Subgroups — #11770903

Order 1152.

425 conjugacy classes of subgroups.

The subgroup lattice has 287 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₄⋊(C₃⋊Dic₃)	C₂	1	1	yes	maximal, characteristic
2	C₃×#4926	C₂	1	1	yes	maximal, characteristic
3	C₃×#4926	C₂	1	1	yes	maximal, characteristic
4	#67750	—	3	1	no	maximal
5	#67749	—	3	1	no	maximal
6	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
7	C₂×C₄⋊(C₃⋊Dic₃)	—	2	1	no	—
8	C₂×C₄×C₃⋊Dic₃	C₄	1	2	yes	—
9	#63658	—	2	1	no	—
10	C₃×#830	—	2	1	no	—
11	C₃×#830	—	2	1	no	—
12	C₃×C₄⋊(C₃⋊C₈)	—	2	1	no	—
13	C₃×C₄⋊(C₃⋊C₈)	C₄	1	2	yes	complemented
14	C₃×#803	—	2	1	no	—
15	C₃×#803	C₄	1	2	yes	complemented
16	C₃×#432	—	3	1	no	—
17	C₃×#432	—	3	1	no	—
18	C₄×C₄⋊Dic₃	—	3	1	no	—
19	C₄×C₄⋊Dic₃	—	3	1	no	—
20	C₄×C₄⋊Dic₃	—	6	1	no	—
21	#4926	D₃	1	1	yes	characteristic
22	#4926	D₃	1	1	yes	characteristic
23	C₂²×C₃²×C₄	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
25	C₂²×C₃²×C₄	D₄	1	1	yes	characteristic
26	C₂²×C₃⋊Dic₃	—	2	2	no	—
27	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
28	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
29	C₃²×C₄²	D₄	1	1	yes	characteristic
30	C₃²×C₄²	Q₈	1	1	yes	characteristic
31	C₄⋊(C₃⋊Dic₃)	—	2	4	no	—
32	C₄×C₃⋊Dic₃	—	4	2	no	—
33	C₂×C₃×C₃⋊C₈	—	2	2	no	—
34	C₂×C₃×C₃⋊C₈	—	2	2	no	—
35	#1285	—	9	1	no	Sylow
36	C₂×C₃×C₄²	—	2	1	no	—
37	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
38	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
39	C₂×C₄⋊Dic₃	—	6	2	no	—
40	C₂×C₄⋊Dic₃	—	6	1	no	—
41	C₂×C₄⋊Dic₃	—	6	1	no	—
42	C₂×C₄×Dic₃	—	3	2	no	—
43	C₂×C₄×Dic₃	—	3	2	no	—
44	C₂×C₄×Dic₃	—	6	2	no	—
45	C₃×C₄⋊C₈	—	3	2	no	—
46	C₃×C₄⋊C₈	—	6	1	no	—
47	C₃×C₂²⋊C₈	—	6	1	no	—
48	C₃×C₂²⋊C₈	—	6	1	no	—
49	C₃×#97	—	3	2	no	—
50	C₃×#97	—	6	1	no	—
51	C₃⋊#95	—	6	2	no	—
52	C₃⋊#95	—	6	1	no	—
53	C₃⋊#95	—	6	1	no	—
54	#830	—	2	1	no	—
55	#830	—	2	1	no	—
56	C₄⋊(C₃⋊C₈)	—	2	1	no	—
57	C₄⋊(C₃⋊C₈)	Dic₃	1	2	yes	complemented
58	#803	—	2	1	no	—
59	#803	Dic₃	1	2	yes	complemented
60	C₂³×C₃²	C₂²⋊C₄	1	1	yes	characteristic
61	C₂×C₃²×C₄	—	2	1	no	—
62	C₂×C₃²×C₄	—	2	1	no	—
63	C₂×C₃²×C₄	—	2	2	no	—
64	C₂×C₃²×C₄	—	4	1	no	—
65	C₂×C₃²×C₄	C₄²	1	1	yes	characteristic
66	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
67	C₂×C₃²×C₄	C₂²⋊C₄	1	1	yes	characteristic
68	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
69	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
