Subgroups — #36707998

Order 22784.

552 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#13083573	C₂	1	1	yes	maximal, characteristic
2	#26022159	C₂	1	1	yes	maximal, characteristic, complemented
3	#26022158	C₂	1	1	yes	maximal, characteristic, complemented
4	#26022080	C₂	1	1	yes	maximal, characteristic, complemented
5	#26022078	C₂	1	1	yes	maximal, characteristic, complemented
6	#26022075	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₆×C₂²⋊D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
8	#26022069	C₂	1	1	yes	maximal, characteristic, complemented
9	#26022054	C₂	1	1	yes	maximal, characteristic, complemented
10	#26022052	C₂	1	1	yes	maximal, characteristic, complemented
11	#26022052	C₂	1	1	yes	maximal, characteristic, complemented
12	M₃₂×Dic₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#19151373	C₂	1	1	yes	maximal, characteristic, complemented
14	#346×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈₉×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#13083573	C₄	1	1	yes	characteristic
17	C₂×#15667952	C₂²	1	1	yes	characteristic
18	C₂²×#13083549	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
20	C₂×C₁₆×D₈₉	C₂²	1	1	yes	characteristic
21	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic
22	#19151722	C₄	1	1	yes	characteristic
23	D₄×#10623494	C₄	1	1	yes	characteristic
24	C₈×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
25	C₈×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
26	#19151661	C₄	1	1	yes	characteristic
27	#19151661	C₄	1	1	yes	characteristic
28	#19151650	C₄	1	1	yes	characteristic
29	#19151648	C₄	1	1	yes	characteristic
30	#19151648	C₄	1	1	yes	characteristic
31	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₈₉	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
34	C₄⋊#13083549	C₂²	1	1	yes	characteristic
35	#19151416	C₂²	1	1	yes	characteristic
36	#19151416	C₂²	1	1	yes	characteristic
37	#19151416	C₂²	1	1	yes	characteristic
38	#19151416	C₂²	1	1	yes	characteristic
39	C₂²⋊#13083549	C₂²	1	1	yes	characteristic
40	C₂²⋊#13083549	C₂²	1	1	yes	characteristic
41	#19151377	C₂²	1	1	yes	characteristic
42	#19151377	C₂²	1	1	yes	characteristic
43	#19151374	C₂²	1	1	yes	characteristic
44	#19151373	C₂²	1	1	yes	characteristic
45	#19151373	C₂²	1	1	yes	characteristic
46	#19151373	C₂²	1	1	yes	characteristic
47	#19151373	C₂²	1	1	yes	characteristic
48	#19151373	C₂²	1	1	yes	characteristic
49	#19151373	C₂²	1	1	yes	characteristic
50	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
51	C₁₆×Dic₈₉	C₂²	1	1	yes	characteristic
52	C₂×M₃₂×C₈₉	C₂²	1	1	yes	characteristic
53	C₂²×C₁₆×C₈₉	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
55	C₄⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
56	C₂²⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
57	C₂²⋊C₁₆×C₈₉	C₂²	1	1	yes	characteristic
58	#346×C₈₉	C₂²	1	1	yes	characteristic
59	C₂×#13083573	C₈	1	1	yes	characteristic
