Subgroups — C₈₉×#35277 #36413125

Order 22784.

2370 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#542×C₈₉	C₂	1	2	yes	maximal, complemented
2	C₈₉×#2868	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2858	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2857	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2856	C₂	1	1	yes	maximal, characteristic
6	C₈₉×#2640	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2620	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2512	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2491	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2452	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2422	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2326	C₂	1	2	yes	maximal, complemented
13	C₄×C₄⋊Q₈×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#127×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	#542×C₈₉	—	2	16	no	—
17	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
19	C₂×C₄⋊Q₈×C₈₉	C₂²	1	4	yes	—
20	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#126×C₈₉	C₂²	1	4	yes	—
22	C₂×#124×C₈₉	C₂²	1	2	yes	—
23	C₂×#124×C₈₉	C₂²	1	2	yes	—
24	C₂×#124×C₈₉	C₂²	1	4	yes	—
25	C₂×#123×C₈₉	C₂²	1	4	yes	—
26	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
28	C₂×#121×C₈₉	C₂²	1	2	yes	—
29	C₂×#121×C₈₉	C₂²	1	4	yes	—
30	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
33	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
34	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
36	#397×C₈₉	C₂²	1	8	yes	—
37	#396×C₈₉	C₂²	1	8	yes	—
38	#394×C₈₉	C₂²	1	8	yes	—
39	#393×C₈₉	C₂²	1	8	yes	—
40	#391×C₈₉	C₂²	1	2	yes	—
41	#391×C₈₉	C₂²	1	2	yes	—
42	#390×C₈₉	C₂²	1	2	yes	—
43	#390×C₈₉	C₂²	1	4	yes	—
44	#390×C₈₉	C₂²	1	2	yes	—
45	#390×C₈₉	C₂²	1	4	yes	—
46	#390×C₈₉	C₂²	1	4	yes	—
47	#390×C₈₉	C₂²	1	4	yes	—
48	#389×C₈₉	C₂²	1	4	yes	—
49	#389×C₈₉	C₂²	1	4	yes	—
50	#388×C₈₉	C₂²	1	8	yes	—
51	#385×C₈₉	C₂²	1	8	yes	—
52	#384×C₈₉	C₂²	1	1	yes	characteristic
53	#384×C₈₉	C₂²	1	1	yes	characteristic
54	#384×C₈₉	C₂²	1	2	yes	—
55	#384×C₈₉	C₂²	1	4	yes	—
56	#380×C₈₉	C₂²	1	4	yes	—
57	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
58	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
59	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
60	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
61	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
62	#376×C₈₉	C₂²	1	1	yes	characteristic
63	#376×C₈₉	C₂²	1	1	yes	characteristic
64	C₄³×C₈₉	C₂²	1	1	yes	characteristic
65	C₄³×C₈₉	C₂²	1	1	yes	characteristic
66	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
67	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
68	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
69	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
70	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
71	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
72	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
73	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
74	C₄⋊Q₈×C₈₉	—	2	8	no	—
75	C₄⋊Q₈×C₈₉	—	2	4	no	—
76	C₄⋊Q₈×C₈₉	—	4	8	no	—
77	#127×C₈₉	—	2	4	no	—
78	#126×C₈₉	—	2	16	no	—
79	#124×C₈₉	—	2	16	no	—
80	#124×C₈₉	—	2	8	no	—
81	#124×C₈₉	—	2	8	no	—
82	#123×C₈₉	—	2	16	no	—
83	C₂²⋊Q₈×C₈₉	—	2	8	no	—
84	C₂²⋊Q₈×C₈₉	—	2	16	no	—
85	#121×C₈₉	—	2	8	no	—
86	#121×C₈₉	—	4	8	no	—
87	C₄×Q₈×C₈₉	—	2	8	no	—
88	C₄×D₄×C₈₉	—	2	8	no	—
89	C₄×D₄×C₈₉	—	4	8	no	—
90	#117×C₈₉	—	2	4	no	—
