Subgroups — C₈₉×#35529 #36413377

Order 22784.

2618 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#544×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#518×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#2566	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2566	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2563	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2542	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2454	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2452	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2437	C₂	1	8	yes	maximal, complemented
10	C₈₉×#2317	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2309	C₂	1	1	yes	maximal, characteristic
12	C₈₉×#2296	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#390×C₈₉	C₂	1	1	yes	maximal, characteristic
14	C₈₉×#2285	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂³×D₄×C₈₉	C₂²	1	1	yes	characteristic
16	#544×C₈₉	—	2	8	no	—
17	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
18	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
19	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
20	C₂×#125×C₈₉	C₂²	1	2	yes	complemented
21	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	4	yes	—
22	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	8	yes	complemented
23	#518×C₈₉	—	2	8	no	—
24	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
25	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
26	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
28	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
29	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
34	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
35	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
36	#399×C₈₉	C₂²	1	8	yes	complemented
37	#396×C₈₉	C₂²	1	8	yes	complemented
38	#396×C₈₉	C₂²	1	8	yes	complemented
39	#393×C₈₉	C₂²	1	8	yes	complemented
40	#390×C₈₉	C₂²	1	2	yes	—
41	#390×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	#389×C₈₉	C₂²	1	2	yes	complemented
47	#389×C₈₉	C₂²	1	2	yes	complemented
48	#389×C₈₉	C₂²	1	4	yes	complemented
49	#385×C₈₉	C₂²	1	4	yes	—
50	#385×C₈₉	C₂²	1	4	yes	—
51	#385×C₈₉	C₂²	1	8	yes	complemented
52	#385×C₈₉	C₂²	1	8	yes	complemented
53	#384×C₈₉	C₂²	1	1	yes	characteristic, complemented
54	#384×C₈₉	C₂²	1	2	yes	complemented
55	#384×C₈₉	C₂²	1	1	yes	characteristic, complemented
56	#382×C₈₉	C₂²	1	1	yes	characteristic, complemented
57	#382×C₈₉	C₂²	1	2	yes	complemented
58	#382×C₈₉	C₂²	1	1	yes	characteristic, complemented
59	#380×C₈₉	C₂²	1	4	yes	—
60	#380×C₈₉	C₂²	1	8	yes	complemented
61	#379×C₈₉	C₂²	1	4	yes	—
62	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
63	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
64	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	complemented
65	C₂⁵×C₈₉	C₂³	1	2	yes	—
66	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
67	C₂²×D₄×C₈₉	—	2	4	no	—
68	C₂²×D₄×C₈₉	—	2	4	no	—
69	C₂²×D₄×C₈₉	Q₈	1	8	yes	complemented
70	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
71	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
72	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
74	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
75	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
76	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
77	C₄⋊Q₈×C₈₉	—	2	8	no	—
78	C₄⋊Q₈×C₈₉	—	2	8	no	—
79	#125×C₈₉	—	2	8	no	—
80	#125×C₈₉	—	2	8	no	—
81	C₂²⋊Q₈×C₈₉	—	2	16	no	—
82	C₂²⋊Q₈×C₈₉	—	4	16	no	—
83	C₄×D₄×C₈₉	—	2	8	no	—
84	C₄×D₄×C₈₉	—	2	8	no	—
85	C₄×D₄×C₈₉	—	2	8	no	—
86	C₄×D₄×C₈₉	—	2	8	no	—
87	#117×C₈₉	—	2	4	no	—
88	#117×C₈₉	—	2	4	no	—
89	#117×C₈₉	—	2	4	no	—
90	#117×C₈₉	D₄	1	8	yes	—
91	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
92	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	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	1	yes	characteristic
