Subgroups — C₈₉×#25292 #36403140

Order 22784.

954 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#459×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2548	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2538	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2067	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2054	C₂	1	2	yes	maximal, complemented
7	C₈₉×#1970	C₂	1	2	yes	maximal, complemented
8	C₈₉×#1957	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#1947	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#1934	C₂	1	2	yes	maximal, complemented
11	C₄×#102×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₈₉	C₂²	1	2	yes	—
13	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
14	C₂×#124×C₈₉	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₈₉	—	2	1	no	—
16	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
18	#459×C₈₉	—	2	4	no	—
19	C₈×Q₈×C₈₉	—	2	4	no	—
20	C₂×#107×C₈₉	C₂²	1	2	yes	—
21	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#102×C₈₉	C₂²	1	2	yes	—
25	C₂×#102×C₈₉	C₂²	1	2	yes	—
26	C₂×#102×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#102×C₈₉	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
29	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
30	#396×C₈₉	—	2	2	no	—
31	#394×C₈₉	—	2	2	no	—
32	#390×C₈₉	—	2	1	no	—
33	#390×C₈₉	C₂²	1	2	yes	—
34	#390×C₈₉	C₂²	1	2	yes	—
35	#390×C₈₉	C₂²	1	2	yes	—
36	#389×C₈₉	C₂²	1	2	yes	—
37	#384×C₈₉	C₂²	1	1	yes	characteristic
38	#380×C₈₉	—	2	1	no	—
39	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
40	#340×C₈₉	C₂²	1	2	yes	—
41	#340×C₈₉	C₂²	1	1	yes	characteristic
42	#340×C₈₉	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₈₉	—	2	1	no	—
45	C₂²×D₄×C₈₉	—	2	1	no	—
46	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
47	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₈₉	—	2	1	no	—
49	C₂×D₈×C₈₉	—	2	4	no	—
50	C₂×D₈×C₈₉	—	2	4	no	—
51	C₂×D₈×C₈₉	—	4	2	no	—
52	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
53	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
54	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
55	#127×C₈₉	—	2	2	no	—
56	#127×C₈₉	—	2	2	no	—
57	#124×C₈₉	—	4	4	no	—
58	C₂²⋊Q₈×C₈₉	—	4	4	no	—
59	C₄×Q₈×C₈₉	—	2	2	no	—
60	C₄×Q₈×C₈₉	—	2	2	no	—
61	C₄×D₄×C₈₉	—	2	2	no	—
62	C₄×D₄×C₈₉	—	2	2	no	—
63	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
65	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
79	C₂×C₄²×C₈₉	—	2	1	no	—
80	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
81	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
82	#107×C₈₉	—	4	2	no	—
83	C₄⋊C₈×C₈₉	—	2	4	no	—
84	C₄⋊C₈×C₈₉	D₄	1	4	yes	—
85	#102×C₈₉	—	2	2	no	—
86	#102×C₈₉	—	2	4	no	—
