Subgroups — #14643272

Order 2816.

636 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13077249	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#4318	C₂	1	1	yes	maximal, characteristic
3	#13066452	C₂	1	4	yes	maximal, complemented
4	C₂×C₁₁×#431	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄²×C₁₁	C₂²	1	1	yes	characteristic
6	C₂²×#4318	—	2	1	no	—
7	C₁₁×#431	—	2	1	no	—
8	C₁₁×#431	—	2	1	no	—
9	C₁₁×#431	C₄	1	2	yes	—
10	C₁₁×#431	C₂²	1	2	yes	—
11	C₂×C₁₁×C₄⋊C₈	C₄	1	2	yes	—
12	C₂×C₁₁×C₂²⋊C₈	—	2	1	no	—
13	C₂×C₄×C₈×C₁₁	—	2	1	no	—
14	#10622820	C₄	1	2	yes	—
15	#10622539	—	2	1	no	—
16	#10622539	—	2	1	no	—
17	#10622538	—	2	1	no	—
18	#10622538	—	2	1	no	—
19	#10622537	C₄	1	2	yes	—
20	C₄×#4318	—	2	1	no	—
21	C₄×#4318	—	2	1	no	—
22	C₄×#4318	C₄	1	2	yes	—
23	C₄×#4318	C₄	1	2	yes	—
24	C₄×#4318	C₂²	1	2	yes	—
25	C₂×#66867	—	2	1	no	—
26	C₂×C₄×C₁₁⋊C₈	C₂²	1	2	yes	—
27	C₂³×C₄×C₁₁	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₁₁	D₄	1	1	yes	characteristic
29	C₂³×C₄×C₁₁	Q₈	1	1	yes	characteristic
30	C₂²×C₈×C₁₁	—	2	2	no	—
31	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₁	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
37	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
38	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
41	C₂×C₄²×C₁₁	Q₈	1	1	yes	characteristic
42	C₂×C₄²×C₁₁	C₂³	1	1	yes	characteristic
43	C₂×#4318	—	2	8	no	—
44	C₂×#4318	—	2	2	no	—
45	C₂×#4318	—	2	2	no	—
46	C₂×#4318	C₂×C₄	1	4	yes	—
47	C₂²×C₁₁⋊C₈	—	2	2	no	—
48	C₁₁×C₄⋊C₈	—	2	2	no	—
49	C₁₁×C₄⋊C₈	C₂×C₄	1	4	yes	—
50	C₁₁×C₂²⋊C₈	—	2	2	no	—
51	C₁₁×C₂²⋊C₈	—	2	2	no	—
52	C₄×C₈×C₁₁	—	2	2	no	—
53	C₄×C₈×C₁₁	—	2	2	no	—
54	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
55	C₂²⋊(C₁₁⋊C₈)	—	2	2	no	—
56	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
57	C₄⋊(C₁₁⋊C₈)	—	2	2	no	—
58	#66867	—	2	2	no	—
59	#66867	—	2	2	no	—
60	#66867	—	2	2	no	—
61	C₄×C₁₁⋊C₈	—	2	2	no	—
62	C₄×C₁₁⋊C₈	—	2	2	no	—
63	C₄×C₁₁⋊C₈	C₂×C₄	1	4	yes	—
64	#7883	—	11	1	no	maximal, Sylow
65	C₂⁴×C₁₁	C₄⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₁₁	—	2	4	no	—
67	C₂²×C₄×C₁₁	—	2	4	no	—
68	C₂²×C₄×C₁₁	—	4	2	no	—
69	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
70	C₂²×C₄×C₁₁	C₄²	1	1	yes	characteristic
71	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₁₁	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₁	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₁	C₂×Q₈	1	1	yes	characteristic
87	C₂×C₈×C₁₁	—	2	4	no	—
88	C₂×C₈×C₁₁	—	4	4	no	—
89	C₄²×C₁₁	C₄²	1	1	yes	characteristic
90	C₄²×C₁₁	C₄²	1	1	yes	characteristic
91	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
92	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
93	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
94	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
95	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
96	C₄²×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
97	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
