Subgroups — #22625058

Order 9344.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17989496	C₂	1	1	yes	maximal, characteristic, complemented
2	#17989494	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988974	C₂	1	1	yes	maximal, characteristic
4	#14556652	—	2	1	no	—
5	#14556650	—	2	1	no	—
6	C₂×#11924016	—	2	1	no	—
7	C₂×#11924013	—	2	1	no	—
8	#14556579	C₂²	1	1	yes	characteristic
9	#14556502	C₄	1	1	yes	characteristic, complemented
10	#127×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	#11924016	—	4	2	no	—
16	#11924013	—	4	2	no	—
17	C₂×#10596831	—	2	1	no	—
18	#11924005	—	4	1	no	—
19	C₂×D₄×C₇₃	—	2	1	no	—
20	C₂×D₄×C₇₃	—	4	1	no	—
21	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
22	C₂³×C₇₃	—	4	1	no	—
23	C₂²×D₇₃	—	2	1	no	—
24	C₂×#64408	—	8	1	no	—
25	D₄×C₇₃	—	4	1	no	—
26	D₄×C₇₃	—	4	1	no	—
27	D₄×C₇₃	—	8	2	no	—
28	C₂×C₄×C₇₃	—	2	1	no	—
29	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×Dic₇₃	—	2	1	no	—
31	D₂₉₂	—	4	1	no	—
32	Dic₁₄₆	—	4	1	no	—
33	#10596833	—	8	1	no	—
34	#10596831	—	2	2	no	—
35	C₂²×C₇₃	—	8	2	no	—
36	C₂²×C₇₃	—	8	1	no	—
37	C₂²×C₇₃	#99	1	1	yes	characteristic
38	C₂×D₇₃	—	4	1	no	—
39	C₂×D₇₃	—	8	1	no	—
40	#64408	—	16	1	no	—
41	C₄×C₇₃	—	2	1	no	—
42	C₄×C₇₃	—	4	1	no	—
43	Dic₇₃	—	4	1	no	—
44	C₂×C₇₃	—	2	1	no	—
45	C₂×C₇₃	—	16	1	no	—
46	C₂×C₇₃	#353	1	1	yes	characteristic
47	D₇₃	—	8	1	no	—
48	#1406	—	73	1	no	maximal, Sylow
49	C₇₃	#1406	1	1	yes	characteristic, complemented, Sylow
50	#496	—	73	1	no	—
51	#355	—	73	1	no	—
52	#354	—	73	1	no	—
53	C₂×SD₁₆	—	146	1	no	—
54	C₂×D₈	—	146	1	no	—
55	#127	#64408	1	1	yes	characteristic, complemented
56	#124	—	73	1	no	—
57	#101	—	146	1	no	—
58	#99	—	146	1	no	—
59	#97	—	73	1	no	—
60	C₂×Q₈	—	73	1	no	—
61	C₂×D₄	—	2	1	no	—
62	C₂×D₄	—	4	1	no	—
63	C₂×D₄	—	73	1	no	—
64	SD₁₆	—	292	2	no	—
65	D₈	—	292	2	no	—
66	M₁₆	—	292	1	no	—
67	C₂×C₈	—	146	1	no	—
68	C₂²⋊C₄	—	292	1	no	—
69	C₂²⋊C₄	—	292	1	no	—
70	C₄²	C₂×#64408	1	1	yes	characteristic
71	C₂³	—	4	1	no	—
72	C₂³	—	146	1	no	—
73	Q₈	—	292	1	no	—
74	D₄	—	4	1	no	—
75	D₄	—	4	1	no	—
76	D₄	—	8	2	no	—
77	D₄	—	292	1	no	—
78	C₂×C₄	—	2	1	no	—
79	C₂×C₄	—	584	1	no	—
80	C₂×C₄	—	146	1	no	—
81	C₂×C₄	C₂²⋊#64408	1	1	yes	characteristic
82	C₈	—	584	1	no	—
83	C₈	—	146	2	no	—
84	C₂²	—	8	2	no	—
85	C₂²	—	8	1	no	—
86	C₂²	—	292	1	no	—
87	C₂²	—	584	1	no	—
88	C₂²	#14556649	1	1	yes	characteristic
89	C₄	—	2	1	no	—
90	C₄	—	4	1	no	—
91	C₄	—	292	1	no	—
92	C₄	—	1168	1	no	—
93	C₂	—	2	1	no	—
94	C₂	—	16	1	no	—
95	C₂	—	584	1	no	—
96	C₂	#17989491	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#17989491
commutator	C₄²×C₇₃	C₂×C₄
Frattini	C₄²	C₂×#64408
Fitting	#127×C₇₃	C₄
socle	C₂×C₇₃	#353
hypercenter	#127	#64408
hypocenter	C₇₃	#1406
LCS	G ▷ C₄²×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄² ◁ #127

Complements

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

N	H ≅ G/N	type
1. #17989496	C₂	semidirect
2. #17989494	C₂	semidirect
9. #14556502	C₄	semidirect
10. #127×C₇₃	C₄	semidirect
49. C₇₃	#1406	semidirect
55. #127	#64408	semidirect