Subgroups — C₈₉×#61427 #36439275

Order 22784.

1890 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3475	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3380	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#3360	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3341	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3336	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3303	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3296	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3283	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3280	C₂	1	2	yes	maximal, complemented
11	C₈₉×#3170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#3168	C₂	1	2	yes	maximal, complemented
13	C₈₉×#3102	C₂	1	4	yes	maximal, complemented
14	C₈₉×#3101	C₂	1	2	yes	maximal, complemented
15	C₈×#41×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#135×C₈₉	C₂	1	2	yes	maximal, complemented
17	C₂×C₄×D₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#135×C₈₉	C₂²	1	2	yes	—
19	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
20	#556×C₈₉	C₂²	1	2	yes	complemented
21	#555×C₈₉	C₂²	1	2	yes	complemented
22	#554×C₈₉	C₂²	1	2	yes	complemented
23	#553×C₈₉	—	2	2	no	—
24	#552×C₈₉	—	2	2	no	—
25	#552×C₈₉	C₂²	1	4	yes	—
26	#551×C₈₉	—	2	4	no	—
27	#547×C₈₉	C₂²	1	2	yes	complemented
28	#546×C₈₉	C₂²	1	4	yes	—
29	#533×C₈₉	C₂²	1	2	yes	—
30	#529×C₈₉	—	2	4	no	—
31	#529×C₈₉	C₂²	1	4	yes	complemented
32	#525×C₈₉	—	2	2	no	—
33	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
34	C₄×#41×C₈₉	C₂²	1	4	yes	complemented
35	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
36	C₂×#117×C₈₉	—	2	2	no	—
37	#500×C₈₉	C₂²	1	1	yes	characteristic, complemented
38	#499×C₈₉	C₂²	1	2	yes	complemented
39	#495×C₈₉	C₂²	1	2	yes	—
40	#494×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	#488×C₈₉	C₂²	1	4	yes	complemented
42	#487×C₈₉	C₂²	1	2	yes	complemented
43	#485×C₈₉	C₂²	1	4	yes	complemented
44	#483×C₈₉	C₂²	1	4	yes	—
45	#482×C₈₉	C₂²	1	4	yes	complemented
46	#479×C₈₉	C₂²	1	4	yes	complemented
47	#478×C₈₉	C₂²	1	4	yes	complemented
48	#476×C₈₉	C₂²	1	2	yes	complemented
49	#476×C₈₉	C₂²	1	2	yes	complemented
50	#467×C₈₉	C₂²	1	2	yes	—
51	#467×C₈₉	C₂²	1	2	yes	—
52	#467×C₈₉	C₂²	1	2	yes	complemented
53	#466×C₈₉	C₂²	1	2	yes	—
54	#465×C₈₉	C₂²	1	4	yes	complemented
55	#464×C₈₉	C₂²	1	4	yes	complemented
56	#463×C₈₉	C₂²	1	4	yes	—
57	#461×C₈₉	C₂²	1	2	yes	complemented
58	#461×C₈₉	C₂²	1	2	yes	complemented
59	#452×C₈₉	C₂²	1	4	yes	complemented
60	#450×C₈₉	C₂²	1	4	yes	—
61	#449×C₈₉	C₂²	1	4	yes	—
62	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
63	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
65	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
66	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	complemented
67	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
68	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
69	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	complemented
70	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
71	C₄×D₈×C₈₉	C₂²	1	2	yes	—
72	C₄×D₈×C₈₉	C₂²	1	2	yes	—
73	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
74	C₄×D₈×C₈₉	C₂²	1	2	yes	—
75	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
76	C₄×D₈×C₈₉	C₂²	1	1	yes	characteristic
77	C₈×D₄×C₈₉	C₂²	1	2	yes	—
78	C₈×D₄×C₈₉	C₂²	1	2	yes	—
79	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
80	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
81	#431×C₈₉	C₂²	1	1	yes	characteristic
82	#431×C₈₉	C₂²	1	2	yes	complemented
83	#427×C₈₉	C₂²	1	2	yes	complemented
84	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
85	#416×C₈₉	C₂²	1	4	yes	complemented
86	C₂×#102×C₈₉	C₂²	1	2	yes	—
87	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
