Subgroups — C₂×#10592381 #11874946

Order 1152.

1272 conjugacy classes of subgroups.

The subgroup lattice has 159 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#64078	C₂	1	2	yes	maximal
2	C₂×C₃²×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#63645	C₂	1	4	yes	maximal
4	#10592381	C₂	1	8	yes	maximal, direct product factor
5	C₂×#4682	—	3	4	no	maximal
6	C₂²×#634	—	2	2	no	—
7	C₂²×C₃²×C₈	C₂²	1	2	yes	—
8	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
9	C₂×C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
10	C₂×C₄⋊(C₃⋊Dic₃)	C₂²	1	4	yes	—
11	#64078	—	2	4	no	—
12	#64078	C₂²	1	8	yes	—
13	C₃²×C₄×C₈	C₂²	1	4	yes	—
14	#63645	C₂²	1	16	yes	—
15	C₂×#869	—	3	8	no	—
16	C₂×C₃×C₄×C₈	D₃	1	4	yes	—
17	C₂×#818	—	3	16	no	—
18	#4682	—	3	32	no	—
19	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
20	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
21	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
22	C₂²×C₃⋊Dic₃	—	2	4	no	—
23	C₂×#634	—	2	8	no	—
24	C₂×#634	—	4	8	no	—
25	C₂×C₃²×C₈	Q₈	1	8	yes	complemented
26	C₂×C₃²×C₈	C₂³	1	4	yes	—
27	C₃²×C₄²	D₄	1	2	yes	—
28	C₃²×C₄²	C₂³	1	2	yes	—
29	C₄⋊(C₃⋊Dic₃)	—	2	4	no	—
30	C₄⋊(C₃⋊Dic₃)	—	2	8	no	—
31	C₄⋊(C₃⋊Dic₃)	C₂³	1	8	yes	—
32	C₂×#500	—	9	1	no	Sylow
33	C₂²×Dic₆	—	6	8	no	—
34	C₂²×C₃×C₈	C₂×D₃	1	8	yes	—
35	C₂×C₃×C₄²	C₂×D₃	1	4	yes	—
36	C₂×C₄⋊Dic₃	—	3	16	no	—
37	C₂×C₄⋊Dic₃	—	6	8	no	—
38	#869	—	3	32	no	—
39	#869	—	6	16	no	—
40	C₃×C₄×C₈	C₂×D₃	1	16	yes	—
41	#818	—	3	64	no	—
42	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
43	C₂×C₃²×C₄	D₈	1	4	yes	—
44	C₂×C₃²×C₄	Q₁₆	1	4	yes	—
45	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
46	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
47	C₂×C₃²×C₄	C₂×D₄	1	2	yes	—
48	C₂×C₃²×C₄	C₂×Q₈	1	4	yes	—
49	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
50	C₂×C₃⋊Dic₃	—	2	8	no	—
51	C₂×C₃⋊Dic₃	—	4	8	no	—
52	#634	—	4	16	no	—
53	C₃²×C₈	C₂×Q₈	1	8	yes	complemented
54	C₂×C₄⋊Q₈	—	9	2	no	—
55	#500	—	9	8	no	—
56	C₂×#107	—	9	4	no	—
57	C₂×C₄×C₈	C₃⋊D₃	1	1	yes	characteristic
58	C₂²×C₃×C₄	D₁₂	1	4	yes	—
59	C₂²×C₃×C₄	D₁₂	1	4	yes	—
60	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
61	C₂²×Dic₃	—	6	16	no	—
62	C₂×Dic₆	—	6	32	no	—
63	C₂×Dic₆	—	12	32	no	—
64	C₂×C₃×C₈	Dic₆	1	32	yes	complemented
65	C₂×C₃×C₈	C₂²×D₃	1	16	yes	—
66	C₃×C₄²	D₁₂	1	8	yes	—
67	C₃×C₄²	C₂²×D₃	1	8	yes	—
68	C₄⋊Dic₃	—	3	32	no	—
69	C₄⋊Dic₃	—	6	32	no	—
70	C₄⋊Dic₃	—	6	16	no	—
71	C₂²×C₃²	C₄⋊Q₈	1	2	yes	—
72	C₂²×C₃²	C₂×D₈	1	2	yes	—
73	C₂²×C₃²	C₂×Q₁₆	1	2	yes	—
74	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
75	C₃²×C₄	C₄⋊Q₈	1	2	yes	—
76	C₃²×C₄	C₂×D₈	1	4	yes	—
77	C₃²×C₄	C₂×Q₁₆	1	4	yes	—
78	C₃²×C₄	C₂²×Q₈	1	2	yes	—
79	C₃⋊Dic₃	—	4	8	no	—
80	C₂²×Q₈	—	18	2	no	—
81	C₂²×C₈	C₂×C₃⋊D₃	1	2	yes	—
82	C₄⋊Q₈	—	9	8	no	—
83	C₄⋊Q₈	—	18	4	no	—
84	C₂×C₄⋊C₄	—	9	4	no	—
85	C₂×C₄⋊C₄	—	18	2	no	—
86	C₂×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
87	#107	—	9	16	no	—
88	C₄×C₈	C₂×C₃⋊D₃	1	4	yes	—
89	C₂³×C₃	C₂×D₁₂	1	4	yes	—
90	C₂×C₃×C₄	D₂₄	1	16	yes	—
91	C₂×C₃×C₄	Dic₁₂	1	16	yes	—
92	C₂×C₃×C₄	C₂×Dic₆	1	16	yes	—
93	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
