Finite Group Databasebeta

Subgroups — #22627099

Order 9344.

260 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14556688	C₂	1	2	yes	maximal, complemented
2	#17989684	C₂	1	2	yes	maximal, complemented
3	C₂²⋊#11924040	C₂	1	2	yes	maximal, complemented
4	C₂²×#11924036	C₂	1	1	yes	maximal, characteristic
5	#14556688	—	2	4	no	—
6	C₂×#11924040	C₂²	1	4	yes	complemented
7	C₂×#11924036	—	2	4	no	—
8	C₂×#11924036	C₄	1	1	yes	characteristic
9	C₂×#11924036	C₄	1	1	yes	characteristic
10	C₂×#11924036	C₂²	1	1	yes	characteristic
11	C₂×#11924036	C₂²	1	1	yes	characteristic
12	C₂²×#10596833	C₄	1	1	yes	characteristic
13	C₂²×#10596833	C₂²	1	1	yes	characteristic
14	C₂²×C₄×D₇₃	C₄	1	1	yes	characteristic
15	#11924040	—	2	4	no	—
16	#11924036	—	2	2	no	—
17	#11924036	—	2	2	no	—
18	#11924036	—	2	2	no	—
19	#11924036	D₄	1	4	yes	—
20	C₂×#10596833	—	2	2	no	—
21	C₂×#10596833	—	2	2	no	—
22	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
23	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
24	C₂×#10596833	C₂×C₄	1	1	yes	characteristic
25	C₂×#10596833	C₂³	1	1	yes	characteristic
26	C₂³×D₇₃	C₈	1	1	yes	characteristic
27	C₂²×Dic₇₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₄×D₇₃	—	2	2	no	—
29	C₂×C₄×D₇₃	—	2	2	no	—
30	C₂×C₄×D₇₃	C₈	1	1	yes	characteristic
31	C₂×C₄×D₇₃	C₈	1	1	yes	characteristic
32	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×C₇₃	C₈	1	1	yes	characteristic
35	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
36	C₂²×D₇₃	—	2	2	no	—
37	C₂²×D₇₃	—	2	2	no	—
38	C₂²×D₇₃	—	2	2	no	—
39	C₂²×D₇₃	C₂×C₈	1	1	yes	characteristic
40	C₂²×D₇₃	C₂×C₈	1	1	yes	characteristic
41	C₂×C₄×C₇₃	—	2	2	no	—
42	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
43	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
44	C₂×Dic₇₃	—	2	1	no	—
45	C₂×Dic₇₃	—	2	1	no	—
46	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
47	C₂×Dic₇₃	C₂²×C₄	1	1	yes	characteristic
48	C₄×D₇₃	—	2	2	no	—
49	C₄×D₇₃	—	2	2	no	—
50	C₄×D₇₃	—	2	1	no	—
51	C₄×D₇₃	—	2	1	no	—
52	C₄×D₇₃	C₂²⋊C₄	1	2	yes	—
53	C₄×D₇₃	M₁₆	1	2	yes	—
54	#10596833	—	2	1	no	—
55	#10596833	—	2	1	no	—
56	#10596833	C₂²⋊C₄	1	2	yes	—
57	#10596833	C₂×D₄	1	2	yes	—
58	C₂²×C₇₃	—	2	1	no	—
59	C₂²×C₇₃	—	2	1	no	—
60	C₂²×C₇₃	M₃₂	1	2	yes	complemented
61	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
62	C₂×D₇₃	—	2	8	no	—
63	C₂×D₇₃	—	2	1	no	—
64	C₂×D₇₃	—	2	1	no	—
65	C₂×D₇₃	—	2	1	no	—
66	C₂×D₇₃	—	2	1	no	—
67	C₂×D₇₃	C₂²⋊C₈	1	2	yes	—
68	C₂×D₇₃	M₃₂	1	2	yes	complemented
69	C₄×C₇₃	—	2	1	no	—
70	C₄×C₇₃	C₂²⋊C₈	1	2	yes	—
71	Dic₇₃	—	2	1	no	—
72	Dic₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
73	Dic₇₃	C₂×M₁₆	1	1	yes	characteristic
74	C₂×C₇₃	—	2	2	no	—
75	C₂×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