98	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
99	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
100	C₄²×C₁₁	C₄⋊C₄	1	1	yes	characteristic
101	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
102	C₄²×C₁₁	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₁₁	C₂×D₄	1	1	yes	characteristic
105	#4318	—	2	8	no	—
106	#4318	—	2	8	no	—
107	#4318	—	2	8	no	—
108	C₂×C₁₁⋊C₈	—	2	8	no	—
109	C₂×C₁₁⋊C₈	—	2	4	no	—
110	C₂×C₁₁⋊C₈	—	2	4	no	—
111	#2920	—	11	1	no	—
112	C₂×#431	D₁₁	1	1	yes	characteristic
113	C₂×C₄×M₁₆	—	11	1	no	—
114	#1278	—	11	4	no	—
115	C₂³×C₁₁	—	2	2	no	—
116	C₂³×C₁₁	—	2	2	no	—
117	C₂³×C₁₁	—	4	1	no	—
118	C₂³×C₁₁	#95	1	1	yes	characteristic
119	C₂³×C₁₁	#95	1	1	yes	characteristic
120	C₂³×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₁₁	—	2	2	no	—
122	C₂×C₄×C₁₁	—	2	2	no	—
123	C₂×C₄×C₁₁	—	2	2	no	—
124	C₂×C₄×C₁₁	—	2	2	no	—
125	C₂×C₄×C₁₁	—	2	2	no	—
126	C₂×C₄×C₁₁	—	2	2	no	—
127	C₂×C₄×C₁₁	—	2	2	no	—
128	C₂×C₄×C₁₁	—	2	2	no	—
129	C₂×C₄×C₁₁	—	2	2	no	—
130	C₂×C₄×C₁₁	—	2	2	no	—
131	C₂×C₄×C₁₁	—	2	2	no	—
132	C₂×C₄×C₁₁	—	2	2	no	—
133	C₂×C₄×C₁₁	—	2	2	no	—
134	C₂×C₄×C₁₁	—	4	1	no	—
135	C₂×C₄×C₁₁	—	4	1	no	—
136	C₂×C₄×C₁₁	—	4	1	no	—
137	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
138	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
139	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
140	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
141	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
142	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
143	C₂×C₄×C₁₁	#104	1	4	yes	—
144	C₂×C₄×C₁₁	C₂×C₄²	1	1	yes	characteristic
145	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₁₁	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₁₁	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₁₁	#131	1	4	yes	—
151	C₈×C₁₁	—	4	4	no	—
152	C₁₁⋊C₈	—	2	8	no	—
153	C₁₁⋊C₈	—	4	4	no	—
154	C₂²×M₁₆	—	22	1	no	—
155	C₂²×C₄²	C₂×D₁₁	1	1	yes	characteristic
156	#432	—	22	1	no	—
157	#432	—	22	1	no	—
158	#431	—	2	1	no	—
159	#431	—	2	1	no	—
160	#431	—	22	1	no	—
161	#431	—	22	1	no	—
162	#431	Dic₁₁	1	2	yes	—
163	#431	C₂×D₁₁	1	2	yes	—
164	#423	—	11	2	no	—
165	C₂×C₄⋊C₈	Dic₁₁	1	2	yes	—
166	#407	—	11	2	no	—
167	C₂×C₂²⋊C₈	—	2	1	no	—
168	C₄×M₁₆	—	11	2	no	—
169	C₄×M₁₆	—	11	2	no	—
170	C₄×M₁₆	—	11	2	no	—
171	C₄×M₁₆	—	22	1	no	—
172	C₄×M₁₆	—	22	1	no	—
173	C₂×#97	—	22	1	no	—
174	C₂×C₄×C₈	—	2	1	no	—
175	C₂×C₄×C₈	—	11	2	no	—
176	C₂²×C₁₁	—	2	1	no	—
177	C₂²×C₁₁	—	2	1	no	—
178	C₂²×C₁₁	—	2	1	no	—
179	C₂²×C₁₁	—	2	1	no	—
180	C₂²×C₁₁	—	2	1	no	—
181	C₂²×C₁₁	—	2	1	no	—
182	C₂²×C₁₁	—	2	1	no	—
183	C₂²×C₁₁	—	4	4	no	—
184	C₂²×C₁₁	#339	1	2	yes	—
185	C₂²×C₁₁	C₂×#95	1	1	yes	characteristic
186	C₂²×C₁₁	#424	1	2	yes	—
187	C₄×C₁₁	—	2	1	no	—
188	C₄×C₁₁	—	2	1	no	—
189	C₄×C₁₁	—	2	1	no	—
190	C₄×C₁₁	—	2	1	no	—
191	C₄×C₁₁	—	2	1	no	—
192	C₄×C₁₁	—	2	1	no	—
193	C₄×C₁₁	—	2	1	no	—
194	C₄×C₁₁	#339	1	2	yes	—
195	C₄×C₁₁	#405	1	2	yes	—
196	C₄×C₁₁	#408	1	2	yes	—
197	C₄×C₁₁	C₂×#104	1	2	yes	—
198	C₄×C₁₁	#430	1	2	yes	—
