Subgroups — #11771130

Order 1152.

359 conjugacy classes of subgroups.

The subgroup lattice has 265 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10592624	C₂	1	1	yes	maximal, characteristic
2	C₃×#4924	C₂	1	1	yes	maximal, characteristic
3	C₃×C₄×#208	C₂	1	1	yes	maximal, characteristic
4	#67710	—	3	1	no	maximal
5	#67669	—	3	1	no	maximal
6	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
7	C₂×C₃×#208	—	2	1	no	—
8	C₂×C₃×#208	C₄	1	2	yes	—
9	#63657	—	2	1	no	—
10	C₄⋊(C₃⋊(C₃⋊C₈))	C₄	1	2	yes	—
11	C₄×C₃⋊(C₃⋊C₈)	—	2	1	no	—
12	C₃×C₄⋊(C₃⋊C₈)	—	2	1	no	—
13	C₃×C₄⋊(C₃⋊C₈)	—	2	1	no	—
14	C₃×#803	C₄	1	2	yes	—
15	C₃×C₄×C₃⋊C₈	—	2	1	no	—
16	C₃×#423	—	3	1	no	—
17	C₃×C₄×M₁₆	—	3	1	no	—
18	#4925	—	3	1	no	—
19	#4925	—	3	1	no	—
20	#4925	—	6	1	no	—
21	#4924	D₃	1	1	yes	characteristic
22	C₄×#208	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	Q₈	1	1	yes	characteristic
26	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
27	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
28	C₃²×C₄²	D₄	1	1	yes	characteristic
29	C₃²×C₄²	D₄	1	1	yes	characteristic
30	C₂×C₃⋊(C₃⋊C₈)	—	2	2	no	—
31	C₃×#208	—	2	4	no	—
32	C₃×#208	—	4	2	no	—
33	C₂×C₃×C₃⋊C₈	—	2	2	no	—
34	C₂×C₃×C₃⋊C₈	—	2	2	no	—
35	#1299	—	9	1	no	Sylow
36	C₂×C₃×M₁₆	—	3	2	no	—
37	C₂×C₃×M₁₆	—	6	1	no	—
38	C₂×C₃×C₄²	—	2	1	no	—
39	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
40	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
41	C₂×#208	—	2	1	no	—
42	C₂×#208	Dic₃	1	2	yes	—
43	C₃×C₄⋊C₈	—	6	1	no	—
44	C₃×C₄⋊C₈	—	6	1	no	—
45	C₃×#97	—	3	2	no	—
46	C₃×C₄×C₈	—	6	1	no	—
47	#830	—	6	2	no	—
48	#830	—	6	1	no	—
49	#830	—	6	1	no	—
50	C₄⋊(C₃⋊C₈)	—	2	1	no	—
51	C₄⋊(C₃⋊C₈)	—	2	1	no	—
52	C₄⋊(C₃⋊C₈)	—	3	2	no	—
53	C₄⋊(C₃⋊C₈)	—	3	2	no	—
54	C₄⋊(C₃⋊C₈)	—	6	2	no	—
55	#803	Dic₃	1	2	yes	—
56	C₄×C₃⋊C₈	—	2	1	no	—
57	C₄×C₃⋊C₈	—	6	2	no	—
58	C₄×C₃⋊C₈	—	6	1	no	—
59	C₄×C₃⋊C₈	—	6	1	no	—
60	C₂³×C₃²	C₄⋊C₄	1	1	yes	characteristic
61	C₂×C₃²×C₄	—	2	2	no	—
62	C₂×C₃²×C₄	—	2	1	no	—
63	C₂×C₃²×C₄	—	2	1	no	—
64	C₂×C₃²×C₄	—	2	2	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	C₂²⋊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	C₃⋊(C₃⋊C₈)	—	4	2	no	—
72	C₃×C₃⋊C₈	—	2	4	no	—
73	C₃×C₃⋊C₈	—	4	2	no	—
74	#431	—	9	1	no	—
75	#423	—	3	1	no	—
76	C₄×M₁₆	—	3	1	no	—
77	C₂²×C₃×C₄	—	2	1	no	—
78	C₂²×C₃×C₄	—	2	1	no	—
79	C₂²×C₃×C₄	—	2	1	no	—
80	C₂²×C₃×C₄	Dic₆	1	1	yes	characteristic
81	C₂²×C₃×C₄	Dic₆	1	1	yes	characteristic
82	C₂²×C₃×C₄	C₄×D₃	1	1	yes	characteristic
83	C₂²×C₃×C₄	D₁₂	1	1	yes	characteristic
84	C₂²×C₃×C₄	C₂×Dic₃	1	1	yes	characteristic
85	C₂²×C₃×C₄	#67	1	1	yes	characteristic
86	C₃×M₁₆	—	6	4	no	—
87	C₃×M₁₆	—	12	2	no	—
88	C₂×C₃×C₈	—	6	2	no	—
89	C₂×C₃×C₈	—	6	2	no	—
90	C₃×C₄²	—	2	1	no	—
91	C₃×C₄²	—	2	1	no	—
92	C₃×C₄²	—	2	1	no	—
93	C₃×C₄²	—	2	1	no	—
94	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
