Subgroups — #36369939

Order 22144.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012414	C₂	1	2	yes	maximal, complemented
2	#26012388	C₂	1	2	yes	maximal
3	#26012384	C₂	1	2	yes	maximal, complemented
4	#26011448	C₂	1	1	yes	maximal, characteristic
5	#19149753	C₂²	1	4	yes	—
6	C₂×#14583809	C₂²	1	1	yes	characteristic
7	C₂×C₈×D₁₇₃	C₄	1	1	yes	characteristic
8	#19149636	C₄	1	1	yes	characteristic
9	#19149589	C₂²	1	1	yes	characteristic
10	C₄×#13063436	C₂²	1	1	yes	characteristic
11	C₈×Dic₁₇₃	C₄	1	1	yes	characteristic
12	#97×C₁₇₃	C₄	1	1	yes	characteristic
13	#14583829	—	2	4	no	—
14	C₂×C₄×D₁₇₃	C₂×C₄	1	1	yes	characteristic
15	#14583809	—	2	2	no	—
16	C₂×#13063436	C₂×C₄	1	1	yes	characteristic
17	C₂×#13063436	C₂³	1	1	yes	characteristic
18	C₈×D₁₇₃	—	2	2	no	—
19	#14583805	—	2	1	no	—
20	#14583803	—	2	1	no	—
21	C₄×Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×C₁₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₈×C₁₇₃	C₂×C₄	1	1	yes	characteristic
24	C₄²×C₁₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂²×D₁₇₃	M₁₆	1	1	yes	characteristic
26	C₂×Dic₁₇₃	—	2	1	no	—
27	C₂×Dic₁₇₃	M₁₆	1	1	yes	characteristic
28	C₄×D₁₇₃	—	2	1	no	—
29	C₄×D₁₇₃	—	2	1	no	—
30	#13063436	M₁₆	1	2	yes	—
31	#13063436	#41	1	2	yes	—
32	C₂×C₄×C₁₇₃	—	2	1	no	—
33	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
34	C₈×C₁₇₃	—	2	1	no	—
35	C₈×C₁₇₃	—	2	1	no	—
36	C₂²×C₁₇₃	C₂×M₁₆	1	1	yes	characteristic
37	C₂×D₁₇₃	—	2	1	no	—
38	C₂×D₁₇₃	—	4	1	no	—
39	C₄×C₁₇₃	—	4	1	no	—
40	C₄×C₁₇₃	#117	1	1	yes	characteristic
41	C₄×C₁₇₃	C₂×M₁₆	1	1	yes	characteristic
42	Dic₁₇₃	—	2	1	no	—
43	Dic₁₇₃	—	4	1	no	—
44	C₂×C₁₇₃	—	2	1	no	—
45	C₂×C₁₇₃	#432	1	1	yes	characteristic
46	D₁₇₃	—	4	1	no	—
47	C₁₇₃	#2166	1	1	yes	characteristic, complemented, Sylow
48	#2166	—	173	1	no	maximal, Sylow
49	#405	—	173	1	no	—
50	#364	—	173	2	no	—
51	#349	—	173	2	no	—
52	#347	—	173	2	no	—
53	C₂×M₁₆	—	173	1	no	—
54	C₂²×C₈	—	173	1	no	—
55	#117	—	173	1	no	—
56	M₃₂	—	173	4	no	—
57	#97	—	173	1	no	—
58	#97	#10621924	1	1	yes	characteristic
59	C₄×C₈	—	173	1	no	—
60	C₄×C₈	—	173	1	no	—
61	C₂²×C₄	—	173	1	no	—
62	M₁₆	—	346	2	no	—
63	C₂×C₈	—	346	2	no	—
64	C₂×C₈	—	173	1	no	—
65	C₂×C₈	—	173	1	no	—
66	C₂×C₈	C₂×#10621924	1	1	yes	characteristic
67	C₂×C₈	C₂×#10621924	1	1	yes	characteristic
68	C₄⋊C₄	—	346	1	no	—
69	C₂²⋊C₄	—	346	1	no	—
70	C₄²	—	173	1	no	—
71	C₄²	C₂×#10621924	1	1	yes	characteristic
72	C₁₆	—	346	4	no	—
73	C₂³	—	173	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	346	1	no	—
76	C₂×C₄	—	346	1	no	—
77	C₂×C₄	—	346	1	no	—
78	C₂×C₄	—	173	1	no	—
79	C₂×C₄	C₂²×#10621924	1	1	yes	characteristic
80	C₈	—	2	1	no	—
81	C₈	—	2	1	no	—
82	C₈	—	173	2	no	—
83	C₈	—	173	2	no	—
84	C₂²	—	346	1	no	—
85	C₂²	—	692	1	no	—
86	C₂²	D₁₇₃⋊M₁₆	1	1	yes	characteristic
87	C₄	—	4	1	no	—
88	C₄	—	346	1	no	—
89	C₄	—	692	1	no	—
90	C₄	#19149758	1	1	yes	characteristic
91	C₄	D₁₇₃⋊M₁₆	1	1	yes	characteristic
92	C₂	—	2	1	no	—
93	C₂	—	692	1	no	—
94	C₂	#26012514	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19149758
commutator	C₂×C₄×C₁₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#10621924
Fitting	#97×C₁₇₃	C₄
socle	C₂×C₁₇₃	#432
prime radical	C₂²×D₁₇₃	M₁₆
cosocle	C₂×#13063436	C₂³
hypercenter	#97	#10621924
hypocenter	C₁₇₃	#2166
LCS	G ▷ C₂×C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #97

Complements

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

N	H ≅ G/N	type
1. #26012414	C₂	semidirect
3. #26012384	C₂	semidirect
47. C₁₇₃	#2166	semidirect

Maximal subgroups

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

subgroup	index
#26012414	2
#26012388	2
#26012384	2
#26011448	2
#2166	173