91	#117×C₈₉	D₄	1	8	yes	complemented
92	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
93	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
94	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
95	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
96	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
99	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
102	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
105	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
106	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
107	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
108	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
109	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
110	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
111	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
112	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
113	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₄²×C₈₉	—	2	4	no	—
116	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
118	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
119	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
120	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
121	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
122	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
123	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
124	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
128	#95×C₈₉	C₂³	1	2	yes	—
129	#95×C₈₉	C₂³	1	2	yes	—
130	#95×C₈₉	C₂³	1	2	yes	—
131	#95×C₈₉	C₂³	1	2	yes	—
132	#95×C₈₉	C₂³	1	8	yes	—
133	#95×C₈₉	C₂³	1	8	yes	—
134	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
135	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
136	C₂×Q₈×C₈₉	—	2	4	no	—
137	C₂×Q₈×C₈₉	—	2	8	no	—
138	C₂×Q₈×C₈₉	—	2	4	no	—
139	C₂×Q₈×C₈₉	—	2	4	no	—
140	C₂×Q₈×C₈₉	—	4	8	no	—
141	C₂×D₄×C₈₉	—	2	8	no	—
142	C₂×D₄×C₈₉	—	2	4	no	—
143	C₂×D₄×C₈₉	—	2	4	no	—
144	C₂×D₄×C₈₉	—	2	4	no	—
145	C₂×D₄×C₈₉	—	2	8	no	—
146	C₂×D₄×C₈₉	—	2	8	no	—
147	C₂×D₄×C₈₉	—	2	8	no	—
148	C₂×D₄×C₈₉	—	4	8	no	—
149	C₂²×C₄×C₈₉	—	2	2	no	—
150	C₂²×C₄×C₈₉	—	2	2	no	—
151	C₂²×C₄×C₈₉	—	2	4	no	—
152	C₂²×C₄×C₈₉	—	2	4	no	—
153	C₂²×C₄×C₈₉	—	2	4	no	—
154	C₂²×C₄×C₈₉	—	2	8	no	—
155	C₂²×C₄×C₈₉	—	4	8	no	—
156	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
157	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
158	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
159	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
161	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
163	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
164	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
165	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
166	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
167	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
170	C₄⋊C₄×C₈₉	—	2	4	no	—
171	C₄⋊C₄×C₈₉	—	2	4	no	—
172	C₄⋊C₄×C₈₉	—	2	8	no	—
173	C₄⋊C₄×C₈₉	—	2	8	no	—
174	C₄⋊C₄×C₈₉	—	2	8	no	—
175	C₄⋊C₄×C₈₉	—	2	4	no	—
176	C₄⋊C₄×C₈₉	—	2	8	no	—
177	C₄⋊C₄×C₈₉	—	2	8	no	—
178	C₄⋊C₄×C₈₉	—	2	8	no	—
179	C₄⋊C₄×C₈₉	—	4	8	no	—
180	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
181	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
182	C₂²⋊C₄×C₈₉	—	2	8	no	—
183	C₂²⋊C₄×C₈₉	—	2	8	no	—
184	C₂²⋊C₄×C₈₉	—	2	8	no	—
185	C₂²⋊C₄×C₈₉	—	2	8	no	—
186	C₂²⋊C₄×C₈₉	—	2	8	no	—
187	C₂²⋊C₄×C₈₉	—	2	4	no	—
188	C₂²⋊C₄×C₈₉	—	2	16	no	—
