Subgroups — C₂×Q₈×Dic₁₈ #11903718

Order 1152.

1668 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₈×Dic₉	C₂	1	2	yes	maximal
3	Q₈×Dic₁₈	C₂	1	16	yes	maximal, direct product factor
4	C₂×#63450	C₂	1	6	yes	maximal
5	C₂×#63431	C₂	1	3	yes	maximal
6	C₂×C₄×Dic₁₈	C₂	1	3	yes	maximal
7	C₂×Q₈×Dic₆	—	3	1	no	maximal
8	C₂²×Q₈×C₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₁₈	C₂²	1	6	yes	—
10	C₂²×Dic₁₈	C₂²	1	1	yes	characteristic
11	C₄×Q₈×C₉	C₂²	1	8	yes	—
12	C₂×C₉×C₄⋊C₄	C₂²	1	3	yes	—
13	C₂×C₄²×C₉	C₂²	1	3	yes	—
14	Q₈×Dic₉	C₂²	1	16	yes	—
15	C₂×C₄⋊Dic₉	C₂²	1	3	yes	—
16	C₂×C₄⋊Dic₉	C₂²	1	6	yes	—
17	C₂×Dic₉⋊C₄	C₂²	1	6	yes	—
18	C₂×C₄×Dic₉	C₂²	1	6	yes	—
19	#63450	C₂²	1	48	yes	—
20	#63431	C₂²	1	24	yes	—
21	C₄×Dic₁₈	C₂²	1	24	yes	—
22	C₂×C₃×C₄×Q₈	D₃	1	1	yes	characteristic
23	C₂×Q₈×Dic₃	—	3	2	no	—
24	Q₈×Dic₆	—	3	16	no	—
25	C₂×#888	—	3	6	no	—
26	C₂×#869	—	3	3	no	—
27	C₂×C₄×Dic₆	—	3	3	no	—
28	C₂×Q₈×C₉	Q₈	1	8	yes	complemented
29	C₂×Q₈×C₉	C₂³	1	4	yes	—
30	C₂²×C₄×C₉	C₂³	1	3	yes	—
31	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₉	C₂³	1	3	yes	—
33	C₂²×Dic₉	C₂³	1	6	yes	—
34	C₂²×Dic₉	C₂³	1	2	yes	—
35	C₂×Dic₁₈	—	4	12	no	—
36	C₂×Dic₁₈	Q₈	1	8	yes	direct product factor
37	C₂×Dic₁₈	C₂³	1	24	yes	—
38	C₂×Dic₁₈	C₂³	1	4	yes	—
39	C₉×C₄⋊C₄	C₂³	1	12	yes	—
40	C₄²×C₉	C₂³	1	12	yes	—
41	C₄⋊Dic₉	C₂³	1	24	yes	—
42	C₄⋊Dic₉	C₂³	1	12	yes	—
43	Dic₉⋊C₄	C₂³	1	24	yes	—
44	C₄×Dic₉	C₂³	1	24	yes	—
45	C₂×Q₈²	—	9	1	no	Sylow
46	C₂²×C₃×Q₈	C₂×D₃	1	1	yes	characteristic
47	C₂²×Dic₆	—	3	1	no	—
48	C₂²×Dic₆	—	3	6	no	—
49	C₃×C₄×Q₈	C₂×D₃	1	8	yes	—
50	C₂×C₃×C₄⋊C₄	C₂×D₃	1	3	yes	—
51	C₂×C₃×C₄²	C₂×D₃	1	3	yes	—
52	Q₈×Dic₃	—	3	16	no	—
53	C₂×C₄⋊Dic₃	—	3	3	no	—
54	C₂×C₄⋊Dic₃	—	3	6	no	—
55	C₂×Dic₃⋊C₄	—	3	6	no	—
56	C₂×C₄×Dic₃	—	3	6	no	—
57	#888	—	3	48	no	—
58	#869	—	3	24	no	—
59	C₄×Dic₆	—	3	24	no	—
60	C₂³×C₉	C₂⁴	1	1	yes	characteristic
61	Q₈×C₉	C₂×Q₈	1	16	yes	complemented
62	C₂×C₄×C₉	—	2	6	no	—
63	C₂×C₄×C₉	C₂×Q₈	1	12	yes	—
64	C₂×C₄×C₉	C₂×Q₈	1	4	yes	—
65	C₂×C₄×C₉	C₂⁴	1	6	yes	—
66	C₂×C₄×C₉	C₂⁴	1	6	yes	—
67	C₂×C₄×C₉	C₂⁴	1	2	yes	—
68	C₂×Dic₉	—	2	12	no	—
69	C₂×Dic₉	C₂×Q₈	1	8	yes	—
70	C₂×Dic₉	C₂⁴	1	12	yes	—
71	C₂×Dic₉	C₂⁴	1	4	yes	—
72	Dic₁₈	—	4	24	no	—
73	Dic₁₈	C₂×Q₈	1	16	yes	direct product factor
