Subgroups — C₂×C₈₉×#2496 #36412608

Order 22784.

2574 conjugacy classes of subgroups.

The subgroup lattice has 548 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	2	yes	maximal
2	C₈₉×#2496	C₂	1	16	yes	maximal, direct product factor
3	C₂×#400×C₈₉	C₂	1	2	yes	maximal, complemented
4	C₂×#397×C₈₉	C₂	1	2	yes	maximal
5	C₂×#389×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#389×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#387×C₈₉	C₂	1	2	yes	maximal, complemented
8	C₂×#384×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#380×C₈₉	C₂	1	1	yes	maximal, characteristic
10	C₂×#380×C₈₉	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄×C₂²⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic
13	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×#126×C₈₉	—	2	16	no	—
15	C₂×#126×C₈₉	C₂²	1	16	yes	—
16	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
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	2	yes	—
20	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
22	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
29	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
31	#400×C₈₉	C₂²	1	16	yes	complemented
32	#397×C₈₉	C₂²	1	16	yes	—
33	#389×C₈₉	C₂²	1	8	yes	complemented
34	#389×C₈₉	C₂²	1	8	yes	complemented
35	#387×C₈₉	C₂²	1	16	yes	complemented
36	#384×C₈₉	C₂²	1	8	yes	complemented
37	#380×C₈₉	C₂²	1	8	yes	—
38	#380×C₈₉	C₂²	1	8	yes	—
39	C₄×C₄⋊C₄×C₈₉	C₂²	1	8	yes	complemented
40	C₄×C₂²⋊C₄×C₈₉	C₂²	1	8	yes	—
41	C₂×#95×C₈₉	C₂²	1	2	yes	—
42	C₂×#95×C₈₉	C₂²	1	2	yes	—
43	C₂×#95×C₈₉	C₂²	1	2	yes	—
44	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#95×C₈₉	C₂²	1	2	yes	—
46	C₂×#95×C₈₉	C₂²	1	2	yes	—
47	C₂×#95×C₈₉	C₂²	1	1	yes	characteristic
48	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₈₉	—	2	4	no	—
50	C₂³×C₄×C₈₉	—	2	4	no	—
51	C₂³×C₄×C₈₉	—	2	4	no	—
52	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
53	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
56	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
57	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
59	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
60	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
63	#126×C₈₉	—	2	64	no	—
64	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
65	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
66	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
67	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
68	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
69	C₂×C₄⋊C₄×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	C₂³	1	4	yes	—
73	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
74	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
76	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
77	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
78	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
79	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
80	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
81	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
82	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
83	C₂×C₂²⋊C₄×C₈₉	D₄	1	8	yes	—
84	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
85	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
