Subgroups — C₈₉×#35557 #36413405

Order 22784.

1890 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2512	C₂	1	4	yes	maximal, complemented
2	C₈₉×#2511	C₂	1	4	yes	maximal, complemented
3	C₈₉×#2497	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2496	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2481	C₂	1	8	yes	maximal, complemented
6	C₈₉×#2316	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2311	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#2311	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#2297	C₂	1	1	yes	maximal, characteristic
10	C₈₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#384×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2274	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×#126×C₈₉	C₂²	1	8	yes	—
15	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
21	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
22	#400×C₈₉	C₂²	1	8	yes	—
23	#400×C₈₉	C₂²	1	8	yes	—
24	#397×C₈₉	C₂²	1	8	yes	—
25	#396×C₈₉	C₂²	1	8	yes	—
26	#391×C₈₉	C₂²	1	2	yes	—
27	#391×C₈₉	C₂²	1	2	yes	—
28	#391×C₈₉	C₂²	1	2	yes	—
29	#390×C₈₉	C₂²	1	2	yes	—
30	#390×C₈₉	C₂²	1	2	yes	—
31	#390×C₈₉	C₂²	1	2	yes	—
32	#389×C₈₉	C₂²	1	2	yes	—
33	#389×C₈₉	C₂²	1	2	yes	—
34	#389×C₈₉	C₂²	1	4	yes	—
35	#389×C₈₉	C₂²	1	4	yes	—
36	#388×C₈₉	C₂²	1	8	yes	—
37	#387×C₈₉	C₂²	1	8	yes	—
38	#387×C₈₉	C₂²	1	8	yes	—
39	#386×C₈₉	C₂²	1	4	yes	—
40	#386×C₈₉	C₂²	1	4	yes	—
41	#386×C₈₉	C₂²	1	4	yes	—
42	#385×C₈₉	C₂²	1	4	yes	—
43	#384×C₈₉	C₂²	1	2	yes	—
44	#384×C₈₉	C₂²	1	2	yes	—
45	#384×C₈₉	C₂²	1	4	yes	—
46	#380×C₈₉	C₂²	1	4	yes	—
47	#380×C₈₉	C₂²	1	4	yes	—
48	#380×C₈₉	C₂²	1	4	yes	—
49	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
50	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
51	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
52	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
53	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
54	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
55	C₂×#41×C₈₉	—	2	4	no	—
56	C₂×#41×C₈₉	—	2	4	no	—
57	C₂×#41×C₈₉	—	2	4	no	—
58	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
59	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
60	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
64	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
65	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
66	#126×C₈₉	—	4	16	no	—
67	#117×C₈₉	—	2	4	no	—
68	#117×C₈₉	—	2	4	no	—
69	#117×C₈₉	—	2	4	no	—
70	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
71	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
72	C₂×C₄⋊C₄×C₈₉	—	4	8	no	—
73	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
76	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
77	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
78	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
79	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
82	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
83	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
84	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
85	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
86	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
87	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
88	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	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	8	yes	—
