Subgroups — C₈₉×#21546 #36399394

Order 22784.

958 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3050	C₂	1	1	yes	maximal, characteristic
2	C₂×#444×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2929	C₂	1	2	yes	maximal, complemented
4	C₂²×#97×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#1975	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#1946	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#1938	C₂	1	2	yes	maximal, complemented
8	C₈₉×#1896	C₂	1	2	yes	maximal, complemented
9	C₈₉×#1810	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1773	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1765	C₂	1	2	yes	maximal, complemented
12	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×#131×C₈₉	C₂²	1	2	yes	—
14	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
16	#525×C₈₉	C₂²	1	2	yes	—
17	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
18	#467×C₈₉	C₄	1	2	yes	complemented
19	#466×C₈₉	C₄	1	2	yes	complemented
20	#465×C₈₉	C₄	1	4	yes	complemented
21	#444×C₈₉	—	2	4	no	—
22	#435×C₈₉	—	2	4	no	—
23	C₈×D₄×C₈₉	—	2	4	no	—
24	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#108×C₈₉	C₂²	1	1	yes	characteristic
26	#427×C₈₉	C₂²	1	1	yes	characteristic
27	#424×C₈₉	C₂²	1	2	yes	—
28	C₂×#104×C₈₉	C₂²	1	2	yes	—
29	C₂×#104×C₈₉	C₂²	1	2	yes	—
30	#416×C₈₉	C₂²	1	2	yes	—
31	#408×C₈₉	C₂²	1	2	yes	—
32	#407×C₈₉	C₂²	1	2	yes	—
33	#405×C₈₉	C₂²	1	2	yes	—
34	C₂×#97×C₈₉	—	2	4	no	—
35	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
39	#341×C₈₉	C₂²	1	2	yes	—
40	#339×C₈₉	C₂²	1	2	yes	—
41	#339×C₈₉	C₂²	1	2	yes	—
42	C₂×#41×C₈₉	C₂³	1	2	yes	—
43	C₂³×C₄×C₈₉	—	2	1	no	—
44	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
45	#135×C₈₉	—	2	2	no	—
46	#135×C₈₉	—	2	2	no	—
47	C₂×Q₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂×SD₁₆×C₈₉	C₂×C₄	1	2	yes	complemented
49	C₂×D₈×C₈₉	C₂×C₄	1	1	yes	characteristic, complemented
50	#131×C₈₉	—	2	4	no	—
51	#131×C₈₉	—	2	4	no	—
52	C₂×M₁₆×C₈₉	—	2	2	no	—
53	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
54	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₈₉	—	2	2	no	—
56	C₂²×C₈×C₈₉	—	2	2	no	—
57	C₂²×C₈×C₈₉	—	2	2	no	—
58	C₂²×C₈×C₈₉	—	2	2	no	—
59	C₂²×C₈×C₈₉	—	2	2	no	—
60	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
61	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
62	C₂²×C₈×C₈₉	D₄	1	4	yes	—
63	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
64	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
67	#123×C₈₉	—	2	2	no	—
68	C₂²⋊Q₈×C₈₉	C₂×C₄	1	4	yes	—
69	#121×C₈₉	C₂×C₄	1	4	yes	—
70	#120×C₈₉	—	2	2	no	—
71	C₄×D₄×C₈₉	—	2	4	no	—
72	#117×C₈₉	C₂³	1	2	yes	—
73	C₂×C₄²×C₈₉	—	2	1	no	—
74	C₂×C₄²×C₈₉	—	2	2	no	—
75	C₂×C₄²×C₈₉	—	2	2	no	—
76	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
78	#108×C₈₉	—	2	2	no	—
79	#108×C₈₉	—	2	2	no	—
80	#107×C₈₉	C₂×C₄	1	2	yes	complemented
81	#106×C₈₉	C₂×C₄	1	2	yes	complemented
82	C₄⋊C₈×C₈₉	—	2	4	no	—
83	#104×C₈₉	—	2	4	no	—
84	#104×C₈₉	—	2	4	no	—
85	#103×C₈₉	C₂×C₄	1	4	yes	complemented
