Subgroups — C₈₉×#60517 #36438365

Order 22784.

2178 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3449	C₂	1	1	yes	maximal, characteristic
2	C₂×#520×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3099	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3098	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3097	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3096	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3093	C₂	1	4	yes	maximal, complemented
8	C₈₉×#3092	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2911	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#428×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2896	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#417×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2879	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
15	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
16	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
18	#537×C₈₉	C₂²	1	2	yes	—
19	#537×C₈₉	C₂²	1	2	yes	—
20	#536×C₈₉	—	2	1	no	—
21	#536×C₈₉	C₂²	1	2	yes	—
22	#535×C₈₉	—	2	1	no	—
23	#535×C₈₉	C₂²	1	2	yes	—
24	#534×C₈₉	—	2	2	no	—
25	#532×C₈₉	—	2	2	no	—
26	#525×C₈₉	—	2	2	no	—
27	#525×C₈₉	C₂²	1	4	yes	—
28	#520×C₈₉	—	2	2	no	—
29	#520×C₈₉	—	2	2	no	—
30	#520×C₈₉	C₂²	1	4	yes	—
31	#520×C₈₉	C₂²	1	4	yes	complemented
32	C₂×C₄×Q₈×C₈₉	—	2	1	no	—
33	C₂×C₄×D₄×C₈₉	—	2	1	no	—
34	C₂×C₄×D₄×C₈₉	—	2	2	no	—
35	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
38	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
39	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
40	#485×C₈₉	C₂²	1	8	yes	complemented
41	#485×C₈₉	C₂²	1	8	yes	complemented
42	#484×C₈₉	C₂²	1	8	yes	complemented
43	#483×C₈₉	C₂²	1	8	yes	complemented
44	#482×C₈₉	C₂²	1	8	yes	complemented
45	#482×C₈₉	C₂²	1	8	yes	complemented
46	#481×C₈₉	C₂²	1	8	yes	complemented
47	#480×C₈₉	C₂²	1	8	yes	complemented
48	#428×C₈₉	C₂²	1	2	yes	complemented
49	#428×C₈₉	C₂²	1	4	yes	complemented
50	#428×C₈₉	C₂²	1	2	yes	complemented
51	#428×C₈₉	C₂²	1	4	yes	complemented
52	#428×C₈₉	C₂²	1	2	yes	complemented
53	#428×C₈₉	C₂²	1	2	yes	complemented
54	#427×C₈₉	C₂²	1	4	yes	complemented
55	C₂×#107×C₈₉	C₂²	1	2	yes	complemented
56	C₂×#106×C₈₉	C₂²	1	2	yes	complemented
57	#419×C₈₉	C₂²	1	2	yes	complemented
58	#418×C₈₉	C₂²	1	2	yes	complemented
59	#417×C₈₉	C₂²	1	2	yes	—
60	#417×C₈₉	C₂²	1	4	yes	—
61	#417×C₈₉	C₂²	1	2	yes	—
62	#417×C₈₉	C₂²	1	4	yes	complemented
63	#416×C₈₉	C₂²	1	4	yes	complemented
64	C₂×#103×C₈₉	C₂²	1	2	yes	complemented
65	C₂×#102×C₈₉	C₂²	1	2	yes	complemented
66	#408×C₈₉	C₂²	1	4	yes	—
67	#408×C₈₉	C₂²	1	4	yes	complemented
68	#407×C₈₉	C₂²	1	4	yes	complemented
69	C₂×#41×C₈₉	—	2	1	no	—
70	C₂×#41×C₈₉	—	2	1	no	—
71	C₂×#41×C₈₉	—	2	4	no	—
72	C₂×#41×C₈₉	—	2	4	no	—
73	C₂×#41×C₈₉	—	2	4	no	—
74	C₂×#41×C₈₉	—	2	4	no	—
75	C₂×#41×C₈₉	D₄	1	2	yes	—
76	C₂×#41×C₈₉	D₄	1	2	yes	—
77	C₂×#41×C₈₉	C₂³	1	2	yes	—
78	C₂×#41×C₈₉	C₂³	1	2	yes	—
79	C₂×#41×C₈₉	C₂³	1	2	yes	—
80	C₂×#41×C₈₉	C₂³	1	2	yes	—
81	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
82	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₈₉	—	2	1	no	—
84	C₂²×D₄×C₈₉	D₄	1	2	yes	—
85	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
86	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₈₉	—	2	1	no	—
88	C₂³×C₄×C₈₉	—	2	2	no	—
89	C₂³×C₄×C₈₉	—	2	1	no	—
90	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
91	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
