Subgroups — #36526181

Order 22784.

722 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030828	C₂	1	1	yes	maximal, characteristic
2	#26028991	C₂	1	2	yes	maximal, complemented
3	#26019138	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019137	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019084	C₂	1	2	yes	maximal, complemented
6	#26019081	C₂	1	2	yes	maximal, complemented
7	#26019046	C₂	1	1	yes	maximal, characteristic, complemented
8	#335×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018649	C₂	1	2	yes	maximal, complemented
10	C₈×#13083557	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668018	—	2	2	no	—
13	#19152145	C₂²	1	2	yes	—
14	#19152002	C₄	1	1	yes	characteristic
15	#19151973	C₄	1	1	yes	characteristic
16	#19151943	C₄	1	2	yes	—
17	#19151835	C₄	1	1	yes	characteristic
18	#19151833	C₄	1	2	yes	—
19	#19151831	C₄	1	1	yes	characteristic
20	C₄×D₇₁₂	C₂²	1	1	yes	characteristic
21	C₄×#13083559	C₂²	1	2	yes	—
22	#19151677	C₂²	1	2	yes	—
23	#19151676	C₂²	1	2	yes	—
24	#19151672	—	2	2	no	—
25	#19151669	—	2	2	no	—
26	#19151663	C₂²	1	2	yes	—
27	#19151649	C₂²	1	1	yes	characteristic
28	C₄⋊C₈×D₈₉	C₂²	1	2	yes	—
29	#19151563	—	2	2	no	—
30	C₄×#13083557	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
32	#19151351	C₂²	1	1	yes	characteristic
33	#19151350	C₂²	1	2	yes	—
34	#19151327	C₂²	1	2	yes	—
35	D₄⋊#10623494	C₂²	1	2	yes	—
36	#19151325	C₂²	1	2	yes	—
37	#19151320	C₂²	1	1	yes	characteristic
38	#19151319	C₂²	1	1	yes	characteristic
39	C₈×#10623494	C₂²	1	1	yes	characteristic
40	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₈₉	C₂²	1	2	yes	—
42	#335×C₈₉	C₂²	1	1	yes	characteristic
43	D₄⋊C₈×C₈₉	C₂²	1	2	yes	—
44	C₈²×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#13083574	—	2	2	no	—
46	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
47	C₂×#13083559	C₂×C₄	1	2	yes	—
48	#15668018	—	4	8	no	—
49	C₂×#13083558	—	2	2	no	—
50	C₂×#13083557	—	2	2	no	—
51	C₂×#13083557	D₄	1	1	yes	characteristic
52	C₂×#13083557	D₄	1	1	yes	characteristic
53	C₂×C₈×D₈₉	—	2	2	no	—
54	C₂×C₈×D₈₉	—	2	2	no	—
55	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
57	#15668011	C₂×C₄	1	2	yes	—
58	#15668008	C₂×C₄	1	2	yes	—
59	#15667998	—	2	2	no	—
60	#15667987	C₂×C₄	1	2	yes	—
61	#15667985	—	2	2	no	—
62	#15667983	C₂×C₄	1	2	yes	—
63	C₄×D₃₅₆	C₂³	1	2	yes	—
64	C₄×C₂²⋊D₈₉	—	2	2	no	—
65	C₄²×D₈₉	C₂³	1	1	yes	characteristic
66	#15667946	C₂×C₄	1	1	yes	characteristic
67	#15667945	C₂×C₄	1	2	yes	—
68	C₄⋊#10623494	C₂³	1	2	yes	—
69	#15667941	—	2	2	no	—
70	#15667941	—	2	1	no	—
71	#15667934	C₂×C₄	1	2	yes	—
72	#15667933	C₂×C₄	1	2	yes	—
73	#15667932	C₂×C₄	1	2	yes	—
74	C₂²⋊#10623494	—	2	2	no	—
75	#15667924	—	2	1	no	—
