Subgroups — C₂×C₈₉×#2664 #36412439

Order 22784.

2354 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#126×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#125×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2664	C₂	1	16	yes	maximal, direct product factor
4	C₂×#400×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#399×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂×#398×C₈₉	C₂	1	2	yes	maximal, complemented
7	C₂×#398×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#397×C₈₉	C₂	1	1	yes	maximal, characteristic
9	C₂×#396×C₈₉	C₂	1	2	yes	maximal
10	C₂×#389×C₈₉	C₂	1	2	yes	maximal, complemented
11	C₂×#388×C₈₉	C₂	1	2	yes	maximal
12	C₂×C₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#126×C₈₉	—	2	8	no	—
14	C₂×#126×C₈₉	C₂²	1	8	yes	—
15	C₂×#125×C₈₉	—	2	8	no	—
16	C₂×#125×C₈₉	C₂²	1	8	yes	complemented
17	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
18	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
19	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
25	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
26	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
30	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
31	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
32	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
33	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
34	#400×C₈₉	C₂²	1	8	yes	complemented
35	#399×C₈₉	C₂²	1	8	yes	—
36	#398×C₈₉	C₂²	1	8	yes	complemented
37	#398×C₈₉	C₂²	1	16	yes	complemented
38	#397×C₈₉	C₂²	1	8	yes	—
39	#396×C₈₉	C₂²	1	16	yes	—
40	#389×C₈₉	C₂²	1	16	yes	complemented
41	#388×C₈₉	C₂²	1	16	yes	—
42	C₄×C₄⋊C₄×C₈₉	C₂²	1	8	yes	complemented
43	C₂×#95×C₈₉	C₂²	1	2	yes	—
44	C₂×#95×C₈₉	C₂²	1	2	yes	—
45	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×#95×C₈₉	C₂²	1	2	yes	—
47	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
48	C₂×#95×C₈₉	C₂²	1	2	yes	—
49	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
51	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
53	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
55	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
57	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
58	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
59	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
60	#126×C₈₉	—	2	32	no	—
61	#125×C₈₉	—	2	32	no	—
62	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
63	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
64	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
65	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
66	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
67	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
68	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
69	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
70	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
71	C₂×C₄⋊C₄×C₈₉	—	4	4	no	—
72	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
73	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
74	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
76	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	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	4	yes	—
80	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
82	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
83	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
84	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
86	C₂×C₂²⋊C₄×C₈₉	—	4	4	no	—
87	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
88	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
89	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
90	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
91	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
92	C₂×C₄²×C₈₉	—	4	4	no	—
93	C₂×C₄²×C₈₉	D₄	1	8	yes	—
94	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
95	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
96	#95×C₈₉	C₂³	1	4	yes	—
97	#95×C₈₉	C₂³	1	4	yes	—
98	#95×C₈₉	C₂³	1	8	yes	—
99	#95×C₈₉	C₂³	1	8	yes	—
100	#95×C₈₉	C₂³	1	8	yes	—
101	#95×C₈₉	C₂³	1	8	yes	—
102	C₂⁴×C₈₉	—	2	2	no	—
103	C₂⁴×C₈₉	—	2	4	no	—
104	C₂⁴×C₈₉	—	2	2	no	—
105	C₂⁴×C₈₉	—	2	4	no	—
106	C₂⁴×C₈₉	—	2	2	no	—
107	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
108	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
109	C₂²×C₄×C₈₉	—	2	4	no	—
110	C₂²×C₄×C₈₉	—	2	2	no	—
111	C₂²×C₄×C₈₉	—	2	4	no	—
