Subgroups — C₂×#10592883 #11860105

Order 1152.

1440 conjugacy classes of subgroups.

The subgroup lattice has 207 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×Q₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×C₃⋊Dic₃	C₂	1	2	yes	maximal
3	C₂×#63662	C₂	1	2	yes	maximal
4	#10592883	C₂	1	8	yes	maximal, direct product factor
5	C₂×#63644	C₂	1	1	yes	maximal, characteristic
6	C₂×#63642	C₂	1	1	yes	maximal, characteristic
7	C₂×#5184	—	3	4	no	maximal
8	C₂²×C₃²×Q₈	C₂²	1	2	yes	—
9	C₂×C₃²×Q₁₆	C₄	1	8	yes	complemented
10	C₂×C₃²×Q₁₆	C₂²	1	4	yes	—
11	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
12	Q₈×C₃⋊Dic₃	—	2	4	no	—
13	Q₈×C₃⋊Dic₃	C₂²	1	8	yes	—
14	C₂×C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
15	C₂×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
16	C₂×C₄×C₃⋊Dic₃	—	2	2	no	—
17	C₂×C₄×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
18	C₂²×C₃⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
19	#63662	C₂²	1	8	yes	—
20	#63644	C₂²	1	4	yes	—
21	#63642	C₂²	1	4	yes	—
22	C₂²×C₃×Q₁₆	D₃	1	4	yes	—
23	C₂×Q₈×Dic₃	—	3	8	no	—
24	C₂×#835	—	3	8	no	—
25	#5184	—	3	32	no	—
26	C₂×#817	—	3	4	no	—
27	C₂×#815	—	3	4	no	—
28	C₂×C₃²×Q₈	—	2	2	no	—
29	C₂×C₃²×Q₈	—	2	4	no	—
30	C₂×C₃²×Q₈	C₂×C₄	1	8	yes	—
31	C₂×C₃²×Q₈	C₂³	1	4	yes	—
32	C₂²×C₃²×C₄	—	2	2	no	—
33	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
34	C₂²×C₃⋊Dic₃	—	2	2	no	—
35	C₂²×C₃⋊Dic₃	D₄	1	2	yes	—
36	C₃²×Q₁₆	C₂×C₄	1	16	yes	complemented
37	C₂×C₃²×C₈	C₂×C₄	1	4	yes	—
38	C₂×C₃²×C₈	C₂³	1	2	yes	—
39	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
40	C₄⋊(C₃⋊Dic₃)	—	2	8	no	—
41	C₄⋊(C₃⋊Dic₃)	C₂³	1	4	yes	—
42	C₄×C₃⋊Dic₃	—	2	8	no	—
43	C₄×C₃⋊Dic₃	D₄	1	2	yes	—
44	C₄×C₃⋊Dic₃	C₂³	1	2	yes	—
45	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
46	C₂×C₃⋊(C₃⋊C₈)	C₂³	1	2	yes	—
47	C₂×#441	—	9	1	no	Sylow
48	C₂²×C₃×Q₈	C₂×D₃	1	8	yes	—
49	C₂×C₃×Q₁₆	Dic₃	1	32	yes	complemented
50	C₂×C₃×Q₁₆	C₂×D₃	1	16	yes	—
51	C₂²×C₃×C₈	C₂×D₃	1	4	yes	—
52	Q₈×Dic₃	—	3	32	no	—
53	Q₈×Dic₃	—	6	16	no	—
54	C₂×C₄⋊Dic₃	—	3	8	no	—
55	C₂×C₄⋊Dic₃	—	6	8	no	—
56	C₂×C₄×Dic₃	—	3	4	no	—
57	C₂×C₄×Dic₃	—	6	8	no	—
58	C₂²×C₃⋊C₈	—	3	4	no	—
59	#835	—	3	32	no	—
60	#817	—	3	16	no	—
61	#815	—	3	16	no	—
62	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
63	C₃²×Q₈	—	2	8	no	—
64	C₃²×Q₈	—	2	4	no	—
65	C₃²×Q₈	C₂²×C₄	1	8	yes	—
66	C₂×C₃²×C₄	—	2	8	no	—
67	C₂×C₃²×C₄	—	2	4	no	—
68	C₂×C₃²×C₄	C₂²×C₄	1	2	yes	—
69	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
