Subgroups — C₈₉×#35263 #36413111

Order 22784.

2626 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#525×C₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂²×#117×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2855	C₂	1	2	yes	maximal, complemented
4	C₈₉×#2854	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2625	C₂	1	2	yes	maximal, complemented
6	C₈₉×#2624	C₂	1	2	yes	maximal, complemented
7	C₈₉×#2498	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2487	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2486	C₂	1	2	yes	maximal, complemented
10	C₈₉×#2485	C₂	1	4	yes	maximal, complemented
11	C₈₉×#2412	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2316	C₂	1	2	yes	maximal, complemented
13	C₈₉×#2311	C₂	1	2	yes	maximal, complemented
14	C₂×#380×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₈₉	C₂²	1	1	yes	characteristic
17	#525×C₈₉	—	2	8	no	—
18	C₂×#123×C₈₉	C₂²	1	2	yes	—
19	C₂×#123×C₈₉	C₂²	1	4	yes	—
20	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
22	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
23	C₂×#121×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×#120×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×#117×C₈₉	—	2	8	no	—
28	C₂×#117×C₈₉	C₂²	1	2	yes	—
29	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
30	C₂×#117×C₈₉	C₂²	1	2	yes	—
31	C₂×#117×C₈₉	C₂²	1	2	yes	—
32	C₂×#117×C₈₉	C₂²	1	2	yes	—
33	C₂²×C₄⋊C₄×C₈₉	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
35	C₂²×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
36	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
37	C₂²×C₂²⋊C₄×C₈₉	C₂²	1	2	yes	—
38	C₂²×C₄²×C₈₉	C₂²	1	2	yes	—
39	#400×C₈₉	C₂²	1	4	yes	complemented
40	#399×C₈₉	C₂²	1	4	yes	complemented
41	#398×C₈₉	C₂²	1	4	yes	complemented
42	#397×C₈₉	C₂²	1	8	yes	—
43	#397×C₈₉	C₂²	1	4	yes	complemented
44	#394×C₈₉	C₂²	1	8	yes	—
45	#391×C₈₉	C₂²	1	4	yes	complemented
46	#390×C₈₉	C₂²	1	4	yes	complemented
47	#389×C₈₉	C₂²	1	4	yes	complemented
48	#389×C₈₉	C₂²	1	4	yes	complemented
49	#389×C₈₉	C₂²	1	4	yes	complemented
50	#389×C₈₉	C₂²	1	4	yes	complemented
51	#388×C₈₉	C₂²	1	8	yes	complemented
52	#387×C₈₉	C₂²	1	8	yes	complemented
53	#386×C₈₉	C₂²	1	8	yes	—
54	#386×C₈₉	C₂²	1	4	yes	—
55	#385×C₈₉	C₂²	1	4	yes	—
56	#381×C₈₉	C₂²	1	4	yes	—
57	#380×C₈₉	C₂²	1	8	yes	—
58	#380×C₈₉	C₂²	1	2	yes	—
59	#380×C₈₉	C₂²	1	2	yes	—
60	#380×C₈₉	C₂²	1	2	yes	—
61	#380×C₈₉	C₂²	1	2	yes	—
62	#380×C₈₉	C₂²	1	4	yes	complemented
63	#380×C₈₉	C₂²	1	4	yes	complemented
64	C₂×#95×C₈₉	C₂²	1	2	yes	—
65	C₂⁵×C₈₉	C₂³	1	1	yes	characteristic
66	C₂×#41×C₈₉	—	2	4	no	—
67	C₂×#41×C₈₉	—	2	8	no	—
68	C₂²×Q₈×C₈₉	C₂³	1	1	yes	characteristic
69	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
70	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
71	C₂²×D₄×C₈₉	C₂³	1	1	yes	characteristic
72	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
73	C₂³×C₄×C₈₉	—	2	8	no	—
74	C₂³×C₄×C₈₉	D₄	1	8	yes	—