86	#102×C₈₉	C₂×C₄	1	4	yes	complemented
87	C₂²⋊C₈×C₈₉	—	2	4	no	—
88	C₂²⋊C₈×C₈₉	—	2	4	no	—
89	#97×C₈₉	—	2	2	no	—
90	#97×C₈₉	—	2	2	no	—
91	#97×C₈₉	—	2	2	no	—
92	#97×C₈₉	—	2	2	no	—
93	#97×C₈₉	D₄	1	4	yes	complemented
94	C₄×C₈×C₈₉	—	2	2	no	—
95	C₂⁴×C₈₉	#41	1	1	yes	characteristic
96	#41×C₈₉	—	2	2	no	—
97	#41×C₈₉	—	2	2	no	—
98	#41×C₈₉	—	2	2	no	—
99	#41×C₈₉	—	2	2	no	—
100	C₂×Q₈×C₈₉	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₈₉	—	2	4	no	—
102	C₂×D₄×C₈₉	—	2	2	no	—
103	C₂×D₄×C₈₉	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₈₉	—	2	1	no	—
105	C₂²×C₄×C₈₉	—	2	1	no	—
106	C₂²×C₄×C₈₉	—	2	1	no	—
107	C₂²×C₄×C₈₉	—	2	1	no	—
108	C₂²×C₄×C₈₉	—	2	4	no	—
109	C₂²×C₄×C₈₉	—	2	1	no	—
110	C₂²×C₄×C₈₉	—	2	1	no	—
111	C₂²×C₄×C₈₉	—	2	2	no	—
112	C₂²×C₄×C₈₉	—	4	4	no	—
113	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
117	Q₁₆×C₈₉	—	2	2	no	—
118	SD₁₆×C₈₉	—	2	4	no	—
119	D₈×C₈₉	—	2	2	no	—
120	M₁₆×C₈₉	—	2	2	no	—
121	M₁₆×C₈₉	—	2	2	no	—
122	M₁₆×C₈₉	—	2	2	no	—
123	M₁₆×C₈₉	—	2	2	no	—
124	M₁₆×C₈₉	—	4	4	no	—
125	C₂×C₈×C₈₉	—	2	1	no	—
126	C₂×C₈×C₈₉	—	2	1	no	—
127	C₂×C₈×C₈₉	—	2	1	no	—
128	C₂×C₈×C₈₉	—	2	1	no	—
129	C₂×C₈×C₈₉	—	2	4	no	—
130	C₂×C₈×C₈₉	—	2	4	no	—
131	C₂×C₈×C₈₉	—	2	8	no	—
132	C₂×C₈×C₈₉	—	2	2	no	—
133	C₂×C₈×C₈₉	—	2	2	no	—
134	C₂×C₈×C₈₉	—	4	4	no	—
135	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
136	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
139	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
141	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₈₉	#41	1	2	yes	—
143	C₂×C₈×C₈₉	#41	1	2	yes	—
144	C₄⋊C₄×C₈₉	—	2	4	no	—
145	C₄⋊C₄×C₈₉	C₂²×C₄	1	4	yes	—
146	C₂²⋊C₄×C₈₉	—	2	4	no	—
147	C₂²⋊C₄×C₈₉	—	2	2	no	—
148	C₂²⋊C₄×C₈₉	—	2	4	no	—
149	C₄²×C₈₉	—	2	4	no	—
150	C₄²×C₈₉	—	2	1	no	—
151	C₄²×C₈₉	—	2	2	no	—
152	C₄²×C₈₉	—	2	1	no	—
153	C₄²×C₈₉	C₂×D₄	1	2	yes	—
154	C₄²×C₈₉	#41	1	2	yes	—
155	C₂³×C₈₉	—	2	1	no	—
156	C₂³×C₈₉	—	2	1	no	—
157	C₂³×C₈₉	—	2	4	no	—
158	C₂³×C₈₉	—	2	2	no	—
159	C₂³×C₈₉	C₄×D₄	1	2	yes	—
160	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
161	Q₈×C₈₉	—	2	2	no	—
162	Q₈×C₈₉	—	2	2	no	—
163	D₄×C₈₉	—	2	2	no	—
164	D₄×C₈₉	—	2	2	no	—
165	D₄×C₈₉	—	4	2	no	—
166	D₄×C₈₉	—	4	2	no	—
167	D₄×C₈₉	—	4	8	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	2	1	no	—
170	C₂×C₄×C₈₉	—	2	2	no	—
171	C₂×C₄×C₈₉	—	2	2	no	—
172	C₂×C₄×C₈₉	—	2	2	no	—
173	C₂×C₄×C₈₉	—	2	2	no	—
174	C₂×C₄×C₈₉	—	2	4	no	—
175	C₂×C₄×C₈₉	—	2	2	no	—
176	C₂×C₄×C₈₉	—	2	2	no	—
177	C₂×C₄×C₈₉	—	2	2	no	—
178	C₂×C₄×C₈₉	—	4	8	no	—
179	C₂×C₄×C₈₉	—	4	2	no	—
180	C₂×C₄×C₈₉	—	4	2	no	—
181	C₂×C₄×C₈₉	—	4	2	no	—
182	C₂×C₄×C₈₉	—	4	2	no	—
183	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
184	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
189	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
190	C₈×C₈₉	—	2	2	no	—
191	C₈×C₈₉	—	2	2	no	—
192	C₈×C₈₉	—	4	2	no	—
193	C₈×C₈₉	—	4	2	no	—
194	C₈×C₈₉	C₄×D₄	1	2	yes	—
195	C₈×C₈₉	C₄×D₄	1	2	yes	—
196	C₈×C₈₉	#121	1	4	yes	—
197	C₂²×C₈₉	—	2	4	no	—
198	C₂²×C₈₉	—	2	4	no	—
