Subgroups — C₈₉×#60459 #36438307

Order 22784.

2688 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#578×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#131×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3489	C₂	1	2	yes	maximal, complemented
4	C₈₉×#3063	C₂	1	6	yes	maximal, complemented
5	C₈₉×#3061	C₂	1	3	yes	maximal, complemented
6	C₈₉×#3059	C₂	1	3	yes	maximal, complemented
7	C₈₉×#3056	C₂	1	6	yes	maximal, complemented
8	C₈₉×#3050	C₂	1	3	yes	maximal, complemented
9	C₂×#467×C₈₉	C₂	1	3	yes	maximal, complemented
10	C₈₉×#2913	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2898	C₂	1	2	yes	maximal, complemented
12	C₂×2₋¹⁺⁴×C₈₉	C₂²	1	2	yes	—
13	C₂²×#41×C₈₉	C₂²	1	1	yes	characteristic
14	#578×C₈₉	—	2	8	no	—
15	C₂×#137×C₈₉	C₂²	1	6	yes	complemented
16	C₂×#135×C₈₉	C₂²	1	3	yes	complemented
17	C₂²×Q₁₆×C₈₉	C₂²	1	3	yes	complemented
18	C₂×#131×C₈₉	—	2	8	no	—
19	C₂×#131×C₈₉	C₂²	1	3	yes	—
20	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
21	C₂×#131×C₈₉	C₂²	1	3	yes	—
22	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
23	C₂²×M₁₆×C₈₉	C₂²	1	3	yes	—
24	C₂³×C₈×C₈₉	C₂²	1	3	yes	—
25	D₄×Q₈×C₈₉	—	2	2	no	—
26	#548×C₈₉	—	2	2	no	—
27	#547×C₈₉	—	2	6	no	—
28	#546×C₈₉	—	2	6	no	—
29	#537×C₈₉	C₂²	1	6	yes	—
30	#536×C₈₉	C₂²	1	6	yes	—
31	#525×C₈₉	C₂²	1	6	yes	—
32	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	6	yes	—
33	#520×C₈₉	C₂²	1	2	yes	—
34	#470×C₈₉	C₂²	1	12	yes	complemented
35	#468×C₈₉	C₂²	1	12	yes	complemented
36	#467×C₈₉	C₂²	1	3	yes	—
37	#467×C₈₉	C₂²	1	6	yes	—
38	#467×C₈₉	C₂²	1	6	yes	complemented
39	#467×C₈₉	C₂²	1	6	yes	complemented
40	#467×C₈₉	C₂²	1	3	yes	complemented
41	#466×C₈₉	C₂²	1	1	yes	characteristic
42	#466×C₈₉	C₂²	1	3	yes	complemented
43	#465×C₈₉	C₂²	1	6	yes	—
44	#465×C₈₉	C₂²	1	6	yes	complemented
45	#428×C₈₉	C₂²	1	6	yes	complemented
46	#427×C₈₉	C₂²	1	3	yes	complemented
47	C₂×#107×C₈₉	C₂²	1	3	yes	complemented
48	#419×C₈₉	C₂²	1	6	yes	complemented
49	#417×C₈₉	C₂²	1	6	yes	complemented
50	#416×C₈₉	C₂²	1	6	yes	complemented
51	C₂×#103×C₈₉	C₂²	1	6	yes	complemented
52	2₋¹⁺⁴×C₈₉	—	2	8	no	—
53	2₋¹⁺⁴×C₈₉	—	2	8	no	—
54	C₂×#41×C₈₉	—	2	4	no	—
55	C₂×#41×C₈₉	—	2	4	no	—
56	C₂×#41×C₈₉	—	2	6	no	—
57	C₂×#41×C₈₉	D₄	1	3	yes	—
58	C₂×#41×C₈₉	D₄	1	1	yes	characteristic
59	C₂×#41×C₈₉	C₂³	1	6	yes	—
