Subgroups — C₈₉×#60868 #36438716

Order 22784.

1754 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#3458	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#540×C₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈₉×#3241	C₂	1	16	yes	maximal, complemented
4	C₈₉×#3166	C₂	1	2	yes	maximal, complemented
5	C₈₉×#3138	C₂	1	2	yes	maximal, complemented
6	C₈₉×#3094	C₂	1	4	yes	maximal, complemented
7	C₈₉×#3077	C₂	1	4	yes	maximal, complemented
8	C₈₉×#2921	C₂	1	1	yes	maximal, characteristic, complemented
9	#544×C₈₉	—	2	2	no	—
10	#544×C₈₉	C₂²	1	8	yes	complemented
11	#543×C₈₉	—	2	2	no	—
12	#540×C₈₉	—	2	4	no	—
13	#540×C₈₉	C₂²	1	8	yes	—
14	#533×C₈₉	—	2	4	no	—
15	#533×C₈₉	C₂²	1	2	yes	—
16	#533×C₈₉	C₂²	1	2	yes	—
17	C₂×#127×C₈₉	C₂²	1	1	yes	characteristic
18	C₂×#125×C₈₉	C₂²	1	1	yes	characteristic
19	C₂×#123×C₈₉	—	2	2	no	—
20	C₂×#121×C₈₉	—	2	2	no	—
21	C₂×#121×C₈₉	C₂²	1	2	yes	—
22	C₂×C₄×D₄×C₈₉	C₂²	1	2	yes	—
23	C₂×#117×C₈₉	C₂²	1	2	yes	—
24	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
25	#501×C₈₉	C₂²	1	8	yes	complemented
26	#499×C₈₉	C₂²	1	8	yes	complemented
27	#490×C₈₉	C₂²	1	8	yes	complemented
28	#486×C₈₉	C₂²	1	8	yes	complemented
29	#482×C₈₉	C₂²	1	16	yes	complemented
30	#481×C₈₉	C₂²	1	8	yes	complemented
31	#480×C₈₉	C₂²	1	8	yes	complemented
32	#478×C₈₉	C₂²	1	16	yes	complemented
33	#476×C₈₉	C₂²	1	8	yes	complemented
34	#474×C₈₉	C₂²	1	8	yes	complemented
35	#433×C₈₉	C₂²	1	8	yes	complemented
36	#428×C₈₉	C₂²	1	8	yes	—
37	#423×C₈₉	C₂²	1	2	yes	—
38	#418×C₈₉	C₂²	1	8	yes	—
39	#407×C₈₉	C₂²	1	2	yes	—
40	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
41	C₂²×D₄×C₈₉	—	2	2	no	—
42	C₂²×D₄×C₈₉	—	2	2	no	—
43	C₂²×D₄×C₈₉	C₂³	1	2	yes	—
44	C₂³×C₄×C₈₉	—	2	2	no	—
45	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
46	C₂×M₁₆×C₈₉	C₂³	1	4	yes	—
47	C₄⋊Q₈×C₈₉	—	2	8	no	—
48	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
49	C₄⋊Q₈×C₈₉	C₂³	1	4	yes	—
50	#127×C₈₉	—	2	2	no	—
51	#127×C₈₉	C₂³	1	4	yes	—
52	#125×C₈₉	—	2	8	no	—
53	#125×C₈₉	—	2	2	no	—
54	#125×C₈₉	C₂³	1	4	yes	—
55	#125×C₈₉	C₂³	1	4	yes	—
56	#125×C₈₉	C₂³	1	4	yes	—
57	#123×C₈₉	—	2	16	no	—
58	C₂²⋊Q₈×C₈₉	—	2	4	no	—
59	C₂²⋊Q₈×C₈₉	—	2	4	no	—
60	C₂²⋊Q₈×C₈₉	—	2	8	no	—
61	C₂²⋊Q₈×C₈₉	—	2	8	no	—
62	#121×C₈₉	—	2	4	no	—
63	#121×C₈₉	—	2	16	no	—
64	#121×C₈₉	C₂³	1	8	yes	—
65	C₄×Q₈×C₈₉	—	2	4	no	—
66	C₄×Q₈×C₈₉	—	2	4	no	—
67	C₄×D₄×C₈₉	—	2	4	no	—
68	C₄×D₄×C₈₉	C₂³	1	8	yes	—
69	#117×C₈₉	—	2	2	no	—
70	#117×C₈₉	—	2	2	no	—
71	#117×C₈₉	D₄	1	4	yes	—
72	#117×C₈₉	C₂³	1	4	yes	—
73	#117×C₈₉	C₂³	1	4	yes	—
74	#117×C₈₉	C₂³	1	4	yes	—
75	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
