Subgroups — #26011766

Order 11072.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19149709	C₂	1	2	yes	maximal
2	C₂×Dic₆₉₂	C₂	1	1	yes	maximal, characteristic, complemented
3	#19149615	C₂	1	1	yes	maximal, characteristic, complemented
4	#19149597	C₂	1	2	yes	maximal, complemented
5	#131×C₁₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×Dic₃₄₆	C₂²	1	2	yes	—
7	Dic₆₉₂	—	2	1	no	—
8	Dic₆₉₂	—	2	1	no	—
9	#14583816	—	2	2	no	—
10	#14583814	—	2	2	no	—
11	#14583810	C₂²	1	2	yes	—
12	#41×C₁₇₃	C₂²	1	1	yes	characteristic
13	M₁₆×C₁₇₃	—	2	1	no	—
14	M₁₆×C₁₇₃	C₂²	1	1	yes	characteristic
15	C₂×C₈×C₁₇₃	—	2	1	no	—
16	C₂×C₈×C₁₇₃	C₂²	1	1	yes	characteristic
17	Dic₃₄₆	—	2	2	no	—
18	Dic₃₄₆	—	2	2	no	—
19	C₂×Dic₁₇₃	—	2	2	no	—
20	#13063436	—	2	2	no	—
21	Q₈×C₁₇₃	D₄	1	1	yes	characteristic
22	D₄×C₁₇₃	—	2	1	no	—
23	D₄×C₁₇₃	D₄	1	1	yes	characteristic
24	C₂×C₄×C₁₇₃	—	2	1	no	—
25	C₂×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
26	C₈×C₁₇₃	—	2	1	no	—
27	C₈×C₁₇₃	D₄	1	1	yes	characteristic
28	C₈×C₁₇₃	D₄	1	1	yes	characteristic
29	C₂²×C₁₇₃	—	2	1	no	—
30	C₂²×C₁₇₃	#41	1	1	yes	characteristic
31	C₄×C₁₇₃	—	2	1	no	—
32	C₄×C₁₇₃	C₂×D₄	1	1	yes	characteristic
33	C₄×C₁₇₃	C₂×D₄	1	1	yes	characteristic
34	Dic₁₇₃	—	4	2	no	—
35	C₂×C₁₇₃	—	2	1	no	—
36	C₂×C₁₇₃	—	4	1	no	—
37	C₂×C₁₇₃	#121	1	1	yes	characteristic
38	C₁₇₃	#473	1	1	yes	characteristic, complemented, Sylow
39	#473	—	173	1	no	maximal, Sylow
40	#137	—	173	2	no	—
41	C₂×Q₁₆	—	173	1	no	—
42	#131	D₁₇₃	1	1	yes	characteristic
43	#108	—	173	1	no	—
44	#101	—	173	2	no	—
45	#41	C₂×D₁₇₃	1	1	yes	characteristic
46	C₂×Q₈	—	173	2	no	—
47	Q₁₆	—	346	2	no	—
48	Q₁₆	—	346	1	no	—
49	Q₁₆	—	346	1	no	—
50	SD₁₆	—	346	2	no	—
51	M₁₆	—	2	1	no	—
52	M₁₆	—	173	2	no	—
53	M₁₆	C₂×D₁₇₃	1	1	yes	characteristic
54	C₂×C₈	—	2	1	no	—
55	C₂×C₈	C₂×D₁₇₃	1	1	yes	characteristic
56	Q₈	—	346	2	no	—
57	Q₈	—	346	2	no	—
58	Q₈	D₆₉₂	1	1	yes	characteristic
59	D₄	—	2	1	no	—
60	D₄	D₆₉₂	1	1	yes	characteristic
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	346	2	no	—
63	C₂×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
64	C₈	—	2	1	no	—
65	C₈	—	346	2	no	—
66	C₈	C₂²⋊D₁₇₃	1	1	yes	characteristic
67	C₈	C₂²⋊D₁₇₃	1	1	yes	characteristic
68	C₂²	—	2	1	no	—
69	C₂²	#14583826	1	1	yes	characteristic
70	C₄	—	2	1	no	—
71	C₄	—	692	2	no	—
72	C₄	C₂×C₂²⋊D₁₇₃	1	1	yes	characteristic
73	C₄	C₂×D₆₉₂	1	1	yes	characteristic
74	C₂	—	2	1	no	—
75	C₂	—	4	1	no	—
76	C₂	#19149653	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#19149653
commutator, cosocle	C₂×C₄×C₁₇₃	C₂³
Frattini	C₂×C₄	C₂²×D₁₇₃
Fitting	#131×C₁₇₃	C₂
socle	C₂×C₁₇₃	#121
prime radical	#41×C₁₇₃	C₂²
hypercenter	#131	D₁₇₃
hypocenter	C₁₇₃	#473
LCS	G ▷ C₂×C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #131

Complements

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

N	H ≅ G/N	type
2. C₂×Dic₆₉₂	C₂	semidirect
3. #19149615	C₂	semidirect
4. #19149597	C₂	semidirect
38. C₁₇₃	#473	semidirect

Maximal subgroups

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

subgroup	index
#19149709	2
C₂×Dic₆₉₂	2
#19149615	2
#19149597	2
#131×C₁₇₃	2
#473	173