189	C₂²⋊C₄×C₈₉	—	4	8	no	—
190	C₂²⋊C₄×C₈₉	—	4	8	no	—
191	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
192	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
193	C₄²×C₈₉	—	2	8	no	—
194	C₄²×C₈₉	—	2	4	no	—
195	C₄²×C₈₉	—	2	2	no	—
196	C₄²×C₈₉	—	2	2	no	—
197	C₄²×C₈₉	—	2	4	no	—
198	C₄²×C₈₉	—	2	4	no	—
199	C₄²×C₈₉	—	2	4	no	—
200	C₄²×C₈₉	—	2	4	no	—
201	C₄²×C₈₉	C₂×D₄	1	4	yes	—
202	C₄²×C₈₉	C₂×D₄	1	4	yes	—
203	C₄²×C₈₉	#41	1	4	yes	—
204	C₄²×C₈₉	#41	1	4	yes	—
205	C₂³×C₈₉	—	2	1	no	—
206	C₂³×C₈₉	—	2	1	no	—
207	C₂³×C₈₉	—	2	2	no	—
208	C₂³×C₈₉	—	2	2	no	—
209	C₂³×C₈₉	—	2	4	no	—
210	C₂³×C₈₉	—	2	4	no	—
211	C₂³×C₈₉	—	2	4	no	—
212	C₂³×C₈₉	—	2	8	no	—
213	C₂³×C₈₉	—	2	8	no	—
214	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
215	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
216	Q₈×C₈₉	—	4	8	no	—
217	Q₈×C₈₉	—	8	8	no	—
218	D₄×C₈₉	—	4	8	no	—
219	D₄×C₈₉	—	4	16	no	—
220	D₄×C₈₉	—	8	8	no	—
221	C₂×C₄×C₈₉	—	2	1	no	—
222	C₂×C₄×C₈₉	—	2	1	no	—
223	C₂×C₄×C₈₉	—	2	2	no	—
224	C₂×C₄×C₈₉	—	2	2	no	—
225	C₂×C₄×C₈₉	—	2	2	no	—
226	C₂×C₄×C₈₉	—	2	2	no	—
227	C₂×C₄×C₈₉	—	2	2	no	—
228	C₂×C₄×C₈₉	—	2	2	no	—
229	C₂×C₄×C₈₉	—	2	8	no	—
230	C₂×C₄×C₈₉	—	2	4	no	—
231	C₂×C₄×C₈₉	—	2	4	no	—
232	C₂×C₄×C₈₉	—	2	4	no	—
233	C₂×C₄×C₈₉	—	2	2	no	—
234	C₂×C₄×C₈₉	—	2	2	no	—
235	C₂×C₄×C₈₉	—	2	4	no	—
236	C₂×C₄×C₈₉	—	2	4	no	—
237	C₂×C₄×C₈₉	—	2	2	no	—
238	C₂×C₄×C₈₉	—	2	2	no	—
239	C₂×C₄×C₈₉	—	2	8	no	—
240	C₂×C₄×C₈₉	—	2	8	no	—
241	C₂×C₄×C₈₉	—	2	2	no	—
242	C₂×C₄×C₈₉	—	2	2	no	—
243	C₂×C₄×C₈₉	—	4	8	no	—
244	C₂×C₄×C₈₉	—	8	8	no	—
245	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
246	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
252	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
253	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
254	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
255	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
256	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
257	C₂²×C₈₉	—	2	2	no	—
258	C₂²×C₈₉	—	2	2	no	—
259	C₂²×C₈₉	—	2	2	no	—
260	C₂²×C₈₉	—	4	2	no	—
261	C₂²×C₈₉	—	4	2	no	—
262	C₂²×C₈₉	—	4	4	no	—
263	C₂²×C₈₉	—	4	8	no	—
264	C₂²×C₈₉	—	4	4	no	—
265	C₂²×C₈₉	—	4	4	no	—
266	C₂²×C₈₉	—	4	8	no	—
267	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
268	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
269	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
270	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
271	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
272	C₄×C₈₉	—	2	2	no	—
273	C₄×C₈₉	—	2	2	no	—
274	C₄×C₈₉	—	2	2	no	—
275	C₄×C₈₉	—	2	2	no	—
276	C₄×C₈₉	—	2	2	no	—
277	C₄×C₈₉	—	2	4	no	—
278	C₄×C₈₉	—	4	4	no	—
279	C₄×C₈₉	—	4	2	no	—
280	C₄×C₈₉	—	4	4	no	—
281	C₄×C₈₉	—	4	4	no	—
282	C₄×C₈₉	—	4	2	no	—
283	C₄×C₈₉	#532	1	4	yes	—
284	C₄×C₈₉	#542	1	8	yes	complemented
285	#35277	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂×C₈₉	—	4	2	no	—
287	C₂×C₈₉	—	8	4	no	—
288	C₂×C₈₉	C₂×#532	1	1	yes	characteristic
289	C₂×C₈₉	C₂×#542	1	2	yes	—
290	C₂×C₈₉	#3498	1	1	yes	characteristic
291	C₂×C₈₉	#3499	1	1	yes	characteristic
292	C₂×C₈₉	#3511	1	2	yes	—
293	C₂×#542	C₂×C₈₉	1	2	yes	complemented
294	#2868	C₂×C₈₉	1	1	yes	characteristic, complemented
295	#2858	C₂×C₈₉	1	1	yes	characteristic, complemented
296	#2857	C₂×C₈₉	1	1	yes	characteristic, complemented
297	#2856	C₂×C₈₉	1	1	yes	characteristic
298	#2640	C₂×C₈₉	1	2	yes	complemented
299	#2620	C₂×C₈₉	1	2	yes	complemented
300	#2512	C₂×C₈₉	1	4	yes	complemented
