Subgroups — #22624878

Order 9344.

96 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989483	C₂	1	2	yes	maximal
2	#17988610	C₂	1	1	yes	maximal, characteristic
3	#14556665	—	2	2	no	—
4	C₂×#11924012	C₂²	1	1	yes	characteristic
5	C₂×C₄×Dic₇₃	C₄	1	1	yes	characteristic
6	#14556520	—	2	2	no	—
7	C₂×M₁₆×C₇₃	C₄	1	1	yes	characteristic
8	#11924031	—	4	2	no	—
9	C₂²×Dic₇₃	—	2	1	no	—
10	#11924012	—	4	1	no	—
11	C₂×#10596831	D₄	1	2	yes	—
12	C₄×Dic₇₃	—	2	1	no	—
13	C₄×Dic₇₃	C₈	1	1	yes	characteristic
14	C₄×Dic₇₃	C₈	1	1	yes	characteristic
15	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
16	M₁₆×C₇₃	—	4	1	no	—
17	C₂×C₈×C₇₃	—	2	1	no	—
18	C₂³×C₇₃	M₁₆	1	1	yes	characteristic
19	C₂×C₄×C₇₃	—	2	1	no	—
20	C₂×C₄×C₇₃	—	2	1	no	—
21	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
22	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
23	C₂×Dic₇₃	—	2	1	no	—
24	C₂×Dic₇₃	—	2	1	no	—
25	C₂×Dic₇₃	—	4	2	no	—
26	C₈×C₇₃	—	4	1	no	—
27	#10596831	—	2	2	no	—
28	C₂²×C₇₃	—	2	1	no	—
29	C₂²×C₇₃	—	4	1	no	—
30	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
31	C₄×C₇₃	—	2	1	no	—
32	C₄×C₇₃	#99	1	1	yes	characteristic
33	C₄×C₇₃	#101	1	1	yes	characteristic
34	Dic₇₃	—	2	2	no	—
35	Dic₇₃	—	4	1	no	—
36	C₂×C₇₃	—	2	1	no	—
37	C₂×C₇₃	—	4	1	no	—
38	C₂×C₇₃	#324	1	1	yes	characteristic
39	#1327	—	73	1	no	maximal, Sylow
40	C₇₃	#1327	1	1	yes	characteristic, complemented, Sylow
41	#423	—	73	1	no	—
42	#349	—	73	2	no	—
43	C₂×M₁₆	—	73	1	no	—
44	C₂×M₁₆	#64408	1	1	yes	characteristic
45	C₂×C₄²	—	73	1	no	—
46	M₃₂	—	146	2	no	—
47	C₄⋊C₈	—	146	2	no	—
48	C₂²×C₄	—	146	1	no	—
49	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
50	M₁₆	—	4	1	no	—
51	M₁₆	—	292	1	no	—
52	C₂×C₈	—	2	1	no	—
53	C₂×C₈	—	73	2	no	—
54	C₄²	—	73	1	no	—
55	C₄²	—	73	1	no	—
56	C₄²	—	146	1	no	—
57	C₁₆	—	292	2	no	—
58	C₂³	#11924038	1	1	yes	characteristic
59	C₂×C₄	—	2	1	no	—
60	C₂×C₄	—	2	1	no	—
61	C₂×C₄	—	292	2	no	—
62	C₂×C₄	—	146	1	no	—
63	C₂×C₄	—	146	1	no	—
64	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
65	C₂×C₄	#11924036	1	1	yes	characteristic
66	C₈	—	4	1	no	—
67	C₈	—	146	2	no	—
68	C₂²	—	2	1	no	—
69	C₂²	—	4	1	no	—
70	C₂²	#14556648	1	1	yes	characteristic
71	C₄	—	2	1	no	—
72	C₄	—	292	1	no	—
73	C₄	—	146	2	no	—
74	C₄	#14556649	1	1	yes	characteristic
75	C₄	#14556652	1	1	yes	characteristic
76	C₂	—	2	1	no	—
77	C₂	—	4	1	no	—
78	C₂	#17989433	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#14556649
commutator	C₂×C₄×C₇₃	C₂×C₈
Frattini	C₂²×C₄	C₂×#64408
Fitting	C₂×M₁₆×C₇₃	C₄
socle	C₂×C₇₃	#324
hypercenter	C₂×M₁₆	#64408
hypocenter	C₇₃	#1327
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×M₁₆

Complements

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

N	H ≅ G/N	type
40. C₇₃	#1327	semidirect