Subgroups — #35504358

Order 21248.

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	#24917975	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#19127817	C₂	1	1	yes	maximal, characteristic
3	#24908638	C₂	1	2	yes	maximal, complemented
4	#24908634	C₂	1	2	yes	maximal, complemented
5	#24908361	C₂	1	1	yes	maximal, characteristic
6	#24908359	C₂	1	1	yes	maximal, characteristic
7	#24907588	C₂	1	1	yes	maximal, characteristic, complemented
8	#24907516	C₂	1	2	yes	maximal, complemented
9	#24907508	C₂	1	2	yes	maximal, complemented
10	#24907343	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₃×#1833	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14581814	C₂²	1	1	yes	characteristic
13	C₂×#14581800	C₂²	1	2	yes	—
14	#19128254	C₂²	1	2	yes	—
15	#19128105	—	2	1	no	—
16	#19128102	—	2	1	no	—
17	#19128101	—	2	1	no	—
18	#19128098	—	2	1	no	—
19	#19127817	—	2	1	no	—
20	#19127817	—	2	1	no	—
21	#19127817	—	2	1	no	—
22	#19127817	—	2	1	no	—
23	C₂×#14581727	C₂²	1	1	yes	characteristic
24	#19127739	C₂²	1	1	yes	characteristic
25	#19127737	C₂²	1	1	yes	characteristic
26	#19127737	C₂²	1	2	yes	—
27	#19127719	C₂²	1	2	yes	—
28	#19127717	C₂²	1	2	yes	—
29	C₂×#14581718	C₂²	1	2	yes	—
30	#19127674	C₂²	1	2	yes	—
31	#19127674	C₂²	1	2	yes	—
32	#19127656	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₈₃	C₂²	1	1	yes	characteristic
34	#19127473	C₂²	1	2	yes	—
35	#19127462	C₂²	1	1	yes	characteristic
36	#19127460	C₂²	1	1	yes	characteristic
37	#19127458	C₂²	1	2	yes	—
38	C₂×#108×C₈₃	C₂²	1	1	yes	characteristic
39	#427×C₈₃	C₂²	1	1	yes	characteristic
40	#405×C₈₃	C₂²	1	1	yes	characteristic
41	#344×C₈₃	C₂²	1	2	yes	—
42	H(3,ℤ/4)×C₈₃	C₂²	1	2	yes	—
43	C₂×#13050590	C₂³	1	2	yes	—
44	#14581814	—	2	1	no	—
45	#14581814	—	2	1	no	—
46	#14581814	—	2	1	no	—
47	#14581814	—	2	1	no	—
48	C₂×Dic₃₃₂	Q₈	1	1	yes	characteristic, complemented
49	C₂×#13050579	Q₈	1	2	yes	complemented
50	C₂×D₆₆₄	Q₈	1	1	yes	characteristic, complemented
51	#14581800	—	2	2	no	—
52	#14581800	—	2	2	no	—
53	#14581800	—	2	2	no	—
54	#14581800	—	2	2	no	—
55	C₂×#13050574	C₂³	1	1	yes	characteristic
56	C₂×#13050573	—	2	2	no	—
57	C₂²×C₈₃⋊C₈	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₈₃	—	2	2	no	—
59	#14581791	—	2	2	no	—
60	#14581783	—	2	2	no	—
61	#14581769	—	4	2	no	—
62	C₄×Dic₁₆₆	—	4	2	no	—
63	#14581751	C₂³	1	1	yes	characteristic
64	#14581751	C₂³	1	2	yes	—
65	C₂×C₄×Dic₈₃	C₂³	1	1	yes	characteristic
66	#14581727	—	2	1	no	—
67	#14581727	—	2	1	no	—
68	#14581726	—	2	1	no	—
69	#14581725	—	2	2	no	—
70	#14581725	—	2	1	no	—
71	#14581724	—	2	1	no	—
72	#14581723	—	2	2	no	—
73	#14581723	—	2	1	no	—
74	#14581720	—	4	2	no	—
75	#14581718	—	2	2	no	—
76	#14581718	—	2	2	no	—
77	#14581718	—	4	2	no	—