75	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
78	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
80	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
81	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
82	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
83	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
84	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
85	#123×C₈₉	—	2	8	no	—
86	#123×C₈₉	—	4	8	no	—
87	C₂²⋊Q₈×C₈₉	—	2	4	no	—
88	C₂²⋊Q₈×C₈₉	—	2	4	no	—
89	#121×C₈₉	—	2	4	no	—
90	#121×C₈₉	—	2	4	no	—
91	#120×C₈₉	—	2	8	no	—
92	C₄×D₄×C₈₉	—	2	8	no	—
93	C₄×D₄×C₈₉	—	2	8	no	—
94	#117×C₈₉	—	2	8	no	—
95	#117×C₈₉	—	2	8	no	—
96	#117×C₈₉	—	2	8	no	—
97	#117×C₈₉	—	2	8	no	—
98	#117×C₈₉	—	2	4	no	—
99	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
100	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
101	C₂×C₄⋊C₄×C₈₉	—	2	8	no	—
102	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	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	1	yes	characteristic
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	8	yes	—
113	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
114	C₂×C₂²⋊C₄×C₈₉	—	2	8	no	—
115	C₂×C₂²⋊C₄×C₈₉	—	4	4	no	—
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	4	yes	—
119	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
122	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
123	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
124	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
125	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
126	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
127	C₂×C₄²×C₈₉	—	2	8	no	—
128	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
129	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
130	C₂×C₄²×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	#95×C₈₉	C₂³	1	8	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	2	no	—
139	C₂⁴×C₈₉	—	2	2	no	—
140	C₂⁴×C₈₉	—	4	2	no	—
141	C₂⁴×C₈₉	C₂×D₄	1	4	yes	—
142	C₂⁴×C₈₉	C₂⁴	1	2	yes	—
143	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
144	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
145	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
146	#41×C₈₉	—	4	16	no	—
147	C₂×Q₈×C₈₉	—	2	2	no	—
148	C₂×Q₈×C₈₉	—	2	4	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	8	no	—
153	C₂×D₄×C₈₉	—	2	4	no	—
154	C₂×D₄×C₈₉	—	2	4	no	—
155	C₂×D₄×C₈₉	—	2	2	no	—
156	C₂×D₄×C₈₉	—	2	4	no	—
157	C₂×D₄×C₈₉	—	4	4	no	—
158	C₂²×C₄×C₈₉	—	2	4	no	—
159	C₂²×C₄×C₈₉	—	2	32	no	—
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	4	no	—
164	C₂²×C₄×C₈₉	—	2	4	no	—
165	C₂²×C₄×C₈₉	—	2	4	no	—
166	C₂²×C₄×C₈₉	—	2	4	no	—
167	C₂²×C₄×C₈₉	—	2	4	no	—
168	C₂²×C₄×C₈₉	—	2	8	no	—
169	C₂²×C₄×C₈₉	—	2	4	no	—
170	C₂²×C₄×C₈₉	—	2	8	no	—
171	C₂²×C₄×C₈₉	—	4	4	no	—
172	C₂²×C₄×C₈₉	—	4	4	no	—
173	C₂²×C₄×C₈₉	—	4	4	no	—
174	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
175	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