199	C₂²×C₈₉	—	2	2	no	—
200	C₂²×C₈₉	—	2	2	no	—
201	C₂²×C₈₉	—	2	2	no	—
202	C₂²×C₈₉	—	4	4	no	—
203	C₂²×C₈₉	—	4	2	no	—
204	C₂²×C₈₉	#444	1	4	yes	complemented
205	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
206	C₂²×C₈₉	#525	1	1	yes	characteristic
207	C₂²×C₈₉	#529	1	1	yes	characteristic
208	C₄×C₈₉	—	2	2	no	—
209	C₄×C₈₉	—	4	2	no	—
210	C₄×C₈₉	—	4	2	no	—
211	C₄×C₈₉	—	4	4	no	—
212	C₄×C₈₉	—	4	2	no	—
213	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
214	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
215	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
216	C₄×C₈₉	#532	1	1	yes	characteristic
217	#21546	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂×C₈₉	—	2	1	no	—
219	C₂×C₈₉	—	2	1	no	—
220	C₂×C₈₉	—	2	4	no	—
221	C₂×C₈₉	—	8	2	no	—
222	C₂×C₈₉	C₄×#121	1	1	yes	characteristic
223	C₂×C₈₉	C₂×#444	1	2	yes	—
224	#3050	C₂×C₈₉	1	1	yes	characteristic
225	C₂×#444	C₂×C₈₉	1	1	yes	characteristic, complemented
226	#2929	C₂×C₈₉	1	2	yes	complemented
227	C₂²×#97	C₂×C₈₉	1	1	yes	characteristic, complemented
228	#1975	C₂×C₈₉	1	1	yes	characteristic, complemented
229	#1946	C₂×C₈₉	1	1	yes	characteristic, complemented
230	#1938	C₂×C₈₉	1	2	yes	complemented
231	#1896	C₂×C₈₉	1	2	yes	complemented
232	#1810	C₂×C₈₉	1	1	yes	characteristic, complemented
233	#1773	C₂×C₈₉	1	1	yes	characteristic, complemented
234	#1765	C₂×C₈₉	1	2	yes	complemented
235	C₈₉	#21546	1	1	yes	characteristic, direct product factor, Sylow
236	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
237	C₂×#131	C₂²×C₈₉	1	2	yes	—
238	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
239	C₂³×C₈	C₂²×C₈₉	1	1	yes	characteristic
240	#525	C₂²×C₈₉	1	2	yes	—
241	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
242	#467	C₄×C₈₉	1	2	yes	complemented
243	#466	C₄×C₈₉	1	2	yes	complemented
244	#465	C₄×C₈₉	1	4	yes	complemented
245	#444	—	2	4	no	—
246	#435	—	2	4	no	—
247	C₈×D₄	—	2	4	no	—
248	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic
249	C₂×#108	C₂²×C₈₉	1	1	yes	characteristic
250	#427	C₂²×C₈₉	1	1	yes	characteristic
251	#424	C₂²×C₈₉	1	2	yes	—
252	C₂×#104	C₂²×C₈₉	1	2	yes	—
253	C₂×#104	C₂²×C₈₉	1	2	yes	—
254	#416	C₂²×C₈₉	1	2	yes	—
255	#408	C₂²×C₈₉	1	2	yes	—
256	#407	C₂²×C₈₉	1	2	yes	—
257	#405	C₂²×C₈₉	1	2	yes	—
258	C₂×#97	—	2	4	no	—
259	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
260	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
261	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
262	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
263	#341	C₂²×C₈₉	1	2	yes	—
264	#339	C₂²×C₈₉	1	2	yes	—
265	#339	C₂²×C₈₉	1	2	yes	—
266	C₂×#41	C₂³×C₈₉	1	2	yes	—
267	C₂³×C₄	—	2	1	no	—
268	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
269	#135	—	2	2	no	—
270	#135	—	2	2	no	—
271	C₂×Q₁₆	C₂×C₄×C₈₉	1	1	yes	characteristic, complemented
272	C₂×SD₁₆	C₂×C₄×C₈₉	1	2	yes	complemented
273	C₂×D₈	C₂×C₄×C₈₉	1	1	yes	characteristic, complemented
274	#131	—	2	4	no	—
275	#131	—	2	4	no	—
276	C₂×M₁₆	—	2	2	no	—
