Finite Group Databasebeta

Subgroups — #22625997

Order 9344.

186 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 60 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	#17989594	C₂	1	1	yes	maximal, characteristic
2	#17989552	C₂	1	1	yes	maximal, characteristic
3	#17989463	C₂	1	1	yes	maximal, characteristic
4	#17989457	C₂	1	1	yes	maximal, characteristic
5	#17989457	C₂	1	1	yes	maximal, characteristic
6	#17989452	C₂	1	1	yes	maximal, characteristic
7	#17988622	C₂	1	1	yes	maximal, characteristic
8	C₂×#11924038	C₂²	1	1	yes	characteristic
9	C₂×#11924038	C₂²	1	1	yes	characteristic
10	C₂×#11924036	C₂²	1	1	yes	characteristic
11	C₂×C₄×#64408	C₂²	1	1	yes	characteristic
12	#14556658	—	2	1	no	—
13	C₄⋊#10596833	—	2	1	no	—
14	#14556646	—	2	1	no	—
15	C₄×#10596833	—	2	1	no	—
16	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
17	#14556549	C₂²	1	1	yes	characteristic
18	#14556549	C₂²	1	1	yes	characteristic
19	#14556524	C₄	1	1	yes	characteristic, complemented
20	#14556524	C₄	1	1	yes	characteristic, complemented
21	#14556523	C₄	1	1	yes	characteristic, complemented
22	#106×C₇₃	C₄	1	1	yes	characteristic, complemented
23	C₂²×#64408	—	2	1	no	—
24	#11924038	—	2	1	no	—
25	#11924038	—	2	1	no	—
26	#11924038	—	2	1	no	—
27	#11924038	Q₈	1	2	yes	—
28	#11924036	—	2	1	no	—
29	#11924036	—	2	1	no	—
30	C₂×#10596833	—	2	1	no	—
31	C₂×#10596833	—	2	1	no	—
32	C₂×#10596833	D₄	1	1	yes	characteristic
33	C₂×#10596833	D₄	1	1	yes	characteristic
34	C₄×#64408	—	2	1	no	—
35	C₄×#64408	—	2	1	no	—
36	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
37	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
38	C₈×D₇₃	—	2	1	no	—
39	C₈×D₇₃	—	2	1	no	—
40	C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
41	C₄⋊Dic₇₃	C₂×C₄	1	1	yes	characteristic
42	#11924005	—	2	1	no	—
43	#11924005	—	2	1	no	—
44	C₄×Dic₇₃	—	2	1	no	—
45	C₄×Dic₇₃	—	2	1	no	—
46	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
47	C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
48	C₄⋊C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
49	C₂²×D₇₃	#41	1	1	yes	characteristic
50	C₂×#64408	—	2	2	no	—
51	C₂×#64408	—	4	1	no	—
52	C₂×#64408	—	4	1	no	—
53	C₂×C₄×C₇₃	—	2	1	no	—
54	C₂×C₄×C₇₃	—	2	1	no	—
55	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
56	C₂×Dic₇₃	—	2	1	no	—
57	C₂×Dic₇₃	—	2	1	no	—
58	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
59	C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
60	C₄×D₇₃	#41	1	1	yes	characteristic
61	C₄×D₇₃	#41	1	1	yes	characteristic
62	C₄×D₇₃	#41	1	1	yes	characteristic
63	#10596833	—	2	2	no	—
64	#10596833	—	2	1	no	—
65	#10596833	—	2	1	no	—
66	#10596833	—	4	1	no	—
67	C₈×C₇₃	—	2	1	no	—
68	#10596831	—	2	1	no	—
69	C₂²×C₇₃	C₄×D₄	1	1	yes	characteristic
70	C₂×D₇₃	—	2	1	no	—
71	C₂×D₇₃	—	2	1	no	—
72	C₂×D₇₃	#125	1	1	yes	characteristic
73	C₂×D₇₃	#126	1	1	yes	characteristic
74	#64408	—	4	2	no	—
75	C₄×C₇₃	—	4	1	no	—
76	C₄×C₇₃	—	4	1	no	—
77	C₄×C₇₃	#117	1	1	yes	characteristic
