Subgroups — #36368486

Order 22144.

116 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²⋊#14583829	C₂	1	2	yes	maximal, complemented
2	#26011459	C₂	1	1	yes	maximal, characteristic
3	C₂×#14583829	—	2	2	no	—
4	C₂×#14583826	C₄	1	1	yes	characteristic
5	C₂²×#13063436	C₂²	1	1	yes	characteristic
6	#19149591	—	2	2	no	—
7	C₂×M₁₆×C₁₇₃	C₄	1	1	yes	characteristic
8	#14583829	—	4	2	no	—
9	#14583826	—	4	1	no	—
10	#14583826	—	4	1	no	—
11	C₂×Dic₃₄₆	C₈	1	1	yes	characteristic
12	C₂×D₆₉₂	C₈	1	1	yes	characteristic
13	C₂×C₂²⋊D₁₇₃	—	2	1	no	—
14	C₂×C₄×D₁₇₃	—	2	1	no	—
15	C₂×#13063436	—	4	1	no	—
16	C₂×#13063436	D₄	1	2	yes	—
17	C₂²×C₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
18	M₁₆×C₁₇₃	—	4	1	no	—
19	C₂×C₈×C₁₇₃	—	2	1	no	—
20	C₂²×D₁₇₃	—	2	1	no	—
21	Dic₃₄₆	—	4	1	no	—
22	D₆₉₂	—	4	1	no	—
23	C₂²⋊D₁₇₃	—	4	2	no	—
24	C₂×Dic₁₇₃	—	2	1	no	—
25	C₄×D₁₇₃	—	4	1	no	—
26	C₄×D₁₇₃	—	4	1	no	—
27	#13063436	—	2	2	no	—
28	C₂³×C₁₇₃	M₁₆	1	1	yes	characteristic
29	C₂×C₄×C₁₇₃	—	2	1	no	—
30	C₂×C₄×C₁₇₃	—	2	1	no	—
31	C₂×C₄×C₁₇₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₁₇₃	C₂×C₈	1	1	yes	characteristic
33	C₈×C₁₇₃	—	4	1	no	—
34	C₂²×C₁₇₃	—	2	1	no	—
35	C₂²×C₁₇₃	—	2	2	no	—
36	C₂²×C₁₇₃	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×D₁₇₃	—	4	1	no	—
38	C₂×D₁₇₃	—	4	2	no	—
39	C₄×C₁₇₃	—	2	1	no	—
40	C₄×C₁₇₃	#99	1	1	yes	characteristic
41	C₄×C₁₇₃	#100	1	1	yes	characteristic
42	Dic₁₇₃	—	4	1	no	—
43	C₂×C₁₇₃	—	4	1	no	—
44	C₂×C₁₇₃	#323	1	1	yes	characteristic
45	C₂×C₁₇₃	#350	1	2	yes	—
46	D₁₇₃	—	8	1	no	—
47	C₁₇₃	#1315	1	1	yes	characteristic, complemented, Sylow
48	#1315	—	173	1	no	maximal, Sylow
49	#408	—	173	1	no	—
50	C₂²⋊C₁₆	—	173	2	no	—
51	C₂×#41	—	173	1	no	—
52	C₂×M₁₆	#10621924	1	1	yes	characteristic
53	C₂²×C₈	—	173	1	no	—
54	C₂×C₁₆	—	346	2	no	—
55	C₂²⋊C₈	—	346	2	no	—
56	#41	—	692	1	no	—
57	#41	—	692	1	no	—
58	C₂×Q₈	—	173	1	no	—
59	C₂×D₄	—	346	1	no	—
60	C₂×D₄	—	173	1	no	—
61	C₂²×C₄	—	346	1	no	—
62	C₂²×C₄	C₂×#10621924	1	1	yes	characteristic
63	M₁₆	—	4	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	173	2	no	—
66	C₂×C₈	—	692	1	no	—
67	C₁₆	—	692	2	no	—
68	C₂³	—	346	1	no	—
69	C₂³	#14583836	1	1	yes	characteristic
70	Q₈	—	692	1	no	—
71	D₄	—	692	1	no	—
72	D₄	—	692	2	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	2	1	no	—
75	C₂×C₄	—	346	1	no	—
76	C₂×C₄	—	692	1	no	—
77	C₂×C₄	—	692	1	no	—
78	C₂×C₄	C₂²⋊#10621924	1	1	yes	characteristic
79	C₂×C₄	D₁₇₃⋊C₈	1	1	yes	characteristic
80	C₈	—	4	1	no	—
81	C₈	—	346	2	no	—
82	C₂²	—	2	1	no	—
83	C₂²	—	2	2	no	—
84	C₂²	—	692	1	no	—
85	C₂²	—	692	2	no	—
86	C₂²	#19149736	1	1	yes	characteristic
87	C₄	—	2	1	no	—
88	C₄	—	692	1	no	—
89	C₄	#19149738	1	1	yes	characteristic
90	C₄	#19149739	1	1	yes	characteristic
91	C₂	—	4	1	no	—
92	C₂	—	1384	1	no	—
93	C₂	#26012335	1	1	yes	characteristic
94	C₂	#26012390	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊#10621924
commutator	C₂×C₄×C₁₇₃	C₂×C₈
Frattini	C₂²×C₄	C₂×#10621924
Fitting	C₂×M₁₆×C₁₇₃	C₄
socle	C₂²×C₁₇₃	C₂²⋊C₈
prime radical	C₂×#14583826	C₄
cosocle	C₂²×#13063436	C₂²
hypercenter	C₂×M₁₆	#10621924
hypocenter	C₁₇₃	#1315
LCS	G ▷ C₂×C₄×C₁₇₃ ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²⋊#14583829	C₂	semidirect
47. C₁₇₃	#1315	semidirect

Maximal subgroups

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

subgroup	index
C₂²⋊#14583829	2
#26011459	2
#1315	173