Subgroups — #32097406

Order 18176.

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	#22598852	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17986115	C₂	1	1	yes	maximal, characteristic
3	#22589515	C₂	1	2	yes	maximal, complemented
4	#22589511	C₂	1	2	yes	maximal, complemented
5	#22589238	C₂	1	1	yes	maximal, characteristic
6	#22589236	C₂	1	1	yes	maximal, characteristic
7	#22588465	C₂	1	1	yes	maximal, characteristic, complemented
8	#22588393	C₂	1	2	yes	maximal, complemented
9	#22588385	C₂	1	2	yes	maximal, complemented
10	#22588220	C₂	1	1	yes	maximal, characteristic, complemented
11	C₇₁×#1833	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14556150	C₂²	1	1	yes	characteristic
13	C₂×#14556136	C₂²	1	2	yes	—
14	#17986552	C₂²	1	2	yes	—
15	#17986403	—	2	1	no	—
16	#17986400	—	2	1	no	—
17	#17986399	—	2	1	no	—
18	#17986396	—	2	1	no	—
19	#17986115	—	2	1	no	—
20	#17986115	—	2	1	no	—
21	#17986115	—	2	1	no	—
22	#17986115	—	2	1	no	—
23	C₂×#14556063	C₂²	1	1	yes	characteristic
24	#17986037	C₂²	1	1	yes	characteristic
25	#17986035	C₂²	1	1	yes	characteristic
26	#17986035	C₂²	1	2	yes	—
27	#17986017	C₂²	1	2	yes	—
28	#17986015	C₂²	1	2	yes	—
29	C₂×#14556054	C₂²	1	2	yes	—
30	#17985972	C₂²	1	2	yes	—
31	#17985972	C₂²	1	2	yes	—
32	#17985954	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₇₁	C₂²	1	1	yes	characteristic
34	#17985771	C₂²	1	2	yes	—
35	#17985760	C₂²	1	1	yes	characteristic
36	#17985758	C₂²	1	1	yes	characteristic
37	#17985756	C₂²	1	2	yes	—
38	C₂×#108×C₇₁	C₂²	1	1	yes	characteristic
39	#427×C₇₁	C₂²	1	1	yes	characteristic
40	#405×C₇₁	C₂²	1	1	yes	characteristic
41	#344×C₇₁	C₂²	1	2	yes	—
42	H(3,ℤ/4)×C₇₁	C₂²	1	2	yes	—
43	C₂×#11765865	C₂³	1	2	yes	—
44	#14556150	—	2	1	no	—
45	#14556150	—	2	1	no	—
46	#14556150	—	2	1	no	—
47	#14556150	—	2	1	no	—
48	C₂×Dic₂₈₄	Q₈	1	1	yes	characteristic, complemented
49	C₂×#11765854	Q₈	1	2	yes	complemented
50	C₂×D₅₆₈	Q₈	1	1	yes	characteristic, complemented
51	#14556136	—	2	2	no	—
52	#14556136	—	2	2	no	—
53	#14556136	—	2	2	no	—
54	#14556136	—	2	2	no	—
55	C₂×#11765849	C₂³	1	1	yes	characteristic
56	C₂×#11765848	—	2	2	no	—
57	C₂²×C₇₁⋊C₈	C₂³	1	1	yes	characteristic
58	C₂×C₈×D₇₁	—	2	2	no	—
59	#14556127	—	2	2	no	—
60	#14556119	—	2	2	no	—
