Subgroups — C₈₉×#60820 #36438668

Order 22784.

2122 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#3499	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3221	C₂	1	8	yes	maximal, complemented
4	C₈₉×#3207	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3206	C₂	1	4	yes	maximal, complemented
6	C₈₉×#3151	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#492×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈₉×#3139	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈₉×#3131	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#3042	C₂	1	4	yes	maximal, complemented
11	C₈₉×#3010	C₂	1	4	yes	maximal, complemented
12	C₈₉×#2922	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	2	yes	—
14	C₂×AGL(1,ℤ/8)×C₈₉	C₂²	1	4	yes	—
15	C₂²×SD₁₆×C₈₉	C₂²	1	4	yes	—
16	#559×C₈₉	—	2	2	no	—
17	#550×C₈₉	—	2	2	no	—
18	D₄×Q₈×C₈₉	—	2	2	no	—
19	#547×C₈₉	—	2	4	no	—
20	#547×C₈₉	—	2	2	no	—
21	#546×C₈₉	—	2	4	no	—
22	#540×C₈₉	C₂²	1	4	yes	—
23	#536×C₈₉	C₂²	1	2	yes	—
24	#536×C₈₉	C₂²	1	4	yes	complemented
25	#535×C₈₉	C₂²	1	2	yes	—
26	#533×C₈₉	C₂²	1	1	yes	characteristic
27	#532×C₈₉	C₂²	1	1	yes	characteristic
28	#532×C₈₉	C₂²	1	4	yes	—
29	#532×C₈₉	C₂²	1	2	yes	complemented
30	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	complemented
32	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
33	#518×C₈₉	C₂²	1	2	yes	—
34	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
35	#496×C₈₉	C₂²	1	4	yes	—
36	#493×C₈₉	C₂²	1	2	yes	—
37	#492×C₈₉	C₂²	1	4	yes	—
38	#492×C₈₉	C₂²	1	4	yes	—
39	#492×C₈₉	C₂²	1	2	yes	—
40	#491×C₈₉	C₂²	1	4	yes	complemented
41	#488×C₈₉	C₂²	1	4	yes	complemented
42	#487×C₈₉	C₂²	1	2	yes	complemented
43	#487×C₈₉	C₂²	1	4	yes	complemented
44	#486×C₈₉	C₂²	1	2	yes	complemented
45	#463×C₈₉	C₂²	1	16	yes	complemented
46	#461×C₈₉	C₂²	1	16	yes	complemented
47	#449×C₈₉	C₂²	1	16	yes	complemented
48	#448×C₈₉	C₂²	1	16	yes	complemented
49	#433×C₈₉	C₂²	1	4	yes	complemented
50	#431×C₈₉	C₂²	1	4	yes	complemented
51	#424×C₈₉	C₂²	1	2	yes	—
52	#419×C₈₉	C₂²	1	4	yes	—
53	#416×C₈₉	C₂²	1	4	yes	—
54	#408×C₈₉	C₂²	1	2	yes	—
55	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
57	2₋¹⁺⁴×C₈₉	—	4	8	no	—
58	C₂×#41×C₈₉	—	2	4	no	—
59	C₂×#41×C₈₉	—	2	2	no	—
60	C₂×#41×C₈₉	—	2	4	no	—
61	C₂×#41×C₈₉	C₂³	1	2	yes	—
62	C₂×#41×C₈₉	C₂³	1	4	yes	—
63	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
64	C₂²×Q₈×C₈₉	—	2	2	no	—
65	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
66	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
67	C₂²×D₄×C₈₉	—	2	2	no	—
68	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
69	AGL(1,ℤ/8)×C₈₉	—	4	8	no	—
70	C₂×SD₁₆×C₈₉	—	4	8	no	—
71	C₂×SD₁₆×C₈₉	C₂³	1	8	yes	—
72	C₂×SD₁₆×C₈₉	C₂³	1	16	yes	—
73	C₂×D₈×C₈₉	C₂³	1	8	yes	—
