Subgroups — C₈₉×#60804 #36438652

Order 22784.

2164 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#532×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3216	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3215	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3210	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3209	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3208	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3152	C₂	1	2	yes	maximal, complemented
9	C₈₉×#3141	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3037	C₂	1	4	yes	maximal, complemented
11	C₈₉×#3007	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2920	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₈₉	C₂²	1	2	yes	—
14	C₂×#137×C₈₉	C₂²	1	8	yes	complemented
15	#533×C₈₉	—	2	1	no	—
16	#533×C₈₉	—	2	1	no	—
17	#533×C₈₉	—	2	1	no	—
18	#533×C₈₉	—	2	1	no	—
19	#533×C₈₉	C₂²	1	2	yes	—
20	#533×C₈₉	C₂²	1	2	yes	—
21	#533×C₈₉	C₂²	1	2	yes	complemented
22	#533×C₈₉	C₂²	1	2	yes	complemented
23	#532×C₈₉	—	2	1	no	—
24	#532×C₈₉	—	2	1	no	—
25	#532×C₈₉	—	2	1	no	—
26	#532×C₈₉	—	2	1	no	—
27	#532×C₈₉	C₂²	1	2	yes	—
28	#532×C₈₉	C₂²	1	2	yes	—
29	#532×C₈₉	C₂²	1	2	yes	—
30	#532×C₈₉	C₂²	1	2	yes	—
31	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
33	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
34	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#125×C₈₉	—	2	1	no	—
36	C₂×#124×C₈₉	C₂²	1	2	yes	—
37	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
38	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
39	C₂×#121×C₈₉	—	2	1	no	—
40	C₂×#121×C₈₉	—	2	1	no	—
41	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
42	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
43	C₂×C₄×D₄×C₈₉	—	2	1	no	—
44	C₂×C₄×D₄×C₈₉	—	2	1	no	—
45	C₂×#117×C₈₉	—	2	1	no	—
46	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
47	#497×C₈₉	C₂²	1	8	yes	complemented
48	#494×C₈₉	C₂²	1	4	yes	complemented
49	#492×C₈₉	C₂²	1	4	yes	complemented
50	#489×C₈₉	C₂²	1	8	yes	complemented
51	#487×C₈₉	C₂²	1	4	yes	complemented
52	#486×C₈₉	C₂²	1	4	yes	complemented
53	#464×C₈₉	C₂²	1	16	yes	complemented
54	#462×C₈₉	C₂²	1	8	yes	complemented
55	#460×C₈₉	C₂²	1	8	yes	complemented
56	#452×C₈₉	C₂²	1	16	yes	complemented
57	#451×C₈₉	C₂²	1	8	yes	—
58	#450×C₈₉	C₂²	1	8	yes	—
59	#432×C₈₉	C₂²	1	2	yes	—
60	#432×C₈₉	C₂²	1	2	yes	complemented
61	#431×C₈₉	C₂²	1	2	yes	—
62	#431×C₈₉	C₂²	1	2	yes	complemented
63	#423×C₈₉	C₂²	1	2	yes	complemented
64	#417×C₈₉	C₂²	1	8	yes	complemented
65	#407×C₈₉	C₂²	1	2	yes	—
66	C₄×M₁₆×C₈₉	C₂²	1	2	yes	complemented
67	C₂×#41×C₈₉	—	2	2	no	—
68	C₂×#41×C₈₉	—	2	2	no	—
69	C₂×#41×C₈₉	—	4	8	no	—
70	C₂×#41×C₈₉	C₂³	1	4	yes	—
71	C₂×#41×C₈₉	C₂³	1	4	yes	—
72	C₂²×Q₈×C₈₉	—	2	1	no	—
73	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
74	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
75	C₂²×D₄×C₈₉	—	2	2	no	—
76	C₂²×D₄×C₈₉	—	2	1	no	—
77	C₂²×D₄×C₈₉	—	2	1	no	—
78	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
79	C₂³×C₄×C₈₉	—	2	2	no	—
80	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
81	C₂³×C₄×C₈₉	D₄	1	1	yes	characteristic
82	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
83	#137×C₈₉	—	4	16	no	—
84	C₂×Q₁₆×C₈₉	C₂³	1	16	yes	—
85	C₂×SD₁₆×C₈₉	C₂³	1	16	yes	—
86	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
87	C₄⋊Q₈×C₈₉	—	2	1	no	—
88	C₄⋊Q₈×C₈₉	—	2	1	no	—
89	C₄⋊Q₈×C₈₉	—	2	1	no	—
90	C₄⋊Q₈×C₈₉	—	2	1	no	—
91	C₄⋊Q₈×C₈₉	—	2	1	no	—
92	C₄⋊Q₈×C₈₉	—	2	1	no	—
