Subgroups — C₈₉×#35311 #36413159

Order 22784.

2462 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₂²⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2855	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2625	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2503	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2502	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2499	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2484	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2483	C₂	1	4	yes	maximal
10	C₈₉×#2317	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2310	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2280	C₂	1	1	yes	maximal, characteristic
13	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₈₉	—	2	8	no	—
16	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
18	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
20	C₂×#117×C₈₉	—	2	8	no	—
21	C₂×#117×C₈₉	C₂²	1	2	yes	—
22	C₂×#117×C₈₉	C₂²	1	2	yes	—
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	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
27	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
28	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
30	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
31	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
32	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
33	#400×C₈₉	C₂²	1	8	yes	complemented
34	#398×C₈₉	C₂²	1	8	yes	complemented
35	#397×C₈₉	C₂²	1	16	yes	—
36	#391×C₈₉	C₂²	1	8	yes	complemented
37	#391×C₈₉	C₂²	1	4	yes	complemented
38	#391×C₈₉	C₂²	1	4	yes	complemented
39	#389×C₈₉	C₂²	1	8	yes	complemented
40	#387×C₈₉	C₂²	1	16	yes	complemented
41	#385×C₈₉	C₂²	1	8	yes	—
42	#385×C₈₉	C₂²	1	8	yes	—
43	#384×C₈₉	C₂²	1	4	yes	complemented
44	#382×C₈₉	C₂²	1	4	yes	complemented
45	#381×C₈₉	C₂²	1	8	yes	—
46	#381×C₈₉	C₂²	1	8	yes	—
47	#381×C₈₉	C₂²	1	2	yes	—
48	#380×C₈₉	C₂²	1	2	yes	—
49	#380×C₈₉	C₂²	1	2	yes	—
50	#379×C₈₉	C₂²	1	2	yes	—
51	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
52	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
53	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
54	C₂²×Q₈×C₈₉	—	2	4	no	—
55	C₂²×Q₈×C₈₉	—	2	8	no	—
56	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
57	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
58	C₂³×C₄×C₈₉	—	2	8	no	—
59	C₂³×C₄×C₈₉	D₄	1	8	yes	—
60	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
66	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
67	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
68	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
69	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
70	C₂²⋊Q₈×C₈₉	—	2	8	no	—
71	C₂²⋊Q₈×C₈₉	—	2	8	no	—
72	C₂²⋊Q₈×C₈₉	—	2	8	no	—
73	C₂²⋊Q₈×C₈₉	—	2	8	no	—
74	#117×C₈₉	—	2	8	no	—
75	#117×C₈₉	—	2	8	no	—
76	#117×C₈₉	—	2	8	no	—
77	#117×C₈₉	—	2	8	no	—
78	#117×C₈₉	—	2	8	no	—
79	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
80	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
81	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
82	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
83	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
85	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	4	yes	—
91	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
93	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
94	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
95	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
96	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
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×C₄²×C₈₉	—	2	8	no	—
103	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
