Subgroups — #2226×D₈₉ #36709033

Order 22784.

638 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×D₈×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#26022400	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022399	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022398	C₂	1	2	yes	maximal, complemented
6	#26022397	C₂	1	2	yes	maximal, complemented
7	#26022396	C₂	1	1	yes	maximal, characteristic, complemented
8	#367×D₈₉	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#357×D₈₉	C₂	1	2	yes	maximal
11	C₈₉×#2226	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₈₉	C₂²	1	1	yes	characteristic
13	C₄⋊Q₈×D₈₉	—	2	1	no	—
14	C₄×D₄×D₈₉	—	2	1	no	—
15	C₂×C₁₆×D₈₉	C₂²	1	2	yes	—
16	#19152003	C₂²	1	1	yes	characteristic, complemented
17	#19152002	—	2	1	no	—
18	#19152002	C₂²	1	2	yes	complemented
19	#19152001	—	2	1	no	—
20	C₄×D₇₁₂	C₂²	1	1	yes	characteristic
21	D₈×Dic₈₉	C₂²	1	1	yes	characteristic
22	#19151680	C₂²	1	1	yes	characteristic
23	C₄×#13083559	—	2	1	no	—
24	#19151678	—	2	1	no	—
25	#107×D₈₉	—	2	1	no	—
26	#107×D₈₉	C₂²	1	2	yes	—
27	#107×D₈₉	C₂²	1	1	yes	characteristic
28	#102×D₈₉	—	2	1	no	—
29	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
30	#19151426	C₂²	1	2	yes	complemented
31	#19151425	C₂²	1	2	yes	complemented
32	#19151425	C₂²	1	2	yes	complemented
33	C₄⋊#13083549	C₂²	1	1	yes	characteristic, complemented
34	#19151416	C₂²	1	2	yes	complemented
35	#19151400	C₂²	1	2	yes	—
36	#19151399	C₂²	1	2	yes	—
37	#19151398	C₂²	1	2	yes	—
38	#500×C₈₉	C₂²	1	1	yes	characteristic, complemented
39	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
40	#367×C₈₉	C₂²	1	2	yes	complemented
41	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	#357×C₈₉	C₂²	1	2	yes	—
43	C₂×Q₈×D₈₉	—	4	1	no	—
44	C₂×D₄×D₈₉	—	2	1	no	—
45	C₂²×C₄×D₈₉	—	4	1	no	—
46	C₂×D₇₁₂	C₂³	1	1	yes	characteristic
47	C₂×#13083559	—	2	1	no	—
48	D₈×D₈₉	—	2	2	no	—
49	D₈×D₈₉	Q₈	1	4	yes	complemented
50	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
51	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
52	#15668012	—	2	1	no	—
53	#15668011	—	2	2	no	—
54	#15668011	—	4	1	no	—
55	#15668010	—	4	1	no	—
56	C₄×D₃₅₆	—	2	1	no	—
57	D₄×Dic₈₉	—	2	1	no	—
58	#15667974	—	2	1	no	—
59	C₄×C₂²⋊D₈₉	—	4	1	no	—
60	#15667972	—	4	1	no	—
