Subgroups — #11795895

Order 1152.

433 conjugacy classes of subgroups.

The subgroup lattice has 288 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10592388	C₂	1	1	yes	maximal, characteristic
2	C₂×#63544	C₂	1	1	yes	maximal, characteristic
3	C₂×#63542	C₂	1	1	yes	maximal, characteristic
4	C₃×#4461	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#10589104	C₂	1	1	yes	maximal, characteristic, complemented
7	#10589102	C₂	1	1	yes	maximal, characteristic, complemented
8	#69072	—	3	1	no	maximal
9	#69051	—	3	1	no	maximal
10	C₂×#3743	C₄	1	1	yes	characteristic
11	C₂×C₈×C₃⋊D₃	C₂²	1	1	yes	characteristic
12	#64081	C₄	1	1	yes	characteristic
13	C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
14	#63642	C₄	1	1	yes	characteristic
15	C₈×C₃⋊Dic₃	C₂²	1	1	yes	characteristic
16	#63630	C₄	1	1	yes	characteristic
17	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₃⋊C₁₆	C₂²	1	1	yes	characteristic
21	#63544	C₄	1	4	yes	complemented
22	#63542	C₄	1	4	yes	complemented
23	C₂×#798	—	3	1	no	—
24	C₂×#798	—	3	1	no	—
25	C₂×D₃×C₁₆	—	3	1	no	—
26	C₂×D₃×C₁₆	—	3	1	no	—
27	#4689	—	3	1	no	—
28	#4689	—	3	1	no	—
29	#4689	—	6	1	no	—
30	C₃×#346	—	3	1	no	—
31	C₃×C₄×C₁₆	—	3	1	no	—
32	#4502	—	3	1	no	—
33	#4502	—	3	1	no	—
34	Dic₃×C₁₆	—	3	1	no	—
35	Dic₃×C₁₆	—	3	1	no	—
36	#4461	D₃	1	1	yes	characteristic, complemented
37	C₄×C₃⋊C₁₆	D₃	1	1	yes	characteristic, complemented
38	C₂×C₄×C₃⋊D₃	C₂×C₄	1	1	yes	characteristic
39	C₂×C₃²×C₈	C₂×C₄	1	1	yes	characteristic
40	C₂×C₃²×C₈	C₂³	1	1	yes	characteristic
41	C₃²×C₄²	C₂×C₄	1	1	yes	characteristic
42	#3752	C₈	1	2	yes	—
43	#3750	C₈	1	2	yes	—
44	C₄×C₃⋊Dic₃	C₂×C₄	1	1	yes	characteristic
45	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
46	C₂×C₃⋊(C₃⋊C₈)	C₂×C₄	1	1	yes	characteristic
47	#3743	C₈	1	4	yes	—
48	C₈×C₃⋊D₃	C₂×C₄	1	2	yes	—
49	C₈×C₃⋊D₃	C₂×C₄	1	2	yes	—
50	C₃×C₃⋊C₁₆	C₂×C₄	1	2	yes	—
51	C₃×C₃⋊C₁₆	C₂×C₄	1	2	yes	—
52	C₃×C₃⋊C₁₆	C₂×C₄	1	2	yes	—
53	C₃×C₃⋊C₁₆	C₂×C₄	1	2	yes	—
54	#2108	—	9	1	no	Sylow
55	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
56	C₂×ΓL(1,𝔽₂₅)	—	3	1	no	—
57	C₂×ΓL(1,𝔽₂₅)	—	6	1	no	—
58	C₂×D₃×C₈	—	3	1	no	—
59	C₂×D₃×C₈	—	3	1	no	—
60	C₂×D₃×C₈	—	6	1	no	—
61	#872	—	3	1	no	—
62	#872	—	3	1	no	—
63	#872	—	6	1	no	—
64	C₂×C₃×C₁₆	—	3	1	no	—
65	C₂×C₃×C₁₆	—	3	1	no	—
66	C₂×C₃×C₁₆	—	3	1	no	—
67	C₂×C₃×C₁₆	—	3	1	no	—
68	C₃×C₄×C₈	—	2	1	no	—