60	C₂×#41×C₈₉	C₂³	1	3	yes	—
61	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
62	C₂²×Q₈×C₈₉	—	2	2	no	—
63	C₂²×Q₈×C₈₉	D₄	1	1	yes	characteristic
64	C₂²×Q₈×C₈₉	C₂³	1	6	yes	—
65	C₂²×D₄×C₈₉	D₄	1	3	yes	—
66	C₂³×C₄×C₈₉	C₂³	1	3	yes	—
67	#137×C₈₉	—	2	24	no	—
68	#135×C₈₉	—	2	12	no	—
69	C₂×Q₁₆×C₈₉	—	2	12	no	—
70	C₂×Q₁₆×C₈₉	C₂³	1	3	yes	—
71	C₂×Q₁₆×C₈₉	C₂³	1	6	yes	—
72	C₂×SD₁₆×C₈₉	C₂³	1	6	yes	—
73	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
74	#131×C₈₉	—	2	4	no	—
75	#131×C₈₉	—	2	12	no	—
76	#131×C₈₉	—	2	12	no	—
77	#131×C₈₉	D₄	1	8	yes	complemented
78	C₂×M₁₆×C₈₉	—	2	12	no	—
79	C₂×M₁₆×C₈₉	C₂³	1	3	yes	—
80	C₂×M₁₆×C₈₉	C₂³	1	6	yes	—
81	C₂×M₁₆×C₈₉	C₂³	1	3	yes	—
82	C₂²×C₈×C₈₉	—	2	12	no	—
83	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
84	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
85	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
86	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
88	C₂²×C₈×C₈₉	C₂³	1	3	yes	—
89	C₄⋊Q₈×C₈₉	—	2	6	no	—
90	#124×C₈₉	—	2	6	no	—
91	#123×C₈₉	—	2	12	no	—
92	#123×C₈₉	—	2	6	no	—
93	C₂²⋊Q₈×C₈₉	—	2	6	no	—
94	C₂²⋊Q₈×C₈₉	—	2	6	no	—
95	C₂²⋊Q₈×C₈₉	—	2	6	no	—
96	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
97	C₂²⋊Q₈×C₈₉	C₂³	1	6	yes	—
98	C₂²⋊Q₈×C₈₉	C₂³	1	12	yes	—
99	#121×C₈₉	—	2	12	no	—
100	#121×C₈₉	—	2	6	no	—
101	#121×C₈₉	C₂³	1	2	yes	—
102	#121×C₈₉	C₂³	1	6	yes	—
103	#120×C₈₉	—	2	6	no	—
104	C₄×Q₈×C₈₉	—	2	2	no	—
105	C₄×D₄×C₈₉	—	2	6	no	—
106	C₄×D₄×C₈₉	—	2	6	no	—
107	C₄×D₄×C₈₉	—	2	6	no	—
108	#117×C₈₉	C₂³	1	6	yes	—
109	C₂×C₄⋊C₄×C₈₉	—	2	6	no	—
110	C₂×C₄⋊C₄×C₈₉	C₂³	1	6	yes	—
111	C₂×C₂²⋊C₄×C₈₉	—	2	6	no	—
112	#107×C₈₉	C₂³	1	3	yes	—
113	#107×C₈₉	C₂³	1	6	yes	—
114	#107×C₈₉	C₂³	1	1	yes	characteristic
115	#106×C₈₉	C₂³	1	6	yes	—
116	#103×C₈₉	C₂³	1	6	yes	—
117	#103×C₈₉	C₂³	1	12	yes	—
118	#103×C₈₉	C₂³	1	6	yes	—
119	#102×C₈₉	C₂³	1	2	yes	—
120	#102×C₈₉	C₂³	1	6	yes	—
121	C₂⁴×C₈₉	C₂×D₄	1	3	yes	—
122	#41×C₈₉	—	2	4	no	—
123	#41×C₈₉	—	2	12	no	—
124	#41×C₈₉	—	2	6	no	—
125	#41×C₈₉	—	2	6	no	—
126	#41×C₈₉	—	2	12	no	—
127	#41×C₈₉	—	2	12	no	—
128	#41×C₈₉	—	4	24	no	—
129	#41×C₈₉	C₂×D₄	1	4	yes	—
130	#41×C₈₉	#41	1	4	yes	—
131	C₂×Q₈×C₈₉	—	2	4	no	—
132	C₂×Q₈×C₈₉	—	2	6	no	—
133	C₂×Q₈×C₈₉	—	2	12	no	—
134	C₂×Q₈×C₈₉	—	2	12	no	—
135	C₂×Q₈×C₈₉	—	4	8	no	—
136	C₂×Q₈×C₈₉	C₂×D₄	1	3	yes	—