92	C₂×C₄²×C₈₉	—	2	4	no	—
93	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
94	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
95	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
97	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
98	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
99	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
100	#95×C₈₉	C₂³	1	8	yes	—
101	#95×C₈₉	C₂³	1	4	yes	—
102	#95×C₈₉	C₂³	1	4	yes	—
103	#95×C₈₉	C₂³	1	4	yes	—
104	#95×C₈₉	C₂³	1	4	yes	—
105	#95×C₈₉	C₂³	1	8	yes	—
106	#95×C₈₉	C₂³	1	8	yes	—
107	#95×C₈₉	C₂³	1	8	yes	—
108	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
109	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
110	#41×C₈₉	—	4	16	no	—
111	C₂×Q₈×C₈₉	—	2	2	no	—
112	C₂×Q₈×C₈₉	—	2	2	no	—
113	C₂×Q₈×C₈₉	—	2	2	no	—
114	C₂×D₄×C₈₉	—	2	4	no	—
115	C₂×D₄×C₈₉	—	2	4	no	—
116	C₂×D₄×C₈₉	—	2	4	no	—
117	C₂×D₄×C₈₉	—	2	2	no	—
118	C₂×D₄×C₈₉	—	2	2	no	—
119	C₂×D₄×C₈₉	—	2	2	no	—
120	C₂²×C₄×C₈₉	—	2	4	no	—
121	C₂²×C₄×C₈₉	—	2	4	no	—
122	C₂²×C₄×C₈₉	—	2	4	no	—
123	C₂²×C₄×C₈₉	—	2	4	no	—
124	C₂²×C₄×C₈₉	—	2	4	no	—
125	C₂²×C₄×C₈₉	—	2	4	no	—
126	C₂²×C₄×C₈₉	—	2	4	no	—
127	C₂²×C₄×C₈₉	—	2	4	no	—
128	C₂²×C₄×C₈₉	—	4	4	no	—
129	C₂²×C₄×C₈₉	—	4	4	no	—
130	C₂²×C₄×C₈₉	#41	1	4	yes	—
131	C₂²×C₄×C₈₉	#41	1	4	yes	—
132	C₂²×C₄×C₈₉	#41	1	4	yes	—
133	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
134	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
140	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
141	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
143	C₄⋊C₄×C₈₉	—	2	4	no	—
144	C₄⋊C₄×C₈₉	—	2	4	no	—
145	C₄⋊C₄×C₈₉	—	2	4	no	—
146	C₄⋊C₄×C₈₉	—	2	4	no	—
147	C₄⋊C₄×C₈₉	—	2	4	no	—
148	C₄⋊C₄×C₈₉	—	2	4	no	—
149	C₄⋊C₄×C₈₉	—	2	4	no	—
150	C₄⋊C₄×C₈₉	—	2	16	no	—
151	C₄⋊C₄×C₈₉	—	2	8	no	—
152	C₄⋊C₄×C₈₉	—	2	8	no	—
153	C₄⋊C₄×C₈₉	—	4	8	no	—
154	C₄⋊C₄×C₈₉	—	4	8	no	—
155	C₂²⋊C₄×C₈₉	—	2	4	no	—
156	C₂²⋊C₄×C₈₉	—	2	4	no	—
157	C₂²⋊C₄×C₈₉	—	2	4	no	—
158	C₂²⋊C₄×C₈₉	—	2	8	no	—
159	C₂²⋊C₄×C₈₉	—	2	8	no	—
160	C₂²⋊C₄×C₈₉	—	4	8	no	—
161	C₂²⋊C₄×C₈₉	—	4	8	no	—
162	C₄²×C₈₉	—	2	4	no	—
163	C₄²×C₈₉	—	2	2	no	—
164	C₄²×C₈₉	—	2	2	no	—
165	C₄²×C₈₉	—	2	4	no	—
166	C₄²×C₈₉	—	2	4	no	—
167	C₄²×C₈₉	—	2	4	no	—
168	C₄²×C₈₉	—	4	8	no	—
169	C₂³×C₈₉	—	2	2	no	—
170	C₂³×C₈₉	—	2	2	no	—
171	C₂³×C₈₉	—	2	2	no	—
172	C₂³×C₈₉	—	2	2	no	—
173	C₂³×C₈₉	—	2	2	no	—
174	C₂³×C₈₉	—	2	4	no	—
175	C₂³×C₈₉	—	2	4	no	—
176	C₂³×C₈₉	C₂×#41	1	2	yes	—
177	C₂³×C₈₉	C₂×#41	1	2	yes	—
178	C₂³×C₈₉	C₂×#41	1	2	yes	—
179	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
180	Q₈×C₈₉	—	4	4	no	—
181	D₄×C₈₉	—	4	8	no	—
182	D₄×C₈₉	—	4	4	no	—
183	C₂×C₄×C₈₉	—	2	16	no	—
184	C₂×C₄×C₈₉	—	2	2	no	—
185	C₂×C₄×C₈₉	—	2	2	no	—
186	C₂×C₄×C₈₉	—	2	2	no	—
187	C₂×C₄×C₈₉	—	2	2	no	—
188	C₂×C₄×C₈₉	—	2	4	no	—
189	C₂×C₄×C₈₉	—	2	4	no	—
190	C₂×C₄×C₈₉	—	2	4	no	—
191	C₂×C₄×C₈₉	—	2	4	no	—
192	C₂×C₄×C₈₉	—	2	4	no	—
193	C₂×C₄×C₈₉	—	2	2	no	—
194	C₂×C₄×C₈₉	—	2	2	no	—
195	C₂×C₄×C₈₉	—	2	2	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	8	no	—
201	C₂×C₄×C₈₉	—	2	4	no	—
202	C₂×C₄×C₈₉	—	2	4	no	—
203	C₂×C₄×C₈₉	—	2	4	no	—
204	C₂×C₄×C₈₉	—	4	8	no	—
205	C₂×C₄×C₈₉	—	8	4	no	—
206	C₂×C₄×C₈₉	—	8	4	no	—
207	C₂×C₄×C₈₉	#126	1	16	yes	complemented
208	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
209	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