93	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
94	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
95	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
96	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
97	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
98	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
99	#127×C₈₉	—	2	1	no	—
100	#127×C₈₉	—	2	1	no	—
101	#127×C₈₉	C₂³	1	2	yes	—
102	#127×C₈₉	C₂³	1	2	yes	—
103	#125×C₈₉	—	2	2	no	—
104	#125×C₈₉	—	2	2	no	—
105	#125×C₈₉	—	2	2	no	—
106	#125×C₈₉	—	2	2	no	—
107	#124×C₈₉	—	2	2	no	—
108	#124×C₈₉	—	2	2	no	—
109	#124×C₈₉	C₂³	1	4	yes	—
110	#124×C₈₉	C₂³	1	4	yes	—
111	C₂²⋊Q₈×C₈₉	—	2	2	no	—
112	C₂²⋊Q₈×C₈₉	—	2	2	no	—
113	C₂²⋊Q₈×C₈₉	—	2	2	no	—
114	C₂²⋊Q₈×C₈₉	—	2	2	no	—
115	C₂²⋊Q₈×C₈₉	—	2	2	no	—
116	C₂²⋊Q₈×C₈₉	—	2	2	no	—
117	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
118	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
119	#121×C₈₉	—	2	2	no	—
120	#121×C₈₉	—	2	2	no	—
121	#121×C₈₉	—	2	2	no	—
122	#121×C₈₉	—	2	2	no	—
123	#121×C₈₉	—	2	2	no	—
124	#121×C₈₉	—	2	2	no	—
125	#121×C₈₉	—	2	2	no	—
126	#121×C₈₉	—	2	2	no	—
127	C₄×Q₈×C₈₉	—	2	2	no	—
128	C₄×Q₈×C₈₉	—	2	2	no	—
129	C₄×Q₈×C₈₉	—	2	2	no	—
130	C₄×Q₈×C₈₉	—	2	2	no	—
131	C₄×Q₈×C₈₉	—	2	2	no	—
132	C₄×Q₈×C₈₉	—	2	2	no	—
133	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
134	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
135	C₄×D₄×C₈₉	—	2	2	no	—
136	C₄×D₄×C₈₉	—	2	2	no	—
137	C₄×D₄×C₈₉	—	2	2	no	—
138	C₄×D₄×C₈₉	—	2	2	no	—
139	C₄×D₄×C₈₉	—	2	2	no	—
140	C₄×D₄×C₈₉	—	2	2	no	—
141	C₄×D₄×C₈₉	—	2	2	no	—
142	C₄×D₄×C₈₉	—	2	2	no	—
143	#117×C₈₉	—	2	2	no	—
144	#117×C₈₉	—	2	2	no	—
145	#117×C₈₉	—	2	2	no	—
146	#117×C₈₉	—	2	2	no	—
147	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
148	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
149	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
150	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
151	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
152	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
153	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
154	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
156	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
157	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
158	C₂×C₄²×C₈₉	—	2	2	no	—
159	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
160	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
161	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
162	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
163	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
164	C₂×C₄²×C₈₉	D₄	1	1	yes	characteristic
165	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
169	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
170	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
171	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
172	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
173	#103×C₈₉	C₂³	1	16	yes	—
174	#102×C₈₉	C₂³	1	16	yes	—
175	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
176	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
177	#97×C₈₉	C₂³	1	4	yes	—
178	C₄×C₈×C₈₉	C₂³	1	4	yes	—
179	C₂⁴×C₈₉	—	2	2	no	—
180	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
181	#41×C₈₉	—	2	16	no	—
182	#41×C₈₉	—	4	8	no	—
183	#41×C₈₉	—	4	8	no	—
184	#41×C₈₉	—	4	8	no	—
185	C₂×Q₈×C₈₉	—	2	2	no	—
186	C₂×Q₈×C₈₉	—	2	2	no	—
187	C₂×Q₈×C₈₉	—	2	2	no	—
188	C₂×Q₈×C₈₉	—	2	2	no	—
