Subgroups — C₈₉×#60921 #36438769

Order 22784.

1758 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3455	C₂	1	1	yes	maximal, characteristic
2	C₂×#541×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#3261	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3260	C₂	1	4	yes	maximal, complemented
5	C₈₉×#3258	C₂	1	8	yes	maximal, complemented
6	C₈₉×#3080	C₂	1	2	yes	maximal, complemented
7	C₈₉×#3078	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3056	C₂	1	4	yes	maximal, complemented
9	C₈₉×#3039	C₂	1	2	yes	maximal, complemented
10	C₈₉×#3037	C₂	1	2	yes	maximal, complemented
11	C₈₉×#2905	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#137×C₈₉	C₂²	1	4	yes	—
13	C₂²×M₁₆×C₈₉	C₂²	1	2	yes	—
14	#542×C₈₉	C₂²	1	4	yes	—
15	#541×C₈₉	—	2	4	no	—
16	#541×C₈₉	C₂²	1	4	yes	—
17	#541×C₈₉	C₂²	1	4	yes	—
18	#541×C₈₉	C₂²	1	2	yes	—
19	#540×C₈₉	C₂²	1	2	yes	—
20	#539×C₈₉	—	2	2	no	—
21	#538×C₈₉	—	2	2	no	—
22	#533×C₈₉	C₂²	1	1	yes	characteristic
23	#532×C₈₉	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
25	#529×C₈₉	—	2	4	no	—
26	C₂×#126×C₈₉	—	2	2	no	—
27	C₂×#125×C₈₉	—	2	2	no	—
28	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
29	#525×C₈₉	C₂²	1	2	yes	—
30	C₂×C₂²⋊Q₈×C₈₉	C₂²	1	2	yes	—
31	C₄×#41×C₈₉	C₂²	1	2	yes	—
32	C₂×C₄×Q₈×C₈₉	C₂²	1	2	yes	—
33	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
34	#479×C₈₉	C₂²	1	8	yes	complemented
35	#479×C₈₉	C₂²	1	8	yes	complemented
36	#478×C₈₉	C₂²	1	8	yes	complemented
37	#477×C₈₉	C₂²	1	4	yes	complemented
38	#475×C₈₉	C₂²	1	4	yes	complemented
39	#470×C₈₉	C₂²	1	8	yes	—
40	#468×C₈₉	C₂²	1	8	yes	—
41	#467×C₈₉	C₂²	1	8	yes	—
42	#465×C₈₉	C₂²	1	8	yes	—
43	#464×C₈₉	C₂²	1	8	yes	complemented
44	#462×C₈₉	C₂²	1	8	yes	complemented
45	#462×C₈₉	C₂²	1	4	yes	complemented
46	#461×C₈₉	C₂²	1	8	yes	complemented
47	#460×C₈₉	C₂²	1	4	yes	complemented
48	#428×C₈₉	C₂²	1	4	yes	—
49	#424×C₈₉	C₂²	1	4	yes	—
50	#424×C₈₉	C₂²	1	4	yes	—
51	#423×C₈₉	C₂²	1	2	yes	—
52	#423×C₈₉	C₂²	1	2	yes	—
53	#419×C₈₉	C₂²	1	4	yes	—
54	#417×C₈₉	C₂²	1	4	yes	—
55	C₂×#41×C₈₉	C₂³	1	2	yes	—
56	C₂²×Q₈×C₈₉	C₂³	1	2	yes	—
57	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
58	#137×C₈₉	—	4	8	no	—
59	C₂×Q₁₆×C₈₉	C₂³	1	8	yes	—
60	C₂×SD₁₆×C₈₉	C₂³	1	8	yes	—
61	C₂×M₁₆×C₈₉	—	4	4	no	—
62	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
63	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
64	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
65	C₄⋊Q₈×C₈₉	—	2	2	no	—
66	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
67	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
68	C₄⋊Q₈×C₈₉	C₂³	1	2	yes	—
69	#127×C₈₉	C₂³	1	1	yes	characteristic
70	#126×C₈₉	—	2	4	no	—
71	#126×C₈₉	—	2	8	no	—
72	#126×C₈₉	—	2	8	no	—
73	#126×C₈₉	—	2	4	no	—
74	#125×C₈₉	—	2	8	no	—
75	#125×C₈₉	—	2	8	no	—
76	#125×C₈₉	—	2	4	no	—
77	#125×C₈₉	—	2	2	no	—
78	#125×C₈₉	C₂³	1	4	yes	—
79	#125×C₈₉	C₂³	1	2	yes	—
80	#124×C₈₉	—	2	4	no	—
81	#124×C₈₉	C₂³	1	2	yes	—
82	#123×C₈₉	—	2	2	no	—
83	#123×C₈₉	—	2	4	no	—
84	#123×C₈₉	—	2	4	no	—
85	C₂²⋊Q₈×C₈₉	—	2	4	no	—