176	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
177	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
178	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
179	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
180	C₂²×C₄×C₈₉	#41	1	8	yes	—
181	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
182	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
183	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
185	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
186	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
187	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
191	C₄⋊C₄×C₈₉	—	2	4	no	—
192	C₄⋊C₄×C₈₉	—	2	4	no	—
193	C₄⋊C₄×C₈₉	—	2	4	no	—
194	C₄⋊C₄×C₈₉	—	2	4	no	—
195	C₄⋊C₄×C₈₉	—	2	2	no	—
196	C₄⋊C₄×C₈₉	—	2	2	no	—
197	C₄⋊C₄×C₈₉	—	2	4	no	—
198	C₄⋊C₄×C₈₉	—	2	4	no	—
199	C₄⋊C₄×C₈₉	—	2	8	no	—
200	C₄⋊C₄×C₈₉	—	2	8	no	—
201	C₄⋊C₄×C₈₉	—	4	8	no	—
202	C₄⋊C₄×C₈₉	—	4	8	no	—
203	C₂²⋊C₄×C₈₉	—	2	8	no	—
204	C₂²⋊C₄×C₈₉	—	2	8	no	—
205	C₂²⋊C₄×C₈₉	—	2	4	no	—
206	C₂²⋊C₄×C₈₉	—	2	4	no	—
207	C₂²⋊C₄×C₈₉	—	2	4	no	—
208	C₂²⋊C₄×C₈₉	—	2	8	no	—
209	C₂²⋊C₄×C₈₉	—	2	4	no	—
210	C₂²⋊C₄×C₈₉	—	2	4	no	—
211	C₂²⋊C₄×C₈₉	—	4	4	no	—
212	C₂²⋊C₄×C₈₉	—	4	8	no	—
213	C₂²⋊C₄×C₈₉	—	4	8	no	—
214	C₄²×C₈₉	—	2	8	no	—
215	C₄²×C₈₉	—	2	8	no	—
216	C₄²×C₈₉	—	2	4	no	—
217	C₂³×C₈₉	—	2	2	no	—
218	C₂³×C₈₉	—	2	1	no	—
219	C₂³×C₈₉	—	2	1	no	—
220	C₂³×C₈₉	—	2	2	no	—
221	C₂³×C₈₉	—	2	2	no	—
222	C₂³×C₈₉	—	2	8	no	—
223	C₂³×C₈₉	—	2	8	no	—
224	C₂³×C₈₉	—	2	2	no	—
225	C₂³×C₈₉	—	2	1	no	—
226	C₂³×C₈₉	—	2	1	no	—
227	C₂³×C₈₉	—	2	2	no	—
228	C₂³×C₈₉	—	2	2	no	—
229	C₂³×C₈₉	—	2	4	no	—
230	C₂³×C₈₉	—	2	2	no	—
231	C₂³×C₈₉	—	2	2	no	—
232	C₂³×C₈₉	—	2	4	no	—
233	C₂³×C₈₉	—	4	4	no	—
234	C₂³×C₈₉	—	4	8	no	—
235	C₂³×C₈₉	—	4	8	no	—
236	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
237	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
238	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
239	C₂³×C₈₉	C₂×#41	1	4	yes	—
240	C₂³×C₈₉	H(5,𝔽₂)	1	2	yes	—
241	C₂³×C₈₉	2₋¹⁺⁴	1	2	yes	—
242	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
243	Q₈×C₈₉	—	4	4	no	—
244	D₄×C₈₉	—	4	8	no	—
245	D₄×C₈₉	—	4	8	no	—
246	D₄×C₈₉	—	4	8	no	—
247	D₄×C₈₉	—	4	4	no	—
248	C₂×C₄×C₈₉	—	2	8	no	—
249	C₂×C₄×C₈₉	—	2	2	no	—
250	C₂×C₄×C₈₉	—	2	2	no	—
251	C₂×C₄×C₈₉	—	2	8	no	—
252	C₂×C₄×C₈₉	—	2	8	no	—
253	C₂×C₄×C₈₉	—	2	8	no	—
254	C₂×C₄×C₈₉	—	2	8	no	—
255	C₂×C₄×C₈₉	—	2	4	no	—
256	C₂×C₄×C₈₉	—	2	4	no	—
257	C₂×C₄×C₈₉	—	2	2	no	—
258	C₂×C₄×C₈₉	—	2	2	no	—
259	C₂×C₄×C₈₉	—	2	2	no	—
260	C₂×C₄×C₈₉	—	2	8	no	—
261	C₂×C₄×C₈₉	—	2	4	no	—
262	C₂×C₄×C₈₉	—	2	8	no	—
263	C₂×C₄×C₈₉	—	2	4	no	—
264	C₂×C₄×C₈₉	—	2	2	no	—
265	C₂×C₄×C₈₉	—	2	4	no	—
266	C₂×C₄×C₈₉	—	2	2	no	—
267	C₂×C₄×C₈₉	—	2	4	no	—
268	C₂×C₄×C₈₉	—	2	8	no	—
269	C₂×C₄×C₈₉	—	2	4	no	—
270	C₂×C₄×C₈₉	—	2	4	no	—
271	C₂×C₄×C₈₉	—	4	8	no	—
272	C₂×C₄×C₈₉	—	4	8	no	—
273	C₂×C₄×C₈₉	—	4	8	no	—
274	C₂×C₄×C₈₉	—	8	8	no	—
275	C₂×C₄×C₈₉	#123	1	16	yes	complemented
276	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