210	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
211	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
212	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
213	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
214	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
215	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
216	C₂²×C₈₉	—	2	4	no	—
217	C₂²×C₈₉	—	2	2	no	—
218	C₂²×C₈₉	—	2	2	no	—
219	C₂²×C₈₉	—	2	4	no	—
220	C₂²×C₈₉	—	4	2	no	—
221	C₂²×C₈₉	—	4	4	no	—
222	C₂²×C₈₉	—	4	2	no	—
223	C₂²×C₈₉	—	4	2	no	—
224	C₂²×C₈₉	—	4	4	no	—
225	C₂²×C₈₉	C₂×#126	1	4	yes	—
226	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
227	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
228	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
229	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
230	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
231	C₄×C₈₉	—	2	4	no	—
232	C₄×C₈₉	—	2	4	no	—
233	C₄×C₈₉	—	4	2	no	—
234	C₄×C₈₉	—	4	4	no	—
235	C₄×C₈₉	—	4	4	no	—
236	C₄×C₈₉	—	4	4	no	—
237	C₄×C₈₉	—	4	4	no	—
238	C₄×C₈₉	—	4	4	no	—
239	C₄×C₈₉	C₂×#126	1	4	yes	—
240	C₄×C₈₉	C₂×#126	1	4	yes	—
241	#35557	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₂×C₈₉	—	2	4	no	—
243	C₂×C₈₉	—	8	2	no	—
244	C₂×C₈₉	C₂²×#126	1	1	yes	characteristic
245	C₂×C₈₉	#3492	1	2	yes	—
246	C₂×C₈₉	#3508	1	1	yes	characteristic
247	C₂×C₈₉	#3509	1	1	yes	characteristic
248	C₂×C₈₉	#3511	1	2	yes	—
249	#2512	C₂×C₈₉	1	4	yes	complemented
250	#2511	C₂×C₈₉	1	4	yes	complemented
251	#2497	C₂×C₈₉	1	4	yes	complemented
252	#2496	C₂×C₈₉	1	4	yes	complemented
253	#2481	C₂×C₈₉	1	8	yes	complemented
254	#2316	C₂×C₈₉	1	1	yes	characteristic, complemented
255	#2311	C₂×C₈₉	1	1	yes	characteristic
256	#2311	C₂×C₈₉	1	1	yes	characteristic
257	#2297	C₂×C₈₉	1	1	yes	characteristic
258	#2296	C₂×C₈₉	1	1	yes	characteristic, complemented
259	C₂×#384	C₂×C₈₉	1	1	yes	characteristic, complemented
260	#2274	C₂×C₈₉	1	1	yes	characteristic, complemented
261	C₈₉	#35557	1	1	yes	characteristic, direct product factor, Sylow
262	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
263	C₂×#126	C₂²×C₈₉	1	8	yes	—
264	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
265	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
266	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
269	C₂²×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
270	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
271	#400	C₂²×C₈₉	1	8	yes	—
272	#400	C₂²×C₈₉	1	8	yes	—
273	#397	C₂²×C₈₉	1	8	yes	—
274	#396	C₂²×C₈₉	1	8	yes	—
275	#391	C₂²×C₈₉	1	2	yes	—
276	#391	C₂²×C₈₉	1	2	yes	—
277	#391	C₂²×C₈₉	1	2	yes	—
278	#390	C₂²×C₈₉	1	2	yes	—
279	#390	C₂²×C₈₉	1	2	yes	—
280	#390	C₂²×C₈₉	1	2	yes	—
281	#389	C₂²×C₈₉	1	4	yes	—
282	#389	C₂²×C₈₉	1	4	yes	—
283	#389	C₂²×C₈₉	1	2	yes	—
284	#389	C₂²×C₈₉	1	2	yes	—
285	#388	C₂²×C₈₉	1	8	yes	—
286	#387	C₂²×C₈₉	1	8	yes	—
287	#387	C₂²×C₈₉	1	8	yes	—
288	#386	C₂²×C₈₉	1	4	yes	—
289	#386	C₂²×C₈₉	1	4	yes	—
290	#386	C₂²×C₈₉	1	4	yes	—
291	#385	C₂²×C₈₉	1	4	yes	—
292	#384	C₂²×C₈₉	1	2	yes	—
293	#384	C₂²×C₈₉	1	2	yes	—
294	#384	C₂²×C₈₉	1	4	yes	—
295	#380	C₂²×C₈₉	1	4	yes	—
296	#380	C₂²×C₈₉	1	4	yes	—
297	#380	C₂²×C₈₉	1	4	yes	—
298	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
299	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
300	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
