Subgroups — C₂×#10588361 #11873392

Order 1152.

636 conjugacy classes of subgroups.

The subgroup lattice has 210 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63431	C₂	1	1	yes	maximal, characteristic
2	C₂×#63431	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×C₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#63376	C₂	1	4	yes	maximal
5	#10588361	C₂	1	8	yes	maximal, direct product factor
6	C₂×#4681	—	3	1	no	maximal
7	C₂²×Dic₁₈	—	2	1	no	—
8	C₂²×Dic₁₈	C₂²	1	2	yes	—
9	C₂²×C₈×C₉	C₂²	1	2	yes	—
10	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Dic₉	—	2	1	no	—
12	C₂×C₄⋊Dic₉	—	2	1	no	—
13	C₂×C₄⋊Dic₉	—	2	1	no	—
14	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
15	#63431	—	2	2	no	—
16	#63431	—	2	2	no	—
17	#63431	C₂²	1	4	yes	—
18	#63431	C₂²	1	4	yes	—
19	C₄×C₈×C₉	C₂²	1	4	yes	—
20	#63376	C₂²	1	16	yes	—
21	C₂×#869	—	3	1	no	—
22	C₂×#869	—	3	1	no	—
23	C₂×C₃×C₄×C₈	D₃	1	1	yes	characteristic
24	C₂×#816	—	3	4	no	—
25	#4681	—	3	8	no	—
26	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
27	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
28	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
29	C₂²×Dic₉	—	2	2	no	—
30	C₂²×Dic₉	—	2	2	no	—
31	C₂×Dic₁₈	—	2	8	no	—
32	C₂×Dic₁₈	—	2	2	no	—
33	C₂×Dic₁₈	—	2	4	no	—
34	C₂×Dic₁₈	—	4	4	no	—
35	C₂×Dic₁₈	C₂³	1	4	yes	—
36	C₂×C₈×C₉	—	2	4	no	—
37	C₂×C₈×C₉	C₂³	1	4	yes	—
38	C₄²×C₉	D₄	1	2	yes	—
39	C₄²×C₉	C₂³	1	2	yes	—
40	C₄⋊Dic₉	—	2	2	no	—
41	C₄⋊Dic₉	—	2	4	no	—
42	C₄⋊Dic₉	—	2	4	no	—
43	C₄⋊Dic₉	—	2	4	no	—
44	C₄⋊Dic₉	C₂³	1	4	yes	—
45	C₂×#487	—	9	1	no	Sylow
46	C₂²×Dic₆	—	3	2	no	—
47	C₂²×Dic₆	—	6	1	no	—
48	C₂²×C₃×C₈	C₂×D₃	1	2	yes	—
49	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
50	C₂×C₄⋊Dic₃	—	3	2	no	—
51	C₂×C₄⋊Dic₃	—	6	1	no	—
52	C₂×C₄⋊Dic₃	—	6	1	no	—
53	C₂×C₄⋊Dic₃	—	6	1	no	—
54	#869	—	3	4	no	—
55	#869	—	3	4	no	—
56	#869	—	6	2	no	—
57	#869	—	6	2	no	—
58	C₃×C₄×C₈	C₂×D₃	1	4	yes	—
59	#816	—	3	16	no	—
60	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄×C₉	SD₁₆	1	4	yes	—
62	C₂×C₄×C₉	Q₁₆	1	4	yes	—
63	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
64	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
65	C₂×C₄×C₉	C₂×D₄	1	2	yes	—
66	C₂×C₄×C₉	#41	1	4	yes	—
67	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
68	C₂×Dic₉	—	2	4	no	—
69	C₂×Dic₉	—	2	4	no	—
70	C₂×Dic₉	—	4	4	no	—
71	C₂×Dic₉	—	4	4	no	—
72	Dic₁₈	—	2	8	no	—