86	C₂²⋊Q₈×C₈₉	—	2	2	no	—
87	C₂²⋊Q₈×C₈₉	—	2	4	no	—
88	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
89	C₂²⋊Q₈×C₈₉	C₂³	1	4	yes	—
90	#121×C₈₉	—	2	2	no	—
91	#121×C₈₉	—	2	4	no	—
92	#121×C₈₉	C₂³	1	4	yes	—
93	#120×C₈₉	—	2	2	no	—
94	C₄×Q₈×C₈₉	—	2	2	no	—
95	C₄×Q₈×C₈₉	—	2	2	no	—
96	C₄×Q₈×C₈₉	—	2	2	no	—
97	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
98	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
99	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
100	C₄×D₄×C₈₉	—	2	4	no	—
101	C₄×D₄×C₈₉	—	2	4	no	—
102	C₄×D₄×C₈₉	—	2	2	no	—
103	C₄×D₄×C₈₉	C₂³	1	4	yes	—
104	#117×C₈₉	—	2	2	no	—
105	#117×C₈₉	D₄	1	4	yes	—
106	#117×C₈₉	C₂³	1	2	yes	—
107	#117×C₈₉	C₂³	1	2	yes	—
108	#117×C₈₉	C₂³	1	2	yes	—
109	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
110	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
111	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
112	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
113	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
114	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
115	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
116	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
117	C₂×C₄²×C₈₉	—	2	2	no	—
118	C₂×C₄²×C₈₉	—	2	2	no	—
119	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
121	#107×C₈₉	C₂³	1	8	yes	—
122	#106×C₈₉	C₂³	1	8	yes	—
123	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
124	C₄⋊C₈×C₈₉	C₂³	1	8	yes	—
125	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
126	#103×C₈₉	C₂³	1	8	yes	—
127	#103×C₈₉	C₂³	1	8	yes	—
128	#103×C₈₉	C₂³	1	8	yes	—
129	#102×C₈₉	C₂³	1	8	yes	—
130	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
131	#41×C₈₉	—	2	4	no	—
132	#41×C₈₉	—	2	4	no	—
133	C₂×Q₈×C₈₉	—	2	2	no	—
134	C₂×Q₈×C₈₉	—	2	2	no	—
135	C₂×Q₈×C₈₉	—	2	4	no	—
136	C₂×Q₈×C₈₉	—	2	4	no	—
137	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
138	C₂×Q₈×C₈₉	C₂⁴	1	4	yes	—
139	C₂×D₄×C₈₉	—	2	2	no	—
140	C₂×D₄×C₈₉	—	2	4	no	—
141	C₂×D₄×C₈₉	—	2	2	no	—
142	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
143	C₂²×C₄×C₈₉	—	2	2	no	—
144	C₂²×C₄×C₈₉	—	2	2	no	—
145	C₂²×C₄×C₈₉	—	2	2	no	—
146	C₂²×C₄×C₈₉	—	2	2	no	—
147	C₂²×C₄×C₈₉	—	2	2	no	—
148	C₂²×C₄×C₈₉	—	2	4	no	—
149	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
151	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
152	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
153	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
154	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
155	Q₁₆×C₈₉	—	4	8	no	—
156	SD₁₆×C₈₉	—	4	8	no	—
157	M₁₆×C₈₉	—	2	8	no	—
158	M₁₆×C₈₉	—	4	4	no	—
159	C₂×C₈×C₈₉	—	4	4	no	—
160	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
161	C₄⋊C₄×C₈₉	—	2	4	no	—
162	C₄⋊C₄×C₈₉	—	2	4	no	—
163	C₄⋊C₄×C₈₉	—	2	8	no	—
164	C₄⋊C₄×C₈₉	—	2	8	no	—
165	C₄⋊C₄×C₈₉	—	2	8	no	—
166	C₄⋊C₄×C₈₉	—	2	2	no	—
167	C₄⋊C₄×C₈₉	—	2	4	no	—
168	C₄⋊C₄×C₈₉	—	2	2	no	—
169	C₄⋊C₄×C₈₉	—	2	4	no	—
170	C₄⋊C₄×C₈₉	—	2	4	no	—
171	C₄⋊C₄×C₈₉	—	2	2	no	—