189	C₂×Q₈×C₈₉	—	2	8	no	—
190	C₂×Q₈×C₈₉	—	4	4	no	—
191	C₂×Q₈×C₈₉	—	4	4	no	—
192	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
193	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
194	C₂×D₄×C₈₉	—	2	4	no	—
195	C₂×D₄×C₈₉	—	2	4	no	—
196	C₂×D₄×C₈₉	—	2	2	no	—
197	C₂×D₄×C₈₉	—	2	2	no	—
198	C₂×D₄×C₈₉	—	2	2	no	—
199	C₂×D₄×C₈₉	—	2	2	no	—
200	C₂×D₄×C₈₉	—	2	2	no	—
201	C₂×D₄×C₈₉	—	4	4	no	—
202	C₂×D₄×C₈₉	—	4	4	no	—
203	C₂×D₄×C₈₉	—	4	8	no	—
204	C₂×D₄×C₈₉	—	4	4	no	—
205	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
206	C₂²×C₄×C₈₉	—	2	4	no	—
207	C₂²×C₄×C₈₉	—	2	4	no	—
208	C₂²×C₄×C₈₉	—	2	2	no	—
209	C₂²×C₄×C₈₉	—	2	2	no	—
210	C₂²×C₄×C₈₉	—	2	2	no	—
211	C₂²×C₄×C₈₉	—	2	4	no	—
212	C₂²×C₄×C₈₉	—	2	4	no	—
213	C₂²×C₄×C₈₉	—	4	2	no	—
214	C₂²×C₄×C₈₉	—	4	8	no	—
215	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
217	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
218	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
222	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
225	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
227	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
228	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
229	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
230	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
231	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
232	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
233	Q₁₆×C₈₉	—	4	16	no	—
234	SD₁₆×C₈₉	—	4	16	no	—
235	M₁₆×C₈₉	—	2	8	no	—
236	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
237	C₄⋊C₄×C₈₉	—	2	2	no	—
238	C₄⋊C₄×C₈₉	—	2	2	no	—
239	C₄⋊C₄×C₈₉	—	2	2	no	—
240	C₄⋊C₄×C₈₉	—	2	2	no	—
241	C₄⋊C₄×C₈₉	—	2	2	no	—
242	C₄⋊C₄×C₈₉	—	2	2	no	—
243	C₄⋊C₄×C₈₉	—	2	2	no	—
244	C₄⋊C₄×C₈₉	—	2	2	no	—
245	C₄⋊C₄×C₈₉	—	2	2	no	—
246	C₄⋊C₄×C₈₉	—	2	2	no	—
247	C₄⋊C₄×C₈₉	—	2	4	no	—
248	C₄⋊C₄×C₈₉	—	2	4	no	—
249	C₄⋊C₄×C₈₉	—	2	4	no	—
250	C₄⋊C₄×C₈₉	—	2	4	no	—
251	C₄⋊C₄×C₈₉	—	2	2	no	—
252	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
253	C₂²⋊C₄×C₈₉	—	2	4	no	—
254	C₂²⋊C₄×C₈₉	—	2	4	no	—
255	C₂²⋊C₄×C₈₉	—	2	4	no	—
256	C₂²⋊C₄×C₈₉	—	2	4	no	—
257	C₂²⋊C₄×C₈₉	—	2	4	no	—
258	C₂²⋊C₄×C₈₉	—	2	4	no	—
259	C₄²×C₈₉	—	2	4	no	—
260	C₄²×C₈₉	—	2	4	no	—
261	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
262	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
263	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
264	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
267	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
268	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
269	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
270	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
271	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
272	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
273	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
274	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
275	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
276	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
277	C₂³×C₈₉	—	2	2	no	—
278	C₂³×C₈₉	—	2	2	no	—
279	C₂³×C₈₉	—	2	4	no	—
280	C₂³×C₈₉	—	4	1	no	—
281	C₂³×C₈₉	—	4	4	no	—
282	C₂³×C₈₉	—	4	4	no	—
283	C₂³×C₈₉	—	4	4	no	—
284	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
285	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
286	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
287	Q₈×C₈₉	—	2	8	no	—
288	Q₈×C₈₉	—	2	8	no	—
289	Q₈×C₈₉	—	4	4	no	—
290	Q₈×C₈₉	—	4	4	no	—
