Subgroups — C₈₉×#35454 #36413302

Order 22784.

2402 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#126×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#520×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2534	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2487	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2484	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#2482	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈₉×#2481	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2479	C₂	1	4	yes	maximal, complemented
9	C₈₉×#2469	C₂	1	4	yes	maximal, complemented
10	C₈₉×#2467	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2406	C₂	1	1	yes	maximal, characteristic, complemented
12	C₈₉×#2404	C₂	1	1	yes	maximal, characteristic
13	C₈₉×#2321	C₂	1	2	yes	maximal, complemented
14	C₈₉×#2313	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×#123×C₈₉	C₂	1	2	yes	maximal, complemented
16	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
17	C₂×#126×C₈₉	—	2	8	no	—
18	C₂×#126×C₈₉	C₂²	1	4	yes	—
19	C₂×#126×C₈₉	C₂²	1	4	yes	—
20	C₂×#123×C₈₉	C₂²	1	2	yes	—
21	C₂×#120×C₈₉	C₂²	1	2	yes	—
22	#520×C₈₉	—	2	8	no	—
23	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	complemented
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	complemented
27	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
28	C₂×#117×C₈₉	C₂²	1	2	yes	complemented
29	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
30	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
31	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
32	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	complemented
33	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
34	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
35	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
36	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
37	#400×C₈₉	C₂²	1	4	yes	complemented
38	#400×C₈₉	C₂²	1	2	yes	complemented
39	#399×C₈₉	C₂²	1	2	yes	—
40	#399×C₈₉	C₂²	1	4	yes	complemented
41	#398×C₈₉	C₂²	1	2	yes	complemented
42	#397×C₈₉	C₂²	1	2	yes	—
43	#396×C₈₉	C₂²	1	4	yes	—
44	#395×C₈₉	C₂²	1	2	yes	complemented
45	#394×C₈₉	C₂²	1	4	yes	—
46	#394×C₈₉	C₂²	1	2	yes	complemented
47	#393×C₈₉	C₂²	1	2	yes	—
48	#392×C₈₉	C₂²	1	2	yes	—
49	#390×C₈₉	C₂²	1	4	yes	—
50	#389×C₈₉	C₂²	1	4	yes	complemented
51	#388×C₈₉	C₂²	1	4	yes	—
52	#388×C₈₉	C₂²	1	4	yes	—
53	#388×C₈₉	C₂²	1	4	yes	—
54	#388×C₈₉	C₂²	1	4	yes	—
55	#388×C₈₉	C₂²	1	4	yes	complemented
56	#387×C₈₉	C₂²	1	4	yes	complemented
57	#387×C₈₉	C₂²	1	4	yes	complemented
58	#387×C₈₉	C₂²	1	4	yes	complemented
59	#387×C₈₉	C₂²	1	4	yes	complemented
60	#386×C₈₉	C₂²	1	2	yes	—
61	#386×C₈₉	C₂²	1	2	yes	—
62	#386×C₈₉	C₂²	1	4	yes	—
63	#386×C₈₉	C₂²	1	4	yes	—
64	#386×C₈₉	C₂²	1	4	yes	—
65	#385×C₈₉	C₂²	1	2	yes	—
66	#385×C₈₉	C₂²	1	2	yes	—
67	#385×C₈₉	C₂²	1	4	yes	complemented
68	#381×C₈₉	C₂²	1	2	yes	—
69	#381×C₈₉	C₂²	1	1	yes	characteristic
70	#381×C₈₉	C₂²	1	1	yes	characteristic
71	#380×C₈₉	C₂²	1	2	yes	—
72	#380×C₈₉	C₂²	1	4	yes	complemented
73	#379×C₈₉	C₂²	1	2	yes	—
74	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	complemented
75	C₄×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
76	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	complemented
