Subgroups — C₂×#10590891 #11874958

Order 1152.

913 conjugacy classes of subgroups.

The subgroup lattice has 311 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63918	C₂	1	2	yes	maximal
2	C₂×#63645	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#818	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₈×Dic₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#63575	C₂	1	2	yes	maximal
6	#10590891	C₂	1	8	yes	maximal, direct product factor
7	C₂×#4874	—	3	1	no	maximal
8	C₂×#4682	—	3	1	no	maximal
9	C₂²×#627	—	2	2	no	—
10	C₂²×C₃²×C₈	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
12	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
13	C₂×C₃×C₄×Dic₃	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₃⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×Dic₃⋊Dic₃	—	2	2	no	—
16	#63918	—	2	4	no	—
17	#63918	C₂²	1	8	yes	—
18	#63645	C₂²	1	4	yes	—
19	C₃×#818	C₂²	1	4	yes	—
20	C₃×C₈×Dic₃	C₂²	1	4	yes	—
21	#63575	C₂²	1	8	yes	—
22	C₂×#888	—	3	2	no	—
23	C₂×#869	—	3	2	no	—
24	C₂×C₃×#107	—	3	1	no	—
25	C₂×C₃×C₄×C₈	—	3	1	no	—
26	C₂×#818	—	3	1	no	—
27	C₂×#818	—	3	1	no	—
28	C₂×#818	—	3	2	no	—
29	C₂×#818	—	6	1	no	—
30	C₂×#818	D₃	1	1	yes	characteristic
31	C₂×C₈×Dic₃	D₃	1	1	yes	characteristic
32	C₂×#807	—	3	2	no	—
33	#4874	—	3	8	no	—
34	#4682	—	3	8	no	—
35	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
36	C₂²×C₃⋊Dic₃	—	2	2	no	—
37	C₂²×C₃×Dic₃	—	2	2	no	—
38	C₂²×C₃×Dic₃	D₄	1	1	yes	characteristic
39	C₂²×C₃×Dic₃	D₄	1	1	yes	characteristic
40	C₂×#627	—	2	8	no	—
41	C₂×#627	—	4	8	no	—
42	C₂×C₃²×C₈	Q₈	1	4	yes	complemented
43	C₂×C₃²×C₈	C₂³	1	2	yes	—
44	C₄⋊(C₃⋊Dic₃)	—	2	2	no	—
45	C₄⋊(C₃⋊Dic₃)	C₂³	1	4	yes	—
46	C₃×C₄⋊Dic₃	—	2	2	no	—
47	C₃×C₄⋊Dic₃	C₂³	1	4	yes	—
48	C₃×C₄×Dic₃	D₄	1	2	yes	—
49	C₃×C₄×Dic₃	C₂³	1	2	yes	—
50	C₂×C₃×C₃⋊C₈	Q₈	1	4	yes	complemented
51	C₂×C₃×C₃⋊C₈	C₂³	1	2	yes	—
52	Dic₃⋊Dic₃	—	2	8	no	—
53	C₂×#500	—	9	1	no	Sylow
54	C₂²×Dic₆	—	6	2	no	—
55	C₂²×Dic₆	—	6	2	no	—
56	C₂²×C₃×C₈	—	2	1	no	—
57	C₂²×C₃×C₈	—	3	1	no	—
58	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
59	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
60	C₂×C₃×C₄⋊C₄	—	3	2	no	—