76	#15667924	—	2	2	no	—
77	#15667924	—	2	2	no	—
78	#15667922	D₄	1	1	yes	characteristic
79	#15667922	D₄	1	1	yes	characteristic
80	C₄×#10623494	C₂³	1	1	yes	characteristic
81	C₄×#10623494	C₂³	1	1	yes	characteristic
82	C₄×#10623494	C₂³	1	1	yes	characteristic
83	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
84	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
85	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₈₉	—	2	2	no	—
87	C₄×D₄×C₈₉	C₂³	1	2	yes	—
88	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
90	#102×C₈₉	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₈₉	—	2	2	no	—
92	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
95	#13083574	—	4	4	no	—
96	#13083574	—	4	4	no	—
97	C₂×Dic₁₇₈	—	2	2	no	—
98	C₂×D₃₅₆	—	2	2	no	—
99	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
100	C₂×C₂²⋊D₈₉	—	2	2	no	—
101	C₂×C₂²⋊D₈₉	—	2	2	no	—
102	C₂×C₂²⋊D₈₉	—	2	2	no	—
103	C₂×C₄×D₈₉	—	2	2	no	—
104	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
106	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
107	D₇₁₂	—	2	2	no	—
108	#13083559	—	4	2	no	—
109	#13083558	—	4	4	no	—
110	#13083557	—	2	2	no	—
111	#13083557	—	4	4	no	—
112	#13083557	D₈	1	4	yes	complemented
113	C₂×#10623494	—	2	2	no	—
114	C₂×#10623494	—	2	1	no	—
115	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
116	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
117	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
118	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
119	C₈×D₈₉	—	2	2	no	—
120	C₈×D₈₉	—	4	1	no	—
121	C₈×D₈₉	—	4	4	no	—
122	C₈×D₈₉	—	4	4	no	—
123	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
124	#13083553	—	2	2	no	—
125	C₂²⋊Dic₈₉	—	2	2	no	—
126	#13083551	—	2	2	no	—
127	#13083551	—	2	2	no	—
128	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
130	C₄×Dic₈₉	#41	1	1	yes	characteristic
131	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
132	C₂²×C₄×C₈₉	—	2	2	no	—
133	D₈×C₈₉	—	2	2	no	—
134	C₂×C₈×C₈₉	—	2	2	no	—
135	C₂×C₈×C₈₉	—	2	1	no	—
136	C₂×C₈×C₈₉	—	4	4	no	—
137	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
142	C₂²⋊C₄×C₈₉	—	2	2	no	—
143	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
144	C₂³×C₈₉	—	2	2	no	—
145	C₂²×D₈₉	—	2	2	no	—
146	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
147	D₄×C₈₉	—	2	2	no	—
148	D₄×C₈₉	—	2	2	no	—
149	C₂×C₄×C₈₉	—	2	2	no	—
150	C₂×C₄×C₈₉	—	4	2	no	—
151	C₂×C₄×C₈₉	—	4	2	no	—
152	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
155	C₂²⋊D₈₉	—	4	4	no	—
156	C₂²⋊D₈₉	—	4	4	no	—
157	C₂²⋊D₈₉	—	8	2	no	—
158	C₂×Dic₈₉	—	2	2	no	—
159	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
160	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