92	C₂×M₁₆×C₈₉	—	2	4	no	—
93	C₂×M₁₆×C₈₉	—	2	4	no	—
94	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
95	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
96	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
97	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
98	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
99	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
100	C₄⋊Q₈×C₈₉	—	2	2	no	—
101	#127×C₈₉	—	2	2	no	—
102	#124×C₈₉	—	2	2	no	—
103	#124×C₈₉	—	2	2	no	—
104	#123×C₈₉	—	2	4	no	—
105	#123×C₈₉	—	2	4	no	—
106	C₂²⋊Q₈×C₈₉	—	2	2	no	—
107	C₂²⋊Q₈×C₈₉	—	2	2	no	—
108	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
109	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
110	#121×C₈₉	—	2	2	no	—
111	#121×C₈₉	—	2	2	no	—
112	#121×C₈₉	—	2	4	no	—
113	#121×C₈₉	—	2	4	no	—
114	#121×C₈₉	C₂³	1	4	yes	—
115	#121×C₈₉	C₂³	1	4	yes	—
116	#120×C₈₉	—	2	4	no	—
117	#120×C₈₉	—	2	4	no	—
118	C₄×Q₈×C₈₉	—	2	4	no	—
119	C₄×Q₈×C₈₉	—	2	4	no	—
120	C₄×D₄×C₈₉	—	2	8	no	—
121	C₄×D₄×C₈₉	—	2	4	no	—
122	C₄×D₄×C₈₉	—	2	8	no	—
123	C₄×D₄×C₈₉	—	2	4	no	—
124	C₄×D₄×C₈₉	—	2	4	no	—
125	C₄×D₄×C₈₉	—	2	4	no	—
126	#117×C₈₉	—	2	1	no	—
127	#117×C₈₉	—	2	1	no	—
128	#117×C₈₉	—	2	1	no	—
129	#117×C₈₉	—	2	1	no	—
130	#117×C₈₉	—	2	4	no	—
131	#117×C₈₉	C₂³	1	2	yes	—
132	#117×C₈₉	C₂³	1	2	yes	—
133	#117×C₈₉	C₂³	1	2	yes	—
134	#117×C₈₉	C₂³	1	2	yes	—
135	#117×C₈₉	C₂³	1	8	yes	—
136	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
137	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
138	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
139	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
140	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
141	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
143	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
144	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
145	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
146	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
147	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
148	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
149	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
150	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
151	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
152	C₂×C₄²×C₈₉	—	2	1	no	—
153	C₂×C₄²×C₈₉	—	2	1	no	—
154	C₂×C₄²×C₈₉	—	2	2	no	—
155	#107×C₈₉	C₂³	1	8	yes	—
156	#107×C₈₉	C₂³	1	4	yes	—
157	#107×C₈₉	C₂³	1	4	yes	—
158	#106×C₈₉	C₂³	1	8	yes	—
159	#106×C₈₉	C₂³	1	4	yes	—
160	#106×C₈₉	C₂³	1	4	yes	—
161	#103×C₈₉	C₂³	1	8	yes	—
162	#103×C₈₉	C₂³	1	4	yes	—
163	#103×C₈₉	C₂³	1	4	yes	—
164	#102×C₈₉	C₂³	1	8	yes	—
165	#102×C₈₉	C₂³	1	4	yes	—
166	#102×C₈₉	C₂³	1	4	yes	—
167	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
168	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
169	C₂⁴×C₈₉	—	2	1	no	—
170	C₂⁴×C₈₉	C₂×D₄	1	2	yes	—
171	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
172	#41×C₈₉	—	2	8	no	—
173	#41×C₈₉	—	2	8	no	—
174	#41×C₈₉	—	2	4	no	—
175	#41×C₈₉	—	2	4	no	—
176	#41×C₈₉	—	2	4	no	—
177	#41×C₈₉	—	2	4	no	—
178	#41×C₈₉	—	2	4	no	—
179	#41×C₈₉	—	2	4	no	—
180	#41×C₈₉	—	2	4	no	—
181	#41×C₈₉	—	2	4	no	—
182	#41×C₈₉	—	4	4	no	—
183	#41×C₈₉	—	4	4	no	—
184	C₂×Q₈×C₈₉	—	2	4	no	—
185	C₂×Q₈×C₈₉	—	2	1	no	—
186	C₂×Q₈×C₈₉	—	2	2	no	—
187	C₂×Q₈×C₈₉	—	2	2	no	—
188	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
189	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
