Subgroups — C₈₉×#36536 #36414384

Order 22784.

1918 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2864	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2855	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2600	C₂	1	4	yes	maximal, complemented
4	C₈₉×#2578	C₂	1	4	yes	maximal, complemented
5	C₈₉×#2577	C₂	1	4	yes	maximal, complemented
6	C₈₉×#2536	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2535	C₂	1	1	yes	maximal, characteristic
8	C₈₉×#2495	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2427	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2356	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2353	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2349	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#124×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#121×C₈₉	C₂	1	2	yes	maximal, complemented
15	C₄²×D₄×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#124×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
18	C₂×#121×C₈₉	C₂²	1	2	yes	—
19	C₂×C₄×Q₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
21	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
23	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
25	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
26	#400×C₈₉	C₂²	1	4	yes	—
27	#398×C₈₉	C₂²	1	2	yes	—
28	#397×C₈₉	C₂²	1	2	yes	—
29	#397×C₈₉	C₂²	1	4	yes	—
30	#397×C₈₉	C₂²	1	4	yes	—
31	#394×C₈₉	C₂²	1	4	yes	—
32	#394×C₈₉	C₂²	1	2	yes	—
33	#392×C₈₉	C₂²	1	2	yes	—
34	#391×C₈₉	C₂²	1	1	yes	characteristic
35	#391×C₈₉	C₂²	1	2	yes	—
36	#390×C₈₉	C₂²	1	1	yes	characteristic
37	#389×C₈₉	C₂²	1	2	yes	—
38	#389×C₈₉	C₂²	1	2	yes	—
39	#389×C₈₉	C₂²	1	2	yes	—
40	#388×C₈₉	C₂²	1	4	yes	—
41	#388×C₈₉	C₂²	1	4	yes	—
42	#388×C₈₉	C₂²	1	4	yes	—
43	#388×C₈₉	C₂²	1	4	yes	—
44	#387×C₈₉	C₂²	1	4	yes	—
45	#387×C₈₉	C₂²	1	4	yes	—
46	#387×C₈₉	C₂²	1	4	yes	—
47	#387×C₈₉	C₂²	1	4	yes	—
48	#387×C₈₉	C₂²	1	4	yes	—
49	#386×C₈₉	C₂²	1	4	yes	—
50	#386×C₈₉	C₂²	1	4	yes	—
51	#386×C₈₉	C₂²	1	4	yes	—
52	#385×C₈₉	C₂²	1	4	yes	—
53	#385×C₈₉	C₂²	1	4	yes	—
54	#383×C₈₉	C₂²	1	4	yes	—
55	#383×C₈₉	C₂²	1	2	yes	—
56	#382×C₈₉	C₂²	1	1	yes	characteristic
57	#382×C₈₉	C₂²	1	1	yes	characteristic
58	#382×C₈₉	C₂²	1	1	yes	characteristic
59	#381×C₈₉	C₂²	1	4	yes	—
60	#380×C₈₉	C₂²	1	2	yes	—
61	#380×C₈₉	C₂²	1	4	yes	—
62	#380×C₈₉	C₂²	1	2	yes	—
63	#380×C₈₉	C₂²	1	2	yes	—
64	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
65	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
67	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
68	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
69	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
70	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
71	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
72	#376×C₈₉	C₂²	1	2	yes	—
73	C₂×#95×C₈₉	C₂²	1	2	yes	—
74	C₄³×C₈₉	C₂²	1	1	yes	characteristic
75	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
76	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
77	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
