Subgroups — #36708033

Order 22784.

574 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028946	C₂	1	1	yes	maximal, characteristic
2	#26022081	C₂	1	2	yes	maximal, complemented
3	#26022080	C₂	1	2	yes	maximal, complemented
4	#26022077	C₂	1	2	yes	maximal, complemented
5	C₁₆×C₂²⋊D₈₉	C₂	1	2	yes	maximal, complemented
6	#26022056	C₂	1	2	yes	maximal, complemented
7	#26021864	C₂	1	2	yes	maximal, complemented
8	#26021863	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₂²⋊C₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15668018	C₂²	1	1	yes	characteristic
11	#19152109	C₄	1	1	yes	characteristic
12	C₂×#15667952	C₂²	1	1	yes	characteristic
13	C₂×#15667952	C₂²	1	1	yes	characteristic
14	C₂×#15667951	C₂²	1	2	yes	complemented
15	C₂×C₁₆×D₈₉	C₂²	1	2	yes	complemented
16	#19151669	C₄	1	2	yes	—
17	#19151669	C₄	1	2	yes	—
18	C₈×C₂²⋊D₈₉	C₂²	1	2	yes	—
19	C₈×C₂²⋊D₈₉	C₂²	1	2	yes	—
20	#19151624	C₄	1	1	yes	characteristic
21	#19151564	C₄	1	1	yes	characteristic
22	#19151562	C₄	1	1	yes	characteristic
23	#19151553	C₂²	1	1	yes	characteristic
24	#19151416	C₂²	1	2	yes	complemented
25	#19151416	C₂²	1	2	yes	complemented
26	C₂²⋊#13083549	C₂²	1	2	yes	—
27	C₂²⋊#13083549	C₂²	1	2	yes	—
28	#19151377	C₂²	1	2	yes	complemented
29	#19151377	C₂²	1	2	yes	complemented
30	#19151373	C₂²	1	2	yes	complemented
31	C₁₆×Dic₈₉	C₂²	1	2	yes	complemented
32	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
34	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
35	C₂²⋊C₁₆×C₈₉	C₂²	1	2	yes	—
36	C₂²⋊C₁₆×C₈₉	C₂²	1	2	yes	—
37	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
38	#15668018	—	4	1	no	—
39	#15668018	—	4	1	no	—
40	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
41	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
42	C₂×#13083557	C₂×C₄	1	2	yes	—
43	C₂×C₈×D₈₉	C₂³	1	2	yes	—
44	#15667995	C₈	1	2	yes	—
45	#15667991	C₈	1	1	yes	characteristic
46	#15667991	C₈	1	1	yes	characteristic
47	#15667986	C₈	1	1	yes	characteristic
48	#15667986	C₈	1	1	yes	characteristic
49	#15667981	C₈	1	2	yes	—
50	C₄×C₂²⋊D₈₉	C₂×C₄	1	2	yes	—
51	C₄×C₂²⋊D₈₉	C₂×C₄	1	2	yes	—
52	#15667971	C₂×C₄	1	1	yes	characteristic
53	#15667952	—	4	1	no	—
54	#15667952	—	4	1	no	—
55	#15667951	—	4	2	no	—
56	C₂×#13083549	C₂³	1	2	yes	—
57	C₂×#13083549	C₂³	1	2	yes	—
58	C₁₆×D₈₉	—	4	2	no	—
59	#15667941	C₂×C₄	1	2	yes	—
60	#15667941	C₂×C₄	1	2	yes	—
61	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
62	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
63	#15667924	C₂×C₄	1	2	yes	—
64	#15667924	C₂×C₄	1	2	yes	—
65	#15667922	C₂×C₄	1	2	yes	—
66	C₈×Dic₈₉	C₂³	1	2	yes	—
67	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₈×C₈₉	—	4	1	no	—
69	C₂²×C₈×C₈₉	—	4	1	no	—
70	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
73	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₂×C₁₆×C₈₉	—	4	1	no	—
77	C₂×C₁₆×C₈₉	—	4	1	no	—
78	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
79	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
80	#13083574	—	4	1	no	—
81	#13083574	—	4	1	no	—
82	C₂×Dic₁₇₈	C₂×C₈	1	1	yes	characteristic
83	C₂×D₃₅₆	C₂×C₈	1	1	yes	characteristic
84	C₂×C₂²⋊D₈₉	C₂×C₈	1	2	yes	—
85	C₂×C₂²⋊D₈₉	C₂×C₈	1	2	yes	—