88	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	complemented
89	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
90	C₂×#41×C₈₉	C₂³	1	4	yes	—
91	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
92	C₂³×C₄×C₈₉	—	2	2	no	—
93	#135×C₈₉	—	2	8	no	—
94	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
95	C₂×Q₁₆×C₈₉	C₂³	1	2	yes	—
96	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
97	C₂×SD₁₆×C₈₉	C₂³	1	4	yes	—
98	C₂×D₈×C₈₉	—	2	4	no	—
99	C₂×D₈×C₈₉	C₂³	1	2	yes	—
100	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
104	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
106	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
107	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
108	#126×C₈₉	—	2	4	no	—
109	#126×C₈₉	—	2	4	no	—
110	#126×C₈₉	—	2	4	no	—
111	#125×C₈₉	—	2	4	no	—
112	#125×C₈₉	—	2	2	no	—
113	#125×C₈₉	C₂³	1	4	yes	—
114	#124×C₈₉	—	2	4	no	—
115	#124×C₈₉	C₂³	1	4	yes	—
116	#123×C₈₉	—	2	4	no	—
117	#123×C₈₉	—	2	4	no	—
118	#123×C₈₉	—	2	4	no	—
119	#123×C₈₉	—	2	4	no	—
120	C₂²⋊Q₈×C₈₉	—	2	2	no	—
121	C₂²⋊Q₈×C₈₉	—	2	2	no	—
122	C₂²⋊Q₈×C₈₉	—	2	2	no	—
123	C₂²⋊Q₈×C₈₉	—	2	4	no	—
124	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
125	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
126	#121×C₈₉	—	2	2	no	—
127	#121×C₈₉	—	2	2	no	—
128	#121×C₈₉	—	2	4	no	—
129	#121×C₈₉	C₂³	1	4	yes	—
130	#120×C₈₉	—	2	4	no	—
131	C₄×Q₈×C₈₉	—	2	2	no	—
132	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
133	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
134	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
135	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
136	C₄×D₄×C₈₉	—	2	4	no	—
137	C₄×D₄×C₈₉	—	2	4	no	—
138	C₄×D₄×C₈₉	—	2	4	no	—
139	C₄×D₄×C₈₉	—	2	2	no	—
140	C₄×D₄×C₈₉	—	2	2	no	—
141	C₄×D₄×C₈₉	D₄	1	2	yes	—
142	C₄×D₄×C₈₉	D₄	1	1	yes	characteristic
143	C₄×D₄×C₈₉	C₂³	1	2	yes	—
144	C₄×D₄×C₈₉	C₂³	1	2	yes	—
145	C₄×D₄×C₈₉	C₂³	1	2	yes	—
146	C₄×D₄×C₈₉	C₂³	1	2	yes	—
147	C₄×D₄×C₈₉	C₂³	1	4	yes	—
148	C₄×D₄×C₈₉	C₂³	1	2	yes	—
149	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
150	#117×C₈₉	—	2	2	no	—
151	#117×C₈₉	—	2	2	no	—
152	#117×C₈₉	—	2	2	no	—
153	#117×C₈₉	—	2	4	no	—
154	#117×C₈₉	—	2	4	no	—
155	#117×C₈₉	—	2	4	no	—
156	#117×C₈₉	D₄	1	1	yes	characteristic
157	#117×C₈₉	D₄	1	2	yes	—
158	#117×C₈₉	C₂³	1	4	yes	—
159	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
160	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
161	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
163	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
164	C₂×C₄²×C₈₉	—	2	4	no	—
165	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
167	#107×C₈₉	C₂³	1	1	yes	characteristic
168	#107×C₈₉	C₂³	1	1	yes	characteristic
169	#107×C₈₉	C₂³	1	2	yes	—
170	#107×C₈₉	C₂³	1	2	yes	—
171	#107×C₈₉	C₂³	1	2	yes	—
172	#106×C₈₉	C₂³	1	4	yes	—
173	#106×C₈₉	C₂³	1	4	yes	—
174	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
175	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
176	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
177	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
178	#103×C₈₉	C₂³	1	4	yes	—
179	#103×C₈₉	C₂³	1	4	yes	—
180	#103×C₈₉	C₂³	1	4	yes	—
181	#103×C₈₉	C₂³	1	4	yes	—
182	#102×C₈₉	C₂³	1	2	yes	—
183	#102×C₈₉	C₂³	1	2	yes	—
184	#102×C₈₉	C₂³	1	2	yes	—
185	#102×C₈₉	C₂³	1	2	yes	—
186	#102×C₈₉	C₂³	1	4	yes	—
187	#102×C₈₉	C₂³	1	4	yes	—
188	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
189	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
190	C₂²⋊C₈×C₈₉	C₂³	1	2	yes	—
191	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
192	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
193	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₈₉	C₂³	1	2	yes	—