78	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
80	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
81	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
82	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
83	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
84	#124×C₈₉	—	2	4	no	—
85	C₂²⋊Q₈×C₈₉	—	4	4	no	—
86	#121×C₈₉	—	2	8	no	—
87	C₄×Q₈×C₈₉	—	2	4	no	—
88	C₄×D₄×C₈₉	—	2	8	no	—
89	C₄×D₄×C₈₉	—	2	16	no	—
90	C₄×D₄×C₈₉	—	2	4	no	—
91	C₄×D₄×C₈₉	—	2	4	no	—
92	C₄×D₄×C₈₉	—	4	4	no	—
93	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
95	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
96	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
97	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
100	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
101	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
104	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
105	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
106	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
107	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	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	2	yes	—
112	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
113	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
114	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
115	C₂×C₄²×C₈₉	—	4	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	1	yes	characteristic
119	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
120	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
121	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
122	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
123	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
124	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
125	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
126	#95×C₈₉	C₂³	1	1	yes	characteristic
127	#95×C₈₉	C₂³	1	2	yes	—
128	#95×C₈₉	C₂³	1	4	yes	—
129	#95×C₈₉	C₂³	1	4	yes	—
130	#95×C₈₉	C₂³	1	2	yes	—
131	#95×C₈₉	C₂³	1	2	yes	—
132	#95×C₈₉	C₂³	1	1	yes	characteristic
133	#95×C₈₉	C₂³	1	2	yes	—
134	#95×C₈₉	C₂³	1	4	yes	—
135	#95×C₈₉	C₂³	1	4	yes	—
136	#95×C₈₉	C₂³	1	4	yes	—
137	#95×C₈₉	C₂³	1	4	yes	—
138	#95×C₈₉	C₂³	1	4	yes	—
139	#95×C₈₉	C₂³	1	4	yes	—
140	#95×C₈₉	C₂³	1	2	yes	—
141	#95×C₈₉	C₂³	1	2	yes	—
142	#95×C₈₉	C₂³	1	4	yes	—
143	#95×C₈₉	C₂³	1	4	yes	—
144	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
145	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
146	C₂×Q₈×C₈₉	—	2	2	no	—
147	C₂×Q₈×C₈₉	—	2	2	no	—
148	C₂×Q₈×C₈₉	—	2	2	no	—
149	C₂×D₄×C₈₉	—	2	4	no	—
150	C₂×D₄×C₈₉	—	2	8	no	—
151	C₂×D₄×C₈₉	—	2	8	no	—
152	C₂×D₄×C₈₉	—	2	2	no	—
153	C₂×D₄×C₈₉	—	2	2	no	—
154	C₂×D₄×C₈₉	—	2	2	no	—
155	C₂×D₄×C₈₉	—	4	4	no	—
156	C₂×D₄×C₈₉	#41	1	4	yes	—
157	C₂²×C₄×C₈₉	—	2	4	no	—
158	C₂²×C₄×C₈₉	—	2	4	no	—
159	C₂²×C₄×C₈₉	—	2	4	no	—
160	C₂²×C₄×C₈₉	—	2	4	no	—
161	C₂²×C₄×C₈₉	—	2	4	no	—
162	C₂²×C₄×C₈₉	—	2	8	no	—
163	C₂²×C₄×C₈₉	—	4	2	no	—
164	C₂²×C₄×C₈₉	—	4	2	no	—
165	C₂²×C₄×C₈₉	—	4	2	no	—
166	C₂²×C₄×C₈₉	—	4	2	no	—
167	C₂²×C₄×C₈₉	—	4	4	no	—
