Subgroups — #36707680

Order 22784.

648 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26033353	C₂	1	2	yes	maximal, complemented
2	#443×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#26022095	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022094	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022093	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022087	C₂	1	2	yes	maximal, complemented
7	#26022086	C₂	1	2	yes	maximal, complemented
8	#364×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#26021878	C₂	1	2	yes	maximal, complemented
10	#26021845	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2171	C₂	1	1	yes	maximal, characteristic, complemented
12	#135×D₈₉	C₄	1	1	yes	characteristic
13	#131×D₈₉	C₂²	1	2	yes	—
14	#19152016	—	2	2	no	—
15	#19152016	C₂²	1	2	yes	complemented
16	#19152015	C₂²	1	2	yes	complemented
17	#19152014	—	2	2	no	—
18	#19152014	C₂²	1	2	yes	complemented
19	C₂×#15667951	—	2	2	no	—
20	C₂×#15667951	C₂²	1	1	yes	characteristic
21	C₂×#15667951	C₂²	1	1	yes	characteristic
22	M₃₂×D₈₉	—	2	2	no	—
23	M₃₂×D₈₉	C₂²	1	2	yes	—
24	#19151716	C₂²	1	1	yes	characteristic
25	#19151715	C₄	1	1	yes	characteristic
26	#19151714	C₄	1	1	yes	characteristic
27	#19151713	C₂²	1	2	yes	—
28	#19151712	C₄	1	2	yes	—
29	#108×D₈₉	C₄	1	1	yes	characteristic
30	#104×D₈₉	C₄	1	2	yes	—
31	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
32	#19151419	C₂²	1	1	yes	characteristic, complemented
33	#19151418	C₂²	1	2	yes	complemented
34	#19151383	C₂²	1	2	yes	complemented
35	#19151382	C₂²	1	2	yes	complemented
36	#19151381	C₂²	1	2	yes	complemented
37	#19151374	C₂²	1	1	yes	characteristic, complemented
38	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic, complemented
40	#504×C₈₉	C₂²	1	2	yes	complemented
41	#443×C₈₉	C₂²	1	1	yes	characteristic
42	#364×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	#350×C₈₉	C₂²	1	2	yes	complemented
44	#346×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	#41×D₈₉	C₂×C₄	1	2	yes	—
46	#15668035	C₈	1	1	yes	characteristic
47	#15668034	C₂×C₄	1	1	yes	characteristic
48	#15668033	C₈	1	2	yes	—
49	#15668032	C₂×C₄	1	2	yes	—
50	#15668031	C₈	1	1	yes	characteristic
51	Q₁₆×D₈₉	C₈	1	1	yes	characteristic
52	SD₁₆×D₈₉	C₈	1	2	yes	—
53	D₈×D₈₉	C₈	1	1	yes	characteristic
54	#15668020	—	2	2	no	—
55	#15668020	C₂×C₄	1	2	yes	—
56	#15668019	C₂×C₄	1	2	yes	—
57	#15668018	—	2	2	no	—
58	#15668018	C₂³	1	2	yes	—
59	M₁₆×D₈₉	—	2	2	no	—
60	M₁₆×D₈₉	C₂×C₄	1	2	yes	—
61	C₂×C₈×D₈₉	—	2	2	no	—
62	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
64	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
65	#15667952	—	2	2	no	—
66	#15667952	C₂³	1	2	yes	—
67	#15667951	—	2	2	no	—
68	#15667951	—	2	1	no	—
69	#15667951	—	2	1	no	—
70	#15667951	—	2	2	no	—
71	#15667951	—	2	2	no	—
72	#15667951	D₄	1	2	yes	—
