Subgroups — C₂×#13092374 #15681811

Order 2944.

592 conjugacy classes of subgroups.

The subgroup lattice has 182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#67262	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×D₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×#10625043	C₂	1	1	yes	maximal, characteristic
4	#13092374	C₂	1	8	yes	maximal, direct product factor
5	C₂×#10624997	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄×C₂₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₈×Dic₂₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂₃×#97	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×C₄×D₂₃	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₂₃	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
13	C₂×(C₂×D₂₃)⋊C₄	C₄	1	2	yes	—
14	C₂×Dic₂₃⋊C₄	C₄	1	2	yes	—
15	C₂×C₄×Dic₂₃	C₂²	1	1	yes	characteristic
16	C₂²×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂²×C₂₃⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×#67262	C₄	1	8	yes	complemented
19	C₂×#67262	C₂²	1	4	yes	—
20	C₂×C₈×D₂₃	C₄	1	8	yes	complemented
21	C₂×C₈×D₂₃	C₂²	1	4	yes	—
22	#10625043	C₄	1	4	yes	—
23	#10625043	C₂²	1	4	yes	—
24	C₂₃×#97	C₂²	1	4	yes	complemented
25	#10624997	C₂²	1	4	yes	complemented
26	C₈×Dic₂₃	C₂²	1	4	yes	complemented
27	C₄×C₂₃⋊C₈	C₂²	1	4	yes	complemented
28	C₂³×D₂₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×C₂₃	C₂×C₄	1	2	yes	—
30	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
31	C₂²×Dic₂₃	C₂×C₄	1	2	yes	—
32	C₂²×Dic₂₃	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄×D₂₃	C₂×C₄	1	2	yes	—
34	C₂×C₄×D₂₃	C₂×C₄	1	4	yes	—
35	C₂×C₄×D₂₃	C₂×C₄	1	4	yes	—
36	C₂×C₄×D₂₃	C₂³	1	2	yes	—
37	C₂×C₈×C₂₃	C₂×C₄	1	4	yes	—
38	C₂×C₈×C₂₃	C₂×C₄	1	4	yes	—
39	C₂×C₈×C₂₃	C₂³	1	2	yes	—
40	C₂×C₈×C₂₃	C₂³	1	2	yes	—
41	C₄²×C₂₃	C₂×C₄	1	2	yes	—
42	C₄²×C₂₃	C₂³	1	2	yes	—
43	(C₂×D₂₃)⋊C₄	C₂×C₄	1	8	yes	—
44	Dic₂₃⋊C₄	C₂×C₄	1	8	yes	—
45	C₄×Dic₂₃	C₂×C₄	1	2	yes	—
46	C₄×Dic₂₃	C₂³	1	2	yes	—
47	C₂×C₂₃⋊C₈	C₂×C₄	1	4	yes	—
48	C₂×C₂₃⋊C₈	C₂×C₄	1	4	yes	—
49	C₂×C₂₃⋊C₈	C₂³	1	2	yes	—
50	C₂×C₂₃⋊C₈	C₂³	1	2	yes	—
51	#67262	C₂×C₄	1	16	yes	complemented
52	C₈×D₂₃	C₂×C₄	1	16	yes	complemented
53	C₂³×C₂₃	C₂²×C₄	1	1	yes	characteristic
54	C₂²×D₂₃	—	2	4	no	—
55	C₂²×D₂₃	C₄²	1	4	yes	—
56	C₂²×D₂₃	C₂²×C₄	1	2	yes	—
57	C₂×C₄×C₂₃	—	2	4	no	—
