Subgroups — C₈₉×#25335 #36403183

Order 22784.

872 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#489×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#463×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2563	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2367	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2074	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2073	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2055	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#2054	C₂	1	1	yes	maximal, characteristic
9	C₈₉×#1988	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1940	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1880	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#1879	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#1805	C₂	1	1	yes	maximal, characteristic, complemented
14	C₈₉×#1804	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#1762	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×D₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
23	#489×C₈₉	—	2	4	no	—
24	#463×C₈₉	—	2	4	no	—
25	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#103×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
32	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
33	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
35	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
36	C₂×#97×C₈₉	C₂²	1	1	yes	characteristic
37	#393×C₈₉	—	2	1	no	—
38	#393×C₈₉	—	2	1	no	—
39	#391×C₈₉	C₂²	1	1	yes	characteristic
40	#390×C₈₉	C₂²	1	1	yes	characteristic
41	#390×C₈₉	C₂²	1	1	yes	characteristic
42	#390×C₈₉	C₂²	1	1	yes	characteristic
43	#388×C₈₉	—	2	1	no	—
44	#388×C₈₉	—	2	1	no	—
45	#385×C₈₉	—	2	1	no	—
46	#382×C₈₉	C₂²	1	1	yes	characteristic
47	#382×C₈₉	C₂²	1	1	yes	characteristic
48	#380×C₈₉	—	2	1	no	—
49	#380×C₈₉	—	2	1	no	—
50	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
52	C₄×C₂²⋊C₄×C₈₉	—	2	1	no	—
53	#340×C₈₉	C₂²	1	1	yes	characteristic
54	#340×C₈₉	C₂²	1	1	yes	characteristic
55	#340×C₈₉	C₂²	1	1	yes	characteristic
56	#340×C₈₉	C₂²	1	1	yes	characteristic
57	#340×C₈₉	C₂²	1	1	yes	characteristic
58	#340×C₈₉	C₂²	1	1	yes	characteristic
59	#336×C₈₉	C₂²	1	1	yes	characteristic
60	#336×C₈₉	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₈₉	—	2	1	no	—
62	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₈₉	—	2	1	no	—
66	C₂³×C₄×C₈₉	—	2	1	no	—
67	C₂×SD₁₆×C₈₉	—	2	2	no	—
68	C₂×SD₁₆×C₈₉	—	2	2	no	—
69	C₂×SD₁₆×C₈₉	—	4	1	no	—
70	C₂×D₈×C₈₉	—	2	2	no	—
71	C₂×D₈×C₈₉	—	2	2	no	—
72	C₂×D₈×C₈₉	—	4	1	no	—
73	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
77	C₄⋊Q₈×C₈₉	—	2	2	no	—