301	#2491	C₂×C₈₉	1	4	yes	complemented
302	#2452	C₂×C₈₉	1	4	yes	complemented
303	#2422	C₂×C₈₉	1	4	yes	complemented
304	#2326	C₂×C₈₉	1	2	yes	complemented
305	C₄×C₄⋊Q₈	C₂×C₈₉	1	1	yes	characteristic, complemented
306	C₄×#127	C₂×C₈₉	1	1	yes	characteristic, complemented
307	C₄×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
308	C₈₉	#35277	1	1	yes	characteristic, direct product factor, Sylow
309	#542	—	2	16	no	—
310	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
311	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
312	C₂×C₄⋊Q₈	C₂²×C₈₉	1	4	yes	—
313	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
314	C₂×#126	C₂²×C₈₉	1	4	yes	—
315	C₂×#124	C₂²×C₈₉	1	2	yes	—
316	C₂×#124	C₂²×C₈₉	1	2	yes	—
317	C₂×#124	C₂²×C₈₉	1	4	yes	—
318	C₂×#123	C₂²×C₈₉	1	4	yes	—
319	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
320	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
321	C₂×#121	C₂²×C₈₉	1	2	yes	—
322	C₂×#121	C₂²×C₈₉	1	4	yes	—
323	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
324	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
325	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
326	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
327	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
328	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
329	#397	C₂²×C₈₉	1	8	yes	—
330	#396	C₂²×C₈₉	1	8	yes	—
331	#394	C₂²×C₈₉	1	8	yes	—
332	#393	C₂²×C₈₉	1	8	yes	—
333	#391	C₂²×C₈₉	1	2	yes	—
334	#391	C₂²×C₈₉	1	2	yes	—
335	#390	C₂²×C₈₉	1	2	yes	—
336	#390	C₂²×C₈₉	1	4	yes	—
337	#390	C₂²×C₈₉	1	2	yes	—
338	#390	C₂²×C₈₉	1	4	yes	—
339	#390	C₂²×C₈₉	1	4	yes	—
340	#390	C₂²×C₈₉	1	4	yes	—
341	#389	C₂²×C₈₉	1	4	yes	—
342	#389	C₂²×C₈₉	1	4	yes	—
343	#388	C₂²×C₈₉	1	8	yes	—
344	#385	C₂²×C₈₉	1	8	yes	—
345	#384	C₂²×C₈₉	1	1	yes	characteristic
346	#384	C₂²×C₈₉	1	1	yes	characteristic
347	#384	C₂²×C₈₉	1	2	yes	—
348	#384	C₂²×C₈₉	1	4	yes	—
349	#380	C₂²×C₈₉	1	4	yes	—
350	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
351	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
352	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
353	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
354	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
355	#376	C₂²×C₈₉	1	1	yes	characteristic
356	#376	C₂²×C₈₉	1	1	yes	characteristic
357	C₄³	C₂²×C₈₉	1	1	yes	characteristic
358	C₄³	C₂²×C₈₉	1	1	yes	characteristic
359	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
360	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
361	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
362	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
363	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
364	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
365	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
366	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
367	C₄⋊Q₈	—	2	8	no	—
368	C₄⋊Q₈	—	2	4	no	—
369	C₄⋊Q₈	—	4	8	no	—
370	#127	—	2	4	no	—
371	#126	—	2	16	no	—
372	#124	—	2	16	no	—
373	#124	—	2	8	no	—
374	#124	—	2	8	no	—
375	#123	—	2	16	no	—
376	C₂²⋊Q₈	—	2	8	no	—
377	C₂²⋊Q₈	—	2	16	no	—
378	#121	—	2	8	no	—
379	#121	—	4	8	no	—
380	C₄×Q₈	—	2	8	no	—
381	C₄×D₄	—	2	8	no	—
382	C₄×D₄	—	4	8	no	—
383	#117	—	2	4	no	—
384	#117	D₄×C₈₉	1	8	yes	complemented
385	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
388	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
389	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
