Subgroups — C₈₉×#35336 #36413184

Order 22784.

1538 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2859	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2851	C₂	1	2	yes	maximal
4	C₈₉×#2647	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2629	C₂	1	2	yes	maximal
6	C₈₉×#2590	C₂	1	8	yes	maximal, complemented
7	C₈₉×#2587	C₂	1	8	yes	maximal
8	C₈₉×#2330	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2314	C₂	1	2	yes	maximal
10	C₄×#125×C₈₉	C₂	1	2	yes	maximal, complemented
11	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×#125×C₈₉	C₂²	1	2	yes	—
13	C₂×#125×C₈₉	C₂²	1	2	yes	—
14	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
17	#400×C₈₉	C₂²	1	8	yes	—
18	#398×C₈₉	C₂²	1	8	yes	—
19	#398×C₈₉	C₂²	1	8	yes	—
20	#396×C₈₉	C₂²	1	8	yes	—
21	#389×C₈₉	C₂²	1	4	yes	—
22	#389×C₈₉	C₂²	1	8	yes	—
23	#389×C₈₉	C₂²	1	4	yes	—
24	#389×C₈₉	C₂²	1	8	yes	—
25	#389×C₈₉	C₂²	1	8	yes	—
26	#388×C₈₉	C₂²	1	8	yes	—
27	#387×C₈₉	C₂²	1	8	yes	—
28	#387×C₈₉	C₂²	1	8	yes	—
29	#387×C₈₉	C₂²	1	8	yes	—
30	#387×C₈₉	C₂²	1	8	yes	—
31	#385×C₈₉	C₂²	1	8	yes	—
32	#384×C₈₉	C₂²	1	2	yes	—
33	#384×C₈₉	C₂²	1	2	yes	—
34	#382×C₈₉	C₂²	1	2	yes	—
35	#382×C₈₉	C₂²	1	2	yes	—
36	#380×C₈₉	C₂²	1	4	yes	—
37	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
38	C₄×C₄⋊C₄×C₈₉	C₂²	1	8	yes	—
39	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
40	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
41	#376×C₈₉	C₂²	1	1	yes	characteristic
42	#376×C₈₉	C₂²	1	1	yes	characteristic
43	C₄³×C₈₉	C₂²	1	1	yes	characteristic
44	C₄³×C₈₉	C₂²	1	1	yes	characteristic
45	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
47	#125×C₈₉	—	2	8	no	—
48	#125×C₈₉	—	2	8	no	—
49	#117×C₈₉	—	2	4	no	—
50	#117×C₈₉	Q₈	1	8	yes	—
51	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
53	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
54	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
55	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
56	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
57	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
58	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
59	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
60	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
61	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
63	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
64	C₂×C₄²×C₈₉	—	2	4	no	—
65	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
66	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
68	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
69	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
70	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
71	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
75	#95×C₈₉	C₂³	1	4	yes	—
76	#95×C₈₉	C₂³	1	4	yes	—
77	#95×C₈₉	C₂³	1	8	yes	—
78	#95×C₈₉	C₂³	1	8	yes	—
79	#95×C₈₉	C₂³	1	8	yes	—
80	#95×C₈₉	C₂³	1	8	yes	—
81	#95×C₈₉	C₂³	1	8	yes	—
82	#95×C₈₉	C₂³	1	8	yes	—
83	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
84	C₂²×C₄×C₈₉	—	2	2	no	—
85	C₂²×C₄×C₈₉	—	2	2	no	—
86	C₂²×C₄×C₈₉	—	2	4	no	—
87	C₂²×C₄×C₈₉	—	4	4	no	—
88	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
89	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
90	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
91	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
