Subgroups — C₈₉×#35337 #36413185

Order 22784.

1554 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈₉×#2862	C₂	1	1	yes	maximal, characteristic, complemented
2	C₈₉×#2859	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈₉×#2851	C₂	1	2	yes	maximal
4	C₈₉×#2647	C₂	1	2	yes	maximal, complemented
5	C₈₉×#2628	C₂	1	2	yes	maximal
6	C₈₉×#2589	C₂	1	8	yes	maximal
7	C₈₉×#2588	C₂	1	8	yes	maximal, complemented
8	C₈₉×#2331	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2314	C₂	1	2	yes	maximal
10	C₄×#125×C₈₉	C₂	1	2	yes	maximal, complemented
11	C₄×#117×C₈₉	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊Q₈×C₈₉	C₂²	1	2	yes	—
13	C₂×#125×C₈₉	C₂²	1	2	yes	—
14	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
15	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
17	#400×C₈₉	C₂²	1	4	yes	—
18	#400×C₈₉	C₂²	1	8	yes	—
19	#399×C₈₉	C₂²	1	4	yes	—
20	#398×C₈₉	C₂²	1	8	yes	—
21	#395×C₈₉	C₂²	1	4	yes	—
22	#393×C₈₉	C₂²	1	4	yes	—
23	#391×C₈₉	C₂²	1	8	yes	—
24	#391×C₈₉	C₂²	1	8	yes	—
25	#389×C₈₉	C₂²	1	4	yes	—
26	#389×C₈₉	C₂²	1	4	yes	—
27	#389×C₈₉	C₂²	1	8	yes	—
28	#388×C₈₉	C₂²	1	8	yes	—
29	#387×C₈₉	C₂²	1	8	yes	—
30	#387×C₈₉	C₂²	1	8	yes	—
31	#387×C₈₉	C₂²	1	8	yes	—
32	#387×C₈₉	C₂²	1	8	yes	—
33	#385×C₈₉	C₂²	1	8	yes	—
34	#384×C₈₉	C₂²	1	2	yes	—
35	#382×C₈₉	C₂²	1	2	yes	—
36	#382×C₈₉	C₂²	1	2	yes	—
37	#382×C₈₉	C₂²	1	2	yes	—
38	#380×C₈₉	C₂²	1	4	yes	—
39	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
40	C₄×C₄⋊C₄×C₈₉	C₂²	1	8	yes	—
41	C₄×C₄⋊C₄×C₈₉	C₂²	1	4	yes	—
42	C₄×C₂²⋊C₄×C₈₉	C₂²	1	4	yes	—
43	#376×C₈₉	C₂²	1	1	yes	characteristic
44	#376×C₈₉	C₂²	1	1	yes	characteristic
45	C₄³×C₈₉	C₂²	1	1	yes	characteristic
46	C₄³×C₈₉	C₂²	1	1	yes	characteristic
47	C₂²×Q₈×C₈₉	C₂³	1	4	yes	—
48	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₈₉	C₂³	1	2	yes	—
50	C₄⋊Q₈×C₈₉	—	2	8	no	—
51	#125×C₈₉	—	2	8	no	—
52	#117×C₈₉	—	2	4	no	—
53	#117×C₈₉	Q₈	1	8	yes	complemented
54	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
56	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
57	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
58	C₂×C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
59	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
60	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
61	C₂×C₄⋊C₄×C₈₉	C₂³	1	8	yes	—
62	C₂×C₄⋊C₄×C₈₉	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₈₉	C₂³	1	8	yes	—
65	C₂×C₂²⋊C₄×C₈₉	C₂³	1	2	yes	—
66	C₂×C₄²×C₈₉	—	2	4	no	—
67	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₈₉	C₂³	1	2	yes	—
