Subgroups — C₈₉×#35262 #36413110

Order 22784.

2950 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2854	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2624	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2504	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2501	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2500	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2482	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2405	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2317	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2309	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2280	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
14	C₂³×D₄×C₈₉	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×#123×C₈₉	C₂²	1	8	yes	complemented
17	C₂×#121×C₈₉	—	2	8	no	—
18	C₂×#121×C₈₉	C₂²	1	2	yes	—
19	C₂×#121×C₈₉	C₂²	1	2	yes	—
20	C₂×#121×C₈₉	C₂²	1	2	yes	—
21	C₂×#121×C₈₉	C₂²	1	2	yes	—
22	C₂×#117×C₈₉	—	2	8	no	—
23	C₂×#117×C₈₉	C₂²	1	2	yes	—
24	C₂×#117×C₈₉	C₂²	1	2	yes	—
25	C₂×#117×C₈₉	C₂²	1	2	yes	—
26	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
27	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
28	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
30	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
31	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
32	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
33	C₂²×C₄²×C₈₉	C₂²	1	2	yes	complemented
34	#399×C₈₉	C₂²	1	8	yes	complemented
35	#397×C₈₉	C₂²	1	8	yes	complemented
36	#394×C₈₉	C₂²	1	16	yes	complemented
37	#390×C₈₉	C₂²	1	8	yes	complemented
38	#390×C₈₉	C₂²	1	4	yes	complemented
39	#390×C₈₉	C₂²	1	4	yes	complemented
40	#389×C₈₉	C₂²	1	8	yes	complemented
41	#388×C₈₉	C₂²	1	16	yes	complemented
42	#386×C₈₉	C₂²	1	8	yes	complemented
43	#385×C₈₉	C₂²	1	8	yes	—
44	#384×C₈₉	C₂²	1	4	yes	complemented
45	#382×C₈₉	C₂²	1	4	yes	complemented
46	#381×C₈₉	C₂²	1	2	yes	—
47	#380×C₈₉	C₂²	1	2	yes	complemented
48	#380×C₈₉	C₂²	1	2	yes	complemented
49	#379×C₈₉	C₂²	1	8	yes	—
50	#379×C₈₉	C₂²	1	2	yes	—
51	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
52	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	complemented
53	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
54	C₂⁵×C₈₉	C₂³	1	2	yes	—
55	C₂²×D₄×C₈₉	—	2	8	no	—
56	C₂²×D₄×C₈₉	—	2	4	no	—
57	C₂²×D₄×C₈₉	—	2	8	no	—
58	C₂²×D₄×C₈₉	—	4	8	no	—
59	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
60	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
61	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
62	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
63	C₂³×C₄×C₈₉	—	2	8	no	—
64	C₂³×C₄×C₈₉	D₄	1	8	yes	—
65	C₂³×C₄×C₈₉	C₂³	1	2	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	1	yes	characteristic
70	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
72	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
74	#123×C₈₉	—	4	16	no	—
75	#121×C₈₉	—	2	8	no	—
76	#121×C₈₉	—	2	8	no	—
77	#121×C₈₉	—	2	8	no	—
78	#121×C₈₉	—	2	8	no	—
79	#117×C₈₉	—	2	8	no	—
80	#117×C₈₉	—	2	8	no	—
81	#117×C₈₉	—	2	8	no	—
82	#117×C₈₉	—	2	8	no	—
83	#117×C₈₉	—	2	8	no	—
84	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
85	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
86	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
88	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	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	16	yes	—
95	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
96	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
97	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