92	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
93	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
94	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
95	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
96	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
97	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
98	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
99	C₄⋊C₄×C₈₉	—	2	4	no	—
100	C₄⋊C₄×C₈₉	—	2	16	no	—
101	C₄⋊C₄×C₈₉	—	2	16	no	—
102	C₄⋊C₄×C₈₉	—	2	8	no	—
103	C₄⋊C₄×C₈₉	—	2	8	no	—
104	C₄⋊C₄×C₈₉	—	4	8	no	—
105	C₄⋊C₄×C₈₉	—	4	8	no	—
106	C₄⋊C₄×C₈₉	—	4	8	no	—
107	C₄⋊C₄×C₈₉	—	4	8	no	—
108	C₄⋊C₄×C₈₉	C₂×Q₈	1	8	yes	—
109	C₂²⋊C₄×C₈₉	—	2	4	no	—
110	C₂²⋊C₄×C₈₉	—	4	8	no	—
111	C₂²⋊C₄×C₈₉	C₂×Q₈	1	8	yes	—
112	C₄²×C₈₉	—	2	4	no	—
113	C₄²×C₈₉	—	2	2	no	—
114	C₄²×C₈₉	—	2	2	no	—
115	C₄²×C₈₉	—	4	4	no	—
116	C₄²×C₈₉	—	4	8	no	—
117	C₄²×C₈₉	—	4	4	no	—
118	C₄²×C₈₉	C₂×Q₈	1	4	yes	—
119	C₄²×C₈₉	C₂×Q₈	1	4	yes	—
120	C₄²×C₈₉	#41	1	4	yes	—
121	C₄²×C₈₉	#41	1	4	yes	—
122	C₂³×C₈₉	—	2	1	no	—
123	C₂³×C₈₉	—	2	1	no	—
124	C₂³×C₈₉	—	2	4	no	—
125	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
126	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
127	C₂×C₄×C₈₉	—	2	1	no	—
128	C₂×C₄×C₈₉	—	2	1	no	—
129	C₂×C₄×C₈₉	—	2	4	no	—
130	C₂×C₄×C₈₉	—	2	4	no	—
131	C₂×C₄×C₈₉	—	2	4	no	—
132	C₂×C₄×C₈₉	—	2	4	no	—
133	C₂×C₄×C₈₉	—	2	8	no	—
134	C₂×C₄×C₈₉	—	2	2	no	—
135	C₂×C₄×C₈₉	—	2	2	no	—
136	C₂×C₄×C₈₉	—	2	8	no	—
137	C₂×C₄×C₈₉	—	2	8	no	—
138	C₂×C₄×C₈₉	—	2	8	no	—
139	C₂×C₄×C₈₉	—	2	4	no	—
140	C₂×C₄×C₈₉	—	2	8	no	—
141	C₂×C₄×C₈₉	—	2	8	no	—
142	C₂×C₄×C₈₉	—	2	8	no	—
143	C₂×C₄×C₈₉	—	2	4	no	—
144	C₂×C₄×C₈₉	—	4	8	no	—
145	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
146	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
147	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
148	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
149	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
150	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
151	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
152	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
153	C₂²×C₈₉	—	2	2	no	—
154	C₂²×C₈₉	—	2	4	no	—
155	C₂²×C₈₉	—	4	2	no	—
156	C₂²×C₈₉	—	4	2	no	—
157	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
158	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
159	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
160	C₂²×C₈₉	#585	1	4	yes	—
161	C₄×C₈₉	—	2	2	no	—
162	C₄×C₈₉	—	2	4	no	—
163	C₄×C₈₉	—	2	4	no	—
164	C₄×C₈₉	—	2	4	no	—
165	C₄×C₈₉	—	2	4	no	—
166	C₄×C₈₉	—	4	8	no	—
167	C₄×C₈₉	—	4	2	no	—
168	C₄×C₈₉	—	4	2	no	—
169	C₄×C₈₉	—	4	8	no	—
170	C₄×C₈₉	#533	1	4	yes	—
171	#35336	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂×C₈₉	—	4	2	no	—
173	C₂×C₈₉	C₂×#533	1	1	yes	characteristic
174	C₂×C₈₉	#3455	1	2	yes	—
175	C₂×C₈₉	#3504	1	2	yes	—
176	C₂×C₈₉	#3512	1	2	yes	—
177	#2859	C₂×C₈₉	1	1	yes	characteristic, complemented
178	#2859	C₂×C₈₉	1	1	yes	characteristic, complemented
179	#2851	C₂×C₈₉	1	2	yes	—
180	#2647	C₂×C₈₉	1	2	yes	complemented
181	#2629	C₂×C₈₉	1	2	yes	—
182	#2590	C₂×C₈₉	1	8	yes	complemented
183	#2587	C₂×C₈₉	1	8	yes	—
184	#2330	C₂×C₈₉	1	2	yes	complemented
185	#2314	C₂×C₈₉	1	2	yes	—
186	C₄×#125	C₂×C₈₉	1	2	yes	complemented
187	C₄×#117	C₂×C₈₉	1	1	yes	characteristic
188	C₈₉	#35336	1	1	yes	characteristic, direct product factor, Sylow
