Subgroups — #36707641

Order 22784.

734 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₈₉	C₂	1	2	yes	maximal, complemented
2	C₈×D₄×D₈₉	C₂	1	1	yes	maximal, characteristic
3	#26022084	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022080	C₂	1	2	yes	maximal, complemented
5	#26022075	C₂	1	2	yes	maximal, complemented
6	C₁₆×D₃₅₆	C₂	1	1	yes	maximal, characteristic, complemented
7	#26022071	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022006	C₂	1	1	yes	maximal, characteristic, complemented
9	#26021861	C₂	1	2	yes	maximal, complemented
10	C₄×#15667951	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2169	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₈₉	C₂²	1	2	yes	—
13	C₄×D₄×D₈₉	C₄	1	1	yes	characteristic
14	C₂×#15667952	C₂²	1	2	yes	complemented
15	C₂×#15667951	C₂²	1	2	yes	—
16	C₂×#15667951	C₂²	1	1	yes	characteristic
17	C₂×#15667951	C₂²	1	1	yes	characteristic
18	M₃₂×D₈₉	—	2	8	no	—
19	C₂×C₁₆×D₈₉	C₂²	1	2	yes	complemented
20	C₂×C₁₆×D₈₉	C₂²	1	2	yes	complemented
21	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
22	D₄×#10623494	C₄	1	1	yes	characteristic
23	#19151663	C₄	1	1	yes	characteristic
24	C₈×C₂²⋊D₈₉	C₂²	1	2	yes	—
25	#19151661	C₄	1	2	yes	—
26	C₄⋊C₈×D₈₉	C₄	1	1	yes	characteristic
27	C₂²⋊C₈×D₈₉	C₄	1	2	yes	—
28	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
29	C₄⋊#13083549	C₂²	1	1	yes	characteristic, complemented
30	#19151416	C₂²	1	2	yes	complemented
31	C₂²⋊#13083549	C₂²	1	2	yes	complemented
32	#19151377	C₂²	1	2	yes	complemented
33	#19151377	C₂²	1	2	yes	complemented
34	#19151373	C₂²	1	1	yes	characteristic, complemented
35	#19151373	C₂²	1	1	yes	characteristic, complemented
36	C₄×#13083549	C₂²	1	1	yes	characteristic, complemented
37	C₂×M₃₂×C₈₉	C₂²	1	2	yes	complemented
38	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
39	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
40	C₂²⋊C₁₆×C₈₉	C₂²	1	2	yes	complemented
41	C₄×C₁₆×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	C₂×D₄×D₈₉	C₈	1	1	yes	characteristic
43	C₂²×C₄×D₈₉	C₂×C₄	1	2	yes	—
44	C₂²×#10623494	C₂×C₄	1	2	yes	—
45	C₂×C₈×D₈₉	—	2	4	no	—
46	C₂×C₈×D₈₉	—	2	4	no	—
47	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
48	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
49	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₈₉	C₂³	1	2	yes	—
51	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
52	C₄×D₃₅₆	C₂×C₄	1	1	yes	characteristic
53	D₄×Dic₈₉	C₈	1	1	yes	characteristic
54	#15667974	C₈	1	1	yes	characteristic
55	C₄×C₂²⋊D₈₉	C₂×C₄	1	2	yes	—
56	#15667972	C₈	1	2	yes	—
57	C₄⋊C₄×D₈₉	C₈	1	1	yes	characteristic
58	C₂²⋊C₄×D₈₉	C₈	1	2	yes	—
59	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
60	#15667952	—	2	4	no	—
61	#15667951	—	2	4	no	—
62	#15667951	—	2	2	no	—
63	#15667951	D₄	1	4	yes	complemented
64	C₂×#13083549	C₂³	1	1	yes	characteristic
65	C₂×#13083549	C₂³	1	2	yes	—
