Subgroups — #26011796

Order 11072.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19149670	C₂	1	1	yes	maximal, characteristic
2	Q₈×Dic₁₇₃	C₂	1	1	yes	maximal, characteristic
3	#19149612	C₂	1	1	yes	maximal, characteristic
4	#19149611	C₂	1	1	yes	maximal, characteristic
5	#19149608	C₂	1	1	yes	maximal, characteristic
6	#19149603	C₂	1	1	yes	maximal, characteristic
7	#103×C₁₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×#13063436	C₂²	1	1	yes	characteristic
9	C₄⋊Dic₁₇₃	—	2	1	no	—
10	C₄⋊Dic₁₇₃	—	2	1	no	—
11	C₄⋊Dic₁₇₃	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₇₃	C₂²	1	1	yes	characteristic
13	#14583805	—	2	1	no	—
14	C₄×Dic₁₇₃	—	2	1	no	—
15	C₄×Dic₁₇₃	C₂²	1	1	yes	characteristic
16	C₂×Q₈×C₁₇₃	C₂²	1	1	yes	characteristic
17	C₂×C₈×C₁₇₃	C₂²	1	1	yes	characteristic
18	C₄⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic
19	C₂×Dic₁₇₃	—	2	1	no	—
20	C₂×Dic₁₇₃	—	2	1	no	—
21	C₂×Dic₁₇₃	D₄	1	1	yes	characteristic
22	C₂×Dic₁₇₃	D₄	1	1	yes	characteristic
23	#13063436	—	2	1	no	—
24	Q₈×C₁₇₃	—	2	1	no	—
25	Q₈×C₁₇₃	Q₈	1	2	yes	—
26	C₂×C₄×C₁₇₃	—	2	1	no	—
27	C₂×C₄×C₁₇₃	—	2	1	no	—
28	C₂×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
29	C₈×C₁₇₃	—	2	1	no	—
30	C₂²×C₁₇₃	C₂×D₄	1	1	yes	characteristic
31	C₄×C₁₇₃	—	2	2	no	—
32	C₄×C₁₇₃	—	4	1	no	—
33	C₄×C₁₇₃	C₂×Q₈	1	1	yes	characteristic
34	C₄×C₁₇₃	#41	1	1	yes	characteristic
35	Dic₁₇₃	—	2	1	no	—
36	Dic₁₇₃	—	2	1	no	—
37	Dic₁₇₃	—	4	1	no	—
38	Dic₁₇₃	—	4	1	no	—
39	C₂×C₁₇₃	C₂²⋊Q₈	1	1	yes	characteristic
40	C₂×C₁₇₃	#135	1	1	yes	characteristic
41	C₂×C₁₇₃	#137	1	1	yes	characteristic
42	C₁₇₃	#479	1	1	yes	characteristic, complemented, Sylow
43	#479	—	173	1	no	maximal, Sylow
44	#125	—	173	1	no	—
45	C₄×Q₈	—	173	1	no	—
46	#107	—	173	1	no	—
47	#106	—	173	1	no	—
48	C₄⋊C₈	—	173	1	no	—
49	#103	—	173	1	no	—
50	#103	D₁₇₃	1	1	yes	characteristic
51	C₂×Q₈	C₂×D₁₇₃	1	1	yes	characteristic
52	C₂×C₈	—	173	1	no	—
53	C₂×C₈	C₂×D₁₇₃	1	1	yes	characteristic
54	C₄⋊C₄	—	346	1	no	—
55	C₄⋊C₄	—	346	1	no	—
56	C₄⋊C₄	—	346	1	no	—
57	C₄⋊C₄	—	173	1	no	—
58	C₄⋊C₄	—	173	1	no	—
59	C₄⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic
60	C₄²	—	346	1	no	—
61	C₄²	—	173	1	no	—
62	Q₈	—	2	1	no	—
63	Q₈	Dic₃₄₆	1	2	yes	—
64	C₂×C₄	—	2	1	no	—
65	C₂×C₄	—	2	1	no	—
66	C₂×C₄	—	346	1	no	—
67	C₂×C₄	—	346	1	no	—
68	C₂×C₄	—	173	1	no	—
69	C₂×C₄	—	173	1	no	—
70	C₂×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
71	C₈	—	2	1	no	—
72	C₈	—	346	1	no	—
73	C₂²	D₄×D₁₇₃	1	1	yes	characteristic
74	C₄	—	2	2	no	—
75	C₄	—	4	1	no	—
76	C₄	—	346	1	no	—
77	C₄	—	346	1	no	—
78	C₄	—	692	1	no	—
79	C₄	—	692	1	no	—
80	C₄	C₂×Dic₃₄₆	1	1	yes	characteristic
81	C₄	#14583825	1	1	yes	characteristic
82	C₂	#19149656	1	1	yes	characteristic
83	C₂	#19149700	1	1	yes	characteristic
84	C₂	#19149711	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₁₇₃
commutator, cosocle	C₂×C₄×C₁₇₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₇₃
Fitting	#103×C₁₇₃	C₂
socle, prime radical	C₂²×C₁₇₃	C₂×D₄
hypercenter	#103	D₁₇₃
hypocenter	C₁₇₃	#479
LCS	G ▷ C₂×C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #103

Complements

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

N	H ≅ G/N	type
42. C₁₇₃	#479	semidirect

Maximal subgroups

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

subgroup	index
#19149670	2
Q₈×Dic₁₇₃	2
#19149612	2
#19149611	2
#19149608	2
#19149603	2
#103×C₁₇₃	2
#479	173