Subgroups — C₈₉×#35236 #36413084

Order 22784.

2986 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#529×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2848	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2847	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2636	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2562	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2540	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2538	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2537	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2487	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2411	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2408	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2324	C₂	1	4	yes	maximal, complemented
14	C₈₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₈₉	C₂²	1	2	yes	—
17	#529×C₈₉	—	2	8	no	—
18	C₂×#126×C₈₉	C₂²	1	2	yes	complemented
19	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic, complemented
20	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic, complemented
21	C₂×#123×C₈₉	C₂²	1	2	yes	—
22	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
24	C₂×#121×C₈₉	C₂²	1	4	yes	—
25	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#121×C₈₉	C₂²	1	4	yes	complemented
27	C₂×#120×C₈₉	C₂²	1	4	yes	—
28	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₄×D₄×C₈₉	—	2	8	no	—
30	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic, complemented
36	C₂×#117×C₈₉	C₂²	1	2	yes	—
37	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
38	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
39	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
40	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
41	#400×C₈₉	C₂²	1	4	yes	complemented
42	#399×C₈₉	C₂²	1	4	yes	complemented
43	#396×C₈₉	C₂²	1	8	yes	complemented
44	#394×C₈₉	C₂²	1	4	yes	—
45	#394×C₈₉	C₂²	1	8	yes	complemented
46	#392×C₈₉	C₂²	1	4	yes	—
47	#390×C₈₉	C₂²	1	4	yes	—
48	#390×C₈₉	C₂²	1	8	yes	complemented
49	#389×C₈₉	C₂²	1	4	yes	complemented
50	#388×C₈₉	C₂²	1	8	yes	complemented
51	#386×C₈₉	C₂²	1	4	yes	—
52	#386×C₈₉	C₂²	1	8	yes	complemented
53	#385×C₈₉	C₂²	1	4	yes	—
54	#385×C₈₉	C₂²	1	8	yes	complemented
55	#384×C₈₉	C₂²	1	2	yes	complemented
56	#382×C₈₉	C₂²	1	2	yes	complemented
57	#380×C₈₉	C₂²	1	2	yes	—
58	#380×C₈₉	C₂²	1	2	yes	—
59	#380×C₈₉	C₂²	1	4	yes	complemented
60	#380×C₈₉	C₂²	1	4	yes	complemented
61	#380×C₈₉	C₂²	1	4	yes	complemented
62	#379×C₈₉	C₂²	1	4	yes	—
63	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
64	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
65	C₂⁵×C₈₉	C₂³	1	2	yes	—
66	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
67	C₂²×D₄×C₈₉	—	2	8	no	—
68	C₂²×D₄×C₈₉	—	2	4	no	—
69	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
70	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
71	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
73	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
74	C₂³×C₄×C₈₉	—	2	8	no	—
75	C₂³×C₄×C₈₉	—	4	8	no	—
76	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
78	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
82	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
83	#126×C₈₉	—	2	8	no	—
84	#125×C₈₉	—	2	4	no	—
85	#124×C₈₉	—	2	4	no	—
86	#123×C₈₉	—	2	8	no	—
87	C₂²⋊Q₈×C₈₉	—	2	4	no	—
88	C₂²⋊Q₈×C₈₉	—	4	8	no	—
89	#121×C₈₉	—	2	16	no	—
90	#121×C₈₉	—	2	4	no	—
