Subgroups — C₂×#10589141 #11797180

Order 1152.

401 conjugacy classes of subgroups.

The subgroup lattice has 244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63645	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#818	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic
4	#10589141	C₂	1	4	yes	maximal, direct product factor
5	C₂×#4505	—	3	1	no	maximal
6	C₂×#4490	—	3	1	no	maximal
7	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
9	C₂×C₃×C₄⋊Dic₃	—	2	1	no	—
10	#63645	—	2	1	no	—
11	#63645	C₂²	1	2	yes	—
12	C₃×#818	—	2	1	no	—
13	C₃×#818	C₂²	1	2	yes	—
14	C₂×C₃×C₃⋊C₁₆	C₄	1	4	yes	complemented
15	C₂×C₃×C₃⋊C₁₆	C₂²	1	2	yes	—
16	C₂²×C₃×C₁₆	—	3	1	no	—
17	C₂×C₃×#107	—	3	1	no	—
18	C₂×#818	—	3	1	no	—
19	C₂×#818	—	3	1	no	—
20	C₂×#818	—	6	1	no	—
21	C₂×#818	D₃	1	1	yes	characteristic
22	C₂²×C₃⋊C₁₆	D₃	1	1	yes	characteristic
23	#4505	—	3	4	no	—
24	#4490	—	3	4	no	—
25	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
26	C₂²×C₃⋊Dic₃	—	4	1	no	—
27	C₂²×C₃×Dic₃	—	4	1	no	—
28	C₂×C₃²×C₈	C₂×C₄	1	2	yes	—
29	C₂×C₃²×C₈	D₄	1	1	yes	characteristic
30	C₂×C₃²×C₈	Q₈	1	2	yes	—
31	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
32	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
33	C₄⋊(C₃⋊Dic₃)	—	4	1	no	—
34	C₃×C₄⋊Dic₃	—	2	2	no	—
35	C₃×C₄⋊Dic₃	—	4	1	no	—
36	C₃×C₃⋊C₁₆	C₂×C₄	1	4	yes	complemented
37	C₂×#367	—	9	1	no	Sylow
38	C₂²×C₃×C₈	—	2	1	no	—
39	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
40	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
41	C₂×C₃×C₄⋊C₄	—	6	1	no	—
42	C₂×C₄⋊Dic₃	—	2	1	no	—
43	C₂×C₄⋊Dic₃	—	6	2	no	—
44	C₂×C₄⋊Dic₃	—	6	1	no	—
45	C₂×C₄⋊Dic₃	—	6	1	no	—
46	C₂×C₃×C₁₆	—	3	4	no	—
47	C₂×C₃×C₁₆	—	3	2	no	—
48	C₃×#107	—	3	2	no	—
49	C₃×#107	—	6	1	no	—
50	#818	—	2	1	no	—
51	#818	—	3	2	no	—
52	#818	—	3	2	no	—
53	#818	—	6	2	no	—
54	#818	—	6	2	no	—
55	#818	—	6	1	no	—
56	#818	—	6	1	no	—
57	#818	C₂×D₃	1	2	yes	—
58	C₂×C₃⋊C₁₆	Dic₃	1	4	yes	complemented
59	C₂×C₃⋊C₁₆	C₂×D₃	1	2	yes	—
60	C₂³×C₃²	D₈	1	1	yes	characteristic
61	C₂×C₃²×C₄	C₄⋊C₄	1	2	yes	—
62	C₂×C₃²×C₄	D₈	1	1	yes	characteristic
63	C₂×C₃²×C₄	Q₁₆	1	2	yes	—