74	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
75	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
76	C₄⋊Q₈×C₈₉	—	2	2	no	—
77	C₄⋊Q₈×C₈₉	—	2	4	no	—
78	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
79	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
80	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
81	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
82	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
83	#127×C₈₉	—	2	2	no	—
84	#127×C₈₉	—	2	2	no	—
85	#127×C₈₉	C₂³	1	1	yes	characteristic
86	#127×C₈₉	C₂³	1	2	yes	—
87	#127×C₈₉	C₂³	1	2	yes	—
88	#125×C₈₉	C₂³	1	2	yes	—
89	#124×C₈₉	—	2	2	no	—
90	#124×C₈₉	—	2	4	no	—
91	#124×C₈₉	C₂³	1	4	yes	—
92	#124×C₈₉	C₂³	1	2	yes	—
93	#123×C₈₉	—	2	8	no	—
94	#123×C₈₉	—	2	4	no	—
95	#123×C₈₉	—	2	8	no	—
96	C₂²⋊Q₈×C₈₉	—	2	2	no	—
97	C₂²⋊Q₈×C₈₉	—	2	4	no	—
98	C₂²⋊Q₈×C₈₉	—	2	8	no	—
99	#121×C₈₉	—	2	4	no	—
100	#121×C₈₉	—	2	2	no	—
101	#121×C₈₉	—	2	4	no	—
102	#121×C₈₉	—	2	8	no	—
103	#121×C₈₉	C₂³	1	8	yes	—
104	#120×C₈₉	—	2	4	no	—
105	C₄×Q₈×C₈₉	—	2	2	no	—
106	C₄×Q₈×C₈₉	D₄	1	2	yes	—
107	C₄×D₄×C₈₉	—	2	4	no	—
108	C₄×D₄×C₈₉	—	2	4	no	—
109	C₄×D₄×C₈₉	—	2	2	no	—
110	C₄×D₄×C₈₉	—	2	4	no	—
111	C₄×D₄×C₈₉	D₄	1	4	yes	—
112	C₄×D₄×C₈₉	D₄	1	2	yes	—
113	C₄×D₄×C₈₉	C₂³	1	8	yes	—
114	#117×C₈₉	C₂³	1	2	yes	—
115	#117×C₈₉	C₂³	1	1	yes	characteristic
116	#117×C₈₉	C₂³	1	2	yes	—
117	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
118	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
119	C₂×C₂²⋊C₄×C₈₉	—	2	4	no	—
120	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
122	C₄⋊C₈×C₈₉	C₂³	1	8	yes	—
123	#103×C₈₉	C₂³	1	8	yes	—
124	#103×C₈₉	C₂³	1	16	yes	—
125	#102×C₈₉	C₂³	1	8	yes	—
126	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
127	#97×C₈₉	C₂³	1	2	yes	—
128	C₄×C₈×C₈₉	C₂³	1	2	yes	—
129	C₄×C₈×C₈₉	C₂³	1	2	yes	—
130	C₄×C₈×C₈₉	C₂³	1	2	yes	—
131	C₂⁴×C₈₉	—	2	2	no	—
132	#41×C₈₉	—	2	4	no	—
133	#41×C₈₉	—	2	8	no	—
134	#41×C₈₉	—	4	8	no	—
135	#41×C₈₉	—	4	16	no	—
136	#41×C₈₉	—	4	8	no	—
137	#41×C₈₉	—	8	8	no	—
138	C₂×Q₈×C₈₉	—	2	2	no	—
139	C₂×Q₈×C₈₉	—	2	4	no	—
140	C₂×Q₈×C₈₉	—	2	2	no	—
141	C₂×Q₈×C₈₉	—	2	8	no	—
142	C₂×Q₈×C₈₉	—	4	8	no	—
143	C₂×Q₈×C₈₉	—	4	8	no	—
144	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
145	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
146	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
147	C₂×D₄×C₈₉	—	2	4	no	—
148	C₂×D₄×C₈₉	—	2	2	no	—
149	C₂×D₄×C₈₉	—	2	8	no	—
150	C₂×D₄×C₈₉	—	2	2	no	—
151	C₂×D₄×C₈₉	—	2	2	no	—
152	C₂×D₄×C₈₉	—	2	4	no	—
153	C₂×D₄×C₈₉	—	2	4	no	—
154	C₂×D₄×C₈₉	—	2	8	no	—
155	C₂×D₄×C₈₉	—	8	4	no	—
156	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
157	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
159	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