61	C₄⋊C₄×D₈₉	—	2	2	no	—
62	C₄⋊C₄×D₈₉	—	2	1	no	—
63	C₄⋊C₄×D₈₉	—	4	1	no	—
64	C₂²⋊C₄×D₈₉	—	4	1	no	—
65	C₄²×D₈₉	D₄	1	1	yes	characteristic
66	C₂×#13083549	C₂³	1	2	yes	—
67	C₁₆×D₈₉	—	2	4	no	—
68	#15667946	—	2	1	no	—
69	#15667946	C₂³	1	2	yes	—
70	#15667946	C₂³	1	1	yes	characteristic
71	#15667945	—	2	2	no	—
72	#15667945	—	2	1	no	—
73	#15667945	—	2	2	no	—
74	#15667934	—	2	1	no	—
75	#15667933	—	2	1	no	—
76	#15667932	—	2	1	no	—
77	C₄×#10623494	D₄	1	1	yes	characteristic
78	C₈×Dic₈₉	D₄	1	1	yes	characteristic
79	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
80	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
81	C₄⋊Q₈×C₈₉	—	2	1	no	—
82	C₄×D₄×C₈₉	—	2	1	no	—
83	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
84	#107×C₈₉	—	2	1	no	—
85	#107×C₈₉	C₂³	1	2	yes	—
86	#107×C₈₉	C₂³	1	1	yes	characteristic
87	#102×C₈₉	—	2	1	no	—
88	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
89	C₂³×D₈₉	—	4	1	no	—
90	C₂×Dic₁₇₈	—	4	1	no	—
91	C₂×Dic₁₇₈	—	4	2	no	—
92	Q₈×D₈₉	—	8	4	no	—
93	C₂×D₃₅₆	—	2	1	no	—
94	C₂×C₂²⋊D₈₉	—	4	1	no	—
95	D₄×D₈₉	—	2	4	no	—
96	D₄×D₈₉	—	4	2	no	—
97	C₂²×Dic₈₉	—	4	1	no	—
98	C₂×C₄×D₈₉	—	4	1	no	—
99	C₂×C₄×D₈₉	—	4	2	no	—
100	C₂×C₄×D₈₉	—	4	1	no	—
101	C₂×C₄×D₈₉	—	4	1	no	—
102	C₂×C₄×D₈₉	—	8	4	no	—
103	C₂×C₄×D₈₉	D₈	1	1	yes	characteristic
104	C₂×C₄×D₈₉	D₈	1	1	yes	characteristic
105	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
106	D₇₁₂	—	2	1	no	—
107	D₇₁₂	C₂×Q₈	1	2	yes	complemented
108	#13083559	—	2	4	no	—
109	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
110	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
111	C₈×D₈₉	—	2	2	no	—
112	C₈×D₈₉	C₂×Q₈	1	2	yes	—
113	C₈×D₈₉	#41	1	2	yes	—
114	C₄⋊Dic₈₉	—	2	1	no	—
115	C₄⋊Dic₈₉	—	2	2	no	—
116	C₄⋊Dic₈₉	—	4	1	no	—
117	#13083553	—	4	1	no	—
118	#13083553	—	4	2	no	—
119	#13083553	—	4	2	no	—
120	C₂²⋊Dic₈₉	—	4	1	no	—
121	#13083551	—	4	1	no	—
122	#13083551	—	4	1	no	—
123	C₄×Dic₈₉	D₈	1	1	yes	characteristic
124	C₄×Dic₈₉	D₈	1	1	yes	characteristic
125	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
126	#13083549	—	2	2	no	—
127	C₂×Q₈×C₈₉	—	4	1	no	—
128	C₂×D₄×C₈₉	—	2	1	no	—
129	C₂²×C₄×C₈₉	—	4	1	no	—
130	D₈×C₈₉	—	2	1	no	—
131	D₈×C₈₉	C₂×Q₈	1	2	yes	complemented
132	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
