Subgroups — C₂×#10588558 #11874909

Order 1152.

540 conjugacy classes of subgroups.

The subgroup lattice has 204 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63452	C₂	1	2	yes	maximal
2	C₂×C₉×#107	C₂	1	1	yes	maximal, characteristic
3	C₂×#63378	C₂	1	1	yes	maximal, characteristic
4	C₂×C₈×Dic₉	C₂	1	1	yes	maximal, characteristic
5	C₂×#63367	C₂	1	2	yes	maximal
6	#10588558	C₂	1	8	yes	maximal, direct product factor
7	C₂×#4878	—	3	1	no	maximal
8	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
9	C₂×C₉×C₄⋊C₄	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₉	—	2	2	no	—
11	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
12	C₂×Dic₉⋊C₄	—	2	2	no	—
13	C₂×C₄×Dic₉	C₂²	1	1	yes	characteristic
14	C₂²×C₉⋊C₈	C₂²	1	1	yes	characteristic
15	#63452	—	2	4	no	—
16	#63452	C₂²	1	8	yes	—
17	C₉×#107	C₂²	1	4	yes	—
18	#63378	C₂²	1	4	yes	—
19	C₈×Dic₉	C₂²	1	4	yes	—
20	#63367	C₂²	1	8	yes	—
21	C₂×#890	—	3	2	no	—
22	C₂×C₃×#107	D₃	1	1	yes	characteristic
23	C₂×#818	—	3	1	no	—
24	C₂×C₈×Dic₃	—	3	1	no	—
25	C₂×#808	—	3	2	no	—
26	#4878	—	3	8	no	—
27	C₂²×C₄×C₉	—	2	2	no	—
28	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
29	C₂²×Dic₉	—	2	2	no	—
30	C₂²×Dic₉	D₄	1	1	yes	characteristic
31	C₂²×Dic₉	D₄	1	1	yes	characteristic
32	C₂×C₈×C₉	Q₈	1	4	yes	—
33	C₂×C₈×C₉	C₂³	1	2	yes	—
34	C₉×C₄⋊C₄	—	2	2	no	—
35	C₉×C₄⋊C₄	C₂³	1	4	yes	—
36	C₄⋊Dic₉	—	2	2	no	—
37	C₄⋊Dic₉	—	2	8	no	—
38	C₄⋊Dic₉	C₂³	1	4	yes	—
39	Dic₉⋊C₄	—	2	8	no	—
40	C₄×Dic₉	D₄	1	2	yes	—
41	C₄×Dic₉	C₂³	1	2	yes	—
42	C₂×C₉⋊C₈	Q₈	1	4	yes	—
43	C₂×C₉⋊C₈	C₂³	1	2	yes	—
44	C₂×#499	—	9	1	no	Sylow
45	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
46	C₂×C₃×C₄⋊C₄	C₂×D₃	1	2	yes	—
47	C₂×C₄⋊Dic₃	—	3	2	no	—
48	C₂×C₄⋊Dic₃	—	6	2	no	—
49	C₂×Dic₃⋊C₄	—	6	2	no	—
50	C₂×C₄×Dic₃	—	3	1	no	—
51	C₂²×C₃⋊C₈	—	3	1	no	—
52	#890	—	3	8	no	—
53	#890	—	6	4	no	—
54	C₃×#107	C₂×D₃	1	4	yes	—
55	#818	—	3	4	no	—
56	C₈×Dic₃	—	3	4	no	—
57	#808	—	3	8	no	—
58	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄×C₉	—	2	4	no	—
60	C₂×C₄×C₉	—	4	4	no	—
61	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
63	C₂×C₄×C₉	C₂×Q₈	1	2	yes	—
64	C₂×C₄×C₉	C₂⁴	1	1	yes	characteristic
65	C₂×Dic₉	—	2	2	no	—
66	C₂×Dic₉	—	2	2	no	—
67	C₂×Dic₉	—	2	4	no	—
68	C₂×Dic₉	—	4	4	no	—
69	C₂×Dic₉	C₂×D₄	1	2	yes	—
70	C₂×Dic₉	C₂×D₄	1	2	yes	—
71	C₈×C₉	C₂×Q₈	1	4	yes	—