96	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
97	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
98	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
100	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
103	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
104	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₈₉	—	2	16	no	—
110	C₂×C₂²⋊C₄×C₈₉	—	4	8	no	—
111	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
112	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
113	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
114	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
115	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
117	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
118	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
119	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
120	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
121	C₂×C₄²×C₈₉	—	2	4	no	—
122	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
123	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
124	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
126	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
127	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
128	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
129	#95×C₈₉	C₂³	1	4	yes	—
130	#95×C₈₉	C₂³	1	4	yes	—
131	#95×C₈₉	C₂³	1	4	yes	—
132	#95×C₈₉	C₂³	1	4	yes	—
133	#95×C₈₉	C₂³	1	8	yes	—
134	C₂⁴×C₈₉	—	2	4	no	—
135	C₂⁴×C₈₉	—	2	4	no	—
136	C₂⁴×C₈₉	—	4	4	no	—
137	C₂⁴×C₈₉	—	4	4	no	—
138	C₂⁴×C₈₉	C₂×Q₈	1	8	yes	—
139	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
140	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
141	C₂×Q₈×C₈₉	—	2	8	no	—
142	C₂×Q₈×C₈₉	—	4	8	no	—
143	C₂×D₄×C₈₉	—	2	32	no	—
144	C₂×D₄×C₈₉	—	2	4	no	—
145	C₂×D₄×C₈₉	—	2	4	no	—
146	C₂×D₄×C₈₉	—	2	4	no	—
147	C₂×D₄×C₈₉	—	2	4	no	—
148	C₂×D₄×C₈₉	C₂×Q₈	1	8	yes	—
149	C₂×D₄×C₈₉	C₂×Q₈	1	8	yes	—
150	C₂²×C₄×C₈₉	—	2	4	no	—
151	C₂²×C₄×C₈₉	—	2	4	no	—
152	C₂²×C₄×C₈₉	—	2	4	no	—
153	C₂²×C₄×C₈₉	—	2	8	no	—
154	C₂²×C₄×C₈₉	—	2	8	no	—
155	C₂²×C₄×C₈₉	—	4	2	no	—
156	C₂²×C₄×C₈₉	—	4	4	no	—
157	C₂²×C₄×C₈₉	—	4	8	no	—
158	C₂²×C₄×C₈₉	—	4	8	no	—
159	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
161	C₂²×C₄×C₈₉	#41	1	4	yes	—
162	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
165	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
166	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
167	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
173	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
174	C₄⋊C₄×C₈₉	—	2	4	no	—
175	C₄⋊C₄×C₈₉	—	2	4	no	—
176	C₄⋊C₄×C₈₉	—	2	2	no	—
177	C₄⋊C₄×C₈₉	—	2	2	no	—
178	C₄⋊C₄×C₈₉	—	2	2	no	—
179	C₄⋊C₄×C₈₉	—	2	2	no	—
180	C₄⋊C₄×C₈₉	—	2	8	no	—
181	C₄⋊C₄×C₈₉	—	2	8	no	—
182	C₄⋊C₄×C₈₉	—	2	8	no	—
183	C₄⋊C₄×C₈₉	—	2	4	no	—
184	C₄⋊C₄×C₈₉	—	2	8	no	—
185	C₄⋊C₄×C₈₉	—	2	8	no	—
186	C₄⋊C₄×C₈₉	—	4	4	no	—
187	C₄⋊C₄×C₈₉	—	4	4	no	—
188	C₄⋊C₄×C₈₉	—	4	8	no	—
189	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
190	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
191	C₂²⋊C₄×C₈₉	—	2	4	no	—
192	C₂²⋊C₄×C₈₉	—	2	4	no	—
193	C₂²⋊C₄×C₈₉	—	2	4	no	—
194	C₂²⋊C₄×C₈₉	—	2	8	no	—
195	C₂²⋊C₄×C₈₉	—	2	8	no	—
196	C₂²⋊C₄×C₈₉	—	2	16	no	—
197	C₂²⋊C₄×C₈₉	—	4	8	no	—
198	C₂²⋊C₄×C₈₉	—	4	8	no	—
199	C₂²⋊C₄×C₈₉	—	4	8	no	—
200	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
201	C₄²×C₈₉	—	2	4	no	—
202	C₄²×C₈₉	—	2	4	no	—
203	C₄²×C₈₉	—	2	2	no	—
204	C₄²×C₈₉	—	2	4	no	—
205	C₄²×C₈₉	—	2	2	no	—
206	C₄²×C₈₉	—	2	4	no	—
207	C₄²×C₈₉	C₂×D₄	1	8	yes	—
208	C₂³×C₈₉	—	2	2	no	—
209	C₂³×C₈₉	—	2	2	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	—	2	16	no	—
215	C₂³×C₈₉	—	4	16	no	—
216	C₂³×C₈₉	—	8	8	no	—
217	C₂³×C₈₉	—	8	4	no	—
218	C₂³×C₈₉	—	8	4	no	—
219	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
220	C₂³×C₈₉	C₂²×Q₈	1	8	yes	—
221	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
222	C₂³×C₈₉	C₂×#41	1	2	yes	—
