Subgroups — M₃₂×C₂²⋊D₈₉ #36707639

Order 22784.

734 conjugacy classes of subgroups.

The subgroup lattice has 526 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	1	yes	maximal, characteristic, complemented
2	C₂×C₈×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic
3	#26022082	C₂	1	2	yes	maximal, complemented
4	#26022077	C₂	1	2	yes	maximal, complemented
5	#26022075	C₂	1	2	yes	maximal, complemented
6	C₁₆×C₂²⋊D₈₉	C₂	1	2	yes	maximal, complemented
7	#26022007	C₂	1	1	yes	maximal, characteristic, complemented
8	#26021863	C₂	1	1	yes	maximal, characteristic, complemented
9	#26021862	C₂	1	1	yes	maximal, characteristic, complemented
10	M₃₂×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×M₃₂×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₈₉	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₂²⋊D₈₉	C₄	1	1	yes	characteristic
14	C₂×#15667952	C₂²	1	1	yes	characteristic
15	C₂×#15667952	C₂²	1	1	yes	characteristic
16	C₂×#15667951	C₂²	1	2	yes	complemented
17	M₃₂×D₈₉	—	2	4	no	—
18	C₂×C₁₆×D₈₉	C₂²	1	2	yes	complemented
19	C₈×C₂²⋊D₈₉	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₈₉	C₄	1	1	yes	characteristic
21	C₈×C₂²⋊D₈₉	C₄	1	1	yes	characteristic
22	C₈×C₂²⋊D₈₉	C₄	1	1	yes	characteristic
23	C₈×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
24	C₈×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
25	C₈×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
26	C₈×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
27	C₂×#15667941	C₄	1	1	yes	characteristic
28	C₂×C₂²⋊#10623494	C₄	1	1	yes	characteristic
29	C₂×#15667924	C₄	1	1	yes	characteristic
30	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
31	#19151416	C₂²	1	2	yes	complemented
32	#19151416	C₂²	1	2	yes	complemented
33	C₂²⋊#13083549	C₂²	1	2	yes	complemented
34	C₂²⋊#13083549	C₂²	1	2	yes	complemented
35	#19151377	C₂²	1	2	yes	complemented
36	#19151377	C₂²	1	2	yes	complemented
37	#19151373	C₂²	1	2	yes	complemented
38	C₁₆×Dic₈₉	C₂²	1	2	yes	complemented
39	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
40	C₂×M₃₂×C₈₉	—	2	4	no	—
41	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
42	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
43	C₂×M₃₂×C₈₉	C₂²	1	2	yes	complemented
44	C₂²×C₁₆×C₈₉	C₂²	1	2	yes	complemented
45	C₂²×C₂²⋊D₈₉	C₈	1	1	yes	characteristic
46	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
47	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
48	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₈₉	—	2	2	no	—
50	C₂×C₈×D₈₉	—	2	2	no	—
51	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
52	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
54	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
55	C₄×C₂²⋊D₈₉	C₈	1	1	yes	characteristic
56	C₄×C₂²⋊D₈₉	C₈	1	1	yes	characteristic
57	C₄×C₂²⋊D₈₉	C₈	1	1	yes	characteristic
58	C₄×C₂²⋊D₈₉	C₈	1	1	yes	characteristic
59	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
60	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
61	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
62	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
63	C₂×#13083553	C₈	1	1	yes	characteristic
