Subgroups — C₈₉×#22510 #36400358

Order 22784.

1292 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#446×C₈₉	C₂	1	2	yes	maximal, complemented
3	C₈₉×#1985	C₂	1	4	yes	maximal, complemented
4	C₈₉×#1984	C₂	1	2	yes	maximal, complemented
5	C₈₉×#1797	C₂	1	2	yes	maximal
6	C₈₉×#1797	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#1749	C₂	1	2	yes	maximal
8	C₄×C₂²⋊C₈×C₈₉	C₂	1	1	yes	maximal, characteristic
9	C₂³×Q₈×C₈₉	C₄	1	1	yes	characteristic
10	C₂×C₄×Q₈×C₈₉	—	2	8	no	—
11	C₂×C₄×Q₈×C₈₉	C₄	1	1	yes	characteristic
12	C₂×C₄×Q₈×C₈₉	C₄	1	2	yes	—
13	C₂×C₄×Q₈×C₈₉	C₄	1	1	yes	characteristic
14	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₈₉	C₄	1	2	yes	—
18	C₂²×C₄⋊C₄×C₈₉	C₄	1	1	yes	characteristic
19	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
21	#446×C₈₉	—	2	8	no	—
22	C₂×C₄⋊C₈×C₈₉	C₂²	1	2	yes	—
23	C₂×C₄⋊C₈×C₈₉	C₂²	1	4	yes	—
24	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊C₈×C₈₉	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
27	C₂×#97×C₈₉	C₂²	1	4	yes	—
28	C₂×C₄×C₈×C₈₉	C₂²	1	2	yes	—
29	#336×C₈₉	C₂²	1	4	yes	—
30	#336×C₈₉	C₂²	1	2	yes	—
31	#336×C₈₉	C₂²	1	4	yes	—
32	#336×C₈₉	C₂²	1	2	yes	—
33	C₂²×Q₈×C₈₉	—	2	4	no	—
34	C₂²×Q₈×C₈₉	—	2	4	no	—
35	C₂²×Q₈×C₈₉	—	2	4	no	—
36	C₂²×Q₈×C₈₉	C₂×C₄	1	2	yes	—
37	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
38	C₂²×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
39	C₂³×C₄×C₈₉	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₈₉	C₂×C₄	1	2	yes	—
42	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
45	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
46	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
47	C₄×Q₈×C₈₉	—	2	4	no	—
48	C₄×Q₈×C₈₉	—	2	8	no	—
49	C₄×Q₈×C₈₉	—	2	4	no	—
50	C₄×Q₈×C₈₉	—	2	4	no	—
51	C₄×Q₈×C₈₉	—	2	8	no	—
52	C₄×Q₈×C₈₉	D₄	1	8	yes	—
53	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
54	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
55	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
58	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
61	C₂×C₄⋊C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₈₉	—	2	4	no	—
63	C₂×C₄²×C₈₉	—	2	8	no	—
64	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
65	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
70	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
72	C₄⋊C₈×C₈₉	—	2	4	no	—
73	C₄⋊C₈×C₈₉	—	2	8	no	—
74	C₂²⋊C₈×C₈₉	—	2	2	no	—
75	C₂²⋊C₈×C₈₉	—	2	4	no	—
76	C₂²⋊C₈×C₈₉	Q₈	1	4	yes	complemented
77	#97×C₈₉	—	2	8	no	—
78	C₄×C₈×C₈₉	—	2	4	no	—
79	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
80	C₂×Q₈×C₈₉	—	2	32	no	—
81	C₂×Q₈×C₈₉	—	2	4	no	—
82	C₂×Q₈×C₈₉	—	2	2	no	—
83	C₂×Q₈×C₈₉	—	2	4	no	—
84	C₂×Q₈×C₈₉	—	2	4	no	—
85	C₂×Q₈×C₈₉	—	2	2	no	—
86	C₂×Q₈×C₈₉	—	2	2	no	—
87	C₂×Q₈×C₈₉	—	2	2	no	—