160	C₂²×C₄×C₈₉	—	2	4	no	—
161	C₂²×C₄×C₈₉	—	2	2	no	—
162	C₂²×C₄×C₈₉	—	2	4	no	—
163	C₂²×C₄×C₈₉	—	2	2	no	—
164	C₂²×C₄×C₈₉	—	2	8	no	—
165	C₂²×C₄×C₈₉	C₂×D₄	1	4	yes	—
166	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
167	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
168	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
169	SD₁₆×C₈₉	—	4	16	no	—
170	SD₁₆×C₈₉	—	4	8	no	—
171	D₈×C₈₉	—	4	8	no	—
172	M₁₆×C₈₉	—	2	4	no	—
173	C₂×C₈×C₈₉	—	2	4	no	—
174	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
175	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
176	C₄⋊C₄×C₈₉	—	2	4	no	—
177	C₄⋊C₄×C₈₉	—	2	2	no	—
178	C₄⋊C₄×C₈₉	—	2	8	no	—
179	C₄⋊C₄×C₈₉	—	2	4	no	—
180	C₄⋊C₄×C₈₉	—	2	2	no	—
181	C₄⋊C₄×C₈₉	—	2	4	no	—
182	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
183	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
184	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
185	C₂²⋊C₄×C₈₉	—	2	2	no	—
186	C₂²⋊C₄×C₈₉	—	2	8	no	—
187	C₂²⋊C₄×C₈₉	—	2	8	no	—
188	C₂²⋊C₄×C₈₉	—	2	8	no	—
189	C₂²⋊C₄×C₈₉	—	2	4	no	—
190	C₂²⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
191	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
192	C₄²×C₈₉	—	2	2	no	—
193	C₄²×C₈₉	C₂×D₄	1	4	yes	—
194	C₄²×C₈₉	C₂×D₄	1	2	yes	—
195	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
196	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
197	C₄²×C₈₉	C₂⁴	1	2	yes	—
198	C₂³×C₈₉	—	2	2	no	—
199	C₂³×C₈₉	—	2	4	no	—
200	C₂³×C₈₉	—	4	4	no	—
201	C₂³×C₈₉	—	8	4	no	—
202	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
203	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
204	Q₈×C₈₉	—	2	2	no	—
205	Q₈×C₈₉	—	2	8	no	—
206	Q₈×C₈₉	—	2	4	no	—
207	Q₈×C₈₉	—	4	8	no	—
208	Q₈×C₈₉	—	4	4	no	—
209	Q₈×C₈₉	—	4	4	no	—
210	D₄×C₈₉	—	2	4	no	—
211	D₄×C₈₉	—	2	2	no	—
212	D₄×C₈₉	—	2	4	no	—
213	D₄×C₈₉	—	2	8	no	—
214	D₄×C₈₉	—	4	8	no	—
215	D₄×C₈₉	—	4	4	no	—
216	D₄×C₈₉	—	4	4	no	—
217	D₄×C₈₉	—	4	4	no	—
218	D₄×C₈₉	—	4	8	no	—
219	D₄×C₈₉	—	8	4	no	—
220	D₄×C₈₉	—	8	8	no	—
221	C₂×C₄×C₈₉	—	2	4	no	—
222	C₂×C₄×C₈₉	—	2	8	no	—
223	C₂×C₄×C₈₉	—	2	4	no	—
224	C₂×C₄×C₈₉	—	2	4	no	—
225	C₂×C₄×C₈₉	—	2	4	no	—
226	C₂×C₄×C₈₉	—	2	2	no	—
227	C₂×C₄×C₈₉	—	4	8	no	—
228	C₂×C₄×C₈₉	—	4	8	no	—
229	C₂×C₄×C₈₉	—	4	4	no	—
230	C₂×C₄×C₈₉	—	4	4	no	—
231	C₂×C₄×C₈₉	—	8	8	no	—
232	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
233	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
234	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
235	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
237	C₂×C₄×C₈₉	H(5,𝔽₂)	1	4	yes	—
238	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
239	C₈×C₈₉	—	2	4	no	—
240	C₈×C₈₉	—	2	4	no	—
241	C₂²×C₈₉	—	2	2	no	—
242	C₂²×C₈₉	—	2	2	no	—
243	C₂²×C₈₉	—	2	4	no	—
244	C₂²×C₈₉	—	4	2	no	—