277	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
278	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
279	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
281	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
282	C₂²×C₈₉	—	2	2	no	—
283	C₂²×C₈₉	—	2	2	no	—
284	C₂²×C₈₉	—	2	2	no	—
285	C₂²×C₈₉	—	2	2	no	—
286	C₂²×C₈₉	—	2	4	no	—
287	C₂²×C₈₉	—	2	4	no	—
288	C₂²×C₈₉	—	2	4	no	—
289	C₂²×C₈₉	—	2	4	no	—
290	C₂²×C₈₉	—	2	2	no	—
291	C₂²×C₈₉	—	2	2	no	—
292	C₂²×C₈₉	—	2	2	no	—
293	C₂²×C₈₉	—	4	16	no	—
294	C₂²×C₈₉	—	4	2	no	—
295	C₂²×C₈₉	—	4	2	no	—
296	C₂²×C₈₉	—	4	2	no	—
297	C₂²×C₈₉	—	4	2	no	—
298	C₂²×C₈₉	—	4	2	no	—
299	C₂²×C₈₉	—	4	4	no	—
300	C₂²×C₈₉	—	4	4	no	—
301	C₂²×C₈₉	C₂×#123	1	4	yes	—
302	C₂²×C₈₉	#537	1	4	yes	—
303	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
304	C₂²×C₈₉	C₂²×#41	1	2	yes	—
305	C₂²×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
306	C₂²×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
307	C₂²×C₈₉	#585	1	2	yes	—
308	C₄×C₈₉	—	2	2	no	—
309	C₄×C₈₉	—	2	2	no	—
310	C₄×C₈₉	—	4	2	no	—
311	C₄×C₈₉	—	4	4	no	—
312	C₄×C₈₉	—	4	2	no	—
313	C₄×C₈₉	—	4	4	no	—
314	C₄×C₈₉	—	4	2	no	—
315	C₄×C₈₉	—	4	8	no	—
316	C₄×C₈₉	C₂×#123	1	4	yes	—
317	C₄×C₈₉	C₂×#123	1	4	yes	—
318	#35263	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
319	C₂×C₈₉	—	2	4	no	—
320	C₂×C₈₉	—	2	4	no	—
321	C₂×C₈₉	—	4	2	no	—
322	C₂×C₈₉	—	8	2	no	—
323	C₂×C₈₉	C₂²×#123	1	1	yes	characteristic
324	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
325	C₂×C₈₉	#3449	1	1	yes	characteristic
326	C₂×C₈₉	#3494	1	2	yes	—
327	C₂×C₈₉	#3495	1	2	yes	—
328	C₂×#525	C₂×C₈₉	1	1	yes	characteristic
329	C₂²×#117	C₂×C₈₉	1	1	yes	characteristic, complemented
330	#2855	C₂×C₈₉	1	2	yes	complemented
331	#2854	C₂×C₈₉	1	2	yes	complemented
332	#2625	C₂×C₈₉	1	2	yes	complemented
333	#2624	C₂×C₈₉	1	2	yes	complemented
334	#2498	C₂×C₈₉	1	4	yes	complemented
335	#2487	C₂×C₈₉	1	2	yes	complemented
336	#2486	C₂×C₈₉	1	2	yes	complemented
337	#2485	C₂×C₈₉	1	4	yes	complemented
338	#2412	C₂×C₈₉	1	4	yes	complemented
339	#2316	C₂×C₈₉	1	2	yes	complemented
340	#2311	C₂×C₈₉	1	2	yes	complemented
341	C₂×#380	C₂×C₈₉	1	1	yes	characteristic, complemented
342	C₈₉	#35263	1	1	yes	characteristic, direct product factor, Sylow
343	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
344	C₂⁴×C₄	C₂²×C₈₉	1	1	yes	characteristic
345	#525	—	2	8	no	—
346	C₂×#123	C₂²×C₈₉	1	2	yes	—
347	C₂×#123	C₂²×C₈₉	1	4	yes	—
348	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
349	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
350	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
351	C₂×#121	C₂²×C₈₉	1	1	yes	characteristic
352	C₂×#120	C₂²×C₈₉	1	2	yes	—
353	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
354	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
355	C₂×#117	—	2	8	no	—
356	C₂×#117	C₂²×C₈₉	1	2	yes	—
357	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
358	C₂×#117	C₂²×C₈₉	1	2	yes	—
