Subgroups — C₈₉×#35317 #36413165

Order 22784.

3406 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	C₂×#536×C₈₉	C₂	1	4	yes	maximal, complemented
2	C₂×#532×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2868	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2858	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2658	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2542	C₂	1	8	yes	maximal, complemented
8	C₈₉×#2501	C₂	1	8	yes	maximal, complemented
9	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₈₉	C₂²	1	2	yes	—
11	C₂³×Q₈×C₈₉	C₂²	1	2	yes	—
12	#536×C₈₉	—	2	32	no	—
13	#532×C₈₉	—	2	8	no	—
14	C₂×C₄⋊Q₈×C₈₉	—	2	8	no	—
15	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
16	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₈₉	C₂²	1	8	yes	—
18	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
19	C₂×C₄⋊Q₈×C₈₉	C₂²	1	4	yes	—
20	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#124×C₈₉	C₂²	1	8	yes	—
22	C₂×#124×C₈₉	C₂²	1	2	yes	—
23	C₂×#123×C₈₉	C₂²	1	16	yes	—
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	16	yes	—
25	C₂×#121×C₈₉	C₂²	1	4	yes	—
26	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
27	C₂×#117×C₈₉	C₂²	1	2	yes	—
28	C₂²×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
29	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
30	#399×C₈₉	C₂²	1	32	yes	—
31	#390×C₈₉	C₂²	1	16	yes	—
32	#384×C₈₉	C₂²	1	16	yes	—
33	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
34	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
35	#376×C₈₉	C₂²	1	2	yes	—
36	C₄³×C₈₉	C₂²	1	2	yes	—
37	C₂×#41×C₈₉	—	2	8	no	—
38	C₂×#41×C₈₉	—	2	16	no	—
39	C₂²×Q₈×C₈₉	—	2	8	no	—
40	C₂²×Q₈×C₈₉	—	2	16	no	—
41	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
42	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
43	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
44	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
45	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
46	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
47	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
48	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
49	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
50	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
51	C₄⋊Q₈×C₈₉	—	2	16	no	—
52	C₄⋊Q₈×C₈₉	—	2	8	no	—
53	C₄⋊Q₈×C₈₉	—	2	8	no	—
54	C₄⋊Q₈×C₈₉	—	2	4	no	—
55	C₄⋊Q₈×C₈₉	—	2	32	no	—
56	#127×C₈₉	—	2	4	no	—
57	#124×C₈₉	—	2	8	no	—
58	#124×C₈₉	—	2	32	no	—
59	#123×C₈₉	—	2	64	no	—
60	C₂²⋊Q₈×C₈₉	—	2	64	no	—
61	#121×C₈₉	—	2	16	no	—
62	C₄×D₄×C₈₉	—	2	16	no	—
63	#117×C₈₉	D₄	1	16	yes	complemented
64	C₂×C₄⋊C₄×C₈₉	—	2	16	no	—
65	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
67	C₂×C₄⋊C₄×C₈₉	C₂³	1	32	yes	—
68	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
69	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
70	C₂×C₂²⋊C₄×C₈₉	C₂³	1	32	yes	—
71	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
72	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
73	C₂×C₄²×C₈₉	D₄	1	8	yes	—
74	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
75	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
77	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
79	#95×C₈₉	C₂³	1	8	yes	—
80	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
81	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
82	#41×C₈₉	—	4	32	no	—
83	C₂×Q₈×C₈₉	—	2	16	no	—
84	C₂×Q₈×C₈₉	—	2	16	no	—
85	C₂×Q₈×C₈₉	—	2	4	no	—
86	C₂×Q₈×C₈₉	—	2	8	no	—
87	C₂×Q₈×C₈₉	—	2	8	no	—