87	#102×C₈₉	—	2	2	no	—
88	#102×C₈₉	—	2	4	no	—
89	#102×C₈₉	—	4	2	no	—
90	C₄×C₈×C₈₉	—	2	4	no	—
91	C₄×C₈×C₈₉	—	2	2	no	—
92	#95×C₈₉	—	2	1	no	—
93	#95×C₈₉	—	2	2	no	—
94	C₂⁴×C₈₉	—	2	1	no	—
95	C₂⁴×C₈₉	—	2	2	no	—
96	C₂×Q₈×C₈₉	—	2	2	no	—
97	C₂×Q₈×C₈₉	—	2	2	no	—
98	C₂×Q₈×C₈₉	D₈	1	4	yes	complemented
99	C₂×D₄×C₈₉	—	2	1	no	—
100	C₂×D₄×C₈₉	—	2	2	no	—
101	C₂×D₄×C₈₉	—	2	1	no	—
102	C₂×D₄×C₈₉	—	2	1	no	—
103	C₂×D₄×C₈₉	—	2	2	no	—
104	C₂×D₄×C₈₉	—	2	2	no	—
105	C₂×D₄×C₈₉	—	2	2	no	—
106	C₂×D₄×C₈₉	—	2	1	no	—
107	C₂×D₄×C₈₉	—	2	2	no	—
108	C₂×D₄×C₈₉	—	2	1	no	—
109	C₂×D₄×C₈₉	—	2	2	no	—
110	C₂×D₄×C₈₉	—	4	2	no	—
111	C₂×D₄×C₈₉	—	4	2	no	—
112	C₂×D₄×C₈₉	—	4	2	no	—
113	C₂×D₄×C₈₉	—	4	2	no	—
114	C₂×D₄×C₈₉	—	8	1	no	—
115	C₂×D₄×C₈₉	—	8	1	no	—
116	C₂×D₄×C₈₉	#41	1	2	yes	—
117	C₂²×C₄×C₈₉	—	2	1	no	—
118	C₂²×C₄×C₈₉	—	2	1	no	—
119	C₂²×C₄×C₈₉	—	2	1	no	—
120	C₂²×C₄×C₈₉	—	2	2	no	—
121	C₂²×C₄×C₈₉	—	4	2	no	—
122	C₂²×C₄×C₈₉	—	4	2	no	—
123	C₂²×C₄×C₈₉	—	4	2	no	—
124	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
125	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
129	D₈×C₈₉	—	4	8	no	—
130	C₂×C₈×C₈₉	—	2	1	no	—
131	C₂×C₈×C₈₉	—	2	2	no	—
132	C₂×C₈×C₈₉	—	2	2	no	—
133	C₂×C₈×C₈₉	—	2	1	no	—
134	C₂×C₈×C₈₉	—	2	1	no	—
135	C₂×C₈×C₈₉	—	2	1	no	—
136	C₂×C₈×C₈₉	—	2	1	no	—
137	C₂×C₈×C₈₉	C₂×D₄	1	4	yes	—
138	C₂×C₈×C₈₉	#41	1	2	yes	—
139	C₄⋊C₄×C₈₉	—	2	4	no	—
140	C₄⋊C₄×C₈₉	—	2	2	no	—
141	C₄⋊C₄×C₈₉	—	2	1	no	—
142	C₄⋊C₄×C₈₉	—	2	1	no	—
143	C₄⋊C₄×C₈₉	—	2	1	no	—
144	C₄⋊C₄×C₈₉	—	2	2	no	—
145	C₄⋊C₄×C₈₉	—	2	1	no	—
146	C₄⋊C₄×C₈₉	—	2	2	no	—
147	C₄⋊C₄×C₈₉	—	2	1	no	—
148	C₄⋊C₄×C₈₉	—	2	1	no	—
149	C₄⋊C₄×C₈₉	—	4	2	no	—
150	C₄⋊C₄×C₈₉	—	4	4	no	—
151	C₄⋊C₄×C₈₉	—	8	1	no	—
152	C₂²⋊C₄×C₈₉	—	4	2	no	—
153	C₂²⋊C₄×C₈₉	—	4	4	no	—
154	C₂²⋊C₄×C₈₉	—	4	4	no	—
155	C₂²⋊C₄×C₈₉	—	4	4	no	—
156	C₂²⋊C₄×C₈₉	—	8	2	no	—
157	C₂²⋊C₄×C₈₉	—	8	2	no	—
158	C₂²⋊C₄×C₈₉	—	8	2	no	—
159	C₄²×C₈₉	—	2	2	no	—
160	C₄²×C₈₉	—	2	2	no	—
161	C₄²×C₈₉	—	4	2	no	—
162	C₄²×C₈₉	C₂×D₄	1	2	yes	—
163	C₄²×C₈₉	#41	1	2	yes	—
164	C₂³×C₈₉	—	2	2	no	—
165	C₂³×C₈₉	—	4	1	no	—
166	C₂³×C₈₉	—	4	1	no	—
167	C₂³×C₈₉	—	4	1	no	—
168	C₂³×C₈₉	—	4	1	no	—
169	C₂³×C₈₉	—	4	1	no	—
170	C₂³×C₈₉	—	4	1	no	—
171	C₂³×C₈₉	—	4	2	no	—
172	C₂³×C₈₉	—	4	2	no	—
173	C₂³×C₈₉	—	4	2	no	—
174	C₂³×C₈₉	—	4	2	no	—
175	C₂³×C₈₉	—	4	2	no	—
176	C₂³×C₈₉	—	4	2	no	—
177	C₂³×C₈₉	—	4	2	no	—
178	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₈₉	—	2	8	no	—
180	D₄×C₈₉	—	2	2	no	—
181	D₄×C₈₉	—	2	2	no	—
182	D₄×C₈₉	—	4	2	no	—
183	D₄×C₈₉	—	4	1	no	—
184	D₄×C₈₉	—	4	2	no	—
185	D₄×C₈₉	—	4	2	no	—
186	D₄×C₈₉	—	4	1	no	—
187	D₄×C₈₉	—	4	2	no	—
188	D₄×C₈₉	—	8	4	no	—
189	D₄×C₈₉	—	8	4	no	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	—	2	2	no	—
192	C₂×C₄×C₈₉	—	2	1	no	—
