Subgroups — C₈₉×#23736 #36401584

Order 22784.

1050 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#428×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#427×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#419×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂²×#103×C₈₉	C₂	1	1	yes	maximal, characteristic
5	C₈₉×#2317	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#2310	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#2097	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2097	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2096	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2095	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1729	C₂	1	1	yes	maximal, characteristic
12	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
19	#428×C₈₉	—	2	4	no	—
20	#427×C₈₉	—	2	4	no	—
21	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#107×C₈₉	C₂²	1	2	yes	—
23	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#106×C₈₉	C₂²	1	2	yes	—
26	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
27	#419×C₈₉	—	2	4	no	—
28	C₂×#103×C₈₉	—	2	4	no	—
29	C₂×#103×C₈₉	C₂²	1	2	yes	—
30	C₂×#103×C₈₉	C₂²	1	2	yes	—
31	C₂×#103×C₈₉	C₂²	1	2	yes	—
32	C₂×#103×C₈₉	C₂²	1	2	yes	—
33	#391×C₈₉	—	2	2	no	—
34	#391×C₈₉	C₂²	1	2	yes	—
35	#391×C₈₉	C₂²	1	2	yes	—
36	#389×C₈₉	—	2	2	no	—
37	#385×C₈₉	—	2	2	no	—
38	#384×C₈₉	C₂²	1	2	yes	—
39	#382×C₈₉	C₂²	1	2	yes	—
40	#381×C₈₉	—	2	2	no	—
41	#336×C₈₉	C₂²	1	2	yes	—
42	#336×C₈₉	C₂²	1	2	yes	—
43	C₂²×Q₈×C₈₉	—	2	1	no	—
44	C₂²×Q₈×C₈₉	—	2	2	no	—
45	C₂²×Q₈×C₈₉	—	2	2	no	—
46	C₂²×Q₈×C₈₉	—	2	2	no	—
47	C₂²×Q₈×C₈₉	—	2	2	no	—
48	C₂²×Q₈×C₈₉	—	2	2	no	—
49	C₂²×Q₈×C₈₉	Q₈	1	4	yes	—
50	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₈₉	—	2	1	no	—
52	C₂³×C₄×C₈₉	—	2	1	no	—
53	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
54	C₂×M₁₆×C₈₉	—	2	2	no	—
55	C₂×M₁₆×C₈₉	—	2	2	no	—
56	C₂×M₁₆×C₈₉	D₄	1	4	yes	—
57	C₂²×C₈×C₈₉	—	2	2	no	—
58	C₂²×C₈×C₈₉	—	2	2	no	—
59	C₂²×C₈×C₈₉	D₄	1	4	yes	—
60	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
62	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
63	#117×C₈₉	—	2	2	no	—
64	#117×C₈₉	—	2	2	no	—
65	#117×C₈₉	—	2	2	no	—
66	#117×C₈₉	—	2	2	no	—
67	#117×C₈₉	—	2	2	no	—
68	#117×C₈₉	—	2	2	no	—
69	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
70	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
72	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
73	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
74	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
80	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
81	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
82	C₂×C₄²×C₈₉	—	2	1	no	—
83	C₂×C₄²×C₈₉	—	2	1	no	—
84	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
85	#107×C₈₉	—	2	2	no	—
86	#107×C₈₉	—	2	2	no	—
