Finite Group Databasebeta

Subgroups — #22626203

Order 9344.

258 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 52 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	#17989568	C₂	1	2	yes	maximal, complemented
2	#17989494	C₂	1	2	yes	maximal, complemented
3	#17989491	C₂	1	2	yes	maximal, complemented
4	#17989136	C₂	1	1	yes	maximal, characteristic
5	#14556670	—	2	2	no	—
6	#14556650	—	2	2	no	—
7	#14556650	C₂²	1	4	yes	—
8	C₂×#11924029	C₂²	1	1	yes	characteristic
9	C₂×#11924027	C₄	1	1	yes	characteristic, complemented
10	#14556589	C₄	1	1	yes	characteristic, complemented
11	#14556587	C₂²	1	1	yes	characteristic
12	#14556579	C₂²	1	1	yes	characteristic
13	#14556564	—	2	2	no	—
14	#14556551	—	2	2	no	—
15	C₄²×D₇₃	C₄	1	1	yes	characteristic, complemented
16	#124×C₇₃	C₄	1	1	yes	characteristic, complemented
17	C₄⋊#64408	—	4	2	no	—
18	C₂²⋊#64408	—	2	4	no	—
19	C₄×#64408	—	4	2	no	—
20	#11924029	—	4	1	no	—
21	#11924029	—	4	1	no	—
22	#11924027	—	4	1	no	—
23	#11924027	—	4	1	no	—
24	C₂×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
25	C₂×D₂₉₂	D₄	1	2	yes	—
26	C₂×D₂₉₂	C₂³	1	1	yes	characteristic
27	C₂×C₂²⋊D₇₃	—	2	1	no	—
28	C₂×C₂²⋊D₇₃	—	2	2	no	—
29	C₂²×Dic₇₃	—	2	1	no	—
30	C₂×C₄×D₇₃	—	2	1	no	—
31	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄×D₇₃	D₄	1	2	yes	—
33	#11924007	—	2	2	no	—
34	#11924005	—	2	2	no	—
35	C₄×Dic₇₃	—	2	1	no	—
36	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
37	C₂×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
38	C₂×D₄×C₇₃	C₂×C₄	1	1	yes	characteristic
39	C₂²⋊C₄×C₇₃	—	2	2	no	—
40	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₇₃	—	2	1	no	—
42	C₂²×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
43	C₂²×D₇₃	C₂×D₄	1	2	yes	—
44	C₂×#64408	—	4	4	no	—
45	Q₈×C₇₃	—	4	1	no	—
46	D₄×C₇₃	—	4	1	no	—
47	C₂×C₄×C₇₃	—	2	1	no	—
48	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
49	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
50	C₂²⋊D₇₃	—	4	4	no	—
51	C₂²⋊D₇₃	—	4	2	no	—
52	C₂×Dic₇₃	—	2	1	no	—
53	C₂×Dic₇₃	—	2	1	no	—
54	C₂×Dic₇₃	—	4	1	no	—
55	C₂×Dic₇₃	—	4	1	no	—
56	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
57	D₂₉₂	—	4	2	no	—
58	D₂₉₂	—	4	1	no	—
59	C₄×D₇₃	—	2	1	no	—
60	C₄×D₇₃	—	2	1	no	—
61	C₄×D₇₃	—	2	2	no	—
62	C₄×D₇₃	—	2	2	no	—
63	C₄×D₇₃	—	4	2	no	—
64	Dic₁₄₆	—	4	1	no	—
65	C₂²×C₇₃	—	4	2	no	—
66	C₂²×C₇₃	—	4	1	no	—
67	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
68	C₂×D₇₃	—	2	1	no	—
69	C₂×D₇₃	—	2	2	no	—
70	C₂×D₇₃	—	4	1	no	—
71	C₂×D₇₃	—	4	2	no	—
72	#64408	—	8	4	no	—
73	C₄×C₇₃	—	2	1	no	—
74	C₄×C₇₃	—	2	2	no	—
75	C₄×C₇₃	—	4	1	no	—
76	Dic₇₃	—	2	2	no	—
77	Dic₇₃	—	4	1	no	—
78	Dic₇₃	#99	1	1	yes	characteristic
79	Dic₇₃	#99	1	1	yes	characteristic
80	C₂×C₇₃	—	2	1	no	—
81	C₂×C₇₃	—	8	1	no	—