76	C₂×C₄⋊C₄×C₈₉	D₄	1	2	yes	—
77	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
78	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
79	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₈₉	—	2	2	no	—
82	C₂×C₂²⋊C₄×C₈₉	D₄	1	2	yes	—
83	C₂×C₄²×C₈₉	—	2	2	no	—
84	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
86	#107×C₈₉	C₂³	1	16	yes	—
87	#106×C₈₉	C₂³	1	16	yes	—
88	C₄⋊C₈×C₈₉	C₂³	1	8	yes	—
89	#102×C₈₉	C₂³	1	16	yes	—
90	#102×C₈₉	C₂³	1	16	yes	—
91	C₂²⋊C₈×C₈₉	C₂³	1	8	yes	—
92	#97×C₈₉	C₂³	1	4	yes	—
93	C₄×C₈×C₈₉	C₂³	1	4	yes	—
94	C₂⁴×C₈₉	—	2	2	no	—
95	C₂⁴×C₈₉	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₈₉	—	2	4	no	—
97	C₂×Q₈×C₈₉	—	2	4	no	—
98	C₂×D₄×C₈₉	—	2	8	no	—
99	C₂×D₄×C₈₉	—	2	2	no	—
100	C₂×D₄×C₈₉	—	2	8	no	—
101	C₂×D₄×C₈₉	—	2	8	no	—
102	C₂×D₄×C₈₉	—	8	4	no	—
103	C₂×D₄×C₈₉	—	8	4	no	—
104	C₂×D₄×C₈₉	C₂⁴	1	4	yes	—
105	C₂²×C₄×C₈₉	—	2	4	no	—
106	C₂²×C₄×C₈₉	—	2	2	no	—
107	C₂²×C₄×C₈₉	—	2	4	no	—
108	C₂²×C₄×C₈₉	—	2	8	no	—
109	C₂²×C₄×C₈₉	—	8	4	no	—
110	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
115	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
116	M₁₆×C₈₉	—	2	8	no	—
117	C₂×C₈×C₈₉	C₂⁴	1	8	yes	—
118	C₄⋊C₄×C₈₉	—	2	8	no	—
119	C₄⋊C₄×C₈₉	—	2	4	no	—
120	C₄⋊C₄×C₈₉	—	2	2	no	—
121	C₄⋊C₄×C₈₉	—	2	4	no	—
122	C₄⋊C₄×C₈₉	—	2	4	no	—
123	C₄⋊C₄×C₈₉	—	2	8	no	—
124	C₄⋊C₄×C₈₉	—	2	8	no	—
125	C₄⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
126	C₄⋊C₄×C₈₉	C₂⁴	1	8	yes	—
127	C₄⋊C₄×C₈₉	C₂⁴	1	4	yes	—
128	C₂²⋊C₄×C₈₉	—	2	4	no	—
129	C₂²⋊C₄×C₈₉	—	2	4	no	—
130	C₂²⋊C₄×C₈₉	—	2	8	no	—
131	C₂²⋊C₄×C₈₉	—	2	8	no	—
132	C₂²⋊C₄×C₈₉	C₂×D₄	1	8	yes	—
133	C₄²×C₈₉	—	2	4	no	—
134	C₄²×C₈₉	—	2	4	no	—
135	C₄²×C₈₉	C₂×D₄	1	2	yes	—
136	C₄²×C₈₉	C₂×D₄	1	2	yes	—
137	C₄²×C₈₉	C₂⁴	1	2	yes	—
138	C₄²×C₈₉	C₂⁴	1	2	yes	—
139	C₂³×C₈₉	—	2	2	no	—
140	C₂³×C₈₉	—	2	4	no	—
141	C₂³×C₈₉	—	4	2	no	—
142	C₂³×C₈₉	—	4	4	no	—
143	C₂³×C₈₉	—	4	4	no	—
144	C₂³×C₈₉	—	4	4	no	—
145	C₂³×C₈₉	C₂²×D₄	1	2	yes	—
146	C₂³×C₈₉	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₈₉	—	8	4	no	—
148	Q₈×C₈₉	—	8	4	no	—
149	D₄×C₈₉	—	2	8	no	—
150	D₄×C₈₉	—	4	4	no	—
151	D₄×C₈₉	—	8	8	no	—
152	D₄×C₈₉	—	8	8	no	—
153	C₂×C₄×C₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	4	no	—
155	C₂×C₄×C₈₉	—	2	4	no	—
156	C₂×C₄×C₈₉	—	2	8	no	—
157	C₂×C₄×C₈₉	—	2	4	no	—
158	C₂×C₄×C₈₉	—	4	2	no	—
159	C₂×C₄×C₈₉	—	4	2	no	—
160	C₂×C₄×C₈₉	—	4	4	no	—
161	C₂×C₄×C₈₉	—	8	8	no	—
162	C₂×C₄×C₈₉	—	8	4	no	—
163	C₂×C₄×C₈₉	C₂²×D₄	1	2	yes	—
164	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
165	C₂×C₄×C₈₉	C₂²×D₄	1	4	yes	—
