Subgroups — #26216642

Order 12032.

616 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13094030	C₂	1	1	yes	maximal, characteristic
2	#20243534	C₂	1	2	yes	maximal, complemented
3	#20243513	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243511	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243491	C₂	1	2	yes	maximal
6	#20243435	C₂	1	1	yes	maximal, characteristic
7	#20243431	C₂	1	1	yes	maximal, characteristic
8	#20243267	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243189	C₂	1	2	yes	maximal
10	#20243143	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1772	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094030	C₂²	1	1	yes	characteristic
13	C₂×#13094030	C₂²	1	1	yes	characteristic
14	C₄×#10625350	C₂²	1	1	yes	characteristic
15	C₂×#13093960	C₂²	1	1	yes	characteristic
16	#15689161	C₂²	1	1	yes	characteristic
17	#15689105	C₂²	1	2	yes	—
18	#15689096	C₂²	1	2	yes	—
19	#15689078	C₂²	1	2	yes	—
20	#15689078	C₂²	1	1	yes	characteristic
21	#15689078	C₂²	1	1	yes	characteristic
22	#15689077	C₄	1	2	yes	complemented
23	#15689077	C₄	1	2	yes	complemented
24	C₄×#10625329	C₂²	1	1	yes	characteristic
25	C₄×#10625324	C₄	1	2	yes	complemented
26	C₄×C₈×D₄₇	C₄	1	2	yes	complemented
27	#15688895	C₂²	1	2	yes	—
28	#15688893	C₂²	1	2	yes	—
29	#15688883	C₂²	1	2	yes	—
30	C₄₇⋊#338	C₂²	1	2	yes	—
31	#15688880	C₂²	1	2	yes	—
32	#15688879	C₂²	1	2	yes	—
33	#15688879	C₂²	1	2	yes	—
34	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#427	C₂²	1	1	yes	characteristic
36	C₄₇×#405	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#339	C₂²	1	2	yes	—
39	C₂×#10625350	C₂³	1	1	yes	characteristic
40	#13094030	—	2	1	no	—
41	#13094030	—	2	1	no	—
42	#13094030	—	2	1	no	—
43	#13094030	—	2	1	no	—
44	#13094030	—	2	1	no	—
45	#13094030	—	2	1	no	—
46	#13094030	—	2	1	no	—
47	#13094030	—	2	1	no	—
48	C₂×#10625329	C₂³	1	2	yes	—
49	C₂×#10625329	C₂³	1	1	yes	characteristic
50	C₂×#10625329	C₂³	1	1	yes	characteristic
51	C₂×#10625324	C₂×C₄	1	2	yes	—
52	C₂×#10625324	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
55	C₄×Dic₉₄	—	2	1	no	—
56	C₄×D₁₈₈	—	2	1	no	—
57	C₄×C₂²⋊D₄₇	—	2	2	no	—
58	#13093983	C₂³	1	2	yes	—
59	#13093983	C₂³	1	1	yes	characteristic
60	#13093981	C₂×C₄	1	2	yes	—
61	C₄²×D₄₇	C₂×C₄	1	2	yes	—
62	#13093960	—	2	1	no	—
63	#13093960	—	2	1	no	—
64	#13093958	—	2	1	no	—
65	#13093956	—	2	1	no	—
66	#13093942	—	2	2	no	—
67	#13093940	—	2	2	no	—
68	#13093938	—	2	4	no	—
69	#13093935	C₂×C₄	1	2	yes	—
70	#13093934	—	2	2	no	—
71	#13093934	C₂×C₄	1	2	yes	—
72	#13093934	C₂×C₄	1	2	yes	—
73	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
74	C₈×Dic₄₇	—	2	2	no	—
75	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
76	C₈×Dic₄₇	C₂×C₄	1	2	yes	—
77	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
78	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	#117×C₄₇	C₂³	1	2	yes	—
81	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
82	#108×C₄₇	—	2	1	no	—
83	#108×C₄₇	—	2	1	no	—
84	#107×C₄₇	—	2	1	no	—
85	#106×C₄₇	—	2	1	no	—
86	#97×C₄₇	—	2	2	no	—
87	C₄×C₈×C₄₇	—	2	2	no	—
88	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	—	2	1	no	—
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂×C₂²⋊D₄₇	#41	1	2	yes	—
95	#10625350	—	2	1	no	—
96	#10625350	—	2	1	no	—
97	#10625350	—	2	1	no	—