190	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
191	C₂×D₄×C₈₉	—	2	8	no	—
192	C₂×D₄×C₈₉	—	2	2	no	—
193	C₂×D₄×C₈₉	—	2	2	no	—
194	C₂×D₄×C₈₉	—	2	4	no	—
195	C₂×D₄×C₈₉	—	2	4	no	—
196	C₂×D₄×C₈₉	—	2	4	no	—
197	C₂×D₄×C₈₉	—	2	1	no	—
198	C₂×D₄×C₈₉	—	2	2	no	—
199	C₂×D₄×C₈₉	—	2	2	no	—
200	C₂×D₄×C₈₉	—	4	4	no	—
201	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
202	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
203	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
204	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
205	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₈₉	—	2	4	no	—
207	C₂²×C₄×C₈₉	—	2	4	no	—
208	C₂²×C₄×C₈₉	—	2	1	no	—
209	C₂²×C₄×C₈₉	—	2	1	no	—
210	C₂²×C₄×C₈₉	—	2	2	no	—
211	C₂²×C₄×C₈₉	—	2	1	no	—
212	C₂²×C₄×C₈₉	—	2	1	no	—
213	C₂²×C₄×C₈₉	—	2	1	no	—
214	C₂²×C₄×C₈₉	—	2	8	no	—
215	C₂²×C₄×C₈₉	—	2	2	no	—
216	C₂²×C₄×C₈₉	—	2	2	no	—
217	C₂²×C₄×C₈₉	—	2	2	no	—
218	C₂²×C₄×C₈₉	—	2	2	no	—
219	C₂²×C₄×C₈₉	—	4	4	no	—
220	C₂²×C₄×C₈₉	—	8	2	no	—
221	C₂²×C₄×C₈₉	—	8	4	no	—
222	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
223	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
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	#41	1	4	yes	—
228	C₂²×C₄×C₈₉	#41	1	4	yes	—
229	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
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	M₁₆×C₈₉	—	2	4	no	—
234	M₁₆×C₈₉	—	2	4	no	—
235	M₁₆×C₈₉	—	2	4	no	—
236	M₁₆×C₈₉	—	2	4	no	—
237	C₂×C₈×C₈₉	—	2	4	no	—
238	C₂×C₈×C₈₉	—	2	4	no	—
239	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
240	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
241	C₄⋊C₄×C₈₉	—	2	2	no	—
242	C₄⋊C₄×C₈₉	—	2	1	no	—
243	C₄⋊C₄×C₈₉	—	2	8	no	—
244	C₄⋊C₄×C₈₉	—	2	2	no	—
245	C₄⋊C₄×C₈₉	—	2	2	no	—
246	C₄⋊C₄×C₈₉	—	2	1	no	—
247	C₄⋊C₄×C₈₉	—	2	1	no	—
248	C₄⋊C₄×C₈₉	—	2	1	no	—
249	C₄⋊C₄×C₈₉	—	2	4	no	—
250	C₄⋊C₄×C₈₉	—	2	4	no	—
251	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
252	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
253	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
254	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
255	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
256	C₂²⋊C₄×C₈₉	—	2	8	no	—
257	C₂²⋊C₄×C₈₉	—	2	2	no	—
258	C₂²⋊C₄×C₈₉	—	2	2	no	—
259	C₂²⋊C₄×C₈₉	—	2	2	no	—
260	C₂²⋊C₄×C₈₉	—	2	2	no	—
261	C₂²⋊C₄×C₈₉	—	2	4	no	—
262	C₂²⋊C₄×C₈₉	—	2	4	no	—
263	C₂²⋊C₄×C₈₉	—	2	4	no	—
264	C₂²⋊C₄×C₈₉	—	2	4	no	—
265	C₄²×C₈₉	—	2	2	no	—
266	C₄²×C₈₉	—	2	8	no	—
267	C₄²×C₈₉	—	2	2	no	—
268	C₄²×C₈₉	—	2	2	no	—
269	C₄²×C₈₉	—	2	2	no	—
270	C₂³×C₈₉	—	2	4	no	—
271	C₂³×C₈₉	—	2	2	no	—
272	C₂³×C₈₉	—	4	1	no	—
273	C₂³×C₈₉	—	4	2	no	—
274	C₂³×C₈₉	—	4	1	no	—
275	C₂³×C₈₉	—	4	2	no	—
276	C₂³×C₈₉	—	4	2	no	—
277	C₂³×C₈₉	—	8	1	no	—
278	C₂³×C₈₉	—	8	1	no	—
279	C₂³×C₈₉	#123	1	4	yes	—
280	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
281	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
282	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
283	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
284	Q₈×C₈₉	—	2	4	no	—
285	Q₈×C₈₉	—	2	4	no	—
286	Q₈×C₈₉	—	2	2	no	—
287	Q₈×C₈₉	—	2	2	no	—
288	Q₈×C₈₉	—	4	2	no	—
289	D₄×C₈₉	—	2	8	no	—
290	D₄×C₈₉	—	2	8	no	—
291	D₄×C₈₉	—	2	4	no	—
292	D₄×C₈₉	—	2	4	no	—
293	D₄×C₈₉	—	2	2	no	—
294	D₄×C₈₉	—	2	2	no	—
295	D₄×C₈₉	—	4	4	no	—
296	D₄×C₈₉	—	4	4	no	—
297	D₄×C₈₉	—	4	2	no	—
298	D₄×C₈₉	—	8	4	no	—
299	D₄×C₈₉	—	8	4	no	—
300	C₂×C₄×C₈₉	—	2	4	no	—