172	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
173	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
174	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
175	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
176	C₂²⋊C₄×C₈₉	—	2	8	no	—
177	C₂²⋊C₄×C₈₉	—	2	2	no	—
178	C₂²⋊C₄×C₈₉	—	2	4	no	—
179	C₂²⋊C₄×C₈₉	—	2	4	no	—
180	C₂²⋊C₄×C₈₉	—	2	4	no	—
181	C₂²⋊C₄×C₈₉	—	2	4	no	—
182	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
183	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
184	C₄²×C₈₉	—	2	2	no	—
185	C₄²×C₈₉	—	2	4	no	—
186	C₄²×C₈₉	—	2	4	no	—
187	C₄²×C₈₉	—	2	4	no	—
188	C₄²×C₈₉	C₂×D₄	1	2	yes	—
189	C₄²×C₈₉	C₂×D₄	1	2	yes	—
190	C₄²×C₈₉	C₂⁴	1	2	yes	—
191	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
192	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
193	C₂³×C₈₉	—	2	2	no	—
194	C₂³×C₈₉	—	2	2	no	—
195	C₂³×C₈₉	—	4	2	no	—
196	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
197	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
198	Q₈×C₈₉	—	2	4	no	—
199	Q₈×C₈₉	—	2	2	no	—
200	Q₈×C₈₉	—	2	4	no	—
201	Q₈×C₈₉	—	2	2	no	—
202	Q₈×C₈₉	—	4	4	no	—
203	Q₈×C₈₉	—	8	2	no	—
204	D₄×C₈₉	—	2	2	no	—
205	D₄×C₈₉	—	2	2	no	—
206	D₄×C₈₉	—	4	4	no	—
207	D₄×C₈₉	—	8	2	no	—
208	D₄×C₈₉	—	8	4	no	—
209	C₂×C₄×C₈₉	—	2	2	no	—
210	C₂×C₄×C₈₉	—	2	4	no	—
211	C₂×C₄×C₈₉	—	2	2	no	—
212	C₂×C₄×C₈₉	—	2	2	no	—
213	C₂×C₄×C₈₉	—	2	2	no	—
214	C₂×C₄×C₈₉	—	2	4	no	—
215	C₂×C₄×C₈₉	—	2	4	no	—
216	C₂×C₄×C₈₉	—	2	4	no	—
217	C₂×C₄×C₈₉	—	4	2	no	—
218	C₂×C₄×C₈₉	—	4	2	no	—
219	C₂×C₄×C₈₉	—	4	4	no	—
220	C₂×C₄×C₈₉	—	4	4	no	—
221	C₂×C₄×C₈₉	—	4	4	no	—
222	C₂×C₄×C₈₉	—	8	4	no	—
223	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
224	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
225	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
226	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
227	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₈₉	H(5,𝔽₂)	1	2	yes	—
229	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
230	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
231	C₈×C₈₉	—	2	8	no	—
232	C₂²×C₈₉	—	2	2	no	—
233	C₂²×C₈₉	—	2	4	no	—
234	C₂²×C₈₉	—	2	2	no	—
235	C₂²×C₈₉	—	4	4	no	—
236	C₂²×C₈₉	—	4	2	no	—
237	C₂²×C₈₉	—	8	2	no	—
238	C₂²×C₈₉	#537	1	2	yes	—
239	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
240	C₄×C₈₉	—	2	4	no	—
241	C₄×C₈₉	—	2	2	no	—
242	C₄×C₈₉	—	2	2	no	—
243	C₄×C₈₉	—	2	2	no	—
244	C₄×C₈₉	—	4	4	no	—
245	C₄×C₈₉	—	4	4	no	—
246	C₄×C₈₉	—	4	2	no	—
247	C₄×C₈₉	—	4	4	no	—
248	C₄×C₈₉	#537	1	2	yes	—
249	C₄×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
250	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
251	#60921	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
252	C₂×C₈₉	—	2	2	no	—
253	C₂×C₈₉	—	4	2	no	—
254	C₂×C₈₉	—	8	2	no	—
255	C₂×C₈₉	C₂×#537	1	1	yes	characteristic
256	C₂×C₈₉	#3586	1	2	yes	—
257	#3455	C₂×C₈₉	1	1	yes	characteristic
258	C₂×#541	C₂×C₈₉	1	1	yes	characteristic, complemented
259	#3261	C₂×C₈₉	1	4	yes	complemented
260	#3260	C₂×C₈₉	1	4	yes	complemented
