Subgroups — C₈₉×#35248 #36413096

Order 22784.

2230 conjugacy classes of subgroups.

The subgroup lattice has 454 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
2	C₂²×C₄×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2855	C₂	1	4	yes	maximal
4	C₈₉×#2634	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2581	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2568	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2546	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2503	C₂	1	2	yes	maximal
9	C₈₉×#2484	C₂	1	4	yes	maximal
10	C₈₉×#2434	C₂	1	2	yes	maximal
11	C₈₉×#2327	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2283	C₂	1	1	yes	maximal, characteristic
13	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
14	#533×C₈₉	—	2	8	no	—
15	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₈₉	C₂²	1	4	yes	—
17	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×#125×C₈₉	C₂²	1	2	yes	—
19	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
20	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
21	C₂×C₄×Q₈×C₈₉	—	2	8	no	—
22	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
23	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
24	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
25	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
27	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
28	C₂×#117×C₈₉	C₂²	1	2	yes	—
29	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
30	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
32	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
33	#400×C₈₉	C₂²	1	8	yes	—
34	#400×C₈₉	C₂²	1	8	yes	—
35	#398×C₈₉	C₂²	1	8	yes	—
36	#395×C₈₉	C₂²	1	8	yes	—
37	#391×C₈₉	C₂²	1	8	yes	—
38	#391×C₈₉	C₂²	1	4	yes	—
39	#391×C₈₉	C₂²	1	4	yes	—
40	#389×C₈₉	C₂²	1	8	yes	—
41	#387×C₈₉	C₂²	1	16	yes	—
42	#387×C₈₉	C₂²	1	16	yes	—
43	#385×C₈₉	C₂²	1	8	yes	—
44	#383×C₈₉	C₂²	1	2	yes	—
45	#382×C₈₉	C₂²	1	4	yes	—
46	#382×C₈₉	C₂²	1	2	yes	—
47	#381×C₈₉	C₂²	1	8	yes	—
48	#381×C₈₉	C₂²	1	2	yes	—
49	#380×C₈₉	C₂²	1	2	yes	—
50	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
51	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
52	#376×C₈₉	C₂²	1	2	yes	—
53	C₂²×Q₈×C₈₉	—	2	8	no	—
54	C₂²×Q₈×C₈₉	—	2	4	no	—
55	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
56	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
57	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
58	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
59	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
60	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
61	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₄⋊Q₈×C₈₉	—	2	16	no	—
65	C₄⋊Q₈×C₈₉	—	2	4	no	—
66	C₄⋊Q₈×C₈₉	—	2	4	no	—
67	#125×C₈₉	—	2	8	no	—
68	C₂²⋊Q₈×C₈₉	—	2	8	no	—
69	C₂²⋊Q₈×C₈₉	—	2	8	no	—
70	C₄×Q₈×C₈₉	—	2	8	no	—
71	C₄×Q₈×C₈₉	—	2	8	no	—
72	C₄×Q₈×C₈₉	—	2	8	no	—
73	C₄×Q₈×C₈₉	—	2	8	no	—
74	C₄×Q₈×C₈₉	—	2	8	no	—
75	C₄×Q₈×C₈₉	—	2	8	no	—
76	#117×C₈₉	—	2	8	no	—
77	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
78	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
79	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
80	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
81	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
83	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
87	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
88	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
89	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
90	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
92	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
93	C₂×C₄²×C₈₉	—	2	8	no	—
94	C₂×C₄²×C₈₉	D₄	1	8	yes	—
95	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
96	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
97	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
98	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
99	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
100	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
101	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
103	#95×C₈₉	C₂³	1	4	yes	—
104	#95×C₈₉	C₂³	1	4	yes	—
