Subgroups — C₈₉×#35268 #36413116

Order 22784.

1894 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×#2860	C₂	1	2	yes	maximal, complemented
3	C₈₉×#2858	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈₉×#2628	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈₉×#2624	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2619	C₂	1	1	yes	maximal, characteristic
7	C₈₉×#2521	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2516	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2467	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2459	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2328	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈₉×#2319	C₂	1	2	yes	maximal, complemented
14	C₄×#121×C₈₉	C₂	1	2	yes	maximal, complemented
15	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×#126×C₈₉	C₂²	1	4	yes	—
19	C₂×#124×C₈₉	C₂²	1	4	yes	—
20	C₂×#121×C₈₉	C₂²	1	2	yes	—
21	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₈₉	C₂²	1	4	yes	—
23	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
26	#400×C₈₉	C₂²	1	2	yes	—
27	#399×C₈₉	C₂²	1	4	yes	—
28	#399×C₈₉	C₂²	1	2	yes	—
29	#397×C₈₉	C₂²	1	4	yes	—
30	#395×C₈₉	C₂²	1	2	yes	—
31	#394×C₈₉	C₂²	1	2	yes	—
32	#394×C₈₉	C₂²	1	2	yes	—
33	#394×C₈₉	C₂²	1	4	yes	—
34	#394×C₈₉	C₂²	1	4	yes	—
35	#393×C₈₉	C₂²	1	2	yes	—
36	#392×C₈₉	C₂²	1	2	yes	—
37	#392×C₈₉	C₂²	1	2	yes	—
38	#391×C₈₉	C₂²	1	4	yes	—
39	#390×C₈₉	C₂²	1	2	yes	—
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	#389×C₈₉	C₂²	1	2	yes	—
45	#389×C₈₉	C₂²	1	2	yes	—
46	#389×C₈₉	C₂²	1	2	yes	—
47	#389×C₈₉	C₂²	1	2	yes	—
48	#388×C₈₉	C₂²	1	4	yes	—
49	#388×C₈₉	C₂²	1	4	yes	—
50	#388×C₈₉	C₂²	1	4	yes	—
51	#388×C₈₉	C₂²	1	4	yes	—
52	#388×C₈₉	C₂²	1	4	yes	—
53	#388×C₈₉	C₂²	1	4	yes	—
54	#387×C₈₉	C₂²	1	4	yes	—
55	#387×C₈₉	C₂²	1	4	yes	—
56	#387×C₈₉	C₂²	1	4	yes	—
57	#386×C₈₉	C₂²	1	4	yes	—
58	#386×C₈₉	C₂²	1	4	yes	—
59	#386×C₈₉	C₂²	1	4	yes	—
60	#382×C₈₉	C₂²	1	1	yes	characteristic
61	#382×C₈₉	C₂²	1	1	yes	characteristic
62	#381×C₈₉	C₂²	1	4	yes	—
63	#380×C₈₉	C₂²	1	2	yes	—
64	#380×C₈₉	C₂²	1	4	yes	—
65	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
66	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
67	C₄×C₄⋊C₄×C₈₉	C₂²	1	2	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	#376×C₈₉	C₂²	1	1	yes	characteristic
72	#376×C₈₉	C₂²	1	1	yes	characteristic
73	C₄³×C₈₉	C₂²	1	1	yes	characteristic
74	C₄³×C₈₉	C₂²	1	1	yes	characteristic
75	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
76	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
77	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
78	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
79	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
80	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
81	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
83	C₄⋊Q₈×C₈₉	—	2	4	no	—
84	#127×C₈₉	—	2	4	no	—
85	#126×C₈₉	—	4	8	no	—
86	#124×C₈₉	—	4	8	no	—
87	#121×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	—	2	4	no	—
92	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	2	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	2	yes	—
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	4	yes	—
103	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
104	C₂×C₂²⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
