Subgroups — C₈₉×#26265 #36404113

Order 22784.

802 conjugacy classes of subgroups.

The subgroup lattice has 410 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
2	C₂×#441×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2446	C₂	1	2	yes	maximal
4	C₈₉×#2056	C₂	1	2	yes	maximal
5	C₈₉×#2043	C₂	1	2	yes	maximal
6	C₈₉×#1971	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#1971	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#1971	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#1941	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#1878	C₂	1	2	yes	maximal
11	C₈₉×#1771	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	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
17	#494×C₈₉	—	2	4	no	—
18	#441×C₈₉	—	2	4	no	—
19	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×#106×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#103×C₈₉	C₂²	1	2	yes	—
23	C₂×#103×C₈₉	C₂²	1	2	yes	—
24	C₂×#103×C₈₉	C₂²	1	2	yes	—
25	C₂×#103×C₈₉	C₂²	1	2	yes	—
26	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
29	#400×C₈₉	—	2	2	no	—
30	#398×C₈₉	—	2	2	no	—
31	#391×C₈₉	C₂²	1	2	yes	—
32	#391×C₈₉	C₂²	1	2	yes	—
33	#391×C₈₉	C₂²	1	2	yes	—
34	#389×C₈₉	C₂²	1	2	yes	—
35	#387×C₈₉	—	2	2	no	—
36	#387×C₈₉	—	2	2	no	—
37	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
38	#340×C₈₉	C₂²	1	2	yes	—
39	#336×C₈₉	C₂²	1	1	yes	characteristic
40	#336×C₈₉	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
42	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
43	C₂×Q₁₆×C₈₉	—	2	4	no	—
44	C₂×Q₁₆×C₈₉	—	2	2	no	—
45	C₂×Q₁₆×C₈₉	—	2	2	no	—
46	C₂×Q₁₆×C₈₉	—	2	2	no	—
47	C₂×Q₁₆×C₈₉	—	2	4	no	—
48	C₂×Q₁₆×C₈₉	—	2	2	no	—
49	C₂×Q₁₆×C₈₉	—	2	2	no	—
50	C₂×Q₁₆×C₈₉	—	4	2	no	—
51	C₂×Q₁₆×C₈₉	D₄	1	4	yes	—
52	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
56	C₄⋊Q₈×C₈₉	—	2	4	no	—
57	C₄⋊Q₈×C₈₉	—	4	2	no	—
58	C₄×Q₈×C₈₉	—	2	4	no	—
59	C₄×Q₈×C₈₉	—	4	2	no	—
60	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
61	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
62	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
64	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
67	C₂×C₄²×C₈₉	—	2	2	no	—
68	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
70	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
71	#106×C₈₉	—	2	2	no	—
72	#106×C₈₉	—	2	2	no	—
73	C₄⋊C₈×C₈₉	—	2	2	no	—
74	#103×C₈₉	—	2	4	no	—
75	#103×C₈₉	—	4	2	no	—
76	#103×C₈₉	—	4	2	no	—
77	#103×C₈₉	—	4	2	no	—
78	#97×C₈₉	—	2	2	no	—
79	#97×C₈₉	—	2	2	no	—
80	C₄×C₈×C₈₉	—	2	2	no	—
81	#95×C₈₉	—	2	2	no	—
82	#95×C₈₉	—	2	2	no	—
83	#95×C₈₉	—	2	2	no	—
84	#95×C₈₉	—	2	2	no	—
85	#95×C₈₉	—	2	2	no	—
86	#95×C₈₉	—	2	2	no	—
87	#95×C₈₉	—	2	2	no	—
88	#95×C₈₉	D₄	1	2	yes	—
89	C₂×Q₈×C₈₉	—	2	2	no	—
90	C₂×Q₈×C₈₉	—	2	2	no	—
91	C₂×Q₈×C₈₉	—	2	2	no	—
92	C₂×Q₈×C₈₉	—	2	2	no	—