86	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
87	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
88	C₂×C₄²×C₈₉	—	2	8	no	—
89	C₂×C₄²×C₈₉	—	2	4	no	—
90	C₂×C₄²×C₈₉	—	2	4	no	—
91	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
92	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
93	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
94	#95×C₈₉	C₂³	1	4	yes	—
95	#95×C₈₉	C₂³	1	4	yes	—
96	#95×C₈₉	C₂³	1	8	yes	—
97	#95×C₈₉	C₂³	1	8	yes	—
98	#95×C₈₉	C₂³	1	8	yes	—
99	#95×C₈₉	C₂³	1	8	yes	—
100	#95×C₈₉	C₂³	1	8	yes	—
101	C₂⁴×C₈₉	—	2	2	no	—
102	C₂⁴×C₈₉	—	2	2	no	—
103	C₂⁴×C₈₉	—	2	2	no	—
104	C₂⁴×C₈₉	—	2	2	no	—
105	C₂⁴×C₈₉	—	2	2	no	—
106	C₂⁴×C₈₉	—	2	2	no	—
107	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
108	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
109	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	—	2	2	no	—
111	C₂²×C₄×C₈₉	—	2	2	no	—
112	C₂²×C₄×C₈₉	—	2	2	no	—
113	C₂²×C₄×C₈₉	—	2	2	no	—
114	C₂²×C₄×C₈₉	—	2	2	no	—
115	C₂²×C₄×C₈₉	—	2	2	no	—
116	C₂²×C₄×C₈₉	—	2	4	no	—
117	C₂²×C₄×C₈₉	—	2	4	no	—
118	C₂²×C₄×C₈₉	—	2	4	no	—
119	C₂²×C₄×C₈₉	—	2	4	no	—
120	C₂²×C₄×C₈₉	—	2	2	no	—
121	C₂²×C₄×C₈₉	—	2	2	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	—	2	2	no	—
129	C₂²×C₄×C₈₉	—	2	2	no	—
130	C₂²×C₄×C₈₉	—	2	2	no	—
131	C₂²×C₄×C₈₉	—	2	4	no	—
132	C₂²×C₄×C₈₉	—	2	4	no	—
133	C₂²×C₄×C₈₉	—	2	2	no	—
134	C₂²×C₄×C₈₉	—	2	8	no	—
135	C₂²×C₄×C₈₉	—	2	8	no	—
136	C₂²×C₄×C₈₉	—	2	8	no	—
137	C₂²×C₄×C₈₉	—	4	16	no	—
138	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₈₉	#41	1	4	yes	—
141	C₂²×C₄×C₈₉	#41	1	4	yes	—
142	C₂²×C₄×C₈₉	#41	1	4	yes	—
143	C₂²×C₄×C₈₉	#41	1	4	yes	—
144	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
145	C₂²×C₄×C₈₉	C₂⁴	1	2	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	4	yes	—
150	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
151	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
152	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
153	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
154	C₄⋊C₄×C₈₉	—	2	16	no	—
155	C₄⋊C₄×C₈₉	—	2	16	no	—
156	C₄⋊C₄×C₈₉	—	2	16	no	—
157	C₄⋊C₄×C₈₉	—	2	16	no	—
158	C₄⋊C₄×C₈₉	—	2	8	no	—
159	C₄⋊C₄×C₈₉	—	2	8	no	—
160	C₄⋊C₄×C₈₉	—	2	8	no	—
161	C₄⋊C₄×C₈₉	—	2	8	no	—
162	C₂²⋊C₄×C₈₉	—	2	16	no	—
163	C₂²⋊C₄×C₈₉	—	2	16	no	—
164	C₂²⋊C₄×C₈₉	—	2	8	no	—
165	C₂²⋊C₄×C₈₉	C₂×D₄	1	16	yes	—
166	C₄²×C₈₉	—	2	16	no	—
167	C₄²×C₈₉	—	2	8	no	—
168	C₄²×C₈₉	—	2	8	no	—
169	C₂³×C₈₉	—	2	8	no	—
170	C₂³×C₈₉	—	2	8	no	—
171	C₂³×C₈₉	—	2	8	no	—
172	C₂³×C₈₉	—	2	2	no	—
173	C₂³×C₈₉	—	2	2	no	—
174	C₂³×C₈₉	—	2	2	no	—
175	C₂³×C₈₉	—	2	2	no	—
176	C₂³×C₈₉	—	2	2	no	—
177	C₂³×C₈₉	—	2	2	no	—
178	C₂³×C₈₉	—	4	4	no	—
179	C₂³×C₈₉	—	4	4	no	—
180	C₂³×C₈₉	—	4	4	no	—
181	C₂³×C₈₉	—	4	4	no	—
182	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
183	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
184	C₂³×C₈₉	C₂×#41	1	2	yes	—
185	C₂³×C₈₉	C₂×#41	1	2	yes	—
186	C₂³×C₈₉	C₂×#41	1	2	yes	—
187	C₂³×C₈₉	C₂×#41	1	2	yes	—
188	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
189	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
190	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
191	C₂×C₄×C₈₉	—	2	8	no	—
192	C₂×C₄×C₈₉	—	2	8	no	—
193	C₂×C₄×C₈₉	—	2	8	no	—
