Subgroups — C₈₉×#35232 #36413080

Order 22784.

2902 conjugacy classes of subgroups.

The subgroup lattice has 616 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×#2849	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2633	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2631	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2603	C₂	1	4	yes	maximal, complemented
7	C₈₉×#2580	C₂	1	2	yes	maximal, complemented
8	C₈₉×#2561	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2539	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2535	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2486	C₂	1	2	yes	maximal, complemented
12	C₈₉×#2408	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2324	C₂	1	4	yes	maximal, complemented
14	C₈₉×#2283	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×#123×C₈₉	C₂²	1	4	yes	—
23	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#121×C₈₉	C₂²	1	4	yes	—
25	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
26	C₂×#120×C₈₉	C₂²	1	4	yes	—
27	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
28	C₂×C₄×D₄×C₈₉	—	2	8	no	—
29	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
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	1	yes	characteristic, complemented
35	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
36	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
37	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
38	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
39	#399×C₈₉	C₂²	1	4	yes	complemented
40	#398×C₈₉	C₂²	1	4	yes	complemented
41	#397×C₈₉	C₂²	1	4	yes	complemented
42	#397×C₈₉	C₂²	1	4	yes	complemented
43	#394×C₈₉	C₂²	1	4	yes	—
44	#393×C₈₉	C₂²	1	4	yes	complemented
45	#392×C₈₉	C₂²	1	4	yes	—
46	#392×C₈₉	C₂²	1	4	yes	complemented
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	8	yes	complemented
52	#386×C₈₉	C₂²	1	8	yes	complemented
53	#385×C₈₉	C₂²	1	8	yes	complemented
54	#385×C₈₉	C₂²	1	8	yes	complemented
55	#383×C₈₉	C₂²	1	2	yes	complemented
56	#382×C₈₉	C₂²	1	2	yes	complemented
57	#381×C₈₉	C₂²	1	4	yes	—
58	#381×C₈₉	C₂²	1	2	yes	—
59	#380×C₈₉	C₂²	1	2	yes	—
60	#380×C₈₉	C₂²	1	4	yes	complemented
61	#379×C₈₉	C₂²	1	4	yes	—
62	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
63	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
64	#376×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	2	yes	—
72	C₂²×D₄×C₈₉	C₂³	1	8	yes	—
73	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	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	4	yes	—
81	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
82	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
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	#123×C₈₉	—	4	8	no	—
88	C₂²⋊Q₈×C₈₉	—	2	4	no	—
89	#121×C₈₉	—	2	16	no	—
90	#121×C₈₉	—	2	4	no	—
91	#120×C₈₉	—	4	8	no	—
92	C₄×Q₈×C₈₉	—	2	4	no	—
93	C₄×D₄×C₈₉	—	2	8	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	4	no	—
99	#117×C₈₉	—	2	8	no	—
100	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
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	2	yes	—
105	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
