Subgroups — C₈₉×#35455 #36413303

Order 22784.

2506 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#543×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#123×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2561	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2503	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2488	C₂	1	16	yes	maximal, complemented
6	C₈₉×#2308	C₂	1	2	yes	maximal
7	C₂×#381×C₈₉	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2273	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
10	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
11	#543×C₈₉	—	2	8	no	—
12	C₂×#123×C₈₉	—	2	8	no	—
13	C₂×#123×C₈₉	C₂²	1	8	yes	—
14	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
15	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	8	yes	complemented
16	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
17	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
19	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
20	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
21	#400×C₈₉	C₂²	1	16	yes	complemented
22	#397×C₈₉	C₂²	1	8	yes	complemented
23	#393×C₈₉	C₂²	1	8	yes	complemented
24	#391×C₈₉	C₂²	1	8	yes	complemented
25	#388×C₈₉	C₂²	1	16	yes	complemented
26	#386×C₈₉	C₂²	1	8	yes	—
27	#386×C₈₉	C₂²	1	8	yes	—
28	#382×C₈₉	C₂²	1	8	yes	complemented
29	#381×C₈₉	C₂²	1	8	yes	—
30	#381×C₈₉	C₂²	1	4	yes	—
31	#381×C₈₉	C₂²	1	8	yes	complemented
32	#379×C₈₉	C₂²	1	4	yes	—
33	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
34	C₄×C₂²⋊C₄×C₈₉	C₂²	1	8	yes	complemented
35	C₂×#95×C₈₉	C₂²	1	8	yes	complemented
36	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
37	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
38	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
39	C₂²×D₄×C₈₉	—	2	4	no	—
40	C₂²×D₄×C₈₉	—	2	8	no	—
41	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
42	C₂³×C₄×C₈₉	—	2	4	no	—
43	C₂³×C₄×C₈₉	—	2	8	no	—
44	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
45	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
46	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
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	#123×C₈₉	—	2	32	no	—
51	C₂²⋊Q₈×C₈₉	—	2	16	no	—
52	C₂²⋊Q₈×C₈₉	—	2	32	no	—
53	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
54	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
55	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
56	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
57	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
58	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
59	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
60	C₂×C₂²⋊C₄×C₈₉	D₄	1	8	yes	—
61	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
62	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
63	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
64	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
65	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
66	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
67	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
68	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
69	#95×C₈₉	C₂³	1	16	yes	—
70	#95×C₈₉	C₂³	1	16	yes	—
71	#95×C₈₉	C₂³	1	8	yes	—
72	#95×C₈₉	C₂³	1	16	yes	—
73	C₂⁴×C₈₉	—	2	2	no	—
74	C₂⁴×C₈₉	—	2	4	no	—
75	C₂⁴×C₈₉	—	4	4	no	—
76	C₂⁴×C₈₉	—	4	4	no	—
77	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
78	C₂⁴×C₈₉	#41	1	8	yes	—
