Subgroups — C₈₉×#35331 #36413179

Order 22784.

2202 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₈₉	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2862	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2858	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2850	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2640	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2621	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2619	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#2560	C₂	1	8	yes	maximal, complemented
9	C₈₉×#2557	C₂	1	8	yes	maximal, complemented
10	C₈₉×#2328	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2327	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#124×C₈₉	C₂	1	2	yes	maximal, complemented
13	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#542×C₈₉	—	2	16	no	—
15	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
17	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×#126×C₈₉	C₂²	1	4	yes	—
19	C₂×#124×C₈₉	C₂²	1	4	yes	—
20	C₂×#124×C₈₉	C₂²	1	2	yes	—
21	C₂×#124×C₈₉	C₂²	1	2	yes	—
22	C₂×#123×C₈₉	C₂²	1	4	yes	—
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
24	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
25	C₂×#121×C₈₉	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
28	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
31	#398×C₈₉	C₂²	1	4	yes	—
32	#397×C₈₉	C₂²	1	4	yes	—
33	#397×C₈₉	C₂²	1	8	yes	—
34	#394×C₈₉	C₂²	1	4	yes	—
35	#393×C₈₉	C₂²	1	8	yes	—
36	#392×C₈₉	C₂²	1	4	yes	—
37	#391×C₈₉	C₂²	1	8	yes	—
38	#391×C₈₉	C₂²	1	2	yes	—
39	#391×C₈₉	C₂²	1	2	yes	—
40	#390×C₈₉	C₂²	1	8	yes	—
41	#390×C₈₉	C₂²	1	2	yes	—
42	#390×C₈₉	C₂²	1	2	yes	—
43	#388×C₈₉	C₂²	1	8	yes	—
44	#388×C₈₉	C₂²	1	8	yes	—
45	#387×C₈₉	C₂²	1	8	yes	—
46	#386×C₈₉	C₂²	1	8	yes	—
47	#386×C₈₉	C₂²	1	8	yes	—
48	#382×C₈₉	C₂²	1	2	yes	—
49	#382×C₈₉	C₂²	1	1	yes	characteristic
50	#382×C₈₉	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
52	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
53	C₄×C₂²⋊C₄×C₈₉	C₂²	1	8	yes	—
54	#376×C₈₉	C₂²	1	1	yes	characteristic
55	#376×C₈₉	C₂²	1	1	yes	characteristic
56	C₄³×C₈₉	C₂²	1	1	yes	characteristic
57	C₄³×C₈₉	C₂²	1	1	yes	characteristic
58	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
59	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
60	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
61	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
62	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
65	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
66	C₄⋊Q₈×C₈₉	—	2	8	no	—
67	C₄⋊Q₈×C₈₉	—	2	4	no	—
68	#127×C₈₉	—	2	4	no	—
69	#126×C₈₉	—	2	16	no	—
70	#124×C₈₉	—	2	16	no	—
71	#124×C₈₉	—	2	8	no	—
72	#124×C₈₉	—	2	8	no	—
73	#123×C₈₉	—	2	16	no	—
74	C₂²⋊Q₈×C₈₉	—	2	8	no	—
75	C₂²⋊Q₈×C₈₉	—	2	16	no	—
76	#121×C₈₉	—	2	8	no	—
77	C₄×Q₈×C₈₉	—	2	8	no	—
78	C₄×D₄×C₈₉	—	2	8	no	—
79	#117×C₈₉	—	2	4	no	—
80	#117×C₈₉	D₄	1	8	yes	complemented
81	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
86	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
90	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
91	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
93	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
94	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
97	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
98	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
99	C₂×C₄²×C₈₉	—	2	4	no	—
100	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
103	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
