Subgroups — C₈₉×#35179 #36413027

Order 22784.

2234 conjugacy classes of subgroups.

The subgroup lattice has 478 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×#2627	C₂	1	4	yes	maximal
5	C₈₉×#2582	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2581	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2568	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2567	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2565	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2317	C₂	1	2	yes	maximal
11	C₈₉×#2310	C₂	1	2	yes	maximal
12	C₈₉×#2285	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	1	yes	characteristic
17	C₂×#125×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×C₄×Q₈×C₈₉	—	2	8	no	—
21	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
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×#117×C₈₉	C₂²	1	2	yes	—
28	C₂×#117×C₈₉	C₂²	1	2	yes	—
29	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
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	#398×C₈₉	C₂²	1	16	yes	—
35	#395×C₈₉	C₂²	1	8	yes	—
36	#391×C₈₉	C₂²	1	4	yes	—
37	#391×C₈₉	C₂²	1	4	yes	—
38	#391×C₈₉	C₂²	1	8	yes	—
39	#391×C₈₉	C₂²	1	8	yes	—
40	#389×C₈₉	C₂²	1	8	yes	—
41	#389×C₈₉	C₂²	1	8	yes	—
42	#387×C₈₉	C₂²	1	16	yes	—
43	#385×C₈₉	C₂²	1	8	yes	—
44	#384×C₈₉	C₂²	1	4	yes	—
45	#384×C₈₉	C₂²	1	2	yes	—
46	#382×C₈₉	C₂²	1	4	yes	—
47	#382×C₈₉	C₂²	1	2	yes	—
48	#381×C₈₉	C₂²	1	8	yes	—
49	#380×C₈₉	C₂²	1	2	yes	—
50	#380×C₈₉	C₂²	1	2	yes	—
51	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
52	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
53	C₂²×Q₈×C₈₉	—	2	4	no	—
54	C₂²×Q₈×C₈₉	—	2	4	no	—
55	C₂²×Q₈×C₈₉	Q₈	1	8	yes	complemented
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	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
60	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
61	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
62	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
63	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
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	#117×C₈₉	—	2	8	no	—
78	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
79	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
80	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
81	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
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	4	yes	—
86	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	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	4	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	4	yes	—
93	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
94	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
95	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
96	C₂×C₄²×C₈₉	—	2	8	no	—
97	C₂×C₄²×C₈₉	D₄	1	8	yes	—
98	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
99	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
100	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
101	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
102	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
105	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
112	C₂×Q₈×C₈₉	—	2	32	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	4	no	—
117	C₂×Q₈×C₈₉	—	2	4	no	—
118	C₂×Q₈×C₈₉	—	2	4	no	—
119	C₂×Q₈×C₈₉	—	2	8	no	—
120	C₂×Q₈×C₈₉	—	4	4	no	—
121	C₂×Q₈×C₈₉	C₂×Q₈	1	8	yes	—
122	C₂×Q₈×C₈₉	C₂×Q₈	1	8	yes	—
123	C₂²×C₄×C₈₉	—	2	4	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	—	4	2	no	—
128	C₂²×C₄×C₈₉	—	4	4	no	—
129	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
130	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
131	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
132	C₂²×C₄×C₈₉	C₂×Q₈	1	8	yes	—
133	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
134	C₂²×C₄×C₈₉	#41	1	4	yes	—
135	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
136	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
137	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
138	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
139	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
140	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
