Subgroups — #11786080

Order 1152.

525 conjugacy classes of subgroups.

The subgroup lattice has 252 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10592635	C₂	1	1	yes	maximal, characteristic
2	C₃×#4935	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#803	C₂	1	1	yes	maximal, characteristic
4	#10589164	C₂	1	4	yes	maximal
5	#69815	—	3	1	no	maximal
6	#69575	—	3	1	no	maximal
7	C₂×C₃²×C₄²	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊(C₃⋊Dic₃)	C₂²	1	2	yes	—
9	C₂×C₃×C₄⋊Dic₃	—	2	2	no	—
10	C₂×C₃×C₄⋊Dic₃	C₂²	1	2	yes	—
11	C₂²×C₃×C₃⋊C₈	C₂²	1	2	yes	—
12	#63658	—	2	2	no	—
13	C₃×#803	C₄	1	4	yes	complemented
14	C₂×C₃×#97	—	3	1	no	—
15	C₃×#384	—	3	1	no	—
16	#4936	—	3	1	no	—
17	#4936	—	3	1	no	—
18	#4936	—	6	1	no	—
19	#4935	D₃	1	1	yes	characteristic
20	C₂×#803	D₃	1	1	yes	characteristic
21	#4551	—	3	4	no	—
22	#4529	—	3	4	no	—
23	C₂²×C₃²×C₄	D₄	1	2	yes	—
24	C₂²×C₃²×C₄	C₂³	1	1	yes	characteristic
25	C₂²×C₃⋊Dic₃	—	2	2	no	—
26	C₂²×C₃×Dic₃	—	2	2	no	—
27	C₃²×C₄²	C₂×C₄	1	2	yes	—
28	C₃²×C₄²	Q₈	1	2	yes	—
29	C₄⋊(C₃⋊Dic₃)	—	2	4	no	—
30	C₃×C₄⋊Dic₃	—	2	4	no	—
31	C₃×C₄⋊Dic₃	—	4	4	no	—
32	C₂×C₃×C₃⋊C₈	—	2	2	no	—
33	C₂×C₃×C₃⋊C₈	—	2	2	no	—
34	C₂×C₃×C₃⋊C₈	C₂×C₄	1	4	yes	—
35	#1836	—	9	1	no	Sylow
36	C₂²×C₃×C₈	—	3	2	no	—
37	C₂×C₃×C₄⋊C₄	—	3	2	no	—
38	C₂×C₃×C₄⋊C₄	—	6	2	no	—
39	C₂×C₃×C₄²	—	2	1	no	—
40	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
41	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
42	C₂×C₄⋊Dic₃	—	2	2	no	—
43	C₂×C₄⋊Dic₃	—	3	2	no	—
44	C₂×C₄⋊Dic₃	—	3	2	no	—
45	C₂×C₄⋊Dic₃	—	6	2	no	—
46	C₂×C₄⋊Dic₃	C₂×D₃	1	2	yes	—
47	C₂²×C₃⋊C₈	C₂×D₃	1	2	yes	—
48	C₃×#97	—	3	4	no	—
49	C₃⋊#95	—	6	4	no	—
50	C₃⋊#95	—	6	2	no	—
51	C₃⋊#95	—	6	2	no	—
52	#803	Dic₃	1	4	yes	complemented
53	C₂³×C₃²	C₂×D₄	1	1	yes	characteristic
54	C₂×C₃²×C₄	—	2	2	no	—
55	C₂×C₃²×C₄	—	2	2	no	—
56	C₂×C₃²×C₄	C₄⋊C₄	1	4	yes	—
57	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
58	C₂×C₃²×C₄	C₂×Q₈	1	1	yes	characteristic
59	C₂×C₃²×C₄	#41	1	2	yes	—
60	C₂×C₃²×C₄	#41	1	2	yes	—
