Subgroups — #36538359

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	#26030064	C₂	1	2	yes	maximal
3	C₈×#13083573	C₂	1	1	yes	maximal, characteristic
4	#26019657	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019655	C₂	1	2	yes	maximal, complemented
6	#26019653	C₂	1	1	yes	maximal, characteristic, complemented
7	#26019651	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019649	C₂	1	2	yes	maximal, complemented
9	#26019009	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018931	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1675	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄⋊Q₈×D₈₉	C₂²	1	2	yes	—
13	C₄×#13083573	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	#19151894	C₂²	1	2	yes	—
19	#19151890	C₂²	1	2	yes	—
20	#19151888	C₂²	1	2	yes	—
21	#19151882	—	2	2	no	—
22	#19151876	—	2	2	no	—
23	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
24	#19151722	C₂²	1	1	yes	characteristic
25	D₄×#10623494	C₂²	1	1	yes	characteristic
26	C₈×C₂²⋊D₈₉	—	2	1	no	—
27	#19151661	—	2	1	no	—
28	#19151650	C₂²	1	1	yes	characteristic
29	#19151648	—	2	1	no	—
30	#19151637	—	2	2	no	—
31	#107×D₈₉	—	2	1	no	—
32	#107×D₈₉	—	2	1	no	—
33	#19151620	C₂²	1	2	yes	—
34	#19151596	—	2	2	no	—
35	C₂×C₈×Dic₈₉	—	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	#476×C₈₉	C₂²	1	2	yes	—
44	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
45	#335×C₈₉	C₂²	1	1	yes	characteristic
46	#333×C₈₉	C₂²	1	2	yes	—
47	C₂×#13083573	D₄	1	1	yes	characteristic
48	C₂×Q₈×D₈₉	—	2	2	no	—
49	C₂×#13083557	—	2	2	no	—
50	C₂²×#10623494	—	2	1	no	—
51	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
52	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
53	#15668012	C₂³	1	2	yes	—
54	#15668011	—	2	2	no	—
55	#15668011	—	2	2	no	—
56	#15668010	—	2	2	no	—
57	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
58	#15667977	D₄	1	1	yes	characteristic
59	D₄×Dic₈₉	D₄	1	1	yes	characteristic
60	C₄×C₂²⋊D₈₉	—	2	1	no	—
61	#15667972	—	2	1	no	—
62	#15667970	D₄	1	1	yes	characteristic
63	#15667968	—	2	1	no	—
64	C₄⋊C₄×D₈₉	—	2	2	no	—
65	C₄⋊C₄×D₈₉	—	2	2	no	—
66	C₂×C₄×Dic₈₉	—	2	1	no	—
67	C₄²×D₈₉	C₂³	1	1	yes	characteristic
68	#15667946	—	2	2	no	—
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	#15667943	—	2	2	no	—
75	C₄⋊#10623494	C₂³	1	2	yes	—
76	C₄⋊#10623494	C₂³	1	1	yes	characteristic
77	#15667941	—	2	1	no	—
78	#15667941	—	2	2	no	—
79	#15667941	—	2	1	no	—
80	#15667937	—	2	2	no	—
81	#15667935	—	2	2	no	—
82	#15667933	—	2	2	no	—
83	C₂²⋊#10623494	—	2	1	no	—
84	#15667924	—	2	1	no	—
85	C₄×#10623494	C₂³	1	1	yes	characteristic
86	C₈×Dic₈₉	—	2	1	no	—
87	C₈×Dic₈₉	—	2	1	no	—
88	C₈×Dic₈₉	—	2	1	no	—
89	C₈×Dic₈₉	D₄	1	1	yes	characteristic
90	C₈×Dic₈₉	D₄	1	1	yes	characteristic
91	C₂²×C₈×C₈₉	—	2	1	no	—
92	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
93	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
94	#107×C₈₉	—	2	1	no	—
95	#107×C₈₉	—	2	1	no	—
96	#106×C₈₉	—	2	2	no	—
97	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
98	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
99	#102×C₈₉	—	2	2	no	—
100	C₂²⋊C₈×C₈₉	—	2	1	no	—
101	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	#13083573	—	2	2	no	—
103	#13083573	Q₁₆	1	4	yes	—
104	C₂×Dic₁₇₈	—	2	2	no	—
105	C₂×Dic₁₇₈	—	4	2	no	—
106	C₂×Dic₁₇₈	C₂×D₄	1	1	yes	characteristic
107	Q₈×D₈₉	—	8	4	no	—
108	C₂×C₂²⋊D₈₉	—	2	1	no	—
109	C₂²×Dic₈₉	—	2	1	no	—
110	C₂²×Dic₈₉	—	2	1	no	—
111	C₂×C₄×D₈₉	—	4	2	no	—
112	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