166	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	2₋¹⁺⁴	1	4	yes	—
168	C₂×C₄×C₈₉	C₂⁵	1	1	yes	characteristic
169	C₈×C₈₉	—	2	8	no	—
170	C₂²×C₈₉	—	2	2	no	—
171	C₂²×C₈₉	—	2	4	no	—
172	C₂²×C₈₉	—	2	2	no	—
173	C₂²×C₈₉	—	4	4	no	—
174	C₂²×C₈₉	—	4	4	no	—
175	C₂²×C₈₉	—	4	4	no	—
176	C₂²×C₈₉	—	8	2	no	—
177	C₂²×C₈₉	—	8	8	no	—
178	C₂²×C₈₉	#536	1	2	yes	—
179	C₂²×C₈₉	C₂³×D₄	1	1	yes	characteristic
180	C₄×C₈₉	—	2	4	no	—
181	C₄×C₈₉	—	2	4	no	—
182	C₄×C₈₉	—	2	2	no	—
183	C₄×C₈₉	—	4	4	no	—
184	C₄×C₈₉	—	4	8	no	—
185	C₄×C₈₉	#536	1	2	yes	—
186	C₄×C₈₉	C₂×2₋¹⁺⁴	1	2	yes	—
187	#60868	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
188	C₂×C₈₉	—	2	2	no	—
189	C₂×C₈₉	—	4	2	no	—
190	C₂×C₈₉	—	8	4	no	—
191	C₂×C₈₉	C₂×#536	1	1	yes	characteristic
192	C₂×C₈₉	#3585	1	2	yes	—
193	#3458	C₂×C₈₉	1	1	yes	characteristic, complemented
194	C₂×#540	C₂×C₈₉	1	1	yes	characteristic
195	#3241	C₂×C₈₉	1	16	yes	complemented
196	#3166	C₂×C₈₉	1	2	yes	complemented
197	#3138	C₂×C₈₉	1	2	yes	complemented
198	#3094	C₂×C₈₉	1	4	yes	complemented
199	#3077	C₂×C₈₉	1	4	yes	complemented
200	#2921	C₂×C₈₉	1	1	yes	characteristic, complemented
201	C₈₉	#60868	1	1	yes	characteristic, direct product factor, Sylow
202	#544	—	2	2	no	—
203	#544	C₂²×C₈₉	1	8	yes	complemented
204	#543	—	2	2	no	—
205	#540	—	2	4	no	—
206	#540	C₂²×C₈₉	1	8	yes	—
207	#533	—	2	4	no	—
208	#533	C₂²×C₈₉	1	2	yes	—
209	#533	C₂²×C₈₉	1	2	yes	—
210	C₂×#127	C₂²×C₈₉	1	1	yes	characteristic
211	C₂×#125	C₂²×C₈₉	1	1	yes	characteristic
212	C₂×#123	—	2	2	no	—
213	C₂×#121	—	2	2	no	—
214	C₂×#121	C₂²×C₈₉	1	2	yes	—
215	C₂×C₄×D₄	C₂²×C₈₉	1	2	yes	—
216	C₂×#117	C₂²×C₈₉	1	2	yes	—
217	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
218	#501	C₂²×C₈₉	1	8	yes	complemented
219	#499	C₂²×C₈₉	1	8	yes	complemented
220	#490	C₂²×C₈₉	1	8	yes	complemented
221	#486	C₂²×C₈₉	1	8	yes	complemented
222	#482	C₂²×C₈₉	1	16	yes	complemented
223	#481	C₂²×C₈₉	1	8	yes	complemented
224	#480	C₂²×C₈₉	1	8	yes	complemented
225	#478	C₂²×C₈₉	1	16	yes	complemented
226	#476	C₂²×C₈₉	1	8	yes	complemented
227	#474	C₂²×C₈₉	1	8	yes	complemented
228	#433	C₂²×C₈₉	1	8	yes	complemented
229	#428	C₂²×C₈₉	1	8	yes	—
230	#423	C₂²×C₈₉	1	2	yes	—
231	#418	C₂²×C₈₉	1	8	yes	—
232	#407	C₂²×C₈₉	1	2	yes	—
233	C₄×M₁₆	C₂²×C₈₉	1	2	yes	—
234	C₂²×D₄	—	2	2	no	—
235	C₂²×D₄	—	2	2	no	—
236	C₂²×D₄	C₂³×C₈₉	1	2	yes	—
237	C₂³×C₄	—	2	2	no	—
238	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
239	C₂×M₁₆	C₂³×C₈₉	1	4	yes	—
240	C₄⋊Q₈	—	2	8	no	—
241	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
242	C₄⋊Q₈	C₂³×C₈₉	1	4	yes	—
243	#127	—	2	2	no	—
244	#127	C₂³×C₈₉	1	4	yes	—
245	#125	—	2	8	no	—