61	C₂×C₃⋊Dic₃	—	4	2	no	—
62	C₂×C₃⋊Dic₃	—	4	2	no	—
63	C₂×C₃⋊Dic₃	—	4	2	no	—
64	C₂×C₃×Dic₃	—	4	2	no	—
65	C₂×C₃×Dic₃	—	4	4	no	—
66	C₃×C₃⋊C₈	—	2	4	no	—
67	C₂×#97	—	3	1	no	—
68	#384	—	3	1	no	—
69	#382	—	9	1	no	—
70	#340	—	9	4	no	—
71	C₂²×C₃×C₄	—	2	2	no	—
72	C₂²×C₃×C₄	—	2	1	no	—
73	C₂²×C₃×C₄	—	6	2	no	—
74	C₂²×C₃×C₄	D₁₂	1	2	yes	—
75	C₂²×C₃×C₄	#67	1	2	yes	—
76	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
77	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
78	C₂²×Dic₃	—	2	2	no	—
79	C₂²×Dic₃	—	6	4	no	—
80	C₂²×Dic₃	—	6	2	no	—
81	C₂²×Dic₃	—	6	2	no	—
82	C₂×C₃×C₈	—	3	4	no	—
83	C₂×C₃×C₈	—	6	2	no	—
84	C₂×C₃×C₈	—	6	2	no	—
85	C₃×C₄⋊C₄	—	6	4	no	—
86	C₃×C₄⋊C₄	—	12	4	no	—
87	C₃×C₄²	—	2	2	no	—
88	C₃×C₄²	—	2	2	no	—
89	C₃×C₄²	Dic₆	1	2	yes	—
90	C₃×C₄²	Dic₆	1	2	yes	—
91	C₃×C₄²	C₄×D₃	1	2	yes	—
92	C₃×C₄²	C₂×Dic₃	1	2	yes	—
93	C₄⋊Dic₃	—	2	4	no	—
94	C₄⋊Dic₃	—	4	4	no	—
95	C₄⋊Dic₃	—	6	4	no	—
96	C₄⋊Dic₃	—	6	4	no	—
97	C₄⋊Dic₃	—	12	4	no	—
98	C₂×C₃⋊C₈	—	2	2	no	—
99	C₂×C₃⋊C₈	—	2	2	no	—
100	C₂×C₃⋊C₈	C₂×Dic₃	1	4	yes	—
101	C₂²×C₃²	C₂×C₄⋊C₄	1	1	yes	characteristic
102	C₂²×C₃²	#124	1	1	yes	characteristic
103	C₂²×C₃²	#124	1	1	yes	characteristic
104	C₂²×C₃²	AGL(1,ℤ/8)	1	2	yes	—
105	C₂²×C₃²	#137	1	2	yes	—
106	C₃²×C₄	—	2	4	no	—
107	C₃²×C₄	#117	1	2	yes	—
108	C₃²×C₄	#125	1	2	yes	—
109	C₃⋊Dic₃	—	8	2	no	—
110	C₃×Dic₃	—	8	2	no	—
111	C₂²×C₈	—	3	2	no	—
112	C₂×C₄⋊C₄	—	3	2	no	—
113	C₂×C₄⋊C₄	—	6	2	no	—
114	C₂×C₄⋊C₄	—	9	2	no	—
115	C₂×C₄²	D₃²	1	1	yes	characteristic
116	#97	—	3	4	no	—
117	#95	—	18	2	no	—
118	C₂³×C₃	—	2	1	no	—
119	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
120	C₂³×C₃	C₂×#67	1	1	yes	characteristic
121	C₂×C₃×C₄	—	2	2	no	—
122	C₂×C₃×C₄	—	2	2	no	—
123	C₂×C₃×C₄	—	2	2	no	—
124	C₂×C₃×C₄	—	2	2	no	—
125	C₂×C₃×C₄	—	2	4	no	—
126	C₂×C₃×C₄	—	2	2	no	—
127	C₂×C₃×C₄	—	2	2	no	—
128	C₂×C₃×C₄	—	2	1	no	—
129	C₂×C₃×C₄	—	2	1	no	—
130	C₂×C₃×C₄	—	4	2	no	—
131	C₂×C₃×C₄	—	4	2	no	—
132	C₂×C₃×C₄	—	12	2	no	—
133	C₂×C₃×C₄	—	12	4	no	—
134	C₂×C₃×C₄	Dic₃⋊C₄	1	4	yes	—