79	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
80	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
81	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
82	C₂×Q₈×C₈₉	—	2	8	no	—
83	C₂×Q₈×C₈₉	—	4	8	no	—
84	C₂×D₄×C₈₉	—	2	8	no	—
85	C₂×D₄×C₈₉	—	2	8	no	—
86	C₂×D₄×C₈₉	—	2	8	no	—
87	C₂×D₄×C₈₉	—	4	16	no	—
88	C₂²×C₄×C₈₉	—	2	4	no	—
89	C₂²×C₄×C₈₉	—	2	2	no	—
90	C₂²×C₄×C₈₉	—	2	8	no	—
91	C₂²×C₄×C₈₉	—	2	8	no	—
92	C₂²×C₄×C₈₉	—	2	8	no	—
93	C₂²×C₄×C₈₉	—	2	8	no	—
94	C₂²×C₄×C₈₉	—	2	4	no	—
95	C₂²×C₄×C₈₉	—	2	8	no	—
96	C₂²×C₄×C₈₉	—	2	8	no	—
97	C₂²×C₄×C₈₉	—	4	4	no	—
98	C₂²×C₄×C₈₉	—	4	8	no	—
99	C₂²×C₄×C₈₉	—	4	8	no	—
100	C₂²×C₄×C₈₉	—	4	16	no	—
101	C₂²×C₄×C₈₉	C₂×D₄	1	8	yes	—
102	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
103	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
104	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
105	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
106	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
107	C₄⋊C₄×C₈₉	—	2	16	no	—
108	C₄⋊C₄×C₈₉	—	2	8	no	—
109	C₄⋊C₄×C₈₉	—	2	16	no	—
110	C₂²⋊C₄×C₈₉	—	2	8	no	—
111	C₂²⋊C₄×C₈₉	—	2	8	no	—
112	C₂²⋊C₄×C₈₉	—	2	8	no	—
113	C₂²⋊C₄×C₈₉	—	2	8	no	—
114	C₂²⋊C₄×C₈₉	—	2	16	no	—
115	C₂²⋊C₄×C₈₉	—	4	16	no	—
116	C₂²⋊C₄×C₈₉	C₂×D₄	1	16	yes	—
117	C₄²×C₈₉	—	4	8	no	—
118	C₂³×C₈₉	—	2	8	no	—
119	C₂³×C₈₉	—	2	4	no	—
120	C₂³×C₈₉	—	2	2	no	—
121	C₂³×C₈₉	—	2	4	no	—
122	C₂³×C₈₉	—	2	8	no	—
123	C₂³×C₈₉	—	4	8	no	—
124	C₂³×C₈₉	—	4	16	no	—
125	C₂³×C₈₉	—	4	8	no	—
126	C₂³×C₈₉	—	4	4	no	—
127	C₂³×C₈₉	—	8	8	no	—
128	C₂³×C₈₉	#124	1	16	yes	—
129	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
130	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
131	C₂³×C₈₉	C₂×#41	1	4	yes	—
132	C₂³×C₈₉	C₂×#41	1	4	yes	—
133	C₂³×C₈₉	C₂×#41	1	4	yes	—
134	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
135	Q₈×C₈₉	—	8	8	no	—
136	D₄×C₈₉	—	4	16	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	2	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	—	2	16	no	—
145	C₂×C₄×C₈₉	—	2	16	no	—
146	C₂×C₄×C₈₉	—	4	8	no	—
147	C₂×C₄×C₈₉	—	4	8	no	—
148	C₂×C₄×C₈₉	—	4	16	no	—
149	C₂×C₄×C₈₉	—	4	4	no	—
150	C₂×C₄×C₈₉	—	8	8	no	—
151	C₂×C₄×C₈₉	—	8	8	no	—
152	C₂×C₄×C₈₉	C₂²×D₄	1	8	yes	—
153	C₂²×C₈₉	—	2	4	no	—
154	C₂²×C₈₉	—	2	8	no	—
155	C₂²×C₈₉	—	2	8	no	—
156	C₂²×C₈₉	—	2	8	no	—
157	C₂²×C₈₉	—	2	8	no	—
158	C₂²×C₈₉	—	4	16	no	—
159	C₂²×C₈₉	—	4	2	no	—
160	C₂²×C₈₉	—	4	4	no	—
161	C₂²×C₈₉	—	4	8	no	—
162	C₂²×C₈₉	—	8	8	no	—
163	C₂²×C₈₉	C₂×#124	1	4	yes	—
164	C₂²×C₈₉	C₂×#124	1	8	yes	—
165	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
166	C₂²×C₈₉	C₂²×#41	1	2	yes	—
167	C₂²×C₈₉	#585	1	4	yes	—
168	C₄×C₈₉	—	2	8	no	—
169	C₄×C₈₉	—	4	4	no	—
170	C₄×C₈₉	—	4	2	no	—
171	C₄×C₈₉	—	4	8	no	—
172	C₄×C₈₉	—	4	8	no	—
173	#35455	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂×C₈₉	—	2	4	no	—
175	C₂×C₈₉	—	2	8	no	—
176	C₂×C₈₉	—	8	2	no	—
177	C₂×C₈₉	C₂²×#124	1	1	yes	characteristic
178	C₂×C₈₉	#3485	1	2	yes	—
179	C₂×C₈₉	#3491	1	4	yes	—
180	C₂×#543	C₂×C₈₉	1	1	yes	characteristic, complemented
181	C₂²×#123	C₂×C₈₉	1	1	yes	characteristic
182	#2561	C₂×C₈₉	1	4	yes	complemented
183	#2503	C₂×C₈₉	1	4	yes	complemented
184	#2488	C₂×C₈₉	1	16	yes	complemented
185	#2308	C₂×C₈₉	1	2	yes	—
186	C₂×#381	C₂×C₈₉	1	2	yes	complemented
187	#2273	C₂×C₈₉	1	1	yes	characteristic, complemented
188	C₈₉	#35455	1	1	yes	characteristic, direct product factor, Sylow
189	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
190	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