301	C₂×C₄×C₈₉	—	2	8	no	—
302	C₂×C₄×C₈₉	—	2	4	no	—
303	C₂×C₄×C₈₉	—	2	4	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	4	no	—
308	C₂×C₄×C₈₉	—	2	2	no	—
309	C₂×C₄×C₈₉	—	2	2	no	—
310	C₂×C₄×C₈₉	—	4	2	no	—
311	C₂×C₄×C₈₉	—	4	2	no	—
312	C₂×C₄×C₈₉	—	4	4	no	—
313	C₂×C₄×C₈₉	—	4	2	no	—
314	C₂×C₄×C₈₉	—	4	4	no	—
315	C₂×C₄×C₈₉	—	4	4	no	—
316	C₂×C₄×C₈₉	—	8	1	no	—
317	C₂×C₄×C₈₉	—	8	1	no	—
318	C₂×C₄×C₈₉	—	8	2	no	—
319	C₂×C₄×C₈₉	—	8	2	no	—
320	C₂×C₄×C₈₉	—	8	8	no	—
321	C₂×C₄×C₈₉	#123	1	4	yes	—
322	C₂×C₄×C₈₉	#123	1	4	yes	—
323	C₂×C₄×C₈₉	#123	1	4	yes	—
324	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
325	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
327	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
329	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
330	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
331	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
332	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
333	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
334	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
335	C₈×C₈₉	—	2	4	no	—
336	C₈×C₈₉	—	2	4	no	—
337	C₂²×C₈₉	—	2	1	no	—
338	C₂²×C₈₉	—	2	1	no	—
339	C₂²×C₈₉	—	2	1	no	—
340	C₂²×C₈₉	—	2	1	no	—
341	C₂²×C₈₉	—	2	1	no	—
342	C₂²×C₈₉	—	2	1	no	—
343	C₂²×C₈₉	—	2	4	no	—
344	C₂²×C₈₉	—	2	4	no	—
345	C₂²×C₈₉	—	2	4	no	—
346	C₂²×C₈₉	—	4	4	no	—
347	C₂²×C₈₉	—	4	8	no	—
348	C₂²×C₈₉	—	4	2	no	—
349	C₂²×C₈₉	—	4	2	no	—
350	C₂²×C₈₉	—	4	2	no	—
351	C₂²×C₈₉	—	8	4	no	—
352	C₂²×C₈₉	C₂×#123	1	2	yes	—
353	C₂²×C₈₉	C₂×#123	1	2	yes	—
354	C₂²×C₈₉	C₂×#123	1	2	yes	—
355	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
356	C₄×C₈₉	—	2	4	no	—
357	C₄×C₈₉	—	4	4	no	—
358	C₄×C₈₉	—	4	2	no	—
359	C₄×C₈₉	—	4	2	no	—
360	C₄×C₈₉	—	4	2	no	—
361	C₄×C₈₉	—	4	2	no	—
362	C₄×C₈₉	—	4	2	no	—
363	C₄×C₈₉	C₂×#123	1	2	yes	—
364	C₄×C₈₉	C₂×#123	1	2	yes	—
365	C₄×C₈₉	C₂×#123	1	2	yes	—
366	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
367	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
368	#60517	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
369	C₂×C₈₉	—	2	2	no	—
370	C₂×C₈₉	—	2	2	no	—
371	C₂×C₈₉	—	2	2	no	—
372	C₂×C₈₉	—	4	4	no	—
373	C₂×C₈₉	—	8	2	no	—
374	C₂×C₈₉	C₂²×#123	1	1	yes	characteristic
375	C₂×C₈₉	#3585	1	1	yes	characteristic
376	C₂×C₈₉	#3586	1	1	yes	characteristic
377	#3449	C₂×C₈₉	1	1	yes	characteristic
378	C₂×#520	C₂×C₈₉	1	1	yes	characteristic, complemented
379	#3099	C₂×C₈₉	1	4	yes	complemented
380	#3098	C₂×C₈₉	1	4	yes	complemented
381	#3097	C₂×C₈₉	1	4	yes	complemented
382	#3096	C₂×C₈₉	1	4	yes	complemented
383	#3093	C₂×C₈₉	1	4	yes	complemented
384	#3092	C₂×C₈₉	1	4	yes	complemented
385	#2911	C₂×C₈₉	1	1	yes	characteristic, complemented
386	C₂×#428	C₂×C₈₉	1	1	yes	characteristic, complemented
387	#2896	C₂×C₈₉	1	1	yes	characteristic, complemented
388	C₂×#417	C₂×C₈₉	1	1	yes	characteristic, complemented
389	#2879	C₂×C₈₉	1	1	yes	characteristic, complemented
390	C₈₉	#60517	1	1	yes	characteristic, direct product factor, Sylow
391	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
392	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
393	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
394	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
395	#537	C₂²×C₈₉	1	2	yes	—
396	#537	C₂²×C₈₉	1	2	yes	—
397	#536	—	2	1	no	—
398	#536	C₂²×C₈₉	1	2	yes	—
399	#535	—	2	1	no	—
400	#535	C₂²×C₈₉	1	2	yes	—
401	#534	—	2	2	no	—
402	#532	—	2	2	no	—