168	C₂²×C₄×C₈₉	—	4	4	no	—
169	C₂²×C₄×C₈₉	—	4	4	no	—
170	C₂²×C₄×C₈₉	#41	1	8	yes	—
171	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
172	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
173	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
174	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₈₉	C₂⁴	1	2	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	1	yes	characteristic
180	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
181	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
183	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
184	C₄⋊C₄×C₈₉	—	2	4	no	—
185	C₄⋊C₄×C₈₉	—	2	8	no	—
186	C₄⋊C₄×C₈₉	—	2	2	no	—
187	C₄⋊C₄×C₈₉	—	2	2	no	—
188	C₄⋊C₄×C₈₉	—	2	2	no	—
189	C₄⋊C₄×C₈₉	—	2	4	no	—
190	C₄⋊C₄×C₈₉	—	2	4	no	—
191	C₄⋊C₄×C₈₉	—	2	4	no	—
192	C₄⋊C₄×C₈₉	—	4	4	no	—
193	C₄⋊C₄×C₈₉	—	4	4	no	—
194	C₄⋊C₄×C₈₉	—	4	4	no	—
195	C₂²⋊C₄×C₈₉	—	2	4	no	—
196	C₂²⋊C₄×C₈₉	—	2	8	no	—
197	C₂²⋊C₄×C₈₉	—	2	8	no	—
198	C₂²⋊C₄×C₈₉	—	2	8	no	—
199	C₂²⋊C₄×C₈₉	—	2	4	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	—	4	4	no	—
204	C₂²⋊C₄×C₈₉	—	4	4	no	—
205	C₂²⋊C₄×C₈₉	—	4	4	no	—
206	C₄²×C₈₉	—	2	4	no	—
207	C₄²×C₈₉	—	2	8	no	—
208	C₄²×C₈₉	—	2	4	no	—
209	C₄²×C₈₉	—	2	2	no	—
210	C₄²×C₈₉	—	2	2	no	—
211	C₄²×C₈₉	—	2	4	no	—
212	C₄²×C₈₉	—	4	2	no	—
213	C₄²×C₈₉	—	4	2	no	—
214	C₄²×C₈₉	—	4	2	no	—
215	C₄²×C₈₉	#41	1	4	yes	—
216	C₂³×C₈₉	—	2	2	no	—
217	C₂³×C₈₉	—	2	2	no	—
218	C₂³×C₈₉	—	2	2	no	—
219	C₂³×C₈₉	—	2	4	no	—
220	C₂³×C₈₉	—	2	2	no	—
221	C₂³×C₈₉	—	2	2	no	—
222	C₂³×C₈₉	—	2	2	no	—
223	C₂³×C₈₉	—	2	2	no	—
224	C₂³×C₈₉	—	2	4	no	—
225	C₂³×C₈₉	—	2	2	no	—
226	C₂³×C₈₉	C₂×#41	1	4	yes	—
227	C₂³×C₈₉	C₂×#41	1	4	yes	—
228	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
229	Q₈×C₈₉	—	4	4	no	—
230	D₄×C₈₉	—	2	8	no	—
231	D₄×C₈₉	—	2	8	no	—
232	D₄×C₈₉	—	4	16	no	—
233	C₂×C₄×C₈₉	—	2	2	no	—
234	C₂×C₄×C₈₉	—	2	2	no	—
235	C₂×C₄×C₈₉	—	2	2	no	—
236	C₂×C₄×C₈₉	—	2	2	no	—
237	C₂×C₄×C₈₉	—	2	2	no	—
238	C₂×C₄×C₈₉	—	2	2	no	—
239	C₂×C₄×C₈₉	—	2	4	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	4	no	—
244	C₂×C₄×C₈₉	—	2	2	no	—
245	C₂×C₄×C₈₉	—	2	2	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	2	no	—
251	C₂×C₄×C₈₉	—	2	4	no	—
252	C₂×C₄×C₈₉	—	2	2	no	—
253	C₂×C₄×C₈₉	—	2	2	no	—
254	C₂×C₄×C₈₉	—	2	4	no	—
255	C₂×C₄×C₈₉	—	2	2	no	—
256	C₂×C₄×C₈₉	—	2	2	no	—
257	C₂×C₄×C₈₉	—	2	4	no	—
258	C₂×C₄×C₈₉	—	2	4	no	—
259	C₂×C₄×C₈₉	—	2	2	no	—
260	C₂×C₄×C₈₉	—	2	4	no	—
261	C₂×C₄×C₈₉	—	4	8	no	—
262	C₂×C₄×C₈₉	—	4	8	no	—
263	C₂×C₄×C₈₉	—	4	8	no	—
264	C₂×C₄×C₈₉	—	8	8	no	—
265	C₂×C₄×C₈₉	—	8	4	no	—
266	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
267	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
268	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
269	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
270	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
271	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
272	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
273	C₂²×C₈₉	—	2	4	no	—
274	C₂²×C₈₉	—	2	4	no	—
275	C₂²×C₈₉	—	2	4	no	—
276	C₂²×C₈₉	—	2	8	no	—
277	C₂²×C₈₉	—	2	4	no	—