137	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂×Q₈×C₈₉	C₂⁴	1	6	yes	—
139	C₂×D₄×C₈₉	—	2	12	no	—
140	C₂×D₄×C₈₉	—	2	2	no	—
141	C₂×D₄×C₈₉	—	2	6	no	—
142	C₂×D₄×C₈₉	—	2	6	no	—
143	C₂×D₄×C₈₉	C₂×D₄	1	6	yes	—
144	C₂×D₄×C₈₉	C₂×D₄	1	3	yes	—
145	C₂×D₄×C₈₉	C₂×D₄	1	3	yes	—
146	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
147	C₂²×C₄×C₈₉	—	2	6	no	—
148	C₂²×C₄×C₈₉	—	2	6	no	—
149	C₂²×C₄×C₈₉	—	2	6	no	—
150	C₂²×C₄×C₈₉	—	2	6	no	—
151	C₂²×C₄×C₈₉	—	2	6	no	—
152	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
153	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
154	C₂²×C₄×C₈₉	C₂×D₄	1	3	yes	—
155	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
156	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
157	C₂²×C₄×C₈₉	C₂⁴	1	3	yes	—
158	Q₁₆×C₈₉	—	2	6	no	—
159	Q₁₆×C₈₉	—	2	12	no	—
160	SD₁₆×C₈₉	—	2	12	no	—
161	D₈×C₈₉	—	2	2	no	—
162	M₁₆×C₈₉	—	2	6	no	—
163	M₁₆×C₈₉	—	2	12	no	—
164	M₁₆×C₈₉	C₂×D₄	1	12	yes	—
165	C₂×C₈×C₈₉	—	2	6	no	—
166	C₂×C₈×C₈₉	—	2	2	no	—
167	C₂×C₈×C₈₉	—	2	6	no	—
168	C₂×C₈×C₈₉	—	2	6	no	—
169	C₂×C₈×C₈₉	—	2	6	no	—
170	C₂×C₈×C₈₉	C₂×D₄	1	12	yes	—
171	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
172	C₂×C₈×C₈₉	C₂⁴	1	3	yes	—
173	C₂×C₈×C₈₉	C₂⁴	1	3	yes	—
174	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
175	C₄⋊C₄×C₈₉	—	2	6	no	—
176	C₄⋊C₄×C₈₉	—	2	12	no	—
177	C₄⋊C₄×C₈₉	—	2	6	no	—
178	C₄⋊C₄×C₈₉	—	2	6	no	—
179	C₄⋊C₄×C₈₉	C₂⁴	1	2	yes	—
180	C₄⋊C₄×C₈₉	C₂⁴	1	6	yes	—
181	C₂²⋊C₄×C₈₉	—	2	6	no	—
182	C₂²⋊C₄×C₈₉	—	2	12	no	—
183	C₂²⋊C₄×C₈₉	—	2	6	no	—
184	C₂²⋊C₄×C₈₉	—	2	6	no	—
185	C₂²⋊C₄×C₈₉	—	2	2	no	—
186	C₂²⋊C₄×C₈₉	—	2	6	no	—
187	C₄²×C₈₉	—	2	6	no	—
188	C₂³×C₈₉	—	2	6	no	—
189	C₂³×C₈₉	—	2	6	no	—
190	C₂³×C₈₉	—	2	2	no	—
191	C₂³×C₈₉	—	4	3	no	—
192	C₂³×C₈₉	C₂²×D₄	1	3	yes	—
193	C₂³×C₈₉	C₂²×D₄	1	3	yes	—
194	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
195	Q₈×C₈₉	—	2	6	no	—
196	Q₈×C₈₉	—	2	6	no	—
197	Q₈×C₈₉	—	2	6	no	—
198	Q₈×C₈₉	—	4	12	no	—
199	Q₈×C₈₉	#121	1	4	yes	—
200	D₄×C₈₉	—	2	12	no	—
201	D₄×C₈₉	—	2	6	no	—
202	D₄×C₈₉	—	2	2	no	—
203	D₄×C₈₉	—	2	2	no	—
204	D₄×C₈₉	—	4	12	no	—
205	D₄×C₈₉	—	4	4	no	—
206	D₄×C₈₉	—	8	6	no	—
207	D₄×C₈₉	#121	1	12	yes	—
208	C₂×C₄×C₈₉	—	2	6	no	—
209	C₂×C₄×C₈₉	—	2	6	no	—
210	C₂×C₄×C₈₉	—	2	6	no	—
211	C₂×C₄×C₈₉	—	2	1	no	—
212	C₂×C₄×C₈₉	—	2	3	no	—
213	C₂×C₄×C₈₉	—	2	1	no	—