105	#95×C₈₉	C₂³	1	4	yes	—
106	#95×C₈₉	C₂³	1	4	yes	—
107	#95×C₈₉	C₂³	1	16	yes	—
108	#95×C₈₉	C₂³	1	16	yes	—
109	#95×C₈₉	C₂³	1	16	yes	—
110	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
111	C₂×Q₈×C₈₉	—	2	32	no	—
112	C₂×Q₈×C₈₉	—	2	4	no	—
113	C₂×Q₈×C₈₉	—	2	4	no	—
114	C₂×Q₈×C₈₉	—	2	4	no	—
115	C₂×Q₈×C₈₉	—	2	4	no	—
116	C₂×Q₈×C₈₉	—	2	8	no	—
117	C₂×Q₈×C₈₉	—	2	4	no	—
118	C₂×Q₈×C₈₉	—	2	8	no	—
119	C₂×Q₈×C₈₉	—	2	8	no	—
120	C₂×Q₈×C₈₉	#41	1	8	yes	—
121	C₂²×C₄×C₈₉	—	2	4	no	—
122	C₂²×C₄×C₈₉	—	2	4	no	—
123	C₂²×C₄×C₈₉	—	2	8	no	—
124	C₂²×C₄×C₈₉	—	2	4	no	—
125	C₂²×C₄×C₈₉	—	2	4	no	—
126	C₂²×C₄×C₈₉	—	2	4	no	—
127	C₂²×C₄×C₈₉	—	2	8	no	—
128	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
132	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
133	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
135	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
140	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
142	C₄⋊C₄×C₈₉	—	2	8	no	—
143	C₄⋊C₄×C₈₉	—	2	8	no	—
144	C₄⋊C₄×C₈₉	—	2	4	no	—
145	C₄⋊C₄×C₈₉	—	2	4	no	—
146	C₄⋊C₄×C₈₉	—	2	4	no	—
147	C₄⋊C₄×C₈₉	—	2	4	no	—
148	C₄⋊C₄×C₈₉	—	2	8	no	—
149	C₄⋊C₄×C₈₉	—	2	8	no	—
150	C₄⋊C₄×C₈₉	—	2	4	no	—
151	C₄⋊C₄×C₈₉	—	2	4	no	—
152	C₄⋊C₄×C₈₉	—	2	32	no	—
153	C₄⋊C₄×C₈₉	—	2	8	no	—
154	C₂²⋊C₄×C₈₉	—	2	8	no	—
155	C₂²⋊C₄×C₈₉	—	2	8	no	—
156	C₄²×C₈₉	—	2	8	no	—
157	C₄²×C₈₉	—	2	8	no	—
158	C₄²×C₈₉	—	2	8	no	—
159	C₄²×C₈₉	—	2	8	no	—
160	C₄²×C₈₉	C₂×D₄	1	4	yes	—
161	C₄²×C₈₉	C₂×D₄	1	4	yes	—
162	C₄²×C₈₉	C₂×D₄	1	4	yes	—
163	C₄²×C₈₉	C₂×D₄	1	4	yes	—
164	C₂³×C₈₉	—	2	2	no	—
165	C₂³×C₈₉	—	2	2	no	—
166	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
167	C₂³×C₈₉	2₋¹⁺⁴	1	4	yes	—
168	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
169	Q₈×C₈₉	—	2	16	no	—
170	Q₈×C₈₉	—	2	16	no	—
171	Q₈×C₈₉	—	4	8	no	—
172	Q₈×C₈₉	—	4	8	no	—
173	C₂×C₄×C₈₉	—	2	16	no	—
174	C₂×C₄×C₈₉	—	2	8	no	—
175	C₂×C₄×C₈₉	—	2	4	no	—
176	C₂×C₄×C₈₉	—	2	2	no	—
177	C₂×C₄×C₈₉	—	2	4	no	—
178	C₂×C₄×C₈₉	—	2	2	no	—
179	C₂×C₄×C₈₉	—	2	2	no	—
180	C₂×C₄×C₈₉	—	2	2	no	—
181	C₂×C₄×C₈₉	—	2	8	no	—
182	C₂×C₄×C₈₉	—	2	8	no	—
183	C₂×C₄×C₈₉	—	2	4	no	—
184	C₂×C₄×C₈₉	—	2	4	no	—
185	C₂×C₄×C₈₉	—	2	4	no	—
186	C₂×C₄×C₈₉	—	2	8	no	—
187	C₂×C₄×C₈₉	—	2	8	no	—
188	C₂×C₄×C₈₉	—	2	8	no	—
189	C₂×C₄×C₈₉	—	2	8	no	—
190	C₂×C₄×C₈₉	—	2	8	no	—
191	C₂×C₄×C₈₉	—	2	8	no	—
192	C₂×C₄×C₈₉	—	4	8	no	—
193	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
196	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
198	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
199	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
200	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
201	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
202	C₂²×C₈₉	—	2	2	no	—
203	C₂²×C₈₉	—	2	2	no	—
204	C₂²×C₈₉	—	2	8	no	—
205	C₂²×C₈₉	#536	1	4	yes	—
206	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
207	C₂²×C₈₉	C₂²×#41	1	2	yes	—
208	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
209	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
210	C₄×C₈₉	—	2	2	no	—
211	C₄×C₈₉	—	2	8	no	—
212	C₄×C₈₉	—	2	2	no	—
213	C₄×C₈₉	—	2	2	no	—
214	C₄×C₈₉	—	2	2	no	—
215	C₄×C₈₉	—	4	4	no	—
216	C₄×C₈₉	—	4	4	no	—
217	C₄×C₈₉	—	4	4	no	—
218	C₄×C₈₉	—	4	8	no	—
219	C₄×C₈₉	#525	1	4	yes	—
220	C₄×C₈₉	#536	1	4	yes	—
221	#35248	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
222	C₂×C₈₉	—	2	4	no	—
223	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
224	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
225	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
226	C₂×C₈₉	#3523	1	4	yes	—
227	C₂×#533	C₂×C₈₉	1	1	yes	characteristic
228	C₂²×C₄×Q₈	C₂×C₈₉	1	1	yes	characteristic
229	#2855	C₂×C₈₉	1	4	yes	—
230	#2634	C₂×C₈₉	1	4	yes	complemented
231	#2581	C₂×C₈₉	1	4	yes	complemented
232	#2568	C₂×C₈₉	1	2	yes	complemented
233	#2546	C₂×C₈₉	1	2	yes	complemented
234	#2503	C₂×C₈₉	1	2	yes	—
235	#2484	C₂×C₈₉	1	4	yes	—
236	#2434	C₂×C₈₉	1	2	yes	—
237	#2327	C₂×C₈₉	1	4	yes	complemented
238	#2283	C₂×C₈₉	1	1	yes	characteristic
239	C₈₉	#35248	1	1	yes	characteristic, direct product factor, Sylow
240	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
241	#533	—	2	8	no	—