403	#525	—	2	2	no	—
404	#525	C₂²×C₈₉	1	4	yes	—
405	#520	—	2	2	no	—
406	#520	—	2	2	no	—
407	#520	C₂²×C₈₉	1	4	yes	—
408	#520	C₂²×C₈₉	1	4	yes	complemented
409	C₂×C₄×Q₈	—	2	1	no	—
410	C₂×C₄×D₄	—	2	1	no	—
411	C₂×C₄×D₄	—	2	2	no	—
412	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
413	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
414	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
415	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
416	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
417	#485	C₂²×C₈₉	1	8	yes	complemented
418	#485	C₂²×C₈₉	1	8	yes	complemented
419	#484	C₂²×C₈₉	1	8	yes	complemented
420	#483	C₂²×C₈₉	1	8	yes	complemented
421	#482	C₂²×C₈₉	1	8	yes	complemented
422	#482	C₂²×C₈₉	1	8	yes	complemented
423	#481	C₂²×C₈₉	1	8	yes	complemented
424	#480	C₂²×C₈₉	1	8	yes	complemented
425	#428	C₂²×C₈₉	1	2	yes	complemented
426	#428	C₂²×C₈₉	1	4	yes	complemented
427	#428	C₂²×C₈₉	1	2	yes	complemented
428	#428	C₂²×C₈₉	1	4	yes	complemented
429	#428	C₂²×C₈₉	1	2	yes	complemented
430	#428	C₂²×C₈₉	1	2	yes	complemented
431	#427	C₂²×C₈₉	1	4	yes	complemented
432	C₂×#107	C₂²×C₈₉	1	2	yes	complemented
433	C₂×#106	C₂²×C₈₉	1	2	yes	complemented
434	#419	C₂²×C₈₉	1	2	yes	complemented
435	#418	C₂²×C₈₉	1	2	yes	complemented
436	#417	C₂²×C₈₉	1	2	yes	—
437	#417	C₂²×C₈₉	1	4	yes	—
438	#417	C₂²×C₈₉	1	2	yes	—
439	#417	C₂²×C₈₉	1	4	yes	complemented
440	#416	C₂²×C₈₉	1	4	yes	complemented
441	C₂×#103	C₂²×C₈₉	1	2	yes	complemented
442	C₂×#102	C₂²×C₈₉	1	2	yes	complemented
443	#408	C₂²×C₈₉	1	4	yes	—
444	#408	C₂²×C₈₉	1	4	yes	complemented
445	#407	C₂²×C₈₉	1	4	yes	complemented
446	C₂×#41	—	2	1	no	—
447	C₂×#41	—	2	1	no	—
448	C₂×#41	—	2	4	no	—
449	C₂×#41	—	2	4	no	—
450	C₂×#41	—	2	4	no	—
451	C₂×#41	—	2	4	no	—
452	C₂×#41	D₄×C₈₉	1	2	yes	—
453	C₂×#41	D₄×C₈₉	1	2	yes	—
454	C₂×#41	C₂³×C₈₉	1	2	yes	—
455	C₂×#41	C₂³×C₈₉	1	2	yes	—
456	C₂×#41	C₂³×C₈₉	1	2	yes	—
457	C₂×#41	C₂³×C₈₉	1	2	yes	—
458	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
459	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
460	C₂²×D₄	—	2	1	no	—
461	C₂²×D₄	D₄×C₈₉	1	2	yes	—
462	C₂²×D₄	D₄×C₈₉	1	1	yes	characteristic
463	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
464	C₂³×C₄	—	2	1	no	—
465	C₂³×C₄	—	2	2	no	—
466	C₂³×C₄	—	2	1	no	—
467	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
468	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
469	C₂×M₁₆	—	2	4	no	—
470	C₂×M₁₆	—	2	4	no	—
471	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
472	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
473	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
474	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
475	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
476	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
477	C₄⋊Q₈	—	2	2	no	—
478	#127	—	2	2	no	—
479	#124	—	2	2	no	—
480	#124	—	2	2	no	—
481	#123	—	2	4	no	—
482	#123	—	2	4	no	—
483	C₂²⋊Q₈	—	2	2	no	—
484	C₂²⋊Q₈	—	2	2	no	—
485	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
486	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
487	#121	—	2	2	no	—
488	#121	—	2	2	no	—
489	#121	—	2	4	no	—
490	#121	—	2	4	no	—
491	#121	C₂³×C₈₉	1	4	yes	—
492	#121	C₂³×C₈₉	1	4	yes	—
493	#120	—	2	4	no	—
494	#120	—	2	4	no	—
495	C₄×Q₈	—	2	4	no	—
496	C₄×Q₈	—	2	4	no	—
497	C₄×D₄	—	2	8	no	—
498	C₄×D₄	—	2	4	no	—
499	C₄×D₄	—	2	8	no	—
500	C₄×D₄	—	2	4	no	—
501	C₄×D₄	—	2	4	no	—