214	C₂×C₄×C₈₉	—	2	3	no	—
215	C₂×C₄×C₈₉	—	2	2	no	—
216	C₂×C₄×C₈₉	—	2	6	no	—
217	C₂×C₄×C₈₉	—	2	6	no	—
218	C₂×C₄×C₈₉	—	4	12	no	—
219	C₂×C₄×C₈₉	—	4	12	no	—
220	C₂×C₄×C₈₉	—	8	6	no	—
221	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
223	C₂×C₄×C₈₉	C₂²×D₄	1	3	yes	—
224	C₂×C₄×C₈₉	C₂²×D₄	1	6	yes	—
225	C₂×C₄×C₈₉	C₂×#41	1	6	yes	—
226	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
227	C₈×C₈₉	—	2	1	no	—
228	C₈×C₈₉	—	2	3	no	—
229	C₈×C₈₉	C₂²×D₄	1	2	yes	—
230	C₈×C₈₉	C₂²×D₄	1	6	yes	—
231	C₂²×C₈₉	—	2	3	no	—
232	C₂²×C₈₉	—	2	1	no	—
233	C₂²×C₈₉	—	2	1	no	—
234	C₂²×C₈₉	—	2	3	no	—
235	C₂²×C₈₉	—	2	3	no	—
236	C₂²×C₈₉	—	2	3	no	—
237	C₂²×C₈₉	—	2	3	no	—
238	C₂²×C₈₉	—	4	12	no	—
239	C₂²×C₈₉	—	4	2	no	—
240	C₂²×C₈₉	—	4	2	no	—
241	C₂²×C₈₉	—	4	2	no	—
242	C₂²×C₈₉	C₂×#121	1	6	yes	—
243	C₂²×C₈₉	#578	1	2	yes	complemented
244	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
245	C₄×C₈₉	—	2	1	no	—
246	C₄×C₈₉	—	2	3	no	—
247	C₄×C₈₉	—	4	6	no	—
248	C₄×C₈₉	—	4	6	no	—
249	C₄×C₈₉	—	4	2	no	—
250	C₄×C₈₉	C₂×#121	1	6	yes	—
251	C₄×C₈₉	C₂³×D₄	1	1	yes	characteristic
252	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
253	#60459	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
254	C₂×C₈₉	—	2	2	no	—
255	C₂×C₈₉	—	2	6	no	—
256	C₂×C₈₉	—	4	3	no	—
257	C₂×C₈₉	—	8	2	no	—
258	C₂×C₈₉	C₂²×#121	1	1	yes	characteristic
259	C₂×C₈₉	C₂×#578	1	1	yes	characteristic
260	C₂×C₈₉	#3584	1	1	yes	characteristic
261	C₂×#578	C₂×C₈₉	1	1	yes	characteristic, complemented
262	C₂²×#131	C₂×C₈₉	1	1	yes	characteristic, complemented
263	#3489	C₂×C₈₉	1	2	yes	complemented
264	#3063	C₂×C₈₉	1	6	yes	complemented
265	#3061	C₂×C₈₉	1	3	yes	complemented
266	#3059	C₂×C₈₉	1	3	yes	complemented
267	#3056	C₂×C₈₉	1	6	yes	complemented
268	#3050	C₂×C₈₉	1	3	yes	complemented
269	C₂×#467	C₂×C₈₉	1	3	yes	complemented
270	#2913	C₂×C₈₉	1	1	yes	characteristic, complemented
271	#2898	C₂×C₈₉	1	2	yes	complemented
272	C₈₉	#60459	1	1	yes	characteristic, direct product factor, Sylow
273	C₂×2₋¹⁺⁴	C₂²×C₈₉	1	2	yes	—
274	C₂²×#41	C₂²×C₈₉	1	1	yes	characteristic
275	#578	—	2	8	no	—
276	C₂×#137	C₂²×C₈₉	1	6	yes	complemented
277	C₂×#135	C₂²×C₈₉	1	3	yes	complemented
278	C₂²×Q₁₆	C₂²×C₈₉	1	3	yes	complemented
279	C₂×#131	—	2	8	no	—
280	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
