Subgroups — C₈₉×#62595 #36440443

Order 22784.

1966 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3517	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3359	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3358	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3332	C₂	1	6	yes	maximal, complemented
6	C₈₉×#3330	C₂	1	6	yes	maximal, complemented
7	C₈₉×#3239	C₂	1	3	yes	maximal, complemented
8	C₈₉×#3214	C₂	1	3	yes	maximal, complemented
9	C₈₉×#3171	C₂	1	3	yes	maximal, complemented
10	C₈₉×#3141	C₂	1	3	yes	maximal, complemented
11	C₈₉×#2971	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₈₉	—	2	1	no	—
13	#557×C₈₉	C₂²	1	1	yes	characteristic
14	#553×C₈₉	—	2	3	no	—
15	#550×C₈₉	—	2	1	no	—
16	#550×C₈₉	C₂²	1	3	yes	—
17	#550×C₈₉	C₂²	1	1	yes	characteristic
18	D₄×Q₈×C₈₉	—	2	1	no	—
19	D₄×Q₈×C₈₉	C₂²	1	2	yes	—
20	#547×C₈₉	—	2	3	no	—
21	#547×C₈₉	C₂²	1	3	yes	—
22	#547×C₈₉	C₂²	1	6	yes	—
23	#540×C₈₉	—	2	3	no	—
24	#536×C₈₉	—	2	3	no	—
25	#532×C₈₉	C₂²	1	3	yes	—
26	#532×C₈₉	C₂²	1	3	yes	—
27	C₂×C₄⋊Q₈×C₈₉	C₂²	1	3	yes	—
28	#529×C₈₉	C₂²	1	3	yes	—
29	#520×C₈₉	—	2	1	no	—
30	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
31	#501×C₈₉	C₂²	1	3	yes	—
32	#496×C₈₉	C₂²	1	3	yes	—
33	#490×C₈₉	C₂²	1	1	yes	characteristic
34	#489×C₈₉	C₂²	1	3	yes	—
35	#489×C₈₉	C₂²	1	6	yes	—
36	#487×C₈₉	C₂²	1	6	yes	—
37	#486×C₈₉	C₂²	1	6	yes	—
38	#484×C₈₉	C₂²	1	6	yes	—
39	#481×C₈₉	C₂²	1	6	yes	—
40	#475×C₈₉	C₂²	1	6	yes	—
41	#474×C₈₉	C₂²	1	6	yes	—
42	#469×C₈₉	C₂²	1	6	yes	—
43	#468×C₈₉	C₂²	1	6	yes	—
44	#461×C₈₉	C₂²	1	6	yes	—
45	#459×C₈₉	C₂²	1	6	yes	—
46	#449×C₈₉	C₂²	1	12	yes	—
47	C₈×Q₈×C₈₉	C₂²	1	2	yes	—
48	C₄×SD₁₆×C₈₉	C₂²	1	6	yes	—
49	C₄×D₈×C₈₉	C₂²	1	6	yes	—
50	#436×C₈₉	C₂²	1	6	yes	—
51	#432×C₈₉	C₂²	1	3	yes	—
52	#417×C₈₉	C₂²	1	12	yes	—
53	C₄×M₁₆×C₈₉	C₂²	1	3	yes	—
54	2₋¹⁺⁴×C₈₉	—	4	8	no	—
55	C₂×#41×C₈₉	—	2	1	no	—
56	C₂×#41×C₈₉	—	2	6	no	—
57	C₂×#41×C₈₉	—	2	3	no	—
58	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
59	C₂×#41×C₈₉	C₂³	1	6	yes	—
60	C₂²×Q₈×C₈₉	—	2	2	no	—
61	C₂²×Q₈×C₈₉	—	2	3	no	—
62	C₂×SD₁₆×C₈₉	C₂³	1	6	yes	—
63	C₂×D₈×C₈₉	C₂³	1	6	yes	—
64	C₂×M₁₆×C₈₉	C₂³	1	6	yes	—
65	C₄⋊Q₈×C₈₉	—	2	3	no	—
66	C₄⋊Q₈×C₈₉	—	2	3	no	—
67	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