112	C₂²×C₄×C₈₉	—	2	4	no	—
113	C₂²×C₄×C₈₉	—	2	2	no	—
114	C₂²×C₄×C₈₉	—	2	4	no	—
115	C₂²×C₄×C₈₉	—	2	2	no	—
116	C₂²×C₄×C₈₉	—	2	2	no	—
117	C₂²×C₄×C₈₉	—	2	2	no	—
118	C₂²×C₄×C₈₉	—	2	4	no	—
119	C₂²×C₄×C₈₉	—	2	4	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	2	no	—
127	C₂²×C₄×C₈₉	—	2	4	no	—
128	C₂²×C₄×C₈₉	—	2	2	no	—
129	C₂²×C₄×C₈₉	—	2	4	no	—
130	C₂²×C₄×C₈₉	—	2	4	no	—
131	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₈₉	#41	1	8	yes	—
135	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
137	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
138	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
139	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
141	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
142	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
144	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
145	C₄⋊C₄×C₈₉	—	2	16	no	—
146	C₄⋊C₄×C₈₉	—	2	16	no	—
147	C₄⋊C₄×C₈₉	—	2	8	no	—
148	C₄⋊C₄×C₈₉	—	2	8	no	—
149	C₄⋊C₄×C₈₉	—	2	8	no	—
150	C₄⋊C₄×C₈₉	—	2	8	no	—
151	C₄⋊C₄×C₈₉	—	2	8	no	—
152	C₄⋊C₄×C₈₉	—	2	16	no	—
153	C₄⋊C₄×C₈₉	—	2	16	no	—
154	C₄⋊C₄×C₈₉	—	4	8	no	—
155	C₂²⋊C₄×C₈₉	—	2	8	no	—
156	C₂²⋊C₄×C₈₉	—	2	8	no	—
157	C₂²⋊C₄×C₈₉	—	2	8	no	—
158	C₂²⋊C₄×C₈₉	—	2	16	no	—
159	C₂²⋊C₄×C₈₉	—	4	8	no	—
160	C₄²×C₈₉	—	4	8	no	—
161	C₄²×C₈₉	C₂×D₄	1	16	yes	—
162	C₂³×C₈₉	—	2	2	no	—
163	C₂³×C₈₉	—	2	4	no	—
164	C₂³×C₈₉	—	2	2	no	—
165	C₂³×C₈₉	—	2	4	no	—
166	C₂³×C₈₉	—	2	2	no	—
167	C₂³×C₈₉	—	4	4	no	—
168	C₂³×C₈₉	—	4	4	no	—
169	C₂³×C₈₉	—	4	4	no	—
170	C₂³×C₈₉	—	4	8	no	—
171	C₂³×C₈₉	—	4	8	no	—
172	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
173	C₂³×C₈₉	C₂×#41	1	4	yes	—
174	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
175	C₂³×C₈₉	2₋¹⁺⁴	1	4	yes	—
176	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
177	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
178	C₂×C₄×C₈₉	—	2	8	no	—
179	C₂×C₄×C₈₉	—	2	8	no	—
180	C₂×C₄×C₈₉	—	2	8	no	—
181	C₂×C₄×C₈₉	—	2	16	no	—
182	C₂×C₄×C₈₉	—	2	4	no	—
183	C₂×C₄×C₈₉	—	2	2	no	—
184	C₂×C₄×C₈₉	—	2	4	no	—
185	C₂×C₄×C₈₉	—	2	4	no	—
186	C₂×C₄×C₈₉	—	2	2	no	—
187	C₂×C₄×C₈₉	—	2	4	no	—
188	C₂×C₄×C₈₉	—	2	2	no	—
189	C₂×C₄×C₈₉	—	2	2	no	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	—	2	4	no	—
192	C₂×C₄×C₈₉	—	2	4	no	—
193	C₂×C₄×C₈₉	—	2	4	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	4	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	4	no	—
204	C₂×C₄×C₈₉	—	4	4	no	—
205	C₂×C₄×C₈₉	—	4	8	no	—
206	C₂×C₄×C₈₉	—	4	4	no	—
207	C₂×C₄×C₈₉	—	4	4	no	—
208	C₂×C₄×C₈₉	—	4	8	no	—
209	C₂×C₄×C₈₉	—	4	8	no	—
210	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
211	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
212	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
213	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
214	C₂²×C₈₉	—	4	2	no	—
215	C₂²×C₈₉	—	4	2	no	—
216	C₂²×C₈₉	—	4	2	no	—
217	C₂²×C₈₉	—	4	4	no	—
218	C₂²×C₈₉	—	4	4	no	—
219	C₂²×C₈₉	—	8	8	no	—
220	C₂²×C₈₉	#532	1	4	yes	—
221	C₂²×C₈₉	#536	1	4	yes	—
222	C₂²×C₈₉	#537	1	4	yes	—
223	C₂²×C₈₉	#539	1	8	yes	—
224	C₂²×C₈₉	#541	1	8	yes	—
225	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
226	C₂²×C₈₉	C₂²×#41	1	2	yes	—
227	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
228	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
229	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
230	C₄×C₈₉	—	2	4	no	—
231	C₄×C₈₉	—	2	4	no	—
232	C₄×C₈₉	—	2	4	no	—
233	C₄×C₈₉	—	2	8	no	—
234	C₄×C₈₉	—	4	2	no	—
235	C₄×C₈₉	—	4	4	no	—
236	C₄×C₈₉	—	4	2	no	—
237	C₄×C₈₉	—	4	2	no	—
238	C₄×C₈₉	—	4	4	no	—
239	C₄×C₈₉	—	4	4	no	—
240	C₂×#2664	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂×C₈₉	—	8	2	no	—
242	C₂×C₈₉	#2664	1	8	yes	direct product factor
243	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
244	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
245	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
246	C₂×C₈₉	C₂×#539	1	2	yes	—
247	C₂×C₈₉	C₂×#541	1	2	yes	—
248	C₂²×#126	C₂×C₈₉	1	1	yes	characteristic
249	C₂²×#125	C₂×C₈₉	1	1	yes	characteristic, complemented
250	#2664	C₂×C₈₉	1	16	yes	direct product factor
251	C₂×#400	C₂×C₈₉	1	1	yes	characteristic, complemented
252	C₂×#399	C₂×C₈₉	1	1	yes	characteristic
253	C₂×#398	C₂×C₈₉	1	2	yes	complemented
254	C₂×#398	C₂×C₈₉	1	1	yes	characteristic, complemented
255	C₂×#397	C₂×C₈₉	1	1	yes	characteristic
256	C₂×#396	C₂×C₈₉	1	2	yes	—
257	C₂×#389	C₂×C₈₉	1	2	yes	complemented
258	C₂×#388	C₂×C₈₉	1	2	yes	—