281	C₂×#131	C₂²×C₈₉	1	3	yes	—
282	C₂×#131	C₂²×C₈₉	1	3	yes	—
283	C₂×#131	C₂²×C₈₉	1	1	yes	characteristic
284	C₂²×M₁₆	C₂²×C₈₉	1	3	yes	—
285	C₂³×C₈	C₂²×C₈₉	1	3	yes	—
286	D₄×Q₈	—	2	2	no	—
287	#548	—	2	2	no	—
288	#547	—	2	6	no	—
289	#546	—	2	6	no	—
290	#537	C₂²×C₈₉	1	6	yes	—
291	#536	C₂²×C₈₉	1	6	yes	—
292	#525	C₂²×C₈₉	1	6	yes	—
293	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	6	yes	—
294	#520	C₂²×C₈₉	1	2	yes	—
295	#470	C₂²×C₈₉	1	12	yes	complemented
296	#468	C₂²×C₈₉	1	12	yes	complemented
297	#467	C₂²×C₈₉	1	3	yes	—
298	#467	C₂²×C₈₉	1	6	yes	—
299	#467	C₂²×C₈₉	1	6	yes	complemented
300	#467	C₂²×C₈₉	1	6	yes	complemented
301	#467	C₂²×C₈₉	1	3	yes	complemented
302	#466	C₂²×C₈₉	1	1	yes	characteristic
303	#466	C₂²×C₈₉	1	3	yes	complemented
304	#465	C₂²×C₈₉	1	6	yes	—
305	#465	C₂²×C₈₉	1	6	yes	complemented
306	#428	C₂²×C₈₉	1	6	yes	complemented
307	#427	C₂²×C₈₉	1	3	yes	complemented
308	C₂×#107	C₂²×C₈₉	1	3	yes	complemented
309	#419	C₂²×C₈₉	1	6	yes	complemented
310	#417	C₂²×C₈₉	1	6	yes	complemented
311	#416	C₂²×C₈₉	1	6	yes	complemented
312	C₂×#103	C₂²×C₈₉	1	6	yes	complemented
313	2₋¹⁺⁴	—	2	8	no	—
314	2₋¹⁺⁴	—	2	8	no	—
315	C₂×#41	—	2	4	no	—
316	C₂×#41	—	2	4	no	—
317	C₂×#41	—	2	6	no	—
318	C₂×#41	D₄×C₈₉	1	3	yes	—
319	C₂×#41	D₄×C₈₉	1	1	yes	characteristic
320	C₂×#41	C₂³×C₈₉	1	6	yes	—
321	C₂×#41	C₂³×C₈₉	1	3	yes	—
322	C₂×#41	C₂³×C₈₉	1	1	yes	characteristic
323	C₂²×Q₈	—	2	2	no	—
324	C₂²×Q₈	D₄×C₈₉	1	1	yes	characteristic
325	C₂²×Q₈	C₂³×C₈₉	1	6	yes	—
326	C₂²×D₄	D₄×C₈₉	1	3	yes	—
327	C₂³×C₄	C₂³×C₈₉	1	3	yes	—
328	#137	—	2	24	no	—
329	#135	—	2	12	no	—
330	C₂×Q₁₆	—	2	12	no	—
331	C₂×Q₁₆	C₂³×C₈₉	1	3	yes	—
332	C₂×Q₁₆	C₂³×C₈₉	1	6	yes	—
333	C₂×SD₁₆	C₂³×C₈₉	1	6	yes	—
334	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
335	#131	—	2	4	no	—
336	#131	—	2	12	no	—
337	#131	—	2	12	no	—
338	#131	D₄×C₈₉	1	8	yes	complemented
339	C₂×M₁₆	—	2	12	no	—
340	C₂×M₁₆	C₂³×C₈₉	1	3	yes	—
341	C₂×M₁₆	C₂³×C₈₉	1	6	yes	—
342	C₂×M₁₆	C₂³×C₈₉	1	3	yes	—
343	C₂²×C₈	—	2	12	no	—
344	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
345	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
346	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
347	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
348	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