196	C₄×C₈×C₈₉	C₂³	1	2	yes	—
197	C₄×C₈×C₈₉	C₂³	1	2	yes	—
198	C₂⁴×C₈₉	—	2	2	no	—
199	#41×C₈₉	—	2	4	no	—
200	#41×C₈₉	—	2	8	no	—
201	#41×C₈₉	—	4	4	no	—
202	C₂×Q₈×C₈₉	—	2	2	no	—
203	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
204	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
205	C₂×D₄×C₈₉	—	2	4	no	—
206	C₂×D₄×C₈₉	—	2	4	no	—
207	C₂×D₄×C₈₉	—	2	4	no	—
208	C₂×D₄×C₈₉	—	2	2	no	—
209	C₂×D₄×C₈₉	—	4	2	no	—
210	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
211	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
212	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
213	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₈₉	—	2	2	no	—
215	C₂²×C₄×C₈₉	—	2	4	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	—	2	2	no	—
220	C₂²×C₄×C₈₉	—	2	4	no	—
221	C₂²×C₄×C₈₉	—	4	8	no	—
222	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
223	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
224	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
225	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
226	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
227	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
228	Q₁₆×C₈₉	—	2	4	no	—
229	Q₁₆×C₈₉	—	4	2	no	—
230	SD₁₆×C₈₉	—	2	8	no	—
231	SD₁₆×C₈₉	—	4	4	no	—
232	D₈×C₈₉	—	2	4	no	—
233	D₈×C₈₉	—	2	2	no	—
234	D₈×C₈₉	#41	1	4	yes	complemented
235	C₂×C₈×C₈₉	—	2	2	no	—
236	C₂×C₈×C₈₉	—	2	4	no	—
237	C₂×C₈×C₈₉	—	4	2	no	—
238	C₂×C₈×C₈₉	—	4	1	no	—
239	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
242	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
243	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
244	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
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	2	no	—
250	C₄⋊C₄×C₈₉	—	2	4	no	—
251	C₄⋊C₄×C₈₉	—	2	4	no	—
252	C₄⋊C₄×C₈₉	—	2	4	no	—
253	C₄⋊C₄×C₈₉	—	2	4	no	—
254	C₄⋊C₄×C₈₉	—	2	2	no	—
255	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
256	C₄⋊C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
257	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
259	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
261	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
262	C₂²⋊C₄×C₈₉	—	2	4	no	—
263	C₂²⋊C₄×C₈₉	—	2	4	no	—
264	C₂²⋊C₄×C₈₉	—	2	4	no	—
265	C₂²⋊C₄×C₈₉	—	2	2	no	—
266	C₂²⋊C₄×C₈₉	—	2	4	no	—
267	C₂²⋊C₄×C₈₉	—	2	4	no	—
268	C₂²⋊C₄×C₈₉	—	2	2	no	—
269	C₂²⋊C₄×C₈₉	—	2	2	no	—
270	C₂²⋊C₄×C₈₉	—	2	2	no	—
271	C₂²⋊C₄×C₈₉	—	2	4	no	—
272	C₂²⋊C₄×C₈₉	—	2	4	no	—
273	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
274	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
275	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
276	C₄²×C₈₉	—	2	4	no	—
277	C₄²×C₈₉	—	2	4	no	—
278	C₄²×C₈₉	—	2	4	no	—
279	C₄²×C₈₉	C₂×D₄	1	2	yes	—
280	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
281	C₄²×C₈₉	C₂×D₄	1	2	yes	—
282	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
283	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
284	C₄²×C₈₉	C₂⁴	1	2	yes	—
285	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
286	C₂³×C₈₉	—	2	2	no	—
287	C₂³×C₈₉	—	2	2	no	—
288	C₂³×C₈₉	—	4	4	no	—
289	C₂³×C₈₉	—	4	4	no	—
290	C₂³×C₈₉	—	8	2	no	—
291	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
292	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
293	Q₈×C₈₉	—	2	2	no	—
294	Q₈×C₈₉	—	2	4	no	—
295	Q₈×C₈₉	—	2	4	no	—
296	Q₈×C₈₉	—	8	2	no	—
297	D₄×C₈₉	—	2	4	no	—
298	D₄×C₈₉	—	2	2	no	—
299	D₄×C₈₉	—	2	2	no	—
300	D₄×C₈₉	—	2	2	no	—
301	D₄×C₈₉	—	2	2	no	—
302	D₄×C₈₉	—	4	4	no	—
303	D₄×C₈₉	—	4	8	no	—
304	D₄×C₈₉	—	8	4	no	—
305	D₄×C₈₉	C₂×#41	1	4	yes	—
306	C₂×C₄×C₈₉	—	2	4	no	—
307	C₂×C₄×C₈₉	—	2	1	no	—
308	C₂×C₄×C₈₉	—	2	2	no	—
309	C₂×C₄×C₈₉	—	2	1	no	—
310	C₂×C₄×C₈₉	—	2	2	no	—
311	C₂×C₄×C₈₉	—	2	2	no	—
312	C₂×C₄×C₈₉	—	2	4	no	—