359	C₂×#117	C₂²×C₈₉	1	2	yes	—
360	C₂×#117	C₂²×C₈₉	1	2	yes	—
361	C₂²×C₄⋊C₄	C₂²×C₈₉	1	2	yes	—
362	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
363	C₂²×C₄⋊C₄	C₂²×C₈₉	1	1	yes	characteristic
364	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
365	C₂²×C₂²⋊C₄	C₂²×C₈₉	1	2	yes	—
366	C₂²×C₄²	C₂²×C₈₉	1	2	yes	—
367	#400	C₂²×C₈₉	1	4	yes	complemented
368	#399	C₂²×C₈₉	1	4	yes	complemented
369	#398	C₂²×C₈₉	1	4	yes	complemented
370	#397	C₂²×C₈₉	1	8	yes	—
371	#397	C₂²×C₈₉	1	4	yes	complemented
372	#394	C₂²×C₈₉	1	8	yes	—
373	#391	C₂²×C₈₉	1	4	yes	complemented
374	#390	C₂²×C₈₉	1	4	yes	complemented
375	#389	C₂²×C₈₉	1	4	yes	complemented
376	#389	C₂²×C₈₉	1	4	yes	complemented
377	#389	C₂²×C₈₉	1	4	yes	complemented
378	#389	C₂²×C₈₉	1	4	yes	complemented
379	#388	C₂²×C₈₉	1	8	yes	complemented
380	#387	C₂²×C₈₉	1	8	yes	complemented
381	#386	C₂²×C₈₉	1	8	yes	—
382	#386	C₂²×C₈₉	1	4	yes	—
383	#385	C₂²×C₈₉	1	4	yes	—
384	#381	C₂²×C₈₉	1	4	yes	—
385	#380	C₂²×C₈₉	1	8	yes	—
386	#380	C₂²×C₈₉	1	2	yes	—
387	#380	C₂²×C₈₉	1	2	yes	—
388	#380	C₂²×C₈₉	1	2	yes	—
389	#380	C₂²×C₈₉	1	2	yes	—
390	#380	C₂²×C₈₉	1	4	yes	complemented
391	#380	C₂²×C₈₉	1	4	yes	complemented
392	C₂×#95	C₂²×C₈₉	1	2	yes	—
393	C₂⁵	C₂³×C₈₉	1	1	yes	characteristic
394	C₂×#41	—	2	4	no	—
395	C₂×#41	—	2	8	no	—
396	C₂²×Q₈	C₂³×C₈₉	1	1	yes	characteristic
397	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
398	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
399	C₂²×D₄	C₂³×C₈₉	1	1	yes	characteristic
400	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
401	C₂³×C₄	—	2	8	no	—
402	C₂³×C₄	D₄×C₈₉	1	8	yes	—
403	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
404	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
405	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
406	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
407	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
408	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
409	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
410	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
411	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
412	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
413	#123	—	2	8	no	—
414	#123	—	4	8	no	—
415	C₂²⋊Q₈	—	2	4	no	—
416	C₂²⋊Q₈	—	2	4	no	—
417	#121	—	2	4	no	—
418	#121	—	2	4	no	—
419	#120	—	2	8	no	—
420	C₄×D₄	—	2	8	no	—
421	C₄×D₄	—	2	8	no	—
422	#117	—	2	8	no	—
423	#117	—	2	8	no	—
424	#117	—	2	8	no	—
425	#117	—	2	8	no	—
426	#117	—	2	4	no	—
427	C₂×C₄⋊C₄	—	2	4	no	—
428	C₂×C₄⋊C₄	—	2	4	no	—
429	C₂×C₄⋊C₄	—	2	8	no	—
430	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
431	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
432	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
433	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
434	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
435	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
