Subgroups — #26216496

Order 12032.

926 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	#20245791	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688988	C₂	1	1	yes	maximal, characteristic
4	#20243520	C₂	1	4	yes	maximal, complemented
5	#20243517	C₂	1	4	yes	maximal, complemented
6	#20243109	C₂	1	1	yes	maximal, characteristic
7	#20243108	C₂	1	1	yes	maximal, characteristic
8	#20243107	C₂	1	1	yes	maximal, characteristic
9	C₄₇×#1736	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂×#13093983	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
14	M₁₆×Dic₄₇	C₄	1	8	yes	complemented
15	C₂×#13093934	C₂²	1	2	yes	—
16	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
17	#15688992	C₂²	1	2	yes	—
18	#15688988	—	2	2	no	—
19	#15688988	C₂²	1	2	yes	—
20	#15688988	C₂²	1	2	yes	—
21	#15688988	C₂²	1	2	yes	—
22	#15688981	—	2	2	no	—
23	C₄×Dic₄₇⋊C₄	—	2	2	no	—
24	C₂×C₄₇⋊#95	—	2	2	no	—
25	#15688886	C₂²	1	4	yes	—
26	#15688885	C₂²	1	4	yes	—
27	#15688885	C₂²	1	4	yes	—
28	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#340	C₂²	1	4	yes	—
32	C₂³×Dic₄₇	—	2	1	no	—
33	C₂³×Dic₄₇	D₄	1	2	yes	—
34	C₂×#10625329	—	2	2	no	—
35	C₂×#10625329	—	2	2	no	—
36	C₂×#10625329	C₂×C₄	1	4	yes	—
37	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
38	#13093983	—	2	2	no	—
39	#13093983	—	2	2	no	—
40	C₂×C₄⋊Dic₄₇	—	2	2	no	—
41	C₂×C₄⋊Dic₄₇	—	2	2	no	—
42	C₂×C₄⋊Dic₄₇	—	2	1	no	—
43	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
44	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
45	C₂×Dic₄₇⋊C₄	—	2	2	no	—
46	C₂×Dic₄₇⋊C₄	—	2	2	no	—
47	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
48	C₂×C₄×Dic₄₇	—	2	1	no	—
49	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
50	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
51	C₂×C₄×Dic₄₇	Q₈	1	4	yes	—
52	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
53	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
54	#13093934	C₂×C₄	1	8	yes	complemented
55	C₈×Dic₄₇	C₂×C₄	1	8	yes	complemented
56	C₄₇⋊#95	—	2	4	no	—
57	C₄₇⋊#95	—	2	4	no	—
58	C₄₇⋊#95	—	2	4	no	—
59	C₂³×C₄×C₄₇	—	2	1	no	—
60	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
61	C₂×M₁₆×C₄₇	—	2	2	no	—
62	C₂×M₁₆×C₄₇	—	2	2	no	—
63	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
64	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
65	#117×C₄₇	—	2	2	no	—
66	#117×C₄₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₄²×C₄₇	—	2	1	no	—
74	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	—	2	2	no	—
76	C₂²×C₄×C₄₇	—	2	2	no	—
77	C₂²×C₄×C₄₇	—	4	4	no	—
78	C₂²×C₄×C₄₇	—	4	2	no	—
79	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₄₇	#41	1	2	yes	—
83	C₂²×C₄×C₄₇	#41	1	2	yes	—
84	C₂²×C₄×C₄₇	#41	1	2	yes	—
85	C₂²×C₄×C₄₇	#41	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
87	C₂²×Dic₄₇	—	2	2	no	—
88	C₂²×Dic₄₇	—	2	2	no	—
89	C₂²×Dic₄₇	—	4	2	no	—
90	C₂²×Dic₄₇	—	4	2	no	—
91	C₂²×Dic₄₇	—	4	4	no	—
92	C₂²×Dic₄₇	—	4	2	no	—
93	C₂²×Dic₄₇	C₄⋊C₄	1	8	yes	—
94	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