87	#107×C₈₉	—	2	4	no	—
88	#106×C₈₉	—	2	2	no	—
89	#106×C₈₉	—	2	2	no	—
90	#106×C₈₉	—	2	4	no	—
91	#103×C₈₉	—	2	4	no	—
92	#103×C₈₉	—	2	4	no	—
93	#103×C₈₉	—	2	4	no	—
94	#103×C₈₉	—	2	4	no	—
95	#95×C₈₉	—	2	4	no	—
96	#95×C₈₉	—	2	4	no	—
97	#95×C₈₉	—	2	4	no	—
98	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
99	C₂×Q₈×C₈₉	—	2	4	no	—
100	C₂×Q₈×C₈₉	—	2	2	no	—
101	C₂×Q₈×C₈₉	—	2	8	no	—
102	C₂×Q₈×C₈₉	—	2	8	no	—
103	C₂×Q₈×C₈₉	—	2	2	no	—
104	C₂×Q₈×C₈₉	—	2	2	no	—
105	C₂×Q₈×C₈₉	—	2	2	no	—
106	C₂×Q₈×C₈₉	—	2	2	no	—
107	C₂×Q₈×C₈₉	—	4	2	no	—
108	C₂×Q₈×C₈₉	—	4	4	no	—
109	C₂×Q₈×C₈₉	—	4	4	no	—
110	C₂×Q₈×C₈₉	—	4	2	no	—
111	C₂×Q₈×C₈₉	C₂×Q₈	1	4	yes	—
112	C₂²×C₄×C₈₉	—	2	4	no	—
113	C₂²×C₄×C₈₉	—	2	2	no	—
114	C₂²×C₄×C₈₉	—	2	1	no	—
115	C₂²×C₄×C₈₉	—	2	1	no	—
116	C₂²×C₄×C₈₉	—	2	1	no	—
117	C₂²×C₄×C₈₉	—	2	2	no	—
118	C₂²×C₄×C₈₉	—	2	1	no	—
119	C₂²×C₄×C₈₉	—	4	2	no	—
120	C₂²×C₄×C₈₉	—	4	2	no	—
121	C₂²×C₄×C₈₉	—	4	2	no	—
122	C₂²×C₄×C₈₉	—	8	2	no	—
123	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
124	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
128	C₂²×C₄×C₈₉	#41	1	2	yes	—
129	C₂²×C₄×C₈₉	#41	1	2	yes	—
130	C₂²×C₄×C₈₉	#41	1	2	yes	—
131	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
132	M₁₆×C₈₉	—	2	8	no	—
133	C₂×C₈×C₈₉	—	2	8	no	—
134	C₂×C₈×C₈₉	—	2	1	no	—
135	C₂×C₈×C₈₉	—	2	1	no	—
136	C₂×C₈×C₈₉	—	2	1	no	—
137	C₂×C₈×C₈₉	—	2	1	no	—
138	C₂×C₈×C₈₉	—	2	2	no	—
139	C₂×C₈×C₈₉	—	2	2	no	—
140	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
142	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
143	C₄⋊C₄×C₈₉	—	2	4	no	—
144	C₄⋊C₄×C₈₉	—	2	2	no	—
145	C₄⋊C₄×C₈₉	—	2	1	no	—
146	C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₄⋊C₄×C₈₉	—	2	1	no	—
148	C₄⋊C₄×C₈₉	—	2	2	no	—
149	C₄⋊C₄×C₈₉	—	2	1	no	—
150	C₄⋊C₄×C₈₉	—	2	1	no	—
151	C₄⋊C₄×C₈₉	—	2	1	no	—
152	C₄⋊C₄×C₈₉	—	2	1	no	—
153	C₄⋊C₄×C₈₉	—	2	1	no	—
154	C₄⋊C₄×C₈₉	—	4	2	no	—
155	C₄⋊C₄×C₈₉	—	8	4	no	—
156	C₂²⋊C₄×C₈₉	—	2	4	no	—
157	C₂²⋊C₄×C₈₉	—	4	2	no	—
158	C₂²⋊C₄×C₈₉	—	4	2	no	—
159	C₄²×C₈₉	—	2	2	no	—
160	C₄²×C₈₉	—	2	2	no	—
161	C₄²×C₈₉	—	4	2	no	—
162	C₄²×C₈₉	—	4	2	no	—
163	C₂³×C₈₉	—	2	2	no	—
164	C₂³×C₈₉	—	2	2	no	—
165	C₂³×C₈₉	C₂²⋊Q₈	1	2	yes	—
166	C₂³×C₈₉	#123	1	2	yes	—
167	C₂³×C₈₉	#127	1	2	yes	—
168	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₈₉	—	2	4	no	—
170	Q₈×C₈₉	—	2	4	no	—
171	Q₈×C₈₉	—	4	2	no	—
172	Q₈×C₈₉	—	4	2	no	—
173	Q₈×C₈₉	—	4	8	no	—
174	C₂×C₄×C₈₉	—	2	4	no	—
175	C₂×C₄×C₈₉	—	2	4	no	—
176	C₂×C₄×C₈₉	—	2	4	no	—
177	C₂×C₄×C₈₉	—	2	4	no	—
178	C₂×C₄×C₈₉	—	4	2	no	—
179	C₂×C₄×C₈₉	—	4	2	no	—
180	C₂×C₄×C₈₉	—	4	8	no	—
181	C₂×C₄×C₈₉	—	4	1	no	—
182	C₂×C₄×C₈₉	—	4	1	no	—
183	C₂×C₄×C₈₉	—	4	1	no	—
184	C₂×C₄×C₈₉	—	4	1	no	—
185	C₂×C₄×C₈₉	—	4	2	no	—
186	C₂×C₄×C₈₉	—	4	2	no	—
187	C₂×C₄×C₈₉	—	4	4	no	—
188	C₂×C₄×C₈₉	—	4	2	no	—
189	C₂×C₄×C₈₉	—	4	2	no	—
190	C₂×C₄×C₈₉	—	4	2	no	—
191	C₂×C₄×C₈₉	—	8	4	no	—
