Subgroups — #22625070

Order 9344.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989492	C₂	1	2	yes	maximal
2	#17988953	C₂	1	1	yes	maximal, characteristic
3	#14556650	—	2	2	no	—
4	#14556588	C₂²	1	1	yes	characteristic
5	#14556511	—	2	2	no	—
6	#14556502	C₄	1	1	yes	characteristic, complemented
7	#125×C₇₃	C₄	1	1	yes	characteristic, complemented
8	C₂²⋊#64408	—	4	2	no	—
9	C₂×D₂₉₂	—	4	1	no	—
10	C₂×D₂₉₂	D₄	1	2	yes	—
11	C₂×#10596831	—	2	1	no	—
12	C₄⋊C₄×C₇₃	—	2	1	no	—
13	C₄⋊C₄×C₇₃	—	4	1	no	—
14	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
15	C₂²×D₇₃	—	2	2	no	—
16	C₂×#64408	—	8	2	no	—
17	C₂×C₄×C₇₃	—	2	1	no	—
18	C₂×C₄×C₇₃	—	4	1	no	—
19	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
20	D₂₉₂	—	4	2	no	—
21	D₂₉₂	—	8	2	no	—
22	#10596831	—	4	1	no	—
23	C₂²×C₇₃	#99	1	1	yes	characteristic
24	C₂×D₇₃	—	4	2	no	—
25	C₂×D₇₃	—	8	2	no	—
26	#64408	—	16	2	no	—
27	C₄×C₇₃	—	2	1	no	—
28	C₄×C₇₃	—	4	1	no	—
29	C₄×C₇₃	—	8	1	no	—
30	C₂×C₇₃	—	2	1	no	—
31	C₂×C₇₃	#354	1	1	yes	characteristic
32	D₇₃	—	8	2	no	—
33	#1412	—	73	1	no	maximal, Sylow
34	C₇₃	#1412	1	1	yes	characteristic, complemented, Sylow
35	#490	—	73	1	no	—
36	#353	—	73	2	no	—
37	#127	—	73	1	no	—
38	#125	#64408	1	1	yes	characteristic, complemented
39	#102	—	146	2	no	—
40	#99	—	146	2	no	—
41	#97	—	73	1	no	—
42	C₂×D₄	—	292	1	no	—
43	C₂×D₄	—	73	2	no	—
44	C₂×C₈	—	146	1	no	—
45	C₄⋊C₄	—	2	1	no	—
46	C₄⋊C₄	—	4	1	no	—
47	C₂²⋊C₄	—	292	2	no	—
48	C₄²	C₂×#64408	1	1	yes	characteristic
49	C₂³	—	146	2	no	—
50	D₄	—	292	2	no	—
51	D₄	—	584	2	no	—
52	C₂×C₄	—	2	1	no	—
53	C₂×C₄	—	4	1	no	—
54	C₂×C₄	—	584	2	no	—
55	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
56	C₈	—	292	1	no	—
57	C₂²	—	292	2	no	—
58	C₂²	—	584	2	no	—
59	C₂²	#14556649	1	1	yes	characteristic
60	C₄	—	2	1	no	—
61	C₄	—	4	1	no	—
62	C₄	—	8	1	no	—
63	C₄	—	1168	2	no	—
64	C₂	—	2	1	no	—
65	C₂	—	584	2	no	—
66	C₂	#17989493	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17989493
commutator	C₄²×C₇₃	C₂×C₄
Frattini	C₄²	C₂×#64408
Fitting	#125×C₇₃	C₄
socle	C₂×C₇₃	#354
hypercenter	#125	#64408
hypocenter	C₇₃	#1412
LCS	G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
6. #14556502	C₄	semidirect
7. #125×C₇₃	C₄	semidirect
34. C₇₃	#1412	semidirect
38. #125	#64408	semidirect