Subgroups — #36707647

Order 22784.

682 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19152016	C₂	1	1	yes	maximal, characteristic, complemented
2	#26028962	C₂	1	1	yes	maximal, characteristic
3	#26022082	C₂	1	2	yes	maximal, complemented
4	#26022077	C₂	1	2	yes	maximal, complemented
5	#26022075	C₂	1	2	yes	maximal, complemented
6	C₁₆×C₂²⋊D₈₉	C₂	1	2	yes	maximal, complemented
7	C₂×#19151416	C₂	1	1	yes	maximal, characteristic, complemented
8	#26021866	C₂	1	1	yes	maximal, characteristic, complemented
9	#26021865	C₂	1	1	yes	maximal, characteristic, complemented
10	M₃₂×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#504×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668018	C₂²	1	1	yes	characteristic
13	#19152144	C₄	1	1	yes	characteristic
14	#19152016	—	2	4	no	—
15	C₂×#15667952	C₂²	1	1	yes	characteristic
16	C₂×#15667951	C₂²	1	2	yes	—
17	C₂²×#13083549	C₂²	1	1	yes	characteristic
18	C₂×C₁₆×D₈₉	C₂²	1	2	yes	—
19	#19151674	C₄	1	2	yes	—
20	#19151674	C₄	1	2	yes	—
21	C₈×C₂²⋊D₈₉	C₂²	1	2	yes	—
22	C₈×C₂²⋊D₈₉	C₂²	1	2	yes	—
23	#19151621	C₄	1	1	yes	characteristic
24	#19151566	C₄	1	1	yes	characteristic
25	#19151565	C₄	1	1	yes	characteristic
26	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
27	#19151416	C₂²	1	1	yes	characteristic
28	#19151416	C₂²	1	1	yes	characteristic
29	#19151416	C₂²	1	1	yes	characteristic
30	#19151416	C₂²	1	1	yes	characteristic
31	C₂²⋊#13083549	C₂²	1	2	yes	—
32	C₂²⋊#13083549	C₂²	1	2	yes	—
33	#19151377	C₂²	1	2	yes	—
34	#19151377	C₂²	1	2	yes	—
35	#19151373	C₂²	1	2	yes	—
36	C₁₆×Dic₈₉	C₂²	1	2	yes	—
37	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
38	#504×C₈₉	—	2	4	no	—
39	C₂×M₃₂×C₈₉	C₂²	1	2	yes	—
40	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
41	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
42	C₂²×C₁₆×C₈₉	C₂²	1	2	yes	—
43	C₂×#13083574	C₂×C₄	1	1	yes	characteristic
44	#15668018	—	2	2	no	—
45	#15668018	—	2	2	no	—
46	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
47	C₂×#13083557	C₂×C₄	1	2	yes	—
48	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₈₉	C₂³	1	2	yes	—
50	#15668010	C₈	1	1	yes	characteristic
51	#15668008	C₈	1	1	yes	characteristic
52	#15668001	C₈	1	1	yes	characteristic
53	#15667999	C₈	1	1	yes	characteristic
54	#15667984	C₈	1	2	yes	—
55	#15667984	C₈	1	2	yes	—
56	C₄×C₂²⋊D₈₉	C₂×C₄	1	2	yes	—
57	C₄×C₂²⋊D₈₉	C₂×C₄	1	2	yes	—
58	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
59	#15667952	—	2	2	no	—
60	#15667951	—	2	4	no	—
61	C₂×#13083549	—	2	2	no	—
62	C₂×#13083549	C₂³	1	2	yes	—
63	C₂×#13083549	C₂³	1	1	yes	characteristic
64	C₂×#13083549	C₂³	1	1	yes	characteristic
65	C₁₆×D₈₉	—	2	4	no	—
66	#15667941	C₂×C₄	1	2	yes	—
67	#15667941	C₂×C₄	1	2	yes	—
68	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