291	Q₈×C₈₉	—	4	4	no	—
292	Q₈×C₈₉	—	4	4	no	—
293	D₄×C₈₉	—	2	8	no	—
294	D₄×C₈₉	—	4	4	no	—
295	D₄×C₈₉	—	4	4	no	—
296	D₄×C₈₉	—	4	8	no	—
297	D₄×C₈₉	—	4	8	no	—
298	D₄×C₈₉	—	4	4	no	—
299	D₄×C₈₉	—	4	4	no	—
300	D₄×C₈₉	—	4	4	no	—
301	C₂×C₄×C₈₉	—	2	2	no	—
302	C₂×C₄×C₈₉	—	2	2	no	—
303	C₂×C₄×C₈₉	—	2	2	no	—
304	C₂×C₄×C₈₉	—	2	2	no	—
305	C₂×C₄×C₈₉	—	2	2	no	—
306	C₂×C₄×C₈₉	—	2	2	no	—
307	C₂×C₄×C₈₉	—	2	2	no	—
308	C₂×C₄×C₈₉	—	2	2	no	—
309	C₂×C₄×C₈₉	—	2	2	no	—
310	C₂×C₄×C₈₉	—	2	2	no	—
311	C₂×C₄×C₈₉	—	2	2	no	—
312	C₂×C₄×C₈₉	—	2	2	no	—
313	C₂×C₄×C₈₉	—	2	2	no	—
314	C₂×C₄×C₈₉	—	2	4	no	—
315	C₂×C₄×C₈₉	—	2	4	no	—
316	C₂×C₄×C₈₉	—	2	4	no	—
317	C₂×C₄×C₈₉	—	4	1	no	—
318	C₂×C₄×C₈₉	—	4	1	no	—
319	C₂×C₄×C₈₉	—	4	1	no	—
320	C₂×C₄×C₈₉	—	4	8	no	—
321	C₂×C₄×C₈₉	—	4	4	no	—
322	C₂×C₄×C₈₉	—	4	4	no	—
323	C₂×C₄×C₈₉	—	4	4	no	—
324	C₂×C₄×C₈₉	—	4	8	no	—
325	C₂×C₄×C₈₉	#137	1	4	yes	complemented
326	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
330	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
331	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
334	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
335	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
336	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
337	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
338	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
339	C₈×C₈₉	—	2	8	no	—
340	C₂²×C₈₉	—	2	1	no	—
341	C₂²×C₈₉	—	2	1	no	—
342	C₂²×C₈₉	—	2	1	no	—
343	C₂²×C₈₉	—	2	1	no	—
344	C₂²×C₈₉	—	2	1	no	—
345	C₂²×C₈₉	—	2	1	no	—
346	C₂²×C₈₉	—	2	1	no	—
347	C₂²×C₈₉	—	4	4	no	—
348	C₂²×C₈₉	—	4	4	no	—
349	C₂²×C₈₉	—	4	4	no	—
350	C₂²×C₈₉	—	4	4	no	—
351	C₂²×C₈₉	—	8	8	no	—
352	C₂²×C₈₉	#535	1	2	yes	—
353	C₂²×C₈₉	C₂×#137	1	2	yes	—
354	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
355	C₄×C₈₉	—	2	1	no	—
356	C₄×C₈₉	—	2	1	no	—
357	C₄×C₈₉	—	2	1	no	—
358	C₄×C₈₉	—	2	1	no	—
359	C₄×C₈₉	—	2	1	no	—
360	C₄×C₈₉	—	2	1	no	—
361	C₄×C₈₉	—	2	1	no	—
362	C₄×C₈₉	—	4	4	no	—
363	C₄×C₈₉	—	4	4	no	—
364	C₄×C₈₉	—	4	4	no	—
365	C₄×C₈₉	#535	1	2	yes	—
366	C₄×C₈₉	C₂×#137	1	2	yes	—
367	C₄×C₈₉	C₂×#137	1	2	yes	—
368	C₄×C₈₉	#575	1	2	yes	—
369	C₄×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
370	#60804	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
371	C₂×C₈₉	—	2	2	no	—
372	C₂×C₈₉	—	2	2	no	—
373	C₂×C₈₉	—	4	1	no	—
374	C₂×C₈₉	—	8	4	no	—
375	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
376	C₂×C₈₉	C₂²×#137	1	1	yes	characteristic
377	C₂×C₈₉	C₂×#575	1	1	yes	characteristic
378	C₂×#533	C₂×C₈₉	1	1	yes	characteristic, complemented
379	C₂×#532	C₂×C₈₉	1	1	yes	characteristic
380	#3216	C₂×C₈₉	1	4	yes	complemented
381	#3215	C₂×C₈₉	1	4	yes	complemented
382	#3210	C₂×C₈₉	1	4	yes	complemented
383	#3209	C₂×C₈₉	1	2	yes	complemented
384	#3208	C₂×C₈₉	1	2	yes	complemented
385	#3152	C₂×C₈₉	1	2	yes	complemented
386	#3141	C₂×C₈₉	1	2	yes	complemented
387	#3037	C₂×C₈₉	1	4	yes	complemented
388	#3007	C₂×C₈₉	1	4	yes	complemented
389	#2920	C₂×C₈₉	1	1	yes	characteristic, complemented
390	C₈₉	#60804	1	1	yes	characteristic, direct product factor, Sylow
391	C₂²×#41	C₂²×C₈₉	1	2	yes	—
392	C₂×#137	C₂²×C₈₉	1	8	yes	complemented
393	#533	—	2	1	no	—
394	#533	—	2	1	no	—
395	#533	—	2	1	no	—
396	#533	—	2	1	no	—
397	#533	C₂²×C₈₉	1	2	yes	—
398	#533	C₂²×C₈₉	1	2	yes	—
399	#533	C₂²×C₈₉	1	2	yes	complemented
400	#533	C₂²×C₈₉	1	2	yes	complemented
401	#532	—	2	1	no	—
402	#532	—	2	1	no	—
403	#532	—	2	1	no	—
404	#532	—	2	1	no	—
405	#532	C₂²×C₈₉	1	2	yes	—
