Subgroups — C₈₉×#35241 #36413089

Order 22784.

2266 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#533×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#529×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2857	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2850	C₂	1	2	yes	maximal
5	C₈₉×#2664	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2568	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2565	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2547	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#2546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2545	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2542	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2498	C₂	1	4	yes	maximal, complemented
13	C₈₉×#2417	C₂	1	4	yes	maximal, complemented
14	C₈₉×#2323	C₂	1	4	yes	maximal, complemented
15	C₂×C₄×C₄⋊C₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#533×C₈₉	—	2	8	no	—
17	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
20	#529×C₈₉	—	2	8	no	—
21	C₂×#126×C₈₉	C₂²	1	2	yes	—
22	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#125×C₈₉	C₂²	1	2	yes	—
24	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#124×C₈₉	C₂²	1	2	yes	—
26	C₂×#123×C₈₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
28	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
29	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
31	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
36	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₂×#117×C₈₉	C₂²	1	2	yes	—
38	C₂×#117×C₈₉	C₂²	1	2	yes	—
39	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
40	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
41	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
42	#400×C₈₉	C₂²	1	4	yes	—
43	#399×C₈₉	C₂²	1	4	yes	—
44	#398×C₈₉	C₂²	1	8	yes	—
45	#398×C₈₉	C₂²	1	4	yes	—
46	#397×C₈₉	C₂²	1	4	yes	—
47	#396×C₈₉	C₂²	1	8	yes	—
48	#391×C₈₉	C₂²	1	2	yes	—
49	#391×C₈₉	C₂²	1	2	yes	—
50	#391×C₈₉	C₂²	1	4	yes	—
51	#391×C₈₉	C₂²	1	2	yes	—
52	#390×C₈₉	C₂²	1	2	yes	—
53	#389×C₈₉	C₂²	1	8	yes	—
54	#389×C₈₉	C₂²	1	4	yes	—
55	#388×C₈₉	C₂²	1	8	yes	—
56	#388×C₈₉	C₂²	1	8	yes	—
57	#387×C₈₉	C₂²	1	8	yes	—
58	#386×C₈₉	C₂²	1	8	yes	—
59	#384×C₈₉	C₂²	1	2	yes	—
60	#382×C₈₉	C₂²	1	2	yes	—
61	#380×C₈₉	C₂²	1	4	yes	—
62	#380×C₈₉	C₂²	1	8	yes	—
63	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
65	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
68	C₂×#95×C₈₉	C₂²	1	2	yes	—
69	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
70	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
71	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
72	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
73	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
76	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
77	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₄⋊Q₈×C₈₉	—	2	4	no	—
80	C₄⋊Q₈×C₈₉	—	2	4	no	—
81	C₄⋊Q₈×C₈₉	—	4	4	no	—
82	#126×C₈₉	—	2	8	no	—
83	#125×C₈₉	—	2	4	no	—
84	#125×C₈₉	—	2	8	no	—
85	#124×C₈₉	—	2	4	no	—
86	#124×C₈₉	—	4	4	no	—
87	#123×C₈₉	—	2	8	no	—
88	C₂²⋊Q₈×C₈₉	—	2	4	no	—
89	C₂²⋊Q₈×C₈₉	—	2	8	no	—
90	C₂²⋊Q₈×C₈₉	—	2	8	no	—
91	C₂²⋊Q₈×C₈₉	—	2	16	no	—
92	#121×C₈₉	—	2	4	no	—
93	C₄×Q₈×C₈₉	—	2	4	no	—
94	C₄×Q₈×C₈₉	—	2	8	no	—
95	C₄×Q₈×C₈₉	—	2	8	no	—
96	C₄×D₄×C₈₉	—	2	8	no	—
97	C₄×D₄×C₈₉	—	2	4	no	—
98	#117×C₈₉	—	2	8	no	—
99	#117×C₈₉	—	2	8	no	—