68	C₄⋊Q₈×C₈₉	C₂³	1	6	yes	—
69	C₄⋊Q₈×C₈₉	C₂³	1	3	yes	—
70	#127×C₈₉	—	2	3	no	—
71	#127×C₈₉	C₂³	1	3	yes	—
72	#127×C₈₉	C₂³	1	1	yes	characteristic
73	#126×C₈₉	—	2	3	no	—
74	#125×C₈₉	—	2	3	no	—
75	#125×C₈₉	C₂³	1	1	yes	characteristic
76	#124×C₈₉	—	2	3	no	—
77	#124×C₈₉	C₂³	1	3	yes	—
78	#123×C₈₉	—	2	3	no	—
79	#123×C₈₉	—	2	12	no	—
80	#123×C₈₉	—	2	6	no	—
81	C₂²⋊Q₈×C₈₉	—	2	6	no	—
82	C₂²⋊Q₈×C₈₉	—	2	6	no	—
83	C₂²⋊Q₈×C₈₉	C₂³	1	3	yes	—
84	#121×C₈₉	—	2	3	no	—
85	#121×C₈₉	—	2	3	no	—
86	#121×C₈₉	—	2	3	no	—
87	#121×C₈₉	—	2	3	no	—
88	#121×C₈₉	—	2	3	no	—
89	#121×C₈₉	—	2	6	no	—
90	#121×C₈₉	C₂³	1	6	yes	—
91	#121×C₈₉	C₂³	1	3	yes	—
92	C₄×Q₈×C₈₉	—	2	1	no	—
93	C₄×Q₈×C₈₉	D₄	1	1	yes	characteristic
94	C₄×Q₈×C₈₉	C₂³	1	3	yes	—
95	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
96	C₄×D₄×C₈₉	—	2	3	no	—
97	C₄×D₄×C₈₉	—	2	3	no	—
98	C₄×D₄×C₈₉	—	2	3	no	—
99	C₄×D₄×C₈₉	—	2	3	no	—
100	C₄×D₄×C₈₉	—	2	3	no	—
101	C₄×D₄×C₈₉	D₄	1	3	yes	—
102	C₄×D₄×C₈₉	C₂³	1	3	yes	—
103	C₄×D₄×C₈₉	C₂³	1	6	yes	—
104	C₄×D₄×C₈₉	C₂³	1	3	yes	—
105	#117×C₈₉	—	2	3	no	—
106	#117×C₈₉	D₄	1	3	yes	—
107	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
108	C₂×C₄⋊C₄×C₈₉	—	2	3	no	—
109	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
110	C₂×C₄²×C₈₉	C₂³	1	3	yes	—
111	#107×C₈₉	C₂³	1	6	yes	—
112	#106×C₈₉	C₂³	1	6	yes	—
113	C₄⋊C₈×C₈₉	C₂³	1	6	yes	—
114	#103×C₈₉	C₂³	1	6	yes	—
115	#103×C₈₉	C₂³	1	12	yes	—
116	#102×C₈₉	C₂³	1	6	yes	—
117	#102×C₈₉	C₂³	1	12	yes	—
118	#102×C₈₉	C₂³	1	2	yes	—
119	#102×C₈₉	C₂³	1	2	yes	—
120	C₂²⋊C₈×C₈₉	C₂³	1	6	yes	—
121	#97×C₈₉	C₂³	1	1	yes	characteristic
122	#97×C₈₉	C₂³	1	3	yes	—
123	C₄×C₈×C₈₉	C₂³	1	6	yes	—
124	#41×C₈₉	—	2	4	no	—
125	#41×C₈₉	—	4	12	no	—
126	#41×C₈₉	—	4	12	no	—
127	#41×C₈₉	—	4	24	no	—
128	#41×C₈₉	—	4	4	no	—
129	C₂×Q₈×C₈₉	—	2	6	no	—
130	C₂×Q₈×C₈₉	—	2	3	no	—
131	C₂×Q₈×C₈₉	—	4	12	no	—
132	C₂×Q₈×C₈₉	—	4	8	no	—
133	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
134	C₂×Q₈×C₈₉	C₂⁴	1	3	yes	—
135	C₂×D₄×C₈₉	—	2	6	no	—
136	C₂×D₄×C₈₉	—	2	3	no	—
137	C₂×D₄×C₈₉	—	2	6	no	—
138	C₂×D₄×C₈₉	—	2	1	no	—
139	C₂×D₄×C₈₉	—	2	3	no	—
140	C₂×D₄×C₈₉	—	2	1	no	—
141	C₂×D₄×C₈₉	—	2	3	no	—
142	C₂×D₄×C₈₉	C₂×D₄	1	3	yes	—
143	C₂×D₄×C₈₉	C₂⁴	1	3	yes	—
144	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₈₉	—	2	6	no	—