73	#15667951	D₄	1	2	yes	—
74	C₂×#13083549	—	2	2	no	—
75	C₂×#13083549	C₂³	1	1	yes	characteristic
76	C₂×#13083549	C₂³	1	1	yes	characteristic
77	C₁₆×D₈₉	—	2	2	no	—
78	C₁₆×D₈₉	—	2	2	no	—
79	C₁₆×D₈₉	—	2	2	no	—
80	#15667948	C₂×C₄	1	1	yes	characteristic
81	#15667947	C₂×C₄	1	2	yes	—
82	#15667940	C₂×C₄	1	2	yes	—
83	#15667939	C₂×C₄	1	2	yes	—
84	#15667938	C₂×C₄	1	2	yes	—
85	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
88	#135×C₈₉	C₂×C₄	1	1	yes	characteristic
89	#131×C₈₉	C₂³	1	2	yes	—
90	M₃₂×C₈₉	—	2	2	no	—
91	M₃₂×C₈₉	C₂³	1	2	yes	—
92	C₂×C₁₆×C₈₉	—	2	2	no	—
93	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
95	#108×C₈₉	C₂×C₄	1	1	yes	characteristic
96	#104×C₈₉	C₂×C₄	1	2	yes	—
97	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
98	#13083575	C₂×C₈	1	2	yes	—
99	#13083574	—	2	2	no	—
100	#13083574	C₂²×C₄	1	2	yes	—
101	#13083573	—	2	2	no	—
102	#13083573	C₂×C₈	1	2	yes	—
103	Q₈×D₈₉	C₂×C₈	1	2	yes	—
104	D₄×D₈₉	—	2	2	no	—
105	D₄×D₈₉	C₂×C₈	1	2	yes	—
106	C₂×C₄×D₈₉	—	2	2	no	—
107	C₂×C₄×D₈₉	—	2	1	no	—
108	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
109	Dic₃₅₆	C₂×C₈	1	1	yes	characteristic
110	#13083564	C₂×C₈	1	2	yes	—
111	#13083563	C₂×C₈	1	2	yes	—
112	#13083562	C₂×C₈	1	2	yes	—
113	#13083561	C₂×C₈	1	2	yes	—
114	D₇₁₂	C₂×C₈	1	1	yes	characteristic
115	#13083559	C₂×C₈	1	2	yes	—
116	#13083558	—	2	2	no	—
117	#13083558	C₂²×C₄	1	2	yes	—
118	#13083557	—	2	2	no	—
119	#13083557	—	2	2	no	—
120	#13083557	—	2	2	no	—
121	C₂×#10623494	—	2	2	no	—
122	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
123	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
124	C₈×D₈₉	—	2	2	no	—
125	C₈×D₈₉	—	2	2	no	—
126	C₈×D₈₉	—	2	2	no	—
127	C₈×D₈₉	C₂×C₈	1	1	yes	characteristic
128	C₈×D₈₉	C₂×C₈	1	1	yes	characteristic
129	C₈×D₈₉	C₂×C₈	1	1	yes	characteristic
130	C₈×D₈₉	C₂×C₈	1	1	yes	characteristic
131	C₈×D₈₉	C₂×D₄	1	1	yes	characteristic
132	C₈×D₈₉	C₂×D₄	1	1	yes	characteristic
133	C₈×D₈₉	#41	1	1	yes	characteristic
134	C₈×D₈₉	#41	1	1	yes	characteristic
135	C₄×Dic₈₉	—	2	1	no	—
136	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
137	#13083549	—	2	2	no	—
138	#13083549	—	2	1	no	—
139	#13083549	C₂×D₄	1	2	yes	—
140	#41×C₈₉	C₂²×C₄	1	2	yes	—
141	Q₁₆×C₈₉	C₂×C₈	1	1	yes	characteristic
142	SD₁₆×C₈₉	C₂×C₈	1	2	yes	—
143	D₈×C₈₉	C₂×C₈	1	1	yes	characteristic
144	M₁₆×C₈₉	—	2	2	no	—
145	M₁₆×C₈₉	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₈₉	—	2	2	no	—
147	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
149	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
150	C₁₆×C₈₉	—	2	2	no	—
151	C₁₆×C₈₉	—	2	1	no	—
152	C₁₆×C₈₉	C₂×D₄	1	2	yes	—
153	C₂²×D₈₉	—	2	2	no	—
154	C₂²×D₈₉	#131	1	1	yes	characteristic
155	Q₈×C₈₉	C₂²×C₈	1	2	yes	—
156	D₄×C₈₉	—	2	2	no	—
157	D₄×C₈₉	C₂²×C₈	1	2	yes	—
158	C₂×C₄×C₈₉	—	2	2	no	—
159	C₂×C₄×C₈₉	—	2	1	no	—
160	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
