Subgroups — #36523883

Order 22784.

782 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029273	C₂	1	2	yes	maximal, complemented
2	C₄×D₈×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#26019077	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019076	C₂	1	1	yes	maximal, characteristic, complemented
5	#26019075	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×#13083559	C₂	1	2	yes	maximal, complemented
7	#26019044	C₂	1	2	yes	maximal, complemented
8	#26018997	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018641	C₂	1	2	yes	maximal, complemented
10	#26018537	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1580	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₈₉	C₄	1	1	yes	characteristic
13	C₄×D₄×D₈₉	C₂²	1	2	yes	—
14	C₄×D₇₁₂	C₂²	1	1	yes	characteristic
15	D₈×Dic₈₉	C₄	1	1	yes	characteristic
16	#19151680	C₄	1	1	yes	characteristic
17	C₄×#13083559	C₂²	1	2	yes	—
18	#19151678	C₄	1	2	yes	—
19	C₈×D₃₅₆	C₂²	1	2	yes	complemented
20	D₄×#10623494	C₂²	1	2	yes	complemented
21	#19151663	C₂²	1	2	yes	complemented
22	C₈×C₂²⋊D₈₉	—	2	2	no	—
23	#19151661	—	2	2	no	—
24	#19151650	C₂²	1	2	yes	—
25	#19151649	C₂²	1	1	yes	characteristic
26	#19151649	C₂²	1	1	yes	characteristic
27	#107×D₈₉	C₄	1	1	yes	characteristic
28	#102×D₈₉	C₄	1	2	yes	—
29	C₂×#15667924	—	2	2	no	—
30	C₂²⋊C₈×D₈₉	—	2	2	no	—
31	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
32	#19151350	C₂²	1	2	yes	complemented
33	#19151349	C₂²	1	1	yes	characteristic, complemented
34	#19151327	C₂²	1	2	yes	complemented
35	D₄⋊#10623494	C₂²	1	2	yes	complemented
36	#19151325	C₂²	1	2	yes	complemented
37	#19151319	C₂²	1	1	yes	characteristic, complemented
38	C₈×#10623494	C₂²	1	1	yes	characteristic, complemented
39	C₈×#10623494	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₈₉	C₂²	1	2	yes	complemented
42	#334×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	D₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
44	#322×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₄×D₈₉	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₈₉	—	2	2	no	—
47	C₂×D₇₁₂	C₂×C₄	1	1	yes	characteristic
48	C₂×#13083559	C₂×C₄	1	2	yes	—
49	D₈×D₈₉	C₈	1	8	yes	complemented
50	C₂²×#10623494	—	2	2	no	—
51	C₂×C₈×D₈₉	—	2	2	no	—
52	C₂×C₈×D₈₉	—	2	2	no	—
53	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
55	C₄×D₃₅₆	C₂³	1	2	yes	—
56	D₄×Dic₈₉	C₂×C₄	1	2	yes	—
57	#15667974	C₂×C₄	1	2	yes	—
58	C₄×C₂²⋊D₈₉	—	2	2	no	—
59	#15667972	—	2	2	no	—
60	C₄⋊C₄×D₈₉	C₂×C₄	1	2	yes	—
61	C₂²⋊C₄×D₈₉	—	2	2	no	—
62	C₄²×D₈₉	C₂³	1	1	yes	characteristic
63	#15667946	C₂×C₄	1	1	yes	characteristic
64	#15667945	C₂×C₄	1	2	yes	—
65	C₄⋊#10623494	C₂³	1	2	yes	—
66	#15667941	—	2	1	no	—
67	#15667941	D₄	1	2	yes	—
68	#15667934	C₂×C₄	1	2	yes	—
69	#15667933	C₂×C₄	1	2	yes	—