77	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×#41×C₈₉	—	2	8	no	—
79	C₂×#41×C₈₉	—	2	4	no	—
80	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
81	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
82	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
83	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
84	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
86	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
87	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
88	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
89	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
90	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
91	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
92	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
93	#126×C₈₉	—	2	16	no	—
94	#126×C₈₉	—	2	16	no	—
95	#123×C₈₉	—	2	8	no	—
96	#120×C₈₉	—	2	8	no	—
97	C₄×Q₈×C₈₉	—	2	8	no	—
98	C₄×D₄×C₈₉	—	2	8	no	—
99	C₄×D₄×C₈₉	—	2	8	no	—
100	C₄×D₄×C₈₉	—	2	8	no	—
101	#117×C₈₉	—	2	4	no	—
102	#117×C₈₉	—	2	8	no	—
103	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
104	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
105	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
106	C₂×C₄⋊C₄×C₈₉	D₄	1	8	yes	complemented
107	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
108	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	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	1	yes	characteristic
114	C₂×C₄⋊C₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
116	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
117	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
118	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
119	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
121	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
122	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
123	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
125	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
126	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
127	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
128	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
129	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
130	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
131	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
132	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
133	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
134	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
135	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
136	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
137	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
138	C₂×C₄²×C₈₉	—	2	4	no	—
139	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
140	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
141	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
142	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
143	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
144	#95×C₈₉	C₂³	1	4	yes	—
145	#95×C₈₉	C₂³	1	4	yes	—
146	#95×C₈₉	C₂³	1	4	yes	—
147	#95×C₈₉	C₂³	1	4	yes	—
148	#95×C₈₉	C₂³	1	4	yes	—
149	#95×C₈₉	C₂³	1	4	yes	—
150	#95×C₈₉	C₂³	1	4	yes	—