259	C₂×C₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
260	C₈₉	C₂×#2664	1	1	yes	characteristic, direct product factor, Sylow
261	C₂×#126	—	2	8	no	—
262	C₂×#126	C₂²×C₈₉	1	8	yes	—
263	C₂×#125	—	2	8	no	—
264	C₂×#125	C₂²×C₈₉	1	8	yes	complemented
265	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
266	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
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	2	yes	—
270	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
271	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
272	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
273	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
274	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
275	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
276	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
277	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
278	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
279	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
280	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
281	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
282	#400	C₂²×C₈₉	1	8	yes	complemented
283	#399	C₂²×C₈₉	1	8	yes	—
284	#398	C₂²×C₈₉	1	8	yes	complemented
285	#398	C₂²×C₈₉	1	16	yes	complemented
286	#397	C₂²×C₈₉	1	8	yes	—
287	#396	C₂²×C₈₉	1	16	yes	—
288	#389	C₂²×C₈₉	1	16	yes	complemented
289	#388	C₂²×C₈₉	1	16	yes	—
290	C₄×C₄⋊C₄	C₂²×C₈₉	1	8	yes	complemented
291	C₂×#95	C₂²×C₈₉	1	2	yes	—
292	C₂×#95	C₂²×C₈₉	1	2	yes	—
293	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
294	C₂×#95	C₂²×C₈₉	1	2	yes	—
295	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
296	C₂×#95	C₂²×C₈₉	1	2	yes	—
297	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
298	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
299	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
300	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
301	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
302	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
304	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
305	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
306	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
307	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
308	#126	—	2	32	no	—
309	#125	—	2	32	no	—
310	C₂×C₄⋊C₄	—	2	8	no	—
311	C₂×C₄⋊C₄	—	2	4	no	—
312	C₂×C₄⋊C₄	—	2	4	no	—
313	C₂×C₄⋊C₄	—	2	8	no	—
314	C₂×C₄⋊C₄	—	2	4	no	—
315	C₂×C₄⋊C₄	—	2	4	no	—
316	C₂×C₄⋊C₄	—	2	4	no	—
317	C₂×C₄⋊C₄	—	2	8	no	—
318	C₂×C₄⋊C₄	—	2	8	no	—
319	C₂×C₄⋊C₄	—	4	4	no	—
320	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
321	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
322	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
324	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
325	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
327	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
328	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
329	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
330	C₂×C₂²⋊C₄	—	2	4	no	—
331	C₂×C₂²⋊C₄	—	2	4	no	—
332	C₂×C₂²⋊C₄	—	2	4	no	—
333	C₂×C₂²⋊C₄	—	2	8	no	—
334	C₂×C₂²⋊C₄	—	4	4	no	—
335	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
336	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
337	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
338	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
340	C₂×C₄²	—	4	4	no	—
341	C₂×C₄²	D₄×C₈₉	1	8	yes	—
342	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
343	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
344	#95	C₂³×C₈₉	1	4	yes	—
345	#95	C₂³×C₈₉	1	4	yes	—
346	#95	C₂³×C₈₉	1	8	yes	—
347	#95	C₂³×C₈₉	1	8	yes	—
348	#95	C₂³×C₈₉	1	8	yes	—
349	#95	C₂³×C₈₉	1	8	yes	—
350	C₂⁴	—	2	2	no	—
351	C₂⁴	—	2	4	no	—
352	C₂⁴	—	2	2	no	—
353	C₂⁴	—	2	4	no	—
354	C₂⁴	—	2	2	no	—
355	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
356	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	—	2	4	no	—
368	C₂²×C₄	—	2	4	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	2	no	—
375	C₂²×C₄	—	2	4	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	4	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
380	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
381	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
382	C₂²×C₄	#41×C₈₉	1	8	yes	—
383	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