193	C₂×C₄×C₈₉	—	2	1	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	—	4	1	no	—
198	C₂×C₄×C₈₉	—	4	1	no	—
199	C₂×C₄×C₈₉	—	4	2	no	—
200	C₂×C₄×C₈₉	—	4	1	no	—
201	C₂×C₄×C₈₉	—	4	1	no	—
202	C₂×C₄×C₈₉	—	4	1	no	—
203	C₂×C₄×C₈₉	—	4	2	no	—
204	C₂×C₄×C₈₉	—	4	1	no	—
205	C₂×C₄×C₈₉	—	4	1	no	—
206	C₂×C₄×C₈₉	—	4	1	no	—
207	C₂×C₄×C₈₉	—	4	2	no	—
208	C₂×C₄×C₈₉	—	4	1	no	—
209	C₂×C₄×C₈₉	—	8	4	no	—
210	C₂×C₄×C₈₉	#121	1	2	yes	—
211	C₂×C₄×C₈₉	#121	1	2	yes	—
212	C₂×C₄×C₈₉	C₂×D₈	1	4	yes	—
213	C₂×C₄×C₈₉	C₂×D₈	1	2	yes	—
214	C₂×C₄×C₈₉	#135	1	2	yes	—
215	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
216	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
217	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
218	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
219	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
220	C₂×C₄×C₈₉	2₋¹⁺⁴	1	1	yes	characteristic
221	C₈×C₈₉	—	2	4	no	—
222	C₈×C₈₉	—	2	2	no	—
223	C₈×C₈₉	—	4	1	no	—
224	C₂²×C₈₉	—	4	2	no	—
225	C₂²×C₈₉	—	4	2	no	—
226	C₂²×C₈₉	—	4	2	no	—
227	C₂²×C₈₉	—	8	1	no	—
228	C₂²×C₈₉	—	8	1	no	—
229	C₂²×C₈₉	—	8	1	no	—
230	C₂²×C₈₉	—	8	1	no	—
231	C₂²×C₈₉	—	8	2	no	—
232	C₂²×C₈₉	—	8	2	no	—
233	C₂²×C₈₉	—	8	2	no	—
234	C₂²×C₈₉	—	8	2	no	—
235	C₂²×C₈₉	—	8	2	no	—
236	C₂²×C₈₉	—	8	2	no	—
237	C₂²×C₈₉	—	8	2	no	—
238	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
239	C₂²×C₈₉	#548	1	1	yes	characteristic
240	C₂²×C₈₉	#550	1	1	yes	characteristic
241	C₂²×C₈₉	C₂²×D₈	1	1	yes	characteristic
242	C₂²×C₈₉	C₂×#135	1	1	yes	characteristic
243	C₂²×C₈₉	#576	1	1	yes	characteristic
244	C₂²×C₈₉	#577	1	1	yes	characteristic
245	C₄×C₈₉	—	2	4	no	—
246	C₄×C₈₉	—	2	2	no	—
247	C₄×C₈₉	—	4	2	no	—
248	C₄×C₈₉	—	8	1	no	—
249	C₄×C₈₉	—	8	1	no	—
250	C₄×C₈₉	—	8	2	no	—
251	C₄×C₈₉	—	8	1	no	—
252	C₄×C₈₉	#466	1	4	yes	—
253	C₄×C₈₉	#529	1	1	yes	characteristic
254	C₄×C₈₉	#542	1	1	yes	characteristic
255	C₄×C₈₉	#546	1	1	yes	characteristic
256	C₄×C₈₉	#548	1	1	yes	characteristic
257	#25292	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
258	C₂×C₈₉	—	8	2	no	—
259	C₂×C₈₉	—	16	2	no	—
260	C₂×C₈₉	#2426	1	1	yes	characteristic
261	C₂×C₈₉	C₂×#466	1	1	yes	characteristic
262	C₂×C₈₉	#3062	1	1	yes	characteristic
263	C₂×C₈₉	#3358	1	1	yes	characteristic
264	C₂×C₈₉	#3361	1	1	yes	characteristic
265	C₂×C₈₉	#3391	1	1	yes	characteristic
266	C₂×C₈₉	#3394	1	1	yes	characteristic
267	C₂×#459	C₂×C₈₉	1	1	yes	characteristic
268	C₂×C₈×Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
269	#2548	C₂×C₈₉	1	1	yes	characteristic, complemented
270	#2538	C₂×C₈₉	1	1	yes	characteristic, complemented
271	#2067	C₂×C₈₉	1	2	yes	complemented
272	#2054	C₂×C₈₉	1	2	yes	complemented
273	#1970	C₂×C₈₉	1	2	yes	complemented