69	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
70	C₃×C₄×C₈	C₂×D₃	1	1	yes	characteristic
71	#815	—	3	1	no	—
72	#815	—	3	1	no	—
73	#815	—	6	1	no	—
74	C₈×Dic₃	—	3	1	no	—
75	C₈×Dic₃	—	3	1	no	—
76	C₈×Dic₃	—	6	1	no	—
77	C₂×C₃⋊C₁₆	C₂×D₃	1	1	yes	characteristic
78	C₂×C₃⋊C₁₆	C₂×D₃	1	1	yes	characteristic
79	C₂×C₃⋊C₁₆	C₂×D₃	1	1	yes	characteristic
80	C₂×C₃⋊C₁₆	C₂×D₃	1	1	yes	characteristic
81	#803	—	3	1	no	—
82	#803	—	3	1	no	—
83	#803	—	6	1	no	—
84	#798	—	3	4	no	—
85	#798	—	3	4	no	—
86	D₃×C₁₆	—	3	4	no	—
87	D₃×C₁₆	—	3	4	no	—
88	C₂²×C₃⋊D₃	C₂×C₈	1	1	yes	characteristic
89	C₂×C₃²×C₄	C₂×C₈	1	2	yes	—
90	C₂×C₃²×C₄	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₃⋊Dic₃	C₂×C₈	1	2	yes	—
92	C₂×C₃⋊Dic₃	C₂×C₈	1	1	yes	characteristic
93	C₄×C₃⋊D₃	C₄²	1	2	yes	—
94	C₄×C₃⋊D₃	C₂×C₈	1	2	yes	—
95	C₃²×C₈	C₂×C₈	1	2	yes	—
96	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
97	C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
98	C₃⋊(C₃⋊C₈)	C₄²	1	2	yes	—
99	C₃⋊(C₃⋊C₈)	C₂×C₈	1	2	yes	—
100	C₂×M₃₂	—	9	1	no	—
101	C₂²×C₁₆	—	9	1	no	—
102	#405	—	9	1	no	—
103	#346	—	3	1	no	—
104	#346	—	9	1	no	—
105	C₄×C₁₆	—	3	1	no	—
106	C₄×C₁₆	—	9	1	no	—
107	C₂×C₄×D₃	—	3	1	no	—
108	C₂×C₄×D₃	—	3	1	no	—
109	C₂×C₄×D₃	—	6	1	no	—
110	C₂×C₃×C₈	—	2	1	no	—
111	C₂×C₃×C₈	—	2	1	no	—
112	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
113	C₂×C₃×C₈	C₄×D₃	1	1	yes	characteristic
114	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
115	C₂×C₃×C₈	C₂²×D₃	1	1	yes	characteristic
116	C₃×C₄²	—	2	1	no	—
117	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
118	C₃×C₄²	C₄×D₃	1	1	yes	characteristic
119	(C₂×D₃)⋊C₄	—	3	2	no	—
120	(C₂×D₃)⋊C₄	—	3	2	no	—
121	(C₂×D₃)⋊C₄	—	6	2	no	—
122	Dic₃⋊C₄	—	3	2	no	—
123	Dic₃⋊C₄	—	3	2	no	—
124	Dic₃⋊C₄	—	6	2	no	—
125	C₄×Dic₃	—	3	1	no	—
126	C₄×Dic₃	—	3	1	no	—
127	C₄×Dic₃	—	6	1	no	—
128	C₂×C₃⋊C₈	—	3	1	no	—
129	C₂×C₃⋊C₈	—	3	1	no	—
130	C₂×C₃⋊C₈	—	3	1	no	—
131	C₂×C₃⋊C₈	—	3	1	no	—
132	C₂×C₃⋊C₈	—	6	1	no	—
133	C₂×C₃⋊C₈	—	6	1	no	—
134	ΓL(1,𝔽₂₅)	—	3	4	no	—
135	ΓL(1,𝔽₂₅)	—	3	4	no	—
136	ΓL(1,𝔽₂₅)	—	6	4	no	—
137	D₃×C₈	—	3	2	no	—
138	D₃×C₈	—	3	2	no	—
139	D₃×C₈	—	3	2	no	—
140	D₃×C₈	—	3	2	no	—
141	D₃×C₈	—	6	2	no	—
142	D₃×C₈	—	6	2	no	—
143	C₃×C₁₆	—	3	2	no	—
144	C₃×C₁₆	—	3	2	no	—
145	C₃×C₁₆	—	3	2	no	—
146	C₃×C₁₆	—	3	2	no	—
147	C₃⋊C₁₆	C₄×D₃	1	2	yes	—
148	C₃⋊C₁₆	C₄×D₃	1	2	yes	—
