Subgroups — C₈₉×#62860 #36440708

Order 22784.

6866 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3510	C₂	1	8	yes	maximal, complemented
2	C₈₉×#3509	C₂	1	8	yes	maximal, complemented
3	C₈₉×#3507	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3495	C₂	1	16	yes	maximal, complemented
5	C₈₉×#3491	C₂	1	8	yes	maximal, complemented
6	C₈₉×#3461	C₂	1	8	yes	maximal, complemented
7	C₈₉×#3458	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3449	C₂	1	1	yes	maximal, characteristic
9	C₂×#536×C₈₉	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3428	C₂	1	2	yes	maximal, complemented
11	C₂×#519×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₈₉	C₂²	1	2	yes	—
13	C₂³×Q₈×C₈₉	C₂²	1	1	yes	characteristic
14	#559×C₈₉	C₂²	1	16	yes	complemented
15	#557×C₈₉	C₂²	1	16	yes	complemented
16	#556×C₈₉	C₂²	1	16	yes	complemented
17	#556×C₈₉	C₂²	1	32	yes	complemented
18	#554×C₈₉	C₂²	1	16	yes	complemented
19	#552×C₈₉	C₂²	1	64	yes	complemented
20	#552×C₈₉	C₂²	1	32	yes	complemented
21	#551×C₈₉	C₂²	1	64	yes	complemented
22	#544×C₈₉	C₂²	1	4	yes	complemented
23	#544×C₈₉	C₂²	1	8	yes	complemented
24	#543×C₈₉	C₂²	1	4	yes	—
25	#542×C₈₉	C₂²	1	32	yes	complemented
26	#541×C₈₉	C₂²	1	32	yes	complemented
27	#539×C₈₉	C₂²	1	32	yes	complemented
28	#537×C₈₉	C₂²	1	4	yes	—
29	#536×C₈₉	C₂²	1	8	yes	—
30	#536×C₈₉	C₂²	1	8	yes	—
31	#536×C₈₉	C₂²	1	4	yes	—
32	#536×C₈₉	C₂²	1	8	yes	complemented
33	#536×C₈₉	C₂²	1	8	yes	complemented
34	#535×C₈₉	C₂²	1	4	yes	—
35	#534×C₈₉	C₂²	1	4	yes	—
36	#533×C₈₉	C₂²	1	4	yes	complemented
37	#533×C₈₉	C₂²	1	8	yes	complemented
38	#533×C₈₉	C₂²	1	32	yes	complemented
39	#532×C₈₉	C₂²	1	4	yes	—
40	C₂×C₄⋊Q₈×C₈₉	C₂²	1	4	yes	complemented
41	#529×C₈₉	C₂²	1	32	yes	complemented
42	#529×C₈₉	C₂²	1	32	yes	complemented
43	C₂×#124×C₈₉	C₂²	1	4	yes	complemented
44	#525×C₈₉	C₂²	1	8	yes	—
45	C₂×#123×C₈₉	C₂²	1	8	yes	—
46	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	8	yes	complemented
47	#520×C₈₉	C₂²	1	8	yes	—
48	#520×C₈₉	C₂²	1	8	yes	complemented
49	#519×C₈₉	C₂²	1	8	yes	complemented
50	#519×C₈₉	C₂²	1	8	yes	complemented
51	#519×C₈₉	C₂²	1	4	yes	complemented
52	#518×C₈₉	C₂²	1	8	yes	—
53	#518×C₈₉	C₂²	1	4	yes	complemented
54	C₄×#41×C₈₉	C₂²	1	8	yes	—
55	C₄×#41×C₈₉	C₂²	1	8	yes	complemented
56	C₂×C₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
57	C₂×C₄×Q₈×C₈₉	C₂²	1	4	yes	complemented
58	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
60	C₂×#117×C₈₉	C₂²	1	4	yes	—
61	C₂×#117×C₈₉	C₂²	1	2	yes	—
62	C₂×#117×C₈₉	C₂²	1	8	yes	complemented
63	C₂×#41×C₈₉	—	2	16	no	—
64	C₂×#41×C₈₉	C₂³	1	4	yes	—
65	C₂×#41×C₈₉	C₂³	1	4	yes	—
66	C₂×#41×C₈₉	C₂³	1	4	yes	—
67	C₂×#41×C₈₉	C₂³	1	4	yes	—
68	C₂²×Q₈×C₈₉	—	2	8	no	—
69	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
70	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
71	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
72	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
