Subgroups — C₂×#13093145 #15686969

Order 2944.

1048 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13093145	C₂	1	16	yes	maximal, direct product factor
2	C₂×#10625040	C₂	1	1	yes	maximal, characteristic
3	C₂×#10625115	C₂	1	2	yes	maximal
4	C₂×#10625041	C₂	1	2	yes	maximal
5	C₂×#10625060	C₂	1	4	yes	maximal
6	C₂×C₄×Dic₄₆	C₂	1	2	yes	maximal
7	C₂×C₄×Dic₄₆	C₂	1	1	yes	maximal, characteristic
8	C₂×#10625058	C₂	1	2	yes	maximal
9	C₂×C₄×Q₈×C₂₃	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₈×C₂₃	C₂²	1	1	yes	characteristic
11	C₂²×Dic₄₆	C₂²	1	2	yes	—
12	C₂²×Dic₄₆	C₂²	1	1	yes	characteristic
13	C₄×Q₈×C₂₃	C₂²	1	8	yes	—
14	C₂×C₄⋊C₄×C₂₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×C₂₃	C₂²	1	2	yes	—
16	C₂×C₄²×C₂₃	C₂²	1	2	yes	—
17	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
18	#10625115	C₂²	1	16	yes	—
19	C₂×C₄⋊Dic₂₃	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Dic₂₃	C₂²	1	2	yes	—
21	C₂×C₄⋊Dic₂₃	C₂²	1	2	yes	—
22	C₂×Dic₂₃⋊C₄	C₂²	1	4	yes	—
23	C₂×Dic₂₃⋊C₄	C₂²	1	2	yes	—
24	C₂×Dic₂₃⋊C₄	C₂²	1	4	yes	—
25	C₂×Dic₂₃⋊C₄	C₂²	1	4	yes	—
26	C₂×C₄×Dic₂₃	C₂²	1	4	yes	—
27	C₂×C₄×Dic₂₃	C₂²	1	2	yes	—
28	#10625060	C₂²	1	32	yes	—
29	#10625058	C₂²	1	16	yes	—
30	#10625041	C₂²	1	16	yes	—
31	#10625040	C₂²	1	8	yes	—
32	C₄×Dic₄₆	C₂²	1	16	yes	—
33	C₄×Dic₄₆	C₂²	1	8	yes	—
34	C₂×Q₈×C₂₃	—	2	4	no	—
35	C₂×Q₈×C₂₃	C₂³	1	4	yes	—
36	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
37	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
38	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
40	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
41	C₂²×Dic₂₃	C₂³	1	2	yes	—
42	C₂²×Dic₂₃	C₂³	1	4	yes	—
43	C₂²×Dic₂₃	C₂³	1	2	yes	—
44	C₂×Dic₄₆	—	2	8	no	—
45	C₂×Dic₄₆	Q₈	1	8	yes	complemented
46	C₂×Dic₄₆	C₂³	1	8	yes	—
47	C₂×Dic₄₆	C₂³	1	4	yes	—
48	C₄⋊C₄×C₂₃	C₂³	1	4	yes	—
49	C₄⋊C₄×C₂₃	C₂³	1	8	yes	—
50	C₄²×C₂₃	C₂³	1	4	yes	—
51	C₄²×C₂₃	C₂³	1	8	yes	—
52	C₄⋊Dic₂₃	C₂³	1	8	yes	—
53	C₄⋊Dic₂₃	C₂³	1	4	yes	—
54	C₄⋊Dic₂₃	C₂³	1	8	yes	—
55	Dic₂₃⋊C₄	C₂³	1	8	yes	—
56	Dic₂₃⋊C₄	C₂³	1	16	yes	—
57	Dic₂₃⋊C₄	C₂³	1	16	yes	—
58	Dic₂₃⋊C₄	C₂³	1	16	yes	—
59	C₄×Dic₂₃	C₂³	1	16	yes	—
60	C₄×Dic₂₃	C₂³	1	8	yes	—
61	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
62	Q₈×C₂₃	—	2	8	no	—
63	C₂×C₄×C₂₃	—	2	4	no	—
64	C₂×C₄×C₂₃	—	2	4	no	—
65	C₂×C₄×C₂₃	—	2	2	no	—
66	C₂×C₄×C₂₃	C₂×Q₈	1	4	yes	—
