Subgroups — #11794638

Order 1152.

411 conjugacy classes of subgroups.

The subgroup lattice has 279 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#390	C₂	1	1	yes	maximal, characteristic
2	C₂×#63392	C₂	1	2	yes	maximal
3	#10588615	C₂	1	1	yes	maximal, characteristic, complemented
4	#10588206	C₂	1	2	yes	maximal, complemented
5	#10588200	C₂	1	1	yes	maximal, characteristic, complemented
6	#69640	—	3	1	no	maximal
7	C₂²×D₄×C₉	C₂²	1	1	yes	characteristic
8	C₂×C₉×C₄⋊C₄	C₂²	1	1	yes	characteristic
9	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
10	C₂×C₉×C₂²⋊C₄	—	2	1	no	—
11	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Dic₉	—	2	1	no	—
13	C₂×C₄⋊Dic₉	—	2	1	no	—
14	C₂×C₄⋊Dic₉	C₂²	1	2	yes	—
15	C₂²×C₉⋊C₈	C₂²	1	2	yes	—
16	#63392	—	2	4	no	—
17	C₃×#390	D₃	1	1	yes	characteristic
18	C₂×#832	—	3	2	no	—
19	#4935	—	3	1	no	—
20	#4529	—	3	2	no	—
21	#4524	—	3	1	no	—
22	C₂⁴×C₉	—	2	1	no	—
23	C₂×D₄×C₉	—	2	2	no	—
24	C₂×D₄×C₉	—	2	2	no	—
25	C₂×D₄×C₉	—	2	1	no	—
26	C₂×D₄×C₉	D₄	1	2	yes	—
27	C₂²×C₄×C₉	—	2	1	no	—
28	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
29	C₂²×C₄×C₉	D₄	1	1	yes	characteristic
30	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
31	C₂²×Dic₉	—	2	2	no	—
32	C₉×C₄⋊C₄	—	2	2	no	—
33	C₉×C₂²⋊C₄	—	4	2	no	—
34	C₉×C₂²⋊C₄	—	4	2	no	—
35	C₄²×C₉	—	2	2	no	—
36	C₄⋊Dic₉	—	2	2	no	—
37	C₄⋊Dic₉	—	2	2	no	—
38	C₄⋊Dic₉	—	4	2	no	—
39	C₄⋊Dic₉	—	4	2	no	—
40	C₂×C₉⋊C₈	—	2	2	no	—
41	C₂×C₉⋊C₈	—	2	2	no	—
42	C₂×C₉⋊C₈	—	2	2	no	—
43	#2071	—	9	1	no	Sylow
44	C₂²×C₃×D₄	C₂×D₃	1	1	yes	characteristic
45	C₂×C₃×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
46	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
47	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
48	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
49	C₂×C₄⋊Dic₃	—	3	2	no	—
50	C₂×C₄⋊Dic₃	—	6	1	no	—
51	C₂×C₄⋊Dic₃	—	6	1	no	—
52	C₂²×C₃⋊C₈	—	3	2	no	—
53	#832	—	6	4	no	—
54	C₂³×C₉	—	2	2	no	—
55	C₂³×C₉	—	4	1	no	—
56	C₂³×C₉	—	4	1	no	—
57	C₂³×C₉	—	4	1	no	—
58	C₂³×C₉	—	4	1	no	—
59	C₂³×C₉	—	4	1	no	—
60	C₂³×C₉	—	4	1	no	—
61	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
62	D₄×C₉	—	2	4	no	—
63	D₄×C₉	—	4	2	no	—
64	C₂×C₄×C₉	—	2	1	no	—
65	C₂×C₄×C₉	—	2	1	no	—