78	C₄⋊Q₈×C₈₉	—	2	2	no	—
79	#124×C₈₉	—	2	2	no	—
80	#124×C₈₉	D₄	1	4	yes	—
81	C₄×Q₈×C₈₉	—	2	2	no	—
82	C₄×Q₈×C₈₉	—	4	1	no	—
83	C₄×D₄×C₈₉	—	2	2	no	—
84	C₄×D₄×C₈₉	—	2	2	no	—
85	C₄×D₄×C₈₉	—	2	2	no	—
86	C₄×D₄×C₈₉	—	4	1	no	—
87	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
88	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
89	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
99	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
100	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
101	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
102	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
103	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
104	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
105	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
106	C₂×C₄²×C₈₉	—	2	1	no	—
107	C₂×C₄²×C₈₉	—	2	1	no	—
108	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
111	C₄⋊C₈×C₈₉	—	2	2	no	—
112	C₄⋊C₈×C₈₉	—	4	1	no	—
113	C₄⋊C₈×C₈₉	—	4	1	no	—
114	#103×C₈₉	—	2	2	no	—
115	#103×C₈₉	—	2	2	no	—
116	#103×C₈₉	—	2	2	no	—
117	#102×C₈₉	—	2	2	no	—
118	#102×C₈₉	—	2	2	no	—
119	#102×C₈₉	—	2	2	no	—
120	#102×C₈₉	—	2	2	no	—
121	#102×C₈₉	—	2	2	no	—
122	#97×C₈₉	—	2	2	no	—
123	#95×C₈₉	—	2	1	no	—
124	#95×C₈₉	—	2	1	no	—
125	#95×C₈₉	—	2	1	no	—
126	#95×C₈₉	—	2	1	no	—
127	#95×C₈₉	—	2	1	no	—
128	#95×C₈₉	—	2	1	no	—
129	#95×C₈₉	—	2	1	no	—
130	#95×C₈₉	D₄	1	1	yes	characteristic
131	#95×C₈₉	D₄	1	1	yes	characteristic
132	C₂⁴×C₈₉	—	2	1	no	—
133	C₂⁴×C₈₉	—	2	1	no	—
134	C₂×Q₈×C₈₉	—	2	1	no	—
135	C₂×Q₈×C₈₉	—	2	1	no	—
136	C₂×Q₈×C₈₉	—	2	1	no	—
137	C₂×Q₈×C₈₉	—	2	1	no	—
138	C₂×Q₈×C₈₉	—	2	1	no	—
139	C₂×Q₈×C₈₉	—	4	2	no	—
140	C₂×Q₈×C₈₉	—	8	1	no	—
141	C₂×Q₈×C₈₉	—	8	1	no	—
142	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
143	C₂×D₄×C₈₉	—	2	1	no	—
144	C₂×D₄×C₈₉	—	2	1	no	—
145	C₂×D₄×C₈₉	—	2	1	no	—
146	C₂×D₄×C₈₉	—	2	1	no	—
147	C₂×D₄×C₈₉	—	2	1	no	—
148	C₂×D₄×C₈₉	—	2	1	no	—
149	C₂×D₄×C₈₉	—	2	1	no	—
150	C₂×D₄×C₈₉	—	2	1	no	—
151	C₂×D₄×C₈₉	—	2	1	no	—
152	C₂×D₄×C₈₉	—	2	1	no	—
153	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
154	C₂×D₄×C₈₉	#41	1	2	yes	—
155	C₂²×C₄×C₈₉	—	2	1	no	—
156	C₂²×C₄×C₈₉	—	2	1	no	—
157	C₂²×C₄×C₈₉	—	2	1	no	—
158	C₂²×C₄×C₈₉	—	2	1	no	—
159	C₂²×C₄×C₈₉	—	2	1	no	—
160	C₂²×C₄×C₈₉	—	2	1	no	—
161	C₂²×C₄×C₈₉	—	4	2	no	—
162	C₂²×C₄×C₈₉	—	4	2	no	—
163	C₂²×C₄×C₈₉	—	4	2	no	—
164	C₂²×C₄×C₈₉	—	4	2	no	—
165	C₂²×C₄×C₈₉	—	4	2	no	—
166	C₂²×C₄×C₈₉	—	8	1	no	—
167	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
174	SD₁₆×C₈₉	—	4	4	no	—
175	D₈×C₈₉	—	4	4	no	—
176	C₂×C₈×C₈₉	—	2	1	no	—
177	C₂×C₈×C₈₉	—	2	1	no	—
178	C₂×C₈×C₈₉	—	2	1	no	—
