Subgroups — C₈₉×#61289 #36439137

Order 22784.

1774 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3512	C₂	1	2	yes	maximal, complemented
2	C₈₉×#3351	C₂	1	8	yes	maximal, complemented
3	C₈₉×#3339	C₂	1	4	yes	maximal, complemented
4	C₈₉×#3336	C₂	1	4	yes	maximal, complemented
5	C₂×#499×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈₉×#3099	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3080	C₂	1	2	yes	maximal, complemented
8	C₈₉×#3061	C₂	1	2	yes	maximal, complemented
9	C₄×#135×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈₉×#2931	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2913	C₂	1	2	yes	maximal, complemented
12	C₂×#135×C₈₉	C₂²	1	1	yes	characteristic
13	C₂×#131×C₈₉	C₂²	1	2	yes	—
14	#553×C₈₉	—	2	8	no	—
15	#553×C₈₉	C₂²	1	8	yes	—
16	#552×C₈₉	C₂²	1	8	yes	—
17	#541×C₈₉	—	2	2	no	—
18	#540×C₈₉	—	2	2	no	—
19	#537×C₈₉	C₂²	1	4	yes	—
20	#532×C₈₉	C₂²	1	1	yes	characteristic
21	#529×C₈₉	—	2	4	no	—
22	C₂×#125×C₈₉	C₂²	1	2	yes	—
23	#520×C₈₉	C₂²	1	4	yes	—
24	C₄×#41×C₈₉	C₂²	1	2	yes	—
25	#499×C₈₉	C₂²	1	4	yes	—
26	#499×C₈₉	C₂²	1	4	yes	—
27	#485×C₈₉	C₂²	1	8	yes	—
28	#483×C₈₉	C₂²	1	8	yes	—
29	#482×C₈₉	C₂²	1	8	yes	—
30	#481×C₈₉	C₂²	1	8	yes	—
31	#479×C₈₉	C₂²	1	8	yes	—
32	#478×C₈₉	C₂²	1	8	yes	—
33	#468×C₈₉	C₂²	1	8	yes	—
34	#467×C₈₉	C₂²	1	4	yes	—
35	#466×C₈₉	C₂²	1	4	yes	—
36	C₄×Q₁₆×C₈₉	C₂²	1	2	yes	—
37	C₄×SD₁₆×C₈₉	C₂²	1	4	yes	—
38	C₄×D₈×C₈₉	C₂²	1	2	yes	—
39	#436×C₈₉	C₂²	1	4	yes	—
40	C₈×D₄×C₈₉	C₂²	1	4	yes	—
41	#428×C₈₉	C₂²	1	4	yes	—
42	#428×C₈₉	C₂²	1	8	yes	—
43	#427×C₈₉	C₂²	1	4	yes	—
44	#427×C₈₉	C₂²	1	1	yes	characteristic
45	C₂×#107×C₈₉	C₂²	1	4	yes	—
46	C₂×#107×C₈₉	C₂²	1	2	yes	—
47	C₂×#106×C₈₉	C₂²	1	2	yes	—
48	#423×C₈₉	C₂²	1	1	yes	characteristic
49	#417×C₈₉	C₂²	1	4	yes	—
50	#416×C₈₉	C₂²	1	2	yes	—
51	#408×C₈₉	C₂²	1	2	yes	—
52	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
53	C₂×#41×C₈₉	C₂³	1	2	yes	—
54	C₂×#41×C₈₉	C₂³	1	2	yes	—
55	#135×C₈₉	—	2	4	no	—
56	C₂×Q₁₆×C₈₉	C₂³	1	1	yes	characteristic
57	C₂×SD₁₆×C₈₉	C₂³	1	2	yes	—
58	C₂×D₈×C₈₉	C₂³	1	1	yes	characteristic
59	#131×C₈₉	—	2	8	no	—
60	C₂×M₁₆×C₈₉	C₂³	1	2	yes	—
61	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
62	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₈₉	C₂³	1	4	yes	—
64	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
65	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
66	#127×C₈₉	D₄	1	1	yes	characteristic
67	#126×C₈₉	—	2	8	no	—
68	#126×C₈₉	—	2	8	no	—
69	#125×C₈₉	—	2	8	no	—
70	#125×C₈₉	—	2	2	no	—
71	#125×C₈₉	—	2	2	no	—