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	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	4	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×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
116	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
117	C₂×C₄²×C₈₉	—	2	4	no	—
118	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
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	2	yes	—
126	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
127	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
128	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
130	#95×C₈₉	C₂³	1	2	yes	—
131	#95×C₈₉	C₂³	1	2	yes	—
132	#95×C₈₉	C₂³	1	2	yes	—
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	2	yes	—
140	#95×C₈₉	C₂³	1	2	yes	—
141	#95×C₈₉	C₂³	1	2	yes	—
142	#95×C₈₉	C₂³	1	2	yes	—
143	#95×C₈₉	C₂³	1	4	yes	—
144	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
145	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
146	C₂×Q₈×C₈₉	—	2	4	no	—
147	C₂×Q₈×C₈₉	—	4	4	no	—
148	C₂×D₄×C₈₉	—	2	8	no	—
149	C₂×D₄×C₈₉	—	2	4	no	—
150	C₂×D₄×C₈₉	—	2	4	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	—	4	4	no	—
155	C₂×D₄×C₈₉	—	4	4	no	—
156	C₂×D₄×C₈₉	—	4	4	no	—
157	C₂×D₄×C₈₉	—	4	4	no	—
158	C₂²×C₄×C₈₉	—	2	2	no	—
159	C₂²×C₄×C₈₉	—	2	2	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	4	no	—
165	C₂²×C₄×C₈₉	—	4	4	no	—
166	C₂²×C₄×C₈₉	#41	1	4	yes	—
167	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
168	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
170	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
172	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
174	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
175	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
176	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
177	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
178	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
179	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
180	C₄⋊C₄×C₈₉	—	2	2	no	—
181	C₄⋊C₄×C₈₉	—	2	2	no	—
182	C₄⋊C₄×C₈₉	—	2	4	no	—
183	C₄⋊C₄×C₈₉	—	2	4	no	—
184	C₄⋊C₄×C₈₉	—	2	4	no	—
185	C₄⋊C₄×C₈₉	—	2	4	no	—
186	C₄⋊C₄×C₈₉	—	2	4	no	—
187	C₄⋊C₄×C₈₉	—	2	8	no	—
188	C₄⋊C₄×C₈₉	—	4	4	no	—
189	C₄⋊C₄×C₈₉	—	4	4	no	—
190	C₄⋊C₄×C₈₉	—	4	4	no	—
191	C₂²⋊C₄×C₈₉	—	2	4	no	—
192	C₂²⋊C₄×C₈₉	—	2	2	no	—
193	C₂²⋊C₄×C₈₉	—	2	2	no	—
194	C₂²⋊C₄×C₈₉	—	2	8	no	—
195	C₂²⋊C₄×C₈₉	—	2	8	no	—
196	C₂²⋊C₄×C₈₉	—	2	8	no	—
197	C₂²⋊C₄×C₈₉	—	2	8	no	—
198	C₂²⋊C₄×C₈₉	—	4	4	no	—
199	C₂²⋊C₄×C₈₉	—	4	4	no	—
200	C₂²⋊C₄×C₈₉	—	4	4	no	—
201	C₂²⋊C₄×C₈₉	—	4	4	no	—
202	C₂²⋊C₄×C₈₉	—	4	4	no	—
203	C₂²⋊C₄×C₈₉	—	4	4	no	—
204	C₂²⋊C₄×C₈₉	—	4	4	no	—
205	C₄²×C₈₉	—	2	4	no	—
206	C₄²×C₈₉	—	2	2	no	—
207	C₄²×C₈₉	—	2	2	no	—
208	C₄²×C₈₉	—	2	2	no	—
209	C₄²×C₈₉	—	2	2	no	—
210	C₄²×C₈₉	—	2	4	no	—
211	C₄²×C₈₉	—	2	4	no	—
212	C₄²×C₈₉	—	4	2	no	—
213	C₄²×C₈₉	—	4	2	no	—
214	C₄²×C₈₉	—	4	4	no	—
215	C₄²×C₈₉	#41	1	4	yes	—
216	C₄²×C₈₉	#41	1	4	yes	—
217	C₂³×C₈₉	—	2	1	no	—
218	C₂³×C₈₉	—	2	1	no	—
219	C₂³×C₈₉	—	2	2	no	—
220	C₂³×C₈₉	—	2	2	no	—
221	C₂³×C₈₉	—	2	4	no	—
222	C₂³×C₈₉	—	2	4	no	—
223	C₂³×C₈₉	—	2	4	no	—
224	C₂³×C₈₉	—	2	4	no	—
225	C₂³×C₈₉	—	2	4	no	—
226	C₂³×C₈₉	—	2	4	no	—
227	C₂³×C₈₉	—	2	4	no	—
228	C₂³×C₈₉	C₂×#41	1	2	yes	—