72	C₉⋊C₈	C₂×Q₈	1	4	yes	—
73	C₂×#125	—	9	2	no	—
74	#499	—	9	8	no	—
75	C₂×#107	—	9	1	no	—
76	C₂×#107	D₉	1	1	yes	characteristic
77	C₂×#106	—	9	2	no	—
78	C₂×C₄×C₈	—	9	1	no	—
79	C₂²×C₃×C₄	—	2	2	no	—
80	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
81	C₂²×Dic₃	—	3	1	no	—
82	C₂²×Dic₃	—	3	1	no	—
83	C₂²×Dic₃	—	6	2	no	—
84	C₂×C₃×C₈	Dic₆	1	4	yes	—
85	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
86	C₃×C₄⋊C₄	—	2	2	no	—
87	C₃×C₄⋊C₄	C₂²×D₃	1	4	yes	—
88	C₄⋊Dic₃	—	3	4	no	—
89	C₄⋊Dic₃	—	6	8	no	—
90	C₄⋊Dic₃	—	6	2	no	—
91	Dic₃⋊C₄	—	6	8	no	—
92	C₄×Dic₃	—	3	2	no	—
93	C₄×Dic₃	—	3	2	no	—
94	C₂×C₃⋊C₈	—	3	4	no	—
95	C₂×C₃⋊C₈	—	3	2	no	—
96	C₂²×C₉	C₄⋊Q₈	1	2	yes	—
97	C₂²×C₉	#135	1	2	yes	—
98	C₂²×C₉	#135	1	2	yes	—
99	C₂²×C₉	C₂²×D₄	1	1	yes	characteristic
100	C₄×C₉	—	4	4	no	—
101	C₄×C₉	C₄⋊Q₈	1	2	yes	—
102	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
103	C₄×C₉	C₂²×Q₈	1	1	yes	characteristic
104	Dic₉	—	2	2	no	—
105	Dic₉	—	2	2	no	—
106	Dic₉	—	4	4	no	—
107	C₂²×C₈	—	9	1	no	—
108	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
109	#125	—	9	8	no	—
110	#125	—	18	4	no	—
111	C₂×C₄⋊C₄	—	9	2	no	—
112	C₂×C₄⋊C₄	—	18	2	no	—
113	C₂×C₄⋊C₄	—	18	2	no	—
114	C₂×C₄⋊C₄	C₂×D₉	1	2	yes	—
115	C₂×C₄²	—	9	1	no	—
116	#107	—	9	4	no	—
117	#107	C₂×D₉	1	4	yes	—
118	#106	—	9	8	no	—
119	C₄×C₈	—	9	4	no	—
120	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
121	C₂×C₃×C₄	—	2	4	no	—
122	C₂×C₃×C₄	—	4	4	no	—
123	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
124	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
125	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
126	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
127	C₂×Dic₃	—	3	2	no	—
128	C₂×Dic₃	—	3	2	no	—
129	C₂×Dic₃	—	6	2	no	—
130	C₂×Dic₃	—	6	2	no	—
131	C₂×Dic₃	—	6	4	no	—
132	C₂×Dic₃	—	12	4	no	—
133	C₃×C₈	C₂×Dic₆	1	4	yes	—
134	C₃⋊C₈	—	3	4	no	—
135	C₂×C₉	#499	1	4	yes	complemented
136	C₂×C₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
137	C₂×C₉	C₂×#135	1	1	yes	characteristic
138	C₂×C₉	C₂×#135	1	1	yes	characteristic
139	C₂²×C₄	—	2	2	no	—
140	C₂²×C₄	—	9	1	no	—
141	C₂²×C₄	—	9	1	no	—
142	C₂²×C₄	—	18	2	no	—
143	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
144	C₂×C₈	—	9	4	no	—
145	C₂×C₈	—	9	2	no	—
146	C₂×C₈	Dic₁₈	1	4	yes	—
147	C₂×C₈	C₂²×D₉	1	2	yes	—
148	C₄⋊C₄	—	2	2	no	—
149	C₄⋊C₄	—	9	4	no	—