135	C₂×C₃×C₄	C₄⋊Dic₃	1	4	yes	—
136	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
137	C₂×C₃×C₄	C₂×Dic₆	1	1	yes	characteristic
138	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
139	C₂×C₃×C₄	#235	1	2	yes	—
140	C₂×C₃×C₄	#235	1	2	yes	—
141	C₂×C₃×C₄	#237	1	2	yes	—
142	C₂×C₃×C₄	#239	1	2	yes	—
143	C₂×C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
144	C₂×Dic₃	—	4	4	no	—
145	C₂×Dic₃	—	4	2	no	—
146	C₂×Dic₃	—	12	4	no	—
147	C₂×Dic₃	—	12	4	no	—
148	C₂×Dic₃	—	12	4	no	—
149	C₂×Dic₃	—	12	2	no	—
150	C₂×Dic₃	—	12	2	no	—
151	C₂×Dic₃	—	12	2	no	—
152	C₂×Dic₃	—	12	2	no	—
153	C₂×Dic₃	—	12	2	no	—
154	C₂×Dic₃	—	12	2	no	—
155	C₃×C₈	—	6	4	no	—
156	C₃⋊C₈	—	2	4	no	—
157	C₂×C₃²	#382	1	1	yes	characteristic
158	C₂×C₃²	#428	1	2	yes	—
159	C₂×C₃²	#489	1	2	yes	—
160	C₂×C₃²	#490	1	1	yes	characteristic
161	C₂×C₃²	#491	1	1	yes	characteristic
162	C₂²×C₄	—	6	2	no	—
163	C₂²×C₄	—	18	2	no	—
164	C₂²×C₄	#626	1	2	yes	—
165	C₂²×C₄	C₂×D₃²	1	1	yes	characteristic
166	C₂×C₈	—	3	4	no	—
167	C₂×C₈	—	6	2	no	—
168	C₂×C₈	—	6	2	no	—
169	C₄⋊C₄	—	6	4	no	—
170	C₄⋊C₄	—	12	4	no	—
171	C₄⋊C₄	—	18	4	no	—
172	C₄²	D₃×Dic₃	1	2	yes	—
173	C₄²	#627	1	2	yes	—
174	C₂²×C₃	—	2	2	no	—
175	C₂²×C₃	—	2	2	no	—
176	C₂²×C₃	—	2	1	no	—
177	C₂²×C₃	—	2	1	no	—
178	C₂²×C₃	—	2	1	no	—
179	C₂²×C₃	#875	1	1	yes	characteristic
180	C₂²×C₃	#875	1	1	yes	characteristic
181	C₂²×C₃	#908	1	2	yes	—
182	C₂²×C₃	#909	1	2	yes	—
183	C₂²×C₃	C₂×Dic₃⋊C₄	1	1	yes	characteristic
184	C₂²×C₃	C₂×C₄⋊Dic₃	1	1	yes	characteristic
185	C₂²×C₃	#932	1	2	yes	—
186	C₂²×C₃	#936	1	1	yes	characteristic
187	C₂²×C₃	#942	1	2	yes	—
188	C₂²×C₃	#947	1	1	yes	characteristic
189	C₃×C₄	—	2	4	no	—
190	C₃×C₄	—	2	4	no	—
191	C₃×C₄	—	2	2	no	—
192	C₃×C₄	—	2	2	no	—
193	C₃×C₄	—	4	4	no	—
194	C₃×C₄	—	24	2	no	—
195	C₃×C₄	#870	1	2	yes	—
196	C₃×C₄	#890	1	2	yes	—
197	C₃×C₄	#892	1	2	yes	—
198	C₃×C₄	#926	1	2	yes	—
199	Dic₃	—	8	2	no	—
200	Dic₃	—	24	4	no	—
201	Dic₃	—	24	2	no	—
202	Dic₃	—	24	2	no	—
203	C₃²	#1836	1	1	yes	characteristic, complemented, Sylow
