Subgroups — #36524367

Order 22784.

766 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030253	C₂	1	1	yes	maximal, characteristic
2	#26028965	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₈×D₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019118	C₂	1	4	yes	maximal, complemented
5	#26019077	C₂	1	4	yes	maximal, complemented
6	#26019023	C₂	1	1	yes	maximal, characteristic, complemented
7	#26018678	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018652	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15668018	—	2	1	no	—
11	C₂²×C₈×D₈₉	—	2	1	no	—
12	#19152148	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
14	#19151912	C₄	1	2	yes	—
15	#19151879	C₄	1	2	yes	—
16	#19151794	C₄	1	2	yes	—
17	#19151734	C₄	1	2	yes	—
18	C₄×D₇₁₂	C₂²	1	4	yes	—
19	#19151677	—	2	1	no	—
20	#19151677	C₂²	1	2	yes	complemented
21	C₈×D₃₅₆	—	2	1	no	—
22	C₈×D₃₅₆	—	2	1	no	—
23	C₈×D₃₅₆	—	2	1	no	—
24	C₈×D₃₅₆	C₂²	1	2	yes	—
25	C₈×D₃₅₆	C₂²	1	2	yes	—
26	C₈×D₃₅₆	C₂²	1	2	yes	complemented
27	#19151622	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
29	#19151564	—	2	1	no	—
30	C₂×#15667924	—	2	1	no	—
31	#19151349	C₂²	1	4	yes	complemented
32	#19151327	C₂²	1	4	yes	—
33	#19151327	C₂²	1	4	yes	complemented
34	#431×C₈₉	C₂²	1	1	yes	characteristic
35	#431×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
37	#322×C₈₉	C₂²	1	2	yes	complemented
38	#322×C₈₉	C₂²	1	2	yes	complemented
39	C₂×#13083574	—	2	1	no	—
40	C₂²×D₃₅₆	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄×D₈₉	—	2	1	no	—
42	C₂×D₇₁₂	C₂×C₄	1	4	yes	—
43	#15668018	—	4	4	no	—
44	C₂×#13083558	—	2	1	no	—
45	C₂×#13083557	—	2	2	no	—
46	C₂²×#10623494	—	2	1	no	—
47	C₂×C₈×D₈₉	—	2	2	no	—
48	C₂×C₈×D₈₉	—	2	2	no	—
49	C₂×C₈×D₈₉	—	2	2	no	—
50	C₂×C₈×D₈₉	—	4	4	no	—
51	#15668012	C₂×C₄	1	1	yes	characteristic
52	#15668009	C₂×C₄	1	1	yes	characteristic
53	#15668000	—	2	1	no	—
54	#15667986	—	2	1	no	—
55	#15667986	C₂×C₄	1	2	yes	—
56	C₄×D₃₅₆	—	2	1	no	—
57	C₄×D₃₅₆	—	2	1	no	—
58	C₄×D₃₅₆	—	2	1	no	—
59	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
60	C₄×D₃₅₆	C₂³	1	2	yes	—
61	C₄×D₃₅₆	C₂³	1	2	yes	—
62	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
63	C₂×#13083551	—	2	1	no	—
64	#15667946	C₂×C₄	1	4	yes	—
65	C₄⋊#10623494	—	2	1	no	—
66	C₄⋊#10623494	—	2	1	no	—
67	C₄⋊#10623494	C₂³	1	2	yes	—
68	C₄⋊#10623494	C₂³	1	2	yes	—
69	#15667934	C₂×C₄	1	4	yes	—
70	#15667934	C₂×C₄	1	4	yes	—
71	#15667924	—	2	2	no	—
72	#15667924	—	2	2	no	—
73	#15667924	—	2	2	no	—
74	#15667924	—	2	2	no	—
75	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
76	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
77	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₈₉	—	2	1	no	—
79	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
80	C₂²⋊C₈×C₈₉	—	2	1	no	—
81	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
82	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
83	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
84	C₄×C₈×C₈₉	C₂³	1	2	yes	—
85	C₄×C₈×C₈₉	C₂³	1	2	yes	—
86	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
88	C₂³×D₈₉	—	2	1	no	—
89	#13083574	—	4	2	no	—
90	#13083574	—	4	2	no	—
91	C₂×Dic₁₇₈	—	2	1	no	—
92	C₂×D₃₅₆	—	2	1	no	—
93	C₂×D₃₅₆	—	2	4	no	—
94	C₂×D₃₅₆	—	2	1	no	—