406	#532	C₂²×C₈₉	1	2	yes	—
407	#532	C₂²×C₈₉	1	2	yes	—
408	#532	C₂²×C₈₉	1	2	yes	—
409	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
410	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
411	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
412	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×#125	—	2	1	no	—
414	C₂×#124	C₂²×C₈₉	1	2	yes	—
415	C₂×C₂²⋊Q₈	—	2	1	no	—
416	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
417	C₂×#121	—	2	1	no	—
418	C₂×#121	—	2	1	no	—
419	C₂×C₄×Q₈	—	2	1	no	—
420	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
421	C₂×C₄×D₄	—	2	1	no	—
422	C₂×C₄×D₄	—	2	1	no	—
423	C₂×#117	—	2	1	no	—
424	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
425	#497	C₂²×C₈₉	1	8	yes	complemented
426	#494	C₂²×C₈₉	1	4	yes	complemented
427	#492	C₂²×C₈₉	1	4	yes	complemented
428	#489	C₂²×C₈₉	1	8	yes	complemented
429	#487	C₂²×C₈₉	1	4	yes	complemented
430	#486	C₂²×C₈₉	1	4	yes	complemented
431	#464	C₂²×C₈₉	1	16	yes	complemented
432	#462	C₂²×C₈₉	1	8	yes	complemented
433	#460	C₂²×C₈₉	1	8	yes	complemented
434	#452	C₂²×C₈₉	1	16	yes	complemented
435	#451	C₂²×C₈₉	1	8	yes	—
436	#450	C₂²×C₈₉	1	8	yes	—
437	#432	C₂²×C₈₉	1	2	yes	—
438	#432	C₂²×C₈₉	1	2	yes	complemented
439	#431	C₂²×C₈₉	1	2	yes	—
440	#431	C₂²×C₈₉	1	2	yes	complemented
441	#423	C₂²×C₈₉	1	2	yes	complemented
442	#417	C₂²×C₈₉	1	8	yes	complemented
443	#407	C₂²×C₈₉	1	2	yes	—
444	C₄×M₁₆	C₂²×C₈₉	1	2	yes	complemented
445	C₂×#41	—	2	2	no	—
446	C₂×#41	—	2	2	no	—
447	C₂×#41	—	4	8	no	—
448	C₂×#41	C₂³×C₈₉	1	4	yes	—
449	C₂×#41	C₂³×C₈₉	1	4	yes	—
450	C₂²×Q₈	—	2	1	no	—
451	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
452	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
453	C₂²×D₄	—	2	2	no	—
454	C₂²×D₄	—	2	1	no	—
455	C₂²×D₄	—	2	1	no	—
456	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
457	C₂³×C₄	—	2	2	no	—
458	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
459	C₂³×C₄	D₄×C₈₉	1	1	yes	characteristic
460	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
461	#137	—	4	16	no	—
462	C₂×Q₁₆	C₂³×C₈₉	1	16	yes	—
463	C₂×SD₁₆	C₂³×C₈₉	1	16	yes	—
464	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
465	C₄⋊Q₈	—	2	1	no	—
466	C₄⋊Q₈	—	2	1	no	—
467	C₄⋊Q₈	—	2	1	no	—
468	C₄⋊Q₈	—	2	1	no	—
469	C₄⋊Q₈	—	2	1	no	—
470	C₄⋊Q₈	—	2	1	no	—
471	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
472	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
473	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
474	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
475	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
476	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
477	#127	—	2	1	no	—
478	#127	—	2	1	no	—
479	#127	C₂³×C₈₉	1	2	yes	—
480	#127	C₂³×C₈₉	1	2	yes	—
481	#125	—	2	2	no	—
482	#125	—	2	2	no	—
483	#125	—	2	2	no	—
484	#125	—	2	2	no	—
485	#124	—	2	2	no	—
486	#124	—	2	2	no	—
487	#124	C₂³×C₈₉	1	4	yes	—
488	#124	C₂³×C₈₉	1	4	yes	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	2	no	—
492	C₂²⋊Q₈	—	2	2	no	—
493	C₂²⋊Q₈	—	2	2	no	—
494	C₂²⋊Q₈	—	2	2	no	—
495	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
496	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
497	#121	—	2	2	no	—
498	#121	—	2	2	no	—
499	#121	—	2	2	no	—
500	#121	—	2	2	no	—
501	#121	—	2	2	no	—
502	#121	—	2	2	no	—
503	#121	—	2	2	no	—
504	#121	—	2	2	no	—
505	C₄×Q₈	—	2	2	no	—
506	C₄×Q₈	—	2	2	no	—
507	C₄×Q₈	—	2	2	no	—
508	C₄×Q₈	—	2	2	no	—
509	C₄×Q₈	—	2	2	no	—
510	C₄×Q₈	—	2	2	no	—