502	C₄×D₄	—	2	4	no	—
503	#117	—	2	1	no	—
504	#117	—	2	1	no	—
505	#117	—	2	1	no	—
506	#117	—	2	1	no	—
507	#117	—	2	4	no	—
508	#117	C₂³×C₈₉	1	2	yes	—
509	#117	C₂³×C₈₉	1	2	yes	—
510	#117	C₂³×C₈₉	1	2	yes	—
511	#117	C₂³×C₈₉	1	2	yes	—
512	#117	C₂³×C₈₉	1	8	yes	—
513	C₂×C₄⋊C₄	—	2	1	no	—
514	C₂×C₄⋊C₄	—	2	1	no	—
515	C₂×C₄⋊C₄	—	2	1	no	—
516	C₂×C₄⋊C₄	—	2	2	no	—
517	C₂×C₄⋊C₄	—	2	4	no	—
518	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
519	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
520	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
521	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
522	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
523	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
524	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
525	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
526	C₂×C₂²⋊C₄	—	2	1	no	—
527	C₂×C₂²⋊C₄	—	2	1	no	—
528	C₂×C₂²⋊C₄	—	2	2	no	—
529	C₂×C₄²	—	2	1	no	—
530	C₂×C₄²	—	2	1	no	—
531	C₂×C₄²	—	2	2	no	—
532	#107	C₂³×C₈₉	1	8	yes	—
533	#107	C₂³×C₈₉	1	4	yes	—
534	#107	C₂³×C₈₉	1	4	yes	—
535	#106	C₂³×C₈₉	1	8	yes	—
536	#106	C₂³×C₈₉	1	4	yes	—
537	#106	C₂³×C₈₉	1	4	yes	—
538	#103	C₂³×C₈₉	1	8	yes	—
539	#103	C₂³×C₈₉	1	4	yes	—
540	#103	C₂³×C₈₉	1	4	yes	—
541	#102	C₂³×C₈₉	1	8	yes	—
542	#102	C₂³×C₈₉	1	4	yes	—
543	#102	C₂³×C₈₉	1	4	yes	—
544	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
545	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
546	C₂⁴	—	2	1	no	—
547	C₂⁴	C₂×D₄×C₈₉	1	2	yes	—
548	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
549	#41	—	2	8	no	—
550	#41	—	2	8	no	—
551	#41	—	2	4	no	—
552	#41	—	2	4	no	—
553	#41	—	2	4	no	—
554	#41	—	2	4	no	—
555	#41	—	2	4	no	—
556	#41	—	2	4	no	—
557	#41	—	2	4	no	—
558	#41	—	2	4	no	—
559	#41	—	4	4	no	—
560	#41	—	4	4	no	—
561	C₂×Q₈	—	2	4	no	—
562	C₂×Q₈	—	2	1	no	—
563	C₂×Q₈	—	2	2	no	—
564	C₂×Q₈	—	2	2	no	—
565	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
566	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
567	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
568	C₂×D₄	—	2	8	no	—
569	C₂×D₄	—	2	2	no	—
570	C₂×D₄	—	2	2	no	—
571	C₂×D₄	—	2	4	no	—
572	C₂×D₄	—	2	4	no	—
573	C₂×D₄	—	2	4	no	—
574	C₂×D₄	—	2	1	no	—
575	C₂×D₄	—	2	2	no	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	4	4	no	—
578	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
579	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
580	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
581	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
582	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
583	C₂²×C₄	—	2	4	no	—
584	C₂²×C₄	—	2	4	no	—
585	C₂²×C₄	—	2	1	no	—
586	C₂²×C₄	—	2	1	no	—
587	C₂²×C₄	—	2	2	no	—
588	C₂²×C₄	—	2	1	no	—
589	C₂²×C₄	—	2	1	no	—
590	C₂²×C₄	—	2	1	no	—
591	C₂²×C₄	—	2	8	no	—
592	C₂²×C₄	—	2	2	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	4	4	no	—
597	C₂²×C₄	—	8	2	no	—
598	C₂²×C₄	—	8	4	no	—
599	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
600	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
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	#41×C₈₉	1	4	yes	—
605	C₂²×C₄	#41×C₈₉	1	4	yes	—
606	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
607	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
608	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
609	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
610	M₁₆	—	2	4	no	—
611	M₁₆	—	2	4	no	—