86	C₂×C₂²⋊D₈₉	C₂×C₈	1	2	yes	—
87	C₂×C₄×D₈₉	C₂²×C₄	1	2	yes	—
88	#13083558	—	4	1	no	—
89	#13083558	—	4	1	no	—
90	#13083557	—	4	2	no	—
91	C₂×#10623494	C₂²×C₄	1	2	yes	—
92	C₂×#10623494	C₂²×C₄	1	2	yes	—
93	C₈×D₈₉	—	2	2	no	—
94	C₈×D₈₉	—	2	2	no	—
95	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
96	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
97	#13083553	C₂×C₈	1	2	yes	—
98	#13083553	C₂×C₈	1	2	yes	—
99	C₂²⋊Dic₈₉	C₂×C₈	1	2	yes	—
100	C₂²⋊Dic₈₉	C₂×C₈	1	2	yes	—
101	C₂²⋊Dic₈₉	C₂×C₈	1	2	yes	—
102	#13083551	C₂×C₈	1	2	yes	—
103	#13083551	C₂×C₈	1	2	yes	—
104	C₄×Dic₈₉	C₂²×C₄	1	2	yes	—
105	#13083549	—	2	2	no	—
106	#13083549	—	2	2	no	—
107	C₂⁴×C₈₉	C₂×C₈	1	1	yes	characteristic
108	C₂²×C₄×C₈₉	—	4	1	no	—
109	C₂²×C₄×C₈₉	—	4	1	no	—
110	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
111	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
112	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
113	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₈₉	—	2	1	no	—
117	C₂×C₈×C₈₉	—	2	1	no	—
118	C₂×C₈×C₈₉	—	2	1	no	—
119	C₂×C₈×C₈₉	—	2	1	no	—
120	C₂×C₈×C₈₉	—	2	1	no	—
121	C₂×C₈×C₈₉	—	2	1	no	—
122	C₂×C₈×C₈₉	—	4	1	no	—
123	C₂×C₈×C₈₉	—	4	1	no	—
124	C₂×C₈×C₈₉	—	4	1	no	—
125	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
129	C₁₆×C₈₉	—	2	2	no	—
130	C₁₆×C₈₉	—	2	2	no	—
131	C₂³×C₈₉	—	2	2	no	—
132	C₂³×C₈₉	—	4	1	no	—
133	C₂³×C₈₉	—	4	1	no	—
134	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
135	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
136	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
137	C₂²×D₈₉	C₂²×C₈	1	2	yes	—
138	C₂×C₄×C₈₉	—	2	1	no	—
139	C₂×C₄×C₈₉	—	2	1	no	—
140	C₂×C₄×C₈₉	—	2	1	no	—
141	C₂×C₄×C₈₉	—	2	1	no	—
142	C₂×C₄×C₈₉	—	2	1	no	—
143	C₂×C₄×C₈₉	—	2	1	no	—
144	C₂×C₄×C₈₉	—	4	1	no	—
145	C₂×C₄×C₈₉	—	4	1	no	—
146	C₂×C₄×C₈₉	—	4	1	no	—
147	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
148	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
149	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
150	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
151	C₂²⋊D₈₉	—	2	4	no	—
152	C₂²⋊D₈₉	—	4	2	no	—
153	C₂²⋊D₈₉	—	4	2	no	—
154	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
155	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
156	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
157	D₃₅₆	—	4	1	no	—
158	C₄×D₈₉	—	2	2	no	—
159	C₄×D₈₉	—	2	2	no	—
160	Dic₁₇₈	—	4	1	no	—
161	C₈×C₈₉	—	2	1	no	—
162	C₈×C₈₉	—	2	1	no	—
163	C₈×C₈₉	—	2	1	no	—
164	C₈×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
165	C₈×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
166	#10623494	—	2	2	no	—
167	#10623494	—	2	2	no	—
168	C₂²×C₈₉	—	2	1	no	—
169	C₂²×C₈₉	—	2	1	no	—
170	C₂²×C₈₉	—	2	1	no	—
171	C₂²×C₈₉	—	2	1	no	—
172	C₂²×C₈₉	—	2	1	no	—
173	C₂²×C₈₉	—	2	1	no	—
174	C₂²×C₈₉	—	2	1	no	—
175	C₂²×C₈₉	—	2	1	no	—
176	C₂²×C₈₉	—	4	4	no	—
177	C₂²×C₈₉	#504	1	2	yes	—
178	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
179	C₂×D₈₉	—	2	2	no	—
180	C₂×D₈₉	—	2	2	no	—
181	C₂×D₈₉	—	2	2	no	—
182	C₄×C₈₉	—	2	1	no	—
183	C₄×C₈₉	—	2	1	no	—
184	C₄×C₈₉	—	2	1	no	—
185	C₄×C₈₉	#518	1	1	yes	characteristic
186	C₄×C₈₉	#568	1	1	yes	characteristic