151	#95×C₈₉	C₂³	1	2	yes	—
152	#95×C₈₉	C₂³	1	2	yes	—
153	#95×C₈₉	C₂³	1	2	yes	—
154	#95×C₈₉	C₂³	1	2	yes	—
155	#95×C₈₉	C₂³	1	4	yes	—
156	C₂⁴×C₈₉	—	2	2	no	—
157	C₂⁴×C₈₉	—	2	4	no	—
158	C₂⁴×C₈₉	—	4	2	no	—
159	C₂⁴×C₈₉	—	4	2	no	—
160	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
161	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
162	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
163	#41×C₈₉	—	2	32	no	—
164	C₂×Q₈×C₈₉	—	2	2	no	—
165	C₂×Q₈×C₈₉	—	2	4	no	—
166	C₂×D₄×C₈₉	—	2	4	no	—
167	C₂×D₄×C₈₉	—	2	4	no	—
168	C₂×D₄×C₈₉	—	2	4	no	—
169	C₂×D₄×C₈₉	—	2	8	no	—
170	C₂×D₄×C₈₉	—	2	2	no	—
171	C₂×D₄×C₈₉	—	4	4	no	—
172	C₂×D₄×C₈₉	—	4	4	no	—
173	C₂×D₄×C₈₉	#41	1	8	yes	—
174	C₂²×C₄×C₈₉	—	2	4	no	—
175	C₂²×C₄×C₈₉	—	2	4	no	—
176	C₂²×C₄×C₈₉	—	2	4	no	—
177	C₂²×C₄×C₈₉	—	2	4	no	—
178	C₂²×C₄×C₈₉	—	2	2	no	—
179	C₂²×C₄×C₈₉	—	2	2	no	—
180	C₂²×C₄×C₈₉	—	2	2	no	—
181	C₂²×C₄×C₈₉	—	2	4	no	—
182	C₂²×C₄×C₈₉	—	2	4	no	—
183	C₂²×C₄×C₈₉	—	2	4	no	—
184	C₂²×C₄×C₈₉	—	4	2	no	—
185	C₂²×C₄×C₈₉	—	4	2	no	—
186	C₂²×C₄×C₈₉	—	4	2	no	—
187	C₂²×C₄×C₈₉	—	4	2	no	—
188	C₂²×C₄×C₈₉	—	4	4	no	—
189	C₂²×C₄×C₈₉	—	4	4	no	—
190	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
191	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
192	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
193	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
194	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
195	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
196	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
197	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
198	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
199	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
200	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
201	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
202	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
203	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
204	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
205	C₄⋊C₄×C₈₉	—	2	2	no	—
206	C₄⋊C₄×C₈₉	—	2	4	no	—
207	C₄⋊C₄×C₈₉	—	2	4	no	—
208	C₄⋊C₄×C₈₉	—	2	4	no	—
209	C₄⋊C₄×C₈₉	—	2	8	no	—
210	C₄⋊C₄×C₈₉	—	2	4	no	—
211	C₄⋊C₄×C₈₉	—	2	2	no	—
212	C₄⋊C₄×C₈₉	—	2	8	no	—
213	C₄⋊C₄×C₈₉	—	4	4	no	—
214	C₄⋊C₄×C₈₉	—	4	4	no	—
215	C₄⋊C₄×C₈₉	—	4	4	no	—
216	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
217	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
218	C₂²⋊C₄×C₈₉	—	2	4	no	—
219	C₂²⋊C₄×C₈₉	—	2	4	no	—
220	C₂²⋊C₄×C₈₉	—	2	4	no	—
221	C₂²⋊C₄×C₈₉	—	2	8	no	—
222	C₂²⋊C₄×C₈₉	—	2	4	no	—
223	C₂²⋊C₄×C₈₉	—	2	8	no	—
224	C₂²⋊C₄×C₈₉	—	2	4	no	—
225	C₂²⋊C₄×C₈₉	—	2	8	no	—
226	C₂²⋊C₄×C₈₉	—	2	4	no	—
227	C₂²⋊C₄×C₈₉	—	2	4	no	—
228	C₂²⋊C₄×C₈₉	—	2	8	no	—
229	C₂²⋊C₄×C₈₉	—	4	4	no	—
230	C₂²⋊C₄×C₈₉	—	4	4	no	—
231	C₂²⋊C₄×C₈₉	—	4	4	no	—
232	C₂²⋊C₄×C₈₉	—	4	4	no	—
233	C₄²×C₈₉	—	2	8	no	—
234	C₄²×C₈₉	—	2	4	no	—
235	C₄²×C₈₉	—	2	4	no	—
236	C₄²×C₈₉	—	2	4	no	—
237	C₄²×C₈₉	—	4	4	no	—
238	C₂³×C₈₉	—	2	2	no	—
239	C₂³×C₈₉	—	2	2	no	—
240	C₂³×C₈₉	—	2	2	no	—
241	C₂³×C₈₉	—	2	2	no	—
242	C₂³×C₈₉	—	2	4	no	—
243	C₂³×C₈₉	—	2	4	no	—
244	C₂³×C₈₉	—	2	2	no	—
245	C₂³×C₈₉	—	2	4	no	—
246	C₂³×C₈₉	—	2	2	no	—
247	C₂³×C₈₉	—	2	4	no	—
248	C₂³×C₈₉	—	2	2	no	—
249	C₂³×C₈₉	—	4	4	no	—
250	C₂³×C₈₉	—	4	4	no	—
251	C₂³×C₈₉	—	4	4	no	—