104	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
105	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
106	#95×C₈₉	C₂³	1	4	yes	—
107	#95×C₈₉	C₂³	1	4	yes	—
108	#95×C₈₉	C₂³	1	16	yes	—
109	#95×C₈₉	C₂³	1	16	yes	—
110	#95×C₈₉	C₂³	1	16	yes	—
111	C₂⁴×C₈₉	—	2	4	no	—
112	C₂⁴×C₈₉	—	2	4	no	—
113	C₂⁴×C₈₉	—	4	2	no	—
114	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
115	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
116	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
117	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
118	C₂×Q₈×C₈₉	—	2	4	no	—
119	C₂×Q₈×C₈₉	—	2	4	no	—
120	C₂×Q₈×C₈₉	—	2	8	no	—
121	C₂×Q₈×C₈₉	—	2	8	no	—
122	C₂×Q₈×C₈₉	—	4	16	no	—
123	C₂²×C₄×C₈₉	—	2	4	no	—
124	C₂²×C₄×C₈₉	—	2	32	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	4	no	—
129	C₂²×C₄×C₈₉	—	2	4	no	—
130	C₂²×C₄×C₈₉	—	2	4	no	—
131	C₂²×C₄×C₈₉	—	2	4	no	—
132	C₂²×C₄×C₈₉	—	2	4	no	—
133	C₂²×C₄×C₈₉	—	2	8	no	—
134	C₂²×C₄×C₈₉	—	2	8	no	—
135	C₂²×C₄×C₈₉	—	4	4	no	—
136	C₂²×C₄×C₈₉	—	4	4	no	—
137	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
140	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
143	C₂²×C₄×C₈₉	#41	1	8	yes	—
144	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
145	C₂²×C₄×C₈₉	C₂⁴	1	8	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	1	yes	characteristic
150	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
151	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
152	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
153	C₄⋊C₄×C₈₉	—	2	4	no	—
154	C₄⋊C₄×C₈₉	—	2	4	no	—
155	C₄⋊C₄×C₈₉	—	2	4	no	—
156	C₄⋊C₄×C₈₉	—	2	4	no	—
157	C₄⋊C₄×C₈₉	—	2	4	no	—
158	C₄⋊C₄×C₈₉	—	2	4	no	—
159	C₄⋊C₄×C₈₉	—	2	8	no	—
160	C₄⋊C₄×C₈₉	—	2	8	no	—
161	C₄⋊C₄×C₈₉	—	2	8	no	—
162	C₄⋊C₄×C₈₉	—	4	16	no	—
163	C₂²⋊C₄×C₈₉	—	2	8	no	—
164	C₂²⋊C₄×C₈₉	—	2	8	no	—
165	C₂²⋊C₄×C₈₉	—	2	8	no	—
166	C₂²⋊C₄×C₈₉	—	2	8	no	—
167	C₂²⋊C₄×C₈₉	—	2	8	no	—
168	C₂²⋊C₄×C₈₉	—	2	8	no	—
169	C₂²⋊C₄×C₈₉	—	4	4	no	—
170	C₄²×C₈₉	—	2	8	no	—
171	C₄²×C₈₉	—	2	8	no	—
172	C₄²×C₈₉	—	2	8	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	8	no	—
178	C₂³×C₈₉	—	2	8	no	—
179	C₂³×C₈₉	—	2	2	no	—
180	C₂³×C₈₉	—	2	2	no	—
181	C₂³×C₈₉	—	2	2	no	—
182	C₂³×C₈₉	—	4	4	no	—
183	C₂³×C₈₉	—	4	16	no	—
184	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
185	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
186	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
187	C₂³×C₈₉	C₂×#41	1	4	yes	—
188	C₂³×C₈₉	2₋¹⁺⁴	1	4	yes	—
189	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
190	Q₈×C₈₉	—	4	8	no	—
191	Q₈×C₈₉	—	4	8	no	—
192	C₂×C₄×C₈₉	—	2	8	no	—
193	C₂×C₄×C₈₉	—	2	2	no	—
194	C₂×C₄×C₈₉	—	2	2	no	—
195	C₂×C₄×C₈₉	—	2	8	no	—
196	C₂×C₄×C₈₉	—	2	8	no	—
197	C₂×C₄×C₈₉	—	2	8	no	—
198	C₂×C₄×C₈₉	—	2	8	no	—
199	C₂×C₄×C₈₉	—	2	4	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	8	no	—
204	C₂×C₄×C₈₉	—	2	8	no	—
205	C₂×C₄×C₈₉	—	2	8	no	—
206	C₂×C₄×C₈₉	—	2	8	no	—
207	C₂×C₄×C₈₉	—	2	8	no	—
208	C₂×C₄×C₈₉	—	2	8	no	—
209	C₂×C₄×C₈₉	—	2	8	no	—
210	C₂×C₄×C₈₉	—	4	8	no	—
211	C₂×C₄×C₈₉	—	4	8	no	—
212	C₂×C₄×C₈₉	—	4	8	no	—
213	C₂×C₄×C₈₉	—	4	8	no	—
214	C₂×C₄×C₈₉	#123	1	16	yes	—
215	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
216	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
217	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
218	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
219	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
220	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
221	C₂²×C₈₉	—	2	2	no	—
222	C₂²×C₈₉	—	2	2	no	—
223	C₂²×C₈₉	—	2	2	no	—
224	C₂²×C₈₉	—	2	2	no	—
225	C₂²×C₈₉	—	2	8	no	—
226	C₂²×C₈₉	—	2	8	no	—
227	C₂²×C₈₉	—	2	2	no	—
228	C₂²×C₈₉	—	2	2	no	—
229	C₂²×C₈₉	—	2	2	no	—
230	C₂²×C₈₉	—	4	16	no	—
231	C₂²×C₈₉	—	4	4	no	—
