Subgroups — #22624880

Order 9344.

90 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989483	C₂	1	2	yes	maximal
2	#17988613	C₂	1	1	yes	maximal, characteristic
3	#14556665	—	2	2	no	—
4	C₂×#11924012	C₂²	1	1	yes	characteristic
5	#14556550	C₄	1	1	yes	characteristic
6	#14556520	—	2	2	no	—
7	C₂²×C₈×C₇₃	C₄	1	1	yes	characteristic
8	#11924031	—	4	2	no	—
9	#11924012	—	4	1	no	—
10	C₂×#10596831	D₄	1	2	yes	—
11	C₄⋊Dic₇₃	—	2	1	no	—
12	C₂²⋊Dic₇₃	C₈	1	2	yes	—
13	C₄×Dic₇₃	—	2	1	no	—
14	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
15	C₂×C₈×C₇₃	—	2	1	no	—
16	C₂×C₈×C₇₃	—	4	1	no	—
17	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
18	C₂×C₄×C₇₃	—	2	1	no	—
19	C₂×C₄×C₇₃	—	2	1	no	—
20	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
21	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
22	C₂×Dic₇₃	—	2	2	no	—
23	C₈×C₇₃	—	4	1	no	—
24	#10596831	—	2	2	no	—
25	C₂²×C₇₃	—	2	1	no	—
26	C₂²×C₇₃	—	4	1	no	—
27	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
28	C₄×C₇₃	—	2	1	no	—
29	C₄×C₇₃	#99	1	1	yes	characteristic
30	C₄×C₇₃	#101	1	1	yes	characteristic
31	Dic₇₃	—	4	2	no	—
32	C₂×C₇₃	—	2	1	no	—
33	C₂×C₇₃	—	4	1	no	—
34	C₂×C₇₃	#324	1	1	yes	characteristic
35	#1328	—	73	1	no	maximal, Sylow
36	C₇₃	#1328	1	1	yes	characteristic, complemented, Sylow
37	#424	—	73	1	no	—
38	#349	—	73	2	no	—
39	C₂×M₁₆	—	73	1	no	—
40	C₂²×C₈	#64408	1	1	yes	characteristic
41	#117	—	73	1	no	—
42	M₃₂	—	146	2	no	—
43	C₄⋊C₈	—	146	2	no	—
44	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
45	M₁₆	—	292	1	no	—
46	C₂×C₈	—	2	1	no	—
47	C₂×C₈	—	4	1	no	—
48	C₂×C₈	—	73	2	no	—
49	C₄⋊C₄	—	146	1	no	—
50	C₂²⋊C₄	—	73	2	no	—
51	C₄²	—	146	1	no	—
52	C₁₆	—	292	2	no	—
53	C₂³	#11924036	1	1	yes	characteristic
54	C₂×C₄	—	2	1	no	—
55	C₂×C₄	—	2	1	no	—
56	C₂×C₄	—	146	2	no	—
57	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
58	C₂×C₄	#11924038	1	1	yes	characteristic
59	C₈	—	4	1	no	—
60	C₈	—	146	2	no	—
61	C₂²	—	2	1	no	—
62	C₂²	—	4	1	no	—
63	C₂²	#14556648	1	1	yes	characteristic
64	C₄	—	2	1	no	—
65	C₄	—	292	2	no	—
66	C₄	#14556649	1	1	yes	characteristic
67	C₄	#14556652	1	1	yes	characteristic
68	C₂	—	2	1	no	—
69	C₂	—	4	1	no	—
70	C₂	#17989433	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556649
commutator	C₂³×C₇₃	C₂×C₈
Frattini	C₂²×C₄	C₂×#64408
Fitting	C₂²×C₈×C₇₃	C₄
socle	C₂×C₇₃	#324
hypercenter	C₂²×C₈	#64408
hypocenter	C₇₃	#1328
LCS	G ▷ C₂³×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
36. C₇₃	#1328	semidirect