70	C₂×C₃²×C₄	C₄⋊C₄	1	1	yes	characteristic
71	C₂×C₃⋊Dic₃	—	2	4	no	—
72	C₂×C₃⋊Dic₃	—	4	2	no	—
73	C₂×C₃⋊Dic₃	—	4	2	no	—
74	C₃×C₃⋊C₈	—	4	2	no	—
75	C₃×C₃⋊C₈	—	4	2	no	—
76	#432	—	3	1	no	—
77	#432	—	3	1	no	—
78	C₄×C₄⋊C₄	—	9	1	no	—
79	C₂²×C₃×C₄	—	2	1	no	—
80	C₂²×C₃×C₄	—	2	1	no	—
81	C₂²×C₃×C₄	—	2	1	no	—
82	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
83	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
84	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
85	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
86	C₂²×C₃×C₄	#67	1	1	yes	characteristic
87	C₂²×C₃×C₄	#67	1	1	yes	characteristic
88	C₂²×Dic₃	—	6	4	no	—
89	C₂²×Dic₃	—	6	2	no	—
90	C₂²×Dic₃	—	6	2	no	—
91	C₂×C₃×C₈	—	6	2	no	—
92	C₂×C₃×C₈	—	6	2	no	—
93	C₃×C₄²	—	2	1	no	—
94	C₃×C₄²	—	2	1	no	—
95	C₃×C₄²	—	2	1	no	—
96	C₃×C₄²	—	2	1	no	—
97	C₃×C₄²	Dic₆	1	1	yes	characteristic
98	C₃×C₄²	Dic₆	1	1	yes	characteristic
99	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
100	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
101	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
102	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
103	C₃×C₄²	#67	1	1	yes	characteristic
104	C₃×C₄²	#67	1	1	yes	characteristic
105	C₄⋊Dic₃	—	6	8	no	—
106	C₄⋊Dic₃	—	6	4	no	—
107	C₄⋊Dic₃	—	6	4	no	—
108	C₄×Dic₃	—	12	4	no	—
109	C₄×Dic₃	—	12	2	no	—
110	C₄×Dic₃	—	12	2	no	—
111	C₂×C₃⋊C₈	—	2	2	no	—
112	C₂×C₃⋊C₈	—	2	2	no	—
113	C₂²×C₃²	—	2	1	no	—
114	C₂²×C₃²	—	2	1	no	—
115	C₂²×C₃²	#95	1	1	yes	characteristic
116	C₂²×C₃²	#100	1	1	yes	characteristic
117	C₂²×C₃²	#101	1	1	yes	characteristic
118	C₃²×C₄	—	2	1	no	—
119	C₃²×C₄	—	2	1	no	—
120	C₃²×C₄	—	2	1	no	—
121	C₃²×C₄	—	2	1	no	—
122	C₃²×C₄	—	2	1	no	—
123	C₃²×C₄	#104	1	2	yes	—
124	C₃⋊Dic₃	—	4	4	no	—
125	C₂×C₄⋊C₄	—	18	1	no	—
126	C₂×C₄²	—	9	2	no	—
127	C₂×C₄²	D₃²	1	1	yes	characteristic
128	C₄⋊C₈	—	3	2	no	—
129	C₄⋊C₈	—	6	1	no	—
130	C₂²⋊C₈	—	6	1	no	—
131	C₂²⋊C₈	—	6	1	no	—
132	#97	—	3	2	no	—
133	#97	—	6	1	no	—
134	#95	—	18	1	no	—
135	C₂³×C₃	—	2	1	no	—
136	C₂³×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
137	C₂³×C₃	(C₂×D₃)⋊C₄	1	1	yes	characteristic
138	C₂×C₃×C₄	—	2	2	no	—
139	C₂×C₃×C₄	—	2	4	no	—
140	C₂×C₃×C₄	—	2	2	no	—
141	C₂×C₃×C₄	—	2	1	no	—
142	C₂×C₃×C₄	—	2	1	no	—
143	C₂×C₃×C₄	—	2	1	no	—
144	C₂×C₃×C₄	—	2	1	no	—
145	C₂×C₃×C₄	—	2	2	no	—
146	C₂×C₃×C₄	—	2	2	no	—
147	C₂×C₃×C₄	—	2	1	no	—
148	C₂×C₃×C₄	—	2	1	no	—
149	C₂×C₃×C₄	—	2	1	no	—