194	C₂×C₄×C₈₉	—	2	2	no	—
195	C₂×C₄×C₈₉	—	2	2	no	—
196	C₂×C₄×C₈₉	—	2	2	no	—
197	C₂×C₄×C₈₉	—	2	2	no	—
198	C₂×C₄×C₈₉	—	2	2	no	—
199	C₂×C₄×C₈₉	—	2	2	no	—
200	C₂×C₄×C₈₉	—	2	4	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	—	2	2	no	—
205	C₂×C₄×C₈₉	—	2	2	no	—
206	C₂×C₄×C₈₉	—	2	4	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	4	no	—
212	C₂×C₄×C₈₉	—	2	2	no	—
213	C₂×C₄×C₈₉	—	2	2	no	—
214	C₂×C₄×C₈₉	—	2	2	no	—
215	C₂×C₄×C₈₉	—	2	4	no	—
216	C₂×C₄×C₈₉	—	2	4	no	—
217	C₂×C₄×C₈₉	—	2	2	no	—
218	C₂×C₄×C₈₉	—	4	4	no	—
219	C₂×C₄×C₈₉	—	4	8	no	—
220	C₂×C₄×C₈₉	—	4	8	no	—
221	C₂×C₄×C₈₉	—	4	8	no	—
222	C₂×C₄×C₈₉	—	4	8	no	—
223	C₂×C₄×C₈₉	—	4	4	no	—
224	C₂×C₄×C₈₉	—	4	16	no	—
225	C₂×C₄×C₈₉	#126	1	16	yes	complemented
226	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
227	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
228	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
229	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
230	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
231	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
232	C₂²×C₈₉	—	2	4	no	—
233	C₂²×C₈₉	—	2	4	no	—
234	C₂²×C₈₉	—	2	4	no	—
235	C₂²×C₈₉	—	4	2	no	—
236	C₂²×C₈₉	—	4	2	no	—
237	C₂²×C₈₉	—	4	2	no	—
238	C₂²×C₈₉	—	4	2	no	—
239	C₂²×C₈₉	—	4	16	no	—
240	C₂²×C₈₉	C₂×#126	1	4	yes	—
241	C₂²×C₈₉	#532	1	4	yes	—
242	C₂²×C₈₉	#541	1	4	yes	—
243	C₂²×C₈₉	#547	1	4	yes	—
244	C₂²×C₈₉	#547	1	4	yes	—
245	C₂²×C₈₉	#552	1	4	yes	—
246	C₂²×C₈₉	#556	1	4	yes	—
247	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
248	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
249	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
250	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
251	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
252	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
253	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
254	C₄×C₈₉	—	2	4	no	—
255	C₄×C₈₉	—	2	4	no	—
256	C₄×C₈₉	—	2	4	no	—
257	C₄×C₈₉	—	4	2	no	—
258	C₄×C₈₉	—	4	4	no	—
259	C₄×C₈₉	—	4	4	no	—
260	C₄×C₈₉	—	4	4	no	—
261	C₄×C₈₉	—	4	4	no	—
262	C₄×C₈₉	—	4	2	no	—
263	C₄×C₈₉	C₂×#126	1	8	yes	complemented
264	C₂×#2496	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
265	C₂×C₈₉	—	4	4	no	—
266	C₂×C₈₉	#2496	1	8	yes	direct product factor
267	C₂×C₈₉	C₂²×#126	1	1	yes	characteristic
268	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
269	C₂×C₈₉	C₂×#541	1	1	yes	characteristic
270	C₂×C₈₉	C₂×#547	1	1	yes	characteristic
271	C₂×C₈₉	C₂×#547	1	1	yes	characteristic
272	C₂×C₈₉	C₂×#552	1	1	yes	characteristic
273	C₂×C₈₉	C₂×#556	1	1	yes	characteristic
274	C₂²×#126	C₂×C₈₉	1	2	yes	—
275	#2496	C₂×C₈₉	1	16	yes	direct product factor
276	C₂×#400	C₂×C₈₉	1	2	yes	complemented
277	C₂×#397	C₂×C₈₉	1	2	yes	—
278	C₂×#389	C₂×C₈₉	1	1	yes	characteristic, complemented
279	C₂×#389	C₂×C₈₉	1	1	yes	characteristic, complemented
280	C₂×#387	C₂×C₈₉	1	2	yes	complemented
281	C₂×#384	C₂×C₈₉	1	1	yes	characteristic, complemented
282	C₂×#380	C₂×C₈₉	1	1	yes	characteristic
283	C₂×#380	C₂×C₈₉	1	1	yes	characteristic
284	C₂×C₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
285	C₂×C₄×C₂²⋊C₄	C₂×C₈₉	1	1	yes	characteristic
286	C₈₉	C₂×#2496	1	1	yes	characteristic, direct product factor, Sylow
287	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