94	C₂×C₃×C₄	C₂×D₁₂	1	8	yes	—
95	C₂×C₃×C₄	C₂×D₁₂	1	8	yes	—
96	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
97	C₂×Dic₃	—	6	32	no	—
98	C₂×Dic₃	—	12	32	no	—
99	Dic₆	—	12	64	no	—
100	C₃×C₈	C₂×Dic₆	1	32	yes	complemented
101	C₂×C₃²	#500	1	4	yes	complemented
102	C₂×C₃²	C₂×C₄⋊Q₈	1	1	yes	characteristic
103	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
104	C₂×C₃²	C₂²×Q₁₆	1	1	yes	characteristic
105	C₂×Q₈	—	18	8	no	—
106	C₂×Q₈	—	36	8	no	—
107	C₂²×C₄	—	18	4	no	—
108	C₂²×C₄	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
109	C₂²×C₄	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
110	C₂²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
111	C₂×C₈	#634	1	8	yes	complemented
112	C₂×C₈	C₂²×C₃⋊D₃	1	4	yes	—
113	C₄⋊C₄	—	9	8	no	—
114	C₄⋊C₄	—	18	4	no	—
115	C₄⋊C₄	—	18	8	no	—
116	C₄²	C₄⋊(C₃⋊D₃)	1	2	yes	—
117	C₄²	C₂²×C₃⋊D₃	1	2	yes	—
118	C₂²×C₃	#869	1	8	yes	—
119	C₂²×C₃	C₂×D₂₄	1	8	yes	—
120	C₂²×C₃	C₂×Dic₁₂	1	8	yes	—
121	C₂²×C₃	C₂²×D₁₂	1	4	yes	—
122	C₃×C₄	#869	1	8	yes	—
123	C₃×C₄	C₂×D₂₄	1	16	yes	—
124	C₃×C₄	C₂×Dic₁₂	1	16	yes	—
125	C₃×C₄	C₂²×Dic₆	1	8	yes	—
126	Dic₃	—	12	32	no	—
127	C₃²	C₂×#500	1	1	yes	characteristic, complemented, Sylow
128	C₂³	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
129	Q₈	—	36	16	no	—
130	C₂×C₄	—	18	8	no	—
131	C₂×C₄	—	36	8	no	—
132	C₂×C₄	#3745	1	4	yes	—
133	C₂×C₄	#3746	1	4	yes	—
134	C₂×C₄	C₂×#634	1	4	yes	—
135	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
136	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
137	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
138	C₂×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
139	C₈	C₂×#634	1	8	yes	complemented
140	C₂×C₃	#4682	1	16	yes	complemented
141	C₂×C₃	C₂×#869	1	4	yes	—
142	C₂×C₃	C₂²×D₂₄	1	4	yes	—
143	C₂×C₃	C₂²×Dic₁₂	1	4	yes	—
144	C₂²	#64078	1	2	yes	—
145	C₂²	C₂×#3745	1	2	yes	—
146	C₂²	C₂×#3746	1	2	yes	—
147	C₂²	C₂²×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
148	C₄	—	36	8	no	—
149	C₄	#64078	1	2	yes	—
150	C₄	C₂×#3745	1	4	yes	—
151	C₄	C₂×#3746	1	4	yes	—
152	C₄	C₂²×#634	1	2	yes	—
153	C₃	C₂×#4682	1	4	yes	complemented
154	C₂	#10592381	1	4	yes	direct product factor
155	C₂	C₂×#64078	1	1	yes	characteristic
156	C₂	C₂²×#3745	1	1	yes	characteristic
157	C₂	C₂²×#3746	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₄⋊(C₃⋊D₃)
commutator, cosocle	C₂×C₃²×C₄	C₂⁴
Frattini	C₂×C₄	C₂³×C₃⋊D₃
Fitting	C₂×C₃²×C₄×C₈	C₂
socle, prime radical	C₂³×C₃²	C₂×D₄
hypercenter	C₂×C₄×C₈	C₃⋊D₃
hypocenter	C₃²	C₂×#500
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
4. #10592381	C₂	direct (N × H)
25. C₂×C₃²×C₈	Q₈	semidirect
53. C₃²×C₈	C₂×Q₈	semidirect
64. C₂×C₃×C₈	Dic₆	semidirect
100. C₃×C₈	C₂×Dic₆	semidirect
101. C₂×C₃²	#500	semidirect
111. C₂×C₈	#634	semidirect
127. C₃²	C₂×#500	semidirect
139. C₈	C₂×#634	semidirect
140. C₂×C₃	#4682	semidirect
153. C₃	C₂×#4682	semidirect
154. C₂	#10592381	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#64078	2
C₂×C₃²×C₄×C₈	2
C₂×#63645	2
#10592381	2
C₂×#4682	3

Subgroups — C2×#10592381 #11874946

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10592381 #11874946