143	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
144	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
145	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
146	C₄⋊C₄×C₈₉	—	2	8	no	—
147	C₄⋊C₄×C₈₉	—	2	8	no	—
148	C₄⋊C₄×C₈₉	—	2	4	no	—
149	C₄⋊C₄×C₈₉	—	2	4	no	—
150	C₄⋊C₄×C₈₉	—	2	4	no	—
151	C₄⋊C₄×C₈₉	—	2	4	no	—
152	C₄⋊C₄×C₈₉	—	2	8	no	—
153	C₄⋊C₄×C₈₉	—	2	8	no	—
154	C₄⋊C₄×C₈₉	—	2	4	no	—
155	C₄⋊C₄×C₈₉	—	2	4	no	—
156	C₄⋊C₄×C₈₉	—	2	8	no	—
157	C₄⋊C₄×C₈₉	—	2	8	no	—
158	C₄⋊C₄×C₈₉	—	4	4	no	—
159	C₄⋊C₄×C₈₉	—	4	16	no	—
160	C₂²⋊C₄×C₈₉	—	2	8	no	—
161	C₂²⋊C₄×C₈₉	—	2	8	no	—
162	C₄²×C₈₉	—	2	8	no	—
163	C₄²×C₈₉	—	2	8	no	—
164	C₄²×C₈₉	—	2	8	no	—
165	C₄²×C₈₉	—	2	8	no	—
166	C₄²×C₈₉	C₂×D₄	1	4	yes	—
167	C₄²×C₈₉	C₂×D₄	1	4	yes	—
168	C₄²×C₈₉	C₂×D₄	1	4	yes	—
169	C₄²×C₈₉	C₂×D₄	1	4	yes	—
170	C₂³×C₈₉	—	2	2	no	—
171	C₂³×C₈₉	—	2	2	no	—
172	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
173	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
174	C₂³×C₈₉	C₂×#41	1	2	yes	—
175	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
176	Q₈×C₈₉	—	2	16	no	—
177	Q₈×C₈₉	—	2	16	no	—
178	Q₈×C₈₉	—	4	8	no	—
179	Q₈×C₈₉	—	4	8	no	—
180	C₂×C₄×C₈₉	—	2	16	no	—
181	C₂×C₄×C₈₉	—	2	4	no	—
182	C₂×C₄×C₈₉	—	2	4	no	—
183	C₂×C₄×C₈₉	—	2	2	no	—
184	C₂×C₄×C₈₉	—	2	2	no	—
185	C₂×C₄×C₈₉	—	2	2	no	—
186	C₂×C₄×C₈₉	—	2	8	no	—
187	C₂×C₄×C₈₉	—	2	4	no	—
188	C₂×C₄×C₈₉	—	2	4	no	—
189	C₂×C₄×C₈₉	—	2	4	no	—
190	C₂×C₄×C₈₉	—	2	8	no	—
191	C₂×C₄×C₈₉	—	2	8	no	—
192	C₂×C₄×C₈₉	—	2	8	no	—
193	C₂×C₄×C₈₉	—	2	8	no	—
194	C₂×C₄×C₈₉	—	2	8	no	—
195	C₂×C₄×C₈₉	—	2	8	no	—
196	C₂×C₄×C₈₉	—	4	4	no	—
197	C₂×C₄×C₈₉	—	4	8	no	—
198	C₂×C₄×C₈₉	C₂²⋊Q₈	1	16	yes	—
199	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
200	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
201	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
202	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
203	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
204	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
205	C₂×C₄×C₈₉	C₂²×Q₈	1	8	yes	—
206	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
207	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
208	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
209	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
210	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
211	C₂²×C₈₉	—	2	2	no	—
212	C₂²×C₈₉	—	2	2	no	—
213	C₂²×C₈₉	—	2	4	no	—
214	C₂²×C₈₉	—	2	4	no	—
215	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
216	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
217	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
218	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
219	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
220	C₂²×C₈₉	#585	1	2	yes	—
221	C₄×C₈₉	—	2	8	no	—
222	C₄×C₈₉	—	2	2	no	—
223	C₄×C₈₉	—	2	2	no	—
224	C₄×C₈₉	—	2	2	no	—
225	C₄×C₈₉	—	4	4	no	—
226	C₄×C₈₉	—	4	4	no	—
227	C₄×C₈₉	—	4	4	no	—
228	C₄×C₈₉	—	4	8	no	—
229	C₄×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
230	C₄×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
231	C₄×C₈₉	#536	1	4	yes	—
232	#35179	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂×C₈₉	—	2	4	no	—
234	C₂×C₈₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
235	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
236	C₂×C₈₉	#3449	1	1	yes	characteristic
237	C₂×C₈₉	#3502	1	2	yes	—
238	C₂×C₈₉	#3507	1	2	yes	—
239	C₂×#533	C₂×C₈₉	1	1	yes	characteristic
240	C₂²×C₄×Q₈	C₂×C₈₉	1	1	yes	characteristic
241	#2855	C₂×C₈₉	1	4	yes	—
242	#2627	C₂×C₈₉	1	4	yes	—
243	#2582	C₂×C₈₉	1	4	yes	complemented
244	#2581	C₂×C₈₉	1	4	yes	complemented
245	#2568	C₂×C₈₉	1	2	yes	complemented
246	#2567	C₂×C₈₉	1	2	yes	complemented
247	#2565	C₂×C₈₉	1	4	yes	complemented
248	#2317	C₂×C₈₉	1	2	yes	—
249	#2310	C₂×C₈₉	1	2	yes	—
250	#2285	C₂×C₈₉	1	1	yes	characteristic
251	C₈₉	#35179	1	1	yes	characteristic, direct product factor, Sylow
252	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
253	#533	—	2	8	no	—
254	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
255	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
256	C₂×#125	C₂²×C₈₉	1	2	yes	—
257	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