66	C₂×#13083549	C₂³	1	1	yes	characteristic
67	C₁₆×D₈₉	—	2	4	no	—
68	C₁₆×D₈₉	—	2	4	no	—
69	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
70	#15667941	C₂×C₄	1	2	yes	—
71	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
72	#15667924	C₂×C₄	1	2	yes	—
73	#15667924	C₂×C₄	1	2	yes	—
74	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
75	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
76	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
77	C₂²×C₈×C₈₉	C₂³	1	2	yes	—
78	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
79	M₃₂×C₈₉	—	2	4	no	—
80	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
81	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
82	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
84	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
85	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
86	C₂³×D₈₉	C₂×C₈	1	2	yes	—
87	C₂×D₃₅₆	C₂×C₈	1	1	yes	characteristic
88	C₂×C₂²⋊D₈₉	C₂×C₈	1	2	yes	—
89	D₄×D₈₉	—	2	4	no	—
90	C₂²×Dic₈₉	C₂×C₈	1	2	yes	—
91	C₂×C₄×D₈₉	—	2	4	no	—
92	C₂×C₄×D₈₉	—	2	4	no	—
93	C₂×C₄×D₈₉	C₂×C₈	1	2	yes	—
94	C₂×C₄×D₈₉	C₂×C₈	1	2	yes	—
95	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
97	C₂×C₄×D₈₉	C₂²×C₄	1	2	yes	—
98	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
99	C₂×#10623494	—	2	4	no	—
100	C₂×#10623494	C₂²×C₄	1	2	yes	—
101	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
102	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
103	C₈×D₈₉	—	2	4	no	—
104	C₈×D₈₉	—	2	2	no	—
105	C₈×D₈₉	—	2	2	no	—
106	C₈×D₈₉	—	2	2	no	—
107	C₈×D₈₉	—	2	4	no	—
108	C₈×D₈₉	C₂×D₄	1	2	yes	—
109	C₈×D₈₉	#41	1	2	yes	—
110	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
111	#13083553	C₂×C₈	1	2	yes	—
112	C₂²⋊Dic₈₉	C₂×C₈	1	2	yes	—
113	#13083551	C₂×C₈	1	2	yes	—
114	#13083551	C₂×C₈	1	2	yes	—
115	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
116	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
117	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
118	#13083549	—	2	2	no	—
119	#13083549	—	2	1	no	—
120	#13083549	C₂×D₄	1	2	yes	complemented
121	C₂×D₄×C₈₉	C₂×C₈	1	1	yes	characteristic
122	C₂²×C₄×C₈₉	C₂²×C₄	1	2	yes	—
123	C₂×C₈×C₈₉	—	2	2	no	—
124	C₂×C₈×C₈₉	—	2	2	no	—
125	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
128	C₄⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
129	C₂²⋊C₄×C₈₉	C₂×C₈	1	2	yes	—
130	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₁₆×C₈₉	—	2	2	no	—
132	C₁₆×C₈₉	—	2	1	no	—
133	C₁₆×C₈₉	C₂×D₄	1	2	yes	complemented
134	C₂³×C₈₉	C₂²×C₈	1	2	yes	—
135	C₂²×D₈₉	—	2	4	no	—
136	C₂²×D₈₉	—	2	4	no	—
137	C₂²×D₈₉	—	4	2	no	—
138	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
139	C₂²×D₈₉	C₂²×C₈	1	2	yes	—
140	D₄×C₈₉	—	2	2	no	—
141	C₂×C₄×C₈₉	—	2	2	no	—
142	C₂×C₄×C₈₉	—	2	2	no	—
143	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
144	C₂×C₄×C₈₉	C₂²×C₈	1	2	yes	—
145	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