60	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
61	C₂²×#10623494	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
63	C₂×C₈×D₈₉	C₂³	1	1	yes	characteristic
64	C₄×Dic₁₇₈	C₂×C₄	1	1	yes	characteristic
65	#15667977	C₈	1	1	yes	characteristic
66	D₄×Dic₈₉	C₈	1	1	yes	characteristic
67	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
68	C₄×C₂²⋊D₈₉	C₂×C₄	1	1	yes	characteristic
69	#15667972	C₈	1	1	yes	characteristic
70	#15667972	C₈	1	1	yes	characteristic
71	#15667970	C₈	1	1	yes	characteristic
72	#15667968	C₈	1	1	yes	characteristic
73	#15667968	C₈	1	1	yes	characteristic
74	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
76	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
77	#15667952	—	2	2	no	—
78	C₂×#13083549	—	2	2	no	—
79	C₂×#13083549	C₂³	1	1	yes	characteristic
80	C₂×#13083549	C₂³	1	1	yes	characteristic
81	C₂×#13083549	C₂³	1	1	yes	characteristic
82	C₂×#13083549	C₂³	1	1	yes	characteristic
83	C₁₆×D₈₉	—	2	2	no	—
84	C₁₆×D₈₉	—	2	2	no	—
85	C₄⋊#10623494	C₂×C₄	1	1	yes	characteristic
86	#15667941	C₂×C₄	1	1	yes	characteristic
87	#15667941	C₂×C₄	1	1	yes	characteristic
88	#15667941	C₂×C₄	1	1	yes	characteristic
89	#15667941	C₂×C₄	1	1	yes	characteristic
90	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
91	C₂²⋊#10623494	C₂×C₄	1	1	yes	characteristic
92	#15667924	C₂×C₄	1	1	yes	characteristic
93	#15667924	C₂×C₄	1	1	yes	characteristic
94	C₄×#10623494	C₂×C₄	1	1	yes	characteristic
95	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
96	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
97	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
98	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
99	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
100	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
101	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
102	C₈×Dic₈₉	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
105	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
106	M₃₂×C₈₉	—	2	2	no	—
107	C₂×C₁₆×C₈₉	—	2	2	no	—
108	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
109	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
110	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
111	C₂×C₁₆×C₈₉	C₂³	1	1	yes	characteristic
112	C₄⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊C₈×C₈₉	C₂×C₄	1	1	yes	characteristic
115	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
116	#13083573	—	2	4	no	—
117	C₂×Dic₁₇₈	C₂×C₈	1	1	yes	characteristic
118	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
119	C₂×C₂²⋊D₈₉	C₂×C₈	1	1	yes	characteristic
120	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
121	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
122	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
123	C₂²×Dic₈₉	C₂×C₈	1	1	yes	characteristic
124	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
125	C₂×C₄×D₈₉	C₂×C₈	1	1	yes	characteristic
126	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