113	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
114	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
115	#13083557	—	4	4	no	—
116	C₂×#10623494	—	2	1	no	—
117	C₂×#10623494	—	2	2	no	—
118	C₂×#10623494	—	4	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	C₄⋊Dic₈₉	—	2	2	no	—
124	C₄⋊Dic₈₉	—	2	2	no	—
125	C₄⋊Dic₈₉	C₂×D₄	1	1	yes	characteristic
126	#13083553	—	2	1	no	—
127	#13083553	—	2	1	no	—
128	#13083553	—	4	2	no	—
129	#13083553	—	4	2	no	—
130	C₂²⋊Dic₈₉	—	2	1	no	—
131	#13083551	—	2	1	no	—
132	C₄×Dic₈₉	—	2	1	no	—
133	C₄×Dic₈₉	—	2	1	no	—
134	C₄×Dic₈₉	—	2	1	no	—
135	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
136	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
137	C₄×Dic₈₉	#41	1	1	yes	characteristic
138	C₂×Q₈×C₈₉	—	2	2	no	—
139	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₈₉	—	2	1	no	—
141	C₂×C₈×C₈₉	—	2	2	no	—
142	C₂×C₈×C₈₉	—	2	1	no	—
143	C₂×C₈×C₈₉	—	4	2	no	—
144	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
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	C₂²⋊C₄×C₈₉	—	2	1	no	—
150	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
151	C₂³×C₈₉	—	2	1	no	—
152	C₂²×D₈₉	#121	1	1	yes	characteristic
153	Q₈×C₈₉	—	8	2	no	—
154	D₄×C₈₉	—	2	1	no	—
155	D₄×C₈₉	C₂×Q₁₆	1	2	yes	—
156	C₂×C₄×C₈₉	—	2	1	no	—
157	C₂×C₄×C₈₉	—	4	1	no	—
158	C₂×C₄×C₈₉	—	4	1	no	—
159	C₂×C₄×C₈₉	—	4	2	no	—
160	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
163	C₂²⋊D₈₉	—	2	4	no	—
164	C₂×Dic₈₉	—	2	1	no	—
165	C₂×Dic₈₉	—	2	4	no	—
166	C₂×Dic₈₉	—	2	1	no	—
167	C₂×Dic₈₉	—	4	2	no	—
168	C₂×Dic₈₉	—	4	2	no	—
169	C₂×Dic₈₉	#121	1	1	yes	characteristic
170	C₂×Dic₈₉	#121	1	1	yes	characteristic
171	C₂×Dic₈₉	#121	1	1	yes	characteristic
172	C₄×D₈₉	—	2	1	no	—
173	C₄×D₈₉	—	2	1	no	—
174	C₄×D₈₉	—	2	2	no	—
175	C₄×D₈₉	—	8	4	no	—
176	C₄×D₈₉	C₂×Q₁₆	1	2	yes	—
177	C₄×D₈₉	#135	1	2	yes	—
178	Dic₁₇₈	—	2	1	no	—
179	Dic₁₇₈	—	8	4	no	—
180	Dic₁₇₈	—	8	2	no	—
181	Dic₁₇₈	C₂×Q₁₆	1	2	yes	—
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	—	2	2	no	—
191	C₂²×C₈₉	—	4	1	no	—
192	C₂²×C₈₉	—	4	1	no	—
193	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
194	C₂×D₈₉	—	2	1	no	—
195	C₂×D₈₉	—	2	1	no	—
196	C₂×D₈₉	#467	1	2	yes	—
197	C₄×C₈₉	—	2	1	no	—
198	C₄×C₈₉	—	4	1	no	—
199	C₄×C₈₉	—	8	2	no	—
200	C₄×C₈₉	C₂²×Q₁₆	1	1	yes	characteristic
201	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
202	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
203	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
204	Dic₈₉	—	2	1	no	—
205	Dic₈₉	—	2	2	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	—	4	2	no	—
212	C₂×C₈₉	#3039	1	1	yes	characteristic
213	C₂×C₈₉	C₂×#467	1	1	yes	characteristic
214	C₂×C₈₉	C₂×#472	1	1	yes	characteristic
215	D₈₉	—	2	2	no	—
216	C₂×#500	—	89	1	no	—
217	#3079	—	89	2	no	—
218	C₈×#41	—	89	1	no	—
219	#1676	—	89	1	no	—
220	#1676	—	89	1	no	—
221	#1676	—	89	2	no	—
222	#1675	—	89	2	no	—
223	#1675	—	89	1	no	—
224	#1675	D₈₉	1	1	yes	characteristic, complemented
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	—	89	2	no	—
237	#476	—	89	2	no	—
238	#476	C₂×D₈₉	1	2	yes	—
239	#475	—	178	2	no	—
240	#474	—	178	2	no	—
241	C₈×Q₈	—	89	1	no	—
242	C₈×Q₈	—	89	1	no	—
243	C₈×D₄	—	89	1	no	—
244	C₈×D₄	—	178	1	no	—
245	C₈×D₄	—	178	1	no	—
246	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
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	—	2	1	no	—
267	C₂²×C₈	—	89	1	no	—
268	C₂²×C₈	—	89	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	—	89	1	no	—
277	C₄×D₄	—	89	1	no	—