78	#14581706	—	4	2	no	—
79	#14581706	—	4	2	no	—
80	#14581702	—	2	1	no	—
81	C₈×Dic₈₃	—	2	1	no	—
82	C₈×Dic₈₃	D₄	1	1	yes	characteristic
83	C₈×Dic₈₃	D₄	1	1	yes	characteristic
84	C₈×Dic₈₃	D₄	1	1	yes	characteristic
85	C₈×Dic₈₃	D₄	1	1	yes	characteristic
86	C₂×M₁₆×C₈₃	C₂³	1	2	yes	—
87	C₂×M₁₆×C₈₃	C₂³	1	1	yes	characteristic
88	C₂²×C₈×C₈₃	C₂³	1	1	yes	characteristic
89	#117×C₈₃	C₂³	1	1	yes	characteristic
90	#117×C₈₃	C₂³	1	2	yes	—
91	#108×C₈₃	—	2	1	no	—
92	#108×C₈₃	—	2	1	no	—
93	#107×C₈₃	—	2	1	no	—
94	#106×C₈₃	—	2	1	no	—
95	#97×C₈₃	—	2	1	no	—
96	C₄×C₈×C₈₃	—	2	1	no	—
97	#13050590	—	2	2	no	—
98	#13050590	—	2	2	no	—
99	#13050590	—	2	2	no	—
100	#13050590	—	2	2	no	—
101	C₂×Dic₁₆₆	—	4	2	no	—
102	C₂×Dic₁₆₆	C₂×Q₈	1	2	yes	—
103	C₂×D₃₃₂	C₂×Q₈	1	2	yes	—
104	C₂×C₂²⋊D₈₃	—	2	2	no	—
105	C₂²×Dic₈₃	—	2	1	no	—
106	C₂×C₄×D₈₃	—	2	2	no	—
107	Dic₃₃₂	—	2	1	no	—
108	Dic₃₃₂	—	2	1	no	—
109	#13050579	—	2	2	no	—
110	#13050579	—	2	2	no	—
111	D₆₆₄	—	2	1	no	—
112	D₆₆₄	—	2	1	no	—
113	#13050574	—	2	1	no	—
114	#13050574	—	2	1	no	—
115	#13050573	—	4	2	no	—
116	#13050573	—	4	2	no	—
117	C₂×C₈₃⋊C₈	—	2	1	no	—
118	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈₃⋊C₈	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈₃⋊C₈	#41	1	1	yes	characteristic
121	C₂×C₈₃⋊C₈	#41	1	1	yes	characteristic
122	C₂×C₈₃⋊C₈	#41	1	1	yes	characteristic
123	C₂×C₈₃⋊C₈	#41	1	1	yes	characteristic
124	C₈×D₈₃	—	4	2	no	—
125	C₈×D₈₃	—	4	2	no	—
126	C₄⋊Dic₈₃	—	2	2	no	—
127	C₄⋊Dic₈₃	—	2	1	no	—
128	C₄⋊Dic₈₃	—	4	2	no	—
129	Dic₈₃⋊C₄	—	4	2	no	—
130	Dic₈₃⋊C₄	—	4	2	no	—
131	C₂²⋊Dic₈₃	—	2	2	no	—
132	C₂²⋊Dic₈₃	—	2	1	no	—
133	C₄×Dic₈₃	—	2	1	no	—
134	C₄×Dic₈₃	—	2	1	no	—
135	C₄×Dic₈₃	—	2	2	no	—
136	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
137	C₄×Dic₈₃	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₃	C₂⁴	1	1	yes	characteristic
139	M₁₆×C₈₃	—	2	2	no	—
140	M₁₆×C₈₃	—	2	2	no	—
141	M₁₆×C₈₃	—	2	1	no	—
142	M₁₆×C₈₃	—	2	1	no	—
143	C₂×C₈×C₈₃	—	2	2	no	—
144	C₂×C₈×C₈₃	—	2	1	no	—
145	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₈₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₈₃	C₂×Q₈	1	1	yes	characteristic
148	C₂×C₈×C₈₃	C₂×Q₈	1	1	yes	characteristic
149	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
150	C₂×C₈×C₈₃	#41	1	1	yes	characteristic
151	C₄⋊C₄×C₈₃	—	2	2	no	—
152	C₄⋊C₄×C₈₃	—	2	1	no	—
153	C₂²⋊C₄×C₈₃	—	2	2	no	—
154	C₂²⋊C₄×C₈₃	—	2	1	no	—
155	C₄²×C₈₃	—	2	1	no	—
156	C₄²×C₈₃	—	2	2	no	—
157	C₂³×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
158	C₂²×D₈₃	—	2	2	no	—
159	C₂×C₄×C₈₃	—	4	2	no	—
160	C₂×C₄×C₈₃	—	4	1	no	—
161	C₂×C₄×C₈₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₈₃	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₈₃	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₈₃	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂²⋊D₈₃	—	4	2	no	—