199	C₂³×C₄	Dic₂₂	1	1	yes	characteristic
200	C₂³×C₄	C₄×D₁₁	1	1	yes	characteristic
201	C₂³×C₄	C₂²⋊D₁₁	1	1	yes	characteristic
202	C₂×M₁₆	—	11	4	no	—
203	C₂×M₁₆	—	22	8	no	—
204	C₂×M₁₆	—	22	2	no	—
205	C₂×M₁₆	—	22	2	no	—
206	C₂²×C₈	—	2	2	no	—
207	C₂²×C₈	—	22	2	no	—
208	C₂×C₄²	Dic₂₂	1	1	yes	characteristic
209	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
210	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
211	C₂×C₄²	C₄×D₁₁	1	1	yes	characteristic
212	C₂×C₄²	D₄₄	1	1	yes	characteristic
213	C₂×C₄²	D₄₄	1	1	yes	characteristic
214	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
215	C₂×C₄²	C₂×Dic₁₁	1	1	yes	characteristic
216	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
217	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
218	C₂×C₄²	C₂²⋊D₁₁	1	1	yes	characteristic
219	C₂×C₄²	C₂²×D₁₁	1	1	yes	characteristic
220	C₄⋊C₈	—	2	2	no	—
221	C₄⋊C₈	—	22	2	no	—
222	C₄⋊C₈	—	22	2	no	—
223	C₄⋊C₈	C₂×Dic₁₁	1	4	yes	—
224	C₂²⋊C₈	—	2	2	no	—
225	C₂²⋊C₈	—	2	2	no	—
226	C₂²⋊C₈	—	22	2	no	—
227	C₂²⋊C₈	—	22	2	no	—
228	#97	—	22	2	no	—
229	#97	—	22	2	no	—
230	#97	—	22	2	no	—
231	C₄×C₈	—	2	2	no	—
232	C₄×C₈	—	2	2	no	—
233	C₄×C₈	—	11	4	no	—
234	C₄×C₈	—	22	2	no	—
235	C₄×C₈	—	22	2	no	—
236	C₂×C₁₁	—	2	2	no	—
237	C₂×C₁₁	—	2	2	no	—
238	C₂×C₁₁	—	4	1	no	—
239	C₂×C₁₁	#1729	1	1	yes	characteristic
240	C₂×C₁₁	C₂×#339	1	1	yes	characteristic
241	C₂×C₁₁	#1738	1	1	yes	characteristic
242	C₂⁴	Dic₁₁⋊C₄	1	1	yes	characteristic
243	C₂²×C₄	—	2	4	no	—
244	C₂²×C₄	—	2	4	no	—
245	C₂²×C₄	—	4	2	no	—
246	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
247	C₂²×C₄	C₄×Dic₁₁	1	1	yes	characteristic
248	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
249	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
250	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
251	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
252	C₂²×C₄	Dic₁₁⋊C₄	1	1	yes	characteristic
253	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
254	C₂²×C₄	C₄⋊Dic₁₁	1	1	yes	characteristic
255	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
256	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
257	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
258	C₂²×C₄	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
259	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊Dic₁₁	1	1	yes	characteristic
261	C₂²×C₄	C₂×Dic₂₂	1	1	yes	characteristic
262	C₂²×C₄	C₂×C₄×D₁₁	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
264	M₁₆	—	22	8	no	—
265	M₁₆	—	22	8	no	—
266	M₁₆	—	22	8	no	—
267	C₂×C₈	—	2	4	no	—
268	C₂×C₈	—	4	4	no	—
269	C₂×C₈	—	22	8	no	—
270	C₂×C₈	—	22	4	no	—
271	C₂×C₈	—	22	4	no	—
272	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
273	C₄²	C₄×Dic₁₁	1	1	yes	characteristic
274	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
275	C₄²	Dic₁₁⋊C₄	1	1	yes	characteristic
276	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
277	C₄²	C₄⋊Dic₁₁	1	1	yes	characteristic
278	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