277	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
278	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
279	C₂²×C₈	—	2	2	no	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	2	no	—
283	C₂²×C₈	—	2	2	no	—
284	C₂²×C₈	C₂×C₄×C₈₉	1	2	yes	—
285	C₂²×C₈	C₂×C₄×C₈₉	1	2	yes	—
286	C₂²×C₈	D₄×C₈₉	1	4	yes	—
287	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
288	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
289	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
291	#123	—	2	2	no	—
292	C₂²⋊Q₈	C₂×C₄×C₈₉	1	4	yes	—
293	#121	C₂×C₄×C₈₉	1	4	yes	—
294	#120	—	2	2	no	—
295	C₄×D₄	—	2	4	no	—
296	#117	C₂³×C₈₉	1	2	yes	—
297	C₂×C₄²	—	2	1	no	—
298	C₂×C₄²	—	2	2	no	—
299	C₂×C₄²	—	2	2	no	—
300	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
302	#108	—	2	2	no	—
303	#108	—	2	2	no	—
304	#107	C₂×C₄×C₈₉	1	2	yes	complemented
305	#106	C₂×C₄×C₈₉	1	2	yes	complemented
306	C₄⋊C₈	—	2	4	no	—
307	#104	—	2	4	no	—
308	#104	—	2	4	no	—
309	#103	C₂×C₄×C₈₉	1	4	yes	complemented
310	#102	C₂×C₄×C₈₉	1	4	yes	complemented
311	C₂²⋊C₈	—	2	4	no	—
312	C₂²⋊C₈	—	2	4	no	—
313	#97	—	2	2	no	—
314	#97	—	2	2	no	—
315	#97	—	2	2	no	—
316	#97	—	2	2	no	—
317	#97	D₄×C₈₉	1	4	yes	complemented
318	C₄×C₈	—	2	2	no	—
319	C₂⁴	#41×C₈₉	1	1	yes	characteristic
320	#41	—	2	2	no	—
321	#41	—	2	2	no	—
322	#41	—	2	2	no	—
323	#41	—	2	2	no	—
324	C₂×Q₈	C₂²×C₄×C₈₉	1	2	yes	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	C₂²×C₄×C₈₉	1	2	yes	—
328	C₂²×C₄	—	2	1	no	—
329	C₂²×C₄	—	2	1	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
338	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
339	C₂²×C₄	#41×C₈₉	1	1	yes	characteristic
340	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
341	Q₁₆	—	2	2	no	—
342	SD₁₆	—	2	4	no	—
343	D₈	—	2	2	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	2	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	2	2	no	—
348	M₁₆	—	4	4	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	4	no	—
354	C₂×C₈	—	2	4	no	—
355	C₂×C₈	—	2	8	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	4	4	no	—
359	C₂×C₈	C₂²×C₄×C₈₉	1	2	yes	—
360	C₂×C₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
361	C₂×C₈	C₂²×C₄×C₈₉	1	1	yes	characteristic
362	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
363	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
364	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
365	C₂×C₈	C₂×D₄×C₈₉	1	2	yes	—
366	C₂×C₈	#41×C₈₉	1	2	yes	—
367	C₂×C₈	#41×C₈₉	1	2	yes	—
368	C₄⋊C₄	—	2	4	no	—
369	C₄⋊C₄	C₂²×C₄×C₈₉	1	4	yes	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₄²	—	2	4	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂×D₄×C₈₉	1	2	yes	—
378	C₄²	#41×C₈₉	1	2	yes	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	1	no	—
382	C₂³	—	2	2	no	—
383	C₂³	C₄×D₄×C₈₉	1	2	yes	—
384	C₂³	C₂×#41×C₈₉	1	1	yes	characteristic
385	Q₈	—	2	2	no	—
386	Q₈	—	2	2	no	—
387	D₄	—	2	2	no	—
388	D₄	—	2	2	no	—
389	D₄	—	4	8	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	C₄×D₄×C₈₉	1	2	yes	—