168	C₂²⋊D₈₃	—	4	2	no	—
169	C₂×Dic₈₃	—	2	1	no	—
170	C₂×Dic₈₃	—	2	1	no	—
171	C₂×Dic₈₃	—	2	2	no	—
172	C₂×Dic₈₃	—	4	2	no	—
173	C₂×Dic₈₃	—	4	2	no	—
174	C₂×Dic₈₃	—	4	1	no	—
175	D₃₃₂	—	2	2	no	—
176	D₃₃₂	—	2	2	no	—
177	C₄×D₈₃	—	4	2	no	—
178	C₄×D₈₃	—	4	2	no	—
179	Dic₁₆₆	—	2	2	no	—
180	Dic₁₆₆	—	2	2	no	—
181	Dic₁₆₆	—	8	4	no	—
182	C₈×C₈₃	—	4	2	no	—
183	C₈×C₈₃	—	4	1	no	—
184	C₈×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
185	C₈×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
186	C₈×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
187	C₈×C₈₃	C₂²⋊Q₈	1	1	yes	characteristic
188	C₈₃⋊C₈	—	4	1	no	—
189	C₈₃⋊C₈	#124	1	1	yes	characteristic
190	C₈₃⋊C₈	#124	1	1	yes	characteristic
191	C₈₃⋊C₈	#124	1	1	yes	characteristic
192	C₈₃⋊C₈	#124	1	1	yes	characteristic
193	C₂²×C₈₃	—	4	1	no	—
194	C₂²×C₈₃	#535	1	1	yes	characteristic
195	C₂²×C₈₃	#554	1	1	yes	characteristic
196	C₂²×C₈₃	#555	1	1	yes	characteristic
197	C₂×D₈₃	—	4	2	no	—
198	C₂×D₈₃	—	8	2	no	—
199	C₄×C₈₃	—	8	2	no	—
200	C₄×C₈₃	—	8	1	no	—
201	C₄×C₈₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
202	C₄×C₈₃	C₂×#124	1	1	yes	characteristic
203	C₄×C₈₃	#554	1	1	yes	characteristic
204	C₄×C₈₃	#555	1	1	yes	characteristic
205	Dic₈₃	—	2	2	no	—
206	Dic₈₃	—	4	1	no	—
207	Dic₈₃	—	4	2	no	—
208	Dic₈₃	—	8	2	no	—
209	Dic₈₃	—	8	1	no	—
210	#29154	—	83	1	no	maximal, Sylow
211	C₂×C₈₃	—	2	1	no	—
212	C₂×C₈₃	—	2	1	no	—
213	C₂×C₈₃	—	2	1	no	—
214	C₂×C₈₃	#2563	1	1	yes	characteristic
215	D₈₃	—	8	2	no	—
216	#3160	—	83	1	no	—
217	C₂×#443	—	83	1	no	—
218	#2031	—	83	2	no	—
219	#2031	—	83	2	no	—
220	#1976	—	83	1	no	—
221	#1976	—	83	1	no	—
222	#1833	—	83	1	no	—
223	#1833	D₈₃	1	1	yes	characteristic, complemented
224	#1814	—	83	2	no	—
225	#1812	—	83	2	no	—
226	#1772	—	83	1	no	—
227	C₈₃	#29154	1	1	yes	characteristic, complemented, Sylow
228	C₂×#135	—	83	1	no	—
229	C₂×#131	—	83	2	no	—
230	#533	—	83	2	no	—
231	#500	—	166	1	no	—
232	#499	—	166	1	no	—
233	#499	—	166	1	no	—
234	#498	—	166	1	no	—
235	#443	—	166	1	no	—
236	#443	—	166	1	no	—
237	#443	—	166	1	no	—
238	#443	—	166	1	no	—
239	C₂×#108	—	83	1	no	—
240	C₂×#108	C₂×D₈₃	1	1	yes	characteristic
241	#427	—	83	1	no	—
242	#427	—	83	1	no	—
243	#427	—	83	2	no	—
244	#427	C₂×D₈₃	1	1	yes	characteristic
245	#421	—	83	2	no	—
246	#421	—	83	2	no	—
247	C₂×#104	—	83	2	no	—
248	#410	—	83	2	no	—
249	#410	—	83	2	no	—
250	#405	—	83	1	no	—
251	#405	C₂×D₈₃	1	1	yes	characteristic
252	C₂×C₄×C₈	—	83	1	no	—
253	#344	—	83	2	no	—
254	#344	C₂×D₈₃	1	2	yes	—
255	#339	—	83	1	no	—
256	#339	—	83	1	no	—
257	H(3,ℤ/4)	—	83	2	no	—
258	H(3,ℤ/4)	C₂×D₈₃	1	2	yes	—