100	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
101	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
102	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
110	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
112	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
114	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
120	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
121	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
126	C₂×C₄²×C₈₉	—	4	4	no	—
127	C₂×C₄²×C₈₉	D₄	1	8	yes	—
128	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
129	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
130	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
131	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
132	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
133	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
135	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
136	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
137	#95×C₈₉	C₂³	1	4	yes	—
138	#95×C₈₉	C₂³	1	2	yes	—
139	#95×C₈₉	C₂³	1	2	yes	—
140	#95×C₈₉	C₂³	1	8	yes	—
141	#95×C₈₉	C₂³	1	8	yes	—
142	#95×C₈₉	C₂³	1	8	yes	—
143	#95×C₈₉	C₂³	1	8	yes	—
144	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
145	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
146	C₂×Q₈×C₈₉	—	2	2	no	—
147	C₂×Q₈×C₈₉	—	2	4	no	—
148	C₂×Q₈×C₈₉	—	2	4	no	—
149	C₂×Q₈×C₈₉	—	2	8	no	—
150	C₂×Q₈×C₈₉	—	2	4	no	—
151	C₂×Q₈×C₈₉	—	2	2	no	—
152	C₂×Q₈×C₈₉	—	2	2	no	—
153	C₂×Q₈×C₈₉	—	2	4	no	—
154	C₂×D₄×C₈₉	—	2	4	no	—
155	C₂×D₄×C₈₉	—	2	8	no	—
156	C₂×D₄×C₈₉	—	2	2	no	—
157	C₂×D₄×C₈₉	—	2	2	no	—
158	C₂×D₄×C₈₉	—	2	2	no	—
159	C₂²×C₄×C₈₉	—	2	4	no	—
160	C₂²×C₄×C₈₉	—	2	4	no	—
161	C₂²×C₄×C₈₉	—	2	2	no	—
162	C₂²×C₄×C₈₉	—	2	2	no	—
163	C₂²×C₄×C₈₉	—	2	8	no	—
164	C₂²×C₄×C₈₉	—	2	4	no	—
165	C₂²×C₄×C₈₉	—	2	8	no	—
166	C₂²×C₄×C₈₉	—	2	8	no	—
167	C₂²×C₄×C₈₉	—	4	4	no	—
168	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
169	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
170	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
171	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
175	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
176	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
180	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
182	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
184	C₄⋊C₄×C₈₉	—	2	4	no	—
185	C₄⋊C₄×C₈₉	—	2	4	no	—
186	C₄⋊C₄×C₈₉	—	2	4	no	—
187	C₄⋊C₄×C₈₉	—	2	4	no	—
188	C₄⋊C₄×C₈₉	—	2	2	no	—
189	C₄⋊C₄×C₈₉	—	2	4	no	—
190	C₄⋊C₄×C₈₉	—	2	2	no	—
191	C₄⋊C₄×C₈₉	—	2	8	no	—
192	C₄⋊C₄×C₈₉	—	2	8	no	—
193	C₄⋊C₄×C₈₉	—	2	4	no	—
194	C₄⋊C₄×C₈₉	—	2	4	no	—
195	C₄⋊C₄×C₈₉	—	2	4	no	—
196	C₄⋊C₄×C₈₉	—	2	8	no	—
197	C₄⋊C₄×C₈₉	—	2	4	no	—
198	C₄⋊C₄×C₈₉	—	2	16	no	—
199	C₄⋊C₄×C₈₉	—	4	8	no	—
200	C₄⋊C₄×C₈₉	#41	1	8	yes	—
201	C₂²⋊C₄×C₈₉	—	2	8	no	—
202	C₂²⋊C₄×C₈₉	—	2	4	no	—
203	C₂²⋊C₄×C₈₉	—	2	4	no	—
204	C₂²⋊C₄×C₈₉	—	2	4	no	—
205	C₂²⋊C₄×C₈₉	—	2	4	no	—
206	C₂²⋊C₄×C₈₉	—	2	4	no	—
207	C₂²⋊C₄×C₈₉	—	2	16	no	—
208	C₂²⋊C₄×C₈₉	—	4	8	no	—
209	C₄²×C₈₉	—	2	4	no	—
210	C₄²×C₈₉	—	2	8	no	—
211	C₄²×C₈₉	—	2	4	no	—
212	C₄²×C₈₉	—	2	4	no	—
213	C₄²×C₈₉	—	4	4	no	—
214	C₄²×C₈₉	C₂×D₄	1	4	yes	—
215	C₄²×C₈₉	C₂×D₄	1	4	yes	—
216	C₄²×C₈₉	C₂×D₄	1	4	yes	—
217	C₄²×C₈₉	C₂×D₄	1	4	yes	—
218	C₂³×C₈₉	—	2	2	no	—
219	C₂³×C₈₉	—	2	1	no	—
220	C₂³×C₈₉	—	2	1	no	—
221	C₂³×C₈₉	—	2	2	no	—
222	C₂³×C₈₉	—	2	4	no	—
223	C₂³×C₈₉	—	2	2	no	—