61	#14556105	—	4	2	no	—
62	C₄×Dic₁₄₂	—	4	2	no	—
63	#14556087	C₂³	1	1	yes	characteristic
64	#14556087	C₂³	1	2	yes	—
65	C₂×C₄×Dic₇₁	C₂³	1	1	yes	characteristic
66	#14556063	—	2	1	no	—
67	#14556063	—	2	1	no	—
68	#14556062	—	2	1	no	—
69	#14556061	—	2	2	no	—
70	#14556061	—	2	1	no	—
71	#14556060	—	2	1	no	—
72	#14556059	—	2	2	no	—
73	#14556059	—	2	1	no	—
74	#14556056	—	4	2	no	—
75	#14556054	—	2	2	no	—
76	#14556054	—	2	2	no	—
77	#14556054	—	4	2	no	—
78	#14556042	—	4	2	no	—
79	#14556042	—	4	2	no	—
80	#14556038	—	2	1	no	—
81	C₈×Dic₇₁	—	2	1	no	—
82	C₈×Dic₇₁	D₄	1	1	yes	characteristic
83	C₈×Dic₇₁	D₄	1	1	yes	characteristic
84	C₈×Dic₇₁	D₄	1	1	yes	characteristic
85	C₈×Dic₇₁	D₄	1	1	yes	characteristic
86	C₂×M₁₆×C₇₁	C₂³	1	1	yes	characteristic
87	C₂×M₁₆×C₇₁	C₂³	1	2	yes	—
88	C₂²×C₈×C₇₁	C₂³	1	1	yes	characteristic
89	#117×C₇₁	C₂³	1	1	yes	characteristic
90	#117×C₇₁	C₂³	1	2	yes	—
91	#108×C₇₁	—	2	1	no	—
92	#108×C₇₁	—	2	1	no	—
93	#107×C₇₁	—	2	1	no	—
94	#106×C₇₁	—	2	1	no	—
95	#97×C₇₁	—	2	1	no	—
96	C₄×C₈×C₇₁	—	2	1	no	—
97	#11765865	—	2	2	no	—
98	#11765865	—	2	2	no	—
99	#11765865	—	2	2	no	—
100	#11765865	—	2	2	no	—
101	C₂×Dic₁₄₂	—	4	2	no	—
102	C₂×Dic₁₄₂	C₂×Q₈	1	2	yes	—
103	C₂×D₂₈₄	C₂×Q₈	1	2	yes	—
104	C₂×C₂²⋊D₇₁	—	2	2	no	—
105	C₂²×Dic₇₁	—	2	1	no	—
106	C₂×C₄×D₇₁	—	2	2	no	—
107	Dic₂₈₄	—	2	1	no	—
108	Dic₂₈₄	—	2	1	no	—
109	#11765854	—	2	2	no	—
110	#11765854	—	2	2	no	—
111	D₅₆₈	—	2	1	no	—
112	D₅₆₈	—	2	1	no	—
113	#11765849	—	2	1	no	—
114	#11765849	—	2	1	no	—
115	#11765848	—	4	2	no	—
116	#11765848	—	4	2	no	—
117	C₂×C₇₁⋊C₈	—	2	1	no	—
118	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
119	C₂×C₇₁⋊C₈	C₂×D₄	1	1	yes	characteristic
120	C₂×C₇₁⋊C₈	#41	1	1	yes	characteristic
121	C₂×C₇₁⋊C₈	#41	1	1	yes	characteristic
122	C₂×C₇₁⋊C₈	#41	1	1	yes	characteristic
123	C₂×C₇₁⋊C₈	#41	1	1	yes	characteristic
124	C₈×D₇₁	—	4	2	no	—
125	C₈×D₇₁	—	4	2	no	—
126	C₄⋊Dic₇₁	—	2	2	no	—
127	C₄⋊Dic₇₁	—	2	1	no	—
128	C₄⋊Dic₇₁	—	4	2	no	—
129	Dic₇₁⋊C₄	—	4	2	no	—
130	Dic₇₁⋊C₄	—	4	2	no	—
131	C₂²⋊Dic₇₁	—	2	1	no	—
132	C₂²⋊Dic₇₁	—	2	2	no	—
133	C₄×Dic₇₁	—	2	1	no	—
134	C₄×Dic₇₁	—	2	1	no	—
135	C₄×Dic₇₁	—	2	2	no	—
136	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
137	C₄×Dic₇₁	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₇₁	C₂⁴	1	1	yes	characteristic