64	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
65	C₂×C₃⋊Dic₃	—	4	2	no	—
66	C₂×C₃⋊Dic₃	—	8	2	no	—
67	C₂×C₃×Dic₃	—	4	2	no	—
68	C₂×C₃×Dic₃	—	8	2	no	—
69	C₃²×C₈	C₄⋊C₄	1	2	yes	—
70	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
71	C₃²×C₈	C₂×Q₈	1	1	yes	characteristic
72	C₂²×C₁₆	—	3	1	no	—
73	C₂×#107	—	3	1	no	—
74	C₂×#107	—	9	1	no	—
75	#367	—	9	4	no	—
76	C₂²×C₃×C₄	—	2	1	no	—
77	C₂²×C₃×C₄	—	12	1	no	—
78	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
79	C₂²×C₃×C₄	#67	1	1	yes	characteristic
80	C₂²×Dic₃	—	4	1	no	—
81	C₂²×Dic₃	—	12	2	no	—
82	C₂²×Dic₃	—	12	1	no	—
83	C₂²×Dic₃	—	12	1	no	—
84	C₂×C₃×C₈	—	2	2	no	—
85	C₂×C₃×C₈	—	2	1	no	—
86	C₂×C₃×C₈	—	2	2	no	—
87	C₂×C₃×C₈	—	2	1	no	—
88	C₂×C₃×C₈	Dic₆	1	2	yes	—
89	C₂×C₃×C₈	Dic₆	1	2	yes	—
90	C₂×C₃×C₈	C₄×D₃	1	2	yes	—
91	C₂×C₃×C₈	D₁₂	1	1	yes	characteristic
92	C₂×C₃×C₈	C₂×Dic₃	1	2	yes	—
93	C₂×C₃×C₈	#67	1	1	yes	characteristic
94	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
95	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
96	C₃×C₄⋊C₄	—	6	2	no	—
97	C₃×C₄⋊C₄	—	12	1	no	—
98	C₄⋊Dic₃	—	2	2	no	—
99	C₄⋊Dic₃	—	4	1	no	—
100	C₄⋊Dic₃	—	6	4	no	—
101	C₄⋊Dic₃	—	6	2	no	—
102	C₄⋊Dic₃	—	6	2	no	—
103	C₄⋊Dic₃	—	12	2	no	—
104	C₄⋊Dic₃	—	12	1	no	—
105	C₄⋊Dic₃	—	12	1	no	—
106	C₃×C₁₆	—	3	4	no	—
107	C₃⋊C₁₆	C₂×Dic₃	1	4	yes	complemented
108	C₂²×C₃²	#107	1	2	yes	—
109	C₂²×C₃²	SD₃₂	1	2	yes	—
110	C₂²×C₃²	SD₃₂	1	2	yes	—
111	C₂²×C₃²	C₂×D₈	1	1	yes	characteristic
112	C₃²×C₄	#107	1	2	yes	—
113	C₃²×C₄	C₂×C₄⋊C₄	1	1	yes	characteristic
114	C₃²×C₄	C₂×Q₁₆	1	1	yes	characteristic
115	C₃⋊Dic₃	—	8	2	no	—
116	C₃×Dic₃	—	8	2	no	—
117	C₂²×C₈	D₃²	1	1	yes	characteristic
118	C₂×C₄⋊C₄	—	6	1	no	—
119	C₂×C₄⋊C₄	—	18	1	no	—
120	C₂×C₁₆	—	3	4	no	—
121	C₂×C₁₆	—	3	2	no	—
122	#107	—	3	2	no	—
123	#107	—	6	1	no	—
124	#107	—	9	2	no	—
125	#107	—	18	1	no	—
126	C₂³×C₃	—	2	1	no	—
127	C₂³×C₃	D₂₄	1	1	yes	characteristic
128	C₂³×C₃	#213	1	1	yes	characteristic
129	C₂×C₃×C₄	—	2	1	no	—
130	C₂×C₃×C₄	—	2	2	no	—
131	C₂×C₃×C₄	—	2	2	no	—
132	C₂×C₃×C₄	—	2	1	no	—
133	C₂×C₃×C₄	—	12	2	no	—
134	C₂×C₃×C₄	—	24	2	no	—
135	C₂×C₃×C₄	D₂₄	1	1	yes	characteristic
136	C₂×C₃×C₄	Dic₁₂	1	2	yes	—
