Subgroups — #26316232

Order 12032.

612 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253900	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689239	C₂	1	1	yes	maximal, characteristic
3	#20244563	C₂	1	2	yes	maximal, complemented
4	#20244559	C₂	1	2	yes	maximal, complemented
5	#20244286	C₂	1	1	yes	maximal, characteristic
6	#20244284	C₂	1	1	yes	maximal, characteristic
7	#20243513	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243441	C₂	1	2	yes	maximal, complemented
9	#20243433	C₂	1	2	yes	maximal, complemented
10	#20243268	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1833	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094046	C₂²	1	1	yes	characteristic
13	C₂×#13094032	C₂²	1	2	yes	—
14	#15689676	C₂²	1	2	yes	—
15	#15689527	—	2	1	no	—
16	#15689524	—	2	1	no	—
17	#15689523	—	2	1	no	—
18	#15689520	—	2	1	no	—
19	#15689239	—	2	1	no	—
20	#15689239	—	2	1	no	—
21	#15689239	—	2	1	no	—
22	#15689239	—	2	1	no	—
23	C₂×#13093959	C₂²	1	1	yes	characteristic
24	#15689161	C₂²	1	1	yes	characteristic
25	#15689159	C₂²	1	1	yes	characteristic
26	#15689159	C₂²	1	2	yes	—
27	#15689141	C₂²	1	2	yes	—
28	#15689139	C₂²	1	2	yes	—
29	C₂×#13093950	C₂²	1	2	yes	—
30	#15689096	C₂²	1	2	yes	—
31	#15689096	C₂²	1	2	yes	—
32	#15689078	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
34	#15688895	C₂²	1	2	yes	—
35	#15688884	C₂²	1	1	yes	characteristic
36	#15688882	C₂²	1	1	yes	characteristic
37	#15688880	C₂²	1	2	yes	—
38	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#427	C₂²	1	1	yes	characteristic
40	C₄₇×#405	C₂²	1	1	yes	characteristic
41	C₄₇×#344	C₂²	1	2	yes	—
42	C₄₇×H(3,ℤ/4)	C₂²	1	2	yes	—
43	C₂×#10625350	C₂³	1	2	yes	—
44	#13094046	—	2	1	no	—
45	#13094046	—	2	1	no	—
46	#13094046	—	2	1	no	—
47	#13094046	—	2	1	no	—
48	C₂×Dic₁₈₈	Q₈	1	1	yes	characteristic, complemented
49	C₂×#10625325	Q₈	1	2	yes	complemented
50	C₂×D₃₇₆	Q₈	1	1	yes	characteristic, complemented
51	#13094032	—	2	2	no	—
52	#13094032	—	2	2	no	—
53	#13094032	—	2	2	no	—
54	#13094032	—	2	2	no	—
55	C₂×#10625329	C₂³	1	1	yes	characteristic
56	C₂×#10625324	—	2	2	no	—
57	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₄₇	—	2	2	no	—
59	#13094023	—	2	2	no	—
60	#13094015	—	2	2	no	—
61	#13094001	—	4	2	no	—
62	C₄×Dic₉₄	—	4	2	no	—
63	#13093983	C₂³	1	1	yes	characteristic
64	#13093983	C₂³	1	2	yes	—
65	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
66	#13093959	—	2	1	no	—
67	#13093959	—	2	1	no	—
68	#13093958	—	2	1	no	—
69	#13093957	—	2	2	no	—
70	#13093957	—	2	1	no	—
71	#13093956	—	2	1	no	—
72	#13093955	—	2	2	no	—
73	#13093955	—	2	1	no	—
74	#13093952	—	4	2	no	—
75	#13093950	—	2	2	no	—
76	#13093950	—	2	2	no	—