384	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
386	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
387	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
388	C₂²×C₄	C₂⁴×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	2	yes	—
392	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
393	C₄⋊C₄	—	2	16	no	—
394	C₄⋊C₄	—	2	16	no	—
395	C₄⋊C₄	—	2	8	no	—
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	2	8	no	—
400	C₄⋊C₄	—	2	16	no	—
401	C₄⋊C₄	—	2	16	no	—
402	C₄⋊C₄	—	4	8	no	—
403	C₂²⋊C₄	—	2	8	no	—
404	C₂²⋊C₄	—	2	8	no	—
405	C₂²⋊C₄	—	2	8	no	—
406	C₂²⋊C₄	—	2	16	no	—
407	C₂²⋊C₄	—	4	8	no	—
408	C₄²	—	4	8	no	—
409	C₄²	C₂×D₄×C₈₉	1	16	yes	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	4	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	4	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	4	4	no	—
416	C₂³	—	4	4	no	—
417	C₂³	—	4	4	no	—
418	C₂³	—	4	8	no	—
419	C₂³	—	4	8	no	—
420	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
421	C₂³	C₂×#41×C₈₉	1	4	yes	—
422	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
423	C₂³	2₋¹⁺⁴×C₈₉	1	4	yes	—
424	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
425	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	8	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	2	16	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	4	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	4	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	4	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	4	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	4	4	no	—
453	C₂×C₄	—	4	8	no	—
454	C₂×C₄	—	4	4	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	8	no	—
457	C₂×C₄	—	4	8	no	—
458	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
459	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
460	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
461	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
462	C₂²	—	4	2	no	—
463	C₂²	—	4	2	no	—
464	C₂²	—	4	2	no	—
465	C₂²	—	4	4	no	—
466	C₂²	—	4	4	no	—
467	C₂²	—	8	8	no	—
468	C₂²	#532×C₈₉	1	4	yes	—
469	C₂²	#536×C₈₉	1	4	yes	—
470	C₂²	#537×C₈₉	1	4	yes	—
471	C₂²	#539×C₈₉	1	8	yes	—
472	C₂²	#541×C₈₉	1	8	yes	—
473	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
474	C₂²	C₂²×#41×C₈₉	1	2	yes	—
475	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
476	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
477	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
478	C₄	—	2	4	no	—
479	C₄	—	2	4	no	—
480	C₄	—	2	4	no	—
481	C₄	—	2	8	no	—
482	C₄	—	4	2	no	—
483	C₄	—	4	4	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	4	no	—
487	C₄	—	4	4	no	—
488	C₂	—	8	2	no	—
489	C₂	C₈₉×#2664	1	8	yes	direct product factor
490	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
491	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
492	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
493	C₂	C₂×#539×C₈₉	1	2	yes	—
494	C₂	C₂×#541×C₈₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₈₉	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁵×C₈₉	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#125×C₈₉	C₂	semidirect
3. C₈₉×#2664	C₂	direct (N × H)
4. C₂×#400×C₈₉	C₂	semidirect
6. C₂×#398×C₈₉	C₂	semidirect
7. C₂×#398×C₈₉	C₂	semidirect
10. C₂×#389×C₈₉	C₂	semidirect
12. C₂×C₄×C₄⋊C₄×C₈₉	C₂	semidirect
16. C₂×#125×C₈₉	C₂²	semidirect
34. #400×C₈₉	C₂²	semidirect
36. #398×C₈₉	C₂²	semidirect
37. #398×C₈₉	C₂²	semidirect
40. #389×C₈₉	C₂²	semidirect
42. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
240. C₂×#2664	C₈₉	direct (N × H)
242. C₂×C₈₉	#2664	direct (N × H)
249. C₂²×#125	C₂×C₈₉	semidirect
250. #2664	C₂×C₈₉	direct (N × H)
251. C₂×#400	C₂×C₈₉	semidirect
253. C₂×#398	C₂×C₈₉	semidirect
254. C₂×#398	C₂×C₈₉	semidirect
257. C₂×#389	C₂×C₈₉	semidirect
259. C₂×C₄×C₄⋊C₄	C₂×C₈₉	semidirect
260. C₈₉	C₂×#2664	direct (N × H)
264. C₂×#125	C₂²×C₈₉	semidirect
282. #400	C₂²×C₈₉	semidirect
284. #398	C₂²×C₈₉	semidirect
285. #398	C₂²×C₈₉	semidirect
288. #389	C₂²×C₈₉	semidirect
290. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
489. C₂	C₈₉×#2664	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#126×C₈₉	2
C₂²×#125×C₈₉	2
C₈₉×#2664	2
C₂×#400×C₈₉	2
C₂×#399×C₈₉	2
C₂×#398×C₈₉	2
C₂×#397×C₈₉	2
C₂×#396×C₈₉	2
C₂×#389×C₈₉	2
C₂×#388×C₈₉	2
C₂×C₄×C₄⋊C₄×C₈₉	2
C₂×#2664	89

Subgroups — C2×C89×#2664 #36412439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#2664 #36412439