Subgroups — #36563171

Order 22784.

774 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19151999	C₂	1	1	yes	maximal, characteristic
2	#26022811	C₂	1	2	yes	maximal
3	#26021215	C₂	1	2	yes	maximal
4	#26020985	C₂	1	1	yes	maximal, characteristic
5	#26020977	C₂	1	2	yes	maximal
6	#26020415	C₂	1	1	yes	maximal, characteristic
7	#107×Dic₈₉	C₂	1	1	yes	maximal, characteristic
8	#107×Dic₈₉	C₂	1	1	yes	maximal, characteristic
9	#26020140	C₂	1	2	yes	maximal
10	C₄×C₈×Dic₈₉	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1942	C₂	1	1	yes	maximal, characteristic
12	C₂×#15668003	C₂²	1	2	yes	—
13	#19151999	C₄	1	8	yes	complemented
14	C₂×#15667946	C₂²	1	1	yes	characteristic
15	C₂×#15667946	C₂²	1	1	yes	characteristic
16	C₂×#15667943	C₂²	1	2	yes	—
17	C₂×#15667943	C₂²	1	2	yes	—
18	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
19	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
23	#19151496	C₂²	1	2	yes	—
24	#19151483	—	2	2	no	—
25	#19151479	—	2	2	no	—
26	#19151463	C₂²	1	2	yes	—
27	C₄⋊C₄×Dic₈₉	—	2	2	no	—
28	C₄⋊C₄×Dic₈₉	C₂²	1	2	yes	—
29	C₄⋊C₄×Dic₈₉	C₂²	1	2	yes	—
30	#19151449	—	2	2	no	—
31	C₄²×Dic₈₉	C₂²	1	1	yes	characteristic
32	#19151361	C₂²	1	2	yes	—
33	#19151360	C₂²	1	2	yes	—
34	#19151360	C₂²	1	2	yes	—
35	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
38	#389×C₈₉	C₂²	1	2	yes	—
39	#340×C₈₉	C₂²	1	2	yes	—
40	C₂²×#10623494	C₂³	1	1	yes	characteristic
41	C₂²×#10623494	C₂³	1	1	yes	characteristic
42	#15668003	—	2	4	no	—
43	#15668003	C₂×C₄	1	8	yes	—
44	C₂×C₄⋊Dic₈₉	—	2	2	no	—
45	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
46	C₂×C₄⋊Dic₈₉	C₂³	1	2	yes	—
47	C₂×#13083553	—	2	2	no	—
48	C₂×#13083553	—	2	2	no	—
49	C₂×C₄×Dic₈₉	—	2	2	no	—
50	C₂×C₄×Dic₈₉	—	2	2	no	—
51	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
52	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
53	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
54	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
55	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₈₉	C₂³	1	1	yes	characteristic
57	#15667946	—	2	2	no	—
58	#15667946	C₂×C₄	1	4	yes	—
59	#15667943	—	2	4	no	—
60	#15667943	C₂×C₄	1	8	yes	—
61	C₄×#10623494	—	2	2	no	—
62	C₈×Dic₈₉	—	2	2	no	—
63	C₈×Dic₈₉	C₂×C₄	1	4	yes	—
64	C₈×Dic₈₉	Q₈	1	4	yes	—
65	C₈×Dic₈₉	Q₈	1	4	yes	—
66	#15667919	—	2	2	no	—
67	#15667919	—	2	2	no	—
68	#15667919	—	2	2	no	—
69	#15667919	—	2	2	no	—
70	#15667919	—	2	2	no	—
71	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