139	M₁₆×C₇₁	—	2	2	no	—
140	M₁₆×C₇₁	—	2	1	no	—
141	M₁₆×C₇₁	—	2	2	no	—
142	M₁₆×C₇₁	—	2	1	no	—
143	C₂×C₈×C₇₁	—	2	1	no	—
144	C₂×C₈×C₇₁	—	2	2	no	—
145	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₇₁	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
148	C₂×C₈×C₇₁	C₂×Q₈	1	1	yes	characteristic
149	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
150	C₂×C₈×C₇₁	#41	1	1	yes	characteristic
151	C₄⋊C₄×C₇₁	—	2	2	no	—
152	C₄⋊C₄×C₇₁	—	2	1	no	—
153	C₂²⋊C₄×C₇₁	—	2	1	no	—
154	C₂²⋊C₄×C₇₁	—	2	2	no	—
155	C₄²×C₇₁	—	2	1	no	—
156	C₄²×C₇₁	—	2	2	no	—
157	C₂³×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
158	C₂²×D₇₁	—	2	2	no	—
159	C₂×C₄×C₇₁	—	4	2	no	—
160	C₂×C₄×C₇₁	—	4	1	no	—
161	C₂×C₄×C₇₁	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₇₁	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
165	C₂×C₄×C₇₁	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₇₁	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂²⋊D₇₁	—	4	2	no	—
168	C₂²⋊D₇₁	—	4	2	no	—
169	C₂×Dic₇₁	—	2	1	no	—
170	C₂×Dic₇₁	—	2	1	no	—
171	C₂×Dic₇₁	—	2	2	no	—
172	C₂×Dic₇₁	—	4	2	no	—
173	C₂×Dic₇₁	—	4	2	no	—
174	C₂×Dic₇₁	—	4	1	no	—
175	D₂₈₄	—	2	2	no	—
176	D₂₈₄	—	2	2	no	—
177	C₄×D₇₁	—	4	2	no	—
178	C₄×D₇₁	—	4	2	no	—
179	Dic₁₄₂	—	2	2	no	—
180	Dic₁₄₂	—	2	2	no	—
181	Dic₁₄₂	—	8	4	no	—
182	C₈×C₇₁	—	4	2	no	—
183	C₈×C₇₁	—	4	1	no	—
184	C₈×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
185	C₈×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
186	C₈×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
187	C₈×C₇₁	C₂²⋊Q₈	1	1	yes	characteristic
188	C₇₁⋊C₈	—	4	1	no	—
189	C₇₁⋊C₈	#124	1	1	yes	characteristic
190	C₇₁⋊C₈	#124	1	1	yes	characteristic
191	C₇₁⋊C₈	#124	1	1	yes	characteristic
192	C₇₁⋊C₈	#124	1	1	yes	characteristic
193	C₂²×C₇₁	—	4	1	no	—
194	C₂²×C₇₁	#535	1	1	yes	characteristic
195	C₂²×C₇₁	#554	1	1	yes	characteristic
196	C₂²×C₇₁	#555	1	1	yes	characteristic
197	C₂×D₇₁	—	4	2	no	—
198	C₂×D₇₁	—	8	2	no	—
199	C₄×C₇₁	—	8	2	no	—
200	C₄×C₇₁	—	8	1	no	—
201	C₄×C₇₁	C₂×C₂²⋊Q₈	1	1	yes	characteristic
202	C₄×C₇₁	C₂×#124	1	1	yes	characteristic
203	C₄×C₇₁	#554	1	1	yes	characteristic
204	C₄×C₇₁	#555	1	1	yes	characteristic
205	Dic₇₁	—	2	2	no	—
206	Dic₇₁	—	4	1	no	—
207	Dic₇₁	—	4	2	no	—