229	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
230	Q₈×C₈₉	—	8	4	no	—
231	D₄×C₈₉	—	4	16	no	—
232	D₄×C₈₉	—	4	8	no	—
233	D₄×C₈₉	—	8	4	no	—
234	D₄×C₈₉	—	8	4	no	—
235	C₂×C₄×C₈₉	—	2	1	no	—
236	C₂×C₄×C₈₉	—	2	2	no	—
237	C₂×C₄×C₈₉	—	2	1	no	—
238	C₂×C₄×C₈₉	—	2	2	no	—
239	C₂×C₄×C₈₉	—	2	2	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	8	no	—
244	C₂×C₄×C₈₉	—	2	2	no	—
245	C₂×C₄×C₈₉	—	2	2	no	—
246	C₂×C₄×C₈₉	—	2	1	no	—
247	C₂×C₄×C₈₉	—	2	1	no	—
248	C₂×C₄×C₈₉	—	2	4	no	—
249	C₂×C₄×C₈₉	—	2	4	no	—
250	C₂×C₄×C₈₉	—	2	4	no	—
251	C₂×C₄×C₈₉	—	2	2	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	4	no	—
256	C₂×C₄×C₈₉	—	2	4	no	—
257	C₂×C₄×C₈₉	—	2	4	no	—
258	C₂×C₄×C₈₉	—	2	2	no	—
259	C₂×C₄×C₈₉	—	2	2	no	—
260	C₂×C₄×C₈₉	—	2	2	no	—
261	C₂×C₄×C₈₉	—	2	4	no	—
262	C₂×C₄×C₈₉	—	2	4	no	—
263	C₂×C₄×C₈₉	—	4	8	no	—
264	C₂×C₄×C₈₉	—	8	8	no	—
265	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
266	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
267	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
268	C₂×C₄×C₈₉	C₂×#41	1	2	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	4	yes	—
273	C₂²×C₈₉	—	2	2	no	—
274	C₂²×C₈₉	—	2	4	no	—
275	C₂²×C₈₉	—	4	2	no	—
276	C₂²×C₈₉	—	4	1	no	—
277	C₂²×C₈₉	—	4	1	no	—
278	C₂²×C₈₉	—	4	4	no	—
279	C₂²×C₈₉	—	4	4	no	—
280	C₂²×C₈₉	—	4	4	no	—
281	C₂²×C₈₉	—	4	4	no	—
282	C₂²×C₈₉	—	4	4	no	—
283	C₂²×C₈₉	—	4	4	no	—
284	C₂²×C₈₉	—	4	4	no	—
285	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
286	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
287	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
288	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
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	—	2	2	no	—
295	C₄×C₈₉	—	4	2	no	—
296	C₄×C₈₉	—	4	2	no	—
297	C₄×C₈₉	—	4	4	no	—
298	C₄×C₈₉	—	4	4	no	—
299	C₄×C₈₉	—	4	1	no	—
300	C₄×C₈₉	—	4	4	no	—
301	C₄×C₈₉	—	4	1	no	—
302	C₄×C₈₉	#529	1	4	yes	—
303	#35268	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
304	C₂×C₈₉	—	4	2	no	—
305	C₂×C₈₉	—	8	4	no	—
306	C₂×C₈₉	C₂×#529	1	1	yes	characteristic
307	C₂×C₈₉	#3460	1	2	yes	—
308	C₂×C₈₉	#3494	1	2	yes	—
309	C₂×C₈₉	#3508	1	1	yes	characteristic
310	C₂×C₈₉	#3510	1	1	yes	characteristic
311	#2864	C₂×C₈₉	1	1	yes	characteristic, complemented
312	#2860	C₂×C₈₉	1	2	yes	complemented
313	#2858	C₂×C₈₉	1	1	yes	characteristic, complemented
314	#2628	C₂×C₈₉	1	1	yes	characteristic, complemented
315	#2624	C₂×C₈₉	1	2	yes	complemented
316	#2619	C₂×C₈₉	1	1	yes	characteristic
317	#2521	C₂×C₈₉	1	4	yes	complemented
318	#2516	C₂×C₈₉	1	4	yes	complemented
319	#2467	C₂×C₈₉	1	4	yes	complemented
320	#2459	C₂×C₈₉	1	4	yes	complemented
321	#2331	C₂×C₈₉	1	1	yes	characteristic, complemented
322	#2328	C₂×C₈₉	1	1	yes	characteristic, complemented
323	#2319	C₂×C₈₉	1	2	yes	complemented
324	C₄×#121	C₂×C₈₉	1	2	yes	complemented
325	C₄×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
326	C₈₉	#35268	1	1	yes	characteristic, direct product factor, Sylow
327	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
328	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
329	C₂×#126	C₂²×C₈₉	1	4	yes	—
330	C₂×#124	C₂²×C₈₉	1	4	yes	—
331	C₂×#121	C₂²×C₈₉	1	2	yes	—
332	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
333	C₂×C₄×D₄	C₂²×C₈₉	1	4	yes	—
334	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