88	C₂×Q₈×C₈₉	C₂²⋊C₄	1	4	yes	—
89	C₂×Q₈×C₈₉	M₁₆	1	4	yes	—
90	C₂²×C₄×C₈₉	—	2	4	no	—
91	C₂²×C₄×C₈₉	—	2	4	no	—
92	C₂²×C₄×C₈₉	—	2	2	no	—
93	C₂²×C₄×C₈₉	—	2	4	no	—
94	C₂²×C₄×C₈₉	—	2	2	no	—
95	C₂²×C₄×C₈₉	—	2	2	no	—
96	C₂²×C₄×C₈₉	—	2	2	no	—
97	C₂²×C₄×C₈₉	—	2	2	no	—
98	C₂²×C₄×C₈₉	—	2	4	no	—
99	C₂²×C₄×C₈₉	—	2	2	no	—
100	C₂²×C₄×C₈₉	—	2	4	no	—
101	C₂²×C₄×C₈₉	—	4	1	no	—
102	C₂²×C₄×C₈₉	—	4	2	no	—
103	C₂²×C₄×C₈₉	M₁₆	1	4	yes	—
104	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₈₉	C₂×Q₈	1	2	yes	—
114	C₂²×C₄×C₈₉	#41	1	2	yes	—
115	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₈₉	—	2	2	no	—
117	C₂×C₈×C₈₉	—	2	2	no	—
118	C₂×C₈×C₈₉	—	2	2	no	—
119	C₂×C₈×C₈₉	—	2	4	no	—
120	C₂×C₈×C₈₉	—	2	2	no	—
121	C₂×C₈×C₈₉	—	2	4	no	—
122	C₂×C₈×C₈₉	—	2	2	no	—
123	C₂×C₈×C₈₉	—	2	4	no	—
124	C₂×C₈×C₈₉	C₂×Q₈	1	4	yes	complemented
125	C₄⋊C₄×C₈₉	—	2	4	no	—
126	C₄⋊C₄×C₈₉	—	2	4	no	—
127	C₄⋊C₄×C₈₉	—	2	4	no	—
128	C₄⋊C₄×C₈₉	—	2	4	no	—
129	C₄⋊C₄×C₈₉	—	2	2	no	—
130	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	8	yes	—
131	C₄⋊C₄×C₈₉	C₂²⋊C₄	1	4	yes	—
132	C₄²×C₈₉	—	2	2	no	—
133	C₄²×C₈₉	—	2	4	no	—
134	C₄²×C₈₉	—	2	4	no	—
135	C₄²×C₈₉	—	2	2	no	—
136	C₄²×C₈₉	—	2	2	no	—
137	C₄²×C₈₉	—	2	4	no	—
138	C₄²×C₈₉	C₂×D₄	1	4	yes	—
139	C₄²×C₈₉	C₂×D₄	1	8	yes	—
140	C₂³×C₈₉	—	2	1	no	—
141	C₂³×C₈₉	—	2	1	no	—
142	C₂³×C₈₉	—	2	1	no	—
143	C₂³×C₈₉	—	2	1	no	—
144	C₂³×C₈₉	C₄×Q₈	1	2	yes	—
145	C₂³×C₈₉	C₂×M₁₆	1	2	yes	—
146	C₂³×C₈₉	#131	1	2	yes	—
147	C₂³×C₈₉	C₂³×C₄	1	1	yes	characteristic
148	Q₈×C₈₉	—	2	16	no	—
149	Q₈×C₈₉	—	2	8	no	—
150	Q₈×C₈₉	—	2	8	no	—
151	C₂×C₄×C₈₉	—	2	16	no	—
152	C₂×C₄×C₈₉	—	2	1	no	—
153	C₂×C₄×C₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	1	no	—
155	C₂×C₄×C₈₉	—	2	1	no	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	—	2	2	no	—
158	C₂×C₄×C₈₉	—	2	2	no	—
159	C₂×C₄×C₈₉	—	2	1	no	—
160	C₂×C₄×C₈₉	—	2	1	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
162	C₂×C₄×C₈₉	—	2	1	no	—
163	C₂×C₄×C₈₉	—	2	2	no	—
164	C₂×C₄×C₈₉	—	2	4	no	—
165	C₂×C₄×C₈₉	—	2	4	no	—
166	C₂×C₄×C₈₉	—	2	8	no	—
167	C₂×C₄×C₈₉	—	2	2	no	—
168	C₂×C₄×C₈₉	—	2	1	no	—
169	C₂×C₄×C₈₉	—	2	1	no	—
170	C₂×C₄×C₈₉	—	2	2	no	—
171	C₂×C₄×C₈₉	—	2	1	no	—
172	C₂×C₄×C₈₉	—	2	2	no	—
173	C₂×C₄×C₈₉	—	4	4	no	—
174	C₂×C₄×C₈₉	—	4	8	no	—
175	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	4	yes	—
177	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	4	yes	—
178	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₈₉	C₄×Q₈	1	2	yes	—
180	C₂×C₄×C₈₉	C₂×M₁₆	1	4	yes	—
181	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
182	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
183	C₂×C₄×C₈₉	C₂×M₁₆	1	2	yes	—
184	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₈₉	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