252	C₂³×C₈₉	—	8	8	no	—
253	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
254	C₂³×C₈₉	C₂×#41	1	4	yes	—
255	C₂³×C₈₉	C₂×#41	1	4	yes	—
256	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
257	Q₈×C₈₉	—	2	8	no	—
258	D₄×C₈₉	—	2	8	no	—
259	D₄×C₈₉	—	2	16	no	—
260	D₄×C₈₉	—	8	8	no	—
261	C₂×C₄×C₈₉	—	2	16	no	—
262	C₂×C₄×C₈₉	—	2	8	no	—
263	C₂×C₄×C₈₉	—	2	2	no	—
264	C₂×C₄×C₈₉	—	2	2	no	—
265	C₂×C₄×C₈₉	—	2	2	no	—
266	C₂×C₄×C₈₉	—	2	2	no	—
267	C₂×C₄×C₈₉	—	2	4	no	—
268	C₂×C₄×C₈₉	—	2	4	no	—
269	C₂×C₄×C₈₉	—	2	2	no	—
270	C₂×C₄×C₈₉	—	2	2	no	—
271	C₂×C₄×C₈₉	—	2	2	no	—
272	C₂×C₄×C₈₉	—	2	2	no	—
273	C₂×C₄×C₈₉	—	2	2	no	—
274	C₂×C₄×C₈₉	—	2	4	no	—
275	C₂×C₄×C₈₉	—	2	4	no	—
276	C₂×C₄×C₈₉	—	2	4	no	—
277	C₂×C₄×C₈₉	—	2	4	no	—
278	C₂×C₄×C₈₉	—	2	4	no	—
279	C₂×C₄×C₈₉	—	2	4	no	—
280	C₂×C₄×C₈₉	—	2	2	no	—
281	C₂×C₄×C₈₉	—	2	4	no	—
282	C₂×C₄×C₈₉	—	2	4	no	—
283	C₂×C₄×C₈₉	—	2	4	no	—
284	C₂×C₄×C₈₉	—	2	4	no	—
285	C₂×C₄×C₈₉	—	2	2	no	—
286	C₂×C₄×C₈₉	—	4	4	no	—
287	C₂×C₄×C₈₉	—	4	4	no	—
288	C₂×C₄×C₈₉	—	4	4	no	—
289	C₂×C₄×C₈₉	—	4	4	no	—
290	C₂×C₄×C₈₉	—	4	4	no	—
291	C₂×C₄×C₈₉	—	8	4	no	—
292	C₂×C₄×C₈₉	—	8	4	no	—
293	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
294	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
296	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
297	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
298	C₂²×C₈₉	—	2	2	no	—
299	C₂²×C₈₉	—	2	2	no	—
300	C₂²×C₈₉	—	2	8	no	—
301	C₂²×C₈₉	—	2	4	no	—
302	C₂²×C₈₉	—	2	8	no	—
303	C₂²×C₈₉	—	4	2	no	—
304	C₂²×C₈₉	—	4	2	no	—
305	C₂²×C₈₉	—	4	4	no	—
306	C₂²×C₈₉	—	4	2	no	—
307	C₂²×C₈₉	—	4	2	no	—
308	C₂²×C₈₉	—	4	2	no	—
309	C₂²×C₈₉	—	4	4	no	—
310	C₂²×C₈₉	—	4	4	no	—
311	C₂²×C₈₉	—	8	8	no	—
312	C₂²×C₈₉	#525	1	4	yes	—
313	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
314	C₂²×C₈₉	C₂²×#41	1	2	yes	—
315	C₂²×C₈₉	#585	1	2	yes	—
316	C₂²×C₈₉	#585	1	2	yes	—
317	C₄×C₈₉	—	2	2	no	—
318	C₄×C₈₉	—	2	2	no	—
319	C₄×C₈₉	—	2	4	no	—
320	C₄×C₈₉	—	2	4	no	—
321	C₄×C₈₉	—	2	4	no	—
322	C₄×C₈₉	—	4	2	no	—
323	C₄×C₈₉	—	4	2	no	—
324	C₄×C₈₉	—	4	2	no	—
325	C₄×C₈₉	—	4	2	no	—
326	C₄×C₈₉	—	4	2	no	—
327	C₄×C₈₉	—	4	4	no	—
328	C₄×C₈₉	—	4	4	no	—
329	#35454	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
330	C₂×C₈₉	—	2	4	no	—
331	C₂×C₈₉	—	4	4	no	—
332	C₂×C₈₉	—	8	2	no	—
333	C₂×C₈₉	C₂×#525	1	1	yes	characteristic
334	C₂×C₈₉	#3485	1	1	yes	characteristic
335	C₂×C₈₉	#3487	1	1	yes	characteristic
336	C₂×C₈₉	#3521	1	4	yes	—
337	C₂²×#126	C₂×C₈₉	1	1	yes	characteristic, complemented
338	C₂×#520	C₂×C₈₉	1	1	yes	characteristic, complemented
339	#2534	C₂×C₈₉	1	2	yes	complemented
340	#2487	C₂×C₈₉	1	2	yes	complemented
341	#2484	C₂×C₈₉	1	1	yes	characteristic, complemented
342	#2482	C₂×C₈₉	1	1	yes	characteristic, complemented
343	#2481	C₂×C₈₉	1	4	yes	complemented
344	#2479	C₂×C₈₉	1	4	yes	complemented
345	#2469	C₂×C₈₉	1	4	yes	complemented
346	#2467	C₂×C₈₉	1	4	yes	complemented
347	#2406	C₂×C₈₉	1	1	yes	characteristic, complemented
348	#2404	C₂×C₈₉	1	1	yes	characteristic
349	#2321	C₂×C₈₉	1	2	yes	complemented
350	#2313	C₂×C₈₉	1	1	yes	characteristic, complemented
351	C₄×#123	C₂×C₈₉	1	2	yes	complemented
352	C₈₉	#35454	1	1	yes	characteristic, direct product factor, Sylow
353	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
354	C₂×#126	—	2	8	no	—