133	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
134	C₄⋊C₄×C₈₉	—	2	1	no	—
135	C₄⋊C₄×C₈₉	—	2	2	no	—
136	C₄⋊C₄×C₈₉	—	4	1	no	—
137	C₂²⋊C₄×C₈₉	—	4	1	no	—
138	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₁₆×C₈₉	—	2	2	no	—
140	C₂³×C₈₉	—	4	1	no	—
141	C₂²×D₈₉	—	4	1	no	—
142	C₂²×D₈₉	—	4	4	no	—
143	C₂²×D₈₉	—	8	2	no	—
144	C₂²×D₈₉	—	8	2	no	—
145	C₂²×D₈₉	C₂×D₈	1	1	yes	characteristic
146	Q₈×C₈₉	—	8	2	no	—
147	D₄×C₈₉	—	2	2	no	—
148	D₄×C₈₉	—	4	1	no	—
149	C₂×C₄×C₈₉	—	4	1	no	—
150	C₂×C₄×C₈₉	—	4	2	no	—
151	C₂×C₄×C₈₉	—	8	2	no	—
152	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
153	C₂×C₄×C₈₉	C₂×D₈	1	1	yes	characteristic
154	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
155	C₂²⋊D₈₉	—	4	4	no	—
156	C₂×Dic₈₉	—	4	1	no	—
157	C₂×Dic₈₉	—	4	2	no	—
158	C₂×Dic₈₉	—	8	2	no	—
159	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
160	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
161	C₂×Dic₈₉	C₂×D₈	1	1	yes	characteristic
162	D₃₅₆	—	2	2	no	—
163	D₃₅₆	—	4	1	no	—
164	C₄×D₈₉	—	2	2	no	—
165	C₄×D₈₉	—	8	2	no	—
166	C₄×D₈₉	—	8	4	no	—
167	C₄×D₈₉	—	8	2	no	—
168	C₄×D₈₉	—	8	2	no	—
169	C₄×D₈₉	SD₃₂	1	4	yes	—
170	C₄×D₈₉	C₂²⋊Q₈	1	2	yes	—
171	C₄×D₈₉	#137	1	2	yes	—
172	Dic₁₇₈	—	8	4	no	—
173	Dic₁₇₈	—	8	2	no	—
174	C₈×C₈₉	—	2	1	no	—
175	C₈×C₈₉	C₂²×Q₈	1	1	yes	characteristic
176	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
177	#10623494	—	2	1	no	—
178	#10623494	C₂²⋊Q₈	1	2	yes	—
179	C₂²×C₈₉	—	4	2	no	—
180	C₂²×C₈₉	—	8	1	no	—
181	C₂²×C₈₉	—	8	1	no	—
182	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
183	C₂×D₈₉	—	4	2	no	—
184	C₂×D₈₉	—	8	1	no	—
185	C₂×D₈₉	—	8	1	no	—
186	C₂×D₈₉	—	8	8	no	—
187	C₂×D₈₉	#474	1	2	yes	—
188	C₂×D₈₉	C₂×SD₃₂	1	2	yes	—
189	C₂×D₈₉	#509	1	2	yes	—
190	C₄×C₈₉	—	2	1	no	—
191	C₄×C₈₉	—	8	1	no	—
192	C₄×C₈₉	—	8	2	no	—
193	C₄×C₈₉	C₂×SD₃₂	1	2	yes	—
194	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
195	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
196	Dic₈₉	—	2	1	no	—
197	Dic₈₉	—	8	1	no	—
198	Dic₈₉	—	8	2	no	—
199	Dic₈₉	#474	1	2	yes	—
200	Dic₈₉	C₂×SD₃₂	1	2	yes	—
201	C₂×#2226	—	89	1	no	maximal, Sylow
202	C₂×C₈₉	—	8	2	no	—
203	C₂×C₈₉	C₂×#474	1	1	yes	characteristic
204	C₂×C₈₉	C₂²×SD₃₂	1	1	yes	characteristic
205	C₂×C₈₉	C₂×#509	1	1	yes	characteristic
206	D₈₉	—	8	2	no	—
207	D₈₉	#2226	1	4	yes	direct product factor