150	C₂×C₃×C₄	—	2	1	no	—
151	C₂×C₃×C₄	—	2	1	no	—
152	C₂×C₃×C₄	—	2	1	no	—
153	C₂×C₃×C₄	—	4	1	no	—
154	C₂×C₃×C₄	—	4	1	no	—
155	C₂×C₃×C₄	—	4	2	no	—
156	C₂×C₃×C₄	C₄×Dic₃	1	1	yes	characteristic
157	C₂×C₃×C₄	C₄×Dic₃	1	1	yes	characteristic
158	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
159	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
160	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
161	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
162	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
163	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
164	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
165	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
166	C₂×C₃×C₄	#217	1	1	yes	characteristic
167	C₂×C₃×C₄	#217	1	1	yes	characteristic
168	C₂×Dic₃	—	6	8	no	—
169	C₂×Dic₃	—	6	4	no	—
170	C₂×Dic₃	—	6	4	no	—
171	C₂×Dic₃	—	12	4	no	—
172	C₂×Dic₃	—	12	4	no	—
173	C₂×Dic₃	—	12	2	no	—
174	C₂×Dic₃	—	12	2	no	—
175	C₂×Dic₃	—	12	2	no	—
176	C₂×Dic₃	—	12	2	no	—
177	C₃×C₈	—	12	2	no	—
178	C₃×C₈	—	12	2	no	—
179	C₃⋊C₈	—	4	2	no	—
180	C₃⋊C₈	—	4	2	no	—
181	C₂×C₃²	—	2	1	no	—
182	C₂×C₃²	—	2	1	no	—
183	C₂×C₃²	H(3,ℤ/4)	1	1	yes	characteristic
184	C₂×C₃²	#339	1	1	yes	characteristic
185	C₂×C₃²	#343	1	1	yes	characteristic
186	C₂²×C₄	—	18	2	no	—
187	C₂²×C₄	#624	1	1	yes	characteristic
188	C₂²×C₄	#626	1	1	yes	characteristic
189	C₂²×C₄	#626	1	1	yes	characteristic
190	C₂×C₈	—	6	2	no	—
191	C₂×C₈	—	6	2	no	—
192	C₄⋊C₄	—	18	4	no	—
193	C₄²	—	36	2	no	—
194	C₄²	D₃×Dic₃	1	1	yes	characteristic
195	C₄²	D₃×Dic₃	1	1	yes	characteristic
196	C₄²	#625	1	1	yes	characteristic
197	C₄²	#627	1	1	yes	characteristic
198	C₂²×C₃	—	2	2	no	—
199	C₂²×C₃	—	2	2	no	—
200	C₂²×C₃	—	2	1	no	—
201	C₂²×C₃	—	2	1	no	—
202	C₂²×C₃	—	2	1	no	—
203	C₂²×C₃	—	2	1	no	—
204	C₂²×C₃	—	2	1	no	—
205	C₂²×C₃	—	2	1	no	—
206	C₂²×C₃	—	2	1	no	—
207	C₂²×C₃	#823	1	1	yes	characteristic
208	C₂²×C₃	#823	1	1	yes	characteristic
209	C₂²×C₃	#824	1	1	yes	characteristic
210	C₂²×C₃	#824	1	1	yes	characteristic
211	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
212	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
213	C₃×C₄	—	2	2	no	—
214	C₃×C₄	—	2	2	no	—
215	C₃×C₄	—	2	2	no	—
216	C₃×C₄	—	2	1	no	—
217	C₃×C₄	—	2	1	no	—
218	C₃×C₄	—	2	1	no	—
219	C₃×C₄	—	2	1	no	—
220	C₃×C₄	—	2	1	no	—
221	C₃×C₄	—	2	1	no	—
222	C₃×C₄	—	2	1	no	—
223	C₃×C₄	—	2	1	no	—
224	C₃×C₄	—	2	1	no	—
