Subgroups — #36538361

Order 22784.

638 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	#500×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	#26030066	C₂	1	2	yes	maximal
3	C₈×#13083575	C₂	1	1	yes	maximal, characteristic
4	#26019656	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019654	C₂	1	2	yes	maximal, complemented
6	#26019652	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019650	C₂	1	2	yes	maximal, complemented
8	#26019648	C₂	1	1	yes	maximal, characteristic, complemented
9	#26019009	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018931	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1676	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄⋊Q₈×D₈₉	C₂²	1	2	yes	—
13	C₄×#13083575	C₂²	1	1	yes	characteristic
14	#19152003	C₂²	1	1	yes	characteristic
15	#19152002	—	2	1	no	—
16	#19152002	—	2	1	no	—
17	#19152001	C₂²	1	2	yes	—
18	#19151893	C₂²	1	2	yes	—
19	#19151889	C₂²	1	2	yes	—
20	#19151885	C₂²	1	2	yes	—
21	#19151881	—	2	2	no	—
22	#19151877	—	2	2	no	—
23	Q₈×#10623494	C₂²	1	1	yes	characteristic
24	C₈×D₃₅₆	—	2	1	no	—
25	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
26	#19151663	—	2	1	no	—
27	#19151663	C₂²	1	1	yes	characteristic
28	#19151650	—	2	1	no	—
29	#19151650	C₂²	1	1	yes	characteristic
30	#19151639	—	2	2	no	—
31	#107×D₈₉	—	2	1	no	—
32	#107×D₈₉	—	2	1	no	—
33	#19151620	C₂²	1	2	yes	—
34	#19151598	—	2	2	no	—
35	C₄×C₈×D₈₉	—	2	1	no	—
36	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
37	#19151351	C₂²	1	1	yes	characteristic
38	#19151350	C₂²	1	2	yes	—
39	#19151347	C₂²	1	2	yes	—
40	#19151346	C₂²	1	2	yes	—
41	#19151346	C₂²	1	2	yes	—
42	#500×C₈₉	C₂²	1	1	yes	characteristic
43	#477×C₈₉	C₂²	1	2	yes	—
44	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic
45	#335×C₈₉	C₂²	1	1	yes	characteristic
46	#333×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083575	D₄	1	1	yes	characteristic
48	C₂×Q₈×D₈₉	—	2	2	no	—
49	C₂×#13083557	—	2	2	no	—
50	C₂×C₈×D₈₉	—	2	1	no	—
51	C₂×C₈×D₈₉	—	2	1	no	—
52	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
53	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
54	#15668012	C₂³	1	2	yes	—
55	#15668011	—	2	2	no	—
56	#15668011	—	2	2	no	—
57	#15668010	—	2	2	no	—
58	Q₈×Dic₈₉	D₄	1	1	yes	characteristic
59	C₄×D₃₅₆	—	2	1	no	—
60	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
61	#15667974	—	2	1	no	—
62	#15667974	D₄	1	1	yes	characteristic
63	#15667970	—	2	1	no	—
64	#15667970	D₄	1	1	yes	characteristic
65	C₄⋊C₄×D₈₉	—	2	2	no	—
66	C₄⋊C₄×D₈₉	—	2	2	no	—
67	C₄²×D₈₉	—	2	1	no	—
68	C₄²×D₈₉	C₂³	1	1	yes	characteristic
69	#15667946	—	2	1	no	—
70	#15667946	—	2	1	no	—
71	#15667945	—	2	2	no	—
72	#15667945	—	2	2	no	—