192	C₂×C₄×C₈₉	C₂²⋊Q₈	1	4	yes	—
193	C₂×C₄×C₈₉	C₂²⋊Q₈	1	4	yes	—
194	C₂×C₄×C₈₉	C₂²⋊Q₈	1	2	yes	—
195	C₂×C₄×C₈₉	#123	1	4	yes	—
196	C₂×C₄×C₈₉	#123	1	4	yes	—
197	C₂×C₄×C₈₉	#123	1	2	yes	—
198	C₂×C₄×C₈₉	#127	1	2	yes	—
199	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
200	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
202	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
205	C₈×C₈₉	—	2	2	no	—
206	C₈×C₈₉	—	2	2	no	—
207	C₈×C₈₉	—	2	4	no	—
208	C₂²×C₈₉	—	2	4	no	—
209	C₂²×C₈₉	—	2	4	no	—
210	C₂²×C₈₉	—	2	2	no	—
211	C₂²×C₈₉	—	2	2	no	—
212	C₂²×C₈₉	#399	1	4	yes	—
213	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
214	C₂²×C₈₉	C₂×#123	1	1	yes	characteristic
215	C₂²×C₈₉	C₂×#127	1	1	yes	characteristic
216	C₂²×C₈₉	#577	1	2	yes	—
217	C₂²×C₈₉	#578	1	2	yes	—
218	C₄×C₈₉	—	4	4	no	—
219	C₄×C₈₉	—	4	4	no	—
220	C₄×C₈₉	—	8	1	no	—
221	C₄×C₈₉	—	8	1	no	—
222	C₄×C₈₉	—	8	2	no	—
223	C₄×C₈₉	—	8	1	no	—
224	C₄×C₈₉	—	8	1	no	—
225	C₄×C₈₉	#399	1	4	yes	—
226	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
227	C₄×C₈₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
228	C₄×C₈₉	C₂×#123	1	1	yes	characteristic
229	C₄×C₈₉	C₂×#123	1	1	yes	characteristic
230	#23736	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂×C₈₉	—	2	4	no	—
232	C₂×C₈₉	C₂×#399	1	1	yes	characteristic
233	C₂×C₈₉	#3082	1	2	yes	—
234	C₂×C₈₉	#3097	1	2	yes	—
235	C₂×C₈₉	#3154	1	1	yes	characteristic
236	C₂×C₈₉	#3156	1	1	yes	characteristic
237	C₂×#428	C₂×C₈₉	1	1	yes	characteristic
238	C₂×#427	C₂×C₈₉	1	1	yes	characteristic
239	C₂×#419	C₂×C₈₉	1	1	yes	characteristic
240	C₂²×#103	C₂×C₈₉	1	1	yes	characteristic
241	#2317	C₂×C₈₉	1	1	yes	characteristic
242	#2310	C₂×C₈₉	1	1	yes	characteristic
243	#2097	C₂×C₈₉	1	2	yes	complemented
244	#2097	C₂×C₈₉	1	2	yes	complemented
245	#2096	C₂×C₈₉	1	2	yes	complemented
246	#2095	C₂×C₈₉	1	2	yes	complemented
247	#1729	C₂×C₈₉	1	1	yes	characteristic
248	C₈₉	#23736	1	1	yes	characteristic, direct product factor, Sylow
249	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
250	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
251	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
252	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
253	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
254	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
255	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
256	#428	—	2	4	no	—
257	#427	—	2	4	no	—
258	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
259	C₂×#107	C₂²×C₈₉	1	2	yes	—
260	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
261	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
262	C₂×#106	C₂²×C₈₉	1	2	yes	—
263	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
264	#419	—	2	4	no	—
265	C₂×#103	—	2	4	no	—
266	C₂×#103	C₂²×C₈₉	1	2	yes	—