245	C₂²×C₈₉	—	4	4	no	—
246	C₂²×C₈₉	—	4	8	no	—
247	C₂²×C₈₉	—	4	4	no	—
248	C₂²×C₈₉	—	16	4	no	—
249	C₂²×C₈₉	#535	1	2	yes	—
250	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
251	C₄×C₈₉	—	2	2	no	—
252	C₄×C₈₉	—	2	4	no	—
253	C₄×C₈₉	—	2	2	no	—
254	C₄×C₈₉	—	4	4	no	—
255	C₄×C₈₉	—	4	2	no	—
256	C₄×C₈₉	—	4	4	no	—
257	C₄×C₈₉	#535	1	2	yes	—
258	C₄×C₈₉	#577	1	4	yes	—
259	C₄×C₈₉	C₂×H(5,𝔽₂)	1	2	yes	—
260	#60820	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂×C₈₉	—	2	2	no	—
262	C₂×C₈₉	—	4	2	no	—
263	C₂×C₈₉	—	8	2	no	—
264	C₂×C₈₉	—	8	4	no	—
265	C₂×C₈₉	C₂×#535	1	1	yes	characteristic
266	C₂×C₈₉	C₂×#577	1	2	yes	—
267	#3508	C₂×C₈₉	1	1	yes	characteristic, complemented
268	#3499	C₂×C₈₉	1	1	yes	characteristic, complemented
269	#3221	C₂×C₈₉	1	8	yes	complemented
270	#3207	C₂×C₈₉	1	4	yes	complemented
271	#3206	C₂×C₈₉	1	4	yes	complemented
272	#3151	C₂×C₈₉	1	1	yes	characteristic, complemented
273	C₂×#492	C₂×C₈₉	1	1	yes	characteristic, complemented
274	#3139	C₂×C₈₉	1	1	yes	characteristic, complemented
275	#3131	C₂×C₈₉	1	1	yes	characteristic, complemented
276	#3042	C₂×C₈₉	1	4	yes	complemented
277	#3010	C₂×C₈₉	1	4	yes	complemented
278	#2922	C₂×C₈₉	1	1	yes	characteristic, complemented
279	C₈₉	#60820	1	1	yes	characteristic, direct product factor, Sylow
280	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	2	yes	—
281	C₂×AGL(1,ℤ/8)	C₂²×C₈₉	1	4	yes	—
282	C₂²×SD₁₆	C₂²×C₈₉	1	4	yes	—
283	#559	—	2	2	no	—
284	#550	—	2	2	no	—
285	D₄×Q₈	—	2	2	no	—
286	#547	—	2	4	no	—
287	#547	—	2	2	no	—
288	#546	—	2	4	no	—
289	#540	C₂²×C₈₉	1	4	yes	—
290	#536	C₂²×C₈₉	1	2	yes	—
291	#536	C₂²×C₈₉	1	4	yes	complemented
292	#535	C₂²×C₈₉	1	2	yes	—
293	#533	C₂²×C₈₉	1	1	yes	characteristic
294	#532	C₂²×C₈₉	1	1	yes	characteristic
295	#532	C₂²×C₈₉	1	4	yes	—
296	#532	C₂²×C₈₉	1	2	yes	complemented
297	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
298	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	complemented
299	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
300	#518	C₂²×C₈₉	1	2	yes	—
301	C₄×#41	C₂²×C₈₉	1	1	yes	characteristic
302	#496	C₂²×C₈₉	1	4	yes	—
303	#493	C₂²×C₈₉	1	2	yes	—
304	#492	C₂²×C₈₉	1	4	yes	—
305	#492	C₂²×C₈₉	1	4	yes	—
306	#492	C₂²×C₈₉	1	2	yes	—
307	#491	C₂²×C₈₉	1	4	yes	complemented
308	#488	C₂²×C₈₉	1	4	yes	complemented
309	#487	C₂²×C₈₉	1	2	yes	complemented
310	#487	C₂²×C₈₉	1	4	yes	complemented
311	#486	C₂²×C₈₉	1	2	yes	complemented
312	#463	C₂²×C₈₉	1	16	yes	complemented
313	#461	C₂²×C₈₉	1	16	yes	complemented
314	#449	C₂²×C₈₉	1	16	yes	complemented
315	#448	C₂²×C₈₉	1	16	yes	complemented
316	#433	C₂²×C₈₉	1	4	yes	complemented
317	#431	C₂²×C₈₉	1	4	yes	complemented
318	#424	C₂²×C₈₉	1	2	yes	—
319	#419	C₂²×C₈₉	1	4	yes	—
320	#416	C₂²×C₈₉	1	4	yes	—
