Subgroups — C₈₉×#35298 #36413146

Order 22784.

2498 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#532×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2868	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2862	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2858	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2858	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2620	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2566	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2545	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2500	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2432	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2326	C₂	1	4	yes	maximal, complemented
13	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×#41×C₈₉	C₂²	1	2	yes	—
15	#533×C₈₉	—	2	8	no	—
16	#532×C₈₉	—	2	8	no	—
17	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Q₈×C₈₉	C₂²	1	4	yes	—
21	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#125×C₈₉	C₂²	1	2	yes	—
23	C₂×#124×C₈₉	C₂²	1	4	yes	—
24	C₂×#124×C₈₉	C₂²	1	2	yes	—
25	C₂×#124×C₈₉	C₂²	1	4	yes	—
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
28	C₂×#121×C₈₉	C₂²	1	2	yes	—
29	C₂×#121×C₈₉	C₂²	1	2	yes	—
30	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
31	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
34	C₂×#117×C₈₉	C₂²	1	2	yes	—
35	C₂×#117×C₈₉	C₂²	1	2	yes	—
36	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
37	#396×C₈₉	C₂²	1	16	yes	—
38	#394×C₈₉	C₂²	1	16	yes	—
39	#391×C₈₉	C₂²	1	4	yes	—
40	#391×C₈₉	C₂²	1	4	yes	—
41	#390×C₈₉	C₂²	1	4	yes	—
42	#390×C₈₉	C₂²	1	4	yes	—
43	#390×C₈₉	C₂²	1	4	yes	—
44	#390×C₈₉	C₂²	1	4	yes	—
45	#388×C₈₉	C₂²	1	16	yes	—
46	#385×C₈₉	C₂²	1	16	yes	—
47	#384×C₈₉	C₂²	1	4	yes	—
48	#384×C₈₉	C₂²	1	4	yes	—
49	#382×C₈₉	C₂²	1	4	yes	—
50	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
51	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
52	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
53	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
54	#376×C₈₉	C₂²	1	2	yes	—
55	C₄³×C₈₉	C₂²	1	1	yes	characteristic
56	C₄³×C₈₉	C₂²	1	1	yes	characteristic
57	C₂×#41×C₈₉	—	2	8	no	—
58	C₂×#41×C₈₉	—	4	8	no	—
59	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
60	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
61	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
62	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
63	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
64	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
65	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
66	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
69	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
70	C₄⋊Q₈×C₈₉	—	2	4	no	—
71	C₄⋊Q₈×C₈₉	—	2	4	no	—
72	C₄⋊Q₈×C₈₉	—	2	4	no	—
73	C₄⋊Q₈×C₈₉	—	4	8	no	—
74	#127×C₈₉	—	2	4	no	—
75	#125×C₈₉	—	2	8	no	—
76	#124×C₈₉	—	2	8	no	—
77	#124×C₈₉	—	2	16	no	—
78	#124×C₈₉	—	4	8	no	—
79	C₂²⋊Q₈×C₈₉	—	2	8	no	—
80	C₂²⋊Q₈×C₈₉	—	2	8	no	—
81	#121×C₈₉	—	2	8	no	—
82	#121×C₈₉	—	2	8	no	—
83	C₄×Q₈×C₈₉	—	2	8	no	—
84	C₄×Q₈×C₈₉	—	2	8	no	—
85	C₄×D₄×C₈₉	—	2	8	no	—
86	C₄×D₄×C₈₉	—	2	8	no	—
87	#117×C₈₉	—	2	8	no	—
88	#117×C₈₉	—	2	8	no	—
89	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
90	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
98	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
99	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
101	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
102	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
103	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
105	C₂×C₄²×C₈₉	D₄	1	8	yes	—
106	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
107	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
