Subgroups — C₈₉×#2685 #26017159

Order 11392.

666 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#126×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#120×C₈₉	C₂	1	1	yes	maximal, characteristic
3	#399×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#396×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#394×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	#394×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	#394×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#394×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	#390×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#390×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	#388×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#388×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	#388×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#379×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	#379×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂⁵×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic
18	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic
19	C₂²×D₄×C₈₉	C₂²	1	1	yes	characteristic
20	#126×C₈₉	—	2	4	no	—
21	#120×C₈₉	—	2	4	no	—
22	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
23	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
25	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
26	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
46	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
47	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic, complemented
48	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic, complemented
49	#95×C₈₉	C₂²	1	1	yes	characteristic, complemented
50	#95×C₈₉	C₂²	1	1	yes	characteristic, complemented
51	#95×C₈₉	C₂²	1	1	yes	characteristic, complemented
52	#95×C₈₉	C₂²	1	1	yes	characteristic, complemented
53	C₂⁴×C₈₉	—	2	2	no	—
54	C₂⁴×C₈₉	—	2	2	no	—
55	C₂⁴×C₈₉	—	2	2	no	—
56	C₂⁴×C₈₉	—	4	1	no	—
57	C₂⁴×C₈₉	—	4	1	no	—
58	C₂⁴×C₈₉	—	4	1	no	—
59	C₂⁴×C₈₉	—	4	1	no	—
60	C₂⁴×C₈₉	C₂³	1	1	yes	characteristic
61	C₂⁴×C₈₉	C₂³	1	1	yes	characteristic
62	C₂⁴×C₈₉	C₂³	1	1	yes	characteristic
63	C₂⁴×C₈₉	C₂³	1	1	yes	characteristic
64	C₂×D₄×C₈₉	—	2	2	no	—
65	C₂×D₄×C₈₉	—	2	2	no	—
66	C₂×D₄×C₈₉	—	2	2	no	—
67	C₂×D₄×C₈₉	—	2	2	no	—
68	C₂×D₄×C₈₉	—	2	2	no	—
69	C₂×D₄×C₈₉	—	4	1	no	—
70	C₂×D₄×C₈₉	—	4	1	no	—
71	C₂×D₄×C₈₉	—	4	1	no	—
72	C₂×D₄×C₈₉	—	4	1	no	—
73	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
75	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
76	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
77	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
80	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