104	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
105	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
106	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
110	#95×C₈₉	C₂³	1	4	yes	—
111	#95×C₈₉	C₂³	1	4	yes	—
112	#95×C₈₉	C₂³	1	8	yes	—
113	#95×C₈₉	C₂³	1	8	yes	—
114	#95×C₈₉	C₂³	1	4	yes	—
115	#95×C₈₉	C₂³	1	4	yes	—
116	#95×C₈₉	C₂³	1	8	yes	—
117	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
118	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
119	C₂×Q₈×C₈₉	—	2	4	no	—
120	C₂×Q₈×C₈₉	—	2	8	no	—
121	C₂×Q₈×C₈₉	—	2	4	no	—
122	C₂×Q₈×C₈₉	—	2	4	no	—
123	C₂×Q₈×C₈₉	—	4	8	no	—
124	C₂×D₄×C₈₉	—	2	8	no	—
125	C₂×D₄×C₈₉	—	2	4	no	—
126	C₂×D₄×C₈₉	—	2	4	no	—
127	C₂×D₄×C₈₉	—	2	4	no	—
128	C₂×D₄×C₈₉	—	2	8	no	—
129	C₂×D₄×C₈₉	—	4	8	no	—
130	C₂×D₄×C₈₉	—	4	8	no	—
131	C₂²×C₄×C₈₉	—	2	2	no	—
132	C₂²×C₄×C₈₉	—	2	2	no	—
133	C₂²×C₄×C₈₉	—	2	4	no	—
134	C₂²×C₄×C₈₉	—	2	8	no	—
135	C₂²×C₄×C₈₉	—	4	4	no	—
136	C₂²×C₄×C₈₉	—	4	8	no	—
137	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
142	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
146	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
148	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
149	C₄⋊C₄×C₈₉	—	2	4	no	—
150	C₄⋊C₄×C₈₉	—	2	4	no	—
151	C₄⋊C₄×C₈₉	—	2	8	no	—
152	C₄⋊C₄×C₈₉	—	2	8	no	—
153	C₄⋊C₄×C₈₉	—	2	8	no	—
154	C₄⋊C₄×C₈₉	—	2	4	no	—
155	C₄⋊C₄×C₈₉	—	2	8	no	—
156	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
157	C₂²⋊C₄×C₈₉	—	2	8	no	—
158	C₂²⋊C₄×C₈₉	—	2	8	no	—
159	C₂²⋊C₄×C₈₉	—	2	8	no	—
160	C₂²⋊C₄×C₈₉	—	2	8	no	—
161	C₂²⋊C₄×C₈₉	—	2	8	no	—
162	C₂²⋊C₄×C₈₉	—	2	4	no	—
163	C₂²⋊C₄×C₈₉	—	2	16	no	—
164	C₂²⋊C₄×C₈₉	—	4	8	no	—
165	C₂²⋊C₄×C₈₉	—	4	8	no	—
166	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
167	C₄²×C₈₉	—	2	8	no	—
168	C₄²×C₈₉	—	2	4	no	—
169	C₄²×C₈₉	—	2	2	no	—
170	C₄²×C₈₉	—	2	2	no	—
171	C₄²×C₈₉	—	4	4	no	—
172	C₄²×C₈₉	—	4	4	no	—
173	C₄²×C₈₉	C₂×D₄	1	4	yes	—
174	C₄²×C₈₉	C₂×D₄	1	4	yes	—
175	C₄²×C₈₉	#41	1	4	yes	—
176	C₄²×C₈₉	#41	1	4	yes	—
177	C₂³×C₈₉	—	2	1	no	—
178	C₂³×C₈₉	—	2	1	no	—
179	C₂³×C₈₉	—	2	4	no	—
180	C₂³×C₈₉	—	2	4	no	—
181	C₂³×C₈₉	—	2	4	no	—
182	C₂³×C₈₉	—	2	4	no	—
183	C₂³×C₈₉	—	2	8	no	—
184	C₂³×C₈₉	—	2	8	no	—
185	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
186	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
187	Q₈×C₈₉	—	4	8	no	—
188	Q₈×C₈₉	—	8	8	no	—
189	D₄×C₈₉	—	4	8	no	—
190	D₄×C₈₉	—	8	8	no	—
191	D₄×C₈₉	—	8	8	no	—
192	C₂×C₄×C₈₉	—	2	1	no	—
193	C₂×C₄×C₈₉	—	2	1	no	—
194	C₂×C₄×C₈₉	—	2	4	no	—
195	C₂×C₄×C₈₉	—	2	4	no	—
196	C₂×C₄×C₈₉	—	2	4	no	—
197	C₂×C₄×C₈₉	—	2	4	no	—
198	C₂×C₄×C₈₉	—	2	8	no	—
199	C₂×C₄×C₈₉	—	2	4	no	—
200	C₂×C₄×C₈₉	—	2	4	no	—
201	C₂×C₄×C₈₉	—	2	4	no	—
202	C₂×C₄×C₈₉	—	2	2	no	—
203	C₂×C₄×C₈₉	—	2	2	no	—
204	C₂×C₄×C₈₉	—	2	4	no	—
205	C₂×C₄×C₈₉	—	2	4	no	—
206	C₂×C₄×C₈₉	—	2	4	no	—
207	C₂×C₄×C₈₉	—	2	4	no	—
208	C₂×C₄×C₈₉	—	2	8	no	—
209	C₂×C₄×C₈₉	—	2	8	no	—
210	C₂×C₄×C₈₉	—	4	8	no	—
211	C₂×C₄×C₈₉	—	8	8	no	—
212	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
213	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
214	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
215	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
217	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
218	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
219	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
220	C₂²×C₈₉	—	2	2	no	—
221	C₂²×C₈₉	—	2	4	no	—
222	C₂²×C₈₉	—	4	2	no	—
223	C₂²×C₈₉	—	4	2	no	—
224	C₂²×C₈₉	—	4	4	no	—
225	C₂²×C₈₉	—	4	8	no	—
226	C₂²×C₈₉	—	4	4	no	—
227	C₂²×C₈₉	—	4	4	no	—
228	C₂²×C₈₉	—	4	8	no	—