72	#125×C₈₉	C₂³	1	8	yes	—
73	#124×C₈₉	D₄	1	2	yes	—
74	#123×C₈₉	—	2	8	no	—
75	#123×C₈₉	—	2	8	no	—
76	C₂²⋊Q₈×C₈₉	—	2	4	no	—
77	C₂²⋊Q₈×C₈₉	C₂³	1	8	yes	—
78	#121×C₈₉	—	2	4	no	—
79	#121×C₈₉	—	2	8	no	—
80	#121×C₈₉	—	2	8	no	—
81	#121×C₈₉	D₄	1	4	yes	—
82	#121×C₈₉	C₂³	1	8	yes	—
83	C₄×Q₈×C₈₉	—	2	4	no	—
84	C₄×Q₈×C₈₉	C₂³	1	4	yes	—
85	C₄×D₄×C₈₉	—	2	4	no	—
86	C₄×D₄×C₈₉	—	2	8	no	—
87	C₄×D₄×C₈₉	—	2	4	no	—
88	C₄×D₄×C₈₉	—	2	8	no	—
89	C₄×D₄×C₈₉	C₂³	1	4	yes	—
90	C₄×D₄×C₈₉	C₂³	1	4	yes	—
91	#117×C₈₉	—	2	8	no	—
92	#117×C₈₉	—	2	2	no	—
93	#117×C₈₉	C₂³	1	2	yes	—
94	#117×C₈₉	C₂³	1	8	yes	—
95	C₂×C₄⋊C₄×C₈₉	—	2	4	no	—
96	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
97	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
98	C₂×C₄²×C₈₉	—	2	2	no	—
99	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
100	#107×C₈₉	C₂³	1	2	yes	—
101	#107×C₈₉	C₂³	1	4	yes	—
102	#107×C₈₉	C₂³	1	4	yes	—
103	#107×C₈₉	C₂³	1	8	yes	—
104	#106×C₈₉	C₂³	1	8	yes	—
105	#106×C₈₉	C₂³	1	2	yes	—
106	#106×C₈₉	C₂³	1	8	yes	—
107	C₄⋊C₈×C₈₉	C₂³	1	4	yes	—
108	#103×C₈₉	C₂³	1	4	yes	—
109	#103×C₈₉	C₂³	1	8	yes	—
110	#102×C₈₉	C₂³	1	4	yes	—
111	#102×C₈₉	C₂³	1	8	yes	—
112	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
113	C₂²⋊C₈×C₈₉	C₂³	1	4	yes	—
114	C₄×C₈×C₈₉	C₂³	1	2	yes	—
115	C₄×C₈×C₈₉	C₂³	1	2	yes	—
116	#41×C₈₉	—	2	4	no	—
117	#41×C₈₉	—	2	4	no	—
118	#41×C₈₉	—	2	4	no	—
119	#41×C₈₉	—	2	4	no	—
120	C₂×Q₈×C₈₉	C₂×D₄	1	2	yes	—
121	C₂×Q₈×C₈₉	C₂⁴	1	2	yes	—
122	C₂×D₄×C₈₉	—	2	2	no	—
123	C₂×D₄×C₈₉	—	2	8	no	—
124	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
125	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
126	C₂×D₄×C₈₉	C₂×D₄	1	4	yes	—
127	C₂×D₄×C₈₉	C₂⁴	1	2	yes	—
128	C₂²×C₄×C₈₉	—	2	4	no	—
129	C₂²×C₄×C₈₉	—	2	8	no	—
130	C₂²×C₄×C₈₉	—	2	2	no	—
131	C₂²×C₄×C₈₉	—	2	4	no	—
132	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₈₉	C₂⁴	1	4	yes	—
134	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
135	Q₁₆×C₈₉	—	2	2	no	—
136	SD₁₆×C₈₉	—	2	4	no	—
137	D₈×C₈₉	—	2	2	no	—
138	M₁₆×C₈₉	—	2	4	no	—
139	M₁₆×C₈₉	—	2	8	no	—
140	C₂×C₈×C₈₉	—	2	2	no	—
141	C₂×C₈×C₈₉	—	2	8	no	—
142	C₂×C₈×C₈₉	#41	1	4	yes	—
143	C₂×C₈×C₈₉	C₂⁴	1	2	yes	—
144	C₂×C₈×C₈₉	C₂⁴	1	4	yes	—
145	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
146	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
147	C₄⋊C₄×C₈₉	—	2	8	no	—
148	C₄⋊C₄×C₈₉	—	2	8	no	—
149	C₄⋊C₄×C₈₉	—	2	4	no	—
150	C₄⋊C₄×C₈₉	—	2	8	no	—
151	C₄⋊C₄×C₈₉	—	2	4	no	—
152	C₄⋊C₄×C₈₉	—	2	8	no	—
153	C₄⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