511	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
512	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
513	C₄×D₄	—	2	2	no	—
514	C₄×D₄	—	2	2	no	—
515	C₄×D₄	—	2	2	no	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	—	2	2	no	—
518	C₄×D₄	—	2	2	no	—
519	C₄×D₄	—	2	2	no	—
520	C₄×D₄	—	2	2	no	—
521	#117	—	2	2	no	—
522	#117	—	2	2	no	—
523	#117	—	2	2	no	—
524	#117	—	2	2	no	—
525	C₂×C₄⋊C₄	—	2	1	no	—
526	C₂×C₄⋊C₄	—	2	1	no	—
527	C₂×C₄⋊C₄	—	2	1	no	—
528	C₂×C₄⋊C₄	—	2	1	no	—
529	C₂×C₄⋊C₄	—	2	1	no	—
530	C₂×C₄⋊C₄	—	2	2	no	—
531	C₂×C₄⋊C₄	—	2	2	no	—
532	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
533	C₂×C₂²⋊C₄	—	2	2	no	—
534	C₂×C₂²⋊C₄	—	2	2	no	—
535	C₂×C₂²⋊C₄	—	2	2	no	—
536	C₂×C₄²	—	2	2	no	—
537	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
538	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
539	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
540	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
541	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
542	C₂×C₄²	D₄×C₈₉	1	1	yes	characteristic
543	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
544	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
545	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
546	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
547	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
548	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
549	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
550	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
551	#103	C₂³×C₈₉	1	16	yes	—
552	#102	C₂³×C₈₉	1	16	yes	—
553	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
554	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
555	#97	C₂³×C₈₉	1	4	yes	—
556	C₄×C₈	C₂³×C₈₉	1	4	yes	—
557	C₂⁴	—	2	2	no	—
558	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
559	#41	—	2	16	no	—
560	#41	—	4	8	no	—
561	#41	—	4	8	no	—
562	#41	—	4	8	no	—
563	C₂×Q₈	—	2	2	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	—	2	2	no	—
566	C₂×Q₈	—	2	2	no	—
567	C₂×Q₈	—	2	8	no	—
568	C₂×Q₈	—	4	4	no	—
569	C₂×Q₈	—	4	4	no	—
570	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
571	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	2	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	2	no	—
578	C₂×D₄	—	2	2	no	—
579	C₂×D₄	—	4	4	no	—
580	C₂×D₄	—	4	4	no	—
581	C₂×D₄	—	4	8	no	—
582	C₂×D₄	—	4	4	no	—
583	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	4	no	—
586	C₂²×C₄	—	2	2	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	2	no	—
589	C₂²×C₄	—	2	4	no	—
590	C₂²×C₄	—	2	4	no	—
591	C₂²×C₄	—	4	2	no	—
592	C₂²×C₄	—	4	8	no	—
593	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
594	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
595	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
596	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
597	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
598	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
599	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
601	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
602	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
603	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
604	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
605	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
606	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
607	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