229	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
230	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
231	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
232	C₂²×C₈₉	#585	1	4	yes	—
233	C₄×C₈₉	—	2	2	no	—
234	C₄×C₈₉	—	2	4	no	—
235	C₄×C₈₉	—	2	4	no	—
236	C₄×C₈₉	—	2	4	no	—
237	C₄×C₈₉	—	2	4	no	—
238	C₄×C₈₉	—	4	4	no	—
239	C₄×C₈₉	—	4	2	no	—
240	C₄×C₈₉	—	4	4	no	—
241	C₄×C₈₉	—	4	4	no	—
242	C₄×C₈₉	—	4	2	no	—
243	C₄×C₈₉	#532	1	4	yes	—
244	#35331	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
245	C₂×C₈₉	—	4	2	no	—
246	C₂×C₈₉	—	8	4	no	—
247	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
248	C₂×C₈₉	#3455	1	2	yes	—
249	C₂×C₈₉	#3500	1	2	yes	—
250	C₂×C₈₉	#3510	1	2	yes	—
251	C₂×#542	C₂×C₈₉	1	2	yes	complemented
252	#2862	C₂×C₈₉	1	1	yes	characteristic, complemented
253	#2858	C₂×C₈₉	1	1	yes	characteristic, complemented
254	#2850	C₂×C₈₉	1	2	yes	complemented
255	#2640	C₂×C₈₉	1	2	yes	complemented
256	#2621	C₂×C₈₉	1	1	yes	characteristic, complemented
257	#2619	C₂×C₈₉	1	1	yes	characteristic
258	#2560	C₂×C₈₉	1	8	yes	complemented
259	#2557	C₂×C₈₉	1	8	yes	complemented
260	#2328	C₂×C₈₉	1	1	yes	characteristic, complemented
261	#2327	C₂×C₈₉	1	1	yes	characteristic, complemented
262	C₄×#124	C₂×C₈₉	1	2	yes	complemented
263	C₄×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
264	C₈₉	#35331	1	1	yes	characteristic, direct product factor, Sylow
265	#542	—	2	16	no	—
266	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
267	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
268	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
269	C₂×#126	C₂²×C₈₉	1	4	yes	—
270	C₂×#124	C₂²×C₈₉	1	2	yes	—
271	C₂×#124	C₂²×C₈₉	1	2	yes	—
272	C₂×#124	C₂²×C₈₉	1	4	yes	—
273	C₂×#123	C₂²×C₈₉	1	4	yes	—
274	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
275	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
276	C₂×#121	C₂²×C₈₉	1	2	yes	—
277	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
278	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
279	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
280	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
281	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
282	#398	C₂²×C₈₉	1	4	yes	—
283	#397	C₂²×C₈₉	1	8	yes	—
284	#397	C₂²×C₈₉	1	4	yes	—
285	#394	C₂²×C₈₉	1	4	yes	—
286	#393	C₂²×C₈₉	1	8	yes	—
287	#392	C₂²×C₈₉	1	4	yes	—
288	#391	C₂²×C₈₉	1	8	yes	—
289	#391	C₂²×C₈₉	1	2	yes	—
290	#391	C₂²×C₈₉	1	2	yes	—
291	#390	C₂²×C₈₉	1	8	yes	—
292	#390	C₂²×C₈₉	1	2	yes	—
293	#390	C₂²×C₈₉	1	2	yes	—
294	#388	C₂²×C₈₉	1	8	yes	—
295	#388	C₂²×C₈₉	1	8	yes	—
296	#387	C₂²×C₈₉	1	8	yes	—
297	#386	C₂²×C₈₉	1	8	yes	—
298	#386	C₂²×C₈₉	1	8	yes	—
299	#382	C₂²×C₈₉	1	1	yes	characteristic
300	#382	C₂²×C₈₉	1	1	yes	characteristic
301	#382	C₂²×C₈₉	1	2	yes	—
302	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
303	C₄×C₂²⋊C₄	C₂²×C₈₉	1	8	yes	—
304	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
305	#376	C₂²×C₈₉	1	1	yes	characteristic
306	#376	C₂²×C₈₉	1	1	yes	characteristic
307	C₄³	C₂²×C₈₉	1	1	yes	characteristic
308	C₄³	C₂²×C₈₉	1	1	yes	characteristic
309	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
310	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
311	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
312	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
313	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
314	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
316	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
317	C₄⋊Q₈	—	2	8	no	—
318	C₄⋊Q₈	—	2	4	no	—