98	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
99	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
100	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	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×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
106	C₂×C₄²×C₈₉	—	2	8	no	—
107	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
108	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
109	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
110	#95×C₈₉	C₂³	1	4	yes	—
111	#95×C₈₉	C₂³	1	4	yes	—
112	#95×C₈₉	C₂³	1	16	yes	—
113	C₂⁴×C₈₉	—	2	4	no	—
114	C₂⁴×C₈₉	—	2	4	no	—
115	C₂⁴×C₈₉	—	2	4	no	—
116	C₂⁴×C₈₉	—	2	8	no	—
117	C₂⁴×C₈₉	—	4	2	no	—
118	C₂⁴×C₈₉	—	4	4	no	—
119	C₂⁴×C₈₉	—	4	4	no	—
120	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
121	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
122	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
123	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
124	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
125	C₂×D₄×C₈₉	—	2	8	no	—
126	C₂×D₄×C₈₉	—	2	8	no	—
127	C₂×D₄×C₈₉	—	2	16	no	—
128	C₂×D₄×C₈₉	—	2	4	no	—
129	C₂×D₄×C₈₉	—	2	4	no	—
130	C₂×D₄×C₈₉	—	2	8	no	—
131	C₂×D₄×C₈₉	—	2	8	no	—
132	C₂×D₄×C₈₉	—	4	8	no	—
133	C₂×D₄×C₈₉	—	4	32	no	—
134	C₂×D₄×C₈₉	—	4	16	no	—
135	C₂²×C₄×C₈₉	—	2	4	no	—
136	C₂²×C₄×C₈₉	—	2	32	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	4	no	—
141	C₂²×C₄×C₈₉	—	2	4	no	—
142	C₂²×C₄×C₈₉	—	2	4	no	—
143	C₂²×C₄×C₈₉	—	2	4	no	—
144	C₂²×C₄×C₈₉	—	2	8	no	—
145	C₂²×C₄×C₈₉	—	4	4	no	—
146	C₂²×C₄×C₈₉	—	4	4	no	—
147	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
148	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
149	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
150	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
151	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
152	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₈₉	#41	1	8	yes	—
154	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
155	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
156	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
157	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
158	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
159	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
160	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
161	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
162	C₄⋊C₄×C₈₉	—	2	4	no	—
163	C₄⋊C₄×C₈₉	—	2	4	no	—
164	C₄⋊C₄×C₈₉	—	2	4	no	—
165	C₄⋊C₄×C₈₉	—	2	4	no	—
166	C₄⋊C₄×C₈₉	—	2	4	no	—
167	C₄⋊C₄×C₈₉	—	2	4	no	—
168	C₄⋊C₄×C₈₉	—	2	8	no	—
169	C₄⋊C₄×C₈₉	—	4	16	no	—
170	C₂²⋊C₄×C₈₉	—	2	8	no	—
171	C₂²⋊C₄×C₈₉	—	2	8	no	—
172	C₂²⋊C₄×C₈₉	—	2	8	no	—
173	C₂²⋊C₄×C₈₉	—	2	8	no	—
174	C₂²⋊C₄×C₈₉	—	2	8	no	—
175	C₂²⋊C₄×C₈₉	—	2	8	no	—
176	C₂²⋊C₄×C₈₉	—	4	4	no	—
177	C₂²⋊C₄×C₈₉	—	4	16	no	—
178	C₂²⋊C₄×C₈₉	—	4	16	no	—
179	C₄²×C₈₉	—	2	8	no	—
180	C₄²×C₈₉	—	2	8	no	—
181	C₄²×C₈₉	—	2	8	no	—
182	C₂³×C₈₉	—	2	2	no	—
183	C₂³×C₈₉	—	2	2	no	—
184	C₂³×C₈₉	—	2	2	no	—
185	C₂³×C₈₉	—	2	2	no	—
186	C₂³×C₈₉	—	2	8	no	—
187	C₂³×C₈₉	—	2	8	no	—
188	C₂³×C₈₉	—	2	2	no	—
189	C₂³×C₈₉	—	2	2	no	—
190	C₂³×C₈₉	—	2	2	no	—
191	C₂³×C₈₉	—	2	4	no	—
192	C₂³×C₈₉	—	2	8	no	—
193	C₂³×C₈₉	—	2	8	no	—
194	C₂³×C₈₉	—	2	8	no	—
195	C₂³×C₈₉	—	4	4	no	—
196	C₂³×C₈₉	—	4	16	no	—
197	C₂³×C₈₉	—	4	8	no	—
198	C₂³×C₈₉	—	4	8	no	—
199	C₂³×C₈₉	—	4	8	no	—
200	C₂³×C₈₉	—	8	16	no	—
201	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
202	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
203	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
