Subgroups — #22624942

Order 9344.

102 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989510	C₂	1	2	yes	maximal, complemented
2	#17988961	C₂	1	1	yes	maximal, characteristic
3	#14556665	—	2	2	no	—
4	C₂×#11924015	—	2	2	no	—
5	#14556588	C₄	1	1	yes	characteristic
6	C₄×#10596831	C₂²	1	1	yes	characteristic
7	C₄⋊Q₈×C₇₃	C₄	1	1	yes	characteristic
8	#11924031	—	4	2	no	—
9	C₂×D₂₉₂	—	2	1	no	—
10	C₂×D₂₉₂	—	4	1	no	—
11	#11924015	—	4	2	no	—
12	#11924015	—	4	2	no	—
13	C₂×#10596831	D₄	1	2	yes	—
14	C₂×Q₈×C₇₃	—	2	1	no	—
15	C₄⋊C₄×C₇₃	—	4	1	no	—
16	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
17	C₂²×D₇₃	—	4	1	no	—
18	Q₈×C₇₃	—	4	2	no	—
19	C₂×C₄×C₇₃	—	2	1	no	—
20	C₂×C₄×C₇₃	—	4	1	no	—
21	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
22	D₂₉₂	—	4	2	no	—
23	D₂₉₂	—	8	2	no	—
24	#10596831	D₈	1	2	yes	—
25	#10596831	SD₁₆	1	2	yes	—
26	C₂²×C₇₃	#100	1	1	yes	characteristic
27	C₂×D₇₃	—	8	2	no	—
28	C₂×D₇₃	—	8	1	no	—
29	C₄×C₇₃	—	2	2	no	—
30	C₄×C₇₃	—	8	1	no	—
31	C₄×C₇₃	#102	1	2	yes	—
32	C₂×C₇₃	—	2	1	no	—
33	C₂×C₇₃	#331	1	1	yes	characteristic
34	D₇₃	—	16	1	no	—
35	#1359	—	73	1	no	maximal, Sylow
36	C₇₃	#1359	1	1	yes	characteristic, complemented, Sylow
37	#492	—	73	1	no	—
38	#364	—	73	2	no	—
39	C₂×SD₁₆	—	146	2	no	—
40	C₄⋊Q₈	#64408	1	1	yes	characteristic
41	#127	—	73	1	no	—
42	M₃₂	—	146	2	no	—
43	C₄×C₈	—	73	1	no	—
44	C₂×Q₈	—	2	1	no	—
45	C₂×D₄	—	292	1	no	—
46	C₂×D₄	—	146	1	no	—
47	SD₁₆	—	292	2	no	—
48	SD₁₆	—	292	2	no	—
49	C₂×C₈	—	73	2	no	—
50	C₄⋊C₄	—	4	1	no	—
51	C₄²	C₂×#64408	1	1	yes	characteristic
52	C₁₆	—	292	2	no	—
53	C₂³	—	292	1	no	—
54	Q₈	—	4	2	no	—
55	D₄	—	292	2	no	—
56	D₄	—	584	2	no	—
57	C₂×C₄	—	2	1	no	—
58	C₂×C₄	—	4	1	no	—
59	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
60	C₈	—	73	2	no	—
61	C₈	—	73	2	no	—
62	C₂²	—	584	2	no	—
63	C₂²	—	584	1	no	—
64	C₂²	#14556651	1	1	yes	characteristic
65	C₄	—	2	2	no	—
66	C₄	—	8	1	no	—
67	C₄	#14556653	1	2	yes	—
68	C₂	—	2	1	no	—
69	C₂	—	1168	1	no	—
70	C₂	#17989445	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17989445
commutator	C₄²×C₇₃	C₂×C₄
Frattini	C₄²	C₂×#64408
Fitting	C₄⋊Q₈×C₇₃	C₄
socle	C₂×C₇₃	#331
hypercenter	C₄⋊Q₈	#64408
hypocenter	C₇₃	#1359
LCS	G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #17989510	C₂	semidirect
36. C₇₃	#1359	semidirect