319	#127	—	2	4	no	—
320	#126	—	2	16	no	—
321	#124	—	2	16	no	—
322	#124	—	2	8	no	—
323	#124	—	2	8	no	—
324	#123	—	2	16	no	—
325	C₂²⋊Q₈	—	2	8	no	—
326	C₂²⋊Q₈	—	2	16	no	—
327	#121	—	2	8	no	—
328	C₄×Q₈	—	2	8	no	—
329	C₄×D₄	—	2	8	no	—
330	#117	—	2	4	no	—
331	#117	D₄×C₈₉	1	8	yes	complemented
332	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
333	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
334	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
336	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
337	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
338	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
339	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
341	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
342	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
343	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
344	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
345	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
346	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
347	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
348	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
349	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
350	C₂×C₄²	—	2	4	no	—
351	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
352	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
353	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
355	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
356	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
357	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
358	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
359	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
360	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
361	#95	C₂³×C₈₉	1	4	yes	—
362	#95	C₂³×C₈₉	1	4	yes	—
363	#95	C₂³×C₈₉	1	8	yes	—
364	#95	C₂³×C₈₉	1	8	yes	—
365	#95	C₂³×C₈₉	1	4	yes	—
366	#95	C₂³×C₈₉	1	4	yes	—
367	#95	C₂³×C₈₉	1	8	yes	—
368	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
369	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
370	C₂×Q₈	—	2	4	no	—
371	C₂×Q₈	—	2	8	no	—
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	—	4	8	no	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	4	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	2	8	no	—
380	C₂×D₄	—	4	8	no	—
381	C₂×D₄	—	4	8	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	8	no	—
386	C₂²×C₄	—	4	4	no	—
387	C₂²×C₄	—	4	8	no	—
388	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
389	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
390	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
391	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
392	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
393	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
394	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
395	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
396	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
397	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
398	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
399	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
400	C₄⋊C₄	—	2	4	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	8	no	—
403	C₄⋊C₄	—	2	8	no	—
404	C₄⋊C₄	—	2	8	no	—
405	C₄⋊C₄	—	2	4	no	—
406	C₄⋊C₄	—	2	8	no	—
407	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	2	8	no	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	—	2	8	no	—