204	C₂³×C₈₉	C₂×#41	1	4	yes	—
205	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
206	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
207	D₄×C₈₉	—	4	16	no	—
208	D₄×C₈₉	—	4	16	no	—
209	D₄×C₈₉	—	4	8	no	—
210	D₄×C₈₉	—	4	8	no	—
211	C₂×C₄×C₈₉	—	2	8	no	—
212	C₂×C₄×C₈₉	—	2	2	no	—
213	C₂×C₄×C₈₉	—	2	2	no	—
214	C₂×C₄×C₈₉	—	2	8	no	—
215	C₂×C₄×C₈₉	—	2	8	no	—
216	C₂×C₄×C₈₉	—	2	8	no	—
217	C₂×C₄×C₈₉	—	2	8	no	—
218	C₂×C₄×C₈₉	—	2	4	no	—
219	C₂×C₄×C₈₉	—	2	4	no	—
220	C₂×C₄×C₈₉	—	2	4	no	—
221	C₂×C₄×C₈₉	—	2	8	no	—
222	C₂×C₄×C₈₉	—	2	8	no	—
223	C₂×C₄×C₈₉	—	2	8	no	—
224	C₂×C₄×C₈₉	—	2	8	no	—
225	C₂×C₄×C₈₉	—	2	8	no	—
226	C₂×C₄×C₈₉	—	2	8	no	—
227	C₂×C₄×C₈₉	—	4	8	no	—
228	C₂×C₄×C₈₉	—	4	8	no	—
229	C₂×C₄×C₈₉	—	4	8	no	—
230	C₂×C₄×C₈₉	#123	1	16	yes	complemented
231	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
232	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
234	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
236	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
237	C₂²×C₈₉	—	2	2	no	—
238	C₂²×C₈₉	—	2	2	no	—
239	C₂²×C₈₉	—	2	2	no	—
240	C₂²×C₈₉	—	2	2	no	—
241	C₂²×C₈₉	—	2	8	no	—
242	C₂²×C₈₉	—	2	8	no	—
243	C₂²×C₈₉	—	2	2	no	—
244	C₂²×C₈₉	—	2	2	no	—
245	C₂²×C₈₉	—	2	2	no	—
246	C₂²×C₈₉	—	4	16	no	—
247	C₂²×C₈₉	—	4	4	no	—
248	C₂²×C₈₉	—	4	4	no	—
249	C₂²×C₈₉	—	4	4	no	—
250	C₂²×C₈₉	—	4	4	no	—
251	C₂²×C₈₉	—	4	16	no	—
252	C₂²×C₈₉	—	8	16	no	—
253	C₂²×C₈₉	C₂×#123	1	4	yes	—
254	C₂²×C₈₉	#535	1	4	yes	—
255	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
256	C₂²×C₈₉	C₂²×#41	1	2	yes	—
257	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
258	C₂²×C₈₉	#585	1	2	yes	—
259	C₄×C₈₉	—	2	2	no	—
260	C₄×C₈₉	—	2	2	no	—
261	C₄×C₈₉	—	4	4	no	—
262	C₄×C₈₉	—	4	4	no	—
263	C₄×C₈₉	—	4	4	no	—
264	C₄×C₈₉	—	4	8	no	—
265	C₄×C₈₉	C₂×#123	1	4	yes	—
266	C₄×C₈₉	C₂×#123	1	4	yes	—
267	#35262	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
268	C₂×C₈₉	—	2	4	no	—
269	C₂×C₈₉	—	2	4	no	—
270	C₂×C₈₉	—	4	2	no	—
271	C₂×C₈₉	—	8	4	no	—
272	C₂×C₈₉	C₂²×#123	1	1	yes	characteristic
273	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
274	C₂×C₈₉	#3449	1	1	yes	characteristic
275	C₂×C₈₉	#3494	1	4	yes	—
276	C₂²×#121	C₂×C₈₉	1	1	yes	characteristic
277	C₂²×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
278	#2854	C₂×C₈₉	1	4	yes	complemented
279	#2624	C₂×C₈₉	1	4	yes	complemented
280	#2504	C₂×C₈₉	1	2	yes	complemented
281	#2501	C₂×C₈₉	1	2	yes	complemented
282	#2500	C₂×C₈₉	1	4	yes	complemented
283	#2482	C₂×C₈₉	1	4	yes	complemented
284	#2405	C₂×C₈₉	1	4	yes	complemented
285	#2317	C₂×C₈₉	1	2	yes	complemented
286	#2309	C₂×C₈₉	1	2	yes	complemented
287	#2280	C₂×C₈₉	1	1	yes	characteristic, complemented
288	C₈₉	#35262	1	1	yes	characteristic, direct product factor, Sylow
289	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
290	C₂³×D₄	C₂²×C₈₉	1	2	yes	—
291	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
292	C₂×#123	C₂²×C₈₉	1	8	yes	complemented
293	C₂×#121	—	2	8	no	—
294	C₂×#121	C₂²×C₈₉	1	2	yes	—
295	C₂×#121	C₂²×C₈₉	1	2	yes	—
296	C₂×#121	C₂²×C₈₉	1	2	yes	—
297	C₂×#121	C₂²×C₈₉	1	2	yes	—
298	C₂×#117	—	2	8	no	—
299	C₂×#117	C₂²×C₈₉	1	2	yes	—
300	C₂×#117	C₂²×C₈₉	1	2	yes	—
301	C₂×#117	C₂²×C₈₉	1	2	yes	—
302	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
303	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
304	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
305	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
306	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
307	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
