Subgroups — C₂×#13092974 #15686688

Order 2944.

1168 conjugacy classes of subgroups.

The subgroup lattice has 156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13092974	C₂	1	16	yes	maximal, direct product factor
2	C₂×#10625040	C₂	1	2	yes	maximal, complemented
3	C₂×#10625041	C₂	1	2	yes	maximal, complemented
4	C₂×#10625095	C₂	1	4	yes	maximal
5	C₂×C₄×Dic₄₆	C₂	1	4	yes	maximal, complemented
6	C₂×#10625097	C₂	1	2	yes	maximal
7	C₂²×C₄²×C₂₃	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₄×C₂₃	C₂²	1	2	yes	—
9	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic
10	C₂²×Dic₄₆	C₂²	1	4	yes	—
11	C₂×C₄²×C₂₃	C₂²	1	2	yes	—
12	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₂₃	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₂₃	C₂²	1	8	yes	—
15	C₂×C₂²⋊Dic₂₃	C₂²	1	4	yes	—
16	#10625097	C₂²	1	16	yes	—
17	C₂×C₄⋊Dic₂₃	C₂²	1	4	yes	—
18	C₂×C₄⋊Dic₂₃	C₂²	1	4	yes	—
19	#10625095	C₂²	1	32	yes	—
20	C₂×Dic₂₃⋊C₄	C₂²	1	8	yes	—
21	C₂×C₄×Dic₂₃	C₂²	1	4	yes	—
22	#10625041	C₂²	1	16	yes	complemented
23	#10625040	C₂²	1	16	yes	complemented
24	C₄×Dic₄₆	C₂²	1	32	yes	complemented
25	C₂⁴×C₂₃	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₂₃	—	2	8	no	—
27	C₂²×C₄×C₂₃	Q₈	1	8	yes	complemented
28	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
29	C₂²×C₄×C₂₃	C₂³	1	8	yes	—
30	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
31	C₂²×C₄×C₂₃	C₂³	1	4	yes	—
32	C₂²×C₄×C₂₃	C₂³	1	2	yes	—
33	C₂²×C₄×C₂₃	C₂³	1	1	yes	characteristic
34	C₂²×Dic₂₃	C₂³	1	8	yes	—
35	C₂×Dic₄₆	—	2	16	no	—
36	C₂×Dic₄₆	C₂³	1	16	yes	—
37	C₄²×C₂₃	C₂³	1	8	yes	—
38	C₄²×C₂₃	C₂³	1	4	yes	—
39	C₄²×C₂₃	C₂³	1	4	yes	—
40	C₂²⋊Dic₂₃	C₂³	1	16	yes	—
41	C₄⋊Dic₂₃	C₂³	1	16	yes	—
42	C₄⋊Dic₂₃	C₂³	1	16	yes	—
43	Dic₂₃⋊C₄	C₂³	1	32	yes	—
44	C₄×Dic₂₃	C₂³	1	16	yes	—
45	C₂³×C₂₃	—	2	4	no	—
46	C₂³×C₂₃	C₂×Q₈	1	4	yes	—
47	C₂³×C₂₃	C₂⁴	1	2	yes	—
48	C₂³×C₂₃	C₂⁴	1	1	yes	characteristic
49	C₂×C₄×C₂₃	—	2	4	no	—
50	C₂×C₄×C₂₃	—	2	16	no	—
51	C₂×C₄×C₂₃	C₂×Q₈	1	4	yes	—
52	C₂×C₄×C₂₃	C₂×Q₈	1	4	yes	—
53	C₂×C₄×C₂₃	C₂×Q₈	1	16	yes	complemented
54	C₂×C₄×C₂₃	#41	1	8	yes	—
55	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
56	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
57	C₂×C₄×C₂₃	C₂⁴	1	2	yes	—
58	C₂×C₄×C₂₃	C₂⁴	1	4	yes	—
59	C₂×Dic₂₃	—	2	16	no	—
60	C₂×Dic₂₃	C₂⁴	1	16	yes	—
61	Dic₄₆	—	2	32	no	—
62	C₂×#533	—	23	1	no	maximal, Sylow
63	C₂²×C₂₃	—	2	8	no	—
64	C₂²×C₂₃	—	2	4	no	—
65	C₂²×C₂₃	C₂²×Q₈	1	4	yes	—
66	C₂²×C₂₃	C₂²×Q₈	1	2	yes	—
67	C₂²×C₂₃	C₂×#41	1	4	yes	—
68	C₂²×C₂₃	C₂⁵	1	1	yes	characteristic
69	C₄×C₂₃	—	2	4	no	—
70	C₄×C₂₃	C₂²×Q₈	1	4	yes	—
71	C₄×C₂₃	C₂²×Q₈	1	4	yes	—
72	C₄×C₂₃	C₂×#41	1	8	yes	—
73	Dic₂₃	—	2	16	no	—
74	#533	—	23	16	no	—
75	C₂×C₄⋊Q₈	—	23	2	no	—
76	C₂×#125	—	23	2	no	—
77	C₂×C₂²⋊Q₈	—	23	4	no	—
78	C₂×C₄×Q₈	—	23	4	no	—
79	C₂×#117	—	23	2	no	—
80	C₂²×C₄²	D₂₃	1	1	yes	characteristic
81	C₂×C₂₃	—	2	4	no	—
82	C₂×C₂₃	#533	1	4	yes	complemented
83	C₂×C₂₃	C₂³×Q₈	1	1	yes	characteristic
84	C₂×C₂₃	C₂²×#41	1	2	yes	—
85	C₂²×Q₈	—	23	4	no	—
86	C₂³×C₄	C₂×D₂₃	1	2	yes	—