301	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
302	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
303	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
304	C₂×#41	—	2	4	no	—
305	C₂×#41	—	2	4	no	—
306	C₂×#41	—	2	4	no	—
307	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
308	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
309	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
311	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
312	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
313	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
314	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
315	#126	—	4	16	no	—
316	#117	—	2	4	no	—
317	#117	—	2	4	no	—
318	#117	—	2	4	no	—
319	C₂×C₄⋊C₄	—	2	4	no	—
320	C₂×C₄⋊C₄	—	2	4	no	—
321	C₂×C₄⋊C₄	—	4	8	no	—
322	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
323	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
326	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
328	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
331	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
332	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
333	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
334	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
335	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
336	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
340	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
341	C₂×C₄²	—	2	4	no	—
342	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
343	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
344	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
345	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
346	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
347	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
348	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
349	#95	C₂³×C₈₉	1	8	yes	—
350	#95	C₂³×C₈₉	1	4	yes	—
351	#95	C₂³×C₈₉	1	4	yes	—
352	#95	C₂³×C₈₉	1	4	yes	—
353	#95	C₂³×C₈₉	1	4	yes	—
354	#95	C₂³×C₈₉	1	8	yes	—
355	#95	C₂³×C₈₉	1	8	yes	—
356	#95	C₂³×C₈₉	1	8	yes	—
357	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
358	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
359	#41	—	4	16	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	4	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	4	no	—
374	C₂²×C₄	—	2	4	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	4	no	—
377	C₂²×C₄	—	4	4	no	—
378	C₂²×C₄	—	4	4	no	—
379	C₂²×C₄	#41×C₈₉	1	4	yes	—
380	C₂²×C₄	#41×C₈₉	1	4	yes	—
381	C₂²×C₄	#41×C₈₉	1	4	yes	—
382	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
383	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
384	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
385	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
386	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
387	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
388	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
389	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
390	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
391	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	4	no	—
398	C₄⋊C₄	—	2	4	no	—
399	C₄⋊C₄	—	2	16	no	—
400	C₄⋊C₄	—	2	8	no	—
401	C₄⋊C₄	—	2	8	no	—
402	C₄⋊C₄	—	4	8	no	—
403	C₄⋊C₄	—	4	8	no	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	2	4	no	—