70	#15667932	C₂×C₄	1	2	yes	—
71	C₂²⋊#10623494	—	2	2	no	—
72	#15667924	—	2	2	no	—
73	#15667924	—	2	1	no	—
74	#15667924	—	2	2	no	—
75	#15667924	—	2	2	no	—
76	#15667924	D₄	1	2	yes	—
77	C₄×#10623494	C₂³	1	1	yes	characteristic
78	C₄×#10623494	C₂³	1	1	yes	characteristic
79	C₄×#10623494	C₂³	1	1	yes	characteristic
80	C₈×Dic₈₉	—	2	2	no	—
81	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
83	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₈₉	—	2	2	no	—
85	C₄×D₄×C₈₉	C₂³	1	2	yes	—
86	#107×C₈₉	C₂×C₄	1	1	yes	characteristic
87	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
88	#102×C₈₉	C₂×C₄	1	2	yes	—
89	C₂²⋊C₈×C₈₉	—	2	2	no	—
90	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
93	C₂³×D₈₉	—	2	2	no	—
94	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
95	C₂×C₂²⋊D₈₉	—	2	2	no	—
96	D₄×D₈₉	—	2	4	no	—
97	D₄×D₈₉	C₂×C₈	1	8	yes	complemented
98	C₂²×Dic₈₉	—	2	2	no	—
99	C₂×C₄×D₈₉	—	2	2	no	—
100	C₂×C₄×D₈₉	—	2	2	no	—
101	C₂×C₄×D₈₉	—	2	2	no	—
102	C₂×C₄×D₈₉	—	8	2	no	—
103	C₂×C₄×D₈₉	—	8	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	C₂×C₈	1	4	yes	complemented
108	#13083559	C₂×C₈	1	8	yes	complemented
109	C₂×#10623494	—	2	2	no	—
110	C₂×#10623494	—	2	1	no	—
111	C₂×#10623494	—	8	2	no	—
112	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
113	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
114	C₂×#10623494	C₂×D₄	1	2	yes	—
115	C₈×D₈₉	—	2	2	no	—
116	C₈×D₈₉	—	8	2	no	—
117	C₈×D₈₉	—	8	2	no	—
118	C₈×D₈₉	C₂×C₈	1	4	yes	complemented
119	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
120	#13083553	—	2	2	no	—
121	C₂²⋊Dic₈₉	—	2	2	no	—
122	#13083551	—	2	2	no	—
123	#13083551	—	2	2	no	—
124	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
125	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
126	C₄×Dic₈₉	#41	1	1	yes	characteristic
127	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
128	C₂²×C₄×C₈₉	—	2	2	no	—
129	D₈×C₈₉	C₂×C₈	1	4	yes	complemented
130	C₂×C₈×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	—	2	1	no	—
132	C₂×C₈×C₈₉	—	8	2	no	—
133	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
137	C₂²⋊C₄×C₈₉	—	2	2	no	—
138	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
139	C₂³×C₈₉	—	2	2	no	—
140	C₂²×D₈₉	—	2	2	no	—
141	C₂²×D₈₉	—	2	8	no	—
142	C₂²×D₈₉	—	8	2	no	—
143	C₂²×D₈₉	—	8	2	no	—
144	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
145	D₄×C₈₉	—	2	2	no	—
146	D₄×C₈₉	C₂²×C₈	1	4	yes	—
147	C₂×C₄×C₈₉	—	2	2	no	—
148	C₂×C₄×C₈₉	—	4	2	no	—
149	C₂×C₄×C₈₉	—	4	2	no	—
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	—	2	8	no	—
154	C₂×Dic₈₉	—	2	2	no	—
155	C₂×Dic₈₉	—	8	2	no	—
156	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
157	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
158	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
