Subgroups — #36351636

Order 22144.

70 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#14583801	C₂	1	1	yes	maximal, characteristic
2	#26011244	C₂	1	1	yes	maximal, characteristic
3	#335×C₁₇₃	C₂	1	1	yes	maximal, characteristic
4	C₂×#14583801	C₄	1	1	yes	characteristic
5	C₂×#14583801	C₄	1	1	yes	characteristic
6	C₄⋊#13063436	—	2	1	no	—
7	C₄⋊C₈×C₁₇₃	—	2	1	no	—
8	C₄×C₈×C₁₇₃	C₂²	1	1	yes	characteristic
9	C₂×#13063436	—	4	1	no	—
10	#14583801	—	2	1	no	—
11	#14583801	C₈	1	2	yes	complemented
12	C₂×C₈×C₁₇₃	—	4	1	no	—
13	C₂×C₈×C₁₇₃	C₂×C₄	1	1	yes	characteristic
14	C₂×C₈×C₁₇₃	Q₈	1	1	yes	characteristic
15	C₄²×C₁₇₃	D₄	1	1	yes	characteristic
16	#13063436	—	8	1	no	—
17	C₂×C₄×C₁₇₃	C₄⋊C₄	1	1	yes	characteristic
18	C₂×C₄×C₁₇₃	D₈	1	1	yes	characteristic
19	C₂×C₄×C₁₇₃	Q₁₆	1	1	yes	characteristic
20	C₈×C₁₇₃	—	2	1	no	—
21	C₈×C₁₇₃	—	8	1	no	—
22	C₈×C₁₇₃	C₂×C₈	1	1	yes	characteristic
23	C₈×C₁₇₃	M₁₆	1	1	yes	characteristic
24	C₂²×C₁₇₃	#107	1	1	yes	characteristic
25	C₄×C₁₇₃	—	2	1	no	—
26	C₄×C₁₇₃	C₄⋊C₈	1	1	yes	characteristic
27	C₄×C₁₇₃	#108	1	1	yes	characteristic
28	C₄×C₁₇₃	SD₃₂	1	1	yes	characteristic
29	C₄×C₁₇₃	SD₃₂	1	1	yes	characteristic
30	C₂×C₁₇₃	#335	1	1	yes	characteristic
31	C₂×C₁₇₃	#367	1	1	yes	characteristic
32	C₂×C₁₇₃	#368	1	1	yes	characteristic
33	C₁₇₃	#1372	1	1	yes	characteristic, complemented, Sylow
34	#1372	—	173	1	no	maximal, Sylow
35	C₄×C₁₆	—	173	1	no	—
36	#335	—	173	1	no	—
37	#335	D₁₇₃	1	1	yes	characteristic
38	C₂×C₁₆	—	173	1	no	—
39	C₂×C₁₆	—	173	1	no	—
40	C₄⋊C₈	—	2	1	no	—
41	C₄⋊C₈	—	346	1	no	—
42	C₄×C₈	C₂×D₁₇₃	1	1	yes	characteristic
43	C₂×C₈	—	4	1	no	—
44	C₂×C₈	—	692	1	no	—
45	C₂×C₈	C₄×D₁₇₃	1	1	yes	characteristic
46	C₂×C₈	Dic₃₄₆	1	1	yes	characteristic
47	C₄²	C₂²⋊D₁₇₃	1	1	yes	characteristic
48	C₁₆	—	346	1	no	—
49	C₁₆	—	173	2	no	—
50	C₂×C₄	#14583805	1	1	yes	characteristic
51	C₂×C₄	#14583811	1	1	yes	characteristic
52	C₂×C₄	#14583816	1	1	yes	characteristic
53	C₈	—	2	1	no	—
54	C₈	—	8	1	no	—
55	C₈	—	1384	1	no	—
56	C₈	C₈×D₁₇₃	1	1	yes	characteristic
57	C₈	#14583809	1	1	yes	characteristic
58	C₂²	#19149612	1	1	yes	characteristic
59	C₄	—	2	1	no	—
60	C₄	#19149608	1	1	yes	characteristic
61	C₄	#19149614	1	1	yes	characteristic
62	C₄	#19149622	1	1	yes	characteristic
63	C₄	#19149623	1	1	yes	characteristic
64	C₂	#26011243	1	1	yes	characteristic
65	C₂	#26011318	1	1	yes	characteristic
66	C₂	#26011320	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#14583811
commutator	C₈×C₁₇₃	C₂×C₈
Frattini	C₄×C₈	C₂×D₁₇₃
Fitting	#335×C₁₇₃	C₂
socle, prime radical	C₂²×C₁₇₃	#107
cosocle	C₄×C₈×C₁₇₃	C₂²
hypercenter	#335	D₁₇₃
hypocenter	C₁₇₃	#1372
LCS	G ▷ C₈×C₁₇₃ ▷ C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ #335

Complements

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

N	H ≅ G/N	type
11. #14583801	C₈	semidirect
33. C₁₇₃	#1372	semidirect

Maximal subgroups

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

subgroup	index
C₄×#14583801	2
#26011244	2
#335×C₁₇₃	2
#1372	173