66	C₂×C₄×C₉	—	2	1	no	—
67	C₂×C₄×C₉	—	2	1	no	—
68	C₂×C₄×C₉	—	4	1	no	—
69	C₂×C₄×C₉	—	4	1	no	—
70	C₂×C₄×C₉	—	4	1	no	—
71	C₂×C₄×C₉	D₈	1	2	yes	—
72	C₂×C₄×C₉	SD₁₆	1	2	yes	—
73	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
74	C₂×C₄×C₉	#41	1	1	yes	characteristic
75	C₂×C₄×C₉	#41	1	2	yes	—
76	C₂×C₄×C₉	#41	1	2	yes	—
77	C₂×Dic₉	—	4	2	no	—
78	C₂×Dic₉	—	4	2	no	—
79	C₂×Dic₉	—	4	2	no	—
80	C₉⋊C₈	—	4	2	no	—
81	C₂×#102	—	9	2	no	—
82	#390	D₉	1	1	yes	characteristic
83	#384	—	9	1	no	—
84	#340	—	9	2	no	—
85	#336	—	9	1	no	—
86	C₂⁴×C₃	—	2	1	no	—
87	C₂×C₃×D₄	—	2	1	no	—
88	C₂×C₃×D₄	—	2	2	no	—
89	C₂×C₃×D₄	—	2	2	no	—
90	C₂×C₃×D₄	D₁₂	1	2	yes	—
91	C₂²×C₃×C₄	—	2	1	no	—
92	C₂²×C₃×C₄	#67	1	1	yes	characteristic
93	C₂²×C₃×C₄	#67	1	1	yes	characteristic
94	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
95	C₂²×Dic₃	—	6	2	no	—
96	C₃×C₄⋊C₄	—	2	2	no	—
97	C₃×C₂²⋊C₄	—	4	2	no	—
98	C₃×C₂²⋊C₄	—	4	2	no	—
99	C₃×C₄²	—	2	2	no	—
100	C₄⋊Dic₃	—	6	2	no	—
101	C₄⋊Dic₃	—	6	2	no	—
102	C₄⋊Dic₃	—	12	2	no	—
103	C₄⋊Dic₃	—	12	2	no	—
104	C₂×C₃⋊C₈	—	6	2	no	—
105	C₂×C₃⋊C₈	—	6	2	no	—
106	C₂×C₃⋊C₈	—	6	2	no	—
107	C₂²×C₉	—	4	2	no	—
108	C₂²×C₉	—	4	2	no	—
109	C₂²×C₉	—	4	2	no	—
110	C₂²×C₉	—	8	1	no	—
111	C₂²×C₉	—	8	1	no	—
112	C₂²×C₉	—	8	1	no	—
113	C₂²×C₉	—	8	1	no	—
114	C₂²×C₉	#121	1	1	yes	characteristic
115	C₂²×C₉	#123	1	1	yes	characteristic
116	C₂²×C₉	#124	1	1	yes	characteristic
117	C₂²×C₉	C₂×D₈	1	1	yes	characteristic
118	C₂²×C₉	C₂×SD₁₆	1	1	yes	characteristic
119	C₂²×C₉	AGL(1,ℤ/8)	1	1	yes	characteristic
120	C₂²×C₉	#137	1	1	yes	characteristic
121	C₄×C₉	—	2	2	no	—
122	C₄×C₉	—	2	2	no	—
123	C₄×C₉	—	8	1	no	—
124	C₄×C₉	#123	1	2	yes	—
125	C₄×C₉	#126	1	2	yes	—
126	Dic₉	—	8	2	no	—
127	C₂²×D₄	C₂×D₉	1	1	yes	characteristic
128	C₂²×C₈	—	9	2	no	—
129	C₂×C₄⋊C₄	—	9	2	no	—
130	C₂×C₄⋊C₄	—	18	1	no	—
131	C₂×C₄⋊C₄	—	18	1	no	—
132	C₂×C₄⋊C₄	C₂×D₉	1	1	yes	characteristic
133	C₂×C₂²⋊C₄	—	2	1	no	—
134	C₂×C₂²⋊C₄	—	2	1	no	—
135	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
136	#102	—	18	4	no	—
137	C₂³×C₃	—	2	2	no	—
138	C₂³×C₃	—	4	1	no	—
139	C₂³×C₃	—	4	1	no	—
140	C₂³×C₃	—	4	1	no	—
141	C₂³×C₃	—	4	1	no	—
142	C₂³×C₃	—	4	1	no	—
143	C₂³×C₃	—	4	1	no	—
144	C₂³×C₃	C₂×#67	1	1	yes	characteristic
145	C₃×D₄	—	2	4	no	—