612	M₁₆	—	2	4	no	—
613	M₁₆	—	2	4	no	—
614	C₂×C₈	—	2	4	no	—
615	C₂×C₈	—	2	4	no	—
616	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
617	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	1	no	—
620	C₄⋊C₄	—	2	8	no	—
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	1	no	—
624	C₄⋊C₄	—	2	1	no	—
625	C₄⋊C₄	—	2	1	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
629	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
630	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
631	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
632	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
633	C₂²⋊C₄	—	2	8	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	2	no	—
636	C₂²⋊C₄	—	2	2	no	—
637	C₂²⋊C₄	—	2	2	no	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	4	no	—
642	C₄²	—	2	2	no	—
643	C₄²	—	2	8	no	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	2	no	—
646	C₄²	—	2	2	no	—
647	C₂³	—	2	4	no	—
648	C₂³	—	2	2	no	—
649	C₂³	—	4	1	no	—
650	C₂³	—	4	2	no	—
651	C₂³	—	4	1	no	—
652	C₂³	—	4	2	no	—
653	C₂³	—	4	2	no	—
654	C₂³	—	8	1	no	—
655	C₂³	—	8	1	no	—
656	C₂³	#123×C₈₉	1	4	yes	—
657	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
658	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
659	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
660	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
661	Q₈	—	2	4	no	—
662	Q₈	—	2	4	no	—
663	Q₈	—	2	2	no	—
664	Q₈	—	2	2	no	—
665	Q₈	—	4	2	no	—
666	D₄	—	2	8	no	—
667	D₄	—	2	8	no	—
668	D₄	—	2	4	no	—
669	D₄	—	2	4	no	—
670	D₄	—	2	2	no	—
671	D₄	—	2	2	no	—
672	D₄	—	4	4	no	—
673	D₄	—	4	4	no	—
674	D₄	—	4	2	no	—
675	D₄	—	8	4	no	—
676	D₄	—	8	4	no	—
677	C₂×C₄	—	2	4	no	—
678	C₂×C₄	—	2	8	no	—
679	C₂×C₄	—	2	4	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	2	2	no	—
683	C₂×C₄	—	2	2	no	—
684	C₂×C₄	—	2	4	no	—
685	C₂×C₄	—	2	2	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	4	2	no	—
688	C₂×C₄	—	4	2	no	—
689	C₂×C₄	—	4	4	no	—
690	C₂×C₄	—	4	2	no	—
691	C₂×C₄	—	4	4	no	—
692	C₂×C₄	—	4	4	no	—
693	C₂×C₄	—	8	1	no	—
694	C₂×C₄	—	8	1	no	—
695	C₂×C₄	—	8	2	no	—
696	C₂×C₄	—	8	2	no	—
697	C₂×C₄	—	8	8	no	—
698	C₂×C₄	#123×C₈₉	1	4	yes	—
699	C₂×C₄	#123×C₈₉	1	4	yes	—
700	C₂×C₄	#123×C₈₉	1	4	yes	—
701	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
702	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
703	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
704	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
705	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
706	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
707	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
708	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
709	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
710	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
711	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
712	C₈	—	2	4	no	—
713	C₈	—	2	4	no	—
714	C₂²	—	2	1	no	—
715	C₂²	—	2	1	no	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	1	no	—
719	C₂²	—	2	1	no	—
720	C₂²	—	2	4	no	—
721	C₂²	—	2	4	no	—
722	C₂²	—	2	4	no	—
723	C₂²	—	4	4	no	—
724	C₂²	—	4	8	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	4	2	no	—
728	C₂²	—	8	4	no	—
729	C₂²	C₂×#123×C₈₉	1	2	yes	—
730	C₂²	C₂×#123×C₈₉	1	2	yes	—
731	C₂²	C₂×#123×C₈₉	1	2	yes	—
732	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
733	C₄	—	2	4	no	—
734	C₄	—	4	4	no	—