67	C₂×C₄×C₂₃	#41	1	4	yes	—
68	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
69	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
70	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
71	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
72	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
73	C₂×Dic₂₃	—	2	8	no	—
74	C₂×Dic₂₃	—	2	4	no	—
75	C₂×Dic₂₃	C₂×Q₈	1	8	yes	—
76	C₂×Dic₂₃	C₂⁴	1	4	yes	—
77	C₂×Dic₂₃	C₂⁴	1	8	yes	—
78	C₂×Dic₂₃	C₂⁴	1	4	yes	—
79	Dic₄₆	—	2	16	no	—
80	Dic₄₆	C₂×Q₈	1	16	yes	complemented
81	C₂×#557	—	23	1	no	maximal, Sylow
82	C₂²×C₂₃	C₂²×Q₈	1	2	yes	—
83	C₂²×C₂₃	C₂×#41	1	2	yes	—
84	C₂²×C₂₃	2₋¹⁺⁴	1	2	yes	—
85	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
86	C₄×C₂₃	—	2	4	no	—
87	C₄×C₂₃	—	2	4	no	—
88	C₄×C₂₃	—	2	2	no	—
89	C₄×C₂₃	C₂²×Q₈	1	4	yes	—
90	C₄×C₂₃	C₂×#41	1	4	yes	—
91	Dic₂₃	—	2	8	no	—
92	Dic₂₃	—	2	4	no	—
93	Dic₂₃	C₂²×Q₈	1	8	yes	—
94	#557	—	23	16	no	—
95	C₂×C₄⋊Q₈	—	23	2	no	—
96	C₂×C₄⋊Q₈	—	23	1	no	—
97	C₂×#125	—	23	4	no	—
98	C₂×#125	—	23	2	no	—
99	C₂×C₄×Q₈	—	23	2	no	—
100	C₂×C₄×Q₈	—	23	2	no	—
101	C₂×C₄×Q₈	—	23	1	no	—
102	C₂×C₄×Q₈	D₂₃	1	1	yes	characteristic
103	C₂×C₂₃	#557	1	4	yes	complemented
104	C₂×C₂₃	C₂³×Q₈	1	1	yes	characteristic
105	C₂×C₂₃	C₂²×#41	1	1	yes	characteristic
106	C₂×C₂₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
107	C₂²×Q₈	—	23	1	no	—
108	C₂²×Q₈	—	23	2	no	—
109	C₂²×Q₈	C₂×D₂₃	1	1	yes	characteristic
110	C₄⋊Q₈	—	23	16	no	—
111	C₄⋊Q₈	—	23	8	no	—
112	#125	—	23	32	no	—
113	#125	—	23	16	no	—
114	C₄×Q₈	—	23	16	no	—
115	C₄×Q₈	—	23	16	no	—
116	C₄×Q₈	—	23	8	no	—
117	C₄×Q₈	C₂×D₂₃	1	8	yes	—
118	C₂×C₄⋊C₄	—	23	2	no	—
119	C₂×C₄⋊C₄	—	23	4	no	—
120	C₂×C₄⋊C₄	—	23	1	no	—
121	C₂×C₄⋊C₄	—	23	4	no	—
122	C₂×C₄⋊C₄	—	23	2	no	—
123	C₂×C₄⋊C₄	—	23	4	no	—
124	C₂×C₄⋊C₄	—	23	2	no	—
125	C₂×C₄⋊C₄	C₂×D₂₃	1	1	yes	characteristic
126	C₂×C₄⋊C₄	C₂×D₂₃	1	2	yes	—
127	C₂×C₄²	—	23	4	no	—
128	C₂×C₄²	—	23	2	no	—
129	C₂×C₄²	C₂×D₂₃	1	2	yes	—
130	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
131	C₂₃	C₂×#557	1	1	yes	characteristic, complemented, Sylow
132	C₂×Q₈	—	2	4	no	—
133	C₂×Q₈	—	23	8	no	—
134	C₂×Q₈	—	23	4	no	—
135	C₂×Q₈	—	23	8	no	—
136	C₂×Q₈	—	46	8	no	—
137	C₂×Q₈	C₂²×D₂₃	1	4	yes	—
138	C₂²×C₄	—	23	2	no	—
139	C₂²×C₄	—	23	2	no	—
140	C₂²×C₄	—	23	4	no	—
141	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
