Subgroups — #11795379

Order 1152.

411 conjugacy classes of subgroups.

The subgroup lattice has 300 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63380	C₂	1	1	yes	maximal, characteristic
2	C₂×#63380	C₂	1	1	yes	maximal, characteristic
3	C₂×#63378	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#63377	C₂	1	1	yes	maximal, characteristic, complemented
5	#10588619	C₂	1	1	yes	maximal, characteristic
6	#10588616	C₂	1	1	yes	maximal, characteristic, complemented
7	C₉×#336	C₂	1	1	yes	maximal, characteristic, complemented
8	#68680	—	3	1	no	maximal
9	C₂²×D₃₆	C₂²	1	1	yes	characteristic
10	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
11	C₂²×C₈×C₉	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₉	C₂²	1	1	yes	characteristic
13	C₂×(C₂×D₉)⋊C₄	—	2	2	no	—
14	C₂×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Dic₉	C₂²	1	1	yes	characteristic
17	C₉⋊#95	—	2	2	no	—
18	#63380	—	2	2	no	—
19	#63380	—	2	2	no	—
20	#63378	—	2	2	no	—
21	#63377	—	2	2	no	—
22	C₂×#821	—	3	1	no	—
23	C₂×#821	—	3	1	no	—
24	C₂×#818	—	3	1	no	—
25	C₂×#817	—	3	1	no	—
26	#4939	—	3	1	no	—
27	#4936	—	3	1	no	—
28	C₃×#336	D₃	1	1	yes	characteristic
29	C₂³×D₉	—	2	1	no	—
30	C₂²×C₄×C₉	D₄	1	2	yes	—
31	C₂²×C₄×C₉	C₂³	1	1	yes	characteristic
32	C₂²×Dic₉	—	2	1	no	—
33	C₂²×Dic₉	—	2	1	no	—
34	C₂²×Dic₉	—	2	1	no	—
35	C₂×D₃₆	—	2	1	no	—
36	C₂×D₃₆	—	2	1	no	—
37	C₂×D₃₆	—	2	1	no	—
38	C₂×D₃₆	—	2	1	no	—
39	C₂×D₃₆	—	2	1	no	—
40	C₂×D₃₆	Q₈	1	2	yes	—
41	C₂×C₈×C₉	—	2	1	no	—
42	C₂×C₈×C₉	—	2	1	no	—
43	C₂×C₈×C₉	—	2	1	no	—
44	C₂×C₈×C₉	—	2	1	no	—
45	C₂×C₈×C₉	D₄	1	2	yes	—
46	C₂×C₈×C₉	D₄	1	2	yes	—
47	C₄²×C₉	—	2	1	no	—
48	C₄²×C₉	—	2	1	no	—
49	(C₂×D₉)⋊C₄	—	4	4	no	—
50	C₄⋊Dic₉	—	2	1	no	—
51	C₄⋊Dic₉	—	2	1	no	—
52	C₄⋊Dic₉	—	2	1	no	—
53	C₄⋊Dic₉	—	2	1	no	—
54	C₄⋊Dic₉	—	2	1	no	—
55	C₄⋊Dic₉	—	2	1	no	—
56	#2092	—	9	1	no	Sylow
57	C₂²×D₁₂	—	3	1	no	—
58	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
59	C₂²×C₃×C₈	C₂×D₃	1	1	yes	characteristic
60	C₂×C₃×C₄²	C₂×D₃	1	1	yes	characteristic
61	C₂×(C₂×D₃)⋊C₄	—	6	2	no	—
62	C₂×C₄⋊Dic₃	—	3	1	no	—
63	C₂×C₄⋊Dic₃	—	3	1	no	—
64	C₂×C₄⋊Dic₃	—	3	1	no	—
65	C₃⋊#95	—	6	2	no	—
66	#821	—	6	2	no	—
67	#821	—	6	2	no	—
68	#818	—	6	2	no	—
69	#817	—	6	2	no	—
70	C₂³×C₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×D₉	—	2	2	no	—
72	C₂²×D₉	—	4	1	no	—