308	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
309	C₂²×C₄²	C₂²×C₈₉	1	2	yes	complemented
310	#399	C₂²×C₈₉	1	8	yes	complemented
311	#397	C₂²×C₈₉	1	8	yes	complemented
312	#394	C₂²×C₈₉	1	16	yes	complemented
313	#390	C₂²×C₈₉	1	8	yes	complemented
314	#390	C₂²×C₈₉	1	4	yes	complemented
315	#390	C₂²×C₈₉	1	4	yes	complemented
316	#389	C₂²×C₈₉	1	8	yes	complemented
317	#388	C₂²×C₈₉	1	16	yes	complemented
318	#386	C₂²×C₈₉	1	8	yes	complemented
319	#385	C₂²×C₈₉	1	8	yes	—
320	#384	C₂²×C₈₉	1	4	yes	complemented
321	#382	C₂²×C₈₉	1	4	yes	complemented
322	#381	C₂²×C₈₉	1	2	yes	—
323	#380	C₂²×C₈₉	1	2	yes	complemented
324	#380	C₂²×C₈₉	1	2	yes	complemented
325	#379	C₂²×C₈₉	1	8	yes	—
326	#379	C₂²×C₈₉	1	2	yes	—
327	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
328	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	complemented
329	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
330	C₂⁵	C₂³×C₈₉	1	2	yes	—
331	C₂²×D₄	—	2	8	no	—
332	C₂²×D₄	—	2	4	no	—
333	C₂²×D₄	—	2	8	no	—
334	C₂²×D₄	—	4	8	no	—
335	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
336	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
337	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
338	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
339	C₂³×C₄	—	2	8	no	—
340	C₂³×C₄	D₄×C₈₉	1	8	yes	—
341	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
342	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
343	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
344	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
345	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
346	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
347	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
348	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
349	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
350	#123	—	4	16	no	—
351	#121	—	2	8	no	—
352	#121	—	2	8	no	—
353	#121	—	2	8	no	—
354	#121	—	2	8	no	—
355	#117	—	2	8	no	—
356	#117	—	2	8	no	—
357	#117	—	2	8	no	—
358	#117	—	2	8	no	—
359	#117	—	2	8	no	—
360	C₂×C₄⋊C₄	—	2	4	no	—
361	C₂×C₄⋊C₄	—	2	4	no	—
362	C₂×C₄⋊C₄	—	2	4	no	—
363	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
364	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
366	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
367	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
368	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
369	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
370	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
371	C₂×C₂²⋊C₄	—	2	8	no	—
372	C₂×C₂²⋊C₄	—	2	8	no	—
373	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
374	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
375	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
376	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
377	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
378	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
379	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
380	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
381	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
382	C₂×C₄²	—	2	8	no	—
383	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
384	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
385	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
386	#95	C₂³×C₈₉	1	4	yes	—
387	#95	C₂³×C₈₉	1	4	yes	—
388	#95	C₂³×C₈₉	1	16	yes	—
389	C₂⁴	—	2	4	no	—
390	C₂⁴	—	2	4	no	—
391	C₂⁴	—	2	4	no	—
392	C₂⁴	—	2	8	no	—
393	C₂⁴	—	4	2	no	—
394	C₂⁴	—	4	4	no	—
395	C₂⁴	—	4	4	no	—