179	C₂×C₈×C₈₉	—	2	1	no	—
180	C₂×C₈×C₈₉	—	2	1	no	—
181	C₂×C₈×C₈₉	—	2	1	no	—
182	C₂×C₈×C₈₉	—	2	1	no	—
183	C₂×C₈×C₈₉	—	2	1	no	—
184	C₂×C₈×C₈₉	—	2	1	no	—
185	C₂×C₈×C₈₉	—	2	1	no	—
186	C₂×C₈×C₈₉	—	2	1	no	—
187	C₂×C₈×C₈₉	—	2	1	no	—
188	C₄⋊C₄×C₈₉	—	2	1	no	—
189	C₄⋊C₄×C₈₉	—	2	1	no	—
190	C₄⋊C₄×C₈₉	—	2	1	no	—
191	C₄⋊C₄×C₈₉	—	2	1	no	—
192	C₄⋊C₄×C₈₉	—	2	1	no	—
193	C₄⋊C₄×C₈₉	—	2	1	no	—
194	C₄⋊C₄×C₈₉	—	2	1	no	—
195	C₄⋊C₄×C₈₉	—	2	1	no	—
196	C₄⋊C₄×C₈₉	—	2	1	no	—
197	C₄⋊C₄×C₈₉	—	4	1	no	—
198	C₄⋊C₄×C₈₉	—	4	1	no	—
199	C₄⋊C₄×C₈₉	—	4	2	no	—
200	C₄⋊C₄×C₈₉	—	4	2	no	—
201	C₄⋊C₄×C₈₉	#41	1	2	yes	—
202	C₂²⋊C₄×C₈₉	—	2	4	no	—
203	C₂²⋊C₄×C₈₉	—	2	4	no	—
204	C₂²⋊C₄×C₈₉	—	4	2	no	—
205	C₂²⋊C₄×C₈₉	—	4	2	no	—
206	C₂²⋊C₄×C₈₉	—	4	2	no	—
207	C₂²⋊C₄×C₈₉	—	8	1	no	—
208	C₂²⋊C₄×C₈₉	—	8	1	no	—
209	C₂²⋊C₄×C₈₉	—	8	1	no	—
210	C₂²⋊C₄×C₈₉	—	8	1	no	—
211	C₂²⋊C₄×C₈₉	—	8	1	no	—
212	C₄²×C₈₉	—	2	1	no	—
213	C₄²×C₈₉	—	2	1	no	—
214	C₄²×C₈₉	—	2	1	no	—
215	C₄²×C₈₉	—	2	1	no	—
216	C₄²×C₈₉	—	4	2	no	—
217	C₄²×C₈₉	—	8	1	no	—
218	C₄²×C₈₉	C₂×D₄	1	2	yes	—
219	C₄²×C₈₉	#41	1	2	yes	—
220	C₂³×C₈₉	—	2	2	no	—
221	C₂³×C₈₉	—	2	2	no	—
222	C₂³×C₈₉	—	4	1	no	—
223	C₂³×C₈₉	—	4	1	no	—
224	C₂³×C₈₉	—	4	1	no	—
225	C₂³×C₈₉	—	4	1	no	—
226	C₂³×C₈₉	—	4	1	no	—
227	C₂³×C₈₉	—	4	1	no	—
228	C₂³×C₈₉	—	4	1	no	—
229	C₂³×C₈₉	—	4	1	no	—
230	C₂³×C₈₉	—	4	1	no	—
231	C₂³×C₈₉	—	4	1	no	—
232	C₂³×C₈₉	—	4	1	no	—
233	C₂³×C₈₉	—	4	1	no	—
234	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
235	Q₈×C₈₉	—	2	2	no	—
236	Q₈×C₈₉	—	2	2	no	—
237	Q₈×C₈₉	—	4	1	no	—
238	Q₈×C₈₉	—	4	1	no	—
239	Q₈×C₈₉	—	8	4	no	—
240	D₄×C₈₉	—	2	2	no	—
241	D₄×C₈₉	—	2	2	no	—
242	D₄×C₈₉	—	2	2	no	—
243	D₄×C₈₉	—	2	2	no	—
244	D₄×C₈₉	—	4	1	no	—
245	D₄×C₈₉	—	4	1	no	—
246	D₄×C₈₉	—	4	1	no	—
247	D₄×C₈₉	—	4	1	no	—
248	C₂×C₄×C₈₉	—	2	1	no	—
249	C₂×C₄×C₈₉	—	2	1	no	—
250	C₂×C₄×C₈₉	—	2	1	no	—
251	C₂×C₄×C₈₉	—	2	1	no	—
252	C₂×C₄×C₈₉	—	2	2	no	—
253	C₂×C₄×C₈₉	—	2	1	no	—
254	C₂×C₄×C₈₉	—	2	1	no	—
255	C₂×C₄×C₈₉	—	2	1	no	—
256	C₂×C₄×C₈₉	—	2	1	no	—
257	C₂×C₄×C₈₉	—	2	2	no	—
258	C₂×C₄×C₈₉	—	2	1	no	—
259	C₂×C₄×C₈₉	—	2	1	no	—
260	C₂×C₄×C₈₉	—	2	1	no	—
261	C₂×C₄×C₈₉	—	2	1	no	—
262	C₂×C₄×C₈₉	—	2	1	no	—
263	C₂×C₄×C₈₉	—	2	1	no	—
264	C₂×C₄×C₈₉	—	2	1	no	—
265	C₂×C₄×C₈₉	—	2	1	no	—
266	C₂×C₄×C₈₉	—	4	1	no	—
267	C₂×C₄×C₈₉	—	4	1	no	—
268	C₂×C₄×C₈₉	—	4	1	no	—
269	C₂×C₄×C₈₉	—	4	1	no	—
270	C₂×C₄×C₈₉	—	4	1	no	—
271	C₂×C₄×C₈₉	—	4	1	no	—
272	C₂×C₄×C₈₉	—	4	1	no	—
273	C₂×C₄×C₈₉	—	4	1	no	—
274	C₂×C₄×C₈₉	—	4	1	no	—
275	C₂×C₄×C₈₉	—	4	1	no	—
276	C₂×C₄×C₈₉	—	4	1	no	—
277	C₂×C₄×C₈₉	—	4	1	no	—
278	C₂×C₄×C₈₉	—	4	1	no	—
279	C₂×C₄×C₈₉	—	4	1	no	—
280	C₂×C₄×C₈₉	—	4	1	no	—
281	C₂×C₄×C₈₉	—	4	1	no	—
