Subgroups — C₈₉×#22761 #36400609

Order 22784.

782 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₈₉×#2356	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2351	C₂	1	1	yes	maximal, characteristic
4	C₈₉×#1935	C₂	1	2	yes	maximal
5	C₈₉×#1921	C₂	1	2	yes	maximal
6	C₈₉×#1878	C₂	1	2	yes	maximal
7	C₈₉×#1835	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#1805	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#1805	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#1770	C₂	1	1	yes	maximal, characteristic
11	C₈₉×#1763	C₂	1	2	yes	maximal
12	C₂²×Q₁₆×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
16	C₄×Q₁₆×C₈₉	C₄	1	8	yes	complemented
17	C₂×#107×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#103×C₈₉	C₂²	1	2	yes	—
20	C₂×#103×C₈₉	C₂²	1	2	yes	—
21	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#97×C₈₉	C₂²	1	2	yes	—
24	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
25	#391×C₈₉	C₂²	1	2	yes	—
26	#389×C₈₉	—	2	2	no	—
27	#389×C₈₉	C₂²	1	2	yes	—
28	#387×C₈₉	—	2	2	no	—
29	#383×C₈₉	—	2	1	no	—
30	#382×C₈₉	—	2	1	no	—
31	#382×C₈₉	C₂²	1	1	yes	characteristic
32	#382×C₈₉	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₈₉	—	2	1	no	—
34	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
36	#376×C₈₉	—	2	1	no	—
37	#340×C₈₉	C₂²	1	2	yes	—
38	#340×C₈₉	C₂²	1	2	yes	—
39	#340×C₈₉	C₂²	1	2	yes	—
40	#340×C₈₉	C₂²	1	2	yes	—
41	#336×C₈₉	C₂²	1	2	yes	—
42	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆×C₈₉	—	2	2	no	—
45	C₂×Q₁₆×C₈₉	—	2	2	no	—
46	C₂×Q₁₆×C₈₉	C₂×C₄	1	4	yes	—
47	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
48	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
50	C₄×Q₈×C₈₉	—	2	2	no	—
51	C₄×Q₈×C₈₉	—	2	2	no	—
52	C₄×Q₈×C₈₉	—	2	4	no	—
53	C₄×Q₈×C₈₉	—	4	2	no	—
54	C₄×Q₈×C₈₉	C₂×C₄	1	4	yes	—
55	C₄×Q₈×C₈₉	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
57	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
58	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
59	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
60	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₈₉	—	2	1	no	—
66	C₂×C₄²×C₈₉	—	2	1	no	—
67	C₂×C₄²×C₈₉	—	2	2	no	—
68	C₂×C₄²×C₈₉	—	2	2	no	—
69	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
70	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
71	#107×C₈₉	C₂×C₄	1	4	yes	—
72	C₄⋊C₈×C₈₉	—	2	2	no	—
73	#103×C₈₉	—	2	4	no	—
74	#103×C₈₉	—	4	2	no	—
75	#103×C₈₉	C₂×C₄	1	4	yes	—
76	#103×C₈₉	C₂×C₄	1	4	yes	—
77	#97×C₈₉	—	4	2	no	—
78	C₄×C₈×C₈₉	C₂×C₄	1	4	yes	—
79	#95×C₈₉	—	2	1	no	—
80	#95×C₈₉	—	2	2	no	—
81	#95×C₈₉	—	2	1	no	—
82	#95×C₈₉	—	2	2	no	—
83	#95×C₈₉	—	2	2	no	—
84	#95×C₈₉	—	2	1	no	—
85	#95×C₈₉	—	2	1	no	—
86	#95×C₈₉	—	2	2	no	—
87	#95×C₈₉	D₄	1	1	yes	characteristic
88	#95×C₈₉	D₄	1	1	yes	characteristic
89	C₂×Q₈×C₈₉	—	2	1	no	—
90	C₂×Q₈×C₈₉	—	2	1	no	—
91	C₂×Q₈×C₈₉	—	2	1	no	—
92	C₂×Q₈×C₈₉	—	2	1	no	—
93	C₂×Q₈×C₈₉	—	2	1	no	—
94	C₂×Q₈×C₈₉	—	2	1	no	—
95	C₂×Q₈×C₈₉	—	2	1	no	—
96	C₂×Q₈×C₈₉	—	2	1	no	—
97	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
98	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