408	C₂×C₄	C₂³×C₄×C₈₉	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
410	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
412	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
413	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
414	C₈	—	2	2	no	—
415	C₈	—	2	2	no	—
416	C₈	—	4	2	no	—
417	C₈	—	4	2	no	—
418	C₈	C₄×D₄×C₈₉	1	2	yes	—
419	C₈	C₄×D₄×C₈₉	1	2	yes	—
420	C₈	#121×C₈₉	1	4	yes	—
421	C₂²	—	2	4	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	4	no	—
428	C₂²	#444×C₈₉	1	4	yes	complemented
429	C₂²	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
430	C₂²	#525×C₈₉	1	1	yes	characteristic
431	C₂²	#529×C₈₉	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	4	4	no	—
437	C₄	C₂×C₄×D₄×C₈₉	1	1	yes	characteristic
438	C₄	C₄×#41×C₈₉	1	1	yes	characteristic
439	C₄	C₂×#121×C₈₉	1	1	yes	characteristic
440	C₄	#532×C₈₉	1	1	yes	characteristic
441	C₂	—	2	1	no	—
442	C₂	—	2	4	no	—
443	C₂	—	2	1	no	—
444	C₂	—	8	2	no	—
445	C₂	C₄×#121×C₈₉	1	1	yes	characteristic
446	C₂	C₂×#444×C₈₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₈₉	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₈₉
Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₈₉×#3050	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈₉ ◁ C₂³×C₈×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#444×C₈₉	C₂	semidirect
3. C₈₉×#2929	C₂	semidirect
4. C₂²×#97×C₈₉	C₂	semidirect
5. C₈₉×#1975	C₂	semidirect
6. C₈₉×#1946	C₂	semidirect
7. C₈₉×#1938	C₂	semidirect
8. C₈₉×#1896	C₂	semidirect
9. C₈₉×#1810	C₂	semidirect
10. C₈₉×#1773	C₂	semidirect
11. C₈₉×#1765	C₂	semidirect
18. #467×C₈₉	C₄	semidirect
19. #466×C₈₉	C₄	semidirect
20. #465×C₈₉	C₄	semidirect
47. C₂×Q₁₆×C₈₉	C₂×C₄	semidirect
48. C₂×SD₁₆×C₈₉	C₂×C₄	semidirect
49. C₂×D₈×C₈₉	C₂×C₄	semidirect
80. #107×C₈₉	C₂×C₄	semidirect
81. #106×C₈₉	C₂×C₄	semidirect
85. #103×C₈₉	C₂×C₄	semidirect
86. #102×C₈₉	C₂×C₄	semidirect
93. #97×C₈₉	D₄	semidirect
204. C₂²×C₈₉	#444	semidirect
217. #21546	C₈₉	direct (N × H)
225. C₂×#444	C₂×C₈₉	semidirect
226. #2929	C₂×C₈₉	semidirect
227. C₂²×#97	C₂×C₈₉	semidirect
228. #1975	C₂×C₈₉	semidirect
229. #1946	C₂×C₈₉	semidirect
230. #1938	C₂×C₈₉	semidirect
231. #1896	C₂×C₈₉	semidirect
232. #1810	C₂×C₈₉	semidirect
233. #1773	C₂×C₈₉	semidirect
234. #1765	C₂×C₈₉	semidirect
235. C₈₉	#21546	direct (N × H)
242. #467	C₄×C₈₉	semidirect
243. #466	C₄×C₈₉	semidirect
244. #465	C₄×C₈₉	semidirect
271. C₂×Q₁₆	C₂×C₄×C₈₉	semidirect
272. C₂×SD₁₆	C₂×C₄×C₈₉	semidirect
273. C₂×D₈	C₂×C₄×C₈₉	semidirect
304. #107	C₂×C₄×C₈₉	semidirect
305. #106	C₂×C₄×C₈₉	semidirect
309. #103	C₂×C₄×C₈₉	semidirect
310. #102	C₂×C₄×C₈₉	semidirect
317. #97	D₄×C₈₉	semidirect
428. C₂²	#444×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3050	2
C₂×#444×C₈₉	2
C₈₉×#2929	2
C₂²×#97×C₈₉	2
C₈₉×#1975	2
C₈₉×#1946	2
C₈₉×#1938	2
C₈₉×#1896	2
C₈₉×#1810	2
C₈₉×#1773	2
C₈₉×#1765	2
#21546	89

Subgroups — C89×#21546 #36399394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#21546 #36399394