91	#121×C₈₉	—	4	8	no	—
92	#120×C₈₉	—	4	8	no	—
93	C₄×Q₈×C₈₉	—	2	4	no	—
94	C₄×D₄×C₈₉	—	2	8	no	—
95	C₄×D₄×C₈₉	—	2	8	no	—
96	C₄×D₄×C₈₉	—	2	8	no	—
97	C₄×D₄×C₈₉	—	2	8	no	—
98	C₄×D₄×C₈₉	—	2	8	no	—
99	C₄×D₄×C₈₉	—	2	4	no	—
100	#117×C₈₉	—	2	8	no	—
101	#117×C₈₉	—	4	4	no	—
102	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
103	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
112	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
114	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
115	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
116	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
118	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
119	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
121	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
122	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
126	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
127	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
128	C₂×C₄²×C₈₉	D₄	1	8	yes	complemented
129	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
130	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
131	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
134	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
135	#95×C₈₉	C₂³	1	4	yes	—
136	#95×C₈₉	C₂³	1	4	yes	—
137	#95×C₈₉	C₂³	1	8	yes	—
138	#95×C₈₉	C₂³	1	8	yes	—
139	C₂⁴×C₈₉	—	2	4	no	—
140	C₂⁴×C₈₉	—	2	8	no	—
141	C₂⁴×C₈₉	—	2	4	no	—
142	C₂⁴×C₈₉	—	2	4	no	—
143	C₂⁴×C₈₉	—	4	4	no	—
144	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
145	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
146	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
147	C₂×Q₈×C₈₉	—	2	2	no	—
148	C₂×Q₈×C₈₉	—	2	4	no	—
149	C₂×D₄×C₈₉	—	2	32	no	—
150	C₂×D₄×C₈₉	—	2	8	no	—
151	C₂×D₄×C₈₉	—	2	4	no	—
152	C₂×D₄×C₈₉	—	2	4	no	—
153	C₂×D₄×C₈₉	—	2	4	no	—
154	C₂×D₄×C₈₉	—	2	16	no	—
155	C₂×D₄×C₈₉	—	2	4	no	—
156	C₂×D₄×C₈₉	—	2	4	no	—
157	C₂×D₄×C₈₉	—	2	2	no	—
158	C₂×D₄×C₈₉	—	2	4	no	—
159	C₂×D₄×C₈₉	—	2	4	no	—
160	C₂×D₄×C₈₉	—	4	8	no	—
161	C₂×D₄×C₈₉	—	4	8	no	—
162	C₂×D₄×C₈₉	#41	1	8	yes	—
163	C₂²×C₄×C₈₉	—	2	2	no	—
164	C₂²×C₄×C₈₉	—	2	2	no	—
165	C₂²×C₄×C₈₉	—	2	4	no	—
166	C₂²×C₄×C₈₉	—	2	4	no	—
167	C₂²×C₄×C₈₉	—	2	4	no	—
168	C₂²×C₄×C₈₉	—	2	4	no	—
169	C₂²×C₄×C₈₉	—	2	8	no	—
170	C₂²×C₄×C₈₉	—	2	8	no	—
171	C₂²×C₄×C₈₉	—	2	8	no	—
172	C₂²×C₄×C₈₉	—	2	8	no	—
173	C₂²×C₄×C₈₉	—	2	8	no	—
174	C₂²×C₄×C₈₉	—	4	4	no	—
175	C₂²×C₄×C₈₉	—	4	4	no	—
176	C₂²×C₄×C₈₉	—	4	4	no	—
177	C₂²×C₄×C₈₉	—	4	32	no	—
178	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
179	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
181	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
183	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
184	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
192	C₄⋊C₄×C₈₉	—	2	4	no	—
193	C₄⋊C₄×C₈₉	—	2	4	no	—
194	C₄⋊C₄×C₈₉	—	2	4	no	—
195	C₄⋊C₄×C₈₉	—	2	4	no	—
196	C₄⋊C₄×C₈₉	—	2	2	no	—
197	C₄⋊C₄×C₈₉	—	2	4	no	—
198	C₄⋊C₄×C₈₉	—	2	2	no	—
199	C₄⋊C₄×C₈₉	—	2	4	no	—
200	C₄⋊C₄×C₈₉	—	2	8	no	—
201	C₄⋊C₄×C₈₉	—	2	8	no	—
202	C₄⋊C₄×C₈₉	—	4	4	no	—
203	C₄⋊C₄×C₈₉	—	4	8	no	—
204	C₂²⋊C₄×C₈₉	—	2	4	no	—
205	C₂²⋊C₄×C₈₉	—	2	16	no	—
206	C₂²⋊C₄×C₈₉	—	2	8	no	—
207	C₂²⋊C₄×C₈₉	—	2	8	no	—
208	C₂²⋊C₄×C₈₉	—	2	8	no	—
209	C₂²⋊C₄×C₈₉	—	2	4	no	—
210	C₂²⋊C₄×C₈₉	—	2	4	no	—
211	C₂²⋊C₄×C₈₉	—	2	4	no	—
212	C₂²⋊C₄×C₈₉	—	2	4	no	—
213	C₂²⋊C₄×C₈₉	—	4	8	no	—
214	C₂²⋊C₄×C₈₉	—	4	8	no	—