69	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
70	#15667924	C₂×C₄	1	2	yes	—
71	#15667924	C₂×C₄	1	2	yes	—
72	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
73	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
74	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
75	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
76	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
77	#131×C₈₉	—	2	2	no	—
78	#131×C₈₉	—	2	2	no	—
79	C₂×M₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
80	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
81	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
82	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
83	M₃₂×C₈₉	—	2	4	no	—
84	M₃₂×C₈₉	D₄	1	4	yes	complemented
85	C₂×C₁₆×C₈₉	—	2	2	no	—
86	C₂×C₁₆×C₈₉	—	2	4	no	—
87	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
88	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
89	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
90	#13083574	—	2	2	no	—
91	#13083574	—	2	2	no	—
92	C₂×Dic₁₇₈	C₂×C₈	1	1	yes	characteristic
93	C₂×D₃₅₆	C₂×C₈	1	1	yes	characteristic
94	C₂×C₂²⋊D₈₉	C₂×C₈	1	2	yes	—
95	C₂×C₂²⋊D₈₉	C₂×C₈	1	2	yes	—
96	C₂×C₂²⋊D₈₉	C₂×C₈	1	2	yes	—
97	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
98	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
99	C₂×C₄×D₈₉	C₂²×C₄	1	2	yes	—
100	#13083558	—	2	2	no	—
101	#13083557	—	2	4	no	—
102	C₂×#10623494	—	2	2	no	—
103	C₂×#10623494	C₂²×C₄	1	2	yes	—
104	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
105	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
106	C₈×D₈₉	—	2	2	no	—
107	C₈×D₈₉	—	2	2	no	—
108	#13083553	C₂×C₈	1	2	yes	—
109	#13083553	C₂×C₈	1	2	yes	—
110	C₂²⋊Dic₈₉	C₂×C₈	1	2	yes	—
111	C₂²⋊Dic₈₉	C₂×C₈	1	2	yes	—
112	#13083551	C₂×C₈	1	2	yes	—
113	#13083551	C₂×C₈	1	2	yes	—
114	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
115	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
116	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
117	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
118	#13083549	—	2	1	no	—
119	#13083549	—	2	1	no	—
120	#13083549	—	2	2	no	—
121	#41×C₈₉	—	2	2	no	—
122	#41×C₈₉	—	2	2	no	—
123	C₂×Q₈×C₈₉	C₂×C₈	1	1	yes	characteristic
124	C₂×D₄×C₈₉	C₂×C₈	1	2	yes	—
125	C₂×D₄×C₈₉	C₂×C₈	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
128	M₁₆×C₈₉	—	2	2	no	—
129	M₁₆×C₈₉	—	2	4	no	—
130	C₂×C₈×C₈₉	—	2	2	no	—
131	C₂×C₈×C₈₉	—	2	2	no	—
132	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₈₉	#41	1	2	yes	—
136	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
137	C₁₆×C₈₉	—	2	1	no	—
138	C₁₆×C₈₉	—	2	1	no	—
139	C₁₆×C₈₉	C₂×D₄	1	4	yes	—
140	C₂³×C₈₉	C₂²×C₈	1	2	yes	—
141	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
142	C₂²×D₈₉	C₂²×C₈	1	2	yes	—