87	C₂³×C₄	C₂×D₂₃	1	1	yes	characteristic
88	C₄⋊Q₈	—	23	16	no	—
89	#125	—	23	16	no	—
90	C₂²⋊Q₈	—	23	32	no	—
91	C₄×Q₈	—	23	32	no	—
92	#117	—	23	16	no	—
93	C₂×C₄⋊C₄	—	23	4	no	—
94	C₂×C₄⋊C₄	—	23	8	no	—
95	C₂×C₄⋊C₄	—	23	4	no	—
96	C₂×C₂²⋊C₄	—	23	4	no	—
97	C₂×C₄²	—	23	4	no	—
98	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
99	C₂×C₄²	C₂×D₂₃	1	1	yes	characteristic
100	C₂×C₄²	C₂×D₂₃	1	8	yes	—
101	C₂×C₄²	C₂×D₂₃	1	2	yes	—
102	C₂₃	C₂×#533	1	1	yes	characteristic, complemented, Sylow
103	C₂⁴	C₂²×D₂₃	1	1	yes	characteristic
104	C₂×Q₈	—	23	16	no	—
105	C₂×Q₈	—	46	16	no	—
106	C₂²×C₄	—	2	8	no	—
107	C₂²×C₄	—	23	8	no	—
108	C₂²×C₄	Dic₄₆	1	8	yes	complemented
109	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
110	C₂²×C₄	C₂²×D₂₃	1	8	yes	—
111	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
112	C₂²×C₄	C₂²×D₂₃	1	4	yes	—
113	C₂²×C₄	C₂²×D₂₃	1	2	yes	—
114	C₂²×C₄	C₂²×D₂₃	1	1	yes	characteristic
115	C₄⋊C₄	—	23	16	no	—
116	C₄⋊C₄	—	23	32	no	—
117	C₄⋊C₄	—	23	16	no	—
118	C₂²⋊C₄	—	23	16	no	—
119	C₄²	—	23	16	no	—
120	C₄²	C₂²×D₂₃	1	8	yes	—
121	C₄²	C₂²×D₂₃	1	4	yes	—
122	C₄²	C₂²×D₂₃	1	4	yes	—
123	C₂³	—	2	4	no	—
124	C₂³	C₂×Dic₄₆	1	4	yes	—
125	C₂³	C₂³×D₂₃	1	2	yes	—
126	C₂³	C₂³×D₂₃	1	1	yes	characteristic
127	Q₈	—	46	32	no	—
128	C₂×C₄	—	2	4	no	—
129	C₂×C₄	—	2	16	no	—
130	C₂×C₄	—	23	16	no	—
131	C₂×C₄	—	46	16	no	—
132	C₂×C₄	C₂×Dic₄₆	1	4	yes	—
133	C₂×C₄	C₂×Dic₄₆	1	4	yes	—
134	C₂×C₄	C₂×Dic₄₆	1	16	yes	complemented
135	C₂×C₄	#67288	1	8	yes	—
136	C₂×C₄	C₂³×D₂₃	1	4	yes	—
137	C₂×C₄	C₂³×D₂₃	1	2	yes	—
138	C₂×C₄	C₂³×D₂₃	1	2	yes	—
139	C₂×C₄	C₂³×D₂₃	1	4	yes	—
140	C₂²	—	2	8	no	—
141	C₂²	—	2	4	no	—
142	C₂²	C₂²×Dic₄₆	1	4	yes	—
143	C₂²	C₂²×Dic₄₆	1	2	yes	—
144	C₂²	C₂×#67288	1	4	yes	—
145	C₂²	C₂⁴×D₂₃	1	1	yes	characteristic
146	C₄	—	2	4	no	—
147	C₄	—	46	16	no	—
148	C₄	C₂²×Dic₄₆	1	4	yes	—
149	C₄	C₂²×Dic₄₆	1	4	yes	—
150	C₄	C₂×#67288	1	8	yes	—
151	C₂	—	2	4	no	—
152	C₂	#13092974	1	4	yes	direct product factor
153	C₂	C₂³×Dic₄₆	1	1	yes	characteristic
154	C₂	C₂²×#67288	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₂₃
commutator, cosocle	C₂²×C₂₃	C₂⁵
Frattini	C₂²	C₂⁴×D₂₃
Fitting	C₂²×C₄²×C₂₃	C₂
socle	C₂³×C₂₃	C₂⁴
prime radical	C₂⁴×C₂₃	C₂³
hypercenter	C₂²×C₄²	D₂₃
hypocenter	C₂₃	C₂×#533
LCS	G ▷ C₂²×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
1. #13092974	C₂	direct (N × H)
2. C₂×#10625040	C₂	semidirect
3. C₂×#10625041	C₂	semidirect
5. C₂×C₄×Dic₄₆	C₂	semidirect
22. #10625041	C₂²	semidirect
23. #10625040	C₂²	semidirect
24. C₄×Dic₄₆	C₂²	semidirect
27. C₂²×C₄×C₂₃	Q₈	semidirect
53. C₂×C₄×C₂₃	C₂×Q₈	semidirect
82. C₂×C₂₃	#533	semidirect
102. C₂₃	C₂×#533	semidirect
108. C₂²×C₄	Dic₄₆	semidirect
134. C₂×C₄	C₂×Dic₄₆	semidirect
152. C₂	#13092974	direct (N × H)

Maximal subgroups

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

subgroup	index
#13092974	2
C₂×#10625040	2
C₂×#10625041	2
C₂×#10625095	2
C₂×C₄×Dic₄₆	2
C₂×#10625097	2
C₂²×C₄²×C₂₃	2
C₂×#533	23

Subgroups — C2×#13092974 #15686688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13092974 #15686688