Subgroups — C₈₉×#25427 #36403275

Order 22784.

952 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#494×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#470×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#470×C₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#441×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2429	C₂	1	2	yes	maximal
6	C₈₉×#2043	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2001	C₂	1	2	yes	maximal
8	C₈₉×#1971	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1941	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1878	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1753	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₈₉	C₂²	1	2	yes	—
14	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
15	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
20	#494×C₈₉	—	2	4	no	—
21	#470×C₈₉	—	2	4	no	—
22	#470×C₈₉	—	2	4	no	—
23	#441×C₈₉	—	2	4	no	—
24	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#103×C₈₉	C₂²	1	2	yes	—
27	C₂×#103×C₈₉	C₂²	1	2	yes	—
28	C₂×#103×C₈₉	C₂²	1	2	yes	—
29	C₂×#103×C₈₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
33	#398×C₈₉	—	2	2	no	—
34	#396×C₈₉	—	2	2	no	—
35	#391×C₈₉	C₂²	1	2	yes	—
36	#389×C₈₉	—	2	2	no	—
37	#389×C₈₉	C₂²	1	2	yes	—
38	#388×C₈₉	—	2	2	no	—
39	C₄×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
40	#340×C₈₉	C₂²	1	2	yes	—
41	#336×C₈₉	C₂²	1	1	yes	characteristic
42	#336×C₈₉	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
44	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
45	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
46	C₂×Q₁₆×C₈₉	—	2	4	no	—
47	C₂×Q₁₆×C₈₉	—	2	2	no	—
48	C₂×Q₁₆×C₈₉	—	2	2	no	—
49	C₂×Q₁₆×C₈₉	—	2	2	no	—
50	C₂×Q₁₆×C₈₉	—	2	2	no	—
51	C₂×Q₁₆×C₈₉	—	2	4	no	—
52	C₂×Q₁₆×C₈₉	—	2	2	no	—
53	C₂×Q₁₆×C₈₉	—	4	2	no	—
54	C₂×Q₁₆×C₈₉	D₄	1	4	yes	—
55	C₂×M₁₆×C₈₉	—	2	2	no	—
56	C₂×M₁₆×C₈₉	—	2	2	no	—
57	C₂×M₁₆×C₈₉	—	2	2	no	—
58	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₈₉	—	2	4	no	—
63	C₄⋊Q₈×C₈₉	—	4	2	no	—
64	C₂²⋊Q₈×C₈₉	—	2	4	no	—
65	C₂²⋊Q₈×C₈₉	—	2	4	no	—
66	C₂²⋊Q₈×C₈₉	—	4	2	no	—
67	C₂²⋊Q₈×C₈₉	—	4	2	no	—
68	C₄×Q₈×C₈₉	—	2	4	no	—
69	C₄×Q₈×C₈₉	—	4	2	no	—
70	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
71	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
72	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
73	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
74	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
75	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
81	C₂×C₄²×C₈₉	—	2	2	no	—
82	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
84	#106×C₈₉	—	2	2	no	—
85	#106×C₈₉	D₄	1	4	yes	—
86	#103×C₈₉	—	2	4	no	—
87	#103×C₈₉	—	2	4	no	—
88	#103×C₈₉	—	2	4	no	—
89	#103×C₈₉	—	4	2	no	—
90	C₂²⋊C₈×C₈₉	—	2	2	no	—
91	#97×C₈₉	—	2	2	no	—
92	C₄×C₈×C₈₉	—	2	2	no	—
93	#95×C₈₉	—	2	2	no	—
94	#95×C₈₉	—	2	2	no	—
95	#95×C₈₉	—	2	2	no	—
96	#95×C₈₉	D₄	1	2	yes	—
97	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
98	C₂×Q₈×C₈₉	—	2	2	no	—
99	C₂×Q₈×C₈₉	—	2	2	no	—
100	C₂×Q₈×C₈₉	—	2	2	no	—
101	C₂×Q₈×C₈₉	—	2	2	no	—
102	C₂×Q₈×C₈₉	—	2	2	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	—	2	2	no	—
108	C₂×Q₈×C₈₉	—	2	2	no	—
109	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
110	C₂²×C₄×C₈₉	—	2	2	no	—
111	C₂²×C₄×C₈₉	—	2	2	no	—
112	C₂²×C₄×C₈₉	—	2	1	no	—