313	C₂×C₄×C₈₉	—	2	4	no	—
314	C₂×C₄×C₈₉	—	2	2	no	—
315	C₂×C₄×C₈₉	—	4	2	no	—
316	C₂×C₄×C₈₉	—	4	1	no	—
317	C₂×C₄×C₈₉	—	4	8	no	—
318	C₂×C₄×C₈₉	—	4	4	no	—
319	C₂×C₄×C₈₉	—	4	4	no	—
320	C₂×C₄×C₈₉	—	4	4	no	—
321	C₂×C₄×C₈₉	—	4	4	no	—
322	C₂×C₄×C₈₉	—	4	4	no	—
323	C₂×C₄×C₈₉	—	8	4	no	—
324	C₂×C₄×C₈₉	#135	1	4	yes	complemented
325	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
326	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
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	2	yes	—
331	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
332	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
333	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
334	C₈×C₈₉	—	2	1	no	—
335	C₈×C₈₉	—	2	2	no	—
336	C₈×C₈₉	—	2	1	no	—
337	C₈×C₈₉	—	2	2	no	—
338	C₈×C₈₉	—	2	1	no	—
339	C₈×C₈₉	C₂×#41	1	2	yes	—
340	C₂²×C₈₉	—	2	1	no	—
341	C₂²×C₈₉	—	2	1	no	—
342	C₂²×C₈₉	—	2	2	no	—
343	C₂²×C₈₉	—	2	2	no	—
344	C₂²×C₈₉	—	2	4	no	—
345	C₂²×C₈₉	—	2	2	no	—
346	C₂²×C₈₉	—	4	2	no	—
347	C₂²×C₈₉	—	4	2	no	—
348	C₂²×C₈₉	—	4	2	no	—
349	C₂²×C₈₉	—	4	2	no	—
350	C₂²×C₈₉	—	4	2	no	—
351	C₂²×C₈₉	—	8	8	no	—
352	C₂²×C₈₉	C₂×#135	1	2	yes	—
353	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
354	C₄×C₈₉	—	2	1	no	—
355	C₄×C₈₉	—	2	2	no	—
356	C₄×C₈₉	—	2	1	no	—
357	C₄×C₈₉	—	2	2	no	—
358	C₄×C₈₉	—	2	1	no	—
359	C₄×C₈₉	—	2	2	no	—
360	C₄×C₈₉	—	4	4	no	—
361	C₄×C₈₉	—	4	4	no	—
362	C₄×C₈₉	—	4	2	no	—
363	C₄×C₈₉	—	4	2	no	—
364	C₄×C₈₉	C₂×#135	1	2	yes	—
365	C₄×C₈₉	C₂×#135	1	2	yes	—
366	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
367	C₄×C₈₉	#585	1	1	yes	characteristic
368	#61427	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
369	C₂×C₈₉	—	2	2	no	—
370	C₂×C₈₉	—	4	2	no	—
371	C₂×C₈₉	—	4	4	no	—
372	C₂×C₈₉	—	8	2	no	—
373	C₂×C₈₉	D₄×#41	1	1	yes	characteristic
374	C₂×C₈₉	C₂²×#135	1	1	yes	characteristic
375	C₂×C₈₉	#3584	1	1	yes	characteristic
376	#3475	C₂×C₈₉	1	2	yes	complemented
377	#3393	C₂×C₈₉	1	1	yes	characteristic, complemented
378	#3380	C₂×C₈₉	1	1	yes	characteristic, complemented
379	#3360	C₂×C₈₉	1	2	yes	complemented
380	#3341	C₂×C₈₉	1	1	yes	characteristic, complemented
381	#3336	C₂×C₈₉	1	2	yes	complemented
382	#3303	C₂×C₈₉	1	2	yes	complemented
383	#3296	C₂×C₈₉	1	4	yes	complemented
384	#3283	C₂×C₈₉	1	1	yes	characteristic, complemented
385	#3280	C₂×C₈₉	1	2	yes	complemented
386	#3170	C₂×C₈₉	1	1	yes	characteristic, complemented
387	#3168	C₂×C₈₉	1	2	yes	complemented
388	#3102	C₂×C₈₉	1	4	yes	complemented
389	#3101	C₂×C₈₉	1	2	yes	complemented
390	C₈×#41	C₂×C₈₉	1	1	yes	characteristic, complemented
391	C₄×#135	C₂×C₈₉	1	2	yes	complemented
392	C₂×C₄×D₈	C₂×C₈₉	1	1	yes	characteristic, complemented
393	C₈₉	#61427	1	1	yes	characteristic, direct product factor, Sylow
394	C₂×#135	C₂²×C₈₉	1	2	yes	—
395	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
396	#556	C₂²×C₈₉	1	2	yes	complemented
397	#555	C₂²×C₈₉	1	2	yes	complemented
398	#554	C₂²×C₈₉	1	2	yes	complemented
399	#553	—	2	2	no	—
400	#552	—	2	2	no	—
401	#552	C₂²×C₈₉	1	4	yes	—
402	#551	—	2	4	no	—
403	#547	C₂²×C₈₉	1	2	yes	complemented
404	#546	C₂²×C₈₉	1	4	yes	—
405	#533	C₂²×C₈₉	1	2	yes	—
406	#529	—	2	4	no	—
407	#529	C₂²×C₈₉	1	4	yes	complemented
408	#525	—	2	2	no	—
409	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
410	C₄×#41	C₂²×C₈₉	1	4	yes	complemented
411	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
412	C₂×#117	—	2	2	no	—
413	#500	C₂²×C₈₉	1	1	yes	characteristic, complemented
414	#499	C₂²×C₈₉	1	2	yes	complemented
415	#495	C₂²×C₈₉	1	2	yes	—
416	#494	C₂²×C₈₉	1	1	yes	characteristic, complemented
417	#488	C₂²×C₈₉	1	4	yes	complemented
418	#487	C₂²×C₈₉	1	2	yes	complemented
419	#485	C₂²×C₈₉	1	4	yes	complemented
420	#483	C₂²×C₈₉	1	4	yes	—
421	#482	C₂²×C₈₉	1	4	yes	complemented