335	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
336	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
337	#400	C₂²×C₈₉	1	2	yes	—
338	#399	C₂²×C₈₉	1	4	yes	—
339	#399	C₂²×C₈₉	1	2	yes	—
340	#397	C₂²×C₈₉	1	4	yes	—
341	#395	C₂²×C₈₉	1	2	yes	—
342	#394	C₂²×C₈₉	1	2	yes	—
343	#394	C₂²×C₈₉	1	2	yes	—
344	#394	C₂²×C₈₉	1	4	yes	—
345	#394	C₂²×C₈₉	1	4	yes	—
346	#393	C₂²×C₈₉	1	2	yes	—
347	#392	C₂²×C₈₉	1	2	yes	—
348	#392	C₂²×C₈₉	1	2	yes	—
349	#391	C₂²×C₈₉	1	4	yes	—
350	#390	C₂²×C₈₉	1	2	yes	—
351	#390	C₂²×C₈₉	1	2	yes	—
352	#390	C₂²×C₈₉	1	2	yes	—
353	#390	C₂²×C₈₉	1	2	yes	—
354	#390	C₂²×C₈₉	1	4	yes	—
355	#389	C₂²×C₈₉	1	2	yes	—
356	#389	C₂²×C₈₉	1	2	yes	—
357	#389	C₂²×C₈₉	1	2	yes	—
358	#389	C₂²×C₈₉	1	2	yes	—
359	#388	C₂²×C₈₉	1	4	yes	—
360	#388	C₂²×C₈₉	1	4	yes	—
361	#388	C₂²×C₈₉	1	4	yes	—
362	#388	C₂²×C₈₉	1	4	yes	—
363	#388	C₂²×C₈₉	1	4	yes	—
364	#388	C₂²×C₈₉	1	4	yes	—
365	#387	C₂²×C₈₉	1	4	yes	—
366	#387	C₂²×C₈₉	1	4	yes	—
367	#387	C₂²×C₈₉	1	4	yes	—
368	#386	C₂²×C₈₉	1	4	yes	—
369	#386	C₂²×C₈₉	1	4	yes	—
370	#386	C₂²×C₈₉	1	4	yes	—
371	#382	C₂²×C₈₉	1	1	yes	characteristic
372	#382	C₂²×C₈₉	1	1	yes	characteristic
373	#381	C₂²×C₈₉	1	4	yes	—
374	#380	C₂²×C₈₉	1	4	yes	—
375	#380	C₂²×C₈₉	1	2	yes	—
376	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
377	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
378	C₄×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
379	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
380	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
381	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
382	#376	C₂²×C₈₉	1	1	yes	characteristic
383	#376	C₂²×C₈₉	1	1	yes	characteristic
384	C₄³	C₂²×C₈₉	1	1	yes	characteristic
385	C₄³	C₂²×C₈₉	1	1	yes	characteristic
386	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
387	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
388	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
389	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
390	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
391	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
392	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
393	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
394	C₄⋊Q₈	—	2	4	no	—
395	#127	—	2	4	no	—
396	#126	—	4	8	no	—
397	#124	—	4	8	no	—
398	#121	—	2	8	no	—
399	C₄×D₄	—	2	8	no	—
400	C₄×D₄	—	4	8	no	—
401	#117	—	2	4	no	—
402	#117	—	2	4	no	—
403	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
404	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
405	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
406	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
407	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
408	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
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	4	yes	—
412	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
413	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
414	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
415	C₂×C₂²⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
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	4	yes	—
419	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