137	C₂×C₃×C₄	Dic₃⋊C₄	1	2	yes	—
138	C₂×C₃×C₄	C₄⋊Dic₃	1	2	yes	—
139	C₂×C₃×C₄	#213	1	1	yes	characteristic
140	C₂×C₃×C₄	#216	1	2	yes	—
141	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
142	C₂×C₃×C₄	C₂×#67	1	1	yes	characteristic
143	C₂×Dic₃	—	4	2	no	—
144	C₂×Dic₃	—	8	2	no	—
145	C₂×Dic₃	—	12	4	no	—
146	C₂×Dic₃	—	12	2	no	—
147	C₂×Dic₃	—	12	2	no	—
148	C₂×Dic₃	—	24	4	no	—
149	C₂×Dic₃	—	24	2	no	—
150	C₂×Dic₃	—	24	2	no	—
151	C₃×C₈	—	2	2	no	—
152	C₃×C₈	—	2	1	no	—
153	C₃×C₈	—	2	1	no	—
154	C₃×C₈	Dic₃⋊C₄	1	2	yes	—
155	C₃×C₈	C₄⋊Dic₃	1	2	yes	—
156	C₃×C₈	C₂×Dic₆	1	1	yes	characteristic
157	C₃×C₈	C₂×Dic₆	1	1	yes	characteristic
158	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
159	C₃×C₈	C₂²×Dic₃	1	1	yes	characteristic
160	C₂×C₃²	#367	1	4	yes	complemented
161	C₂×C₃²	C₂×#107	1	1	yes	characteristic
162	C₂×C₃²	C₂×SD₃₂	1	1	yes	characteristic
163	C₂×C₃²	C₂×SD₃₂	1	1	yes	characteristic
164	C₂²×C₄	—	12	1	no	—
165	C₂²×C₄	—	36	1	no	—
166	C₂²×C₄	#626	1	1	yes	characteristic
167	C₂×C₈	D₃×Dic₃	1	2	yes	—
168	C₂×C₈	#626	1	1	yes	characteristic
169	C₂×C₈	#627	1	2	yes	—
170	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
171	C₄⋊C₄	—	6	2	no	—
172	C₄⋊C₄	—	12	1	no	—
173	C₄⋊C₄	—	18	2	no	—
174	C₄⋊C₄	—	36	1	no	—
175	C₁₆	—	3	4	no	—
176	C₂²×C₃	—	2	2	no	—
177	C₂²×C₃	—	2	2	no	—
178	C₂²×C₃	—	2	1	no	—
179	C₂²×C₃	—	2	2	no	—
180	C₂²×C₃	#800	1	2	yes	—
181	C₂²×C₃	#800	1	2	yes	—
182	C₂²×C₃	#807	1	2	yes	—
183	C₂²×C₃	#818	1	2	yes	—
184	C₂²×C₃	#827	1	2	yes	—
185	C₂²×C₃	#828	1	2	yes	—
186	C₂²×C₃	C₂×D₂₄	1	1	yes	characteristic
187	C₂²×C₃	C₂×#213	1	1	yes	characteristic
188	C₃×C₄	—	2	2	no	—
189	C₃×C₄	—	2	1	no	—
190	C₃×C₄	—	2	1	no	—
191	C₃×C₄	—	24	2	no	—
192	C₃×C₄	#807	1	2	yes	—
193	C₃×C₄	#818	1	2	yes	—
194	C₃×C₄	C₂×Dic₁₂	1	1	yes	characteristic
195	C₃×C₄	C₂×Dic₃⋊C₄	1	1	yes	characteristic
196	C₃×C₄	C₂×C₄⋊Dic₃	1	1	yes	characteristic
197	C₃×C₄	C₂×#216	1	1	yes	characteristic
198	Dic₃	—	8	2	no	—
199	Dic₃	—	24	4	no	—
200	Dic₃	—	24	2	no	—
201	Dic₃	—	24	2	no	—
202	C₃²	C₂×#367	1	1	yes	characteristic, complemented, Sylow
203	C₂³	#3714	1	1	yes	characteristic
204	C₂×C₄	—	12	2	no	—
205	C₂×C₄	—	24	2	no	—