191	#543	—	2	8	no	—
192	C₂×#123	—	2	8	no	—
193	C₂×#123	C₂²×C₈₉	1	8	yes	—
194	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
195	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	8	yes	complemented
196	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
197	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
198	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
199	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
200	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
201	#400	C₂²×C₈₉	1	16	yes	complemented
202	#397	C₂²×C₈₉	1	8	yes	complemented
203	#393	C₂²×C₈₉	1	8	yes	complemented
204	#391	C₂²×C₈₉	1	8	yes	complemented
205	#388	C₂²×C₈₉	1	16	yes	complemented
206	#386	C₂²×C₈₉	1	8	yes	—
207	#386	C₂²×C₈₉	1	8	yes	—
208	#382	C₂²×C₈₉	1	8	yes	complemented
209	#381	C₂²×C₈₉	1	8	yes	—
210	#381	C₂²×C₈₉	1	4	yes	—
211	#381	C₂²×C₈₉	1	8	yes	complemented
212	#379	C₂²×C₈₉	1	4	yes	—
213	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
214	C₄×C₂²⋊C₄	C₂²×C₈₉	1	8	yes	complemented
215	C₂×#95	C₂²×C₈₉	1	8	yes	complemented
216	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
217	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
218	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
219	C₂²×D₄	—	2	4	no	—
220	C₂²×D₄	—	2	8	no	—
221	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
222	C₂³×C₄	—	2	4	no	—
223	C₂³×C₄	—	2	8	no	—
224	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
225	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
226	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
227	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
228	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
229	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
230	#123	—	2	32	no	—
231	C₂²⋊Q₈	—	2	16	no	—
232	C₂²⋊Q₈	—	2	32	no	—
233	C₂×C₄⋊C₄	—	2	8	no	—
234	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
235	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
236	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
237	C₂×C₂²⋊C₄	—	2	8	no	—
238	C₂×C₂²⋊C₄	—	2	8	no	—
239	C₂×C₂²⋊C₄	—	2	8	no	—
240	C₂×C₂²⋊C₄	D₄×C₈₉	1	8	yes	—
241	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
242	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
243	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
244	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
245	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
246	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
247	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
248	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
249	#95	C₂³×C₈₉	1	16	yes	—
250	#95	C₂³×C₈₉	1	16	yes	—
251	#95	C₂³×C₈₉	1	8	yes	—
252	#95	C₂³×C₈₉	1	16	yes	—
253	C₂⁴	—	2	2	no	—
254	C₂⁴	—	2	4	no	—
255	C₂⁴	—	4	4	no	—
256	C₂⁴	—	4	4	no	—
257	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
258	C₂⁴	#41×C₈₉	1	8	yes	—
259	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
260	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
261	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
262	C₂×Q₈	—	2	8	no	—
263	C₂×Q₈	—	4	8	no	—
264	C₂×D₄	—	2	8	no	—
265	C₂×D₄	—	2	8	no	—
266	C₂×D₄	—	2	8	no	—
267	C₂×D₄	—	4	16	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	8	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	8	no	—
276	C₂²×C₄	—	2	8	no	—
277	C₂²×C₄	—	4	4	no	—
278	C₂²×C₄	—	4	8	no	—
279	C₂²×C₄	—	4	8	no	—
280	C₂²×C₄	—	4	16	no	—
281	C₂²×C₄	C₂×D₄×C₈₉	1	8	yes	—
