Subgroups — C₈×SD₁₆×D₈₉ #36523787

Order 22784.

822 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×Q₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×SD₁₆×D₈₉	C₂	1	1	yes	maximal, characteristic
3	C₈×D₄×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26019055	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×#13083563	C₂	1	1	yes	maximal, characteristic, complemented
6	SD₁₆×#10623494	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×#13083561	C₂	1	1	yes	maximal, characteristic, complemented
8	#26019051	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#13083562	C₂	1	1	yes	maximal, characteristic, complemented
10	#26019049	C₂	1	1	yes	maximal, characteristic, complemented
11	#334×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈⋊C₈×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄⋊C₈×D₈₉	C₂	1	1	yes	maximal, characteristic
14	C₈²×D₈₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₈×SD₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×SD₁₆×D₈₉	C₄	1	1	yes	characteristic
17	C₂²×C₈×D₈₉	—	2	1	no	—
18	C₄×Q₈×D₈₉	C₂²	1	1	yes	characteristic
19	C₄×D₄×D₈₉	C₂²	1	1	yes	characteristic
20	Q₈×#10623494	C₂²	1	1	yes	characteristic, complemented
21	C₈×Dic₁₇₈	—	2	1	no	—
22	C₈×Dic₁₇₈	C₂²	1	1	yes	characteristic, complemented
23	#19151722	—	2	1	no	—
24	#19151722	C₂²	1	1	yes	characteristic, complemented
25	#19151689	C₄	1	1	yes	characteristic
26	C₄×#13083563	C₂²	1	1	yes	characteristic
27	SD₁₆×Dic₈₉	C₄	1	1	yes	characteristic
28	C₄×#13083561	C₂²	1	1	yes	characteristic
29	#19151685	C₄	1	1	yes	characteristic
30	C₄×#13083562	C₂²	1	1	yes	characteristic
31	#19151683	C₄	1	1	yes	characteristic
32	C₈×D₃₅₆	C₂²	1	1	yes	characteristic
33	D₄×#10623494	C₂²	1	1	yes	characteristic
34	#19151663	C₂²	1	1	yes	characteristic
35	C₈×C₂²⋊D₈₉	—	2	1	no	—
36	#19151661	—	2	1	no	—
37	#106×D₈₉	C₄	1	1	yes	characteristic
38	C₄⋊C₈×D₈₉	—	2	1	no	—
39	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
40	C₄⋊C₈×D₈₉	C₂²	1	1	yes	characteristic
41	#103×D₈₉	C₄	1	1	yes	characteristic
42	#102×D₈₉	C₄	1	1	yes	characteristic
43	C₂²⋊C₈×D₈₉	—	2	1	no	—
44	C₄×C₈×D₈₉	—	2	1	no	—
45	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
47	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
48	#19151349	C₂²	1	1	yes	characteristic, complemented
49	#19151348	C₂²	1	1	yes	characteristic, complemented
50	#19151348	C₂²	1	1	yes	characteristic, complemented
51	#19151330	C₂²	1	1	yes	characteristic, complemented
52	Q₈⋊#10623494	C₂²	1	1	yes	characteristic, complemented
53	#19151328	C₂²	1	1	yes	characteristic, complemented
54	#19151327	C₂²	1	1	yes	characteristic
55	D₄⋊#10623494	C₂²	1	1	yes	characteristic
56	#19151325	C₂²	1	1	yes	characteristic
57	C₈×#10623494	C₂²	1	1	yes	characteristic, complemented
58	C₈×#10623494	C₂²	1	1	yes	characteristic, complemented
59	C₈×#10623494	C₂²	1	1	yes	characteristic, complemented
60	C₈×Q₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
61	C₄×SD₁₆×C₈₉	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₈₉	C₂²	1	1	yes	characteristic
63	#334×C₈₉	C₂²	1	1	yes	characteristic, complemented
