Subgroups — #36368520

Order 22144.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012377	C₂	1	1	yes	maximal, characteristic
2	#26012354	C₂	1	1	yes	maximal, characteristic
3	#26011585	C₂	1	1	yes	maximal, characteristic
4	C₂×#14583829	—	2	1	no	—
5	C₄⋊#13063443	—	2	1	no	—
6	C₂×Dic₆₉₂	C₄	1	1	yes	characteristic
7	#19149644	—	2	1	no	—
8	#19149602	—	2	1	no	—
9	C₈×Dic₁₇₃	C₂²	1	1	yes	characteristic
10	#107×C₁₇₃	C₄	1	1	yes	characteristic
11	C₂×#13063443	—	4	1	no	—
12	#14583829	—	2	2	no	—
13	C₂×Dic₃₄₆	—	2	1	no	—
14	Dic₆₉₂	—	2	1	no	—
15	Dic₆₉₂	C₈	1	2	yes	complemented
16	C₂×#13063436	D₄	1	1	yes	characteristic
17	#14583805	—	4	1	no	—
18	C₄×Dic₁₇₃	—	4	1	no	—
19	C₄×Dic₁₇₃	D₄	1	1	yes	characteristic
20	C₂×C₈×C₁₇₃	C₂×C₄	1	1	yes	characteristic
21	C₄⋊C₄×C₁₇₃	—	2	1	no	—
22	#13063443	—	8	1	no	—
23	Dic₃₄₆	—	2	2	no	—
24	Dic₃₄₆	—	4	1	no	—
25	C₂×Dic₁₇₃	—	4	1	no	—
26	C₂×Dic₁₇₃	D₈	1	1	yes	characteristic
27	C₂×Dic₁₇₃	SD₁₆	1	1	yes	characteristic
28	#13063436	—	2	1	no	—
29	C₂×C₄×C₁₇₃	—	4	1	no	—
30	C₂×C₄×C₁₇₃	C₂²⋊C₄	1	1	yes	characteristic
31	C₈×C₁₇₃	C₂×C₈	1	1	yes	characteristic
32	C₈×C₁₇₃	M₁₆	1	1	yes	characteristic
33	C₂²×C₁₇₃	#102	1	1	yes	characteristic
34	C₄×C₁₇₃	—	8	1	no	—
35	C₄×C₁₇₃	C₂²⋊C₈	1	1	yes	characteristic
36	C₄×C₁₇₃	#104	1	1	yes	characteristic
37	Dic₁₇₃	—	2	1	no	—
38	Dic₁₇₃	—	4	2	no	—
39	Dic₁₇₃	SD₃₂	1	1	yes	characteristic
40	Dic₁₇₃	Q₃₂	1	1	yes	characteristic
41	C₂×C₁₇₃	D₄⋊C₈	1	1	yes	characteristic
42	C₂×C₁₇₃	#358	1	1	yes	characteristic
43	C₂×C₁₇₃	#359	1	1	yes	characteristic
44	C₁₇₃	#1332	1	1	yes	characteristic, complemented, Sylow
45	#1332	—	173	1	no	maximal, Sylow
46	C₄×Q₁₆	—	173	1	no	—
47	C₄×C₁₆	—	173	1	no	—
48	#335	—	173	1	no	—
49	C₂×Q₁₆	—	173	1	no	—
50	C₄×Q₈	—	346	1	no	—
51	C₂×C₁₆	—	346	1	no	—
52	#107	#10621924	1	1	yes	characteristic
53	C₄⋊C₈	—	346	1	no	—
54	#103	—	346	1	no	—
55	C₄×C₈	—	173	1	no	—
56	C₂×Q₈	—	346	1	no	—
57	Q₁₆	—	346	1	no	—
58	Q₁₆	—	173	2	no	—
59	C₂×C₈	—	173	1	no	—
60	C₂×C₈	—	692	1	no	—
61	C₂×C₈	C₂×#10621924	1	1	yes	characteristic
62	C₄⋊C₄	—	2	1	no	—
63	C₄⋊C₄	—	692	1	no	—
64	C₄²	—	173	1	no	—
65	C₄²	—	692	1	no	—
66	C₁₆	—	346	2	no	—
67	Q₈	—	346	2	no	—
68	Q₈	—	692	1	no	—
69	C₂×C₄	—	4	1	no	—
70	C₂×C₄	—	173	1	no	—
71	C₂×C₄	—	173	1	no	—
72	C₂×C₄	—	692	1	no	—
73	C₂×C₄	C₂²⋊#10621924	1	1	yes	characteristic
74	C₈	—	346	1	no	—
75	C₈	—	1384	1	no	—
76	C₈	D₁₇₃⋊C₈	1	1	yes	characteristic
77	C₈	#14583836	1	1	yes	characteristic
78	C₂²	#19149741	1	1	yes	characteristic
79	C₄	—	8	1	no	—
80	C₄	—	346	1	no	—
81	C₄	—	173	1	no	—
82	C₄	—	173	1	no	—
83	C₄	—	692	2	no	—
84	C₄	#19149736	1	1	yes	characteristic
85	C₄	#19149744	1	1	yes	characteristic
86	C₂	#26012339	1	1	yes	characteristic
87	C₂	#26012404	1	1	yes	characteristic
88	C₂	#26012405	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#19149741
commutator	C₈×C₁₇₃	C₂×C₈
Frattini	C₂×C₈	C₂×#10621924
Fitting	#107×C₁₇₃	C₄
socle, prime radical	C₂²×C₁₇₃	#102
cosocle	C₈×Dic₁₇₃	C₂²
hypercenter	#107	#10621924
hypocenter	C₁₇₃	#1332
LCS	G ▷ C₈×C₁₇₃ ▷ C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #107

Complements

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

N	H ≅ G/N	type
15. Dic₆₉₂	C₈	semidirect
44. C₁₇₃	#1332	semidirect

Maximal subgroups

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

subgroup	index
#26012377	2
#26012354	2
#26011585	2
#1332	173