161	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
162	D₃₅₆	—	2	2	no	—
163	D₃₅₆	—	2	2	no	—
164	D₃₅₆	—	4	4	no	—
165	C₄×D₈₉	—	2	1	no	—
166	C₄×D₈₉	—	2	1	no	—
167	C₄×D₈₉	—	4	1	no	—
168	C₄×D₈₉	—	4	2	no	—
169	C₄×D₈₉	—	4	2	no	—
170	C₄×D₈₉	C₂×D₈	1	2	yes	—
171	C₄×D₈₉	#135	1	2	yes	—
172	Dic₁₇₈	—	4	4	no	—
173	C₈×C₈₉	—	2	1	no	—
174	C₈×C₈₉	—	2	1	no	—
175	C₈×C₈₉	—	4	1	no	—
176	C₈×C₈₉	—	4	2	no	—
177	C₈×C₈₉	#131	1	2	yes	complemented
178	C₈×C₈₉	C₂×D₈	1	2	yes	—
179	#10623494	—	2	1	no	—
180	#10623494	—	2	1	no	—
181	#10623494	—	2	1	no	—
182	#10623494	—	4	1	no	—
183	#10623494	—	4	2	no	—
184	#10623494	C₂×D₈	1	2	yes	—
185	C₂²×C₈₉	—	4	2	no	—
186	C₂²×C₈₉	—	4	2	no	—
187	C₂²×C₈₉	—	4	2	no	—
188	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
189	C₂×D₈₉	—	2	1	no	—
190	C₂×D₈₉	—	2	1	no	—
191	C₂×D₈₉	—	4	2	no	—
192	C₂×D₈₉	—	4	2	no	—
193	C₂×D₈₉	—	4	2	no	—
194	C₂×D₈₉	C₄×D₈	1	2	yes	—
195	C₄×C₈₉	—	2	1	no	—
196	C₄×C₈₉	—	4	2	no	—
197	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
198	C₄×C₈₉	#568	1	1	yes	characteristic
199	C₄×C₈₉	C₂²×D₈	1	1	yes	characteristic
200	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
201	Dic₈₉	—	2	1	no	—
202	Dic₈₉	—	2	1	no	—
203	Dic₈₉	—	4	2	no	—
204	Dic₈₉	C₄×D₈	1	2	yes	—
205	#18066	—	89	1	no	maximal, Sylow
206	C₂×C₈₉	—	8	2	no	—
207	C₂×C₈₉	#2935	1	1	yes	characteristic
208	C₂×C₈₉	C₂×C₄×D₈	1	1	yes	characteristic
209	C₂×C₈₉	#2957	1	1	yes	characteristic
210	D₈₉	—	2	2	no	—
211	D₈₉	—	8	2	no	—
212	#3169	—	89	1	no	—
213	#2935	—	89	2	no	—
214	#1589	—	89	1	no	—
215	#1589	—	89	1	no	—
216	#1581	—	89	2	no	—
217	#1581	—	89	2	no	—
218	C₈×D₈	—	89	1	no	—
219	C₈×D₈	D₈₉	1	1	yes	characteristic, complemented
220	C₂×#335	—	89	1	no	—
221	#1480	—	89	2	no	—
222	C₈×M₁₆	—	89	1	no	—
223	C₈₉	#18066	1	1	yes	characteristic, complemented, Sylow
224	C₂×#131	—	178	2	no	—
225	#532	—	89	2	no	—
226	#500	—	89	1	no	—
227	#493	—	89	1	no	—
228	#486	—	89	2	no	—
229	#466	—	89	1	no	—
230	#466	—	89	1	no	—
231	#466	—	89	2	no	—
232	C₄×D₈	—	89	2	no	—
233	C₄×D₈	—	89	1	no	—
234	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
235	#436	—	89	2	no	—
236	#436	—	89	2	no	—
237	#435	—	178	2	no	—
238	#435	—	178	2	no	—
239	C₈×D₄	—	89	2	no	—
240	C₈×D₄	C₂×D₈₉	1	2	yes	—
241	#431	—	89	1	no	—
242	C₂×C₄⋊C₈	—	89	2	no	—
243	#408	—	178	2	no	—
244	C₄×M₁₆	—	89	1	no	—
245	C₂×C₄×C₈	—	89	1	no	—
246	#335	—	89	2	no	—
247	#335	—	89	1	no	—
248	#335	C₂×D₈₉	1	1	yes	characteristic
249	D₄⋊C₈	—	89	2	no	—
250	D₄⋊C₈	—	89	2	no	—
251	D₄⋊C₈	—	89	2	no	—
252	D₄⋊C₈	C₂×D₈₉	1	2	yes	—
253	#322	—	89	1	no	—
254	#322	—	89	1	no	—
255	C₈²	—	89	1	no	—
256	C₈²	C₂×D₈₉	1	1	yes	characteristic
257	C₂×#41	—	178	2	no	—
