Subgroups — #22625060

Order 9344.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989496	C₂	1	1	yes	maximal, characteristic
2	#17989494	C₂	1	1	yes	maximal, characteristic
3	#17988979	C₂	1	1	yes	maximal, characteristic
4	#14556652	—	2	1	no	—
5	#14556650	—	2	1	no	—
6	C₂×#11924018	—	2	1	no	—
7	C₂×#11924015	—	2	1	no	—
8	#14556579	C₂²	1	1	yes	characteristic
9	#14556502	C₄	1	1	yes	characteristic, complemented
10	C₄⋊Q₈×C₇₃	C₄	1	1	yes	characteristic, complemented
11	#11924037	—	4	1	no	—
12	C₂²⋊#64408	—	4	1	no	—
13	C₂×Dic₁₄₆	D₄	1	1	yes	characteristic
14	C₂×D₂₉₂	D₄	1	1	yes	characteristic
15	#11924018	—	4	2	no	—
16	#11924015	—	4	2	no	—
17	C₂×#10596831	—	2	1	no	—
18	#11924005	—	4	1	no	—
19	C₂×Q₈×C₇₃	—	2	1	no	—
20	C₄⋊C₄×C₇₃	—	4	1	no	—
21	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂²×D₇₃	—	2	1	no	—
23	C₂×#64408	—	8	1	no	—
24	Q₈×C₇₃	—	4	1	no	—
25	Q₈×C₇₃	—	4	1	no	—
26	C₂×C₄×C₇₃	—	2	1	no	—
27	C₂×C₄×C₇₃	—	4	1	no	—
28	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
29	C₂×Dic₇₃	—	2	1	no	—
30	D₂₉₂	—	4	1	no	—
31	Dic₁₄₆	—	4	1	no	—
32	#10596833	—	8	1	no	—
33	#10596831	—	2	2	no	—
34	C₂²×C₇₃	#99	1	1	yes	characteristic
35	C₂×D₇₃	—	4	1	no	—
36	C₂×D₇₃	—	8	1	no	—
37	#64408	—	16	1	no	—
38	C₄×C₇₃	—	2	1	no	—
39	C₄×C₇₃	—	4	1	no	—
40	C₄×C₇₃	—	8	1	no	—
41	Dic₇₃	—	4	1	no	—
42	C₂×C₇₃	—	2	1	no	—
43	C₂×C₇₃	#353	1	1	yes	characteristic
44	D₇₃	—	8	1	no	—
45	#1407	—	73	1	no	maximal, Sylow
46	C₇₃	#1407	1	1	yes	characteristic, complemented, Sylow
47	#497	—	73	1	no	—
48	#355	—	73	1	no	—
49	#354	—	73	1	no	—
50	C₂×Q₁₆	—	146	1	no	—
51	C₂×SD₁₆	—	146	1	no	—
52	C₄⋊Q₈	#64408	1	1	yes	characteristic, complemented
53	#124	—	73	1	no	—
54	#101	—	146	1	no	—
55	#99	—	146	1	no	—
56	#97	—	73	1	no	—
57	C₂×Q₈	—	2	1	no	—
58	C₂×Q₈	—	73	1	no	—
59	C₂×D₄	—	73	1	no	—
60	Q₁₆	—	292	2	no	—
61	SD₁₆	—	292	2	no	—
62	M₁₆	—	292	1	no	—
63	C₂×C₈	—	146	1	no	—
64	C₄⋊C₄	—	4	1	no	—
65	C₂²⋊C₄	—	292	1	no	—
66	C₂²⋊C₄	—	292	1	no	—
67	C₄²	C₂×#64408	1	1	yes	characteristic
68	C₂³	—	146	1	no	—
69	Q₈	—	4	1	no	—
70	Q₈	—	4	1	no	—
71	Q₈	—	292	1	no	—
72	D₄	—	292	1	no	—
73	C₂×C₄	—	2	1	no	—
74	C₂×C₄	—	4	1	no	—
75	C₂×C₄	—	584	1	no	—
76	C₂×C₄	—	146	1	no	—
77	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
78	C₈	—	584	1	no	—
79	C₈	—	146	2	no	—
80	C₂²	—	292	1	no	—
81	C₂²	—	584	1	no	—
82	C₂²	#14556649	1	1	yes	characteristic
83	C₄	—	2	1	no	—
84	C₄	—	4	1	no	—
85	C₄	—	8	1	no	—
86	C₄	—	292	1	no	—
87	C₄	—	1168	1	no	—
88	C₂	—	2	1	no	—
89	C₂	—	584	1	no	—
90	C₂	#17989491	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17989491
commutator	C₄²×C₇₃	C₂×C₄
Frattini	C₄²	C₂×#64408
Fitting	C₄⋊Q₈×C₇₃	C₄
socle	C₂×C₇₃	#353
hypercenter	C₄⋊Q₈	#64408
hypocenter	C₇₃	#1407
LCS	G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
9. #14556502	C₄	semidirect
10. C₄⋊Q₈×C₇₃	C₄	semidirect
46. C₇₃	#1407	semidirect
52. C₄⋊Q₈	#64408	semidirect