Subgroups — #36524992

Order 22784.

734 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030827	C₂	1	1	yes	maximal, characteristic
2	#26028965	C₂	1	1	yes	maximal, characteristic, complemented
3	#26019164	C₂	1	4	yes	maximal, complemented
4	#26019074	C₂	1	4	yes	maximal, complemented
5	#26019007	C₂	1	1	yes	maximal, characteristic, complemented
6	#26018703	C₂	1	1	yes	maximal, characteristic, complemented
7	#26018702	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#19151320	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15668018	—	2	1	no	—
11	#19152148	C₂²	1	1	yes	characteristic
12	#19152001	C₄	1	1	yes	characteristic
13	#19151974	C₄	1	1	yes	characteristic
14	#19151946	C₄	1	1	yes	characteristic
15	#19151944	C₄	1	1	yes	characteristic
16	#19151832	C₄	1	4	yes	—
17	C₄×#13083559	C₂²	1	4	yes	—
18	#19151677	—	2	1	no	—
19	#19151677	C₂²	1	2	yes	—
20	C₈×D₃₅₆	—	2	1	no	—
21	C₈×D₃₅₆	C₂²	1	2	yes	—
22	#19151622	C₂²	1	1	yes	characteristic
23	#19151564	—	2	1	no	—
24	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
25	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
26	#19151348	C₂²	1	4	yes	—
27	D₄⋊#10623494	C₂²	1	4	yes	—
28	#19151325	C₂²	1	4	yes	—
29	#19151320	C₂²	1	2	yes	—
30	#19151320	C₂²	1	2	yes	—
31	C₂×#131×C₈₉	—	2	1	no	—
32	#532×C₈₉	C₂²	1	1	yes	characteristic
33	#436×C₈₉	—	2	1	no	—
34	#436×C₈₉	C₂²	1	2	yes	—
35	C₈×D₄×C₈₉	—	2	1	no	—
36	C₈×D₄×C₈₉	C₂²	1	2	yes	—
37	#423×C₈₉	C₂²	1	1	yes	characteristic
38	#408×C₈₉	—	2	1	no	—
39	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×#13083574	—	2	1	no	—
41	C₂×#13083559	C₂×C₄	1	4	yes	—
42	#15668018	—	4	4	no	—
43	C₂×#13083558	—	2	1	no	—
44	C₂×#13083557	—	2	2	no	—
45	C₂²×#10623494	—	2	1	no	—
46	C₂²×#10623494	C₂×C₄	1	2	yes	—
47	C₂×C₈×D₈₉	—	2	2	no	—
48	#15668012	C₂×C₄	1	1	yes	characteristic
49	#15668009	C₂×C₄	1	1	yes	characteristic
50	#15668000	—	2	1	no	—
51	#15667986	—	2	1	no	—
52	#15667986	C₂×C₄	1	2	yes	—
53	C₄×D₃₅₆	—	2	1	no	—
54	C₄×D₃₅₆	C₂³	1	2	yes	—
55	#15667945	C₂×C₄	1	4	yes	—
56	C₄⋊#10623494	—	2	1	no	—
57	C₄⋊#10623494	C₂³	1	2	yes	—
58	#15667933	C₂×C₄	1	4	yes	—
59	#15667932	C₂×C₄	1	4	yes	—
60	#15667924	—	2	2	no	—
61	#15667924	—	2	2	no	—
62	C₄×#10623494	—	2	1	no	—
63	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
64	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
65	C₄×#10623494	C₂³	1	2	yes	—
66	C₄×#10623494	C₂³	1	2	yes	—
67	C₂×#41×C₈₉	—	2	1	no	—
68	#131×C₈₉	—	4	4	no	—
69	C₂×M₁₆×C₈₉	—	2	1	no	—
70	C₂×M₁₆×C₈₉	—	2	2	no	—
71	C₂²×C₈×C₈₉	—	2	2	no	—
72	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
73	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
74	C₄⋊Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
75	#127×C₈₉	C₂×C₄	1	1	yes	characteristic
76	#124×C₈₉	—	2	1	no	—
77	#121×C₈₉	—	2	1	no	—
78	#121×C₈₉	C₂×C₄	1	2	yes	—
79	C₄×D₄×C₈₉	—	2	1	no	—
80	C₄×D₄×C₈₉	C₂³	1	2	yes	—
81	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₈₉	—	2	1	no	—
83	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
84	C₂²⋊C₈×C₈₉	—	2	2	no	—
85	C₂²⋊C₈×C₈₉	—	2	2	no	—
86	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
87	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