422	#479	C₂²×C₈₉	1	4	yes	complemented
423	#478	C₂²×C₈₉	1	4	yes	complemented
424	#476	C₂²×C₈₉	1	2	yes	complemented
425	#476	C₂²×C₈₉	1	2	yes	complemented
426	#467	C₂²×C₈₉	1	2	yes	—
427	#467	C₂²×C₈₉	1	2	yes	—
428	#467	C₂²×C₈₉	1	2	yes	complemented
429	#466	C₂²×C₈₉	1	2	yes	—
430	#465	C₂²×C₈₉	1	4	yes	complemented
431	#464	C₂²×C₈₉	1	4	yes	complemented
432	#463	C₂²×C₈₉	1	4	yes	—
433	#461	C₂²×C₈₉	1	2	yes	complemented
434	#461	C₂²×C₈₉	1	2	yes	complemented
435	#452	C₂²×C₈₉	1	4	yes	complemented
436	#450	C₂²×C₈₉	1	4	yes	—
437	#449	C₂²×C₈₉	1	4	yes	—
438	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
439	C₈×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
440	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
441	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
442	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	complemented
443	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
444	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
445	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	complemented
446	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
447	C₄×D₈	C₂²×C₈₉	1	2	yes	—
448	C₄×D₈	C₂²×C₈₉	1	2	yes	—
449	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
450	C₄×D₈	C₂²×C₈₉	1	2	yes	—
451	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
452	C₄×D₈	C₂²×C₈₉	1	1	yes	characteristic
453	C₈×D₄	C₂²×C₈₉	1	2	yes	—
454	C₈×D₄	C₂²×C₈₉	1	2	yes	—
455	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
456	C₈×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
457	#431	C₂²×C₈₉	1	1	yes	characteristic
458	#431	C₂²×C₈₉	1	2	yes	complemented
459	#427	C₂²×C₈₉	1	2	yes	complemented
460	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
461	#416	C₂²×C₈₉	1	4	yes	complemented
462	C₂×#102	C₂²×C₈₉	1	2	yes	—
463	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
464	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	complemented
465	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
466	C₂×#41	C₂³×C₈₉	1	4	yes	—
467	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
468	C₂³×C₄	—	2	2	no	—
469	#135	—	2	8	no	—
470	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
471	C₂×Q₁₆	C₂³×C₈₉	1	2	yes	—
472	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
473	C₂×SD₁₆	C₂³×C₈₉	1	4	yes	—
474	C₂×D₈	—	2	4	no	—
475	C₂×D₈	C₂³×C₈₉	1	2	yes	—
476	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
477	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
478	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
479	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
480	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
481	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
482	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
483	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
484	#126	—	2	4	no	—
485	#126	—	2	4	no	—
486	#126	—	2	4	no	—
487	#125	—	2	4	no	—
488	#125	—	2	2	no	—
489	#125	C₂³×C₈₉	1	4	yes	—
490	#124	—	2	4	no	—
491	#124	C₂³×C₈₉	1	4	yes	—
492	#123	—	2	4	no	—
493	#123	—	2	4	no	—
494	#123	—	2	4	no	—
495	#123	—	2	4	no	—
496	C₂²⋊Q₈	—	2	2	no	—
497	C₂²⋊Q₈	—	2	2	no	—
498	C₂²⋊Q₈	—	2	2	no	—
499	C₂²⋊Q₈	—	2	4	no	—
500	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
501	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
502	#121	—	2	2	no	—
503	#121	—	2	2	no	—
504	#121	—	2	4	no	—
505	#121	C₂³×C₈₉	1	4	yes	—
506	#120	—	2	4	no	—
507	C₄×Q₈	—	2	2	no	—
508	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
509	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
510	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
511	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
512	C₄×D₄	—	2	4	no	—
513	C₄×D₄	—	2	4	no	—
514	C₄×D₄	—	2	4	no	—
515	C₄×D₄	—	2	2	no	—