246	#125	—	2	2	no	—
247	#125	C₂³×C₈₉	1	4	yes	—
248	#125	C₂³×C₈₉	1	4	yes	—
249	#125	C₂³×C₈₉	1	4	yes	—
250	#123	—	2	16	no	—
251	C₂²⋊Q₈	—	2	4	no	—
252	C₂²⋊Q₈	—	2	4	no	—
253	C₂²⋊Q₈	—	2	8	no	—
254	C₂²⋊Q₈	—	2	8	no	—
255	#121	—	2	4	no	—
256	#121	—	2	16	no	—
257	#121	C₂³×C₈₉	1	8	yes	—
258	C₄×Q₈	—	2	4	no	—
259	C₄×Q₈	—	2	4	no	—
260	C₄×D₄	—	2	4	no	—
261	C₄×D₄	C₂³×C₈₉	1	8	yes	—
262	#117	—	2	2	no	—
263	#117	—	2	2	no	—
264	#117	D₄×C₈₉	1	4	yes	—
265	#117	C₂³×C₈₉	1	4	yes	—
266	#117	C₂³×C₈₉	1	4	yes	—
267	#117	C₂³×C₈₉	1	4	yes	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	D₄×C₈₉	1	2	yes	—
270	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
271	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
272	C₂×C₂²⋊C₄	—	2	2	no	—
273	C₂×C₂²⋊C₄	—	2	2	no	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	D₄×C₈₉	1	2	yes	—
276	C₂×C₄²	—	2	2	no	—
277	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
278	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
279	#107	C₂³×C₈₉	1	16	yes	—
280	#106	C₂³×C₈₉	1	16	yes	—
281	C₄⋊C₈	C₂³×C₈₉	1	8	yes	—
282	#102	C₂³×C₈₉	1	16	yes	—
283	#102	C₂³×C₈₉	1	16	yes	—
284	C₂²⋊C₈	C₂³×C₈₉	1	8	yes	—
285	#97	C₂³×C₈₉	1	4	yes	—
286	C₄×C₈	C₂³×C₈₉	1	4	yes	—
287	C₂⁴	—	2	2	no	—
288	C₂⁴	C₂×D₄×C₈₉	1	1	yes	characteristic
289	C₂×Q₈	—	2	4	no	—
290	C₂×Q₈	—	2	4	no	—
291	C₂×D₄	—	2	8	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	8	no	—
294	C₂×D₄	—	2	8	no	—
295	C₂×D₄	—	8	4	no	—
296	C₂×D₄	—	8	4	no	—
297	C₂×D₄	C₂⁴×C₈₉	1	4	yes	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	8	no	—
302	C₂²×C₄	—	8	4	no	—
303	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₈₉	1	1	yes	characteristic
305	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₈₉	1	2	yes	—
307	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
308	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
309	M₁₆	—	2	8	no	—
310	C₂×C₈	C₂⁴×C₈₉	1	8	yes	—
311	C₄⋊C₄	—	2	8	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₄⋊C₄	—	2	4	no	—
316	C₄⋊C₄	—	2	8	no	—
317	C₄⋊C₄	—	2	8	no	—
318	C₄⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
319	C₄⋊C₄	C₂⁴×C₈₉	1	8	yes	—
320	C₄⋊C₄	C₂⁴×C₈₉	1	4	yes	—
321	C₂²⋊C₄	—	2	4	no	—
322	C₂²⋊C₄	—	2	4	no	—
323	C₂²⋊C₄	—	2	8	no	—
324	C₂²⋊C₄	—	2	8	no	—
325	C₂²⋊C₄	C₂×D₄×C₈₉	1	8	yes	—
326	C₄²	—	2	4	no	—
327	C₄²	—	2	4	no	—
328	C₄²	C₂×D₄×C₈₉	1	2	yes	—
329	C₄²	C₂×D₄×C₈₉	1	2	yes	—
330	C₄²	C₂⁴×C₈₉	1	2	yes	—
331	C₄²	C₂⁴×C₈₉	1	2	yes	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	4	no	—
336	C₂³	—	4	4	no	—
337	C₂³	—	4	4	no	—
338	C₂³	C₂²×D₄×C₈₉	1	2	yes	—
339	C₂³	C₂²×D₄×C₈₉	1	1	yes	characteristic