73	Dic₁₈	—	4	4	no	—
74	Dic₁₈	—	4	8	no	—
75	C₈×C₉	—	2	4	no	—
76	C₂×C₄⋊Q₈	—	9	1	no	—
77	C₂×C₄⋊Q₈	—	9	1	no	—
78	#487	—	9	8	no	—
79	C₂×#103	—	9	4	no	—
80	C₂×C₄×C₈	D₉	1	1	yes	characteristic
81	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
82	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
83	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
84	C₂²×Dic₃	—	6	2	no	—
85	C₂²×Dic₃	—	6	2	no	—
86	C₂×Dic₆	—	3	4	no	—
87	C₂×Dic₆	—	6	8	no	—
88	C₂×Dic₆	—	6	4	no	—
89	C₂×Dic₆	—	6	2	no	—
90	C₂×Dic₆	—	12	4	no	—
91	C₂×C₃×C₈	—	2	4	no	—
92	C₂×C₃×C₈	C₂²×D₃	1	4	yes	—
93	C₃×C₄²	D₁₂	1	2	yes	—
94	C₃×C₄²	C₂²×D₃	1	2	yes	—
95	C₄⋊Dic₃	—	3	4	no	—
96	C₄⋊Dic₃	—	6	4	no	—
97	C₄⋊Dic₃	—	6	4	no	—
98	C₄⋊Dic₃	—	6	4	no	—
99	C₄⋊Dic₃	—	6	2	no	—
100	C₂²×C₉	#124	1	2	yes	—
101	C₂²×C₉	C₂×SD₁₆	1	2	yes	—
102	C₂²×C₉	C₂×Q₁₆	1	2	yes	—
103	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
104	C₄×C₉	#124	1	2	yes	—
105	C₄×C₉	C₂×SD₁₆	1	4	yes	—
106	C₄×C₉	C₂×Q₁₆	1	4	yes	—
107	C₄×C₉	C₂×#41	1	2	yes	—
108	Dic₉	—	4	4	no	—
109	Dic₉	—	4	4	no	—
110	C₂²×Q₈	—	9	2	no	—
111	C₂²×Q₈	—	18	1	no	—
112	C₂²×C₈	C₂×D₉	1	2	yes	—
113	C₄⋊Q₈	—	9	4	no	—
114	C₄⋊Q₈	—	9	4	no	—
115	C₄⋊Q₈	—	18	2	no	—
116	C₄⋊Q₈	—	18	2	no	—
117	C₂×C₄⋊C₄	—	9	2	no	—
118	C₂×C₄⋊C₄	—	18	1	no	—
119	C₂×C₄⋊C₄	—	18	1	no	—
120	C₂×C₄⋊C₄	—	18	1	no	—
121	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
122	#103	—	9	16	no	—
123	C₄×C₈	C₂×D₉	1	4	yes	—
124	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
125	C₂×C₃×C₄	#204	1	4	yes	—
126	C₂×C₃×C₄	Dic₁₂	1	4	yes	—
127	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
128	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
129	C₂×C₃×C₄	C₂×D₁₂	1	2	yes	—
130	C₂×C₃×C₄	#235	1	4	yes	—
131	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
132	C₂×Dic₃	—	6	4	no	—
133	C₂×Dic₃	—	6	4	no	—
134	C₂×Dic₃	—	12	4	no	—
135	C₂×Dic₃	—	12	4	no	—
136	Dic₆	—	6	8	no	—
137	Dic₆	—	12	4	no	—
138	Dic₆	—	12	8	no	—
139	C₃×C₈	—	2	4	no	—
140	C₂×C₉	#487	1	4	yes	complemented
141	C₂×C₉	C₂×#124	1	1	yes	characteristic
142	C₂×C₉	C₂²×SD₁₆	1	1	yes	characteristic
143	C₂×C₉	C₂²×Q₁₆	1	1	yes	characteristic
144	C₂×Q₈	—	9	4	no	—
145	C₂×Q₈	—	18	4	no	—
146	C₂×Q₈	—	18	2	no	—
147	C₂×Q₈	—	18	8	no	—
148	C₂×Q₈	—	36	4	no	—
149	C₂²×C₄	—	18	2	no	—
150	C₂²×C₄	—	18	2	no	—
151	C₂²×C₄	D₃₆	1	1	yes	characteristic
152	C₂²×C₄	D₃₆	1	1	yes	characteristic