73	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
74	C₂²×D₄×C₈₉	C₂³	1	4	yes	—
75	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
76	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
77	C₂³×C₄×C₈₉	C₂³	1	4	yes	—
78	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
79	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	—
80	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	—
81	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
82	C₄⋊Q₈×C₈₉	C₂³	1	16	yes	—
83	C₄⋊Q₈×C₈₉	C₂³	1	8	yes	—
84	#127×C₈₉	C₂³	1	4	yes	—
85	#126×C₈₉	C₂³	1	64	yes	—
86	#126×C₈₉	C₂³	1	64	yes	—
87	#125×C₈₉	C₂³	1	16	yes	—
88	#125×C₈₉	C₂³	1	32	yes	—
89	#125×C₈₉	C₂³	1	64	yes	—
90	#125×C₈₉	C₂³	1	8	yes	—
91	#124×C₈₉	C₂³	1	16	yes	—
92	#124×C₈₉	C₂³	1	16	yes	—
93	#124×C₈₉	C₂³	1	32	yes	—
94	#124×C₈₉	C₂³	1	8	yes	—
95	#123×C₈₉	C₂³	1	32	yes	—
96	#123×C₈₉	C₂³	1	32	yes	—
97	#123×C₈₉	C₂³	1	16	yes	—
98	#123×C₈₉	C₂³	1	64	yes	—
99	C₂²⋊Q₈×C₈₉	C₂³	1	32	yes	—
100	C₂²⋊Q₈×C₈₉	C₂³	1	32	yes	—
101	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
102	C₂²⋊Q₈×C₈₉	C₂³	1	16	yes	—
103	C₂²⋊Q₈×C₈₉	C₂³	1	64	yes	—
104	C₂²⋊Q₈×C₈₉	C₂³	1	32	yes	—
105	#121×C₈₉	C₂³	1	16	yes	—
106	#121×C₈₉	C₂³	1	16	yes	—
107	#120×C₈₉	C₂³	1	16	yes	—
108	C₄×Q₈×C₈₉	C₂³	1	32	yes	—
109	C₄×Q₈×C₈₉	C₂³	1	16	yes	—
110	C₄×Q₈×C₈₉	C₂³	1	16	yes	—
111	C₄×Q₈×C₈₉	C₂³	1	16	yes	—
112	C₄×Q₈×C₈₉	C₂³	1	16	yes	—
113	C₄×Q₈×C₈₉	C₂³	1	32	yes	—
114	C₄×Q₈×C₈₉	C₂³	1	16	yes	—
115	C₄×D₄×C₈₉	C₂³	1	32	yes	—
116	C₄×D₄×C₈₉	C₂³	1	16	yes	—
117	C₄×D₄×C₈₉	C₂³	1	32	yes	—
118	C₄×D₄×C₈₉	C₂³	1	16	yes	—
119	C₄×D₄×C₈₉	C₂³	1	16	yes	—
120	C₄×D₄×C₈₉	C₂³	1	32	yes	—
121	#117×C₈₉	C₂³	1	4	yes	—
122	#117×C₈₉	C₂³	1	4	yes	—
123	#117×C₈₉	C₂³	1	4	yes	—
124	#117×C₈₉	C₂³	1	4	yes	—
125	#117×C₈₉	C₂³	1	4	yes	—
126	#117×C₈₉	C₂³	1	4	yes	—
127	#117×C₈₉	C₂³	1	4	yes	—
128	#117×C₈₉	C₂³	1	32	yes	—
129	#117×C₈₉	C₂³	1	4	yes	—
130	#117×C₈₉	C₂³	1	16	yes	—
131	#117×C₈₉	C₂³	1	16	yes	—
132	#117×C₈₉	C₂³	1	16	yes	—
133	#117×C₈₉	C₂³	1	64	yes	—
134	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
135	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
136	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
137	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
138	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
139	C₂×C₄⋊C₄×C₈₉	C₂³	1	16	yes	—
140	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
141	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
142	C₂×C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
143	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
144	C₂×C₂²⋊C₄×C₈₉	C₂³	1	16	yes	—
145	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
146	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
147	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
148	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
149	C₂×C₄²×C₈₉	C₂³	1	16	yes	—
150	C₂⁴×C₈₉	C₂⁴	1	4	yes	—
