Subgroups — C₂×C₃×#4936 #11801086

Order 1152.

1673 conjugacy classes of subgroups.

The subgroup lattice has 274 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₄⋊Dic₃	C₂	1	2	yes	maximal
3	C₂×C₃×C₃⋊#95	C₂	1	4	yes	maximal
4	C₃×#4936	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×#382	—	3	1	no	maximal
6	C₂×#4936	C₃	1	1	yes	maximal, characteristic, direct product factor
7	C₂³×C₃²×C₄	C₂²	1	2	yes	—
8	C₂³×C₃²×C₄	C₂²	1	1	yes	characteristic
9	C₂³×C₃×Dic₃	C₂²	1	4	yes	—
10	C₂×C₃²×C₄²	C₄	1	8	yes	complemented
11	C₂×C₃²×C₄²	C₂²	1	4	yes	—
12	C₂×C₃×C₄⋊Dic₃	—	2	8	no	—
13	C₂×C₃×C₄⋊Dic₃	C₂²	1	8	yes	—
14	C₃×C₃⋊#95	C₂²	1	16	yes	—
15	C₂²×C₃×C₄⋊C₄	—	3	2	no	—
16	C₂²×C₃×C₄²	—	2	1	no	—
17	C₂²×C₃×C₄²	D₃	1	1	yes	characteristic
18	C₂²×C₃×C₄²	C₂×C₃	1	1	yes	characteristic
19	C₂²×C₄⋊Dic₃	C₂×C₃	1	2	yes	—
20	C₃×#382	—	3	8	no	—
21	C₂×C₃×#95	—	3	4	no	—
22	C₂×C₃⋊#95	C₂×C₃	1	4	yes	—
23	#4936	C₂×C₃	1	8	yes	direct product factor
24	C₂⁴×C₃²	C₂³	1	1	yes	characteristic
25	C₂²×C₃²×C₄	—	2	8	no	—
26	C₂²×C₃²×C₄	C₂×C₄	1	8	yes	—
27	C₂²×C₃²×C₄	C₂×C₄	1	4	yes	—
28	C₂²×C₃²×C₄	D₄	1	4	yes	—
29	C₂²×C₃²×C₄	Q₈	1	4	yes	—
30	C₂²×C₃²×C₄	C₂³	1	4	yes	—
31	C₂²×C₃²×C₄	C₂³	1	2	yes	—
32	C₂²×C₃×Dic₃	—	2	8	no	—
33	C₂²×C₃×Dic₃	—	2	16	no	—
34	C₂²×C₃×Dic₃	C₂³	1	8	yes	—
35	C₃²×C₄²	C₂×C₄	1	16	yes	complemented
36	C₃×C₄⋊Dic₃	—	2	16	no	—
37	C₂×#382	—	3	1	no	Sylow
38	C₂³×C₃×C₄	—	2	2	no	—
39	C₂³×C₃×C₄	—	2	1	no	—
40	C₂³×C₃×C₄	—	3	4	no	—
41	C₂³×C₃×C₄	C₂×D₃	1	2	yes	—
42	C₂³×C₃×C₄	C₂×D₃	1	1	yes	characteristic
43	C₂³×C₃×C₄	C₂²×C₃	1	2	yes	—
44	C₂³×C₃×C₄	C₂²×C₃	1	1	yes	characteristic
45	C₂³×Dic₃	C₂²×C₃	1	4	yes	—
46	C₂×C₃×C₄⋊C₄	—	3	8	no	—
47	C₂×C₃×C₄⋊C₄	—	6	8	no	—
48	C₂×C₃×C₄²	—	2	8	no	—
49	C₂×C₃×C₄²	—	2	4	no	—
50	C₂×C₃×C₄²	Dic₃	1	8	yes	complemented
51	C₂×C₃×C₄²	C₃×C₄	1	8	yes	complemented
52	C₂×C₃×C₄²	C₂×D₃	1	4	yes	—
53	C₂×C₃×C₄²	C₂²×C₃	1	4	yes	—
54	C₂×C₄⋊Dic₃	—	2	8	no	—
55	C₂×C₄⋊Dic₃	C₂²×C₃	1	8	yes	—
56	C₃×#95	—	3	16	no	—
57	C₃⋊#95	C₂²×C₃	1	16	yes	—
58	C₂³×C₃²	C₂²×C₄	1	2	yes	—
59	C₂³×C₃²	C₂×D₄	1	2	yes	—
60	C₂³×C₃²	C₂×Q₈	1	2	yes	—
61	C₂³×C₃²	#41	1	8	yes	—
62	C₂³×C₃²	C₂⁴	1	1	yes	characteristic