93	C₂×Q₈×C₈₉	—	2	2	no	—
94	C₂×Q₈×C₈₉	—	2	2	no	—
95	C₂×Q₈×C₈₉	—	2	2	no	—
96	C₂×Q₈×C₈₉	—	2	2	no	—
97	C₂×Q₈×C₈₉	—	2	2	no	—
98	C₂×Q₈×C₈₉	—	2	2	no	—
99	C₂×Q₈×C₈₉	—	2	2	no	—
100	C₂×Q₈×C₈₉	C₂×D₄	1	4	yes	—
101	C₂²×C₄×C₈₉	—	2	2	no	—
102	C₂²×C₄×C₈₉	—	2	2	no	—
103	C₂²×C₄×C₈₉	—	2	2	no	—
104	C₂²×C₄×C₈₉	—	2	2	no	—
105	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
110	Q₁₆×C₈₉	—	2	8	no	—
111	Q₁₆×C₈₉	—	4	8	no	—
112	Q₁₆×C₈₉	—	4	4	no	—
113	C₂×C₈×C₈₉	—	2	1	no	—
114	C₂×C₈×C₈₉	—	2	1	no	—
115	C₂×C₈×C₈₉	—	2	1	no	—
116	C₂×C₈×C₈₉	—	2	1	no	—
117	C₂×C₈×C₈₉	—	2	1	no	—
118	C₂×C₈×C₈₉	—	2	1	no	—
119	C₂×C₈×C₈₉	—	2	1	no	—
120	C₂×C₈×C₈₉	—	2	1	no	—
121	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
122	C₂×C₈×C₈₉	#41	1	2	yes	—
123	C₂×C₈×C₈₉	#41	1	2	yes	—
124	C₂×C₈×C₈₉	#41	1	2	yes	—
125	C₄⋊C₄×C₈₉	—	2	4	no	—
126	C₄⋊C₄×C₈₉	—	2	2	no	—
127	C₄⋊C₄×C₈₉	—	2	2	no	—
128	C₄⋊C₄×C₈₉	—	2	2	no	—
129	C₄⋊C₄×C₈₉	—	2	2	no	—
130	C₄⋊C₄×C₈₉	—	4	4	no	—
131	C₄⋊C₄×C₈₉	—	4	4	no	—
132	C₄⋊C₄×C₈₉	—	4	4	no	—
133	C₄⋊C₄×C₈₉	—	4	4	no	—
134	C₄²×C₈₉	—	2	1	no	—
135	C₄²×C₈₉	—	2	1	no	—
136	C₄²×C₈₉	—	2	1	no	—
137	C₄²×C₈₉	—	2	1	no	—
138	C₄²×C₈₉	—	2	1	no	—
139	C₄²×C₈₉	—	2	1	no	—
140	C₄²×C₈₉	—	4	4	no	—
141	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
142	Q₈×C₈₉	—	2	4	no	—
143	Q₈×C₈₉	—	2	4	no	—
144	Q₈×C₈₉	—	4	2	no	—
145	Q₈×C₈₉	—	4	2	no	—
146	Q₈×C₈₉	—	4	2	no	—
147	Q₈×C₈₉	—	4	2	no	—
148	Q₈×C₈₉	—	4	2	no	—
149	Q₈×C₈₉	—	4	2	no	—
150	C₂×C₄×C₈₉	—	2	2	no	—
151	C₂×C₄×C₈₉	—	2	2	no	—
152	C₂×C₄×C₈₉	—	2	1	no	—
153	C₂×C₄×C₈₉	—	2	1	no	—
154	C₂×C₄×C₈₉	—	2	2	no	—
155	C₂×C₄×C₈₉	—	2	4	no	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	—	2	2	no	—
158	C₂×C₄×C₈₉	—	2	2	no	—
159	C₂×C₄×C₈₉	—	2	2	no	—
160	C₂×C₄×C₈₉	—	4	2	no	—
161	C₂×C₄×C₈₉	—	4	2	no	—
162	C₂×C₄×C₈₉	—	4	2	no	—
163	C₂×C₄×C₈₉	—	4	2	no	—
164	C₂×C₄×C₈₉	—	4	2	no	—
165	C₂×C₄×C₈₉	—	4	2	no	—
166	C₂×C₄×C₈₉	—	4	2	no	—
167	C₂×C₄×C₈₉	—	4	2	no	—
168	C₂×C₄×C₈₉	—	4	2	no	—
169	C₂×C₄×C₈₉	—	4	2	no	—
170	C₂×C₄×C₈₉	—	4	2	no	—
171	C₂×C₄×C₈₉	#137	1	4	yes	—
172	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
177	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
178	C₈×C₈₉	—	2	2	no	—
179	C₈×C₈₉	—	4	1	no	—
180	C₈×C₈₉	—	4	1	no	—
181	C₈×C₈₉	#123	1	4	yes	—
182	C₂²×C₈₉	#532	1	1	yes	characteristic
183	C₂²×C₈₉	D₄²	1	1	yes	characteristic
184	C₂²×C₈₉	#550	1	1	yes	characteristic
185	C₂²×C₈₉	C₂×#137	1	2	yes	—
186	C₂²×C₈₉	#578	1	2	yes	—
187	C₄×C₈₉	—	2	4	no	—
188	C₄×C₈₉	—	4	1	no	—
189	C₄×C₈₉	—	4	1	no	—
190	C₄×C₈₉	—	4	4	no	—
191	C₄×C₈₉	—	4	2	no	—
192	C₄×C₈₉	—	8	2	no	—
193	C₄×C₈₉	—	8	2	no	—
194	C₄×C₈₉	—	8	2	no	—
195	C₄×C₈₉	C₂×#123	1	1	yes	characteristic
196	C₄×C₈₉	#540	1	1	yes	characteristic
197	C₄×C₈₉	#546	1	1	yes	characteristic
198	C₄×C₈₉	#559	1	1	yes	characteristic
199	#26265	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