151	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
152	#41×C₈₉	—	2	16	no	—
153	#41×C₈₉	—	2	16	no	—
154	#41×C₈₉	—	2	16	no	—
155	#41×C₈₉	—	2	16	no	—
156	C₂×Q₈×C₈₉	—	2	16	no	—
157	C₂×Q₈×C₈₉	—	2	16	no	—
158	C₂×Q₈×C₈₉	—	2	8	no	—
159	C₂×Q₈×C₈₉	—	2	8	no	—
160	C₂×Q₈×C₈₉	—	2	8	no	—
161	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
162	C₂×Q₈×C₈₉	C₂⁴	1	8	yes	—
163	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
164	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
165	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
166	C₂×Q₈×C₈₉	C₂⁴	1	16	yes	—
167	C₂×D₄×C₈₉	—	2	16	no	—
168	C₂×D₄×C₈₉	—	2	8	no	—
169	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
170	C₂×D₄×C₈₉	C₂⁴	1	8	yes	—
171	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
172	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
173	C₂×D₄×C₈₉	C₂⁴	1	16	yes	—
174	C₂²×C₄×C₈₉	—	2	8	no	—
175	C₂²×C₄×C₈₉	—	2	16	no	—
176	C₂²×C₄×C₈₉	#41	1	8	yes	—
177	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
178	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
179	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
180	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
181	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
182	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
183	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
184	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
185	C₂²×C₄×C₈₉	C₂⁴	1	32	yes	—
186	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
190	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
191	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
192	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
193	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
194	C₄⋊C₄×C₈₉	C₂⁴	1	32	yes	—
195	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
196	C₄⋊C₄×C₈₉	C₂⁴	1	32	yes	—
197	C₄⋊C₄×C₈₉	C₂⁴	1	64	yes	—
198	C₄⋊C₄×C₈₉	C₂⁴	1	32	yes	—
199	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
200	C₄⋊C₄×C₈₉	C₂⁴	1	16	yes	—
201	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
202	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
203	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
204	C₂²⋊C₄×C₈₉	C₂⁴	1	8	yes	—
205	C₂²⋊C₄×C₈₉	C₂⁴	1	32	yes	—
206	C₂²⋊C₄×C₈₉	C₂⁴	1	64	yes	—
207	C₂²⋊C₄×C₈₉	C₂⁴	1	32	yes	—
208	C₄²×C₈₉	C₂⁴	1	8	yes	—
209	C₄²×C₈₉	C₂⁴	1	8	yes	—
210	C₄²×C₈₉	C₂⁴	1	32	yes	—
211	C₄²×C₈₉	C₂⁴	1	32	yes	—
212	C₄²×C₈₉	C₂⁴	1	4	yes	—
213	C₄²×C₈₉	C₂⁴	1	8	yes	—
214	C₄²×C₈₉	C₂⁴	1	4	yes	—
215	C₂³×C₈₉	—	2	8	no	—
216	C₂³×C₈₉	—	4	2	no	—
217	C₂³×C₈₉	—	4	8	no	—
218	C₂³×C₈₉	C₂×#41	1	4	yes	—
219	C₂³×C₈₉	C₂⁵	1	8	yes	—
220	C₂³×C₈₉	C₂⁵	1	2	yes	—
221	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
222	Q₈×C₈₉	—	2	8	no	—
223	Q₈×C₈₉	—	2	16	no	—
224	Q₈×C₈₉	—	2	8	no	—
225	Q₈×C₈₉	—	2	8	no	—
226	Q₈×C₈₉	—	2	8	no	—
227	Q₈×C₈₉	—	4	16	no	—
228	D₄×C₈₉	—	2	16	no	—
229	D₄×C₈₉	—	2	16	no	—