81	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
82	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
83	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
84	C₄⋊C₄×C₈₉	—	2	2	no	—
85	C₄⋊C₄×C₈₉	—	2	2	no	—
86	C₄⋊C₄×C₈₉	—	2	2	no	—
87	C₄⋊C₄×C₈₉	—	4	1	no	—
88	C₄⋊C₄×C₈₉	—	4	1	no	—
89	C₄⋊C₄×C₈₉	—	4	1	no	—
90	C₂²⋊C₄×C₈₉	—	2	2	no	—
91	C₂²⋊C₄×C₈₉	—	2	2	no	—
92	C₂²⋊C₄×C₈₉	—	2	2	no	—
93	C₂²⋊C₄×C₈₉	—	2	2	no	—
94	C₂²⋊C₄×C₈₉	—	2	2	no	—
95	C₂²⋊C₄×C₈₉	—	2	2	no	—
96	C₂²⋊C₄×C₈₉	—	4	1	no	—
97	C₂²⋊C₄×C₈₉	—	4	1	no	—
98	C₂²⋊C₄×C₈₉	—	4	1	no	—
99	C₂²⋊C₄×C₈₉	—	4	1	no	—
100	C₂²⋊C₄×C₈₉	—	4	1	no	—
101	C₂²⋊C₄×C₈₉	—	4	1	no	—
102	C₂²⋊C₄×C₈₉	—	4	1	no	—
103	C₂²⋊C₄×C₈₉	—	4	1	no	—
104	C₂²⋊C₄×C₈₉	—	4	1	no	—
105	C₂²⋊C₄×C₈₉	—	4	1	no	—
106	C₂²⋊C₄×C₈₉	—	4	1	no	—
107	C₂²⋊C₄×C₈₉	—	4	1	no	—
108	C₂²⋊C₄×C₈₉	D₄	1	4	yes	—
109	C₄²×C₈₉	—	2	2	no	—
110	C₄²×C₈₉	—	4	1	no	—
111	C₂³×C₈₉	—	2	1	no	—
112	C₂³×C₈₉	—	2	1	no	—
113	C₂³×C₈₉	—	2	1	no	—
114	C₂³×C₈₉	—	2	1	no	—
115	C₂³×C₈₉	—	2	1	no	—
116	C₂³×C₈₉	—	2	1	no	—
117	C₂³×C₈₉	—	2	1	no	—
118	C₂³×C₈₉	—	2	1	no	—
119	C₂³×C₈₉	—	2	1	no	—
120	C₂³×C₈₉	—	2	1	no	—
121	C₂³×C₈₉	—	2	1	no	—
122	C₂³×C₈₉	—	2	1	no	—
123	C₂³×C₈₉	—	2	1	no	—
124	C₂³×C₈₉	—	2	1	no	—
125	C₂³×C₈₉	—	2	1	no	—
126	C₂³×C₈₉	—	2	1	no	—
127	C₂³×C₈₉	—	2	1	no	—
128	C₂³×C₈₉	—	2	1	no	—
129	C₂³×C₈₉	—	2	1	no	—
130	C₂³×C₈₉	—	2	1	no	—
131	C₂³×C₈₉	—	2	1	no	—
132	C₂³×C₈₉	—	2	1	no	—
133	C₂³×C₈₉	—	2	1	no	—
134	C₂³×C₈₉	—	2	1	no	—
135	C₂³×C₈₉	—	2	1	no	—
136	C₂³×C₈₉	—	4	4	no	—
137	C₂³×C₈₉	—	4	4	no	—
138	C₂³×C₈₉	—	4	4	no	—
139	C₂³×C₈₉	—	4	4	no	—
140	C₂³×C₈₉	—	4	4	no	—
141	C₂³×C₈₉	—	4	4	no	—
142	C₂³×C₈₉	—	4	4	no	—
143	C₂³×C₈₉	C₂×D₄	1	2	yes	—
144	C₂³×C₈₉	#41	1	2	yes	—
145	C₂³×C₈₉	#41	1	2	yes	—
146	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
147	D₄×C₈₉	—	4	4	no	—
148	D₄×C₈₉	—	4	4	no	—
149	D₄×C₈₉	—	4	4	no	—
150	C₂×C₄×C₈₉	—	2	1	no	—
151	C₂×C₄×C₈₉	—	2	1	no	—
152	C₂×C₄×C₈₉	—	2	1	no	—
153	C₂×C₄×C₈₉	—	2	1	no	—
154	C₂×C₄×C₈₉	—	2	1	no	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	2	1	no	—
157	C₂×C₄×C₈₉	—	2	1	no	—
158	C₂×C₄×C₈₉	—	2	1	no	—
159	C₂×C₄×C₈₉	—	2	1	no	—
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	—	2	1	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	1	no	—
164	C₂×C₄×C₈₉	—	2	1	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	2	1	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	2	1	no	—
170	C₂×C₄×C₈₉	—	2	1	no	—
171	C₂×C₄×C₈₉	—	2	1	no	—
172	C₂×C₄×C₈₉	—	2	1	no	—
173	C₂×C₄×C₈₉	—	2	1	no	—
174	C₂×C₄×C₈₉	—	2	1	no	—
175	C₂×C₄×C₈₉	—	2	1	no	—
176	C₂×C₄×C₈₉	—	2	1	no	—
177	C₂×C₄×C₈₉	—	2	1	no	—
178	C₂×C₄×C₈₉	—	2	1	no	—
179	C₂×C₄×C₈₉	—	2	1	no	—