288	C₂×#126	—	2	16	no	—
289	C₂×#126	C₂²×C₈₉	1	16	yes	—
290	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
291	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
292	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
293	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
294	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
295	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
296	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
297	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
298	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
299	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
300	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
301	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
302	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
303	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
304	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
305	#400	C₂²×C₈₉	1	16	yes	complemented
306	#397	C₂²×C₈₉	1	16	yes	—
307	#389	C₂²×C₈₉	1	8	yes	complemented
308	#389	C₂²×C₈₉	1	8	yes	complemented
309	#387	C₂²×C₈₉	1	16	yes	complemented
310	#384	C₂²×C₈₉	1	8	yes	complemented
311	#380	C₂²×C₈₉	1	8	yes	—
312	#380	C₂²×C₈₉	1	8	yes	—
313	C₄×C₄⋊C₄	C₂²×C₈₉	1	8	yes	complemented
314	C₄×C₂²⋊C₄	C₂²×C₈₉	1	8	yes	—
315	C₂×#95	C₂²×C₈₉	1	2	yes	—
316	C₂×#95	C₂²×C₈₉	1	2	yes	—
317	C₂×#95	C₂²×C₈₉	1	2	yes	—
318	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
319	C₂×#95	C₂²×C₈₉	1	2	yes	—
320	C₂×#95	C₂²×C₈₉	1	2	yes	—
321	C₂×#95	C₂²×C₈₉	1	1	yes	characteristic
322	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
323	C₂³×C₄	—	2	4	no	—
324	C₂³×C₄	—	2	4	no	—
325	C₂³×C₄	—	2	4	no	—
326	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
327	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
328	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
329	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
330	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
331	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
332	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
333	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
336	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
337	#126	—	2	64	no	—
338	C₂×C₄⋊C₄	—	2	8	no	—
339	C₂×C₄⋊C₄	—	2	8	no	—
340	C₂×C₄⋊C₄	—	2	8	no	—
341	C₂×C₄⋊C₄	—	2	8	no	—
342	C₂×C₄⋊C₄	—	2	4	no	—
343	C₂×C₄⋊C₄	—	2	4	no	—
344	C₂×C₄⋊C₄	—	2	4	no	—
345	C₂×C₄⋊C₄	—	2	4	no	—
346	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
347	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
348	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
349	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
350	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	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	8	yes	—
354	C₂×C₂²⋊C₄	—	2	8	no	—
355	C₂×C₂²⋊C₄	—	2	8	no	—
356	C₂×C₂²⋊C₄	—	2	4	no	—
357	C₂×C₂²⋊C₄	D₄×C₈₉	1	8	yes	—
358	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
359	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
360	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
361	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
362	C₂×C₄²	—	2	8	no	—
363	C₂×C₄²	—	2	4	no	—
364	C₂×C₄²	—	2	4	no	—