127	C₂×#10623494	—	2	2	no	—
128	C₂×#10623494	—	2	2	no	—
129	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
130	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
131	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
132	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
133	C₈×D₈₉	—	2	1	no	—
134	C₈×D₈₉	—	2	1	no	—
135	C₈×D₈₉	—	2	2	no	—
136	C₄⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
137	#13083553	C₂×C₈	1	1	yes	characteristic
138	#13083553	C₂×C₈	1	1	yes	characteristic
139	#13083553	C₂×C₈	1	1	yes	characteristic
140	#13083553	C₂×C₈	1	1	yes	characteristic
141	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
142	C₂²⋊Dic₈₉	C₂×C₈	1	1	yes	characteristic
143	#13083551	C₂×C₈	1	1	yes	characteristic
144	#13083551	C₂×C₈	1	1	yes	characteristic
145	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
146	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
147	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
148	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
149	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
150	C₄×Dic₈₉	C₂×C₈	1	1	yes	characteristic
151	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
154	#13083549	—	2	1	no	—
155	#13083549	—	2	1	no	—
156	#13083549	—	2	1	no	—
157	#13083549	#41	1	2	yes	complemented
158	C₂×D₄×C₈₉	C₂×C₈	1	1	yes	characteristic
159	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
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	C₂⁴	1	1	yes	characteristic
169	C₄⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
170	C₂²⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
171	C₂²⋊C₄×C₈₉	C₂×C₈	1	1	yes	characteristic
172	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
173	C₁₆×C₈₉	—	2	1	no	—
174	C₁₆×C₈₉	—	2	1	no	—
175	C₁₆×C₈₉	—	2	1	no	—
176	C₁₆×C₈₉	#41	1	2	yes	complemented
177	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
178	C₂³×C₈₉	C₂²×C₈	1	1	yes	characteristic
179	C₂²×D₈₉	C₂²×C₈	1	1	yes	characteristic
180	D₄×C₈₉	—	2	2	no	—
181	C₂×C₄×C₈₉	—	2	1	no	—
182	C₂×C₄×C₈₉	—	2	1	no	—
183	C₂×C₄×C₈₉	—	2	1	no	—
184	C₂×C₄×C₈₉	—	2	1	no	—
185	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₂²×C₈	1	1	yes	characteristic
189	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
190	C₂²⋊D₈₉	—	2	2	no	—
191	C₂²⋊D₈₉	M₃₂	1	4	yes	complemented
192	C₂×Dic₈₉	—	2	2	no	—
193	C₂×Dic₈₉	—	2	2	no	—
194	C₂×Dic₈₉	—	4	1	no	—
195	C₂×Dic₈₉	—	4	1	no	—
196	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
197	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
198	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
199	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
200	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
201	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
202	C₂×Dic₈₉	C₂²×C₈	1	1	yes	characteristic
203	C₄×D₈₉	—	2	2	no	—
204	C₄×D₈₉	—	2	1	no	—
205	C₄×D₈₉	—	2	1	no	—
206	C₄×D₈₉	—	4	1	no	—
207	Dic₁₇₈	—	2	2	no	—