63	C₂×C₃²×C₄	—	2	16	no	—
64	C₂×C₃²×C₄	—	2	8	no	—
65	C₂×C₃²×C₄	C₄⋊C₄	1	16	yes	—
66	C₂×C₃²×C₄	C₂²×C₄	1	8	yes	—
67	C₂×C₃²×C₄	C₂²×C₄	1	4	yes	—
68	C₂×C₃²×C₄	C₂×D₄	1	4	yes	—
69	C₂×C₃²×C₄	C₂×Q₈	1	4	yes	—
70	C₂×C₃×Dic₃	—	2	8	no	—
71	C₂×C₃×Dic₃	—	2	16	no	—
72	C₂×C₃×Dic₃	—	4	16	no	—
73	C₂²×C₄⋊C₄	—	3	2	no	—
74	C₂²×C₄²	C₃×D₃	1	1	yes	characteristic
75	#382	—	3	8	no	—
76	C₂×#95	—	3	4	no	—
77	C₂⁴×C₃	—	2	1	no	—
78	C₂⁴×C₃	C₂²×D₃	1	1	yes	characteristic
79	C₂⁴×C₃	C₂³×C₃	1	1	yes	characteristic
80	C₂²×C₃×C₄	—	2	16	no	—
81	C₂²×C₃×C₄	—	2	8	no	—
82	C₂²×C₃×C₄	—	2	8	no	—
83	C₂²×C₃×C₄	—	2	4	no	—
84	C₂²×C₃×C₄	—	2	4	no	—
85	C₂²×C₃×C₄	—	2	8	no	—
86	C₂²×C₃×C₄	—	2	4	no	—
87	C₂²×C₃×C₄	—	2	4	no	—
88	C₂²×C₃×C₄	—	2	2	no	—
89	C₂²×C₃×C₄	—	3	8	no	—
90	C₂²×C₃×C₄	—	6	8	no	—
91	C₂²×C₃×C₄	—	6	16	no	—
92	C₂²×C₃×C₄	Dic₆	1	4	yes	—
93	C₂²×C₃×C₄	D₁₂	1	4	yes	—
94	C₂²×C₃×C₄	C₂×Dic₃	1	8	yes	—
95	C₂²×C₃×C₄	C₂×Dic₃	1	4	yes	—
96	C₂²×C₃×C₄	C₂×C₃×C₄	1	8	yes	—
97	C₂²×C₃×C₄	C₂×C₃×C₄	1	4	yes	—
98	C₂²×C₃×C₄	C₃×D₄	1	4	yes	—
99	C₂²×C₃×C₄	C₃×Q₈	1	4	yes	—
100	C₂²×C₃×C₄	C₂²×D₃	1	4	yes	—
101	C₂²×C₃×C₄	C₂²×D₃	1	2	yes	—
102	C₂²×C₃×C₄	C₂³×C₃	1	4	yes	—
103	C₂²×C₃×C₄	C₂³×C₃	1	2	yes	—
104	C₂²×Dic₃	—	2	8	no	—
105	C₂²×Dic₃	—	2	16	no	—
106	C₂²×Dic₃	C₂³×C₃	1	8	yes	—
107	C₃×C₄⋊C₄	—	6	16	no	—
108	C₃×C₄²	—	2	16	no	—
109	C₃×C₄²	C₂×Dic₃	1	16	yes	complemented
110	C₃×C₄²	C₂×C₃×C₄	1	16	yes	complemented
111	C₄⋊Dic₃	—	2	16	no	—
112	C₂²×C₃²	C₂×C₄⋊C₄	1	4	yes	—
113	C₂²×C₃²	#117	1	8	yes	—
114	C₂²×C₃²	#124	1	8	yes	—
115	C₂²×C₃²	#125	1	8	yes	—
116	C₂²×C₃²	C₂³×C₄	1	1	yes	characteristic
117	C₂²×C₃²	C₂²×D₄	1	1	yes	characteristic
118	C₂²×C₃²	C₂²×Q₈	1	1	yes	characteristic
119	C₂²×C₃²	C₂×#41	1	4	yes	—
120	C₃²×C₄	—	2	8	no	—
121	C₃²×C₄	C₂×C₄⋊C₄	1	8	yes	—
122	C₃×Dic₃	—	4	8	no	—
123	C₂³×C₄	—	3	4	no	—
124	C₂³×C₄	C₂×C₃×D₃	1	2	yes	—
125	C₂³×C₄	C₂×C₃×D₃	1	1	yes	characteristic
126	C₂×C₄⋊C₄	—	3	8	no	—
127	C₂×C₄⋊C₄	—	6	8	no	—
128	C₂×C₄²	C₃×Dic₃	1	8	yes	complemented
129	C₂×C₄²	C₂×C₃×D₃	1	4	yes	—
130	#95	—	3	16	no	—
131	C₂³×C₃	—	2	1	no	—
132	C₂³×C₃	—	2	2	no	—
133	C₂³×C₃	—	2	2	no	—
134	C₂³×C₃	—	2	8	no	—
135	C₂³×C₃	—	2	2	no	—