610	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
611	Q₁₆	—	4	16	no	—
612	SD₁₆	—	4	16	no	—
613	M₁₆	—	2	8	no	—
614	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
615	C₄⋊C₄	—	2	2	no	—
616	C₄⋊C₄	—	2	2	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	2	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	2	no	—
624	C₄⋊C₄	—	2	2	no	—
625	C₄⋊C₄	—	2	4	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	2	no	—
630	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
631	C₂²⋊C₄	—	2	4	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	4	no	—
634	C₂²⋊C₄	—	2	4	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₄²	—	2	4	no	—
638	C₄²	—	2	4	no	—
639	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
640	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
641	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
642	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
643	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
644	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
645	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
646	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
647	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
648	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
649	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
650	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
651	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
652	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
653	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
654	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
655	C₂³	—	2	2	no	—
656	C₂³	—	2	2	no	—
657	C₂³	—	2	4	no	—
658	C₂³	—	4	1	no	—
659	C₂³	—	4	4	no	—
660	C₂³	—	4	4	no	—
661	C₂³	—	4	4	no	—
662	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
663	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
664	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
665	Q₈	—	2	8	no	—
666	Q₈	—	2	8	no	—
667	Q₈	—	4	4	no	—
668	Q₈	—	4	4	no	—
669	Q₈	—	4	4	no	—
670	Q₈	—	4	4	no	—
671	D₄	—	2	8	no	—
672	D₄	—	4	4	no	—
673	D₄	—	4	4	no	—
674	D₄	—	4	8	no	—
675	D₄	—	4	8	no	—
676	D₄	—	4	4	no	—
677	D₄	—	4	4	no	—
678	D₄	—	4	4	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	2	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	2	no	—
689	C₂×C₄	—	2	2	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	2	2	no	—
692	C₂×C₄	—	2	4	no	—
693	C₂×C₄	—	2	4	no	—
694	C₂×C₄	—	2	4	no	—
695	C₂×C₄	—	4	1	no	—
696	C₂×C₄	—	4	1	no	—
697	C₂×C₄	—	4	1	no	—
698	C₂×C₄	—	4	8	no	—
699	C₂×C₄	—	4	4	no	—
700	C₂×C₄	—	4	4	no	—
701	C₂×C₄	—	4	4	no	—
702	C₂×C₄	—	4	8	no	—
703	C₂×C₄	#137×C₈₉	1	4	yes	complemented
704	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
705	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
706	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
707	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
709	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
710	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
711	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
712	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
713	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
714	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
715	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
716	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
717	C₈	—	2	8	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	1	no	—
721	C₂²	—	2	1	no	—