108	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
109	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
110	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
111	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
112	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
117	#95×C₈₉	C₂³	1	4	yes	—
118	#95×C₈₉	C₂³	1	4	yes	—
119	#95×C₈₉	C₂³	1	16	yes	—
120	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
121	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
122	#41×C₈₉	—	4	32	no	—
123	C₂×Q₈×C₈₉	—	2	4	no	—
124	C₂×Q₈×C₈₉	—	2	4	no	—
125	C₂×Q₈×C₈₉	—	2	4	no	—
126	C₂×Q₈×C₈₉	—	2	8	no	—
127	C₂×Q₈×C₈₉	—	2	8	no	—
128	C₂×Q₈×C₈₉	—	2	8	no	—
129	C₂×D₄×C₈₉	—	2	8	no	—
130	C₂×D₄×C₈₉	—	2	4	no	—
131	C₂×D₄×C₈₉	—	2	4	no	—
132	C₂×D₄×C₈₉	—	2	4	no	—
133	C₂×D₄×C₈₉	—	2	8	no	—
134	C₂×D₄×C₈₉	—	2	8	no	—
135	C₂×D₄×C₈₉	—	2	8	no	—
136	C₂×D₄×C₈₉	—	4	8	no	—
137	C₂²×C₄×C₈₉	—	2	4	no	—
138	C₂²×C₄×C₈₉	—	2	4	no	—
139	C₂²×C₄×C₈₉	—	2	4	no	—
140	C₂²×C₄×C₈₉	—	2	8	no	—
141	C₂²×C₄×C₈₉	—	4	8	no	—
142	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
144	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
145	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
146	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
147	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
148	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
149	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
151	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
153	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
154	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
155	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
156	C₄⋊C₄×C₈₉	—	2	4	no	—
157	C₄⋊C₄×C₈₉	—	2	4	no	—
158	C₄⋊C₄×C₈₉	—	2	4	no	—
159	C₄⋊C₄×C₈₉	—	2	4	no	—
160	C₄⋊C₄×C₈₉	—	2	8	no	—
161	C₄⋊C₄×C₈₉	—	2	8	no	—
162	C₄⋊C₄×C₈₉	—	2	4	no	—
163	C₄⋊C₄×C₈₉	—	2	4	no	—
164	C₄⋊C₄×C₈₉	—	2	8	no	—
165	C₄⋊C₄×C₈₉	—	4	16	no	—
166	C₂²⋊C₄×C₈₉	—	2	8	no	—
167	C₂²⋊C₄×C₈₉	—	2	8	no	—
168	C₂²⋊C₄×C₈₉	—	2	8	no	—
169	C₂²⋊C₄×C₈₉	—	2	8	no	—
170	C₂²⋊C₄×C₈₉	—	2	32	no	—
171	C₂²⋊C₄×C₈₉	—	4	16	no	—
172	C₄²×C₈₉	—	2	8	no	—
173	C₄²×C₈₉	—	2	4	no	—
174	C₄²×C₈₉	—	2	4	no	—
175	C₄²×C₈₉	—	2	4	no	—
176	C₄²×C₈₉	—	2	4	no	—
177	C₄²×C₈₉	—	2	4	no	—
178	C₄²×C₈₉	C₂×D₄	1	4	yes	—
179	C₄²×C₈₉	C₂×D₄	1	4	yes	—
180	C₄²×C₈₉	C₂×D₄	1	4	yes	—
181	C₄²×C₈₉	C₂×D₄	1	4	yes	—
182	C₄²×C₈₉	#41	1	8	yes	complemented
183	C₂³×C₈₉	—	2	2	no	—
184	C₂³×C₈₉	—	2	2	no	—
185	C₂³×C₈₉	—	2	2	no	—
186	C₂³×C₈₉	—	2	4	no	—
187	C₂³×C₈₉	—	2	8	no	—
188	C₂³×C₈₉	—	2	8	no	—
189	C₂³×C₈₉	—	2	8	no	—
190	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
191	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
192	Q₈×C₈₉	—	4	8	no	—
193	Q₈×C₈₉	—	4	8	no	—
194	Q₈×C₈₉	—	4	8	no	—
195	D₄×C₈₉	—	4	16	no	—
196	D₄×C₈₉	—	4	8	no	—
197	D₄×C₈₉	—	4	8	no	—
198	D₄×C₈₉	—	4	8	no	—
199	C₂×C₄×C₈₉	—	2	2	no	—
200	C₂×C₄×C₈₉	—	2	4	no	—
201	C₂×C₄×C₈₉	—	2	2	no	—
202	C₂×C₄×C₈₉	—	2	4	no	—
203	C₂×C₄×C₈₉	—	2	2	no	—
204	C₂×C₄×C₈₉	—	2	8	no	—
205	C₂×C₄×C₈₉	—	2	8	no	—
206	C₂×C₄×C₈₉	—	2	8	no	—
207	C₂×C₄×C₈₉	—	2	4	no	—
208	C₂×C₄×C₈₉	—	2	4	no	—
209	C₂×C₄×C₈₉	—	2	4	no	—
210	C₂×C₄×C₈₉	—	2	4	no	—
211	C₂×C₄×C₈₉	—	2	8	no	—
212	C₂×C₄×C₈₉	—	2	4	no	—
213	C₂×C₄×C₈₉	—	2	8	no	—
214	C₂×C₄×C₈₉	—	2	8	no	—
215	C₂×C₄×C₈₉	—	2	4	no	—
216	C₂×C₄×C₈₉	—	4	16	no	—
217	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
220	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
221	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
222	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
223	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
224	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
225	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
