Subgroups — #22626266

Order 9344.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556665	C₂	1	1	yes	maximal, characteristic
2	C₂²×#11924031	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#11924031	C₂	1	4	yes	maximal, complemented
4	#17988543	C₂	1	1	yes	maximal, characteristic
5	#14556665	—	2	2	no	—
6	C₂×#11924031	—	2	2	no	—
7	C₂×#11924031	C₂²	1	2	yes	—
8	C₂×#11924031	C₂²	1	2	yes	—
9	C₂×#11924012	C₄	1	1	yes	characteristic
10	C₂²×#10596831	C₂²	1	1	yes	characteristic
11	#14556502	C₄	1	2	yes	—
12	C₄×#10596831	C₂²	1	2	yes	—
13	#117×C₇₃	C₄	1	1	yes	characteristic
14	#11924031	—	2	2	no	—
15	#11924031	—	2	2	no	—
16	#11924012	—	2	2	no	—
17	C₂×#10596831	C₂×C₄	1	2	yes	—
18	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
19	C₂×#10596831	D₄	1	2	yes	—
20	C₂×#10596831	Q₈	1	2	yes	—
21	C₂×#10596831	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₄⋊C₄×C₇₃	C₈	1	2	yes	—
24	C₂²⋊C₄×C₇₃	C₈	1	2	yes	—
25	C₄²×C₇₃	C₂×C₄	1	2	yes	—
26	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₇₃	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₇₃	C₂×C₈	1	4	yes	—
29	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₇₃	M₁₆	1	2	yes	—
31	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
32	#10596831	—	2	2	no	—
33	#10596831	C₄⋊C₄	1	2	yes	—
34	#10596831	C₂×D₄	1	1	yes	characteristic
35	#10596831	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₇₃	—	2	2	no	—
37	C₂²×C₇₃	C₄⋊C₈	1	2	yes	—
38	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₇₃	—	2	4	no	—
40	C₄×C₇₃	C₄⋊C₈	1	2	yes	—
41	C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
42	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
43	C₂×C₇₃	—	2	2	no	—
44	C₂×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
45	C₂×C₇₃	#504	1	2	yes	—
46	#2151	—	73	1	no	maximal, Sylow
47	C₇₃	#2151	1	1	yes	characteristic, complemented, Sylow
48	C₂×M₃₂	—	73	1	no	—
49	C₂²×C₁₆	—	73	1	no	—
50	#405	—	73	1	no	—
51	C₄⋊C₁₆	—	73	4	no	—
52	C₂×M₁₆	—	73	1	no	—
53	C₂²×C₈	—	73	1	no	—
54	#117	#64408	1	1	yes	characteristic
55	M₃₂	—	146	2	no	—
56	C₂×C₁₆	—	73	2	no	—
57	C₂×C₁₆	—	73	2	no	—
58	C₂×C₁₆	—	146	2	no	—
59	#97	—	73	2	no	—
60	C₄×C₈	—	73	2	no	—
61	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
62	M₁₆	—	146	2	no	—
63	C₂×C₈	—	73	2	no	—
64	C₂×C₈	—	73	2	no	—
65	C₂×C₈	—	73	1	no	—
66	C₂×C₈	—	73	1	no	—
67	C₂×C₈	—	73	2	no	—
68	C₄⋊C₄	#10596833	1	2	yes	—
69	C₂²⋊C₄	#10596833	1	2	yes	—
70	C₄²	C₂×#64408	1	2	yes	—
71	C₁₆	—	146	2	no	—
72	C₁₆	—	146	2	no	—
73	C₂³	C₂×#10596833	1	1	yes	characteristic
74	C₂×C₄	C₄⋊#64408	1	2	yes	—
75	C₂×C₄	C₂×#10596833	1	4	yes	—
76	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
77	C₂×C₄	#11924038	1	2	yes	—
78	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
79	C₈	—	73	1	no	—
80	C₈	—	73	2	no	—
81	C₈	—	73	1	no	—
82	C₈	—	146	2	no	—
83	C₂²	—	2	2	no	—
84	C₂²	C₄⋊#10596833	1	2	yes	—
85	C₂²	C₂²×#10596833	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	C₄⋊#10596833	1	2	yes	—
88	C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
89	C₄	C₂×#11924038	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×C₄⋊#10596833	1	1	yes	characteristic
92	C₂	#17989645	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₈
Fitting	#117×C₇₃	C₄
hypercenter	#117	#64408
hypocenter	C₇₃	#2151
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. C₄⋊#11924031	C₂	semidirect
47. C₇₃	#2151	semidirect