95	C₂×D₃₅₆	—	2	1	no	—
96	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
97	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
98	C₂×C₂²⋊D₈₉	—	2	2	no	—
99	C₂²×Dic₈₉	—	2	1	no	—
100	C₂×C₄×D₈₉	—	2	2	no	—
101	C₂×C₄×D₈₉	—	2	2	no	—
102	C₂×C₄×D₈₉	—	2	2	no	—
103	C₂×C₄×D₈₉	—	4	2	no	—
104	C₂×C₄×D₈₉	—	4	2	no	—
105	D₇₁₂	—	2	8	no	—
106	#13083558	—	4	2	no	—
107	#13083557	—	4	4	no	—
108	C₂×#10623494	—	2	2	no	—
109	C₂×#10623494	—	2	2	no	—
110	C₂×#10623494	—	4	2	no	—
111	C₈×D₈₉	—	4	4	no	—
112	C₈×D₈₉	—	4	4	no	—
113	C₈×D₈₉	—	4	4	no	—
114	C₄⋊Dic₈₉	—	2	1	no	—
115	C₄⋊Dic₈₉	—	2	1	no	—
116	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
117	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
118	#13083551	—	2	2	no	—
119	#13083551	—	2	2	no	—
120	#13083551	—	2	2	no	—
121	#13083551	—	2	2	no	—
122	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
125	C₂×C₈×C₈₉	—	2	2	no	—
126	C₂×C₈×C₈₉	—	2	2	no	—
127	C₂×C₈×C₈₉	—	2	2	no	—
128	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
129	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
132	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₈₉	#41	1	1	yes	characteristic
136	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
137	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
138	C₂²×D₈₉	—	2	4	no	—
139	C₂²×D₈₉	—	2	2	no	—
140	C₂²×D₈₉	—	2	2	no	—
141	C₂²×D₈₉	—	4	2	no	—
142	C₂²×D₈₉	—	4	2	no	—
143	C₂×C₄×C₈₉	—	2	2	no	—
144	C₂×C₄×C₈₉	—	4	1	no	—
145	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
147	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
148	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
149	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
150	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
153	C₂²⋊D₈₉	—	4	4	no	—
154	C₂×Dic₈₉	—	2	2	no	—
155	C₂×Dic₈₉	—	2	2	no	—
156	C₂×Dic₈₉	—	4	2	no	—
157	D₃₅₆	—	2	4	no	—
158	D₃₅₆	—	2	2	no	—
159	D₃₅₆	—	2	4	no	—
160	D₃₅₆	—	4	2	no	—
161	D₃₅₆	—	4	2	no	—
162	D₃₅₆	#131	1	4	yes	complemented
163	C₄×D₈₉	—	4	2	no	—
164	C₄×D₈₉	—	4	2	no	—
165	C₄×D₈₉	—	4	2	no	—
166	C₄×D₈₉	—	4	2	no	—
167	C₄×D₈₉	—	4	4	no	—
168	Dic₁₇₈	—	4	2	no	—
169	C₈×C₈₉	—	2	4	no	—
170	C₈×C₈₉	—	2	1	no	—
171	C₈×C₈₉	—	2	1	no	—
172	C₈×C₈₉	—	2	1	no	—
173	C₈×C₈₉	—	2	1	no	—
174	C₈×C₈₉	—	4	2	no	—
175	#10623494	—	4	2	no	—
176	#10623494	—	4	2	no	—
177	C₂²×C₈₉	—	2	1	no	—
178	C₂²×C₈₉	—	2	1	no	—
179	C₂²×C₈₉	#442	1	2	yes	—
180	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
181	C₂×D₈₉	—	2	4	no	—
182	C₂×D₈₉	—	4	8	no	—
183	C₂×D₈₉	—	4	2	no	—
184	C₂×D₈₉	—	4	2	no	—
185	C₂×D₈₉	—	4	2	no	—
186	C₂×D₈₉	—	4	2	no	—
187	C₂×D₈₉	—	4	2	no	—
188	C₄×C₈₉	—	2	1	no	—
189	C₄×C₈₉	—	2	1	no	—
190	C₄×C₈₉	—	2	1	no	—
191	C₄×C₈₉	#442	1	2	yes	—
192	C₄×C₈₉	C₂×#131	1	2	yes	—
193	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
195	Dic₈₉	—	4	2	no	—
196	Dic₈₉	—	4	2	no	—
197	#17907	—	89	1	no	maximal, Sylow
198	C₂×C₈₉	—	2	2	no	—
199	C₂×C₈₉	#2929	1	1	yes	characteristic
200	C₂×C₈₉	C₂×#442	1	1	yes	characteristic
201	C₂×C₈₉	#2955	1	1	yes	characteristic
202	D₈₉	—	4	4	no	—
203	D₈₉	—	8	2	no	—
204	#3100	—	89	1	no	—
205	#2931	—	89	1	no	—
206	C₂×C₈×D₄	—	89	1	no	—
207	#1586	—	89	4	no	—
208	#1580	—	89	4	no	—
209	#1570	—	89	1	no	—
210	#1486	—	89	1	no	—
211	#1480	—	89	1	no	—