95	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
96	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
97	C₃×C₄²	D₁₂	1	1	yes	characteristic
98	C₃×C₄²	C₂×Dic₃	1	1	yes	characteristic
99	C₃×C₄²	#67	1	1	yes	characteristic
100	C₃×C₄²	#67	1	1	yes	characteristic
101	C₃×C₄²	#67	1	1	yes	characteristic
102	#208	—	2	4	no	—
103	#208	—	4	2	no	—
104	C₂×C₃⋊C₈	—	2	2	no	—
105	C₂×C₃⋊C₈	—	2	2	no	—
106	C₂×C₃⋊C₈	—	6	4	no	—
107	C₂×C₃⋊C₈	—	6	2	no	—
108	C₂×C₃⋊C₈	—	6	2	no	—
109	C₂²×C₃²	—	2	1	no	—
110	C₂²×C₃²	—	2	1	no	—
111	C₂²×C₃²	—	2	1	no	—
112	C₂²×C₃²	#95	1	1	yes	characteristic
113	C₃²×C₄	—	2	1	no	—
114	C₃²×C₄	—	2	1	no	—
115	C₃²×C₄	—	2	1	no	—
116	C₃²×C₄	#100	1	1	yes	characteristic
117	C₃²×C₄	#101	1	1	yes	characteristic
118	C₃²×C₄	#104	1	2	yes	—
119	C₃²×C₄	#108	1	2	yes	—
120	C₂×M₁₆	—	3	2	no	—
121	C₂×M₁₆	—	6	1	no	—
122	C₂×C₄²	D₃²	1	1	yes	characteristic
123	C₄⋊C₈	—	6	1	no	—
124	C₄⋊C₈	—	6	1	no	—
125	C₄⋊C₈	—	9	2	no	—
126	C₂²⋊C₈	—	18	1	no	—
127	#97	—	3	2	no	—
128	C₄×C₈	—	6	1	no	—
129	C₄×C₈	—	18	1	no	—
130	C₂³×C₃	—	2	1	no	—
131	C₂³×C₃	Dic₃⋊C₄	1	1	yes	characteristic
132	C₂³×C₃	C₄⋊Dic₃	1	1	yes	characteristic
133	C₂×C₃×C₄	—	2	4	no	—
134	C₂×C₃×C₄	—	2	2	no	—
135	C₂×C₃×C₄	—	2	2	no	—
136	C₂×C₃×C₄	—	2	2	no	—
137	C₂×C₃×C₄	—	2	1	no	—
138	C₂×C₃×C₄	—	2	1	no	—
139	C₂×C₃×C₄	—	2	2	no	—
140	C₂×C₃×C₄	—	2	1	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	1	no	—
146	C₂×C₃×C₄	—	2	1	no	—
147	C₂×C₃×C₄	—	2	1	no	—
148	C₂×C₃×C₄	—	4	1	no	—
149	C₂×C₃×C₄	—	4	1	no	—
150	C₂×C₃×C₄	—	4	2	no	—
151	C₂×C₃×C₄	C₄×Dic₃	1	1	yes	characteristic
152	C₂×C₃×C₄	C₄×Dic₃	1	1	yes	characteristic
153	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
154	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
155	C₂×C₃×C₄	Dic₃⋊C₄	1	1	yes	characteristic
156	C₂×C₃×C₄	C₄⋊Dic₃	1	1	yes	characteristic
157	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
158	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
159	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
160	C₂×C₃×C₄	(C₂×D₃)⋊C₄	1	1	yes	characteristic
161	C₂×C₃×C₄	#217	1	1	yes	characteristic
162	C₂×C₃×C₄	#217	1	1	yes	characteristic
163	C₃×C₈	—	6	4	no	—
164	C₃×C₈	—	12	2	no	—
165	C₃⋊C₈	—	2	4	no	—
166	C₃⋊C₈	—	4	2	no	—
167	C₃⋊C₈	—	12	4	no	—
168	C₃⋊C₈	—	12	2	no	—
169	C₃⋊C₈	—	12	2	no	—
170	C₂×C₃²	—	4	1	no	—
171	C₂×C₃²	#339	1	1	yes	characteristic
172	C₂×C₃²	#341	1	1	yes	characteristic
173	C₂×C₃²	#343	1	1	yes	characteristic
174	C₂²×C₄	D₃×Dic₃	1	1	yes	characteristic
175	C₂²×C₄	#626	1	1	yes	characteristic
176	C₂²×C₄	#627	1	1	yes	characteristic
177	M₁₆	—	6	4	no	—
178	M₁₆	—	12	2	no	—
179	C₂×C₈	—	6	2	no	—
180	C₂×C₈	—	6	2	no	—
181	C₂×C₈	—	18	2	no	—
182	C₄²	D₃×Dic₃	1	1	yes	characteristic
183	C₄²	#624	1	1	yes	characteristic
184	C₄²	#625	1	1	yes	characteristic
185	C₄²	#626	1	1	yes	characteristic
186	C₂²×C₃	—	2	2	no	—