223	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
224	Q₈×C₈₉	—	8	8	no	—
225	D₄×C₈₉	—	2	16	no	—
226	D₄×C₈₉	—	2	16	no	—
227	C₂×C₄×C₈₉	—	2	2	no	—
228	C₂×C₄×C₈₉	—	2	4	no	—
229	C₂×C₄×C₈₉	—	2	2	no	—
230	C₂×C₄×C₈₉	—	2	4	no	—
231	C₂×C₄×C₈₉	—	2	2	no	—
232	C₂×C₄×C₈₉	—	2	2	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	2	no	—
237	C₂×C₄×C₈₉	—	2	4	no	—
238	C₂×C₄×C₈₉	—	2	8	no	—
239	C₂×C₄×C₈₉	—	2	2	no	—
240	C₂×C₄×C₈₉	—	2	4	no	—
241	C₂×C₄×C₈₉	—	2	4	no	—
242	C₂×C₄×C₈₉	—	2	4	no	—
243	C₂×C₄×C₈₉	—	2	4	no	—
244	C₂×C₄×C₈₉	—	2	4	no	—
245	C₂×C₄×C₈₉	—	2	2	no	—
246	C₂×C₄×C₈₉	—	2	4	no	—
247	C₂×C₄×C₈₉	—	4	8	no	—
248	C₂×C₄×C₈₉	—	8	8	no	—
249	C₂×C₄×C₈₉	—	8	8	no	—
250	C₂×C₄×C₈₉	—	8	4	no	—
251	C₂×C₄×C₈₉	C₂²⋊Q₈	1	16	yes	complemented
252	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
253	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
254	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
255	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
256	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
257	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
258	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
259	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
260	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
261	C₂²×C₈₉	—	2	4	no	—
262	C₂²×C₈₉	—	2	2	no	—
263	C₂²×C₈₉	—	2	2	no	—
264	C₂²×C₈₉	—	2	4	no	—
265	C₂²×C₈₉	—	2	8	no	—
266	C₂²×C₈₉	—	2	16	no	—
267	C₂²×C₈₉	—	4	8	no	—
268	C₂²×C₈₉	—	4	4	no	—
269	C₂²×C₈₉	—	4	4	no	—
270	C₂²×C₈₉	—	8	16	no	—
271	C₂²×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
272	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
273	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
274	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
275	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
276	C₂²×C₈₉	#585	1	2	yes	—
277	C₄×C₈₉	—	2	4	no	—
278	C₄×C₈₉	—	2	4	no	—
279	C₄×C₈₉	—	2	4	no	—
280	C₄×C₈₉	—	4	4	no	—
281	C₄×C₈₉	—	4	2	no	—
282	C₄×C₈₉	—	4	2	no	—
283	C₄×C₈₉	—	4	4	no	—
284	C₄×C₈₉	—	4	2	no	—
285	C₄×C₈₉	—	4	2	no	—
286	C₄×C₈₉	—	4	2	no	—
287	C₄×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
288	C₄×C₈₉	C₂×C₂²⋊Q₈	1	4	yes	—
289	#35529	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
290	C₂×C₈₉	—	2	4	no	—
291	C₂×C₈₉	—	4	8	no	—
292	C₂×C₈₉	C₂²×C₂²⋊Q₈	1	1	yes	characteristic
293	C₂×C₈₉	#3494	1	2	yes	—
294	C₂×C₈₉	#3498	1	1	yes	characteristic
295	C₂×C₈₉	#3500	1	1	yes	characteristic
296	C₂×C₈₉	#3501	1	2	yes	—
297	C₂×#544	C₂×C₈₉	1	1	yes	characteristic, complemented
298	C₂×#518	C₂×C₈₉	1	1	yes	characteristic
299	#2566	C₂×C₈₉	1	2	yes	complemented
300	#2566	C₂×C₈₉	1	2	yes	complemented
301	#2563	C₂×C₈₉	1	2	yes	complemented
302	#2542	C₂×C₈₉	1	2	yes	complemented
303	#2454	C₂×C₈₉	1	4	yes	complemented
304	#2452	C₂×C₈₉	1	4	yes	complemented
305	#2437	C₂×C₈₉	1	8	yes	complemented
306	#2317	C₂×C₈₉	1	1	yes	characteristic, complemented
307	#2309	C₂×C₈₉	1	1	yes	characteristic
308	#2296	C₂×C₈₉	1	1	yes	characteristic, complemented
309	C₂×#390	C₂×C₈₉	1	1	yes	characteristic
310	#2285	C₂×C₈₉	1	1	yes	characteristic, complemented
311	C₈₉	#35529	1	1	yes	characteristic, direct product factor, Sylow
312	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
313	#544	—	2	8	no	—
314	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
315	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
316	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
317	C₂×#125	C₂²×C₈₉	1	2	yes	complemented
318	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	4	yes	—
319	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	8	yes	complemented
320	#518	—	2	8	no	—
321	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
322	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
323	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
324	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
325	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