225	C₃×C₄	—	2	1	no	—
226	C₃×C₄	—	2	2	no	—
227	C₃×C₄	—	4	1	no	—
228	C₃×C₄	—	4	1	no	—
229	C₃×C₄	#825	1	2	yes	—
230	C₃×C₄	#837	1	2	yes	—
231	Dic₃	—	12	8	no	—
232	Dic₃	—	12	4	no	—
233	Dic₃	—	12	4	no	—
234	C₃²	#1285	1	1	yes	characteristic, complemented, Sylow
235	C₂³	#3722	1	1	yes	characteristic
236	C₂×C₄	—	2	1	no	—
237	C₂×C₄	—	2	1	no	—
238	C₂×C₄	—	2	2	no	—
239	C₂×C₄	—	4	1	no	—
240	C₂×C₄	—	18	4	no	—
241	C₂×C₄	—	36	2	no	—
242	C₂×C₄	—	36	2	no	—
243	C₂×C₄	Dic₃²	1	1	yes	characteristic
244	C₂×C₄	(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
245	C₂×C₄	(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
246	C₂×C₄	Dic₃⋊Dic₃	1	1	yes	characteristic
247	C₂×C₄	Dic₃⋊Dic₃	1	1	yes	characteristic
248	C₂×C₄	#3724	1	1	yes	characteristic
249	C₈	—	12	2	no	—
250	C₈	—	12	2	no	—
251	C₂×C₃	—	2	2	no	—
252	C₂×C₃	—	2	2	no	—
253	C₂×C₃	—	2	1	no	—
254	C₂×C₃	—	2	1	no	—
255	C₂×C₃	—	2	1	no	—
256	C₂×C₃	—	2	1	no	—
257	C₂×C₃	—	2	1	no	—
258	C₂×C₃	—	2	1	no	—
259	C₂×C₃	—	2	1	no	—
260	C₂×C₃	#4531	1	1	yes	characteristic
261	C₂×C₃	#4532	1	1	yes	characteristic
262	C₂×C₃	#4554	1	1	yes	characteristic
263	C₂×C₃	#4554	1	1	yes	characteristic
264	C₂×C₃	#4555	1	1	yes	characteristic
265	C₂×C₃	#4557	1	1	yes	characteristic
266	C₂²	—	2	1	no	—
267	C₂²	—	2	1	no	—
268	C₂²	#63559	1	1	yes	characteristic
269	C₂²	#63561	1	1	yes	characteristic
270	C₂²	#63579	1	1	yes	characteristic
271	C₄	—	2	1	no	—
272	C₄	—	2	1	no	—
273	C₄	—	2	1	no	—
274	C₄	—	2	1	no	—
275	C₄	—	2	1	no	—
276	C₄	—	36	4	no	—
277	C₄	#63568	1	2	yes	—
278	C₃	—	2	1	no	—
279	C₃	#67749	1	1	yes	characteristic, complemented
280	C₃	#67750	1	1	yes	characteristic, complemented
281	C₂	—	2	1	no	—
282	C₂	—	2	1	no	—
283	C₂	#10589158	1	1	yes	characteristic
284	C₂	#10589160	1	1	yes	characteristic
285	C₂	#10589168	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#63579
commutator	C₂×C₃²×C₄	C₄²
Frattini, hypercenter	C₂×C₄²	D₃²
Fitting, cosocle	C₂×C₃²×C₄²	C₂²
socle	C₂²×C₃²	#95
prime radical	C₂³×C₃²	C₂²⋊C₄
hypocenter	C₃²	#1285
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂² ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
13. C₃×C₄⋊(C₃⋊C₈)	C₄	semidirect
15. C₃×#803	C₄	semidirect
57. C₄⋊(C₃⋊C₈)	Dic₃	semidirect
59. #803	Dic₃	semidirect
234. C₃²	#1285	semidirect
279. C₃	#67749	semidirect
280. C₃	#67750	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₄⋊(C₃⋊Dic₃)	2
C₃×#4926	2
#67750	3
#67749	3