88	C₂×Q₈×C₈₉	—	2	8	no	—
89	C₂×Q₈×C₈₉	—	4	32	no	—
90	C₂×D₄×C₈₉	—	2	8	no	—
91	C₂×D₄×C₈₉	—	2	16	no	—
92	C₂×D₄×C₈₉	—	2	8	no	—
93	C₂×D₄×C₈₉	—	2	8	no	—
94	C₂×D₄×C₈₉	—	2	4	no	—
95	C₂×D₄×C₈₉	—	2	16	no	—
96	C₂²×C₄×C₈₉	—	2	8	no	—
97	C₂²×C₄×C₈₉	—	2	8	no	—
98	C₂²×C₄×C₈₉	—	2	16	no	—
99	C₂²×C₄×C₈₉	—	2	8	no	—
100	C₂²×C₄×C₈₉	—	2	16	no	—
101	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
102	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
104	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
105	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
106	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
107	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
108	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
109	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
111	C₄⋊C₄×C₈₉	—	2	16	no	—
112	C₄⋊C₄×C₈₉	—	2	16	no	—
113	C₄⋊C₄×C₈₉	—	2	8	no	—
114	C₄⋊C₄×C₈₉	—	2	64	no	—
115	C₄⋊C₄×C₈₉	C₂×D₄	1	16	yes	—
116	C₂²⋊C₄×C₈₉	—	2	16	no	—
117	C₂²⋊C₄×C₈₉	—	2	64	no	—
118	C₂²⋊C₄×C₈₉	C₂×D₄	1	16	yes	—
119	C₄²×C₈₉	—	2	16	no	—
120	C₄²×C₈₉	C₂×D₄	1	8	yes	—
121	C₄²×C₈₉	C₂×D₄	1	4	yes	—
122	C₄²×C₈₉	C₂×D₄	1	4	yes	—
123	C₄²×C₈₉	C₂×D₄	1	16	yes	—
124	C₂³×C₈₉	—	2	4	no	—
125	C₂³×C₈₉	—	2	8	no	—
126	C₂³×C₈₉	—	2	4	no	—
127	C₂³×C₈₉	—	2	16	no	—
128	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
129	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
130	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
131	Q₈×C₈₉	—	4	16	no	—
132	Q₈×C₈₉	—	4	16	no	—
133	Q₈×C₈₉	—	4	8	no	—
134	D₄×C₈₉	—	4	16	no	—
135	D₄×C₈₉	—	4	8	no	—
136	D₄×C₈₉	—	4	16	no	—
137	C₂×C₄×C₈₉	—	2	16	no	—
138	C₂×C₄×C₈₉	—	2	4	no	—
139	C₂×C₄×C₈₉	—	2	16	no	—
140	C₂×C₄×C₈₉	—	2	4	no	—
141	C₂×C₄×C₈₉	—	2	16	no	—
142	C₂×C₄×C₈₉	—	2	8	no	—
143	C₂×C₄×C₈₉	—	2	8	no	—
144	C₂×C₄×C₈₉	—	4	16	no	—
145	C₂×C₄×C₈₉	—	4	16	no	—
146	C₂×C₄×C₈₉	#127	1	16	yes	—
147	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
148	C₂×C₄×C₈₉	C₂²×D₄	1	16	yes	—
149	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
150	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
151	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
152	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
153	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
154	C₂×C₄×C₈₉	2₋¹⁺⁴	1	8	yes	—
155	C₂²×C₈₉	—	2	4	no	—
156	C₂²×C₈₉	—	2	8	no	—
157	C₂²×C₈₉	—	4	4	no	—
158	C₂²×C₈₉	—	4	8	no	—
159	C₂²×C₈₉	—	4	16	no	—
160	C₂²×C₈₉	C₂×#127	1	4	yes	—
161	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
162	C₂²×C₈₉	C₂³×D₄	1	2	yes	—
163	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	4	yes	—
164	C₄×C₈₉	—	2	4	no	—
165	C₄×C₈₉	—	2	16	no	—
166	C₄×C₈₉	—	4	4	no	—
167	C₄×C₈₉	—	4	8	no	—
168	C₄×C₈₉	C₂×#127	1	4	yes	—
169	C₄×C₈₉	C₂×#127	1	4	yes	—
170	C₄×C₈₉	#536	1	8	yes	complemented
171	#35317	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂×C₈₉	—	2	4	no	—
173	C₂×C₈₉	—	8	4	no	—
174	C₂×C₈₉	C₂²×#127	1	1	yes	characteristic
175	C₂×C₈₉	C₂×#536	1	2	yes	—
176	C₂×C₈₉	#3499	1	4	yes	—
177	C₂×#536	C₂×C₈₉	1	4	yes	complemented
178	C₂×#532	C₂×C₈₉	1	1	yes	characteristic
179	C₂²×C₄⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
180	#2868	C₂×C₈₉	1	2	yes	complemented
181	#2858	C₂×C₈₉	1	2	yes	complemented
182	#2658	C₂×C₈₉	1	4	yes	complemented
183	#2542	C₂×C₈₉	1	8	yes	complemented
184	#2501	C₂×C₈₉	1	8	yes	complemented
185	C₄×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
186	C₈₉	#35317	1	1	yes	characteristic, direct product factor, Sylow
187	C₂²×#41	C₂²×C₈₉	1	2	yes	—
188	C₂³×Q₈	C₂²×C₈₉	1	2	yes	—