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	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×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
427	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
428	C₂×C₄²	—	2	4	no	—
429	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
430	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
431	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
432	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
433	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
434	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
435	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
436	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
437	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
438	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
439	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
441	#95	C₂³×C₈₉	1	2	yes	—
442	#95	C₂³×C₈₉	1	2	yes	—
443	#95	C₂³×C₈₉	1	2	yes	—
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	2	yes	—
451	#95	C₂³×C₈₉	1	2	yes	—
452	#95	C₂³×C₈₉	1	2	yes	—
453	#95	C₂³×C₈₉	1	2	yes	—
454	#95	C₂³×C₈₉	1	4	yes	—
455	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
456	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
457	C₂×Q₈	—	2	4	no	—
458	C₂×Q₈	—	4	4	no	—
459	C₂×D₄	—	2	8	no	—
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	4	no	—
462	C₂×D₄	—	2	4	no	—
463	C₂×D₄	—	2	4	no	—
464	C₂×D₄	—	2	4	no	—
465	C₂×D₄	—	4	4	no	—
466	C₂×D₄	—	4	4	no	—
467	C₂×D₄	—	4	4	no	—
468	C₂×D₄	—	4	4	no	—
469	C₂²×C₄	—	2	2	no	—
470	C₂²×C₄	—	2	2	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	4	no	—
476	C₂²×C₄	—	4	4	no	—
477	C₂²×C₄	#41×C₈₉	1	4	yes	—
478	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
479	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
480	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
481	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
482	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
483	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
484	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
485	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
486	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
487	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
488	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
489	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
490	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	4	no	—
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	8	no	—
499	C₄⋊C₄	—	4	4	no	—
500	C₄⋊C₄	—	4	4	no	—
501	C₄⋊C₄	—	4	4	no	—
502	C₂²⋊C₄	—	2	4	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	8	no	—
506	C₂²⋊C₄	—	2	8	no	—
507	C₂²⋊C₄	—	2	8	no	—
508	C₂²⋊C₄	—	2	8	no	—
509	C₂²⋊C₄	—	4	4	no	—
510	C₂²⋊C₄	—	4	4	no	—
511	C₂²⋊C₄	—	4	4	no	—
512	C₂²⋊C₄	—	4	4	no	—
513	C₂²⋊C₄	—	4	4	no	—
514	C₂²⋊C₄	—	4	4	no	—
515	C₂²⋊C₄	—	4	4	no	—
516	C₄²	—	2	4	no	—
517	C₄²	—	2	2	no	—
518	C₄²	—	2	2	no	—
519	C₄²	—	2	2	no	—
520	C₄²	—	2	2	no	—
521	C₄²	—	2	4	no	—
522	C₄²	—	2	4	no	—
523	C₄²	—	4	4	no	—
524	C₄²	—	4	2	no	—
525	C₄²	—	4	2	no	—
526	C₄²	#41×C₈₉	1	4	yes	—
527	C₄²	#41×C₈₉	1	4	yes	—
528	C₂³	—	2	1	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	2	2	no	—
531	C₂³	—	2	2	no	—
532	C₂³	—	2	4	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	4	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	4	no	—