61	C₂×C₃×C₄²	—	3	1	no	—
62	C₂×C₄⋊Dic₃	—	3	2	no	—
63	C₂×C₄⋊Dic₃	—	3	2	no	—
64	C₂×C₄⋊Dic₃	—	6	2	no	—
65	C₂×C₄⋊Dic₃	—	6	2	no	—
66	C₂×C₄⋊Dic₃	C₂×D₃	1	2	yes	—
67	C₂×Dic₃⋊C₄	—	6	2	no	—
68	C₂×C₄×Dic₃	C₂×D₃	1	1	yes	characteristic
69	C₂²×C₃⋊C₈	C₂×D₃	1	1	yes	characteristic
70	#888	—	3	8	no	—
71	#888	—	6	4	no	—
72	#869	—	3	8	no	—
73	#869	—	6	4	no	—
74	C₃×#107	—	3	4	no	—
75	C₃×C₄×C₈	—	3	4	no	—
76	#818	—	3	4	no	—
77	#818	—	3	4	no	—
78	#818	—	3	8	no	—
79	#818	—	6	4	no	—
80	#818	C₂×D₃	1	4	yes	—
81	C₈×Dic₃	C₂×D₃	1	4	yes	—
82	#807	—	3	8	no	—
83	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
84	C₂×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
85	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
86	C₂×C₃²×C₄	C₂×Q₈	1	2	yes	—
87	C₂×C₃²×C₄	C₂⁴	1	1	yes	characteristic
88	C₂×C₃⋊Dic₃	—	2	4	no	—
89	C₂×C₃⋊Dic₃	—	4	4	no	—
90	C₂×C₃×Dic₃	—	2	4	no	—
91	C₂×C₃×Dic₃	—	4	4	no	—
92	C₂×C₃×Dic₃	D₈	1	4	yes	—
93	C₂×C₃×Dic₃	Q₁₆	1	4	yes	—
94	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
95	C₂×C₃×Dic₃	C₂×D₄	1	2	yes	—
96	#627	—	4	16	no	—
97	C₃²×C₈	C₂×Q₈	1	4	yes	complemented
98	C₃×C₃⋊C₈	C₂×Q₈	1	4	yes	complemented
99	C₂×C₄⋊Q₈	—	9	2	no	—
100	#500	—	9	8	no	—
101	C₂×#107	—	3	1	no	—
102	C₂×#107	—	9	2	no	—
103	C₂×#107	—	9	1	no	—
104	C₂×C₄×C₈	—	3	1	no	—
105	C₂²×C₃×C₄	—	2	1	no	—
106	C₂²×C₃×C₄	—	3	1	no	—
107	C₂²×C₃×C₄	—	3	1	no	—
108	C₂²×C₃×C₄	—	6	2	no	—
109	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
110	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
111	C₂²×Dic₃	—	2	2	no	—
112	C₂²×Dic₃	—	6	2	no	—
113	C₂²×Dic₃	—	6	2	no	—
114	C₂²×Dic₃	—	12	2	no	—
115	C₂²×Dic₃	D₁₂	1	1	yes	characteristic
116	C₂²×Dic₃	D₁₂	1	1	yes	characteristic
117	C₂×Dic₆	—	6	8	no	—
118	C₂×Dic₆	—	6	8	no	—
119	C₂×Dic₆	—	12	8	no	—
120	C₂×Dic₆	—	12	8	no	—
121	C₂×C₃×C₈	—	2	4	no	—
122	C₂×C₃×C₈	—	2	2	no	—
123	C₂×C₃×C₈	—	3	4	no	—
124	C₂×C₃×C₈	—	3	2	no	—
125	C₂×C₃×C₈	Dic₆	1	4	yes	complemented
126	C₂×C₃×C₈	Dic₆	1	4	yes	complemented
127	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
128	C₂×C₃×C₈	C₂²×D₃	1	2	yes	—
129	C₃×C₄⋊C₄	—	3	4	no	—
130	C₃×C₄⋊C₄	—	6	2	no	—
131	C₃×C₄²	—	3	2	no	—
132	C₃×C₄²	—	3	2	no	—