208	Dic₇₁	—	8	2	no	—
209	Dic₇₁	—	8	1	no	—
210	#29154	—	71	1	no	maximal, Sylow
211	C₂×C₇₁	—	2	1	no	—
212	C₂×C₇₁	—	2	1	no	—
213	C₂×C₇₁	—	2	1	no	—
214	C₂×C₇₁	#2563	1	1	yes	characteristic
215	D₇₁	—	8	2	no	—
216	#3160	—	71	1	no	—
217	C₂×#443	—	71	1	no	—
218	#2031	—	71	2	no	—
219	#2031	—	71	2	no	—
220	#1976	—	71	1	no	—
221	#1976	—	71	1	no	—
222	#1833	—	71	1	no	—
223	#1833	D₇₁	1	1	yes	characteristic, complemented
224	#1814	—	71	2	no	—
225	#1812	—	71	2	no	—
226	#1772	—	71	1	no	—
227	C₇₁	#29154	1	1	yes	characteristic, complemented, Sylow
228	C₂×#135	—	71	1	no	—
229	C₂×#131	—	71	2	no	—
230	#533	—	71	2	no	—
231	#500	—	142	1	no	—
232	#499	—	142	1	no	—
233	#499	—	142	1	no	—
234	#498	—	142	1	no	—
235	#443	—	142	1	no	—
236	#443	—	142	1	no	—
237	#443	—	142	1	no	—
238	#443	—	142	1	no	—
239	C₂×#108	—	71	1	no	—
240	C₂×#108	C₂×D₇₁	1	1	yes	characteristic
241	#427	—	71	1	no	—
242	#427	—	71	1	no	—
243	#427	—	71	2	no	—
244	#427	C₂×D₇₁	1	1	yes	characteristic
245	#421	—	71	2	no	—
246	#421	—	71	2	no	—
247	C₂×#104	—	71	2	no	—
248	#410	—	71	2	no	—
249	#410	—	71	2	no	—
250	#405	—	71	1	no	—
251	#405	C₂×D₇₁	1	1	yes	characteristic
252	C₂×C₄×C₈	—	71	1	no	—
253	#344	—	71	2	no	—
254	#344	C₂×D₇₁	1	2	yes	—
255	#339	—	71	1	no	—
256	#339	—	71	1	no	—
257	H(3,ℤ/4)	—	71	2	no	—
258	H(3,ℤ/4)	C₂×D₇₁	1	2	yes	—
259	C₂×#41	—	71	2	no	—
260	#135	—	142	1	no	—
261	#135	—	142	1	no	—
262	#135	—	142	1	no	—
263	#135	—	142	1	no	—
264	C₂×Q₁₆	—	71	1	no	—
265	C₂×SD₁₆	—	71	2	no	—
266	C₂×D₈	—	71	1	no	—
267	#131	—	142	2	no	—
268	#131	—	142	2	no	—
269	#131	—	142	2	no	—
270	#131	—	142	2	no	—
271	C₂×M₁₆	—	71	1	no	—
272	C₂×M₁₆	—	142	2	no	—
273	C₂×M₁₆	C₂²×D₇₁	1	2	yes	—
274	C₂×M₁₆	C₂²×D₇₁	1	1	yes	characteristic
275	C₂²×C₈	—	71	1	no	—
276	C₂²×C₈	—	142	2	no	—
277	C₂²×C₈	C₂²×D₇₁	1	1	yes	characteristic
278	C₄⋊Q₈	—	142	2	no	—
279	#125	—	142	2	no	—
280	C₂²⋊Q₈	—	284	2	no	—
281	C₄×Q₈	—	284	2	no	—
282	#117	—	71	2	no	—
283	#117	—	71	1	no	—
284	#117	C₂²×D₇₁	1	2	yes	—
285	#117	C₂²×D₇₁	1	1	yes	characteristic
286	C₂×C₄²	—	71	1	no	—
287	#108	—	2	1	no	—
288	#108	—	2	1	no	—
289	#108	—	142	1	no	—
290	#108	—	142	1	no	—
291	#107	—	2	1	no	—
292	#107	—	142	1	no	—
293	#107	—	142	2	no	—
294	#107	—	142	1	no	—
295	#106	—	2	1	no	—
296	#106	—	142	1	no	—