180	C₂×C₄×C₈₉	—	2	1	no	—
181	C₂×C₄×C₈₉	C₂×D₄	1	2	yes	—
182	C₂×C₄×C₈₉	C₂×D₄	1	2	yes	—
183	C₂²×C₈₉	—	2	2	no	—
184	C₂²×C₈₉	—	2	2	no	—
185	C₂²×C₈₉	—	2	2	no	—
186	C₂²×C₈₉	—	2	2	no	—
187	C₂²×C₈₉	—	2	2	no	—
188	C₂²×C₈₉	—	2	2	no	—
189	C₂²×C₈₉	—	2	2	no	—
190	C₂²×C₈₉	—	2	2	no	—
191	C₂²×C₈₉	—	2	2	no	—
192	C₂²×C₈₉	—	4	16	no	—
193	C₂²×C₈₉	—	4	1	no	—
194	C₂²×C₈₉	—	4	1	no	—
195	C₂²×C₈₉	—	4	1	no	—
196	C₂²×C₈₉	—	4	1	no	—
197	C₂²×C₈₉	—	4	1	no	—
198	C₂²×C₈₉	—	4	1	no	—
199	C₂²×C₈₉	—	4	1	no	—
200	C₂²×C₈₉	—	4	1	no	—
201	C₂²×C₈₉	—	4	1	no	—
202	C₂²×C₈₉	—	4	1	no	—
203	C₂²×C₈₉	—	4	1	no	—
204	C₂²×C₈₉	—	4	1	no	—
205	C₂²×C₈₉	—	4	1	no	—
206	C₂²×C₈₉	—	4	1	no	—
207	C₂²×C₈₉	—	4	1	no	—
208	C₂²×C₈₉	—	4	1	no	—
209	C₂²×C₈₉	—	4	1	no	—
210	C₂²×C₈₉	—	4	1	no	—
211	C₂²×C₈₉	—	4	1	no	—
212	C₂²×C₈₉	C₂²×D₄	1	1	yes	characteristic
213	C₂²×C₈₉	C₂×#41	1	1	yes	characteristic
214	C₂²×C₈₉	C₂×#41	1	1	yes	characteristic
215	C₂²×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂²×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
217	C₂²×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
218	C₂²×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
219	C₄×C₈₉	—	2	2	no	—
220	C₄×C₈₉	—	2	2	no	—
221	C₄×C₈₉	—	4	1	no	—
222	C₄×C₈₉	—	4	1	no	—
223	C₄×C₈₉	—	4	1	no	—
224	C₄×C₈₉	—	4	1	no	—
225	C₄×C₈₉	—	4	1	no	—
226	C₄×C₈₉	—	4	1	no	—
227	C₄×C₈₉	—	4	1	no	—
228	C₄×C₈₉	—	4	1	no	—
229	C₄×C₈₉	—	4	1	no	—
230	C₂×C₈₉	—	4	2	no	—
231	C₂×C₈₉	—	4	2	no	—
232	C₂×C₈₉	—	4	2	no	—
233	C₂×C₈₉	—	8	1	no	—
234	C₂×C₈₉	#535	1	1	yes	characteristic
235	C₂×C₈₉	#538	1	1	yes	characteristic
236	C₂×C₈₉	#538	1	1	yes	characteristic
237	C₂×C₈₉	#546	1	1	yes	characteristic
238	C₂×C₈₉	#546	1	1	yes	characteristic
239	C₂×C₈₉	#551	1	1	yes	characteristic
240	C₂×C₈₉	#560	1	1	yes	characteristic
241	#2685	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
242	C₈₉	#2685	1	1	yes	characteristic, direct product factor, Sylow
243	C₂×#126	C₂×C₈₉	1	1	yes	characteristic, complemented
244	C₂×#120	C₂×C₈₉	1	1	yes	characteristic
245	#399	C₂×C₈₉	1	1	yes	characteristic, complemented
246	#396	C₂×C₈₉	1	1	yes	characteristic, complemented
247	#394	C₂×C₈₉	1	1	yes	characteristic, complemented
248	#394	C₂×C₈₉	1	1	yes	characteristic, complemented
249	#394	C₂×C₈₉	1	1	yes	characteristic, complemented
250	#394	C₂×C₈₉	1	1	yes	characteristic, complemented
251	#390	C₂×C₈₉	1	1	yes	characteristic, complemented
252	#390	C₂×C₈₉	1	1	yes	characteristic, complemented
253	#388	C₂×C₈₉	1	1	yes	characteristic, complemented
254	#388	C₂×C₈₉	1	1	yes	characteristic, complemented
255	#388	C₂×C₈₉	1	1	yes	characteristic, complemented
256	#379	C₂×C₈₉	1	1	yes	characteristic, complemented