159	D₃₅₆	—	2	2	no	—
160	D₃₅₆	C₂²×C₈	1	4	yes	—
161	C₄×D₈₉	—	2	2	no	—
162	C₄×D₈₉	—	4	1	no	—
163	C₄×D₈₉	—	4	2	no	—
164	C₄×D₈₉	—	4	2	no	—
165	C₄×D₈₉	—	8	2	no	—
166	C₄×D₈₉	—	8	2	no	—
167	C₄×D₈₉	C₂²×C₈	1	2	yes	—
168	C₄×D₈₉	#131	1	2	yes	—
169	C₈×C₈₉	—	2	1	no	—
170	C₈×C₈₉	—	2	2	no	—
171	C₈×C₈₉	—	4	1	no	—
172	C₈×C₈₉	—	4	2	no	—
173	C₈×C₈₉	C₂²×C₈	1	2	yes	—
174	#10623494	—	2	1	no	—
175	#10623494	—	2	2	no	—
176	#10623494	—	4	1	no	—
177	#10623494	—	4	2	no	—
178	#10623494	C₂²×C₈	1	2	yes	—
179	C₂²×C₈₉	—	2	4	no	—
180	C₂²×C₈₉	—	4	2	no	—
181	C₂²×C₈₉	—	4	2	no	—
182	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
183	C₂×D₈₉	—	2	1	no	—
184	C₂×D₈₉	—	2	1	no	—
185	C₂×D₈₉	—	2	4	no	—
186	C₂×D₈₉	—	4	2	no	—
187	C₂×D₈₉	—	4	2	no	—
188	C₂×D₈₉	—	8	8	no	—
189	C₂×D₈₉	C₈×D₄	1	2	yes	—
190	C₄×C₈₉	—	2	1	no	—
191	C₄×C₈₉	—	4	2	no	—
192	C₄×C₈₉	C₂³×C₈	1	1	yes	characteristic
193	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
194	C₄×C₈₉	#576	1	2	yes	—
195	Dic₈₉	—	2	1	no	—
196	Dic₈₉	—	2	1	no	—
197	Dic₈₉	—	4	2	no	—
198	Dic₈₉	C₈×D₄	1	2	yes	—
199	#17854	—	89	1	no	maximal, Sylow
200	C₂×C₈₉	—	4	4	no	—
201	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
202	C₂×C₈₉	#2948	1	1	yes	characteristic
203	C₂×C₈₉	#2957	1	1	yes	characteristic
204	D₈₉	—	2	2	no	—
205	D₈₉	—	4	4	no	—
206	#2972	—	89	2	no	—
207	C₂×C₄×D₈	—	89	1	no	—
208	#1580	—	89	1	no	—
209	#1580	—	89	1	no	—
210	#1580	—	89	1	no	—
211	#1580	D₈₉	1	1	yes	characteristic, complemented
212	C₈×D₈	—	89	2	no	—
213	C₈×D₈	—	89	2	no	—
214	#1564	—	89	1	no	—
215	#1478	—	89	2	no	—
216	#1450	—	89	1	no	—
217	C₈₉	#17854	1	1	yes	characteristic, complemented, Sylow
218	C₂²×D₈	—	89	1	no	—
219	C₂×C₄×D₄	—	89	2	no	—
220	C₄×D₈	—	89	1	no	—
221	C₄×D₈	—	89	2	no	—
222	C₄×D₈	—	89	1	no	—
223	C₄×D₈	—	89	2	no	—
224	C₄×D₈	—	89	1	no	—
225	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
226	C₈×D₄	—	89	2	no	—
227	C₈×D₄	—	89	2	no	—
228	C₈×D₄	—	89	2	no	—
229	C₈×D₄	—	178	2	no	—
230	C₈×D₄	—	178	2	no	—
231	C₈×D₄	C₂×D₈₉	1	2	yes	complemented
232	#431	—	89	1	no	—
233	#431	—	89	1	no	—
234	#431	—	89	2	no	—
235	C₂×#107	—	89	1	no	—
236	C₂×#102	—	89	2	no	—
237	C₂×C₂²⋊C₈	—	178	2	no	—
238	C₂×C₂²⋊C₈	—	178	2	no	—
239	C₂×C₄×C₈	—	89	1	no	—
240	#335	—	89	2	no	—
241	#334	—	89	1	no	—
242	#334	C₂×D₈₉	1	1	yes	characteristic, complemented
243	D₄⋊C₈	—	89	2	no	—
244	D₄⋊C₈	—	89	2	no	—
245	D₄⋊C₈	—	89	2	no	—
246	D₄⋊C₈	C₂×D₈₉	1	2	yes	complemented
247	#322	—	89	1	no	—
248	#322	C₂×D₈₉	1	1	yes	characteristic, complemented
249	C₈²	—	89	1	no	—
250	C₈²	—	89	1	no	—
251	C₂²×D₄	—	89	2	no	—
252	C₂³×C₄	—	178	2	no	—
253	C₂×D₈	—	89	2	no	—
254	C₂×D₈	—	89	8	no	—
255	C₂×D₈	—	89	1	no	—
256	C₂×D₈	C₄×D₈₉	1	1	yes	characteristic
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	—	89	1	no	—
