Subgroups — #22625063

Order 9344.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989492	C₂	1	2	yes	maximal, complemented
2	#17988964	C₂	1	1	yes	maximal, characteristic
3	#14556650	—	2	2	no	—
4	C₂×D₅₈₄	—	2	2	no	—
5	#14556588	C₄	1	1	yes	characteristic, complemented
6	#14556588	C₂²	1	1	yes	characteristic
7	C₄×C₈×C₇₃	C₄	1	1	yes	characteristic, complemented
8	C₂²⋊#64408	—	4	2	no	—
9	C₂×D₂₉₂	—	2	1	no	—
10	C₂×D₂₉₂	—	4	1	no	—
11	C₂×D₂₉₂	—	4	1	no	—
12	C₂×D₂₉₂	D₄	1	2	yes	—
13	D₅₈₄	—	4	4	no	—
14	C₂×C₈×C₇₃	—	2	1	no	—
15	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
16	C₂²×D₇₃	—	2	2	no	—
17	C₂²×D₇₃	—	4	1	no	—
18	C₂×#64408	—	8	2	no	—
19	C₂×C₄×C₇₃	—	2	1	no	—
20	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
21	D₂₉₂	—	4	2	no	—
22	D₂₉₂	—	4	2	no	—
23	D₂₉₂	—	8	2	no	—
24	D₂₉₂	—	8	2	no	—
25	C₈×C₇₃	—	2	2	no	—
26	C₂²×C₇₃	#99	1	1	yes	characteristic
27	C₂×D₇₃	—	4	2	no	—
28	C₂×D₇₃	—	8	2	no	—
29	C₂×D₇₃	—	8	2	no	—
30	C₂×D₇₃	—	8	1	no	—
31	#64408	—	16	2	no	—
32	C₄×C₇₃	—	2	2	no	—
33	C₄×C₇₃	—	2	1	no	—
34	C₂×C₇₃	—	2	1	no	—
35	C₂×C₇₃	#353	1	1	yes	characteristic
36	D₇₃	—	8	2	no	—
37	D₇₃	—	16	1	no	—
38	#1408	—	73	1	no	maximal, Sylow
39	C₇₃	#1408	1	1	yes	characteristic, complemented, Sylow
40	#493	—	73	1	no	—
41	#353	—	73	2	no	—
42	C₂×D₈	—	146	2	no	—
43	#127	—	73	1	no	—
44	#127	—	73	1	no	—
45	#99	—	146	2	no	—
46	C₄×C₈	#64408	1	1	yes	characteristic, complemented
47	C₂×D₄	—	292	1	no	—
48	C₂×D₄	—	292	1	no	—
49	C₂×D₄	—	73	2	no	—
50	C₂×D₄	—	146	1	no	—
51	D₈	—	292	4	no	—
52	C₂×C₈	—	2	1	no	—
53	C₂²⋊C₄	—	292	2	no	—
54	C₄²	C₂×#64408	1	1	yes	characteristic
55	C₂³	—	292	1	no	—
56	C₂³	—	146	2	no	—
57	D₄	—	292	2	no	—
58	D₄	—	292	2	no	—
59	D₄	—	584	2	no	—
60	D₄	—	584	2	no	—
61	C₂×C₄	—	2	1	no	—
62	C₂×C₄	—	584	2	no	—
63	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
64	C₈	—	2	2	no	—
65	C₂²	—	292	2	no	—
66	C₂²	—	584	2	no	—
67	C₂²	—	584	2	no	—
68	C₂²	—	584	1	no	—
69	C₂²	#14556650	1	1	yes	characteristic
70	C₄	—	2	2	no	—
71	C₄	—	2	1	no	—
72	C₄	—	1168	2	no	—
73	C₂	—	2	1	no	—
74	C₂	—	584	2	no	—
75	C₂	—	1168	1	no	—
76	C₂	#17989492	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17989492
commutator	C₄²×C₇₃	C₂×C₄
Frattini	C₄²	C₂×#64408
Fitting	C₄×C₈×C₇₃	C₄
socle	C₂×C₇₃	#353
hypercenter	C₄×C₈	#64408
hypocenter	C₇₃	#1408
LCS	G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
1. #17989492	C₂	semidirect
5. #14556588	C₄	semidirect
7. C₄×C₈×C₇₃	C₄	semidirect
39. C₇₃	#1408	semidirect
46. C₄×C₈	#64408	semidirect