208	C₂×#500	—	89	1	no	—
209	C₂×C₄×D₈	—	89	1	no	—
210	#2226	—	89	1	no	—
211	#2226	—	89	1	no	—
212	#2226	—	89	2	no	—
213	#2226	—	89	1	no	—
214	#2226	—	89	2	no	—
215	#2226	D₈₉	1	1	yes	characteristic, direct product factor
216	C₂×#367	—	89	2	no	—
217	C₂×C₄⋊C₁₆	—	89	1	no	—
218	C₂×#357	—	89	2	no	—
219	C₈₉	C₂×#2226	1	1	yes	characteristic, complemented, Sylow
220	C₂²×D₈	—	89	1	no	—
221	C₂×C₄⋊Q₈	—	178	1	no	—
222	C₂×C₄×D₄	—	178	1	no	—
223	C₂²×C₁₆	—	89	2	no	—
224	#500	—	89	2	no	—
225	#500	—	89	1	no	—
226	#500	—	178	1	no	—
227	#500	—	178	1	no	—
228	#500	C₂×D₈₉	1	1	yes	characteristic, complemented
229	C₄×D₈	—	89	1	no	—
230	C₄×D₈	—	89	1	no	—
231	C₄×D₈	—	89	1	no	—
232	C₄×D₈	—	178	1	no	—
233	C₄×D₈	—	178	1	no	—
234	C₄×D₈	C₂×D₈₉	1	1	yes	characteristic
235	C₂×#107	—	89	2	no	—
236	C₂×#107	—	89	1	no	—
237	C₂×#107	—	178	1	no	—
238	C₂×#102	—	178	1	no	—
239	C₂×C₄×C₈	—	89	1	no	—
240	#367	—	89	2	no	—
241	#367	—	89	2	no	—
242	#367	—	89	2	no	—
243	#367	C₂×D₈₉	1	2	yes	complemented
244	C₄⋊C₁₆	—	89	2	no	—
245	C₄⋊C₁₆	—	89	1	no	—
246	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
247	#357	—	89	2	no	—
248	#357	—	89	2	no	—
249	#357	—	89	2	no	—
250	#357	C₂×D₈₉	1	2	yes	—
251	C₂²×Q₈	—	356	1	no	—
252	C₂²×D₄	—	178	1	no	—
253	C₂³×C₄	—	356	1	no	—
254	C₂×D₈	—	89	4	no	—
255	C₂×D₈	—	89	1	no	—
256	C₂×D₈	—	178	2	no	—
257	C₂×D₈	—	178	1	no	—
258	C₂×D₈	C₂²×D₈₉	1	1	yes	characteristic
259	C₂²×C₈	—	89	1	no	—
260	C₂²×C₈	—	89	1	no	—
261	C₄⋊Q₈	—	2	1	no	—
262	C₄⋊Q₈	—	356	1	no	—
263	C₄⋊Q₈	—	356	1	no	—
264	C₄⋊Q₈	—	178	2	no	—
265	C₄⋊Q₈	—	178	1	no	—
266	C₄×D₄	—	2	1	no	—
267	C₄×D₄	—	356	1	no	—
268	C₄×D₄	—	356	1	no	—
269	C₄×D₄	—	178	1	no	—
270	C₄×D₄	—	178	1	no	—
271	C₄×D₄	—	178	1	no	—
272	C₂×C₄⋊C₄	—	356	1	no	—
273	C₂×C₄⋊C₄	—	178	1	no	—
274	C₂×C₄⋊C₄	—	178	2	no	—
275	C₂×C₂²⋊C₄	—	356	1	no	—
276	C₂×C₄²	—	89	1	no	—
277	C₂×C₁₆	—	89	2	no	—
278	C₂×C₁₆	—	178	4	no	—
279	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
280	#107	—	2	1	no	—
281	#107	—	89	2	no	—
282	#107	—	89	1	no	—
283	#107	—	178	1	no	—
284	#107	—	178	2	no	—
285	#107	—	178	2	no	—
286	#107	—	178	1	no	—
287	#107	C₂²×D₈₉	1	2	yes	—
288	#107	C₂²×D₈₉	1	1	yes	characteristic
289	#102	—	2	1	no	—
290	#102	—	178	1	no	—
291	#102	—	178	1	no	—
292	#102	—	178	1	no	—