267	C₂×#103	C₂²×C₈₉	1	2	yes	—
268	C₂×#103	C₂²×C₈₉	1	2	yes	—
269	C₂×#103	C₂²×C₈₉	1	2	yes	—
270	#391	—	2	2	no	—
271	#391	C₂²×C₈₉	1	2	yes	—
272	#391	C₂²×C₈₉	1	2	yes	—
273	#389	—	2	2	no	—
274	#385	—	2	2	no	—
275	#384	C₂²×C₈₉	1	2	yes	—
276	#382	C₂²×C₈₉	1	2	yes	—
277	#381	—	2	2	no	—
278	#336	C₂²×C₈₉	1	2	yes	—
279	#336	C₂²×C₈₉	1	2	yes	—
280	C₂²×Q₈	—	2	1	no	—
281	C₂²×Q₈	—	2	2	no	—
282	C₂²×Q₈	—	2	2	no	—
283	C₂²×Q₈	—	2	2	no	—
284	C₂²×Q₈	—	2	2	no	—
285	C₂²×Q₈	—	2	2	no	—
286	C₂²×Q₈	Q₈×C₈₉	1	4	yes	—
287	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
288	C₂³×C₄	—	2	1	no	—
289	C₂³×C₄	—	2	1	no	—
290	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
291	C₂×M₁₆	—	2	2	no	—
292	C₂×M₁₆	—	2	2	no	—
293	C₂×M₁₆	D₄×C₈₉	1	4	yes	—
294	C₂²×C₈	—	2	2	no	—
295	C₂²×C₈	—	2	2	no	—
296	C₂²×C₈	D₄×C₈₉	1	4	yes	—
297	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
298	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
299	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
300	#117	—	2	2	no	—
301	#117	—	2	2	no	—
302	#117	—	2	2	no	—
303	#117	—	2	2	no	—
304	#117	—	2	2	no	—
305	#117	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	2	4	no	—
310	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
313	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
319	C₂×C₄²	—	2	1	no	—
320	C₂×C₄²	—	2	1	no	—
321	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
322	#107	—	2	2	no	—
323	#107	—	2	2	no	—
324	#107	—	2	4	no	—
325	#106	—	2	2	no	—
326	#106	—	2	2	no	—
327	#106	—	2	4	no	—
328	#103	—	2	4	no	—
329	#103	—	2	4	no	—
330	#103	—	2	4	no	—
331	#103	—	2	4	no	—
332	#95	—	2	4	no	—
333	#95	—	2	4	no	—
334	#95	—	2	4	no	—
335	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	8	no	—
339	C₂×Q₈	—	2	8	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	4	4	no	—
345	C₂×Q₈	—	4	4	no	—
346	C₂×Q₈	—	4	2	no	—
347	C₂×Q₈	—	4	2	no	—
348	C₂×Q₈	C₂×Q₈×C₈₉	1	4	yes	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	4	2	no	—
357	C₂²×C₄	—	4	2	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	8	2	no	—
360	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
361	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
363	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
364	C₂²×C₄	C₂×Q₈×C₈₉	1	2	yes	—
365	C₂²×C₄	#41×C₈₉	1	2	yes	—
366	C₂²×C₄	#41×C₈₉	1	2	yes	—
367	C₂²×C₄	#41×C₈₉	1	2	yes	—
368	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
369	M₁₆	—	2	8	no	—
370	C₂×C₈	—	2	8	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
378	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
379	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
380	C₄⋊C₄	—	2	4	no	—
381	C₄⋊C₄	—	2	2	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	1	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	4	2	no	—
392	C₄⋊C₄	—	8	4	no	—