70	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
71	C₂×C₄²×C₈₉	C₂³	1	4	yes	—
72	C₂×C₄²×C₈₉	C₂³	1	8	yes	—
73	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
77	#95×C₈₉	C₂³	1	4	yes	—
78	#95×C₈₉	C₂³	1	4	yes	—
79	#95×C₈₉	C₂³	1	8	yes	—
80	#95×C₈₉	C₂³	1	8	yes	—
81	#95×C₈₉	C₂³	1	8	yes	—
82	#95×C₈₉	C₂³	1	8	yes	—
83	#95×C₈₉	C₂³	1	4	yes	—
84	#95×C₈₉	C₂³	1	8	yes	—
85	#95×C₈₉	C₂³	1	4	yes	—
86	#95×C₈₉	C₂³	1	8	yes	—
87	C₂⁴×C₈₉	C₂⁴	1	1	yes	characteristic
88	C₂×Q₈×C₈₉	—	2	8	no	—
89	C₂×Q₈×C₈₉	—	4	8	no	—
90	C₂²×C₄×C₈₉	—	2	2	no	—
91	C₂²×C₄×C₈₉	—	2	2	no	—
92	C₂²×C₄×C₈₉	—	2	4	no	—
93	C₂²×C₄×C₈₉	—	4	4	no	—
94	C₂²×C₄×C₈₉	C₂×Q₈	1	4	yes	—
95	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
96	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
97	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
98	C₂²×C₄×C₈₉	C₂⁴	1	8	yes	—
99	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
100	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
101	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
102	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
103	C₂²×C₄×C₈₉	C₂⁴	1	2	yes	—
104	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
105	C₄⋊C₄×C₈₉	—	2	4	no	—
106	C₄⋊C₄×C₈₉	—	2	16	no	—
107	C₄⋊C₄×C₈₉	—	2	8	no	—
108	C₄⋊C₄×C₈₉	—	2	8	no	—
109	C₄⋊C₄×C₈₉	—	2	8	no	—
110	C₄⋊C₄×C₈₉	—	4	8	no	—
111	C₄⋊C₄×C₈₉	—	4	8	no	—
112	C₄⋊C₄×C₈₉	—	4	8	no	—
113	C₄⋊C₄×C₈₉	C₂×Q₈	1	8	yes	—
114	C₂²⋊C₄×C₈₉	—	2	4	no	—
115	C₂²⋊C₄×C₈₉	—	4	8	no	—
116	C₂²⋊C₄×C₈₉	C₂×Q₈	1	8	yes	—
117	C₄²×C₈₉	—	2	4	no	—
118	C₄²×C₈₉	—	2	2	no	—
119	C₄²×C₈₉	—	2	2	no	—
120	C₄²×C₈₉	—	4	4	no	—
121	C₄²×C₈₉	—	4	8	no	—
122	C₄²×C₈₉	—	4	4	no	—
123	C₄²×C₈₉	C₂×Q₈	1	4	yes	—
124	C₄²×C₈₉	C₂×Q₈	1	4	yes	—
125	C₄²×C₈₉	#41	1	4	yes	—
126	C₄²×C₈₉	#41	1	4	yes	—
127	C₂³×C₈₉	—	2	1	no	—
128	C₂³×C₈₉	—	2	1	no	—
129	C₂³×C₈₉	—	2	4	no	—
130	C₂³×C₈₉	C₂²×Q₈	1	2	yes	—
131	C₂³×C₈₉	C₂⁵	1	1	yes	characteristic
132	Q₈×C₈₉	—	8	8	no	—
133	C₂×C₄×C₈₉	—	2	1	no	—
134	C₂×C₄×C₈₉	—	2	1	no	—
135	C₂×C₄×C₈₉	—	2	4	no	—
136	C₂×C₄×C₈₉	—	2	4	no	—
137	C₂×C₄×C₈₉	—	2	4	no	—
138	C₂×C₄×C₈₉	—	2	4	no	—
139	C₂×C₄×C₈₉	—	2	8	no	—
140	C₂×C₄×C₈₉	—	2	2	no	—
141	C₂×C₄×C₈₉	—	2	2	no	—
142	C₂×C₄×C₈₉	—	2	8	no	—
143	C₂×C₄×C₈₉	—	2	8	no	—
144	C₂×C₄×C₈₉	—	2	8	no	—
145	C₂×C₄×C₈₉	—	2	8	no	—
146	C₂×C₄×C₈₉	—	2	4	no	—
147	C₂×C₄×C₈₉	—	2	8	no	—
148	C₂×C₄×C₈₉	—	2	4	no	—
149	C₂×C₄×C₈₉	—	2	8	no	—
150	C₂×C₄×C₈₉	—	4	8	no	—
151	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
152	C₂×C₄×C₈₉	C₂²×Q₈	1	4	yes	—
153	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