95	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
96	M₁₆×C₄₇	—	2	8	no	—
97	C₂×C₈×C₄₇	—	2	2	no	—
98	C₂×C₈×C₄₇	—	2	2	no	—
99	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
100	C₄⋊C₄×C₄₇	—	2	2	no	—
101	C₄⋊C₄×C₄₇	—	2	2	no	—
102	C₄⋊C₄×C₄₇	—	2	2	no	—
103	C₄⋊C₄×C₄₇	—	2	2	no	—
104	C₄⋊C₄×C₄₇	—	4	2	no	—
105	C₂²⋊C₄×C₄₇	—	4	2	no	—
106	C₄²×C₄₇	—	4	2	no	—
107	C₂²⋊Dic₄₇	—	4	2	no	—
108	C₄⋊Dic₄₇	—	2	2	no	—
109	C₄⋊Dic₄₇	—	2	2	no	—
110	C₄⋊Dic₄₇	—	2	2	no	—
111	C₄⋊Dic₄₇	—	2	2	no	—
112	C₄⋊Dic₄₇	—	4	2	no	—
113	Dic₄₇⋊C₄	—	4	4	no	—
114	Dic₄₇⋊C₄	—	4	4	no	—
115	C₄×Dic₄₇	—	4	2	no	—
116	C₄×Dic₄₇	C₄⋊C₄	1	8	yes	—
117	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
118	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
119	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
120	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
121	#10625329	—	2	8	no	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
125	C₂³×C₄₇	—	2	2	no	—
126	C₂³×C₄₇	—	2	2	no	—
127	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
128	C₂³×C₄₇	#124	1	2	yes	—
129	C₂³×C₄₇	#124	1	2	yes	—
130	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
131	C₂×C₄×C₄₇	—	4	2	no	—
132	C₂×C₄×C₄₇	—	4	2	no	—
133	C₂×C₄×C₄₇	—	4	2	no	—
134	C₂×C₄×C₄₇	—	4	2	no	—
135	C₂×C₄×C₄₇	—	4	4	no	—
136	C₂×C₄×C₄₇	—	8	4	no	—
137	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
138	C₂×C₄×C₄₇	#117	1	4	yes	—
139	C₂×C₄×C₄₇	#117	1	4	yes	—
140	C₂×C₄×C₄₇	#124	1	2	yes	—
141	C₂×C₄×C₄₇	#124	1	2	yes	—
142	C₂×C₄×C₄₇	#125	1	4	yes	—
143	C₂×C₄×C₄₇	#125	1	4	yes	—
144	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
150	C₂×Dic₄₇	—	2	2	no	—
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	2	2	no	—
153	C₂×Dic₄₇	—	2	2	no	—
154	C₂×Dic₄₇	—	4	8	no	—
155	C₂×Dic₄₇	—	4	2	no	—
156	C₂×Dic₄₇	—	4	2	no	—
157	C₂×Dic₄₇	—	4	2	no	—
158	C₂×Dic₄₇	—	4	2	no	—
159	C₂×Dic₄₇	—	4	4	no	—
160	C₂×Dic₄₇	—	8	4	no	—
161	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
162	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
163	C₈×C₄₇	—	2	4	no	—
164	C₄₇⋊C₈	—	2	4	no	—
165	#20765	—	47	1	no	maximal, Sylow
166	C₂²×C₄₇	—	2	2	no	—
167	C₂²×C₄₇	—	2	2	no	—
168	C₂²×C₄₇	—	2	4	no	—
169	C₂²×C₄₇	—	2	4	no	—
170	C₂²×C₄₇	#382	1	4	yes	—
171	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
172	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
173	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
174	C₂²×C₄₇	#575	1	2	yes	—
175	C₂²×C₄₇	#575	1	2	yes	—
176	C₄×C₄₇	—	8	2	no	—
177	C₄×C₄₇	—	8	2	no	—
178	C₄×C₄₇	#382	1	4	yes	—
179	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
180	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
181	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
182	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
183	Dic₄₇	—	2	4	no	—
184	Dic₄₇	—	2	4	no	—
185	Dic₄₇	—	8	2	no	—
186	Dic₄₇	—	8	2	no	—
187	C₂×C₄×M₁₆	—	47	1	no	—
188	#2285	—	47	1	no	—
189	C₂×#382	—	47	1	no	—
190	#1836	—	47	4	no	—
191	#1835	—	47	4	no	—
192	#1736	—	47	1	no	—
193	#1736	—	47	1	no	—
194	#1736	—	47	1	no	—