274	#1957	C₂×C₈₉	1	1	yes	characteristic, complemented
275	#1947	C₂×C₈₉	1	1	yes	characteristic, complemented
276	#1934	C₂×C₈₉	1	2	yes	complemented
277	C₄×#102	C₂×C₈₉	1	1	yes	characteristic, complemented
278	C₈₉	#25292	1	1	yes	characteristic, direct product factor, Sylow
279	C₂²×D₈	C₂²×C₈₉	1	2	yes	—
280	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
281	C₂×#124	—	2	1	no	—
282	C₂×C₂²⋊Q₈	—	2	1	no	—
283	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
284	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
285	#459	—	2	4	no	—
286	C₈×Q₈	—	2	4	no	—
287	C₂×#107	C₂²×C₈₉	1	2	yes	—
288	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
289	C₂×C₄⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
290	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
291	C₂×#102	C₂²×C₈₉	1	2	yes	—
292	C₂×#102	C₂²×C₈₉	1	2	yes	—
293	C₂×#102	C₂²×C₈₉	1	1	yes	characteristic
294	C₂×#102	C₂²×C₈₉	1	2	yes	—
295	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
296	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
297	#396	—	2	2	no	—
298	#394	—	2	2	no	—
299	#390	—	2	1	no	—
300	#390	C₂²×C₈₉	1	2	yes	—
301	#390	C₂²×C₈₉	1	2	yes	—
302	#390	C₂²×C₈₉	1	2	yes	—
303	#389	C₂²×C₈₉	1	2	yes	—
304	#384	C₂²×C₈₉	1	1	yes	characteristic
305	#380	—	2	1	no	—
306	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
307	#340	C₂²×C₈₉	1	2	yes	—
308	#340	C₂²×C₈₉	1	1	yes	characteristic
309	#340	C₂²×C₈₉	1	1	yes	characteristic
310	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
311	C₂²×D₄	—	2	1	no	—
312	C₂²×D₄	—	2	1	no	—
313	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
314	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
315	C₂³×C₄	—	2	1	no	—
316	C₂×D₈	—	2	4	no	—
317	C₂×D₈	—	2	4	no	—
318	C₂×D₈	—	4	2	no	—
319	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
320	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
321	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
322	#127	—	2	2	no	—
323	#127	—	2	2	no	—
324	#124	—	4	4	no	—
325	C₂²⋊Q₈	—	4	4	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×D₄	—	2	2	no	—
329	C₄×D₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	2	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	D₄×C₈₉	1	1	yes	characteristic
334	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
335	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
336	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
337	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
338	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
339	C₂×C₂²⋊C₄	—	2	1	no	—
340	C₂×C₂²⋊C₄	—	2	2	no	—
341	C₂×C₂²⋊C₄	—	2	2	no	—
342	C₂×C₂²⋊C₄	—	2	2	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₄²	—	2	1	no	—