282	C₂×C₄×C₈₉	—	8	4	no	—
283	C₂×C₄×C₈₉	—	8	4	no	—
284	C₂×C₄×C₈₉	#121	1	2	yes	—
285	C₂×C₄×C₈₉	#121	1	2	yes	—
286	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
288	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
289	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
290	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
291	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
292	C₈×C₈₉	—	4	1	no	—
293	C₈×C₈₉	—	4	1	no	—
294	C₈×C₈₉	—	4	1	no	—
295	C₈×C₈₉	—	4	1	no	—
296	C₂²×C₈₉	—	4	2	no	—
297	C₂²×C₈₉	—	4	2	no	—
298	C₂²×C₈₉	—	4	2	no	—
299	C₂²×C₈₉	—	4	2	no	—
300	C₂²×C₈₉	—	4	2	no	—
301	C₂²×C₈₉	—	4	2	no	—
302	C₂²×C₈₉	—	8	1	no	—
303	C₂²×C₈₉	—	8	1	no	—
304	C₂²×C₈₉	—	8	1	no	—
305	C₂²×C₈₉	—	8	1	no	—
306	C₂²×C₈₉	—	8	1	no	—
307	C₂²×C₈₉	—	8	1	no	—
308	C₂²×C₈₉	—	8	1	no	—
309	C₂²×C₈₉	—	8	1	no	—
310	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
311	C₂²×C₈₉	#546	1	1	yes	characteristic
312	C₂²×C₈₉	#548	1	1	yes	characteristic
313	C₂²×C₈₉	#575	1	1	yes	characteristic
314	C₂²×C₈₉	#575	1	1	yes	characteristic
315	C₂²×C₈₉	#576	1	1	yes	characteristic
316	C₂²×C₈₉	#577	1	1	yes	characteristic
317	C₄×C₈₉	—	2	2	no	—
318	C₄×C₈₉	—	2	2	no	—
319	C₄×C₈₉	—	4	2	no	—
320	C₄×C₈₉	—	4	1	no	—
321	C₄×C₈₉	—	4	1	no	—
322	C₄×C₈₉	—	4	2	no	—
323	C₄×C₈₉	—	4	1	no	—
324	C₄×C₈₉	—	4	1	no	—
325	C₄×C₈₉	—	8	1	no	—
326	C₄×C₈₉	—	8	1	no	—
327	C₄×C₈₉	—	8	1	no	—
328	C₄×C₈₉	—	8	1	no	—
329	C₄×C₈₉	#529	1	1	yes	characteristic
330	C₄×C₈₉	#542	1	1	yes	characteristic
331	C₄×C₈₉	#546	1	1	yes	characteristic
332	C₄×C₈₉	#547	1	1	yes	characteristic
333	#25335	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
334	C₂×C₈₉	—	8	2	no	—
335	C₂×C₈₉	—	8	2	no	—
336	C₂×C₈₉	#2427	1	1	yes	characteristic
337	C₂×C₈₉	#3040	1	1	yes	characteristic
338	C₂×C₈₉	#3045	1	1	yes	characteristic
339	C₂×C₈₉	#3319	1	1	yes	characteristic
340	C₂×C₈₉	#3321	1	1	yes	characteristic
341	C₂×C₈₉	#3370	1	1	yes	characteristic
342	C₂×C₈₉	#3376	1	1	yes	characteristic
343	C₂×#489	C₂×C₈₉	1	1	yes	characteristic, complemented
344	C₂×#463	C₂×C₈₉	1	1	yes	characteristic
345	#2563	C₂×C₈₉	1	1	yes	characteristic, complemented
346	#2367	C₂×C₈₉	1	1	yes	characteristic, complemented
347	#2074	C₂×C₈₉	1	1	yes	characteristic, complemented
348	#2073	C₂×C₈₉	1	1	yes	characteristic, complemented
349	#2055	C₂×C₈₉	1	1	yes	characteristic, complemented
350	#2054	C₂×C₈₉	1	1	yes	characteristic
351	#1988	C₂×C₈₉	1	1	yes	characteristic, complemented
352	#1940	C₂×C₈₉	1	1	yes	characteristic, complemented
353	#1880	C₂×C₈₉	1	1	yes	characteristic, complemented
354	#1879	C₂×C₈₉	1	1	yes	characteristic
355	#1805	C₂×C₈₉	1	1	yes	characteristic, complemented