189	#536	—	2	32	no	—
190	#532	—	2	8	no	—
191	C₂×C₄⋊Q₈	—	2	8	no	—
192	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
193	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
194	C₂×C₄⋊Q₈	C₂²×C₈₉	1	8	yes	—
195	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
196	C₂×C₄⋊Q₈	C₂²×C₈₉	1	4	yes	—
197	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
198	C₂×#124	C₂²×C₈₉	1	8	yes	—
199	C₂×#124	C₂²×C₈₉	1	2	yes	—
200	C₂×#123	C₂²×C₈₉	1	16	yes	—
201	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	16	yes	—
202	C₂×#121	C₂²×C₈₉	1	4	yes	—
203	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
204	C₂×#117	C₂²×C₈₉	1	2	yes	—
205	C₂²×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
206	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
207	#399	C₂²×C₈₉	1	32	yes	—
208	#390	C₂²×C₈₉	1	16	yes	—
209	#384	C₂²×C₈₉	1	16	yes	—
210	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
211	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
212	#376	C₂²×C₈₉	1	2	yes	—
213	C₄³	C₂²×C₈₉	1	2	yes	—
214	C₂×#41	—	2	8	no	—
215	C₂×#41	—	2	16	no	—
216	C₂²×Q₈	—	2	8	no	—
217	C₂²×Q₈	—	2	16	no	—
218	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
219	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
220	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
221	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
222	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
223	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
224	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
225	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
226	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
227	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
228	C₄⋊Q₈	—	2	16	no	—
229	C₄⋊Q₈	—	2	8	no	—
230	C₄⋊Q₈	—	2	8	no	—
231	C₄⋊Q₈	—	2	4	no	—
232	C₄⋊Q₈	—	2	32	no	—
233	#127	—	2	4	no	—
234	#124	—	2	8	no	—
235	#124	—	2	32	no	—
236	#123	—	2	64	no	—
237	C₂²⋊Q₈	—	2	64	no	—
238	#121	—	2	16	no	—
239	C₄×D₄	—	2	16	no	—
240	#117	D₄×C₈₉	1	16	yes	complemented
241	C₂×C₄⋊C₄	—	2	16	no	—
242	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
243	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
244	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
245	C₂×C₄⋊C₄	C₂³×C₈₉	1	32	yes	—
246	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
247	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
248	C₂×C₂²⋊C₄	C₂³×C₈₉	1	32	yes	—
249	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
250	C₂×C₄²	D₄×C₈₉	1	8	yes	—
251	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
252	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
253	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
254	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
255	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
256	#95	C₂³×C₈₉	1	8	yes	—
257	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
258	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
259	#41	—	4	32	no	—
260	C₂×Q₈	—	2	16	no	—
261	C₂×Q₈	—	2	16	no	—
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	—	2	8	no	—
264	C₂×Q₈	—	2	8	no	—
265	C₂×Q₈	—	2	8	no	—
266	C₂×Q₈	—	4	32	no	—
267	C₂×D₄	—	2	8	no	—
268	C₂×D₄	—	2	16	no	—
269	C₂×D₄	—	2	8	no	—
270	C₂×D₄	—	2	8	no	—
271	C₂×D₄	—	2	4	no	—
272	C₂×D₄	—	2	16	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	8	no	—
275	C₂²×C₄	—	2	16	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	2	16	no	—
278	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