355	C₂×#126	C₂²×C₈₉	1	4	yes	—
356	C₂×#126	C₂²×C₈₉	1	4	yes	—
357	C₂×#123	C₂²×C₈₉	1	2	yes	—
358	C₂×#120	C₂²×C₈₉	1	2	yes	—
359	#520	—	2	8	no	—
360	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	complemented
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	2	yes	complemented
364	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
365	C₂×#117	C₂²×C₈₉	1	2	yes	complemented
366	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
367	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
368	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
369	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	complemented
370	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
371	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
372	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
373	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
374	#400	C₂²×C₈₉	1	4	yes	complemented
375	#400	C₂²×C₈₉	1	2	yes	complemented
376	#399	C₂²×C₈₉	1	2	yes	—
377	#399	C₂²×C₈₉	1	4	yes	complemented
378	#398	C₂²×C₈₉	1	2	yes	complemented
379	#397	C₂²×C₈₉	1	2	yes	—
380	#396	C₂²×C₈₉	1	4	yes	—
381	#395	C₂²×C₈₉	1	2	yes	complemented
382	#394	C₂²×C₈₉	1	4	yes	—
383	#394	C₂²×C₈₉	1	2	yes	complemented
384	#393	C₂²×C₈₉	1	2	yes	—
385	#392	C₂²×C₈₉	1	2	yes	—
386	#390	C₂²×C₈₉	1	4	yes	—
387	#389	C₂²×C₈₉	1	4	yes	complemented
388	#388	C₂²×C₈₉	1	4	yes	—
389	#388	C₂²×C₈₉	1	4	yes	—
390	#388	C₂²×C₈₉	1	4	yes	—
391	#388	C₂²×C₈₉	1	4	yes	—
392	#388	C₂²×C₈₉	1	4	yes	complemented
393	#387	C₂²×C₈₉	1	4	yes	complemented
394	#387	C₂²×C₈₉	1	4	yes	complemented
395	#387	C₂²×C₈₉	1	4	yes	complemented
396	#387	C₂²×C₈₉	1	4	yes	complemented
397	#386	C₂²×C₈₉	1	2	yes	—
398	#386	C₂²×C₈₉	1	4	yes	—
399	#386	C₂²×C₈₉	1	4	yes	—
400	#386	C₂²×C₈₉	1	2	yes	—
401	#386	C₂²×C₈₉	1	4	yes	—
402	#385	C₂²×C₈₉	1	2	yes	—
403	#385	C₂²×C₈₉	1	2	yes	—
404	#385	C₂²×C₈₉	1	4	yes	complemented
405	#381	C₂²×C₈₉	1	1	yes	characteristic
406	#381	C₂²×C₈₉	1	1	yes	characteristic
407	#381	C₂²×C₈₉	1	2	yes	—
408	#380	C₂²×C₈₉	1	2	yes	—
409	#380	C₂²×C₈₉	1	4	yes	complemented
410	#379	C₂²×C₈₉	1	2	yes	—
411	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	complemented
412	C₄×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
413	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	complemented
414	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
415	C₂×#41	—	2	8	no	—
416	C₂×#41	—	2	4	no	—
417	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
418	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
419	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
420	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
421	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
422	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
423	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
424	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
425	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
426	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
427	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
428	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
429	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
430	#126	—	2	16	no	—
431	#126	—	2	16	no	—
432	#123	—	2	8	no	—
433	#120	—	2	8	no	—