224	C₂³×C₈₉	—	2	4	no	—
225	C₂³×C₈₉	—	2	2	no	—
226	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
227	C₂³×C₈₉	2₋¹⁺⁴	1	4	yes	—
228	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
229	Q₈×C₈₉	—	4	8	no	—
230	Q₈×C₈₉	—	4	4	no	—
231	Q₈×C₈₉	—	4	8	no	—
232	D₄×C₈₉	—	4	8	no	—
233	D₄×C₈₉	—	4	4	no	—
234	C₂×C₄×C₈₉	—	2	8	no	—
235	C₂×C₄×C₈₉	—	2	2	no	—
236	C₂×C₄×C₈₉	—	2	4	no	—
237	C₂×C₄×C₈₉	—	2	1	no	—
238	C₂×C₄×C₈₉	—	2	2	no	—
239	C₂×C₄×C₈₉	—	2	2	no	—
240	C₂×C₄×C₈₉	—	2	1	no	—
241	C₂×C₄×C₈₉	—	2	4	no	—
242	C₂×C₄×C₈₉	—	2	8	no	—
243	C₂×C₄×C₈₉	—	2	8	no	—
244	C₂×C₄×C₈₉	—	2	2	no	—
245	C₂×C₄×C₈₉	—	2	2	no	—
246	C₂×C₄×C₈₉	—	2	4	no	—
247	C₂×C₄×C₈₉	—	2	4	no	—
248	C₂×C₄×C₈₉	—	2	2	no	—
249	C₂×C₄×C₈₉	—	2	8	no	—
250	C₂×C₄×C₈₉	—	2	4	no	—
251	C₂×C₄×C₈₉	—	2	4	no	—
252	C₂×C₄×C₈₉	—	2	4	no	—
253	C₂×C₄×C₈₉	—	2	4	no	—
254	C₂×C₄×C₈₉	—	2	2	no	—
255	C₂×C₄×C₈₉	—	2	4	no	—
256	C₂×C₄×C₈₉	—	2	4	no	—
257	C₂×C₄×C₈₉	—	2	2	no	—
258	C₂×C₄×C₈₉	—	2	4	no	—
259	C₂×C₄×C₈₉	—	4	16	no	—
260	C₂×C₄×C₈₉	—	4	8	no	—
261	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
262	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
263	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
268	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
269	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
270	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
271	C₂²×C₈₉	—	2	2	no	—
272	C₂²×C₈₉	—	2	2	no	—
273	C₂²×C₈₉	—	2	4	no	—
274	C₂²×C₈₉	—	2	4	no	—
275	C₂²×C₈₉	—	4	2	no	—
276	C₂²×C₈₉	—	4	2	no	—
277	C₂²×C₈₉	—	4	2	no	—
278	C₂²×C₈₉	—	4	4	no	—
279	C₂²×C₈₉	—	4	4	no	—
280	C₂²×C₈₉	#536	1	4	yes	—
281	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
282	C₂²×C₈₉	C₂²×#41	1	2	yes	—
283	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
284	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
285	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
286	C₄×C₈₉	—	2	2	no	—
287	C₄×C₈₉	—	2	2	no	—
288	C₄×C₈₉	—	2	2	no	—
289	C₄×C₈₉	—	2	2	no	—
290	C₄×C₈₉	—	2	8	no	—
291	C₄×C₈₉	—	4	2	no	—
292	C₄×C₈₉	—	4	4	no	—
293	C₄×C₈₉	—	4	2	no	—
294	C₄×C₈₉	—	4	2	no	—
295	C₄×C₈₉	—	4	4	no	—
296	C₄×C₈₉	—	4	4	no	—
297	C₄×C₈₉	#532	1	4	yes	—
298	C₄×C₈₉	#537	1	4	yes	—
299	#35241	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
300	C₂×C₈₉	—	2	4	no	—
301	C₂×C₈₉	—	8	2	no	—
302	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
303	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
304	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
305	C₂×C₈₉	#3520	1	2	yes	—
306	C₂×C₈₉	#3523	1	2	yes	—
307	C₂×#533	C₂×C₈₉	1	1	yes	characteristic, complemented
308	C₂×#529	C₂×C₈₉	1	1	yes	characteristic
309	#2857	C₂×C₈₉	1	2	yes	complemented
310	#2850	C₂×C₈₉	1	2	yes	—
311	#2664	C₂×C₈₉	1	4	yes	complemented
312	#2568	C₂×C₈₉	1	1	yes	characteristic, complemented
313	#2565	C₂×C₈₉	1	2	yes	complemented
314	#2547	C₂×C₈₉	1	1	yes	characteristic, complemented
315	#2546	C₂×C₈₉	1	1	yes	characteristic, complemented
316	#2545	C₂×C₈₉	1	2	yes	complemented
317	#2542	C₂×C₈₉	1	1	yes	characteristic, complemented
318	#2498	C₂×C₈₉	1	4	yes	complemented
319	#2417	C₂×C₈₉	1	4	yes	complemented
320	#2323	C₂×C₈₉	1	4	yes	complemented
321	C₂×C₄×C₄⋊C₄	C₂×C₈₉	1	1	yes	characteristic, complemented
322	C₈₉	#35241	1	1	yes	characteristic, direct product factor, Sylow
323	#533	—	2	8	no	—
324	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
325	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