436	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
437	C₂×C₄⋊C₄	C₂³×C₈₉	1	1	yes	characteristic
438	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
439	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
440	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
441	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
442	C₂×C₂²⋊C₄	—	2	8	no	—
443	C₂×C₂²⋊C₄	—	4	4	no	—
444	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
445	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
446	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
447	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
448	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
449	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
450	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
451	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
452	C₂×C₂²⋊C₄	C₂³×C₈₉	1	4	yes	—
453	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
454	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
455	C₂×C₄²	—	2	8	no	—
456	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
457	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
458	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
459	#95	C₂³×C₈₉	1	4	yes	—
460	#95	C₂³×C₈₉	1	4	yes	—
461	#95	C₂³×C₈₉	1	8	yes	—
462	#95	C₂³×C₈₉	1	8	yes	—
463	#95	C₂³×C₈₉	1	8	yes	—
464	#95	C₂³×C₈₉	1	8	yes	—
465	C₂⁴	—	2	4	no	—
466	C₂⁴	—	2	2	no	—
467	C₂⁴	—	2	2	no	—
468	C₂⁴	—	4	2	no	—
469	C₂⁴	C₂×D₄×C₈₉	1	4	yes	—
470	C₂⁴	C₂⁴×C₈₉	1	2	yes	—
471	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
472	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
473	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
474	#41	—	4	16	no	—
475	C₂×Q₈	—	2	2	no	—
476	C₂×Q₈	—	2	4	no	—
477	C₂×D₄	—	2	4	no	—
478	C₂×D₄	—	2	4	no	—
479	C₂×D₄	—	2	4	no	—
480	C₂×D₄	—	2	8	no	—
481	C₂×D₄	—	2	4	no	—
482	C₂×D₄	—	2	4	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	4	no	—
485	C₂×D₄	—	4	4	no	—
486	C₂²×C₄	—	2	4	no	—
487	C₂²×C₄	—	2	32	no	—
488	C₂²×C₄	—	2	4	no	—
489	C₂²×C₄	—	2	4	no	—
490	C₂²×C₄	—	2	4	no	—
491	C₂²×C₄	—	2	4	no	—
492	C₂²×C₄	—	2	4	no	—
493	C₂²×C₄	—	2	4	no	—
494	C₂²×C₄	—	2	4	no	—
495	C₂²×C₄	—	2	4	no	—
496	C₂²×C₄	—	2	8	no	—
497	C₂²×C₄	—	2	4	no	—
498	C₂²×C₄	—	2	8	no	—
499	C₂²×C₄	—	4	4	no	—
500	C₂²×C₄	—	4	4	no	—
501	C₂²×C₄	—	4	4	no	—
502	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
503	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
504	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
505	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
506	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
507	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
508	C₂²×C₄	#41×C₈₉	1	8	yes	—
509	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
510	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
511	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
512	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