242	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
243	C₂×C₄⋊Q₈	C₂²×C₈₉	1	4	yes	—
244	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
245	C₂×#125	C₂²×C₈₉	1	2	yes	—
246	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
247	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
248	C₂×C₄×Q₈	—	2	8	no	—
249	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
250	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
251	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
252	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
253	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
254	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
255	C₂×#117	C₂²×C₈₉	1	2	yes	—
256	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
257	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
258	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
259	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
260	#400	C₂²×C₈₉	1	8	yes	—
261	#400	C₂²×C₈₉	1	8	yes	—
262	#398	C₂²×C₈₉	1	8	yes	—
263	#395	C₂²×C₈₉	1	8	yes	—
264	#391	C₂²×C₈₉	1	8	yes	—
265	#391	C₂²×C₈₉	1	4	yes	—
266	#391	C₂²×C₈₉	1	4	yes	—
267	#389	C₂²×C₈₉	1	8	yes	—
268	#387	C₂²×C₈₉	1	16	yes	—
269	#387	C₂²×C₈₉	1	16	yes	—
270	#385	C₂²×C₈₉	1	8	yes	—
271	#383	C₂²×C₈₉	1	2	yes	—
272	#382	C₂²×C₈₉	1	4	yes	—
273	#382	C₂²×C₈₉	1	2	yes	—
274	#381	C₂²×C₈₉	1	8	yes	—
275	#381	C₂²×C₈₉	1	2	yes	—
276	#380	C₂²×C₈₉	1	2	yes	—
277	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
278	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
279	#376	C₂²×C₈₉	1	2	yes	—
280	C₂²×Q₈	—	2	8	no	—
281	C₂²×Q₈	—	2	4	no	—
282	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
283	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
284	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
285	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
286	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
287	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
288	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
289	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
291	C₄⋊Q₈	—	2	16	no	—
292	C₄⋊Q₈	—	2	4	no	—
293	C₄⋊Q₈	—	2	4	no	—
294	#125	—	2	8	no	—
295	C₂²⋊Q₈	—	2	8	no	—
296	C₂²⋊Q₈	—	2	8	no	—
297	C₄×Q₈	—	2	8	no	—
298	C₄×Q₈	—	2	8	no	—
299	C₄×Q₈	—	2	8	no	—
300	C₄×Q₈	—	2	8	no	—
301	C₄×Q₈	—	2	8	no	—
302	C₄×Q₈	—	2	8	no	—
303	#117	—	2	8	no	—
304	C₂×C₄⋊C₄	—	2	8	no	—
305	C₂×C₄⋊C₄	—	2	4	no	—
306	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
308	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
309	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
310	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
311	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
313	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
314	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
315	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
316	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
317	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
318	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
319	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
320	C₂×C₄²	—	2	8	no	—
321	C₂×C₄²	D₄×C₈₉	1	8	yes	—
322	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
323	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
324	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
325	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
326	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
327	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
328	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
329	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
330	#95	C₂³×C₈₉	1	4	yes	—
331	#95	C₂³×C₈₉	1	4	yes	—
332	#95	C₂³×C₈₉	1	4	yes	—
333	#95	C₂³×C₈₉	1	4	yes	—
334	#95	C₂³×C₈₉	1	16	yes	—
335	#95	C₂³×C₈₉	1	16	yes	—
336	#95	C₂³×C₈₉	1	16	yes	—
337	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
338	C₂×Q₈	—	2	32	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	—	2	4	no	—
341	C₂×Q₈	—	2	4	no	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	—	2	8	no	—
344	C₂×Q₈	—	2	4	no	—
345	C₂×Q₈	—	2	8	no	—
346	C₂×Q₈	—	2	8	no	—