142	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
143	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
144	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
145	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
146	C₄⋊C₄	—	23	8	no	—
147	C₄⋊C₄	—	23	16	no	—
148	C₄⋊C₄	—	23	4	no	—
149	C₄⋊C₄	—	23	16	no	—
150	C₄⋊C₄	—	23	8	no	—
151	C₄⋊C₄	—	23	16	no	—
152	C₄⋊C₄	—	23	8	no	—
153	C₄⋊C₄	C₂²×D₂₃	1	4	yes	—
154	C₄⋊C₄	C₂²×D₂₃	1	8	yes	—
155	C₄²	—	23	16	no	—
156	C₄²	—	23	8	no	—
157	C₄²	C₂²×D₂₃	1	8	yes	—
158	C₄²	C₂²×D₂₃	1	4	yes	—
159	C₂³	C₂³×D₂₃	1	1	yes	characteristic
160	Q₈	—	2	8	no	—
161	Q₈	—	23	16	no	—
162	Q₈	—	46	16	no	—
163	C₂×C₄	—	2	4	no	—
164	C₂×C₄	—	2	4	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	23	8	no	—
167	C₂×C₄	—	23	4	no	—
168	C₂×C₄	—	23	4	no	—
169	C₂×C₄	—	23	8	no	—
170	C₂×C₄	—	46	8	no	—
171	C₂×C₄	—	46	4	no	—
172	C₂×C₄	#67288	1	4	yes	—
173	C₂×C₄	Q₈×D₂₃	1	4	yes	—
174	C₂×C₄	C₂³×D₂₃	1	4	yes	—
175	C₂×C₄	C₂³×D₂₃	1	2	yes	—
176	C₂×C₄	C₂³×D₂₃	1	4	yes	—
177	C₂×C₄	C₂³×D₂₃	1	2	yes	—
178	C₂×C₄	C₂³×D₂₃	1	2	yes	—
179	C₂²	C₂×#67288	1	2	yes	—
180	C₂²	C₂×Q₈×D₂₃	1	2	yes	—
181	C₂²	#10625161	1	2	yes	—
182	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
183	C₄	—	2	4	no	—
184	C₄	—	2	4	no	—
185	C₄	—	2	2	no	—
186	C₄	—	23	8	no	—
187	C₄	—	46	8	no	—
188	C₄	—	46	4	no	—
189	C₄	C₂×#67288	1	4	yes	—
190	C₄	C₂×Q₈×D₂₃	1	4	yes	—
191	C₂	#13093145	1	4	yes	direct product factor
192	C₂	C₂²×Q₈×D₂₃	1	1	yes	characteristic
193	C₂	C₂²×#67288	1	1	yes	characteristic
194	C₂	C₂×#10625161	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₂₃
commutator, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂×C₄×Q₈×C₂₃	C₂
socle, prime radical	C₂³×C₂₃	C₂⁴
hypercenter	C₂×C₄×Q₈	D₂₃
hypocenter	C₂₃	C₂×#557
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #13093145	C₂	direct (N × H)
45. C₂×Dic₄₆	Q₈	semidirect
80. Dic₄₆	C₂×Q₈	semidirect
103. C₂×C₂₃	#557	semidirect
131. C₂₃	C₂×#557	semidirect
191. C₂	#13093145	direct (N × H)

Maximal subgroups

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

subgroup	index
#13093145	2
C₂×#10625040	2
C₂×#10625115	2
C₂×#10625041	2
C₂×#10625060	2
C₂×C₄×Dic₄₆	2
C₂×#10625058	2
C₂×C₄×Q₈×C₂₃	2
C₂×#557	23

Subgroups — C2×#13093145 #15686969

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13093145 #15686969