393	C₂²⋊C₄	—	2	4	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	—	4	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	4	2	no	—
399	C₄²	—	4	2	no	—
400	C₂³	—	2	2	no	—
401	C₂³	—	2	2	no	—
402	C₂³	C₂²⋊Q₈×C₈₉	1	2	yes	—
403	C₂³	#123×C₈₉	1	2	yes	—
404	C₂³	#127×C₈₉	1	2	yes	—
405	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
406	Q₈	—	2	4	no	—
407	Q₈	—	2	4	no	—
408	Q₈	—	4	8	no	—
409	Q₈	—	4	2	no	—
410	Q₈	—	4	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	4	8	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	1	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	4	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	8	4	no	—
429	C₂×C₄	C₂²⋊Q₈×C₈₉	1	2	yes	—
430	C₂×C₄	C₂²⋊Q₈×C₈₉	1	4	yes	—
431	C₂×C₄	C₂²⋊Q₈×C₈₉	1	4	yes	—
432	C₂×C₄	#123×C₈₉	1	2	yes	—
433	C₂×C₄	#123×C₈₉	1	4	yes	—
434	C₂×C₄	#123×C₈₉	1	4	yes	—
435	C₂×C₄	#127×C₈₉	1	2	yes	—
436	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
437	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
438	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
439	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
440	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
441	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
442	C₈	—	2	2	no	—
443	C₈	—	2	2	no	—
444	C₈	—	2	4	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	2	no	—
448	C₂²	—	2	2	no	—
449	C₂²	#399×C₈₉	1	4	yes	—
450	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
451	C₂²	C₂×#123×C₈₉	1	1	yes	characteristic
452	C₂²	C₂×#127×C₈₉	1	1	yes	characteristic
453	C₂²	#577×C₈₉	1	2	yes	—
454	C₂²	#578×C₈₉	1	2	yes	—
455	C₄	—	4	4	no	—
456	C₄	—	4	4	no	—
457	C₄	—	8	2	no	—
458	C₄	—	8	1	no	—
459	C₄	—	8	1	no	—
460	C₄	—	8	1	no	—
461	C₄	—	8	1	no	—
462	C₄	#399×C₈₉	1	4	yes	—
463	C₄	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
464	C₄	C₂×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
465	C₄	C₂×#123×C₈₉	1	1	yes	characteristic
466	C₄	C₂×#123×C₈₉	1	1	yes	characteristic
467	C₂	—	2	4	no	—
468	C₂	C₂×#399×C₈₉	1	1	yes	characteristic
469	C₂	C₈₉×#3082	1	2	yes	—
470	C₂	C₈₉×#3097	1	2	yes	—
471	C₂	C₈₉×#3154	1	1	yes	characteristic
472	C₂	C₈₉×#3156	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂⁴×C₈₉	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
7. C₈₉×#2097	C₂	semidirect
8. C₈₉×#2097	C₂	semidirect
9. C₈₉×#2096	C₂	semidirect
10. C₈₉×#2095	C₂	semidirect
230. #23736	C₈₉	direct (N × H)
243. #2097	C₂×C₈₉	semidirect
244. #2097	C₂×C₈₉	semidirect
245. #2096	C₂×C₈₉	semidirect
246. #2095	C₂×C₈₉	semidirect
248. C₈₉	#23736	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#428×C₈₉	2
C₂×#427×C₈₉	2
C₂×#419×C₈₉	2
C₂²×#103×C₈₉	2
C₈₉×#2317	2
C₈₉×#2310	2
C₈₉×#2097	2
C₈₉×#2096	2
C₈₉×#2095	2
C₈₉×#1729	2
#23736	89

Subgroups — C89×#23736 #36401584

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#23736 #36401584