76	C₂×C₇₃	C₂×M₃₂	1	1	yes	characteristic
77	C₂×C₇₃	C₂×M₃₂	1	1	yes	characteristic
78	D₇₃	—	2	2	no	—
79	D₇₃	—	2	2	no	—
80	#2112	—	73	1	no	maximal, Sylow
81	C₇₃	#2112	1	1	yes	characteristic, complemented, Sylow
82	C₂³×C₈	—	73	1	no	—
83	C₂×M₃₂	—	73	2	no	—
84	C₂²⋊C₁₆	—	73	2	no	—
85	C₂²⋊C₁₆	—	73	2	no	—
86	C₂³×C₄	—	73	1	no	—
87	C₂²×C₈	—	73	1	no	—
88	C₂²×C₈	—	73	1	no	—
89	C₂²×C₈	—	73	1	no	—
90	C₂²×C₈	—	73	1	no	—
91	C₂²×C₈	—	73	1	no	—
92	C₂²×C₈	—	73	1	no	—
93	C₂²×C₈	—	146	4	no	—
94	M₃₂	—	146	4	no	—
95	C₂×C₁₆	—	73	4	no	—
96	C₂⁴	—	73	1	no	—
97	C₂²×C₄	—	73	1	no	—
98	C₂²×C₄	—	73	1	no	—
99	C₂²×C₄	—	73	1	no	—
100	C₂²×C₄	—	73	1	no	—
101	C₂²×C₄	—	73	1	no	—
102	C₂²×C₄	—	146	2	no	—
103	C₂²×C₄	—	146	2	no	—
104	C₂²×C₄	#10596842	1	1	yes	characteristic
105	C₂×C₈	—	73	1	no	—
106	C₂×C₈	—	73	1	no	—
107	C₂×C₈	—	73	4	no	—
108	C₂×C₈	—	73	1	no	—
109	C₂×C₈	—	73	1	no	—
110	C₂×C₈	—	146	2	no	—
111	C₂×C₈	—	146	2	no	—
112	C₂×C₈	—	146	2	no	—
113	C₂×C₈	—	146	2	no	—
114	C₂×C₈	—	146	2	no	—
115	C₁₆	—	146	4	no	—
116	C₂³	—	73	1	no	—
117	C₂³	—	73	1	no	—
118	C₂³	—	146	2	no	—
119	C₂³	—	146	2	no	—
120	C₂³	—	146	2	no	—
121	C₂³	C₂×#10596842	1	1	yes	characteristic
122	C₂×C₄	—	2	2	no	—
123	C₂×C₄	—	73	1	no	—
124	C₂×C₄	—	73	2	no	—
125	C₂×C₄	—	73	2	no	—
126	C₂×C₄	—	73	1	no	—
127	C₂×C₄	—	146	1	no	—
128	C₂×C₄	—	146	1	no	—
129	C₂×C₄	—	146	2	no	—
130	C₂×C₄	—	146	1	no	—
131	C₂×C₄	—	146	1	no	—
132	C₂×C₄	—	146	2	no	—
133	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
134	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
135	C₈	—	73	2	no	—
136	C₈	—	73	2	no	—
137	C₈	—	146	1	no	—
138	C₈	—	146	1	no	—
139	C₂²	—	2	1	no	—
140	C₂²	—	2	1	no	—
141	C₂²	—	73	2	no	—
142	C₂²	—	73	2	no	—
143	C₂²	—	146	8	no	—
144	C₂²	—	146	1	no	—
145	C₂²	—	146	1	no	—
146	C₂²	—	146	1	no	—
147	C₂²	—	146	1	no	—
148	C₂²	#14556688	1	2	yes	complemented
149	C₂²	C₂²×#10596842	1	1	yes	characteristic
150	C₄	—	2	1	no	—
151	C₄	—	73	1	no	—
152	C₄	—	73	1	no	—
153	C₄	—	146	1	no	—
154	C₄	C₂²⋊#10596842	1	2	yes	—
155	C₂	—	2	2	no	—
156	C₂	—	146	2	no	—
157	C₂	—	146	2	no	—
158	C₂	C₂×C₂²⋊#10596842	1	1	yes	characteristic
159	C₂	#17989706	1	1	yes	characteristic
160	C₂	C₂×#14556688	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#10596842
commutator, socle	C₂²×C₇₃	C₂²×C₈
Fitting	C₂²×C₄×C₇₃	C₈
hypercenter	C₂²×C₄	#10596842
hypocenter	C₇₃	#2112
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄

Complements

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

N	H ≅ G/N	type
1. C₂×#14556688	C₂	semidirect
2. #17989684	C₂	semidirect
3. C₂²⋊#11924040	C₂	semidirect
6. C₂×#11924040	C₂²	semidirect
60. C₂²×C₇₃	M₃₂	semidirect
68. C₂×D₇₃	M₃₂	semidirect
81. C₇₃	#2112	semidirect
148. C₂²	#14556688	semidirect