Subgroups — C₂×#10589332 #11795915

Order 1152.

504 conjugacy classes of subgroups.

The subgroup lattice has 150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#97	C₂	1	1	yes	maximal, characteristic
2	C₂×#63639	C₂	1	2	yes	maximal
3	#10589332	C₂	1	4	yes	maximal, direct product factor
4	C₂×#4466	—	3	4	no	maximal
5	C₂²×C₃²×C₈	C₄	1	1	yes	characteristic
6	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
7	C₂×C₃²×C₄²	C₄	1	1	yes	characteristic
8	C₃²×#97	C₄	1	2	yes	—
9	C₃²×#97	C₂²	1	2	yes	—
10	#63639	C₄	1	4	yes	complemented
11	#63639	C₂²	1	4	yes	—
12	C₂×C₃⋊(C₃⋊C₁₆)	C₄	1	4	yes	complemented
13	C₂×C₃×#97	D₃	1	4	yes	—
14	C₂×#812	—	3	8	no	—
15	#4466	—	3	16	no	—
16	C₂²×C₃²×C₄	—	2	1	no	—
17	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
18	C₂×C₃²×C₈	—	2	1	no	—
19	C₂×C₃²×C₈	—	2	1	no	—
20	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
21	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
22	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
23	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
24	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
25	C₃²×C₄²	—	2	1	no	—
26	C₃²×C₄²	C₂×C₄	1	2	yes	—
27	C₃⋊(C₃⋊C₁₆)	C₂×C₄	1	8	yes	complemented
28	C₂×#347	—	9	1	no	Sylow
29	C₂²×C₃×C₈	Dic₃	1	4	yes	—
30	C₂²×C₃×C₈	C₂×D₃	1	4	yes	—
31	C₂×C₃×C₄²	Dic₃	1	4	yes	—
32	C₃×#97	Dic₃	1	8	yes	—
33	C₃×#97	C₂×D₃	1	8	yes	—
34	#812	—	3	16	no	—
35	#812	—	3	16	no	—
36	C₂×C₃⋊C₁₆	—	3	16	no	—
37	C₂³×C₃²	M₁₆	1	1	yes	characteristic
38	C₂×C₃²×C₄	—	2	2	no	—
39	C₂×C₃²×C₄	—	4	2	no	—
40	C₂×C₃²×C₄	C₄²	1	1	yes	characteristic
41	C₂×C₃²×C₄	C₄²	1	1	yes	characteristic
42	C₂×C₃²×C₄	M₁₆	1	1	yes	characteristic
43	C₂×C₃²×C₄	M₁₆	1	1	yes	characteristic
44	C₂×C₃²×C₄	M₁₆	1	1	yes	characteristic
45	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
46	C₃²×C₈	—	2	2	no	—
47	C₃²×C₈	C₄²	1	2	yes	—
48	C₃²×C₈	C₂²×C₄	1	2	yes	—
49	C₂×M₃₂	—	9	2	no	—
50	C₂×#97	C₃⋊D₃	1	1	yes	characteristic
51	#347	—	9	4	no	—
52	C₂²×C₃×C₄	—	2	4	no	—
53	C₂²×C₃×C₄	C₂×Dic₃	1	4	yes	—
54	C₂×C₃×C₈	—	2	4	no	—
55	C₂×C₃×C₈	—	2	4	no	—
56	C₂×C₃×C₈	C₄×D₃	1	8	yes	—
57	C₂×C₃×C₈	C₄×D₃	1	8	yes	—
58	C₂×C₃×C₈	C₂×Dic₃	1	8	yes	—
59	C₂×C₃×C₈	C₂×Dic₃	1	4	yes	—
60	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
61	C₃×C₄²	—	2	4	no	—
62	C₃×C₄²	C₂×Dic₃	1	8	yes	—
63	C₃⋊C₁₆	—	3	32	no	—
64	C₂²×C₃²	—	2	2	no	—
65	C₂²×C₃²	#97	1	1	yes	characteristic
66	C₂²×C₃²	#97	1	1	yes	characteristic
67	C₂²×C₃²	C₂×M₁₆	1	1	yes	characteristic
68	C₃²×C₄	—	4	2	no	—
69	C₃²×C₄	#97	1	1	yes	characteristic
70	C₃²×C₄	#97	1	1	yes	characteristic
71	C₃²×C₄	C₂×C₄²	1	1	yes	characteristic
72	C₃²×C₄	C₂×M₁₆	1	1	yes	characteristic
73	C₂²×C₈	C₃⋊Dic₃	1	1	yes	characteristic
74	C₂²×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
75	C₂×C₄²	C₃⋊Dic₃	1	1	yes	characteristic
76	M₃₂	—	9	4	no	—
77	M₃₂	—	9	4	no	—
78	C₂×C₁₆	—	9	4	no	—
79	#97	C₃⋊Dic₃	1	2	yes	—
80	#97	C₂×C₃⋊D₃	1	2	yes	—
81	C₂³×C₃	#208	1	4	yes	—
82	C₂×C₃×C₄	—	2	8	no	—
83	C₂×C₃×C₄	—	4	8	no	—