326	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
327	#529	—	2	8	no	—
328	C₂×#126	C₂²×C₈₉	1	2	yes	—
329	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
330	C₂×#125	C₂²×C₈₉	1	2	yes	—
331	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
332	C₂×#124	C₂²×C₈₉	1	2	yes	—
333	C₂×#123	C₂²×C₈₉	1	2	yes	—
334	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
335	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
336	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
337	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
338	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
339	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
340	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
341	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
342	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
343	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
344	C₂×#117	C₂²×C₈₉	1	2	yes	—
345	C₂×#117	C₂²×C₈₉	1	2	yes	—
346	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
347	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
348	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
349	#400	C₂²×C₈₉	1	4	yes	—
350	#399	C₂²×C₈₉	1	4	yes	—
351	#398	C₂²×C₈₉	1	8	yes	—
352	#398	C₂²×C₈₉	1	4	yes	—
353	#397	C₂²×C₈₉	1	4	yes	—
354	#396	C₂²×C₈₉	1	8	yes	—
355	#391	C₂²×C₈₉	1	2	yes	—
356	#391	C₂²×C₈₉	1	2	yes	—
357	#391	C₂²×C₈₉	1	4	yes	—
358	#391	C₂²×C₈₉	1	2	yes	—
359	#390	C₂²×C₈₉	1	2	yes	—
360	#389	C₂²×C₈₉	1	8	yes	—
361	#389	C₂²×C₈₉	1	4	yes	—
362	#388	C₂²×C₈₉	1	8	yes	—
363	#388	C₂²×C₈₉	1	8	yes	—
364	#387	C₂²×C₈₉	1	8	yes	—
365	#386	C₂²×C₈₉	1	8	yes	—
366	#384	C₂²×C₈₉	1	2	yes	—
367	#382	C₂²×C₈₉	1	2	yes	—
368	#380	C₂²×C₈₉	1	4	yes	—
369	#380	C₂²×C₈₉	1	8	yes	—
370	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
371	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
372	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
373	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
374	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
375	C₂×#95	C₂²×C₈₉	1	2	yes	—
376	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
377	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
378	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
379	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
380	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
381	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
382	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
383	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
384	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
385	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
386	C₄⋊Q₈	—	2	4	no	—
387	C₄⋊Q₈	—	2	4	no	—
388	C₄⋊Q₈	—	4	4	no	—
389	#126	—	2	8	no	—
390	#125	—	2	4	no	—
391	#125	—	2	8	no	—
392	#124	—	2	4	no	—
393	#124	—	4	4	no	—
394	#123	—	2	8	no	—
395	C₂²⋊Q₈	—	2	4	no	—
396	C₂²⋊Q₈	—	2	8	no	—
397	C₂²⋊Q₈	—	2	8	no	—
398	C₂²⋊Q₈	—	2	16	no	—
399	#121	—	2	4	no	—
400	C₄×Q₈	—	2	4	no	—
401	C₄×Q₈	—	2	8	no	—
402	C₄×Q₈	—	2	8	no	—
403	C₄×D₄	—	2	8	no	—
404	C₄×D₄	—	2	4	no	—
405	#117	—	2	8	no	—
406	#117	—	2	8	no	—
407	C₂×C₄⋊C₄	—	2	8	no	—
408	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
409	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
410	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
416	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