347	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
348	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
349	#107	—	4	2	no	—
350	C₄⋊C₈	—	2	4	no	—
351	C₄⋊C₈	D₄×C₈₉	1	4	yes	—
352	#102	—	2	2	no	—
353	#102	—	2	4	no	—
354	#102	—	2	2	no	—
355	#102	—	2	4	no	—
356	#102	—	4	2	no	—
357	C₄×C₈	—	2	4	no	—
358	C₄×C₈	—	2	2	no	—
359	#95	—	2	1	no	—
360	#95	—	2	2	no	—
361	C₂⁴	—	2	1	no	—
362	C₂⁴	—	2	2	no	—
363	C₂×Q₈	—	2	2	no	—
364	C₂×Q₈	—	2	2	no	—
365	C₂×Q₈	D₈×C₈₉	1	4	yes	complemented
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	2	1	no	—
370	C₂×D₄	—	2	2	no	—
371	C₂×D₄	—	2	2	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	1	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	8	1	no	—
382	C₂×D₄	—	8	1	no	—
383	C₂×D₄	#41×C₈₉	1	2	yes	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	1	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	4	2	no	—
389	C₂²×C₄	—	4	2	no	—
390	C₂²×C₄	—	4	2	no	—
391	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
392	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
394	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
395	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
396	D₈	—	4	8	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	2	2	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	2	1	no	—
404	C₂×C₈	C₂×D₄×C₈₉	1	4	yes	—
405	C₂×C₈	#41×C₈₉	1	2	yes	—
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	2	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	4	2	no	—
417	C₄⋊C₄	—	4	4	no	—
418	C₄⋊C₄	—	8	1	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₂²⋊C₄	—	4	4	no	—
421	C₂²⋊C₄	—	4	4	no	—
422	C₂²⋊C₄	—	4	4	no	—
423	C₂²⋊C₄	—	8	2	no	—
424	C₂²⋊C₄	—	8	2	no	—
425	C₂²⋊C₄	—	8	2	no	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	2	no	—
428	C₄²	—	4	2	no	—
429	C₄²	C₂×D₄×C₈₉	1	2	yes	—
430	C₄²	#41×C₈₉	1	2	yes	—
431	C₂³	—	2	2	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	1	no	—
438	C₂³	—	4	2	no	—
439	C₂³	—	4	2	no	—
440	C₂³	—	4	2	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
446	Q₈	—	2	8	no	—
447	D₄	—	2	2	no	—
448	D₄	—	2	2	no	—
449	D₄	—	4	2	no	—
450	D₄	—	4	1	no	—
451	D₄	—	4	2	no	—
452	D₄	—	4	2	no	—
453	D₄	—	4	1	no	—
454	D₄	—	4	2	no	—
455	D₄	—	8	4	no	—
456	D₄	—	8	4	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	1	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	1	no	—
468	C₂×C₄	—	4	1	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	8	4	no	—
477	C₂×C₄	#121×C₈₉	1	2	yes	—
478	C₂×C₄	#121×C₈₉	1	2	yes	—
479	C₂×C₄	C₂×D₈×C₈₉	1	4	yes	—
480	C₂×C₄	C₂×D₈×C₈₉	1	2	yes	—
481	C₂×C₄	#135×C₈₉	1	2	yes	—
482	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
483	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