321	#408	C₂²×C₈₉	1	2	yes	—
322	C₄×M₁₆	C₂²×C₈₉	1	1	yes	characteristic
323	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
324	2₋¹⁺⁴	—	4	8	no	—
325	C₂×#41	—	2	4	no	—
326	C₂×#41	—	2	2	no	—
327	C₂×#41	—	2	4	no	—
328	C₂×#41	C₂³×C₈₉	1	2	yes	—
329	C₂×#41	C₂³×C₈₉	1	4	yes	—
330	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
331	C₂²×Q₈	—	2	2	no	—
332	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
333	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
334	C₂²×D₄	—	2	2	no	—
335	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
336	AGL(1,ℤ/8)	—	4	8	no	—
337	C₂×SD₁₆	—	4	8	no	—
338	C₂×SD₁₆	C₂³×C₈₉	1	16	yes	—
339	C₂×SD₁₆	C₂³×C₈₉	1	8	yes	—
340	C₂×D₈	C₂³×C₈₉	1	8	yes	—
341	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
342	C₂²×C₈	C₂³×C₈₉	1	2	yes	—
343	C₄⋊Q₈	—	2	2	no	—
344	C₄⋊Q₈	—	2	4	no	—
345	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
346	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
347	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
348	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
349	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
350	#127	—	2	2	no	—
351	#127	—	2	2	no	—
352	#127	C₂³×C₈₉	1	2	yes	—
353	#127	C₂³×C₈₉	1	2	yes	—
354	#127	C₂³×C₈₉	1	1	yes	characteristic
355	#125	C₂³×C₈₉	1	2	yes	—
356	#124	—	2	2	no	—
357	#124	—	2	4	no	—
358	#124	C₂³×C₈₉	1	2	yes	—
359	#124	C₂³×C₈₉	1	4	yes	—
360	#123	—	2	8	no	—
361	#123	—	2	4	no	—
362	#123	—	2	8	no	—
363	C₂²⋊Q₈	—	2	2	no	—
364	C₂²⋊Q₈	—	2	4	no	—
365	C₂²⋊Q₈	—	2	8	no	—
366	#121	—	2	4	no	—
367	#121	—	2	2	no	—
368	#121	—	2	4	no	—
369	#121	—	2	8	no	—
370	#121	C₂³×C₈₉	1	8	yes	—
371	#120	—	2	4	no	—
372	C₄×Q₈	—	2	2	no	—
373	C₄×Q₈	D₄×C₈₉	1	2	yes	—
374	C₄×D₄	—	2	4	no	—
375	C₄×D₄	—	2	4	no	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	4	no	—
378	C₄×D₄	D₄×C₈₉	1	4	yes	—
379	C₄×D₄	D₄×C₈₉	1	2	yes	—
380	C₄×D₄	C₂³×C₈₉	1	8	yes	—
381	#117	C₂³×C₈₉	1	2	yes	—
382	#117	C₂³×C₈₉	1	1	yes	characteristic
383	#117	C₂³×C₈₉	1	2	yes	—
384	C₂×C₄⋊C₄	—	2	2	no	—
385	C₂×C₄⋊C₄	—	2	4	no	—
386	C₂×C₂²⋊C₄	—	2	4	no	—
387	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
388	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
389	C₄⋊C₈	C₂³×C₈₉	1	8	yes	—
390	#103	C₂³×C₈₉	1	8	yes	—
391	#103	C₂³×C₈₉	1	16	yes	—
392	#102	C₂³×C₈₉	1	8	yes	—
393	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
394	#97	C₂³×C₈₉	1	2	yes	—
395	C₄×C₈	C₂³×C₈₉	1	2	yes	—
396	C₄×C₈	C₂³×C₈₉	1	2	yes	—
397	C₄×C₈	C₂³×C₈₉	1	2	yes	—
398	C₂⁴	—	2	2	no	—
399	#41	—	2	4	no	—
400	#41	—	2	8	no	—
401	#41	—	4	8	no	—
402	#41	—	4	16	no	—
403	#41	—	4	8	no	—
404	#41	—	8	8	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	4	no	—
407	C₂×Q₈	—	2	2	no	—
408	C₂×Q₈	—	2	8	no	—
409	C₂×Q₈	—	4	8	no	—
410	C₂×Q₈	—	4	8	no	—