297	#106	—	142	2	no	—
298	#106	—	142	1	no	—
299	#104	—	284	2	no	—
300	#104	—	284	2	no	—
301	#104	—	142	2	no	—
302	#104	—	142	2	no	—
303	#99	—	284	2	no	—
304	#99	—	284	2	no	—
305	#97	—	2	1	no	—
306	#97	—	142	1	no	—
307	C₄×C₈	—	2	1	no	—
308	C₄×C₈	—	71	1	no	—
309	C₄×C₈	—	71	1	no	—
310	C₄×C₈	—	71	1	no	—
311	C₄×C₈	—	71	1	no	—
312	C₄×C₈	—	142	1	no	—
313	#41	—	142	2	no	—
314	#41	—	142	2	no	—
315	#41	—	142	2	no	—
316	#41	—	142	2	no	—
317	C₂×Q₈	—	284	2	no	—
318	C₂×Q₈	—	71	2	no	—
319	C₂×D₄	—	71	2	no	—
320	C₂×D₄	—	142	2	no	—
321	C₂²×C₄	—	142	1	no	—
322	C₂²×C₄	—	142	2	no	—
323	C₂²×C₄	C₂³×D₇₁	1	1	yes	characteristic
324	Q₁₆	—	142	1	no	—
325	Q₁₆	—	142	1	no	—
326	SD₁₆	—	142	2	no	—
327	SD₁₆	—	142	2	no	—
328	D₈	—	142	1	no	—
329	D₈	—	142	1	no	—
330	M₁₆	—	2	2	no	—
331	M₁₆	—	2	1	no	—
332	M₁₆	—	2	2	no	—
333	M₁₆	—	2	1	no	—
334	M₁₆	—	284	2	no	—
335	M₁₆	—	284	2	no	—
336	M₁₆	—	142	1	no	—
337	M₁₆	—	142	1	no	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	2	1	no	—
340	C₂×C₈	—	284	2	no	—
341	C₂×C₈	—	284	2	no	—
342	C₂×C₈	—	71	1	no	—
343	C₂×C₈	—	71	1	no	—
344	C₂×C₈	—	71	1	no	—
345	C₂×C₈	—	71	1	no	—
346	C₂×C₈	—	71	1	no	—
347	C₂×C₈	—	71	1	no	—
348	C₂×C₈	—	142	1	no	—
349	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
350	C₂×C₈	D₄×D₇₁	1	1	yes	characteristic
351	C₂×C₈	Q₈×D₇₁	1	1	yes	characteristic
352	C₂×C₈	Q₈×D₇₁	1	1	yes	characteristic
353	C₂×C₈	#11765865	1	1	yes	characteristic
354	C₂×C₈	#11765865	1	1	yes	characteristic
355	C₄⋊C₄	—	2	2	no	—
356	C₄⋊C₄	—	2	1	no	—
357	C₄⋊C₄	—	284	2	no	—
358	C₄⋊C₄	—	284	2	no	—
359	C₄⋊C₄	—	284	2	no	—
360	C₄⋊C₄	—	142	2	no	—
361	C₄⋊C₄	—	142	1	no	—
362	C₂²⋊C₄	—	2	1	no	—
363	C₂²⋊C₄	—	2	2	no	—
364	C₂²⋊C₄	—	142	1	no	—
365	C₂²⋊C₄	—	142	2	no	—
366	C₄²	—	2	1	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	71	1	no	—
369	C₄²	—	71	1	no	—
370	C₄²	—	142	1	no	—
371	C₄²	—	142	2	no	—
372	C₄²	—	142	1	no	—
373	C₂³	—	142	2	no	—
374	C₂³	#14556174	1	1	yes	characteristic
375	Q₈	—	568	4	no	—
376	Q₈	—	142	2	no	—
377	Q₈	—	142	2	no	—
378	D₄	—	284	2	no	—
379	D₄	—	284	2	no	—
380	D₄	—	142	2	no	—
381	D₄	—	142	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	1	no	—
384	C₂×C₄	—	284	2	no	—
385	C₂×C₄	—	284	2	no	—
386	C₂×C₄	—	284	2	no	—
387	C₂×C₄	—	284	2	no	—