111	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
112	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	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	2	yes	—
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	2	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	8	yes	—
122	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
123	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
124	C₂×C₄²×C₈₉	D₄	1	8	yes	complemented
125	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
126	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
127	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
130	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
131	#95×C₈₉	C₂³	1	4	yes	—
132	#95×C₈₉	C₂³	1	4	yes	—
133	#95×C₈₉	C₂³	1	4	yes	—
134	#95×C₈₉	C₂³	1	4	yes	—
135	#95×C₈₉	C₂³	1	8	yes	—
136	#95×C₈₉	C₂³	1	8	yes	—
137	C₂⁴×C₈₉	—	2	4	no	—
138	C₂⁴×C₈₉	—	2	8	no	—
139	C₂⁴×C₈₉	—	2	8	no	—
140	C₂⁴×C₈₉	—	4	4	no	—
141	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
142	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
143	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
144	C₂×Q₈×C₈₉	—	2	2	no	—
145	C₂×Q₈×C₈₉	—	4	2	no	—
146	C₂×D₄×C₈₉	—	2	32	no	—
147	C₂×D₄×C₈₉	—	2	8	no	—
148	C₂×D₄×C₈₉	—	2	4	no	—
149	C₂×D₄×C₈₉	—	2	4	no	—
150	C₂×D₄×C₈₉	—	2	4	no	—
151	C₂×D₄×C₈₉	—	2	16	no	—
152	C₂×D₄×C₈₉	—	2	4	no	—
153	C₂×D₄×C₈₉	—	2	4	no	—
154	C₂×D₄×C₈₉	—	2	2	no	—
155	C₂×D₄×C₈₉	—	2	4	no	—
156	C₂×D₄×C₈₉	—	4	2	no	—
157	C₂×D₄×C₈₉	—	4	8	no	—
158	C₂×D₄×C₈₉	—	4	8	no	—
159	C₂×D₄×C₈₉	#41	1	8	yes	—
160	C₂²×C₄×C₈₉	—	2	4	no	—
161	C₂²×C₄×C₈₉	—	2	4	no	—
162	C₂²×C₄×C₈₉	—	2	4	no	—
163	C₂²×C₄×C₈₉	—	2	8	no	—
164	C₂²×C₄×C₈₉	—	2	4	no	—
165	C₂²×C₄×C₈₉	—	2	8	no	—
166	C₂²×C₄×C₈₉	—	2	8	no	—
167	C₂²×C₄×C₈₉	—	2	8	no	—
168	C₂²×C₄×C₈₉	—	4	8	no	—
169	C₂²×C₄×C₈₉	—	4	8	no	—
170	C₂²×C₄×C₈₉	—	4	2	no	—
171	C₂²×C₄×C₈₉	—	4	32	no	—
172	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
173	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
174	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
175	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
176	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
177	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
178	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
179	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
180	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
184	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
186	C₄⋊C₄×C₈₉	—	2	4	no	—
187	C₄⋊C₄×C₈₉	—	2	4	no	—
188	C₄⋊C₄×C₈₉	—	2	4	no	—
189	C₄⋊C₄×C₈₉	—	2	4	no	—
190	C₄⋊C₄×C₈₉	—	2	2	no	—
191	C₄⋊C₄×C₈₉	—	2	4	no	—
192	C₄⋊C₄×C₈₉	—	2	2	no	—
193	C₄⋊C₄×C₈₉	—	2	4	no	—
194	C₄⋊C₄×C₈₉	—	2	8	no	—
195	C₄⋊C₄×C₈₉	—	4	8	no	—
196	C₂²⋊C₄×C₈₉	—	2	4	no	—
197	C₂²⋊C₄×C₈₉	—	2	16	no	—
198	C₂²⋊C₄×C₈₉	—	2	8	no	—
199	C₂²⋊C₄×C₈₉	—	2	8	no	—
200	C₂²⋊C₄×C₈₉	—	2	8	no	—
201	C₂²⋊C₄×C₈₉	—	2	4	no	—
202	C₂²⋊C₄×C₈₉	—	2	4	no	—
203	C₂²⋊C₄×C₈₉	—	2	4	no	—
204	C₂²⋊C₄×C₈₉	—	2	4	no	—
205	C₂²⋊C₄×C₈₉	—	4	8	no	—
206	C₂²⋊C₄×C₈₉	—	4	8	no	—
207	C₂²⋊C₄×C₈₉	—	4	8	no	—
208	C₄²×C₈₉	—	2	4	no	—
209	C₄²×C₈₉	—	4	4	no	—
210	C₄²×C₈₉	C₂×D₄	1	4	yes	—
211	C₄²×C₈₉	C₂×D₄	1	4	yes	—
212	C₄²×C₈₉	C₂×D₄	1	4	yes	—