146	C₂²×C₄×C₈₉	—	2	3	no	—
147	C₂²×C₄×C₈₉	—	2	6	no	—
148	C₂²×C₄×C₈₉	—	2	6	no	—
149	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
150	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
151	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
152	SD₁₆×C₈₉	—	4	6	no	—
153	D₈×C₈₉	—	4	6	no	—
154	M₁₆×C₈₉	—	4	6	no	—
155	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
156	C₂×C₈×C₈₉	C₂⁴	1	6	yes	—
157	C₄⋊C₄×C₈₉	—	2	3	no	—
158	C₄⋊C₄×C₈₉	—	2	3	no	—
159	C₄⋊C₄×C₈₉	—	2	3	no	—
160	C₄⋊C₄×C₈₉	—	2	6	no	—
161	C₄⋊C₄×C₈₉	—	2	6	no	—
162	C₄⋊C₄×C₈₉	—	2	1	no	—
163	C₄⋊C₄×C₈₉	—	2	1	no	—
164	C₄⋊C₄×C₈₉	—	2	3	no	—
165	C₄⋊C₄×C₈₉	—	2	3	no	—
166	C₄⋊C₄×C₈₉	C₂×D₄	1	3	yes	—
167	C₄⋊C₄×C₈₉	C₂×D₄	1	3	yes	—
168	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
169	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
170	C₄⋊C₄×C₈₉	C₂⁴	1	1	yes	characteristic
171	C₂²⋊C₄×C₈₉	—	2	3	no	—
172	C₂²⋊C₄×C₈₉	—	2	3	no	—
173	C₂²⋊C₄×C₈₉	—	2	3	no	—
174	C₂²⋊C₄×C₈₉	—	2	3	no	—
175	C₂²⋊C₄×C₈₉	—	2	6	no	—
176	C₂²⋊C₄×C₈₉	—	2	3	no	—
177	C₂²⋊C₄×C₈₉	—	2	6	no	—
178	C₂²⋊C₄×C₈₉	C₂×D₄	1	6	yes	—
179	C₄²×C₈₉	—	2	3	no	—
180	C₄²×C₈₉	C₂×D₄	1	3	yes	—
181	C₄²×C₈₉	C₂×D₄	1	3	yes	—
182	C₄²×C₈₉	C₂⁴	1	3	yes	—
183	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
184	C₂³×C₈₉	—	2	2	no	—
185	C₂³×C₈₉	—	2	3	no	—
186	C₂³×C₈₉	C₂²×D₄	1	3	yes	—
187	Q₈×C₈₉	—	2	6	no	—
188	Q₈×C₈₉	—	4	6	no	—
189	Q₈×C₈₉	—	4	12	no	—
190	Q₈×C₈₉	AGL(1,ℤ/8)	1	4	yes	—
191	D₄×C₈₉	—	2	6	no	—
192	D₄×C₈₉	—	2	2	no	—
193	D₄×C₈₉	—	2	6	no	—
194	D₄×C₈₉	—	2	2	no	—
195	D₄×C₈₉	—	4	2	no	—
196	D₄×C₈₉	—	4	2	no	—
197	D₄×C₈₉	—	4	12	no	—
198	D₄×C₈₉	—	4	6	no	—
199	D₄×C₈₉	—	8	3	no	—
200	D₄×C₈₉	—	8	3	no	—
201	D₄×C₈₉	—	8	6	no	—
202	C₂×C₄×C₈₉	—	2	6	no	—
203	C₂×C₄×C₈₉	—	2	6	no	—
204	C₂×C₄×C₈₉	—	2	1	no	—
205	C₂×C₄×C₈₉	—	2	3	no	—
206	C₂×C₄×C₈₉	—	2	1	no	—
207	C₂×C₄×C₈₉	—	2	6	no	—
208	C₂×C₄×C₈₉	—	4	3	no	—
209	C₂×C₄×C₈₉	—	4	12	no	—
210	C₂×C₄×C₈₉	—	4	12	no	—
211	C₂×C₄×C₈₉	—	4	6	no	—
212	C₂×C₄×C₈₉	—	8	6	no	—
213	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
216	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
217	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
218	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