73	C₂²×D₉	—	4	1	no	—
74	C₂²×D₉	—	4	2	no	—
75	C₂²×D₉	—	4	2	no	—
76	C₂×C₄×C₉	—	2	2	no	—
77	C₂×C₄×C₉	—	2	2	no	—
78	C₂×C₄×C₉	—	2	2	no	—
79	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
80	C₂×C₄×C₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₉	C₂×Q₈	1	1	yes	characteristic
82	C₂×C₄×C₉	#41	1	1	yes	characteristic
83	C₂×C₄×C₉	#41	1	1	yes	characteristic
84	C₂×C₄×C₉	#41	1	1	yes	characteristic
85	C₂×Dic₉	—	4	1	no	—
86	C₂×Dic₉	—	4	1	no	—
87	C₂×Dic₉	—	4	1	no	—
88	C₂×Dic₉	—	4	2	no	—
89	C₂×Dic₉	—	4	2	no	—
90	C₂×Dic₉	—	4	2	no	—
91	D₃₆	—	2	2	no	—
92	D₃₆	—	2	2	no	—
93	D₃₆	—	4	1	no	—
94	D₃₆	—	4	1	no	—
95	C₈×C₉	—	2	2	no	—
96	C₈×C₉	—	2	2	no	—
97	C₂×#107	—	9	1	no	—
98	C₂×#106	—	9	1	no	—
99	C₂×#102	—	9	1	no	—
100	C₂×#102	—	9	1	no	—
101	#390	—	9	1	no	—
102	#382	—	9	1	no	—
103	#336	D₉	1	1	yes	characteristic, complemented
104	C₂³×D₃	—	6	1	no	—
105	C₂²×C₃×C₄	D₁₂	1	2	yes	—
106	C₂²×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
107	C₂²×Dic₃	—	6	1	no	—
108	C₂²×Dic₃	—	6	1	no	—
109	C₂²×Dic₃	—	6	1	no	—
110	C₂×D₁₂	—	3	2	no	—
111	C₂×D₁₂	—	6	1	no	—
112	C₂×D₁₂	—	6	1	no	—
113	C₂×D₁₂	—	6	1	no	—
114	C₂×D₁₂	—	6	1	no	—
115	C₂×D₁₂	—	6	1	no	—
116	C₂×C₃×C₈	—	2	1	no	—
117	C₂×C₃×C₈	—	2	1	no	—
118	C₂×C₃×C₈	—	2	1	no	—
119	C₂×C₃×C₈	—	2	1	no	—
120	C₂×C₃×C₈	D₁₂	1	2	yes	—
121	C₂×C₃×C₈	D₁₂	1	2	yes	—
122	C₃×C₄²	—	2	1	no	—
123	C₃×C₄²	—	2	1	no	—
124	(C₂×D₃)⋊C₄	—	12	4	no	—
125	C₄⋊Dic₃	—	6	1	no	—
126	C₄⋊Dic₃	—	6	1	no	—
127	C₄⋊Dic₃	—	6	1	no	—
128	C₄⋊Dic₃	—	6	1	no	—
129	C₄⋊Dic₃	—	6	1	no	—
130	C₄⋊Dic₃	—	6	1	no	—
131	C₂²×C₉	C₂²⋊Q₈	1	1	yes	characteristic
132	C₂²×C₉	#123	1	1	yes	characteristic
133	C₂²×C₉	#127	1	1	yes	characteristic
134	C₂²×C₉	#135	1	2	yes	—
135	C₂²×C₉	AGL(1,ℤ/8)	1	2	yes	—
136	C₂×D₉	—	4	2	no	—
137	C₂×D₉	—	4	4	no	—
138	C₂×D₉	—	8	2	no	—
139	C₂×D₉	—	8	1	no	—
140	C₂×D₉	—	8	1	no	—
141	C₄×C₉	—	4	2	no	—
142	C₄×C₉	C₂²⋊Q₈	1	1	yes	characteristic
143	C₄×C₉	C₂²⋊Q₈	1	1	yes	characteristic
144	C₄×C₉	#123	1	1	yes	characteristic
145	C₄×C₉	#123	1	1	yes	characteristic
146	Dic₉	—	8	1	no	—
147	Dic₉	—	8	1	no	—
148	Dic₉	—	8	1	no	—
149	C₂²×D₄	—	9	1	no	—
150	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
151	C₂²×C₈	C₂×D₉	1	1	yes	characteristic
152	C₂×C₄⋊C₄	—	9	1	no	—
153	C₂×C₄⋊C₄	—	9	1	no	—
154	C₂×C₄⋊C₄	—	9	1	no	—
155	C₂×C₂²⋊C₄	—	18	2	no	—