232	C₂²×C₈₉	C₂×#123	1	4	yes	—
233	C₂²×C₈₉	#536	1	4	yes	—
234	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
235	C₂²×C₈₉	C₂²×#41	1	2	yes	—
236	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
237	C₂²×C₈₉	#585	1	2	yes	—
238	C₄×C₈₉	—	2	2	no	—
239	C₄×C₈₉	—	2	2	no	—
240	C₄×C₈₉	—	4	4	no	—
241	C₄×C₈₉	—	4	4	no	—
242	C₄×C₈₉	—	4	4	no	—
243	C₄×C₈₉	—	4	4	no	—
244	C₄×C₈₉	—	4	8	no	—
245	C₄×C₈₉	C₂×#123	1	4	yes	—
246	C₄×C₈₉	C₂×#123	1	4	yes	—
247	#35311	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
248	C₂×C₈₉	—	2	4	no	—
249	C₂×C₈₉	—	2	4	no	—
250	C₂×C₈₉	—	4	2	no	—
251	C₂×C₈₉	C₂²×#123	1	1	yes	characteristic
252	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
253	C₂×C₈₉	#3449	1	1	yes	characteristic
254	C₂×C₈₉	#3495	1	4	yes	—
255	C₂²×C₂²⋊Q₈	C₂×C₈₉	1	1	yes	characteristic
256	C₂²×#117	C₂×C₈₉	1	1	yes	characteristic
257	#2855	C₂×C₈₉	1	4	yes	complemented
258	#2625	C₂×C₈₉	1	4	yes	complemented
259	#2503	C₂×C₈₉	1	2	yes	complemented
260	#2502	C₂×C₈₉	1	2	yes	complemented
261	#2499	C₂×C₈₉	1	4	yes	complemented
262	#2484	C₂×C₈₉	1	4	yes	complemented
263	#2483	C₂×C₈₉	1	4	yes	—
264	#2317	C₂×C₈₉	1	2	yes	complemented
265	#2310	C₂×C₈₉	1	2	yes	complemented
266	#2280	C₂×C₈₉	1	1	yes	characteristic
267	C₈₉	#35311	1	1	yes	characteristic, direct product factor, Sylow
268	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
269	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
270	C₂×C₂²⋊Q₈	—	2	8	no	—
271	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
272	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
273	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
274	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
275	C₂×#117	—	2	8	no	—
276	C₂×#117	C₂²×C₈₉	1	2	yes	—
277	C₂×#117	C₂²×C₈₉	1	2	yes	—
278	C₂×#117	C₂²×C₈₉	1	2	yes	—
279	C₂×#117	C₂²×C₈₉	1	2	yes	—
280	C₂×#117	C₂²×C₈₉	1	2	yes	—
281	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
282	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
283	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
284	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
285	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
286	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
287	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
288	#400	C₂²×C₈₉	1	8	yes	complemented
289	#398	C₂²×C₈₉	1	8	yes	complemented
290	#397	C₂²×C₈₉	1	16	yes	—
291	#391	C₂²×C₈₉	1	8	yes	complemented
292	#391	C₂²×C₈₉	1	4	yes	complemented
293	#391	C₂²×C₈₉	1	4	yes	complemented
294	#389	C₂²×C₈₉	1	8	yes	complemented
295	#387	C₂²×C₈₉	1	16	yes	complemented
296	#385	C₂²×C₈₉	1	8	yes	—
297	#385	C₂²×C₈₉	1	8	yes	—
298	#384	C₂²×C₈₉	1	4	yes	complemented
299	#382	C₂²×C₈₉	1	4	yes	complemented
300	#381	C₂²×C₈₉	1	8	yes	—
301	#381	C₂²×C₈₉	1	8	yes	—
302	#381	C₂²×C₈₉	1	2	yes	—
303	#380	C₂²×C₈₉	1	2	yes	—
304	#380	C₂²×C₈₉	1	2	yes	—
305	#379	C₂²×C₈₉	1	2	yes	—
306	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
307	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
308	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
309	C₂²×Q₈	—	2	4	no	—
310	C₂²×Q₈	—	2	8	no	—
311	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
312	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
313	C₂³×C₄	—	2	8	no	—
314	C₂³×C₄	D₄×C₈₉	1	8	yes	—
315	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
316	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
317	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
318	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
319	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
322	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
323	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