219	C₈×C₈₉	—	2	2	no	—
220	C₈×C₈₉	—	2	6	no	—
221	C₂²×C₈₉	—	2	3	no	—
222	C₂²×C₈₉	—	2	3	no	—
223	C₂²×C₈₉	—	2	3	no	—
224	C₂²×C₈₉	—	4	2	no	—
225	C₂²×C₈₉	—	4	3	no	—
226	C₂²×C₈₉	—	4	3	no	—
227	C₂²×C₈₉	—	4	2	no	—
228	C₂²×C₈₉	—	4	2	no	—
229	C₂²×C₈₉	—	4	3	no	—
230	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
231	C₄×C₈₉	—	2	1	no	—
232	C₄×C₈₉	—	2	3	no	—
233	C₄×C₈₉	—	2	3	no	—
234	C₄×C₈₉	—	2	1	no	—
235	C₄×C₈₉	—	4	1	no	—
236	C₄×C₈₉	—	4	3	no	—
237	C₄×C₈₉	—	4	1	no	—
238	C₄×C₈₉	—	4	6	no	—
239	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	6	yes	—
240	C₄×C₈₉	#585	1	2	yes	—
241	#62595	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂×C₈₉	—	4	3	no	—
243	C₂×C₈₉	—	8	2	no	—
244	C₂×C₈₉	—	8	3	no	—
245	C₂×C₈₉	#3500	1	1	yes	characteristic
246	C₂×C₈₉	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
247	C₂×C₈₉	#3586	1	1	yes	characteristic
248	#3517	C₂×C₈₉	1	1	yes	characteristic, complemented
249	#3499	C₂×C₈₉	1	1	yes	characteristic, complemented
250	#3359	C₂×C₈₉	1	2	yes	complemented
251	#3358	C₂×C₈₉	1	2	yes	complemented
252	#3332	C₂×C₈₉	1	6	yes	complemented
253	#3330	C₂×C₈₉	1	6	yes	complemented
254	#3239	C₂×C₈₉	1	3	yes	complemented
255	#3214	C₂×C₈₉	1	3	yes	complemented
256	#3171	C₂×C₈₉	1	3	yes	complemented
257	#3141	C₂×C₈₉	1	3	yes	complemented
258	#2971	C₂×C₈₉	1	1	yes	characteristic, complemented
259	C₈₉	#62595	1	1	yes	characteristic, direct product factor, Sylow
260	C₂×2₋¹⁺⁴	—	2	1	no	—
261	#557	C₂²×C₈₉	1	1	yes	characteristic
262	#553	—	2	3	no	—
263	#550	—	2	1	no	—
264	#550	C₂²×C₈₉	1	3	yes	—
265	#550	C₂²×C₈₉	1	1	yes	characteristic
266	D₄×Q₈	—	2	1	no	—
267	D₄×Q₈	C₂²×C₈₉	1	2	yes	—
268	#547	—	2	3	no	—
269	#547	C₂²×C₈₉	1	3	yes	—
270	#547	C₂²×C₈₉	1	6	yes	—
271	#540	—	2	3	no	—
272	#536	—	2	3	no	—
273	#532	C₂²×C₈₉	1	3	yes	—
274	#532	C₂²×C₈₉	1	3	yes	—
275	C₂×C₄⋊Q₈	C₂²×C₈₉	1	3	yes	—
276	#529	C₂²×C₈₉	1	3	yes	—
277	#520	—	2	1	no	—
278	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
279	#501	C₂²×C₈₉	1	3	yes	—
280	#496	C₂²×C₈₉	1	3	yes	—
281	#490	C₂²×C₈₉	1	1	yes	characteristic
282	#489	C₂²×C₈₉	1	3	yes	—
283	#489	C₂²×C₈₉	1	6	yes	—
284	#487	C₂²×C₈₉	1	6	yes	—
285	#486	C₂²×C₈₉	1	6	yes	—
286	#484	C₂²×C₈₉	1	6	yes	—
287	#481	C₂²×C₈₉	1	6	yes	—
288	#475	C₂²×C₈₉	1	6	yes	—