215	C₂²⋊C₄×C₈₉	—	4	8	no	—
216	C₄²×C₈₉	—	2	4	no	—
217	C₄²×C₈₉	—	4	4	no	—
218	C₄²×C₈₉	C₂×D₄	1	4	yes	—
219	C₄²×C₈₉	C₂×D₄	1	4	yes	—
220	C₄²×C₈₉	C₂×D₄	1	4	yes	—
221	C₄²×C₈₉	C₂×D₄	1	4	yes	—
222	C₂³×C₈₉	—	2	2	no	—
223	C₂³×C₈₉	—	2	2	no	—
224	C₂³×C₈₉	—	2	16	no	—
225	C₂³×C₈₉	—	2	4	no	—
226	C₂³×C₈₉	—	2	4	no	—
227	C₂³×C₈₉	—	2	4	no	—
228	C₂³×C₈₉	—	2	4	no	—
229	C₂³×C₈₉	—	2	4	no	—
230	C₂³×C₈₉	—	2	4	no	—
231	C₂³×C₈₉	—	2	2	no	—
232	C₂³×C₈₉	—	2	4	no	—
233	C₂³×C₈₉	—	2	4	no	—
234	C₂³×C₈₉	—	2	2	no	—
235	C₂³×C₈₉	—	2	2	no	—
236	C₂³×C₈₉	—	4	16	no	—
237	C₂³×C₈₉	—	4	16	no	—
238	C₂³×C₈₉	—	4	8	no	—
239	C₂³×C₈₉	—	4	8	no	—
240	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
241	C₂³×C₈₉	C₂×#41	1	8	yes	—
242	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
243	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
244	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
245	Q₈×C₈₉	—	4	4	no	—
246	D₄×C₈₉	—	2	16	no	—
247	D₄×C₈₉	—	2	16	no	—
248	D₄×C₈₉	—	4	8	no	—
249	D₄×C₈₉	—	4	4	no	—
250	D₄×C₈₉	—	8	16	no	—
251	C₂×C₄×C₈₉	—	2	8	no	—
252	C₂×C₄×C₈₉	—	2	2	no	—
253	C₂×C₄×C₈₉	—	2	1	no	—
254	C₂×C₄×C₈₉	—	2	1	no	—
255	C₂×C₄×C₈₉	—	2	2	no	—
256	C₂×C₄×C₈₉	—	2	1	no	—
257	C₂×C₄×C₈₉	—	2	1	no	—
258	C₂×C₄×C₈₉	—	2	8	no	—
259	C₂×C₄×C₈₉	—	2	8	no	—
260	C₂×C₄×C₈₉	—	2	2	no	—
261	C₂×C₄×C₈₉	—	2	2	no	—
262	C₂×C₄×C₈₉	—	2	2	no	—
263	C₂×C₄×C₈₉	—	2	4	no	—
264	C₂×C₄×C₈₉	—	2	4	no	—
265	C₂×C₄×C₈₉	—	2	8	no	—
266	C₂×C₄×C₈₉	—	2	8	no	—
267	C₂×C₄×C₈₉	—	2	2	no	—
268	C₂×C₄×C₈₉	—	2	8	no	—
269	C₂×C₄×C₈₉	—	2	4	no	—
270	C₂×C₄×C₈₉	—	2	4	no	—
271	C₂×C₄×C₈₉	—	2	4	no	—
272	C₂×C₄×C₈₉	—	2	2	no	—
273	C₂×C₄×C₈₉	—	4	16	no	—
274	C₂×C₄×C₈₉	—	4	8	no	—
275	C₂×C₄×C₈₉	—	4	8	no	—
276	C₂×C₄×C₈₉	—	4	16	no	—
277	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
279	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
281	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
282	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
283	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
284	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
285	C₂²×C₈₉	—	2	2	no	—
286	C₂²×C₈₉	—	2	2	no	—
287	C₂²×C₈₉	—	2	4	no	—
288	C₂²×C₈₉	—	2	4	no	—
289	C₂²×C₈₉	—	2	8	no	—
290	C₂²×C₈₉	—	2	8	no	—
291	C₂²×C₈₉	—	2	8	no	—
292	C₂²×C₈₉	—	4	32	no	—
293	C₂²×C₈₉	—	4	4	no	—
294	C₂²×C₈₉	—	4	4	no	—
295	C₂²×C₈₉	—	4	4	no	—
296	C₂²×C₈₉	—	4	4	no	—
297	C₂²×C₈₉	—	4	2	no	—
298	C₂²×C₈₉	—	4	2	no	—
299	C₂²×C₈₉	—	4	2	no	—
300	C₂²×C₈₉	—	4	4	no	—
301	C₂²×C₈₉	—	4	4	no	—
302	C₂²×C₈₉	#537	1	4	yes	—
303	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
304	C₂²×C₈₉	C₂²×#41	1	2	yes	—
305	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
306	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
307	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
308	C₄×C₈₉	—	2	2	no	—
309	C₄×C₈₉	—	2	2	no	—
310	C₄×C₈₉	—	2	2	no	—
311	C₄×C₈₉	—	2	2	no	—
312	C₄×C₈₉	—	4	2	no	—
313	C₄×C₈₉	—	4	4	no	—
314	C₄×C₈₉	—	4	2	no	—
315	C₄×C₈₉	—	4	2	no	—
316	C₄×C₈₉	—	4	8	no	—
317	C₄×C₈₉	#525	1	4	yes	—
318	C₄×C₈₉	#535	1	4	yes	—
319	#35236	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
320	C₂×C₈₉	—	2	4	no	—
321	C₂×C₈₉	—	4	8	no	—
322	C₂×C₈₉	—	8	2	no	—
323	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
324	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
325	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
326	C₂×C₈₉	#3519	1	2	yes	—
327	C₂×C₈₉	#3520	1	2	yes	—
328	C₂×#529	C₂×C₈₉	1	1	yes	characteristic, complemented