136	C₂³×C₃	C₂×Dic₆	1	2	yes	—
137	C₂³×C₃	C₂×D₁₂	1	2	yes	—
138	C₂³×C₃	#235	1	8	yes	—
139	C₂³×C₃	C₂²×Dic₃	1	2	yes	—
140	C₂³×C₃	C₂²×C₃×C₄	1	2	yes	—
141	C₂³×C₃	C₂×C₃×D₄	1	2	yes	—
142	C₂³×C₃	C₂×C₃×Q₈	1	2	yes	—
143	C₂³×C₃	C₃×#41	1	8	yes	—
144	C₂³×C₃	C₂³×D₃	1	1	yes	characteristic
145	C₂³×C₃	C₂⁴×C₃	1	1	yes	characteristic
146	C₂×C₃×C₄	—	2	32	no	—
147	C₂×C₃×C₄	—	2	16	no	—
148	C₂×C₃×C₄	—	2	16	no	—
149	C₂×C₃×C₄	—	2	16	no	—
150	C₂×C₃×C₄	—	2	8	no	—
151	C₂×C₃×C₄	—	2	8	no	—
152	C₂×C₃×C₄	—	2	16	no	—
153	C₂×C₃×C₄	—	2	4	no	—
154	C₂×C₃×C₄	—	2	4	no	—
155	C₂×C₃×C₄	—	2	8	no	—
156	C₂×C₃×C₄	—	2	4	no	—
157	C₂×C₃×C₄	—	6	8	no	—
158	C₂×C₃×C₄	—	6	16	no	—
159	C₂×C₃×C₄	—	12	16	no	—
160	C₂×C₃×C₄	C₄⋊Dic₃	1	16	yes	—
161	C₂×C₃×C₄	C₃×C₄⋊C₄	1	16	yes	—
162	C₂×C₃×C₄	C₂×Dic₆	1	4	yes	—
163	C₂×C₃×C₄	C₂×D₁₂	1	4	yes	—
164	C₂×C₃×C₄	C₂²×Dic₃	1	8	yes	—
165	C₂×C₃×C₄	C₂²×Dic₃	1	4	yes	—
166	C₂×C₃×C₄	C₂²×C₃×C₄	1	8	yes	—
167	C₂×C₃×C₄	C₂²×C₃×C₄	1	4	yes	—
168	C₂×C₃×C₄	C₂×C₃×D₄	1	4	yes	—
169	C₂×C₃×C₄	C₂×C₃×Q₈	1	4	yes	—
170	C₂×Dic₃	—	2	8	no	—
171	C₂×Dic₃	—	2	16	no	—
172	C₂×Dic₃	—	4	16	no	—
173	C₂×C₃²	#382	1	8	yes	complemented
174	C₂×C₃²	C₂²×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₃²	C₂×#117	1	2	yes	—
176	C₂×C₃²	C₂×#124	1	2	yes	—
177	C₂×C₃²	C₂×#125	1	2	yes	—
178	C₂⁴	C₂²×C₃×D₃	1	1	yes	characteristic
179	C₂²×C₄	—	2	8	no	—
180	C₂²×C₄	—	3	8	no	—
181	C₂²×C₄	—	6	8	no	—
182	C₂²×C₄	—	6	16	no	—
183	C₂²×C₄	C₃×Dic₆	1	4	yes	—
184	C₂²×C₄	C₃×D₁₂	1	4	yes	—
185	C₂²×C₄	C₂×C₃×Dic₃	1	8	yes	—
186	C₂²×C₄	C₂×C₃×Dic₃	1	4	yes	—
187	C₂²×C₄	C₂²×C₃×D₃	1	4	yes	—
188	C₂²×C₄	C₂²×C₃×D₃	1	2	yes	—
189	C₄⋊C₄	—	6	16	no	—
190	C₄²	C₂×C₃×Dic₃	1	16	yes	complemented
191	C₂²×C₃	—	2	4	no	—
192	C₂²×C₃	—	2	8	no	—
193	C₂²×C₃	—	2	1	no	—
194	C₂²×C₃	—	2	1	no	—
195	C₂²×C₃	—	2	4	no	—
196	C₂²×C₃	—	2	1	no	—
197	C₂²×C₃	—	2	8	no	—
198	C₂²×C₃	—	2	8	no	—
199	C₂²×C₃	#870	1	8	yes	—
200	C₂²×C₃	#875	1	8	yes	—
201	C₂²×C₃	C₂×C₄⋊Dic₃	1	4	yes	—
202	C₂²×C₃	#926	1	8	yes	—
203	C₂²×C₃	C₂×C₃×C₄⋊C₄	1	4	yes	—
204	C₂²×C₃	C₃×#117	1	8	yes	—
205	C₂²×C₃	C₃×#124	1	8	yes	—
206	C₂²×C₃	C₃×#125	1	8	yes	—
207	C₂²×C₃	C₂²×Dic₆	1	1	yes	characteristic