64	C₂×C₂²⋊Dic₈₉	C₈	1	1	yes	characteristic
65	C₂×#13083551	C₈	1	1	yes	characteristic
66	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
67	#15667952	—	2	2	no	—
68	#15667952	—	2	2	no	—
69	#15667951	—	2	4	no	—
70	C₂×#13083549	C₂³	1	2	yes	—
71	C₂×#13083549	C₂³	1	2	yes	—
72	C₁₆×D₈₉	—	2	4	no	—
73	#15667941	C₂×C₄	1	1	yes	characteristic
74	#15667941	C₂×C₄	1	1	yes	characteristic
75	#15667941	C₂×C₄	1	1	yes	characteristic
76	#15667941	C₂×C₄	1	1	yes	characteristic
77	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
78	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
79	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
80	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
81	#15667924	C₂×C₄	1	1	yes	characteristic
82	#15667924	C₂×C₄	1	1	yes	characteristic
83	#15667924	C₂×C₄	1	1	yes	characteristic
84	#15667924	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
88	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
89	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₈×C₈₉	—	2	2	no	—
91	C₂²×C₈×C₈₉	—	2	2	no	—
92	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
93	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
94	C₂²×C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
95	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
96	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
98	M₃₂×C₈₉	—	2	2	no	—
99	M₃₂×C₈₉	—	2	4	no	—
100	M₃₂×C₈₉	D₄	1	4	yes	complemented
101	C₂×C₁₆×C₈₉	—	2	4	no	—
102	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
103	C₂×C₁₆×C₈₉	C₂³	1	2	yes	—
104	C₂³×D₈₉	C₂×C₈	1	1	yes	characteristic
105	C₂×C₂²⋊D₈₉	—	2	4	no	—
106	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
107	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
108	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
109	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
110	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
111	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
112	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
113	C₂×C₄×D₈₉	—	2	2	no	—
114	C₂×C₄×D₈₉	—	2	2	no	—
115	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
116	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
117	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
119	C₂×#10623494	—	2	2	no	—
120	C₂×#10623494	—	2	2	no	—
121	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
122	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
123	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
124	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
125	C₈×D₈₉	—	2	2	no	—
126	C₈×D₈₉	—	2	2	no	—
127	C₈×D₈₉	—	2	1	no	—
128	C₈×D₈₉	—	2	1	no	—
129	C₈×D₈₉	—	2	1	no	—
130	C₈×D₈₉	—	2	1	no	—
131	#13083553	C₂×C₈	1	1	yes	characteristic
132	#13083553	C₂×C₈	1	1	yes	characteristic
133	#13083553	C₂×C₈	1	1	yes	characteristic
134	#13083553	C₂×C₈	1	1	yes	characteristic
135	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
136	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
137	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
138	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