434	C₄×Q₈	—	2	8	no	—
435	C₄×D₄	—	2	8	no	—
436	C₄×D₄	—	2	8	no	—
437	C₄×D₄	—	2	8	no	—
438	#117	—	2	4	no	—
439	#117	—	2	8	no	—
440	C₂×C₄⋊C₄	—	2	4	no	—
441	C₂×C₄⋊C₄	—	2	4	no	—
442	C₂×C₄⋊C₄	—	2	8	no	—
443	C₂×C₄⋊C₄	D₄×C₈₉	1	8	yes	complemented
444	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
445	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
446	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
447	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
449	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
450	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
451	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
452	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
453	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
454	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
455	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
456	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
457	C₂×C₂²⋊C₄	—	2	4	no	—
458	C₂×C₂²⋊C₄	—	2	4	no	—
459	C₂×C₂²⋊C₄	—	2	4	no	—
460	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
461	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
462	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
463	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
464	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
469	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
471	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
472	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
473	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
474	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
475	C₂×C₄²	—	2	4	no	—
476	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
477	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
478	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
479	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
480	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
481	#95	C₂³×C₈₉	1	4	yes	—
482	#95	C₂³×C₈₉	1	4	yes	—
483	#95	C₂³×C₈₉	1	4	yes	—
484	#95	C₂³×C₈₉	1	4	yes	—
485	#95	C₂³×C₈₉	1	4	yes	—
486	#95	C₂³×C₈₉	1	4	yes	—
487	#95	C₂³×C₈₉	1	4	yes	—
488	#95	C₂³×C₈₉	1	2	yes	—
489	#95	C₂³×C₈₉	1	2	yes	—
490	#95	C₂³×C₈₉	1	2	yes	—
491	#95	C₂³×C₈₉	1	2	yes	—
492	#95	C₂³×C₈₉	1	4	yes	—
493	C₂⁴	—	2	2	no	—
494	C₂⁴	—	2	4	no	—
495	C₂⁴	—	4	2	no	—
496	C₂⁴	—	4	2	no	—
497	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
498	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
499	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
500	#41	—	2	32	no	—
501	C₂×Q₈	—	2	2	no	—
502	C₂×Q₈	—	2	4	no	—
503	C₂×D₄	—	2	4	no	—
504	C₂×D₄	—	2	4	no	—
505	C₂×D₄	—	2	4	no	—
506	C₂×D₄	—	2	8	no	—
507	C₂×D₄	—	2	2	no	—
508	C₂×D₄	—	4	4	no	—
509	C₂×D₄	—	4	4	no	—
510	C₂×D₄	#41×C₈₉	1	8	yes	—
511	C₂²×C₄	—	2	4	no	—
512	C₂²×C₄	—	2	4	no	—
513	C₂²×C₄	—	2	4	no	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	2	2	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	2	4	no	—
519	C₂²×C₄	—	2	4	no	—
520	C₂²×C₄	—	2	4	no	—
521	C₂²×C₄	—	4	2	no	—
522	C₂²×C₄	—	4	2	no	—
523	C₂²×C₄	—	4	2	no	—
524	C₂²×C₄	—	4	2	no	—
525	C₂²×C₄	—	4	4	no	—
526	C₂²×C₄	—	4	4	no	—
527	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
528	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