258	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
259	C₂×C₄×Q₈	—	2	8	no	—
260	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
261	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
262	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
263	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
264	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
265	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
266	C₂×#117	C₂²×C₈₉	1	2	yes	—
267	C₂×#117	C₂²×C₈₉	1	2	yes	—
268	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
269	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
270	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
271	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
272	#400	C₂²×C₈₉	1	8	yes	—
273	#398	C₂²×C₈₉	1	16	yes	—
274	#395	C₂²×C₈₉	1	8	yes	—
275	#391	C₂²×C₈₉	1	4	yes	—
276	#391	C₂²×C₈₉	1	4	yes	—
277	#391	C₂²×C₈₉	1	8	yes	—
278	#391	C₂²×C₈₉	1	8	yes	—
279	#389	C₂²×C₈₉	1	8	yes	—
280	#389	C₂²×C₈₉	1	8	yes	—
281	#387	C₂²×C₈₉	1	16	yes	—
282	#385	C₂²×C₈₉	1	8	yes	—
283	#384	C₂²×C₈₉	1	4	yes	—
284	#384	C₂²×C₈₉	1	2	yes	—
285	#382	C₂²×C₈₉	1	4	yes	—
286	#382	C₂²×C₈₉	1	2	yes	—
287	#381	C₂²×C₈₉	1	8	yes	—
288	#380	C₂²×C₈₉	1	2	yes	—
289	#380	C₂²×C₈₉	1	2	yes	—
290	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
291	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
292	C₂²×Q₈	—	2	4	no	—
293	C₂²×Q₈	—	2	4	no	—
294	C₂²×Q₈	Q₈×C₈₉	1	8	yes	complemented
295	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
296	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
297	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
298	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
299	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
300	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
301	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
302	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
303	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
304	C₄⋊Q₈	—	2	4	no	—
305	C₄⋊Q₈	—	2	4	no	—
306	#125	—	2	8	no	—
307	C₂²⋊Q₈	—	2	8	no	—
308	C₂²⋊Q₈	—	2	8	no	—
309	C₄×Q₈	—	2	8	no	—
310	C₄×Q₈	—	2	8	no	—
311	C₄×Q₈	—	2	8	no	—
312	C₄×Q₈	—	2	8	no	—
313	C₄×Q₈	—	2	8	no	—
314	C₄×Q₈	—	2	8	no	—
315	#117	—	2	8	no	—
316	#117	—	2	8	no	—
317	C₂×C₄⋊C₄	—	2	8	no	—
318	C₂×C₄⋊C₄	—	2	4	no	—
319	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
320	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
322	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
326	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
327	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
328	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
330	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
331	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
332	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
333	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
334	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
335	C₂×C₄²	—	2	8	no	—
336	C₂×C₄²	D₄×C₈₉	1	8	yes	—
337	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
338	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
339	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
340	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
341	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
342	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
343	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
344	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
345	#95	C₂³×C₈₉	1	4	yes	—
346	#95	C₂³×C₈₉	1	4	yes	—
347	#95	C₂³×C₈₉	1	16	yes	—
348	#95	C₂³×C₈₉	1	16	yes	—
349	#95	C₂³×C₈₉	1	16	yes	—
350	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
351	C₂×Q₈	—	2	32	no	—
352	C₂×Q₈	—	2	4	no	—
353	C₂×Q₈	—	2	4	no	—
354	C₂×Q₈	—	2	4	no	—
355	C₂×Q₈	—	2	4	no	—
356	C₂×Q₈	—	2	4	no	—
357	C₂×Q₈	—	2	4	no	—
358	C₂×Q₈	—	2	8	no	—
359	C₂×Q₈	—	4	4	no	—
360	C₂×Q₈	C₂×Q₈×C₈₉	1	8	yes	—
361	C₂×Q₈	C₂×Q₈×C₈₉	1	8	yes	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	4	4	no	—
368	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
369	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
370	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