230	D₄×C₈₉	—	2	8	no	—
231	D₄×C₈₉	—	2	8	no	—
232	D₄×C₈₉	—	4	16	no	—
233	C₂×C₄×C₈₉	—	2	8	no	—
234	C₂×C₄×C₈₉	—	2	16	no	—
235	C₂×C₄×C₈₉	—	2	8	no	—
236	C₂×C₄×C₈₉	—	2	16	no	—
237	C₂×C₄×C₈₉	—	2	16	no	—
238	C₂×C₄×C₈₉	—	4	4	no	—
239	C₂×C₄×C₈₉	—	4	32	no	—
240	C₂×C₄×C₈₉	—	4	8	no	—
241	C₂×C₄×C₈₉	—	4	4	no	—
242	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
243	C₂×C₄×C₈₉	C₂×#41	1	8	yes	—
244	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
245	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
246	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
247	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
248	C₂×C₄×C₈₉	C₂⁵	1	16	yes	—
249	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
250	C₂×C₄×C₈₉	C₂⁵	1	8	yes	—
251	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
252	C₂×C₄×C₈₉	C₂⁵	1	2	yes	—
253	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
254	C₂²×C₈₉	—	2	2	no	—
255	C₂²×C₈₉	—	2	4	no	—
256	C₂²×C₈₉	—	2	8	no	—
257	C₂²×C₈₉	—	2	16	no	—
258	C₂²×C₈₉	—	4	4	no	—
259	C₂²×C₈₉	—	8	8	no	—
260	C₂²×C₈₉	C₂²×#41	1	4	yes	—
261	C₂²×C₈₉	C₂²×#41	1	2	yes	—
262	C₂²×C₈₉	C₂⁶	1	1	yes	characteristic
263	C₄×C₈₉	—	2	8	no	—
264	C₄×C₈₉	—	2	8	no	—
265	C₄×C₈₉	—	2	8	no	—
266	C₄×C₈₉	—	2	16	no	—
267	C₄×C₈₉	—	2	8	no	—
268	C₄×C₈₉	C₂²×#41	1	2	yes	—
269	C₄×C₈₉	C₂²×#41	1	4	yes	—
270	C₄×C₈₉	C₂²×#41	1	2	yes	—
271	#62860	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
272	C₂×C₈₉	—	2	4	no	—
273	C₂×C₈₉	—	2	2	no	—
274	C₂×C₈₉	—	4	8	no	—
275	C₂×C₈₉	C₂³×#41	1	1	yes	characteristic
276	C₂×C₈₉	2₋¹⁺⁶	1	2	yes	—
277	#3510	C₂×C₈₉	1	8	yes	complemented
278	#3509	C₂×C₈₉	1	8	yes	complemented
279	#3507	C₂×C₈₉	1	8	yes	complemented
280	#3495	C₂×C₈₉	1	16	yes	complemented
281	#3491	C₂×C₈₉	1	8	yes	complemented
282	#3461	C₂×C₈₉	1	8	yes	complemented
283	#3458	C₂×C₈₉	1	1	yes	characteristic, complemented
284	#3449	C₂×C₈₉	1	1	yes	characteristic
285	C₂×#536	C₂×C₈₉	1	2	yes	complemented
286	#3428	C₂×C₈₉	1	2	yes	complemented
287	C₂×#519	C₂×C₈₉	1	1	yes	characteristic, complemented
288	C₈₉	#62860	1	1	yes	characteristic, direct product factor, Sylow
289	C₂²×#41	C₂²×C₈₉	1	2	yes	—
290	C₂³×Q₈	C₂²×C₈₉	1	1	yes	characteristic
291	#559	C₂²×C₈₉	1	16	yes	complemented
292	#557	C₂²×C₈₉	1	16	yes	complemented
293	#556	C₂²×C₈₉	1	16	yes	complemented
294	#556	C₂²×C₈₉	1	32	yes	complemented
295	#554	C₂²×C₈₉	1	16	yes	complemented
296	#552	C₂²×C₈₉	1	64	yes	complemented
297	#552	C₂²×C₈₉	1	32	yes	complemented
298	#551	C₂²×C₈₉	1	64	yes	complemented
299	#544	C₂²×C₈₉	1	4	yes	complemented
300	#544	C₂²×C₈₉	1	8	yes	complemented
301	#543	C₂²×C₈₉	1	4	yes	—
302	#542	C₂²×C₈₉	1	32	yes	complemented
303	#541	C₂²×C₈₉	1	32	yes	complemented
304	#539	C₂²×C₈₉	1	32	yes	complemented
305	#537	C₂²×C₈₉	1	4	yes	—
306	#536	C₂²×C₈₉	1	8	yes	—
307	#536	C₂²×C₈₉	1	8	yes	—
308	#536	C₂²×C₈₉	1	4	yes	—
309	#536	C₂²×C₈₉	1	8	yes	complemented
310	#536	C₂²×C₈₉	1	8	yes	complemented
311	#535	C₂²×C₈₉	1	4	yes	—