257	#379	C₂×C₈₉	1	1	yes	characteristic, complemented
258	C₂⁵	C₂²×C₈₉	1	1	yes	characteristic
259	C₂²×D₄	C₂²×C₈₉	1	1	yes	characteristic
260	C₂²×D₄	C₂²×C₈₉	1	1	yes	characteristic
261	C₂²×D₄	C₂²×C₈₉	1	1	yes	characteristic
262	#126	—	2	4	no	—
263	#120	—	2	4	no	—
264	C₂×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
265	C₂×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
266	C₂×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
267	C₂×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
268	C₂×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
269	C₂×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
270	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
271	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
276	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
277	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
278	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
279	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
280	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
281	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
282	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
283	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
284	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
285	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
286	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
287	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
288	C₂×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
289	C₂×C₄²	C₂²×C₈₉	1	1	yes	characteristic, complemented
290	C₂×C₄²	C₂²×C₈₉	1	1	yes	characteristic, complemented
291	#95	C₂²×C₈₉	1	1	yes	characteristic, complemented
292	#95	C₂²×C₈₉	1	1	yes	characteristic, complemented
293	#95	C₂²×C₈₉	1	1	yes	characteristic, complemented
294	#95	C₂²×C₈₉	1	1	yes	characteristic, complemented
295	C₂⁴	—	2	2	no	—
296	C₂⁴	—	2	2	no	—
297	C₂⁴	—	2	2	no	—
298	C₂⁴	—	4	1	no	—
299	C₂⁴	—	4	1	no	—
300	C₂⁴	—	4	1	no	—
301	C₂⁴	—	4	1	no	—
302	C₂⁴	C₂³×C₈₉	1	1	yes	characteristic
303	C₂⁴	C₂³×C₈₉	1	1	yes	characteristic
304	C₂⁴	C₂³×C₈₉	1	1	yes	characteristic
305	C₂⁴	C₂³×C₈₉	1	1	yes	characteristic
306	C₂×D₄	—	2	2	no	—
307	C₂×D₄	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	2	no	—
310	C₂×D₄	—	2	2	no	—
311	C₂×D₄	—	4	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	4	1	no	—
314	C₂×D₄	—	4	1	no	—
315	C₂²×C₄	C₂³×C₈₉	1	1	yes	characteristic
316	C₂²×C₄	C₂³×C₈₉	1	1	yes	characteristic
317	C₂²×C₄	C₂³×C₈₉	1	1	yes	characteristic
318	C₂²×C₄	C₂³×C₈₉	1	1	yes	characteristic
319	C₂²×C₄	C₂³×C₈₉	1	1	yes	characteristic
320	C₂²×C₄	C₂³×C₈₉	1	1	yes	characteristic
321	C₂²×C₄	C₂³×C₈₉	1	1	yes	characteristic