113	C₂²×C₄×C₈₉	—	2	1	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	1	no	—
118	C₂²×C₄×C₈₉	—	2	2	no	—
119	C₂²×C₄×C₈₉	—	2	2	no	—
120	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
124	Q₁₆×C₈₉	—	2	8	no	—
125	Q₁₆×C₈₉	—	4	8	no	—
126	Q₁₆×C₈₉	—	4	4	no	—
127	M₁₆×C₈₉	—	4	4	no	—
128	C₂×C₈×C₈₉	—	2	1	no	—
129	C₂×C₈×C₈₉	—	2	1	no	—
130	C₂×C₈×C₈₉	—	2	1	no	—
131	C₂×C₈×C₈₉	—	2	1	no	—
132	C₂×C₈×C₈₉	—	2	1	no	—
133	C₂×C₈×C₈₉	—	2	1	no	—
134	C₂×C₈×C₈₉	—	2	1	no	—
135	C₂×C₈×C₈₉	—	2	1	no	—
136	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
137	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
138	C₂×C₈×C₈₉	#41	1	2	yes	—
139	C₂×C₈×C₈₉	#41	1	2	yes	—
140	C₄⋊C₄×C₈₉	—	2	2	no	—
141	C₄⋊C₄×C₈₉	—	2	2	no	—
142	C₄⋊C₄×C₈₉	—	2	2	no	—
143	C₄⋊C₄×C₈₉	—	4	4	no	—
144	C₄⋊C₄×C₈₉	—	4	4	no	—
145	C₄⋊C₄×C₈₉	—	4	4	no	—
146	C₄⋊C₄×C₈₉	—	4	4	no	—
147	C₄⋊C₄×C₈₉	—	4	4	no	—
148	C₄⋊C₄×C₈₉	—	4	4	no	—
149	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
150	C₂²⋊C₄×C₈₉	—	2	4	no	—
151	C₂²⋊C₄×C₈₉	—	4	4	no	—
152	C₂²⋊C₄×C₈₉	—	4	4	no	—
153	C₄²×C₈₉	—	2	1	no	—
154	C₄²×C₈₉	—	2	1	no	—
155	C₄²×C₈₉	—	2	1	no	—
156	C₄²×C₈₉	—	2	1	no	—
157	C₄²×C₈₉	—	4	4	no	—
158	C₂³×C₈₉	—	2	1	no	—
159	C₂³×C₈₉	—	2	1	no	—
160	C₂³×C₈₉	—	2	1	no	—
161	C₂³×C₈₉	—	2	2	no	—
162	C₂³×C₈₉	—	2	2	no	—
163	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
164	Q₈×C₈₉	—	2	4	no	—
165	Q₈×C₈₉	—	2	4	no	—
166	Q₈×C₈₉	—	4	2	no	—
167	Q₈×C₈₉	—	4	2	no	—
168	Q₈×C₈₉	—	4	2	no	—
169	Q₈×C₈₉	—	4	2	no	—
170	Q₈×C₈₉	—	4	2	no	—
171	Q₈×C₈₉	—	4	2	no	—
172	C₂×C₄×C₈₉	—	2	2	no	—
173	C₂×C₄×C₈₉	—	2	2	no	—
174	C₂×C₄×C₈₉	—	2	1	no	—
175	C₂×C₄×C₈₉	—	2	2	no	—
176	C₂×C₄×C₈₉	—	2	4	no	—
177	C₂×C₄×C₈₉	—	2	4	no	—
178	C₂×C₄×C₈₉	—	2	1	no	—
179	C₂×C₄×C₈₉	—	2	1	no	—
180	C₂×C₄×C₈₉	—	2	2	no	—
181	C₂×C₄×C₈₉	—	2	2	no	—
182	C₂×C₄×C₈₉	—	4	2	no	—
183	C₂×C₄×C₈₉	—	4	2	no	—
184	C₂×C₄×C₈₉	—	4	2	no	—
185	C₂×C₄×C₈₉	—	4	2	no	—
186	C₂×C₄×C₈₉	—	4	1	no	—
187	C₂×C₄×C₈₉	—	4	1	no	—
188	C₂×C₄×C₈₉	—	4	1	no	—
189	C₂×C₄×C₈₉	—	4	1	no	—
190	C₂×C₄×C₈₉	—	4	2	no	—
191	C₂×C₄×C₈₉	—	4	2	no	—
192	C₂×C₄×C₈₉	—	4	2	no	—
193	C₂×C₄×C₈₉	—	4	2	no	—
194	C₂×C₄×C₈₉	—	4	2	no	—
195	C₂×C₄×C₈₉	—	4	2	no	—
196	C₂×C₄×C₈₉	#137	1	4	yes	—
197	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
199	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
200	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
201	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
203	C₈×C₈₉	—	2	2	no	—
204	C₈×C₈₉	—	4	1	no	—
205	C₈×C₈₉	—	4	1	no	—
206	C₈×C₈₉	#121	1	4	yes	—
207	C₂²×C₈₉	—	4	1	no	—
208	C₂²×C₈₉	—	4	1	no	—
209	C₂²×C₈₉	—	4	1	no	—
210	C₂²×C₈₉	—	4	2	no	—
211	C₂²×C₈₉	—	4	2	no	—
212	C₂²×C₈₉	#532	1	1	yes	characteristic
213	C₂²×C₈₉	D₄²	1	1	yes	characteristic
214	C₂²×C₈₉	D₄²	1	1	yes	characteristic
215	C₂²×C₈₉	C₂×#137	1	2	yes	—
216	C₂²×C₈₉	#578	1	2	yes	—
217	C₄×C₈₉	—	2	4	no	—
218	C₄×C₈₉	—	4	1	no	—
219	C₄×C₈₉	—	4	4	no	—
220	C₄×C₈₉	—	4	2	no	—
221	C₄×C₈₉	—	4	4	no	—
222	C₄×C₈₉	—	8	2	no	—
223	C₄×C₈₉	—	8	2	no	—
224	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
225	C₄×C₈₉	#540	1	1	yes	characteristic
226	C₄×C₈₉	#546	1	1	yes	characteristic
227	C₄×C₈₉	#550	1	1	yes	characteristic
228	#25427	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂×C₈₉	—	8	1	no	—
230	C₂×C₈₉	#2428	1	1	yes	characteristic
231	C₂×C₈₉	#3177	1	1	yes	characteristic
232	C₂×C₈₉	#3185	1	1	yes	characteristic