278	C₂²×C₈₉	—	4	2	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	2	no	—
284	C₂²×C₈₉	—	4	2	no	—
285	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
286	C₂²×C₈₉	C₂²×#41	1	2	yes	—
287	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
288	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
289	C₂²×C₈₉	#585	1	2	yes	—
290	C₄×C₈₉	—	2	2	no	—
291	C₄×C₈₉	—	2	4	no	—
292	C₄×C₈₉	—	2	4	no	—
293	C₄×C₈₉	—	2	2	no	—
294	C₄×C₈₉	—	4	2	no	—
295	C₄×C₈₉	—	4	2	no	—
296	C₄×C₈₉	—	4	2	no	—
297	C₄×C₈₉	—	4	2	no	—
298	C₄×C₈₉	—	4	4	no	—
299	C₄×C₈₉	—	4	2	no	—
300	C₄×C₈₉	—	4	4	no	—
301	C₄×C₈₉	—	4	2	no	—
302	C₄×C₈₉	#553	1	4	yes	—
303	#36536	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
304	C₂×C₈₉	—	4	4	no	—
305	C₂×C₈₉	—	4	4	no	—
306	C₂×C₈₉	#3444	1	1	yes	characteristic
307	C₂×C₈₉	C₂×#553	1	1	yes	characteristic
308	C₂×C₈₉	#3475	1	2	yes	—
309	C₂×C₈₉	#3505	1	2	yes	—
310	C₂×C₈₉	#3510	1	1	yes	characteristic
311	#2864	C₂×C₈₉	1	1	yes	characteristic, complemented
312	#2855	C₂×C₈₉	1	2	yes	complemented
313	#2600	C₂×C₈₉	1	4	yes	complemented
314	#2578	C₂×C₈₉	1	4	yes	complemented
315	#2577	C₂×C₈₉	1	4	yes	complemented
316	#2536	C₂×C₈₉	1	1	yes	characteristic, complemented
317	#2535	C₂×C₈₉	1	1	yes	characteristic
318	#2495	C₂×C₈₉	1	2	yes	complemented
319	#2427	C₂×C₈₉	1	2	yes	complemented
320	#2356	C₂×C₈₉	1	1	yes	characteristic, complemented
321	#2353	C₂×C₈₉	1	4	yes	complemented
322	#2349	C₂×C₈₉	1	1	yes	characteristic, complemented
323	C₄×#124	C₂×C₈₉	1	1	yes	characteristic, complemented
324	C₄×#121	C₂×C₈₉	1	2	yes	complemented
325	C₄²×D₄	C₂×C₈₉	1	1	yes	characteristic, complemented
326	C₈₉	#36536	1	1	yes	characteristic, direct product factor, Sylow
327	C₂×#124	C₂²×C₈₉	1	1	yes	characteristic
328	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
329	C₂×#121	C₂²×C₈₉	1	2	yes	—
330	C₂×C₄×Q₈	C₂²×C₈₉	1	1	yes	characteristic
331	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
332	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
333	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
334	C₂×C₄×D₄	C₂²×C₈₉	1	1	yes	characteristic
335	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
336	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
337	#400	C₂²×C₈₉	1	4	yes	—
338	#398	C₂²×C₈₉	1	2	yes	—
339	#397	C₂²×C₈₉	1	2	yes	—
340	#397	C₂²×C₈₉	1	4	yes	—
341	#397	C₂²×C₈₉	1	4	yes	—
342	#394	C₂²×C₈₉	1	4	yes	—
343	#394	C₂²×C₈₉	1	2	yes	—
344	#392	C₂²×C₈₉	1	2	yes	—
345	#391	C₂²×C₈₉	1	1	yes	characteristic
346	#391	C₂²×C₈₉	1	2	yes	—
347	#390	C₂²×C₈₉	1	1	yes	characteristic
348	#389	C₂²×C₈₉	1	2	yes	—
349	#389	C₂²×C₈₉	1	2	yes	—
350	#389	C₂²×C₈₉	1	2	yes	—
351	#388	C₂²×C₈₉	1	4	yes	—
352	#388	C₂²×C₈₉	1	4	yes	—
353	#388	C₂²×C₈₉	1	4	yes	—
354	#388	C₂²×C₈₉	1	4	yes	—
355	#387	C₂²×C₈₉	1	4	yes	—
356	#387	C₂²×C₈₉	1	4	yes	—
357	#387	C₂²×C₈₉	1	4	yes	—
358	#387	C₂²×C₈₉	1	4	yes	—
359	#387	C₂²×C₈₉	1	4	yes	—
360	#386	C₂²×C₈₉	1	4	yes	—
361	#386	C₂²×C₈₉	1	4	yes	—
362	#386	C₂²×C₈₉	1	4	yes	—
363	#385	C₂²×C₈₉	1	4	yes	—
364	#385	C₂²×C₈₉	1	4	yes	—
365	#383	C₂²×C₈₉	1	4	yes	—
