Subgroups — #22624884

Order 9344.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊#11924031	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989475	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988664	C₂	1	1	yes	maximal, characteristic
4	C₂×#11924031	—	2	1	no	—
5	C₂×#11924031	—	2	1	no	—
6	C₂×#11924011	—	2	1	no	—
7	C₄×D₂₉₂	C₄	1	1	yes	characteristic
8	#14556503	—	2	1	no	—
9	C₄×#10596831	C₂²	1	1	yes	characteristic
10	C₄⋊C₈×C₇₃	C₄	1	1	yes	characteristic
11	#11924031	—	2	2	no	—
12	#11924031	—	4	1	no	—
13	C₂×D₂₉₂	C₈	1	1	yes	characteristic
14	C₂×C₄×D₇₃	—	2	1	no	—
15	#11924011	—	4	1	no	—
16	#11924011	—	4	1	no	—
17	C₂×#10596831	D₄	1	1	yes	characteristic
18	C₂×#10596831	D₄	1	1	yes	characteristic
19	C₄⋊Dic₇₃	C₈	1	1	yes	characteristic
20	#11924005	—	2	1	no	—
21	C₂×C₈×C₇₃	—	2	1	no	—
22	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂²×D₇₃	—	2	1	no	—
24	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
25	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₇₃	M₁₆	1	1	yes	characteristic
27	C₂×Dic₇₃	—	2	1	no	—
28	D₂₉₂	—	4	1	no	—
29	C₄×D₇₃	—	4	1	no	—
30	C₄×D₇₃	—	4	1	no	—
31	C₈×C₇₃	—	4	1	no	—
32	#10596831	—	2	1	no	—
33	#10596831	D₈	1	1	yes	characteristic
34	#10596831	SD₁₆	1	1	yes	characteristic
35	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
36	C₂×D₇₃	—	4	1	no	—
37	C₂×D₇₃	—	4	1	no	—
38	C₂×D₇₃	—	4	1	no	—
39	C₄×C₇₃	—	2	1	no	—
40	C₄×C₇₃	—	2	1	no	—
41	C₄×C₇₃	#102	1	1	yes	characteristic
42	C₄×C₇₃	#104	1	1	yes	characteristic
43	Dic₇₃	—	4	1	no	—
44	C₂×C₇₃	D₄⋊C₈	1	1	yes	characteristic
45	C₂×C₇₃	#349	1	1	yes	characteristic
46	C₂×C₇₃	#350	1	1	yes	characteristic
47	D₇₃	—	8	1	no	—
48	#1330	—	73	1	no	maximal, Sylow
49	C₇₃	#1330	1	1	yes	characteristic, complemented, Sylow
50	#436	—	73	1	no	—
51	C₄⋊C₁₆	—	73	1	no	—
52	#346	—	73	1	no	—
53	C₂×M₁₆	—	146	1	no	—
54	C₄×D₄	—	73	1	no	—
55	C₂×C₁₆	—	146	1	no	—
56	C₂×C₁₆	—	146	1	no	—
57	C₄⋊C₈	#64408	1	1	yes	characteristic
58	C₂²⋊C₈	—	146	1	no	—
59	C₄×C₈	—	73	1	no	—
60	C₂×D₄	—	73	1	no	—
61	C₂²×C₄	—	146	1	no	—
62	M₁₆	—	292	1	no	—
63	M₁₆	—	292	1	no	—
64	C₂×C₈	—	2	1	no	—
65	C₂×C₈	—	73	1	no	—
66	C₂×C₈	—	73	1	no	—
67	C₄⋊C₄	—	73	1	no	—
68	C₂²⋊C₄	—	146	1	no	—
69	C₄²	C₂×#64408	1	1	yes	characteristic
70	C₁₆	—	292	1	no	—
71	C₁₆	—	146	2	no	—
72	C₂³	—	146	1	no	—
73	D₄	—	292	1	no	—
74	C₂×C₄	—	292	1	no	—
75	C₂×C₄	—	292	1	no	—
76	C₂×C₄	—	146	1	no	—
77	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
78	C₂×C₄	#11924036	1	1	yes	characteristic
79	C₂×C₄	#11924038	1	1	yes	characteristic
80	C₈	—	4	1	no	—
81	C₈	—	73	1	no	—
82	C₈	—	73	1	no	—
83	C₈	—	146	1	no	—
84	C₂²	—	292	1	no	—
85	C₂²	—	292	1	no	—
86	C₂²	—	292	1	no	—
87	C₂²	#14556648	1	1	yes	characteristic
88	C₄	—	2	1	no	—
89	C₄	—	2	1	no	—
90	C₄	—	292	1	no	—
91	C₄	#14556653	1	1	yes	characteristic
92	C₄	#14556656	1	1	yes	characteristic
93	C₂	—	584	1	no	—
94	C₂	#17989435	1	1	yes	characteristic
95	C₂	#17989484	1	1	yes	characteristic
96	C₂	#17989486	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊#64408
commutator	C₂×C₄×C₇₃	C₂×C₈
Frattini	C₄²	C₂×#64408
Fitting	C₄⋊C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂²⋊C₈
hypercenter	C₄⋊C₈	#64408
hypocenter	C₇₃	#1330
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₄⋊#11924031	C₂	semidirect
2. #17989475	C₂	semidirect
49. C₇₃	#1330	semidirect