279	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
280	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
281	C₄²	(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
282	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
283	C₄²	C₂²⋊Dic₁₁	1	1	yes	characteristic
284	C₄²	C₂×C₄×D₁₁	1	1	yes	characteristic
285	C₄²	C₂×D₄₄	1	1	yes	characteristic
286	C₄²	C₂²×Dic₁₁	1	1	yes	characteristic
287	C₄²	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
288	C₁₁	#7883	1	1	yes	characteristic, complemented, Sylow
289	C₂³	—	2	2	no	—
290	C₂³	—	2	2	no	—
291	C₂³	—	4	1	no	—
292	C₂³	C₁₁⋊#95	1	1	yes	characteristic
293	C₂³	C₁₁⋊#95	1	1	yes	characteristic
294	C₂³	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
295	C₂×C₄	—	2	2	no	—
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	2	2	no	—
301	C₂×C₄	—	2	2	no	—
302	C₂×C₄	—	2	2	no	—
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	4	1	no	—
309	C₂×C₄	—	4	1	no	—
310	C₂×C₄	—	4	1	no	—
311	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
312	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
313	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
314	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
315	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
316	C₂×C₄	C₁₁⋊#95	1	1	yes	characteristic
317	C₂×C₄	#66901	1	4	yes	—
318	C₂×C₄	#66954	1	4	yes	—
319	C₂×C₄	C₂×C₄×Dic₁₁	1	1	yes	characteristic
320	C₂×C₄	C₂×Dic₁₁⋊C₄	1	1	yes	characteristic
321	C₂×C₄	C₂×C₄⋊Dic₁₁	1	1	yes	characteristic
322	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
323	C₂×C₄	C₂×(C₂×D₁₁)⋊C₄	1	1	yes	characteristic
324	C₂×C₄	C₂×C₂²⋊Dic₁₁	1	1	yes	characteristic
325	C₈	—	4	4	no	—
326	C₈	—	22	8	no	—
327	C₈	—	44	4	no	—
328	C₂²	—	2	1	no	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	1	no	—
333	C₂²	—	2	1	no	—
334	C₂²	—	2	1	no	—
335	C₂²	—	4	4	no	—
336	C₂²	#10622170	1	2	yes	—
337	C₂²	#10622715	1	2	yes	—
338	C₂²	C₂×C₁₁⋊#95	1	1	yes	characteristic
339	C₄	—	2	1	no	—
340	C₄	—	2	1	no	—
341	C₄	—	2	1	no	—
342	C₄	—	2	1	no	—
343	C₄	—	2	1	no	—
344	C₄	—	2	1	no	—
345	C₄	—	2	1	no	—
346	C₄	#10622170	1	2	yes	—
347	C₄	#10622714	1	2	yes	—
348	C₄	#10622723	1	2	yes	—
349	C₄	#10622737	1	2	yes	—
350	C₄	C₂×#66901	1	2	yes	—
351	C₂	—	2	2	no	—
352	C₂	—	2	2	no	—
353	C₂	—	4	1	no	—
354	C₂	#13068312	1	1	yes	characteristic
355	C₂	C₂×#10622170	1	1	yes	characteristic
356	C₂	#13068342	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂×C₂²⋊D₁₁
commutator	C₂×C₄×C₁₁	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₁₁
Fitting	C₂×C₁₁×#431	C₂
socle	C₂²×C₁₁	C₂×#95
prime radical	C₂⁴×C₁₁	C₄⋊C₄
cosocle	C₂×C₄²×C₁₁	C₂³
hypercenter	C₂×#431	D₁₁
hypocenter	C₁₁	#7883
LCS	G ▷ C₂×C₄×C₁₁ ▷ C₂×C₁₁ ▷ C₁₁
UCS	C₁ ◁ C₄² ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. #13066452	C₂	semidirect
288. C₁₁	#7883	semidirect

Maximal subgroups

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

subgroup	index
#13077249	2
C₂×C₄×#4318	2
#13066452	2
C₂×C₁₁×#431	2
#7883	11