289	#474	C₂²×C₈₉	1	6	yes	—
290	#469	C₂²×C₈₉	1	6	yes	—
291	#468	C₂²×C₈₉	1	6	yes	—
292	#461	C₂²×C₈₉	1	6	yes	—
293	#459	C₂²×C₈₉	1	6	yes	—
294	#449	C₂²×C₈₉	1	12	yes	—
295	C₈×Q₈	C₂²×C₈₉	1	2	yes	—
296	C₄×SD₁₆	C₂²×C₈₉	1	6	yes	—
297	C₄×D₈	C₂²×C₈₉	1	6	yes	—
298	#436	C₂²×C₈₉	1	6	yes	—
299	#432	C₂²×C₈₉	1	3	yes	—
300	#417	C₂²×C₈₉	1	12	yes	—
301	C₄×M₁₆	C₂²×C₈₉	1	3	yes	—
302	2₋¹⁺⁴	—	4	8	no	—
303	C₂×#41	—	2	1	no	—
304	C₂×#41	—	2	6	no	—
305	C₂×#41	—	2	3	no	—
306	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
307	C₂×#41	C₂³×C₈₉	1	6	yes	—
308	C₂²×Q₈	—	2	2	no	—
309	C₂²×Q₈	—	2	3	no	—
310	C₂×SD₁₆	C₂³×C₈₉	1	6	yes	—
311	C₂×D₈	C₂³×C₈₉	1	6	yes	—
312	C₂×M₁₆	C₂³×C₈₉	1	6	yes	—
313	C₄⋊Q₈	—	2	3	no	—
314	C₄⋊Q₈	—	2	3	no	—
315	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
316	C₄⋊Q₈	C₂³×C₈₉	1	3	yes	—
317	C₄⋊Q₈	C₂³×C₈₉	1	6	yes	—
318	#127	—	2	3	no	—
319	#127	C₂³×C₈₉	1	1	yes	characteristic
320	#127	C₂³×C₈₉	1	3	yes	—
321	#126	—	2	3	no	—
322	#125	—	2	3	no	—
323	#125	C₂³×C₈₉	1	1	yes	characteristic
324	#124	—	2	3	no	—
325	#124	C₂³×C₈₉	1	3	yes	—
326	#123	—	2	3	no	—
327	#123	—	2	12	no	—
328	#123	—	2	6	no	—
329	C₂²⋊Q₈	—	2	6	no	—
330	C₂²⋊Q₈	—	2	6	no	—
331	C₂²⋊Q₈	C₂³×C₈₉	1	3	yes	—
332	#121	—	2	3	no	—
333	#121	—	2	3	no	—
334	#121	—	2	3	no	—
335	#121	—	2	3	no	—
336	#121	—	2	3	no	—
337	#121	—	2	6	no	—
338	#121	C₂³×C₈₉	1	3	yes	—
339	#121	C₂³×C₈₉	1	6	yes	—
340	C₄×Q₈	—	2	1	no	—
341	C₄×Q₈	D₄×C₈₉	1	1	yes	characteristic
342	C₄×Q₈	C₂³×C₈₉	1	3	yes	—
343	C₄×Q₈	C₂³×C₈₉	1	1	yes	characteristic
344	C₄×D₄	—	2	3	no	—
345	C₄×D₄	—	2	3	no	—
346	C₄×D₄	—	2	3	no	—
347	C₄×D₄	—	2	3	no	—
348	C₄×D₄	—	2	3	no	—
349	C₄×D₄	D₄×C₈₉	1	3	yes	—
350	C₄×D₄	C₂³×C₈₉	1	3	yes	—
351	C₄×D₄	C₂³×C₈₉	1	6	yes	—
352	C₄×D₄	C₂³×C₈₉	1	3	yes	—
353	#117	—	2	3	no	—
354	#117	D₄×C₈₉	1	3	yes	—
355	C₂×C₄⋊C₄	—	2	3	no	—
356	C₂×C₄⋊C₄	—	2	3	no	—
357	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
358	C₂×C₄²	C₂³×C₈₉	1	3	yes	—
359	#107	C₂³×C₈₉	1	6	yes	—
360	#106	C₂³×C₈₉	1	6	yes	—
361	C₄⋊C₈	C₂³×C₈₉	1	6	yes	—
362	#103	C₂³×C₈₉	1	6	yes	—
363	#103	C₂³×C₈₉	1	12	yes	—
364	#102	C₂³×C₈₉	1	6	yes	—
365	#102	C₂³×C₈₉	1	12	yes	—
366	#102	C₂³×C₈₉	1	2	yes	—
367	#102	C₂³×C₈₉	1	2	yes	—
368	C₂²⋊C₈	C₂³×C₈₉	1	6	yes	—
369	#97	C₂³×C₈₉	1	1	yes	characteristic
