Subgroups — #22626345

Order 9344.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989508	C₂	1	2	yes	maximal
2	C₄⋊#11924031	C₂	1	1	yes	maximal, characteristic
3	#17989473	C₂	1	2	yes	maximal
4	C₄×#11924031	C₂	1	1	yes	maximal, characteristic
5	#17988711	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924031	C₂²	1	1	yes	characteristic
7	C₂×#11924031	C₂²	1	2	yes	—
8	C₂×#11924031	C₂²	1	1	yes	characteristic
9	C₄×Dic₁₄₆	C₄	1	1	yes	characteristic
10	#14556520	C₄	1	2	yes	—
11	C₄×#10596831	C₂²	1	1	yes	characteristic
12	C₈×Dic₇₃	C₂²	1	2	yes	—
13	C₄⋊C₈×C₇₃	C₄	1	1	yes	characteristic
14	#11924031	—	2	1	no	—
15	#11924031	—	2	2	no	—
16	#11924031	Q₈	1	2	yes	complemented
17	C₂×Dic₁₄₆	C₈	1	1	yes	characteristic
18	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
19	C₂×#10596831	C₂³	1	1	yes	characteristic
20	C₄⋊Dic₇₃	C₈	1	1	yes	characteristic
21	#11924007	C₈	1	2	yes	—
22	C₄×Dic₇₃	C₂×C₄	1	2	yes	—
23	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
24	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
28	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
29	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
30	Dic₁₄₆	C₁₆	1	4	yes	complemented
31	C₈×C₇₃	—	2	2	no	—
32	#10596831	—	2	1	no	—
33	#10596831	C₂×Q₈	1	1	yes	characteristic
34	#10596831	#41	1	1	yes	characteristic
35	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
36	C₄×C₇₃	—	2	1	no	—
37	C₄×C₇₃	C₂×C₁₆	1	2	yes	—
38	C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
39	C₄×C₇₃	#131	1	1	yes	characteristic
40	Dic₇₃	—	2	2	no	—
41	Dic₇₃	C₂×C₁₆	1	4	yes	—
42	C₂×C₇₃	C₈×Q₈	1	1	yes	characteristic
43	C₂×C₇₃	C₂²×C₁₆	1	1	yes	characteristic
44	C₂×C₇₃	#504	1	1	yes	characteristic
45	Q₈×C₁₆	—	73	1	no	maximal, Sylow
46	C₇₃	Q₈×C₁₆	1	1	yes	characteristic, complemented, Sylow
47	C₈×Q₈	—	73	1	no	—
48	C₄⋊C₁₆	—	73	1	no	—
49	C₄⋊C₁₆	—	73	2	no	—
50	C₄×C₁₆	—	73	1	no	—
51	C₄×C₁₆	—	73	2	no	—
52	C₄×Q₈	—	73	1	no	—
53	C₂×C₁₆	—	73	1	no	—
54	C₂×C₁₆	—	73	1	no	—
55	C₂×C₁₆	—	73	2	no	—
56	C₄⋊C₈	—	73	2	no	—
57	C₄⋊C₈	#64408	1	1	yes	characteristic
58	C₄×C₈	—	73	2	no	—
59	C₄×C₈	—	73	1	no	—
60	C₂×Q₈	—	73	1	no	—
61	C₂×C₈	—	73	1	no	—
62	C₂×C₈	—	73	1	no	—
63	C₂×C₈	C₂×#64408	1	2	yes	—
64	C₄⋊C₄	—	73	2	no	—
65	C₄⋊C₄	—	73	1	no	—
66	C₄²	—	73	2	no	—
67	C₄²	C₂×#64408	1	1	yes	characteristic
68	C₁₆	—	73	2	no	—
69	C₁₆	—	146	1	no	—
70	C₁₆	—	146	2	no	—
71	Q₈	—	73	4	no	—
72	C₂×C₄	—	73	2	no	—
73	C₂×C₄	—	73	2	no	—
74	C₂×C₄	#11924036	1	1	yes	characteristic
75	C₂×C₄	#11924036	1	1	yes	characteristic
76	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
77	C₈	—	2	2	no	—
78	C₈	—	73	1	no	—
79	C₈	—	73	1	no	—
80	C₈	—	146	1	no	—
81	C₂²	C₂×#11924036	1	1	yes	characteristic
82	C₄	—	2	1	no	—
83	C₄	—	73	4	no	—
84	C₄	—	146	2	no	—
85	C₄	#14556664	1	2	yes	—
86	C₄	Q₈×#64408	1	1	yes	characteristic
87	C₄	#14556678	1	1	yes	characteristic
88	C₂	#17989636	1	1	yes	characteristic
89	C₂	C₂×#14556664	1	1	yes	characteristic
90	C₂	#17989646	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#64408
commutator	C₂×C₇₃	C₂²×C₁₆
Fitting	C₄⋊C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂²×C₈
hypercenter	C₄⋊C₈	#64408
hypocenter	C₇₃	Q₈×C₁₆
LCS	G ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
16. #11924031	Q₈	semidirect
30. Dic₁₄₆	C₁₆	semidirect
46. C₇₃	Q₈×C₁₆	semidirect