154	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
155	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
156	C₂²⋊C₄×C₈₉	—	2	8	no	—
157	C₂²⋊C₄×C₈₉	—	2	2	no	—
158	C₂²⋊C₄×C₈₉	—	2	8	no	—
159	C₂²⋊C₄×C₈₉	—	2	4	no	—
160	C₂²⋊C₄×C₈₉	—	2	8	no	—
161	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
162	C₂²⋊C₄×C₈₉	C₂×D₄	1	4	yes	—
163	C₄²×C₈₉	—	2	4	no	—
164	C₄²×C₈₉	—	2	2	no	—
165	C₄²×C₈₉	—	2	8	no	—
166	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
167	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₈₉	C₂⁴	1	2	yes	—
169	C₂³×C₈₉	—	2	2	no	—
170	C₂³×C₈₉	C₂²×D₄	1	4	yes	—
171	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
172	Q₈×C₈₉	—	2	4	no	—
173	Q₈×C₈₉	—	2	2	no	—
174	Q₈×C₈₉	—	2	2	no	—
175	D₄×C₈₉	—	2	8	no	—
176	D₄×C₈₉	—	2	4	no	—
177	D₄×C₈₉	—	2	2	no	—
178	D₄×C₈₉	—	2	2	no	—
179	D₄×C₈₉	—	4	4	no	—
180	D₄×C₈₉	—	4	4	no	—
181	D₄×C₈₉	—	8	8	no	—
182	C₂×C₄×C₈₉	—	2	4	no	—
183	C₂×C₄×C₈₉	—	2	4	no	—
184	C₂×C₄×C₈₉	—	2	4	no	—
185	C₂×C₄×C₈₉	—	2	2	no	—
186	C₂×C₄×C₈₉	—	2	8	no	—
187	C₂×C₄×C₈₉	—	4	2	no	—
188	C₂×C₄×C₈₉	—	4	4	no	—
189	C₂×C₄×C₈₉	—	8	4	no	—
190	C₂×C₄×C₈₉	—	8	8	no	—
191	C₂×C₄×C₈₉	—	8	4	no	—
192	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
194	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
195	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
197	C₂×C₄×C₈₉	2₋¹⁺⁴	1	2	yes	—
198	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
199	C₈×C₈₉	—	2	4	no	—
200	C₈×C₈₉	—	2	2	no	—
201	C₈×C₈₉	C₂×#41	1	2	yes	—
202	C₈×C₈₉	C₂×#41	1	2	yes	—
203	C₂²×C₈₉	—	2	2	no	—
204	C₂²×C₈₉	—	2	4	no	—
205	C₂²×C₈₉	—	2	4	no	—
206	C₂²×C₈₉	—	2	4	no	—
207	C₂²×C₈₉	—	4	4	no	—
208	C₂²×C₈₉	—	4	2	no	—
209	C₂²×C₈₉	#547	1	2	yes	—
210	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
211	C₄×C₈₉	—	2	2	no	—
212	C₄×C₈₉	—	2	2	no	—
213	C₄×C₈₉	—	2	4	no	—
214	C₄×C₈₉	—	4	4	no	—
215	C₄×C₈₉	—	4	8	no	—
216	C₄×C₈₉	—	4	2	no	—
217	C₄×C₈₉	#547	1	2	yes	—
218	C₄×C₈₉	C₂²×#41	1	1	yes	characteristic
219	C₄×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
220	#61289	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
221	C₂×C₈₉	—	2	2	no	—
222	C₂×C₈₉	—	4	4	no	—
223	C₂×C₈₉	—	8	2	no	—
224	C₂×C₈₉	C₂×#547	1	1	yes	characteristic
225	C₂×C₈₉	#3584	1	2	yes	—
226	#3512	C₂×C₈₉	1	2	yes	complemented
227	#3351	C₂×C₈₉	1	8	yes	complemented
228	#3339	C₂×C₈₉	1	4	yes	complemented
229	#3336	C₂×C₈₉	1	4	yes	complemented
230	C₂×#499	C₂×C₈₉	1	1	yes	characteristic, complemented
231	#3099	C₂×C₈₉	1	4	yes	complemented