411	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
412	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
413	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
414	C₂×D₄	—	2	4	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	8	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	8	no	—
422	C₂×D₄	—	8	4	no	—
423	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
424	C₂×D₄	C₂×D₄×C₈₉	1	1	yes	characteristic
425	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
426	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
427	C₂²×C₄	—	2	4	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	8	no	—
432	C₂²×C₄	C₂×D₄×C₈₉	1	4	yes	—
433	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
434	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
435	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
436	SD₁₆	—	4	16	no	—
437	SD₁₆	—	4	8	no	—
438	D₈	—	4	8	no	—
439	M₁₆	—	2	4	no	—
440	C₂×C₈	—	2	4	no	—
441	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
442	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	8	no	—
446	C₄⋊C₄	—	2	4	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	4	no	—
449	C₄⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
450	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
451	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	8	no	—
454	C₂²⋊C₄	—	2	8	no	—
455	C₂²⋊C₄	—	2	8	no	—
456	C₂²⋊C₄	—	2	4	no	—
457	C₂²⋊C₄	C₂×D₄×C₈₉	1	2	yes	—
458	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
459	C₄²	—	2	2	no	—
460	C₄²	C₂×D₄×C₈₉	1	4	yes	—
461	C₄²	C₂×D₄×C₈₉	1	2	yes	—
462	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
463	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
464	C₄²	C₂⁴×C₈₉	1	2	yes	—
465	C₂³	—	2	2	no	—
466	C₂³	—	2	4	no	—
467	C₂³	—	4	4	no	—
468	C₂³	—	8	4	no	—
469	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
470	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
471	Q₈	—	2	2	no	—
472	Q₈	—	2	8	no	—
473	Q₈	—	2	4	no	—
474	Q₈	—	4	8	no	—
475	Q₈	—	4	4	no	—
476	Q₈	—	4	4	no	—
477	D₄	—	2	4	no	—
478	D₄	—	2	2	no	—
479	D₄	—	2	4	no	—
480	D₄	—	2	8	no	—
481	D₄	—	4	8	no	—
482	D₄	—	4	4	no	—
483	D₄	—	4	4	no	—
484	D₄	—	4	4	no	—
485	D₄	—	4	8	no	—
486	D₄	—	8	4	no	—
487	D₄	—	8	8	no	—
488	C₂×C₄	—	2	4	no	—
489	C₂×C₄	—	2	8	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	4	no	—
492	C₂×C₄	—	2	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	4	8	no	—
495	C₂×C₄	—	4	8	no	—
496	C₂×C₄	—	4	4	no	—
497	C₂×C₄	—	4	4	no	—
498	C₂×C₄	—	8	8	no	—
499	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
500	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
501	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
502	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