233	C₂×C₈₉	#3270	1	2	yes	—
234	C₂×C₈₉	#3276	1	2	yes	—
235	C₂×#494	C₂×C₈₉	1	1	yes	characteristic, complemented
236	C₂×#470	C₂×C₈₉	1	1	yes	characteristic
237	C₂×#470	C₂×C₈₉	1	1	yes	characteristic
238	C₂×#441	C₂×C₈₉	1	1	yes	characteristic, complemented
239	#2429	C₂×C₈₉	1	2	yes	—
240	#2043	C₂×C₈₉	1	2	yes	complemented
241	#2001	C₂×C₈₉	1	2	yes	—
242	#1971	C₂×C₈₉	1	1	yes	characteristic, complemented
243	#1941	C₂×C₈₉	1	1	yes	characteristic, complemented
244	#1878	C₂×C₈₉	1	2	yes	complemented
245	#1753	C₂×C₈₉	1	1	yes	characteristic
246	C₈₉	#25427	1	1	yes	characteristic, direct product factor, Sylow
247	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
248	C₂²×Q₁₆	C₂²×C₈₉	1	2	yes	—
249	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
250	C₂²×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
251	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
252	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
253	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
254	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
255	#494	—	2	4	no	—
256	#470	—	2	4	no	—
257	#470	—	2	4	no	—
258	#441	—	2	4	no	—
259	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
260	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
261	C₂×#103	C₂²×C₈₉	1	2	yes	—
262	C₂×#103	C₂²×C₈₉	1	2	yes	—
263	C₂×#103	C₂²×C₈₉	1	2	yes	—
264	C₂×#103	C₂²×C₈₉	1	2	yes	—
265	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
266	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
267	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
268	#398	—	2	2	no	—
269	#396	—	2	2	no	—
270	#391	C₂²×C₈₉	1	2	yes	—
271	#389	—	2	2	no	—
272	#389	C₂²×C₈₉	1	2	yes	—
273	#388	—	2	2	no	—
274	C₄×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
275	#340	C₂²×C₈₉	1	2	yes	—
276	#336	C₂²×C₈₉	1	1	yes	characteristic
277	#336	C₂²×C₈₉	1	1	yes	characteristic
278	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
279	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
280	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
281	C₂×Q₁₆	—	2	4	no	—
282	C₂×Q₁₆	—	2	2	no	—
283	C₂×Q₁₆	—	2	2	no	—
284	C₂×Q₁₆	—	2	2	no	—
285	C₂×Q₁₆	—	2	2	no	—
286	C₂×Q₁₆	—	2	4	no	—
287	C₂×Q₁₆	—	2	2	no	—
288	C₂×Q₁₆	—	4	2	no	—
289	C₂×Q₁₆	D₄×C₈₉	1	4	yes	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	—	2	2	no	—
292	C₂×M₁₆	—	2	2	no	—
293	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
294	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
297	C₄⋊Q₈	—	2	4	no	—
298	C₄⋊Q₈	—	4	2	no	—
299	C₂²⋊Q₈	—	2	4	no	—
300	C₂²⋊Q₈	—	2	4	no	—
301	C₂²⋊Q₈	—	4	2	no	—
302	C₂²⋊Q₈	—	4	2	no	—
303	C₄×Q₈	—	2	4	no	—
304	C₄×Q₈	—	4	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	—	2	2	no	—
315	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
316	C₂×C₄²	—	2	2	no	—
317	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
318	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
319	#106	—	2	2	no	—
320	#106	D₄×C₈₉	1	4	yes	—
321	#103	—	2	4	no	—
322	#103	—	2	4	no	—
323	#103	—	2	4	no	—
324	#103	—	4	2	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	#97	—	2	2	no	—
327	C₄×C₈	—	2	2	no	—
328	#95	—	2	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	#95	D₄×C₈₉	1	2	yes	—