88	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
90	#13083574	—	4	2	no	—
91	#13083574	—	4	2	no	—
92	C₂×Dic₁₇₈	—	2	1	no	—
93	C₂×D₃₅₆	—	2	1	no	—
94	C₂×D₃₅₆	—	2	1	no	—
95	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
96	C₂×C₂²⋊D₈₉	—	2	2	no	—
97	C₂×C₄×D₈₉	—	2	2	no	—
98	#13083559	—	2	8	no	—
99	#13083558	—	4	2	no	—
100	#13083557	—	4	4	no	—
101	C₂×#10623494	—	2	4	no	—
102	C₂×#10623494	—	2	2	no	—
103	C₂×#10623494	—	2	2	no	—
104	C₂×#10623494	—	4	2	no	—
105	C₂×#10623494	C₂²×C₄	1	2	yes	—
106	C₂×#10623494	C₂²×C₄	1	2	yes	—
107	C₈×D₈₉	—	4	4	no	—
108	C₄⋊Dic₈₉	—	2	1	no	—
109	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
110	#13083551	—	2	2	no	—
111	#13083551	—	2	2	no	—
112	#41×C₈₉	—	4	2	no	—
113	#41×C₈₉	—	4	2	no	—
114	C₂×Q₈×C₈₉	—	2	1	no	—
115	C₂×D₄×C₈₉	—	2	2	no	—
116	C₂×D₄×C₈₉	—	2	1	no	—
117	C₂×D₄×C₈₉	—	2	1	no	—
118	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₈₉	—	2	2	no	—
120	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
123	M₁₆×C₈₉	—	4	4	no	—
124	M₁₆×C₈₉	—	4	2	no	—
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	—	4	4	no	—
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	C₄⋊C₄×C₈₉	—	2	1	no	—
134	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
135	C₂²⋊C₄×C₈₉	—	2	2	no	—
136	C₂²⋊C₄×C₈₉	—	2	2	no	—
137	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₈₉	#41	1	1	yes	characteristic
140	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
141	C₂³×C₈₉	—	2	2	no	—
142	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
143	C₂²×D₈₉	—	2	2	no	—
144	Q₈×C₈₉	—	4	2	no	—
145	D₄×C₈₉	—	2	4	no	—
146	D₄×C₈₉	—	4	4	no	—
147	D₄×C₈₉	—	4	2	no	—
148	D₄×C₈₉	—	4	2	no	—
149	C₂×C₄×C₈₉	—	2	2	no	—
150	C₂×C₄×C₈₉	—	2	2	no	—
151	C₂×C₄×C₈₉	—	2	2	no	—
152	C₂×C₄×C₈₉	—	4	2	no	—
153	C₂×C₄×C₈₉	—	4	2	no	—
154	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
158	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
159	C₂×C₄×C₈₉	C₂³×C₄	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	C₂²⋊D₈₉	—	4	4	no	—
163	C₂×Dic₈₉	—	2	2	no	—
164	D₃₅₆	—	2	4	no	—
165	D₃₅₆	—	4	2	no	—
166	D₃₅₆	—	4	2	no	—
167	C₄×D₈₉	—	4	2	no	—
168	C₄×D₈₉	—	4	2	no	—
169	Dic₁₇₈	—	4	2	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	—	2	2	no	—
176	#10623494	—	4	2	no	—
177	#10623494	—	4	2	no	—
178	#10623494	#131	1	4	yes	complemented
179	C₂²×C₈₉	—	2	1	no	—
180	C₂²×C₈₉	—	2	1	no	—
181	C₂²×C₈₉	—	4	2	no	—
182	C₂²×C₈₉	—	4	2	no	—
183	C₂²×C₈₉	—	4	2	no	—
184	C₂²×C₈₉	#442	1	2	yes	—
185	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
186	C₂×D₈₉	—	4	2	no	—
187	C₂×D₈₉	—	4	2	no	—
188	C₂×D₈₉	—	4	2	no	—
189	C₄×C₈₉	—	2	1	no	—
190	C₄×C₈₉	—	2	1	no	—
191	C₄×C₈₉	—	4	2	no	—
192	C₄×C₈₉	#442	1	2	yes	—
193	C₄×C₈₉	#444	1	2	yes	—
194	C₄×C₈₉	C₂×#131	1	2	yes	—
195	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
196	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	Dic₈₉	—	4	2	no	—
198	#17962	—	89	1	no	maximal, Sylow
199	C₂×C₈₉	—	2	2	no	—
200	C₂×C₈₉	—	8	2	no	—
201	C₂×C₈₉	#2931	1	1	yes	characteristic
202	C₂×C₈₉	C₂×#442	1	1	yes	characteristic
203	C₂×C₈₉	C₂×#444	1	1	yes	characteristic
204	D₈₉	—	8	2	no	—
205	#3169	—	89	1	no	—
206	#2931	—	89	1	no	—
207	#2931	D₈₉	1	1	yes	characteristic, complemented