261	#3258	C₂×C₈₉	1	8	yes	complemented
262	#3080	C₂×C₈₉	1	2	yes	complemented
263	#3078	C₂×C₈₉	1	2	yes	complemented
264	#3056	C₂×C₈₉	1	4	yes	complemented
265	#3039	C₂×C₈₉	1	2	yes	complemented
266	#3037	C₂×C₈₉	1	2	yes	complemented
267	#2905	C₂×C₈₉	1	1	yes	characteristic, complemented
268	C₈₉	#60921	1	1	yes	characteristic, direct product factor, Sylow
269	C₂×#137	C₂²×C₈₉	1	4	yes	—
270	C₂²×M₁₆	C₂²×C₈₉	1	2	yes	—
271	#542	C₂²×C₈₉	1	4	yes	—
272	#541	—	2	4	no	—
273	#541	C₂²×C₈₉	1	4	yes	—
274	#541	C₂²×C₈₉	1	4	yes	—
275	#541	C₂²×C₈₉	1	2	yes	—
276	#540	C₂²×C₈₉	1	2	yes	—
277	#539	—	2	2	no	—
278	#538	—	2	2	no	—
279	#533	C₂²×C₈₉	1	1	yes	characteristic
280	#532	C₂²×C₈₉	1	1	yes	characteristic
281	C₂×C₄⋊Q₈	C₂²×C₈₉	1	1	yes	characteristic
282	#529	—	2	4	no	—
283	C₂×#126	—	2	2	no	—
284	C₂×#125	—	2	2	no	—
285	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
286	#525	C₂²×C₈₉	1	2	yes	—
287	C₂×C₂²⋊Q₈	C₂²×C₈₉	1	2	yes	—
288	C₄×#41	C₂²×C₈₉	1	2	yes	—
289	C₂×C₄×Q₈	C₂²×C₈₉	1	2	yes	—
290	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
291	#479	C₂²×C₈₉	1	8	yes	complemented
292	#479	C₂²×C₈₉	1	8	yes	complemented
293	#478	C₂²×C₈₉	1	8	yes	complemented
294	#477	C₂²×C₈₉	1	4	yes	complemented
295	#475	C₂²×C₈₉	1	4	yes	complemented
296	#470	C₂²×C₈₉	1	8	yes	—
297	#468	C₂²×C₈₉	1	8	yes	—
298	#467	C₂²×C₈₉	1	8	yes	—
299	#465	C₂²×C₈₉	1	8	yes	—
300	#464	C₂²×C₈₉	1	8	yes	complemented
301	#462	C₂²×C₈₉	1	8	yes	complemented
302	#462	C₂²×C₈₉	1	4	yes	complemented
303	#461	C₂²×C₈₉	1	8	yes	complemented
304	#460	C₂²×C₈₉	1	4	yes	complemented
305	#428	C₂²×C₈₉	1	4	yes	—
306	#424	C₂²×C₈₉	1	4	yes	—
307	#424	C₂²×C₈₉	1	4	yes	—
308	#423	C₂²×C₈₉	1	2	yes	—
309	#423	C₂²×C₈₉	1	2	yes	—
310	#419	C₂²×C₈₉	1	4	yes	—
311	#417	C₂²×C₈₉	1	4	yes	—
312	C₂×#41	C₂³×C₈₉	1	2	yes	—
313	C₂²×Q₈	C₂³×C₈₉	1	2	yes	—
314	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
315	#137	—	4	8	no	—
316	C₂×Q₁₆	C₂³×C₈₉	1	8	yes	—
317	C₂×SD₁₆	C₂³×C₈₉	1	8	yes	—
318	C₂×M₁₆	—	4	4	no	—
319	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
320	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
321	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
322	C₄⋊Q₈	—	2	2	no	—
323	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
324	C₄⋊Q₈	C₂³×C₈₉	1	1	yes	characteristic
325	C₄⋊Q₈	C₂³×C₈₉	1	2	yes	—
326	#127	C₂³×C₈₉	1	1	yes	characteristic
327	#126	—	2	4	no	—
328	#126	—	2	8	no	—
329	#126	—	2	8	no	—
330	#126	—	2	4	no	—
331	#125	—	2	8	no	—
332	#125	—	2	8	no	—
333	#125	—	2	4	no	—
334	#125	—	2	2	no	—
335	#125	C₂³×C₈₉	1	4	yes	—
336	#125	C₂³×C₈₉	1	2	yes	—
337	#124	—	2	4	no	—
338	#124	C₂³×C₈₉	1	2	yes	—
339	#123	—	2	2	no	—
340	#123	—	2	4	no	—
341	#123	—	2	4	no	—
342	C₂²⋊Q₈	—	2	4	no	—
343	C₂²⋊Q₈	—	2	2	no	—
344	C₂²⋊Q₈	—	2	4	no	—
345	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
346	C₂²⋊Q₈	C₂³×C₈₉	1	4	yes	—
347	#121	—	2	2	no	—
348	#121	—	2	4	no	—
349	#121	C₂³×C₈₉	1	4	yes	—
350	#120	—	2	2	no	—
351	C₄×Q₈	—	2	2	no	—
352	C₄×Q₈	—	2	2	no	—
353	C₄×Q₈	—	2	2	no	—
354	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