259	C₂×#41	—	83	2	no	—
260	#135	—	166	1	no	—
261	#135	—	166	1	no	—
262	#135	—	166	1	no	—
263	#135	—	166	1	no	—
264	C₂×Q₁₆	—	83	1	no	—
265	C₂×SD₁₆	—	83	2	no	—
266	C₂×D₈	—	83	1	no	—
267	#131	—	166	2	no	—
268	#131	—	166	2	no	—
269	#131	—	166	2	no	—
270	#131	—	166	2	no	—
271	C₂×M₁₆	—	83	1	no	—
272	C₂×M₁₆	—	166	2	no	—
273	C₂×M₁₆	C₂²×D₈₃	1	2	yes	—
274	C₂×M₁₆	C₂²×D₈₃	1	1	yes	characteristic
275	C₂²×C₈	—	83	1	no	—
276	C₂²×C₈	—	166	2	no	—
277	C₂²×C₈	C₂²×D₈₃	1	1	yes	characteristic
278	C₄⋊Q₈	—	166	2	no	—
279	#125	—	166	2	no	—
280	C₂²⋊Q₈	—	332	2	no	—
281	C₄×Q₈	—	332	2	no	—
282	#117	—	83	2	no	—
283	#117	—	83	1	no	—
284	#117	C₂²×D₈₃	1	2	yes	—
285	#117	C₂²×D₈₃	1	1	yes	characteristic
286	C₂×C₄²	—	83	1	no	—
287	#108	—	2	1	no	—
288	#108	—	2	1	no	—
289	#108	—	166	1	no	—
290	#108	—	166	1	no	—
291	#107	—	2	1	no	—
292	#107	—	166	1	no	—
293	#107	—	166	2	no	—
294	#107	—	166	1	no	—
295	#106	—	2	1	no	—
296	#106	—	166	1	no	—
297	#106	—	166	2	no	—
298	#106	—	166	1	no	—
299	#104	—	332	2	no	—
300	#104	—	332	2	no	—
301	#104	—	166	2	no	—
302	#104	—	166	2	no	—
303	#99	—	332	2	no	—
304	#99	—	332	2	no	—
305	#97	—	2	1	no	—
306	#97	—	166	1	no	—
307	C₄×C₈	—	2	1	no	—
308	C₄×C₈	—	83	1	no	—
309	C₄×C₈	—	83	1	no	—
310	C₄×C₈	—	83	1	no	—
311	C₄×C₈	—	83	1	no	—
312	C₄×C₈	—	166	1	no	—
313	#41	—	166	2	no	—
314	#41	—	166	2	no	—
315	#41	—	166	2	no	—
316	#41	—	166	2	no	—
317	C₂×Q₈	—	332	2	no	—
318	C₂×Q₈	—	83	2	no	—
319	C₂×D₄	—	83	2	no	—
320	C₂×D₄	—	166	2	no	—
321	C₂²×C₄	—	166	1	no	—
322	C₂²×C₄	—	166	2	no	—
323	C₂²×C₄	C₂³×D₈₃	1	1	yes	characteristic
324	Q₁₆	—	166	1	no	—
325	Q₁₆	—	166	1	no	—
326	SD₁₆	—	166	2	no	—
327	SD₁₆	—	166	2	no	—
328	D₈	—	166	1	no	—
329	D₈	—	166	1	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	1	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	1	no	—
334	M₁₆	—	332	2	no	—
335	M₁₆	—	332	2	no	—
336	M₁₆	—	166	1	no	—
337	M₁₆	—	166	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	332	2	no	—
341	C₂×C₈	—	332	2	no	—
342	C₂×C₈	—	83	1	no	—
343	C₂×C₈	—	83	1	no	—
344	C₂×C₈	—	83	1	no	—
345	C₂×C₈	—	83	1	no	—
346	C₂×C₈	—	83	1	no	—
347	C₂×C₈	—	83	1	no	—
348	C₂×C₈	—	166	1	no	—
349	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
350	C₂×C₈	D₄×D₈₃	1	1	yes	characteristic
351	C₂×C₈	Q₈×D₈₃	1	1	yes	characteristic
352	C₂×C₈	Q₈×D₈₃	1	1	yes	characteristic
353	C₂×C₈	#13050590	1	1	yes	characteristic
354	C₂×C₈	#13050590	1	1	yes	characteristic
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	332	2	no	—
358	C₄⋊C₄	—	332	2	no	—
359	C₄⋊C₄	—	332	2	no	—
360	C₄⋊C₄	—	166	2	no	—
361	C₄⋊C₄	—	166	1	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	166	1	no	—
365	C₂²⋊C₄	—	166	2	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	83	1	no	—