516	C₄×D₄	—	2	2	no	—
517	C₄×D₄	D₄×C₈₉	1	2	yes	—
518	C₄×D₄	D₄×C₈₉	1	1	yes	characteristic
519	C₄×D₄	C₂³×C₈₉	1	2	yes	—
520	C₄×D₄	C₂³×C₈₉	1	2	yes	—
521	C₄×D₄	C₂³×C₈₉	1	2	yes	—
522	C₄×D₄	C₂³×C₈₉	1	2	yes	—
523	C₄×D₄	C₂³×C₈₉	1	4	yes	—
524	C₄×D₄	C₂³×C₈₉	1	2	yes	—
525	C₄×D₄	C₂³×C₈₉	1	1	yes	characteristic
526	#117	—	2	2	no	—
527	#117	—	2	2	no	—
528	#117	—	2	2	no	—
529	#117	—	2	4	no	—
530	#117	—	2	4	no	—
531	#117	—	2	4	no	—
532	#117	D₄×C₈₉	1	1	yes	characteristic
533	#117	D₄×C₈₉	1	2	yes	—
534	#117	C₂³×C₈₉	1	4	yes	—
535	C₂×C₄⋊C₄	—	2	2	no	—
536	C₂×C₄⋊C₄	—	2	2	no	—
537	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
538	C₂×C₂²⋊C₄	—	2	2	no	—
539	C₂×C₂²⋊C₄	—	2	4	no	—
540	C₂×C₄²	—	2	4	no	—
541	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
542	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
543	#107	C₂³×C₈₉	1	1	yes	characteristic
544	#107	C₂³×C₈₉	1	1	yes	characteristic
545	#107	C₂³×C₈₉	1	2	yes	—
546	#107	C₂³×C₈₉	1	2	yes	—
547	#107	C₂³×C₈₉	1	2	yes	—
548	#106	C₂³×C₈₉	1	4	yes	—
549	#106	C₂³×C₈₉	1	4	yes	—
550	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
551	C₄⋊C₈	C₂³×C₈₉	1	1	yes	characteristic
552	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
553	C₄⋊C₈	C₂³×C₈₉	1	2	yes	—
554	#103	C₂³×C₈₉	1	4	yes	—
555	#103	C₂³×C₈₉	1	4	yes	—
556	#103	C₂³×C₈₉	1	4	yes	—
557	#103	C₂³×C₈₉	1	4	yes	—
558	#102	C₂³×C₈₉	1	2	yes	—
559	#102	C₂³×C₈₉	1	2	yes	—
560	#102	C₂³×C₈₉	1	2	yes	—
561	#102	C₂³×C₈₉	1	2	yes	—
562	#102	C₂³×C₈₉	1	4	yes	—
563	#102	C₂³×C₈₉	1	4	yes	—
564	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
565	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
566	C₂²⋊C₈	C₂³×C₈₉	1	2	yes	—
567	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
568	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
569	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
570	C₄×C₈	C₂³×C₈₉	1	1	yes	characteristic
571	C₄×C₈	C₂³×C₈₉	1	2	yes	—
572	C₄×C₈	C₂³×C₈₉	1	2	yes	—
573	C₄×C₈	C₂³×C₈₉	1	2	yes	—
574	C₂⁴	—	2	2	no	—
575	#41	—	2	4	no	—
576	#41	—	2	8	no	—
577	#41	—	4	4	no	—
578	C₂×Q₈	—	2	2	no	—
579	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
580	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
581	C₂×D₄	—	2	4	no	—
582	C₂×D₄	—	2	4	no	—
583	C₂×D₄	—	2	4	no	—
584	C₂×D₄	—	2	2	no	—
585	C₂×D₄	—	4	2	no	—
586	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
587	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
588	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
589	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
590	C₂²×C₄	—	2	2	no	—
591	C₂²×C₄	—	2	2	no	—
592	C₂²×C₄	—	2	4	no	—
593	C₂²×C₄	—	2	2	no	—
594	C₂²×C₄	—	2	2	no	—
595	C₂²×C₄	—	2	2	no	—
596	C₂²×C₄	—	2	4	no	—
597	C₂²×C₄	—	4	8	no	—
598	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
599	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
600	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
601	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
602	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
603	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
604	Q₁₆	—	2	4	no	—
605	Q₁₆	—	4	2	no	—
606	SD₁₆	—	2	8	no	—
607	SD₁₆	—	4	4	no	—
608	D₈	—	2	4	no	—
609	D₈	—	2	2	no	—
610	D₈	#41×C₈₉	1	4	yes	complemented
611	C₂×C₈	—	2	2	no	—
612	C₂×C₈	—	2	4	no	—
613	C₂×C₈	—	4	2	no	—
614	C₂×C₈	—	4	1	no	—
615	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
616	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
617	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
618	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
619	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
620	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
621	C₄⋊C₄	—	2	2	no	—
622	C₄⋊C₄	—	2	2	no	—
623	C₄⋊C₄	—	2	4	no	—
624	C₄⋊C₄	—	2	4	no	—