226	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
227	C₂²×C₈₉	—	2	2	no	—
228	C₂²×C₈₉	—	2	2	no	—
229	C₂²×C₈₉	—	2	2	no	—
230	C₂²×C₈₉	—	4	4	no	—
231	C₂²×C₈₉	—	4	4	no	—
232	C₂²×C₈₉	—	4	4	no	—
233	C₂²×C₈₉	—	4	4	no	—
234	C₂²×C₈₉	—	4	16	no	—
235	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
236	C₂²×C₈₉	C₂²×#41	1	2	yes	—
237	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
238	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
239	C₄×C₈₉	—	2	2	no	—
240	C₄×C₈₉	—	2	2	no	—
241	C₄×C₈₉	—	2	2	no	—
242	C₄×C₈₉	—	2	8	no	—
243	C₄×C₈₉	—	4	4	no	—
244	C₄×C₈₉	—	4	4	no	—
245	C₄×C₈₉	—	4	4	no	—
246	C₄×C₈₉	—	4	4	no	—
247	C₄×C₈₉	#532	1	4	yes	—
248	C₄×C₈₉	#535	1	4	yes	—
249	C₄×C₈₉	#536	1	4	yes	—
250	#35298	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
251	C₂×C₈₉	—	4	2	no	—
252	C₂×C₈₉	—	8	4	no	—
253	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
254	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
255	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
256	C₂×C₈₉	#3511	1	4	yes	—
257	C₂×#533	C₂×C₈₉	1	1	yes	characteristic, complemented
258	C₂×#532	C₂×C₈₉	1	1	yes	characteristic
259	#2868	C₂×C₈₉	1	1	yes	characteristic, complemented
260	#2862	C₂×C₈₉	1	1	yes	characteristic, complemented
261	#2858	C₂×C₈₉	1	1	yes	characteristic, complemented
262	#2858	C₂×C₈₉	1	1	yes	characteristic, complemented
263	#2620	C₂×C₈₉	1	4	yes	complemented
264	#2566	C₂×C₈₉	1	4	yes	complemented
265	#2545	C₂×C₈₉	1	4	yes	complemented
266	#2500	C₂×C₈₉	1	4	yes	complemented
267	#2432	C₂×C₈₉	1	4	yes	complemented
268	#2326	C₂×C₈₉	1	4	yes	complemented
269	C₄×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
270	C₈₉	#35298	1	1	yes	characteristic, direct product factor, Sylow
271	C₂²×#41	C₂²×C₈₉	1	2	yes	—
272	#533	—	2	8	no	—
273	#532	—	2	8	no	—
274	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
275	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
276	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
277	C₂×C₄⋊Q₈	C₂²×C₈₉	1	4	yes	—
278	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
279	C₂×#125	C₂²×C₈₉	1	2	yes	—
280	C₂×#124	C₂²×C₈₉	1	4	yes	—
281	C₂×#124	C₂²×C₈₉	1	2	yes	—
282	C₂×#124	C₂²×C₈₉	1	4	yes	—
283	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
284	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
285	C₂×#121	C₂²×C₈₉	1	2	yes	—
286	C₂×#121	C₂²×C₈₉	1	2	yes	—
287	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
288	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
289	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
290	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
291	C₂×#117	C₂²×C₈₉	1	2	yes	—
292	C₂×#117	C₂²×C₈₉	1	2	yes	—
293	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
294	#396	C₂²×C₈₉	1	16	yes	—
295	#394	C₂²×C₈₉	1	16	yes	—
296	#391	C₂²×C₈₉	1	4	yes	—
297	#391	C₂²×C₈₉	1	4	yes	—
298	#390	C₂²×C₈₉	1	4	yes	—
299	#390	C₂²×C₈₉	1	4	yes	—
300	#390	C₂²×C₈₉	1	4	yes	—
301	#390	C₂²×C₈₉	1	4	yes	—
302	#388	C₂²×C₈₉	1	16	yes	—
303	#385	C₂²×C₈₉	1	16	yes	—
304	#384	C₂²×C₈₉	1	4	yes	—
305	#384	C₂²×C₈₉	1	4	yes	—
306	#382	C₂²×C₈₉	1	4	yes	—
307	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
308	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
309	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
310	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
311	#376	C₂²×C₈₉	1	2	yes	—
312	C₄³	C₂²×C₈₉	1	1	yes	characteristic
313	C₄³	C₂²×C₈₉	1	1	yes	characteristic
314	C₂×#41	—	2	8	no	—
315	C₂×#41	—	4	8	no	—
316	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
317	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
318	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
319	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
