Subgroups — #36351647

Order 22144.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19149619	C₂	1	2	yes	maximal
2	C₂×#97×C₁₇₃	C₂	1	1	yes	maximal, characteristic
3	#19149619	—	2	2	no	—
4	#19149619	C₄	1	4	yes	complemented
5	C₂×#14583801	—	2	2	no	—
6	C₂²×C₈×C₁₇₃	C₄	1	1	yes	characteristic
7	C₂²×C₈×C₁₇₃	C₂²	1	1	yes	characteristic
8	C₂×C₄²×C₁₇₃	C₄	1	1	yes	characteristic
9	#97×C₁₇₃	—	2	2	no	—
10	#14583801	—	2	4	no	—
11	C₂²×C₄×C₁₇₃	C₈	1	2	yes	—
12	C₂²×C₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
13	C₂×C₈×C₁₇₃	—	2	1	no	—
14	C₂×C₈×C₁₇₃	—	2	1	no	—
15	C₂×C₈×C₁₇₃	C₈	1	2	yes	—
16	C₂×C₈×C₁₇₃	C₂×C₄	1	2	yes	—
17	C₂×C₈×C₁₇₃	D₄	1	1	yes	characteristic
18	C₂×C₈×C₁₇₃	D₄	1	2	yes	—
19	C₂×C₈×C₁₇₃	Q₈	1	1	yes	characteristic
20	C₄²×C₁₇₃	—	2	1	no	—
21	C₄²×C₁₇₃	—	2	1	no	—
22	C₂³×C₁₇₃	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₁₇₃	—	2	2	no	—
24	C₂×C₄×C₁₇₃	—	4	2	no	—
25	C₂×C₄×C₁₇₃	C₄²	1	1	yes	characteristic
26	C₂×C₄×C₁₇₃	C₂²⋊C₄	1	1	yes	characteristic
27	C₂×C₄×C₁₇₃	C₄⋊C₄	1	1	yes	characteristic
28	C₂×C₄×C₁₇₃	C₂×C₈	1	1	yes	characteristic
29	C₂×C₄×C₁₇₃	M₁₆	1	1	yes	characteristic
30	C₂×C₄×C₁₇₃	M₁₆	1	1	yes	characteristic
31	C₈×C₁₇₃	—	2	2	no	—
32	C₈×C₁₇₃	C₂²⋊C₄	1	2	yes	—
33	C₈×C₁₇₃	C₄⋊C₄	1	2	yes	—
34	C₂²×C₁₇₃	—	2	2	no	—
35	C₂²×C₁₇₃	C₄×C₈	1	1	yes	characteristic
36	C₂²×C₁₇₃	C₂²⋊C₈	1	1	yes	characteristic
37	C₂²×C₁₇₃	C₄⋊C₈	1	1	yes	characteristic
38	C₄×C₁₇₃	—	4	2	no	—
39	C₄×C₁₇₃	#95	1	1	yes	characteristic
40	C₄×C₁₇₃	#97	1	1	yes	characteristic
41	C₄×C₁₇₃	C₂²⋊C₈	1	1	yes	characteristic
42	C₄×C₁₇₃	C₄⋊C₈	1	1	yes	characteristic
43	C₂×C₁₇₃	—	2	1	no	—
44	C₂×C₁₇₃	—	2	1	no	—
45	C₂×C₁₇₃	#336	1	1	yes	characteristic
46	C₂×C₁₇₃	#349	1	2	yes	—
47	C₁₇₃	#1377	1	1	yes	characteristic, complemented, Sylow
48	#1377	—	173	1	no	maximal, Sylow
49	C₂×M₃₂	—	173	2	no	—
50	C₂×#97	D₁₇₃	1	1	yes	characteristic
51	C₂²×C₈	Dic₁₇₃	1	1	yes	characteristic
52	C₂²×C₈	C₂×D₁₇₃	1	1	yes	characteristic
53	C₂×C₄²	Dic₁₇₃	1	1	yes	characteristic
54	M₃₂	—	346	2	no	—
55	M₃₂	—	173	4	no	—
56	C₂×C₁₆	—	346	2	no	—
57	#97	—	2	2	no	—
58	C₂²×C₄	#13063436	1	2	yes	—
59	C₂²×C₄	C₂×Dic₁₇₃	1	1	yes	characteristic
60	C₂×C₈	—	2	1	no	—
61	C₂×C₈	—	2	1	no	—
62	C₂×C₈	#13063436	1	2	yes	—
63	C₂×C₈	C₄×D₁₇₃	1	2	yes	—
64	C₂×C₈	C₂²⋊D₁₇₃	1	2	yes	—
65	C₂×C₈	D₆₉₂	1	1	yes	characteristic
66	C₂×C₈	Dic₃₄₆	1	1	yes	characteristic
67	C₄²	—	2	1	no	—
68	C₄²	—	2	1	no	—
69	C₁₆	—	346	4	no	—
70	C₂³	C₂×#13063436	1	1	yes	characteristic
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	4	2	no	—
73	C₂×C₄	C₄×Dic₁₇₃	1	1	yes	characteristic
74	C₂×C₄	C₂²⋊Dic₁₇₃	1	1	yes	characteristic
75	C₂×C₄	C₄⋊Dic₁₇₃	1	1	yes	characteristic
76	C₂×C₄	C₂×#13063436	1	1	yes	characteristic
77	C₂×C₄	#14583810	1	1	yes	characteristic
78	C₂×C₄	#14583810	1	1	yes	characteristic
79	C₈	—	2	2	no	—
80	C₈	#14583803	1	2	yes	—
81	C₈	#14583805	1	2	yes	—
82	C₂²	—	2	2	no	—
83	C₂²	C₄×#13063436	1	1	yes	characteristic
84	C₂²	C₂²⋊#13063436	1	1	yes	characteristic
85	C₂²	C₄⋊#13063436	1	1	yes	characteristic
86	C₄	—	4	2	no	—
87	C₄	#19149586	1	1	yes	characteristic
88	C₄	#19149590	1	1	yes	characteristic
89	C₄	C₂²⋊#13063436	1	1	yes	characteristic
90	C₄	C₄⋊#13063436	1	1	yes	characteristic
91	C₂	—	2	1	no	—
92	C₂	—	2	1	no	—
93	C₂	#26011246	1	1	yes	characteristic
94	C₂	#26011273	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊Dic₁₇₃
commutator	C₂²×C₁₇₃	C₄×C₈
Frattini	C₂²×C₈	C₂×D₁₇₃
Fitting	C₂×#97×C₁₇₃	C₂
socle	C₂²×C₁₇₃	C₂²⋊C₈
prime radical	C₂³×C₁₇₃	C₂×C₈
cosocle	C₂²×C₈×C₁₇₃	C₂²
hypercenter	C₂×#97	D₁₇₃
hypocenter	C₁₇₃	#1377
LCS	G ▷ C₂²×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
4. #19149619	C₄	semidirect
47. C₁₇₃	#1377	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19149619	2
C₂×#97×C₁₇₃	2
#1377	173