392	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
393	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
394	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
395	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
397	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
398	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
399	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
400	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
401	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
407	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
408	C₂×C₄²	—	2	4	no	—
409	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
411	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
412	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
413	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
414	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
415	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
416	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
417	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
419	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
421	#95	C₂³×C₈₉	1	2	yes	—
422	#95	C₂³×C₈₉	1	2	yes	—
423	#95	C₂³×C₈₉	1	2	yes	—
424	#95	C₂³×C₈₉	1	2	yes	—
425	#95	C₂³×C₈₉	1	8	yes	—
426	#95	C₂³×C₈₉	1	8	yes	—
427	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
428	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
429	C₂×Q₈	—	2	4	no	—
430	C₂×Q₈	—	2	8	no	—
431	C₂×Q₈	—	2	4	no	—
432	C₂×Q₈	—	2	4	no	—
433	C₂×Q₈	—	4	8	no	—
434	C₂×D₄	—	2	8	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂×D₄	—	2	4	no	—
437	C₂×D₄	—	2	4	no	—
438	C₂×D₄	—	2	8	no	—
439	C₂×D₄	—	2	8	no	—
440	C₂×D₄	—	2	8	no	—
441	C₂×D₄	—	4	8	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	8	no	—
448	C₂²×C₄	—	4	8	no	—
449	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
450	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
453	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
454	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
457	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
459	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
460	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
461	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
462	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
463	C₄⋊C₄	—	2	4	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	8	no	—
466	C₄⋊C₄	—	2	8	no	—
467	C₄⋊C₄	—	2	8	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	8	no	—
470	C₄⋊C₄	—	2	8	no	—
471	C₄⋊C₄	—	2	8	no	—
472	C₄⋊C₄	—	4	8	no	—
473	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
474	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
475	C₂²⋊C₄	—	2	8	no	—
476	C₂²⋊C₄	—	2	8	no	—
477	C₂²⋊C₄	—	2	8	no	—
478	C₂²⋊C₄	—	2	8	no	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	16	no	—
482	C₂²⋊C₄	—	4	8	no	—
483	C₂²⋊C₄	—	4	8	no	—
484	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
485	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
486	C₄²	—	2	8	no	—
487	C₄²	—	2	4	no	—
488	C₄²	—	2	2	no	—
489	C₄²	—	2	2	no	—
490	C₄²	—	2	4	no	—
491	C₄²	—	2	4	no	—
492	C₄²	—	2	4	no	—
493	C₄²	—	2	4	no	—
494	C₄²	C₂×D₄×C₈₉	1	4	yes	—
495	C₄²	C₂×D₄×C₈₉	1	4	yes	—
496	C₄²	#41×C₈₉	1	4	yes	—
497	C₄²	#41×C₈₉	1	4	yes	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	2	4	no	—
503	C₂³	—	2	4	no	—
504	C₂³	—	2	4	no	—
505	C₂³	—	2	8	no	—
