Subgroups — C₂×#10589360 #11797095

Order 1152.

456 conjugacy classes of subgroups.

The subgroup lattice has 171 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃²×#108	C₂	1	1	yes	maximal, characteristic
2	C₂×#63644	C₂	1	1	yes	maximal, characteristic
3	C₂×#63639	C₂	1	1	yes	maximal, characteristic
4	#10589360	C₂	1	4	yes	maximal, direct product factor
5	C₂×#4494	—	3	4	no	maximal
6	C₂×C₃²×M₁₆	—	2	1	no	—
7	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
9	C₃²×#108	—	2	1	no	—
10	C₃²×#108	C₂²	1	2	yes	—
11	#63644	—	2	1	no	—
12	#63644	C₂²	1	2	yes	—
13	#63639	C₄	1	2	yes	complemented
14	#63639	C₂²	1	2	yes	—
15	C₂×C₃⋊(C₃⋊C₁₆)	C₄	1	2	yes	complemented
16	C₂×C₃×#108	D₃	1	4	yes	—
17	C₂×#817	—	3	4	no	—
18	C₂×#812	—	3	4	no	—
19	#4494	—	3	16	no	—
20	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
21	C₂²×C₃⋊Dic₃	—	4	1	no	—
22	C₃²×M₁₆	—	2	2	no	—
23	C₃²×M₁₆	—	4	1	no	—
24	C₂×C₃²×C₈	—	4	1	no	—
25	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
26	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
27	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
28	C₂×C₃²×C₈	Q₈	1	1	yes	characteristic
29	C₂×C₃²×C₈	Q₈	1	1	yes	characteristic
30	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
31	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
32	C₄⋊(C₃⋊Dic₃)	—	4	1	no	—
33	C₃⋊(C₃⋊C₁₆)	C₂×C₄	1	4	yes	complemented
34	C₂×#365	—	9	1	no	Sylow
35	C₂×C₃×M₁₆	—	2	4	no	—
36	C₂²×C₃×C₈	C₂×D₃	1	4	yes	—
37	C₂×C₄⋊Dic₃	—	6	4	no	—
38	C₃×#108	—	2	4	no	—
39	C₃×#108	C₂×D₃	1	8	yes	—
40	#817	—	3	8	no	—
41	#817	—	6	4	no	—
42	#812	—	3	8	no	—
43	#812	—	3	8	no	—
44	C₂×C₃⋊C₁₆	—	3	8	no	—
45	C₂³×C₃²	SD₁₆	1	1	yes	characteristic
46	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
47	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
48	C₂×C₃²×C₄	SD₁₆	1	1	yes	characteristic
49	C₂×C₃²×C₄	SD₁₆	1	1	yes	characteristic
50	C₂×C₃²×C₄	SD₁₆	1	1	yes	characteristic
51	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
52	C₂×C₃⋊Dic₃	—	4	2	no	—
53	C₂×C₃⋊Dic₃	—	8	2	no	—
54	C₃²×C₈	—	4	2	no	—
55	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
56	C₃²×C₈	C₄⋊C₄	1	1	yes	characteristic
57	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
58	C₃²×C₈	C₂×Q₈	1	1	yes	characteristic
59	C₂×M₃₂	—	9	1	no	—
60	C₂×#108	C₃⋊D₃	1	1	yes	characteristic
61	C₂×#106	—	9	1	no	—
62	#365	—	9	4	no	—
63	C₂²×C₃×C₄	#67	1	4	yes	—
64	C₂²×Dic₃	—	12	4	no	—
65	C₃×M₁₆	—	2	8	no	—
66	C₃×M₁₆	—	4	4	no	—
67	C₂×C₃×C₈	—	4	4	no	—
68	C₂×C₃×C₈	Dic₆	1	4	yes	—
69	C₂×C₃×C₈	Dic₆	1	4	yes	—
70	C₂×C₃×C₈	C₄×D₃	1	4	yes	—
71	C₂×C₃×C₈	C₄×D₃	1	4	yes	—
72	C₂×C₃×C₈	#67	1	4	yes	—
73	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
74	C₄⋊Dic₃	—	6	8	no	—
75	C₄⋊Dic₃	—	12	4	no	—
76	C₃⋊C₁₆	—	3	16	no	—
77	C₂²×C₃²	—	2	2	no	—
78	C₂²×C₃²	#106	1	1	yes	characteristic
79	C₂²×C₃²	#106	1	1	yes	characteristic
80	C₂²×C₃²	C₂×SD₁₆	1	1	yes	characteristic
81	C₃²×C₄	#106	1	1	yes	characteristic
82	C₃²×C₄	#106	1	1	yes	characteristic
83	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
84	C₃²×C₄	C₂×SD₁₆	1	1	yes	characteristic
85	C₃⋊Dic₃	—	8	2	no	—
86	C₂×M₁₆	—	2	1	no	—
87	C₂²×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
88	C₂×C₄⋊C₄	—	18	1	no	—
89	M₃₂	—	9	2	no	—
90	M₃₂	—	9	2	no	—
91	C₂×C₁₆	—	9	2	no	—
92	#108	—	2	1	no	—
93	#108	C₂×C₃⋊D₃	1	2	yes	—
