Subgroups — C₂×#26012549 #36370527

Order 22144.

368 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012549	C₂	1	8	yes	maximal, direct product factor
2	C₂×#19149753	C₂	1	3	yes	maximal, complemented
3	C₂²×#14583829	C₂	1	3	yes	maximal, complemented
4	C₂×#19149686	C₂	1	1	yes	maximal, characteristic
5	#19149753	C₂²	1	12	yes	complemented
6	C₂×#14583829	C₂²	1	1	yes	characteristic
7	C₂×#14583829	C₂²	1	3	yes	—
8	C₂×#14583829	C₂²	1	12	yes	complemented
9	#19149686	C₄	1	4	yes	—
10	#19149686	C₂²	1	4	yes	—
11	C₂×#14583810	C₄	1	3	yes	—
12	C₂²×#13063436	C₂²	1	3	yes	—
13	C₂×#41×C₁₇₃	C₄	1	1	yes	characteristic
14	#14583829	C₂³	1	2	yes	—
15	#14583829	C₂³	1	6	yes	—
16	#14583810	C₂×C₄	1	12	yes	—
17	C₂×#13063436	C₂×C₄	1	3	yes	—
18	C₂×#13063436	C₂×C₄	1	6	yes	—
19	C₂×#13063436	C₂³	1	1	yes	characteristic
20	C₂×#13063436	C₂³	1	6	yes	—
21	#41×C₁₇₃	C₈	1	4	yes	—
22	#41×C₁₇₃	C₂×C₄	1	4	yes	—
23	C₂×Q₈×C₁₇₃	C₈	1	1	yes	characteristic
24	C₂×D₄×C₁₇₃	C₈	1	3	yes	—
25	C₂²×C₄×C₁₇₃	C₂×C₄	1	3	yes	—
26	#13063436	C₂²×C₄	1	1	yes	characteristic
27	#13063436	C₂²×C₄	1	6	yes	—
28	#13063436	C₂⁴	1	1	yes	characteristic
29	C₂³×C₁₇₃	C₂×C₈	1	3	yes	—
30	Q₈×C₁₇₃	C₂×C₈	1	4	yes	—
31	D₄×C₁₇₃	C₂×C₈	1	12	yes	—
32	C₂×C₄×C₁₇₃	C₂×C₈	1	3	yes	—
33	C₂×C₄×C₁₇₃	C₂×C₈	1	6	yes	—
34	C₂×C₄×C₁₇₃	C₂²×C₄	1	6	yes	—
35	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
36	C₂²×C₁₇₃	—	2	6	no	—
37	C₂²×C₁₇₃	C₂²×C₈	1	6	yes	—
38	C₂²×C₁₇₃	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₁₇₃	C₂²×C₈	1	1	yes	characteristic
40	C₄×C₁₇₃	C₂²×C₈	1	6	yes	—
41	C₄×C₁₇₃	C₂³×C₄	1	1	yes	characteristic
42	C₂×C₁₇₃	—	2	6	no	—
43	C₂×C₁₇₃	#504	1	2	yes	complemented
44	C₂×C₁₇₃	C₂³×C₈	1	1	yes	characteristic
45	C₁₇₃	C₂×#504	1	1	yes	characteristic, complemented, Sylow
46	C₂×#504	—	173	1	no	maximal, Sylow
47	C₂×#131	—	173	1	no	—
48	#504	—	173	8	no	—
49	C₂×M₃₂	—	173	3	no	—
50	C₂²×C₁₆	—	173	3	no	—
51	C₂×#41	#10621924	1	1	yes	characteristic
52	#131	—	173	4	no	—
53	#131	—	173	4	no	—
54	C₂×M₁₆	—	173	3	no	—
55	C₂²×C₈	—	173	3	no	—
56	M₃₂	—	173	12	no	—
57	C₂×C₁₆	—	173	1	no	—
58	C₂×C₁₆	—	173	3	no	—
59	C₂×C₁₆	—	173	12	no	—
60	#41	#13063443	1	4	yes	—
61	#41	C₂×#10621924	1	4	yes	—
62	C₂×Q₈	#13063443	1	1	yes	characteristic
63	C₂×D₄	#13063443	1	3	yes	—
64	C₂²×C₄	C₂×#10621924	1	3	yes	—
65	M₁₆	—	173	12	no	—
66	C₂×C₈	—	173	6	no	—
67	C₂×C₈	—	173	6	no	—
68	C₂×C₈	—	173	3	no	—
69	C₂×C₈	—	173	1	no	—
70	C₁₆	—	173	2	no	—
71	C₁₆	—	173	6	no	—
72	C₂³	C₂×#13063443	1	3	yes	—
73	Q₈	C₂×#13063443	1	4	yes	—
74	D₄	C₂×#13063443	1	12	yes	—
75	C₂×C₄	C₂×#13063443	1	3	yes	—
76	C₂×C₄	C₂×#13063443	1	6	yes	—
77	C₂×C₄	C₂²×#10621924	1	6	yes	—
78	C₂×C₄	C₂²×#10621924	1	1	yes	characteristic
79	C₈	—	173	1	no	—
80	C₈	—	173	6	no	—
81	C₈	—	173	1	no	—
82	C₂²	—	2	6	no	—
83	C₂²	C₂²×#13063443	1	6	yes	—
84	C₂²	C₂²×#13063443	1	1	yes	characteristic
85	C₄	C₂²×#13063443	1	1	yes	characteristic
86	C₄	C₂²×#13063443	1	6	yes	—
87	C₄	C₂³×#10621924	1	1	yes	characteristic
88	C₂	—	2	6	no	—
89	C₂	#26012549	1	2	yes	direct product factor
90	C₂	C₂³×#13063443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×#10621924
commutator	C₂×C₁₇₃	C₂³×C₈
Frattini	C₄	C₂³×#10621924
Fitting, prime radical	C₂×#41×C₁₇₃	C₄
socle	C₂²×C₁₇₃	C₂²×C₈
cosocle	#13063436	C₂⁴
hypercenter	C₂×#41	#10621924
hypocenter	C₁₇₃	C₂×#504
LCS	G ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#41

Complements

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

N	H ≅ G/N	type
1. #26012549	C₂	direct (N × H)
2. C₂×#19149753	C₂	semidirect
3. C₂²×#14583829	C₂	semidirect
5. #19149753	C₂²	semidirect
8. C₂×#14583829	C₂²	semidirect
43. C₂×C₁₇₃	#504	semidirect
45. C₁₇₃	C₂×#504	semidirect
89. C₂	#26012549	direct (N × H)

Maximal subgroups

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

subgroup	index
#26012549	2
C₂×#19149753	2
C₂²×#14583829	2
C₂×#19149686	2
C₂×#504	173

Subgroups — C2×#26012549 #36370527

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#26012549 #36370527