187	Dic₈₉	—	2	2	no	—
188	Dic₈₉	—	2	2	no	—
189	Dic₈₉	—	2	2	no	—
190	#33490	—	89	1	no	maximal, Sylow
191	C₂×C₈₉	—	2	2	no	—
192	C₂×C₈₉	—	4	1	no	—
193	C₂×C₈₉	—	4	1	no	—
194	C₂×C₈₉	#2972	1	1	yes	characteristic
195	C₂×C₈₉	C₂×#504	1	1	yes	characteristic
196	C₂×C₈₉	#3407	1	1	yes	characteristic
197	D₈₉	—	4	2	no	—
198	#2929	—	89	1	no	—
199	#2169	—	89	2	no	—
200	#2168	—	89	2	no	—
201	#2168	—	89	2	no	—
202	D₄×C₁₆	—	89	2	no	—
203	#2164	—	89	2	no	—
204	#2113	—	89	2	no	—
205	#2112	—	89	1	no	—
206	C₂×C₂²⋊C₁₆	D₈₉	1	1	yes	characteristic, complemented
207	C₈₉	#33490	1	1	yes	characteristic, complemented, Sylow
208	C₂×#131	—	89	1	no	—
209	C₂³×C₈	C₂×D₈₉	1	1	yes	characteristic
210	#525	—	89	1	no	—
211	C₂×M₃₂	—	89	1	no	—
212	C₂×M₃₂	—	89	1	no	—
213	C₂×M₃₂	—	89	2	no	—
214	C₂²×C₁₆	—	89	2	no	—
215	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
216	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
217	#435	—	89	2	no	—
218	#435	—	89	2	no	—
219	C₈×D₄	—	89	2	no	—
220	C₈×D₄	—	89	2	no	—
221	#424	—	89	1	no	—
222	#408	—	89	1	no	—
223	#407	—	89	1	no	—
224	#405	—	89	1	no	—
225	C₄⋊C₁₆	—	89	2	no	—
226	C₄⋊C₁₆	—	89	2	no	—
227	C₂²⋊C₁₆	—	89	2	no	—
228	C₂²⋊C₁₆	—	89	2	no	—
229	C₂²⋊C₁₆	—	89	2	no	—
230	C₂²⋊C₁₆	—	89	2	no	—
231	C₂²⋊C₁₆	C₂×D₈₉	1	2	yes	—
232	C₂²⋊C₁₆	C₂×D₈₉	1	2	yes	—
233	#346	—	89	2	no	—
234	C₄×C₁₆	—	89	2	no	—
235	C₂×#41	—	89	1	no	—
236	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
237	#131	—	356	1	no	—
238	#131	—	356	1	no	—
239	C₂×M₁₆	—	89	1	no	—
240	C₂×M₁₆	—	89	1	no	—
241	C₂×M₁₆	—	89	2	no	—
242	C₂²×C₈	—	4	1	no	—
243	C₂²×C₈	—	4	1	no	—
244	C₂²×C₈	—	89	2	no	—
245	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
246	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
247	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
248	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
249	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
250	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
251	#123	—	89	2	no	—
252	C₂²⋊Q₈	—	89	1	no	—
253	C₂²⋊Q₈	—	89	1	no	—
254	#121	—	89	1	no	—
255	#121	—	89	1	no	—
256	#120	—	89	2	no	—
257	C₄×D₄	—	89	2	no	—
258	C₄×D₄	—	89	2	no	—
259	#117	—	89	1	no	—
260	M₃₂	—	356	2	no	—
261	M₃₂	—	356	1	no	—
262	M₃₂	—	356	1	no	—
263	C₂×C₁₆	—	4	1	no	—
264	C₂×C₁₆	—	4	1	no	—
265	C₂×C₁₆	—	89	2	no	—
266	C₂×C₁₆	—	89	2	no	—
267	C₂×C₁₆	—	356	2	no	—
268	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
269	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
270	C₄⋊C₈	—	89	2	no	—
271	C₄⋊C₈	—	89	2	no	—
272	C₂²⋊C₈	—	89	2	no	—
273	C₂²⋊C₈	—	89	2	no	—
274	C₂²⋊C₈	—	89	2	no	—
275	C₂²⋊C₈	—	89	2	no	—
276	#97	—	89	2	no	—
277	C₄×C₈	—	89	2	no	—
278	C₂⁴	C₈×D₈₉	1	1	yes	characteristic
279	#41	—	356	1	no	—
280	#41	—	356	1	no	—
281	C₂×Q₈	—	89	1	no	—
282	C₂×D₄	—	89	2	no	—
283	C₂×D₄	—	89	2	no	—
284	C₂×D₄	—	89	2	no	—
285	C₂×D₄	—	89	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	89	2	no	—
289	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
290	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
291	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
295	M₁₆	—	356	2	no	—
296	M₁₆	—	356	1	no	—