76	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
77	#107×C₈₉	—	2	2	no	—
78	#107×C₈₉	C₂×C₄	1	4	yes	—
79	C₄×C₈×C₈₉	—	2	2	no	—
80	#95×C₈₉	—	2	2	no	—
81	C₂²×Dic₈₉	—	2	2	no	—
82	C₂²×Dic₈₉	—	2	2	no	—
83	C₂²×Dic₈₉	C₂×D₄	1	1	yes	characteristic
84	C₂²×Dic₈₉	C₂×D₄	1	1	yes	characteristic
85	C₂²×Dic₈₉	C₂×D₄	1	1	yes	characteristic
86	C₂²×Dic₈₉	C₂×D₄	1	1	yes	characteristic
87	C₂×#10623494	—	2	1	no	—
88	C₂×#10623494	—	2	1	no	—
89	C₂×#10623494	C₂²×C₄	1	2	yes	—
90	C₂×#10623494	C₂×Q₈	1	2	yes	—
91	C₂×#10623494	C₂×Q₈	1	2	yes	—
92	C₂×#10623494	#41	1	2	yes	—
93	C₄⋊Dic₈₉	—	2	2	no	—
94	C₄⋊Dic₈₉	—	2	8	no	—
95	C₄⋊Dic₈₉	—	2	2	no	—
96	C₄⋊Dic₈₉	—	2	2	no	—
97	C₄⋊Dic₈₉	C₂²×C₄	1	4	yes	—
98	#13083553	—	2	8	no	—
99	#13083553	—	4	4	no	—
100	C₄×Dic₈₉	—	2	2	no	—
101	C₄×Dic₈₉	—	2	2	no	—
102	C₄×Dic₈₉	—	2	2	no	—
103	C₄×Dic₈₉	—	2	2	no	—
104	C₄×Dic₈₉	—	4	4	no	—
105	C₄×Dic₈₉	—	4	4	no	—
106	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
107	C₄×Dic₈₉	C₂×Q₈	1	2	yes	—
108	C₄×Dic₈₉	C₂×Q₈	1	2	yes	—
109	C₄×Dic₈₉	#41	1	2	yes	—
110	C₂²×C₄×C₈₉	—	2	2	no	—
111	C₂²×C₄×C₈₉	—	2	2	no	—
112	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
115	C₂×C₈×C₈₉	—	2	1	no	—
116	C₂×C₈×C₈₉	—	2	1	no	—
117	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
119	C₂×C₈×C₈₉	C₂×Q₈	1	2	yes	—
120	C₂×C₈×C₈₉	#41	1	2	yes	—
121	C₄⋊C₄×C₈₉	—	2	2	no	—
122	C₄⋊C₄×C₈₉	—	2	2	no	—
123	C₄⋊C₄×C₈₉	—	2	2	no	—
124	C₄⋊C₄×C₈₉	—	4	4	no	—
125	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
126	C₄²×C₈₉	—	2	1	no	—
127	C₄²×C₈₉	—	2	1	no	—
128	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
129	C₂×C₄×C₈₉	—	2	1	no	—
130	C₂×C₄×C₈₉	—	2	1	no	—
131	C₂×C₄×C₈₉	—	2	1	no	—
132	C₂×C₄×C₈₉	—	2	1	no	—
133	C₂×C₄×C₈₉	—	2	4	no	—
134	C₂×C₄×C₈₉	—	4	2	no	—
135	C₂×C₄×C₈₉	—	4	2	no	—
136	C₂×C₄×C₈₉	—	4	2	no	—
137	C₂×C₄×C₈₉	—	4	2	no	—
138	C₂×C₄×C₈₉	—	4	2	no	—
139	C₂×C₄×C₈₉	#135	1	2	yes	—
140	C₂×C₄×C₈₉	#135	1	2	yes	—
141	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
142	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
143	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
145	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
147	C₂×Dic₈₉	—	2	1	no	—
148	C₂×Dic₈₉	—	2	1	no	—
149	C₂×Dic₈₉	—	2	1	no	—
150	C₂×Dic₈₉	—	2	1	no	—
151	C₂×Dic₈₉	—	2	1	no	—
152	C₂×Dic₈₉	—	2	1	no	—
153	C₂×Dic₈₉	—	2	4	no	—
154	C₂×Dic₈₉	—	4	2	no	—
155	C₂×Dic₈₉	—	4	2	no	—
156	C₂×Dic₈₉	—	4	2	no	—
157	C₂×Dic₈₉	—	4	2	no	—
158	C₂×Dic₈₉	—	4	2	no	—
159	C₂×Dic₈₉	C₄×D₄	1	2	yes	—
160	C₂×Dic₈₉	C₄×D₄	1	2	yes	—