232	#3080	C₂×C₈₉	1	2	yes	complemented
233	#3061	C₂×C₈₉	1	2	yes	complemented
234	C₄×#135	C₂×C₈₉	1	1	yes	characteristic, complemented
235	#2931	C₂×C₈₉	1	1	yes	characteristic, complemented
236	#2913	C₂×C₈₉	1	2	yes	complemented
237	C₈₉	#61289	1	1	yes	characteristic, direct product factor, Sylow
238	C₂×#135	C₂²×C₈₉	1	1	yes	characteristic
239	C₂×#131	C₂²×C₈₉	1	2	yes	—
240	#553	—	2	8	no	—
241	#553	C₂²×C₈₉	1	8	yes	—
242	#552	C₂²×C₈₉	1	8	yes	—
243	#541	—	2	2	no	—
244	#540	—	2	2	no	—
245	#537	C₂²×C₈₉	1	4	yes	—
246	#532	C₂²×C₈₉	1	1	yes	characteristic
247	#529	—	2	4	no	—
248	C₂×#125	C₂²×C₈₉	1	2	yes	—
249	#520	C₂²×C₈₉	1	4	yes	—
250	C₄×#41	C₂²×C₈₉	1	2	yes	—
251	#499	C₂²×C₈₉	1	4	yes	—
252	#499	C₂²×C₈₉	1	4	yes	—
253	#485	C₂²×C₈₉	1	8	yes	—
254	#483	C₂²×C₈₉	1	8	yes	—
255	#482	C₂²×C₈₉	1	8	yes	—
256	#481	C₂²×C₈₉	1	8	yes	—
257	#479	C₂²×C₈₉	1	8	yes	—
258	#478	C₂²×C₈₉	1	8	yes	—
259	#468	C₂²×C₈₉	1	8	yes	—
260	#467	C₂²×C₈₉	1	4	yes	—
261	#466	C₂²×C₈₉	1	4	yes	—
262	C₄×Q₁₆	C₂²×C₈₉	1	2	yes	—
263	C₄×SD₁₆	C₂²×C₈₉	1	4	yes	—
264	C₄×D₈	C₂²×C₈₉	1	2	yes	—
265	#436	C₂²×C₈₉	1	4	yes	—
266	C₈×D₄	C₂²×C₈₉	1	4	yes	—
267	#428	C₂²×C₈₉	1	4	yes	—
268	#428	C₂²×C₈₉	1	8	yes	—
269	#427	C₂²×C₈₉	1	4	yes	—
270	#427	C₂²×C₈₉	1	1	yes	characteristic
271	C₂×#107	C₂²×C₈₉	1	4	yes	—
272	C₂×#107	C₂²×C₈₉	1	2	yes	—
273	C₂×#106	C₂²×C₈₉	1	2	yes	—
274	#423	C₂²×C₈₉	1	1	yes	characteristic
275	#417	C₂²×C₈₉	1	4	yes	—
276	#416	C₂²×C₈₉	1	2	yes	—
277	#408	C₂²×C₈₉	1	2	yes	—
278	C₂×C₄×C₈	C₂²×C₈₉	1	1	yes	characteristic
279	C₂×#41	C₂³×C₈₉	1	2	yes	—
280	C₂×#41	C₂³×C₈₉	1	2	yes	—
281	#135	—	2	4	no	—
282	C₂×Q₁₆	C₂³×C₈₉	1	1	yes	characteristic
283	C₂×SD₁₆	C₂³×C₈₉	1	2	yes	—
284	C₂×D₈	C₂³×C₈₉	1	1	yes	characteristic
285	#131	—	2	8	no	—
286	C₂×M₁₆	C₂³×C₈₉	1	2	yes	—
287	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
288	C₂²×C₈	C₂³×C₈₉	1	4	yes	—
289	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
290	C₂²×C₈	C₂³×C₈₉	1	1	yes	characteristic
291	C₄⋊Q₈	D₄×C₈₉	1	1	yes	characteristic
292	#127	D₄×C₈₉	1	1	yes	characteristic
293	#126	—	2	8	no	—
294	#126	—	2	8	no	—
295	#125	—	2	8	no	—
296	#125	—	2	2	no	—
297	#125	—	2	2	no	—
298	#125	C₂³×C₈₉	1	8	yes	—
299	#124	D₄×C₈₉	1	2	yes	—
300	#123	—	2	8	no	—
301	#123	—	2	8	no	—
302	C₂²⋊Q₈	—	2	4	no	—
303	C₂²⋊Q₈	C₂³×C₈₉	1	8	yes	—
304	#121	—	2	4	no	—
305	#121	—	2	8	no	—
306	#121	—	2	8	no	—
307	#121	D₄×C₈₉	1	4	yes	—
308	#121	C₂³×C₈₉	1	8	yes	—
309	C₄×Q₈	—	2	4	no	—
310	C₄×Q₈	C₂³×C₈₉	1	4	yes	—
311	C₄×D₄	—	2	4	no	—
312	C₄×D₄	—	2	8	no	—
313	C₄×D₄	—	2	4	no	—
314	C₄×D₄	—	2	8	no	—