356	#1804	C₂×C₈₉	1	1	yes	characteristic, complemented
357	#1762	C₂×C₈₉	1	1	yes	characteristic, complemented
358	C₈₉	#25335	1	1	yes	characteristic, direct product factor, Sylow
359	C₂²×SD₁₆	C₂²×C₈₉	1	1	yes	characteristic
360	C₂²×D₈	C₂²×C₈₉	1	1	yes	characteristic
361	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
362	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
363	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
364	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
365	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
366	#489	—	2	4	no	—
367	#463	—	2	4	no	—
368	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
369	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
370	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
371	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
372	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
373	C₂×#103	C₂²×C₈₉	1	1	yes	characteristic
374	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
375	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
376	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
377	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
378	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
379	C₂×#97	C₂²×C₈₉	1	1	yes	characteristic
380	#393	—	2	1	no	—
381	#393	—	2	1	no	—
382	#391	C₂²×C₈₉	1	1	yes	characteristic
383	#390	C₂²×C₈₉	1	1	yes	characteristic
384	#390	C₂²×C₈₉	1	1	yes	characteristic
385	#390	C₂²×C₈₉	1	1	yes	characteristic
386	#388	—	2	1	no	—
387	#388	—	2	1	no	—
388	#385	—	2	1	no	—
389	#382	C₂²×C₈₉	1	1	yes	characteristic
390	#382	C₂²×C₈₉	1	1	yes	characteristic
391	#380	—	2	1	no	—
392	#380	—	2	1	no	—
393	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
394	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
395	C₄×C₂²⋊C₄	—	2	1	no	—
396	#340	C₂²×C₈₉	1	1	yes	characteristic
397	#340	C₂²×C₈₉	1	1	yes	characteristic
398	#340	C₂²×C₈₉	1	1	yes	characteristic
399	#340	C₂²×C₈₉	1	1	yes	characteristic
400	#340	C₂²×C₈₉	1	1	yes	characteristic
401	#340	C₂²×C₈₉	1	1	yes	characteristic
402	#336	C₂²×C₈₉	1	1	yes	characteristic
403	#336	C₂²×C₈₉	1	1	yes	characteristic
404	C₂²×Q₈	—	2	1	no	—
405	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
406	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
407	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
408	C₂³×C₄	—	2	1	no	—
409	C₂³×C₄	—	2	1	no	—
410	C₂×SD₁₆	—	2	2	no	—
411	C₂×SD₁₆	—	2	2	no	—
412	C₂×SD₁₆	—	4	1	no	—
413	C₂×D₈	—	2	2	no	—
414	C₂×D₈	—	2	2	no	—
415	C₂×D₈	—	4	1	no	—
416	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