259	C₂²×C₈	—	89	1	no	—
260	C₂²×C₈	—	178	2	no	—
261	C₂²×C₈	—	178	2	no	—
262	C₂²×C₈	—	178	2	no	—
263	C₄×D₄	—	89	2	no	—
264	C₄×D₄	—	89	2	no	—
265	C₄×D₄	—	89	2	no	—
266	C₄×D₄	—	178	2	no	—
267	C₄×D₄	—	178	2	no	—
268	C₄×D₄	C₂²×D₈₉	1	2	yes	—
269	C₂×C₄⋊C₄	—	89	2	no	—
270	C₂×C₂²⋊C₄	—	178	2	no	—
271	C₂×C₄²	—	89	1	no	—
272	#107	—	89	1	no	—
273	#107	—	89	2	no	—
274	#107	C₄×D₈₉	1	1	yes	characteristic
275	C₄⋊C₈	—	89	2	no	—
276	C₄⋊C₈	—	89	2	no	—
277	C₄⋊C₈	—	178	1	no	—
278	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
279	#102	—	89	2	no	—
280	#102	—	89	2	no	—
281	#102	—	89	2	no	—
282	#102	C₄×D₈₉	1	2	yes	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	89	2	no	—
285	C₂²⋊C₈	—	178	2	no	—
286	C₂²⋊C₈	—	178	2	no	—
287	C₂²⋊C₈	—	178	1	no	—
288	C₂²⋊C₈	—	178	2	no	—
289	C₂²⋊C₈	—	178	2	no	—
290	C₄×C₈	—	89	1	no	—
291	C₄×C₈	—	89	1	no	—
292	C₄×C₈	—	89	1	no	—
293	C₄×C₈	—	89	1	no	—
294	C₄×C₈	—	89	1	no	—
295	C₄×C₈	—	178	2	no	—
296	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
297	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
299	C₂⁴	—	178	2	no	—
300	C₂×D₄	—	89	8	no	—
301	C₂×D₄	—	89	2	no	—
302	C₂×D₄	—	178	4	no	—
303	C₂×D₄	—	178	2	no	—
304	C₂×D₄	C₂×C₄×D₈₉	1	2	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	89	1	no	—
307	C₂²×C₄	—	89	1	no	—
308	C₂²×C₄	—	89	1	no	—
309	C₂²×C₄	—	178	2	no	—
310	C₂²×C₄	—	178	2	no	—
311	C₂²×C₄	—	178	2	no	—
312	C₂²×C₄	—	178	2	no	—
313	C₂²×C₄	—	712	2	no	—
314	C₂²×C₄	—	712	2	no	—
315	D₈	—	89	8	no	—
316	D₈	—	89	4	no	—
317	D₈	C₈×D₈₉	1	4	yes	complemented
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	8	2	no	—
321	C₂×C₈	—	89	1	no	—
322	C₂×C₈	—	89	4	no	—
323	C₂×C₈	—	89	1	no	—
324	C₂×C₈	—	89	2	no	—
325	C₂×C₈	—	178	2	no	—
326	C₂×C₈	—	178	2	no	—
327	C₂×C₈	—	178	1	no	—
328	C₂×C₈	—	712	2	no	—
329	C₂×C₈	—	712	2	no	—
330	C₂×C₈	—	712	2	no	—
331	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
332	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
333	C₂×C₈	D₄×D₈₉	1	2	yes	—
334	C₄⋊C₄	—	89	2	no	—
335	C₄⋊C₄	—	178	2	no	—
336	C₄⋊C₄	C₂×C₄×D₈₉	1	2	yes	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	178	2	no	—
339	C₂²⋊C₄	—	178	2	no	—
340	C₂²⋊C₄	—	178	2	no	—
341	C₄²	—	89	1	no	—
342	C₄²	—	89	1	no	—
343	C₄²	—	89	1	no	—
344	C₄²	C₂³×D₈₉	1	1	yes	characteristic
345	C₂³	—	2	2	no	—
346	C₂³	—	89	1	no	—
347	C₂³	—	178	8	no	—
348	C₂³	—	178	2	no	—
349	C₂³	—	712	2	no	—
350	C₂³	—	712	2	no	—
351	D₄	—	2	2	no	—
352	D₄	—	89	4	no	—
353	D₄	—	178	8	no	—
354	D₄	—	178	2	no	—
355	D₄	C₂×C₈×D₈₉	1	4	yes	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	89	1	no	—
360	C₂×C₄	—	89	2	no	—
361	C₂×C₄	—	89	2	no	—
362	C₂×C₄	—	89	1	no	—
363	C₂×C₄	—	89	1	no	—
364	C₂×C₄	—	356	1	no	—
365	C₂×C₄	—	356	2	no	—
366	C₂×C₄	—	356	2	no	—
367	C₂×C₄	—	178	2	no	—
368	C₂×C₄	—	178	2	no	—