278	C₄×D₄	—	178	1	no	—
279	C₄×D₄	—	178	1	no	—
280	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
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	—	178	2	no	—
290	#107	—	178	2	no	—
291	#107	—	178	2	no	—
292	#107	—	178	2	no	—
293	#107	—	178	1	no	—
294	#107	—	178	1	no	—
295	#106	—	2	2	no	—
296	#106	—	178	2	no	—
297	C₄⋊C₈	—	89	1	no	—
298	C₄⋊C₈	—	89	2	no	—
299	C₄⋊C₈	—	178	2	no	—
300	C₄⋊C₈	—	178	1	no	—
301	C₄⋊C₈	—	178	1	no	—
302	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
303	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
304	#103	—	178	2	no	—
305	#103	—	178	2	no	—
306	#102	—	2	2	no	—
307	#102	—	178	2	no	—
308	C₂²⋊C₈	—	2	1	no	—
309	C₂²⋊C₈	—	178	1	no	—
310	C₂²⋊C₈	—	178	1	no	—
311	C₄×C₈	—	89	1	no	—
312	C₄×C₈	—	89	1	no	—
313	C₄×C₈	—	89	1	no	—
314	C₄×C₈	—	178	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	—	89	1	no	—
322	C₂×Q₈	—	356	2	no	—
323	C₂×Q₈	—	178	2	no	—
324	C₂×Q₈	—	712	4	no	—
325	C₂×D₄	—	178	1	no	—
326	C₂×D₄	D₄×D₈₉	1	1	yes	characteristic
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	89	1	no	—
329	C₂²×C₄	—	89	1	no	—
330	C₂²×C₄	—	89	1	no	—
331	C₂²×C₄	—	356	2	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	—	4	2	no	—
338	C₂×C₈	—	89	1	no	—
339	C₂×C₈	—	89	1	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	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	89	1	no	—
350	C₄⋊C₄	—	356	2	no	—
351	C₄⋊C₄	—	356	2	no	—
352	C₄⋊C₄	—	178	1	no	—
353	C₄⋊C₄	—	178	2	no	—
354	C₄⋊C₄	—	178	2	no	—
355	C₄⋊C₄	—	178	1	no	—
356	C₄⋊C₄	D₄×D₈₉	1	1	yes	characteristic
357	C₂²⋊C₄	—	2	1	no	—
358	C₂²⋊C₄	—	178	1	no	—
359	C₂²⋊C₄	—	178	1	no	—
360	C₄²	—	89	1	no	—
361	C₄²	—	89	1	no	—
362	C₄²	—	89	1	no	—
363	C₄²	—	178	1	no	—
364	C₄²	—	178	1	no	—
365	C₄²	—	178	1	no	—
366	C₄²	C₂³×D₈₉	1	1	yes	characteristic
367	C₂³	—	2	1	no	—
368	C₂³	—	89	1	no	—
369	Q₈	—	8	2	no	—
370	Q₈	—	89	2	no	—
371	Q₈	—	178	1	no	—
372	Q₈	—	712	2	no	—
373	Q₈	—	712	4	no	—
374	D₄	—	2	1	no	—
375	D₄	—	178	4	no	—
376	D₄	Q₁₆×D₈₉	1	2	yes	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	89	1	no	—
382	C₂×C₄	—	89	1	no	—
383	C₂×C₄	—	89	2	no	—
384	C₂×C₄	—	89	2	no	—
385	C₂×C₄	—	89	1	no	—
386	C₂×C₄	—	356	2	no	—
387	C₂×C₄	—	356	2	no	—
388	C₂×C₄	—	178	2	no	—
389	C₂×C₄	—	178	4	no	—
390	C₂×C₄	—	178	1	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	#15668041	1	2	yes	—
406	C₂²	—	2	2	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	—	89	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	—	4	1	no	—
415	C₄	—	8	2	no	—
416	C₄	—	89	2	no	—
417	C₄	—	89	2	no	—
418	C₄	—	356	1	no	—
419	C₄	—	178	1	no	—
420	C₄	—	178	2	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×#15668041	1	1	yes	characteristic
426	C₂	—	4	2	no	—
427	C₂	—	178	2	no	—
428	C₂	#26029734	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×#1675	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	C₂×#13083573	D₄
hypercenter	#1675	D₈₉
hypocenter	C₈₉	#19272
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1675

Complements

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

N	H ≅ G/N	type
1. #500×D₈₉	C₂	semidirect
4. #26019657	C₂	semidirect
5. #26019655	C₂	semidirect
6. #26019653	C₂	semidirect
7. #26019651	C₂	semidirect
8. #26019649	C₂	semidirect
9. #26019009	C₂	semidirect
10. #26018931	C₂	semidirect
11. C₈₉×#1675	C₂	semidirect
224. #1675	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
#26030064	2
C₈×#13083573	2
#26019657	2
#26019655	2
#26019653	2
#26019651	2
#26019649	2
#26019009	2
#26018931	2
C₈₉×#1675	2
#19272	89