293	C₄×C₈	—	89	1	no	—
294	C₄×C₈	—	89	1	no	—
295	C₄×C₈	—	89	1	no	—
296	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
297	C₂⁴	—	356	1	no	—
298	C₂×Q₈	—	4	1	no	—
299	C₂×Q₈	—	356	2	no	—
300	C₂×Q₈	—	356	1	no	—
301	C₂×Q₈	—	712	4	no	—
302	C₂×D₄	—	2	1	no	—
303	C₂×D₄	—	356	2	no	—
304	C₂×D₄	—	356	1	no	—
305	C₂×D₄	—	178	4	no	—
306	C₂×D₄	—	178	1	no	—
307	C₂²×C₄	—	4	1	no	—
308	C₂²×C₄	—	89	1	no	—
309	C₂²×C₄	—	89	1	no	—
310	C₂²×C₄	—	89	1	no	—
311	C₂²×C₄	—	356	1	no	—
312	C₂²×C₄	—	356	1	no	—
313	C₂²×C₄	—	356	2	no	—
314	C₂²×C₄	—	356	1	no	—
315	C₂²×C₄	—	356	1	no	—
316	C₂²×C₄	—	712	4	no	—
317	D₈	—	2	1	no	—
318	D₈	—	89	2	no	—
319	D₈	—	178	4	no	—
320	D₈	—	178	1	no	—
321	D₈	Q₈×D₈₉	1	2	yes	complemented
322	C₂×C₈	—	89	1	no	—
323	C₂×C₈	—	89	2	no	—
324	C₂×C₈	—	89	2	no	—
325	C₂×C₈	—	89	1	no	—
326	C₂×C₈	—	178	2	no	—
327	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
328	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₄⋊C₄	—	356	2	no	—
333	C₄⋊C₄	—	356	1	no	—
334	C₄⋊C₄	—	356	2	no	—
335	C₄⋊C₄	—	356	1	no	—
336	C₄⋊C₄	—	178	1	no	—
337	C₄⋊C₄	—	178	2	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	356	1	no	—
340	C₂²⋊C₄	—	356	1	no	—
341	C₂²⋊C₄	—	356	1	no	—
342	C₄²	—	89	1	no	—
343	C₄²	—	89	1	no	—
344	C₄²	—	89	1	no	—
345	C₄²	D₄×D₈₉	1	1	yes	characteristic
346	C₁₆	—	2	2	no	—
347	C₁₆	—	178	2	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	89	1	no	—
350	C₂³	—	356	4	no	—
351	C₂³	—	356	1	no	—
352	C₂³	—	712	2	no	—
353	C₂³	—	712	2	no	—
354	Q₈	—	8	2	no	—
355	Q₈	—	712	2	no	—
356	Q₈	—	712	4	no	—
357	D₄	—	2	2	no	—
358	D₄	—	4	1	no	—
359	D₄	—	356	4	no	—
360	D₄	—	356	1	no	—
361	D₄	—	178	2	no	—
362	C₂×C₄	—	4	1	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	89	1	no	—
366	C₂×C₄	—	89	1	no	—
367	C₂×C₄	—	89	2	no	—
368	C₂×C₄	—	89	4	no	—
369	C₂×C₄	—	89	2	no	—
370	C₂×C₄	—	89	1	no	—
371	C₂×C₄	—	356	1	no	—
372	C₂×C₄	—	356	2	no	—
373	C₂×C₄	—	178	2	no	—
374	C₂×C₄	—	712	2	no	—
375	C₂×C₄	—	712	2	no	—
376	C₂×C₄	—	712	4	no	—
377	C₂×C₄	—	712	2	no	—
378	C₂×C₄	—	712	2	no	—
379	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
380	C₂×C₄	D₈×D₈₉	1	1	yes	characteristic
381	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
382	C₈	—	2	1	no	—
383	C₈	—	89	2	no	—
384	C₈	—	178	1	no	—
385	C₈	C₂×Q₈×D₈₉	1	1	yes	characteristic