418	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
419	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
420	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
421	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
422	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
423	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
424	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
432	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
433	C₂×C₄²	—	4	4	no	—
434	C₂×C₄²	D₄×C₈₉	1	8	yes	—
435	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
436	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
437	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
438	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
439	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
440	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
441	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
442	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
443	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
444	#95	C₂³×C₈₉	1	4	yes	—
445	#95	C₂³×C₈₉	1	2	yes	—
446	#95	C₂³×C₈₉	1	2	yes	—
447	#95	C₂³×C₈₉	1	8	yes	—
448	#95	C₂³×C₈₉	1	8	yes	—
449	#95	C₂³×C₈₉	1	8	yes	—
450	#95	C₂³×C₈₉	1	8	yes	—
451	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
452	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
453	C₂×Q₈	—	2	2	no	—
454	C₂×Q₈	—	2	4	no	—
455	C₂×Q₈	—	2	4	no	—
456	C₂×Q₈	—	2	8	no	—
457	C₂×Q₈	—	2	4	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	2	2	no	—
460	C₂×Q₈	—	2	4	no	—
461	C₂×D₄	—	2	4	no	—
462	C₂×D₄	—	2	8	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂²×C₄	—	2	4	no	—
467	C₂²×C₄	—	2	4	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	8	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	8	no	—
473	C₂²×C₄	—	2	8	no	—
474	C₂²×C₄	—	4	4	no	—
475	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
476	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
477	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
478	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
479	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
480	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
481	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
482	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
483	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
484	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
486	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
488	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
489	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
491	C₄⋊C₄	—	2	4	no	—
492	C₄⋊C₄	—	2	4	no	—
493	C₄⋊C₄	—	2	4	no	—
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	2	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	8	no	—
499	C₄⋊C₄	—	2	8	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	4	no	—
503	C₄⋊C₄	—	2	8	no	—
504	C₄⋊C₄	—	2	4	no	—
505	C₄⋊C₄	—	2	16	no	—
506	C₄⋊C₄	—	4	8	no	—
507	C₄⋊C₄	#41×C₈₉	1	8	yes	—
508	C₂²⋊C₄	—	2	8	no	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	2	16	no	—
515	C₂²⋊C₄	—	4	8	no	—
516	C₄²	—	2	4	no	—
517	C₄²	—	2	8	no	—
518	C₄²	—	2	4	no	—
519	C₄²	—	2	4	no	—
520	C₄²	—	4	4	no	—
521	C₄²	C₂×D₄×C₈₉	1	4	yes	—
522	C₄²	C₂×D₄×C₈₉	1	4	yes	—
523	C₄²	C₂×D₄×C₈₉	1	4	yes	—
524	C₄²	C₂×D₄×C₈₉	1	4	yes	—
525	C₂³	—	2	2	no	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	4	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	2	no	—