58	C₂×C₄×C₂₃	C₂²×C₄	1	4	yes	—
59	C₂×C₄×C₂₃	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₄×C₂₃	C₂²×C₄	1	2	yes	—
61	C₂×C₄×C₂₃	C₂²×C₄	1	2	yes	—
62	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
63	C₂×Dic₂₃	—	2	4	no	—
64	C₂×Dic₂₃	C₄²	1	4	yes	—
65	C₂×Dic₂₃	C₂²×C₄	1	4	yes	—
66	C₂×Dic₂₃	C₂²×C₄	1	2	yes	—
67	C₄×D₂₃	C₄²	1	8	yes	—
68	C₄×D₂₃	C₂²×C₄	1	4	yes	—
69	C₄×D₂₃	C₂²×C₄	1	4	yes	—
70	C₈×C₂₃	C₂²×C₄	1	4	yes	—
71	C₈×C₂₃	C₂²×C₄	1	4	yes	—
72	C₂₃⋊C₈	C₂²×C₄	1	4	yes	—
73	C₂₃⋊C₈	C₂²×C₄	1	4	yes	—
74	C₂×#405	—	23	1	no	maximal, Sylow
75	C₂²×C₂₃	C₂×C₄²	1	2	yes	—
76	C₂²×C₂₃	#131	1	4	yes	—
77	C₂²×C₂₃	C₂³×C₄	1	1	yes	characteristic
78	C₂×D₂₃	—	2	4	no	—
79	C₂×D₂₃	—	2	8	no	—
80	C₂×D₂₃	C₂×C₄²	1	4	yes	—
81	C₄×C₂₃	—	2	4	no	—
82	C₄×C₂₃	C₂×C₄²	1	2	yes	—
83	C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
84	C₄×C₂₃	C₂³×C₄	1	1	yes	characteristic
85	Dic₂₃	—	2	4	no	—
86	Dic₂₃	C₂×C₄²	1	4	yes	—
87	C₂²×M₁₆	—	23	1	no	—
88	C₂³×C₈	—	23	1	no	—
89	C₂×#117	—	23	1	no	—
90	#405	—	23	8	no	—
91	C₂×#97	—	23	1	no	—
92	C₂×#97	D₂₃	1	1	yes	characteristic, complemented
93	C₂×C₄×C₈	—	23	1	no	—
94	C₂×C₄×C₈	—	23	1	no	—
95	C₂×C₂₃	#405	1	4	yes	complemented
96	C₂×C₂₃	C₂²×C₄²	1	1	yes	characteristic
97	C₂×C₂₃	C₂×#131	1	2	yes	—
98	D₂₃	—	2	4	no	—
99	C₂³×C₄	—	23	1	no	—
100	C₂×M₁₆	—	23	8	no	—
101	C₂×M₁₆	—	23	4	no	—
102	C₂²×C₈	—	23	1	no	—
103	C₂²×C₈	—	23	1	no	—
104	C₂²×C₈	—	23	8	no	—
105	C₂²×C₈	—	23	4	no	—
106	C₂²×C₈	C₂×D₂₃	1	1	yes	characteristic
107	C₂²×C₈	C₂×D₂₃	1	1	yes	characteristic
108	#117	—	23	4	no	—
109	#117	—	23	4	no	—
110	C₂×C₄⋊C₄	—	23	2	no	—
111	C₂×C₂²⋊C₄	—	23	2	no	—
112	C₂×C₄²	—	23	1	no	—
113	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
114	#97	—	23	4	no	—
115	#97	C₂×D₂₃	1	4	yes	complemented
116	C₄×C₈	—	23	4	no	—
117	C₄×C₈	—	23	4	no	—
118	C₂₃	C₂×#405	1	1	yes	characteristic, complemented, Sylow
119	C₂⁴	—	23	1	no	—
120	C₂²×C₄	—	23	1	no	—
121	C₂²×C₄	—	23	2	no	—
122	C₂²×C₄	—	23	4	no	—
123	C₂²×C₄	—	23	4	no	—
124	C₂²×C₄	—	23	2	no	—
125	C₂²×C₄	—	23	2	no	—
126	C₂²×C₄	C₄×D₂₃	1	2	yes	—
127	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
128	M₁₆	—	23	16	no	—
129	C₂×C₈	—	23	4	no	—
130	C₂×C₈	—	23	4	no	—
131	C₂×C₈	—	23	2	no	—
132	C₂×C₈	—	23	2	no	—
133	C₂×C₈	—	23	16	no	—
134	C₂×C₈	C₄×D₂₃	1	4	yes	—
135	C₂×C₈	C₄×D₂₃	1	4	yes	—
136	C₂×C₈	C₂²×D₂₃	1	2	yes	—