150	C₄⋊C₄	—	18	8	no	—
151	C₄⋊C₄	—	18	8	no	—
152	C₄⋊C₄	—	18	2	no	—
153	C₄⋊C₄	C₂²×D₉	1	4	yes	—
154	C₄²	—	9	2	no	—
155	C₄²	—	9	2	no	—
156	C₂²×C₃	#888	1	2	yes	—
157	C₂²×C₃	#912	1	2	yes	—
158	C₂²×C₃	#919	1	2	yes	—
159	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
160	C₃×C₄	—	4	4	no	—
161	C₃×C₄	#888	1	2	yes	—
162	C₃×C₄	C₂²×Dic₆	1	1	yes	characteristic
163	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
164	Dic₃	—	6	2	no	—
165	Dic₃	—	6	2	no	—
166	Dic₃	—	12	4	no	—
167	C₉	C₂×#499	1	1	yes	characteristic, complemented, Sylow
168	C₂³	D₄×D₉	1	1	yes	characteristic
169	C₂×C₄	—	2	4	no	—
170	C₂×C₄	—	4	4	no	—
171	C₂×C₄	—	9	2	no	—
172	C₂×C₄	—	9	2	no	—
173	C₂×C₄	—	18	2	no	—
174	C₂×C₄	—	18	2	no	—
175	C₂×C₄	—	18	4	no	—
176	C₂×C₄	—	36	4	no	—
177	C₂×C₄	C₂×Dic₁₈	1	2	yes	—
178	C₂×C₄	D₄×D₉	1	1	yes	characteristic
179	C₂×C₄	Q₈×D₉	1	2	yes	—
180	C₂×C₄	C₂³×D₉	1	1	yes	characteristic
181	C₈	—	9	4	no	—
182	C₈	C₂×Dic₁₈	1	4	yes	—
183	C₂×C₃	#4878	1	4	yes	—
184	C₂×C₃	C₂×#888	1	1	yes	characteristic
185	C₂×C₃	C₂×#912	1	1	yes	characteristic
186	C₂×C₃	C₂×#919	1	1	yes	characteristic
187	C₂²	#63450	1	2	yes	—
188	C₂²	#63474	1	2	yes	—
189	C₂²	#63481	1	2	yes	—
190	C₂²	C₂×D₄×D₉	1	1	yes	characteristic
191	C₄	—	4	4	no	—
192	C₄	—	18	2	no	—
193	C₄	—	18	2	no	—
194	C₄	—	36	4	no	—
195	C₄	#63450	1	2	yes	—
196	C₄	C₂²×Dic₁₈	1	1	yes	characteristic
197	C₄	C₂×Q₈×D₉	1	1	yes	characteristic
198	C₃	C₂×#4878	1	1	yes	characteristic
199	C₂	#10588558	1	4	yes	direct product factor
200	C₂	C₂×#63450	1	1	yes	characteristic
201	C₂	C₂×#63474	1	1	yes	characteristic
202	C₂	C₂×#63481	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₄×D₉
commutator, cosocle	C₂×C₄×C₉	C₂⁴
Frattini	C₂×C₃×C₄	C₂³×D₃
Fitting	C₂×C₉×#107	C₂
socle, prime radical	C₂³×C₃	D₃×D₄
hypercenter	C₂×#107	D₉
hypocenter	C₉	C₂×#499
LCS	G ▷ C₂×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂×#107

Complements

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

N	H ≅ G/N	type
6. #10588558	C₂	direct (N × H)
135. C₂×C₉	#499	semidirect
167. C₉	C₂×#499	semidirect
199. C₂	#10588558	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×#63452	2
C₂×C₉×#107	2
C₂×#63378	2
C₂×C₈×Dic₉	2
C₂×#63367	2
#10588558	2
C₂×#4878	3

Subgroups — C2×#10588558 #11874909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10588558 #11874909