₈	—	173	2	no	—
58	C₂²×C₄	—	173	2	no	—
59	C₂²×C₄	C₂×#10621924	1	1	yes	characteristic
60	C₂×C₈	—	346	8	no	—
61	C₂×C₈	—	173	8	no	—
62	C₂×C₈	—	173	4	no	—
63	C₂×C₈	—	173	2	no	—
64	C₂×C₈	#13063443	1	4	yes	complemented
65	C₂×C₈	C₂×#10621924	1	2	yes	—
66	C₄²	—	173	2	no	—
67	C₄²	—	173	1	no	—
68	C₄²	—	173	1	no	—
69	C₂³	C₄×#10621924	1	1	yes	characteristic
70	C₂×C₄	—	173	8	no	—
71	C₂×C₄	—	173	2	no	—
72	C₂×C₄	—	173	2	no	—
73	C₂×C₄	C₄×#10621924	1	1	yes	characteristic
74	C₂×C₄	C₂×#13063443	1	2	yes	—
75	C₂×C₄	D₁₇₃⋊C₈	1	2	yes	—
76	C₂×C₄	C₂²×#10621924	1	1	yes	characteristic
77	C₈	—	346	8	no	—
78	C₈	—	173	4	no	—
79	C₈	C₂×#13063443	1	4	yes	complemented
80	C₂²	C₄×#13063443	1	2	yes	—
81	C₂²	#19149733	1	4	yes	—
82	C₂²	C₂×C₄×#10621924	1	1	yes	characteristic
83	C₄	—	173	4	no	—
84	C₄	—	173	4	no	—
85	C₄	C₄×#13063443	1	2	yes	—
86	C₄	C₂²×#13063443	1	1	yes	characteristic
87	C₄	C₂×D₁₇₃⋊C₈	1	1	yes	characteristic
88	C₂	#26012332	1	4	yes	direct product factor
89	C₂	C₂×C₄×#13063443	1	1	yes	characteristic
90	C₂	C₂×#19149733	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×#10621924
commutator	C₂×C₁₇₃	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#10621924
Fitting	C₂²×C₈×C₁₇₃	C₄
socle, prime radical	C₂³×C₁₇₃	C₄²
cosocle	C₄×Dic₁₇₃	C₂³
hypercenter	C₂²×C₈	#10621924
hypocenter	C₁₇₃	C₂×#322
LCS	G ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. #26012332	C₂	direct (N × H)
15. C₂×#13063436	C₈	semidirect
21. C₂×C₈×C₁₇₃	C₈	semidirect
27. #13063436	C₂×C₈	semidirect
33. C₈×C₁₇₃	C₂×C₈	semidirect
42. C₂×C₁₇₃	#322	semidirect
45. C₁₇₃	C₂×#322	semidirect
64. C₂×C₈	#13063443	semidirect
79. C₈	C₂×#13063443	semidirect
88. C₂	#26012332	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#13063443	2
#26012332	2
C₂×C₈×Dic₁₇₃	2
C₂×#322	173

Subgroups — C2×#26012332 #36368756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26012332 #36368756