Subgroups — #36369935

Order 22144.

128 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	C₄×#14583809	C₂	1	1	yes	maximal, characteristic
5	#19149753	C₂²	1	4	yes	—
6	C₂×#14583809	C₄	1	1	yes	characteristic
7	C₂×#14583809	C₂²	1	1	yes	characteristic
8	C₄²×D₁₇₃	C₄	1	1	yes	characteristic
9	#19149589	C₄	1	1	yes	characteristic
10	#19149589	C₂²	1	1	yes	characteristic
11	C₄×#13063436	C₂²	1	1	yes	characteristic
12	C₄×C₈×C₁₇₃	C₄	1	1	yes	characteristic
13	#14583829	—	2	4	no	—
14	C₂×C₄×D₁₇₃	—	2	1	no	—
15	C₂×C₄×D₁₇₃	C₂×C₄	1	1	yes	characteristic
16	#14583809	—	2	2	no	—
17	#14583809	—	2	2	no	—
18	C₂×#13063436	C₂×C₄	1	1	yes	characteristic
19	C₂×#13063436	C₂³	1	1	yes	characteristic
20	C₄×Dic₁₇₃	—	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	C₄×D₁₇₃	—	4	2	no	—
31	#13063436	M₁₆	1	2	yes	—
32	#13063436	#41	1	2	yes	—
33	C₂×C₄×C₁₇₃	—	2	1	no	—
34	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
35	C₈×C₁₇₃	—	2	1	no	—
36	C₈×C₁₇₃	—	2	1	no	—
37	C₂²×C₁₇₃	C₂×M₁₆	1	1	yes	characteristic
38	C₂×D₁₇₃	—	2	1	no	—
39	C₂×D₁₇₃	—	4	1	no	—
40	C₄×C₁₇₃	—	2	2	no	—
41	C₄×C₁₇₃	#117	1	1	yes	characteristic
42	C₄×C₁₇₃	C₂×M₁₆	1	1	yes	characteristic
43	Dic₁₇₃	—	2	1	no	—
44	Dic₁₇₃	—	4	1	no	—
45	C₂×C₁₇₃	—	2	1	no	—
46	C₂×C₁₇₃	#432	1	1	yes	characteristic
47	D₁₇₃	—	4	1	no	—
48	C₁₇₃	#2165	1	1	yes	characteristic, complemented, Sylow
49	#2165	—	173	1	no	maximal, Sylow
50	C₄×M₁₆	—	173	1	no	—
51	#364	—	173	2	no	—
52	#349	—	173	2	no	—
53	#347	—	173	2	no	—
54	C₂×M₁₆	—	173	1	no	—
55	C₂×M₁₆	—	173	1	no	—
56	C₂×C₄²	—	173	1	no	—
57	M₃₂	—	173	4	no	—
58	#97	—	173	1	no	—
59	#97	—	173	1	no	—
60	C₄×C₈	—	173	1	no	—
61	C₄×C₈	#10621924	1	1	yes	characteristic
62	C₂²×C₄	—	346	1	no	—
63	C₂²×C₄	—	173	1	no	—
64	M₁₆	—	346	2	no	—
65	M₁₆	—	346	2	no	—
66	C₂×C₈	—	173	1	no	—
67	C₂×C₈	—	173	1	no	—
68	C₂×C₈	C₂×#10621924	1	1	yes	characteristic
69	C₂×C₈	C₂×#10621924	1	1	yes	characteristic
70	C₄²	—	346	1	no	—
71	C₄²	—	173	1	no	—
72	C₄²	C₂×#10621924	1	1	yes	characteristic
73	C₁₆	—	346	4	no	—
74	C₂³	—	173	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	346	1	no	—
77	C₂×C₄	—	346	1	no	—
78	C₂×C₄	—	346	1	no	—
79	C₂×C₄	—	173	1	no	—
80	C₂×C₄	—	692	2	no	—
81	C₂×C₄	C₂²×#10621924	1	1	yes	characteristic
82	C₈	—	2	1	no	—
83	C₈	—	2	1	no	—
84	C₈	—	173	2	no	—
85	C₈	—	173	2	no	—
86	C₂²	—	346	1	no	—
87	C₂²	—	692	1	no	—
88	C₂²	D₁₇₃⋊M₁₆	1	1	yes	characteristic
89	C₄	—	2	2	no	—
90	C₄	—	346	1	no	—
91	C₄	—	692	1	no	—
92	C₄	#19149758	1	1	yes	characteristic
93	C₄	D₁₇₃⋊M₁₆	1	1	yes	characteristic
94	C₂	—	2	1	no	—
95	C₂	—	692	1	no	—
96	C₂	#26012514	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19149758
commutator	C₂×C₄×C₁₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#10621924
Fitting	C₄×C₈×C₁₇₃	C₄
socle	C₂×C₁₇₃	#432
prime radical	C₂²×D₁₇₃	M₁₆
cosocle	C₂×#13063436	C₂³
hypercenter	C₄×C₈	#10621924
hypocenter	C₁₇₃	#2165
LCS	G ▷ C₂×C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. #26012414	C₂	semidirect
3. #26012384	C₂	semidirect
48. C₁₇₃	#2165	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
C₄×#14583809	2
#2165	173