139	#13083551	C₂×C₈	1	1	yes	characteristic
140	#13083551	C₂×C₈	1	1	yes	characteristic
141	#13083551	C₂×C₈	1	1	yes	characteristic
142	#13083551	C₂×C₈	1	1	yes	characteristic
143	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
144	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
145	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
146	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
147	#13083549	—	2	2	no	—
148	#13083549	—	2	2	no	—
149	C₂⁴×C₈₉	C₂×C₈	1	1	yes	characteristic
150	C₂²×C₄×C₈₉	—	2	2	no	—
151	C₂²×C₄×C₈₉	—	2	2	no	—
152	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
153	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
154	C₂²×C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
155	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₈₉	—	2	2	no	—
159	C₂×C₈×C₈₉	—	2	2	no	—
160	C₂×C₈×C₈₉	—	2	2	no	—
161	C₂×C₈×C₈₉	—	2	1	no	—
162	C₂×C₈×C₈₉	—	2	1	no	—
163	C₂×C₈×C₈₉	—	2	1	no	—
164	C₂×C₈×C₈₉	—	2	1	no	—
165	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
168	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
169	C₂×C₈×C₈₉	#41	1	2	yes	—
170	C₂×C₈×C₈₉	C₂⁴	1	1	yes	characteristic
171	C₁₆×C₈₉	—	2	2	no	—
172	C₁₆×C₈₉	C₂×D₄	1	4	yes	complemented
173	C₂³×C₈₉	—	2	2	no	—
174	C₂³×C₈₉	—	2	2	no	—
175	C₂³×C₈₉	—	4	1	no	—
176	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
177	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
178	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
179	C₂²×D₈₉	—	2	2	no	—
180	C₂²×D₈₉	—	2	2	no	—
181	C₂²×D₈₉	—	4	1	no	—
182	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
183	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
184	C₂×C₄×C₈₉	—	2	2	no	—
185	C₂×C₄×C₈₉	—	2	1	no	—
186	C₂×C₄×C₈₉	—	2	1	no	—
187	C₂×C₄×C₈₉	—	2	1	no	—
188	C₂×C₄×C₈₉	—	2	1	no	—
189	C₂×C₄×C₈₉	—	2	2	no	—
190	C₂×C₄×C₈₉	—	2	2	no	—
191	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
193	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
194	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
195	C₂×C₄×C₈₉	#131	1	2	yes	—
196	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
197	C₂²⋊D₈₉	—	2	2	no	—
198	C₂²⋊D₈₉	—	2	2	no	—
199	C₂²⋊D₈₉	—	2	2	no	—
200	C₂²⋊D₈₉	M₃₂	1	4	yes	direct product factor
201	C₂×Dic₈₉	—	2	2	no	—
202	C₂×Dic₈₉	—	2	2	no	—
203	C₂×Dic₈₉	—	4	1	no	—
204	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
205	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
206	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
207	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
208	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
209	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
210	C₄×D₈₉	—	2	1	no	—
211	C₄×D₈₉	—	2	1	no	—
212	C₄×D₈₉	—	2	1	no	—
213	C₄×D₈₉	—	2	1	no	—
214	C₄×D₈₉	—	2	2	no	—
215	C₄×D₈₉	—	2	2	no	—
216	C₈×C₈₉	—	2	1	no	—
217	C₈×C₈₉	—	2	1	no	—
218	C₈×C₈₉	C₄×D₄	1	2	yes	—
219	C₈×C₈₉	C₂²×D₄	1	1	yes	characteristic
220	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
221	#10623494	—	2	1	no	—
222	#10623494	—	2	1	no	—
223	#10623494	—	2	1	no	—
224	#10623494	—	2	1	no	—
225	C₂²×C₈₉	—	2	1	no	—
226	C₂²×C₈₉	—	2	1	no	—
227	C₂²×C₈₉	—	2	1	no	—