195	#1736	D₄₇	1	1	yes	characteristic
196	C₂×C₄₇	—	2	4	no	—
197	C₂×C₄₇	C₂×#382	1	1	yes	characteristic
198	C₂×C₄₇	#2911	1	2	yes	—
199	C₂×C₄₇	#3140	1	1	yes	characteristic
200	C₂×C₄₇	#3140	1	1	yes	characteristic
201	C₂×C₄₇	#3142	1	2	yes	—
202	C₂²×M₁₆	—	47	1	no	—
203	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
204	C₂×#117	—	47	1	no	—
205	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
206	C₂²×C₄⋊C₄	—	47	1	no	—
207	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
208	C₂²×C₄²	—	47	1	no	—
209	C₄×M₁₆	—	47	8	no	—
210	C₂×#97	—	47	2	no	—
211	C₂×C₄×C₈	—	47	2	no	—
212	#384	—	47	2	no	—
213	#382	—	47	2	no	—
214	#382	—	47	2	no	—
215	#382	—	47	2	no	—
216	#382	—	94	2	no	—
217	#380	—	94	2	no	—
218	C₄×C₄⋊C₄	—	94	2	no	—
219	C₂×#95	—	94	2	no	—
220	#340	—	47	4	no	—
221	#340	—	47	4	no	—
222	#340	—	47	4	no	—
223	#340	C₂×D₄₇	1	4	yes	—
224	C₄₇	#20765	1	1	yes	characteristic, complemented, Sylow
225	C₂³×C₄	—	2	1	no	—
226	C₂³×C₄	—	47	2	no	—
227	C₂³×C₄	—	94	1	no	—
228	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	47	4	no	—
232	C₂×M₁₆	—	94	2	no	—
233	C₂×M₁₆	—	94	2	no	—
234	C₂×M₁₆	C₄×D₄₇	1	4	yes	—
235	C₂²×C₈	—	47	2	no	—
236	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
237	#117	—	2	2	no	—
238	#117	—	2	2	no	—
239	#117	—	94	2	no	—
240	#117	—	94	2	no	—
241	C₂×C₄⋊C₄	—	2	2	no	—
242	C₂×C₄⋊C₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	47	2	no	—
245	C₂×C₄⋊C₄	—	47	2	no	—
246	C₂×C₄⋊C₄	—	94	2	no	—
247	C₂×C₄⋊C₄	—	94	2	no	—
248	C₂×C₄⋊C₄	—	94	2	no	—
249	C₂×C₄⋊C₄	—	94	2	no	—
250	C₂×C₄⋊C₄	—	94	1	no	—
251	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
252	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
253	C₂×C₂²⋊C₄	—	2	1	no	—
254	C₂×C₂²⋊C₄	—	94	1	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	—	47	4	no	—
257	C₂×C₄²	—	47	2	no	—
258	C₂×C₄²	—	47	4	no	—
259	C₂×C₄²	—	47	1	no	—
260	C₂×C₄²	—	47	1	no	—
261	C₂×C₄²	—	94	1	no	—
262	#97	—	47	8	no	—
263	C₄×C₈	—	47	8	no	—
264	#95	—	94	4	no	—
265	#95	—	94	4	no	—
266	#95	—	94	4	no	—
267	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	4	4	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	47	2	no	—
273	C₂²×C₄	—	47	2	no	—
274	C₂²×C₄	—	47	8	no	—
275	C₂²×C₄	—	94	2	no	—
276	C₂²×C₄	—	94	2	no	—
277	C₂²×C₄	—	188	2	no	—
278	C₂²×C₄	—	188	2	no	—
279	C₂²×C₄	—	188	4	no	—
280	C₂²×C₄	—	188	2	no	—
281	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
282	C₂²×C₄	#10625350	1	2	yes	—
283	C₂²×C₄	#10625350	1	2	yes	—
284	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
285	C₂²×C₄	#10625352	1	2	yes	—
286	C₂²×C₄	#10625352	1	2	yes	—
287	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
288	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
289	M₁₆	—	2	8	no	—
290	M₁₆	—	94	8	no	—
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	47	4	no	—
294	C₂×C₈	—	94	2	no	—
295	C₂×C₈	—	94	2	no	—
296	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
297	C₄⋊C₄	—	2	2	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₄⋊C₄	—	94	2	no	—
303	C₄⋊C₄	—	94	2	no	—