78	C₄×C₇₃	C₄×Q₈	1	1	yes	characteristic
79	Dic₇₃	—	4	1	no	—
80	Dic₇₃	—	4	1	no	—
81	Dic₇₃	C₂²⋊Q₈	1	1	yes	characteristic
82	Dic₇₃	#123	1	1	yes	characteristic
83	C₂×C₇₃	#387	1	1	yes	characteristic
84	C₂×C₇₃	#443	1	1	yes	characteristic
85	C₂×C₇₃	#444	1	1	yes	characteristic
86	D₇₃	—	2	1	no	—
87	D₇₃	—	2	1	no	—
88	#1922	—	73	1	no	maximal, Sylow
89	C₇₃	#1922	1	1	yes	characteristic, complemented, Sylow
90	#427	—	73	1	no	—
91	#424	—	73	1	no	—
92	#405	—	73	1	no	—
93	#341	—	73	1	no	—
94	#339	—	73	1	no	—
95	#339	—	73	1	no	—
96	#336	—	73	1	no	—
97	C₂×M₁₆	—	73	1	no	—
98	C₂×M₁₆	—	73	1	no	—
99	C₂²×C₈	—	73	1	no	—
100	C₂²×C₈	—	73	1	no	—
101	#117	—	73	1	no	—
102	#117	—	73	1	no	—
103	C₂×C₄²	—	73	1	no	—
104	#107	—	73	1	no	—
105	#107	—	73	1	no	—
106	#106	—	73	1	no	—
107	#106	#64408	1	1	yes	characteristic, complemented
108	C₄⋊C₈	—	146	1	no	—
109	C₄⋊C₈	—	146	1	no	—
110	#97	—	146	1	no	—
111	C₄×C₈	—	146	1	no	—
112	C₂²×C₄	—	73	1	no	—
113	C₂²×C₄	—	146	1	no	—
114	M₁₆	—	73	2	no	—
115	M₁₆	—	146	1	no	—
116	M₁₆	—	146	1	no	—
117	M₁₆	—	146	1	no	—
118	C₂×C₈	—	73	1	no	—
119	C₂×C₈	—	73	1	no	—
120	C₂×C₈	—	73	1	no	—
121	C₂×C₈	—	146	1	no	—
122	C₂×C₈	—	146	1	no	—
123	C₂×C₈	—	146	1	no	—
124	C₂×C₈	—	146	1	no	—
125	C₂×C₈	—	146	1	no	—
126	C₂×C₈	—	146	1	no	—
127	C₂×C₈	C₂×#64408	1	1	yes	characteristic
128	C₄⋊C₄	—	73	1	no	—
129	C₄⋊C₄	—	73	1	no	—
130	C₄⋊C₄	C₂×#64408	1	1	yes	characteristic
131	C₄⋊C₄	C₂×#64408	1	1	yes	characteristic
132	C₂²⋊C₄	—	146	1	no	—
133	C₂²⋊C₄	—	146	1	no	—
134	C₄²	—	146	1	no	—
135	C₄²	—	146	1	no	—
136	C₄²	—	146	1	no	—
137	C₄²	—	146	1	no	—
138	C₂³	—	73	1	no	—
139	C₂×C₄	—	2	1	no	—
140	C₂×C₄	—	2	1	no	—
141	C₂×C₄	—	292	1	no	—
142	C₂×C₄	—	292	1	no	—
143	C₂×C₄	—	73	1	no	—
144	C₂×C₄	—	73	1	no	—
145	C₂×C₄	—	73	1	no	—
146	C₂×C₄	—	73	1	no	—
147	C₂×C₄	—	73	1	no	—
148	C₂×C₄	—	146	2	no	—
149	C₂×C₄	—	146	1	no	—
150	C₂×C₄	—	146	1	no	—
151	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
152	C₈	—	2	1	no	—
153	C₈	—	292	1	no	—
154	C₈	—	146	1	no	—
155	C₈	—	146	1	no	—
156	C₈	—	146	2	no	—
157	C₈	—	146	1	no	—
158	C₂²	—	73	1	no	—
159	C₂²	—	73	1	no	—
160	C₂²	—	146	1	no	—
161	C₂²	—	146	1	no	—
162	C₂²	D₄×#64408	1	1	yes	characteristic
163	C₄	—	4	1	no	—
164	C₄	—	4	1	no	—
165	C₄	—	292	2	no	—
166	C₄	—	292	1	no	—
167	C₄	—	292	1	no	—
168	C₄	—	73	1	no	—
169	C₄	—	73	1	no	—
170	C₄	#14556670	1	1	yes	characteristic
171	C₄	Q₈×#64408	1	1	yes	characteristic
172	C₂	—	146	1	no	—
173	C₂	—	146	1	no	—
174	C₂	#17989536	1	1	yes	characteristic
175	C₂	#17989630	1	1	yes	characteristic
176	C₂	#17989632	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	#106×C₇₃	C₄
socle	C₂²×C₇₃	C₄×D₄
hypercenter	#106	#64408
hypocenter	C₇₃	#1922
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #106

Complements

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

N	H ≅ G/N	type
19. #14556524	C₄	semidirect
20. #14556524	C₄	semidirect
21. #14556523	C₄	semidirect
22. #106×C₇₃	C₄	semidirect
89. C₇₃	#1922	semidirect
107. #106	#64408	semidirect