77	#13093950	—	4	2	no	—
78	#13093938	—	4	2	no	—
79	#13093938	—	4	2	no	—
80	#13093934	—	2	1	no	—
81	C₈×Dic₄₇	—	2	1	no	—
82	C₈×Dic₄₇	D₄	1	1	yes	characteristic
83	C₈×Dic₄₇	D₄	1	1	yes	characteristic
84	C₈×Dic₄₇	D₄	1	1	yes	characteristic
85	C₈×Dic₄₇	D₄	1	1	yes	characteristic
86	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
87	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
89	#117×C₄₇	C₂³	1	1	yes	characteristic
90	#117×C₄₇	C₂³	1	2	yes	—
91	#108×C₄₇	—	2	1	no	—
92	#108×C₄₇	—	2	1	no	—
93	#107×C₄₇	—	2	1	no	—
94	#106×C₄₇	—	2	1	no	—
95	#97×C₄₇	—	2	1	no	—
96	C₄×C₈×C₄₇	—	2	1	no	—
97	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
98	C₂×C₂²⋊D₄₇	—	2	2	no	—
99	C₂²×Dic₄₇	—	2	1	no	—
100	#10625350	—	2	2	no	—
101	#10625350	—	2	2	no	—
102	#10625350	—	2	2	no	—
103	#10625350	—	2	2	no	—
104	C₂×D₁₈₈	C₂×Q₈	1	2	yes	—
105	C₂×C₄×D₄₇	—	2	2	no	—
106	C₂×Dic₉₄	—	4	2	no	—
107	C₂×Dic₉₄	C₂×Q₈	1	2	yes	—
108	M₁₆×C₄₇	—	2	2	no	—
109	M₁₆×C₄₇	—	2	1	no	—
110	M₁₆×C₄₇	—	2	2	no	—
111	M₁₆×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	1	no	—
114	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
117	C₂×C₈×C₄₇	C₂×Q₈	1	1	yes	characteristic
118	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
119	C₂×C₈×C₄₇	#41	1	1	yes	characteristic
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	1	no	—
122	C₂²⋊C₄×C₄₇	—	2	1	no	—
123	C₂²⋊C₄×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	—	2	1	no	—
125	C₄²×C₄₇	—	2	2	no	—
126	C₂²⋊Dic₄₇	—	2	1	no	—
127	C₂²⋊Dic₄₇	—	2	2	no	—
128	C₄⋊Dic₄₇	—	2	2	no	—
129	C₄⋊Dic₄₇	—	2	1	no	—
130	C₄⋊Dic₄₇	—	4	2	no	—
131	Dic₄₇⋊C₄	—	4	2	no	—
132	Dic₄₇⋊C₄	—	4	2	no	—
133	C₄×Dic₄₇	—	2	1	no	—
134	C₄×Dic₄₇	—	2	1	no	—
135	C₄×Dic₄₇	—	2	2	no	—
136	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
137	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
138	#10625329	—	2	1	no	—
139	#10625329	—	2	1	no	—
140	C₂×C₄₇⋊C₈	—	2	1	no	—
141	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄₇⋊C₈	#41	1	1	yes	characteristic
144	C₂×C₄₇⋊C₈	#41	1	1	yes	characteristic
145	C₂×C₄₇⋊C₈	#41	1	1	yes	characteristic
146	C₂×C₄₇⋊C₈	#41	1	1	yes	characteristic
147	Dic₁₈₈	—	2	1	no	—
148	Dic₁₈₈	—	2	1	no	—
149	D₃₇₆	—	2	1	no	—
150	D₃₇₆	—	2	1	no	—
151	#10625325	—	2	2	no	—
152	#10625325	—	2	2	no	—
153	#10625324	—	4	2	no	—
154	#10625324	—	4	2	no	—
155	C₈×D₄₇	—	4	2	no	—
156	C₈×D₄₇	—	4	2	no	—
157	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
158	C₂²×D₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	1	no	—
161	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂²⋊D₄₇	—	4	2	no	—
168	C₂²⋊D₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	2	1	no	—
170	C₂×Dic₄₇	—	2	1	no	—
171	C₂×Dic₄₇	—	2	2	no	—