625	C₄⋊C₄	—	2	2	no	—
626	C₄⋊C₄	—	2	4	no	—
627	C₄⋊C₄	—	2	4	no	—
628	C₄⋊C₄	—	2	4	no	—
629	C₄⋊C₄	—	2	4	no	—
630	C₄⋊C₄	—	2	2	no	—
631	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
632	C₄⋊C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
633	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
634	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
635	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
636	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
637	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
638	C₂²⋊C₄	—	2	4	no	—
639	C₂²⋊C₄	—	2	4	no	—
640	C₂²⋊C₄	—	2	4	no	—
641	C₂²⋊C₄	—	2	2	no	—
642	C₂²⋊C₄	—	2	4	no	—
643	C₂²⋊C₄	—	2	4	no	—
644	C₂²⋊C₄	—	2	2	no	—
645	C₂²⋊C₄	—	2	2	no	—
646	C₂²⋊C₄	—	2	2	no	—
647	C₂²⋊C₄	—	2	4	no	—
648	C₂²⋊C₄	—	2	4	no	—
649	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
650	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
651	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
652	C₄²	—	2	4	no	—
653	C₄²	—	2	4	no	—
654	C₄²	—	2	4	no	—
655	C₄²	C₂×D₄×C₈₉	1	2	yes	—
656	C₄²	C₂×D₄×C₈₉	1	2	yes	—
657	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
658	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
659	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
660	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
661	C₄²	C₂⁴×C₈₉	1	2	yes	—
662	C₂³	—	2	2	no	—
663	C₂³	—	2	2	no	—
664	C₂³	—	4	4	no	—
665	C₂³	—	4	4	no	—
666	C₂³	—	8	2	no	—
667	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
668	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
669	Q₈	—	2	2	no	—
670	Q₈	—	2	4	no	—
671	Q₈	—	2	4	no	—
672	Q₈	—	8	2	no	—
673	D₄	—	2	4	no	—
674	D₄	—	2	2	no	—
675	D₄	—	2	2	no	—
676	D₄	—	2	2	no	—
677	D₄	—	2	2	no	—
678	D₄	—	4	4	no	—
679	D₄	—	4	8	no	—
680	D₄	—	8	4	no	—
681	D₄	C₂×#41×C₈₉	1	4	yes	—
682	C₂×C₄	—	2	4	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	2	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	2	no	—
687	C₂×C₄	—	2	2	no	—
688	C₂×C₄	—	2	4	no	—
689	C₂×C₄	—	2	4	no	—
690	C₂×C₄	—	2	2	no	—
691	C₂×C₄	—	4	2	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	—	4	8	no	—
694	C₂×C₄	—	4	4	no	—
695	C₂×C₄	—	4	4	no	—
696	C₂×C₄	—	4	4	no	—
697	C₂×C₄	—	4	4	no	—
698	C₂×C₄	—	4	4	no	—
699	C₂×C₄	—	8	4	no	—
700	C₂×C₄	#135×C₈₉	1	4	yes	complemented
701	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
702	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
703	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
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	2	yes	—
707	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
708	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
709	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
710	C₈	—	2	1	no	—
711	C₈	—	2	2	no	—
712	C₈	—	2	1	no	—
713	C₈	—	2	2	no	—
714	C₈	—	2	1	no	—
715	C₈	C₂×#41×C₈₉	1	2	yes	—
716	C₂²	—	2	1	no	—
717	C₂²	—	2	1	no	—
718	C₂²	—	2	2	no	—
719	C₂²	—	2	2	no	—
720	C₂²	—	2	2	no	—
721	C₂²	—	2	4	no	—
722	C₂²	—	4	2	no	—
723	C₂²	—	4	2	no	—
724	C₂²	—	4	2	no	—
725	C₂²	—	4	2	no	—
726	C₂²	—	4	2	no	—
727	C₂²	—	8	8	no	—
728	C₂²	C₂×#135×C₈₉	1	2	yes	—
729	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
730	C₄	—	2	2	no	—
731	C₄	—	2	1	no	—
732	C₄	—	2	2	no	—
733	C₄	—	2	1	no	—
734	C₄	—	2	2	no	—
735	C₄	—	2	1	no	—
736	C₄	—	4	2	no	—
737	C₄	—	4	2	no	—
738	C₄	—	4	4	no	—
739	C₄	—	4	4	no	—
740	C₄	C₂×#135×C₈₉	1	2	yes	—
741	C₄	C₂×#135×C₈₉	1	2	yes	—
742	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
743	C₄	#585×C₈₉	1	1	yes	characteristic
744	C₂	—	2	2	no	—
745	C₂	—	4	2	no	—
746	C₂	—	4	4	no	—
747	C₂	—	8	2	no	—
748	C₂	D₄×#41×C₈₉	1	1	yes	characteristic
749	C₂	C₂²×#135×C₈₉	1	1	yes	characteristic
750	C₂	C₈₉×#3584	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3475	C₂	semidirect