161	C₂²⋊D₈₉	—	2	2	no	—
162	C₂²⋊D₈₉	—	2	2	no	—
163	C₂²⋊D₈₉	—	2	2	no	—
164	C₂×Dic₈₉	—	2	1	no	—
165	C₂×Dic₈₉	—	2	2	no	—
166	C₂×Dic₈₉	#131	1	1	yes	characteristic
167	D₃₅₆	—	2	2	no	—
168	D₃₅₆	C₂²×C₈	1	2	yes	—
169	C₄×D₈₉	—	2	2	no	—
170	C₄×D₈₉	—	2	2	no	—
171	C₄×D₈₉	—	2	2	no	—
172	C₄×D₈₉	—	4	2	no	—
173	C₄×D₈₉	C₄×D₄	1	1	yes	characteristic
174	C₄×D₈₉	C₄×D₄	1	1	yes	characteristic
175	C₄×D₈₉	C₂²×C₈	1	1	yes	characteristic
176	C₄×D₈₉	C₂²×C₈	1	1	yes	characteristic
177	Dic₁₇₈	—	2	2	no	—
178	Dic₁₇₈	C₂²×C₈	1	2	yes	—
179	C₈×C₈₉	—	2	2	no	—
180	C₈×C₈₉	C₂²×C₈	1	1	yes	characteristic
181	C₈×C₈₉	C₂²×C₈	1	1	yes	characteristic
182	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
183	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
184	#10623494	—	2	2	no	—
185	#10623494	C₄×D₄	1	1	yes	characteristic
186	#10623494	C₄×D₄	1	1	yes	characteristic
187	#10623494	C₂²×C₈	1	1	yes	characteristic
188	#10623494	C₂²×C₈	1	1	yes	characteristic
189	C₂²×C₈₉	—	2	2	no	—
190	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
191	C₂×D₈₉	—	2	2	no	—
192	C₂×D₈₉	—	4	1	no	—
193	C₂×D₈₉	—	8	2	no	—
194	C₂×D₈₉	C₈×D₄	1	1	yes	characteristic
195	C₂×D₈₉	C₈×D₄	1	1	yes	characteristic
196	C₄×C₈₉	—	2	2	no	—
197	C₄×C₈₉	—	4	1	no	—
198	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
199	C₄×C₈₉	C₂³×C₈	1	1	yes	characteristic
200	Dic₈₉	—	2	2	no	—
201	Dic₈₉	—	2	2	no	—
202	Dic₈₉	C₈×D₄	1	1	yes	characteristic
203	Dic₈₉	C₈×D₄	1	1	yes	characteristic
204	#33443	—	89	1	no	maximal, Sylow
205	C₂×C₈₉	—	2	1	no	—
206	C₂×C₈₉	—	4	2	no	—
207	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
208	D₈₉	—	2	1	no	—
209	D₈₉	—	2	1	no	—
210	D₈₉	—	4	2	no	—
211	#3407	—	89	2	no	—
212	C₂×#443	—	89	1	no	—
213	#2171	—	89	1	no	—
214	#2171	—	89	1	no	—
215	#2171	—	89	1	no	—
216	#2171	D₈₉	1	1	yes	characteristic, complemented
217	#2170	—	89	2	no	—
218	#2170	—	89	2	no	—
219	C₂×#364	—	89	1	no	—
220	#2117	—	89	2	no	—
221	C₄×M₃₂	—	89	1	no	—
222	C₈₉	#33443	1	1	yes	characteristic, complemented, Sylow
223	C₂×#135	—	89	1	no	—
224	C₂×#131	—	89	2	no	—
225	#504	—	89	2	no	—
226	#504	—	89	2	no	—
227	#504	—	89	2	no	—
228	#504	—	178	2	no	—
229	#504	—	178	2	no	—
230	#504	C₂×D₈₉	1	2	yes	complemented
231	C₂×M₃₂	—	89	1	no	—
232	C₂×M₃₂	—	89	1	no	—
233	C₂×M₃₂	—	89	2	no	—
234	C₂×M₃₂	—	178	2	no	—
235	C₂×M₃₂	—	178	2	no	—
236	#443	—	89	1	no	—
237	#443	—	89	2	no	—
238	#443	—	89	1	no	—
239	#443	—	89	2	no	—
240	#443	—	89	1	no	—
241	#443	C₂×D₈₉	1	1	yes	characteristic
242	C₂×#108	—	89	1	no	—
243	C₂×#104	—	89	2	no	—
244	C₂×C₄×C₈	—	89	1	no	—
245	#364	—	89	2	no	—
246	#364	—	89	1	no	—
247	#364	C₂×D₈₉	1	1	yes	characteristic, complemented
248	#350	—	89	2	no	—
249	#350	—	89	2	no	—
250	#350	—	89	2	no	—
251	#350	C₂×D₈₉	1	2	yes	complemented
252	#346	—	89	1	no	—
253	#346	C₂×D₈₉	1	1	yes	characteristic, complemented