172	C₂×Dic₄₇	—	4	2	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	—	4	1	no	—
175	D₁₈₈	—	2	2	no	—
176	D₁₈₈	—	2	2	no	—
177	C₄×D₄₇	—	4	2	no	—
178	C₄×D₄₇	—	4	2	no	—
179	Dic₉₄	—	2	2	no	—
180	Dic₉₄	—	2	2	no	—
181	Dic₉₄	—	8	4	no	—
182	C₈×C₄₇	—	4	2	no	—
183	C₈×C₄₇	—	4	1	no	—
184	C₈×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
185	C₈×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
186	C₈×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
187	C₈×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
188	C₄₇⋊C₈	—	4	1	no	—
189	C₄₇⋊C₈	#124	1	1	yes	characteristic
190	C₄₇⋊C₈	#124	1	1	yes	characteristic
191	C₄₇⋊C₈	#124	1	1	yes	characteristic
192	C₄₇⋊C₈	#124	1	1	yes	characteristic
193	#29154	—	47	1	no	maximal, Sylow
194	C₂²×C₄₇	—	4	1	no	—
195	C₂²×C₄₇	#535	1	1	yes	characteristic
196	C₂²×C₄₇	#554	1	1	yes	characteristic
197	C₂²×C₄₇	#555	1	1	yes	characteristic
198	C₂×D₄₇	—	4	2	no	—
199	C₂×D₄₇	—	8	2	no	—
200	C₄×C₄₇	—	8	2	no	—
201	C₄×C₄₇	—	8	1	no	—
202	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
203	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
204	C₄×C₄₇	#554	1	1	yes	characteristic
205	C₄×C₄₇	#555	1	1	yes	characteristic
206	Dic₄₇	—	2	2	no	—
207	Dic₄₇	—	4	1	no	—
208	Dic₄₇	—	4	2	no	—
209	Dic₄₇	—	8	2	no	—
210	Dic₄₇	—	8	1	no	—
211	#3160	—	47	1	no	—
212	C₂×#443	—	47	1	no	—
213	#2031	—	47	2	no	—
214	#2031	—	47	2	no	—
215	#1976	—	47	1	no	—
216	#1976	—	47	1	no	—
217	#1833	—	47	1	no	—
218	#1833	D₄₇	1	1	yes	characteristic, complemented
219	#1814	—	47	2	no	—
220	#1812	—	47	2	no	—
221	#1772	—	47	1	no	—
222	C₂×C₄₇	—	2	1	no	—
223	C₂×C₄₇	—	2	1	no	—
224	C₂×C₄₇	—	2	1	no	—
225	C₂×C₄₇	#2563	1	1	yes	characteristic
226	D₄₇	—	8	2	no	—
227	C₂×#135	—	47	1	no	—
228	C₂×#131	—	47	2	no	—
229	#533	—	47	2	no	—
230	#500	—	94	1	no	—
231	#499	—	94	1	no	—
232	#499	—	94	1	no	—
233	#498	—	94	1	no	—
234	#443	—	94	1	no	—
235	#443	—	94	1	no	—
236	#443	—	94	1	no	—
237	#443	—	94	1	no	—
238	C₂×#108	—	47	1	no	—
239	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
240	#427	—	47	1	no	—
241	#427	—	47	1	no	—
242	#427	—	47	2	no	—
243	#427	C₂×D₄₇	1	1	yes	characteristic
244	#421	—	47	2	no	—
245	#421	—	47	2	no	—
246	C₂×#104	—	47	2	no	—
247	#410	—	47	2	no	—
248	#410	—	47	2	no	—
249	#405	—	47	1	no	—
250	#405	C₂×D₄₇	1	1	yes	characteristic
251	C₂×C₄×C₈	—	47	1	no	—
252	#344	—	47	2	no	—
253	#344	C₂×D₄₇	1	2	yes	—
254	#339	—	47	1	no	—
255	#339	—	47	1	no	—
256	H(3,ℤ/4)	—	47	2	no	—
257	H(3,ℤ/4)	C₂×D₄₇	1	2	yes	—
258	C₄₇	#29154	1	1	yes	characteristic, complemented, Sylow
259	C₂×#41	—	47	2	no	—
260	#135	—	94	1	no	—
261	#135	—	94	1	no	—
262	#135	—	94	1	no	—
263	#135	—	94	1	no	—