326	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
327	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
328	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
329	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
330	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
331	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
332	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
333	#399	C₂²×C₈₉	1	8	yes	complemented
334	#396	C₂²×C₈₉	1	8	yes	complemented
335	#396	C₂²×C₈₉	1	8	yes	complemented
336	#393	C₂²×C₈₉	1	8	yes	complemented
337	#390	C₂²×C₈₉	1	2	yes	—
338	#390	C₂²×C₈₉	1	2	yes	—
339	#390	C₂²×C₈₉	1	2	yes	—
340	#390	C₂²×C₈₉	1	4	yes	—
341	#390	C₂²×C₈₉	1	2	yes	—
342	#390	C₂²×C₈₉	1	4	yes	—
343	#389	C₂²×C₈₉	1	4	yes	complemented
344	#389	C₂²×C₈₉	1	2	yes	complemented
345	#389	C₂²×C₈₉	1	2	yes	complemented
346	#385	C₂²×C₈₉	1	4	yes	—
347	#385	C₂²×C₈₉	1	4	yes	—
348	#385	C₂²×C₈₉	1	8	yes	complemented
349	#385	C₂²×C₈₉	1	8	yes	complemented
350	#384	C₂²×C₈₉	1	1	yes	characteristic, complemented
351	#384	C₂²×C₈₉	1	2	yes	complemented
352	#384	C₂²×C₈₉	1	1	yes	characteristic, complemented
353	#382	C₂²×C₈₉	1	1	yes	characteristic, complemented
354	#382	C₂²×C₈₉	1	2	yes	complemented
355	#382	C₂²×C₈₉	1	1	yes	characteristic, complemented
356	#380	C₂²×C₈₉	1	4	yes	—
357	#380	C₂²×C₈₉	1	8	yes	complemented
358	#379	C₂²×C₈₉	1	4	yes	—
359	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
360	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
361	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	complemented
362	C₂⁵	C₂³×C₈₉	1	2	yes	—
363	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
364	C₂²×D₄	—	2	4	no	—
365	C₂²×D₄	—	2	4	no	—
366	C₂²×D₄	Q₈×C₈₉	1	8	yes	complemented
367	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
368	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
369	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
370	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
371	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
372	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
373	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
374	C₄⋊Q₈	—	2	8	no	—
375	C₄⋊Q₈	—	2	8	no	—
376	#125	—	2	8	no	—
377	#125	—	2	8	no	—
378	C₂²⋊Q₈	—	2	16	no	—
379	C₂²⋊Q₈	—	4	16	no	—
380	C₄×D₄	—	2	8	no	—
381	C₄×D₄	—	2	8	no	—
382	C₄×D₄	—	2	8	no	—
383	C₄×D₄	—	2	8	no	—
384	#117	—	2	4	no	—
385	#117	—	2	4	no	—
386	#117	—	2	4	no	—
387	#117	D₄×C₈₉	1	8	yes	—
388	C₂×C₄⋊C₄	—	2	4	no	—
389	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
390	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
391	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
396	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
397	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
398	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
399	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
400	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
401	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
402	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
403	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
404	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
406	C₂×C₂²⋊C₄	—	2	16	no	—
407	C₂×C₂²⋊C₄	—	4	8	no	—
408	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
411	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
412	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
413	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
418	C₂×C₄²	—	2	4	no	—
419	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
420	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
421	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
422	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
423	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
424	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
425	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