213	C₄²×C₈₉	C₂×D₄	1	4	yes	—
214	C₂³×C₈₉	—	2	2	no	—
215	C₂³×C₈₉	—	2	2	no	—
216	C₂³×C₈₉	—	2	16	no	—
217	C₂³×C₈₉	—	2	4	no	—
218	C₂³×C₈₉	—	2	4	no	—
219	C₂³×C₈₉	—	2	8	no	—
220	C₂³×C₈₉	—	2	8	no	—
221	C₂³×C₈₉	—	2	2	no	—
222	C₂³×C₈₉	—	2	4	no	—
223	C₂³×C₈₉	—	2	2	no	—
224	C₂³×C₈₉	—	2	2	no	—
225	C₂³×C₈₉	—	2	4	no	—
226	C₂³×C₈₉	—	4	32	no	—
227	C₂³×C₈₉	—	4	8	no	—
228	C₂³×C₈₉	—	4	8	no	—
229	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
230	C₂³×C₈₉	C₂×#41	1	8	yes	—
231	C₂³×C₈₉	H(5,𝔽₂)	1	4	yes	—
232	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
233	Q₈×C₈₉	—	4	4	no	—
234	D₄×C₈₉	—	2	16	no	—
235	D₄×C₈₉	—	2	16	no	—
236	D₄×C₈₉	—	4	4	no	—
237	D₄×C₈₉	—	4	8	no	—
238	D₄×C₈₉	—	8	16	no	—
239	C₂×C₄×C₈₉	—	2	8	no	—
240	C₂×C₄×C₈₉	—	2	2	no	—
241	C₂×C₄×C₈₉	—	2	2	no	—
242	C₂×C₄×C₈₉	—	2	2	no	—
243	C₂×C₄×C₈₉	—	2	2	no	—
244	C₂×C₄×C₈₉	—	2	2	no	—
245	C₂×C₄×C₈₉	—	2	8	no	—
246	C₂×C₄×C₈₉	—	2	2	no	—
247	C₂×C₄×C₈₉	—	2	2	no	—
248	C₂×C₄×C₈₉	—	2	2	no	—
249	C₂×C₄×C₈₉	—	2	4	no	—
250	C₂×C₄×C₈₉	—	2	4	no	—
251	C₂×C₄×C₈₉	—	2	8	no	—
252	C₂×C₄×C₈₉	—	2	8	no	—
253	C₂×C₄×C₈₉	—	2	2	no	—
254	C₂×C₄×C₈₉	—	2	8	no	—
255	C₂×C₄×C₈₉	—	2	2	no	—
256	C₂×C₄×C₈₉	—	2	8	no	—
257	C₂×C₄×C₈₉	—	2	4	no	—
258	C₂×C₄×C₈₉	—	4	4	no	—
259	C₂×C₄×C₈₉	—	4	16	no	—
260	C₂×C₄×C₈₉	—	4	16	no	—
261	C₂×C₄×C₈₉	—	4	8	no	—
262	C₂×C₄×C₈₉	—	4	8	no	—
263	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
264	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
265	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
266	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
267	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
268	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
269	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
270	C₂²×C₈₉	—	2	2	no	—
271	C₂²×C₈₉	—	2	2	no	—
272	C₂²×C₈₉	—	2	8	no	—
273	C₂²×C₈₉	—	2	8	no	—
274	C₂²×C₈₉	—	2	16	no	—
275	C₂²×C₈₉	—	4	32	no	—
276	C₂²×C₈₉	—	4	4	no	—
277	C₂²×C₈₉	—	4	4	no	—
278	C₂²×C₈₉	—	4	8	no	—
279	C₂²×C₈₉	—	4	2	no	—
280	C₂²×C₈₉	—	4	2	no	—
281	C₂²×C₈₉	—	4	2	no	—
282	C₂²×C₈₉	—	4	4	no	—
283	C₂²×C₈₉	—	4	4	no	—
284	C₂²×C₈₉	#535	1	4	yes	—
285	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
286	C₂²×C₈₉	C₂²×#41	1	2	yes	—
287	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
288	C₂²×C₈₉	#585	1	2	yes	—
289	C₄×C₈₉	—	2	2	no	—
290	C₄×C₈₉	—	2	2	no	—
291	C₄×C₈₉	—	2	2	no	—
292	C₄×C₈₉	—	2	2	no	—
293	C₄×C₈₉	—	2	2	no	—
294	C₄×C₈₉	—	4	2	no	—
295	C₄×C₈₉	—	4	4	no	—
296	C₄×C₈₉	—	4	2	no	—
297	C₄×C₈₉	—	4	2	no	—
298	C₄×C₈₉	—	4	8	no	—
299	C₄×C₈₉	#525	1	4	yes	—
300	#35232	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
301	C₂×C₈₉	—	2	4	no	—
302	C₂×C₈₉	—	4	8	no	—
303	C₂×C₈₉	—	8	2	no	—
304	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
305	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
306	C₂×C₈₉	#3449	1	1	yes	characteristic
307	C₂×C₈₉	#3513	1	4	yes	—
308	C₂×#529	C₂×C₈₉	1	1	yes	characteristic, complemented
309	C₂²×C₄×D₄	C₂×C₈₉	1	1	yes	characteristic, complemented
310	#2849	C₂×C₈₉	1	4	yes	complemented
311	#2633	C₂×C₈₉	1	2	yes	complemented
312	#2631	C₂×C₈₉	1	2	yes	complemented
313	#2603	C₂×C₈₉	1	4	yes	complemented
314	#2580	C₂×C₈₉	1	2	yes	complemented