264	C₂×Q₁₆	—	47	1	no	—
265	C₂×SD₁₆	—	47	2	no	—
266	C₂×D₈	—	47	1	no	—
267	#131	—	94	2	no	—
268	#131	—	94	2	no	—
269	#131	—	94	2	no	—
270	#131	—	94	2	no	—
271	C₂×M₁₆	—	47	1	no	—
272	C₂×M₁₆	—	94	2	no	—
273	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
274	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
275	C₂²×C₈	—	47	1	no	—
276	C₂²×C₈	—	94	2	no	—
277	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
278	C₄⋊Q₈	—	94	2	no	—
279	#125	—	94	2	no	—
280	C₂²⋊Q₈	—	188	2	no	—
281	C₄×Q₈	—	188	2	no	—
282	#117	—	47	2	no	—
283	#117	—	47	1	no	—
284	#117	C₂²×D₄₇	1	2	yes	—
285	#117	C₂²×D₄₇	1	1	yes	characteristic
286	C₂×C₄²	—	47	1	no	—
287	#108	—	2	1	no	—
288	#108	—	2	1	no	—
289	#108	—	94	1	no	—
290	#108	—	94	1	no	—
291	#107	—	2	1	no	—
292	#107	—	94	1	no	—
293	#107	—	94	2	no	—
294	#107	—	94	1	no	—
295	#106	—	2	1	no	—
296	#106	—	94	1	no	—
297	#106	—	94	2	no	—
298	#106	—	94	1	no	—
299	#104	—	94	2	no	—
300	#104	—	94	2	no	—
301	#104	—	188	2	no	—
302	#104	—	188	2	no	—
303	#99	—	188	2	no	—
304	#99	—	188	2	no	—
305	#97	—	2	1	no	—
306	#97	—	94	1	no	—
307	C₄×C₈	—	2	1	no	—
308	C₄×C₈	—	47	1	no	—
309	C₄×C₈	—	47	1	no	—
310	C₄×C₈	—	47	1	no	—
311	C₄×C₈	—	47	1	no	—
312	C₄×C₈	—	94	1	no	—
313	#41	—	94	2	no	—
314	#41	—	94	2	no	—
315	#41	—	94	2	no	—
316	#41	—	94	2	no	—
317	C₂×Q₈	—	47	2	no	—
318	C₂×Q₈	—	188	2	no	—
319	C₂×D₄	—	47	2	no	—
320	C₂×D₄	—	94	2	no	—
321	C₂²×C₄	—	94	1	no	—
322	C₂²×C₄	—	94	2	no	—
323	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
324	Q₁₆	—	94	1	no	—
325	Q₁₆	—	94	1	no	—
326	SD₁₆	—	94	2	no	—
327	SD₁₆	—	94	2	no	—
328	D₈	—	94	1	no	—
329	D₈	—	94	1	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	1	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	1	no	—
334	M₁₆	—	94	1	no	—
335	M₁₆	—	94	1	no	—
336	M₁₆	—	188	2	no	—
337	M₁₆	—	188	2	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	47	1	no	—
341	C₂×C₈	—	47	1	no	—
342	C₂×C₈	—	47	1	no	—
343	C₂×C₈	—	47	1	no	—
344	C₂×C₈	—	47	1	no	—
345	C₂×C₈	—	47	1	no	—
346	C₂×C₈	—	94	1	no	—
347	C₂×C₈	—	188	2	no	—
348	C₂×C₈	—	188	2	no	—
349	C₂×C₈	#10625350	1	1	yes	characteristic
350	C₂×C₈	#10625350	1	1	yes	characteristic
351	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
352	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
353	C₂×C₈	Q₈×D₄₇	1	1	yes	characteristic
354	C₂×C₈	Q₈×D₄₇	1	1	yes	characteristic
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	94	2	no	—
358	C₄⋊C₄	—	94	1	no	—
359	C₄⋊C₄	—	188	2	no	—
360	C₄⋊C₄	—	188	2	no	—
361	C₄⋊C₄	—	188	2	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	94	1	no	—
365	C₂²⋊C₄	—	94	2	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	47	1	no	—
369	C₄²	—	47	1	no	—