735	C₄	—	4	2	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	2	no	—
739	C₄	—	4	2	no	—
740	C₄	C₂×#123×C₈₉	1	2	yes	—
741	C₄	C₂×#123×C₈₉	1	2	yes	—
742	C₄	C₂×#123×C₈₉	1	2	yes	—
743	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
744	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
745	C₂	—	2	2	no	—
746	C₂	—	2	2	no	—
747	C₂	—	2	2	no	—
748	C₂	—	4	4	no	—
749	C₂	—	8	2	no	—
750	C₂	C₂²×#123×C₈₉	1	1	yes	characteristic
751	C₂	C₈₉×#3585	1	1	yes	characteristic
752	C₂	C₈₉×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3449	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂²×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#520×C₈₉	C₂	semidirect
3. C₈₉×#3099	C₂	semidirect
4. C₈₉×#3098	C₂	semidirect
5. C₈₉×#3097	C₂	semidirect
6. C₈₉×#3096	C₂	semidirect
7. C₈₉×#3093	C₂	semidirect
8. C₈₉×#3092	C₂	semidirect
9. C₈₉×#2911	C₂	semidirect
10. C₂×#428×C₈₉	C₂	semidirect
11. C₈₉×#2896	C₂	semidirect
12. C₂×#417×C₈₉	C₂	semidirect
13. C₈₉×#2879	C₂	semidirect
31. #520×C₈₉	C₂²	semidirect
37. C₂×#117×C₈₉	C₂²	semidirect
39. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
40. #485×C₈₉	C₂²	semidirect
41. #485×C₈₉	C₂²	semidirect
42. #484×C₈₉	C₂²	semidirect
43. #483×C₈₉	C₂²	semidirect
44. #482×C₈₉	C₂²	semidirect
45. #482×C₈₉	C₂²	semidirect
46. #481×C₈₉	C₂²	semidirect
47. #480×C₈₉	C₂²	semidirect
48. #428×C₈₉	C₂²	semidirect
49. #428×C₈₉	C₂²	semidirect
50. #428×C₈₉	C₂²	semidirect
51. #428×C₈₉	C₂²	semidirect
52. #428×C₈₉	C₂²	semidirect
53. #428×C₈₉	C₂²	semidirect
54. #427×C₈₉	C₂²	semidirect
55. C₂×#107×C₈₉	C₂²	semidirect
56. C₂×#106×C₈₉	C₂²	semidirect
57. #419×C₈₉	C₂²	semidirect
58. #418×C₈₉	C₂²	semidirect
62. #417×C₈₉	C₂²	semidirect
63. #416×C₈₉	C₂²	semidirect
64. C₂×#103×C₈₉	C₂²	semidirect
65. C₂×#102×C₈₉	C₂²	semidirect
67. #408×C₈₉	C₂²	semidirect
68. #407×C₈₉	C₂²	semidirect
368. #60517	C₈₉	direct (N × H)
378. C₂×#520	C₂×C₈₉	semidirect
379. #3099	C₂×C₈₉	semidirect
380. #3098	C₂×C₈₉	semidirect
381. #3097	C₂×C₈₉	semidirect
382. #3096	C₂×C₈₉	semidirect
383. #3093	C₂×C₈₉	semidirect
384. #3092	C₂×C₈₉	semidirect
385. #2911	C₂×C₈₉	semidirect
386. C₂×#428	C₂×C₈₉	semidirect
387. #2896	C₂×C₈₉	semidirect
388. C₂×#417	C₂×C₈₉	semidirect
389. #2879	C₂×C₈₉	semidirect
390. C₈₉	#60517	direct (N × H)
408. #520	C₂²×C₈₉	semidirect
414. C₂×#117	C₂²×C₈₉	semidirect
416. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
417. #485	C₂²×C₈₉	semidirect
418. #485	C₂²×C₈₉	semidirect
419. #484	C₂²×C₈₉	semidirect
420. #483	C₂²×C₈₉	semidirect
421. #482	C₂²×C₈₉	semidirect
422. #482	C₂²×C₈₉	semidirect
423. #481	C₂²×C₈₉	semidirect
424. #480	C₂²×C₈₉	semidirect
425. #428	C₂²×C₈₉	semidirect
426. #428	C₂²×C₈₉	semidirect
427. #428	C₂²×C₈₉	semidirect
428. #428	C₂²×C₈₉	semidirect
429. #428	C₂²×C₈₉	semidirect
430. #428	C₂²×C₈₉	semidirect
431. #427	C₂²×C₈₉	semidirect
432. C₂×#107	C₂²×C₈₉	semidirect
433. C₂×#106	C₂²×C₈₉	semidirect
434. #419	C₂²×C₈₉	semidirect
435. #418	C₂²×C₈₉	semidirect
439. #417	C₂²×C₈₉	semidirect
440. #416	C₂²×C₈₉	semidirect
441. C₂×#103	C₂²×C₈₉	semidirect
442. C₂×#102	C₂²×C₈₉	semidirect
444. #408	C₂²×C₈₉	semidirect
445. #407	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3449	2
C₂×#520×C₈₉	2
C₈₉×#3099	2
C₈₉×#3098	2
C₈₉×#3097	2
C₈₉×#3096	2
C₈₉×#3093	2
C₈₉×#3092	2
C₈₉×#2911	2
C₂×#428×C₈₉	2
C₈₉×#2896	2
C₂×#417×C₈₉	2
C₈₉×#2879	2
#60517	89

Subgroups — C89×#60517 #36438365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60517 #36438365