312	#534	C₂²×C₈₉	1	4	yes	—
313	#533	C₂²×C₈₉	1	4	yes	complemented
314	#533	C₂²×C₈₉	1	8	yes	complemented
315	#533	C₂²×C₈₉	1	32	yes	complemented
316	#532	C₂²×C₈₉	1	4	yes	—
317	C₂×C₄⋊Q₈	C₂²×C₈₉	1	4	yes	complemented
318	#529	C₂²×C₈₉	1	32	yes	complemented
319	#529	C₂²×C₈₉	1	32	yes	complemented
320	C₂×#124	C₂²×C₈₉	1	4	yes	complemented
321	#525	C₂²×C₈₉	1	8	yes	—
322	C₂×#123	C₂²×C₈₉	1	8	yes	—
323	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	8	yes	complemented
324	#520	C₂²×C₈₉	1	8	yes	—
325	#520	C₂²×C₈₉	1	8	yes	complemented
326	#519	C₂²×C₈₉	1	8	yes	complemented
327	#519	C₂²×C₈₉	1	8	yes	complemented
328	#519	C₂²×C₈₉	1	4	yes	complemented
329	#518	C₂²×C₈₉	1	8	yes	—
330	#518	C₂²×C₈₉	1	4	yes	complemented
331	C₄×#41	C₂²×C₈₉	1	8	yes	—
332	C₄×#41	C₂²×C₈₉	1	8	yes	complemented
333	C₂×C₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
334	C₂×C₄×Q₈	C₂²×C₈₉	1	4	yes	complemented
335	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
336	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
337	C₂×#117	C₂²×C₈₉	1	4	yes	—
338	C₂×#117	C₂²×C₈₉	1	2	yes	—
339	C₂×#117	C₂²×C₈₉	1	8	yes	complemented
340	C₂×#41	—	2	16	no	—
341	C₂×#41	C₂³×C₈₉	1	4	yes	—
342	C₂×#41	C₂³×C₈₉	1	4	yes	—
343	C₂×#41	C₂³×C₈₉	1	4	yes	—
344	C₂×#41	C₂³×C₈₉	1	4	yes	—
345	C₂²×Q₈	—	2	8	no	—
346	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
347	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
348	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
349	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
350	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
351	C₂²×D₄	C₂³×C₈₉	1	4	yes	—
352	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
353	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
354	C₂³×C₄	C₂³×C₈₉	1	4	yes	—
355	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
356	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	—
357	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	—
358	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
359	C₄⋊Q₈	C₂³×C₈₉	1	16	yes	—
360	C₄⋊Q₈	C₂³×C₈₉	1	8	yes	—
361	#127	C₂³×C₈₉	1	4	yes	—
362	#126	C₂³×C₈₉	1	64	yes	—
363	#126	C₂³×C₈₉	1	64	yes	—
364	#125	C₂³×C₈₉	1	16	yes	—
365	#125	C₂³×C₈₉	1	32	yes	—
366	#125	C₂³×C₈₉	1	64	yes	—
367	#125	C₂³×C₈₉	1	8	yes	—
368	#124	C₂³×C₈₉	1	16	yes	—
369	#124	C₂³×C₈₉	1	16	yes	—
370	#124	C₂³×C₈₉	1	32	yes	—
371	#124	C₂³×C₈₉	1	8	yes	—
372	#123	C₂³×C₈₉	1	32	yes	—
373	#123	C₂³×C₈₉	1	32	yes	—
374	#123	C₂³×C₈₉	1	16	yes	—
375	#123	C₂³×C₈₉	1	64	yes	—
376	C₂²⋊Q₈	C₂³×C₈₉	1	32	yes	—
377	C₂²⋊Q₈	C₂³×C₈₉	1	32	yes	—
378	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
379	C₂²⋊Q₈	C₂³×C₈₉	1	16	yes	—
380	C₂²⋊Q₈	C₂³×C₈₉	1	64	yes	—
381	C₂²⋊Q₈	C₂³×C₈₉	1	32	yes	—
382	#121	C₂³×C₈₉	1	16	yes	—
383	#121	C₂³×C₈₉	1	16	yes	—
384	#120	C₂³×C₈₉	1	16	yes	—
385	C₄×Q₈	C₂³×C₈₉	1	32	yes	—
386	C₄×Q₈	C₂³×C₈₉	1	16	yes	—
387	C₄×Q₈	C₂³×C₈₉	1	16	yes	—