365	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
366	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
367	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
368	#95	C₂³×C₈₉	1	4	yes	—
369	#95	C₂³×C₈₉	1	4	yes	—
370	#95	C₂³×C₈₉	1	8	yes	—
371	#95	C₂³×C₈₉	1	8	yes	—
372	#95	C₂³×C₈₉	1	8	yes	—
373	#95	C₂³×C₈₉	1	8	yes	—
374	#95	C₂³×C₈₉	1	8	yes	—
375	C₂⁴	—	2	2	no	—
376	C₂⁴	—	2	2	no	—
377	C₂⁴	—	2	2	no	—
378	C₂⁴	—	2	2	no	—
379	C₂⁴	—	2	2	no	—
380	C₂⁴	—	2	2	no	—
381	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
382	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
383	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	2	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	4	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	4	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	4	no	—
398	C₂²×C₄	—	2	4	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	—	2	4	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	2	8	no	—
409	C₂²×C₄	—	2	8	no	—
410	C₂²×C₄	—	2	8	no	—
411	C₂²×C₄	—	4	16	no	—
412	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
413	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
414	C₂²×C₄	#41×C₈₉	1	4	yes	—
415	C₂²×C₄	#41×C₈₉	1	4	yes	—
416	C₂²×C₄	#41×C₈₉	1	4	yes	—
417	C₂²×C₄	#41×C₈₉	1	4	yes	—
418	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
419	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
420	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
421	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
422	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
423	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
424	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
425	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
426	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
427	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
428	C₄⋊C₄	—	2	16	no	—
429	C₄⋊C₄	—	2	16	no	—
430	C₄⋊C₄	—	2	16	no	—
431	C₄⋊C₄	—	2	16	no	—
432	C₄⋊C₄	—	2	8	no	—
433	C₄⋊C₄	—	2	8	no	—
434	C₄⋊C₄	—	2	8	no	—
435	C₄⋊C₄	—	2	8	no	—
436	C₂²⋊C₄	—	2	16	no	—
437	C₂²⋊C₄	—	2	16	no	—
438	C₂²⋊C₄	—	2	8	no	—
439	C₂²⋊C₄	C₂×D₄×C₈₉	1	16	yes	—
440	C₄²	—	2	16	no	—
441	C₄²	—	2	8	no	—
442	C₄²	—	2	8	no	—
443	C₂³	—	2	8	no	—
444	C₂³	—	2	8	no	—
445	C₂³	—	2	8	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	2	2	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	4	4	no	—
453	C₂³	—	4	4	no	—
454	C₂³	—	4	4	no	—
455	C₂³	—	4	4	no	—
456	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
457	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
458	C₂³	C₂×#41×C₈₉	1	2	yes	—
459	C₂³	C₂×#41×C₈₉	1	2	yes	—
460	C₂³	C₂×#41×C₈₉	1	2	yes	—
461	C₂³	C₂×#41×C₈₉	1	2	yes	—
462	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
463	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
464	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
465	C₂×C₄	—	2	8	no	—
466	C₂×C₄	—	2	8	no	—
467	C₂×C₄	—	2	8	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	4	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	4	no	—
485	C₂×C₄	—	2	4	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	4	4	no	—
493	C₂×C₄	—	4	8	no	—
494	C₂×C₄	—	4	8	no	—
495	C₂×C₄	—	4	8	no	—
496	C₂×C₄	—	4	8	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	4	16	no	—