279	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
280	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
281	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
282	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
283	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
284	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
285	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
286	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
288	C₄⋊C₄	—	2	16	no	—
289	C₄⋊C₄	—	2	16	no	—
290	C₄⋊C₄	—	2	8	no	—
291	C₄⋊C₄	—	2	64	no	—
292	C₄⋊C₄	C₂×D₄×C₈₉	1	16	yes	—
293	C₂²⋊C₄	—	2	16	no	—
294	C₂²⋊C₄	—	2	64	no	—
295	C₂²⋊C₄	C₂×D₄×C₈₉	1	16	yes	—
296	C₄²	—	2	16	no	—
297	C₄²	C₂×D₄×C₈₉	1	8	yes	—
298	C₄²	C₂×D₄×C₈₉	1	4	yes	—
299	C₄²	C₂×D₄×C₈₉	1	4	yes	—
300	C₄²	C₂×D₄×C₈₉	1	16	yes	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	8	no	—
303	C₂³	—	2	4	no	—
304	C₂³	—	2	16	no	—
305	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
306	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
307	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
308	Q₈	—	4	16	no	—
309	Q₈	—	4	16	no	—
310	Q₈	—	4	8	no	—
311	D₄	—	4	16	no	—
312	D₄	—	4	8	no	—
313	D₄	—	4	16	no	—
314	C₂×C₄	—	2	16	no	—
315	C₂×C₄	—	2	4	no	—
316	C₂×C₄	—	2	16	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	16	no	—
319	C₂×C₄	—	2	8	no	—
320	C₂×C₄	—	2	8	no	—
321	C₂×C₄	—	4	16	no	—
322	C₂×C₄	—	4	16	no	—
323	C₂×C₄	#127×C₈₉	1	16	yes	—
324	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
325	C₂×C₄	C₂²×D₄×C₈₉	1	16	yes	—
326	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
327	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
328	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
329	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
330	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
331	C₂×C₄	2₋¹⁺⁴×C₈₉	1	8	yes	—
332	C₂²	—	2	4	no	—
333	C₂²	—	2	8	no	—
334	C₂²	—	4	4	no	—
335	C₂²	—	4	8	no	—
336	C₂²	—	4	16	no	—
337	C₂²	C₂×#127×C₈₉	1	4	yes	—
338	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
339	C₂²	C₂³×D₄×C₈₉	1	2	yes	—
340	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	4	yes	—
341	C₄	—	2	4	no	—
342	C₄	—	2	16	no	—
343	C₄	—	4	4	no	—
344	C₄	—	4	8	no	—
345	C₄	C₂×#127×C₈₉	1	4	yes	—
346	C₄	C₂×#127×C₈₉	1	4	yes	—
347	C₄	#536×C₈₉	1	8	yes	complemented
348	C₂	—	2	4	no	—
349	C₂	—	8	4	no	—
350	C₂	C₂²×#127×C₈₉	1	1	yes	characteristic
351	C₂	C₂×#536×C₈₉	1	2	yes	—
352	C₂	C₈₉×#3499	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#532×C₈₉	C₂
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. C₂×#536×C₈₉	C₂	semidirect
3. C₂²×C₄⋊Q₈×C₈₉	C₂	semidirect
4. C₈₉×#2868	C₂	semidirect
5. C₈₉×#2858	C₂	semidirect
6. C₈₉×#2658	C₂	semidirect
7. C₈₉×#2542	C₂	semidirect
8. C₈₉×#2501	C₂	semidirect
9. C₄×#117×C₈₉	C₂	semidirect
63. #117×C₈₉	D₄	semidirect
170. C₄×C₈₉	#536	semidirect
171. #35317	C₈₉	direct (N × H)
177. C₂×#536	C₂×C₈₉	semidirect
179. C₂²×C₄⋊Q₈	C₂×C₈₉	semidirect
180. #2868	C₂×C₈₉	semidirect
181. #2858	C₂×C₈₉	semidirect
182. #2658	C₂×C₈₉	semidirect
183. #2542	C₂×C₈₉	semidirect
184. #2501	C₂×C₈₉	semidirect
185. C₄×#117	C₂×C₈₉	semidirect
186. C₈₉	#35317	direct (N × H)
240. #117	D₄×C₈₉	semidirect
347. C₄	#536×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#536×C₈₉	2
C₂×#532×C₈₉	2
C₂²×C₄⋊Q₈×C₈₉	2
C₈₉×#2868	2
C₈₉×#2858	2
C₈₉×#2658	2
C₈₉×#2542	2
C₈₉×#2501	2
C₄×#117×C₈₉	2
#35317	89

Subgroups — C89×#35317 #36413165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35317 #36413165