73	#15667945	—	2	2	no	—
74	#15667944	—	2	2	no	—
75	#15667943	—	2	2	no	—
76	C₄⋊#10623494	—	2	1	no	—
77	C₄⋊#10623494	C₂³	1	2	yes	—
78	C₄⋊#10623494	C₂³	1	1	yes	characteristic
79	#15667941	—	2	2	no	—
80	#15667936	—	2	2	no	—
81	#15667934	—	2	2	no	—
82	#15667932	—	2	2	no	—
83	#15667924	—	2	1	no	—
84	#15667924	—	2	1	no	—
85	#15667924	—	2	1	no	—
86	C₄×#10623494	—	2	1	no	—
87	C₄×#10623494	C₂³	1	1	yes	characteristic
88	C₈×Dic₈₉	—	2	1	no	—
89	C₈×Dic₈₉	D₄	1	1	yes	characteristic
90	C₈×Dic₈₉	D₄	1	1	yes	characteristic
91	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
92	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
93	#107×C₈₉	—	2	1	no	—
94	#107×C₈₉	—	2	1	no	—
95	#107×C₈₉	—	2	2	no	—
96	C₄⋊C₈×C₈₉	—	2	1	no	—
97	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
98	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
99	#103×C₈₉	—	2	2	no	—
100	C₄×C₈×C₈₉	—	2	1	no	—
101	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	#13083575	—	2	2	no	—
103	#13083575	Q₁₆	1	4	yes	—
104	C₂×Dic₁₇₈	—	2	2	no	—
105	C₂×Dic₁₇₈	—	4	2	no	—
106	Q₈×D₈₉	—	8	4	no	—
107	C₂×D₃₅₆	—	2	1	no	—
108	C₂×D₃₅₆	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₈₉	—	2	1	no	—
110	C₂×C₄×D₈₉	—	2	1	no	—
111	C₂×C₄×D₈₉	—	2	1	no	—
112	C₂×C₄×D₈₉	—	4	2	no	—
113	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
115	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
116	#13083557	—	4	4	no	—
117	C₂×#10623494	—	2	1	no	—
118	C₂×#10623494	—	2	2	no	—
119	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
120	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
121	C₈×D₈₉	—	2	2	no	—
122	C₈×D₈₉	—	2	2	no	—
123	C₈×D₈₉	—	4	2	no	—
124	C₈×D₈₉	—	4	2	no	—
125	C₄⋊Dic₈₉	—	2	1	no	—
126	C₄⋊Dic₈₉	—	2	2	no	—
127	C₄⋊Dic₈₉	—	2	2	no	—
128	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
129	#13083553	—	4	2	no	—
130	#13083553	—	4	2	no	—
131	#13083551	—	2	1	no	—
132	#13083551	—	2	1	no	—
133	#13083551	—	2	1	no	—
134	C₄×Dic₈₉	—	2	1	no	—
135	C₄×Dic₈₉	—	2	1	no	—
136	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
137	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
138	C₄×Dic₈₉	#41	1	1	yes	characteristic
139	C₂×Q₈×C₈₉	—	2	2	no	—
140	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₈₉	—	2	1	no	—
142	C₂×C₈×C₈₉	—	2	2	no	—
143	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₄⋊C₄×C₈₉	—	2	1	no	—
146	C₄⋊C₄×C₈₉	—	2	2	no	—
147	C₄⋊C₄×C₈₉	—	2	2	no	—
148	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
149	C₄²×C₈₉	—	2	1	no	—
150	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
151	C₂²×D₈₉	—	2	1	no	—
152	C₂²×D₈₉	#121	1	1	yes	characteristic
153	Q₈×C₈₉	—	2	1	no	—
154	Q₈×C₈₉	—	8	2	no	—
155	Q₈×C₈₉	C₂×Q₁₆	1	2	yes	—