84	C₂×C₃×C₄	#208	1	4	yes	—
85	C₂×C₃×C₄	#208	1	4	yes	—
86	C₂×C₃×C₄	#208	1	4	yes	—
87	C₂×C₃×C₄	C₄×Dic₃	1	4	yes	—
88	C₂×C₃×C₄	C₄×Dic₃	1	4	yes	—
89	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
90	C₃×C₈	—	2	8	no	—
91	C₃×C₈	C₄×Dic₃	1	8	yes	—
92	C₃×C₈	C₂×C₄×D₃	1	8	yes	—
93	C₂×C₃²	—	2	1	no	—
94	C₂×C₃²	—	2	1	no	—
95	C₂×C₃²	#347	1	2	yes	complemented
96	C₂×C₃²	C₂×#97	1	1	yes	characteristic
97	C₂²×C₄	—	2	1	no	—
98	C₂²×C₄	C₂×C₃⋊Dic₃	1	1	yes	characteristic
99	C₂×C₈	—	2	1	no	—
100	C₂×C₈	—	2	1	no	—
101	C₂×C₈	C₄×C₃⋊D₃	1	2	yes	—
102	C₂×C₈	C₄×C₃⋊D₃	1	2	yes	—
103	C₂×C₈	C₂×C₃⋊Dic₃	1	2	yes	—
104	C₂×C₈	C₂×C₃⋊Dic₃	1	1	yes	characteristic
105	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
106	C₄²	—	2	1	no	—
107	C₄²	C₂×C₃⋊Dic₃	1	2	yes	—
108	C₁₆	—	9	8	no	—
109	C₂²×C₃	—	2	8	no	—
110	C₂²×C₃	#803	1	4	yes	—
111	C₂²×C₃	#803	1	4	yes	—
112	C₂²×C₃	C₂×#208	1	4	yes	—
113	C₃×C₄	—	4	8	no	—
114	C₃×C₄	#803	1	4	yes	—
115	C₃×C₄	#803	1	4	yes	—
116	C₃×C₄	C₂×#208	1	4	yes	—
117	C₃×C₄	C₂×C₄×Dic₃	1	4	yes	—
118	C₃²	C₂×#347	1	1	yes	characteristic, complemented, Sylow
119	C₂³	#3748	1	1	yes	characteristic
120	C₂×C₄	—	2	2	no	—
121	C₂×C₄	—	4	2	no	—
122	C₂×C₄	#3748	1	1	yes	characteristic
123	C₂×C₄	#3748	1	1	yes	characteristic
124	C₂×C₄	#3748	1	1	yes	characteristic
125	C₂×C₄	C₄×C₃⋊Dic₃	1	1	yes	characteristic
126	C₂×C₄	C₄×C₃⋊Dic₃	1	1	yes	characteristic
127	C₂×C₄	C₂²×C₃⋊Dic₃	1	1	yes	characteristic
128	C₈	—	2	2	no	—
129	C₈	C₄×C₃⋊Dic₃	1	2	yes	—
130	C₈	C₂×C₄×C₃⋊D₃	1	2	yes	—
131	C₂×C₃	—	2	4	no	—
132	C₂×C₃	—	2	4	no	—
133	C₂×C₃	#4466	1	8	yes	complemented
134	C₂×C₃	C₂×#803	1	4	yes	—
135	C₂²	—	2	2	no	—
136	C₂²	#63630	1	1	yes	characteristic
137	C₂²	#63630	1	1	yes	characteristic
138	C₂²	C₂×#3748	1	1	yes	characteristic
139	C₄	—	4	2	no	—
140	C₄	#63630	1	1	yes	characteristic
141	C₄	#63630	1	1	yes	characteristic
142	C₄	C₂×#3748	1	1	yes	characteristic
143	C₄	C₂×C₄×C₃⋊Dic₃	1	1	yes	characteristic
144	C₃	C₂×#4466	1	4	yes	complemented
145	C₂	—	2	1	no	—
146	C₂	—	2	1	no	—
147	C₂	#10589332	1	2	yes	direct product factor
148	C₂	C₂×#63630	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×C₃⋊Dic₃
commutator	C₃²×C₄	C₂×C₄²
Frattini	C₂×C₈	C₂²×C₃⋊D₃
Fitting	C₂×C₃²×#97	C₂
socle	C₂²×C₃²	#97
prime radical	C₂³×C₃²	M₁₆
cosocle	C₂×C₃²×C₈	C₂³
hypercenter	C₂×#97	C₃⋊D₃
hypocenter	C₃²	C₂×#347
LCS	G ▷ C₃²×C₄ ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97

Complements

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

N	H ≅ G/N	type
3. #10589332	C₂	direct (N × H)
10. #63639	C₄	semidirect
12. C₂×C₃⋊(C₃⋊C₁₆)	C₄	semidirect
27. C₃⋊(C₃⋊C₁₆)	C₂×C₄	semidirect
95. C₂×C₃²	#347	semidirect
118. C₃²	C₂×#347	semidirect
133. C₂×C₃	#4466	semidirect
144. C₃	C₂×#4466	semidirect
147. C₂	#10589332	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×C₃²×#97	2
C₂×#63639	2
#10589332	2
C₂×#4466	3

Subgroups — C2×#10589332 #11795915

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10589332 #11795915