146	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
147	C₂²⋊D₈₉	—	2	4	no	—
148	C₂×Dic₈₉	—	2	4	no	—
149	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
150	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
151	C₂×Dic₈₉	C₂²×C₈	1	2	yes	—
152	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
153	D₃₅₆	M₃₂	1	4	yes	complemented
154	C₄×D₈₉	—	2	4	no	—
155	C₄×D₈₉	—	2	2	no	—
156	C₄×D₈₉	—	2	2	no	—
157	C₄×D₈₉	—	2	2	no	—
158	C₄×D₈₉	—	2	4	no	—
159	C₄×D₈₉	—	4	1	no	—
160	C₄×D₈₉	C₄×D₄	1	2	yes	—
161	C₄×D₈₉	#131	1	2	yes	—
162	C₈×C₈₉	—	2	2	no	—
163	C₈×C₈₉	—	2	1	no	—
164	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
165	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
166	#10623494	—	2	2	no	—
167	#10623494	—	2	1	no	—
168	#10623494	C₄×D₄	1	2	yes	—
169	C₂²×C₈₉	—	2	2	no	—
170	C₂²×C₈₉	—	2	2	no	—
171	C₂²×C₈₉	—	2	2	no	—
172	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
173	C₂×D₈₉	—	2	1	no	—
174	C₂×D₈₉	—	2	1	no	—
175	C₂×D₈₉	—	2	2	no	—
176	C₂×D₈₉	—	2	2	no	—
177	C₂×D₈₉	—	4	8	no	—
178	C₂×D₈₉	C₈×D₄	1	2	yes	—
179	C₂×D₈₉	C₂×M₃₂	1	4	yes	complemented
180	C₄×C₈₉	—	2	1	no	—
181	C₄×C₈₉	—	2	2	no	—
182	C₄×C₈₉	C₂×M₃₂	1	2	yes	complemented
183	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
184	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
185	Dic₈₉	—	2	1	no	—
186	Dic₈₉	—	2	1	no	—
187	Dic₈₉	—	2	2	no	—
188	Dic₈₉	C₈×D₄	1	2	yes	—
189	D₄×M₃₂	—	89	1	no	maximal, Sylow
190	C₂×C₈₉	—	4	2	no	—
191	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
192	C₂×C₈₉	C₂²×M₃₂	1	1	yes	characteristic
193	C₂×C₈₉	#3407	1	1	yes	characteristic
194	D₈₉	—	2	2	no	—
195	D₈₉	—	2	4	no	—
196	C₂²×M₃₂	—	89	2	no	—
197	C₂×C₈×D₄	—	89	1	no	—
198	#2169	—	89	1	no	—
199	#2169	D₈₉	1	1	yes	characteristic, complemented
200	#2168	—	89	2	no	—
201	#2168	—	89	2	no	—
202	D₄×C₁₆	—	89	1	no	—
203	D₄×C₁₆	—	89	1	no	—
204	#2150	—	89	1	no	—
205	#2112	—	89	2	no	—
206	C₄×M₃₂	—	89	1	no	—
207	C₈₉	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
208	C₂³×C₈	—	89	2	no	—
209	C₂×C₄×D₄	—	89	1	no	—
210	C₂×M₃₂	—	89	2	no	—
211	C₂×M₃₂	—	89	1	no	—
212	C₂×M₃₂	—	89	1	no	—
213	C₂×M₃₂	—	89	2	no	—
214	C₂×M₃₂	—	178	8	no	—
215	C₂×M₃₂	C₂×D₈₉	1	2	yes	complemented
216	C₂²×C₁₆	—	89	2	no	—
217	C₂²×C₁₆	—	89	2	no	—
218	C₈×D₄	—	89	2	no	—
219	C₈×D₄	—	89	1	no	—
220	C₈×D₄	—	89	1	no	—
221	C₈×D₄	—	89	2	no	—
222	C₈×D₄	—	89	1	no	—
223	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
224	C₂×C₄⋊C₈	—	89	1	no	—
225	C₂×C₂²⋊C₈	—	89	2	no	—
226	C₂×C₄×C₈	—	89	1	no	—
227	C₄⋊C₁₆	—	89	2	no	—
228	C₄⋊C₁₆	—	89	1	no	—
229	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
230	C₂²⋊C₁₆	—	89	2	no	—
231	C₂²⋊C₁₆	—	89	2	no	—
232	C₂²⋊C₁₆	—	89	2	no	—
233	C₂²⋊C₁₆	C₂×D₈₉	1	2	yes	complemented
234	#346	—	89	1	no	—
235	#346	—	89	1	no	—
236	C₄×C₁₆	—	89	1	no	—
237	C₄×C₁₆	C₂×D₈₉	1	1	yes	characteristic, complemented
238	C₂²×D₄	—	89	1	no	—