320	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
321	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
322	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
323	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
324	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
325	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
326	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
327	C₄⋊Q₈	—	2	4	no	—
328	C₄⋊Q₈	—	2	4	no	—
329	C₄⋊Q₈	—	2	4	no	—
330	C₄⋊Q₈	—	4	8	no	—
331	#127	—	2	4	no	—
332	#125	—	2	8	no	—
333	#124	—	2	8	no	—
334	#124	—	2	16	no	—
335	#124	—	4	8	no	—
336	C₂²⋊Q₈	—	2	8	no	—
337	C₂²⋊Q₈	—	2	8	no	—
338	#121	—	2	8	no	—
339	#121	—	2	8	no	—
340	C₄×Q₈	—	2	8	no	—
341	C₄×Q₈	—	2	8	no	—
342	C₄×D₄	—	2	8	no	—
343	C₄×D₄	—	2	8	no	—
344	#117	—	2	8	no	—
345	#117	—	2	8	no	—
346	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
348	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
349	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
350	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
351	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
352	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
353	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
354	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
355	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
357	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
362	C₂×C₄²	D₄×C₈₉	1	8	yes	—
363	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
364	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
365	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
366	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
367	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
368	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
369	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
370	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
371	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
372	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
373	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
374	#95	C₂³×C₈₉	1	4	yes	—
375	#95	C₂³×C₈₉	1	4	yes	—
376	#95	C₂³×C₈₉	1	16	yes	—
377	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
378	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
379	#41	—	4	32	no	—
380	C₂×Q₈	—	2	4	no	—
381	C₂×Q₈	—	2	4	no	—
382	C₂×Q₈	—	2	4	no	—
383	C₂×Q₈	—	2	8	no	—
384	C₂×Q₈	—	2	8	no	—
385	C₂×Q₈	—	2	8	no	—
386	C₂×D₄	—	2	8	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	4	no	—
390	C₂×D₄	—	2	8	no	—
391	C₂×D₄	—	2	8	no	—
392	C₂×D₄	—	2	8	no	—
393	C₂×D₄	—	4	8	no	—
394	C₂²×C₄	—	2	4	no	—
395	C₂²×C₄	—	2	4	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	8	no	—
398	C₂²×C₄	—	4	8	no	—
399	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
400	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
401	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
402	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
403	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
404	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
405	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
406	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
408	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
409	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
410	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
411	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
412	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	4	no	—
415	C₄⋊C₄	—	2	4	no	—
416	C₄⋊C₄	—	2	4	no	—
417	C₄⋊C₄	—	2	8	no	—
418	C₄⋊C₄	—	2	8	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	8	no	—
422	C₄⋊C₄	—	4	16	no	—
423	C₂²⋊C₄	—	2	8	no	—
424	C₂²⋊C₄	—	2	8	no	—