64	Q₈⋊C₈×C₈₉	C₂²	1	1	yes	characteristic, complemented
65	D₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
66	C₈²×C₈₉	C₂²	1	1	yes	characteristic, complemented
67	C₂×Q₈×D₈₉	C₂×C₄	1	1	yes	characteristic
68	C₂×D₄×D₈₉	C₂×C₄	1	1	yes	characteristic
69	C₂²×C₄×D₈₉	—	2	1	no	—
70	C₂×#13083563	C₂×C₄	1	1	yes	characteristic
71	C₂×#13083562	C₂×C₄	1	1	yes	characteristic
72	C₂×#13083561	C₂×C₄	1	1	yes	characteristic
73	SD₁₆×D₈₉	C₈	1	8	yes	direct product factor
74	C₂²×#10623494	—	2	1	no	—
75	C₂×C₈×D₈₉	—	2	1	no	—
76	C₂×C₈×D₈₉	—	2	1	no	—
77	C₂×C₈×D₈₉	—	2	1	no	—
78	C₂×C₈×D₈₉	—	2	1	no	—
79	C₂×C₈×D₈₉	—	2	1	no	—
80	C₂×C₈×D₈₉	—	4	4	no	—
81	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
82	C₂×C₈×D₈₉	C₂×C₄	1	1	yes	characteristic
83	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
84	C₂×C₈×D₈₉	D₄	1	1	yes	characteristic
85	Q₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
86	C₄×Dic₁₇₈	—	2	1	no	—
87	C₄×Dic₁₇₈	C₂³	1	1	yes	characteristic
88	#15667977	—	2	1	no	—
89	#15667977	C₂×C₄	1	1	yes	characteristic
90	C₄×D₃₅₆	C₂³	1	1	yes	characteristic
91	D₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
92	#15667974	C₂×C₄	1	1	yes	characteristic
93	C₄×C₂²⋊D₈₉	—	2	1	no	—
94	#15667972	—	2	1	no	—
95	C₄⋊C₄×D₈₉	—	2	1	no	—
96	C₄⋊C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
97	C₄⋊C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊C₄×D₈₉	—	2	1	no	—
99	C₄²×D₈₉	—	2	1	no	—
100	C₄²×D₈₉	C₂³	1	1	yes	characteristic
101	#15667944	C₂×C₄	1	1	yes	characteristic
102	#15667943	C₂×C₄	1	1	yes	characteristic
103	#15667943	C₂×C₄	1	1	yes	characteristic
104	C₄⋊#10623494	—	2	1	no	—
105	C₄⋊#10623494	C₂³	1	1	yes	characteristic
106	C₄⋊#10623494	C₂³	1	1	yes	characteristic
107	#15667941	—	2	1	no	—
108	#15667941	—	2	1	no	—
109	#15667941	—	2	1	no	—
110	#15667941	—	2	1	no	—
111	#15667937	C₂×C₄	1	1	yes	characteristic
112	#15667936	C₂×C₄	1	1	yes	characteristic
113	#15667935	C₂×C₄	1	1	yes	characteristic
114	#15667934	C₂×C₄	1	1	yes	characteristic
115	#15667933	C₂×C₄	1	1	yes	characteristic
116	#15667932	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊#10623494	—	2	1	no	—
118	#15667924	—	2	1	no	—
119	#15667924	—	2	1	no	—
120	C₄×#10623494	—	2	1	no	—
121	C₄×#10623494	C₂³	1	1	yes	characteristic
122	C₄×#10623494	C₂³	1	1	yes	characteristic
123	C₄×#10623494	C₂³	1	1	yes	characteristic
124	C₈×Dic₈₉	—	2	1	no	—
125	C₈×Dic₈₉	—	2	1	no	—
126	C₈×Dic₈₉	—	2	1	no	—
127	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
128	C₈×Dic₈₉	C₂×C₄	1	1	yes	characteristic
129	C₈×Dic₈₉	D₄	1	1	yes	characteristic
130	C₈×Dic₈₉	D₄	1	1	yes	characteristic
131	C₂×SD₁₆×C₈₉	C₂×C₄	1	1	yes	characteristic
132	C₂²×C₈×C₈₉	—	2	1	no	—
133	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
134	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
135	#106×C₈₉	C₂×C₄	1	1	yes	characteristic
136	C₄⋊C₈×C₈₉	—	2	1	no	—
137	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
138	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
139	#103×C₈₉	C₂×C₄	1	1	yes	characteristic
140	#102×C₈₉	C₂×C₄	1	1	yes	characteristic
141	C₂²⋊C₈×C₈₉	—	2	1	no	—