206	C₂×C₄	—	36	2	no	—
207	C₂×C₄	—	72	2	no	—
208	C₂×C₄	#3714	1	1	yes	characteristic
209	C₂×C₄	#3719	1	2	yes	—
210	C₂×C₄	Dic₃⋊Dic₃	1	2	yes	—
211	C₂×C₄	C₂×#626	1	1	yes	characteristic
212	C₈	Dic₃⋊Dic₃	1	2	yes	—
213	C₈	C₂×D₃×Dic₃	1	1	yes	characteristic
214	C₈	C₂×#627	1	1	yes	characteristic
215	C₂×C₃	—	2	1	no	—
216	C₂×C₃	—	2	1	no	—
217	C₂×C₃	—	2	1	no	—
218	C₂×C₃	—	2	4	no	—
219	C₂×C₃	#4490	1	4	yes	complemented
220	C₂×C₃	#4505	1	4	yes	complemented
221	C₂×C₃	C₂×#800	1	1	yes	characteristic
222	C₂×C₃	C₂×#800	1	1	yes	characteristic
223	C₂×C₃	C₂×#807	1	1	yes	characteristic
224	C₂×C₃	C₂×#818	1	1	yes	characteristic
225	C₂×C₃	C₂×#827	1	1	yes	characteristic
226	C₂×C₃	C₂×#828	1	1	yes	characteristic
227	C₂²	#63548	1	2	yes	—
228	C₂²	#63549	1	2	yes	—
229	C₂²	#63575	1	2	yes	—
230	C₂²	C₂×#3714	1	1	yes	characteristic
231	C₄	—	24	2	no	—
232	C₄	—	72	2	no	—
233	C₄	#63575	1	2	yes	—
234	C₄	C₂×#3719	1	1	yes	characteristic
235	C₄	C₂×Dic₃⋊Dic₃	1	1	yes	characteristic
236	C₃	—	2	1	no	—
237	C₃	C₂×#4490	1	1	yes	characteristic, complemented
238	C₃	C₂×#4505	1	1	yes	characteristic, complemented
239	C₂	#10589141	1	4	yes	direct product factor
240	C₂	C₂×#63548	1	1	yes	characteristic
241	C₂	C₂×#63549	1	1	yes	characteristic
242	C₂	C₂×#63575	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#3714
commutator	C₃²×C₈	C₂²×C₄
Frattini	C₂×C₈	C₂×D₃²
Fitting	C₂²×C₃²×C₈	C₂²
socle, prime radical	C₂³×C₃²	D₈
cosocle	C₂×C₃²×C₈	C₂³
hypercenter	C₂²×C₈	D₃²
hypocenter	C₃²	C₂×#367
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. #10589141	C₂	direct (N × H)
14. C₂×C₃×C₃⋊C₁₆	C₄	semidirect
36. C₃×C₃⋊C₁₆	C₂×C₄	semidirect
58. C₂×C₃⋊C₁₆	Dic₃	semidirect
107. C₃⋊C₁₆	C₂×Dic₃	semidirect
160. C₂×C₃²	#367	semidirect
202. C₃²	C₂×#367	semidirect
219. C₂×C₃	#4490	semidirect
220. C₂×C₃	#4505	semidirect
237. C₃	C₂×#4490	semidirect
238. C₃	C₂×#4505	semidirect
239. C₂	#10589141	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×#63645	2
C₂×C₃×#818	2
C₂²×C₃×C₃⋊C₁₆	2
#10589141	2
C₂×#4505	3
C₂×#4490	3

Subgroups — C2×#10589141 #11797180

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10589141 #11797180