133	C₄⋊Dic₃	—	2	2	no	—
134	C₄⋊Dic₃	—	3	4	no	—
135	C₄⋊Dic₃	—	3	4	no	—
136	C₄⋊Dic₃	—	6	4	no	—
137	C₄⋊Dic₃	—	6	8	no	—
138	C₄⋊Dic₃	—	6	2	no	—
139	C₄⋊Dic₃	—	6	2	no	—
140	C₄⋊Dic₃	—	12	2	no	—
141	C₄⋊Dic₃	C₂²×D₃	1	4	yes	—
142	Dic₃⋊C₄	—	6	8	no	—
143	C₄×Dic₃	D₁₂	1	2	yes	—
144	C₄×Dic₃	C₂²×D₃	1	2	yes	—
145	C₂×C₃⋊C₈	Dic₆	1	4	yes	complemented
146	C₂×C₃⋊C₈	C₂²×D₃	1	2	yes	—
147	C₂²×C₃²	C₄⋊Q₈	1	2	yes	—
148	C₂²×C₃²	C₂×D₈	1	2	yes	—
149	C₂²×C₃²	C₂×Q₁₆	1	2	yes	—
150	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
151	C₃²×C₄	C₄⋊Q₈	1	2	yes	—
152	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
153	C₃²×C₄	C₂²×Q₈	1	1	yes	characteristic
154	C₃⋊Dic₃	—	4	4	no	—
155	C₃×Dic₃	—	4	4	no	—
156	C₃×Dic₃	C₂×D₈	1	4	yes	—
157	C₃×Dic₃	C₂×Q₁₆	1	4	yes	—
158	C₂²×Q₈	—	18	2	no	—
159	C₂²×C₈	—	3	1	no	—
160	C₂²×C₈	D₃²	1	1	yes	characteristic
161	C₄⋊Q₈	—	9	8	no	—
162	C₄⋊Q₈	—	18	4	no	—
163	C₂×C₄⋊C₄	—	3	2	no	—
164	C₂×C₄⋊C₄	—	9	2	no	—
165	C₂×C₄⋊C₄	—	18	2	no	—
166	C₂×C₄²	—	3	1	no	—
167	#107	—	3	4	no	—
168	#107	—	9	8	no	—
169	#107	—	9	4	no	—
170	C₄×C₈	—	3	4	no	—
171	C₂³×C₃	—	2	1	no	—
172	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
173	C₂³×C₃	D₃×D₄	1	1	yes	characteristic
174	C₂×C₃×C₄	—	2	1	no	—
175	C₂×C₃×C₄	—	2	2	no	—
176	C₂×C₃×C₄	—	2	1	no	—
177	C₂×C₃×C₄	—	2	2	no	—
178	C₂×C₃×C₄	—	3	4	no	—
179	C₂×C₃×C₄	—	3	4	no	—
180	C₂×C₃×C₄	—	3	2	no	—
181	C₂×C₃×C₄	—	3	2	no	—
182	C₂×C₃×C₄	—	6	4	no	—
183	C₂×C₃×C₄	—	12	4	no	—
184	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
185	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
186	C₂×C₃×C₄	C₂×Dic₆	1	2	yes	—
187	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
188	C₂×C₃×C₄	D₃×D₄	1	1	yes	characteristic
189	C₂×C₃×C₄	D₃×Q₈	1	2	yes	—
190	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
191	C₂×C₃×C₄	C₂³×D₃	1	1	yes	characteristic
192	C₂×Dic₃	—	2	4	no	—
193	C₂×Dic₃	—	4	4	no	—
194	C₂×Dic₃	—	6	4	no	—
195	C₂×Dic₃	—	6	4	no	—
196	C₂×Dic₃	—	12	4	no	—
197	C₂×Dic₃	—	12	4	no	—
198	C₂×Dic₃	—	12	4	no	—
199	C₂×Dic₃	—	24	4	no	—
200	C₂×Dic₃	D₂₄	1	4	yes	—
201	C₂×Dic₃	Dic₁₂	1	4	yes	—
202	C₂×Dic₃	C₂×D₁₂	1	2	yes	—
203	C₂×Dic₃	C₂×D₁₂	1	2	yes	—
204	Dic₆	—	12	16	no	—