417	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
418	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
419	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
420	C₄⋊Q₈	—	2	2	no	—
421	C₄⋊Q₈	—	2	2	no	—
422	#124	—	2	2	no	—
423	#124	D₄×C₈₉	1	4	yes	—
424	C₄×Q₈	—	2	2	no	—
425	C₄×Q₈	—	4	1	no	—
426	C₄×D₄	—	2	2	no	—
427	C₄×D₄	—	2	2	no	—
428	C₄×D₄	—	2	2	no	—
429	C₄×D₄	—	4	1	no	—
430	C₂×C₄⋊C₄	—	2	1	no	—
431	C₂×C₄⋊C₄	—	2	1	no	—
432	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
433	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
434	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
435	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
436	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	—	2	1	no	—
440	C₂×C₂²⋊C₄	—	2	1	no	—
441	C₂×C₂²⋊C₄	—	2	1	no	—
442	C₂×C₂²⋊C₄	—	2	1	no	—
443	C₂×C₂²⋊C₄	—	2	1	no	—
444	C₂×C₂²⋊C₄	—	2	1	no	—
445	C₂×C₂²⋊C₄	—	2	1	no	—
446	C₂×C₂²⋊C₄	—	2	1	no	—
447	C₂×C₂²⋊C₄	—	2	1	no	—
448	C₂×C₂²⋊C₄	—	2	1	no	—
449	C₂×C₄²	—	2	1	no	—
450	C₂×C₄²	—	2	1	no	—
451	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
452	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
453	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
454	C₄⋊C₈	—	2	2	no	—
455	C₄⋊C₈	—	4	1	no	—
456	C₄⋊C₈	—	4	1	no	—
457	#103	—	2	2	no	—
458	#103	—	2	2	no	—
459	#103	—	2	2	no	—
460	#102	—	2	2	no	—
461	#102	—	2	2	no	—
462	#102	—	2	2	no	—
463	#102	—	2	2	no	—
464	#102	—	2	2	no	—
465	#97	—	2	2	no	—
466	#95	—	2	1	no	—
467	#95	—	2	1	no	—
468	#95	—	2	1	no	—
469	#95	—	2	1	no	—
470	#95	—	2	1	no	—
471	#95	—	2	1	no	—
472	#95	—	2	1	no	—
473	#95	D₄×C₈₉	1	1	yes	characteristic
474	#95	D₄×C₈₉	1	1	yes	characteristic
475	C₂⁴	—	2	1	no	—
476	C₂⁴	—	2	1	no	—
477	C₂×Q₈	—	2	1	no	—
478	C₂×Q₈	—	2	1	no	—
479	C₂×Q₈	—	2	1	no	—
480	C₂×Q₈	—	2	1	no	—
481	C₂×Q₈	—	2	1	no	—
482	C₂×Q₈	—	4	2	no	—
483	C₂×Q₈	—	8	1	no	—
484	C₂×Q₈	—	8	1	no	—
485	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
486	C₂×D₄	—	2	1	no	—
487	C₂×D₄	—	2	1	no	—
488	C₂×D₄	—	2	1	no	—
489	C₂×D₄	—	2	1	no	—
490	C₂×D₄	—	2	1	no	—
491	C₂×D₄	—	2	1	no	—
492	C₂×D₄	—	2	1	no	—
493	C₂×D₄	—	2	1	no	—
494	C₂×D₄	—	2	1	no	—
495	C₂×D₄	—	2	1	no	—
496	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
497	C₂×D₄	#41×C₈₉	1	2	yes	—
498	C₂²×C₄	—	2	1	no	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	4	2	no	—
505	C₂²×C₄	—	4	2	no	—
506	C₂²×C₄	—	4	2	no	—
507	C₂²×C₄	—	4	2	no	—
508	C₂²×C₄	—	4	2	no	—
509	C₂²×C₄	—	8	1	no	—
510	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
512	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
513	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