94	#106	—	9	2	no	—
95	#106	—	18	1	no	—
96	C₂³×C₃	#215	1	4	yes	—
97	C₂×C₃×C₄	Dic₃⋊C₄	1	4	yes	—
98	C₂×C₃×C₄	Dic₃⋊C₄	1	4	yes	—
99	C₂×C₃×C₄	#214	1	4	yes	—
100	C₂×C₃×C₄	#214	1	4	yes	—
101	C₂×C₃×C₄	#215	1	4	yes	—
102	C₂×C₃×C₄	C₂×#67	1	4	yes	—
103	C₂×Dic₃	—	12	8	no	—
104	C₂×Dic₃	—	24	8	no	—
105	C₃×C₈	—	4	8	no	—
106	C₃×C₈	Dic₃⋊C₄	1	4	yes	—
107	C₃×C₈	Dic₃⋊C₄	1	4	yes	—
108	C₃×C₈	C₂×Dic₆	1	4	yes	—
109	C₃×C₈	C₂×C₄×D₃	1	4	yes	—
110	C₂×C₃²	—	2	1	no	—
111	C₂×C₃²	—	2	1	no	—
112	C₂×C₃²	#365	1	2	yes	complemented
113	C₂×C₃²	C₂×#106	1	1	yes	characteristic
114	C₂²×C₄	—	36	1	no	—
115	C₂²×C₄	#638	1	1	yes	characteristic
116	M₁₆	—	2	2	no	—
117	M₁₆	—	4	1	no	—
118	C₂×C₈	—	4	1	no	—
119	C₂×C₈	#634	1	1	yes	characteristic
120	C₂×C₈	#634	1	1	yes	characteristic
121	C₂×C₈	C₄×C₃⋊D₃	1	1	yes	characteristic
122	C₂×C₈	C₄×C₃⋊D₃	1	1	yes	characteristic
123	C₂×C₈	#638	1	1	yes	characteristic
124	C₂×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
125	C₄⋊C₄	—	18	2	no	—
126	C₄⋊C₄	—	36	1	no	—
127	C₁₆	—	9	4	no	—
128	C₂²×C₃	—	2	8	no	—
129	C₂²×C₃	#808	1	4	yes	—
130	C₂²×C₃	#808	1	4	yes	—
131	C₂²×C₃	C₂×#215	1	4	yes	—
132	C₃×C₄	#808	1	4	yes	—
133	C₃×C₄	#808	1	4	yes	—
134	C₃×C₄	C₂×Dic₃⋊C₄	1	4	yes	—
135	C₃×C₄	C₂×#214	1	4	yes	—
136	Dic₃	—	24	8	no	—
137	C₃²	C₂×#365	1	1	yes	characteristic, complemented, Sylow
138	C₂³	#3755	1	1	yes	characteristic
139	C₂×C₄	—	36	2	no	—
140	C₂×C₄	—	72	2	no	—
141	C₂×C₄	#3750	1	1	yes	characteristic
142	C₂×C₄	#3750	1	1	yes	characteristic
143	C₂×C₄	#3754	1	1	yes	characteristic
144	C₂×C₄	#3754	1	1	yes	characteristic
145	C₂×C₄	#3755	1	1	yes	characteristic
146	C₂×C₄	C₂×#638	1	1	yes	characteristic
147	C₈	—	4	2	no	—
148	C₈	#3750	1	1	yes	characteristic
149	C₈	#3750	1	1	yes	characteristic
150	C₈	C₂×#634	1	1	yes	characteristic
151	C₈	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
152	C₂×C₃	—	2	4	no	—
153	C₂×C₃	—	2	4	no	—
154	C₂×C₃	#4494	1	8	yes	complemented
155	C₂×C₃	C₂×#808	1	4	yes	—
156	C₂²	—	2	2	no	—
157	C₂²	#63635	1	1	yes	characteristic
158	C₂²	#63635	1	1	yes	characteristic
159	C₂²	C₂×#3755	1	1	yes	characteristic
160	C₄	—	72	2	no	—
161	C₄	#63635	1	1	yes	characteristic
162	C₄	#63635	1	1	yes	characteristic
163	C₄	C₂×#3750	1	1	yes	characteristic
164	C₄	C₂×#3754	1	1	yes	characteristic
165	C₃	C₂×#4494	1	4	yes	complemented
166	C₂	—	2	1	no	—
167	C₂	—	2	1	no	—
168	C₂	#10589360	1	2	yes	direct product factor
169	C₂	C₂×#63635	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#63635
commutator	C₃²×C₈	C₂²×C₄
Frattini	C₂×C₈	C₂²×C₃⋊D₃
Fitting	C₂×C₃²×#108	C₂
socle	C₂²×C₃²	#106
prime radical	C₂³×C₃²	SD₁₆
cosocle	C₂×C₃²×C₈	C₂³
hypercenter	C₂×#108	C₃⋊D₃
hypocenter	C₃²	C₂×#365
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#108

Complements

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

N	H ≅ G/N	type
4. #10589360	C₂	direct (N × H)
13. #63639	C₄	semidirect
15. C₂×C₃⋊(C₃⋊C₁₆)	C₄	semidirect
33. C₃⋊(C₃⋊C₁₆)	C₂×C₄	semidirect
112. C₂×C₃²	#365	semidirect
137. C₃²	C₂×#365	semidirect
154. C₂×C₃	#4494	semidirect
165. C₃	C₂×#4494	semidirect
168. C₂	#10589360	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×#108	2
C₂×#63644	2
C₂×#63639	2
#10589360	2
C₂×#4494	3

Subgroups — C2×#10589360 #11797095

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10589360 #11797095