369	C₂×C₄	—	712	2	no	—
370	C₂×C₄	—	712	2	no	—
371	C₂×C₄	—	712	2	no	—
372	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
373	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
374	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	2	1	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	89	2	no	—
380	C₈	—	356	1	no	—
381	C₈	—	356	2	no	—
382	C₈	—	178	2	no	—
383	C₈	—	178	1	no	—
384	C₈	C₂×C₈×D₈₉	1	2	yes	—
385	C₂²	—	2	4	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	89	2	no	—
389	C₂²	—	356	2	no	—
390	C₂²	—	356	2	no	—
391	C₂²	—	178	4	no	—
392	C₂²	—	178	1	no	—
393	C₂²	—	178	1	no	—
394	C₂²	—	712	8	no	—
395	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	4	2	no	—
398	C₄	—	89	2	no	—
399	C₄	—	356	2	no	—
400	C₄	—	178	1	no	—
401	C₄	—	178	1	no	—
402	C₄	C₂²×C₈×D₈₉	1	1	yes	characteristic
403	C₄	#131×D₈₉	1	1	yes	characteristic
404	C₄	#19152402	1	2	yes	—
405	C₂	—	4	4	no	—
406	C₂	—	356	4	no	—
407	C₂	—	178	2	no	—
408	C₂	C₈×D₄×D₈₉	1	1	yes	characteristic
409	C₂	#26029101	1	1	yes	characteristic
410	C₂	#26029166	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₄×C₈₉	C₂³×C₈
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1580	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×D₈×D₈₉	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1580	D₈₉
hypocenter	C₈₉	#17854
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1580

Complements

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

N	H ≅ G/N	type
1. #26029273	C₂	semidirect
3. #26019077	C₂	semidirect
4. #26019076	C₂	semidirect
5. #26019075	C₂	semidirect
6. C₈×#13083559	C₂	semidirect
7. #26019044	C₂	semidirect
8. #26018997	C₂	semidirect
9. #26018641	C₂	semidirect
10. #26018537	C₂	semidirect
11. C₈₉×#1580	C₂	semidirect
19. C₈×D₃₅₆	C₂²	semidirect
20. D₄×#10623494	C₂²	semidirect
21. #19151663	C₂²	semidirect
32. #19151350	C₂²	semidirect
33. #19151349	C₂²	semidirect
34. #19151327	C₂²	semidirect
35. D₄⋊#10623494	C₂²	semidirect
36. #19151325	C₂²	semidirect
37. #19151319	C₂²	semidirect
38. C₈×#10623494	C₂²	semidirect
39. C₈×#10623494	C₂²	semidirect
41. C₈×D₄×C₈₉	C₂²	semidirect
42. #334×C₈₉	C₂²	semidirect
43. D₄⋊C₈×C₈₉	C₂²	semidirect
44. #322×C₈₉	C₂²	semidirect
49. D₈×D₈₉	C₈	semidirect
97. D₄×D₈₉	C₂×C₈	semidirect
107. D₇₁₂	C₂×C₈	semidirect
108. #13083559	C₂×C₈	semidirect
118. C₈×D₈₉	C₂×C₈	semidirect
129. D₈×C₈₉	C₂×C₈	semidirect
211. #1580	D₈₉	semidirect
217. C₈₉	#17854	semidirect
231. C₈×D₄	C₂×D₈₉	semidirect
242. #334	C₂×D₈₉	semidirect
246. D₄⋊C₈	C₂×D₈₉	semidirect
248. #322	C₂×D₈₉	semidirect
317. D₈	C₈×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029273	2
C₄×D₈×D₈₉	2
#26019077	2
#26019076	2
#26019075	2
C₈×#13083559	2
#26019044	2
#26018997	2
#26018641	2
#26018537	2
C₈₉×#1580	2
#17854	89