Subgroups — #36369492

Order 22144.

196 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26012357	C₂	1	6	yes	maximal
2	#26011336	C₂	1	1	yes	maximal, characteristic
3	C₂²×#13063443	C₂²	1	4	yes	—
4	C₂×C₄×Dic₁₇₃	C₂²	1	3	yes	—
5	#19149586	C₄	1	3	yes	—
6	#95×C₁₇₃	C₄	1	1	yes	characteristic
7	C₂×#13063443	—	2	12	no	—
8	C₂²×Dic₁₇₃	C₂×C₄	1	3	yes	—
9	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
10	C₄×Dic₁₇₃	—	2	6	no	—
11	C₂²×C₄×C₁₇₃	C₂×C₄	1	3	yes	—
12	#13063443	—	4	4	no	—
13	C₂×Dic₁₇₃	—	2	3	no	—
14	C₂×Dic₁₇₃	—	2	3	no	—
15	C₂×Dic₁₇₃	—	2	3	no	—
16	C₂×Dic₁₇₃	#41	1	6	yes	—
17	C₂³×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
18	C₂×C₄×C₁₇₃	—	2	3	no	—
19	C₂×C₄×C₁₇₃	—	2	6	no	—
20	C₂²×C₁₇₃	#117	1	3	yes	—
21	C₂²×C₁₇₃	#131	1	3	yes	—
22	C₂²×C₁₇₃	#131	1	1	yes	characteristic
23	C₄×C₁₇₃	—	4	3	no	—
24	Dic₁₇₃	—	4	3	no	—
25	Dic₁₇₃	#126	1	4	yes	—
26	C₂×C₁₇₃	#383	1	1	yes	characteristic
27	C₂×C₁₇₃	#433	1	3	yes	—
28	C₂×C₁₇₃	#433	1	3	yes	—
29	C₁₇₃	#1840	1	1	yes	characteristic, complemented, Sylow
30	#1840	—	173	1	no	maximal, Sylow
31	#376	—	173	1	no	—
32	#336	—	173	6	no	—
33	C₂²×C₈	—	173	4	no	—
34	C₂×C₄²	—	173	3	no	—
35	#95	—	173	3	no	—
36	#95	#10621924	1	1	yes	characteristic
37	C₂²×C₄	—	173	3	no	—
38	C₂²×C₄	—	173	1	no	—
39	C₂²×C₄	C₂×#10621924	1	3	yes	—
40	C₂×C₈	—	346	12	no	—
41	C₄²	—	346	6	no	—
42	C₂³	C₂²×#10621924	1	1	yes	characteristic
43	C₂×C₄	—	2	3	no	—
44	C₂×C₄	—	2	6	no	—
45	C₂×C₄	—	346	3	no	—
46	C₂×C₄	—	346	3	no	—
47	C₂×C₄	—	346	3	no	—
48	C₂×C₄	—	173	6	no	—
49	C₈	—	692	4	no	—
50	C₂²	#19149758	1	3	yes	—
51	C₂²	#19149766	1	3	yes	—
52	C₂²	#19149767	1	1	yes	characteristic
53	C₄	—	4	3	no	—
54	C₄	—	173	4	no	—
55	C₄	—	692	3	no	—
56	C₂	#26012436	1	1	yes	characteristic
57	C₂	#26012515	1	3	yes	—
58	C₂	#26012516	1	3	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂²×#10621924
commutator, socle, prime radical	C₂³×C₁₇₃	C₂²×C₄
Fitting	#95×C₁₇₃	C₄
cosocle	C₂²×Dic₁₇₃	C₂³
hypercenter	#95	#10621924
hypocenter	C₁₇₃	#1840
LCS	G ▷ C₂³×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂³ ◁ #95

Complements

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

N	H ≅ G/N	type
29. C₁₇₃	#1840	semidirect

Maximal subgroups

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

subgroup	index
#26012357	2
#26011336	2
#1840	173