315	C₄×D₄	C₂³×C₈₉	1	4	yes	—
316	C₄×D₄	C₂³×C₈₉	1	4	yes	—
317	#117	—	2	8	no	—
318	#117	—	2	2	no	—
319	#117	C₂³×C₈₉	1	2	yes	—
320	#117	C₂³×C₈₉	1	8	yes	—
321	C₂×C₄⋊C₄	—	2	4	no	—
322	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
323	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
324	C₂×C₄²	—	2	2	no	—
325	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
326	#107	C₂³×C₈₉	1	2	yes	—
327	#107	C₂³×C₈₉	1	4	yes	—
328	#107	C₂³×C₈₉	1	4	yes	—
329	#107	C₂³×C₈₉	1	8	yes	—
330	#106	C₂³×C₈₉	1	8	yes	—
331	#106	C₂³×C₈₉	1	2	yes	—
332	#106	C₂³×C₈₉	1	8	yes	—
333	C₄⋊C₈	C₂³×C₈₉	1	4	yes	—
334	#103	C₂³×C₈₉	1	4	yes	—
335	#103	C₂³×C₈₉	1	8	yes	—
336	#102	C₂³×C₈₉	1	4	yes	—
337	#102	C₂³×C₈₉	1	8	yes	—
338	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
339	C₂²⋊C₈	C₂³×C₈₉	1	4	yes	—
340	C₄×C₈	C₂³×C₈₉	1	2	yes	—
341	C₄×C₈	C₂³×C₈₉	1	2	yes	—
342	#41	—	2	4	no	—
343	#41	—	2	4	no	—
344	#41	—	2	4	no	—
345	#41	—	2	4	no	—
346	C₂×Q₈	C₂×D₄×C₈₉	1	2	yes	—
347	C₂×Q₈	C₂⁴×C₈₉	1	2	yes	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	8	no	—
350	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
351	C₂×D₄	C₂×D₄×C₈₉	1	2	yes	—
352	C₂×D₄	C₂×D₄×C₈₉	1	4	yes	—
353	C₂×D₄	C₂⁴×C₈₉	1	2	yes	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	8	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
359	C₂²×C₄	C₂⁴×C₈₉	1	4	yes	—
360	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
361	Q₁₆	—	2	2	no	—
362	SD₁₆	—	2	4	no	—
363	D₈	—	2	2	no	—
364	M₁₆	—	2	4	no	—
365	M₁₆	—	2	8	no	—
366	C₂×C₈	—	2	2	no	—
367	C₂×C₈	—	2	8	no	—
368	C₂×C₈	#41×C₈₉	1	4	yes	—
369	C₂×C₈	C₂⁴×C₈₉	1	2	yes	—
370	C₂×C₈	C₂⁴×C₈₉	1	4	yes	—
371	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
372	C₂×C₈	C₂⁴×C₈₉	1	1	yes	characteristic
373	C₄⋊C₄	—	2	8	no	—
374	C₄⋊C₄	—	2	8	no	—
375	C₄⋊C₄	—	2	4	no	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	8	no	—
379	C₄⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
380	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
381	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
382	C₂²⋊C₄	—	2	8	no	—
383	C₂²⋊C₄	—	2	2	no	—
384	C₂²⋊C₄	—	2	8	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
388	C₂²⋊C₄	C₂×D₄×C₈₉	1	4	yes	—
389	C₄²	—	2	4	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	8	no	—
392	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
393	C₄²	C₂×D₄×C₈₉	1	1	yes	characteristic
394	C₄²	C₂⁴×C₈₉	1	2	yes	—
395	C₂³	—	2	2	no	—
396	C₂³	C₂²×D₄×C₈₉	1	4	yes	—
397	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