412	C₂²⋊C₄	—	2	8	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	16	no	—
415	C₂²⋊C₄	—	4	8	no	—
416	C₂²⋊C₄	—	4	8	no	—
417	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
418	C₄²	—	2	8	no	—
419	C₄²	—	2	4	no	—
420	C₄²	—	2	2	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	4	4	no	—
423	C₄²	—	4	4	no	—
424	C₄²	C₂×D₄×C₈₉	1	4	yes	—
425	C₄²	C₂×D₄×C₈₉	1	4	yes	—
426	C₄²	#41×C₈₉	1	4	yes	—
427	C₄²	#41×C₈₉	1	4	yes	—
428	C₂³	—	2	1	no	—
429	C₂³	—	2	1	no	—
430	C₂³	—	2	4	no	—
431	C₂³	—	2	4	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	4	no	—
434	C₂³	—	2	8	no	—
435	C₂³	—	2	8	no	—
436	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
437	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
438	Q₈	—	4	8	no	—
439	Q₈	—	8	8	no	—
440	D₄	—	4	8	no	—
441	D₄	—	8	8	no	—
442	D₄	—	8	8	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	4	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	2	4	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	8	no	—
460	C₂×C₄	—	2	8	no	—
461	C₂×C₄	—	4	8	no	—
462	C₂×C₄	—	8	8	no	—
463	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
464	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
465	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
466	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
467	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
468	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
469	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
470	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
471	C₂²	—	2	2	no	—
472	C₂²	—	2	4	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	4	2	no	—
475	C₂²	—	4	4	no	—
476	C₂²	—	4	8	no	—
477	C₂²	—	4	4	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	8	no	—
480	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
481	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
482	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
483	C₂²	#585×C₈₉	1	4	yes	—
484	C₄	—	2	2	no	—
485	C₄	—	2	4	no	—
486	C₄	—	2	4	no	—
487	C₄	—	2	4	no	—
488	C₄	—	2	4	no	—
489	C₄	—	4	4	no	—
490	C₄	—	4	2	no	—
491	C₄	—	4	4	no	—
492	C₄	—	4	4	no	—
493	C₄	—	4	2	no	—
494	C₄	#532×C₈₉	1	4	yes	—
495	C₂	—	4	2	no	—
496	C₂	—	8	4	no	—
497	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
498	C₂	C₈₉×#3455	1	2	yes	—
499	C₂	C₈₉×#3500	1	2	yes	—
500	C₂	C₈₉×#3510	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2619	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#542×C₈₉	C₂	semidirect
2. C₈₉×#2862	C₂	semidirect
3. C₈₉×#2858	C₂	semidirect
4. C₈₉×#2850	C₂	semidirect
5. C₈₉×#2640	C₂	semidirect
6. C₈₉×#2621	C₂	semidirect
8. C₈₉×#2560	C₂	semidirect
9. C₈₉×#2557	C₂	semidirect
10. C₈₉×#2328	C₂	semidirect
11. C₈₉×#2327	C₂	semidirect
12. C₄×#124×C₈₉	C₂	semidirect
13. C₄×#117×C₈₉	C₂	semidirect
80. #117×C₈₉	D₄	semidirect
244. #35331	C₈₉	direct (N × H)
251. C₂×#542	C₂×C₈₉	semidirect
252. #2862	C₂×C₈₉	semidirect
253. #2858	C₂×C₈₉	semidirect
254. #2850	C₂×C₈₉	semidirect
255. #2640	C₂×C₈₉	semidirect
256. #2621	C₂×C₈₉	semidirect
258. #2560	C₂×C₈₉	semidirect
259. #2557	C₂×C₈₉	semidirect
260. #2328	C₂×C₈₉	semidirect
261. #2327	C₂×C₈₉	semidirect
262. C₄×#124	C₂×C₈₉	semidirect
263. C₄×#117	C₂×C₈₉	semidirect
264. C₈₉	#35331	direct (N × H)
331. #117	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#542×C₈₉	2
C₈₉×#2862	2
C₈₉×#2858	2
C₈₉×#2850	2
C₈₉×#2640	2
C₈₉×#2621	2
C₈₉×#2619	2
C₈₉×#2560	2
C₈₉×#2557	2
C₈₉×#2328	2
C₈₉×#2327	2
C₄×#124×C₈₉	2
C₄×#117×C₈₉	2
#35331	89

Subgroups — C89×#35331 #36413179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35331 #36413179