143	Q₈×C₈₉	—	2	2	no	—
144	D₄×C₈₉	—	2	4	no	—
145	D₄×C₈₉	—	2	2	no	—
146	C₂×C₄×C₈₉	—	2	2	no	—
147	C₂×C₄×C₈₉	—	2	2	no	—
148	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
150	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₄×C₈₉	#131	1	2	yes	—
152	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
153	C₂²⋊D₈₉	—	2	4	no	—
154	C₂²⋊D₈₉	—	2	4	no	—
155	C₂²⋊D₈₉	—	4	2	no	—
156	C₂×Dic₈₉	—	2	2	no	—
157	C₂×Dic₈₉	—	4	1	no	—
158	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
159	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
160	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
161	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
162	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
163	D₃₅₆	—	2	2	no	—
164	C₄×D₈₉	—	2	2	no	—
165	C₄×D₈₉	—	2	2	no	—
166	Dic₁₇₈	—	2	2	no	—
167	C₈×C₈₉	—	2	2	no	—
168	C₈×C₈₉	C₄×D₄	1	2	yes	—
169	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
170	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
171	#10623494	—	2	2	no	—
172	#10623494	—	2	1	no	—
173	#10623494	—	2	1	no	—
174	C₂²×C₈₉	—	2	1	no	—
175	C₂²×C₈₉	—	2	1	no	—
176	C₂²×C₈₉	—	2	2	no	—
177	C₂²×C₈₉	—	2	2	no	—
178	C₂²×C₈₉	—	2	2	no	—
179	C₂²×C₈₉	C₈×D₄	1	2	yes	—
180	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
181	C₂×D₈₉	—	2	2	no	—
182	C₂×D₈₉	—	2	2	no	—
183	C₂×D₈₉	—	2	2	no	—
184	C₄×C₈₉	—	2	2	no	—
185	C₄×C₈₉	C₈×D₄	1	2	yes	—
186	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
187	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
188	Dic₈₉	—	2	1	no	—
189	Dic₈₉	—	2	1	no	—
190	Dic₈₉	—	2	1	no	—
191	Dic₈₉	—	2	2	no	—
192	Dic₈₉	#504	1	2	yes	complemented
193	#33438	—	89	1	no	maximal, Sylow
194	C₂×C₈₉	—	2	2	no	—
195	C₂×C₈₉	—	4	2	no	—
196	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
197	C₂×C₈₉	C₂×#504	1	1	yes	characteristic
198	C₂×C₈₉	#3407	1	1	yes	characteristic
199	D₈₉	—	4	2	no	—
200	C₂×#504	—	89	1	no	—
201	C₂×#504	D₈₉	1	1	yes	characteristic, complemented
202	#2931	—	89	1	no	—
203	#2169	—	89	2	no	—
204	#2168	—	89	2	no	—
205	#2168	—	89	2	no	—
206	D₄×C₁₆	—	89	2	no	—
207	C₂×C₄⋊C₁₆	—	89	1	no	—
208	#2113	—	89	1	no	—
209	#2113	—	89	1	no	—
210	C₄×M₃₂	—	89	1	no	—
211	C₈₉	#33438	1	1	yes	characteristic, complemented, Sylow
212	C₂×#131	—	89	1	no	—
213	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
214	#532	—	89	1	no	—
215	#504	—	2	4	no	—
216	#504	—	178	4	no	—
217	C₂×M₃₂	—	89	1	no	—
218	C₂×M₃₂	—	89	2	no	—
219	C₂×M₃₂	C₂×D₈₉	1	2	yes	—
220	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
221	C₂²×C₁₆	—	89	1	no	—
222	C₂²×C₁₆	—	89	2	no	—
223	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
224	C₂²×C₁₆	C₂×D₈₉	1	2	yes	—
225	#436	—	89	2	no	—
226	#436	—	89	2	no	—
227	C₈×D₄	—	89	2	no	—
228	C₈×D₄	—	89	2	no	—
229	#423	—	89	1	no	—