499	C₂×C₄	#126×C₈₉	1	16	yes	complemented
500	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
501	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
502	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
503	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
504	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
505	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
506	C₂²	—	2	4	no	—
507	C₂²	—	2	4	no	—
508	C₂²	—	2	4	no	—
509	C₂²	—	4	2	no	—
510	C₂²	—	4	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	16	no	—
514	C₂²	C₂×#126×C₈₉	1	4	yes	—
515	C₂²	#532×C₈₉	1	4	yes	—
516	C₂²	#541×C₈₉	1	4	yes	—
517	C₂²	#547×C₈₉	1	4	yes	—
518	C₂²	#547×C₈₉	1	4	yes	—
519	C₂²	#552×C₈₉	1	4	yes	—
520	C₂²	#556×C₈₉	1	4	yes	—
521	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
522	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
523	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
524	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
525	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
526	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
527	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
528	C₄	—	2	4	no	—
529	C₄	—	2	4	no	—
530	C₄	—	2	4	no	—
531	C₄	—	4	2	no	—
532	C₄	—	4	4	no	—
533	C₄	—	4	4	no	—
534	C₄	—	4	4	no	—
535	C₄	—	4	4	no	—
536	C₄	—	4	2	no	—
537	C₄	C₂×#126×C₈₉	1	8	yes	complemented
538	C₂	—	4	4	no	—
539	C₂	C₈₉×#2496	1	8	yes	direct product factor
540	C₂	C₂²×#126×C₈₉	1	1	yes	characteristic
541	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
542	C₂	C₂×#541×C₈₉	1	1	yes	characteristic
543	C₂	C₂×#547×C₈₉	1	1	yes	characteristic
544	C₂	C₂×#547×C₈₉	1	1	yes	characteristic
545	C₂	C₂×#552×C₈₉	1	1	yes	characteristic
546	C₂	C₂×#556×C₈₉	1	1	yes	characteristic

	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. C₈₉×#2496	C₂	direct (N × H)
3. C₂×#400×C₈₉	C₂	semidirect
5. C₂×#389×C₈₉	C₂	semidirect
6. C₂×#389×C₈₉	C₂	semidirect
7. C₂×#387×C₈₉	C₂	semidirect
8. C₂×#384×C₈₉	C₂	semidirect
11. C₂×C₄×C₄⋊C₄×C₈₉	C₂	semidirect
31. #400×C₈₉	C₂²	semidirect
33. #389×C₈₉	C₂²	semidirect
34. #389×C₈₉	C₂²	semidirect
35. #387×C₈₉	C₂²	semidirect
36. #384×C₈₉	C₂²	semidirect
39. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
225. C₂×C₄×C₈₉	#126	semidirect
263. C₄×C₈₉	C₂×#126	semidirect
264. C₂×#2496	C₈₉	direct (N × H)
266. C₂×C₈₉	#2496	direct (N × H)
275. #2496	C₂×C₈₉	direct (N × H)
276. C₂×#400	C₂×C₈₉	semidirect
278. C₂×#389	C₂×C₈₉	semidirect
279. C₂×#389	C₂×C₈₉	semidirect
280. C₂×#387	C₂×C₈₉	semidirect
281. C₂×#384	C₂×C₈₉	semidirect
284. C₂×C₄×C₄⋊C₄	C₂×C₈₉	semidirect
286. C₈₉	C₂×#2496	direct (N × H)
305. #400	C₂²×C₈₉	semidirect
307. #389	C₂²×C₈₉	semidirect
308. #389	C₂²×C₈₉	semidirect
309. #387	C₂²×C₈₉	semidirect
310. #384	C₂²×C₈₉	semidirect
313. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
499. C₂×C₄	#126×C₈₉	semidirect
537. C₄	C₂×#126×C₈₉	semidirect
539. C₂	C₈₉×#2496	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
C₈₉×#2496	2
C₂×#400×C₈₉	2
C₂×#397×C₈₉	2
C₂×#389×C₈₉	2
C₂×#387×C₈₉	2
C₂×#384×C₈₉	2
C₂×#380×C₈₉	2
C₂×C₄×C₄⋊C₄×C₈₉	2
C₂×C₄×C₂²⋊C₄×C₈₉	2
C₂×#2496	89

Subgroups — C2×C89×#2496 #36412608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈₉×#2496 #36412608