74	Q₈²	—	9	16	no	—
75	C₂×C₄⋊Q₈	—	9	6	no	—
76	C₂×C₄⋊Q₈	—	9	3	no	—
77	C₂×C₄×Q₈	—	9	2	no	—
78	C₂×C₄×Q₈	—	9	3	no	—
79	C₂×C₄×Q₈	D₉	1	1	yes	characteristic
80	C₂×C₃×Q₈	Dic₆	1	8	yes	—
81	C₂×C₃×Q₈	C₂²×D₃	1	4	yes	—
82	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
83	C₂²×C₃×C₄	C₂²×D₃	1	3	yes	—
84	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
85	C₂²×Dic₃	—	3	2	no	—
86	C₂²×Dic₃	—	3	6	no	—
87	C₂×Dic₆	—	3	8	no	—
88	C₂×Dic₆	—	3	4	no	—
89	C₂×Dic₆	—	3	24	no	—
90	C₂×Dic₆	—	12	12	no	—
91	C₃×C₄⋊C₄	C₂²×D₃	1	12	yes	—
92	C₃×C₄²	C₂²×D₃	1	12	yes	—
93	C₄⋊Dic₃	—	3	12	no	—
94	C₄⋊Dic₃	—	3	24	no	—
95	Dic₃⋊C₄	—	3	24	no	—
96	C₄×Dic₃	—	3	24	no	—
97	C₂²×C₉	C₂²×Q₈	1	2	yes	—
98	C₂²×C₉	C₂²×Q₈	1	2	yes	—
99	C₂²×C₉	H(5,𝔽₂)	1	2	yes	—
100	C₂²×C₉	C₂⁵	1	1	yes	characteristic
101	C₄×C₉	—	2	6	no	—
102	C₄×C₉	C₂²×Q₈	1	12	yes	—
103	C₄×C₉	C₂²×Q₈	1	4	yes	—
104	Dic₉	—	2	12	no	—
105	Dic₉	C₂²×Q₈	1	8	yes	—
106	C₂²×Q₈	—	9	1	no	—
107	C₂²×Q₈	—	9	6	no	—
108	C₂²×Q₈	C₂×D₉	1	1	yes	characteristic
109	C₄⋊Q₈	—	9	48	no	—
110	C₄⋊Q₈	—	9	24	no	—
111	C₄×Q₈	—	9	16	no	—
112	C₄×Q₈	—	9	24	no	—
113	C₄×Q₈	C₂×D₉	1	8	yes	—
114	C₂×C₄⋊C₄	—	9	6	no	—
115	C₂×C₄⋊C₄	—	9	6	no	—
116	C₂×C₄⋊C₄	—	9	3	no	—
117	C₂×C₄⋊C₄	C₂×D₉	1	3	yes	—
118	C₂×C₄²	—	9	6	no	—
119	C₂×C₄²	C₂×D₉	1	3	yes	—
120	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
121	C₃×Q₈	C₂×Dic₆	1	16	yes	—
122	C₂×C₃×C₄	—	2	6	no	—
123	C₂×C₃×C₄	C₂×Dic₆	1	12	yes	—
124	C₂×C₃×C₄	D₃×Q₈	1	4	yes	—
125	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
126	C₂×C₃×C₄	C₂³×D₃	1	6	yes	—
127	C₂×C₃×C₄	C₂³×D₃	1	2	yes	—
128	C₂×Dic₃	—	3	8	no	—
129	C₂×Dic₃	—	3	4	no	—
130	C₂×Dic₃	—	3	12	no	—
131	C₂×Dic₃	—	6	12	no	—
132	Dic₆	—	3	16	no	—
133	Dic₆	—	12	24	no	—
134	C₂×C₉	Q₈²	1	4	yes	complemented
135	C₂×C₉	C₂³×Q₈	1	1	yes	characteristic
136	C₂×C₉	C₂³×Q₈	1	1	yes	characteristic
137	C₂×C₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
138	C₂×Q₈	—	9	8	no	—
139	C₂×Q₈	—	9	4	no	—
140	C₂×Q₈	—	9	24	no	—
141	C₂×Q₈	—	36	12	no	—
142	C₂×Q₈	Dic₁₈	1	8	yes	direct product factor
143	C₂×Q₈	C₂²×D₉	1	4	yes	—
144	C₂²×C₄	—	9	2	no	—
145	C₂²×C₄	—	9	6	no	—
146	C₂²×C₄	C₂²×D₉	1	3	yes	—
147	C₂²×C₄	C₂²×D₉	1	3	yes	—
148	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