388	C₂×C₄	—	284	1	no	—
389	C₂×C₄	—	142	1	no	—
390	C₂×C₄	—	142	2	no	—
391	C₂×C₄	—	142	1	no	—
392	C₂×C₄	C₂×D₄×D₇₁	1	1	yes	characteristic
393	C₂×C₄	C₂×Q₈×D₇₁	1	1	yes	characteristic
394	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
395	C₂×C₄	#41×D₇₁	1	1	yes	characteristic
396	C₂×C₄	C₂×#11765865	1	1	yes	characteristic
397	C₂×C₄	#14556174	1	1	yes	characteristic
398	C₈	—	4	1	no	—
399	C₈	—	4	2	no	—
400	C₈	—	284	1	no	—
401	C₈	—	71	1	no	—
402	C₈	—	71	1	no	—
403	C₈	—	71	1	no	—
404	C₈	—	71	1	no	—
405	C₈	#14556106	1	1	yes	characteristic
406	C₈	#14556106	1	1	yes	characteristic
407	C₈	#14556106	1	1	yes	characteristic
408	C₈	#14556106	1	1	yes	characteristic
409	C₂²	—	4	1	no	—
410	C₂²	—	284	2	no	—
411	C₂²	—	568	2	no	—
412	C₂²	#17986567	1	1	yes	characteristic
413	C₂²	#17986705	1	1	yes	characteristic
414	C₂²	#17986712	1	1	yes	characteristic
415	C₄	—	8	2	no	—
416	C₄	—	8	1	no	—
417	C₄	—	284	1	no	—
418	C₄	—	284	2	no	—
419	C₄	—	568	2	no	—
420	C₄	—	568	1	no	—
421	C₄	—	142	2	no	—
422	C₄	C₂×#14556106	1	1	yes	characteristic
423	C₄	#124×D₇₁	1	1	yes	characteristic
424	C₄	#17986705	1	1	yes	characteristic
425	C₄	#17986712	1	1	yes	characteristic
426	C₂	—	2	1	no	—
427	C₂	—	2	1	no	—
428	C₂	—	2	1	no	—
429	C₂	—	568	2	no	—
430	C₂	#22593512	1	1	yes	characteristic

	subgroup	G/H
center	C₄	#17986712
commutator, cosocle	C₂²×C₄×C₇₁	C₂⁴
Frattini	C₂²×C₄	C₂³×D₇₁
Fitting	C₇₁×#1833	C₂
socle	C₂×C₇₁	#2563
prime radical	C₂×#14556150	C₂²
hypercenter	#1833	D₇₁
hypocenter	C₇₁	#29154
LCS	G ▷ C₂²×C₄×C₇₁ ▷ C₂×C₇₁ ▷ C₇₁
UCS	C₁ ◁ C₄ ◁ C₂²×C₄ ◁ #1833

Complements

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

N	H ≅ G/N	type
1. #22598852	C₂	semidirect
3. #22589515	C₂	semidirect
4. #22589511	C₂	semidirect
7. #22588465	C₂	semidirect
8. #22588393	C₂	semidirect
9. #22588385	C₂	semidirect
10. #22588220	C₂	semidirect
11. C₇₁×#1833	C₂	semidirect
48. C₂×Dic₂₈₄	Q₈	semidirect
49. C₂×#11765854	Q₈	semidirect
50. C₂×D₅₆₈	Q₈	semidirect
223. #1833	D₇₁	semidirect
227. C₇₁	#29154	semidirect

Maximal subgroups

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

subgroup	index
#22598852	2
C₂×#17986115	2
#22589515	2
#22589511	2
#22589238	2
#22589236	2
#22588465	2
#22588393	2
#22588385	2
#22588220	2
C₇₁×#1833	2
#29154	71