315	#2561	C₂×C₈₉	1	2	yes	complemented
316	#2539	C₂×C₈₉	1	2	yes	complemented
317	#2535	C₂×C₈₉	1	2	yes	complemented
318	#2486	C₂×C₈₉	1	2	yes	complemented
319	#2408	C₂×C₈₉	1	2	yes	complemented
320	#2324	C₂×C₈₉	1	4	yes	complemented
321	#2283	C₂×C₈₉	1	1	yes	characteristic, complemented
322	C₈₉	#35232	1	1	yes	characteristic, direct product factor, Sylow
323	C₂³×D₄	C₂²×C₈₉	1	1	yes	characteristic
324	C₂⁴×C₄	C₂²×C₈₉	1	2	yes	—
325	#529	—	2	8	no	—
326	C₂×#126	C₂²×C₈₉	1	2	yes	complemented
327	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic, complemented
328	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic, complemented
329	C₂×#123	C₂²×C₈₉	1	2	yes	—
330	C₂×#123	C₂²×C₈₉	1	4	yes	—
331	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
332	C₂×#121	C₂²×C₈₉	1	4	yes	—
333	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
334	C₂×#120	C₂²×C₈₉	1	4	yes	—
335	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic, complemented
336	C₂×C₄×D₄	—	2	8	no	—
337	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
338	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
339	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
340	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
341	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
342	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic, complemented
343	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
344	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
345	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
346	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
347	#399	C₂²×C₈₉	1	4	yes	complemented
348	#398	C₂²×C₈₉	1	4	yes	complemented
349	#397	C₂²×C₈₉	1	4	yes	complemented
350	#397	C₂²×C₈₉	1	4	yes	complemented
351	#394	C₂²×C₈₉	1	4	yes	—
352	#393	C₂²×C₈₉	1	4	yes	complemented
353	#392	C₂²×C₈₉	1	4	yes	—
354	#392	C₂²×C₈₉	1	4	yes	complemented
355	#390	C₂²×C₈₉	1	4	yes	—
356	#390	C₂²×C₈₉	1	8	yes	complemented
357	#389	C₂²×C₈₉	1	4	yes	complemented
358	#388	C₂²×C₈₉	1	8	yes	complemented
359	#386	C₂²×C₈₉	1	8	yes	complemented
360	#386	C₂²×C₈₉	1	8	yes	complemented
361	#385	C₂²×C₈₉	1	8	yes	complemented
362	#385	C₂²×C₈₉	1	8	yes	complemented
363	#383	C₂²×C₈₉	1	2	yes	complemented
364	#382	C₂²×C₈₉	1	2	yes	complemented
365	#381	C₂²×C₈₉	1	4	yes	—
366	#381	C₂²×C₈₉	1	2	yes	—
367	#380	C₂²×C₈₉	1	2	yes	—
368	#380	C₂²×C₈₉	1	4	yes	complemented
369	#379	C₂²×C₈₉	1	4	yes	—
370	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
371	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
372	#376	C₂²×C₈₉	1	2	yes	complemented
373	C₂⁵	C₂³×C₈₉	1	2	yes	—
374	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
375	C₂²×D₄	—	2	8	no	—
376	C₂²×D₄	—	2	4	no	—
377	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
378	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
379	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
380	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
381	C₂²×D₄	C₂³×C₈₉	1	8	yes	—
382	C₂³×C₄	—	2	8	no	—
383	C₂³×C₄	—	4	8	no	—
384	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
385	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