228	C₂²×C₈₉	—	2	1	no	—
229	C₂²×C₈₉	—	2	1	no	—
230	C₂²×C₈₉	—	2	1	no	—
231	C₂²×C₈₉	—	2	1	no	—
232	C₂²×C₈₉	—	4	4	no	—
233	C₂²×C₈₉	C₈×D₄	1	2	yes	—
234	C₂²×C₈₉	C₂×M₃₂	1	2	yes	complemented
235	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
236	C₂×D₈₉	—	2	1	no	—
237	C₂×D₈₉	—	2	1	no	—
238	C₂×D₈₉	—	2	1	no	—
239	C₂×D₈₉	—	2	1	no	—
240	C₂×D₈₉	—	2	1	no	—
241	C₂×D₈₉	—	4	4	no	—
242	C₂×D₈₉	C₂×M₃₂	1	2	yes	complemented
243	C₄×C₈₉	—	2	1	no	—
244	C₄×C₈₉	—	2	1	no	—
245	C₄×C₈₉	C₈×D₄	1	2	yes	—
246	C₄×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
247	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
248	Dic₈₉	—	2	1	no	—
249	Dic₈₉	—	2	1	no	—
250	Dic₈₉	—	2	1	no	—
251	Dic₈₉	—	2	1	no	—
252	Dic₈₉	—	2	1	no	—
253	Dic₈₉	C₂×M₃₂	1	2	yes	complemented
254	D₄×M₃₂	—	89	1	no	maximal, Sylow
255	C₂×C₈₉	—	2	2	no	—
256	C₂×C₈₉	—	2	2	no	—
257	C₂×C₈₉	—	4	1	no	—
258	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
259	C₂×C₈₉	C₂²×M₃₂	1	1	yes	characteristic
260	C₂×C₈₉	#3407	1	1	yes	characteristic
261	D₈₉	—	2	2	no	—
262	D₈₉	—	4	1	no	—
263	C₂²×M₃₂	—	89	1	no	—
264	C₂²×M₃₂	D₈₉	1	1	yes	characteristic, complemented
265	C₂×C₈×D₄	—	89	1	no	—
266	#2169	—	89	2	no	—
267	#2168	—	89	2	no	—
268	#2168	—	89	2	no	—
269	D₄×C₁₆	—	89	2	no	—
270	#2150	—	89	1	no	—
271	#2112	—	89	1	no	—
272	#2112	—	89	1	no	—
273	C₄×M₃₂	—	89	1	no	—
274	C₈₉	D₄×M₃₂	1	1	yes	characteristic, complemented, Sylow
275	C₂³×C₈	—	89	1	no	—
276	C₂³×C₈	C₂×D₈₉	1	1	yes	characteristic
277	C₂×C₄×D₄	—	89	1	no	—
278	C₂×M₃₂	—	2	4	no	—
279	C₂×M₃₂	—	89	1	no	—
280	C₂×M₃₂	—	89	1	no	—
281	C₂×M₃₂	—	89	2	no	—
282	C₂×M₃₂	—	178	4	no	—
283	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
284	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
285	C₂×M₃₂	C₂×D₈₉	1	2	yes	complemented
286	C₂²×C₁₆	—	89	2	no	—
287	C₂²×C₁₆	C₂×D₈₉	1	2	yes	complemented
288	C₈×D₄	—	89	1	no	—
289	C₈×D₄	—	89	1	no	—
290	C₈×D₄	—	89	1	no	—
291	C₈×D₄	—	89	1	no	—
292	C₈×D₄	—	89	1	no	—
293	C₈×D₄	—	89	1	no	—
294	C₈×D₄	—	89	1	no	—
295	C₈×D₄	—	89	1	no	—
296	C₂×C₄⋊C₈	—	89	1	no	—
297	C₂×C₂²⋊C₈	—	89	1	no	—
298	C₂×C₂²⋊C₈	—	89	1	no	—
299	C₂×C₄×C₈	—	89	1	no	—
300	C₄⋊C₁₆	—	89	2	no	—
301	C₄⋊C₁₆	—	89	2	no	—
302	C₂²⋊C₁₆	—	89	2	no	—
303	C₂²⋊C₁₆	—	89	2	no	—
304	C₂²⋊C₁₆	—	89	2	no	—
305	C₂²⋊C₁₆	—	89	2	no	—
306	#346	—	89	2	no	—
307	C₄×C₁₆	—	89	2	no	—
308	C₂²×D₄	—	89	1	no	—
309	C₂³×C₄	—	89	1	no	—
310	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
311	C₂²×C₈	—	2	2	no	—
312	C₂²×C₈	—	2	2	no	—
313	C₂²×C₈	—	89	1	no	—
314	C₂²×C₈	—	89	1	no	—
315	C₂²×C₈	—	89	1	no	—
316	C₂²×C₈	—	89	1	no	—
317	C₂²×C₈	—	89	1	no	—
318	C₂²×C₈	—	89	1	no	—
319	C₂²×C₈	—	178	2	no	—
320	C₂²×C₈	—	178	2	no	—
321	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
322	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
323	C₂²×C₈	C₄×D₈₉	1	1	yes	characteristic
324	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
325	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
326	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
327	C₄×D₄	—	89	1	no	—
328	C₄×D₄	—	89	1	no	—
329	C₄×D₄	—	89	1	no	—
330	C₄×D₄	—	89	1	no	—
331	C₄×D₄	—	89	1	no	—
332	C₄×D₄	—	89	1	no	—