200	C₂×C₈₉	#2445	1	1	yes	characteristic
201	C₂×C₈₉	#3177	1	1	yes	characteristic
202	C₂×C₈₉	#3185	1	1	yes	characteristic
203	C₂×C₈₉	#3270	1	2	yes	—
204	C₂×C₈₉	#3398	1	2	yes	—
205	C₂×#494	C₂×C₈₉	1	1	yes	characteristic
206	C₂×#441	C₂×C₈₉	1	1	yes	characteristic
207	#2446	C₂×C₈₉	1	2	yes	—
208	#2056	C₂×C₈₉	1	2	yes	—
209	#2043	C₂×C₈₉	1	2	yes	—
210	#1971	C₂×C₈₉	1	1	yes	characteristic
211	#1971	C₂×C₈₉	1	1	yes	characteristic
212	#1971	C₂×C₈₉	1	1	yes	characteristic
213	#1941	C₂×C₈₉	1	1	yes	characteristic
214	#1878	C₂×C₈₉	1	2	yes	—
215	#1771	C₂×C₈₉	1	1	yes	characteristic
216	C₈₉	#26265	1	1	yes	characteristic, direct product factor, Sylow
217	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
218	C₂²×Q₁₆	C₂²×C₈₉	1	2	yes	—
219	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
220	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
221	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
222	#494	—	2	4	no	—
223	#441	—	2	4	no	—
224	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
225	C₂×#106	C₂²×C₈₉	1	1	yes	characteristic
226	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
227	C₂×#103	C₂²×C₈₉	1	2	yes	—
228	C₂×#103	C₂²×C₈₉	1	2	yes	—
229	C₂×#103	C₂²×C₈₉	1	2	yes	—
230	C₂×#103	C₂²×C₈₉	1	2	yes	—
231	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
232	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
233	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
234	#400	—	2	2	no	—
235	#398	—	2	2	no	—
236	#391	C₂²×C₈₉	1	2	yes	—
237	#391	C₂²×C₈₉	1	2	yes	—
238	#391	C₂²×C₈₉	1	2	yes	—
239	#389	C₂²×C₈₉	1	2	yes	—
240	#387	—	2	2	no	—
241	#387	—	2	2	no	—
242	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
243	#340	C₂²×C₈₉	1	2	yes	—
244	#336	C₂²×C₈₉	1	1	yes	characteristic
245	#336	C₂²×C₈₉	1	1	yes	characteristic
246	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
247	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
248	C₂×Q₁₆	—	2	4	no	—
249	C₂×Q₁₆	—	2	2	no	—
250	C₂×Q₁₆	—	2	2	no	—
251	C₂×Q₁₆	—	2	2	no	—
252	C₂×Q₁₆	—	2	4	no	—
253	C₂×Q₁₆	—	2	2	no	—
254	C₂×Q₁₆	—	2	2	no	—
255	C₂×Q₁₆	—	4	2	no	—
256	C₂×Q₁₆	D₄×C₈₉	1	4	yes	—
257	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
258	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
259	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
261	C₄⋊Q₈	—	2	4	no	—
262	C₄⋊Q₈	—	4	2	no	—
263	C₄×Q₈	—	2	4	no	—
264	C₄×Q₈	—	4	2	no	—
265	C₂×C₄⋊C₄	—	2	2	no	—
266	C₂×C₄⋊C₄	—	2	2	no	—
267	C₂×C₄⋊C₄	—	2	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
271	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
272	C₂×C₄²	—	2	2	no	—
273	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
274	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
275	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
276	#106	—	2	2	no	—