347	C₂×Q₈	#41×C₈₉	1	8	yes	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	4	no	—
350	C₂²×C₄	—	2	8	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	4	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	8	no	—
355	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
356	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
357	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
358	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
359	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
360	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
361	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
362	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
363	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
364	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
365	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
366	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
367	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
368	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
369	C₄⋊C₄	—	2	8	no	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	4	no	—
372	C₄⋊C₄	—	2	4	no	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	4	no	—
375	C₄⋊C₄	—	2	8	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	32	no	—
380	C₄⋊C₄	—	2	8	no	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₄²	—	2	8	no	—
384	C₄²	—	2	8	no	—
385	C₄²	—	2	8	no	—
386	C₄²	—	2	8	no	—
387	C₄²	C₂×D₄×C₈₉	1	4	yes	—
388	C₄²	C₂×D₄×C₈₉	1	4	yes	—
389	C₄²	C₂×D₄×C₈₉	1	4	yes	—
390	C₄²	C₂×D₄×C₈₉	1	4	yes	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	2	no	—
393	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
394	C₂³	2₋¹⁺⁴×C₈₉	1	4	yes	—
395	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
396	Q₈	—	2	16	no	—
397	Q₈	—	2	16	no	—
398	Q₈	—	4	8	no	—
399	Q₈	—	4	8	no	—
400	C₂×C₄	—	2	16	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	8	no	—
409	C₂×C₄	—	2	8	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	8	no	—
414	C₂×C₄	—	2	8	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	8	no	—
417	C₂×C₄	—	2	8	no	—
418	C₂×C₄	—	2	8	no	—
419	C₂×C₄	—	4	8	no	—
420	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
421	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
422	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
423	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
424	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
425	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
426	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
427	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
428	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	8	no	—
432	C₂²	#536×C₈₉	1	4	yes	—
433	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
434	C₂²	C₂²×#41×C₈₉	1	2	yes	—
435	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
436	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
437	C₄	—	2	2	no	—
438	C₄	—	2	8	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	4	4	no	—
443	C₄	—	4	4	no	—
444	C₄	—	4	4	no	—
445	C₄	—	4	8	no	—
446	C₄	#525×C₈₉	1	4	yes	—
447	C₄	#536×C₈₉	1	4	yes	—
448	C₂	—	2	4	no	—
449	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
450	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
451	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
452	C₂	C₈₉×#3523	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁴×C₈₉	C₂⁴
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
4. C₈₉×#2634	C₂	semidirect
5. C₈₉×#2581	C₂	semidirect
6. C₈₉×#2568	C₂	semidirect
7. C₈₉×#2546	C₂	semidirect
11. C₈₉×#2327	C₂	semidirect
221. #35248	C₈₉	direct (N × H)
230. #2634	C₂×C₈₉	semidirect
231. #2581	C₂×C₈₉	semidirect
232. #2568	C₂×C₈₉	semidirect
233. #2546	C₂×C₈₉	semidirect
237. #2327	C₂×C₈₉	semidirect
239. C₈₉	#35248	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
C₂²×C₄×Q₈×C₈₉	2
C₈₉×#2855	2
C₈₉×#2634	2
C₈₉×#2581	2
C₈₉×#2568	2
C₈₉×#2546	2
C₈₉×#2503	2
C₈₉×#2484	2
C₈₉×#2434	2
C₈₉×#2327	2
C₈₉×#2283	2
#35248	89

Subgroups — C89×#35248 #36413096

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35248 #36413096