205	Dic₆	—	12	16	no	—
206	C₃×C₈	—	2	4	no	—
207	C₃×C₈	—	3	4	no	—
208	C₃×C₈	C₂×Dic₆	1	4	yes	complemented
209	C₃×C₈	C₂×Dic₆	1	4	yes	complemented
210	C₃⋊C₈	C₂×Dic₆	1	4	yes	complemented
211	C₂×C₃²	#500	1	4	yes	complemented
212	C₂×C₃²	C₂×C₄⋊Q₈	1	1	yes	characteristic
213	C₂×C₃²	C₂²×D₈	1	1	yes	characteristic
214	C₂×C₃²	C₂²×Q₁₆	1	1	yes	characteristic
215	C₂×Q₈	—	18	8	no	—
216	C₂×Q₈	—	36	8	no	—
217	C₂²×C₄	—	3	1	no	—
218	C₂²×C₄	—	3	1	no	—
219	C₂²×C₄	—	6	2	no	—
220	C₂²×C₄	—	18	2	no	—
221	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
222	C₂×C₈	—	3	2	no	—
223	C₂×C₈	—	3	4	no	—
224	C₂×C₈	#627	1	4	yes	complemented
225	C₂×C₈	C₂×D₃²	1	2	yes	—
226	C₄⋊C₄	—	3	4	no	—
227	C₄⋊C₄	—	6	2	no	—
228	C₄⋊C₄	—	9	4	no	—
229	C₄⋊C₄	—	18	8	no	—
230	C₄⋊C₄	—	18	2	no	—
231	C₄²	—	3	2	no	—
232	C₄²	—	3	2	no	—
233	C₂²×C₃	—	2	1	no	—
234	C₂²×C₃	—	2	2	no	—
235	C₂²×C₃	—	2	2	no	—
236	C₂²×C₃	—	2	2	no	—
237	C₂²×C₃	#869	1	2	yes	—
238	C₂²×C₃	#888	1	2	yes	—
239	C₂²×C₃	C₂×D₂₄	1	2	yes	—
240	C₂²×C₃	C₂×Dic₁₂	1	2	yes	—
241	C₂²×C₃	D₃×D₈	1	2	yes	—
242	C₂²×C₃	D₃×Q₁₆	1	2	yes	—
243	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
244	C₂²×C₃	C₂×D₃×D₄	1	1	yes	characteristic
245	C₃×C₄	—	2	1	no	—
246	C₃×C₄	—	2	1	no	—
247	C₃×C₄	—	2	2	no	—
248	C₃×C₄	—	3	4	no	—
249	C₃×C₄	—	3	4	no	—
250	C₃×C₄	—	12	4	no	—
251	C₃×C₄	#869	1	2	yes	—
252	C₃×C₄	#888	1	2	yes	—
253	C₃×C₄	C₂²×Dic₆	1	1	yes	characteristic
254	C₃×C₄	C₂²×Dic₆	1	1	yes	characteristic
255	C₃×C₄	C₂²×Dic₆	1	1	yes	characteristic
256	C₃×C₄	C₂×D₃×Q₈	1	1	yes	characteristic
257	Dic₃	—	4	4	no	—
258	Dic₃	—	12	4	no	—
259	Dic₃	—	12	4	no	—
260	Dic₃	—	24	4	no	—
261	Dic₃	C₂×D₂₄	1	4	yes	—
262	Dic₃	C₂×Dic₁₂	1	4	yes	—
263	C₃²	C₂×#500	1	1	yes	characteristic, complemented, Sylow
264	C₂³	D₃×D₁₂	1	1	yes	characteristic
265	Q₈	—	36	16	no	—
266	C₂×C₄	—	3	2	no	—
267	C₂×C₄	—	3	2	no	—
268	C₂×C₄	—	3	4	no	—
269	C₂×C₄	—	3	4	no	—
270	C₂×C₄	—	6	4	no	—
271	C₂×C₄	—	12	4	no	—
272	C₂×C₄	—	18	4	no	—
273	C₂×C₄	—	36	4	no	—
274	C₂×C₄	D₃×Dic₆	1	2	yes	—
275	C₂×C₄	D₃×D₁₂	1	1	yes	characteristic
276	C₂×C₄	C₂×#627	1	2	yes	—
277	C₂×C₄	C₂²×D₃²	1	1	yes	characteristic
278	C₈	—	3	4	no	—
279	C₈	C₂×#627	1	4	yes	complemented