506	C₂³	—	2	8	no	—
507	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
508	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
509	Q₈	—	4	8	no	—
510	Q₈	—	8	8	no	—
511	D₄	—	4	8	no	—
512	D₄	—	4	16	no	—
513	D₄	—	8	8	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	8	no	—
523	C₂×C₄	—	2	4	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	8	no	—
533	C₂×C₄	—	2	8	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	4	8	no	—
537	C₂×C₄	—	8	8	no	—
538	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
540	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
541	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
542	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
543	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
544	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
545	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
546	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
547	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
548	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
549	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	4	no	—
556	C₂²	—	4	8	no	—
557	C₂²	—	4	4	no	—
558	C₂²	—	4	4	no	—
559	C₂²	—	4	8	no	—
560	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
561	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
562	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
563	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
564	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
565	C₄	—	2	2	no	—
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	4	no	—
571	C₄	—	4	4	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	4	no	—
574	C₄	—	4	4	no	—
575	C₄	—	4	2	no	—
576	C₄	#532×C₈₉	1	4	yes	—
577	C₄	#542×C₈₉	1	8	yes	complemented
578	C₂	—	4	2	no	—
579	C₂	—	8	4	no	—
580	C₂	C₂×#532×C₈₉	1	1	yes	characteristic
581	C₂	C₂×#542×C₈₉	1	2	yes	—
582	C₂	C₈₉×#3498	1	1	yes	characteristic
583	C₂	C₈₉×#3499	1	1	yes	characteristic
584	C₂	C₈₉×#3511	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2856	C₂
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
1. C₂×#542×C₈₉	C₂	semidirect
2. C₈₉×#2868	C₂	semidirect
3. C₈₉×#2858	C₂	semidirect
4. C₈₉×#2857	C₂	semidirect
6. C₈₉×#2640	C₂	semidirect
7. C₈₉×#2620	C₂	semidirect
8. C₈₉×#2512	C₂	semidirect
9. C₈₉×#2491	C₂	semidirect
10. C₈₉×#2452	C₂	semidirect
11. C₈₉×#2422	C₂	semidirect
12. C₈₉×#2326	C₂	semidirect
13. C₄×C₄⋊Q₈×C₈₉	C₂	semidirect
14. C₄×#127×C₈₉	C₂	semidirect
15. C₄×#117×C₈₉	C₂	semidirect
91. #117×C₈₉	D₄	semidirect
284. C₄×C₈₉	#542	semidirect
285. #35277	C₈₉	direct (N × H)
293. C₂×#542	C₂×C₈₉	semidirect
294. #2868	C₂×C₈₉	semidirect
295. #2858	C₂×C₈₉	semidirect
296. #2857	C₂×C₈₉	semidirect
298. #2640	C₂×C₈₉	semidirect
299. #2620	C₂×C₈₉	semidirect
300. #2512	C₂×C₈₉	semidirect
301. #2491	C₂×C₈₉	semidirect
302. #2452	C₂×C₈₉	semidirect
303. #2422	C₂×C₈₉	semidirect
304. #2326	C₂×C₈₉	semidirect
305. C₄×C₄⋊Q₈	C₂×C₈₉	semidirect
306. C₄×#127	C₂×C₈₉	semidirect
307. C₄×#117	C₂×C₈₉	semidirect
308. C₈₉	#35277	direct (N × H)
384. #117	D₄×C₈₉	semidirect
577. C₄	#542×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#542×C₈₉	2
C₈₉×#2868	2
C₈₉×#2858	2
C₈₉×#2857	2
C₈₉×#2856	2
C₈₉×#2640	2
C₈₉×#2620	2
C₈₉×#2512	2
C₈₉×#2491	2
C₈₉×#2452	2
C₈₉×#2422	2
C₈₉×#2326	2
C₄×C₄⋊Q₈×C₈₉	2
C₄×#127×C₈₉	2
C₄×#117×C₈₉	2
#35277	89

Subgroups — C89×#35277 #36413125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35277 #36413125