349	C₂²×C₈	C₂³×C₈₉	1	3	yes	—
350	C₄⋊Q₈	—	2	6	no	—
351	#124	—	2	6	no	—
352	#123	—	2	12	no	—
353	#123	—	2	6	no	—
354	C₂²⋊Q₈	—	2	6	no	—
355	C₂²⋊Q₈	—	2	6	no	—
356	C₂²⋊Q₈	—	2	6	no	—
357	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
358	C₂²⋊Q₈	C₂³×C₈₉	1	12	yes	—
359	C₂²⋊Q₈	C₂³×C₈₉	1	6	yes	—
360	#121	—	2	12	no	—
361	#121	—	2	6	no	—
362	#121	C₂³×C₈₉	1	2	yes	—
363	#121	C₂³×C₈₉	1	6	yes	—
364	#120	—	2	6	no	—
365	C₄×Q₈	—	2	2	no	—
366	C₄×D₄	—	2	6	no	—
367	C₄×D₄	—	2	6	no	—
368	C₄×D₄	—	2	6	no	—
369	#117	C₂³×C₈₉	1	6	yes	—
370	C₂×C₄⋊C₄	—	2	6	no	—
371	C₂×C₄⋊C₄	C₂³×C₈₉	1	6	yes	—
372	C₂×C₂²⋊C₄	—	2	6	no	—
373	#107	C₂³×C₈₉	1	3	yes	—
374	#107	C₂³×C₈₉	1	6	yes	—
375	#107	C₂³×C₈₉	1	1	yes	characteristic
376	#106	C₂³×C₈₉	1	6	yes	—
377	#103	C₂³×C₈₉	1	6	yes	—
378	#103	C₂³×C₈₉	1	12	yes	—
379	#103	C₂³×C₈₉	1	6	yes	—
380	#102	C₂³×C₈₉	1	2	yes	—
381	#102	C₂³×C₈₉	1	6	yes	—
382	C₂⁴	C₂×D₄×C₈₉	1	3	yes	—
383	#41	—	2	4	no	—
384	#41	—	2	12	no	—
385	#41	—	2	6	no	—
386	#41	—	2	6	no	—
387	#41	—	2	12	no	—
388	#41	—	2	12	no	—
389	#41	—	4	24	no	—
390	#41	C₂×D₄×C₈₉	1	4	yes	—
391	#41	#41×C₈₉	1	4	yes	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	6	no	—
394	C₂×Q₈	—	2	12	no	—
395	C₂×Q₈	—	2	12	no	—
396	C₂×Q₈	—	4	8	no	—
397	C₂×Q₈	C₂×D₄×C₈₉	1	3	yes	—
398	C₂×Q₈	C₂×D₄×C₈₉	1	1	yes	characteristic
399	C₂×Q₈	C₂⁴×C₈₉	1	6	yes	—
400	C₂×D₄	—	2	12	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	6	no	—
403	C₂×D₄	—	2	6	no	—
404	C₂×D₄	C₂×D₄×C₈₉	1	6	yes	—
405	C₂×D₄	C₂×D₄×C₈₉	1	3	yes	—
406	C₂×D₄	C₂×D₄×C₈₉	1	3	yes	—
407	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
408	C₂²×C₄	—	2	6	no	—
409	C₂²×C₄	—	2	6	no	—
410	C₂²×C₄	—	2	6	no	—
411	C₂²×C₄	—	2	6	no	—
412	C₂²×C₄	—	2	6	no	—
413	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
414	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
415	C₂²×C₄	C₂×D₄×C₈₉	1	3	yes	—
416	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
417	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
418	C₂²×C₄	C₂⁴×C₈₉	1	3	yes	—
419	Q₁₆	—	2	6	no	—
420	Q₁₆	—	2	12	no	—
421	SD₁₆	—	2	12	no	—
422	D₈	—	2	2	no	—
423	M₁₆	—	2	6	no	—
424	M₁₆	—	2	12	no	—
425	M₁₆	C₂×D₄×C₈₉	1	12	yes	—
426	C₂×C₈	—	2	6	no	—
427	C₂×C₈	—	2	2	no	—
428	C₂×C₈	—	2	6	no	—
429	C₂×C₈	—	2	6	no	—
430	C₂×C₈	—	2	6	no	—
431	C₂×C₈	C₂×D₄×C₈₉	1	12	yes	—