503	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
504	C₂×C₄	H(5,𝔽₂)×C₈₉	1	4	yes	—
505	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
506	C₈	—	2	4	no	—
507	C₈	—	2	4	no	—
508	C₂²	—	2	2	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	4	8	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	4	4	no	—
515	C₂²	—	16	4	no	—
516	C₂²	#535×C₈₉	1	2	yes	—
517	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
518	C₄	—	2	4	no	—
519	C₄	—	2	2	no	—
520	C₄	—	2	2	no	—
521	C₄	—	4	4	no	—
522	C₄	—	4	4	no	—
523	C₄	—	4	2	no	—
524	C₄	#535×C₈₉	1	2	yes	—
525	C₄	#577×C₈₉	1	4	yes	—
526	C₄	C₂×H(5,𝔽₂)×C₈₉	1	2	yes	—
527	C₂	—	2	2	no	—
528	C₂	—	4	2	no	—
529	C₂	—	8	2	no	—
530	C₂	—	8	4	no	—
531	C₂	C₂×#535×C₈₉	1	1	yes	characteristic
532	C₂	C₂×#577×C₈₉	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₄×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3508	C₂	semidirect
2. C₈₉×#3499	C₂	semidirect
3. C₈₉×#3221	C₂	semidirect
4. C₈₉×#3207	C₂	semidirect
5. C₈₉×#3206	C₂	semidirect
6. C₈₉×#3151	C₂	semidirect
7. C₂×#492×C₈₉	C₂	semidirect
8. C₈₉×#3139	C₂	semidirect
9. C₈₉×#3131	C₂	semidirect
10. C₈₉×#3042	C₂	semidirect
11. C₈₉×#3010	C₂	semidirect
12. C₈₉×#2922	C₂	semidirect
24. #536×C₈₉	C₂²	semidirect
29. #532×C₈₉	C₂²	semidirect
31. C₂×C₄⋊Q₈×C₈₉	C₂²	semidirect
40. #491×C₈₉	C₂²	semidirect
41. #488×C₈₉	C₂²	semidirect
42. #487×C₈₉	C₂²	semidirect
43. #487×C₈₉	C₂²	semidirect
44. #486×C₈₉	C₂²	semidirect
45. #463×C₈₉	C₂²	semidirect
46. #461×C₈₉	C₂²	semidirect
47. #449×C₈₉	C₂²	semidirect
48. #448×C₈₉	C₂²	semidirect
49. #433×C₈₉	C₂²	semidirect
50. #431×C₈₉	C₂²	semidirect
260. #60820	C₈₉	direct (N × H)
267. #3508	C₂×C₈₉	semidirect
268. #3499	C₂×C₈₉	semidirect
269. #3221	C₂×C₈₉	semidirect
270. #3207	C₂×C₈₉	semidirect
271. #3206	C₂×C₈₉	semidirect
272. #3151	C₂×C₈₉	semidirect
273. C₂×#492	C₂×C₈₉	semidirect
274. #3139	C₂×C₈₉	semidirect
275. #3131	C₂×C₈₉	semidirect
276. #3042	C₂×C₈₉	semidirect
277. #3010	C₂×C₈₉	semidirect
278. #2922	C₂×C₈₉	semidirect
279. C₈₉	#60820	direct (N × H)
291. #536	C₂²×C₈₉	semidirect
296. #532	C₂²×C₈₉	semidirect
298. C₂×C₄⋊Q₈	C₂²×C₈₉	semidirect
307. #491	C₂²×C₈₉	semidirect
308. #488	C₂²×C₈₉	semidirect
309. #487	C₂²×C₈₉	semidirect
310. #487	C₂²×C₈₉	semidirect
311. #486	C₂²×C₈₉	semidirect
312. #463	C₂²×C₈₉	semidirect
313. #461	C₂²×C₈₉	semidirect
314. #449	C₂²×C₈₉	semidirect
315. #448	C₂²×C₈₉	semidirect
316. #433	C₂²×C₈₉	semidirect
317. #431	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×#3508	2
C₈₉×#3499	2
C₈₉×#3221	2
C₈₉×#3207	2
C₈₉×#3206	2
C₈₉×#3151	2
C₂×#492×C₈₉	2
C₈₉×#3139	2
C₈₉×#3131	2
C₈₉×#3042	2
C₈₉×#3010	2
C₈₉×#2922	2
#60820	89

Subgroups — C89×#60820 #36438668

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60820 #36438668