189	C₂×#125	C₂²×C₈₉	1	2	yes	—
190	C₂×#125	C₂²×C₈₉	1	2	yes	—
191	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
192	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
193	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
194	#400	C₂²×C₈₉	1	8	yes	—
195	#398	C₂²×C₈₉	1	8	yes	—
196	#398	C₂²×C₈₉	1	8	yes	—
197	#396	C₂²×C₈₉	1	8	yes	—
198	#389	C₂²×C₈₉	1	4	yes	—
199	#389	C₂²×C₈₉	1	8	yes	—
200	#389	C₂²×C₈₉	1	4	yes	—
201	#389	C₂²×C₈₉	1	8	yes	—
202	#389	C₂²×C₈₉	1	8	yes	—
203	#388	C₂²×C₈₉	1	8	yes	—
204	#387	C₂²×C₈₉	1	8	yes	—
205	#387	C₂²×C₈₉	1	8	yes	—
206	#387	C₂²×C₈₉	1	8	yes	—
207	#387	C₂²×C₈₉	1	8	yes	—
208	#385	C₂²×C₈₉	1	8	yes	—
209	#384	C₂²×C₈₉	1	2	yes	—
210	#384	C₂²×C₈₉	1	2	yes	—
211	#382	C₂²×C₈₉	1	2	yes	—
212	#382	C₂²×C₈₉	1	2	yes	—
213	#380	C₂²×C₈₉	1	4	yes	—
214	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
215	C₄×C₄⋊C₄	C₂²×C₈₉	1	8	yes	—
216	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
217	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
218	#376	C₂²×C₈₉	1	1	yes	characteristic
219	#376	C₂²×C₈₉	1	1	yes	characteristic
220	C₄³	C₂²×C₈₉	1	1	yes	characteristic
221	C₄³	C₂²×C₈₉	1	1	yes	characteristic
222	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
223	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
224	#125	—	2	8	no	—
225	#125	—	2	8	no	—
226	#117	—	2	4	no	—
227	#117	Q₈×C₈₉	1	8	yes	—
228	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
229	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
230	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
231	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
232	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
233	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
234	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
235	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
236	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
237	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
238	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
239	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
240	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
241	C₂×C₄²	—	2	4	no	—
242	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
243	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
245	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
246	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
247	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
248	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
249	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
250	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
252	#95	C₂³×C₈₉	1	4	yes	—
253	#95	C₂³×C₈₉	1	4	yes	—
254	#95	C₂³×C₈₉	1	8	yes	—
255	#95	C₂³×C₈₉	1	8	yes	—
256	#95	C₂³×C₈₉	1	8	yes	—
257	#95	C₂³×C₈₉	1	8	yes	—
258	#95	C₂³×C₈₉	1	8	yes	—
259	#95	C₂³×C₈₉	1	8	yes	—
260	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
261	C₂²×C₄	—	2	2	no	—
262	C₂²×C₄	—	2	2	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	4	4	no	—
265	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
266	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
267	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
268	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
269	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