156	C₂×C₄×C₈₉	—	2	1	no	—
157	C₂×C₄×C₈₉	—	2	1	no	—
158	C₂×C₄×C₈₉	—	4	2	no	—
159	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
162	C₂×Dic₈₉	—	2	1	no	—
163	C₂×Dic₈₉	—	4	2	no	—
164	C₂×Dic₈₉	#121	1	1	yes	characteristic
165	C₂×Dic₈₉	#121	1	1	yes	characteristic
166	C₂×Dic₈₉	#121	1	1	yes	characteristic
167	D₃₅₆	—	2	4	no	—
168	D₃₅₆	—	2	1	no	—
169	D₃₅₆	C₂×Q₁₆	1	2	yes	—
170	C₄×D₈₉	—	2	1	no	—
171	C₄×D₈₉	—	2	1	no	—
172	C₄×D₈₉	—	2	4	no	—
173	C₄×D₈₉	—	2	2	no	—
174	C₄×D₈₉	—	4	1	no	—
175	C₄×D₈₉	—	4	1	no	—
176	C₄×D₈₉	—	4	2	no	—
177	C₄×D₈₉	—	8	4	no	—
178	C₄×D₈₉	C₂×Q₁₆	1	2	yes	—
179	C₄×D₈₉	#135	1	2	yes	—
180	Dic₁₇₈	—	8	4	no	—
181	Dic₁₇₈	—	8	2	no	—
182	C₈×C₈₉	—	2	1	no	—
183	C₈×C₈₉	—	4	2	no	—
184	C₈×C₈₉	—	4	1	no	—
185	C₈×C₈₉	#137	1	2	yes	—
186	#10623494	—	2	1	no	—
187	#10623494	—	4	2	no	—
188	#10623494	—	4	1	no	—
189	#10623494	#137	1	2	yes	—
190	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
191	C₂×D₈₉	—	2	1	no	—
192	C₂×D₈₉	—	2	1	no	—
193	C₂×D₈₉	—	2	2	no	—
194	C₂×D₈₉	—	4	1	no	—
195	C₂×D₈₉	—	4	1	no	—
196	C₂×D₈₉	#467	1	2	yes	—
197	C₄×C₈₉	—	2	2	no	—
198	C₄×C₈₉	—	2	1	no	—
199	C₄×C₈₉	—	4	1	no	—
200	C₄×C₈₉	—	8	2	no	—
201	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
202	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
203	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
204	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
205	Dic₈₉	—	2	1	no	—
206	Dic₈₉	—	4	1	no	—
207	Dic₈₉	—	8	2	no	—
208	Dic₈₉	#467	1	2	yes	—
209	Dic₈₉	#472	1	2	yes	—
210	#19272	—	89	1	no	maximal, Sylow
211	C₂×C₈₉	#3039	1	1	yes	characteristic
212	C₂×C₈₉	C₂×#467	1	1	yes	characteristic
213	C₂×C₈₉	C₂×#472	1	1	yes	characteristic
214	D₈₉	—	2	2	no	—
215	D₈₉	—	4	2	no	—
216	C₂×#500	—	89	1	no	—
217	#3079	—	89	2	no	—
218	C₈×#41	—	89	1	no	—
219	#1676	—	89	2	no	—
220	#1676	—	89	1	no	—
221	#1676	D₈₉	1	1	yes	characteristic, complemented
222	#1675	—	89	1	no	—
223	#1675	—	89	1	no	—
224	#1675	—	89	2	no	—
225	#1567	—	89	1	no	—
226	#1548	—	89	2	no	—
227	C₈₉	#19272	1	1	yes	characteristic, complemented, Sylow
228	C₂×C₄⋊Q₈	—	89	2	no	—
229	C₄×#41	—	89	1	no	—
230	#500	—	89	2	no	—
231	#500	—	89	1	no	—
232	#500	—	178	1	no	—
233	#500	—	178	1	no	—
234	#500	C₂×D₈₉	1	1	yes	characteristic
235	#477	—	89	2	no	—
236	#477	C₂×D₈₉	1	2	yes	—
237	#476	—	89	2	no	—
238	#476	—	89	2	no	—
239	#475	—	178	2	no	—
240	#474	—	178	2	no	—
241	C₈×Q₈	—	89	1	no	—
242	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic
243	C₈×D₄	—	89	1	no	—
244	C₈×D₄	—	89	1	no	—
245	C₈×D₄	—	178	1	no	—
246	C₈×D₄	—	178	1	no	—
247	#431	—	89	1	no	—
248	#431	—	178	1	no	—
249	#428	—	178	2	no	—
250	C₂×#107	—	178	1	no	—
251	C₂×#107	—	178	1	no	—
252	#423	—	89	2	no	—