212	#1452	D₈₉	1	1	yes	characteristic, complemented
213	C₈₉	#17907	1	1	yes	characteristic, complemented, Sylow
214	C₂×#131	—	178	1	no	—
215	C₂³×C₈	—	178	1	no	—
216	#532	—	89	1	no	—
217	C₂×C₄×D₄	—	89	1	no	—
218	#480	—	89	2	no	—
219	#474	—	89	2	no	—
220	#459	—	89	2	no	—
221	#447	—	89	2	no	—
222	C₄×D₈	—	89	4	no	—
223	#436	—	89	2	no	—
224	#436	—	178	1	no	—
225	C₈×D₄	—	89	2	no	—
226	C₈×D₄	—	89	2	no	—
227	C₈×D₄	—	89	2	no	—
228	C₈×D₄	—	178	1	no	—
229	C₈×D₄	—	178	1	no	—
230	C₈×D₄	—	178	1	no	—
231	#431	C₂×D₈₉	1	1	yes	characteristic
232	#431	C₂×D₈₉	1	1	yes	characteristic
233	#423	—	89	1	no	—
234	C₂×C₄⋊C₈	—	89	1	no	—
235	#408	—	178	1	no	—
236	C₂×C₂²⋊C₈	—	178	1	no	—
237	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
238	#334	—	89	4	no	—
239	D₄⋊C₈	—	89	4	no	—
240	D₄⋊C₈	—	89	4	no	—
241	#322	C₂×D₈₉	1	2	yes	complemented
242	#322	C₂×D₈₉	1	2	yes	complemented
243	C₂×#41	—	178	1	no	—
244	C₂²×D₄	—	89	1	no	—
245	C₂³×C₄	—	178	1	no	—
246	C₂×D₈	—	89	4	no	—
247	#131	—	356	4	no	—
248	C₂×M₁₆	—	178	1	no	—
249	C₂×M₁₆	—	178	2	no	—
250	C₂²×C₈	—	356	4	no	—
251	C₂²×C₈	—	178	1	no	—
252	C₂²×C₈	—	178	2	no	—
253	C₂²×C₈	—	178	2	no	—
254	C₂²×C₈	—	178	2	no	—
255	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
256	C₂²×C₈	D₃₅₆	1	1	yes	characteristic
257	C₄⋊Q₈	—	89	1	no	—
258	#127	—	89	1	no	—
259	#124	—	178	1	no	—
260	#121	—	89	2	no	—
261	#121	—	178	1	no	—
262	C₄×D₄	—	89	2	no	—
263	C₄×D₄	—	89	2	no	—
264	C₄×D₄	—	89	2	no	—
265	C₄×D₄	—	178	1	no	—
266	C₄×D₄	—	178	1	no	—
267	C₄×D₄	—	178	1	no	—
268	C₂×C₄⋊C₄	—	89	1	no	—
269	C₂×C₂²⋊C₄	—	178	1	no	—
270	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
271	#107	—	89	4	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	89	2	no	—
274	C₄⋊C₈	—	89	2	no	—
275	C₄⋊C₈	—	178	1	no	—
276	C₄⋊C₈	—	178	1	no	—
277	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
278	#102	—	89	4	no	—
279	#102	—	89	4	no	—
280	C₂²⋊C₈	—	2	1	no	—
281	C₂²⋊C₈	—	178	2	no	—
282	C₂²⋊C₈	—	178	2	no	—
283	C₂²⋊C₈	—	178	2	no	—
284	C₂²⋊C₈	—	178	2	no	—
285	C₂²⋊C₈	C₄×D₈₉	1	2	yes	—
286	C₄×C₈	D₃₅₆	1	1	yes	characteristic
287	C₄×C₈	D₃₅₆	1	1	yes	characteristic
288	C₄×C₈	C₂²×D₈₉	1	2	yes	—
289	C₄×C₈	C₂²×D₈₉	1	2	yes	—
290	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
291	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
292	C₂⁴	—	178	1	no	—
293	#41	—	356	2	no	—
294	#41	—	356	2	no	—
295	C₂×Q₈	—	178	1	no	—
296	C₂×D₄	—	89	2	no	—
297	C₂×D₄	—	89	2	no	—
298	C₂×D₄	—	178	4	no	—
299	C₂×D₄	—	178	2	no	—
300	C₂×D₄	—	178	1	no	—
301	C₂×D₄	—	178	1	no	—
302	C₂×D₄	—	178	1	no	—
303	C₂²×C₄	—	356	2	no	—
304	C₂²×C₄	—	356	2	no	—
305	C₂²×C₄	—	178	1	no	—
306	C₂²×C₄	—	178	2	no	—
307	C₂²×C₄	—	178	2	no	—
308	C₂²×C₄	—	178	2	no	—
309	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
311	C₂²×C₄	#13083574	1	1	yes	characteristic
312	D₈	—	178	8	no	—
313	M₁₆	—	356	4	no	—
314	M₁₆	—	356	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	356	4	no	—
319	C₂×C₈	—	356	4	no	—
320	C₂×C₈	—	356	4	no	—
321	C₂×C₈	—	356	2	no	—
322	C₂×C₈	—	178	2	no	—
323	C₂×C₈	—	178	2	no	—
324	C₂×C₈	C₂×C₄×D₈₉	1	4	yes	—
325	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
326	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
327	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