513	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
514	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
515	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
516	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
517	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
518	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
519	C₄⋊C₄	—	2	4	no	—
520	C₄⋊C₄	—	2	4	no	—
521	C₄⋊C₄	—	2	4	no	—
522	C₄⋊C₄	—	2	4	no	—
523	C₄⋊C₄	—	2	2	no	—
524	C₄⋊C₄	—	2	2	no	—
525	C₄⋊C₄	—	2	4	no	—
526	C₄⋊C₄	—	2	4	no	—
527	C₄⋊C₄	—	2	8	no	—
528	C₄⋊C₄	—	2	8	no	—
529	C₄⋊C₄	—	4	8	no	—
530	C₄⋊C₄	—	4	8	no	—
531	C₂²⋊C₄	—	2	8	no	—
532	C₂²⋊C₄	—	2	8	no	—
533	C₂²⋊C₄	—	2	4	no	—
534	C₂²⋊C₄	—	2	4	no	—
535	C₂²⋊C₄	—	2	4	no	—
536	C₂²⋊C₄	—	2	8	no	—
537	C₂²⋊C₄	—	2	4	no	—
538	C₂²⋊C₄	—	2	4	no	—
539	C₂²⋊C₄	—	4	4	no	—
540	C₂²⋊C₄	—	4	8	no	—
541	C₂²⋊C₄	—	4	8	no	—
542	C₄²	—	2	8	no	—
543	C₄²	—	2	8	no	—
544	C₄²	—	2	4	no	—
545	C₂³	—	2	2	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	2	no	—
549	C₂³	—	2	2	no	—
550	C₂³	—	2	8	no	—
551	C₂³	—	2	8	no	—
552	C₂³	—	2	2	no	—
553	C₂³	—	2	1	no	—
554	C₂³	—	2	1	no	—
555	C₂³	—	2	2	no	—
556	C₂³	—	2	2	no	—
557	C₂³	—	2	4	no	—
558	C₂³	—	2	2	no	—
559	C₂³	—	2	2	no	—
560	C₂³	—	2	4	no	—
561	C₂³	—	4	4	no	—
562	C₂³	—	4	8	no	—
563	C₂³	—	4	8	no	—
564	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
565	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
566	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
567	C₂³	C₂×#41×C₈₉	1	4	yes	—
568	C₂³	H(5,𝔽₂)×C₈₉	1	2	yes	—
569	C₂³	2₋¹⁺⁴×C₈₉	1	2	yes	—
570	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
571	Q₈	—	4	4	no	—
572	D₄	—	4	8	no	—
573	D₄	—	4	8	no	—
574	D₄	—	4	8	no	—
575	D₄	—	4	4	no	—
576	C₂×C₄	—	2	8	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	2	no	—
579	C₂×C₄	—	2	8	no	—
580	C₂×C₄	—	2	8	no	—
581	C₂×C₄	—	2	8	no	—
582	C₂×C₄	—	2	8	no	—
583	C₂×C₄	—	2	4	no	—
584	C₂×C₄	—	2	4	no	—
585	C₂×C₄	—	2	2	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	8	no	—
589	C₂×C₄	—	2	4	no	—
590	C₂×C₄	—	2	8	no	—
591	C₂×C₄	—	2	4	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	4	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	4	no	—
596	C₂×C₄	—	2	8	no	—
597	C₂×C₄	—	2	4	no	—
598	C₂×C₄	—	2	4	no	—
599	C₂×C₄	—	4	8	no	—
600	C₂×C₄	—	4	8	no	—
601	C₂×C₄	—	4	8	no	—
602	C₂×C₄	—	8	8	no	—
603	C₂×C₄	#123×C₈₉	1	16	yes	complemented
604	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
605	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
606	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
607	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
608	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
609	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	4	no	—
615	C₂²	—	2	4	no	—
616	C₂²	—	2	4	no	—
617	C₂²	—	2	4	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	2	2	no	—
621	C₂²	—	4	16	no	—
622	C₂²	—	4	2	no	—
623	C₂²	—	4	2	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	4	4	no	—