484	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
485	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
486	C₂×C₄	H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
487	C₂×C₄	2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
488	C₈	—	2	4	no	—
489	C₈	—	2	2	no	—
490	C₈	—	4	1	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	8	1	no	—
495	C₂²	—	8	1	no	—
496	C₂²	—	8	1	no	—
497	C₂²	—	8	1	no	—
498	C₂²	—	8	2	no	—
499	C₂²	—	8	2	no	—
500	C₂²	—	8	2	no	—
501	C₂²	—	8	2	no	—
502	C₂²	—	8	2	no	—
503	C₂²	—	8	2	no	—
504	C₂²	—	8	2	no	—
505	C₂²	C₂×#121×C₈₉	1	1	yes	characteristic
506	C₂²	#548×C₈₉	1	1	yes	characteristic
507	C₂²	#550×C₈₉	1	1	yes	characteristic
508	C₂²	C₂²×D₈×C₈₉	1	1	yes	characteristic
509	C₂²	C₂×#135×C₈₉	1	1	yes	characteristic
510	C₂²	#576×C₈₉	1	1	yes	characteristic
511	C₂²	#577×C₈₉	1	1	yes	characteristic
512	C₄	—	2	2	no	—
513	C₄	—	2	4	no	—
514	C₄	—	4	2	no	—
515	C₄	—	8	1	no	—
516	C₄	—	8	1	no	—
517	C₄	—	8	2	no	—
518	C₄	—	8	1	no	—
519	C₄	#466×C₈₉	1	4	yes	—
520	C₄	#529×C₈₉	1	1	yes	characteristic
521	C₄	#542×C₈₉	1	1	yes	characteristic
522	C₄	#546×C₈₉	1	1	yes	characteristic
523	C₄	#548×C₈₉	1	1	yes	characteristic
524	C₂	—	8	2	no	—
525	C₂	—	16	2	no	—
526	C₂	C₈₉×#2426	1	1	yes	characteristic
527	C₂	C₂×#466×C₈₉	1	1	yes	characteristic
528	C₂	C₈₉×#3062	1	1	yes	characteristic
529	C₂	C₈₉×#3358	1	1	yes	characteristic
530	C₂	C₈₉×#3361	1	1	yes	characteristic
531	C₂	C₈₉×#3391	1	1	yes	characteristic
532	C₂	C₈₉×#3394	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₈₉
prime radical	C₂×#459×C₈₉	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ C₂×C₄×Q₈×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×Q₈×C₈₉	C₂	semidirect
3. C₈₉×#2548	C₂	semidirect
4. C₈₉×#2538	C₂	semidirect
5. C₈₉×#2067	C₂	semidirect
6. C₈₉×#2054	C₂	semidirect
7. C₈₉×#1970	C₂	semidirect
8. C₈₉×#1957	C₂	semidirect
9. C₈₉×#1947	C₂	semidirect
10. C₈₉×#1934	C₂	semidirect
11. C₄×#102×C₈₉	C₂	semidirect
98. C₂×Q₈×C₈₉	D₈	semidirect
257. #25292	C₈₉	direct (N × H)
268. C₂×C₈×Q₈	C₂×C₈₉	semidirect
269. #2548	C₂×C₈₉	semidirect
270. #2538	C₂×C₈₉	semidirect
271. #2067	C₂×C₈₉	semidirect
272. #2054	C₂×C₈₉	semidirect
273. #1970	C₂×C₈₉	semidirect
274. #1957	C₂×C₈₉	semidirect
275. #1947	C₂×C₈₉	semidirect
276. #1934	C₂×C₈₉	semidirect
277. C₄×#102	C₂×C₈₉	semidirect
278. C₈₉	#25292	direct (N × H)
365. C₂×Q₈	D₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#459×C₈₉	2
C₂×C₈×Q₈×C₈₉	2
C₈₉×#2548	2
C₈₉×#2538	2
C₈₉×#2067	2
C₈₉×#2054	2
C₈₉×#1970	2
C₈₉×#1957	2
C₈₉×#1947	2
C₈₉×#1934	2
C₄×#102×C₈₉	2
#25292	89

Subgroups — C89×#25292 #36403140

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#25292 #36403140