258	C₂×D₈	—	89	2	no	—
259	C₂×D₈	—	89	1	no	—
260	C₂×D₈	C₄×D₈₉	1	1	yes	characteristic
261	#131	—	356	8	no	—
262	C₂×M₁₆	—	89	1	no	—
263	C₂×M₁₆	—	89	1	no	—
264	C₂×M₁₆	—	178	2	no	—
265	C₂×M₁₆	—	178	2	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	89	1	no	—
268	C₂²×C₈	—	89	1	no	—
269	C₂²×C₈	—	178	2	no	—
270	C₂²×C₈	—	178	2	no	—
271	C₄⋊Q₈	—	89	2	no	—
272	#127	—	89	2	no	—
273	#124	—	178	2	no	—
274	#121	—	89	2	no	—
275	#121	—	89	2	no	—
276	#121	—	178	2	no	—
277	C₄×D₄	—	89	2	no	—
278	C₄×D₄	—	178	2	no	—
279	C₄×D₄	C₂²×D₈₉	1	2	yes	—
280	C₂×C₄²	—	89	1	no	—
281	#107	—	89	1	no	—
282	#107	—	89	2	no	—
283	#107	C₄×D₈₉	1	1	yes	characteristic
284	C₄⋊C₈	—	89	2	no	—
285	C₄⋊C₈	—	178	2	no	—
286	C₄⋊C₈	—	178	1	no	—
287	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
288	#102	—	89	2	no	—
289	#102	—	89	2	no	—
290	#102	—	89	2	no	—
291	#102	C₄×D₈₉	1	2	yes	—
292	C₂²⋊C₈	—	2	2	no	—
293	C₂²⋊C₈	—	178	2	no	—
294	C₂²⋊C₈	—	178	1	no	—
295	C₂²⋊C₈	—	178	2	no	—
296	C₂²⋊C₈	—	178	2	no	—
297	#97	—	89	1	no	—
298	#97	—	89	1	no	—
299	C₄×C₈	—	89	1	no	—
300	C₄×C₈	—	89	1	no	—
301	C₄×C₈	—	89	1	no	—
302	C₄×C₈	—	89	1	no	—
303	C₄×C₈	—	89	1	no	—
304	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
305	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
306	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
307	#41	—	356	4	no	—
308	#41	—	356	4	no	—
309	C₂×Q₈	—	178	2	no	—
310	C₂×D₄	—	89	2	no	—
311	C₂×D₄	—	178	2	no	—
312	C₂×D₄	—	178	2	no	—
313	C₂×D₄	—	178	2	no	—
314	C₂×D₄	—	178	2	no	—
315	C₂×D₄	C₂×C₄×D₈₉	1	2	yes	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	89	1	no	—
318	C₂²×C₄	—	89	1	no	—
319	C₂²×C₄	—	89	1	no	—
320	C₂²×C₄	—	178	2	no	—
321	D₈	—	2	2	no	—
322	D₈	—	356	2	no	—
323	D₈	—	178	2	no	—
324	M₁₆	—	89	4	no	—
325	M₁₆	—	356	4	no	—
326	M₁₆	—	356	4	no	—
327	M₁₆	—	178	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	1	no	—
330	C₂×C₈	—	4	4	no	—
331	C₂×C₈	—	89	1	no	—
332	C₂×C₈	—	89	1	no	—
333	C₂×C₈	—	89	1	no	—
334	C₂×C₈	—	89	1	no	—
335	C₂×C₈	—	356	1	no	—
336	C₂×C₈	—	356	4	no	—
337	C₂×C₈	—	356	4	no	—
338	C₂×C₈	—	178	2	no	—
339	C₂×C₈	—	178	1	no	—
340	C₂×C₈	—	178	2	no	—
341	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
342	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
343	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
344	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
345	C₄⋊C₄	—	89	2	no	—
346	C₄⋊C₄	—	178	2	no	—
347	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
348	C₂²⋊C₄	—	2	2	no	—
349	C₂²⋊C₄	—	178	2	no	—
350	C₂²⋊C₄	—	178	2	no	—
351	C₂²⋊C₄	—	178	2	no	—
352	C₄²	—	89	1	no	—
353	C₄²	—	89	1	no	—
354	C₄²	—	89	1	no	—
355	C₄²	C₂³×D₈₉	1	1	yes	characteristic
356	C₂³	—	2	2	no	—