324	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
325	C₂²⋊Q₈	—	2	8	no	—
326	C₂²⋊Q₈	—	2	8	no	—
327	C₂²⋊Q₈	—	2	8	no	—
328	C₂²⋊Q₈	—	2	8	no	—
329	#117	—	2	8	no	—
330	#117	—	2	8	no	—
331	#117	—	2	8	no	—
332	#117	—	2	8	no	—
333	#117	—	2	8	no	—
334	C₂×C₄⋊C₄	—	2	4	no	—
335	C₂×C₄⋊C₄	—	2	4	no	—
336	C₂×C₄⋊C₄	—	2	4	no	—
337	C₂×C₄⋊C₄	—	2	8	no	—
338	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
339	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
340	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
341	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
344	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
345	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
346	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
347	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
348	C₂×C₂²⋊C₄	—	2	8	no	—
349	C₂×C₂²⋊C₄	—	2	8	no	—
350	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
351	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
352	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
353	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
354	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
355	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
356	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
357	C₂×C₄²	—	2	8	no	—
358	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
359	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
360	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
361	#95	C₂³×C₈₉	1	4	yes	—
362	#95	C₂³×C₈₉	1	4	yes	—
363	#95	C₂³×C₈₉	1	16	yes	—
364	#95	C₂³×C₈₉	1	16	yes	—
365	#95	C₂³×C₈₉	1	16	yes	—
366	C₂⁴	—	2	4	no	—
367	C₂⁴	—	2	4	no	—
368	C₂⁴	—	4	2	no	—
369	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
370	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
371	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
372	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
373	C₂×Q₈	—	2	4	no	—
374	C₂×Q₈	—	2	4	no	—
375	C₂×Q₈	—	2	8	no	—
376	C₂×Q₈	—	2	8	no	—
377	C₂×Q₈	—	4	16	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	32	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	4	no	—
382	C₂²×C₄	—	2	4	no	—
383	C₂²×C₄	—	2	4	no	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	4	no	—
386	C₂²×C₄	—	2	4	no	—
387	C₂²×C₄	—	2	4	no	—
388	C₂²×C₄	—	2	8	no	—
389	C₂²×C₄	—	2	8	no	—
390	C₂²×C₄	—	4	4	no	—
391	C₂²×C₄	—	4	4	no	—
392	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
393	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
394	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
395	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
396	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
397	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
398	C₂²×C₄	#41×C₈₉	1	8	yes	—
399	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
400	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
401	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
402	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
403	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
404	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
405	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
406	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
408	C₄⋊C₄	—	2	4	no	—
409	C₄⋊C₄	—	2	4	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	8	no	—
415	C₄⋊C₄	—	2	8	no	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	4	16	no	—
418	C₂²⋊C₄	—	2	8	no	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	8	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	2	8	no	—
423	C₂²⋊C₄	—	2	8	no	—
424	C₂²⋊C₄	—	4	4	no	—
425	C₄²	—	2	8	no	—
426	C₄²	—	2	8	no	—
427	C₄²	—	2	8	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	8	no	—