340	Q₈	—	8	4	no	—
341	Q₈	—	8	4	no	—
342	D₄	—	2	8	no	—
343	D₄	—	4	4	no	—
344	D₄	—	8	8	no	—
345	D₄	—	8	8	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	8	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	8	8	no	—
355	C₂×C₄	—	8	4	no	—
356	C₂×C₄	C₂²×D₄×C₈₉	1	2	yes	—
357	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
358	C₂×C₄	C₂²×D₄×C₈₉	1	4	yes	—
359	C₂×C₄	C₂²×D₄×C₈₉	1	1	yes	characteristic
360	C₂×C₄	2₋¹⁺⁴×C₈₉	1	4	yes	—
361	C₂×C₄	C₂⁵×C₈₉	1	1	yes	characteristic
362	C₈	—	2	8	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	4	4	no	—
368	C₂²	—	4	4	no	—
369	C₂²	—	8	2	no	—
370	C₂²	—	8	8	no	—
371	C₂²	#536×C₈₉	1	2	yes	—
372	C₂²	C₂³×D₄×C₈₉	1	1	yes	characteristic
373	C₄	—	2	4	no	—
374	C₄	—	2	4	no	—
375	C₄	—	2	2	no	—
376	C₄	—	4	4	no	—
377	C₄	—	4	8	no	—
378	C₄	#536×C₈₉	1	2	yes	—
379	C₄	C₂×2₋¹⁺⁴×C₈₉	1	2	yes	—
380	C₂	—	2	2	no	—
381	C₂	—	4	2	no	—
382	C₂	—	8	4	no	—
383	C₂	C₂×#536×C₈₉	1	1	yes	characteristic
384	C₂	C₈₉×#3585	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₈₉	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₈₉
prime radical	C₂×#540×C₈₉	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
1. C₈₉×#3458	C₂	semidirect
3. C₈₉×#3241	C₂	semidirect
4. C₈₉×#3166	C₂	semidirect
5. C₈₉×#3138	C₂	semidirect
6. C₈₉×#3094	C₂	semidirect
7. C₈₉×#3077	C₂	semidirect
8. C₈₉×#2921	C₂	semidirect
10. #544×C₈₉	C₂²	semidirect
25. #501×C₈₉	C₂²	semidirect
26. #499×C₈₉	C₂²	semidirect
27. #490×C₈₉	C₂²	semidirect
28. #486×C₈₉	C₂²	semidirect
29. #482×C₈₉	C₂²	semidirect
30. #481×C₈₉	C₂²	semidirect
31. #480×C₈₉	C₂²	semidirect
32. #478×C₈₉	C₂²	semidirect
33. #476×C₈₉	C₂²	semidirect
34. #474×C₈₉	C₂²	semidirect
35. #433×C₈₉	C₂²	semidirect
187. #60868	C₈₉	direct (N × H)
193. #3458	C₂×C₈₉	semidirect
195. #3241	C₂×C₈₉	semidirect
196. #3166	C₂×C₈₉	semidirect
197. #3138	C₂×C₈₉	semidirect
198. #3094	C₂×C₈₉	semidirect
199. #3077	C₂×C₈₉	semidirect
200. #2921	C₂×C₈₉	semidirect
201. C₈₉	#60868	direct (N × H)
203. #544	C₂²×C₈₉	semidirect
218. #501	C₂²×C₈₉	semidirect
219. #499	C₂²×C₈₉	semidirect
220. #490	C₂²×C₈₉	semidirect
221. #486	C₂²×C₈₉	semidirect
222. #482	C₂²×C₈₉	semidirect
223. #481	C₂²×C₈₉	semidirect
224. #480	C₂²×C₈₉	semidirect
225. #478	C₂²×C₈₉	semidirect
226. #476	C₂²×C₈₉	semidirect
227. #474	C₂²×C₈₉	semidirect
228. #433	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×#3458	2
C₂×#540×C₈₉	2
C₈₉×#3241	2
C₈₉×#3166	2
C₈₉×#3138	2
C₈₉×#3094	2
C₈₉×#3077	2
C₈₉×#2921	2
#60868	89

Subgroups — C89×#60868 #36438716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#60868 #36438716