82	C₂×C₇₃	C₂×#99	1	1	yes	characteristic
83	D₇₃	—	4	2	no	—
84	D₇₃	—	4	1	no	—
85	#2126	—	73	1	no	maximal, Sylow
86	C₇₃	#2126	1	1	yes	characteristic, complemented, Sylow
87	#532	—	73	1	no	—
88	#410	—	73	2	no	—
89	#354	—	73	2	no	—
90	#353	—	73	2	no	—
91	C₂×#41	—	73	1	no	—
92	C₂×#41	—	73	1	no	—
93	C₄⋊Q₈	—	73	1	no	—
94	#127	—	73	1	no	—
95	#124	—	73	1	no	—
96	#124	#64408	1	1	yes	characteristic, complemented
97	#121	—	146	2	no	—
98	C₄×D₄	—	146	2	no	—
99	#117	—	146	2	no	—
100	C₂×C₄²	—	73	1	no	—
101	#99	—	73	4	no	—
102	#99	—	146	2	no	—
103	#41	—	292	1	no	—
104	#41	—	292	1	no	—
105	#41	—	292	1	no	—
106	#41	—	292	1	no	—
107	C₂×Q₈	—	73	1	no	—
108	C₂×Q₈	C₂×#64408	1	1	yes	characteristic
109	C₂×D₄	—	73	2	no	—
110	C₂×D₄	—	73	1	no	—
111	C₂×D₄	—	146	2	no	—
112	C₂×D₄	—	146	1	no	—
113	C₂×D₄	C₂×#64408	1	1	yes	characteristic
114	C₂²×C₄	—	73	2	no	—
115	C₂²×C₄	—	73	1	no	—
116	C₂²×C₄	—	146	1	no	—
117	C₂²×C₄	—	146	1	no	—
118	C₄⋊C₄	—	292	2	no	—
119	C₄⋊C₄	—	146	2	no	—
120	C₂²⋊C₄	—	2	2	no	—
121	C₂²⋊C₄	—	146	2	no	—
122	C₂²⋊C₄	—	146	4	no	—
123	C₄²	—	292	2	no	—
124	C₄²	—	73	1	no	—
125	C₄²	—	146	1	no	—
126	C₄²	C₂×#64408	1	1	yes	characteristic
127	C₂³	—	2	1	no	—
128	C₂³	—	73	2	no	—
129	C₂³	—	73	1	no	—
130	Q₈	—	4	1	no	—
131	Q₈	—	292	1	no	—
132	D₄	—	4	1	no	—
133	D₄	—	292	2	no	—
134	D₄	—	292	1	no	—
135	D₄	—	292	2	no	—
136	D₄	—	292	4	no	—
137	C₂×C₄	—	2	1	no	—
138	C₂×C₄	—	292	2	no	—
139	C₂×C₄	—	292	1	no	—
140	C₂×C₄	—	292	1	no	—
141	C₂×C₄	—	292	4	no	—
142	C₂×C₄	—	73	1	no	—
143	C₂×C₄	—	146	2	no	—
144	C₂×C₄	—	146	2	no	—
145	C₂×C₄	—	146	1	no	—
146	C₂×C₄	—	146	1	no	—
147	C₂×C₄	—	146	1	no	—
148	C₂×C₄	—	146	1	no	—
149	C₂×C₄	C₂²⋊#64408	1	2	yes	—
150	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
151	C₂²	—	4	2	no	—
152	C₂²	—	4	1	no	—
153	C₂²	—	292	1	no	—
154	C₂²	—	292	2	no	—
155	C₂²	—	146	2	no	—
156	C₂²	—	146	1	no	—
157	C₂²	C₂×C₂²⋊#64408	1	1	yes	characteristic
158	C₄	—	2	2	no	—
159	C₄	—	2	1	no	—
160	C₄	—	4	1	no	—
161	C₄	—	292	1	no	—
162	C₄	—	584	4	no	—
163	C₄	—	73	1	no	—
164	C₄	—	73	1	no	—
165	C₄	—	146	2	no	—
166	C₂	—	2	1	no	—
167	C₂	—	8	1	no	—
168	C₂	—	292	2	no	—
169	C₂	—	292	1	no	—
170	C₂	D₇₃⋊#99	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₇₃⋊#99
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	#124×C₇₃	C₄
socle	C₂×C₇₃	C₂×#99
hypercenter	#124	#64408
hypocenter	C₇₃	#2126
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×Q₈ ◁ #124

Complements

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

N	H ≅ G/N	type
1. #17989568	C₂	semidirect
2. #17989494	C₂	semidirect
3. #17989491	C₂	semidirect
9. C₂×#11924027	C₄	semidirect
10. #14556589	C₄	semidirect
15. C₄²×D₇₃	C₄	semidirect
16. #124×C₇₃	C₄	semidirect
86. C₇₃	#2126	semidirect
96. #124	#64408	semidirect