366	#383	C₂²×C₈₉	1	2	yes	—
367	#382	C₂²×C₈₉	1	1	yes	characteristic
368	#382	C₂²×C₈₉	1	1	yes	characteristic
369	#382	C₂²×C₈₉	1	1	yes	characteristic
370	#381	C₂²×C₈₉	1	4	yes	—
371	#380	C₂²×C₈₉	1	4	yes	—
372	#380	C₂²×C₈₉	1	2	yes	—
373	#380	C₂²×C₈₉	1	2	yes	—
374	#380	C₂²×C₈₉	1	2	yes	—
375	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
376	C₄×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
377	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
378	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
379	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
380	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
381	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
382	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
383	#376	C₂²×C₈₉	1	2	yes	—
384	C₂×#95	C₂²×C₈₉	1	2	yes	—
385	C₄³	C₂²×C₈₉	1	1	yes	characteristic
386	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
387	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
388	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
389	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
390	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
391	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
392	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
393	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
394	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
395	#124	—	2	4	no	—
396	C₂²⋊Q₈	—	4	4	no	—
397	#121	—	2	8	no	—
398	C₄×Q₈	—	2	4	no	—
399	C₄×D₄	—	2	8	no	—
400	C₄×D₄	—	2	16	no	—
401	C₄×D₄	—	2	4	no	—
402	C₄×D₄	—	2	4	no	—
403	C₄×D₄	—	4	4	no	—
404	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
405	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
407	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
408	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
409	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
414	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
415	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
416	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
418	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
420	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
422	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
423	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
424	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
425	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
426	C₂×C₄²	—	4	4	no	—
427	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
428	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
429	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
430	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
431	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
433	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
434	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
435	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
436	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
437	#95	C₂³×C₈₉	1	1	yes	characteristic
438	#95	C₂³×C₈₉	1	2	yes	—
