Subgroups — #22624938

Order 9344.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989479	C₂	1	2	yes	maximal
2	#17988957	C₂	1	1	yes	maximal, characteristic
3	#14556665	—	2	2	no	—
4	#14556591	C₄	1	1	yes	characteristic
5	#14556514	—	2	2	no	—
6	#14556502	C₂²	1	1	yes	characteristic
7	#125×C₇₃	C₄	1	1	yes	characteristic
8	#11924031	—	2	4	no	—
9	C₂×Dic₁₄₆	—	2	1	no	—
10	C₂×#10596831	D₄	1	2	yes	—
11	C₄⋊Dic₇₃	—	4	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	C₂×C₄×C₇₃	—	2	1	no	—
16	C₂×C₄×C₇₃	—	4	1	no	—
17	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
18	C₂×Dic₇₃	—	4	1	no	—
19	Dic₁₄₆	—	4	2	no	—
20	#10596831	—	2	2	no	—
21	C₂²×C₇₃	#100	1	1	yes	characteristic
22	C₄×C₇₃	—	4	1	no	—
23	C₄×C₇₃	—	8	1	no	—
24	C₄×C₇₃	#104	1	2	yes	—
25	Dic₇₃	—	8	1	no	—
26	C₂×C₇₃	—	2	1	no	—
27	C₂×C₇₃	#329	1	1	yes	characteristic
28	#1356	—	73	1	no	maximal, Sylow
29	C₇₃	#1356	1	1	yes	characteristic, complemented, Sylow
30	#491	—	73	1	no	—
31	#347	—	73	2	no	—
32	C₄⋊Q₈	—	73	1	no	—
33	#125	#64408	1	1	yes	characteristic
34	M₃₂	—	146	2	no	—
35	#103	—	146	2	no	—
36	#97	—	73	1	no	—
37	C₂×Q₈	—	146	1	no	—
38	C₂×C₈	—	73	2	no	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	4	1	no	—
41	C₄⋊C₄	—	292	1	no	—
42	C₄²	C₂×#64408	1	1	yes	characteristic
43	C₁₆	—	146	4	no	—
44	Q₈	—	292	2	no	—
45	C₂×C₄	—	2	1	no	—
46	C₂×C₄	—	4	1	no	—
47	C₂×C₄	—	292	1	no	—
48	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
49	C₈	—	146	2	no	—
50	C₂²	#14556651	1	1	yes	characteristic
51	C₄	—	4	1	no	—
52	C₄	—	8	1	no	—
53	C₄	—	584	1	no	—
54	C₄	#14556656	1	2	yes	—
55	C₂	—	2	1	no	—
56	C₂	#17989443	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17989443
commutator	C₄²×C₇₃	C₂×C₄
Frattini	C₄²	C₂×#64408
Fitting	#125×C₇₃	C₄
socle	C₂×C₇₃	#329
hypercenter	#125	#64408
hypocenter	C₇₃	#1356
LCS	G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ C₄² ◁ #125

Complements

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

N	H ≅ G/N	type
29. C₇₃	#1356	semidirect