188	C₈×C₈₉	—	2	4	no	—
189	C₈×C₈₉	—	4	2	no	—
190	C₈×C₈₉	—	4	4	no	—
191	C₂²×C₈₉	—	2	2	no	—
192	C₂²×C₈₉	—	2	2	no	—
193	C₂²×C₈₉	—	2	2	no	—
194	C₂²×C₈₉	—	2	2	no	—
195	C₂²×C₈₉	—	2	2	no	—
196	C₂²×C₈₉	—	2	2	no	—
197	C₂²×C₈₉	#446	1	4	yes	complemented
198	C₂²×C₈₉	C₂²×C₂²⋊C₄	1	1	yes	characteristic
199	C₂²×C₈₉	C₂×C₄×Q₈	1	1	yes	characteristic
200	C₂²×C₈₉	#519	1	1	yes	characteristic
201	C₂²×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
202	C₂²×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
203	C₂²×C₈₉	C₂×#131	1	1	yes	characteristic
204	C₂²×C₈₉	#568	1	1	yes	characteristic
205	C₄×C₈₉	—	2	2	no	—
206	C₄×C₈₉	—	2	4	no	—
207	C₄×C₈₉	—	2	4	no	—
208	C₄×C₈₉	—	2	2	no	—
209	C₄×C₈₉	—	2	2	no	—
210	C₄×C₈₉	—	2	4	no	—
211	C₄×C₈₉	—	4	2	no	—
212	C₄×C₈₉	—	4	1	no	—
213	C₄×C₈₉	#407	1	4	yes	—
214	C₄×C₈₉	#548	1	2	yes	—
215	C₄×C₈₉	D₄×Q₈	1	2	yes	—
216	#22510	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂×C₈₉	—	2	4	no	—
218	C₂×C₈₉	Q₈×C₂²⋊C₄	1	1	yes	characteristic
219	C₂×C₈₉	C₂×#407	1	1	yes	characteristic
220	C₂×C₈₉	#2880	1	1	yes	characteristic
221	C₂×C₈₉	C₂×#446	1	1	yes	characteristic
222	C₂×C₈₉	Q₈×M₁₆	1	1	yes	characteristic
223	C₂×C₈₉	#2983	1	1	yes	characteristic
224	C₂×C₈₉	#2984	1	1	yes	characteristic
225	C₂²×C₄×Q₈	C₂×C₈₉	1	1	yes	characteristic
226	C₂×#446	C₂×C₈₉	1	2	yes	complemented
227	#1985	C₂×C₈₉	1	4	yes	complemented
228	#1984	C₂×C₈₉	1	2	yes	complemented
229	#1797	C₂×C₈₉	1	2	yes	—
230	#1797	C₂×C₈₉	1	1	yes	characteristic
231	#1749	C₂×C₈₉	1	2	yes	—
232	C₄×C₂²⋊C₈	C₂×C₈₉	1	1	yes	characteristic
233	C₈₉	#22510	1	1	yes	characteristic, direct product factor, Sylow
234	C₂³×Q₈	C₄×C₈₉	1	1	yes	characteristic
235	C₂×C₄×Q₈	—	2	8	no	—
236	C₂×C₄×Q₈	C₄×C₈₉	1	1	yes	characteristic
237	C₂×C₄×Q₈	C₄×C₈₉	1	2	yes	—
238	C₂×C₄×Q₈	C₄×C₈₉	1	1	yes	characteristic
239	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
241	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	C₄×C₈₉	1	2	yes	—
243	C₂²×C₄⋊C₄	C₄×C₈₉	1	1	yes	characteristic
244	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
245	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
246	#446	—	2	8	no	—
247	C₂×C₄⋊C₈	C₂²×C₈₉	1	2	yes	—
248	C₂×C₄⋊C₈	C₂²×C₈₉	1	4	yes	—
249	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
250	C₂×C₂²⋊C₈	C₂²×C₈₉	1	2	yes	—
251	C₂×C₂²⋊C₈	C₂²×C₈₉	1	1	yes	characteristic
252	C₂×#97	C₂²×C₈₉	1	4	yes	—
253	C₂×C₄×C₈	C₂²×C₈₉	1	2	yes	—
254	#336	C₂²×C₈₉	1	4	yes	—
255	#336	C₂²×C₈₉	1	2	yes	—
256	#336	C₂²×C₈₉	1	4	yes	—
257	#336	C₂²×C₈₉	1	2	yes	—
258	C₂²×Q₈	—	2	4	no	—
259	C₂²×Q₈	—	2	4	no	—
260	C₂²×Q₈	—	2	4	no	—
261	C₂²×Q₈	C₂×C₄×C₈₉	1	2	yes	—
262	C₂²×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
263	C₂²×Q₈	C₂×C₄×C₈₉	1	1	yes	characteristic
264	C₂³×C₄	C₂×C₄×C₈₉	1	2	yes	—