433	C₂³	—	2	8	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	4	4	no	—
438	C₂³	—	4	16	no	—
439	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
440	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
441	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
442	C₂³	C₂×#41×C₈₉	1	4	yes	—
443	C₂³	2₋¹⁺⁴×C₈₉	1	4	yes	—
444	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
445	Q₈	—	4	8	no	—
446	Q₈	—	4	8	no	—
447	C₂×C₄	—	2	8	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	8	no	—
451	C₂×C₄	—	2	8	no	—
452	C₂×C₄	—	2	8	no	—
453	C₂×C₄	—	2	8	no	—
454	C₂×C₄	—	2	4	no	—
455	C₂×C₄	—	2	4	no	—
456	C₂×C₄	—	2	4	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	8	no	—
459	C₂×C₄	—	2	8	no	—
460	C₂×C₄	—	2	8	no	—
461	C₂×C₄	—	2	8	no	—
462	C₂×C₄	—	2	8	no	—
463	C₂×C₄	—	2	8	no	—
464	C₂×C₄	—	2	8	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	—	4	8	no	—
467	C₂×C₄	—	4	8	no	—
468	C₂×C₄	—	4	8	no	—
469	C₂×C₄	#123×C₈₉	1	16	yes	—
470	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
471	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
472	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
473	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
474	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
475	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
476	C₂²	—	2	2	no	—
477	C₂²	—	2	2	no	—
478	C₂²	—	2	2	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	8	no	—
481	C₂²	—	2	8	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	4	16	no	—
486	C₂²	—	4	4	no	—
487	C₂²	C₂×#123×C₈₉	1	4	yes	—
488	C₂²	#536×C₈₉	1	4	yes	—
489	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
490	C₂²	C₂²×#41×C₈₉	1	2	yes	—
491	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
492	C₂²	#585×C₈₉	1	2	yes	—
493	C₄	—	2	2	no	—
494	C₄	—	2	2	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	4	no	—
497	C₄	—	4	4	no	—
498	C₄	—	4	4	no	—
499	C₄	—	4	8	no	—
500	C₄	C₂×#123×C₈₉	1	4	yes	—
501	C₄	C₂×#123×C₈₉	1	4	yes	—
502	C₂	—	2	4	no	—
503	C₂	—	2	4	no	—
504	C₂	—	4	2	no	—
505	C₂	C₂²×#123×C₈₉	1	1	yes	characteristic
506	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
507	C₂	C₈₉×#3449	1	1	yes	characteristic
508	C₂	C₈₉×#3495	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁵×C₈₉	C₂³
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
3. C₈₉×#2855	C₂	semidirect
4. C₈₉×#2625	C₂	semidirect
5. C₈₉×#2503	C₂	semidirect
6. C₈₉×#2502	C₂	semidirect
7. C₈₉×#2499	C₂	semidirect
8. C₈₉×#2484	C₂	semidirect
10. C₈₉×#2317	C₂	semidirect
11. C₈₉×#2310	C₂	semidirect
33. #400×C₈₉	C₂²	semidirect
34. #398×C₈₉	C₂²	semidirect
36. #391×C₈₉	C₂²	semidirect
37. #391×C₈₉	C₂²	semidirect
38. #391×C₈₉	C₂²	semidirect
39. #389×C₈₉	C₂²	semidirect
40. #387×C₈₉	C₂²	semidirect
43. #384×C₈₉	C₂²	semidirect
44. #382×C₈₉	C₂²	semidirect
247. #35311	C₈₉	direct (N × H)
257. #2855	C₂×C₈₉	semidirect
258. #2625	C₂×C₈₉	semidirect
259. #2503	C₂×C₈₉	semidirect
260. #2502	C₂×C₈₉	semidirect
261. #2499	C₂×C₈₉	semidirect
262. #2484	C₂×C₈₉	semidirect
264. #2317	C₂×C₈₉	semidirect
265. #2310	C₂×C₈₉	semidirect
267. C₈₉	#35311	direct (N × H)
288. #400	C₂²×C₈₉	semidirect
289. #398	C₂²×C₈₉	semidirect
291. #391	C₂²×C₈₉	semidirect
292. #391	C₂²×C₈₉	semidirect
293. #391	C₂²×C₈₉	semidirect
294. #389	C₂²×C₈₉	semidirect
295. #387	C₂²×C₈₉	semidirect
298. #384	C₂²×C₈₉	semidirect
299. #382	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₂²⋊Q₈×C₈₉	2
C₂²×#117×C₈₉	2
C₈₉×#2855	2
C₈₉×#2625	2
C₈₉×#2503	2
C₈₉×#2502	2
C₈₉×#2499	2
C₈₉×#2484	2
C₈₉×#2483	2
C₈₉×#2317	2
C₈₉×#2310	2
C₈₉×#2280	2
#35311	89

Subgroups — C89×#35311 #36413159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35311 #36413159