208	C₈×C₈₉	—	2	1	no	—
209	C₈×C₈₉	—	2	1	no	—
210	C₈×C₈₉	—	2	1	no	—
211	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
212	C₈×C₈₉	C₂×#41	1	1	yes	characteristic
213	#10623494	—	2	1	no	—
214	#10623494	—	2	1	no	—
215	#10623494	—	2	1	no	—
216	#10623494	#131	1	2	yes	—
217	C₂²×C₈₉	—	2	1	no	—
218	C₂²×C₈₉	—	2	1	no	—
219	C₂²×C₈₉	—	2	1	no	—
220	C₂²×C₈₉	—	2	1	no	—
221	C₂²×C₈₉	—	2	1	no	—
222	C₂²×C₈₉	C₂×M₃₂	1	2	yes	—
223	C₂²×C₈₉	C₂³×C₈	1	1	yes	characteristic
224	C₂×D₈₉	—	2	1	no	—
225	C₂×D₈₉	—	2	1	no	—
226	C₂×D₈₉	C₂×M₃₂	1	2	yes	—
227	C₄×C₈₉	—	2	1	no	—
228	C₄×C₈₉	—	2	1	no	—
229	C₄×C₈₉	—	2	1	no	—
230	C₄×C₈₉	—	2	1	no	—
231	C₄×C₈₉	C₄×#41	1	1	yes	characteristic
232	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
233	Dic₈₉	—	2	1	no	—
234	Dic₈₉	—	2	1	no	—
235	Dic₈₉	—	2	1	no	—
236	Dic₈₉	—	2	1	no	—
237	Dic₈₉	—	2	1	no	—
238	Dic₈₉	—	2	1	no	—
239	Dic₈₉	C₂×M₃₂	1	2	yes	—
240	#33484	—	89	1	no	maximal, Sylow
241	C₂×C₈₉	—	2	2	no	—
242	C₂×C₈₉	—	4	1	no	—
243	C₂×C₈₉	C₈×#41	1	1	yes	characteristic
244	C₂×C₈₉	C₂²×M₃₂	1	1	yes	characteristic
245	C₂×C₈₉	#3407	1	1	yes	characteristic
246	D₈₉	—	2	2	no	—
247	C₈×#41	—	89	1	no	—
248	#2183	—	89	1	no	—
249	#2183	—	89	1	no	—
250	#2168	—	89	1	no	—
251	#2168	—	89	1	no	—
252	#2168	—	89	1	no	—
253	#2168	D₈₉	1	1	yes	characteristic, complemented
254	D₄×C₁₆	—	89	1	no	—
255	D₄×C₁₆	—	89	1	no	—
256	#2163	—	89	1	no	—
257	#2163	—	89	1	no	—
258	#2163	—	89	1	no	—
259	C₄×M₃₂	—	89	1	no	—
260	C₂×#346	—	89	1	no	—
261	C₂×#346	—	89	1	no	—
262	C₈₉	#33484	1	1	yes	characteristic, complemented, Sylow
263	C₄×#41	—	89	1	no	—
264	C₂×M₃₂	—	89	1	no	—
265	C₂×M₃₂	C₂×D₈₉	1	1	yes	characteristic
266	C₂²×C₁₆	—	89	1	no	—
267	C₂²×C₁₆	—	89	1	no	—
268	C₂²×C₁₆	—	89	1	no	—
269	C₂²×C₁₆	C₂×D₈₉	1	1	yes	characteristic
270	C₈×Q₈	—	89	1	no	—
271	C₈×Q₈	—	89	1	no	—
272	C₈×D₄	—	89	1	no	—
273	C₈×D₄	—	89	1	no	—
274	C₈×D₄	—	89	1	no	—
275	C₈×D₄	—	89	1	no	—
276	C₈×D₄	—	89	1	no	—
277	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
278	#431	—	89	1	no	—
279	#431	—	89	1	no	—
280	#431	—	89	1	no	—
281	C₂×C₄×C₈	—	89	1	no	—
282	C₂×C₄×C₈	—	89	1	no	—
283	C₂×C₄×C₈	—	89	1	no	—
284	C₄⋊C₁₆	—	89	1	no	—
285	C₄⋊C₁₆	—	89	1	no	—
286	C₄⋊C₁₆	—	89	1	no	—
287	C₄⋊C₁₆	—	89	1	no	—
288	C₄⋊C₁₆	—	89	1	no	—
289	C₄⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
290	C₂²⋊C₁₆	—	89	1	no	—
291	C₂²⋊C₁₆	—	89	1	no	—
292	C₂²⋊C₁₆	—	89	1	no	—
293	C₂²⋊C₁₆	—	89	1	no	—
294	C₂²⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
295	C₂²⋊C₁₆	C₂×D₈₉	1	1	yes	characteristic
296	#346	—	89	1	no	—
297	#346	—	89	1	no	—
298	#346	—	89	1	no	—
299	#346	—	89	1	no	—
300	#346	—	89	1	no	—
301	#346	—	89	1	no	—
302	#346	—	89	1	no	—
303	#346	C₂×D₈₉	1	1	yes	characteristic
304	C₄×C₁₆	—	89	1	no	—
305	C₄×C₁₆	—	89	1	no	—
306	C₂×#41	—	89	1	no	—
307	C₂²×C₈	—	89	1	no	—
308	C₂²×C₈	—	89	1	no	—
309	C₂²×C₈	—	89	1	no	—
310	C₂²×C₈	—	89	1	no	—
311	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