98	#10625350	—	2	1	no	—
99	C₂×D₁₈₈	#41	1	1	yes	characteristic
100	C₂×C₄×D₄₇	—	2	2	no	—
101	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
102	C₂×Dic₉₄	#41	1	1	yes	characteristic
103	M₁₆×C₄₇	—	2	2	no	—
104	M₁₆×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
111	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
112	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
113	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
114	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
115	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
116	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
117	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₂²⋊C₄×C₄₇	—	2	2	no	—
120	C₄²×C₄₇	—	2	1	no	—
121	C₄²×C₄₇	—	2	2	no	—
122	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²⋊Dic₄₇	—	2	1	no	—
125	C₂²⋊Dic₄₇	—	2	2	no	—
126	(C₂×D₄₇)⋊C₄	—	2	2	no	—
127	C₄⋊Dic₄₇	—	2	1	no	—
128	C₄⋊Dic₄₇	—	2	2	no	—
129	Dic₄₇⋊C₄	—	2	2	no	—
130	C₄×Dic₄₇	—	2	2	no	—
131	C₄×Dic₄₇	—	2	2	no	—
132	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
133	#10625329	—	2	1	no	—
134	#10625329	—	2	1	no	—
135	#10625329	—	2	1	no	—
136	#10625329	—	2	1	no	—
137	#10625329	—	2	2	no	—
138	#10625329	—	2	2	no	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
142	#10625324	—	2	2	no	—
143	#10625324	—	2	2	no	—
144	#10625324	—	2	2	no	—
145	#10625324	—	2	2	no	—
146	C₈×D₄₇	—	2	2	no	—
147	C₈×D₄₇	—	2	2	no	—
148	C₈×D₄₇	—	2	2	no	—
149	C₈×D₄₇	—	2	2	no	—
150	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
151	C₂²×D₄₇	#117	1	2	yes	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
162	C₂²⋊D₄₇	—	2	2	no	—
163	C₂²⋊D₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	2	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	#117	1	2	yes	—
167	D₁₈₈	—	2	1	no	—
168	D₁₈₈	—	2	1	no	—
169	C₄×D₄₇	—	2	2	no	—
170	C₄×D₄₇	—	2	2	no	—
171	C₄×D₄₇	—	4	4	no	—
172	Dic₉₄	—	2	1	no	—
173	Dic₉₄	—	2	1	no	—
174	C₈×C₄₇	—	4	2	no	—
175	C₈×C₄₇	#117	1	1	yes	characteristic
176	C₈×C₄₇	#117	1	1	yes	characteristic
177	C₈×C₄₇	#117	1	1	yes	characteristic
178	C₈×C₄₇	#117	1	1	yes	characteristic
179	C₈×C₄₇	#117	1	1	yes	characteristic
180	C₈×C₄₇	#117	1	1	yes	characteristic
181	C₈×C₄₇	#117	1	1	yes	characteristic
182	C₈×C₄₇	#117	1	1	yes	characteristic
183	C₄₇⋊C₈	—	2	2	no	—
184	C₄₇⋊C₈	—	2	2	no	—
185	C₄₇⋊C₈	—	4	2	no	—
186	#20787	—	47	1	no	maximal, Sylow
187	C₂²×C₄₇	—	4	1	no	—
188	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
189	C₂²×C₄₇	#529	1	1	yes	characteristic
190	C₂²×C₄₇	#529	1	1	yes	characteristic
191	C₂×D₄₇	—	2	2	no	—
192	C₂×D₄₇	—	4	2	no	—
193	C₄×C₄₇	—	2	2	no	—
194	C₄×C₄₇	—	4	1	no	—
195	C₄×C₄₇	—	8	2	no	—
196	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
197	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
198	C₄×C₄₇	#529	1	1	yes	characteristic
199	C₄×C₄₇	#529	1	1	yes	characteristic
200	Dic₄₇	—	2	2	no	—
201	Dic₄₇	—	4	2	no	—
202	Dic₄₇	—	8	2	no	—
203	C₄×#131	—	47	1	no	—
204	#1841	—	47	2	no	—
205	#1833	—	47	1	no	—
206	#1833	—	47	1	no	—
207	#1827	—	47	2	no	—
208	#1813	—	47	1	no	—
209	#1812	—	47	1	no	—
210	#1772	—	47	1	no	—
211	#1772	D₄₇	1	1	yes	characteristic, complemented
212	#1757	—	47	2	no	—
213	#1747	—	47	2	no	—
214	C₂×C₄₇	—	2	1	no	—
215	C₂×C₄₇	—	2	1	no	—
216	C₂×C₄₇	—	2	1	no	—