388	C₄×Q₈	C₂³×C₈₉	1	16	yes	—
389	C₄×Q₈	C₂³×C₈₉	1	16	yes	—
390	C₄×Q₈	C₂³×C₈₉	1	32	yes	—
391	C₄×Q₈	C₂³×C₈₉	1	16	yes	—
392	C₄×D₄	C₂³×C₈₉	1	32	yes	—
393	C₄×D₄	C₂³×C₈₉	1	16	yes	—
394	C₄×D₄	C₂³×C₈₉	1	32	yes	—
395	C₄×D₄	C₂³×C₈₉	1	16	yes	—
396	C₄×D₄	C₂³×C₈₉	1	16	yes	—
397	C₄×D₄	C₂³×C₈₉	1	32	yes	—
398	#117	C₂³×C₈₉	1	4	yes	—
399	#117	C₂³×C₈₉	1	4	yes	—
400	#117	C₂³×C₈₉	1	4	yes	—
401	#117	C₂³×C₈₉	1	4	yes	—
402	#117	C₂³×C₈₉	1	4	yes	—
403	#117	C₂³×C₈₉	1	4	yes	—
404	#117	C₂³×C₈₉	1	4	yes	—
405	#117	C₂³×C₈₉	1	32	yes	—
406	#117	C₂³×C₈₉	1	4	yes	—
407	#117	C₂³×C₈₉	1	16	yes	—
408	#117	C₂³×C₈₉	1	16	yes	—
409	#117	C₂³×C₈₉	1	16	yes	—
410	#117	C₂³×C₈₉	1	64	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	8	yes	—
414	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
415	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
416	C₂×C₄⋊C₄	C₂³×C₈₉	1	16	yes	—
417	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	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	16	yes	—
421	C₂×C₂²⋊C₄	C₂³×C₈₉	1	16	yes	—
422	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
423	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
424	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
425	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
426	C₂×C₄²	C₂³×C₈₉	1	16	yes	—
427	C₂⁴	C₂⁴×C₈₉	1	4	yes	—
428	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
429	#41	—	2	16	no	—
430	#41	—	2	16	no	—
431	#41	—	2	16	no	—
432	#41	—	2	16	no	—
433	C₂×Q₈	—	2	16	no	—
434	C₂×Q₈	—	2	16	no	—
435	C₂×Q₈	—	2	8	no	—
436	C₂×Q₈	—	2	8	no	—
437	C₂×Q₈	—	2	8	no	—
438	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
439	C₂×Q₈	C₂⁴×C₈₉	1	8	yes	—
440	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
441	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
442	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
443	C₂×Q₈	C₂⁴×C₈₉	1	16	yes	—
444	C₂×D₄	—	2	16	no	—
445	C₂×D₄	—	2	8	no	—
446	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
447	C₂×D₄	C₂⁴×C₈₉	1	8	yes	—
448	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
449	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
450	C₂×D₄	C₂⁴×C₈₉	1	16	yes	—
451	C₂²×C₄	—	2	8	no	—
452	C₂²×C₄	—	2	16	no	—
453	C₂²×C₄	#41×C₈₉	1	8	yes	—
454	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
455	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
456	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
457	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
458	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
459	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
460	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
461	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
462	C₂²×C₄	C₂⁴×C₈₉	1	32	yes	—
463	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
464	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
466	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