514	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
515	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
516	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
517	SD₁₆	—	4	4	no	—
518	D₈	—	4	4	no	—
519	C₂×C₈	—	2	1	no	—
520	C₂×C₈	—	2	1	no	—
521	C₂×C₈	—	2	1	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	1	no	—
525	C₂×C₈	—	2	1	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₄⋊C₄	—	2	1	no	—
532	C₄⋊C₄	—	2	1	no	—
533	C₄⋊C₄	—	2	1	no	—
534	C₄⋊C₄	—	2	1	no	—
535	C₄⋊C₄	—	2	1	no	—
536	C₄⋊C₄	—	2	1	no	—
537	C₄⋊C₄	—	2	1	no	—
538	C₄⋊C₄	—	2	1	no	—
539	C₄⋊C₄	—	2	1	no	—
540	C₄⋊C₄	—	4	1	no	—
541	C₄⋊C₄	—	4	1	no	—
542	C₄⋊C₄	—	4	2	no	—
543	C₄⋊C₄	—	4	2	no	—
544	C₄⋊C₄	#41×C₈₉	1	2	yes	—
545	C₂²⋊C₄	—	2	4	no	—
546	C₂²⋊C₄	—	2	4	no	—
547	C₂²⋊C₄	—	4	2	no	—
548	C₂²⋊C₄	—	4	2	no	—
549	C₂²⋊C₄	—	4	2	no	—
550	C₂²⋊C₄	—	8	1	no	—
551	C₂²⋊C₄	—	8	1	no	—
552	C₂²⋊C₄	—	8	1	no	—
553	C₂²⋊C₄	—	8	1	no	—
554	C₂²⋊C₄	—	8	1	no	—
555	C₄²	—	2	1	no	—
556	C₄²	—	2	1	no	—
557	C₄²	—	2	1	no	—
558	C₄²	—	2	1	no	—
559	C₄²	—	4	2	no	—
560	C₄²	—	8	1	no	—
561	C₄²	C₂×D₄×C₈₉	1	2	yes	—
562	C₄²	#41×C₈₉	1	2	yes	—
563	C₂³	—	2	2	no	—
564	C₂³	—	2	2	no	—
565	C₂³	—	4	1	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	1	no	—
569	C₂³	—	4	1	no	—
570	C₂³	—	4	1	no	—
571	C₂³	—	4	1	no	—
572	C₂³	—	4	1	no	—
573	C₂³	—	4	1	no	—
574	C₂³	—	4	1	no	—
575	C₂³	—	4	1	no	—
576	C₂³	—	4	1	no	—
577	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
578	Q₈	—	2	2	no	—
579	Q₈	—	2	2	no	—
580	Q₈	—	4	1	no	—
581	Q₈	—	4	1	no	—
582	Q₈	—	8	4	no	—
583	D₄	—	2	2	no	—
584	D₄	—	2	2	no	—
585	D₄	—	2	2	no	—
586	D₄	—	2	2	no	—
587	D₄	—	4	1	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	1	no	—
590	D₄	—	4	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	1	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	4	1	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	1	no	—
613	C₂×C₄	—	4	1	no	—
614	C₂×C₄	—	4	1	no	—
615	C₂×C₄	—	4	1	no	—
616	C₂×C₄	—	4	1	no	—
617	C₂×C₄	—	4	1	no	—
618	C₂×C₄	—	4	1	no	—
619	C₂×C₄	—	4	1	no	—
620	C₂×C₄	—	4	1	no	—
621	C₂×C₄	—	4	1	no	—
622	C₂×C₄	—	4	1	no	—
623	C₂×C₄	—	4	1	no	—
624	C₂×C₄	—	4	1	no	—
625	C₂×C₄	—	8	4	no	—
626	C₂×C₄	—	8	4	no	—
627	C₂×C₄	#121×C₈₉	1	2	yes	—
628	C₂×C₄	#121×C₈₉	1	2	yes	—
629	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
630	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
631	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
632	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
633	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
634	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
635	C₈	—	4	1	no	—
636	C₈	—	4	1	no	—
637	C₈	—	4	1	no	—