254	C₄×C₁₆	—	89	1	no	—
255	C₄×C₁₆	—	89	1	no	—
256	C₂×#41	—	89	2	no	—
257	#135	—	89	2	no	—
258	#135	—	89	1	no	—
259	#135	—	89	2	no	—
260	#135	—	89	1	no	—
261	#135	—	89	1	no	—
262	#135	C₄×D₈₉	1	1	yes	characteristic
263	C₂×Q₁₆	—	89	1	no	—
264	C₂×SD₁₆	—	89	2	no	—
265	C₂×D₈	—	89	1	no	—
266	#131	—	89	2	no	—
267	#131	—	89	2	no	—
268	#131	—	89	2	no	—
269	#131	—	178	2	no	—
270	#131	—	178	2	no	—
271	#131	C₂²×D₈₉	1	2	yes	—
272	C₂×M₁₆	—	89	2	no	—
273	C₂×M₁₆	—	178	2	no	—
274	C₂²×C₈	—	89	1	no	—
275	C₂²×C₈	—	89	1	no	—
276	C₂²×C₈	—	178	2	no	—
277	C₂×C₄²	—	89	1	no	—
278	M₃₂	—	2	2	no	—
279	M₃₂	—	89	2	no	—
280	M₃₂	—	89	2	no	—
281	M₃₂	—	89	2	no	—
282	M₃₂	—	178	2	no	—
283	M₃₂	—	178	1	no	—
284	M₃₂	—	178	1	no	—
285	M₃₂	—	178	2	no	—
286	M₃₂	—	178	2	no	—
287	M₃₂	—	178	2	no	—
288	M₃₂	C₂²×D₈₉	1	2	yes	—
289	C₂×C₁₆	—	2	2	no	—
290	C₂×C₁₆	—	89	1	no	—
291	C₂×C₁₆	—	89	1	no	—
292	C₂×C₁₆	—	178	2	no	—
293	C₂×C₁₆	—	178	2	no	—
294	C₂×C₁₆	—	178	2	no	—
295	C₂×C₁₆	—	178	2	no	—
296	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
297	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
298	#108	—	89	2	no	—
299	#108	—	89	1	no	—
300	#108	C₄×D₈₉	1	1	yes	characteristic
301	#104	—	89	2	no	—
302	#104	—	89	2	no	—
303	#104	—	89	2	no	—
304	#104	C₄×D₈₉	1	2	yes	—
305	C₄×C₈	—	89	1	no	—
306	C₄×C₈	—	89	1	no	—
307	C₄×C₈	—	89	1	no	—
308	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
309	#41	—	89	2	no	—
310	#41	—	89	2	no	—
311	#41	—	89	2	no	—
312	#41	—	178	2	no	—
313	#41	—	178	2	no	—
314	#41	C₂×C₄×D₈₉	1	2	yes	—
315	C₂×Q₈	—	89	2	no	—
316	C₂×D₄	—	89	2	no	—
317	C₂×D₄	—	178	2	no	—
318	C₂²×C₄	—	89	1	no	—
319	C₂²×C₄	—	178	2	no	—
320	C₂²×C₄	—	178	1	no	—
321	Q₁₆	—	89	2	no	—
322	Q₁₆	—	89	1	no	—
323	Q₁₆	C₈×D₈₉	1	1	yes	characteristic
324	SD₁₆	—	89	2	no	—
325	SD₁₆	—	89	2	no	—
326	SD₁₆	—	89	2	no	—
327	SD₁₆	C₈×D₈₉	1	2	yes	—
328	D₈	—	89	2	no	—
329	D₈	—	89	1	no	—
330	D₈	C₈×D₈₉	1	1	yes	characteristic
331	M₁₆	—	2	2	no	—
332	M₁₆	—	89	2	no	—
333	M₁₆	—	178	2	no	—
334	M₁₆	—	178	2	no	—
335	M₁₆	—	178	2	no	—
336	M₁₆	—	178	2	no	—
337	M₁₆	C₂×C₄×D₈₉	1	2	yes	—
338	C₂×C₈	—	2	2	no	—
339	C₂×C₈	—	89	1	no	—
340	C₂×C₈	—	89	1	no	—
341	C₂×C₈	—	89	1	no	—
342	C₂×C₈	—	89	1	no	—
343	C₂×C₈	—	89	1	no	—
344	C₂×C₈	—	89	1	no	—
345	C₂×C₈	—	89	1	no	—
346	C₂×C₈	—	89	1	no	—
347	C₂×C₈	—	89	1	no	—
348	C₂×C₈	—	89	1	no	—
349	C₂×C₈	—	178	2	no	—
350	C₂×C₈	—	178	2	no	—
351	C₂×C₈	—	178	2	no	—
352	C₂×C₈	—	178	2	no	—
353	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
354	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
355	C₄²	—	89	1	no	—
356	C₄²	—	178	1	no	—
357	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
358	C₁₆	—	2	2	no	—
359	C₁₆	—	2	1	no	—
360	C₁₆	—	89	2	no	—
361	C₁₆	—	178	2	no	—
362	C₁₆	—	178	1	no	—
363	C₁₆	D₄×D₈₉	1	2	yes	—
364	C₂³	—	89	1	no	—
365	C₂³	—	178	2	no	—