406	C₂²⋊C₄	—	2	4	no	—
407	C₂²⋊C₄	—	2	8	no	—
408	C₂²⋊C₄	—	2	8	no	—
409	C₂²⋊C₄	—	4	8	no	—
410	C₂²⋊C₄	—	4	8	no	—
411	C₄²	—	2	4	no	—
412	C₄²	—	2	2	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	4	no	—
415	C₄²	—	2	4	no	—
416	C₄²	—	2	4	no	—
417	C₄²	—	4	8	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	4	no	—
424	C₂³	—	2	4	no	—
425	C₂³	C₂×#41×C₈₉	1	2	yes	—
426	C₂³	C₂×#41×C₈₉	1	2	yes	—
427	C₂³	C₂×#41×C₈₉	1	2	yes	—
428	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
429	Q₈	—	4	4	no	—
430	D₄	—	4	8	no	—
431	D₄	—	4	4	no	—
432	C₂×C₄	—	2	16	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	8	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	—	4	8	no	—
454	C₂×C₄	—	8	4	no	—
455	C₂×C₄	—	8	4	no	—
456	C₂×C₄	#126×C₈₉	1	16	yes	complemented
457	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
458	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
459	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
460	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
461	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
462	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
463	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
464	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
465	C₂²	—	2	4	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	2	no	—
468	C₂²	—	2	4	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	4	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	4	no	—
474	C₂²	C₂×#126×C₈₉	1	4	yes	—
475	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
476	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
477	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
478	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
479	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
480	C₄	—	2	4	no	—
481	C₄	—	2	4	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	4	no	—
484	C₄	—	4	4	no	—
485	C₄	—	4	4	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	4	no	—
488	C₄	C₂×#126×C₈₉	1	4	yes	—
489	C₄	C₂×#126×C₈₉	1	4	yes	—
490	C₂	—	2	4	no	—
491	C₂	—	8	2	no	—
492	C₂	C₂²×#126×C₈₉	1	1	yes	characteristic
493	C₂	C₈₉×#3492	1	2	yes	—
494	C₂	C₈₉×#3508	1	1	yes	characteristic
495	C₂	C₈₉×#3509	1	1	yes	characteristic
496	C₂	C₈₉×#3511	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×#41×C₈₉	C₂²
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. C₈₉×#2512	C₂	semidirect
2. C₈₉×#2511	C₂	semidirect
3. C₈₉×#2497	C₂	semidirect
4. C₈₉×#2496	C₂	semidirect
5. C₈₉×#2481	C₂	semidirect
6. C₈₉×#2316	C₂	semidirect
10. C₈₉×#2296	C₂	semidirect
11. C₂×#384×C₈₉	C₂	semidirect
12. C₈₉×#2274	C₂	semidirect
207. C₂×C₄×C₈₉	#126	semidirect
241. #35557	C₈₉	direct (N × H)
249. #2512	C₂×C₈₉	semidirect
250. #2511	C₂×C₈₉	semidirect
251. #2497	C₂×C₈₉	semidirect
252. #2496	C₂×C₈₉	semidirect
253. #2481	C₂×C₈₉	semidirect
254. #2316	C₂×C₈₉	semidirect
258. #2296	C₂×C₈₉	semidirect
259. C₂×#384	C₂×C₈₉	semidirect
260. #2274	C₂×C₈₉	semidirect
261. C₈₉	#35557	direct (N × H)
456. C₂×C₄	#126×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2512	2
C₈₉×#2511	2
C₈₉×#2497	2
C₈₉×#2496	2
C₈₉×#2481	2
C₈₉×#2316	2
C₈₉×#2311	2
C₈₉×#2297	2
C₈₉×#2296	2
C₂×#384×C₈₉	2
C₈₉×#2274	2
#35557	89

Subgroups — C89×#35557 #36413405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35557 #36413405