270	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
271	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
272	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
273	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
274	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
275	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
276	C₄⋊C₄	—	2	4	no	—
277	C₄⋊C₄	—	2	16	no	—
278	C₄⋊C₄	—	2	16	no	—
279	C₄⋊C₄	—	2	8	no	—
280	C₄⋊C₄	—	2	8	no	—
281	C₄⋊C₄	—	4	8	no	—
282	C₄⋊C₄	—	4	8	no	—
283	C₄⋊C₄	—	4	8	no	—
284	C₄⋊C₄	—	4	8	no	—
285	C₄⋊C₄	C₂×Q₈×C₈₉	1	8	yes	—
286	C₂²⋊C₄	—	2	4	no	—
287	C₂²⋊C₄	—	4	8	no	—
288	C₂²⋊C₄	C₂×Q₈×C₈₉	1	8	yes	—
289	C₄²	—	2	4	no	—
290	C₄²	—	2	2	no	—
291	C₄²	—	2	2	no	—
292	C₄²	—	4	4	no	—
293	C₄²	—	4	8	no	—
294	C₄²	—	4	4	no	—
295	C₄²	C₂×Q₈×C₈₉	1	4	yes	—
296	C₄²	C₂×Q₈×C₈₉	1	4	yes	—
297	C₄²	#41×C₈₉	1	4	yes	—
298	C₄²	#41×C₈₉	1	4	yes	—
299	C₂³	—	2	1	no	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	4	no	—
302	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
303	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
304	C₂×C₄	—	2	1	no	—
305	C₂×C₄	—	2	1	no	—
306	C₂×C₄	—	2	4	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	4	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	8	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	8	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	2	4	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	4	8	no	—
322	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
323	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
324	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
325	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
326	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
327	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
328	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
329	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
330	C₂²	—	2	2	no	—
331	C₂²	—	2	4	no	—
332	C₂²	—	4	2	no	—
333	C₂²	—	4	2	no	—
334	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
335	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
336	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
337	C₂²	#585×C₈₉	1	4	yes	—
338	C₄	—	2	2	no	—
339	C₄	—	2	4	no	—
340	C₄	—	2	4	no	—
341	C₄	—	2	4	no	—
342	C₄	—	2	4	no	—
343	C₄	—	4	2	no	—
344	C₄	—	4	8	no	—
345	C₄	—	4	2	no	—
346	C₄	—	4	8	no	—
347	C₄	#533×C₈₉	1	4	yes	—
348	C₂	—	4	2	no	—
349	C₂	C₂×#533×C₈₉	1	1	yes	characteristic
350	C₂	C₈₉×#3455	1	2	yes	—
351	C₂	C₈₉×#3504	1	2	yes	—
352	C₂	C₈₉×#3512	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁴×C₈₉	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#2859	C₂	semidirect
2. C₈₉×#2859	C₂	semidirect
4. C₈₉×#2647	C₂	semidirect
6. C₈₉×#2590	C₂	semidirect
8. C₈₉×#2330	C₂	semidirect
10. C₄×#125×C₈₉	C₂	semidirect
171. #35336	C₈₉	direct (N × H)
177. #2859	C₂×C₈₉	semidirect
178. #2859	C₂×C₈₉	semidirect
180. #2647	C₂×C₈₉	semidirect
182. #2590	C₂×C₈₉	semidirect
184. #2330	C₂×C₈₉	semidirect
186. C₄×#125	C₂×C₈₉	semidirect
188. C₈₉	#35336	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#2859	2
C₈₉×#2851	2
C₈₉×#2647	2
C₈₉×#2629	2
C₈₉×#2590	2
C₈₉×#2587	2
C₈₉×#2330	2
C₈₉×#2314	2
C₄×#125×C₈₉	2
C₄×#117×C₈₉	2
#35336	89

Subgroups — C89×#35336 #36413184

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35336 #36413184