329	C₂²×C₄×D₄	C₂×C₈₉	1	1	yes	characteristic, complemented
330	#2848	C₂×C₈₉	1	2	yes	complemented
331	#2847	C₂×C₈₉	1	2	yes	complemented
332	#2636	C₂×C₈₉	1	4	yes	complemented
333	#2562	C₂×C₈₉	1	2	yes	complemented
334	#2540	C₂×C₈₉	1	2	yes	complemented
335	#2538	C₂×C₈₉	1	2	yes	complemented
336	#2537	C₂×C₈₉	1	2	yes	complemented
337	#2487	C₂×C₈₉	1	2	yes	complemented
338	#2411	C₂×C₈₉	1	4	yes	complemented
339	#2408	C₂×C₈₉	1	2	yes	complemented
340	#2324	C₂×C₈₉	1	4	yes	complemented
341	#2285	C₂×C₈₉	1	1	yes	characteristic, complemented
342	C₈₉	#35236	1	1	yes	characteristic, direct product factor, Sylow
343	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
344	C₂⁴×C₄	C₂²×C₈₉	1	2	yes	—
345	#529	—	2	8	no	—
346	C₂×#126	C₂²×C₈₉	1	2	yes	complemented
347	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic, complemented
348	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic, complemented
349	C₂×#123	C₂²×C₈₉	1	2	yes	—
350	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
351	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
352	C₂×#121	C₂²×C₈₉	1	4	yes	—
353	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
354	C₂×#121	C₂²×C₈₉	1	4	yes	complemented
355	C₂×#120	C₂²×C₈₉	1	4	yes	—
356	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
357	C₂×C₄×D₄	—	2	8	no	—
358	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
359	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
360	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
361	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
362	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
363	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
364	C₂×#117	C₂²×C₈₉	1	2	yes	—
365	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
366	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
367	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
368	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
369	#400	C₂²×C₈₉	1	4	yes	complemented
370	#399	C₂²×C₈₉	1	4	yes	complemented
371	#396	C₂²×C₈₉	1	8	yes	complemented
372	#394	C₂²×C₈₉	1	4	yes	—
373	#394	C₂²×C₈₉	1	8	yes	complemented
374	#392	C₂²×C₈₉	1	4	yes	—
375	#390	C₂²×C₈₉	1	4	yes	—
376	#390	C₂²×C₈₉	1	8	yes	complemented
377	#389	C₂²×C₈₉	1	4	yes	complemented
378	#388	C₂²×C₈₉	1	8	yes	complemented
379	#386	C₂²×C₈₉	1	4	yes	—
380	#386	C₂²×C₈₉	1	8	yes	complemented
381	#385	C₂²×C₈₉	1	4	yes	—
382	#385	C₂²×C₈₉	1	8	yes	complemented
383	#384	C₂²×C₈₉	1	2	yes	complemented
384	#382	C₂²×C₈₉	1	2	yes	complemented
385	#380	C₂²×C₈₉	1	2	yes	—
386	#380	C₂²×C₈₉	1	2	yes	—
387	#380	C₂²×C₈₉	1	4	yes	complemented
388	#380	C₂²×C₈₉	1	4	yes	complemented
389	#380	C₂²×C₈₉	1	4	yes	complemented
390	#379	C₂²×C₈₉	1	4	yes	—
391	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
392	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
393	C₂⁵	C₂³×C₈₉	1	2	yes	—
394	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
395	C₂²×D₄	—	2	8	no	—
396	C₂²×D₄	—	2	4	no	—
397	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
398	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
399	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
400	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
401	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
402	C₂³×C₄	—	2	8	no	—
403	C₂³×C₄	—	4	8	no	—
404	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