297	M₁₆	—	356	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	4	1	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	89	2	no	—
308	C₂×C₈	—	89	2	no	—
309	C₂×C₈	—	178	2	no	—
310	C₂×C₈	—	178	2	no	—
311	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
312	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
313	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
314	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
315	C₄⋊C₄	—	89	1	no	—
316	C₄⋊C₄	—	89	1	no	—
317	C₄⋊C₄	—	89	2	no	—
318	C₄⋊C₄	—	89	2	no	—
319	C₂²⋊C₄	—	89	2	no	—
320	C₂²⋊C₄	—	89	2	no	—
321	C₂²⋊C₄	—	89	2	no	—
322	C₂²⋊C₄	—	89	2	no	—
323	C₂²⋊C₄	—	89	2	no	—
324	C₄²	—	89	2	no	—
325	C₁₆	—	2	2	no	—
326	C₁₆	—	2	2	no	—
327	C₁₆	—	178	2	no	—
328	C₁₆	—	178	2	no	—
329	C₂³	—	2	2	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	4	1	no	—
332	C₂³	—	89	2	no	—
333	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
334	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
335	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
336	Q₈	—	356	1	no	—
337	D₄	—	356	1	no	—
338	D₄	—	356	2	no	—
339	D₄	—	356	2	no	—
340	D₄	—	178	4	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	89	2	no	—
351	C₂×C₄	—	89	2	no	—
352	C₂×C₄	—	89	2	no	—
353	C₂×C₄	—	178	2	no	—
354	C₂×C₄	—	178	2	no	—
355	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
356	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
357	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	—	178	2	no	—
363	C₈	—	178	2	no	—
364	C₈	#15668057	1	1	yes	characteristic
365	C₈	#15668057	1	1	yes	characteristic
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	2	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	178	2	no	—
376	C₂²	—	178	2	no	—
377	C₂²	—	178	2	no	—
378	C₂²	#19152014	1	2	yes	—
379	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	178	2	no	—
384	C₄	—	178	2	no	—
385	C₄	—	178	2	no	—
386	C₄	#19152071	1	1	yes	characteristic
387	C₄	#19152364	1	1	yes	characteristic
388	C₂	—	2	2	no	—
389	C₂	—	4	1	no	—
390	C₂	—	4	1	no	—
391	C₂	—	356	2	no	—
392	C₂	#26029274	1	1	yes	characteristic
393	C₂	C₂×#19152014	1	1	yes	characteristic
394	C₂	#26033354	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂³×C₈
Fitting	C₂×C₂²⋊C₁₆×C₈₉	C₂
prime radical	#19152109	C₄
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	C₂×C₂²⋊C₁₆	D₈₉
hypocenter	C₈₉	#33490
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
2. #26022081	C₂	semidirect
3. #26022080	C₂	semidirect
4. #26022077	C₂	semidirect
5. C₁₆×C₂²⋊D₈₉	C₂	semidirect
6. #26022056	C₂	semidirect
7. #26021864	C₂	semidirect
8. #26021863	C₂	semidirect
9. C₂×C₂²⋊C₁₆×C₈₉	C₂	semidirect
14. C₂×#15667951	C₂²	semidirect
15. C₂×C₁₆×D₈₉	C₂²	semidirect
24. #19151416	C₂²	semidirect
25. #19151416	C₂²	semidirect
28. #19151377	C₂²	semidirect
29. #19151377	C₂²	semidirect
30. #19151373	C₂²	semidirect
31. C₁₆×Dic₈₉	C₂²	semidirect
206. C₂×C₂²⋊C₁₆	D₈₉	semidirect
207. C₈₉	#33490	semidirect

Maximal subgroups

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

subgroup	index
#26028946	2
#26022081	2
#26022080	2
#26022077	2
C₁₆×C₂²⋊D₈₉	2
#26022056	2
#26021864	2
#26021863	2
C₂×C₂²⋊C₁₆×C₈₉	2
#33490	89