149	C₃⋊C₁₆	C₄×D₃	1	2	yes	—
150	C₃⋊C₁₆	C₄×D₃	1	2	yes	—
151	C₂²×C₃²	C₂²×C₈	1	1	yes	characteristic
152	C₂×C₃⋊D₃	—	2	2	no	—
153	C₂×C₃⋊D₃	C₄×C₈	1	2	yes	—
154	C₃²×C₄	—	2	2	no	—
155	C₃²×C₄	C₂×C₄²	1	1	yes	characteristic
156	C₃²×C₄	C₂²×C₈	1	1	yes	characteristic
157	C₃⋊Dic₃	—	2	2	no	—
158	C₃⋊Dic₃	C₄×C₈	1	2	yes	—
159	C₂×M₁₆	—	9	1	no	—
160	C₂²×C₈	—	9	1	no	—
161	#117	—	9	1	no	—
162	M₃₂	—	9	4	no	—
163	C₂×C₁₆	—	3	1	no	—
164	C₂×C₁₆	—	3	1	no	—
165	C₂×C₁₆	—	3	1	no	—
166	C₂×C₁₆	—	3	1	no	—
167	C₂×C₁₆	—	9	4	no	—
168	#97	—	9	1	no	—
169	#97	—	9	1	no	—
170	C₄×C₈	—	9	1	no	—
171	C₄×C₈	D₃²	1	1	yes	characteristic
172	C₂²×D₃	—	3	1	no	—
173	C₂²×D₃	—	3	1	no	—
174	C₂²×D₃	—	6	1	no	—
175	C₂×C₃×C₄	—	2	2	no	—
176	C₂×C₃×C₄	—	2	1	no	—
177	C₂×C₃×C₄	D₃×C₈	1	2	yes	—
178	C₂×C₃×C₄	D₃×C₈	1	2	yes	—
179	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
180	C₂×C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
181	C₂×Dic₃	—	3	1	no	—
182	C₂×Dic₃	—	3	1	no	—
183	C₂×Dic₃	—	3	2	no	—
184	C₂×Dic₃	—	3	2	no	—
185	C₂×Dic₃	—	6	1	no	—
186	C₂×Dic₃	—	6	2	no	—
187	C₄×D₃	—	3	2	no	—
188	C₄×D₃	—	3	2	no	—
189	C₄×D₃	—	3	2	no	—
190	C₄×D₃	—	3	2	no	—
191	C₄×D₃	—	6	2	no	—
192	C₄×D₃	—	6	2	no	—
193	C₃×C₈	—	2	2	no	—
194	C₃×C₈	—	2	1	no	—
195	C₃×C₈	—	2	1	no	—
196	C₃×C₈	D₃×C₈	1	2	yes	—
197	C₃×C₈	D₃×C₈	1	2	yes	—
198	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
199	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
200	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
201	C₃×C₈	C₂×C₄×D₃	1	1	yes	characteristic
202	C₃⋊C₈	—	3	2	no	—
203	C₃⋊C₈	—	3	2	no	—
204	C₃⋊C₈	—	3	2	no	—
205	C₃⋊C₈	—	3	2	no	—
206	C₃⋊C₈	—	6	2	no	—
207	C₃⋊C₈	—	6	2	no	—
208	C₂×C₃²	C₂×C₄×C₈	1	1	yes	characteristic
209	C₂×C₃²	#504	1	2	yes	—
210	C₃⋊D₃	—	2	2	no	—
211	C₂²×C₄	—	9	1	no	—
212	M₁₆	—	9	4	no	—
213	C₂×C₈	—	9	1	no	—
214	C₂×C₈	—	9	1	no	—
215	C₂×C₈	—	9	2	no	—
216	C₂×C₈	—	9	2	no	—
217	C₂×C₈	#624	1	1	yes	characteristic
218	C₂×C₈	C₂×D₃²	1	1	yes	characteristic
219	C₄⋊C₄	—	9	2	no	—
220	C₂²⋊C₄	—	9	2	no	—
221	C₄²	—	9	1	no	—
222	C₄²	#624	1	1	yes	characteristic
223	C₁₆	—	3	2	no	—
224	C₁₆	—	3	2	no	—
225	C₁₆	—	3	2	no	—
226	C₁₆	—	3	2	no	—
227	C₂²×C₃	—	2	1	no	—
228	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
229	C₂²×C₃	C₂×D₃×C₈	1	1	yes	characteristic
230	C₂×D₃	—	3	2	no	—
231	C₂×D₃	—	3	2	no	—
232	C₂×D₃	—	6	2	no	—
233	C₂×D₃	—	6	2	no	—
234	C₂×D₃	—	6	2	no	—