153	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
154	C₂×C₈	—	2	4	no	—
155	C₂×C₈	C₂²×D₉	1	4	yes	—
156	C₄⋊C₄	—	9	4	no	—
157	C₄⋊C₄	—	18	2	no	—
158	C₄⋊C₄	—	18	4	no	—
159	C₄⋊C₄	—	18	4	no	—
160	C₄⋊C₄	—	18	4	no	—
161	C₄²	D₃₆	1	2	yes	—
162	C₄²	C₂²×D₉	1	2	yes	—
163	C₂²×C₃	#875	1	2	yes	—
164	C₂²×C₃	C₂×#204	1	2	yes	—
165	C₂²×C₃	C₂×Dic₁₂	1	2	yes	—
166	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
167	C₃×C₄	#875	1	2	yes	—
168	C₃×C₄	C₂×#204	1	4	yes	—
169	C₃×C₄	C₂×Dic₁₂	1	4	yes	—
170	C₃×C₄	C₂×#235	1	2	yes	—
171	Dic₃	—	12	4	no	—
172	Dic₃	—	12	4	no	—
173	C₉	C₂×#487	1	1	yes	characteristic, complemented, Sylow
174	C₂³	C₂×D₃₆	1	1	yes	characteristic
175	Q₈	—	18	8	no	—
176	Q₈	—	36	4	no	—
177	Q₈	—	36	8	no	—
178	C₂×C₄	—	18	4	no	—
179	C₂×C₄	—	18	4	no	—
180	C₂×C₄	—	36	4	no	—
181	C₂×C₄	—	36	4	no	—
182	C₂×C₄	Dic₃₆	1	4	yes	—
183	C₂×C₄	#3664	1	4	yes	—
184	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
185	C₂×C₄	C₂×D₃₆	1	2	yes	—
186	C₂×C₄	C₂×D₃₆	1	2	yes	—
187	C₂×C₄	#3697	1	4	yes	—
188	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
189	C₈	—	2	4	no	—
190	C₂×C₃	#4681	1	4	yes	—
191	C₂×C₃	C₂×#875	1	1	yes	characteristic
192	C₂×C₃	C₂²×#204	1	1	yes	characteristic
193	C₂×C₃	C₂²×Dic₁₂	1	1	yes	characteristic
194	C₂²	#63437	1	2	yes	—
195	C₂²	C₂×Dic₃₆	1	2	yes	—
196	C₂²	C₂×#3664	1	2	yes	—
197	C₂²	C₂²×D₃₆	1	1	yes	characteristic
198	C₄	—	36	4	no	—
199	C₄	—	36	4	no	—
200	C₄	#63437	1	2	yes	—
201	C₄	C₂×Dic₃₆	1	4	yes	—
202	C₄	C₂×#3664	1	4	yes	—
203	C₄	C₂×#3697	1	2	yes	—
204	C₃	C₂×#4681	1	1	yes	characteristic
205	C₂	#10588361	1	4	yes	direct product factor
206	C₂	C₂×#63437	1	1	yes	characteristic
207	C₂	C₂²×Dic₃₆	1	1	yes	characteristic
208	C₂	C₂²×#3664	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₃₆
commutator, cosocle	C₂×C₄×C₉	C₂⁴
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂×C₄×C₈×C₉	C₂
socle, prime radical	C₂³×C₃	C₂×D₁₂
hypercenter	C₂×C₄×C₈	D₉
hypocenter	C₉	C₂×#487
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
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. #10588361	C₂	direct (N × H)
140. C₂×C₉	#487	semidirect
173. C₉	C₂×#487	semidirect
205. C₂	#10588361	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×#63431	2
C₂×C₄×C₈×C₉	2
C₂×#63376	2
#10588361	2
C₂×#4681	3

Subgroups — C2×#10588361 #11873392

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10588361 #11873392