370	#97	C₂³×C₈₉	1	3	yes	—
371	C₄×C₈	C₂³×C₈₉	1	6	yes	—
372	#41	—	2	4	no	—
373	#41	—	4	12	no	—
374	#41	—	4	12	no	—
375	#41	—	4	24	no	—
376	#41	—	4	4	no	—
377	C₂×Q₈	—	2	6	no	—
378	C₂×Q₈	—	2	3	no	—
379	C₂×Q₈	—	4	12	no	—
380	C₂×Q₈	—	4	8	no	—
381	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
382	C₂×Q₈	C₂⁴×C₈₉	1	3	yes	—
383	C₂×D₄	—	2	6	no	—
384	C₂×D₄	—	2	3	no	—
385	C₂×D₄	—	2	6	no	—
386	C₂×D₄	—	2	1	no	—
387	C₂×D₄	—	2	3	no	—
388	C₂×D₄	—	2	1	no	—
389	C₂×D₄	—	2	3	no	—
390	C₂×D₄	C₂×D₄×C₈₉	1	3	yes	—
391	C₂×D₄	C₂⁴×C₈₉	1	3	yes	—
392	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
393	C₂²×C₄	—	2	6	no	—
394	C₂²×C₄	—	2	3	no	—
395	C₂²×C₄	—	2	6	no	—
396	C₂²×C₄	—	2	6	no	—
397	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
398	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
399	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
400	SD₁₆	—	4	6	no	—
401	D₈	—	4	6	no	—
402	M₁₆	—	4	6	no	—
403	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
404	C₂×C₈	C₂⁴×C₈₉	1	6	yes	—
405	C₄⋊C₄	—	2	3	no	—
406	C₄⋊C₄	—	2	3	no	—
407	C₄⋊C₄	—	2	3	no	—
408	C₄⋊C₄	—	2	6	no	—
409	C₄⋊C₄	—	2	6	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	1	no	—
412	C₄⋊C₄	—	2	3	no	—
413	C₄⋊C₄	—	2	3	no	—
414	C₄⋊C₄	C₂×D₄×C₈₉	1	3	yes	—
415	C₄⋊C₄	C₂×D₄×C₈₉	1	3	yes	—
416	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
417	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
418	C₄⋊C₄	C₂⁴×C₈₉	1	1	yes	characteristic
419	C₂²⋊C₄	—	2	3	no	—
420	C₂²⋊C₄	—	2	3	no	—
421	C₂²⋊C₄	—	2	3	no	—
422	C₂²⋊C₄	—	2	3	no	—
423	C₂²⋊C₄	—	2	6	no	—
424	C₂²⋊C₄	—	2	3	no	—
425	C₂²⋊C₄	—	2	6	no	—
426	C₂²⋊C₄	C₂×D₄×C₈₉	1	6	yes	—
427	C₄²	—	2	3	no	—
428	C₄²	C₂×D₄×C₈₉	1	3	yes	—
429	C₄²	C₂×D₄×C₈₉	1	3	yes	—
430	C₄²	C₂⁴×C₈₉	1	3	yes	—
431	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
432	C₂³	—	2	2	no	—
433	C₂³	—	2	3	no	—
434	C₂³	C₂²×D₄×C₈₉	1	3	yes	—
435	Q₈	—	2	6	no	—
436	Q₈	—	4	6	no	—
437	Q₈	—	4	12	no	—
438	Q₈	AGL(1,ℤ/8)×C₈₉	1	4	yes	—
439	D₄	—	2	6	no	—
440	D₄	—	2	2	no	—
441	D₄	—	2	6	no	—
442	D₄	—	2	2	no	—
443	D₄	—	4	2	no	—
444	D₄	—	4	2	no	—
445	D₄	—	4	12	no	—
446	D₄	—	4	6	no	—
447	D₄	—	8	3	no	—
448	D₄	—	8	3	no	—
449	D₄	—	8	6	no	—
450	C₂×C₄	—	2	6	no	—