426	#95	C₂³×C₈₉	1	4	yes	—
427	#95	C₂³×C₈₉	1	4	yes	—
428	#95	C₂³×C₈₉	1	4	yes	—
429	#95	C₂³×C₈₉	1	4	yes	—
430	#95	C₂³×C₈₉	1	8	yes	—
431	C₂⁴	—	2	4	no	—
432	C₂⁴	—	2	4	no	—
433	C₂⁴	—	4	4	no	—
434	C₂⁴	—	4	4	no	—
435	C₂⁴	C₂×Q₈×C₈₉	1	8	yes	—
436	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
437	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
438	C₂×Q₈	—	2	8	no	—
439	C₂×Q₈	—	4	8	no	—
440	C₂×D₄	—	2	32	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	4	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	4	no	—
445	C₂×D₄	C₂×Q₈×C₈₉	1	8	yes	—
446	C₂×D₄	C₂×Q₈×C₈₉	1	8	yes	—
447	C₂²×C₄	—	2	4	no	—
448	C₂²×C₄	—	2	4	no	—
449	C₂²×C₄	—	2	4	no	—
450	C₂²×C₄	—	2	8	no	—
451	C₂²×C₄	—	2	8	no	—
452	C₂²×C₄	—	4	2	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	—	4	8	no	—
455	C₂²×C₄	—	4	8	no	—
456	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
457	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
458	C₂²×C₄	#41×C₈₉	1	4	yes	—
459	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
460	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
461	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
462	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
463	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
464	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
465	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
466	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
467	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
468	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
469	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
470	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
471	C₄⋊C₄	—	2	4	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	2	no	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	2	8	no	—
478	C₄⋊C₄	—	2	8	no	—
479	C₄⋊C₄	—	2	8	no	—
480	C₄⋊C₄	—	2	4	no	—
481	C₄⋊C₄	—	2	8	no	—
482	C₄⋊C₄	—	2	8	no	—
483	C₄⋊C₄	—	4	8	no	—
484	C₄⋊C₄	—	4	4	no	—
485	C₄⋊C₄	—	4	4	no	—
486	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
487	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	2	4	no	—
490	C₂²⋊C₄	—	2	4	no	—
491	C₂²⋊C₄	—	2	8	no	—
492	C₂²⋊C₄	—	2	8	no	—
493	C₂²⋊C₄	—	2	16	no	—
494	C₂²⋊C₄	—	4	8	no	—
495	C₂²⋊C₄	—	4	8	no	—
496	C₂²⋊C₄	—	4	8	no	—
497	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
498	C₄²	—	2	4	no	—
499	C₄²	—	2	4	no	—
500	C₄²	—	2	2	no	—
501	C₄²	—	2	4	no	—
502	C₄²	—	2	2	no	—
503	C₄²	—	2	4	no	—
504	C₄²	C₂×D₄×C₈₉	1	8	yes	—
505	C₂³	—	2	2	no	—
506	C₂³	—	2	2	no	—
507	C₂³	—	2	4	no	—
508	C₂³	—	2	4	no	—
509	C₂³	—	2	8	no	—
510	C₂³	—	2	8	no	—
511	C₂³	—	2	16	no	—
512	C₂³	—	4	16	no	—
513	C₂³	—	8	8	no	—
514	C₂³	—	8	4	no	—
515	C₂³	—	8	4	no	—
516	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
517	C₂³	C₂²×Q₈×C₈₉	1	8	yes	—
518	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
519	C₂³	C₂×#41×C₈₉	1	2	yes	—
520	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
521	Q₈	—	8	8	no	—
522	D₄	—	2	16	no	—
523	D₄	—	2	16	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	8	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	4	8	no	—
545	C₂×C₄	—	8	8	no	—
546	C₂×C₄	—	8	8	no	—
547	C₂×C₄	—	8	4	no	—
548	C₂×C₄	C₂²⋊Q₈×C₈₉	1	16	yes	complemented
549	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
550	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
551	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
552	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
553	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
554	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
555	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
556	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
557	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
558	C₂²	—	2	4	no	—
559	C₂²	—	2	2	no	—
560	C₂²	—	2	2	no	—
561	C₂²	—	2	4	no	—
562	C₂²	—	2	8	no	—
563	C₂²	—	2	16	no	—