146	C₃×D₄	—	4	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	—	4	1	no	—
152	C₂×C₃×C₄	—	4	1	no	—
153	C₂×C₃×C₄	—	4	1	no	—
154	C₂×C₃×C₄	#213	1	2	yes	—
155	C₂×C₃×C₄	#214	1	2	yes	—
156	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
157	C₂×C₃×C₄	#235	1	1	yes	characteristic
158	C₂×C₃×C₄	#237	1	2	yes	—
159	C₂×C₃×C₄	#237	1	2	yes	—
160	C₂×Dic₃	—	12	2	no	—
161	C₂×Dic₃	—	12	2	no	—
162	C₂×Dic₃	—	12	2	no	—
163	C₃⋊C₈	—	12	2	no	—
164	C₂×C₉	—	8	2	no	—
165	C₂×C₉	#397	1	1	yes	characteristic
166	C₂×C₉	#459	1	1	yes	characteristic
167	C₂×C₉	#461	1	1	yes	characteristic
168	C₂×C₉	#480	1	1	yes	characteristic
169	C₂×C₉	#481	1	1	yes	characteristic
170	C₂×C₉	#486	1	1	yes	characteristic
171	C₂×C₉	#489	1	1	yes	characteristic
172	C₂⁴	—	2	1	no	—
173	C₂×D₄	—	2	1	no	—
174	C₂×D₄	—	2	2	no	—
175	C₂×D₄	—	2	2	no	—
176	C₂×D₄	D₃₆	1	2	yes	—
177	C₂²×C₄	—	2	1	no	—
178	C₂²×C₄	—	18	2	no	—
179	C₂²×C₄	#611	1	1	yes	characteristic
180	C₂²×C₄	#611	1	1	yes	characteristic
181	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
182	C₂×C₈	—	18	2	no	—
183	C₂×C₈	—	18	2	no	—
184	C₂×C₈	—	18	2	no	—
185	C₄⋊C₄	—	2	2	no	—
186	C₄⋊C₄	—	18	2	no	—
187	C₄⋊C₄	—	18	2	no	—
188	C₄⋊C₄	—	36	2	no	—
189	C₄⋊C₄	—	36	2	no	—
190	C₂²⋊C₄	—	4	2	no	—
191	C₂²⋊C₄	—	4	2	no	—
192	C₄²	—	2	2	no	—
193	C₂²×C₃	—	4	2	no	—
194	C₂²×C₃	—	4	2	no	—
195	C₂²×C₃	—	4	2	no	—
196	C₂²×C₃	—	8	1	no	—
197	C₂²×C₃	—	8	1	no	—
198	C₂²×C₃	—	8	1	no	—
199	C₂²×C₃	—	8	1	no	—
200	C₂²×C₃	#930	1	1	yes	characteristic
201	C₂²×C₃	C₂×#213	1	1	yes	characteristic
202	C₂²×C₃	C₂×#214	1	1	yes	characteristic
203	C₂²×C₃	#935	1	1	yes	characteristic
204	C₂²×C₃	#936	1	1	yes	characteristic
205	C₂²×C₃	#949	1	1	yes	characteristic
206	C₂²×C₃	#951	1	1	yes	characteristic
207	C₃×C₄	—	2	2	no	—
208	C₃×C₄	—	2	2	no	—
209	C₃×C₄	—	8	1	no	—
210	C₃×C₄	#879	1	2	yes	—
211	C₃×C₄	#886	1	2	yes	—
212	Dic₃	—	24	2	no	—
213	C₉	#2071	1	1	yes	characteristic, complemented, Sylow
214	C₂³	—	2	2	no	—
215	C₂³	—	4	1	no	—
216	C₂³	—	4	1	no	—
217	C₂³	—	4	1	no	—
218	C₂³	—	4	1	no	—
219	C₂³	—	4	1	no	—
220	C₂³	—	4	1	no	—
221	C₂³	C₂×#611	1	1	yes	characteristic
222	D₄	—	2	4	no	—
223	D₄	—	4	2	no	—
224	C₂×C₄	—	2	1	no	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	1	no	—