638	C₈	—	4	1	no	—
639	C₂²	—	4	2	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	2	no	—
642	C₂²	—	4	2	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	4	2	no	—
645	C₂²	—	8	1	no	—
646	C₂²	—	8	1	no	—
647	C₂²	—	8	1	no	—
648	C₂²	—	8	1	no	—
649	C₂²	—	8	1	no	—
650	C₂²	—	8	1	no	—
651	C₂²	—	8	1	no	—
652	C₂²	—	8	1	no	—
653	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
654	C₂²	#546×C₈₉	1	1	yes	characteristic
655	C₂²	#548×C₈₉	1	1	yes	characteristic
656	C₂²	#575×C₈₉	1	1	yes	characteristic
657	C₂²	#575×C₈₉	1	1	yes	characteristic
658	C₂²	#576×C₈₉	1	1	yes	characteristic
659	C₂²	#577×C₈₉	1	1	yes	characteristic
660	C₄	—	2	2	no	—
661	C₄	—	2	2	no	—
662	C₄	—	4	1	no	—
663	C₄	—	4	1	no	—
664	C₄	—	4	2	no	—
665	C₄	—	4	1	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	2	no	—
668	C₄	—	8	1	no	—
669	C₄	—	8	1	no	—
670	C₄	—	8	1	no	—
671	C₄	—	8	1	no	—
672	C₄	#529×C₈₉	1	1	yes	characteristic
673	C₄	#542×C₈₉	1	1	yes	characteristic
674	C₄	#546×C₈₉	1	1	yes	characteristic
675	C₄	#547×C₈₉	1	1	yes	characteristic
676	C₂	—	8	2	no	—
677	C₂	—	8	2	no	—
678	C₂	C₈₉×#2427	1	1	yes	characteristic
679	C₂	C₈₉×#3040	1	1	yes	characteristic
680	C₂	C₈₉×#3045	1	1	yes	characteristic
681	C₂	C₈₉×#3319	1	1	yes	characteristic
682	C₂	C₈₉×#3321	1	1	yes	characteristic
683	C₂	C₈₉×#3370	1	1	yes	characteristic
684	C₂	C₈₉×#3376	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂²×D₈×C₈₉	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₄×C₄⋊C₄×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#489×C₈₉	C₂	semidirect
3. C₈₉×#2563	C₂	semidirect
4. C₈₉×#2367	C₂	semidirect
5. C₈₉×#2074	C₂	semidirect
6. C₈₉×#2073	C₂	semidirect
7. C₈₉×#2055	C₂	semidirect
9. C₈₉×#1988	C₂	semidirect
10. C₈₉×#1940	C₂	semidirect
11. C₈₉×#1880	C₂	semidirect
13. C₈₉×#1805	C₂	semidirect
14. C₈₉×#1804	C₂	semidirect
15. C₈₉×#1762	C₂	semidirect
333. #25335	C₈₉	direct (N × H)
343. C₂×#489	C₂×C₈₉	semidirect
345. #2563	C₂×C₈₉	semidirect
346. #2367	C₂×C₈₉	semidirect
347. #2074	C₂×C₈₉	semidirect
348. #2073	C₂×C₈₉	semidirect
349. #2055	C₂×C₈₉	semidirect
351. #1988	C₂×C₈₉	semidirect
352. #1940	C₂×C₈₉	semidirect
353. #1880	C₂×C₈₉	semidirect
355. #1805	C₂×C₈₉	semidirect
356. #1804	C₂×C₈₉	semidirect
357. #1762	C₂×C₈₉	semidirect
358. C₈₉	#25335	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×#489×C₈₉	2
C₂×#463×C₈₉	2
C₈₉×#2563	2
C₈₉×#2367	2
C₈₉×#2074	2
C₈₉×#2073	2
C₈₉×#2055	2
C₈₉×#2054	2
C₈₉×#1988	2
C₈₉×#1940	2
C₈₉×#1880	2
C₈₉×#1879	2
C₈₉×#1805	2
C₈₉×#1804	2
C₈₉×#1762	2
#25335	89

Subgroups — C89×#25335 #36403183

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25335 #36403183