332	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	2	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	—	2	2	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	C₂×D₄×C₈₉	1	4	yes	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	2	1	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
356	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
357	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
358	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
359	Q₁₆	—	2	8	no	—
360	Q₁₆	—	4	8	no	—
361	Q₁₆	—	4	4	no	—
362	M₁₆	—	4	4	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
372	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
373	C₂×C₈	#41×C₈₉	1	2	yes	—
374	C₂×C₈	#41×C₈₉	1	2	yes	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	—	4	4	no	—
380	C₄⋊C₄	—	4	4	no	—
381	C₄⋊C₄	—	4	4	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄⋊C₄	—	4	4	no	—
384	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	4	4	no	—
387	C₂²⋊C₄	—	4	4	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	2	1	no	—
390	C₄²	—	2	1	no	—
391	C₄²	—	2	1	no	—
392	C₄²	—	4	4	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	1	no	—
395	C₂³	—	2	1	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	2	no	—
398	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
399	Q₈	—	2	4	no	—
400	Q₈	—	2	4	no	—
401	Q₈	—	4	2	no	—
402	Q₈	—	4	2	no	—
403	Q₈	—	4	2	no	—
404	Q₈	—	4	2	no	—
405	Q₈	—	4	2	no	—
406	Q₈	—	4	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	#137×C₈₉	1	4	yes	—
432	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
433	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
434	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
436	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
437	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
438	C₈	—	2	2	no	—
439	C₈	—	4	1	no	—
440	C₈	—	4	1	no	—
441	C₈	#121×C₈₉	1	4	yes	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	2	no	—
447	C₂²	#532×C₈₉	1	1	yes	characteristic
448	C₂²	D₄²×C₈₉	1	1	yes	characteristic
449	C₂²	D₄²×C₈₉	1	1	yes	characteristic
450	C₂²	C₂×#137×C₈₉	1	2	yes	—
451	C₂²	#578×C₈₉	1	2	yes	—
452	C₄	—	2	4	no	—
453	C₄	—	4	1	no	—
454	C₄	—	4	4	no	—
455	C₄	—	4	2	no	—
456	C₄	—	4	4	no	—
457	C₄	—	8	2	no	—
458	C₄	—	8	2	no	—
459	C₄	C₂×#121×C₈₉	1	1	yes	characteristic
460	C₄	#540×C₈₉	1	1	yes	characteristic
461	C₄	#546×C₈₉	1	1	yes	characteristic
462	C₄	#550×C₈₉	1	1	yes	characteristic
463	C₂	—	8	1	no	—
464	C₂	C₈₉×#2428	1	1	yes	characteristic
465	C₂	C₈₉×#3177	1	1	yes	characteristic
466	C₂	C₈₉×#3185	1	1	yes	characteristic
467	C₂	C₈₉×#3270	1	2	yes	—
468	C₂	C₈₉×#3276	1	2	yes	—

	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 ◁ C₄×C₂²⋊C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#494×C₈₉	C₂	semidirect
4. C₂×#441×C₈₉	C₂	semidirect
6. C₈₉×#2043	C₂	semidirect
8. C₈₉×#1971	C₂	semidirect
9. C₈₉×#1941	C₂	semidirect
10. C₈₉×#1878	C₂	semidirect
228. #25427	C₈₉	direct (N × H)
235. C₂×#494	C₂×C₈₉	semidirect
238. C₂×#441	C₂×C₈₉	semidirect
240. #2043	C₂×C₈₉	semidirect
242. #1971	C₂×C₈₉	semidirect
243. #1941	C₂×C₈₉	semidirect
244. #1878	C₂×C₈₉	semidirect
246. C₈₉	#25427	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×#494×C₈₉	2
C₂×#470×C₈₉	2
C₂×#441×C₈₉	2
C₈₉×#2429	2
C₈₉×#2043	2
C₈₉×#2001	2
C₈₉×#1971	2
C₈₉×#1941	2
C₈₉×#1878	2
C₈₉×#1753	2
#25427	89

Subgroups — C89×#25427 #36403275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25427 #36403275