208	#1594	—	89	4	no	—
209	#1580	—	89	4	no	—
210	#1566	—	89	1	no	—
211	#1492	—	89	1	no	—
212	#1492	—	89	1	no	—
213	C₂×#322	—	89	1	no	—
214	C₈₉	#17962	1	1	yes	characteristic, complemented, Sylow
215	C₂×#131	—	2	1	no	—
216	C₂×#131	—	178	1	no	—
217	#532	—	89	1	no	—
218	#532	C₂×D₈₉	1	1	yes	characteristic
219	#500	—	89	1	no	—
220	#493	—	89	1	no	—
221	#486	—	89	1	no	—
222	#486	—	89	1	no	—
223	#466	—	89	4	no	—
224	C₄×D₈	—	89	4	no	—
225	#436	—	2	1	no	—
226	#436	—	89	2	no	—
227	#436	—	178	1	no	—
228	#436	C₂×D₈₉	1	2	yes	—
229	C₈×D₄	—	2	1	no	—
230	C₈×D₄	—	89	2	no	—
231	C₈×D₄	—	178	1	no	—
232	C₈×D₄	C₂×D₈₉	1	2	yes	—
233	#423	—	89	1	no	—
234	#423	C₂×D₈₉	1	1	yes	characteristic
235	#408	—	2	1	no	—
236	#408	—	178	1	no	—
237	C₂×C₄×C₈	—	89	1	no	—
238	C₂×C₄×C₈	—	89	1	no	—
239	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
240	#334	—	89	4	no	—
241	D₄⋊C₈	—	89	4	no	—
242	D₄⋊C₈	—	89	4	no	—
243	#322	—	89	2	no	—
244	#322	—	89	2	no	—
245	C₂×#41	—	2	1	no	—
246	C₂×#41	—	178	1	no	—
247	C₂×D₈	—	89	4	no	—
248	#131	—	4	4	no	—
249	#131	—	356	4	no	—
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	178	1	no	—
253	C₂×M₁₆	—	178	2	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	—	89	2	no	—
256	C₂²×C₈	—	178	1	no	—
257	C₂²×C₈	—	178	2	no	—
258	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
259	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
260	C₄⋊Q₈	—	89	1	no	—
261	C₄⋊Q₈	C₄×D₈₉	1	1	yes	characteristic
262	#127	—	89	1	no	—
263	#127	C₄×D₈₉	1	1	yes	characteristic
264	#124	—	2	1	no	—
265	#124	—	178	1	no	—
266	#121	—	2	1	no	—
267	#121	—	89	2	no	—
268	#121	—	178	1	no	—
269	#121	C₄×D₈₉	1	2	yes	—
270	C₄×D₄	—	2	1	no	—
271	C₄×D₄	—	89	2	no	—
272	C₄×D₄	—	178	1	no	—
273	C₄×D₄	C₂²×D₈₉	1	2	yes	—
274	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
275	#107	—	89	4	no	—
276	C₄⋊C₈	—	2	1	no	—
277	C₄⋊C₈	—	89	2	no	—
278	C₄⋊C₈	—	178	1	no	—
279	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
280	#102	—	89	4	no	—
281	#102	—	89	4	no	—
282	C₂²⋊C₈	—	2	2	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	178	2	no	—
285	C₂²⋊C₈	—	178	2	no	—
286	C₄×C₈	—	89	1	no	—
287	C₄×C₈	—	89	1	no	—
288	C₄×C₈	—	89	2	no	—
289	C₄×C₈	—	89	2	no	—
290	C₄×C₈	—	178	1	no	—
291	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
292	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
293	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
294	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
295	#41	—	4	2	no	—
296	#41	—	4	2	no	—
297	#41	—	356	2	no	—
298	#41	—	356	2	no	—
299	C₂×Q₈	—	2	1	no	—
300	C₂×Q₈	—	178	1	no	—
301	C₂×D₄	—	2	2	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	2	1	no	—
304	C₂×D₄	—	89	2	no	—
305	C₂×D₄	—	178	2	no	—
306	C₂×D₄	—	178	1	no	—
307	C₂×D₄	—	178	1	no	—
308	C₂×D₄	C₂×C₄×D₈₉	1	2	yes	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	178	2	no	—
311	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
313	C₂²×C₄	#13083574	1	1	yes	characteristic
314	D₈	—	178	8	no	—
315	M₁₆	—	4	4	no	—
316	M₁₆	—	4	2	no	—
317	M₁₆	—	356	4	no	—
318	M₁₆	—	356	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	4	4	no	—
323	C₂×C₈	—	89	2	no	—
324	C₂×C₈	—	89	2	no	—