154	C₂×C₄×C₈₉	C₂²×Q₈	1	2	yes	—
155	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
156	C₂×C₄×C₈₉	C₂×#41	1	4	yes	—
157	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
158	C₂×C₄×C₈₉	C₂×#41	1	2	yes	—
159	C₂²×C₈₉	—	2	2	no	—
160	C₂²×C₈₉	—	2	4	no	—
161	C₂²×C₈₉	—	4	2	no	—
162	C₂²×C₈₉	—	4	2	no	—
163	C₂²×C₈₉	C₂³×Q₈	1	1	yes	characteristic
164	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
165	C₂²×C₈₉	C₂²×#41	1	1	yes	characteristic
166	C₂²×C₈₉	#585	1	4	yes	—
167	C₄×C₈₉	—	2	2	no	—
168	C₄×C₈₉	—	2	4	no	—
169	C₄×C₈₉	—	2	4	no	—
170	C₄×C₈₉	—	2	4	no	—
171	C₄×C₈₉	—	2	4	no	—
172	C₄×C₈₉	—	4	8	no	—
173	C₄×C₈₉	—	4	2	no	—
174	C₄×C₈₉	—	4	2	no	—
175	C₄×C₈₉	—	4	8	no	—
176	C₄×C₈₉	#533	1	4	yes	—
177	#35337	C₈₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂×C₈₉	—	4	2	no	—
179	C₂×C₈₉	C₂×#533	1	1	yes	characteristic
180	C₂×C₈₉	#3455	1	2	yes	—
181	C₂×C₈₉	#3504	1	2	yes	—
182	C₂×C₈₉	#3510	1	2	yes	—
183	#2862	C₂×C₈₉	1	1	yes	characteristic, complemented
184	#2859	C₂×C₈₉	1	1	yes	characteristic, complemented
185	#2851	C₂×C₈₉	1	2	yes	—
186	#2647	C₂×C₈₉	1	2	yes	complemented
187	#2628	C₂×C₈₉	1	2	yes	—
188	#2589	C₂×C₈₉	1	8	yes	—
189	#2588	C₂×C₈₉	1	8	yes	complemented
190	#2331	C₂×C₈₉	1	2	yes	complemented
191	#2314	C₂×C₈₉	1	2	yes	—
192	C₄×#125	C₂×C₈₉	1	2	yes	complemented
193	C₄×#117	C₂×C₈₉	1	1	yes	characteristic
194	C₈₉	#35337	1	1	yes	characteristic, direct product factor, Sylow
195	C₂×C₄⋊Q₈	C₂²×C₈₉	1	2	yes	—
196	C₂×#125	C₂²×C₈₉	1	2	yes	—
197	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
198	C₂×#117	C₂²×C₈₉	1	1	yes	characteristic
199	C₂²×C₄²	C₂²×C₈₉	1	1	yes	characteristic
200	#400	C₂²×C₈₉	1	4	yes	—
201	#400	C₂²×C₈₉	1	8	yes	—
202	#399	C₂²×C₈₉	1	4	yes	—
203	#398	C₂²×C₈₉	1	8	yes	—
204	#395	C₂²×C₈₉	1	4	yes	—
205	#393	C₂²×C₈₉	1	4	yes	—
206	#391	C₂²×C₈₉	1	8	yes	—
207	#391	C₂²×C₈₉	1	8	yes	—
208	#389	C₂²×C₈₉	1	4	yes	—
209	#389	C₂²×C₈₉	1	4	yes	—
210	#389	C₂²×C₈₉	1	8	yes	—
211	#388	C₂²×C₈₉	1	8	yes	—
212	#387	C₂²×C₈₉	1	8	yes	—
213	#387	C₂²×C₈₉	1	8	yes	—
214	#387	C₂²×C₈₉	1	8	yes	—
215	#387	C₂²×C₈₉	1	8	yes	—
216	#385	C₂²×C₈₉	1	8	yes	—
217	#384	C₂²×C₈₉	1	2	yes	—
218	#382	C₂²×C₈₉	1	2	yes	—
219	#382	C₂²×C₈₉	1	2	yes	—
220	#382	C₂²×C₈₉	1	2	yes	—
221	#380	C₂²×C₈₉	1	4	yes	—
222	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
223	C₄×C₄⋊C₄	C₂²×C₈₉	1	8	yes	—
224	C₄×C₄⋊C₄	C₂²×C₈₉	1	4	yes	—
225	C₄×C₂²⋊C₄	C₂²×C₈₉	1	4	yes	—
226	#376	C₂²×C₈₉	1	1	yes	characteristic
227	#376	C₂²×C₈₉	1	1	yes	characteristic
228	C₄³	C₂²×C₈₉	1	1	yes	characteristic
229	C₄³	C₂²×C₈₉	1	1	yes	characteristic