439	#95	C₂³×C₈₉	1	4	yes	—
440	#95	C₂³×C₈₉	1	4	yes	—
441	#95	C₂³×C₈₉	1	2	yes	—
442	#95	C₂³×C₈₉	1	2	yes	—
443	#95	C₂³×C₈₉	1	1	yes	characteristic
444	#95	C₂³×C₈₉	1	2	yes	—
445	#95	C₂³×C₈₉	1	4	yes	—
446	#95	C₂³×C₈₉	1	4	yes	—
447	#95	C₂³×C₈₉	1	4	yes	—
448	#95	C₂³×C₈₉	1	4	yes	—
449	#95	C₂³×C₈₉	1	4	yes	—
450	#95	C₂³×C₈₉	1	4	yes	—
451	#95	C₂³×C₈₉	1	2	yes	—
452	#95	C₂³×C₈₉	1	2	yes	—
453	#95	C₂³×C₈₉	1	4	yes	—
454	#95	C₂³×C₈₉	1	4	yes	—
455	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
456	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
457	C₂×Q₈	—	2	2	no	—
458	C₂×Q₈	—	2	2	no	—
459	C₂×Q₈	—	2	2	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	8	no	—
462	C₂×D₄	—	2	8	no	—
463	C₂×D₄	—	2	2	no	—
464	C₂×D₄	—	2	2	no	—
465	C₂×D₄	—	2	2	no	—
466	C₂×D₄	—	4	4	no	—
467	C₂×D₄	#41×C₈₉	1	4	yes	—
468	C₂²×C₄	—	2	4	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	4	no	—
472	C₂²×C₄	—	2	4	no	—
473	C₂²×C₄	—	2	8	no	—
474	C₂²×C₄	—	4	2	no	—
475	C₂²×C₄	—	4	2	no	—
476	C₂²×C₄	—	4	2	no	—
477	C₂²×C₄	—	4	2	no	—
478	C₂²×C₄	—	4	4	no	—
479	C₂²×C₄	—	4	4	no	—
480	C₂²×C₄	—	4	4	no	—
481	C₂²×C₄	#41×C₈₉	1	8	yes	—
482	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
483	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
484	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
485	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
487	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
488	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
489	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
490	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
491	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
492	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
493	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
494	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
495	C₄⋊C₄	—	2	4	no	—
496	C₄⋊C₄	—	2	8	no	—
497	C₄⋊C₄	—	2	2	no	—
498	C₄⋊C₄	—	2	2	no	—
499	C₄⋊C₄	—	2	2	no	—
500	C₄⋊C₄	—	2	4	no	—
501	C₄⋊C₄	—	2	4	no	—
502	C₄⋊C₄	—	2	4	no	—
503	C₄⋊C₄	—	4	4	no	—
504	C₄⋊C₄	—	4	4	no	—
505	C₄⋊C₄	—	4	4	no	—
506	C₂²⋊C₄	—	2	4	no	—
507	C₂²⋊C₄	—	2	8	no	—
508	C₂²⋊C₄	—	2	8	no	—
509	C₂²⋊C₄	—	2	8	no	—
510	C₂²⋊C₄	—	2	4	no	—
511	C₂²⋊C₄	—	2	8	no	—
512	C₂²⋊C₄	—	2	4	no	—
513	C₂²⋊C₄	—	2	4	no	—
514	C₂²⋊C₄	—	4	4	no	—
515	C₂²⋊C₄	—	4	4	no	—
516	C₂²⋊C₄	—	4	4	no	—
517	C₄²	—	2	4	no	—
518	C₄²	—	2	8	no	—
519	C₄²	—	2	4	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	2	no	—
522	C₄²	—	2	4	no	—
523	C₄²	—	4	2	no	—
524	C₄²	—	4	2	no	—
525	C₄²	—	4	2	no	—
526	C₄²	#41×C₈₉	1	4	yes	—
527	C₂³	—	2	2	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	2	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	2	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	2	no	—
537	C₂³	C₂×#41×C₈₉	1	4	yes	—
538	C₂³	C₂×#41×C₈₉	1	4	yes	—
539	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
540	Q₈	—	4	4	no	—
541	D₄	—	2	8	no	—
542	D₄	—	2	8	no	—