398	Q₈	—	2	4	no	—
399	Q₈	—	2	2	no	—
400	Q₈	—	2	2	no	—
401	D₄	—	2	8	no	—
402	D₄	—	2	4	no	—
403	D₄	—	2	2	no	—
404	D₄	—	2	2	no	—
405	D₄	—	4	4	no	—
406	D₄	—	4	4	no	—
407	D₄	—	8	8	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	8	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	4	no	—
415	C₂×C₄	—	8	4	no	—
416	C₂×C₄	—	8	8	no	—
417	C₂×C₄	—	8	4	no	—
418	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
419	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
420	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
421	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
422	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
423	C₂×C₄	2₋¹⁺⁴×C₈₉	1	2	yes	—
424	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
425	C₈	—	2	4	no	—
426	C₈	—	2	2	no	—
427	C₈	C₂×#41×C₈₉	1	2	yes	—
428	C₈	C₂×#41×C₈₉	1	2	yes	—
429	C₂²	—	2	2	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	4	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	4	2	no	—
435	C₂²	#547×C₈₉	1	2	yes	—
436	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	2	no	—
439	C₄	—	2	4	no	—
440	C₄	—	4	4	no	—
441	C₄	—	4	8	no	—
442	C₄	—	4	2	no	—
443	C₄	#547×C₈₉	1	2	yes	—
444	C₄	C₂²×#41×C₈₉	1	1	yes	characteristic
445	C₄	C₂×2₋¹⁺⁴×C₈₉	1	1	yes	characteristic
446	C₂	—	2	2	no	—
447	C₂	—	4	4	no	—
448	C₂	—	8	2	no	—
449	C₂	C₂×#547×C₈₉	1	1	yes	characteristic
450	C₂	C₈₉×#3584	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 ◁ #532×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#3512	C₂	semidirect
2. C₈₉×#3351	C₂	semidirect
3. C₈₉×#3339	C₂	semidirect
4. C₈₉×#3336	C₂	semidirect
5. C₂×#499×C₈₉	C₂	semidirect
6. C₈₉×#3099	C₂	semidirect
7. C₈₉×#3080	C₂	semidirect
8. C₈₉×#3061	C₂	semidirect
9. C₄×#135×C₈₉	C₂	semidirect
10. C₈₉×#2931	C₂	semidirect
11. C₈₉×#2913	C₂	semidirect
220. #61289	C₈₉	direct (N × H)
226. #3512	C₂×C₈₉	semidirect
227. #3351	C₂×C₈₉	semidirect
228. #3339	C₂×C₈₉	semidirect
229. #3336	C₂×C₈₉	semidirect
230. C₂×#499	C₂×C₈₉	semidirect
231. #3099	C₂×C₈₉	semidirect
232. #3080	C₂×C₈₉	semidirect
233. #3061	C₂×C₈₉	semidirect
234. C₄×#135	C₂×C₈₉	semidirect
235. #2931	C₂×C₈₉	semidirect
236. #2913	C₂×C₈₉	semidirect
237. C₈₉	#61289	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈₉×#3512	2
C₈₉×#3351	2
C₈₉×#3339	2
C₈₉×#3336	2
C₂×#499×C₈₉	2
C₈₉×#3099	2
C₈₉×#3080	2
C₈₉×#3061	2
C₄×#135×C₈₉	2
C₈₉×#2931	2
C₈₉×#2913	2
#61289	89

Subgroups — C89×#61289 #36439137

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#61289 #36439137