280	C₂×C₃	—	2	1	no	—
281	C₂×C₃	—	2	1	no	—
282	C₂×C₃	—	2	4	no	—
283	C₂×C₃	—	2	1	no	—
284	C₂×C₃	#4682	1	4	yes	complemented
285	C₂×C₃	#4874	1	4	yes	complemented
286	C₂×C₃	C₂×#869	1	1	yes	characteristic
287	C₂×C₃	C₂×#888	1	1	yes	characteristic
288	C₂×C₃	C₂²×D₂₄	1	1	yes	characteristic
289	C₂×C₃	C₂²×Dic₁₂	1	1	yes	characteristic
290	C₂×C₃	C₂×D₃×D₈	1	1	yes	characteristic
291	C₂×C₃	C₂×D₃×Q₁₆	1	1	yes	characteristic
292	C₂²	D₃×D₂₄	1	2	yes	—
293	C₂²	D₃×Dic₁₂	1	2	yes	—
294	C₂²	#63918	1	2	yes	—
295	C₂²	C₂×D₃×D₁₂	1	1	yes	characteristic
296	C₄	—	3	4	no	—
297	C₄	—	3	4	no	—
298	C₄	—	12	4	no	—
299	C₄	—	36	4	no	—
300	C₄	#63918	1	2	yes	—
301	C₄	C₂×D₃×Dic₆	1	1	yes	characteristic
302	C₄	C₂²×#627	1	1	yes	characteristic
303	C₃	—	2	1	no	—
304	C₃	C₂×#4682	1	1	yes	characteristic, complemented
305	C₃	C₂×#4874	1	1	yes	characteristic, complemented
306	C₂	#10590891	1	4	yes	direct product factor
307	C₂	C₂×D₃×D₂₄	1	1	yes	characteristic
308	C₂	C₂×D₃×Dic₁₂	1	1	yes	characteristic
309	C₂	C₂×#63918	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₃×D₁₂
commutator, cosocle	C₂×C₃²×C₄	C₂⁴
Frattini	C₂×C₄	C₂²×D₃²
Fitting	C₂²×C₃²×C₈	C₂²
socle, prime radical	C₂³×C₃²	C₂×D₄
hypercenter	C₂²×C₈	D₃²
hypocenter	C₃²	C₂×#500
LCS	G ▷ C₂×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
6. #10590891	C₂	direct (N × H)
42. C₂×C₃²×C₈	Q₈	semidirect
50. C₂×C₃×C₃⋊C₈	Q₈	semidirect
97. C₃²×C₈	C₂×Q₈	semidirect
98. C₃×C₃⋊C₈	C₂×Q₈	semidirect
125. C₂×C₃×C₈	Dic₆	semidirect
126. C₂×C₃×C₈	Dic₆	semidirect
145. C₂×C₃⋊C₈	Dic₆	semidirect
208. C₃×C₈	C₂×Dic₆	semidirect
209. C₃×C₈	C₂×Dic₆	semidirect
210. C₃⋊C₈	C₂×Dic₆	semidirect
211. C₂×C₃²	#500	semidirect
224. C₂×C₈	#627	semidirect
263. C₃²	C₂×#500	semidirect
279. C₈	C₂×#627	semidirect
284. C₂×C₃	#4682	semidirect
285. C₂×C₃	#4874	semidirect
304. C₃	C₂×#4682	semidirect
305. C₃	C₂×#4874	semidirect
306. C₂	#10590891	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×#63918	2
C₂×#63645	2
C₂×C₃×#818	2
C₂×C₃×C₈×Dic₃	2
C₂×#63575	2
#10590891	2
C₂×#4874	3
C₂×#4682	3

Subgroups — C2×#10590891 #11874958

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#10590891 #11874958