543	D₄	—	4	16	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	2	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	4	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	4	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	2	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	4	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	4	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	4	no	—
572	C₂×C₄	—	4	8	no	—
573	C₂×C₄	—	4	8	no	—
574	C₂×C₄	—	4	8	no	—
575	C₂×C₄	—	8	8	no	—
576	C₂×C₄	—	8	4	no	—
577	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
578	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
579	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
580	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
581	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
582	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
583	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
584	C₂²	—	2	4	no	—
585	C₂²	—	2	4	no	—
586	C₂²	—	2	4	no	—
587	C₂²	—	2	8	no	—
588	C₂²	—	2	4	no	—
589	C₂²	—	4	2	no	—
590	C₂²	—	4	2	no	—
591	C₂²	—	4	2	no	—
592	C₂²	—	4	2	no	—
593	C₂²	—	4	4	no	—
594	C₂²	—	4	2	no	—
595	C₂²	—	4	2	no	—
596	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
597	C₂²	C₂²×#41×C₈₉	1	2	yes	—
598	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
599	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
600	C₂²	#585×C₈₉	1	2	yes	—
601	C₄	—	2	2	no	—
602	C₄	—	2	4	no	—
603	C₄	—	2	4	no	—
604	C₄	—	2	2	no	—
605	C₄	—	4	2	no	—
606	C₄	—	4	2	no	—
607	C₄	—	4	2	no	—
608	C₄	—	4	4	no	—
609	C₄	—	4	2	no	—
610	C₄	—	4	2	no	—
611	C₄	—	4	4	no	—
612	C₄	—	4	2	no	—
613	C₄	#553×C₈₉	1	4	yes	—
614	C₂	—	4	4	no	—
615	C₂	—	4	4	no	—
616	C₂	C₈₉×#3444	1	1	yes	characteristic
617	C₂	C₂×#553×C₈₉	1	1	yes	characteristic
618	C₂	C₈₉×#3475	1	2	yes	—
619	C₂	C₈₉×#3505	1	2	yes	—
620	C₂	C₈₉×#3510	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2535	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. C₈₉×#2864	C₂	semidirect
2. C₈₉×#2855	C₂	semidirect
3. C₈₉×#2600	C₂	semidirect
4. C₈₉×#2578	C₂	semidirect
5. C₈₉×#2577	C₂	semidirect
6. C₈₉×#2536	C₂	semidirect
8. C₈₉×#2495	C₂	semidirect
9. C₈₉×#2427	C₂	semidirect
10. C₈₉×#2356	C₂	semidirect
11. C₈₉×#2353	C₂	semidirect
12. C₈₉×#2349	C₂	semidirect
13. C₄×#124×C₈₉	C₂	semidirect
14. C₄×#121×C₈₉	C₂	semidirect
15. C₄²×D₄×C₈₉	C₂	semidirect
303. #36536	C₈₉	direct (N × H)
311. #2864	C₂×C₈₉	semidirect
312. #2855	C₂×C₈₉	semidirect
313. #2600	C₂×C₈₉	semidirect
314. #2578	C₂×C₈₉	semidirect
315. #2577	C₂×C₈₉	semidirect
316. #2536	C₂×C₈₉	semidirect
318. #2495	C₂×C₈₉	semidirect
319. #2427	C₂×C₈₉	semidirect
320. #2356	C₂×C₈₉	semidirect
321. #2353	C₂×C₈₉	semidirect
322. #2349	C₂×C₈₉	semidirect
323. C₄×#124	C₂×C₈₉	semidirect
324. C₄×#121	C₂×C₈₉	semidirect
325. C₄²×D₄	C₂×C₈₉	semidirect
326. C₈₉	#36536	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#2864	2
C₈₉×#2855	2
C₈₉×#2600	2
C₈₉×#2578	2
C₈₉×#2577	2
C₈₉×#2536	2
C₈₉×#2535	2
C₈₉×#2495	2
C₈₉×#2427	2
C₈₉×#2356	2
C₈₉×#2353	2
C₈₉×#2349	2
C₄×#124×C₈₉	2
C₄×#121×C₈₉	2
C₄²×D₄×C₈₉	2
#36536	89

Subgroups — C89×#36536 #36414384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#36536 #36414384