204	C₂³	C₂×#626	1	1	yes	characteristic
205	C₂×C₄	—	2	2	no	—
206	C₂×C₄	—	2	2	no	—
207	C₂×C₄	—	12	4	no	—
208	C₂×C₄	—	12	2	no	—
209	C₂×C₄	—	36	2	no	—
210	C₂×C₄	—	36	2	no	—
211	C₂×C₄	—	36	2	no	—
212	C₂×C₄	Dic₃⋊Dic₃	1	4	yes	—
213	C₂×C₄	#3795	1	2	yes	—
214	C₂×C₄	#3799	1	2	yes	—
215	C₂×C₄	C₂×D₃×Dic₃	1	1	yes	characteristic
216	C₂×C₄	C₂×#627	1	1	yes	characteristic
217	C₈	—	6	4	no	—
218	C₂×C₃	—	2	1	no	—
219	C₂×C₃	—	2	1	no	—
220	C₂×C₃	—	2	2	no	—
221	C₂×C₃	—	2	2	no	—
222	C₂×C₃	—	2	1	no	—
223	C₂×C₃	#4703	1	1	yes	characteristic
224	C₂×C₃	#4713	1	1	yes	characteristic
225	C₂×C₃	#4714	1	2	yes	—
226	C₂×C₃	#4936	1	1	yes	characteristic
227	C₂×C₃	#4964	1	2	yes	—
228	C₂×C₃	#4977	1	1	yes	characteristic
229	C₂×C₃	#5071	1	1	yes	characteristic
230	C₂×C₃	#5082	1	1	yes	characteristic
231	C₂×C₃	#5089	1	2	yes	—
232	C₂×C₃	#5121	1	2	yes	—
233	C₂²	#63830	1	2	yes	—
234	C₂²	#63833	1	2	yes	—
235	C₂²	#63860	1	1	yes	characteristic
236	C₂²	#63864	1	1	yes	characteristic
237	C₂²	C₂×Dic₃⋊Dic₃	1	1	yes	characteristic
238	C₄	—	2	4	no	—
239	C₄	—	24	2	no	—
240	C₄	—	72	2	no	—
241	C₄	#63841	1	2	yes	—
242	C₄	#63869	1	2	yes	—
243	C₃	—	2	1	no	—
244	C₃	#69575	1	1	yes	characteristic, complemented
245	C₃	#69815	1	1	yes	characteristic, complemented
246	C₂	#10590275	1	1	yes	characteristic
247	C₂	#10590289	1	1	yes	characteristic
248	C₂	#10590294	1	2	yes	—
249	C₂	#10591130	1	2	yes	—
250	C₂	#10591224	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#626
commutator	C₂×C₃²×C₄	C₂²×C₄
Frattini	C₂²×C₄	C₂×D₃²
Fitting	C₂×C₃²×C₄²	C₂²
socle, prime radical	C₂³×C₃²	C₂×D₄
cosocle	C₂²×C₃²×C₄	C₂³
hypercenter	C₂×C₄²	D₃²
hypocenter	C₃²	#1836
LCS	G ▷ C₂×C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
13. C₃×#803	C₄	semidirect
52. #803	Dic₃	semidirect
203. C₃²	#1836	semidirect
244. C₃	#69575	semidirect
245. C₃	#69815	semidirect

Maximal subgroups

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

subgroup	index
#10592635	2
C₃×#4935	2
C₂×C₃×#803	2
#10589164	2
#69815	3
#69575	3