161	C₂×Dic₈₉	C₄⋊Q₈	1	2	yes	—
162	C₂×Dic₈₉	C₄⋊Q₈	1	2	yes	—
163	C₂×Dic₈₉	#135	1	2	yes	—
164	C₂×Dic₈₉	#135	1	2	yes	—
165	C₈×C₈₉	—	2	2	no	—
166	C₈×C₈₉	C₄×Q₈	1	4	yes	—
167	#10623494	—	2	2	no	—
168	#10623494	C₄×Q₈	1	4	yes	—
169	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
170	C₂²×C₈₉	C₂×C₄⋊Q₈	1	1	yes	characteristic
171	C₂²×C₈₉	#532	1	1	yes	characteristic
172	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
173	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
174	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
175	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
176	C₄×C₈₉	—	2	2	no	—
177	C₄×C₈₉	—	2	2	no	—
178	C₄×C₈₉	—	4	4	no	—
179	C₄×C₈₉	—	8	2	no	—
180	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
181	C₄×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
182	C₄×C₈₉	#533	1	1	yes	characteristic
183	C₄×C₈₉	#533	1	1	yes	characteristic
184	Dic₈₉	—	2	2	no	—
185	Dic₈₉	—	2	2	no	—
186	Dic₈₉	—	2	2	no	—
187	Dic₈₉	—	4	4	no	—
188	Dic₈₉	—	8	2	no	—
189	Dic₈₉	#499	1	4	yes	complemented
190	C₄×#499	—	89	1	no	maximal, Sylow
191	C₂×C₈₉	C₄×C₄⋊Q₈	1	1	yes	characteristic
192	C₂×C₈₉	C₄×#135	1	1	yes	characteristic
193	C₂×C₈₉	C₄×#135	1	1	yes	characteristic
194	C₂×C₈₉	C₂×#499	1	1	yes	characteristic
195	C₂×C₈₉	#3160	1	1	yes	characteristic
196	C₂×C₈₉	#3168	1	1	yes	characteristic
197	C₂×C₈₉	#3168	1	1	yes	characteristic
198	C₂×#499	—	89	1	no	—
199	C₄×#125	—	89	2	no	—
200	#1991	—	89	2	no	—
201	#1942	—	89	1	no	—
202	#1942	D₈₉	1	1	yes	characteristic
203	#1941	—	89	2	no	—
204	#1846	—	89	1	no	—
205	C₄×#107	—	89	1	no	—
206	C₄×#107	—	89	1	no	—
207	C₄×#106	—	89	2	no	—
208	C₄²×C₈	—	89	1	no	—
209	C₈₉	C₄×#499	1	1	yes	characteristic, complemented, Sylow
210	C₂×#125	—	89	2	no	—
211	#499	—	89	8	no	—
212	C₂×#107	—	89	1	no	—
213	C₂×#107	—	89	1	no	—
214	C₂×#107	C₂×D₈₉	1	1	yes	characteristic
215	C₂×#107	C₂×D₈₉	1	1	yes	characteristic
216	C₂×#106	—	89	2	no	—
217	C₂×#106	—	89	2	no	—
218	C₂×C₄×C₈	—	89	1	no	—
219	C₂×C₄×C₈	—	89	1	no	—
220	C₂×C₄×C₈	—	89	1	no	—
221	C₂×C₄×C₈	—	89	1	no	—
222	C₂×C₄×C₈	—	89	1	no	—
223	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
224	#389	—	89	2	no	—
225	#389	C₂×D₈₉	1	2	yes	—
226	#387	—	178	2	no	—
227	#387	—	178	2	no	—
228	#382	—	89	2	no	—
229	C₄×C₄⋊C₄	—	89	2	no	—
230	C₄×C₄⋊C₄	—	89	2	no	—
231	C₄×C₄⋊C₄	—	178	2	no	—
232	C₄×C₄⋊C₄	—	178	2	no	—
233	C₄³	—	89	1	no	—
234	#340	—	89	2	no	—
235	#340	—	89	2	no	—
236	#340	—	89	2	no	—
237	#340	C₂×D₈₉	1	2	yes	—
238	C₂²×C₈	—	89	1	no	—