322	C₂²×C₄	C₂³×C₈₉	1	1	yes	characteristic
323	C₂²×C₄	C₂³×C₈₉	1	1	yes	characteristic
324	C₂²×C₄	C₂³×C₈₉	1	1	yes	characteristic
325	C₂²×C₄	C₂³×C₈₉	1	1	yes	characteristic
326	C₄⋊C₄	—	2	2	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	4	1	no	—
330	C₄⋊C₄	—	4	1	no	—
331	C₄⋊C₄	—	4	1	no	—
332	C₂²⋊C₄	—	2	2	no	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	4	1	no	—
339	C₂²⋊C₄	—	4	1	no	—
340	C₂²⋊C₄	—	4	1	no	—
341	C₂²⋊C₄	—	4	1	no	—
342	C₂²⋊C₄	—	4	1	no	—
343	C₂²⋊C₄	—	4	1	no	—
344	C₂²⋊C₄	—	4	1	no	—
345	C₂²⋊C₄	—	4	1	no	—
346	C₂²⋊C₄	—	4	1	no	—
347	C₂²⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	4	1	no	—
349	C₂²⋊C₄	—	4	1	no	—
350	C₂²⋊C₄	D₄×C₈₉	1	4	yes	—
351	C₄²	—	2	2	no	—
352	C₄²	—	4	1	no	—
353	C₂³	—	2	1	no	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	1	no	—
361	C₂³	—	2	1	no	—
362	C₂³	—	2	1	no	—
363	C₂³	—	2	1	no	—
364	C₂³	—	2	1	no	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	2	1	no	—
374	C₂³	—	2	1	no	—
375	C₂³	—	2	1	no	—
376	C₂³	—	2	1	no	—
377	C₂³	—	2	1	no	—
378	C₂³	—	4	4	no	—
379	C₂³	—	4	4	no	—
380	C₂³	—	4	4	no	—
381	C₂³	—	4	4	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	4	4	no	—
384	C₂³	—	4	4	no	—
385	C₂³	C₂×D₄×C₈₉	1	2	yes	—
386	C₂³	#41×C₈₉	1	2	yes	—
387	C₂³	#41×C₈₉	1	2	yes	—
388	C₂³	C₂⁴×C₈₉	1	1	yes	characteristic
389	D₄	—	4	4	no	—
390	D₄	—	4	4	no	—
391	D₄	—	4	4	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	2	1	no	—
409	C₂×C₄	—	2	1	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	1	no	—
414	C₂×C₄	—	2	1	no	—
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	C₂×D₄×C₈₉	1	2	yes	—
424	C₂×C₄	C₂×D₄×C₈₉	1	2	yes	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	2	2	no	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	2	no	—
432	C₂²	—	2	2	no	—
433	C₂²	—	2	2	no	—
434	C₂²	—	4	16	no	—
435	C₂²	—	4	1	no	—
436	C₂²	—	4	1	no	—
437	C₂²	—	4	1	no	—
438	C₂²	—	4	1	no	—
439	C₂²	—	4	1	no	—
440	C₂²	—	4	1	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	—	4	1	no	—
444	C₂²	—	4	1	no	—
445	C₂²	—	4	1	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	1	no	—
449	C₂²	—	4	1	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	1	no	—
453	C₂²	—	4	1	no	—
454	C₂²	C₂²×D₄×C₈₉	1	1	yes	characteristic
455	C₂²	C₂×#41×C₈₉	1	1	yes	characteristic
456	C₂²	C₂×#41×C₈₉	1	1	yes	characteristic
457	C₂²	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
458	C₂²	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
459	C₂²	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
460	C₂²	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	4	1	no	—
464	C₄	—	4	1	no	—
465	C₄	—	4	1	no	—
466	C₄	—	4	1	no	—
467	C₄	—	4	1	no	—