230	C₂²×Q₈	C₂³×C₈₉	1	4	yes	—
231	C₂³×C₄	C₂³×C₈₉	1	1	yes	characteristic
232	C₂³×C₄	C₂³×C₈₉	1	2	yes	—
233	C₄⋊Q₈	—	2	8	no	—
234	#125	—	2	8	no	—
235	#117	—	2	4	no	—
236	#117	Q₈×C₈₉	1	8	yes	complemented
237	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
238	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
239	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
240	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
241	C₂×C₄⋊C₄	C₂³×C₈₉	1	4	yes	—
242	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
243	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
244	C₂×C₄⋊C₄	C₂³×C₈₉	1	8	yes	—
245	C₂×C₄⋊C₄	C₂³×C₈₉	1	2	yes	—
246	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
247	C₂×C₂²⋊C₄	C₂³×C₈₉	1	8	yes	—
248	C₂×C₂²⋊C₄	C₂³×C₈₉	1	2	yes	—
249	C₂×C₄²	—	2	4	no	—
250	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
252	C₂×C₄²	C₂³×C₈₉	1	2	yes	—
253	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
254	C₂×C₄²	C₂³×C₈₉	1	4	yes	—
255	C₂×C₄²	C₂³×C₈₉	1	8	yes	—
256	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
257	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
258	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
259	C₂×C₄²	C₂³×C₈₉	1	1	yes	characteristic
260	#95	C₂³×C₈₉	1	4	yes	—
261	#95	C₂³×C₈₉	1	4	yes	—
262	#95	C₂³×C₈₉	1	8	yes	—
263	#95	C₂³×C₈₉	1	8	yes	—
264	#95	C₂³×C₈₉	1	8	yes	—
265	#95	C₂³×C₈₉	1	8	yes	—
266	#95	C₂³×C₈₉	1	4	yes	—
267	#95	C₂³×C₈₉	1	8	yes	—
268	#95	C₂³×C₈₉	1	4	yes	—
269	#95	C₂³×C₈₉	1	8	yes	—
270	C₂⁴	C₂⁴×C₈₉	1	1	yes	characteristic
271	C₂×Q₈	—	2	8	no	—
272	C₂×Q₈	—	4	8	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	C₂×Q₈×C₈₉	1	4	yes	—
278	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
279	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
280	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
281	C₂²×C₄	C₂⁴×C₈₉	1	8	yes	—
282	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
283	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
284	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
285	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
286	C₂²×C₄	C₂⁴×C₈₉	1	2	yes	—
287	C₂²×C₄	C₂⁴×C₈₉	1	1	yes	characteristic
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	16	no	—
290	C₄⋊C₄	—	2	8	no	—
291	C₄⋊C₄	—	2	8	no	—
292	C₄⋊C₄	—	2	8	no	—
293	C₄⋊C₄	—	4	8	no	—
294	C₄⋊C₄	—	4	8	no	—
295	C₄⋊C₄	—	4	8	no	—
296	C₄⋊C₄	C₂×Q₈×C₈₉	1	8	yes	—
297	C₂²⋊C₄	—	2	4	no	—
298	C₂²⋊C₄	—	4	8	no	—
299	C₂²⋊C₄	C₂×Q₈×C₈₉	1	8	yes	—
300	C₄²	—	2	4	no	—
301	C₄²	—	2	2	no	—