312	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
313	C₄×Q₈	—	89	1	no	—
314	C₄×Q₈	—	89	1	no	—
315	C₄×D₄	—	89	1	no	—
316	C₄×D₄	—	89	1	no	—
317	C₄×D₄	—	89	1	no	—
318	C₄×D₄	—	89	1	no	—
319	C₄×D₄	—	89	1	no	—
320	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
321	#117	—	89	1	no	—
322	#117	—	89	1	no	—
323	#117	—	89	1	no	—
324	C₂×C₄²	—	89	1	no	—
325	C₂×C₄²	—	89	1	no	—
326	C₂×C₄²	—	89	1	no	—
327	M₃₂	—	2	2	no	—
328	M₃₂	—	178	2	no	—
329	C₂×C₁₆	—	2	2	no	—
330	C₂×C₁₆	—	89	1	no	—
331	C₂×C₁₆	—	89	1	no	—
332	C₂×C₁₆	—	89	1	no	—
333	C₂×C₁₆	—	89	1	no	—
334	C₂×C₁₆	—	178	2	no	—
335	C₂×C₁₆	—	178	2	no	—
336	C₂×C₁₆	—	178	2	no	—
337	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
338	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
339	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
340	C₂×C₁₆	C₂²×D₈₉	1	1	yes	characteristic
341	C₄⋊C₈	—	89	1	no	—
342	C₄⋊C₈	—	89	1	no	—
343	C₄⋊C₈	—	89	1	no	—
344	C₄⋊C₈	—	89	1	no	—
345	C₄⋊C₈	—	89	1	no	—
346	C₄⋊C₈	C₄×D₈₉	1	1	yes	characteristic
347	C₂²⋊C₈	—	89	1	no	—
348	C₂²⋊C₈	—	89	1	no	—
349	C₂²⋊C₈	—	89	1	no	—
350	C₂²⋊C₈	—	89	1	no	—
351	C₂²⋊C₈	C₄×D₈₉	1	1	yes	characteristic
352	C₂²⋊C₈	C₄×D₈₉	1	1	yes	characteristic
353	C₄×C₈	—	89	1	no	—
354	C₄×C₈	—	89	1	no	—
355	C₄×C₈	—	89	1	no	—
356	C₄×C₈	—	89	1	no	—
357	C₄×C₈	—	89	1	no	—
358	C₄×C₈	—	89	1	no	—
359	C₄×C₈	—	89	1	no	—
360	C₄×C₈	—	89	1	no	—
361	C₄×C₈	—	89	1	no	—
362	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
363	#41	—	178	4	no	—
364	C₂×Q₈	—	89	1	no	—
365	C₂×D₄	—	89	1	no	—
366	C₂×D₄	—	89	1	no	—
367	C₂×D₄	C₈×D₈₉	1	1	yes	characteristic
368	C₂²×C₄	—	89	1	no	—
369	C₂²×C₄	—	89	1	no	—
370	C₂²×C₄	—	89	1	no	—
371	C₂²×C₄	—	89	1	no	—
372	C₂²×C₄	—	89	1	no	—
373	C₂²×C₄	—	89	1	no	—
374	C₂²×C₄	—	89	1	no	—
375	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
376	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	1	no	—
381	C₂×C₈	—	89	1	no	—
382	C₂×C₈	—	89	1	no	—
383	C₂×C₈	—	89	1	no	—
384	C₂×C₈	—	89	1	no	—
385	C₂×C₈	—	178	2	no	—
386	C₂×C₈	—	178	2	no	—
387	C₂×C₈	—	178	2	no	—
388	C₂×C₈	—	178	1	no	—
389	C₂×C₈	—	178	1	no	—
390	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
391	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
392	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
393	C₂×C₈	C₂³×D₈₉	1	1	yes	characteristic
394	C₄⋊C₄	—	89	1	no	—
395	C₄⋊C₄	—	89	1	no	—
396	C₄⋊C₄	—	89	1	no	—
397	C₄⋊C₄	—	89	1	no	—
398	C₄⋊C₄	—	89	1	no	—
399	C₄⋊C₄	C₈×D₈₉	1	1	yes	characteristic
400	C₂²⋊C₄	—	89	1	no	—
401	C₂²⋊C₄	—	89	1	no	—
402	C₂²⋊C₄	—	89	1	no	—
403	C₂²⋊C₄	—	89	1	no	—
404	C₂²⋊C₄	C₈×D₈₉	1	1	yes	characteristic
405	C₂²⋊C₄	C₈×D₈₉	1	1	yes	characteristic
406	C₄²	—	89	1	no	—
407	C₄²	—	89	1	no	—
408	C₄²	—	89	1	no	—
409	C₄²	—	89	1	no	—
410	C₄²	—	89	1	no	—
411	C₄²	—	89	1	no	—
412	C₄²	—	89	1	no	—
413	C₄²	—	89	1	no	—
414	C₄²	—	89	1	no	—
415	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
416	C₁₆	—	2	1	no	—
417	C₁₆	—	2	1	no	—
418	C₁₆	—	2	1	no	—