386	C₈	#41×D₈₉	1	1	yes	characteristic
387	C₂²	—	4	2	no	—
388	C₂²	—	8	1	no	—
389	C₂²	—	8	1	no	—
390	C₂²	—	89	2	no	—
391	C₂²	—	89	2	no	—
392	C₂²	—	89	2	no	—
393	C₂²	—	356	2	no	—
394	C₂²	—	712	8	no	—
395	C₂²	—	712	1	no	—
396	C₂²	—	712	1	no	—
397	C₂²	C₂×D₈×D₈₉	1	1	yes	characteristic
398	C₄	—	2	1	no	—
399	C₄	—	8	1	no	—
400	C₄	—	8	2	no	—
401	C₄	—	89	2	no	—
402	C₄	—	89	2	no	—
403	C₄	—	178	1	no	—
404	C₄	—	712	1	no	—
405	C₄	—	712	2	no	—
406	C₄	SD₃₂×D₈₉	1	2	yes	—
407	C₄	C₂²⋊Q₈×D₈₉	1	1	yes	characteristic
408	C₄	#137×D₈₉	1	1	yes	characteristic
409	C₂	—	8	2	no	—
410	C₂	—	89	4	no	—
411	C₂	—	712	2	no	—
412	C₂	#474×D₈₉	1	1	yes	characteristic
413	C₂	C₂×SD₃₂×D₈₉	1	1	yes	characteristic
414	C₂	#509×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₈×D₈₉
commutator, cosocle	C₂×C₈×C₈₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₈₉
Fitting	C₈₉×#2226	C₂
socle	C₂²×C₈₉	C₂²×D₈
prime radical	C₂×D₈×D₈₉	C₂²
hypercenter	#2226	D₈₉
hypocenter	C₈₉	C₂×#2226
LCS	G ▷ C₂×C₈×C₈₉ ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×C₈ ◁ #2226

Complements

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

N	H ≅ G/N	type
1. #500×D₈₉	C₂	semidirect
3. #26022400	C₂	semidirect
4. #26022399	C₂	semidirect
5. #26022398	C₂	semidirect
6. #26022397	C₂	semidirect
7. #26022396	C₂	semidirect
8. #367×D₈₉	C₂	semidirect
9. C₄⋊C₁₆×D₈₉	C₂	semidirect
11. C₈₉×#2226	C₂	semidirect
16. #19152003	C₂²	semidirect
18. #19152002	C₂²	semidirect
30. #19151426	C₂²	semidirect
31. #19151425	C₂²	semidirect
32. #19151425	C₂²	semidirect
33. C₄⋊#13083549	C₂²	semidirect
34. #19151416	C₂²	semidirect
38. #500×C₈₉	C₂²	semidirect
40. #367×C₈₉	C₂²	semidirect
41. C₄⋊C₁₆×C₈₉	C₂²	semidirect
49. D₈×D₈₉	Q₈	semidirect
107. D₇₁₂	C₂×Q₈	semidirect
131. D₈×C₈₉	C₂×Q₈	semidirect
207. D₈₉	#2226	direct (N × H)
215. #2226	D₈₉	direct (N × H)
219. C₈₉	C₂×#2226	semidirect
228. #500	C₂×D₈₉	semidirect
243. #367	C₂×D₈₉	semidirect
246. C₄⋊C₁₆	C₂×D₈₉	semidirect
321. D₈	Q₈×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#500×D₈₉	2
C₄×D₈×D₈₉	2
#26022400	2
#26022399	2
#26022398	2
#26022397	2
#26022396	2
#367×D₈₉	2
C₄⋊C₁₆×D₈₉	2
#357×D₈₉	2
C₈₉×#2226	2
C₂×#2226	89

Subgroups — #2226×D89 #36709033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #2226×D₈₉ #36709033