405	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
406	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
408	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
409	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
410	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
411	#126	—	2	8	no	—
412	#125	—	2	4	no	—
413	#124	—	2	4	no	—
414	#123	—	2	8	no	—
415	C₂²⋊Q₈	—	2	4	no	—
416	C₂²⋊Q₈	—	4	8	no	—
417	#121	—	2	16	no	—
418	#121	—	2	4	no	—
419	#121	—	4	8	no	—
420	#120	—	4	8	no	—
421	C₄×Q₈	—	2	4	no	—
422	C₄×D₄	—	2	8	no	—
423	C₄×D₄	—	2	8	no	—
424	C₄×D₄	—	2	8	no	—
425	C₄×D₄	—	2	8	no	—
426	C₄×D₄	—	2	8	no	—
427	C₄×D₄	—	2	4	no	—
428	#117	—	2	8	no	—
429	#117	—	4	4	no	—
430	C₂×C₄⋊C₄	—	2	4	no	—
431	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
432	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
433	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
435	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
436	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
440	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
441	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
442	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
443	C₂×C₂²⋊C₄	—	2	8	no	—
444	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
455	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
456	C₂×C₄²	D₄×C₈₉	1	8	yes	complemented
457	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
458	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
459	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
460	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
461	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
462	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
463	#95	C₂³×C₈₉	1	4	yes	—
464	#95	C₂³×C₈₉	1	4	yes	—
465	#95	C₂³×C₈₉	1	8	yes	—
466	#95	C₂³×C₈₉	1	8	yes	—
467	C₂⁴	—	2	4	no	—
468	C₂⁴	—	2	8	no	—
469	C₂⁴	—	2	4	no	—
470	C₂⁴	—	2	4	no	—
471	C₂⁴	—	4	4	no	—
472	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
473	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
474	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
475	C₂×Q₈	—	2	2	no	—
476	C₂×Q₈	—	2	4	no	—
477	C₂×D₄	—	2	32	no	—
478	C₂×D₄	—	2	8	no	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	2	4	no	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	16	no	—
483	C₂×D₄	—	2	4	no	—
484	C₂×D₄	—	2	4	no	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	2	4	no	—
487	C₂×D₄	—	2	4	no	—
488	C₂×D₄	—	4	8	no	—
489	C₂×D₄	—	4	8	no	—
490	C₂×D₄	#41×C₈₉	1	8	yes	—
491	C₂²×C₄	—	2	2	no	—
492	C₂²×C₄	—	2	2	no	—
493	C₂²×C₄	—	2	4	no	—
494	C₂²×C₄	—	2	4	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	4	no	—
497	C₂²×C₄	—	2	8	no	—
498	C₂²×C₄	—	2	8	no	—
499	C₂²×C₄	—	2	8	no	—
500	C₂²×C₄	—	2	8	no	—
501	C₂²×C₄	—	2	8	no	—
502	C₂²×C₄	—	4	4	no	—
503	C₂²×C₄	—	4	4	no	—
504	C₂²×C₄	—	4	4	no	—
505	C₂²×C₄	—	4	32	no	—
506	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
507	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
508	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
509	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
510	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
511	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
512	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
513	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
514	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