396	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
397	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
398	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
399	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
400	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
401	C₂×D₄	—	2	8	no	—
402	C₂×D₄	—	2	8	no	—
403	C₂×D₄	—	2	16	no	—
404	C₂×D₄	—	2	4	no	—
405	C₂×D₄	—	2	4	no	—
406	C₂×D₄	—	2	8	no	—
407	C₂×D₄	—	2	8	no	—
408	C₂×D₄	—	4	8	no	—
409	C₂×D₄	—	4	32	no	—
410	C₂×D₄	—	4	16	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	2	32	no	—
413	C₂²×C₄	—	2	4	no	—
414	C₂²×C₄	—	2	4	no	—
415	C₂²×C₄	—	2	4	no	—
416	C₂²×C₄	—	2	4	no	—
417	C₂²×C₄	—	2	4	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	8	no	—
421	C₂²×C₄	—	4	4	no	—
422	C₂²×C₄	—	4	4	no	—
423	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
424	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
425	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
426	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
427	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
428	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
429	C₂²×C₄	#41×C₈₉	1	8	yes	—
430	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
431	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
432	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
433	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
434	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
435	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
437	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
438	C₄⋊C₄	—	2	4	no	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	8	no	—
445	C₄⋊C₄	—	4	16	no	—
446	C₂²⋊C₄	—	2	8	no	—
447	C₂²⋊C₄	—	2	8	no	—
448	C₂²⋊C₄	—	2	8	no	—
449	C₂²⋊C₄	—	2	8	no	—
450	C₂²⋊C₄	—	2	8	no	—
451	C₂²⋊C₄	—	2	8	no	—
452	C₂²⋊C₄	—	4	16	no	—
453	C₂²⋊C₄	—	4	4	no	—
454	C₂²⋊C₄	—	4	16	no	—
455	C₄²	—	2	8	no	—
456	C₄²	—	2	8	no	—
457	C₄²	—	2	8	no	—
458	C₂³	—	2	2	no	—
459	C₂³	—	2	2	no	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	8	no	—
463	C₂³	—	2	8	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	4	no	—
468	C₂³	—	2	8	no	—
469	C₂³	—	2	8	no	—
470	C₂³	—	2	8	no	—
471	C₂³	—	4	4	no	—
472	C₂³	—	4	16	no	—
473	C₂³	—	4	8	no	—
474	C₂³	—	4	8	no	—
475	C₂³	—	4	8	no	—
476	C₂³	—	8	16	no	—
477	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
478	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
479	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
480	C₂³	C₂×#41×C₈₉	1	4	yes	—
481	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
482	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
483	D₄	—	4	16	no	—
484	D₄	—	4	16	no	—
485	D₄	—	4	8	no	—
486	D₄	—	4	8	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	2	no	—
490	C₂×C₄	—	2	8	no	—
491	C₂×C₄	—	2	8	no	—
492	C₂×C₄	—	2	8	no	—
493	C₂×C₄	—	2	8	no	—
494	C₂×C₄	—	2	4	no	—
495	C₂×C₄	—	2	4	no	—
496	C₂×C₄	—	2	4	no	—
497	C₂×C₄	—	2	8	no	—
498	C₂×C₄	—	2	8	no	—
499	C₂×C₄	—	2	8	no	—
500	C₂×C₄	—	2	8	no	—
501	C₂×C₄	—	2	8	no	—
502	C₂×C₄	—	2	8	no	—
503	C₂×C₄	—	4	8	no	—
504	C₂×C₄	—	4	8	no	—
505	C₂×C₄	—	4	8	no	—
506	C₂×C₄	#123×C₈₉	1	16	yes	complemented
507	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
508	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
509	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
510	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
511	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
512	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
513	C₂²	—	2	2	no	—
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	2	8	no	—