208	C₂²×C₃	C₂²×D₁₂	1	1	yes	characteristic
209	C₂²×C₃	C₂×#235	1	4	yes	—
210	C₂²×C₃	C₂³×Dic₃	1	1	yes	characteristic
211	C₂²×C₃	C₂³×C₃×C₄	1	1	yes	characteristic
212	C₂²×C₃	C₂²×C₃×D₄	1	1	yes	characteristic
213	C₂²×C₃	C₂²×C₃×Q₈	1	1	yes	characteristic
214	C₂²×C₃	C₂×C₃×#41	1	4	yes	—
215	C₃×C₄	—	2	16	no	—
216	C₃×C₄	—	2	8	no	—
217	C₃×C₄	—	2	8	no	—
218	C₃×C₄	—	2	8	no	—
219	C₃×C₄	—	12	8	no	—
220	C₃×C₄	C₂×C₄⋊Dic₃	1	8	yes	—
221	C₃×C₄	C₂×C₃×C₄⋊C₄	1	8	yes	—
222	Dic₃	—	4	8	no	—
223	C₃²	C₂×#382	1	1	yes	characteristic, complemented, Sylow
224	C₂³	C₂×C₃×Dic₆	1	2	yes	—
225	C₂³	C₂×C₃×D₁₂	1	2	yes	—
226	C₂³	C₃×#235	1	8	yes	—
227	C₂³	C₂²×C₃×Dic₃	1	2	yes	—
228	C₂³	C₂³×C₃×D₃	1	1	yes	characteristic
229	C₂×C₄	—	2	16	no	—
230	C₂×C₄	—	2	8	no	—
231	C₂×C₄	—	6	8	no	—
232	C₂×C₄	—	6	16	no	—
233	C₂×C₄	—	12	16	no	—
234	C₂×C₄	C₃×C₄⋊Dic₃	1	16	yes	—
235	C₂×C₄	C₂×C₃×Dic₆	1	4	yes	—
236	C₂×C₄	C₂×C₃×D₁₂	1	4	yes	—
237	C₂×C₄	C₂²×C₃×Dic₃	1	8	yes	—
238	C₂×C₄	C₂²×C₃×Dic₃	1	4	yes	—
239	C₂×C₃	—	2	8	no	—
240	C₂×C₃	—	2	1	no	—
241	C₂×C₃	—	2	2	no	—
242	C₂×C₃	—	2	2	no	—
243	C₂×C₃	—	2	2	no	—
244	C₂×C₃	#4936	1	8	yes	direct product factor
245	C₂×C₃	C₃×#382	1	8	yes	complemented
246	C₂×C₃	C₂×#870	1	2	yes	—
247	C₂×C₃	C₂×#875	1	2	yes	—
248	C₂×C₃	C₂²×C₄⋊Dic₃	1	1	yes	characteristic
249	C₂×C₃	C₂×#926	1	2	yes	—
250	C₂×C₃	C₂²×C₃×C₄⋊C₄	1	1	yes	characteristic
251	C₂×C₃	C₂×C₃×#117	1	2	yes	—
252	C₂×C₃	C₂×C₃×#124	1	2	yes	—
253	C₂×C₃	C₂×C₃×#125	1	2	yes	—
254	C₂²	C₃×#870	1	8	yes	—
255	C₂²	C₃×#875	1	8	yes	—
256	C₂²	C₂×C₃×C₄⋊Dic₃	1	4	yes	—
257	C₂²	C₃×#926	1	8	yes	—
258	C₂²	C₂²×C₃×Dic₆	1	1	yes	characteristic
259	C₂²	C₂²×C₃×D₁₂	1	1	yes	characteristic
260	C₂²	C₂×C₃×#235	1	4	yes	—
261	C₂²	C₂³×C₃×Dic₃	1	1	yes	characteristic
262	C₄	—	2	8	no	—
263	C₄	—	12	8	no	—
264	C₄	C₂×C₃×C₄⋊Dic₃	1	8	yes	—
265	C₃	—	2	1	no	—
266	C₃	C₂×#4936	1	1	yes	characteristic, direct product factor
267	C₃	C₂×C₃×#382	1	1	yes	characteristic, complemented
268	C₂	C₃×#4936	1	8	yes	direct product factor
269	C₂	C₂×C₃×#870	1	2	yes	—
270	C₂	C₂×C₃×#875	1	2	yes	—
271	C₂	C₂²×C₃×C₄⋊Dic₃	1	1	yes	characteristic
272	C₂	C₂×C₃×#926	1	2	yes	—