386	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
387	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
388	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
389	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
390	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
391	#126	—	2	8	no	—
392	#125	—	2	4	no	—
393	#124	—	2	4	no	—
394	#123	—	2	8	no	—
395	#123	—	4	8	no	—
396	C₂²⋊Q₈	—	2	4	no	—
397	#121	—	2	16	no	—
398	#121	—	2	4	no	—
399	#120	—	4	8	no	—
400	C₄×Q₈	—	2	4	no	—
401	C₄×D₄	—	2	8	no	—
402	C₄×D₄	—	2	8	no	—
403	C₄×D₄	—	2	8	no	—
404	C₄×D₄	—	2	8	no	—
405	C₄×D₄	—	2	8	no	—
406	C₄×D₄	—	2	4	no	—
407	#117	—	2	8	no	—
408	C₂×C₄⋊C₄	—	2	4	no	—
409	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
410	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
411	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
412	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
413	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
414	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
415	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
417	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
418	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
419	C₂×C₂²⋊C₄	—	2	8	no	—
420	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
426	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
428	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
429	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
430	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
431	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
432	C₂×C₄²	D₄×C₈₉	1	8	yes	complemented
433	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
434	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
435	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
436	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
437	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
438	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
439	#95	C₂³×C₈₉	1	4	yes	—
440	#95	C₂³×C₈₉	1	4	yes	—
441	#95	C₂³×C₈₉	1	4	yes	—
442	#95	C₂³×C₈₉	1	4	yes	—
443	#95	C₂³×C₈₉	1	8	yes	—
444	#95	C₂³×C₈₉	1	8	yes	—
445	C₂⁴	—	2	4	no	—
446	C₂⁴	—	2	8	no	—
447	C₂⁴	—	2	8	no	—
448	C₂⁴	—	4	4	no	—
449	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
450	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
451	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
452	C₂×Q₈	—	2	2	no	—
453	C₂×Q₈	—	4	2	no	—
454	C₂×D₄	—	2	32	no	—
455	C₂×D₄	—	2	8	no	—
456	C₂×D₄	—	2	4	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	4	no	—
459	C₂×D₄	—	2	16	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	4	no	—
462	C₂×D₄	—	2	2	no	—
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	—	4	2	no	—
465	C₂×D₄	—	4	8	no	—
466	C₂×D₄	—	4	8	no	—
467	C₂×D₄	#41×C₈₉	1	8	yes	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	8	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	8	no	—
474	C₂²×C₄	—	2	8	no	—
475	C₂²×C₄	—	2	8	no	—
476	C₂²×C₄	—	4	8	no	—
477	C₂²×C₄	—	4	8	no	—
478	C₂²×C₄	—	4	2	no	—
479	C₂²×C₄	—	4	32	no	—
480	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
481	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