239	C₂³×C₄	—	89	2	no	—
240	C₂²×C₈	—	89	1	no	—
241	C₂²×C₈	—	89	2	no	—
242	C₂²×C₈	—	89	2	no	—
243	C₂²×C₈	—	89	2	no	—
244	C₂²×C₈	—	89	1	no	—
245	C₂²×C₈	—	89	2	no	—
246	C₂²×C₈	—	178	4	no	—
247	C₂²×C₈	—	178	4	no	—
248	C₂²×C₈	C₂²×D₈₉	1	2	yes	—
249	C₄×D₄	—	89	1	no	—
250	C₄×D₄	—	89	2	no	—
251	C₄×D₄	—	89	1	no	—
252	C₄×D₄	—	89	2	no	—
253	C₄×D₄	—	89	1	no	—
254	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
255	C₂×C₄⋊C₄	—	89	1	no	—
256	C₂×C₂²⋊C₄	—	89	2	no	—
257	C₂×C₄²	—	89	1	no	—
258	M₃₂	—	2	4	no	—
259	M₃₂	—	89	4	no	—
260	M₃₂	—	178	2	no	—
261	M₃₂	—	178	4	no	—
262	M₃₂	—	178	4	no	—
263	C₂×C₁₆	—	89	1	no	—
264	C₂×C₁₆	—	89	1	no	—
265	C₂×C₁₆	—	89	2	no	—
266	C₂×C₁₆	—	178	4	no	—
267	C₂×C₁₆	—	178	4	no	—
268	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
269	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
270	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
271	C₄⋊C₈	—	89	2	no	—
272	C₄⋊C₈	—	89	1	no	—
273	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
274	C₂²⋊C₈	—	89	2	no	—
275	C₂²⋊C₈	—	89	2	no	—
276	C₂²⋊C₈	—	89	2	no	—
277	C₂²⋊C₈	C₄×D₈₉	1	2	yes	—
278	C₄×C₈	—	89	1	no	—
279	C₄×C₈	—	89	1	no	—
280	C₄×C₈	—	89	1	no	—
281	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
282	C₂⁴	—	89	2	no	—
283	C₂×D₄	—	89	2	no	—
284	C₂×D₄	—	89	1	no	—
285	C₂×D₄	—	178	4	no	—
286	C₂×D₄	C₈×D₈₉	1	1	yes	characteristic
287	C₂²×C₄	—	89	1	no	—
288	C₂²×C₄	—	89	2	no	—
289	C₂²×C₄	—	89	1	no	—
290	C₂²×C₄	—	89	1	no	—
291	C₂²×C₄	—	89	2	no	—
292	C₂²×C₄	—	89	2	no	—
293	C₂²×C₄	—	89	2	no	—
294	C₂²×C₄	—	178	4	no	—
295	C₂²×C₄	—	178	4	no	—
296	C₂²×C₄	C₂×C₄×D₈₉	1	2	yes	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	89	1	no	—
300	C₂×C₈	—	89	2	no	—
301	C₂×C₈	—	89	2	no	—
302	C₂×C₈	—	89	1	no	—
303	C₂×C₈	—	89	2	no	—
304	C₂×C₈	—	178	4	no	—
305	C₂×C₈	—	178	4	no	—
306	C₂×C₈	—	178	2	no	—
307	C₂×C₈	—	178	4	no	—
308	C₂×C₈	—	178	2	no	—
309	C₂×C₈	—	178	2	no	—
310	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
311	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
312	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
313	C₄⋊C₄	—	89	2	no	—
314	C₄⋊C₄	—	89	1	no	—
315	C₄⋊C₄	C₈×D₈₉	1	1	yes	characteristic
316	C₂²⋊C₄	—	89	2	no	—
317	C₂²⋊C₄	—	89	2	no	—
318	C₂²⋊C₄	—	89	2	no	—
319	C₂²⋊C₄	C₈×D₈₉	1	2	yes	—
320	C₄²	—	89	1	no	—
321	C₄²	—	89	1	no	—
322	C₄²	—	89	1	no	—
323	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
324	C₁₆	—	2	2	no	—
325	C₁₆	—	2	1	no	—
326	C₁₆	—	89	2	no	—
327	C₁₆	—	178	2	no	—
328	C₁₆	—	178	1	no	—
329	C₁₆	D₄×D₈₉	1	2	yes	complemented
330	C₂³	—	89	2	no	—
331	C₂³	—	89	1	no	—
332	C₂³	—	356	2	no	—
333	C₂³	—	178	4	no	—
334	C₂³	—	178	4	no	—
335	C₂³	C₂×C₈×D₈₉	1	2	yes	—
336	D₄	—	2	2	no	—
337	D₄	—	89	4	no	—
338	D₄	—	178	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	89	1	no	—
342	C₂×C₄	—	89	2	no	—
343	C₂×C₄	—	89	2	no	—
344	C₂×C₄	—	89	1	no	—
345	C₂×C₄	—	89	1	no	—
346	C₂×C₄	—	89	2	no	—