533	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
534	C₂³	2₋¹⁺⁴×C₈₉	1	4	yes	—
535	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
536	Q₈	—	4	8	no	—
537	Q₈	—	4	4	no	—
538	Q₈	—	4	8	no	—
539	D₄	—	4	8	no	—
540	D₄	—	4	4	no	—
541	C₂×C₄	—	2	8	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	4	no	—
549	C₂×C₄	—	2	8	no	—
550	C₂×C₄	—	2	8	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	8	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	4	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	4	16	no	—
567	C₂×C₄	—	4	8	no	—
568	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
569	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
570	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
571	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
572	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
573	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
574	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
575	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
576	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
577	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	2	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	4	4	no	—
587	C₂²	#536×C₈₉	1	4	yes	—
588	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
589	C₂²	C₂²×#41×C₈₉	1	2	yes	—
590	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
591	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
592	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
593	C₄	—	2	2	no	—
594	C₄	—	2	2	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	2	no	—
597	C₄	—	2	8	no	—
598	C₄	—	4	2	no	—
599	C₄	—	4	4	no	—
600	C₄	—	4	2	no	—
601	C₄	—	4	2	no	—
602	C₄	—	4	4	no	—
603	C₄	—	4	4	no	—
604	C₄	#532×C₈₉	1	4	yes	—
605	C₄	#537×C₈₉	1	4	yes	—
606	C₂	—	2	4	no	—
607	C₂	—	8	2	no	—
608	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
609	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
610	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
611	C₂	C₈₉×#3520	1	2	yes	—
612	C₂	C₈₉×#3523	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#121×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. C₂×#533×C₈₉	C₂	semidirect
3. C₈₉×#2857	C₂	semidirect
5. C₈₉×#2664	C₂	semidirect
6. C₈₉×#2568	C₂	semidirect
7. C₈₉×#2565	C₂	semidirect
8. C₈₉×#2547	C₂	semidirect
9. C₈₉×#2546	C₂	semidirect
10. C₈₉×#2545	C₂	semidirect
11. C₈₉×#2542	C₂	semidirect
12. C₈₉×#2498	C₂	semidirect
13. C₈₉×#2417	C₂	semidirect
14. C₈₉×#2323	C₂	semidirect
15. C₂×C₄×C₄⋊C₄×C₈₉	C₂	semidirect
299. #35241	C₈₉	direct (N × H)
307. C₂×#533	C₂×C₈₉	semidirect
309. #2857	C₂×C₈₉	semidirect
311. #2664	C₂×C₈₉	semidirect
312. #2568	C₂×C₈₉	semidirect
313. #2565	C₂×C₈₉	semidirect
314. #2547	C₂×C₈₉	semidirect
315. #2546	C₂×C₈₉	semidirect
316. #2545	C₂×C₈₉	semidirect
317. #2542	C₂×C₈₉	semidirect
318. #2498	C₂×C₈₉	semidirect
319. #2417	C₂×C₈₉	semidirect
320. #2323	C₂×C₈₉	semidirect
321. C₂×C₄×C₄⋊C₄	C₂×C₈₉	semidirect
322. C₈₉	#35241	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#533×C₈₉	2
C₂×#529×C₈₉	2
C₈₉×#2857	2
C₈₉×#2850	2
C₈₉×#2664	2
C₈₉×#2568	2
C₈₉×#2565	2
C₈₉×#2547	2
C₈₉×#2546	2
C₈₉×#2545	2
C₈₉×#2542	2
C₈₉×#2498	2
C₈₉×#2417	2
C₈₉×#2323	2
C₂×C₄×C₄⋊C₄×C₈₉	2
#35241	89

Subgroups — C89×#35241 #36413089

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35241 #36413089