230	#408	—	89	1	no	—
231	#408	—	89	1	no	—
232	C₂×C₄×C₈	—	89	1	no	—
233	C₄⋊C₁₆	—	89	1	no	—
234	C₄⋊C₁₆	—	89	1	no	—
235	C₄⋊C₁₆	—	89	1	no	—
236	C₄⋊C₁₆	—	89	1	no	—
237	C₂²⋊C₁₆	—	89	2	no	—
238	C₂²⋊C₁₆	—	89	2	no	—
239	C₂²⋊C₁₆	—	89	2	no	—
240	C₂²⋊C₁₆	—	89	2	no	—
241	#346	—	89	2	no	—
242	C₄×C₁₆	—	89	2	no	—
243	C₂×#41	—	89	1	no	—
244	C₂×#41	C₄×D₈₉	1	1	yes	characteristic
245	#131	—	2	2	no	—
246	#131	—	2	2	no	—
247	#131	—	178	2	no	—
248	#131	—	178	2	no	—
249	C₂×M₁₆	—	89	1	no	—
250	C₂×M₁₆	—	89	2	no	—
251	C₂×M₁₆	C₄×D₈₉	1	1	yes	characteristic
252	C₂×M₁₆	C₄×D₈₉	1	2	yes	—
253	C₂²×C₈	—	89	1	no	—
254	C₂²×C₈	—	89	2	no	—
255	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
256	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
257	C₄⋊Q₈	—	89	1	no	—
258	#127	—	89	1	no	—
259	#124	—	89	1	no	—
260	#124	—	89	1	no	—
261	#121	—	89	2	no	—
262	#121	—	89	2	no	—
263	C₄×D₄	—	89	2	no	—
264	C₄×D₄	—	89	2	no	—
265	C₂×C₄²	—	89	1	no	—
266	M₃₂	—	2	4	no	—
267	M₃₂	—	178	2	no	—
268	M₃₂	—	178	4	no	—
269	M₃₂	C₂²⋊D₈₉	1	4	yes	complemented
270	C₂×C₁₆	—	2	2	no	—
271	C₂×C₁₆	—	2	4	no	—
272	C₂×C₁₆	—	89	2	no	—
273	C₂×C₁₆	—	89	1	no	—
274	C₂×C₁₆	—	89	1	no	—
275	C₂×C₁₆	—	178	2	no	—
276	C₂×C₁₆	—	178	4	no	—
277	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
278	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
279	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
280	C₄⋊C₈	—	89	2	no	—
281	C₄⋊C₈	—	89	2	no	—
282	C₂²⋊C₈	—	89	2	no	—
283	C₂²⋊C₈	—	89	2	no	—
284	C₂²⋊C₈	—	89	2	no	—
285	C₂²⋊C₈	—	89	2	no	—
286	C₄×C₈	—	89	1	no	—
287	C₄×C₈	—	89	1	no	—
288	C₄×C₈	—	89	1	no	—
289	C₄×C₈	—	89	1	no	—
290	#41	—	2	2	no	—
291	#41	—	2	2	no	—
292	#41	—	178	2	no	—
293	#41	—	178	2	no	—
294	C₂×Q₈	—	89	1	no	—
295	C₂×Q₈	C₈×D₈₉	1	1	yes	characteristic
296	C₂×D₄	—	89	2	no	—
297	C₂×D₄	—	89	2	no	—
298	C₂×D₄	—	89	2	no	—
299	C₂×D₄	—	89	1	no	—
300	C₂×D₄	C₈×D₈₉	1	2	yes	—
301	C₂×D₄	C₈×D₈₉	1	1	yes	characteristic
302	C₂²×C₄	—	89	1	no	—
303	C₂²×C₄	—	89	1	no	—
304	C₂²×C₄	—	89	2	no	—
305	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
306	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
307	M₁₆	—	2	2	no	—
308	M₁₆	—	2	4	no	—
309	M₁₆	—	178	2	no	—
310	M₁₆	—	178	4	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	89	1	no	—
314	C₂×C₈	—	89	1	no	—
315	C₂×C₈	—	89	2	no	—
316	C₂×C₈	—	178	2	no	—
317	C₂×C₈	—	178	2	no	—
318	C₂×C₈	—	178	2	no	—
319	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
320	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
321	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
322	C₂×C₈	#13083574	1	2	yes	—
323	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
324	C₄⋊C₄	—	89	2	no	—
325	C₄⋊C₄	—	89	2	no	—
326	C₂²⋊C₄	—	89	2	no	—
327	C₂²⋊C₄	—	89	2	no	—
328	C₂²⋊C₄	—	89	2	no	—
329	C₂²⋊C₄	—	89	2	no	—