302	C₄²	—	2	2	no	—
303	C₄²	—	4	4	no	—
304	C₄²	—	4	8	no	—
305	C₄²	—	4	4	no	—
306	C₄²	C₂×Q₈×C₈₉	1	4	yes	—
307	C₄²	C₂×Q₈×C₈₉	1	4	yes	—
308	C₄²	#41×C₈₉	1	4	yes	—
309	C₄²	#41×C₈₉	1	4	yes	—
310	C₂³	—	2	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	4	no	—
313	C₂³	C₂²×Q₈×C₈₉	1	2	yes	—
314	C₂³	C₂⁵×C₈₉	1	1	yes	characteristic
315	Q₈	—	8	8	no	—
316	C₂×C₄	—	2	1	no	—
317	C₂×C₄	—	2	1	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	8	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	8	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	4	8	no	—
334	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
335	C₂×C₄	C₂²×Q₈×C₈₉	1	4	yes	—
336	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
337	C₂×C₄	C₂²×Q₈×C₈₉	1	2	yes	—
338	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
339	C₂×C₄	C₂×#41×C₈₉	1	4	yes	—
340	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
341	C₂×C₄	C₂×#41×C₈₉	1	2	yes	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	4	2	no	—
345	C₂²	—	4	2	no	—
346	C₂²	C₂³×Q₈×C₈₉	1	1	yes	characteristic
347	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
348	C₂²	C₂²×#41×C₈₉	1	1	yes	characteristic
349	C₂²	#585×C₈₉	1	4	yes	—
350	C₄	—	2	2	no	—
351	C₄	—	2	4	no	—
352	C₄	—	2	4	no	—
353	C₄	—	2	4	no	—
354	C₄	—	2	4	no	—
355	C₄	—	4	2	no	—
356	C₄	—	4	8	no	—
357	C₄	—	4	8	no	—
358	C₄	—	4	2	no	—
359	C₄	#533×C₈₉	1	4	yes	—
360	C₂	—	4	2	no	—
361	C₂	C₂×#533×C₈₉	1	1	yes	characteristic
362	C₂	C₈₉×#3455	1	2	yes	—
363	C₂	C₈₉×#3504	1	2	yes	—
364	C₂	C₈₉×#3510	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₈₉	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₈₉
prime radical	C₂⁴×C₈₉	C₂⁴
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₈₉ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₈₉×#2862	C₂	semidirect
2. C₈₉×#2859	C₂	semidirect
4. C₈₉×#2647	C₂	semidirect
7. C₈₉×#2588	C₂	semidirect
8. C₈₉×#2331	C₂	semidirect
10. C₄×#125×C₈₉	C₂	semidirect
53. #117×C₈₉	Q₈	semidirect
177. #35337	C₈₉	direct (N × H)
183. #2862	C₂×C₈₉	semidirect
184. #2859	C₂×C₈₉	semidirect
186. #2647	C₂×C₈₉	semidirect
189. #2588	C₂×C₈₉	semidirect
190. #2331	C₂×C₈₉	semidirect
192. C₄×#125	C₂×C₈₉	semidirect
194. C₈₉	#35337	direct (N × H)
236. #117	Q₈×C₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₈₉×#2862	2
C₈₉×#2859	2
C₈₉×#2851	2
C₈₉×#2647	2
C₈₉×#2628	2
C₈₉×#2589	2
C₈₉×#2588	2
C₈₉×#2331	2
C₈₉×#2314	2
C₄×#125×C₈₉	2
C₄×#117×C₈₉	2
#35337	89

Subgroups — C89×#35337 #36413185

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈₉×#35337 #36413185