235	C₂×D₃	—	12	2	no	—
236	C₃×C₄	—	2	2	no	—
237	C₃×C₄	—	2	2	no	—
238	C₃×C₄	—	2	1	no	—
239	C₃×C₄	—	2	1	no	—
240	C₃×C₄	—	4	2	no	—
241	C₃×C₄	C₄²×D₃	1	1	yes	characteristic
242	C₃×C₄	C₄²×D₃	1	1	yes	characteristic
243	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
244	C₃×C₄	C₂×D₃×C₈	1	1	yes	characteristic
245	Dic₃	—	3	2	no	—
246	Dic₃	—	3	2	no	—
247	Dic₃	—	6	2	no	—
248	Dic₃	—	6	2	no	—
249	Dic₃	—	6	2	no	—
250	Dic₃	—	12	2	no	—
251	C₃²	#2108	1	1	yes	characteristic, complemented, Sylow
252	C₂³	—	9	1	no	—
253	C₂×C₄	—	9	1	no	—
254	C₂×C₄	—	9	2	no	—
255	C₂×C₄	—	9	2	no	—
256	C₂×C₄	—	9	2	no	—
257	C₂×C₄	#3710	1	2	yes	—
258	C₂×C₄	C₂×#624	1	1	yes	characteristic
259	C₈	—	9	2	no	—
260	C₈	—	9	2	no	—
261	C₈	#3710	1	2	yes	—
262	C₈	C₄×D₃²	1	1	yes	characteristic
263	C₈	C₄×D₃²	1	1	yes	characteristic
264	C₂×C₃	—	2	1	no	—
265	C₂×C₃	—	2	2	no	—
266	C₂×C₃	C₄×D₃×C₈	1	1	yes	characteristic
267	C₂×C₃	C₄×D₃×C₈	1	1	yes	characteristic
268	C₂×C₃	#4901	1	2	yes	—
269	C₂×C₃	#4907	1	2	yes	—
270	D₃	—	6	2	no	—
271	D₃	—	6	2	no	—
272	D₃	—	12	2	no	—
273	C₂²	—	9	2	no	—
274	C₂²	—	18	2	no	—
275	C₂²	C₂×#3710	1	1	yes	characteristic
276	C₄	—	2	2	no	—
277	C₄	—	9	2	no	—
278	C₄	—	18	2	no	—
279	C₄	C₂×#3710	1	1	yes	characteristic
280	C₄	C₄×#624	1	1	yes	characteristic
281	C₃	—	2	1	no	—
282	C₃	#69051	1	1	yes	characteristic, complemented
283	C₃	#69072	1	1	yes	characteristic, complemented
284	C₂	—	18	2	no	—
285	C₂	C₄×#3710	1	1	yes	characteristic
286	C₂	#10590624	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₈	C₂×D₃²
commutator	C₂×C₃²	C₂×C₄×C₈
Fitting	C₃²×C₄×C₈	C₂²
socle	C₂²×C₃²	C₂²×C₈
prime radical	C₂²×C₃⋊D₃	C₂×C₈
cosocle	C₂×C₃²×C₈	C₂³
hypercenter	C₄×C₈	D₃²
hypocenter	C₃²	#2108
LCS	G ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈

Complements

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

N	H ≅ G/N	type
4. C₃×#4461	C₂	semidirect
5. C₃×C₄×C₃⋊C₁₆	C₂	semidirect
6. #10589104	C₂	semidirect
7. #10589102	C₂	semidirect
21. #63544	C₄	semidirect
22. #63542	C₄	semidirect
36. #4461	D₃	semidirect
37. C₄×C₃⋊C₁₆	D₃	semidirect
251. C₃²	#2108	semidirect
282. C₃	#69051	semidirect
283. C₃	#69072	semidirect

Maximal subgroups

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

subgroup	index
#10592388	2
C₂×#63544	2
C₂×#63542	2
C₃×#4461	2
C₃×C₄×C₃⋊C₁₆	2
#10589104	2
#10589102	2
#69072	3
#69051	3