333	C₄×D₄	—	89	1	no	—
334	C₄×D₄	—	89	1	no	—
335	C₂×C₄⋊C₄	—	89	1	no	—
336	C₂×C₂²⋊C₄	—	89	1	no	—
337	C₂×C₂²⋊C₄	—	89	1	no	—
338	C₂×C₄²	—	89	1	no	—
339	M₃₂	—	2	2	no	—
340	M₃₂	—	2	4	no	—
341	M₃₂	—	178	2	no	—
342	M₃₂	—	178	2	no	—
343	M₃₂	—	178	4	no	—
344	M₃₂	C₂²⋊D₈₉	1	4	yes	direct product factor
345	C₂×C₁₆	—	2	4	no	—
346	C₂×C₁₆	—	89	2	no	—
347	C₂×C₁₆	—	89	2	no	—
348	C₂×C₁₆	—	178	4	no	—
349	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
350	C₂×C₁₆	C₂²×D₈₉	1	2	yes	—
351	C₄⋊C₈	—	89	1	no	—
352	C₄⋊C₈	—	89	1	no	—
353	C₄⋊C₈	—	89	1	no	—
354	C₄⋊C₈	—	89	1	no	—
355	C₂²⋊C₈	—	89	1	no	—
356	C₂²⋊C₈	—	89	1	no	—
357	C₂²⋊C₈	—	89	1	no	—
358	C₂²⋊C₈	—	89	1	no	—
359	C₂²⋊C₈	—	89	1	no	—
360	C₂²⋊C₈	—	89	1	no	—
361	C₂²⋊C₈	—	89	1	no	—
362	C₂²⋊C₈	—	89	1	no	—
363	C₄×C₈	—	89	1	no	—
364	C₄×C₈	—	89	1	no	—
365	C₄×C₈	—	89	1	no	—
366	C₄×C₈	—	89	1	no	—
367	C₂⁴	—	89	1	no	—
368	C₂⁴	C₈×D₈₉	1	1	yes	characteristic
369	C₂×D₄	—	89	1	no	—
370	C₂×D₄	—	89	1	no	—
371	C₂×D₄	—	89	1	no	—
372	C₂×D₄	—	89	1	no	—
373	C₂×D₄	—	178	4	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	89	1	no	—
377	C₂²×C₄	—	89	1	no	—
378	C₂²×C₄	—	89	1	no	—
379	C₂²×C₄	—	89	1	no	—
380	C₂²×C₄	—	89	1	no	—
381	C₂²×C₄	—	89	1	no	—
382	C₂²×C₄	—	89	1	no	—
383	C₂²×C₄	—	178	2	no	—
384	C₂²×C₄	—	178	2	no	—
385	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
386	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
387	C₂²×C₄	C₈×D₈₉	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
389	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	2	2	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	89	1	no	—
399	C₂×C₈	—	89	1	no	—
400	C₂×C₈	—	89	1	no	—
401	C₂×C₈	—	89	1	no	—
402	C₂×C₈	—	178	2	no	—
403	C₂×C₈	—	178	2	no	—
404	C₂×C₈	—	178	2	no	—
405	C₂×C₈	—	178	2	no	—
406	C₂×C₈	—	178	1	no	—
407	C₂×C₈	—	178	1	no	—
408	C₂×C₈	—	178	1	no	—
409	C₂×C₈	—	178	1	no	—
410	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
411	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
412	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
413	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
414	C₂×C₈	#13083574	1	2	yes	—
415	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
416	C₄⋊C₄	—	89	1	no	—
417	C₄⋊C₄	—	89	1	no	—
418	C₄⋊C₄	—	89	1	no	—
419	C₄⋊C₄	—	89	1	no	—
420	C₂²⋊C₄	—	89	1	no	—
421	C₂²⋊C₄	—	89	1	no	—
422	C₂²⋊C₄	—	89	1	no	—
423	C₂²⋊C₄	—	89	1	no	—
424	C₂²⋊C₄	—	89	1	no	—
425	C₂²⋊C₄	—	89	1	no	—
426	C₂²⋊C₄	—	89	1	no	—
427	C₂²⋊C₄	—	89	1	no	—
428	C₄²	—	89	1	no	—
429	C₄²	—	89	1	no	—
430	C₄²	—	89	1	no	—
431	C₄²	—	89	1	no	—
432	C₁₆	—	2	2	no	—
433	C₁₆	—	178	2	no	—
434	C₁₆	—	178	2	no	—
435	C₁₆	C₂×C₂²⋊D₈₉	1	4	yes	complemented
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	4	1	no	—
439	C₂³	—	89	1	no	—
440	C₂³	—	89	1	no	—
441	C₂³	—	356	1	no	—
442	C₂³	—	178	2	no	—
443	C₂³	—	178	2	no	—
444	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
445	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
446	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
447	D₄	—	89	4	no	—
448	D₄	—	178	2	no	—
449	D₄	—	178	2	no	—
450	D₄	—	178	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	89	1	no	—