70	C₂×C₃²×C₄	#41	1	2	yes	—
71	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
72	C₂×C₃⋊Dic₃	—	2	4	no	—
73	C₂×C₃⋊Dic₃	—	2	4	no	—
74	C₂×C₃⋊Dic₃	—	4	4	no	—
75	C₂×C₃⋊Dic₃	C₂×D₄	1	4	yes	—
76	C₃²×C₈	C₂²×C₄	1	4	yes	—
77	C₃⋊(C₃⋊C₈)	—	2	2	no	—
78	C₂²×Q₁₆	C₃⋊D₃	1	1	yes	characteristic
79	C₂×C₄×Q₈	—	9	2	no	—
80	#441	—	9	8	no	—
81	C₂×#106	—	9	1	no	—
82	C₂×#103	—	9	2	no	—
83	C₂×#97	—	9	1	no	—
84	C₂×C₃×Q₈	—	2	8	no	—
85	C₂×C₃×Q₈	—	2	16	no	—
86	C₂×C₃×Q₈	C₂×Dic₃	1	32	yes	—
87	C₂×C₃×Q₈	C₂²×D₃	1	16	yes	—
88	C₂²×C₃×C₄	—	2	8	no	—
89	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
90	C₂²×Dic₃	—	3	8	no	—
91	C₂²×Dic₃	—	6	8	no	—
92	C₃×Q₁₆	C₂×Dic₃	1	64	yes	complemented
93	C₂×C₃×C₈	C₂×Dic₃	1	16	yes	—
94	C₂×C₃×C₈	C₂²×D₃	1	8	yes	—
95	C₄⋊Dic₃	—	3	16	no	—
96	C₄⋊Dic₃	—	6	32	no	—
97	C₄⋊Dic₃	—	6	8	no	—
98	C₄×Dic₃	—	3	8	no	—
99	C₄×Dic₃	—	3	8	no	—
100	C₄×Dic₃	—	6	32	no	—
101	C₂×C₃⋊C₈	—	3	8	no	—
102	C₂×C₃⋊C₈	—	6	8	no	—
103	C₂²×C₃²	C₄×D₄	1	2	yes	—
104	C₂²×C₃²	#137	1	4	yes	—
105	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
106	C₃²×C₄	—	2	8	no	—
107	C₃²×C₄	C₄×D₄	1	2	yes	—
108	C₃²×C₄	C₂³×C₄	1	1	yes	characteristic
109	C₃²×C₄	C₂×#41	1	1	yes	characteristic
110	C₃⋊Dic₃	—	2	4	no	—
111	C₃⋊Dic₃	—	4	4	no	—
112	C₂²×Q₈	C₂×C₃⋊D₃	1	2	yes	—
113	C₂×Q₁₆	C₃⋊Dic₃	1	8	yes	complemented
114	C₂×Q₁₆	C₂×C₃⋊D₃	1	4	yes	—
115	C₂²×C₈	—	9	1	no	—
116	C₂²×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
117	C₄×Q₈	—	9	8	no	—
118	C₄×Q₈	—	18	4	no	—
119	C₂×C₄⋊C₄	—	9	2	no	—
120	C₂×C₄⋊C₄	—	18	2	no	—
121	C₂×C₄²	—	9	1	no	—
122	C₂×C₄²	—	18	2	no	—
123	#106	—	9	4	no	—
124	#103	—	9	8	no	—
125	#97	—	9	4	no	—
126	C₂³×C₃	D₃×D₄	1	4	yes	—
127	C₃×Q₈	—	2	32	no	—
128	C₃×Q₈	—	2	16	no	—
129	C₃×Q₈	C₂²×Dic₃	1	32	yes	—
130	C₂×C₃×C₄	—	2	32	no	—
131	C₂×C₃×C₄	—	2	16	no	—
132	C₂×C₃×C₄	D₃×D₄	1	4	yes	—
133	C₂×C₃×C₄	#237	1	8	yes	—
134	C₂×C₃×C₄	C₂²×Dic₃	1	8	yes	—
135	C₂×C₃×C₄	C₂³×D₃	1	4	yes	—
136	C₂×Dic₃	—	3	16	no	—
137	C₂×Dic₃	—	6	16	no	—
138	C₂×Dic₃	—	6	16	no	—
139	C₂×Dic₃	—	12	16	no	—
140	C₃×C₈	C₂²×Dic₃	1	16	yes	—
141	C₃⋊C₈	—	6	8	no	—
142	C₂×C₃²	#441	1	4	yes	complemented
143	C₂×C₃²	C₂×C₄×D₄	1	1	yes	characteristic
144	C₂×C₃²	C₂×#137	1	2	yes	—
145	C₂×Q₈	—	2	2	no	—
146	C₂×Q₈	—	2	4	no	—
147	C₂×Q₈	C₂×C₃⋊Dic₃	1	8	yes	—
148	C₂×Q₈	C₂²×C₃⋊D₃	1	4	yes	—
149	C₂²×C₄	—	2	2	no	—
150	C₂²×C₄	—	9	2	no	—
151	C₂²×C₄	—	18	2	no	—
152	C₂²×C₄	C₂²×C₃⋊D₃	1	1	yes	characteristic
153	Q₁₆	C₂×C₃⋊Dic₃	1	16	yes	complemented
154	C₂×C₈	—	9	2	no	—