369	C₄²	—	83	1	no	—
370	C₄²	—	166	1	no	—
371	C₄²	—	166	2	no	—
372	C₄²	—	166	1	no	—
373	C₂³	—	166	2	no	—
374	C₂³	#14581838	1	1	yes	characteristic
375	Q₈	—	664	4	no	—
376	Q₈	—	166	2	no	—
377	Q₈	—	166	2	no	—
378	D₄	—	332	2	no	—
379	D₄	—	332	2	no	—
380	D₄	—	166	2	no	—
381	D₄	—	166	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	332	2	no	—
385	C₂×C₄	—	332	2	no	—
386	C₂×C₄	—	332	2	no	—
387	C₂×C₄	—	332	1	no	—
388	C₂×C₄	—	332	2	no	—
389	C₂×C₄	—	166	2	no	—
390	C₂×C₄	—	166	1	no	—
391	C₂×C₄	—	166	1	no	—
392	C₂×C₄	C₂×D₄×D₈₃	1	1	yes	characteristic
393	C₂×C₄	C₂×Q₈×D₈₃	1	1	yes	characteristic
394	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
395	C₂×C₄	#41×D₈₃	1	1	yes	characteristic
396	C₂×C₄	C₂×#13050590	1	1	yes	characteristic
397	C₂×C₄	#14581838	1	1	yes	characteristic
398	C₈	—	4	1	no	—
399	C₈	—	4	2	no	—
400	C₈	—	332	1	no	—
401	C₈	—	83	1	no	—
402	C₈	—	83	1	no	—
403	C₈	—	83	1	no	—
404	C₈	—	83	1	no	—
405	C₈	#14581770	1	1	yes	characteristic
406	C₈	#14581770	1	1	yes	characteristic
407	C₈	#14581770	1	1	yes	characteristic
408	C₈	#14581770	1	1	yes	characteristic
409	C₂²	—	4	1	no	—
410	C₂²	—	332	2	no	—
411	C₂²	—	664	2	no	—
412	C₂²	#19128269	1	1	yes	characteristic
413	C₂²	#19128407	1	1	yes	characteristic
414	C₂²	#19128414	1	1	yes	characteristic
415	C₄	—	8	2	no	—
416	C₄	—	8	1	no	—
417	C₄	—	332	1	no	—
418	C₄	—	332	2	no	—
419	C₄	—	664	2	no	—
420	C₄	—	664	1	no	—
421	C₄	—	166	2	no	—
422	C₄	C₂×#14581770	1	1	yes	characteristic
423	C₄	#124×D₈₃	1	1	yes	characteristic
424	C₄	#19128407	1	1	yes	characteristic
425	C₄	#19128414	1	1	yes	characteristic
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	664	2	no	—
430	C₂	#24912635	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#19128414
commutator, cosocle	C₂²×C₄×C₈₃	C₂⁴
Frattini	C₂²×C₄	C₂³×D₈₃
Fitting	C₈₃×#1833	C₂
socle	C₂×C₈₃	#2563
prime radical	C₂×#14581814	C₂²
hypercenter	#1833	D₈₃
hypocenter	C₈₃	#29154
LCS	G ▷ C₂²×C₄×C₈₃ ▷ C₂×C₈₃ ▷ C₈₃
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1833

Complements

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

N	H ≅ G/N	type
1. #24917975	C₂	semidirect
3. #24908638	C₂	semidirect
4. #24908634	C₂	semidirect
7. #24907588	C₂	semidirect
8. #24907516	C₂	semidirect
9. #24907508	C₂	semidirect
10. #24907343	C₂	semidirect
11. C₈₃×#1833	C₂	semidirect
48. C₂×Dic₃₃₂	Q₈	semidirect
49. C₂×#13050579	Q₈	semidirect
50. C₂×D₆₆₄	Q₈	semidirect
223. #1833	D₈₃	semidirect
227. C₈₃	#29154	semidirect

Maximal subgroups

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

subgroup	index
#24917975	2
C₂×#19127817	2
#24908638	2
#24908634	2
#24908361	2
#24908359	2
#24907588	2
#24907516	2
#24907508	2
#24907343	2
C₈₃×#1833	2
#29154	83