328	C₂×C₈	C₂×D₃₅₆	1	1	yes	characteristic
329	C₄⋊C₄	—	89	2	no	—
330	C₄⋊C₄	—	89	2	no	—
331	C₄⋊C₄	—	178	1	no	—
332	C₄⋊C₄	—	178	1	no	—
333	C₂²⋊C₄	—	178	2	no	—
334	C₂²⋊C₄	—	178	2	no	—
335	C₂²⋊C₄	—	178	2	no	—
336	C₂²⋊C₄	—	178	2	no	—
337	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
338	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
339	C₄²	#13083574	1	1	yes	characteristic
340	C₄²	C₂³×D₈₉	1	1	yes	characteristic
341	C₂³	—	356	2	no	—
342	C₂³	—	356	2	no	—
343	C₂³	—	178	4	no	—
344	C₂³	—	178	2	no	—
345	C₂³	—	178	2	no	—
346	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
347	Q₈	—	356	2	no	—
348	D₄	—	89	4	no	—
349	D₄	—	356	2	no	—
350	D₄	—	356	4	no	—
351	D₄	—	356	2	no	—
352	D₄	—	178	4	no	—
353	D₄	—	178	4	no	—
354	D₄	—	178	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	356	2	no	—
358	C₂×C₄	—	356	2	no	—
359	C₂×C₄	—	356	2	no	—
360	C₂×C₄	—	356	2	no	—
361	C₂×C₄	—	356	2	no	—
362	C₂×C₄	—	356	4	no	—
363	C₂×C₄	—	178	2	no	—
364	C₂×C₄	—	178	2	no	—
365	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
366	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
367	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
368	C₂×C₄	#15668040	1	2	yes	—
369	C₂×C₄	#15668040	1	2	yes	—
370	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
372	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
373	C₈	—	2	1	no	—
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	2	4	no	—
378	C₈	—	4	2	no	—
379	C₈	—	356	2	no	—
380	C₈	—	356	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	356	8	no	—
384	C₂²	—	356	2	no	—
385	C₂²	—	356	2	no	—
386	C₂²	—	356	2	no	—
387	C₂²	—	356	2	no	—
388	C₂²	—	356	2	no	—
389	C₂²	—	178	4	no	—
390	C₂²	#19151711	1	2	yes	—
391	C₂²	C₂×C₄×D₃₅₆	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	356	2	no	—
396	C₄	—	356	2	no	—
397	C₄	#19151711	1	2	yes	—
398	C₄	#131×D₈₉	1	2	yes	—
399	C₄	C₂×#15668040	1	1	yes	characteristic
400	C₄	C₂×#15668040	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	356	4	no	—
403	C₂	—	712	2	no	—
404	C₂	#26028948	1	1	yes	characteristic
405	C₂	C₂×#19151711	1	1	yes	characteristic
406	C₂	#26029156	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₃₅₆
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1452	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#26030253	C₂
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1452	D₈₉
hypocenter	C₈₉	#17907
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #1452

Complements

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

N	H ≅ G/N	type
2. #26028965	C₂	semidirect
3. C₂×C₈×D₃₅₆	C₂	semidirect
4. #26019118	C₂	semidirect
5. #26019077	C₂	semidirect
6. #26019023	C₂	semidirect
7. #26018678	C₂	semidirect
8. #26018652	C₂	semidirect
9. C₈₉×#1452	C₂	semidirect
20. #19151677	C₂²	semidirect
26. C₈×D₃₅₆	C₂²	semidirect
31. #19151349	C₂²	semidirect
33. #19151327	C₂²	semidirect
37. #322×C₈₉	C₂²	semidirect
38. #322×C₈₉	C₂²	semidirect
162. D₃₅₆	#131	semidirect
212. #1452	D₈₉	semidirect
213. C₈₉	#17907	semidirect
241. #322	C₂×D₈₉	semidirect
242. #322	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26030253	2
#26028965	2
C₂×C₈×D₃₅₆	2
#26019118	2
#26019077	2
#26019023	2
#26018678	2
#26018652	2
C₈₉×#1452	2
#17907	89