99	C₂×Q₈×C₈₉	#41	1	2	yes	—
100	C₂×Q₈×C₈₉	#41	1	2	yes	—
101	C₂²×C₄×C₈₉	—	2	1	no	—
102	C₂²×C₄×C₈₉	—	2	1	no	—
103	C₂²×C₄×C₈₉	—	2	1	no	—
104	C₂²×C₄×C₈₉	—	2	1	no	—
105	C₂²×C₄×C₈₉	—	2	2	no	—
106	C₂²×C₄×C₈₉	—	2	2	no	—
107	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
112	Q₁₆×C₈₉	—	2	8	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	2	no	—
118	C₂×C₈×C₈₉	—	2	2	no	—
119	C₂×C₈×C₈₉	—	2	2	no	—
120	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
122	C₄⋊C₄×C₈₉	—	2	4	no	—
123	C₄⋊C₄×C₈₉	—	2	4	no	—
124	C₄⋊C₄×C₈₉	—	2	1	no	—
125	C₄⋊C₄×C₈₉	—	2	1	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	2	no	—
131	C₄⋊C₄×C₈₉	—	4	4	no	—
132	C₄⋊C₄×C₈₉	—	4	4	no	—
133	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
134	C₄⋊C₄×C₈₉	C₂²×C₄	1	2	yes	—
135	C₄²×C₈₉	—	2	4	no	—
136	C₄²×C₈₉	—	2	4	no	—
137	C₄²×C₈₉	—	2	2	no	—
138	C₄²×C₈₉	—	2	2	no	—
139	C₄²×C₈₉	—	4	4	no	—
140	C₄²×C₈₉	—	4	4	no	—
141	C₄²×C₈₉	C₂²×C₄	1	2	yes	—
142	C₄²×C₈₉	#41	1	2	yes	—
143	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₈₉	—	2	2	no	—
145	Q₈×C₈₉	—	2	2	no	—
146	Q₈×C₈₉	—	2	2	no	—
147	Q₈×C₈₉	—	2	2	no	—
148	Q₈×C₈₉	—	2	2	no	—
149	Q₈×C₈₉	—	4	1	no	—
150	Q₈×C₈₉	—	4	1	no	—
151	Q₈×C₈₉	#117	1	4	yes	—
152	C₂×C₄×C₈₉	—	2	2	no	—
153	C₂×C₄×C₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	2	no	—
155	C₂×C₄×C₈₉	—	2	2	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	—	2	2	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	—	2	2	no	—
163	C₂×C₄×C₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	2	2	no	—
165	C₂×C₄×C₈₉	—	2	2	no	—
166	C₂×C₄×C₈₉	—	4	1	no	—
167	C₂×C₄×C₈₉	—	4	1	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	—	4	2	no	—
172	C₂×C₄×C₈₉	—	4	2	no	—
173	C₂×C₄×C₈₉	—	4	2	no	—
174	C₂×C₄×C₈₉	—	4	2	no	—
175	C₂×C₄×C₈₉	—	4	2	no	—
176	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
177	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
183	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
184	C₈×C₈₉	—	2	2	no	—
185	C₈×C₈₉	—	2	2	no	—
186	C₈×C₈₉	—	4	2	no	—
187	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂²×C₈₉	#546	1	1	yes	characteristic
189	C₂²×C₈₉	#548	1	1	yes	characteristic
190	C₂²×C₈₉	#575	1	2	yes	—
191	C₂²×C₈₉	#578	1	2	yes	—
192	C₄×C₈₉	—	2	4	no	—
193	C₄×C₈₉	—	2	2	no	—
194	C₄×C₈₉	—	2	2	no	—
195	C₄×C₈₉	—	4	2	no	—
196	C₄×C₈₉	—	4	2	no	—
197	C₄×C₈₉	—	4	2	no	—
198	C₄×C₈₉	—	4	2	no	—
199	C₄×C₈₉	—	4	2	no	—
200	C₄×C₈₉	—	8	2	no	—
201	C₄×C₈₉	—	8	2	no	—
202	C₄×C₈₉	C₂×#117	1	1	yes	characteristic
203	C₄×C₈₉	#520	1	1	yes	characteristic
204	C₄×C₈₉	#552	1	1	yes	characteristic
205	C₄×C₈₉	#553	1	1	yes	characteristic
206	#22761	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂×C₈₉	#2352	1	1	yes	characteristic
208	C₂×C₈₉	#2943	1	1	yes	characteristic
209	C₂×C₈₉	#2950	1	1	yes	characteristic
210	C₂×C₈₉	#3327	1	2	yes	—
211	C₂×C₈₉	#3377	1	2	yes	—
212	C₂×C₄×Q₁₆	C₂×C₈₉	1	1	yes	characteristic
213	#2356	C₂×C₈₉	1	1	yes	characteristic
214	#2351	C₂×C₈₉	1	1	yes	characteristic
215	#1935	C₂×C₈₉	1	2	yes	—
216	#1921	C₂×C₈₉	1	2	yes	—
217	#1878	C₂×C₈₉	1	2	yes	—
218	#1835	C₂×C₈₉	1	1	yes	characteristic