265	C₂³×C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
266	C₂³×C₄	C₂×C₄×C₈₉	1	2	yes	—
267	C₂³×C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
268	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
269	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
270	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
271	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
272	C₄×Q₈	—	2	4	no	—
273	C₄×Q₈	—	2	8	no	—
274	C₄×Q₈	—	2	4	no	—
275	C₄×Q₈	—	2	4	no	—
276	C₄×Q₈	—	2	8	no	—
277	C₄×Q₈	D₄×C₈₉	1	8	yes	—
278	C₂×C₄⋊C₄	—	2	8	no	—
279	C₂×C₄⋊C₄	—	2	4	no	—
280	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
281	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
283	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
284	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
285	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	2	yes	—
286	C₂×C₄⋊C₄	C₂×C₄×C₈₉	1	1	yes	characteristic
287	C₂×C₄²	—	2	4	no	—
288	C₂×C₄²	—	2	8	no	—
289	C₂×C₄²	C₂×C₄×C₈₉	1	2	yes	—
290	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
291	C₂×C₄²	C₂×C₄×C₈₉	1	1	yes	characteristic
292	C₂×C₄²	C₂×C₄×C₈₉	1	2	yes	—
293	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
294	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
295	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
296	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
297	C₄⋊C₈	—	2	4	no	—
298	C₄⋊C₈	—	2	8	no	—
299	C₂²⋊C₈	—	2	2	no	—
300	C₂²⋊C₈	—	2	4	no	—
301	C₂²⋊C₈	Q₈×C₈₉	1	4	yes	complemented
302	#97	—	2	8	no	—
303	C₄×C₈	—	2	4	no	—
304	C₂⁴	C₂²×C₄×C₈₉	1	1	yes	characteristic
305	C₂×Q₈	—	2	32	no	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	4	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	C₂²⋊C₄×C₈₉	1	4	yes	—
314	C₂×Q₈	M₁₆×C₈₉	1	4	yes	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	M₁₆×C₈₉	1	4	yes	—
329	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
330	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
331	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
332	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
333	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
334	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
335	C₂²×C₄	C₂²×C₄×C₈₉	1	2	yes	—
336	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
337	C₂²×C₄	C₂²×C₄×C₈₉	1	1	yes	characteristic
338	C₂²×C₄	C₂×Q₈×C₈₉	1	2	yes	—
339	C₂²×C₄	#41×C₈₉	1	2	yes	—
340	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	—	2	4	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	C₂×Q₈×C₈₉	1	4	yes	complemented
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	C₂²⋊C₄×C₈₉	1	8	yes	—
356	C₄⋊C₄	C₂²⋊C₄×C₈₉	1	4	yes	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	4	no	—