277	#106	—	2	2	no	—
278	C₄⋊C₈	—	2	2	no	—
279	#103	—	2	4	no	—
280	#103	—	4	2	no	—
281	#103	—	4	2	no	—
282	#103	—	4	2	no	—
283	#97	—	2	2	no	—
284	#97	—	2	2	no	—
285	C₄×C₈	—	2	2	no	—
286	#95	—	2	2	no	—
287	#95	—	2	2	no	—
288	#95	—	2	2	no	—
289	#95	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	#95	D₄×C₈₉	1	2	yes	—
294	C₂×Q₈	—	2	2	no	—
295	C₂×Q₈	—	2	2	no	—
296	C₂×Q₈	—	2	2	no	—
297	C₂×Q₈	—	2	2	no	—
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	—	2	2	no	—
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	C₂×D₄×C₈₉	1	4	yes	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
313	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
314	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
315	Q₁₆	—	2	8	no	—
316	Q₁₆	—	4	8	no	—
317	Q₁₆	—	4	4	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
327	C₂×C₈	#41×C₈₉	1	2	yes	—
328	C₂×C₈	#41×C₈₉	1	2	yes	—
329	C₂×C₈	#41×C₈₉	1	2	yes	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	4	4	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	4	4	no	—
346	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
347	Q₈	—	2	4	no	—
348	Q₈	—	2	4	no	—
349	Q₈	—	4	2	no	—
350	Q₈	—	4	2	no	—
351	Q₈	—	4	2	no	—
352	Q₈	—	4	2	no	—
353	Q₈	—	4	2	no	—
354	Q₈	—	4	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	#137×C₈₉	1	4	yes	—
377	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
378	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
379	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
380	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
381	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
382	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
383	C₈	—	2	2	no	—
384	C₈	—	4	1	no	—
385	C₈	—	4	1	no	—
386	C₈	#123×C₈₉	1	4	yes	—
387	C₂²	#532×C₈₉	1	1	yes	characteristic
388	C₂²	D₄²×C₈₉	1	1	yes	characteristic
389	C₂²	#550×C₈₉	1	1	yes	characteristic
390	C₂²	C₂×#137×C₈₉	1	2	yes	—
391	C₂²	#578×C₈₉	1	2	yes	—
392	C₄	—	2	4	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	4	4	no	—
396	C₄	—	4	2	no	—
397	C₄	—	8	2	no	—
398	C₄	—	8	2	no	—
399	C₄	—	8	2	no	—
400	C₄	C₂×#123×C₈₉	1	1	yes	characteristic
401	C₄	#540×C₈₉	1	1	yes	characteristic
402	C₄	#546×C₈₉	1	1	yes	characteristic
403	C₄	#559×C₈₉	1	1	yes	characteristic
404	C₂	C₈₉×#2445	1	1	yes	characteristic
405	C₂	C₈₉×#3177	1	1	yes	characteristic
406	C₂	C₈₉×#3185	1	1	yes	characteristic
407	C₂	C₈₉×#3270	1	2	yes	—
408	C₂	C₈₉×#3398	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
199. #26265	C₈₉	direct (N × H)
216. C₈₉	#26265	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×#441×C₈₉	2
C₈₉×#2446	2
C₈₉×#2056	2
C₈₉×#2043	2
C₈₉×#1971	2
C₈₉×#1941	2
C₈₉×#1878	2
C₈₉×#1771	2
#26265	89

Subgroups — C89×#26265 #36404113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#26265 #36404113