Subgroups — #22625073

Order 9344.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989498	C₂	1	2	yes	maximal
2	#17988957	C₂	1	1	yes	maximal, characteristic
3	#14556652	—	2	2	no	—
4	#14556591	C₂²	1	1	yes	characteristic
5	#14556514	—	2	2	no	—
6	#14556502	C₄	1	1	yes	characteristic
7	#125×C₇₃	C₄	1	1	yes	characteristic
8	#11924037	—	4	2	no	—
9	C₂×Dic₁₄₆	D₄	1	2	yes	—
10	C₂×#10596831	—	2	1	no	—
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	—	2	2	no	—
19	Dic₁₄₆	—	4	2	no	—
20	#10596833	—	8	2	no	—
21	#10596831	—	4	1	no	—
22	C₂²×C₇₃	#99	1	1	yes	characteristic
23	C₄×C₇₃	—	2	1	no	—
24	C₄×C₇₃	—	4	1	no	—
25	C₄×C₇₃	—	8	1	no	—
26	Dic₇₃	—	4	2	no	—
27	C₂×C₇₃	—	2	1	no	—
28	C₂×C₇₃	#354	1	1	yes	characteristic
29	#1413	—	73	1	no	maximal, Sylow
30	C₇₃	#1413	1	1	yes	characteristic, complemented, Sylow
31	#491	—	73	1	no	—
32	#356	—	73	2	no	—
33	C₄⋊Q₈	—	73	1	no	—
34	#125	#64408	1	1	yes	characteristic
35	#103	—	146	2	no	—
36	#101	—	146	2	no	—
37	#97	—	73	1	no	—
38	C₂×Q₈	—	73	2	no	—
39	M₁₆	—	292	2	no	—
40	C₂×C₈	—	146	1	no	—
41	C₄⋊C₄	—	2	1	no	—
42	C₄⋊C₄	—	4	1	no	—
43	C₄⋊C₄	—	292	1	no	—
44	C₄²	C₂×#64408	1	1	yes	characteristic
45	Q₈	—	292	2	no	—
46	C₂×C₄	—	2	1	no	—
47	C₂×C₄	—	4	1	no	—
48	C₂×C₄	—	146	2	no	—
49	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
50	C₈	—	292	1	no	—
51	C₈	—	584	2	no	—
52	C₂²	#14556649	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	4	1	no	—
55	C₄	—	8	1	no	—
56	C₄	—	292	2	no	—
57	C₂	—	2	1	no	—
58	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	#1413
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
30. C₇₃	#1413	semidirect