722	C₂²	—	2	1	no	—
723	C₂²	—	2	1	no	—
724	C₂²	—	2	1	no	—
725	C₂²	—	4	4	no	—
726	C₂²	—	4	4	no	—
727	C₂²	—	4	4	no	—
728	C₂²	—	4	4	no	—
729	C₂²	—	8	8	no	—
730	C₂²	#535×C₈₉	1	2	yes	—
731	C₂²	C₂×#137×C₈₉	1	2	yes	—
732	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
733	C₄	—	2	1	no	—
734	C₄	—	2	1	no	—
735	C₄	—	2	1	no	—
736	C₄	—	2	1	no	—
737	C₄	—	2	1	no	—
738	C₄	—	2	1	no	—
739	C₄	—	2	1	no	—
740	C₄	—	4	4	no	—
741	C₄	—	4	4	no	—
742	C₄	—	4	4	no	—
743	C₄	#535×C₈₉	1	2	yes	—
744	C₄	C₂×#137×C₈₉	1	2	yes	—
745	C₄	C₂×#137×C₈₉	1	2	yes	—
746	C₄	#575×C₈₉	1	2	yes	—
747	C₄	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
748	C₂	—	2	2	no	—
749	C₂	—	2	2	no	—
750	C₂	—	4	1	no	—
751	C₂	—	8	4	no	—
752	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
753	C₂	C₂²×#137×C₈₉	1	1	yes	characteristic
754	C₂	C₂×#575×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂×#532×C₈₉	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂²×C₄²×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#533×C₈₉	C₂	semidirect
3. C₈₉×#3216	C₂	semidirect
4. C₈₉×#3215	C₂	semidirect
5. C₈₉×#3210	C₂	semidirect
6. C₈₉×#3209	C₂	semidirect
7. C₈₉×#3208	C₂	semidirect
8. C₈₉×#3152	C₂	semidirect
9. C₈₉×#3141	C₂	semidirect
10. C₈₉×#3037	C₂	semidirect
11. C₈₉×#3007	C₂	semidirect
12. C₈₉×#2920	C₂	semidirect
14. C₂×#137×C₈₉	C₂²	semidirect
21. #533×C₈₉	C₂²	semidirect
22. #533×C₈₉	C₂²	semidirect
32. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
33. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
42. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
47. #497×C₈₉	C₂²	semidirect
48. #494×C₈₉	C₂²	semidirect
49. #492×C₈₉	C₂²	semidirect
50. #489×C₈₉	C₂²	semidirect
51. #487×C₈₉	C₂²	semidirect
52. #486×C₈₉	C₂²	semidirect
53. #464×C₈₉	C₂²	semidirect
54. #462×C₈₉	C₂²	semidirect
55. #460×C₈₉	C₂²	semidirect
56. #452×C₈₉	C₂²	semidirect
60. #432×C₈₉	C₂²	semidirect
62. #431×C₈₉	C₂²	semidirect
63. #423×C₈₉	C₂²	semidirect
64. #417×C₈₉	C₂²	semidirect
66. C₄×M₁₆×C₈₉	C₂²	semidirect
325. C₂×C₄×C₈₉	#137	semidirect
370. #60804	C₈₉	direct (N × H)
378. C₂×#533	C₂×C₈₉	semidirect
380. #3216	C₂×C₈₉	semidirect
381. #3215	C₂×C₈₉	semidirect
382. #3210	C₂×C₈₉	semidirect
383. #3209	C₂×C₈₉	semidirect
384. #3208	C₂×C₈₉	semidirect
385. #3152	C₂×C₈₉	semidirect
386. #3141	C₂×C₈₉	semidirect
387. #3037	C₂×C₈₉	semidirect
388. #3007	C₂×C₈₉	semidirect
389. #2920	C₂×C₈₉	semidirect
390. C₈₉	#60804	direct (N × H)
392. C₂×#137	C₂²×C₈₉	semidirect
399. #533	C₂²×C₈₉	semidirect
400. #533	C₂²×C₈₉	semidirect
410. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
411. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
420. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
425. #497	C₂²×C₈₉	semidirect
426. #494	C₂²×C₈₉	semidirect
427. #492	C₂²×C₈₉	semidirect
428. #489	C₂²×C₈₉	semidirect
429. #487	C₂²×C₈₉	semidirect
430. #486	C₂²×C₈₉	semidirect
431. #464	C₂²×C₈₉	semidirect
432. #462	C₂²×C₈₉	semidirect
433. #460	C₂²×C₈₉	semidirect
434. #452	C₂²×C₈₉	semidirect
438. #432	C₂²×C₈₉	semidirect
440. #431	C₂²×C₈₉	semidirect
441. #423	C₂²×C₈₉	semidirect
442. #417	C₂²×C₈₉	semidirect
444. C₄×M₁₆	C₂²×C₈₉	semidirect
703. C₂×C₄	#137×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₈₉	2
C₂×#532×C₈₉	2
C₈₉×#3216	2
C₈₉×#3215	2
C₈₉×#3210	2
C₈₉×#3209	2
C₈₉×#3208	2
C₈₉×#3152	2
C₈₉×#3141	2
C₈₉×#3037	2
C₈₉×#3007	2
C₈₉×#2920	2
#60804	89

Subgroups — C89×#60804 #36438652

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60804 #36438652