357	C₂³	—	89	1	no	—
358	C₂³	—	178	2	no	—
359	Q₈	—	356	4	no	—
360	D₄	—	2	2	no	—
361	D₄	—	2	2	no	—
362	D₄	—	356	4	no	—
363	D₄	—	356	4	no	—
364	D₄	—	356	4	no	—
365	D₄	—	178	2	no	—
366	D₄	—	178	2	no	—
367	D₄	—	712	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	89	1	no	—
372	C₂×C₄	—	89	2	no	—
373	C₂×C₄	—	89	2	no	—
374	C₂×C₄	—	89	1	no	—
375	C₂×C₄	—	89	1	no	—
376	C₂×C₄	—	356	1	no	—
377	C₂×C₄	—	356	2	no	—
378	C₂×C₄	—	356	2	no	—
379	C₂×C₄	—	178	2	no	—
380	C₂×C₄	—	178	1	no	—
381	C₂×C₄	—	178	1	no	—
382	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
383	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
384	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
385	C₈	—	2	1	no	—
386	C₈	—	2	1	no	—
387	C₈	—	4	1	no	—
388	C₈	—	4	2	no	—
389	C₈	—	89	2	no	—
390	C₈	—	356	1	no	—
391	C₈	—	356	2	no	—
392	C₈	—	178	1	no	—
393	C₈	—	178	1	no	—
394	C₈	—	178	1	no	—
395	C₈	#15668018	1	2	yes	complemented
396	C₈	D₈×D₈₉	1	2	yes	—
397	C₂²	—	4	2	no	—
398	C₂²	—	4	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	—	89	2	no	—
401	C₂²	—	356	2	no	—
402	C₂²	—	356	2	no	—
403	C₂²	—	356	2	no	—
404	C₂²	—	178	1	no	—
405	C₂²	—	178	1	no	—
406	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
407	C₄	—	2	1	no	—
408	C₄	—	4	2	no	—
409	C₄	—	89	2	no	—
410	C₄	—	356	2	no	—
411	C₄	—	178	1	no	—
412	C₄	—	178	1	no	—
413	C₄	C₂×#15668018	1	1	yes	characteristic
414	C₄	#19152363	1	1	yes	characteristic
415	C₄	C₂×D₈×D₈₉	1	1	yes	characteristic
416	C₄	#135×D₈₉	1	1	yes	characteristic
417	C₂	—	8	2	no	—
418	C₂	—	178	2	no	—
419	C₂	—	712	2	no	—
420	C₂	#26028991	1	1	yes	characteristic
421	C₂	C₄×D₈×D₈₉	1	1	yes	characteristic
422	C₂	#26029164	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×D₈×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	#26030828	C₂
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₈×D₈	D₈₉
hypocenter	C₈₉	#18066
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×D₈

Complements

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

N	H ≅ G/N	type
2. #26028991	C₂	semidirect
3. #26019138	C₂	semidirect
4. #26019137	C₂	semidirect
5. #26019084	C₂	semidirect
6. #26019081	C₂	semidirect
7. #26019046	C₂	semidirect
8. #335×D₈₉	C₂	semidirect
9. #26018649	C₂	semidirect
10. C₈×#13083557	C₂	semidirect
11. C₈×D₈×C₈₉	C₂	semidirect
112. #13083557	D₈	semidirect
177. C₈×C₈₉	#131	semidirect
219. C₈×D₈	D₈₉	semidirect
223. C₈₉	#18066	semidirect
395. C₈	#15668018	semidirect

Maximal subgroups

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

subgroup	index
#26030828	2
#26028991	2
#26019138	2
#26019137	2
#26019084	2
#26019081	2
#26019046	2
#335×D₈₉	2
#26018649	2
C₈×#13083557	2
C₈×D₈×C₈₉	2
#18066	89