482	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
483	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
484	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
487	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
490	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
492	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
493	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
494	C₄⋊C₄	—	2	4	no	—
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	4	no	—
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	4	no	—
500	C₄⋊C₄	—	2	2	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	8	no	—
503	C₄⋊C₄	—	4	8	no	—
504	C₂²⋊C₄	—	2	4	no	—
505	C₂²⋊C₄	—	2	16	no	—
506	C₂²⋊C₄	—	2	8	no	—
507	C₂²⋊C₄	—	2	8	no	—
508	C₂²⋊C₄	—	2	8	no	—
509	C₂²⋊C₄	—	2	4	no	—
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	2	4	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	4	8	no	—
514	C₂²⋊C₄	—	4	8	no	—
515	C₂²⋊C₄	—	4	8	no	—
516	C₄²	—	2	4	no	—
517	C₄²	—	4	4	no	—
518	C₄²	C₂×D₄×C₈₉	1	4	yes	—
519	C₄²	C₂×D₄×C₈₉	1	4	yes	—
520	C₄²	C₂×D₄×C₈₉	1	4	yes	—
521	C₄²	C₂×D₄×C₈₉	1	4	yes	—
522	C₂³	—	2	2	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	2	16	no	—
525	C₂³	—	2	4	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	2	8	no	—
528	C₂³	—	2	8	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	4	32	no	—
535	C₂³	—	4	8	no	—
536	C₂³	—	4	8	no	—
537	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
538	C₂³	C₂×#41×C₈₉	1	8	yes	—
539	C₂³	H(5,𝔽₂)×C₈₉	1	4	yes	—
540	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
541	Q₈	—	4	4	no	—
542	D₄	—	2	16	no	—
543	D₄	—	2	16	no	—
544	D₄	—	4	4	no	—
545	D₄	—	4	8	no	—
546	D₄	—	8	16	no	—
547	C₂×C₄	—	2	8	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	8	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	4	no	—
559	C₂×C₄	—	2	8	no	—
560	C₂×C₄	—	2	8	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	8	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	8	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	4	4	no	—
567	C₂×C₄	—	4	16	no	—
568	C₂×C₄	—	4	16	no	—
569	C₂×C₄	—	4	8	no	—
570	C₂×C₄	—	4	8	no	—
571	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
572	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
573	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
574	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
575	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
576	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
577	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
578	C₂²	—	2	2	no	—
579	C₂²	—	2	2	no	—
580	C₂²	—	2	8	no	—
581	C₂²	—	2	8	no	—
582	C₂²	—	2	16	no	—
583	C₂²	—	4	32	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	4	8	no	—
587	C₂²	—	4	2	no	—
588	C₂²	—	4	2	no	—
589	C₂²	—	4	2	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	4	no	—
592	C₂²	#535×C₈₉	1	4	yes	—
593	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
594	C₂²	C₂²×#41×C₈₉	1	2	yes	—
595	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
596	C₂²	#585×C₈₉	1	2	yes	—
597	C₄	—	2	2	no	—
598	C₄	—	2	2	no	—
599	C₄	—	2	2	no	—
600	C₄	—	2	2	no	—