325	C₂×C₈	—	356	4	no	—
326	C₂×C₈	—	356	2	no	—
327	C₂×C₈	—	178	4	no	—
328	C₂×C₈	—	178	2	no	—
329	C₂×C₈	—	178	2	no	—
330	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
331	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
332	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
333	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	89	2	no	—
336	C₄⋊C₄	—	178	1	no	—
337	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
338	C₂²⋊C₄	—	2	2	no	—
339	C₂²⋊C₄	—	2	2	no	—
340	C₂²⋊C₄	—	178	2	no	—
341	C₂²⋊C₄	—	178	2	no	—
342	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
343	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
344	C₄²	#13083574	1	1	yes	characteristic
345	C₄²	C₂³×D₈₉	1	1	yes	characteristic
346	C₂³	—	2	2	no	—
347	C₂³	—	178	2	no	—
348	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
349	Q₈	—	4	2	no	—
350	Q₈	—	356	2	no	—
351	D₄	—	2	4	no	—
352	D₄	—	4	4	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	356	4	no	—
356	D₄	—	356	2	no	—
357	D₄	—	356	2	no	—
358	D₄	—	178	4	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	356	2	no	—
365	C₂×C₄	—	356	2	no	—
366	C₂×C₄	—	178	2	no	—
367	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
368	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
369	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
370	C₂×C₄	#15668037	1	2	yes	—
371	C₂×C₄	#15668038	1	2	yes	—
372	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
373	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
374	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	—	2	1	no	—
379	C₈	—	4	2	no	—
380	C₈	—	89	4	no	—
381	C₈	—	356	2	no	—
382	C₈	—	356	2	no	—
383	C₈	—	178	2	no	—
384	C₂²	—	2	1	no	—
385	C₂²	—	2	1	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	356	2	no	—
390	C₂²	—	356	2	no	—
391	C₂²	—	356	2	no	—
392	C₂²	#19151708	1	2	yes	—
393	C₂²	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	4	2	no	—
397	C₄	—	356	2	no	—
398	C₄	#19151708	1	2	yes	—
399	C₄	#19151718	1	2	yes	—
400	C₄	#131×D₈₉	1	2	yes	—
401	C₄	C₂×#15668037	1	1	yes	characteristic
402	C₄	C₂×#15668038	1	1	yes	characteristic
403	C₂	—	2	2	no	—
404	C₂	—	8	2	no	—
405	C₂	—	712	2	no	—
406	C₂	#26028962	1	1	yes	characteristic
407	C₂	C₂×#19151708	1	1	yes	characteristic
408	C₂	C₂×#19151718	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#2931	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#26030827	C₂
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2931	D₈₉
hypocenter	C₈₉	#17962
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2931

Complements

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

N	H ≅ G/N	type
2. #26028965	C₂	semidirect
3. #26019164	C₂	semidirect
4. #26019074	C₂	semidirect
5. #26019007	C₂	semidirect
6. #26018703	C₂	semidirect
7. #26018702	C₂	semidirect
8. C₂×#19151320	C₂	semidirect
9. C₈₉×#2931	C₂	semidirect
178. #10623494	#131	semidirect
207. #2931	D₈₉	semidirect
214. C₈₉	#17962	semidirect

Maximal subgroups

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

subgroup	index
#26030827	2
#26028965	2
#26019164	2
#26019074	2
#26019007	2
#26018703	2
#26018702	2
C₂×#19151320	2
C₈₉×#2931	2
#17962	89