219	#1805	C₂×C₈₉	1	1	yes	characteristic
220	#1805	C₂×C₈₉	1	1	yes	characteristic
221	#1770	C₂×C₈₉	1	1	yes	characteristic
222	#1763	C₂×C₈₉	1	2	yes	—
223	C₈₉	#22761	1	1	yes	characteristic, direct product factor, Sylow
224	C₂²×Q₁₆	C₂²×C₈₉	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
226	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
227	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
228	C₄×Q₁₆	C₄×C₈₉	1	8	yes	complemented
229	C₂×#107	C₂²×C₈₉	1	1	yes	characteristic
230	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
231	C₂×#103	C₂²×C₈₉	1	2	yes	—
232	C₂×#103	C₂²×C₈₉	1	2	yes	—
233	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
234	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
235	C₂×#97	C₂²×C₈₉	1	2	yes	—
236	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
237	#391	C₂²×C₈₉	1	2	yes	—
238	#389	—	2	2	no	—
239	#389	C₂²×C₈₉	1	2	yes	—
240	#387	—	2	2	no	—
241	#383	—	2	1	no	—
242	#382	—	2	1	no	—
243	#382	C₂²×C₈₉	1	1	yes	characteristic
244	#382	C₂²×C₈₉	1	1	yes	characteristic
245	C₄×C₄⋊C₄	—	2	1	no	—
246	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
247	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
248	#376	—	2	1	no	—
249	#340	C₂²×C₈₉	1	2	yes	—
250	#340	C₂²×C₈₉	1	2	yes	—
251	#340	C₂²×C₈₉	1	2	yes	—
252	#340	C₂²×C₈₉	1	2	yes	—
253	#336	C₂²×C₈₉	1	2	yes	—
254	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
255	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
256	C₂×Q₁₆	—	2	2	no	—
257	C₂×Q₁₆	—	2	2	no	—
258	C₂×Q₁₆	C₂×C₄×C₈₉	1	4	yes	—
259	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
260	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
262	C₄×Q₈	—	2	2	no	—
263	C₄×Q₈	—	2	2	no	—
264	C₄×Q₈	—	2	4	no	—
265	C₄×Q₈	—	4	2	no	—
266	C₄×Q₈	C₂×C₄×C₈₉	1	4	yes	—
267	C₄×Q₈	C₂×C₄×C₈₉	1	4	yes	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	1	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
274	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
275	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
276	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
277	C₂×C₄²	—	2	1	no	—
278	C₂×C₄²	—	2	1	no	—
279	C₂×C₄²	—	2	2	no	—
280	C₂×C₄²	—	2	2	no	—
281	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
282	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
283	#107	C₂×C₄×C₈₉	1	4	yes	—
284	C₄⋊C₈	—	2	2	no	—
285	#103	—	2	4	no	—
286	#103	—	4	2	no	—
287	#103	C₂×C₄×C₈₉	1	4	yes	—
288	#103	C₂×C₄×C₈₉	1	4	yes	—
289	#97	—	4	2	no	—
290	C₄×C₈	C₂×C₄×C₈₉	1	4	yes	—
291	#95	—	2	1	no	—
292	#95	—	2	2	no	—
293	#95	—	2	1	no	—
294	#95	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	—	2	1	no	—
297	#95	—	2	1	no	—
298	#95	—	2	2	no	—
299	#95	D₄×C₈₉	1	1	yes	characteristic
300	#95	D₄×C₈₉	1	1	yes	characteristic
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	—	2	1	no	—
303	C₂×Q₈	—	2	1	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	1	no	—
308	C₂×Q₈	—	2	1	no	—
309	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
310	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
311	C₂×Q₈	#41×C₈₉	1	2	yes	—