601	C₄	—	2	2	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	4	no	—
604	C₄	—	4	2	no	—
605	C₄	—	4	2	no	—
606	C₄	—	4	8	no	—
607	C₄	#525×C₈₉	1	4	yes	—
608	C₂	—	2	4	no	—
609	C₂	—	4	8	no	—
610	C₂	—	8	2	no	—
611	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
612	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
613	C₂	C₈₉×#3449	1	1	yes	characteristic
614	C₂	C₈₉×#3513	1	4	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×#2849	C₂	semidirect
4. C₈₉×#2633	C₂	semidirect
5. C₈₉×#2631	C₂	semidirect
6. C₈₉×#2603	C₂	semidirect
7. C₈₉×#2580	C₂	semidirect
8. C₈₉×#2561	C₂	semidirect
9. C₈₉×#2539	C₂	semidirect
10. C₈₉×#2535	C₂	semidirect
11. C₈₉×#2486	C₂	semidirect
12. C₈₉×#2408	C₂	semidirect
13. C₈₉×#2324	C₂	semidirect
14. C₈₉×#2283	C₂	semidirect
18. C₂×#126×C₈₉	C₂²	semidirect
19. C₂×#125×C₈₉	C₂²	semidirect
20. C₂×#124×C₈₉	C₂²	semidirect
27. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
34. C₂×C₄×D₄×C₈₉	C₂²	semidirect
35. C₂×#117×C₈₉	C₂²	semidirect
39. #399×C₈₉	C₂²	semidirect
40. #398×C₈₉	C₂²	semidirect
41. #397×C₈₉	C₂²	semidirect
42. #397×C₈₉	C₂²	semidirect
44. #393×C₈₉	C₂²	semidirect
46. #392×C₈₉	C₂²	semidirect
48. #390×C₈₉	C₂²	semidirect
49. #389×C₈₉	C₂²	semidirect
50. #388×C₈₉	C₂²	semidirect
51. #386×C₈₉	C₂²	semidirect
52. #386×C₈₉	C₂²	semidirect
53. #385×C₈₉	C₂²	semidirect
54. #385×C₈₉	C₂²	semidirect
55. #383×C₈₉	C₂²	semidirect
56. #382×C₈₉	C₂²	semidirect
60. #380×C₈₉	C₂²	semidirect
62. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
64. #376×C₈₉	C₂²	semidirect
124. C₂×C₄²×C₈₉	D₄	semidirect
300. #35232	C₈₉	direct (N × H)
308. C₂×#529	C₂×C₈₉	semidirect
309. C₂²×C₄×D₄	C₂×C₈₉	semidirect
310. #2849	C₂×C₈₉	semidirect
311. #2633	C₂×C₈₉	semidirect
312. #2631	C₂×C₈₉	semidirect
313. #2603	C₂×C₈₉	semidirect
314. #2580	C₂×C₈₉	semidirect
315. #2561	C₂×C₈₉	semidirect
316. #2539	C₂×C₈₉	semidirect
317. #2535	C₂×C₈₉	semidirect
318. #2486	C₂×C₈₉	semidirect
319. #2408	C₂×C₈₉	semidirect
320. #2324	C₂×C₈₉	semidirect
321. #2283	C₂×C₈₉	semidirect
322. C₈₉	#35232	direct (N × H)
326. C₂×#126	C₂²×C₈₉	semidirect
327. C₂×#125	C₂²×C₈₉	semidirect
328. C₂×#124	C₂²×C₈₉	semidirect
335. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
342. C₂×C₄×D₄	C₂²×C₈₉	semidirect
343. C₂×#117	C₂²×C₈₉	semidirect
347. #399	C₂²×C₈₉	semidirect
348. #398	C₂²×C₈₉	semidirect
349. #397	C₂²×C₈₉	semidirect
350. #397	C₂²×C₈₉	semidirect
352. #393	C₂²×C₈₉	semidirect
354. #392	C₂²×C₈₉	semidirect
356. #390	C₂²×C₈₉	semidirect
357. #389	C₂²×C₈₉	semidirect
358. #388	C₂²×C₈₉	semidirect
359. #386	C₂²×C₈₉	semidirect
360. #386	C₂²×C₈₉	semidirect
361. #385	C₂²×C₈₉	semidirect
362. #385	C₂²×C₈₉	semidirect
363. #383	C₂²×C₈₉	semidirect
364. #382	C₂²×C₈₉	semidirect
368. #380	C₂²×C₈₉	semidirect
370. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
372. #376	C₂²×C₈₉	semidirect
432. 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×#2849	2
C₈₉×#2633	2
C₈₉×#2631	2
C₈₉×#2603	2
C₈₉×#2580	2
C₈₉×#2561	2
C₈₉×#2539	2
C₈₉×#2535	2
C₈₉×#2486	2
C₈₉×#2408	2
C₈₉×#2324	2
C₈₉×#2283	2
#35232	89

Subgroups — C89×#35232 #36413080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35232 #36413080