529	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
530	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
531	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
532	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
533	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
534	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
535	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
536	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
537	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
538	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
539	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
540	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
541	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
542	C₄⋊C₄	—	2	2	no	—
543	C₄⋊C₄	—	2	4	no	—
544	C₄⋊C₄	—	2	4	no	—
545	C₄⋊C₄	—	2	4	no	—
546	C₄⋊C₄	—	2	8	no	—
547	C₄⋊C₄	—	2	4	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	8	no	—
550	C₄⋊C₄	—	4	4	no	—
551	C₄⋊C₄	—	4	4	no	—
552	C₄⋊C₄	—	4	4	no	—
553	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
554	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
555	C₂²⋊C₄	—	2	4	no	—
556	C₂²⋊C₄	—	2	4	no	—
557	C₂²⋊C₄	—	2	4	no	—
558	C₂²⋊C₄	—	2	8	no	—
559	C₂²⋊C₄	—	2	4	no	—
560	C₂²⋊C₄	—	2	8	no	—
561	C₂²⋊C₄	—	2	4	no	—
562	C₂²⋊C₄	—	2	8	no	—
563	C₂²⋊C₄	—	2	4	no	—
564	C₂²⋊C₄	—	2	4	no	—
565	C₂²⋊C₄	—	2	8	no	—
566	C₂²⋊C₄	—	4	4	no	—
567	C₂²⋊C₄	—	4	4	no	—
568	C₂²⋊C₄	—	4	4	no	—
569	C₂²⋊C₄	—	4	4	no	—
570	C₄²	—	2	8	no	—
571	C₄²	—	2	4	no	—
572	C₄²	—	2	4	no	—
573	C₄²	—	2	4	no	—
574	C₄²	—	4	4	no	—
575	C₂³	—	2	2	no	—
576	C₂³	—	2	2	no	—
577	C₂³	—	2	2	no	—
578	C₂³	—	2	2	no	—
579	C₂³	—	2	4	no	—
580	C₂³	—	2	4	no	—
581	C₂³	—	2	2	no	—
582	C₂³	—	2	4	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	4	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	4	4	no	—
587	C₂³	—	4	4	no	—
588	C₂³	—	4	4	no	—
589	C₂³	—	8	8	no	—
590	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
591	C₂³	C₂×#41×C₈₉	1	4	yes	—
592	C₂³	C₂×#41×C₈₉	1	4	yes	—
593	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
594	Q₈	—	2	8	no	—
595	D₄	—	2	8	no	—
596	D₄	—	2	16	no	—
597	D₄	—	8	8	no	—
598	C₂×C₄	—	2	16	no	—
599	C₂×C₄	—	2	8	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	4	no	—
605	C₂×C₄	—	2	4	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	4	no	—
612	C₂×C₄	—	2	4	no	—
613	C₂×C₄	—	2	4	no	—
614	C₂×C₄	—	2	4	no	—
615	C₂×C₄	—	2	4	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	4	no	—
621	C₂×C₄	—	2	4	no	—
622	C₂×C₄	—	2	2	no	—
623	C₂×C₄	—	4	4	no	—
624	C₂×C₄	—	4	4	no	—
625	C₂×C₄	—	4	4	no	—
626	C₂×C₄	—	4	4	no	—
627	C₂×C₄	—	4	4	no	—
628	C₂×C₄	—	8	4	no	—
629	C₂×C₄	—	8	4	no	—
630	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
631	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
632	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
633	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
634	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	2	no	—
637	C₂²	—	2	8	no	—
638	C₂²	—	2	4	no	—
639	C₂²	—	2	8	no	—
640	C₂²	—	4	2	no	—
641	C₂²	—	4	2	no	—
642	C₂²	—	4	4	no	—
643	C₂²	—	4	2	no	—
644	C₂²	—	4	2	no	—
645	C₂²	—	4	2	no	—
646	C₂²	—	4	4	no	—
647	C₂²	—	4	4	no	—
648	C₂²	—	8	8	no	—
649	C₂²	#525×C₈₉	1	4	yes	—
