Subgroups — C₂×#10592382 #11874913

Order 1152.

1080 conjugacy classes of subgroups.

The subgroup lattice has 153 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#64079	C₂	1	2	yes	maximal
2	C₂×C₃²×C₄×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×#63645	C₂	1	2	yes	maximal
4	C₂×#63644	C₂	1	2	yes	maximal
5	#10592382	C₂	1	8	yes	maximal, direct product factor
6	C₂×#4683	—	3	4	no	maximal
7	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
8	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
9	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₃⋊Dic₃)	C₂²	1	4	yes	—
11	C₂×#3750	—	2	4	no	—
12	#64079	—	2	4	no	—
13	#64079	C₂²	1	8	yes	—
14	C₃²×C₄×C₈	C₂²	1	4	yes	—
15	#63645	C₂²	1	8	yes	—
16	#63644	C₂²	1	8	yes	—
17	C₂×#870	—	3	8	no	—
18	C₂×C₃×C₄×C₈	D₃	1	4	yes	—
19	C₂×#818	—	3	8	no	—
20	C₂×#817	—	3	8	no	—
21	#4683	—	3	32	no	—
22	C₂²×C₃²×C₄	D₄	1	2	yes	—
23	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
24	C₂²×C₃⋊Dic₃	—	2	4	no	—
25	C₂×C₃²×C₈	Q₈	1	4	yes	—
26	C₂×C₃²×C₈	Q₈	1	4	yes	—
27	C₂×C₃²×C₈	C₂³	1	2	yes	—
28	C₂×C₃²×C₈	C₂³	1	2	yes	—
29	C₃²×C₄²	D₄	1	2	yes	—
30	C₃²×C₄²	C₂³	1	2	yes	—
31	C₄⋊(C₃⋊Dic₃)	—	2	4	no	—
32	C₄⋊(C₃⋊Dic₃)	C₂³	1	8	yes	—
33	#3750	—	2	16	no	—
34	C₂×#499	—	9	1	no	Sylow
35	C₂²×C₃×C₈	C₂×D₃	1	4	yes	—
36	C₂²×C₃×C₈	C₂×D₃	1	4	yes	—
37	C₂×C₃×C₄²	C₂×D₃	1	4	yes	—
38	C₂×C₄⋊Dic₃	—	3	16	no	—
39	C₂×Dic₃⋊C₄	—	6	16	no	—
40	#870	—	3	32	no	—
41	#870	—	6	16	no	—
42	C₃×C₄×C₈	C₂×D₃	1	16	yes	—
43	#818	—	3	32	no	—
44	#817	—	3	32	no	—
45	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
46	C₂×C₃²×C₄	—	2	4	no	—
47	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
48	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
49	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
50	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
51	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
52	C₂×C₃⋊Dic₃	—	2	8	no	—
53	C₂×C₃⋊Dic₃	—	4	8	no	—
54	C₃²×C₈	C₂×Q₈	1	4	yes	—
55	C₃²×C₈	C₂×Q₈	1	4	yes	—
56	C₂×#125	—	9	2	no	—
57	#499	—	9	8	no	—
58	C₂×#107	—	9	2	no	—
59	C₂×#106	—	9	2	no	—
60	C₂×C₄×C₈	C₃⋊D₃	1	1	yes	characteristic
61	C₂²×C₃×C₄	D₁₂	1	8	yes	—
62	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
63	C₂²×Dic₃	—	6	16	no	—
64	C₂×C₃×C₈	Dic₆	1	16	yes	—
65	C₂×C₃×C₈	Dic₆	1	16	yes	—
66	C₂×C₃×C₈	C₂²×D₃	1	8	yes	—
67	C₂×C₃×C₈	C₂²×D₃	1	8	yes	—
68	C₃×C₄²	D₁₂	1	8	yes	—
69	C₃×C₄²	C₂²×D₃	1	8	yes	—
70	C₄⋊Dic₃	—	3	32	no	—
71	C₄⋊Dic₃	—	6	16	no	—
72	Dic₃⋊C₄	—	6	64	no	—
73	C₂²×C₃²	C₄⋊Q₈	1	2	yes	—
74	C₂²×C₃²	#135	1	4	yes	—
75	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
76	C₃²×C₄	—	2	4	no	—
77	C₃²×C₄	C₄⋊Q₈	1	2	yes	—
78	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
79	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
80	C₃⋊Dic₃	—	4	8	no	—
81	C₂²×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