564	C₂²	—	4	8	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	—	8	16	no	—
568	C₂²	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
569	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
570	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
571	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
572	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
573	C₂²	#585×C₈₉	1	2	yes	—
574	C₄	—	2	4	no	—
575	C₄	—	2	4	no	—
576	C₄	—	2	4	no	—
577	C₄	—	4	2	no	—
578	C₄	—	4	4	no	—
579	C₄	—	4	2	no	—
580	C₄	—	4	4	no	—
581	C₄	—	4	2	no	—
582	C₄	—	4	2	no	—
583	C₄	—	4	2	no	—
584	C₄	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
585	C₄	C₂×C₂²⋊Q₈×C₈₉	1	4	yes	—
586	C₂	—	2	4	no	—
587	C₂	—	4	8	no	—
588	C₂	C₂²×C₂²⋊Q₈×C₈₉	1	1	yes	characteristic
589	C₂	C₈₉×#3494	1	2	yes	—
590	C₂	C₈₉×#3498	1	1	yes	characteristic
591	C₂	C₈₉×#3500	1	1	yes	characteristic
592	C₂	C₈₉×#3501	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂³×D₄×C₈₉	C₂²
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×#544×C₈₉	C₂	semidirect
3. C₈₉×#2566	C₂	semidirect
4. C₈₉×#2566	C₂	semidirect
5. C₈₉×#2563	C₂	semidirect
6. C₈₉×#2542	C₂	semidirect
7. C₈₉×#2454	C₂	semidirect
8. C₈₉×#2452	C₂	semidirect
9. C₈₉×#2437	C₂	semidirect
10. C₈₉×#2317	C₂	semidirect
12. C₈₉×#2296	C₂	semidirect
14. C₈₉×#2285	C₂	semidirect
17. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
18. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
19. C₂×#125×C₈₉	C₂²	semidirect
20. C₂×#125×C₈₉	C₂²	semidirect
22. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
36. #399×C₈₉	C₂²	semidirect
37. #396×C₈₉	C₂²	semidirect
38. #396×C₈₉	C₂²	semidirect
39. #393×C₈₉	C₂²	semidirect
46. #389×C₈₉	C₂²	semidirect
47. #389×C₈₉	C₂²	semidirect
48. #389×C₈₉	C₂²	semidirect
51. #385×C₈₉	C₂²	semidirect
52. #385×C₈₉	C₂²	semidirect
53. #384×C₈₉	C₂²	semidirect
54. #384×C₈₉	C₂²	semidirect
55. #384×C₈₉	C₂²	semidirect
56. #382×C₈₉	C₂²	semidirect
57. #382×C₈₉	C₂²	semidirect
58. #382×C₈₉	C₂²	semidirect
60. #380×C₈₉	C₂²	semidirect
62. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
63. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
64. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
69. C₂²×D₄×C₈₉	Q₈	semidirect
251. C₂×C₄×C₈₉	C₂²⋊Q₈	semidirect
289. #35529	C₈₉	direct (N × H)
297. C₂×#544	C₂×C₈₉	semidirect
299. #2566	C₂×C₈₉	semidirect
300. #2566	C₂×C₈₉	semidirect
301. #2563	C₂×C₈₉	semidirect
302. #2542	C₂×C₈₉	semidirect
303. #2454	C₂×C₈₉	semidirect
304. #2452	C₂×C₈₉	semidirect
305. #2437	C₂×C₈₉	semidirect
306. #2317	C₂×C₈₉	semidirect
308. #2296	C₂×C₈₉	semidirect
310. #2285	C₂×C₈₉	semidirect
311. C₈₉	#35529	direct (N × H)
314. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
315. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
316. C₂×#125	C₂²×C₈₉	semidirect
317. C₂×#125	C₂²×C₈₉	semidirect
319. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
333. #399	C₂²×C₈₉	semidirect
334. #396	C₂²×C₈₉	semidirect
335. #396	C₂²×C₈₉	semidirect
336. #393	C₂²×C₈₉	semidirect
343. #389	C₂²×C₈₉	semidirect
344. #389	C₂²×C₈₉	semidirect
345. #389	C₂²×C₈₉	semidirect
348. #385	C₂²×C₈₉	semidirect
349. #385	C₂²×C₈₉	semidirect
350. #384	C₂²×C₈₉	semidirect
351. #384	C₂²×C₈₉	semidirect
352. #384	C₂²×C₈₉	semidirect
353. #382	C₂²×C₈₉	semidirect
354. #382	C₂²×C₈₉	semidirect
355. #382	C₂²×C₈₉	semidirect
357. #380	C₂²×C₈₉	semidirect
359. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
360. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
361. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
366. C₂²×D₄	Q₈×C₈₉	semidirect
548. C₂×C₄	C₂²⋊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×#544×C₈₉	2
C₂×#518×C₈₉	2
C₈₉×#2566	2
C₈₉×#2563	2
C₈₉×#2542	2
C₈₉×#2454	2
C₈₉×#2452	2
C₈₉×#2437	2
C₈₉×#2317	2
C₈₉×#2309	2
C₈₉×#2296	2
C₂×#390×C₈₉	2
C₈₉×#2285	2
#35529	89

Subgroups — C89×#35529 #36413377

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35529 #36413377