217	C₂×C₄₇	#2283	1	1	yes	characteristic
218	D₄₇	—	4	2	no	—
219	C₂×#131	—	47	1	no	—
220	C₂×#131	—	47	1	no	—
221	C₄×#41	—	47	1	no	—
222	C₂×#108	—	47	1	no	—
223	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
224	#427	—	47	1	no	—
225	#427	C₂×D₄₇	1	1	yes	characteristic
226	#413	—	47	2	no	—
227	#410	—	47	2	no	—
228	#405	—	47	1	no	—
229	#405	—	47	1	no	—
230	#405	—	47	2	no	—
231	#405	—	47	2	no	—
232	#405	—	47	2	no	—
233	#405	C₂×D₄₇	1	2	yes	—
234	C₄×M₁₆	—	47	1	no	—
235	C₄×M₁₆	—	47	2	no	—
236	C₂×C₄×C₈	—	47	2	no	—
237	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
238	#344	—	47	2	no	—
239	#344	—	47	2	no	—
240	#339	—	47	2	no	—
241	#339	C₂×D₄₇	1	2	yes	—
242	#338	—	47	2	no	—
243	H(3,ℤ/4)	—	47	2	no	—
244	H(3,ℤ/4)	—	47	2	no	—
245	H(3,ℤ/4)	—	47	2	no	—
246	C₄₇	#20787	1	1	yes	characteristic, complemented, Sylow
247	C₂×#41	—	47	1	no	—
248	#131	—	94	1	no	—
249	#131	—	94	1	no	—
250	#131	—	94	1	no	—
251	#131	—	94	1	no	—
252	#131	—	94	1	no	—
253	#131	—	94	1	no	—
254	#131	—	94	1	no	—
255	#131	—	94	1	no	—
256	C₂×M₁₆	—	47	1	no	—
257	C₂×M₁₆	—	47	1	no	—
258	C₂×M₁₆	—	47	2	no	—
259	C₂×M₁₆	—	47	2	no	—
260	C₂×M₁₆	—	47	2	no	—
261	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
262	C₂²×C₈	—	47	2	no	—
263	C₂²×C₈	—	47	2	no	—
264	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
266	C₄×Q₈	—	94	1	no	—
267	C₄×D₄	—	94	1	no	—
268	C₄×D₄	—	94	2	no	—
269	#117	—	47	1	no	—
270	#117	—	47	2	no	—
271	#117	—	47	2	no	—
272	#117	C₂²×D₄₇	1	2	yes	—
273	C₂×C₄²	—	47	2	no	—
274	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
275	#108	—	2	1	no	—
276	#108	—	2	1	no	—
277	#108	—	94	1	no	—
278	#108	—	94	1	no	—
279	#107	—	2	1	no	—
280	#107	—	94	1	no	—
281	#106	—	2	1	no	—
282	#106	—	94	1	no	—
283	#101	—	94	2	no	—
284	#100	—	94	2	no	—
285	#99	—	94	4	no	—
286	#97	—	2	2	no	—
287	#97	—	47	2	no	—
288	#97	—	47	2	no	—
289	#97	—	47	2	no	—
290	#97	—	94	2	no	—
291	C₄×C₈	—	2	2	no	—
292	C₄×C₈	—	47	2	no	—
293	C₄×C₈	—	47	2	no	—
294	C₄×C₈	—	47	2	no	—
295	C₄×C₈	—	94	2	no	—
296	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
297	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
298	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
299	C₄×C₈	C₄×D₄₇	1	1	yes	characteristic
300	#41	—	94	1	no	—
301	#41	—	94	1	no	—
302	#41	—	94	1	no	—
303	#41	—	94	1	no	—
304	C₂×Q₈	—	47	1	no	—
305	C₂×D₄	—	47	2	no	—
306	C₂×D₄	—	47	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	47	2	no	—
309	C₂²×C₄	—	94	2	no	—
310	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
311	M₁₆	—	2	2	no	—
312	M₁₆	—	2	2	no	—
313	M₁₆	—	94	1	no	—
314	M₁₆	—	94	1	no	—
315	M₁₆	—	94	1	no	—
316	M₁₆	—	94	1	no	—
317	M₁₆	—	94	2	no	—
318	M₁₆	—	94	2	no	—
319	M₁₆	—	94	2	no	—
320	M₁₆	—	94	2	no	—
321	M₁₆	—	94	2	no	—
322	M₁₆	—	94	2	no	—
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	47	2	no	—
325	C₂×C₈	—	47	2	no	—
326	C₂×C₈	—	94	2	no	—
327	C₂×C₈	—	94	2	no	—
328	C₂×C₈	—	94	2	no	—
329	C₂×C₈	—	94	2	no	—
330	C₂×C₈	—	94	2	no	—
331	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
332	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
333	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
335	C₂×C₈	#10625350	1	1	yes	characteristic
336	C₂×C₈	#10625350	1	1	yes	characteristic
337	C₂×C₈	#10625350	1	1	yes	characteristic