330	C₄²	—	89	1	no	—
331	C₄²	—	89	1	no	—
332	C₄²	—	89	1	no	—
333	C₄²	—	89	1	no	—
334	C₁₆	—	2	1	no	—
335	C₁₆	—	2	1	no	—
336	C₁₆	—	178	1	no	—
337	C₁₆	—	178	1	no	—
338	C₁₆	—	178	2	no	—
339	C₁₆	C₂×C₂²⋊D₈₉	1	4	yes	—
340	C₂³	—	89	2	no	—
341	C₂³	C₂×C₈×D₈₉	1	2	yes	—
342	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
343	Q₈	—	2	2	no	—
344	Q₈	—	178	2	no	—
345	D₄	—	2	4	no	—
346	D₄	—	2	2	no	—
347	D₄	—	356	2	no	—
348	D₄	—	178	4	no	—
349	D₄	—	178	4	no	—
350	D₄	—	178	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	89	1	no	—
354	C₂×C₄	—	89	1	no	—
355	C₂×C₄	—	89	1	no	—
356	C₂×C₄	—	89	1	no	—
357	C₂×C₄	—	89	2	no	—
358	C₂×C₄	—	356	1	no	—
359	C₂×C₄	—	178	2	no	—
360	C₂×C₄	—	178	2	no	—
361	C₂×C₄	—	178	2	no	—
362	C₂×C₄	C₄×C₂²⋊D₈₉	1	2	yes	—
363	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
364	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
365	C₂×C₄	#15668018	1	2	yes	—
366	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
367	C₈	—	2	2	no	—
368	C₈	—	178	2	no	—
369	C₈	—	178	1	no	—
370	C₈	—	178	1	no	—
371	C₈	C₄×C₂²⋊D₈₉	1	2	yes	—
372	C₈	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
373	C₈	C₂×#13083574	1	1	yes	characteristic
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	178	2	no	—
380	C₂²	—	178	2	no	—
381	C₂²	—	178	2	no	—
382	C₂²	C₈×C₂²⋊D₈₉	1	2	yes	—
383	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
384	C₄	—	2	2	no	—
385	C₄	—	89	2	no	—
386	C₄	—	178	2	no	—
387	C₄	—	178	1	no	—
388	C₄	—	178	1	no	—
389	C₄	—	178	1	no	—
390	C₄	C₈×C₂²⋊D₈₉	1	2	yes	—
391	C₄	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
392	C₄	C₂×#15668018	1	1	yes	characteristic
393	C₂	—	2	2	no	—
394	C₂	—	4	2	no	—
395	C₂	—	356	2	no	—
396	C₂	C₂×C₈×C₂²⋊D₈₉	1	1	yes	characteristic
397	C₂	#504×D₈₉	1	1	yes	characteristic
398	C₂	#26033353	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂³×C₈
Fitting	C₂×#504×C₈₉	C₂
prime radical	#19152144	C₄
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	C₂×#504	D₈₉
hypocenter	C₈₉	#33438
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₂×#504

Complements

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

N	H ≅ G/N	type
1. C₂×#19152016	C₂	semidirect
3. #26022082	C₂	semidirect
4. #26022077	C₂	semidirect
5. #26022075	C₂	semidirect
6. C₁₆×C₂²⋊D₈₉	C₂	semidirect
7. C₂×#19151416	C₂	semidirect
8. #26021866	C₂	semidirect
9. #26021865	C₂	semidirect
10. M₃₂×Dic₈₉	C₂	semidirect
11. C₂×#504×C₈₉	C₂	semidirect
84. M₃₂×C₈₉	D₄	semidirect
192. Dic₈₉	#504	semidirect
201. C₂×#504	D₈₉	semidirect
211. C₈₉	#33438	semidirect
269. M₃₂	C₂²⋊D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19152016	2
#26028962	2
#26022082	2
#26022077	2
#26022075	2
C₁₆×C₂²⋊D₈₉	2
C₂×#19151416	2
#26021866	2
#26021865	2
M₃₂×Dic₈₉	2
C₂×#504×C₈₉	2
#33438	89