515	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
516	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
517	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
518	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
519	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	4	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	4	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	4	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	4	no	—
528	C₄⋊C₄	—	2	8	no	—
529	C₄⋊C₄	—	2	8	no	—
530	C₄⋊C₄	—	4	4	no	—
531	C₄⋊C₄	—	4	8	no	—
532	C₂²⋊C₄	—	2	4	no	—
533	C₂²⋊C₄	—	2	16	no	—
534	C₂²⋊C₄	—	2	8	no	—
535	C₂²⋊C₄	—	2	8	no	—
536	C₂²⋊C₄	—	2	8	no	—
537	C₂²⋊C₄	—	2	4	no	—
538	C₂²⋊C₄	—	2	4	no	—
539	C₂²⋊C₄	—	2	4	no	—
540	C₂²⋊C₄	—	2	4	no	—
541	C₂²⋊C₄	—	4	8	no	—
542	C₂²⋊C₄	—	4	8	no	—
543	C₂²⋊C₄	—	4	8	no	—
544	C₄²	—	2	4	no	—
545	C₄²	—	4	4	no	—
546	C₄²	C₂×D₄×C₈₉	1	4	yes	—
547	C₄²	C₂×D₄×C₈₉	1	4	yes	—
548	C₄²	C₂×D₄×C₈₉	1	4	yes	—
549	C₄²	C₂×D₄×C₈₉	1	4	yes	—
550	C₂³	—	2	2	no	—
551	C₂³	—	2	2	no	—
552	C₂³	—	2	16	no	—
553	C₂³	—	2	4	no	—
554	C₂³	—	2	4	no	—
555	C₂³	—	2	4	no	—
556	C₂³	—	2	4	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	2	4	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	4	no	—
561	C₂³	—	2	4	no	—
562	C₂³	—	2	2	no	—
563	C₂³	—	2	2	no	—
564	C₂³	—	4	16	no	—
565	C₂³	—	4	16	no	—
566	C₂³	—	4	8	no	—
567	C₂³	—	4	8	no	—
568	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
569	C₂³	C₂×#41×C₈₉	1	8	yes	—
570	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
571	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
572	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
573	Q₈	—	4	4	no	—
574	D₄	—	2	16	no	—
575	D₄	—	2	16	no	—
576	D₄	—	4	8	no	—
577	D₄	—	4	4	no	—
578	D₄	—	8	16	no	—
579	C₂×C₄	—	2	8	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	8	no	—
587	C₂×C₄	—	2	8	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	2	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	4	no	—
593	C₂×C₄	—	2	8	no	—
594	C₂×C₄	—	2	8	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	8	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	4	16	no	—
602	C₂×C₄	—	4	8	no	—
603	C₂×C₄	—	4	8	no	—
604	C₂×C₄	—	4	16	no	—
605	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
606	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
607	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
608	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
609	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
610	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
611	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
612	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	2	4	no	—
616	C₂²	—	2	4	no	—
617	C₂²	—	2	8	no	—
618	C₂²	—	2	8	no	—
619	C₂²	—	2	8	no	—
620	C₂²	—	4	32	no	—
621	C₂²	—	4	4	no	—
622	C₂²	—	4	4	no	—
623	C₂²	—	4	4	no	—
624	C₂²	—	4	4	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	4	2	no	—
628	C₂²	—	4	4	no	—
629	C₂²	—	4	4	no	—
630	C₂²	#537×C₈₉	1	4	yes	—
631	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
632	C₂²	C₂²×#41×C₈₉	1	2	yes	—
633	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
634	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
635	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	2	no	—
640	C₄	—	4	2	no	—
641	C₄	—	4	4	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	2	no	—
644	C₄	—	4	8	no	—