227	C₂×C₄	—	2	1	no	—
228	C₂×C₄	—	4	1	no	—
229	C₂×C₄	—	4	1	no	—
230	C₂×C₄	—	4	1	no	—
231	C₂×C₄	—	36	2	no	—
232	C₂×C₄	—	36	2	no	—
233	C₂×C₄	—	36	2	no	—
234	C₂×C₄	#3672	1	2	yes	—
235	C₂×C₄	#3673	1	2	yes	—
236	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
237	C₂×C₄	#3697	1	1	yes	characteristic
238	C₂×C₄	#3699	1	2	yes	—
239	C₂×C₄	#3699	1	2	yes	—
240	C₈	—	36	2	no	—
241	C₂×C₃	—	8	2	no	—
242	C₂×C₃	#4953	1	1	yes	characteristic
243	C₂×C₃	#5015	1	1	yes	characteristic
244	C₂×C₃	#5019	1	1	yes	characteristic
245	C₂×C₃	#5033	1	1	yes	characteristic
246	C₂×C₃	#5034	1	1	yes	characteristic
247	C₂×C₃	#5055	1	1	yes	characteristic
248	C₂×C₃	#5070	1	1	yes	characteristic
249	C₂²	—	4	2	no	—
250	C₂²	—	4	2	no	—
251	C₂²	—	4	2	no	—
252	C₂²	—	8	1	no	—
253	C₂²	—	8	1	no	—
254	C₂²	—	8	1	no	—
255	C₂²	—	8	1	no	—
256	C₂²	#63492	1	1	yes	characteristic
257	C₂²	C₂×#3672	1	1	yes	characteristic
258	C₂²	C₂×#3673	1	1	yes	characteristic
259	C₂²	#63497	1	1	yes	characteristic
260	C₂²	#63498	1	1	yes	characteristic
261	C₂²	#63511	1	1	yes	characteristic
262	C₂²	#63512	1	1	yes	characteristic
263	C₄	—	2	2	no	—
264	C₄	—	2	2	no	—
265	C₄	—	8	1	no	—
266	C₄	—	72	2	no	—
267	C₄	#63441	1	2	yes	—
268	C₄	#63448	1	2	yes	—
269	C₃	#69640	1	1	yes	characteristic
270	C₂	—	8	2	no	—
271	C₂	#10588633	1	1	yes	characteristic
272	C₂	#10588695	1	1	yes	characteristic
273	C₂	#10588698	1	1	yes	characteristic
274	C₂	#10588713	1	1	yes	characteristic
275	C₂	#10588714	1	1	yes	characteristic
276	C₂	#10588734	1	1	yes	characteristic
277	C₂	#10588750	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×#611
commutator, cosocle	C₂²×C₄×C₉	C₂³
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#390	C₂
socle	C₂³×C₃	C₂×#67
prime radical	C₂²×C₃×D₄	C₂×D₃
hypercenter	#390	D₉
hypocenter	C₉	#2071
LCS	G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #390

Complements

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

N	H ≅ G/N	type
3. #10588615	C₂	semidirect
4. #10588206	C₂	semidirect
5. #10588200	C₂	semidirect
213. C₉	#2071	semidirect

Maximal subgroups

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

subgroup	index
C₉×#390	2
C₂×#63392	2
#10588615	2
#10588206	2
#10588200	2
#69640	3