Subgroups — #26012538

Order 11072.

104 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	#19149749	C₂	1	1	yes	maximal, characteristic, complemented
3	#19149743	C₂	1	2	yes	maximal, complemented
4	#19149733	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	2	yes	—
19	Dic₃₄₆	C₂×C₄	1	2	yes	—
20	C₂²⋊D₁₇₃	—	2	2	no	—
21	C₂×Dic₁₇₃	—	2	2	no	—
22	C₄×D₁₇₃	C₂³	1	1	yes	characteristic
23	#13063436	C₂×C₄	1	1	yes	characteristic
24	D₄×C₁₇₃	C₂×C₄	1	2	yes	—
25	C₈×C₁₇₃	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₁₇₃	—	2	2	no	—
27	C₂×D₁₇₃	#41	1	1	yes	characteristic
28	#10621924	—	4	1	no	—
29	C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
30	Dic₁₇₃	—	2	2	no	—
31	Dic₁₇₃	C₂×D₄	1	1	yes	characteristic
32	C₂×C₁₇₃	—	4	2	no	—
33	C₂×C₁₇₃	C₄×D₄	1	1	yes	characteristic
34	D₁₇₃	—	2	1	no	—
35	C₁₇₃	#444	1	1	yes	characteristic, complemented, Sylow
36	#444	—	173	1	no	maximal, Sylow
37	#135	—	173	1	no	—
38	#131	—	173	2	no	—
39	#108	—	173	1	no	—
40	#104	—	173	2	no	—
41	#97	—	173	1	no	—
42	#41	—	173	2	no	—
43	Q₁₆	—	173	1	no	—
44	SD₁₆	—	173	2	no	—
45	D₈	#10621924	1	1	yes	characteristic, complemented
46	M₁₆	—	346	2	no	—
47	M₁₆	—	173	2	no	—
48	C₂×C₈	—	346	2	no	—
49	C₂×C₈	—	173	1	no	—
50	C₂×C₈	—	173	1	no	—
51	C₄²	—	173	1	no	—
52	Q₈	—	173	2	no	—
53	D₄	—	346	2	no	—
54	D₄	C₂×#10621924	1	2	yes	—
55	C₂×C₄	—	346	2	no	—
56	C₂×C₄	—	346	1	no	—
57	C₂×C₄	—	173	1	no	—
58	C₈	—	346	2	no	—
59	C₈	—	173	2	no	—
60	C₈	—	173	1	no	—
61	C₈	C₂×#10621924	1	1	yes	characteristic
62	C₂²	—	2	2	no	—
63	C₂²	—	173	1	no	—
64	C₄	—	346	2	no	—
65	C₄	—	173	1	no	—
66	C₄	—	692	1	no	—
67	C₄	C₂²×#10621924	1	1	yes	characteristic
68	C₂	—	4	2	no	—
69	C₂	—	346	1	no	—
70	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	#444
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. #19149749	C₂	semidirect
3. #19149743	C₂	semidirect
4. #19149733	C₂	semidirect
12. Dic₆₉₂	C₄	semidirect
13. #14583814	C₄	semidirect
15. D₈×C₁₇₃	C₄	semidirect
35. C₁₇₃	#444	semidirect
45. 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
#19149749	2
#19149743	2
#19149733	2
#19149698	2
#444	173