338	C₂×C₈	#10625350	1	1	yes	characteristic
339	C₂×C₈	#10625352	1	1	yes	characteristic
340	C₂×C₈	#10625352	1	1	yes	characteristic
341	C₂×C₈	#10625354	1	1	yes	characteristic
342	C₂×C₈	#10625354	1	1	yes	characteristic
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	94	2	no	—
345	C₄⋊C₄	—	94	1	no	—
346	C₄⋊C₄	—	94	2	no	—
347	C₂²⋊C₄	—	2	2	no	—
348	C₂²⋊C₄	—	94	2	no	—
349	C₂²⋊C₄	—	94	1	no	—
350	C₂²⋊C₄	—	94	2	no	—
351	C₄²	—	2	1	no	—
352	C₄²	—	2	2	no	—
353	C₄²	—	47	2	no	—
354	C₄²	—	94	2	no	—
355	C₄²	—	94	2	no	—
356	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
357	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
358	C₂³	—	47	2	no	—
359	C₂³	#41×D₄₇	1	1	yes	characteristic
360	Q₈	—	94	1	no	—
361	Q₈	—	94	1	no	—
362	D₄	—	94	2	no	—
363	D₄	—	94	2	no	—
364	D₄	—	94	1	no	—
365	D₄	—	94	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	47	2	no	—
371	C₂×C₄	—	94	2	no	—
372	C₂×C₄	—	94	2	no	—
373	C₂×C₄	—	94	2	no	—
374	C₂×C₄	—	188	4	no	—
375	C₂×C₄	—	188	2	no	—
376	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
377	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
378	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
379	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
380	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
381	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
382	C₈	—	4	2	no	—
383	C₈	—	94	2	no	—
384	C₈	—	94	2	no	—
385	C₈	—	188	2	no	—
386	C₈	#13093981	1	1	yes	characteristic
387	C₈	#13093981	1	1	yes	characteristic
388	C₈	#13093981	1	1	yes	characteristic
389	C₈	#13093981	1	1	yes	characteristic
390	C₈	#13093982	1	1	yes	characteristic
391	C₈	#13093982	1	1	yes	characteristic
392	C₈	#13093982	1	1	yes	characteristic
393	C₈	#13093982	1	1	yes	characteristic
394	C₂²	—	4	1	no	—
395	C₂²	—	94	2	no	—
396	C₂²	—	188	2	no	—
397	C₂²	#117×D₄₇	1	1	yes	characteristic
398	C₂²	#15689655	1	1	yes	characteristic
399	C₂²	#15689660	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	4	1	no	—
402	C₄	—	8	2	no	—
403	C₄	—	94	2	no	—
404	C₄	—	376	2	no	—
405	C₄	—	188	2	no	—
406	C₄	C₂×#13093981	1	1	yes	characteristic
407	C₄	C₂×#13093982	1	1	yes	characteristic
408	C₄	#15689655	1	1	yes	characteristic
409	C₄	#15689660	1	1	yes	characteristic
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	2	1	no	—
413	C₂	—	188	2	no	—
414	C₂	#20245784	1	1	yes	characteristic

	subgroup	G/H
center	C₈	#13093982
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1772	C₂
socle	C₂×C₄₇	#2283
prime radical	C₂×#10625350	C₂³
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1772	D₄₇
hypocenter	C₄₇	#20787
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #1772

Complements

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

N	H ≅ G/N	type
2. #20243534	C₂	semidirect
3. #20243513	C₂	semidirect
4. #20243511	C₂	semidirect
8. #20243267	C₂	semidirect
10. #20243143	C₂	semidirect
11. C₄₇×#1772	C₂	semidirect
22. #15689077	C₄	semidirect
23. #15689077	C₄	semidirect
25. C₄×#10625324	C₄	semidirect
26. C₄×C₈×D₄₇	C₄	semidirect
211. #1772	D₄₇	semidirect
246. C₄₇	#20787	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13094030	2
#20243534	2
#20243513	2
#20243511	2
#20243491	2
#20243435	2
#20243431	2
#20243267	2
#20243189	2
#20243143	2
C₄₇×#1772	2
#20787	47