425	C₂²⋊C₄	—	2	8	no	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	2	32	no	—
428	C₂²⋊C₄	—	4	16	no	—
429	C₄²	—	2	8	no	—
430	C₄²	—	2	4	no	—
431	C₄²	—	2	4	no	—
432	C₄²	—	2	4	no	—
433	C₄²	—	2	4	no	—
434	C₄²	—	2	4	no	—
435	C₄²	C₂×D₄×C₈₉	1	4	yes	—
436	C₄²	C₂×D₄×C₈₉	1	4	yes	—
437	C₄²	C₂×D₄×C₈₉	1	4	yes	—
438	C₄²	C₂×D₄×C₈₉	1	4	yes	—
439	C₄²	#41×C₈₉	1	8	yes	complemented
440	C₂³	—	2	2	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	2	2	no	—
443	C₂³	—	2	4	no	—
444	C₂³	—	2	8	no	—
445	C₂³	—	2	8	no	—
446	C₂³	—	2	8	no	—
447	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
448	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
449	Q₈	—	4	8	no	—
450	Q₈	—	4	8	no	—
451	Q₈	—	4	8	no	—
452	D₄	—	4	16	no	—
453	D₄	—	4	8	no	—
454	D₄	—	4	8	no	—
455	D₄	—	4	8	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	8	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	8	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	4	no	—
466	C₂×C₄	—	2	4	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	8	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	8	no	—
471	C₂×C₄	—	2	8	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	4	16	no	—
474	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
475	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
476	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
477	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
478	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
479	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
480	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
481	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
482	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
483	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	4	4	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	4	4	no	—
490	C₂²	—	4	4	no	—
491	C₂²	—	4	16	no	—
492	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
493	C₂²	C₂²×#41×C₈₉	1	2	yes	—
494	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
495	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	2	no	—
499	C₄	—	2	8	no	—
500	C₄	—	4	4	no	—
501	C₄	—	4	4	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	4	no	—
504	C₄	#532×C₈₉	1	4	yes	—
505	C₄	#535×C₈₉	1	4	yes	—
506	C₄	#536×C₈₉	1	4	yes	—
507	C₂	—	4	2	no	—
508	C₂	—	8	4	no	—
509	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
510	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
511	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
512	C₂	C₈₉×#3511	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#532×C₈₉	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×#533×C₈₉	C₂	semidirect
3. C₈₉×#2868	C₂	semidirect
4. C₈₉×#2862	C₂	semidirect
5. C₈₉×#2858	C₂	semidirect
6. C₈₉×#2858	C₂	semidirect
7. C₈₉×#2620	C₂	semidirect
8. C₈₉×#2566	C₂	semidirect
9. C₈₉×#2545	C₂	semidirect
10. C₈₉×#2500	C₂	semidirect
11. C₈₉×#2432	C₂	semidirect
12. C₈₉×#2326	C₂	semidirect
13. C₄×#117×C₈₉	C₂	semidirect
182. C₄²×C₈₉	#41	semidirect
250. #35298	C₈₉	direct (N × H)
257. C₂×#533	C₂×C₈₉	semidirect
259. #2868	C₂×C₈₉	semidirect
260. #2862	C₂×C₈₉	semidirect
261. #2858	C₂×C₈₉	semidirect
262. #2858	C₂×C₈₉	semidirect
263. #2620	C₂×C₈₉	semidirect
264. #2566	C₂×C₈₉	semidirect
265. #2545	C₂×C₈₉	semidirect
266. #2500	C₂×C₈₉	semidirect
267. #2432	C₂×C₈₉	semidirect
268. #2326	C₂×C₈₉	semidirect
269. C₄×#117	C₂×C₈₉	semidirect
270. C₈₉	#35298	direct (N × H)
439. C₄²	#41×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#533×C₈₉	2
C₂×#532×C₈₉	2
C₈₉×#2868	2
C₈₉×#2862	2
C₈₉×#2858	2
C₈₉×#2620	2
C₈₉×#2566	2
C₈₉×#2545	2
C₈₉×#2500	2
C₈₉×#2432	2
C₈₉×#2326	2
C₄×#117×C₈₉	2
#35298	89

Subgroups — C89×#35298 #36413146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35298 #36413146