282	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
283	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
284	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
285	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
286	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
287	C₄⋊C₄	—	2	16	no	—
288	C₄⋊C₄	—	2	8	no	—
289	C₄⋊C₄	—	2	16	no	—
290	C₂²⋊C₄	—	2	8	no	—
291	C₂²⋊C₄	—	2	8	no	—
292	C₂²⋊C₄	—	2	8	no	—
293	C₂²⋊C₄	—	2	8	no	—
294	C₂²⋊C₄	—	2	16	no	—
295	C₂²⋊C₄	—	4	16	no	—
296	C₂²⋊C₄	C₂×D₄×C₈₉	1	16	yes	—
297	C₄²	—	4	8	no	—
298	C₂³	—	2	8	no	—
299	C₂³	—	2	4	no	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	8	no	—
303	C₂³	—	4	8	no	—
304	C₂³	—	4	16	no	—
305	C₂³	—	4	8	no	—
306	C₂³	—	4	4	no	—
307	C₂³	—	8	8	no	—
308	C₂³	#124×C₈₉	1	16	yes	—
309	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
310	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
311	C₂³	C₂×#41×C₈₉	1	4	yes	—
312	C₂³	C₂×#41×C₈₉	1	4	yes	—
313	C₂³	C₂×#41×C₈₉	1	4	yes	—
314	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
315	Q₈	—	8	8	no	—
316	D₄	—	4	16	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	16	no	—
325	C₂×C₄	—	2	16	no	—
326	C₂×C₄	—	4	8	no	—
327	C₂×C₄	—	4	8	no	—
328	C₂×C₄	—	4	16	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	—	8	8	no	—
331	C₂×C₄	—	8	8	no	—
332	C₂×C₄	C₂²×D₄×C₈₉	1	8	yes	—
333	C₂²	—	2	4	no	—
334	C₂²	—	2	8	no	—
335	C₂²	—	2	8	no	—
336	C₂²	—	2	8	no	—
337	C₂²	—	2	8	no	—
338	C₂²	—	4	16	no	—
339	C₂²	—	4	2	no	—
340	C₂²	—	4	4	no	—
341	C₂²	—	4	8	no	—
342	C₂²	—	8	8	no	—
343	C₂²	C₂×#124×C₈₉	1	4	yes	—
344	C₂²	C₂×#124×C₈₉	1	8	yes	—
345	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
346	C₂²	C₂²×#41×C₈₉	1	2	yes	—
347	C₂²	#585×C₈₉	1	4	yes	—
348	C₄	—	2	8	no	—
349	C₄	—	4	4	no	—
350	C₄	—	4	2	no	—
351	C₄	—	4	8	no	—
352	C₄	—	4	8	no	—
353	C₂	—	2	4	no	—
354	C₂	—	2	8	no	—
355	C₂	—	8	2	no	—
356	C₂	C₂²×#124×C₈₉	1	1	yes	characteristic
357	C₂	C₈₉×#3485	1	2	yes	—
358	C₂	C₈₉×#3491	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂³×D₄×C₈₉	C₂²
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×#543×C₈₉	C₂	semidirect
3. C₈₉×#2561	C₂	semidirect
4. C₈₉×#2503	C₂	semidirect
5. C₈₉×#2488	C₂	semidirect
7. C₂×#381×C₈₉	C₂	semidirect
8. C₈₉×#2273	C₂	semidirect
15. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
21. #400×C₈₉	C₂²	semidirect
22. #397×C₈₉	C₂²	semidirect
23. #393×C₈₉	C₂²	semidirect
24. #391×C₈₉	C₂²	semidirect
25. #388×C₈₉	C₂²	semidirect
28. #382×C₈₉	C₂²	semidirect
31. #381×C₈₉	C₂²	semidirect
34. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
35. C₂×#95×C₈₉	C₂²	semidirect
173. #35455	C₈₉	direct (N × H)
180. C₂×#543	C₂×C₈₉	semidirect
182. #2561	C₂×C₈₉	semidirect
183. #2503	C₂×C₈₉	semidirect
184. #2488	C₂×C₈₉	semidirect
186. C₂×#381	C₂×C₈₉	semidirect
187. #2273	C₂×C₈₉	semidirect
188. C₈₉	#35455	direct (N × H)
195. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
201. #400	C₂²×C₈₉	semidirect
202. #397	C₂²×C₈₉	semidirect
203. #393	C₂²×C₈₉	semidirect
204. #391	C₂²×C₈₉	semidirect
205. #388	C₂²×C₈₉	semidirect
208. #382	C₂²×C₈₉	semidirect
211. #381	C₂²×C₈₉	semidirect
214. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
215. C₂×#95	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#543×C₈₉	2
C₂²×#123×C₈₉	2
C₈₉×#2561	2
C₈₉×#2503	2
C₈₉×#2488	2
C₈₉×#2308	2
C₂×#381×C₈₉	2
C₈₉×#2273	2
#35455	89

Subgroups — C89×#35455 #36413303

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35455 #36413303