432	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
433	C₂×C₈	C₂⁴×C₈₉	1	3	yes	—
434	C₂×C₈	C₂⁴×C₈₉	1	3	yes	—
435	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
436	C₄⋊C₄	—	2	6	no	—
437	C₄⋊C₄	—	2	12	no	—
438	C₄⋊C₄	—	2	6	no	—
439	C₄⋊C₄	—	2	6	no	—
440	C₄⋊C₄	C₂⁴×C₈₉	1	2	yes	—
441	C₄⋊C₄	C₂⁴×C₈₉	1	6	yes	—
442	C₂²⋊C₄	—	2	6	no	—
443	C₂²⋊C₄	—	2	12	no	—
444	C₂²⋊C₄	—	2	6	no	—
445	C₂²⋊C₄	—	2	6	no	—
446	C₂²⋊C₄	—	2	2	no	—
447	C₂²⋊C₄	—	2	6	no	—
448	C₄²	—	2	6	no	—
449	C₂³	—	2	6	no	—
450	C₂³	—	2	6	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	4	3	no	—
453	C₂³	C₂²×D₄×C₈₉	1	3	yes	—
454	C₂³	C₂²×D₄×C₈₉	1	3	yes	—
455	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
456	Q₈	—	2	6	no	—
457	Q₈	—	2	6	no	—
458	Q₈	—	2	6	no	—
459	Q₈	—	4	12	no	—
460	Q₈	#121×C₈₉	1	4	yes	—
461	D₄	—	2	12	no	—
462	D₄	—	2	6	no	—
463	D₄	—	2	2	no	—
464	D₄	—	2	2	no	—
465	D₄	—	4	12	no	—
466	D₄	—	4	4	no	—
467	D₄	—	8	6	no	—
468	D₄	#121×C₈₉	1	12	yes	—
469	C₂×C₄	—	2	6	no	—
470	C₂×C₄	—	2	6	no	—
471	C₂×C₄	—	2	6	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	3	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	3	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	6	no	—
478	C₂×C₄	—	2	6	no	—
479	C₂×C₄	—	4	12	no	—
480	C₂×C₄	—	4	12	no	—
481	C₂×C₄	—	8	6	no	—
482	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
484	C₂×C₄	C₂²×D₄×C₈₉	1	3	yes	—
485	C₂×C₄	C₂²×D₄×C₈₉	1	6	yes	—
486	C₂×C₄	C₂×#41×C₈₉	1	6	yes	—
487	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
488	C₈	—	2	1	no	—
489	C₈	—	2	3	no	—
490	C₈	C₂²×D₄×C₈₉	1	2	yes	—
491	C₈	C₂²×D₄×C₈₉	1	6	yes	—
492	C₂²	—	2	3	no	—
493	C₂²	—	2	3	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	3	no	—
497	C₂²	—	2	3	no	—
498	C₂²	—	2	3	no	—
499	C₂²	—	4	12	no	—
500	C₂²	—	4	2	no	—
501	C₂²	—	4	2	no	—
502	C₂²	—	4	2	no	—
503	C₂²	C₂×#121×C₈₉	1	6	yes	—
504	C₂²	#578×C₈₉	1	2	yes	complemented
505	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	3	no	—
508	C₄	—	4	2	no	—
509	C₄	—	4	6	no	—
510	C₄	—	4	6	no	—
511	C₄	C₂×#121×C₈₉	1	6	yes	—
512	C₄	C₂³×D₄×C₈₉	1	1	yes	characteristic
513	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
514	C₂	—	2	2	no	—
515	C₂	—	2	6	no	—
516	C₂	—	4	3	no	—
517	C₂	—	8	2	no	—
518	C₂	C₂²×#121×C₈₉	1	1	yes	characteristic
519	C₂	C₂×#578×C₈₉	1	1	yes	characteristic