187	C₂²×C₃	—	2	1	no	—
188	C₂²×C₃	—	2	1	no	—
189	C₂²×C₃	—	2	1	no	—
190	C₂²×C₃	—	2	1	no	—
191	C₂²×C₃	—	2	1	no	—
192	C₂²×C₃	—	2	1	no	—
193	C₂²×C₃	—	2	1	no	—
194	C₂²×C₃	—	4	1	no	—
195	C₂²×C₃	—	4	1	no	—
196	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
197	C₂²×C₃	C₃⋊#95	1	1	yes	characteristic
198	C₃×C₄	—	2	2	no	—
199	C₃×C₄	—	2	1	no	—
200	C₃×C₄	—	2	1	no	—
201	C₃×C₄	—	2	1	no	—
202	C₃×C₄	—	2	1	no	—
203	C₃×C₄	—	2	1	no	—
204	C₃×C₄	—	2	1	no	—
205	C₃×C₄	—	2	1	no	—
206	C₃×C₄	—	2	1	no	—
207	C₃×C₄	—	2	2	no	—
208	C₃×C₄	—	2	2	no	—
209	C₃×C₄	—	4	1	no	—
210	C₃×C₄	—	4	1	no	—
211	C₃×C₄	#805	1	2	yes	—
212	C₃×C₄	#822	1	2	yes	—
213	C₃×C₄	#822	1	2	yes	—
214	C₃×C₄	#823	1	1	yes	characteristic
215	C₃×C₄	#824	1	1	yes	characteristic
216	C₃×C₄	#825	1	2	yes	—
217	C₃×C₄	#833	1	1	yes	characteristic
218	C₃×C₄	#836	1	1	yes	characteristic
219	C₃²	#1299	1	1	yes	characteristic, complemented, Sylow
220	C₂³	Dic₃⋊Dic₃	1	1	yes	characteristic
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	2	no	—
224	C₂×C₄	—	2	2	no	—
225	C₂×C₄	Dic₃²	1	1	yes	characteristic
226	C₂×C₄	(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
227	C₂×C₄	(C₂×D₃)⋊Dic₃	1	1	yes	characteristic
228	C₂×C₄	#3722	1	1	yes	characteristic
229	C₂×C₄	Dic₃⋊Dic₃	1	1	yes	characteristic
230	C₂×C₄	#3724	1	1	yes	characteristic
231	C₈	—	6	4	no	—
232	C₈	—	12	2	no	—
233	C₈	—	36	2	no	—
234	C₂×C₃	—	2	1	no	—
235	C₂×C₃	—	2	1	no	—
236	C₂×C₃	—	2	1	no	—
237	C₂×C₃	—	4	2	no	—
238	C₂×C₃	—	4	1	no	—
239	C₂×C₃	—	4	1	no	—
240	C₂×C₃	#4523	1	1	yes	characteristic
241	C₂×C₃	#4530	1	1	yes	characteristic
242	C₂×C₃	#4554	1	1	yes	characteristic
243	C₂×C₃	#4555	1	1	yes	characteristic
244	C₂×C₃	#4558	1	1	yes	characteristic
245	C₂×C₃	#4558	1	1	yes	characteristic
246	C₂²	—	2	1	no	—
247	C₂²	—	2	1	no	—
248	C₂²	—	2	1	no	—
249	C₂²	#63579	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	2	1	no	—
253	C₄	#63558	1	1	yes	characteristic
254	C₄	#63560	1	1	yes	characteristic
255	C₄	#63570	1	2	yes	—
256	C₄	#63578	1	2	yes	—
257	C₃	—	2	1	no	—
258	C₃	#67669	1	1	yes	characteristic, complemented
259	C₃	#67710	1	1	yes	characteristic, complemented
260	C₂	—	4	1	no	—
261	C₂	#10589162	1	1	yes	characteristic
262	C₂	#10589165	1	1	yes	characteristic
263	C₂	#10589167	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	(C₂×D₃)⋊Dic₃
commutator	C₂×C₃²×C₄	C₄²
Frattini, hypercenter	C₂×C₄²	D₃²
Fitting, cosocle	C₂×C₃²×C₄²	C₂²
socle	C₂²×C₃²	#95
prime radical	C₂³×C₃²	C₄⋊C₄
hypocenter	C₃²	#1299
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂²×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
219. C₃²	#1299	semidirect
258. C₃	#67669	semidirect
259. C₃	#67710	semidirect

Maximal subgroups

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

subgroup	index
#10592624	2
C₃×#4924	2
C₃×C₄×#208	2
#67710	3
#67669	3