82	C₂²×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
83	#125	—	9	8	no	—
84	#125	—	18	4	no	—
85	C₂×C₄⋊C₄	—	9	4	no	—
86	C₂×C₄⋊C₄	—	18	4	no	—
87	C₂×C₄²	C₂×C₃⋊D₃	1	1	yes	characteristic
88	#107	—	9	8	no	—
89	#106	—	9	8	no	—
90	C₄×C₈	C₂×C₃⋊D₃	1	4	yes	—
91	C₂³×C₃	C₂×D₁₂	1	4	yes	—
92	C₂×C₃×C₄	—	2	16	no	—
93	C₂×C₃×C₄	C₂×Dic₆	1	8	yes	—
94	C₂×C₃×C₄	C₂×Dic₆	1	8	yes	—
95	C₂×C₃×C₄	C₂×D₁₂	1	16	yes	—
96	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
97	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
98	C₂×Dic₃	—	6	32	no	—
99	C₂×Dic₃	—	12	32	no	—
100	C₃×C₈	C₂×Dic₆	1	16	yes	—
101	C₃×C₈	C₂×Dic₆	1	16	yes	—
102	C₂×C₃²	#499	1	4	yes	complemented
103	C₂×C₃²	C₂×C₄⋊Q₈	1	1	yes	characteristic
104	C₂×C₃²	C₂×#135	1	2	yes	—
105	C₂²×C₄	—	18	4	no	—
106	C₂²×C₄	C₄⋊(C₃⋊D₃)	1	2	yes	—
107	C₂²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
108	C₂×C₈	#634	1	4	yes	—
109	C₂×C₈	#634	1	4	yes	—
110	C₂×C₈	C₂²×C₃⋊D₃	1	2	yes	—
111	C₂×C₈	C₂²×C₃⋊D₃	1	2	yes	—
112	C₄⋊C₄	—	9	8	no	—
113	C₄⋊C₄	—	18	4	no	—
114	C₄⋊C₄	—	18	16	no	—
115	C₄²	C₄⋊(C₃⋊D₃)	1	2	yes	—
116	C₄²	C₂²×C₃⋊D₃	1	2	yes	—
117	C₂²×C₃	#869	1	8	yes	—
118	C₂²×C₃	#904	1	16	yes	—
119	C₂²×C₃	C₂²×D₁₂	1	4	yes	—
120	C₃×C₄	—	2	16	no	—
121	C₃×C₄	#869	1	8	yes	—
122	C₃×C₄	C₂²×Dic₆	1	4	yes	—
123	C₃×C₄	C₂²×Dic₆	1	4	yes	—
124	Dic₃	—	12	32	no	—
125	C₃²	C₂×#499	1	1	yes	characteristic, complemented, Sylow
126	C₂³	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
127	C₂×C₄	—	2	4	no	—
128	C₂×C₄	—	18	8	no	—
129	C₂×C₄	—	36	8	no	—
130	C₂×C₄	C₂×#634	1	2	yes	—
131	C₂×C₄	C₂×#634	1	2	yes	—
132	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	4	yes	—
133	C₂×C₄	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
134	C₂×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
135	C₈	C₂×#634	1	4	yes	—
136	C₈	C₂×#634	1	4	yes	—
137	C₂×C₃	#4683	1	16	yes	complemented
138	C₂×C₃	C₂×#869	1	4	yes	—
139	C₂×C₃	C₂×#904	1	8	yes	—
140	C₂²	#64078	1	2	yes	—
141	C₂²	#64113	1	4	yes	—
142	C₂²	C₂²×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
143	C₄	—	2	4	no	—
144	C₄	—	36	8	no	—
145	C₄	#64078	1	2	yes	—
146	C₄	C₂²×#634	1	1	yes	characteristic
147	C₄	C₂²×#634	1	1	yes	characteristic
148	C₃	C₂×#4683	1	4	yes	complemented
149	C₂	#10592382	1	4	yes	direct product factor
150	C₂	C₂×#64078	1	1	yes	characteristic
151	C₂	C₂×#64113	1	2	yes	—

	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×#499
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
5. #10592382	C₂	direct (N × H)
102. C₂×C₃²	#499	semidirect
125. C₃²	C₂×#499	semidirect
137. C₂×C₃	#4683	semidirect
148. C₃	C₂×#4683	semidirect
149. C₂	#10592382	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×#64079	2
C₂×C₃²×C₄×C₈	2
C₂×#63645	2
C₂×#63644	2
#10592382	2
C₂×#4683	3

Subgroups — C2×#10592382 #11874913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10592382 #11874913