312	C₂×Q₈	#41×C₈₉	1	2	yes	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
320	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
321	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
323	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
324	Q₁₆	—	2	8	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
333	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
334	C₄⋊C₄	—	2	4	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	1	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	2	no	—
339	C₄⋊C₄	—	2	2	no	—
340	C₄⋊C₄	—	2	2	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	4	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
346	C₄⋊C₄	C₂²×C₄×C₈₉	1	2	yes	—
347	C₄²	—	2	4	no	—
348	C₄²	—	2	4	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	2	no	—
351	C₄²	—	4	4	no	—
352	C₄²	—	4	4	no	—
353	C₄²	C₂²×C₄×C₈₉	1	2	yes	—
354	C₄²	#41×C₈₉	1	2	yes	—
355	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
356	Q₈	—	2	2	no	—
357	Q₈	—	2	2	no	—
358	Q₈	—	2	2	no	—
359	Q₈	—	2	2	no	—
360	Q₈	—	2	2	no	—
361	Q₈	—	4	1	no	—
362	Q₈	—	4	1	no	—
363	Q₈	#117×C₈₉	1	4	yes	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	2	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	C₄×D₄×C₈₉	1	2	yes	—
389	C₂×C₄	C₄×D₄×C₈₉	1	2	yes	—
390	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
391	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
392	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
393	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
394	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
395	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
396	C₈	—	2	2	no	—
397	C₈	—	2	2	no	—
398	C₈	—	4	2	no	—
399	C₂²	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
400	C₂²	#546×C₈₉	1	1	yes	characteristic
401	C₂²	#548×C₈₉	1	1	yes	characteristic
402	C₂²	#575×C₈₉	1	2	yes	—
403	C₂²	#578×C₈₉	1	2	yes	—
404	C₄	—	2	4	no	—
405	C₄	—	2	2	no	—
406	C₄	—	2	2	no	—
407	C₄	—	4	2	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	4	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	8	2	no	—
413	C₄	—	8	2	no	—
414	C₄	C₂×#117×C₈₉	1	1	yes	characteristic
415	C₄	#520×C₈₉	1	1	yes	characteristic
416	C₄	#552×C₈₉	1	1	yes	characteristic
417	C₄	#553×C₈₉	1	1	yes	characteristic
418	C₂	C₈₉×#2352	1	1	yes	characteristic
419	C₂	C₈₉×#2943	1	1	yes	characteristic
420	C₂	C₈₉×#2950	1	1	yes	characteristic
421	C₂	C₈₉×#3327	1	2	yes	—
422	C₂	C₈₉×#3377	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³×C₈₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₈₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
LCS	G ▷ C₂×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
16. C₄×Q₁₆×C₈₉	C₄	semidirect
206. #22761	C₈₉	direct (N × H)
223. C₈₉	#22761	direct (N × H)
228. C₄×Q₁₆	C₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×Q₁₆×C₈₉	2
C₈₉×#2356	2
C₈₉×#2351	2
C₈₉×#1935	2
C₈₉×#1921	2
C₈₉×#1878	2
C₈₉×#1835	2
C₈₉×#1805	2
C₈₉×#1770	2
C₈₉×#1763	2
#22761	89

Subgroups — C89×#22761 #36400609

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#22761 #36400609