Subgroups — #26012533

Order 11072.

106 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19149766	C₂	1	2	yes	maximal, complemented
2	#19149750	C₂	1	1	yes	maximal, characteristic, complemented
3	#19149743	C₂	1	2	yes	maximal, complemented
4	C₈×#10621924	C₂	1	1	yes	maximal, characteristic, complemented
5	#19149698	C₂	1	1	yes	maximal, characteristic
6	#14583836	C₂²	1	2	yes	—
7	#14583835	—	2	2	no	—
8	D₁₇₃⋊C₈	C₂²	1	1	yes	characteristic
9	C₂×#13063443	—	2	2	no	—
10	C₄×#10621924	C₂²	1	1	yes	characteristic
11	#14583825	C₂²	1	2	yes	—
12	Dic₆₉₂	C₄	1	1	yes	characteristic, complemented
13	#14583814	C₄	1	2	yes	complemented
14	C₈×D₁₇₃	C₂²	1	1	yes	characteristic
15	D₈×C₁₇₃	C₄	1	1	yes	characteristic, complemented
16	C₂×#10621924	—	2	1	no	—
17	#13063443	—	2	2	no	—
18	#13063443	D₄	1	1	yes	characteristic
19	#13063443	D₄	1	1	yes	characteristic
20	Dic₃₄₆	C₂×C₄	1	2	yes	—
21	C₂²⋊D₁₇₃	—	2	2	no	—
22	C₂×Dic₁₇₃	—	2	2	no	—
23	C₄×D₁₇₃	C₂³	1	1	yes	characteristic
24	#13063436	C₂×C₄	1	1	yes	characteristic
25	D₄×C₁₇₃	C₂×C₄	1	2	yes	—
26	C₈×C₁₇₃	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₁₇₃	—	2	2	no	—
28	C₂×D₁₇₃	#41	1	1	yes	characteristic
29	#10621924	—	2	2	no	—
30	C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
31	Dic₁₇₃	—	2	2	no	—
32	Dic₁₇₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₁₇₃	—	4	2	no	—
34	C₂×C₁₇₃	C₄×D₄	1	1	yes	characteristic
35	D₁₇₃	—	2	1	no	—
36	C₁₇₃	#443	1	1	yes	characteristic, complemented, Sylow
37	#443	—	173	1	no	maximal, Sylow
38	#135	—	173	1	no	—
39	#131	—	173	2	no	—
40	#108	—	173	1	no	—
41	#104	—	173	2	no	—
42	C₄×C₈	—	173	1	no	—
43	#41	—	173	2	no	—
44	Q₁₆	—	173	1	no	—
45	SD₁₆	—	173	2	no	—
46	D₈	#10621924	1	1	yes	characteristic, complemented
47	M₁₆	—	346	2	no	—
48	M₁₆	—	173	2	no	—
49	C₂×C₈	—	346	2	no	—
50	C₂×C₈	—	173	1	no	—
51	C₂×C₈	—	173	1	no	—
52	C₄²	—	173	1	no	—
53	Q₈	—	173	2	no	—
54	D₄	—	346	2	no	—
55	D₄	C₂×#10621924	1	2	yes	—
56	C₂×C₄	—	346	1	no	—
57	C₂×C₄	—	346	2	no	—
58	C₂×C₄	—	173	1	no	—
59	C₈	—	346	2	no	—
60	C₈	—	173	1	no	—
61	C₈	—	173	1	no	—
62	C₈	—	173	1	no	—
63	C₈	C₂×#10621924	1	1	yes	characteristic
64	C₂²	—	2	2	no	—
65	C₂²	—	173	1	no	—
66	C₄	—	346	2	no	—
67	C₄	—	346	2	no	—
68	C₄	—	173	1	no	—
69	C₄	C₂²×#10621924	1	1	yes	characteristic
70	C₂	—	4	2	no	—
71	C₂	—	346	1	no	—
72	C₂	D₄×#10621924	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×#10621924
commutator	C₄×C₁₇₃	C₂²×C₄
Frattini	C₄	C₂²×#10621924
Fitting	D₈×C₁₇₃	C₄
socle	C₂×C₁₇₃	C₄×D₄
prime radical	#19149698	C₂
cosocle	C₄×D₁₇₃	C₂³
hypercenter	D₈	#10621924
hypocenter	C₁₇₃	#443
LCS	G ▷ C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂ ◁ C₄ ◁ D₈

Complements

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

N	H ≅ G/N	type
1. #19149766	C₂	semidirect
2. #19149750	C₂	semidirect
3. #19149743	C₂	semidirect
4. C₈×#10621924	C₂	semidirect
12. Dic₆₉₂	C₄	semidirect
13. #14583814	C₄	semidirect
15. D₈×C₁₇₃	C₄	semidirect
36. C₁₇₃	#443	semidirect
46. D₈	#10621924	semidirect

Maximal subgroups

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

subgroup	index
#19149766	2
#19149750	2
#19149743	2
C₈×#10621924	2
#19149698	2
#443	173