468	C₄	—	4	1	no	—
469	C₄	—	4	1	no	—
470	C₄	—	4	1	no	—
471	C₄	—	4	1	no	—
472	C₂	—	4	2	no	—
473	C₂	—	4	2	no	—
474	C₂	—	4	2	no	—
475	C₂	—	8	1	no	—
476	C₂	#535×C₈₉	1	1	yes	characteristic
477	C₂	#538×C₈₉	1	1	yes	characteristic
478	C₂	#538×C₈₉	1	1	yes	characteristic
479	C₂	#546×C₈₉	1	1	yes	characteristic
480	C₂	#546×C₈₉	1	1	yes	characteristic
481	C₂	#551×C₈₉	1	1	yes	characteristic
482	C₂	#560×C₈₉	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₈₉
prime radical	C₂×#120×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×#126×C₈₉	C₂	semidirect
3. #399×C₈₉	C₂	semidirect
4. #396×C₈₉	C₂	semidirect
5. #394×C₈₉	C₂	semidirect
6. #394×C₈₉	C₂	semidirect
7. #394×C₈₉	C₂	semidirect
8. #394×C₈₉	C₂	semidirect
9. #390×C₈₉	C₂	semidirect
10. #390×C₈₉	C₂	semidirect
11. #388×C₈₉	C₂	semidirect
12. #388×C₈₉	C₂	semidirect
13. #388×C₈₉	C₂	semidirect
14. #379×C₈₉	C₂	semidirect
15. #379×C₈₉	C₂	semidirect
22. C₂×C₄⋊C₄×C₈₉	C₂²	semidirect
23. C₂×C₄⋊C₄×C₈₉	C₂²	semidirect
24. C₂×C₄⋊C₄×C₈₉	C₂²	semidirect
25. C₂×C₄⋊C₄×C₈₉	C₂²	semidirect
26. C₂×C₄⋊C₄×C₈₉	C₂²	semidirect
27. C₂×C₄⋊C₄×C₈₉	C₂²	semidirect
43. C₂×C₂²⋊C₄×C₈₉	C₂²	semidirect
44. C₂×C₂²⋊C₄×C₈₉	C₂²	semidirect
45. C₂×C₂²⋊C₄×C₈₉	C₂²	semidirect
46. C₂×C₂²⋊C₄×C₈₉	C₂²	semidirect
47. C₂×C₄²×C₈₉	C₂²	semidirect
48. C₂×C₄²×C₈₉	C₂²	semidirect
49. #95×C₈₉	C₂²	semidirect
50. #95×C₈₉	C₂²	semidirect
51. #95×C₈₉	C₂²	semidirect
52. #95×C₈₉	C₂²	semidirect
241. #2685	C₈₉	direct (N × H)
242. C₈₉	#2685	direct (N × H)
243. C₂×#126	C₂×C₈₉	semidirect
245. #399	C₂×C₈₉	semidirect
246. #396	C₂×C₈₉	semidirect
247. #394	C₂×C₈₉	semidirect
248. #394	C₂×C₈₉	semidirect
249. #394	C₂×C₈₉	semidirect
250. #394	C₂×C₈₉	semidirect
251. #390	C₂×C₈₉	semidirect
252. #390	C₂×C₈₉	semidirect
253. #388	C₂×C₈₉	semidirect
254. #388	C₂×C₈₉	semidirect
255. #388	C₂×C₈₉	semidirect
256. #379	C₂×C₈₉	semidirect
257. #379	C₂×C₈₉	semidirect
264. C₂×C₄⋊C₄	C₂²×C₈₉	semidirect
265. C₂×C₄⋊C₄	C₂²×C₈₉	semidirect
266. C₂×C₄⋊C₄	C₂²×C₈₉	semidirect
267. C₂×C₄⋊C₄	C₂²×C₈₉	semidirect
268. C₂×C₄⋊C₄	C₂²×C₈₉	semidirect
269. C₂×C₄⋊C₄	C₂²×C₈₉	semidirect
285. C₂×C₂²⋊C₄	C₂²×C₈₉	semidirect
286. C₂×C₂²⋊C₄	C₂²×C₈₉	semidirect
287. C₂×C₂²⋊C₄	C₂²×C₈₉	semidirect
288. C₂×C₂²⋊C₄	C₂²×C₈₉	semidirect
289. C₂×C₄²	C₂²×C₈₉	semidirect
290. C₂×C₄²	C₂²×C₈₉	semidirect
291. #95	C₂²×C₈₉	semidirect
292. #95	C₂²×C₈₉	semidirect
293. #95	C₂²×C₈₉	semidirect
294. #95	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#126×C₈₉	2
C₂×#120×C₈₉	2
#399×C₈₉	2
#396×C₈₉	2
#394×C₈₉	2
#390×C₈₉	2
#388×C₈₉	2
#379×C₈₉	2
#2685	89

Subgroups — C89×#2685 #26017159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#2685 #26017159