	subgroup	G/H
center	C₂⁴×C₃	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₃
Fitting	C₂²×C₃²×C₄²	C₂
socle, prime radical	C₂⁴×C₃²	C₂³
cosocle	C₂³×C₃	C₂⁴×C₃
hypercenter	C₂²×C₃×C₄²	D₃
hypocenter	C₃	C₂×C₃×#382
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₃ ◁ C₂²×C₃×C₄²

Complements

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

N	H ≅ G/N	type
4. C₃×#4936	C₂	direct (N × H)
6. C₂×#4936	C₃	direct (N × H)
10. C₂×C₃²×C₄²	C₄	semidirect
23. #4936	C₂×C₃	direct (N × H)
35. C₃²×C₄²	C₂×C₄	semidirect
50. C₂×C₃×C₄²	Dic₃	semidirect
51. C₂×C₃×C₄²	C₃×C₄	semidirect
109. C₃×C₄²	C₂×Dic₃	semidirect
110. C₃×C₄²	C₂×C₃×C₄	semidirect
128. C₂×C₄²	C₃×Dic₃	semidirect
173. C₂×C₃²	#382	semidirect
190. C₄²	C₂×C₃×Dic₃	semidirect
223. C₃²	C₂×#382	semidirect
244. C₂×C₃	#4936	direct (N × H)
245. C₂×C₃	C₃×#382	semidirect
266. C₃	C₂×#4936	direct (N × H)
267. C₃	C₂×C₃×#382	semidirect
268. C₂	C₃×#4936	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃²×C₄²	2
C₂²×C₃×C₄⋊Dic₃	2
C₂×C₃×C₃⋊#95	2
C₃×#4936	2
C₂×C₃×#382	3
C₂×#4936	3

Subgroups — C2×C3×#4936 #11801086

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#4936 #11801086