371	C₂²×C₄	C₂×Q₈×C₈₉	1	8	yes	—
372	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
373	C₂²×C₄	#41×C₈₉	1	4	yes	—
374	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
375	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
376	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
377	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
378	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
379	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
380	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
381	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
382	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
384	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
385	C₄⋊C₄	—	2	8	no	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	4	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	4	no	—
391	C₄⋊C₄	—	2	8	no	—
392	C₄⋊C₄	—	2	8	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	8	no	—
396	C₄⋊C₄	—	2	8	no	—
397	C₄⋊C₄	—	4	4	no	—
398	C₄⋊C₄	—	4	16	no	—
399	C₂²⋊C₄	—	2	8	no	—
400	C₂²⋊C₄	—	2	8	no	—
401	C₄²	—	2	8	no	—
402	C₄²	—	2	8	no	—
403	C₄²	—	2	8	no	—
404	C₄²	—	2	8	no	—
405	C₄²	C₂×D₄×C₈₉	1	4	yes	—
406	C₄²	C₂×D₄×C₈₉	1	4	yes	—
407	C₄²	C₂×D₄×C₈₉	1	4	yes	—
408	C₄²	C₂×D₄×C₈₉	1	4	yes	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
412	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
413	C₂³	C₂×#41×C₈₉	1	2	yes	—
414	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
415	Q₈	—	2	16	no	—
416	Q₈	—	2	16	no	—
417	Q₈	—	4	8	no	—
418	Q₈	—	4	8	no	—
419	C₂×C₄	—	2	16	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	8	no	—
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	4	4	no	—
436	C₂×C₄	—	4	8	no	—
437	C₂×C₄	C₂²⋊Q₈×C₈₉	1	16	yes	—
438	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
439	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
440	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
441	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
442	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
443	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
444	C₂×C₄	C₂²×Q₈×C₈₉	1	8	yes	—
445	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
446	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
447	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
448	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
449	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
450	C₂²	—	2	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	4	no	—
453	C₂²	—	2	4	no	—
454	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
455	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
456	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
457	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
458	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
459	C₂²	#585×C₈₉	1	2	yes	—
460	C₄	—	2	8	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	2	no	—
463	C₄	—	2	2	no	—
464	C₄	—	4	4	no	—
465	C₄	—	4	4	no	—
466	C₄	—	4	4	no	—
467	C₄	—	4	8	no	—
468	C₄	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
469	C₄	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
470	C₄	#536×C₈₉	1	4	yes	—
471	C₂	—	2	4	no	—
472	C₂	C₂²×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
473	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
474	C₂	C₈₉×#3449	1	1	yes	characteristic
475	C₂	C₈₉×#3502	1	2	yes	—
476	C₂	C₈₉×#3507	1	2	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
5. C₈₉×#2582	C₂	semidirect
6. C₈₉×#2581	C₂	semidirect
7. C₈₉×#2568	C₂	semidirect
8. C₈₉×#2567	C₂	semidirect
9. C₈₉×#2565	C₂	semidirect
55. C₂²×Q₈×C₈₉	Q₈	semidirect
232. #35179	C₈₉	direct (N × H)
243. #2582	C₂×C₈₉	semidirect
244. #2581	C₂×C₈₉	semidirect
245. #2568	C₂×C₈₉	semidirect
246. #2567	C₂×C₈₉	semidirect
247. #2565	C₂×C₈₉	semidirect
251. C₈₉	#35179	direct (N × H)
294. C₂²×Q₈	Q₈×C₈₉	semidirect

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×#2627	2
C₈₉×#2582	2
C₈₉×#2581	2
C₈₉×#2568	2
C₈₉×#2567	2
C₈₉×#2565	2
C₈₉×#2317	2
C₈₉×#2310	2
C₈₉×#2285	2
#35179	89

Subgroups — C89×#35179 #36413027

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35179 #36413027