628	C₂²	—	4	4	no	—
629	C₂²	C₂×#123×C₈₉	1	4	yes	—
630	C₂²	#537×C₈₉	1	4	yes	—
631	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
632	C₂²	C₂²×#41×C₈₉	1	2	yes	—
633	C₂²	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
634	C₂²	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
635	C₂²	#585×C₈₉	1	2	yes	—
636	C₄	—	2	2	no	—
637	C₄	—	2	2	no	—
638	C₄	—	4	2	no	—
639	C₄	—	4	4	no	—
640	C₄	—	4	2	no	—
641	C₄	—	4	4	no	—
642	C₄	—	4	2	no	—
643	C₄	—	4	8	no	—
644	C₄	C₂×#123×C₈₉	1	4	yes	—
645	C₄	C₂×#123×C₈₉	1	4	yes	—
646	C₂	—	2	4	no	—
647	C₂	—	2	4	no	—
648	C₂	—	4	2	no	—
649	C₂	—	8	2	no	—
650	C₂	C₂²×#123×C₈₉	1	1	yes	characteristic
651	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
652	C₂	C₈₉×#3449	1	1	yes	characteristic
653	C₂	C₈₉×#3494	1	2	yes	—
654	C₂	C₈₉×#3495	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂×#525×C₈₉	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
2. C₂²×#117×C₈₉	C₂	semidirect
3. C₈₉×#2855	C₂	semidirect
4. C₈₉×#2854	C₂	semidirect
5. C₈₉×#2625	C₂	semidirect
6. C₈₉×#2624	C₂	semidirect
7. C₈₉×#2498	C₂	semidirect
8. C₈₉×#2487	C₂	semidirect
9. C₈₉×#2486	C₂	semidirect
10. C₈₉×#2485	C₂	semidirect
11. C₈₉×#2412	C₂	semidirect
12. C₈₉×#2316	C₂	semidirect
13. C₈₉×#2311	C₂	semidirect
14. C₂×#380×C₈₉	C₂	semidirect
39. #400×C₈₉	C₂²	semidirect
40. #399×C₈₉	C₂²	semidirect
41. #398×C₈₉	C₂²	semidirect
43. #397×C₈₉	C₂²	semidirect
45. #391×C₈₉	C₂²	semidirect
46. #390×C₈₉	C₂²	semidirect
47. #389×C₈₉	C₂²	semidirect
48. #389×C₈₉	C₂²	semidirect
49. #389×C₈₉	C₂²	semidirect
50. #389×C₈₉	C₂²	semidirect
51. #388×C₈₉	C₂²	semidirect
52. #387×C₈₉	C₂²	semidirect
62. #380×C₈₉	C₂²	semidirect
63. #380×C₈₉	C₂²	semidirect
275. C₂×C₄×C₈₉	#123	semidirect
318. #35263	C₈₉	direct (N × H)
329. C₂²×#117	C₂×C₈₉	semidirect
330. #2855	C₂×C₈₉	semidirect
331. #2854	C₂×C₈₉	semidirect
332. #2625	C₂×C₈₉	semidirect
333. #2624	C₂×C₈₉	semidirect
334. #2498	C₂×C₈₉	semidirect
335. #2487	C₂×C₈₉	semidirect
336. #2486	C₂×C₈₉	semidirect
337. #2485	C₂×C₈₉	semidirect
338. #2412	C₂×C₈₉	semidirect
339. #2316	C₂×C₈₉	semidirect
340. #2311	C₂×C₈₉	semidirect
341. C₂×#380	C₂×C₈₉	semidirect
342. C₈₉	#35263	direct (N × H)
367. #400	C₂²×C₈₉	semidirect
368. #399	C₂²×C₈₉	semidirect
369. #398	C₂²×C₈₉	semidirect
371. #397	C₂²×C₈₉	semidirect
373. #391	C₂²×C₈₉	semidirect
374. #390	C₂²×C₈₉	semidirect
375. #389	C₂²×C₈₉	semidirect
376. #389	C₂²×C₈₉	semidirect
377. #389	C₂²×C₈₉	semidirect
378. #389	C₂²×C₈₉	semidirect
379. #388	C₂²×C₈₉	semidirect
380. #387	C₂²×C₈₉	semidirect
390. #380	C₂²×C₈₉	semidirect
391. #380	C₂²×C₈₉	semidirect
603. C₂×C₄	#123×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#525×C₈₉	2
C₂²×#117×C₈₉	2
C₈₉×#2855	2
C₈₉×#2854	2
C₈₉×#2625	2
C₈₉×#2624	2
C₈₉×#2498	2
C₈₉×#2487	2
C₈₉×#2486	2
C₈₉×#2485	2
C₈₉×#2412	2
C₈₉×#2316	2
C₈₉×#2311	2
C₂×#380×C₈₉	2
#35263	89

Subgroups — C89×#35263 #36413111

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35263 #36413111