537	C₂³	—	2	4	no	—
538	C₂³	—	2	4	no	—
539	C₂³	C₂×#41×C₈₉	1	2	yes	—
540	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
541	Q₈	—	8	4	no	—
542	D₄	—	4	16	no	—
543	D₄	—	4	8	no	—
544	D₄	—	8	4	no	—
545	D₄	—	8	4	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	2	no	—
548	C₂×C₄	—	2	1	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	2	no	—
554	C₂×C₄	—	2	8	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	2	2	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	4	no	—
560	C₂×C₄	—	2	4	no	—
561	C₂×C₄	—	2	4	no	—
562	C₂×C₄	—	2	2	no	—
563	C₂×C₄	—	2	2	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	4	no	—
567	C₂×C₄	—	2	4	no	—
568	C₂×C₄	—	2	4	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	4	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	4	8	no	—
575	C₂×C₄	—	8	8	no	—
576	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
577	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
578	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
579	C₂×C₄	C₂×#41×C₈₉	1	2	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	4	yes	—
584	C₂²	—	2	2	no	—
585	C₂²	—	2	4	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	4	no	—
590	C₂²	—	4	4	no	—
591	C₂²	—	4	4	no	—
592	C₂²	—	4	4	no	—
593	C₂²	—	4	4	no	—
594	C₂²	—	4	4	no	—
595	C₂²	—	4	4	no	—
596	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
597	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
598	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
599	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
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	—	2	2	no	—
606	C₄	—	4	4	no	—
607	C₄	—	4	2	no	—
608	C₄	—	4	2	no	—
609	C₄	—	4	4	no	—
610	C₄	—	4	4	no	—
611	C₄	—	4	1	no	—
612	C₄	—	4	1	no	—
613	C₄	#529×C₈₉	1	4	yes	—
614	C₂	—	4	2	no	—
615	C₂	—	8	4	no	—
616	C₂	C₂×#529×C₈₉	1	1	yes	characteristic
617	C₂	C₈₉×#3460	1	2	yes	—
618	C₂	C₈₉×#3494	1	2	yes	—
619	C₂	C₈₉×#3508	1	1	yes	characteristic
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×#2619	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×#2860	C₂	semidirect
3. C₈₉×#2858	C₂	semidirect
4. C₈₉×#2628	C₂	semidirect
5. C₈₉×#2624	C₂	semidirect
7. C₈₉×#2521	C₂	semidirect
8. C₈₉×#2516	C₂	semidirect
9. C₈₉×#2467	C₂	semidirect
10. C₈₉×#2459	C₂	semidirect
11. C₈₉×#2331	C₂	semidirect
12. C₈₉×#2328	C₂	semidirect
13. C₈₉×#2319	C₂	semidirect
14. C₄×#121×C₈₉	C₂	semidirect
15. C₄×#117×C₈₉	C₂	semidirect
303. #35268	C₈₉	direct (N × H)
311. #2864	C₂×C₈₉	semidirect
312. #2860	C₂×C₈₉	semidirect
313. #2858	C₂×C₈₉	semidirect
314. #2628	C₂×C₈₉	semidirect
315. #2624	C₂×C₈₉	semidirect
317. #2521	C₂×C₈₉	semidirect
318. #2516	C₂×C₈₉	semidirect
319. #2467	C₂×C₈₉	semidirect
320. #2459	C₂×C₈₉	semidirect
321. #2331	C₂×C₈₉	semidirect
322. #2328	C₂×C₈₉	semidirect
323. #2319	C₂×C₈₉	semidirect
324. C₄×#121	C₂×C₈₉	semidirect
325. C₄×#117	C₂×C₈₉	semidirect
326. C₈₉	#35268	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×#2860	2
C₈₉×#2858	2
C₈₉×#2628	2
C₈₉×#2624	2
C₈₉×#2619	2
C₈₉×#2521	2
C₈₉×#2516	2
C₈₉×#2467	2
C₈₉×#2459	2
C₈₉×#2331	2
C₈₉×#2328	2
C₈₉×#2319	2
C₄×#121×C₈₉	2
C₄×#117×C₈₉	2
#35268	89

Subgroups — C89×#35268 #36413116

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35268 #36413116