520	C₂	C₈₉×#3584	1	1	yes	characteristic

	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 ◁ C₂²×#41×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×#578×C₈₉	C₂	semidirect
2. C₂²×#131×C₈₉	C₂	semidirect
3. C₈₉×#3489	C₂	semidirect
4. C₈₉×#3063	C₂	semidirect
5. C₈₉×#3061	C₂	semidirect
6. C₈₉×#3059	C₂	semidirect
7. C₈₉×#3056	C₂	semidirect
8. C₈₉×#3050	C₂	semidirect
9. C₂×#467×C₈₉	C₂	semidirect
10. C₈₉×#2913	C₂	semidirect
11. C₈₉×#2898	C₂	semidirect
15. C₂×#137×C₈₉	C₂²	semidirect
16. C₂×#135×C₈₉	C₂²	semidirect
17. C₂²×Q₁₆×C₈₉	C₂²	semidirect
34. #470×C₈₉	C₂²	semidirect
35. #468×C₈₉	C₂²	semidirect
38. #467×C₈₉	C₂²	semidirect
39. #467×C₈₉	C₂²	semidirect
40. #467×C₈₉	C₂²	semidirect
42. #466×C₈₉	C₂²	semidirect
44. #465×C₈₉	C₂²	semidirect
45. #428×C₈₉	C₂²	semidirect
46. #427×C₈₉	C₂²	semidirect
47. C₂×#107×C₈₉	C₂²	semidirect
48. #419×C₈₉	C₂²	semidirect
49. #417×C₈₉	C₂²	semidirect
50. #416×C₈₉	C₂²	semidirect
51. C₂×#103×C₈₉	C₂²	semidirect
77. #131×C₈₉	D₄	semidirect
243. C₂²×C₈₉	#578	semidirect
253. #60459	C₈₉	direct (N × H)
261. C₂×#578	C₂×C₈₉	semidirect
262. C₂²×#131	C₂×C₈₉	semidirect
263. #3489	C₂×C₈₉	semidirect
264. #3063	C₂×C₈₉	semidirect
265. #3061	C₂×C₈₉	semidirect
266. #3059	C₂×C₈₉	semidirect
267. #3056	C₂×C₈₉	semidirect
268. #3050	C₂×C₈₉	semidirect
269. C₂×#467	C₂×C₈₉	semidirect
270. #2913	C₂×C₈₉	semidirect
271. #2898	C₂×C₈₉	semidirect
272. C₈₉	#60459	direct (N × H)
276. C₂×#137	C₂²×C₈₉	semidirect
277. C₂×#135	C₂²×C₈₉	semidirect
278. C₂²×Q₁₆	C₂²×C₈₉	semidirect
295. #470	C₂²×C₈₉	semidirect
296. #468	C₂²×C₈₉	semidirect
299. #467	C₂²×C₈₉	semidirect
300. #467	C₂²×C₈₉	semidirect
301. #467	C₂²×C₈₉	semidirect
303. #466	C₂²×C₈₉	semidirect
305. #465	C₂²×C₈₉	semidirect
306. #428	C₂²×C₈₉	semidirect
307. #427	C₂²×C₈₉	semidirect
308. C₂×#107	C₂²×C₈₉	semidirect
309. #419	C₂²×C₈₉	semidirect
310. #417	C₂²×C₈₉	semidirect
311. #416	C₂²×C₈₉	semidirect
312. C₂×#103	C₂²×C₈₉	semidirect
338. #131	D₄×C₈₉	semidirect
504. C₂²	#578×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×#578×C₈₉	2
C₂²×#131×C₈₉	2
C₈₉×#3489	2
C₈₉×#3063	2
C₈₉×#3061	2
C₈₉×#3059	2
C₈₉×#3056	2
C₈₉×#3050	2
C₂×#467×C₈₉	2
C₈₉×#2913	2
C₈₉×#2898	2
#60459	89

Subgroups — C89×#60459 #36438307

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60459 #36438307