137	C₂×C₈	C₂²×D₂₃	1	2	yes	—
138	C₄⋊C₄	—	23	8	no	—
139	C₂²⋊C₄	—	23	8	no	—
140	C₄²	—	23	2	no	—
141	C₄²	—	23	2	no	—
142	C₄²	C₄×D₂₃	1	2	yes	—
143	C₄²	C₂²×D₂₃	1	2	yes	—
144	C₂³	—	23	4	no	—
145	C₂³	—	23	2	no	—
146	C₂³	—	46	4	no	—
147	C₂³	C₂×C₄×D₂₃	1	1	yes	characteristic
148	C₂×C₄	—	2	4	no	—
149	C₂×C₄	—	23	4	no	—
150	C₂×C₄	—	23	2	no	—
151	C₂×C₄	—	23	8	no	—
152	C₂×C₄	—	23	4	no	—
153	C₂×C₄	—	23	4	no	—
154	C₂×C₄	—	23	4	no	—
155	C₂×C₄	—	46	4	no	—
156	C₂×C₄	C₂×C₄×D₂₃	1	4	yes	—
157	C₂×C₄	C₂×C₄×D₂₃	1	1	yes	characteristic
158	C₂×C₄	C₂×C₄×D₂₃	1	2	yes	—
159	C₂×C₄	C₂×C₄×D₂₃	1	2	yes	—
160	C₂×C₄	C₂³×D₂₃	1	1	yes	characteristic
161	C₈	—	23	4	no	—
162	C₈	—	23	4	no	—
163	C₈	C₂×C₄×D₂₃	1	4	yes	—
164	C₈	C₂×C₄×D₂₃	1	4	yes	—
165	C₂²	—	23	4	no	—
166	C₂²	—	46	8	no	—
167	C₂²	—	46	4	no	—
168	C₂²	C₄²×D₂₃	1	2	yes	—
169	C₂²	#10625078	1	4	yes	—
170	C₂²	C₂²×C₄×D₂₃	1	1	yes	characteristic
171	C₄	—	2	4	no	—
172	C₄	—	23	4	no	—
173	C₄	—	46	4	no	—
174	C₄	C₄²×D₂₃	1	2	yes	—
175	C₄	C₂²×C₄×D₂₃	1	1	yes	characteristic
176	C₄	C₂²×C₄×D₂₃	1	1	yes	characteristic
177	C₂	—	46	4	no	—
178	C₂	#13092374	1	4	yes	direct product factor
179	C₂	C₂×C₄²×D₂₃	1	1	yes	characteristic
180	C₂	C₂×#10625078	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₂₃
commutator	C₂×C₂₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×D₂₃
Fitting	C₂×C₂₃×#97	C₂
socle	C₂³×C₂₃	C₂²×C₄
prime radical	C₂³×D₂₃	C₂×C₄
cosocle	C₂×C₄×C₂₃	C₂⁴
hypercenter	C₂×#97	D₂₃
hypocenter	C₂₃	C₂×#405
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
4. #13092374	C₂	direct (N × H)
5. C₂×#10624997	C₂	semidirect
6. C₂×C₄×C₂₃⋊C₈	C₂	semidirect
7. C₂×C₈×Dic₂₃	C₂	semidirect
8. C₂×C₂₃×#97	C₂	semidirect
18. C₂×#67262	C₄	semidirect
20. C₂×C₈×D₂₃	C₄	semidirect
24. C₂₃×#97	C₂²	semidirect
25. #10624997	C₂²	semidirect
26. C₈×Dic₂₃	C₂²	semidirect
27. C₄×C₂₃⋊C₈	C₂²	semidirect
51. #67262	C₂×C₄	semidirect
52. C₈×D₂₃	C₂×C₄	semidirect
92. C₂×#97	D₂₃	semidirect
95. C₂×C₂₃	#405	semidirect
115. #97	C₂×D₂₃	semidirect
118. C₂₃	C₂×#405	semidirect
178. C₂	#13092374	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×#67262	2
C₂²×C₈×D₂₃	2
C₂×#10625043	2
#13092374	2
C₂×#10624997	2
C₂×C₄×C₂₃⋊C₈	2
C₂×C₈×Dic₂₃	2
C₂×C₂₃×#97	2
C₂×#405	23

Subgroups — C2×#13092374 #15681811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13092374 #15681811