518	C₂²	—	2	8	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	2	2	no	—
521	C₂²	—	2	2	no	—
522	C₂²	—	4	16	no	—
523	C₂²	—	4	4	no	—
524	C₂²	—	4	4	no	—
525	C₂²	—	4	4	no	—
526	C₂²	—	4	4	no	—
527	C₂²	—	4	16	no	—
528	C₂²	—	8	16	no	—
529	C₂²	C₂×#123×C₈₉	1	4	yes	—
530	C₂²	#535×C₈₉	1	4	yes	—
531	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
532	C₂²	C₂²×#41×C₈₉	1	2	yes	—
533	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
534	C₂²	#585×C₈₉	1	2	yes	—
535	C₄	—	2	2	no	—
536	C₄	—	2	2	no	—
537	C₄	—	4	4	no	—
538	C₄	—	4	4	no	—
539	C₄	—	4	4	no	—
540	C₄	—	4	8	no	—
541	C₄	C₂×#123×C₈₉	1	4	yes	—
542	C₄	C₂×#123×C₈₉	1	4	yes	—
543	C₂	—	2	4	no	—
544	C₂	—	2	4	no	—
545	C₂	—	4	2	no	—
546	C₂	—	8	4	no	—
547	C₂	C₂²×#123×C₈₉	1	1	yes	characteristic
548	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
549	C₂	C₈₉×#3449	1	1	yes	characteristic
550	C₂	C₈₉×#3494	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂²×#121×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
2. C₂²×#117×C₈₉	C₂	semidirect
3. C₈₉×#2854	C₂	semidirect
4. C₈₉×#2624	C₂	semidirect
5. C₈₉×#2504	C₂	semidirect
6. C₈₉×#2501	C₂	semidirect
7. C₈₉×#2500	C₂	semidirect
8. C₈₉×#2482	C₂	semidirect
9. C₈₉×#2405	C₂	semidirect
10. C₈₉×#2317	C₂	semidirect
11. C₈₉×#2309	C₂	semidirect
12. C₈₉×#2280	C₂	semidirect
16. C₂×#123×C₈₉	C₂²	semidirect
26. C₂×#117×C₈₉	C₂²	semidirect
27. C₂×#117×C₈₉	C₂²	semidirect
29. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
30. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
33. C₂²×C₄²×C₈₉	C₂²	semidirect
34. #399×C₈₉	C₂²	semidirect
35. #397×C₈₉	C₂²	semidirect
36. #394×C₈₉	C₂²	semidirect
37. #390×C₈₉	C₂²	semidirect
38. #390×C₈₉	C₂²	semidirect
39. #390×C₈₉	C₂²	semidirect
40. #389×C₈₉	C₂²	semidirect
41. #388×C₈₉	C₂²	semidirect
42. #386×C₈₉	C₂²	semidirect
44. #384×C₈₉	C₂²	semidirect
45. #382×C₈₉	C₂²	semidirect
47. #380×C₈₉	C₂²	semidirect
48. #380×C₈₉	C₂²	semidirect
51. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
52. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
230. C₂×C₄×C₈₉	#123	semidirect
267. #35262	C₈₉	direct (N × H)
277. C₂²×#117	C₂×C₈₉	semidirect
278. #2854	C₂×C₈₉	semidirect
279. #2624	C₂×C₈₉	semidirect
280. #2504	C₂×C₈₉	semidirect
281. #2501	C₂×C₈₉	semidirect
282. #2500	C₂×C₈₉	semidirect
283. #2482	C₂×C₈₉	semidirect
284. #2405	C₂×C₈₉	semidirect
285. #2317	C₂×C₈₉	semidirect
286. #2309	C₂×C₈₉	semidirect
287. #2280	C₂×C₈₉	semidirect
288. C₈₉	#35262	direct (N × H)
292. C₂×#123	C₂²×C₈₉	semidirect
302. C₂×#117	C₂²×C₈₉	semidirect
303. C₂×#117	C₂²×C₈₉	semidirect
305. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
306. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
309. C₂²×C₄²	C₂²×C₈₉	semidirect
310. #399	C₂²×C₈₉	semidirect
311. #397	C₂²×C₈₉	semidirect
312. #394	C₂²×C₈₉	semidirect
313. #390	C₂²×C₈₉	semidirect
314. #390	C₂²×C₈₉	semidirect
315. #390	C₂²×C₈₉	semidirect
316. #389	C₂²×C₈₉	semidirect
317. #388	C₂²×C₈₉	semidirect
318. #386	C₂²×C₈₉	semidirect
320. #384	C₂²×C₈₉	semidirect
321. #382	C₂²×C₈₉	semidirect
323. #380	C₂²×C₈₉	semidirect
324. #380	C₂²×C₈₉	semidirect
327. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
328. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
506. C₂×C₄	#123×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#121×C₈₉	2
C₂²×#117×C₈₉	2
C₈₉×#2854	2
C₈₉×#2624	2
C₈₉×#2504	2
C₈₉×#2501	2
C₈₉×#2500	2
C₈₉×#2482	2
C₈₉×#2405	2
C₈₉×#2317	2
C₈₉×#2309	2
C₈₉×#2280	2
#35262	89

Subgroups — C89×#35262 #36413110

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35262 #36413110