459	C₂×C₄	—	89	1	no	—
460	C₂×C₄	—	89	1	no	—
461	C₂×C₄	—	89	1	no	—
462	C₂×C₄	—	89	1	no	—
463	C₂×C₄	—	89	1	no	—
464	C₂×C₄	—	356	1	no	—
465	C₂×C₄	—	178	2	no	—
466	C₂×C₄	—	178	2	no	—
467	C₂×C₄	—	178	2	no	—
468	C₂×C₄	—	178	2	no	—
469	C₂×C₄	—	178	1	no	—
470	C₂×C₄	—	178	1	no	—
471	C₂×C₄	—	178	1	no	—
472	C₂×C₄	—	178	1	no	—
473	C₂×C₄	C₄×C₂²⋊D₈₉	1	2	yes	—
474	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
475	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
476	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
477	C₂×C₄	#15668018	1	2	yes	—
478	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
479	C₈	—	2	1	no	—
480	C₈	—	2	1	no	—
481	C₈	—	178	1	no	—
482	C₈	—	178	1	no	—
483	C₈	—	178	1	no	—
484	C₈	—	178	1	no	—
485	C₈	C₄×C₂²⋊D₈₉	1	2	yes	—
486	C₈	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
487	C₈	C₂×#13083574	1	1	yes	characteristic
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	1	no	—
493	C₂²	—	2	1	no	—
494	C₂²	—	2	1	no	—
495	C₂²	—	4	4	no	—
496	C₂²	—	89	2	no	—
497	C₂²	—	356	4	no	—
498	C₂²	—	178	1	no	—
499	C₂²	—	178	1	no	—
500	C₂²	—	178	1	no	—
501	C₂²	—	178	1	no	—
502	C₂²	—	178	1	no	—
503	C₂²	C₈×C₂²⋊D₈₉	1	2	yes	—
504	C₂²	M₃₂×D₈₉	1	2	yes	complemented
505	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
506	C₄	—	2	1	no	—
507	C₄	—	2	1	no	—
508	C₄	—	89	2	no	—
509	C₄	—	178	1	no	—
510	C₄	—	178	1	no	—
511	C₄	—	178	1	no	—
512	C₄	—	178	1	no	—
513	C₄	—	178	1	no	—
514	C₄	C₈×C₂²⋊D₈₉	1	2	yes	—
515	C₄	C₂×C₄×C₂²⋊D₈₉	1	1	yes	characteristic
516	C₄	C₂×#15668018	1	1	yes	characteristic
517	C₂	—	2	2	no	—
518	C₂	—	2	2	no	—
519	C₂	—	4	1	no	—
520	C₂	—	356	1	no	—
521	C₂	—	178	2	no	—
522	C₂	C₂×C₈×C₂²⋊D₈₉	1	1	yes	characteristic
523	C₂	C₂×M₃₂×D₈₉	1	1	yes	characteristic
524	C₂	#26033354	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×M₃₂×D₈₉	C₂	semidirect
3. #26022082	C₂	semidirect
4. #26022077	C₂	semidirect
5. #26022075	C₂	semidirect
6. C₁₆×C₂²⋊D₈₉	C₂	semidirect
7. #26022007	C₂	semidirect
8. #26021863	C₂	semidirect
9. #26021862	C₂	semidirect
10. M₃₂×Dic₈₉	C₂	semidirect
11. C₂²×M₃₂×C₈₉	C₂	semidirect
16. C₂×#15667951	C₂²	semidirect
18. C₂×C₁₆×D₈₉	C₂²	semidirect
31. #19151416	C₂²	semidirect
32. #19151416	C₂²	semidirect
33. C₂²⋊#13083549	C₂²	semidirect
34. C₂²⋊#13083549	C₂²	semidirect
35. #19151377	C₂²	semidirect
36. #19151377	C₂²	semidirect
37. #19151373	C₂²	semidirect
38. C₁₆×Dic₈₉	C₂²	semidirect
43. C₂×M₃₂×C₈₉	C₂²	semidirect
44. C₂²×C₁₆×C₈₉	C₂²	semidirect
100. M₃₂×C₈₉	D₄	semidirect
172. C₁₆×C₈₉	C₂×D₄	semidirect
200. C₂²⋊D₈₉	M₃₂	direct (N × H)
234. C₂²×C₈₉	C₂×M₃₂	semidirect
242. C₂×D₈₉	C₂×M₃₂	semidirect
253. Dic₈₉	C₂×M₃₂	semidirect
264. C₂²×M₃₂	D₈₉	semidirect
274. C₈₉	D₄×M₃₂	semidirect
285. C₂×M₃₂	C₂×D₈₉	semidirect
287. C₂²×C₁₆	C₂×D₈₉	semidirect
344. M₃₂	C₂²⋊D₈₉	direct (N × H)
435. C₁₆	C₂×C₂²⋊D₈₉	semidirect
504. C₂²	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
C₂×C₈×C₂²⋊D₈₉	2
#26022082	2
#26022077	2
#26022075	2
C₁₆×C₂²⋊D₈₉	2
#26022007	2
#26021863	2
#26021862	2
M₃₂×Dic₈₉	2
C₂²×M₃₂×C₈₉	2
D₄×M₃₂	89

Subgroups — M32×C22⋊D89 #36707639

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — M₃₂×C₂²⋊D₈₉ #36707639