239	C₂²×C₈	—	89	1	no	—
240	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
241	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
242	#125	—	89	8	no	—
243	#125	—	178	4	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	89	2	no	—
246	C₂×C₄⋊C₄	—	89	2	no	—
247	C₂×C₄⋊C₄	—	178	2	no	—
248	C₂×C₄⋊C₄	—	178	2	no	—
249	C₂×C₄⋊C₄	—	178	2	no	—
250	C₂×C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
251	C₂×C₄⋊C₄	C₂²×D₈₉	1	2	yes	—
252	C₂×C₄²	—	89	1	no	—
253	C₂×C₄²	—	89	1	no	—
254	C₂×C₄²	—	89	1	no	—
255	C₂×C₄²	—	89	1	no	—
256	C₂×C₄²	—	89	1	no	—
257	C₂×C₄²	—	89	1	no	—
258	C₂×C₄²	—	178	2	no	—
259	C₂×C₄²	—	178	2	no	—
260	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
261	#107	—	2	2	no	—
262	#107	—	89	4	no	—
263	#107	—	178	2	no	—
264	#107	C₄×D₈₉	1	4	yes	—
265	#106	—	89	8	no	—
266	#106	—	178	4	no	—
267	C₄×C₈	—	2	2	no	—
268	C₄×C₈	—	89	4	no	—
269	C₄×C₈	—	89	4	no	—
270	C₄×C₈	—	89	4	no	—
271	C₄×C₈	—	178	2	no	—
272	C₄×C₈	—	178	2	no	—
273	#95	—	2	2	no	—
274	#95	—	178	2	no	—
275	#95	—	178	2	no	—
276	#95	—	178	2	no	—
277	#95	—	178	2	no	—
278	#95	—	178	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	89	1	no	—
282	C₂²×C₄	—	89	1	no	—
283	C₂²×C₄	—	89	1	no	—
284	C₂²×C₄	—	89	1	no	—
285	C₂²×C₄	—	178	2	no	—
286	C₂²×C₄	—	178	2	no	—
287	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
288	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
289	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
290	C₂×C₈	—	2	1	no	—
291	C₂×C₈	—	2	1	no	—
292	C₂×C₈	—	89	2	no	—
293	C₂×C₈	—	89	2	no	—
294	C₂×C₈	—	89	2	no	—
295	C₂×C₈	—	89	2	no	—
296	C₂×C₈	—	178	1	no	—
297	C₂×C₈	—	178	1	no	—
298	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
299	C₂×C₈	Q₈×D₈₉	1	2	yes	—
300	C₂×C₈	Q₈×D₈₉	1	2	yes	—
301	C₂×C₈	#13083573	1	2	yes	—
302	C₄⋊C₄	—	2	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	2	no	—
305	C₄⋊C₄	—	4	4	no	—
306	C₄⋊C₄	—	89	4	no	—
307	C₄⋊C₄	—	356	4	no	—
308	C₄⋊C₄	—	178	8	no	—
309	C₄⋊C₄	—	178	8	no	—
310	C₄⋊C₄	—	178	2	no	—
311	C₄⋊C₄	—	178	2	no	—
312	C₄⋊C₄	—	178	2	no	—
313	C₄⋊C₄	C₂×C₄×D₈₉	1	4	yes	—
314	C₄²	—	2	1	no	—
315	C₄²	—	2	1	no	—
316	C₄²	—	89	2	no	—
317	C₄²	—	89	2	no	—
318	C₄²	—	89	2	no	—
319	C₄²	—	89	2	no	—
320	C₄²	—	356	4	no	—
321	C₄²	—	356	4	no	—
322	C₄²	—	178	2	no	—
323	C₄²	—	178	2	no	—
324	C₄²	—	178	2	no	—
325	C₄²	—	178	2	no	—
326	C₂³	C₂×D₄×D₈₉	1	1	yes	characteristic
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	4	2	no	—
334	C₂×C₄	—	4	2	no	—