467	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
468	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
469	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
470	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
471	C₄⋊C₄	C₂⁴×C₈₉	1	32	yes	—
472	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
473	C₄⋊C₄	C₂⁴×C₈₉	1	32	yes	—
474	C₄⋊C₄	C₂⁴×C₈₉	1	64	yes	—
475	C₄⋊C₄	C₂⁴×C₈₉	1	32	yes	—
476	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
477	C₄⋊C₄	C₂⁴×C₈₉	1	16	yes	—
478	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
479	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
480	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
481	C₂²⋊C₄	C₂⁴×C₈₉	1	8	yes	—
482	C₂²⋊C₄	C₂⁴×C₈₉	1	32	yes	—
483	C₂²⋊C₄	C₂⁴×C₈₉	1	64	yes	—
484	C₂²⋊C₄	C₂⁴×C₈₉	1	32	yes	—
485	C₄²	C₂⁴×C₈₉	1	8	yes	—
486	C₄²	C₂⁴×C₈₉	1	8	yes	—
487	C₄²	C₂⁴×C₈₉	1	32	yes	—
488	C₄²	C₂⁴×C₈₉	1	32	yes	—
489	C₄²	C₂⁴×C₈₉	1	4	yes	—
490	C₄²	C₂⁴×C₈₉	1	8	yes	—
491	C₄²	C₂⁴×C₈₉	1	4	yes	—
492	C₂³	—	2	8	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	8	no	—
495	C₂³	C₂×#41×C₈₉	1	4	yes	—
496	C₂³	C₂⁵×C₈₉	1	8	yes	—
497	C₂³	C₂⁵×C₈₉	1	2	yes	—
498	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
499	Q₈	—	2	8	no	—
500	Q₈	—	2	16	no	—
501	Q₈	—	2	8	no	—
502	Q₈	—	2	8	no	—
503	Q₈	—	2	8	no	—
504	Q₈	—	4	16	no	—
505	D₄	—	2	16	no	—
506	D₄	—	2	16	no	—
507	D₄	—	2	8	no	—
508	D₄	—	2	8	no	—
509	D₄	—	4	16	no	—
510	C₂×C₄	—	2	8	no	—
511	C₂×C₄	—	2	16	no	—
512	C₂×C₄	—	2	8	no	—
513	C₂×C₄	—	2	16	no	—
514	C₂×C₄	—	2	16	no	—
515	C₂×C₄	—	4	4	no	—
516	C₂×C₄	—	4	32	no	—
517	C₂×C₄	—	4	8	no	—
518	C₂×C₄	—	4	4	no	—
519	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
520	C₂×C₄	C₂×#41×C₈₉	1	8	yes	—
521	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
522	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
523	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
524	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
525	C₂×C₄	C₂⁵×C₈₉	1	16	yes	—
526	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
527	C₂×C₄	C₂⁵×C₈₉	1	8	yes	—
528	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
529	C₂×C₄	C₂⁵×C₈₉	1	2	yes	—
530	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
531	C₂²	—	2	2	no	—
532	C₂²	—	2	4	no	—
533	C₂²	—	2	8	no	—
534	C₂²	—	2	16	no	—
535	C₂²	—	4	4	no	—
536	C₂²	—	8	8	no	—
537	C₂²	C₂²×#41×C₈₉	1	4	yes	—
538	C₂²	C₂²×#41×C₈₉	1	2	yes	—
539	C₂²	C₂⁶×C₈₉	1	1	yes	characteristic
540	C₄	—	2	8	no	—
541	C₄	—	2	8	no	—
542	C₄	—	2	8	no	—
543	C₄	—	2	16	no	—
544	C₄	—	2	8	no	—
545	C₄	C₂²×#41×C₈₉	1	2	yes	—
546	C₄	C₂²×#41×C₈₉	1	4	yes	—
547	C₄	C₂²×#41×C₈₉	1	2	yes	—
548	C₂	—	2	4	no	—
549	C₂	—	2	2	no	—
550	C₂	—	4	8	no	—
551	C₂	C₂³×#41×C₈₉	1	1	yes	characteristic
552	C₂	C₈₉×2₋¹⁺⁶	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₈₉
prime radical	C₈₉×#3449	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₈₉×#3510	C₂	semidirect
2. C₈₉×#3509	C₂	semidirect