156	C₂×C₄²	C₂×D₉	1	1	yes	characteristic
157	#107	—	18	2	no	—
158	#106	—	18	2	no	—
159	#102	—	18	2	no	—
160	#102	—	18	2	no	—
161	#95	—	18	2	no	—
162	C₂³×C₃	C₂×D₁₂	1	1	yes	characteristic
163	C₂²×D₃	—	6	2	no	—
164	C₂²×D₃	—	12	1	no	—
165	C₂²×D₃	—	12	1	no	—
166	C₂²×D₃	—	12	2	no	—
167	C₂²×D₃	—	12	2	no	—
168	C₂×C₃×C₄	—	2	2	no	—
169	C₂×C₃×C₄	—	2	2	no	—
170	C₂×C₃×C₄	—	2	2	no	—
171	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
172	C₂×C₃×C₄	C₂×D₁₂	1	1	yes	characteristic
173	C₂×C₃×C₄	#237	1	1	yes	characteristic
174	C₂×C₃×C₄	#237	1	1	yes	characteristic
175	C₂×C₃×C₄	#237	1	1	yes	characteristic
176	C₂×C₃×C₄	D₃×Q₈	1	1	yes	characteristic
177	C₂×Dic₃	—	12	1	no	—
178	C₂×Dic₃	—	12	1	no	—
179	C₂×Dic₃	—	12	1	no	—
180	C₂×Dic₃	—	12	2	no	—
181	C₂×Dic₃	—	12	2	no	—
182	C₂×Dic₃	—	12	2	no	—
183	D₁₂	—	6	2	no	—
184	D₁₂	—	6	2	no	—
185	D₁₂	—	12	1	no	—
186	D₁₂	—	12	1	no	—
187	C₃×C₈	—	2	2	no	—
188	C₃×C₈	—	2	2	no	—
189	C₂×C₉	#399	1	1	yes	characteristic
190	C₂×C₉	#478	1	2	yes	—
191	C₂×C₉	#482	1	2	yes	—
192	C₂×C₉	#495	1	1	yes	characteristic
193	C₂×C₉	#496	1	1	yes	characteristic
194	D₉	—	8	2	no	—
195	C₂⁴	—	18	1	no	—
196	C₂×D₄	—	9	2	no	—
197	C₂×D₄	—	18	1	no	—
198	C₂×D₄	—	18	1	no	—
199	C₂×D₄	—	18	1	no	—
200	C₂×D₄	—	18	1	no	—
201	C₂×D₄	—	18	1	no	—
202	C₂²×C₄	—	18	1	no	—
203	C₂²×C₄	—	18	1	no	—
204	C₂²×C₄	—	18	1	no	—
205	C₂²×C₄	D₃₆	1	2	yes	—
206	C₂²×C₄	C₂²×D₉	1	1	yes	characteristic
207	C₂×C₈	—	2	1	no	—
208	C₂×C₈	—	2	1	no	—
209	C₂×C₈	—	2	1	no	—
210	C₂×C₈	—	2	1	no	—
211	C₂×C₈	D₃₆	1	2	yes	—
212	C₂×C₈	D₃₆	1	2	yes	—
213	C₄⋊C₄	—	18	1	no	—
214	C₄⋊C₄	—	18	1	no	—
215	C₄⋊C₄	—	18	1	no	—
216	C₄⋊C₄	—	18	1	no	—
217	C₄⋊C₄	—	18	1	no	—
218	C₄⋊C₄	—	18	1	no	—
219	C₂²⋊C₄	—	36	4	no	—
220	C₄²	—	2	1	no	—
221	C₄²	—	2	1	no	—
222	C₂²×C₃	#874	1	1	yes	characteristic
223	C₂²×C₃	#886	1	1	yes	characteristic
224	C₂²×C₃	#897	1	1	yes	characteristic
225	C₂²×C₃	#904	1	2	yes	—
226	C₂²×C₃	#908	1	2	yes	—
227	C₂×D₃	—	12	2	no	—
228	C₂×D₃	—	12	4	no	—
229	C₂×D₃	—	24	1	no	—
230	C₂×D₃	—	24	1	no	—
231	C₂×D₃	—	24	2	no	—
232	C₃×C₄	—	4	2	no	—
233	C₃×C₄	#886	1	1	yes	characteristic
234	C₃×C₄	#886	1	1	yes	characteristic
235	C₃×C₄	#897	1	1	yes	characteristic
236	C₃×C₄	#897	1	1	yes	characteristic
237	Dic₃	—	24	1	no	—
238	Dic₃	—	24	1	no	—
239	Dic₃	—	24	1	no	—
240	C₉	#2092	1	1	yes	characteristic, complemented, Sylow