304	C₄⋊C₄	—	94	2	no	—
305	C₄⋊C₄	—	94	2	no	—
306	C₄⋊C₄	—	188	4	no	—
307	C₄⋊C₄	—	188	4	no	—
308	C₄⋊C₄	—	188	2	no	—
309	C₂²⋊C₄	—	4	2	no	—
310	C₂²⋊C₄	—	188	2	no	—
311	C₄²	—	4	2	no	—
312	C₄²	—	47	8	no	—
313	C₄²	—	47	2	no	—
314	C₄²	—	47	2	no	—
315	C₄²	—	47	2	no	—
316	C₄²	—	47	2	no	—
317	C₄²	—	188	2	no	—
318	C₂³	—	2	2	no	—
319	C₂³	—	2	2	no	—
320	C₂³	C₄⋊C₄×D₄₇	1	2	yes	—
321	C₂³	#13094010	1	2	yes	—
322	C₂³	#13094010	1	2	yes	—
323	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
324	C₂×C₄	—	4	2	no	—
325	C₂×C₄	—	4	2	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	8	4	no	—
330	C₂×C₄	—	47	4	no	—
331	C₂×C₄	—	47	4	no	—
332	C₂×C₄	—	94	2	no	—
333	C₂×C₄	—	94	2	no	—
334	C₂×C₄	—	94	2	no	—
335	C₂×C₄	—	94	2	no	—
336	C₂×C₄	—	376	4	no	—
337	C₂×C₄	—	188	8	no	—
338	C₂×C₄	—	188	2	no	—
339	C₂×C₄	—	188	2	no	—
340	C₂×C₄	—	188	2	no	—
341	C₂×C₄	—	188	2	no	—
342	C₂×C₄	—	188	4	no	—
343	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
344	C₂×C₄	#13093980	1	4	yes	—
345	C₂×C₄	#13093981	1	4	yes	—
346	C₂×C₄	#13094010	1	2	yes	—
347	C₂×C₄	#13094010	1	2	yes	—
348	C₂×C₄	#13094014	1	4	yes	—
349	C₂×C₄	#13094014	1	4	yes	—
350	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
351	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
352	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
353	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
354	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
355	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
356	C₈	—	2	4	no	—
357	C₈	—	94	4	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	2	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	4	no	—
362	C₂²	#15688987	1	4	yes	—
363	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
364	C₂²	C₂×#13094010	1	1	yes	characteristic
365	C₂²	C₂×#13094010	1	1	yes	characteristic
366	C₂²	#15689919	1	2	yes	—
367	C₂²	#15689922	1	2	yes	—
368	C₄	—	8	2	no	—
369	C₄	—	8	2	no	—
370	C₄	—	94	4	no	—
371	C₄	—	94	4	no	—
372	C₄	—	376	2	no	—
373	C₄	—	376	2	no	—
374	C₄	#15688987	1	4	yes	—
375	C₄	C₂×#13093980	1	1	yes	characteristic
376	C₄	C₂×#13093981	1	1	yes	characteristic
377	C₄	C₂×#13094014	1	1	yes	characteristic
378	C₄	C₂×#13094014	1	1	yes	characteristic
379	C₂	—	2	4	no	—
380	C₂	C₂×#15688987	1	1	yes	characteristic
381	C₂	#20251975	1	2	yes	—
382	C₂	#20253772	1	1	yes	characteristic
383	C₂	#20253776	1	1	yes	characteristic
384	C₂	#20253786	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1736	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1736	D₄₇
hypocenter	C₄₇	#20765
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ #1736

Complements

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

N	H ≅ G/N	type
4. #20243520	C₂	semidirect
5. #20243517	C₂	semidirect
14. M₁₆×Dic₄₇	C₄	semidirect
54. #13093934	C₂×C₄	semidirect
55. C₈×Dic₄₇	C₂×C₄	semidirect
224. C₄₇	#20765	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×Dic₄₇	2
#20245791	2
C₂×#15688988	2
#20243520	2
#20243517	2
#20243109	2
#20243108	2
#20243107	2
C₄₇×#1736	2
#20765	47