2. C₈₉×#3393	C₂	semidirect
3. C₈₉×#3380	C₂	semidirect
4. C₈₉×#3360	C₂	semidirect
5. C₈₉×#3341	C₂	semidirect
6. C₈₉×#3336	C₂	semidirect
7. C₈₉×#3303	C₂	semidirect
8. C₈₉×#3296	C₂	semidirect
9. C₈₉×#3283	C₂	semidirect
10. C₈₉×#3280	C₂	semidirect
11. C₈₉×#3170	C₂	semidirect
12. C₈₉×#3168	C₂	semidirect
13. C₈₉×#3102	C₂	semidirect
14. C₈₉×#3101	C₂	semidirect
15. C₈×#41×C₈₉	C₂	semidirect
16. C₄×#135×C₈₉	C₂	semidirect
17. C₂×C₄×D₈×C₈₉	C₂	semidirect
20. #556×C₈₉	C₂²	semidirect
21. #555×C₈₉	C₂²	semidirect
22. #554×C₈₉	C₂²	semidirect
27. #547×C₈₉	C₂²	semidirect
31. #529×C₈₉	C₂²	semidirect
34. C₄×#41×C₈₉	C₂²	semidirect
37. #500×C₈₉	C₂²	semidirect
38. #499×C₈₉	C₂²	semidirect
40. #494×C₈₉	C₂²	semidirect
41. #488×C₈₉	C₂²	semidirect
42. #487×C₈₉	C₂²	semidirect
43. #485×C₈₉	C₂²	semidirect
45. #482×C₈₉	C₂²	semidirect
46. #479×C₈₉	C₂²	semidirect
47. #478×C₈₉	C₂²	semidirect
48. #476×C₈₉	C₂²	semidirect
49. #476×C₈₉	C₂²	semidirect
52. #467×C₈₉	C₂²	semidirect
54. #465×C₈₉	C₂²	semidirect
55. #464×C₈₉	C₂²	semidirect
57. #461×C₈₉	C₂²	semidirect
58. #461×C₈₉	C₂²	semidirect
59. #452×C₈₉	C₂²	semidirect
62. C₈×Q₈×C₈₉	C₂²	semidirect
63. C₈×Q₈×C₈₉	C₂²	semidirect
64. C₄×Q₁₆×C₈₉	C₂²	semidirect
65. C₄×Q₁₆×C₈₉	C₂²	semidirect
66. C₄×Q₁₆×C₈₉	C₂²	semidirect
67. C₄×SD₁₆×C₈₉	C₂²	semidirect
68. C₄×SD₁₆×C₈₉	C₂²	semidirect
69. C₄×SD₁₆×C₈₉	C₂²	semidirect
79. C₈×D₄×C₈₉	C₂²	semidirect
80. C₈×D₄×C₈₉	C₂²	semidirect
82. #431×C₈₉	C₂²	semidirect
83. #427×C₈₉	C₂²	semidirect
85. #416×C₈₉	C₂²	semidirect
88. C₂×C₄×C₈×C₈₉	C₂²	semidirect
234. D₈×C₈₉	#41	semidirect
324. C₂×C₄×C₈₉	#135	semidirect
368. #61427	C₈₉	direct (N × H)
376. #3475	C₂×C₈₉	semidirect
377. #3393	C₂×C₈₉	semidirect
378. #3380	C₂×C₈₉	semidirect
379. #3360	C₂×C₈₉	semidirect
380. #3341	C₂×C₈₉	semidirect
381. #3336	C₂×C₈₉	semidirect
382. #3303	C₂×C₈₉	semidirect
383. #3296	C₂×C₈₉	semidirect
384. #3283	C₂×C₈₉	semidirect
385. #3280	C₂×C₈₉	semidirect
386. #3170	C₂×C₈₉	semidirect
387. #3168	C₂×C₈₉	semidirect
388. #3102	C₂×C₈₉	semidirect
389. #3101	C₂×C₈₉	semidirect
390. C₈×#41	C₂×C₈₉	semidirect
391. C₄×#135	C₂×C₈₉	semidirect
392. C₂×C₄×D₈	C₂×C₈₉	semidirect
393. C₈₉	#61427	direct (N × H)
396. #556	C₂²×C₈₉	semidirect
397. #555	C₂²×C₈₉	semidirect
398. #554	C₂²×C₈₉	semidirect
403. #547	C₂²×C₈₉	semidirect
407. #529	C₂²×C₈₉	semidirect
410. C₄×#41	C₂²×C₈₉	semidirect
413. #500	C₂²×C₈₉	semidirect
414. #499	C₂²×C₈₉	semidirect
416. #494	C₂²×C₈₉	semidirect
417. #488	C₂²×C₈₉	semidirect
418. #487	C₂²×C₈₉	semidirect
419. #485	C₂²×C₈₉	semidirect
421. #482	C₂²×C₈₉	semidirect
422. #479	C₂²×C₈₉	semidirect
423. #478	C₂²×C₈₉	semidirect
424. #476	C₂²×C₈₉	semidirect
425. #476	C₂²×C₈₉	semidirect
428. #467	C₂²×C₈₉	semidirect
430. #465	C₂²×C₈₉	semidirect
431. #464	C₂²×C₈₉	semidirect
433. #461	C₂²×C₈₉	semidirect
434. #461	C₂²×C₈₉	semidirect
435. #452	C₂²×C₈₉	semidirect
438. C₈×Q₈	C₂²×C₈₉	semidirect
439. C₈×Q₈	C₂²×C₈₉	semidirect
440. C₄×Q₁₆	C₂²×C₈₉	semidirect
441. C₄×Q₁₆	C₂²×C₈₉	semidirect
442. C₄×Q₁₆	C₂²×C₈₉	semidirect
443. C₄×SD₁₆	C₂²×C₈₉	semidirect
444. C₄×SD₁₆	C₂²×C₈₉	semidirect
445. C₄×SD₁₆	C₂²×C₈₉	semidirect
455. C₈×D₄	C₂²×C₈₉	semidirect
456. C₈×D₄	C₂²×C₈₉	semidirect
458. #431	C₂²×C₈₉	semidirect
459. #427	C₂²×C₈₉	semidirect
461. #416	C₂²×C₈₉	semidirect
464. C₂×C₄×C₈	C₂²×C₈₉	semidirect
610. D₈	#41×C₈₉	semidirect
700. C₂×C₄	#135×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3475	2
C₈₉×#3393	2
C₈₉×#3380	2
C₈₉×#3360	2
C₈₉×#3341	2
C₈₉×#3336	2
C₈₉×#3303	2
C₈₉×#3296	2
C₈₉×#3283	2
C₈₉×#3280	2
C₈₉×#3170	2
C₈₉×#3168	2
C₈₉×#3102	2
C₈₉×#3101	2
C₈×#41×C₈₉	2
C₄×#135×C₈₉	2
C₂×C₄×D₈×C₈₉	2
#61427	89

Subgroups — C89×#61427 #36439275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61427 #36439275