241	C₂³	—	18	2	no	—
242	C₂³	—	36	1	no	—
243	C₂³	—	36	1	no	—
244	C₂³	—	36	2	no	—
245	C₂³	—	36	2	no	—
246	C₂³	C₂×D₃₆	1	1	yes	characteristic
247	D₄	—	18	2	no	—
248	D₄	—	18	2	no	—
249	D₄	—	36	1	no	—
250	D₄	—	36	1	no	—
251	C₂×C₄	—	2	2	no	—
252	C₂×C₄	—	2	2	no	—
253	C₂×C₄	—	2	2	no	—
254	C₂×C₄	—	36	1	no	—
255	C₂×C₄	—	36	1	no	—
256	C₂×C₄	—	36	1	no	—
257	C₂×C₄	—	36	2	no	—
258	C₂×C₄	—	36	2	no	—
259	C₂×C₄	—	36	2	no	—
260	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
261	C₂×C₄	C₂×D₃₆	1	1	yes	characteristic
262	C₂×C₄	#3699	1	1	yes	characteristic
263	C₂×C₄	#3699	1	1	yes	characteristic
264	C₂×C₄	#3699	1	1	yes	characteristic
265	C₂×C₄	Q₈×D₉	1	1	yes	characteristic
266	C₈	—	2	2	no	—
267	C₈	—	2	2	no	—
268	C₂×C₃	#4677	1	1	yes	characteristic
269	C₂×C₃	#4696	1	1	yes	characteristic
270	C₂×C₃	#4712	1	1	yes	characteristic
271	C₂×C₃	#4737	1	2	yes	—
272	C₂×C₃	#4847	1	2	yes	—
273	D₃	—	24	2	no	—
274	C₂²	—	36	4	no	—
275	C₂²	—	36	2	no	—
276	C₂²	—	72	2	no	—
277	C₂²	—	72	1	no	—
278	C₂²	—	72	1	no	—
279	C₂²	#63436	1	1	yes	characteristic
280	C₂²	#63448	1	1	yes	characteristic
281	C₂²	#63459	1	1	yes	characteristic
282	C₂²	#63467	1	2	yes	—
283	C₂²	#63470	1	2	yes	—
284	C₄	—	4	2	no	—
285	C₄	—	72	1	no	—
286	C₄	—	72	1	no	—
287	C₄	—	72	1	no	—
288	C₄	#63448	1	1	yes	characteristic
289	C₄	#63448	1	1	yes	characteristic
290	C₄	#63459	1	1	yes	characteristic
291	C₄	#63459	1	1	yes	characteristic
292	C₃	#68680	1	1	yes	characteristic
293	C₂	—	72	2	no	—
294	C₂	#10588357	1	1	yes	characteristic
295	C₂	#10588378	1	1	yes	characteristic
296	C₂	#10588393	1	1	yes	characteristic
297	C₂	#10588419	1	2	yes	—
298	C₂	#10588531	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₃₆
commutator, cosocle	C₂²×C₄×C₉	C₂³
Frattini	C₂²×C₃×C₄	C₂²×D₃
Fitting	C₉×#336	C₂
socle	C₂³×C₃	C₂×D₁₂
prime radical	C₂²×D₃₆	C₂²
hypercenter	#336	D₉
hypocenter	C₉	#2092
LCS	G ▷ C₂²×C₄×C₉ ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #336

Complements

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

N	H ≅ G/N	type
3. C₂×#63378	C₂	semidirect
4. C₂×#63377	C₂	semidirect
6. #10588616	C₂	semidirect
7. C₉×#336	C₂	semidirect
103. #336	D₉	semidirect
240. C₉	#2092	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63380	2
C₂×#63378	2
C₂×#63377	2
#10588619	2
#10588616	2
C₉×#336	2
#68680	3