650	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
651	C₂²	C₂²×#41×C₈₉	1	2	yes	—
652	C₂²	#585×C₈₉	1	2	yes	—
653	C₂²	#585×C₈₉	1	2	yes	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	4	no	—
657	C₄	—	2	4	no	—
658	C₄	—	2	4	no	—
659	C₄	—	4	2	no	—
660	C₄	—	4	2	no	—
661	C₄	—	4	2	no	—
662	C₄	—	4	2	no	—
663	C₄	—	4	2	no	—
664	C₄	—	4	4	no	—
665	C₄	—	4	4	no	—
666	C₂	—	2	4	no	—
667	C₂	—	4	4	no	—
668	C₂	—	8	2	no	—
669	C₂	C₂×#525×C₈₉	1	1	yes	characteristic
670	C₂	C₈₉×#3485	1	1	yes	characteristic
671	C₂	C₈₉×#3487	1	1	yes	characteristic
672	C₂	C₈₉×#3521	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₈₉×#2404	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. C₂²×#126×C₈₉	C₂	semidirect
2. C₂×#520×C₈₉	C₂	semidirect
3. C₈₉×#2534	C₂	semidirect
4. C₈₉×#2487	C₂	semidirect
5. C₈₉×#2484	C₂	semidirect
6. C₈₉×#2482	C₂	semidirect
7. C₈₉×#2481	C₂	semidirect
8. C₈₉×#2479	C₂	semidirect
9. C₈₉×#2469	C₂	semidirect
10. C₈₉×#2467	C₂	semidirect
11. C₈₉×#2406	C₂	semidirect
13. C₈₉×#2321	C₂	semidirect
14. C₈₉×#2313	C₂	semidirect
15. C₄×#123×C₈₉	C₂	semidirect
23. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
26. C₂×C₄×D₄×C₈₉	C₂²	semidirect
28. C₂×#117×C₈₉	C₂²	semidirect
32. C₂²×C₄⋊C₄×C₈₉	C₂²	semidirect
37. #400×C₈₉	C₂²	semidirect
38. #400×C₈₉	C₂²	semidirect
40. #399×C₈₉	C₂²	semidirect
41. #398×C₈₉	C₂²	semidirect
44. #395×C₈₉	C₂²	semidirect
46. #394×C₈₉	C₂²	semidirect
50. #389×C₈₉	C₂²	semidirect
55. #388×C₈₉	C₂²	semidirect
56. #387×C₈₉	C₂²	semidirect
57. #387×C₈₉	C₂²	semidirect
58. #387×C₈₉	C₂²	semidirect
59. #387×C₈₉	C₂²	semidirect
67. #385×C₈₉	C₂²	semidirect
72. #380×C₈₉	C₂²	semidirect
74. C₄×C₄⋊C₄×C₈₉	C₂²	semidirect
76. C₄×C₂²⋊C₄×C₈₉	C₂²	semidirect
106. C₂×C₄⋊C₄×C₈₉	D₄	semidirect
329. #35454	C₈₉	direct (N × H)
337. C₂²×#126	C₂×C₈₉	semidirect
338. C₂×#520	C₂×C₈₉	semidirect
339. #2534	C₂×C₈₉	semidirect
340. #2487	C₂×C₈₉	semidirect
341. #2484	C₂×C₈₉	semidirect
342. #2482	C₂×C₈₉	semidirect
343. #2481	C₂×C₈₉	semidirect
344. #2479	C₂×C₈₉	semidirect
345. #2469	C₂×C₈₉	semidirect
346. #2467	C₂×C₈₉	semidirect
347. #2406	C₂×C₈₉	semidirect
349. #2321	C₂×C₈₉	semidirect
350. #2313	C₂×C₈₉	semidirect
351. C₄×#123	C₂×C₈₉	semidirect
352. C₈₉	#35454	direct (N × H)
360. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
363. C₂×C₄×D₄	C₂²×C₈₉	semidirect
365. C₂×#117	C₂²×C₈₉	semidirect
369. C₂²×C₄⋊C₄	C₂²×C₈₉	semidirect
374. #400	C₂²×C₈₉	semidirect
375. #400	C₂²×C₈₉	semidirect
377. #399	C₂²×C₈₉	semidirect
378. #398	C₂²×C₈₉	semidirect
381. #395	C₂²×C₈₉	semidirect
383. #394	C₂²×C₈₉	semidirect
387. #389	C₂²×C₈₉	semidirect
392. #388	C₂²×C₈₉	semidirect
393. #387	C₂²×C₈₉	semidirect
394. #387	C₂²×C₈₉	semidirect
395. #387	C₂²×C₈₉	semidirect
396. #387	C₂²×C₈₉	semidirect
404. #385	C₂²×C₈₉	semidirect
409. #380	C₂²×C₈₉	semidirect
411. C₄×C₄⋊C₄	C₂²×C₈₉	semidirect
413. C₄×C₂²⋊C₄	C₂²×C₈₉	semidirect
443. C₂×C₄⋊C₄	D₄×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#126×C₈₉	2
C₂×#520×C₈₉	2
C₈₉×#2534	2
C₈₉×#2487	2
C₈₉×#2484	2
C₈₉×#2482	2
C₈₉×#2481	2
C₈₉×#2479	2
C₈₉×#2469	2
C₈₉×#2467	2
C₈₉×#2406	2
C₈₉×#2404	2
C₈₉×#2321	2
C₈₉×#2313	2
C₄×#123×C₈₉	2
#35454	89

Subgroups — C89×#35454 #36413302

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35454 #36413302