355	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
356	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
357	C₄×D₄	—	2	4	no	—
358	C₄×D₄	—	2	4	no	—
359	C₄×D₄	—	2	2	no	—
360	C₄×D₄	C₂³×C₈₉	1	4	yes	—
361	#117	—	2	2	no	—
362	#117	D₄×C₈₉	1	4	yes	—
363	#117	C₂³×C₈₉	1	2	yes	—
364	#117	C₂³×C₈₉	1	2	yes	—
365	#117	C₂³×C₈₉	1	2	yes	—
366	C₂×C₄⋊C₄	—	2	2	no	—
367	C₂×C₄⋊C₄	—	2	2	no	—
368	C₂×C₄⋊C₄	—	2	2	no	—
369	C₂×C₄⋊C₄	—	2	2	no	—
370	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
371	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
374	C₂×C₄²	—	2	2	no	—
375	C₂×C₄²	—	2	2	no	—
376	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
378	#107	C₂³×C₈₉	1	8	yes	—
379	#106	C₂³×C₈₉	1	8	yes	—
380	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
381	C₄⋊C₈	C₂³×C₈₉	1	8	yes	—
382	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
383	#103	C₂³×C₈₉	1	8	yes	—
384	#103	C₂³×C₈₉	1	8	yes	—
385	#103	C₂³×C₈₉	1	8	yes	—
386	#102	C₂³×C₈₉	1	8	yes	—
387	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
388	#41	—	2	4	no	—
389	#41	—	2	4	no	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	4	no	—
394	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
395	C₂×Q₈	C₂⁴×C₈₉	1	4	yes	—
396	C₂×D₄	—	2	2	no	—
397	C₂×D₄	—	2	4	no	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	4	no	—
406	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
408	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
409	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
410	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
411	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
412	Q₁₆	—	4	8	no	—
413	SD₁₆	—	4	8	no	—
414	M₁₆	—	2	8	no	—
415	M₁₆	—	4	4	no	—
416	C₂×C₈	—	4	4	no	—
417	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	2	8	no	—
421	C₄⋊C₄	—	2	8	no	—
422	C₄⋊C₄	—	2	8	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	4	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	4	no	—
427	C₄⋊C₄	—	2	4	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
430	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
431	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
432	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
433	C₂²⋊C₄	—	2	8	no	—
434	C₂²⋊C₄	—	2	2	no	—
435	C₂²⋊C₄	—	2	4	no	—
436	C₂²⋊C₄	—	2	4	no	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₂²⋊C₄	—	2	4	no	—
439	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
440	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
441	C₄²	—	2	2	no	—
442	C₄²	—	2	4	no	—
443	C₄²	—	2	4	no	—
444	C₄²	—	2	4	no	—
445	C₄²	C₂×D₄×C₈₉	1	2	yes	—
446	C₄²	C₂×D₄×C₈₉	1	2	yes	—
447	C₄²	C₂⁴×C₈₉	1	2	yes	—
448	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
449	C₄²	C₂⁴×C₈₉	1	1	yes	characteristic
450	C₂³	—	2	2	no	—
451	C₂³	—	2	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
454	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
455	Q₈	—	2	4	no	—
456	Q₈	—	2	2	no	—
457	Q₈	—	2	4	no	—
458	Q₈	—	2	2	no	—
459	Q₈	—	4	4	no	—