366	Q₈	—	89	2	no	—
367	Q₈	—	178	2	no	—
368	Q₈	C₂×C₈×D₈₉	1	2	yes	—
369	D₄	—	2	2	no	—
370	D₄	—	89	2	no	—
371	D₄	—	178	2	no	—
372	D₄	—	178	2	no	—
373	D₄	—	178	2	no	—
374	D₄	—	178	2	no	—
375	D₄	C₂×C₈×D₈₉	1	2	yes	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	89	1	no	—
379	C₂×C₄	—	89	1	no	—
380	C₂×C₄	—	89	1	no	—
381	C₂×C₄	—	89	1	no	—
382	C₂×C₄	—	89	1	no	—
383	C₂×C₄	—	356	2	no	—
384	C₂×C₄	—	178	2	no	—
385	C₂×C₄	—	178	2	no	—
386	C₂×C₄	—	178	2	no	—
387	C₂×C₄	—	178	1	no	—
388	C₂×C₄	—	178	2	no	—
389	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	—	89	1	no	—
392	C₈	—	89	1	no	—
393	C₈	—	89	1	no	—
394	C₈	—	89	1	no	—
395	C₈	—	178	2	no	—
396	C₈	C₂×C₈×D₈₉	1	1	yes	characteristic
397	C₈	C₂×C₈×D₈₉	1	1	yes	characteristic
398	C₈	C₂×D₄×D₈₉	1	1	yes	characteristic
399	C₈	#41×D₈₉	1	1	yes	characteristic
400	C₂²	—	2	2	no	—
401	C₂²	—	89	1	no	—
402	C₂²	—	89	1	no	—
403	C₂²	—	356	1	no	—
404	C₂²	—	178	2	no	—
405	C₂²	—	712	2	no	—
406	C₂²	#131×D₈₉	1	1	yes	characteristic
407	C₄	—	2	2	no	—
408	C₄	—	4	1	no	—
409	C₄	—	89	1	no	—
410	C₄	—	89	1	no	—
411	C₄	—	178	2	no	—
412	C₄	—	178	2	no	—
413	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
414	C₄	C₂²×C₈×D₈₉	1	1	yes	characteristic
415	C₂	—	2	1	no	—
416	C₂	—	4	2	no	—
417	C₂	—	356	2	no	—
418	C₂	—	178	1	no	—
419	C₂	—	178	1	no	—
420	C₂	C₈×D₄×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂×D₄×D₈₉
commutator	C₄×C₈₉	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₈₉×#2171	C₂
socle	C₂×C₈₉	C₂×C₈×D₄
prime radical	#135×D₈₉	C₄
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	#2171	D₈₉
hypocenter	C₈₉	#33443
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₈ ◁ C₂×C₁₆ ◁ #2171

Complements

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

N	H ≅ G/N	type
1. #26033353	C₂	semidirect
3. #26022095	C₂	semidirect
4. #26022094	C₂	semidirect
5. #26022093	C₂	semidirect
6. #26022087	C₂	semidirect
7. #26022086	C₂	semidirect
8. #364×D₈₉	C₂	semidirect
9. #26021878	C₂	semidirect
10. #26021845	C₂	semidirect
11. C₈₉×#2171	C₂	semidirect
15. #19152016	C₂²	semidirect
16. #19152015	C₂²	semidirect
18. #19152014	C₂²	semidirect
32. #19151419	C₂²	semidirect
33. #19151418	C₂²	semidirect
34. #19151383	C₂²	semidirect
35. #19151382	C₂²	semidirect
36. #19151381	C₂²	semidirect
37. #19151374	C₂²	semidirect
38. C₁₆×Dic₈₉	C₂²	semidirect
39. C₁₆×Dic₈₉	C₂²	semidirect
40. #504×C₈₉	C₂²	semidirect
42. #364×C₈₉	C₂²	semidirect
43. #350×C₈₉	C₂²	semidirect
44. #346×C₈₉	C₂²	semidirect
216. #2171	D₈₉	semidirect
222. C₈₉	#33443	semidirect
230. #504	C₂×D₈₉	semidirect
247. #364	C₂×D₈₉	semidirect
251. #350	C₂×D₈₉	semidirect
253. #346	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26033353	2
#443×D₈₉	2
#26022095	2
#26022094	2
#26022093	2
#26022087	2
#26022086	2
#364×D₈₉	2
#26021878	2
#26021845	2
C₈₉×#2171	2
#33443	89