3. C₈₉×#3507	C₂	semidirect
4. C₈₉×#3495	C₂	semidirect
5. C₈₉×#3491	C₂	semidirect
6. C₈₉×#3461	C₂	semidirect
7. C₈₉×#3458	C₂	semidirect
9. C₂×#536×C₈₉	C₂	semidirect
10. C₈₉×#3428	C₂	semidirect
11. C₂×#519×C₈₉	C₂	semidirect
14. #559×C₈₉	C₂²	semidirect
15. #557×C₈₉	C₂²	semidirect
16. #556×C₈₉	C₂²	semidirect
17. #556×C₈₉	C₂²	semidirect
18. #554×C₈₉	C₂²	semidirect
19. #552×C₈₉	C₂²	semidirect
20. #552×C₈₉	C₂²	semidirect
21. #551×C₈₉	C₂²	semidirect
22. #544×C₈₉	C₂²	semidirect
23. #544×C₈₉	C₂²	semidirect
25. #542×C₈₉	C₂²	semidirect
26. #541×C₈₉	C₂²	semidirect
27. #539×C₈₉	C₂²	semidirect
32. #536×C₈₉	C₂²	semidirect
33. #536×C₈₉	C₂²	semidirect
36. #533×C₈₉	C₂²	semidirect
37. #533×C₈₉	C₂²	semidirect
38. #533×C₈₉	C₂²	semidirect
40. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
41. #529×C₈₉	C₂²	semidirect
42. #529×C₈₉	C₂²	semidirect
43. C₂×#124×C₈₉	C₂²	semidirect
46. C₂×C₂²⋊Q₈×C₈₉	C₂²	semidirect
48. #520×C₈₉	C₂²	semidirect
49. #519×C₈₉	C₂²	semidirect
50. #519×C₈₉	C₂²	semidirect
51. #519×C₈₉	C₂²	semidirect
53. #518×C₈₉	C₂²	semidirect
55. C₄×#41×C₈₉	C₂²	semidirect
56. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
57. C₂×C₄×Q₈×C₈₉	C₂²	semidirect
62. C₂×#117×C₈₉	C₂²	semidirect
271. #62860	C₈₉	direct (N × H)
277. #3510	C₂×C₈₉	semidirect
278. #3509	C₂×C₈₉	semidirect
279. #3507	C₂×C₈₉	semidirect
280. #3495	C₂×C₈₉	semidirect
281. #3491	C₂×C₈₉	semidirect
282. #3461	C₂×C₈₉	semidirect
283. #3458	C₂×C₈₉	semidirect
285. C₂×#536	C₂×C₈₉	semidirect
286. #3428	C₂×C₈₉	semidirect
287. C₂×#519	C₂×C₈₉	semidirect
288. C₈₉	#62860	direct (N × H)
291. #559	C₂²×C₈₉	semidirect
292. #557	C₂²×C₈₉	semidirect
293. #556	C₂²×C₈₉	semidirect
294. #556	C₂²×C₈₉	semidirect
295. #554	C₂²×C₈₉	semidirect
296. #552	C₂²×C₈₉	semidirect
297. #552	C₂²×C₈₉	semidirect
298. #551	C₂²×C₈₉	semidirect
299. #544	C₂²×C₈₉	semidirect
300. #544	C₂²×C₈₉	semidirect
302. #542	C₂²×C₈₉	semidirect
303. #541	C₂²×C₈₉	semidirect
304. #539	C₂²×C₈₉	semidirect
309. #536	C₂²×C₈₉	semidirect
310. #536	C₂²×C₈₉	semidirect
313. #533	C₂²×C₈₉	semidirect
314. #533	C₂²×C₈₉	semidirect
315. #533	C₂²×C₈₉	semidirect
317. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
318. #529	C₂²×C₈₉	semidirect
319. #529	C₂²×C₈₉	semidirect
320. C₂×#124	C₂²×C₈₉	semidirect
323. C₂×C₂²⋊Q₈	C₂²×C₈₉	semidirect
325. #520	C₂²×C₈₉	semidirect
326. #519	C₂²×C₈₉	semidirect
327. #519	C₂²×C₈₉	semidirect
328. #519	C₂²×C₈₉	semidirect
330. #518	C₂²×C₈₉	semidirect
332. C₄×#41	C₂²×C₈₉	semidirect
333. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
334. C₂×C₄×Q₈	C₂²×C₈₉	semidirect
339. C₂×#117	C₂²×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#3510	2
C₈₉×#3509	2
C₈₉×#3507	2
C₈₉×#3495	2
C₈₉×#3491	2
C₈₉×#3461	2
C₈₉×#3458	2
C₈₉×#3449	2
C₂×#536×C₈₉	2
C₈₉×#3428	2
C₂×#519×C₈₉	2
#62860	89

Subgroups — C89×#62860 #36440708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#62860 #36440708