370	C₄²	—	94	1	no	—
371	C₄²	—	94	1	no	—
372	C₄²	—	94	2	no	—
373	C₂³	—	94	2	no	—
374	C₂³	#13094070	1	1	yes	characteristic
375	Q₈	—	94	2	no	—
376	Q₈	—	94	2	no	—
377	Q₈	—	376	4	no	—
378	D₄	—	94	2	no	—
379	D₄	—	94	2	no	—
380	D₄	—	188	2	no	—
381	D₄	—	188	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	94	1	no	—
385	C₂×C₄	—	94	2	no	—
386	C₂×C₄	—	94	1	no	—
387	C₂×C₄	—	188	2	no	—
388	C₂×C₄	—	188	1	no	—
389	C₂×C₄	—	188	2	no	—
390	C₂×C₄	—	188	2	no	—
391	C₂×C₄	—	188	2	no	—
392	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
393	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
394	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
395	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
396	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
397	C₂×C₄	#13094070	1	1	yes	characteristic
398	C₈	—	4	1	no	—
399	C₈	—	4	2	no	—
400	C₈	—	47	1	no	—
401	C₈	—	47	1	no	—
402	C₈	—	47	1	no	—
403	C₈	—	47	1	no	—
404	C₈	—	188	1	no	—
405	C₈	#13094002	1	1	yes	characteristic
406	C₈	#13094002	1	1	yes	characteristic
407	C₈	#13094002	1	1	yes	characteristic
408	C₈	#13094002	1	1	yes	characteristic
409	C₂²	—	4	1	no	—
410	C₂²	—	376	2	no	—
411	C₂²	—	188	2	no	—
412	C₂²	#15689691	1	1	yes	characteristic
413	C₂²	#15689829	1	1	yes	characteristic
414	C₂²	#15689836	1	1	yes	characteristic
415	C₄	—	8	2	no	—
416	C₄	—	8	1	no	—
417	C₄	—	94	2	no	—
418	C₄	—	376	2	no	—
419	C₄	—	376	1	no	—
420	C₄	—	188	1	no	—
421	C₄	—	188	2	no	—
422	C₄	C₂×#13094002	1	1	yes	characteristic
423	C₄	#124×D₄₇	1	1	yes	characteristic
424	C₄	#15689829	1	1	yes	characteristic
425	C₄	#15689836	1	1	yes	characteristic
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	376	2	no	—
430	C₂	#20248560	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#15689836
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1833	C₂
socle	C₂×C₄₇	#2563
prime radical	C₂×#13094046	C₂²
hypercenter	#1833	D₄₇
hypocenter	C₄₇	#29154
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1833

Complements

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

N	H ≅ G/N	type
1. #20253900	C₂	semidirect
3. #20244563	C₂	semidirect
4. #20244559	C₂	semidirect
7. #20243513	C₂	semidirect
8. #20243441	C₂	semidirect
9. #20243433	C₂	semidirect
10. #20243268	C₂	semidirect
11. C₄₇×#1833	C₂	semidirect
48. C₂×Dic₁₈₈	Q₈	semidirect
49. C₂×#10625325	Q₈	semidirect
50. C₂×D₃₇₆	Q₈	semidirect
218. #1833	D₄₇	semidirect
258. C₄₇	#29154	semidirect

Maximal subgroups

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

subgroup	index
#20253900	2
C₂×#15689239	2
#20244563	2
#20244559	2
#20244286	2
#20244284	2
#20243513	2
#20243441	2
#20243433	2
#20243268	2
C₄₇×#1833	2
#29154	47