460	Q₈	—	8	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	2	no	—
463	D₄	—	4	4	no	—
464	D₄	—	8	2	no	—
465	D₄	—	8	4	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	4	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	4	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	8	4	no	—
480	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
481	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
482	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
483	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
485	C₂×C₄	H(5,𝔽₂)×C₈₉	1	2	yes	—
486	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
487	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
488	C₈	—	2	8	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	4	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	8	2	no	—
495	C₂²	#537×C₈₉	1	2	yes	—
496	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
497	C₄	—	2	4	no	—
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	4	4	no	—
502	C₄	—	4	4	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	4	no	—
505	C₄	#537×C₈₉	1	2	yes	—
506	C₄	C₂×H(5,𝔽₂)×C₈₉	1	1	yes	characteristic
507	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
508	C₂	—	2	2	no	—
509	C₂	—	4	2	no	—
510	C₂	—	8	2	no	—
511	C₂	C₂×#537×C₈₉	1	1	yes	characteristic
512	C₂	C₈₉×#3586	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₈₉×#3455	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈₉ ◁ C₂×#117×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×#541×C₈₉	C₂	semidirect
3. C₈₉×#3261	C₂	semidirect
4. C₈₉×#3260	C₂	semidirect
5. C₈₉×#3258	C₂	semidirect
6. C₈₉×#3080	C₂	semidirect
7. C₈₉×#3078	C₂	semidirect
8. C₈₉×#3056	C₂	semidirect
9. C₈₉×#3039	C₂	semidirect
10. C₈₉×#3037	C₂	semidirect
11. C₈₉×#2905	C₂	semidirect
34. #479×C₈₉	C₂²	semidirect
35. #479×C₈₉	C₂²	semidirect
36. #478×C₈₉	C₂²	semidirect
37. #477×C₈₉	C₂²	semidirect
38. #475×C₈₉	C₂²	semidirect
43. #464×C₈₉	C₂²	semidirect
44. #462×C₈₉	C₂²	semidirect
45. #462×C₈₉	C₂²	semidirect
46. #461×C₈₉	C₂²	semidirect
47. #460×C₈₉	C₂²	semidirect
251. #60921	C₈₉	direct (N × H)
258. C₂×#541	C₂×C₈₉	semidirect
259. #3261	C₂×C₈₉	semidirect
260. #3260	C₂×C₈₉	semidirect
261. #3258	C₂×C₈₉	semidirect
262. #3080	C₂×C₈₉	semidirect
263. #3078	C₂×C₈₉	semidirect
264. #3056	C₂×C₈₉	semidirect
265. #3039	C₂×C₈₉	semidirect
266. #3037	C₂×C₈₉	semidirect
267. #2905	C₂×C₈₉	semidirect
268. C₈₉	#60921	direct (N × H)
291. #479	C₂²×C₈₉	semidirect
292. #479	C₂²×C₈₉	semidirect
293. #478	C₂²×C₈₉	semidirect
294. #477	C₂²×C₈₉	semidirect
295. #475	C₂²×C₈₉	semidirect
300. #464	C₂²×C₈₉	semidirect
301. #462	C₂²×C₈₉	semidirect
302. #462	C₂²×C₈₉	semidirect
303. #461	C₂²×C₈₉	semidirect
304. #460	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×#3455	2
C₂×#541×C₈₉	2
C₈₉×#3261	2
C₈₉×#3260	2
C₈₉×#3258	2
C₈₉×#3080	2
C₈₉×#3078	2
C₈₉×#3056	2
C₈₉×#3039	2
C₈₉×#3037	2
C₈₉×#2905	2
#60921	89

Subgroups — C89×#60921 #36438769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60921 #36438769