155	C₂×C₈	—	18	2	no	—
156	C₂×C₈	C₂×C₃⋊Dic₃	1	4	yes	—
157	C₂×C₈	C₂²×C₃⋊D₃	1	2	yes	—
158	C₄⋊C₄	—	9	4	no	—
159	C₄⋊C₄	—	18	8	no	—
160	C₄⋊C₄	—	18	2	no	—
161	C₄²	—	9	2	no	—
162	C₄²	—	9	2	no	—
163	C₄²	—	18	8	no	—
164	C₂²×C₃	#918	1	16	yes	—
165	C₂²×C₃	D₄×Dic₃	1	8	yes	—
166	C₂²×C₃	C₂×D₃×D₄	1	4	yes	—
167	C₃×C₄	—	2	32	no	—
168	C₃×C₄	D₄×Dic₃	1	8	yes	—
169	C₃×C₄	C₂×#237	1	4	yes	—
170	C₃×C₄	C₂³×Dic₃	1	4	yes	—
171	Dic₃	—	6	16	no	—
172	Dic₃	—	12	16	no	—
173	C₃²	C₂×#441	1	1	yes	characteristic, complemented, Sylow
174	C₂³	D₄×C₃⋊D₃	1	1	yes	characteristic
175	Q₈	—	2	4	no	—
176	Q₈	—	2	8	no	—
177	Q₈	C₂²×C₃⋊Dic₃	1	8	yes	—
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	2	8	no	—
180	C₂×C₄	—	9	4	no	—
181	C₂×C₄	—	18	4	no	—
182	C₂×C₄	—	18	4	no	—
183	C₂×C₄	—	36	4	no	—
184	C₂×C₄	D₄×C₃⋊D₃	1	1	yes	characteristic
185	C₂×C₄	#3830	1	2	yes	—
186	C₂×C₄	C₂²×C₃⋊Dic₃	1	2	yes	—
187	C₂×C₄	C₂³×C₃⋊D₃	1	1	yes	characteristic
188	C₈	—	18	2	no	—
189	C₈	C₂²×C₃⋊Dic₃	1	4	yes	—
190	C₂×C₃	#5184	1	16	yes	complemented
191	C₂×C₃	C₂×#918	1	8	yes	—
192	C₂×C₃	C₂×D₄×Dic₃	1	4	yes	—
193	C₂²	#64127	1	4	yes	—
194	C₂²	D₄×C₃⋊Dic₃	1	2	yes	—
195	C₂²	C₂×D₄×C₃⋊D₃	1	1	yes	characteristic
196	C₄	—	2	8	no	—
197	C₄	—	18	4	no	—
198	C₄	—	36	4	no	—
199	C₄	D₄×C₃⋊Dic₃	1	2	yes	—
200	C₄	C₂×#3830	1	1	yes	characteristic
201	C₄	C₂³×C₃⋊Dic₃	1	1	yes	characteristic
202	C₃	C₂×#5184	1	4	yes	complemented
203	C₂	#10592883	1	4	yes	direct product factor
204	C₂	C₂×#64127	1	2	yes	—
205	C₂	C₂×D₄×C₃⋊Dic₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₄×C₃⋊D₃
commutator	C₃²×C₄	C₂³×C₄
Frattini	C₂×C₄	C₂³×C₃⋊D₃
Fitting	C₂²×C₃²×Q₁₆	C₂
socle, prime radical	C₂³×C₃²	C₂×D₄
cosocle	C₂×C₃²×C₄	C₂⁴
hypercenter	C₂²×Q₁₆	C₃⋊D₃
hypocenter	C₃²	C₂×#441
LCS	G ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×Q₁₆

Complements

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

N	H ≅ G/N	type
4. #10592883	C₂	direct (N × H)
9. C₂×C₃²×Q₁₆	C₄	semidirect
36. C₃²×Q₁₆	C₂×C₄	semidirect
49. C₂×C₃×Q₁₆	Dic₃	semidirect
92. C₃×Q₁₆	C₂×Dic₃	semidirect
113. C₂×Q₁₆	C₃⋊Dic₃	semidirect
142. C₂×C₃²	#441	semidirect
153. Q₁₆	C₂×C₃⋊Dic₃	semidirect
173. C₃²	C₂×#441	semidirect
190. C₂×C₃	#5184	semidirect
202. C₃	C₂×#5184	semidirect
203. C₂	#10592883	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃²×Q₁₆	2
C₂×Q₈×C₃⋊Dic₃	2
C₂×#63662	2
#10592883	2
C₂×#63644	2
C₂×#63642	2
C₂×#5184	3

Subgroups — C2×#10592883 #11860105

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10592883 #11860105