335	C₂×C₄	—	4	2	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	89	2	no	—
338	C₂×C₄	—	89	2	no	—
339	C₂×C₄	—	89	2	no	—
340	C₂×C₄	—	89	2	no	—
341	C₂×C₄	—	89	2	no	—
342	C₂×C₄	—	89	2	no	—
343	C₂×C₄	—	356	2	no	—
344	C₂×C₄	—	356	2	no	—
345	C₂×C₄	—	356	2	no	—
346	C₂×C₄	—	356	2	no	—
347	C₂×C₄	—	356	2	no	—
348	C₂×C₄	—	178	4	no	—
349	C₂×C₄	—	178	1	no	—
350	C₂×C₄	—	178	1	no	—
351	C₂×C₄	—	178	1	no	—
352	C₂×C₄	—	178	1	no	—
353	C₂×C₄	—	178	1	no	—
354	C₂×C₄	—	178	1	no	—
355	C₂×C₄	#15668031	1	2	yes	—
356	C₂×C₄	#15668035	1	2	yes	—
357	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
358	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
359	C₂×C₄	C₂×Q₈×D₈₉	1	1	yes	characteristic
360	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
361	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
362	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
363	C₈	—	2	2	no	—
364	C₈	—	89	4	no	—
365	C₈	—	178	2	no	—
366	C₈	#15667977	1	4	yes	—
367	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
368	C₂²	C₄⋊Q₈×D₈₉	1	1	yes	characteristic
369	C₂²	#19152143	1	1	yes	characteristic
370	C₂²	#135×D₈₉	1	1	yes	characteristic
371	C₂²	#135×D₈₉	1	1	yes	characteristic
372	C₂²	C₂×#15668031	1	1	yes	characteristic
373	C₂²	C₂×#15668035	1	1	yes	characteristic
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	4	no	—
377	C₄	—	8	2	no	—
378	C₄	—	89	4	no	—
379	C₄	—	356	4	no	—
380	C₄	—	178	2	no	—
381	C₄	—	178	2	no	—
382	C₄	—	178	2	no	—
383	C₄	—	712	2	no	—
384	C₄	C₄×Q₈×D₈₉	1	1	yes	characteristic
385	C₄	C₂×#15667977	1	1	yes	characteristic
386	C₄	#19152150	1	1	yes	characteristic
387	C₄	#19152154	1	1	yes	characteristic
388	C₂	#26022823	1	1	yes	characteristic
389	C₂	C₄×#15668031	1	1	yes	characteristic
390	C₂	C₄×#15668035	1	1	yes	characteristic
391	C₂	#499×D₈₉	1	1	yes	characteristic
392	C₂	#26030763	1	1	yes	characteristic
393	C₂	#26030817	1	1	yes	characteristic
394	C₂	#26030823	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1942	C₂
socle, prime radical	C₂³×C₈₉	C₂²×D₄
cosocle	C₂²×C₄×C₈₉	C₂⁴
hypercenter	#1942	D₈₉
hypocenter	C₈₉	C₄×#499
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1942

Complements

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

N	H ≅ G/N	type
13. #19151999	C₄	semidirect
189. Dic₈₉	#499	semidirect
209. C₈₉	C₄×#499	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19151999	2
#26022811	2
#26021215	2
#26020985	2
#26020977	2
#26020415	2
#107×Dic₈₉	2
#26020140	2
C₄×C₈×Dic₈₉	2
C₈₉×#1942	2
C₄×#499	89