419	C₁₆	—	89	2	no	—
420	C₁₆	—	178	1	no	—
421	C₁₆	—	178	1	no	—
422	C₁₆	—	178	1	no	—
423	C₁₆	#13083573	1	2	yes	complemented
424	C₂³	—	89	1	no	—
425	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
426	C₂³	C₂×C₈×D₈₉	1	1	yes	characteristic
427	Q₈	—	178	2	no	—
428	D₄	—	2	2	no	—
429	D₄	—	89	4	no	—
430	D₄	—	178	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	89	1	no	—
436	C₂×C₄	—	89	1	no	—
437	C₂×C₄	—	89	1	no	—
438	C₂×C₄	—	89	1	no	—
439	C₂×C₄	—	89	1	no	—
440	C₂×C₄	—	89	1	no	—
441	C₂×C₄	—	89	1	no	—
442	C₂×C₄	—	356	1	no	—
443	C₂×C₄	—	356	1	no	—
444	C₂×C₄	—	356	1	no	—
445	C₂×C₄	—	178	2	no	—
446	C₂×C₄	—	178	2	no	—
447	C₂×C₄	—	178	2	no	—
448	C₂×C₄	—	178	1	no	—
449	C₂×C₄	—	178	1	no	—
450	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
451	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
452	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
453	C₂×C₄	C₂×C₈×D₈₉	1	1	yes	characteristic
454	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
455	C₈	—	2	1	no	—
456	C₈	—	2	1	no	—
457	C₈	—	2	1	no	—
458	C₈	—	89	2	no	—
459	C₈	—	178	1	no	—
460	C₈	—	178	1	no	—
461	C₈	—	178	1	no	—
462	C₈	#41×D₈₉	1	1	yes	characteristic
463	C₈	C₂×#13083573	1	1	yes	characteristic
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	1	no	—
468	C₂²	—	2	1	no	—
469	C₂²	—	89	2	no	—
470	C₂²	—	178	1	no	—
471	C₂²	—	178	1	no	—
472	C₂²	M₃₂×D₈₉	1	2	yes	—
473	C₂²	C₂²×C₈×D₈₉	1	1	yes	characteristic
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	89	2	no	—
479	C₄	—	178	1	no	—
480	C₄	—	178	1	no	—
481	C₄	—	178	1	no	—
482	C₄	—	178	1	no	—
483	C₄	—	178	1	no	—
484	C₄	—	178	1	no	—
485	C₄	C₄×#13083573	1	1	yes	characteristic
486	C₄	#131×D₈₉	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	4	1	no	—
489	C₂	—	178	2	no	—
490	C₂	C₈×#13083573	1	1	yes	characteristic
491	C₂	C₂×M₃₂×D₈₉	1	1	yes	characteristic
492	C₂	#26033353	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂³×C₈
Fitting	C₈₉×#2168	C₂
prime radical	C₂×#13083573	C₈
cosocle	C₂×C₈×C₈₉	C₂⁴
hypercenter	#2168	D₈₉
hypocenter	C₈₉	#33484
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
2. #26022159	C₂	semidirect
3. #26022158	C₂	semidirect
4. #26022080	C₂	semidirect
5. #26022078	C₂	semidirect
6. #26022075	C₂	semidirect
7. C₁₆×C₂²⋊D₈₉	C₂	semidirect
8. #26022069	C₂	semidirect
9. #26022054	C₂	semidirect
10. #26022052	C₂	semidirect
11. #26022052	C₂	semidirect
12. M₃₂×Dic₈₉	C₂	semidirect
13. C₂×#19151373	C₂	semidirect
14. #346×D₈₉	C₂	semidirect
15. C₈₉×#2168	C₂	semidirect
157. #13083549	#41	semidirect
176. C₁₆×C₈₉	#41	semidirect
191. C₂²⋊D₈₉	M₃₂	semidirect
253. #2168	D₈₉	semidirect
262. C₈₉	#33484	semidirect
423. C₁₆	#13083573	semidirect

Maximal subgroups

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

subgroup	index
C₈×#13083573	2
#26022159	2
#26022158	2
#26022080	2
#26022078	2
#26022075	2
C₁₆×C₂²⋊D₈₉	2
#26022069	2
#26022054	2
#26022052	2
M₃₂×Dic₈₉	2
C₂×#19151373	2
#346×D₈₉	2
C₈₉×#2168	2
#33484	89