253	#417	—	178	2	no	—
254	C₂×C₄×C₈	—	89	1	no	—
255	C₂×C₄×C₈	—	178	1	no	—
256	#335	—	89	2	no	—
257	#335	—	89	1	no	—
258	#335	C₂×D₈₉	1	1	yes	characteristic
259	#333	—	89	2	no	—
260	#333	—	89	2	no	—
261	#333	—	89	2	no	—
262	#333	C₂×D₈₉	1	2	yes	—
263	C₂×#41	—	89	1	no	—
264	C₂²×Q₈	—	178	2	no	—
265	C₂×M₁₆	—	178	2	no	—
266	C₂²×C₈	—	89	1	no	—
267	C₂²×C₈	—	89	1	no	—
268	C₂²×C₈	—	178	1	no	—
269	C₂²×C₈	—	178	1	no	—
270	C₄⋊Q₈	—	89	2	no	—
271	C₄⋊Q₈	—	178	2	no	—
272	C₄⋊Q₈	—	178	2	no	—
273	C₄⋊Q₈	—	178	2	no	—
274	C₄⋊Q₈	C₂²×D₈₉	1	2	yes	—
275	C₄×Q₈	—	89	1	no	—
276	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
277	C₄×D₄	—	89	1	no	—
278	C₄×D₄	—	89	1	no	—
279	C₄×D₄	—	178	1	no	—
280	C₄×D₄	—	178	1	no	—
281	#117	—	89	1	no	—
282	#117	—	178	1	no	—
283	C₂×C₄⋊C₄	—	178	2	no	—
284	C₂×C₄⋊C₄	—	178	2	no	—
285	C₂×C₄²	—	89	1	no	—
286	C₂×C₄²	—	178	1	no	—
287	#107	—	2	1	no	—
288	#107	—	2	1	no	—
289	#107	—	2	2	no	—
290	#107	—	178	2	no	—
291	#107	—	178	2	no	—
292	#107	—	178	1	no	—
293	#107	—	178	1	no	—
294	#107	—	178	2	no	—
295	#106	—	178	2	no	—
296	#106	—	178	2	no	—
297	C₄⋊C₈	—	2	1	no	—
298	C₄⋊C₈	—	89	1	no	—
299	C₄⋊C₈	—	89	2	no	—
300	C₄⋊C₈	—	178	1	no	—
301	C₄⋊C₈	—	178	2	no	—
302	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
303	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
304	#103	—	2	2	no	—
305	#103	—	178	2	no	—
306	#102	—	178	2	no	—
307	#102	—	178	2	no	—
308	C₂²⋊C₈	—	178	1	no	—
309	C₂²⋊C₈	—	178	1	no	—
310	C₂²⋊C₈	—	178	1	no	—
311	C₄×C₈	—	2	1	no	—
312	C₄×C₈	—	89	1	no	—
313	C₄×C₈	—	89	1	no	—
314	C₄×C₈	—	89	1	no	—
315	C₄×C₈	—	178	1	no	—
316	C₄×C₈	—	178	1	no	—
317	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
318	#41	—	89	4	no	—
319	#41	—	178	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	356	2	no	—
322	C₂×Q₈	—	178	2	no	—
323	C₂×Q₈	—	712	4	no	—
324	C₂×Q₈	D₄×D₈₉	1	1	yes	characteristic
325	C₂×D₄	—	89	1	no	—
326	C₂×D₄	—	178	1	no	—
327	C₂²×C₄	—	89	1	no	—
328	C₂²×C₄	—	89	1	no	—
329	C₂²×C₄	—	89	1	no	—
330	C₂²×C₄	—	356	2	no	—
331	C₂²×C₄	—	178	1	no	—
332	C₂²×C₄	—	178	1	no	—
333	C₂²×C₄	—	178	1	no	—
334	M₁₆	—	356	4	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	89	1	no	—
338	C₂×C₈	—	89	1	no	—
339	C₂×C₈	—	356	2	no	—
340	C₂×C₈	—	356	2	no	—
341	C₂×C₈	—	178	2	no	—
342	C₂×C₈	—	178	1	no	—
343	C₂×C₈	—	178	2	no	—
344	C₂×C₈	—	178	2	no	—
345	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
346	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	89	1	no	—
351	C₄⋊C₄	—	356	2	no	—
352	C₄⋊C₄	—	356	2	no	—
353	C₄⋊C₄	—	178	1	no	—
354	C₄⋊C₄	—	178	2	no	—
355	C₄⋊C₄	—	178	2	no	—
356	C₄⋊C₄	D₄×D₈₉	1	1	yes	characteristic
357	C₂²⋊C₄	—	178	1	no	—
358	C₂²⋊C₄	—	178	1	no	—