347	C₂×C₄	—	356	1	no	—
348	C₂×C₄	—	178	4	no	—
349	C₂×C₄	—	178	4	no	—
350	C₂×C₄	—	178	4	no	—
351	C₂×C₄	—	178	2	no	—
352	C₂×C₄	—	178	2	no	—
353	C₂×C₄	—	178	2	no	—
354	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
355	C₂×C₄	C₂×C₈×D₈₉	1	2	yes	—
356	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
357	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
358	C₈	—	2	2	no	—
359	C₈	—	2	1	no	—
360	C₈	—	89	2	no	—
361	C₈	—	178	2	no	—
362	C₈	—	178	1	no	—
363	C₈	C₂×D₄×D₈₉	1	1	yes	characteristic
364	C₈	#41×D₈₉	1	1	yes	characteristic
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	89	2	no	—
369	C₂²	—	89	4	no	—
370	C₂²	—	356	8	no	—
371	C₂²	—	178	2	no	—
372	C₂²	—	178	1	no	—
373	C₂²	—	178	1	no	—
374	C₂²	—	178	2	no	—
375	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
376	C₄	—	2	2	no	—
377	C₄	—	2	1	no	—
378	C₄	—	89	2	no	—
379	C₄	—	178	2	no	—
380	C₄	—	178	1	no	—
381	C₄	—	178	1	no	—
382	C₄	M₃₂×D₈₉	1	2	yes	complemented
383	C₄	C₄×D₄×D₈₉	1	1	yes	characteristic
384	C₄	#131×D₈₉	1	1	yes	characteristic
385	C₂	—	4	2	no	—
386	C₂	—	178	2	no	—
387	C₂	—	178	4	no	—
388	C₂	C₈×D₄×D₈₉	1	1	yes	characteristic
389	C₂	C₂×M₃₂×D₈₉	1	1	yes	characteristic
390	C₂	#26033353	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂³×C₈
Fitting	C₈₉×#2169	C₂
prime radical	C₂×D₄×D₈₉	C₈
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	#2169	D₈₉
hypocenter	C₈₉	D₄×M₃₂
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ #2169

Complements

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

N	H ≅ G/N	type
1. C₂×M₃₂×D₈₉	C₂	semidirect
3. #26022084	C₂	semidirect
4. #26022080	C₂	semidirect
5. #26022075	C₂	semidirect
6. C₁₆×D₃₅₆	C₂	semidirect
7. #26022071	C₂	semidirect
8. #26022006	C₂	semidirect
9. #26021861	C₂	semidirect
10. C₄×#15667951	C₂	semidirect
11. C₈₉×#2169	C₂	semidirect
14. C₂×#15667952	C₂²	semidirect
19. C₂×C₁₆×D₈₉	C₂²	semidirect
20. C₂×C₁₆×D₈₉	C₂²	semidirect
29. C₄⋊#13083549	C₂²	semidirect
30. #19151416	C₂²	semidirect
31. C₂²⋊#13083549	C₂²	semidirect
32. #19151377	C₂²	semidirect
33. #19151377	C₂²	semidirect
34. #19151373	C₂²	semidirect
35. #19151373	C₂²	semidirect
36. C₄×#13083549	C₂²	semidirect
37. C₂×M₃₂×C₈₉	C₂²	semidirect
39. C₄⋊C₁₆×C₈₉	C₂²	semidirect
40. C₂²⋊C₁₆×C₈₉	C₂²	semidirect
41. C₄×C₁₆×C₈₉	C₂²	semidirect
63. #15667951	D₄	semidirect
120. #13083549	C₂×D₄	semidirect
133. C₁₆×C₈₉	C₂×D₄	semidirect
153. D₃₅₆	M₃₂	semidirect
179. C₂×D₈₉	C₂×M₃₂	semidirect
182. C₄×C₈₉	C₂×M₃₂	semidirect
199. #2169	D₈₉	semidirect
207. C₈₉	D₄×M₃₂	semidirect
215. C₂×M₃₂	C₂×D₈₉	semidirect
229. C₄⋊C₁₆	C₂×D₈₉	semidirect
233. C₂²⋊C₁₆	C₂×D₈₉	semidirect
237. C₄×C₁₆	C₂×D₈₉	semidirect
329. C₁₆	D₄×D₈₉	semidirect
382. C₄	M₃₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₈₉	2
C₈×D₄×D₈₉	2
#26022084	2
#26022080	2
#26022075	2
C₁₆×D₃₅₆	2
#26022071	2
#26022006	2
#26021861	2
C₄×#15667951	2
C₈₉×#2169	2
D₄×M₃₂	89