359	C₄²	—	2	4	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	4	no	—
363	C₄²	C₂×D₄×C₈₉	1	4	yes	—
364	C₄²	C₂×D₄×C₈₉	1	8	yes	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	C₄×Q₈×C₈₉	1	2	yes	—
370	C₂³	C₂×M₁₆×C₈₉	1	2	yes	—
371	C₂³	#131×C₈₉	1	2	yes	—
372	C₂³	C₂³×C₄×C₈₉	1	1	yes	characteristic
373	Q₈	—	2	16	no	—
374	Q₈	—	2	8	no	—
375	Q₈	—	2	8	no	—
376	C₂×C₄	—	2	16	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	8	no	—
400	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
401	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	4	yes	—
402	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	4	yes	—
403	C₂×C₄	C₂×C₂²⋊C₄×C₈₉	1	2	yes	—
404	C₂×C₄	C₄×Q₈×C₈₉	1	2	yes	—
405	C₂×C₄	C₂×M₁₆×C₈₉	1	4	yes	—
406	C₂×C₄	C₂×M₁₆×C₈₉	1	2	yes	—
407	C₂×C₄	C₂×M₁₆×C₈₉	1	2	yes	—
408	C₂×C₄	C₂×M₁₆×C₈₉	1	2	yes	—
409	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
410	C₂×C₄	C₂²×Q₈×C₈₉	1	1	yes	characteristic
411	C₂×C₄	C₂×#41×C₈₉	1	1	yes	characteristic
412	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
413	C₈	—	2	4	no	—
414	C₈	—	4	2	no	—
415	C₈	—	4	4	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	#446×C₈₉	1	4	yes	complemented
423	C₂²	C₂²×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
424	C₂²	C₂×C₄×Q₈×C₈₉	1	1	yes	characteristic
425	C₂²	#519×C₈₉	1	1	yes	characteristic
426	C₂²	C₂²×M₁₆×C₈₉	1	1	yes	characteristic
427	C₂²	C₂²×M₁₆×C₈₉	1	1	yes	characteristic
428	C₂²	C₂×#131×C₈₉	1	1	yes	characteristic
429	C₂²	#568×C₈₉	1	1	yes	characteristic
430	C₄	—	2	2	no	—
431	C₄	—	2	4	no	—
432	C₄	—	2	4	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	4	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	1	no	—
438	C₄	#407×C₈₉	1	4	yes	—
439	C₄	#548×C₈₉	1	2	yes	—
440	C₄	D₄×Q₈×C₈₉	1	2	yes	—
441	C₂	—	2	4	no	—
442	C₂	Q₈×C₂²⋊C₄×C₈₉	1	1	yes	characteristic
443	C₂	C₂×#407×C₈₉	1	1	yes	characteristic
444	C₂	C₈₉×#2880	1	1	yes	characteristic
445	C₂	C₂×#446×C₈₉	1	1	yes	characteristic
446	C₂	Q₈×M₁₆×C₈₉	1	1	yes	characteristic
447	C₂	C₈₉×#2983	1	1	yes	characteristic
448	C₂	C₈₉×#2984	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×#446×C₈₉	C₂	semidirect
3. C₈₉×#1985	C₂	semidirect
4. C₈₉×#1984	C₂	semidirect
76. C₂²⋊C₈×C₈₉	Q₈	semidirect
124. C₂×C₈×C₈₉	C₂×Q₈	semidirect
197. C₂²×C₈₉	#446	semidirect
216. #22510	C₈₉	direct (N × H)
226. C₂×#446	C₂×C₈₉	semidirect
227. #1985	C₂×C₈₉	semidirect
228. #1984	C₂×C₈₉	semidirect
233. C₈₉	#22510	direct (N × H)
301. C₂²⋊C₈	Q₈×C₈₉	semidirect
349. C₂×C₈	C₂×Q₈×C₈₉	semidirect
422. C₂²	#446×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×Q₈×C₈₉	2
C₂×#446×C₈₉	2
C₈₉×#1985	2
C₈₉×#1984	2
C₈₉×#1797	2
C₈₉×#1749	2
C₄×C₂²⋊C₈×C₈₉	2
#22510	89

Subgroups — C89×#22510 #36400358

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#22510 #36400358