359	C₂²⋊C₄	—	178	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	89	1	no	—
362	C₄²	—	89	1	no	—
363	C₄²	—	89	1	no	—
364	C₄²	—	178	1	no	—
365	C₄²	—	178	1	no	—
366	C₄²	C₂³×D₈₉	1	1	yes	characteristic
367	C₂³	—	89	1	no	—
368	C₂³	—	178	1	no	—
369	Q₈	—	2	1	no	—
370	Q₈	—	8	2	no	—
371	Q₈	—	712	2	no	—
372	Q₈	—	712	4	no	—
373	Q₈	Q₁₆×D₈₉	1	2	yes	—
374	D₄	—	89	2	no	—
375	D₄	—	178	4	no	—
376	D₄	—	178	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	89	1	no	—
381	C₂×C₄	—	89	1	no	—
382	C₂×C₄	—	89	2	no	—
383	C₂×C₄	—	89	2	no	—
384	C₂×C₄	—	89	1	no	—
385	C₂×C₄	—	356	2	no	—
386	C₂×C₄	—	356	1	no	—
387	C₂×C₄	—	356	1	no	—
388	C₂×C₄	—	356	2	no	—
389	C₂×C₄	—	178	2	no	—
390	C₂×C₄	—	178	4	no	—
391	C₂×C₄	—	178	1	no	—
392	C₂×C₄	—	178	1	no	—
393	C₂×C₄	—	178	1	no	—
394	C₂×C₄	—	712	4	no	—
395	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
396	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
397	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
398	C₈	—	2	1	no	—
399	C₈	—	4	1	no	—
400	C₈	—	4	2	no	—
401	C₈	—	89	2	no	—
402	C₈	—	356	1	no	—
403	C₈	—	356	2	no	—
404	C₈	—	178	1	no	—
405	C₈	#15668044	1	2	yes	—
406	C₂²	—	89	2	no	—
407	C₂²	—	356	1	no	—
408	C₂²	—	356	1	no	—
409	C₂²	—	178	2	no	—
410	C₂²	—	178	1	no	—
411	C₂²	—	178	1	no	—
412	C₂²	#121×D₈₉	1	1	yes	characteristic
413	C₄	—	2	1	no	—
414	C₄	—	2	2	no	—
415	C₄	—	4	1	no	—
416	C₄	—	8	2	no	—
417	C₄	—	89	2	no	—
418	C₄	—	89	2	no	—
419	C₄	—	356	1	no	—
420	C₄	—	178	1	no	—
421	C₄	—	712	2	no	—
422	C₄	C₂×Q₁₆×D₈₉	1	1	yes	characteristic
423	C₄	#135×D₈₉	1	1	yes	characteristic
424	C₄	#137×D₈₉	1	1	yes	characteristic
425	C₄	C₂×#15668044	1	1	yes	characteristic
426	C₂	—	356	2	no	—
427	C₂	—	178	2	no	—
428	C₂	#26029736	1	1	yes	characteristic
429	C₂	#467×D₈₉	1	1	yes	characteristic
430	C₂	#472×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₈₉
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1676	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	C₂×#13083575	D₄
hypercenter	#1676	D₈₉
hypocenter	C₈₉	#19272
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1676

Complements

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

N	H ≅ G/N	type
1. #500×D₈₉	C₂	semidirect
4. #26019656	C₂	semidirect
5. #26019654	C₂	semidirect
6. #26019652	C₂	semidirect
7. #26019650	C₂	semidirect
8. #26019648	C₂	semidirect
9. #26019009	C₂	semidirect
10. #26018931	C₂	semidirect
11. C₈₉×#1676	C₂	semidirect
221. #1676	D₈₉	semidirect
227. C₈₉	#19272	semidirect

Maximal subgroups

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

subgroup	index
#500×D₈₉	2
#26030066	2
C₈×#13083575	2
#26019656	2
#26019654	2
#26019652	2
#26019650	2
#26019648	2
#26019009	2
#26018931	2
C₈₉×#1676	2
#19272	89