451	C₂×C₄	—	2	6	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	3	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	6	no	—
456	C₂×C₄	—	4	3	no	—
457	C₂×C₄	—	4	12	no	—
458	C₂×C₄	—	4	12	no	—
459	C₂×C₄	—	4	6	no	—
460	C₂×C₄	—	8	6	no	—
461	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
462	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
463	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
464	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
465	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
466	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
467	C₈	—	2	2	no	—
468	C₈	—	2	6	no	—
469	C₂²	—	2	3	no	—
470	C₂²	—	2	3	no	—
471	C₂²	—	2	3	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	3	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	3	no	—
476	C₂²	—	4	3	no	—
477	C₂²	—	4	2	no	—
478	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	3	no	—
482	C₄	—	2	3	no	—
483	C₄	—	4	6	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	4	3	no	—
487	C₄	C₂×AGL(1,ℤ/8)×C₈₉	1	6	yes	—
488	C₄	#585×C₈₉	1	2	yes	—
489	C₂	—	4	3	no	—
490	C₂	—	8	2	no	—
491	C₂	—	8	3	no	—
492	C₂	C₈₉×#3500	1	1	yes	characteristic
493	C₂	C₂²×AGL(1,ℤ/8)×C₈₉	1	1	yes	characteristic
494	C₂	C₈₉×#3586	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3517	C₂	semidirect
2. C₈₉×#3499	C₂	semidirect
3. C₈₉×#3359	C₂	semidirect
4. C₈₉×#3358	C₂	semidirect
5. C₈₉×#3332	C₂	semidirect
6. C₈₉×#3330	C₂	semidirect
7. C₈₉×#3239	C₂	semidirect
8. C₈₉×#3214	C₂	semidirect
9. C₈₉×#3171	C₂	semidirect
10. C₈₉×#3141	C₂	semidirect
11. C₈₉×#2971	C₂	semidirect
241. #62595	C₈₉	direct (N × H)
248. #3517	C₂×C₈₉	semidirect
249. #3499	C₂×C₈₉	semidirect
250. #3359	C₂×C₈₉	semidirect
251. #3358	C₂×C₈₉	semidirect
252. #3332	C₂×C₈₉	semidirect
253. #3330	C₂×C₈₉	semidirect
254. #3239	C₂×C₈₉	semidirect
255. #3214	C₂×C₈₉	semidirect
256. #3171	C₂×C₈₉	semidirect
257. #3141	C₂×C₈₉	semidirect
258. #2971	C₂×C₈₉	semidirect
259. C₈₉	#62595	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#3517	2
C₈₉×#3499	2
C₈₉×#3359	2
C₈₉×#3358	2
C₈₉×#3332	2
C₈₉×#3330	2
C₈₉×#3239	2
C₈₉×#3214	2
C₈₉×#3171	2
C₈₉×#3141	2
C₈₉×#2971	2
#62595	89

Subgroups — C89×#62595 #36440443

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62595 #36440443