645	C₄	#525×C₈₉	1	4	yes	—
646	C₄	#535×C₈₉	1	4	yes	—
647	C₂	—	2	4	no	—
648	C₂	—	4	8	no	—
649	C₂	—	8	2	no	—
650	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
651	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
652	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
653	C₂	C₈₉×#3519	1	2	yes	—
654	C₂	C₈₉×#3520	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
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×#529×C₈₉	C₂	semidirect
2. C₂²×C₄×D₄×C₈₉	C₂	semidirect
3. C₈₉×#2848	C₂	semidirect
4. C₈₉×#2847	C₂	semidirect
5. C₈₉×#2636	C₂	semidirect
6. C₈₉×#2562	C₂	semidirect
7. C₈₉×#2540	C₂	semidirect
8. C₈₉×#2538	C₂	semidirect
9. C₈₉×#2537	C₂	semidirect
10. C₈₉×#2487	C₂	semidirect
11. C₈₉×#2411	C₂	semidirect
12. C₈₉×#2408	C₂	semidirect
13. C₈₉×#2324	C₂	semidirect
14. C₈₉×#2285	C₂	semidirect
18. C₂×#126×C₈₉	C₂²	semidirect
19. C₂×#125×C₈₉	C₂²	semidirect
20. C₂×#124×C₈₉	C₂²	semidirect
23. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
26. C₂×#121×C₈₉	C₂²	semidirect
28. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
35. C₂×C₄×D₄×C₈₉	C₂²	semidirect
37. C₂×#117×C₈₉	C₂²	semidirect
41. #400×C₈₉	C₂²	semidirect
42. #399×C₈₉	C₂²	semidirect
43. #396×C₈₉	C₂²	semidirect
45. #394×C₈₉	C₂²	semidirect
48. #390×C₈₉	C₂²	semidirect
49. #389×C₈₉	C₂²	semidirect
50. #388×C₈₉	C₂²	semidirect
52. #386×C₈₉	C₂²	semidirect
54. #385×C₈₉	C₂²	semidirect
55. #384×C₈₉	C₂²	semidirect
56. #382×C₈₉	C₂²	semidirect
59. #380×C₈₉	C₂²	semidirect
60. #380×C₈₉	C₂²	semidirect
61. #380×C₈₉	C₂²	semidirect
63. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
64. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
128. C₂×C₄²×C₈₉	D₄	semidirect
319. #35236	C₈₉	direct (N × H)
328. C₂×#529	C₂×C₈₉	semidirect
329. C₂²×C₄×D₄	C₂×C₈₉	semidirect
330. #2848	C₂×C₈₉	semidirect
331. #2847	C₂×C₈₉	semidirect
332. #2636	C₂×C₈₉	semidirect
333. #2562	C₂×C₈₉	semidirect
334. #2540	C₂×C₈₉	semidirect
335. #2538	C₂×C₈₉	semidirect
336. #2537	C₂×C₈₉	semidirect
337. #2487	C₂×C₈₉	semidirect
338. #2411	C₂×C₈₉	semidirect
339. #2408	C₂×C₈₉	semidirect
340. #2324	C₂×C₈₉	semidirect
341. #2285	C₂×C₈₉	semidirect
342. C₈₉	#35236	direct (N × H)
346. C₂×#126	C₂²×C₈₉	semidirect
347. C₂×#125	C₂²×C₈₉	semidirect
348. C₂×#124	C₂²×C₈₉	semidirect
351. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
354. C₂×#121	C₂²×C₈₉	semidirect
356. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
363. C₂×C₄×D₄	C₂²×C₈₉	semidirect
365. C₂×#117	C₂²×C₈₉	semidirect
369. #400	C₂²×C₈₉	semidirect
370. #399	C₂²×C₈₉	semidirect
371. #396	C₂²×C₈₉	semidirect
373. #394	C₂²×C₈₉	semidirect
376. #390	C₂²×C₈₉	semidirect
377. #389	C₂²×C₈₉	semidirect
378. #388	C₂²×C₈₉	semidirect
380. #386	C₂²×C₈₉	semidirect
382. #385	C₂²×C₈₉	semidirect
383. #384	C₂²×C₈₉	semidirect
384. #382	C₂²×C₈₉	semidirect
387. #380	C₂²×C₈₉	semidirect
388. #380	C₂²×C₈₉	semidirect
389. #380	C₂²×C₈₉	semidirect
391. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
392. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
456. C₂×C₄²	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#529×C₈₉	2
C₂²×C₄×D₄×C₈₉	2
C₈₉×#2848	2
C₈₉×#2847	2
C₈₉×#2636	2
C₈₉×#2562	2
C₈₉×#2540	2
C₈₉×#2538	2
C₈₉×#2537	2
C₈₉×#2487	2
C₈₉×#2411	2
C₈₉×#2408	2
C₈₉×#2324	2
C₈₉×#2285	2
#35236	89

Subgroups — C89×#35236 #36413084

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35236 #36413084