149	C₄⋊C₄	—	9	24	no	—
150	C₄⋊C₄	—	9	24	no	—
151	C₄⋊C₄	—	9	12	no	—
152	C₄⋊C₄	C₂²×D₉	1	12	yes	—
153	C₄²	—	9	24	no	—
154	C₄²	C₂²×D₉	1	12	yes	—
155	C₂²×C₃	C₂²×Dic₆	1	2	yes	—
156	C₂²×C₃	C₂×D₃×Q₈	1	2	yes	—
157	C₂²×C₃	#1009	1	2	yes	—
158	C₂²×C₃	C₂⁴×D₃	1	1	yes	characteristic
159	C₃×C₄	—	2	6	no	—
160	C₃×C₄	C₂²×Dic₆	1	12	yes	—
161	C₃×C₄	C₂×D₃×Q₈	1	4	yes	—
162	Dic₃	—	3	8	no	—
163	Dic₃	—	6	12	no	—
164	C₉	C₂×Q₈²	1	1	yes	characteristic, complemented, Sylow
165	C₂³	C₂³×D₉	1	1	yes	characteristic
166	Q₈	—	9	16	no	—
167	Q₈	—	36	24	no	—
168	Q₈	C₂×Dic₁₈	1	16	yes	direct product factor
169	C₂×C₄	—	2	6	no	—
170	C₂×C₄	—	9	4	no	—
171	C₂×C₄	—	9	8	no	—
172	C₂×C₄	—	9	12	no	—
173	C₂×C₄	—	18	12	no	—
174	C₂×C₄	C₂×Dic₁₈	1	12	yes	—
175	C₂×C₄	Q₈×D₉	1	4	yes	—
176	C₂×C₄	C₂³×D₉	1	6	yes	—
177	C₂×C₄	C₂³×D₉	1	6	yes	—
178	C₂×C₄	C₂³×D₉	1	2	yes	—
179	C₂×C₃	Q₈×Dic₆	1	4	yes	—
180	C₂×C₃	C₂³×Dic₆	1	1	yes	characteristic
181	C₂×C₃	C₂²×D₃×Q₈	1	1	yes	characteristic
182	C₂×C₃	C₂×#1009	1	1	yes	characteristic
183	C₂²	C₂²×Dic₁₈	1	2	yes	—
184	C₂²	C₂×Q₈×D₉	1	2	yes	—
185	C₂²	#63715	1	2	yes	—
186	C₂²	C₂⁴×D₉	1	1	yes	characteristic
187	C₄	—	2	6	no	—
188	C₄	—	9	8	no	—
189	C₄	—	18	12	no	—
190	C₄	C₂²×Dic₁₈	1	12	yes	—
191	C₄	C₂×Q₈×D₉	1	4	yes	—
192	C₃	C₂×Q₈×Dic₆	1	1	yes	characteristic
193	C₂	Q₈×Dic₁₈	1	4	yes	direct product factor
194	C₂	C₂³×Dic₁₈	1	1	yes	characteristic
195	C₂	C₂²×Q₈×D₉	1	1	yes	characteristic
196	C₂	C₂×#63715	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₉
commutator, cosocle	C₂²×C₉	C₂⁵
Frattini	C₂²×C₃	C₂⁴×D₃
Fitting	C₂×C₄×Q₈×C₉	C₂
socle, prime radical	C₂³×C₃	C₂³×D₃
hypercenter	C₂×C₄×Q₈	D₉
hypocenter	C₉	C₂×Q₈²
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
3. Q₈×Dic₁₈	C₂	direct (N × H)
28. C₂×Q₈×C₉	Q₈	semidirect
36. C₂×Dic₁₈	Q₈	direct (N × H)
61. Q₈×C₉	C₂×Q₈	semidirect
73. Dic₁₈	C₂×Q₈	direct (N × H)
134. C₂×C₉	Q₈²	semidirect
142. C₂×Q₈	Dic₁₈	direct (N × H)
164. C₉	C₂×Q₈²	semidirect
168. Q₈	C₂×Dic₁₈	direct (N × H)
193. C₂	Q₈×Dic₁₈	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×C₄×Q₈×C₉	2
C₂×Q₈×Dic₉	2
Q₈×Dic₁₈	2
C₂×#63450	2
C₂×#63431	2
C₂×C₄×Dic₁₈	2
C₂×Q₈×Dic₆	3

Subgroups — C2×Q8×Dic18 #11903718

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×Dic₁₈ #11903718