142	C₄×C₈×C₈₉	—	2	1	no	—
143	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
145	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
146	C₂³×D₈₉	—	2	1	no	—
147	C₂×Dic₁₇₈	—	2	1	no	—
148	C₂×Dic₁₇₈	C₂²×C₄	1	1	yes	characteristic
149	Q₈×D₈₉	—	2	2	no	—
150	Q₈×D₈₉	C₂×C₈	1	4	yes	complemented
151	C₂×D₃₅₆	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₂²⋊D₈₉	—	2	1	no	—
153	D₄×D₈₉	—	2	2	no	—
154	D₄×D₈₉	C₂×C₈	1	4	yes	—
155	C₂²×Dic₈₉	—	2	1	no	—
156	C₂×C₄×D₈₉	—	2	1	no	—
157	C₂×C₄×D₈₉	—	2	1	no	—
158	C₂×C₄×D₈₉	—	2	1	no	—
159	C₂×C₄×D₈₉	—	2	1	no	—
160	C₂×C₄×D₈₉	—	2	1	no	—
161	C₂×C₄×D₈₉	—	4	2	no	—
162	C₂×C₄×D₈₉	—	4	2	no	—
163	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₄×D₈₉	C₂×D₄	1	1	yes	characteristic
165	C₂×C₄×D₈₉	#41	1	1	yes	characteristic
166	#13083563	C₂×C₈	1	4	yes	complemented
167	#13083562	C₂×C₈	1	4	yes	complemented
168	#13083561	C₂×C₈	1	4	yes	complemented
169	C₂×#10623494	—	2	1	no	—
170	C₂×#10623494	—	2	1	no	—
171	C₂×#10623494	—	2	1	no	—
172	C₂×#10623494	—	4	2	no	—
173	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
174	C₂×#10623494	C₂²×C₄	1	1	yes	characteristic
175	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
176	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
177	C₈×D₈₉	—	2	4	no	—
178	C₈×D₈₉	—	2	2	no	—
179	C₈×D₈₉	—	2	2	no	—
180	C₈×D₈₉	—	4	2	no	—
181	C₈×D₈₉	—	4	2	no	—
182	C₈×D₈₉	—	4	2	no	—
183	C₈×D₈₉	—	4	2	no	—
184	C₈×D₈₉	C₂×C₈	1	4	yes	complemented
185	C₈×D₈₉	SD₁₆	1	4	yes	direct product factor
186	C₄⋊Dic₈₉	—	2	1	no	—
187	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
188	C₄⋊Dic₈₉	C₂²×C₄	1	1	yes	characteristic
189	#13083553	—	2	1	no	—
190	#13083553	—	2	1	no	—
191	#13083553	—	2	1	no	—
192	#13083553	—	2	1	no	—
193	C₂²⋊Dic₈₉	—	2	1	no	—
194	#13083551	—	2	1	no	—
195	#13083551	—	2	1	no	—
196	C₄×Dic₈₉	—	2	1	no	—
197	C₄×Dic₈₉	—	2	1	no	—
198	C₄×Dic₈₉	—	2	1	no	—
199	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
200	C₄×Dic₈₉	C₂×D₄	1	1	yes	characteristic
201	C₄×Dic₈₉	#41	1	1	yes	characteristic
202	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
203	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
204	C₂²×C₄×C₈₉	—	2	1	no	—
205	SD₁₆×C₈₉	C₂×C₈	1	4	yes	complemented
206	C₂×C₈×C₈₉	—	2	1	no	—
207	C₂×C₈×C₈₉	—	2	1	no	—
208	C₂×C₈×C₈₉	—	2	1	no	—
209	C₂×C₈×C₈₉	—	4	2	no	—
210	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
211	C₂×C₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
212	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
213	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
214	C₄⋊C₄×C₈₉	—	2	1	no	—
215	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
216	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
217	C₂²⋊C₄×C₈₉	—	2	1	no	—
218	C₄²×C₈₉	—	2	1	no	—
219	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
220	C₂³×C₈₉	—	2	1	no	—
221	C₂²×D₈₉	—	2	1	no	—
222	C₂²×D₈₉	—	2	4	no	—
223	C₂²×D₈₉	—	4	2	no	—
224	C₂²×D₈₉	—	4	2	no	—
225	C₂²×D₈₉	C₄×D₄	1	1	yes	characteristic
226	Q₈×C₈₉	—	2	1	no	—
227	Q₈×C₈₉	C₂²×C₈	1	2	yes	complemented
228	D₄×C₈₉	—	2	1	no	—
229	D₄×C₈₉	C₂²×C₈	1	2	yes	—
230	C₂×C₄×C₈₉	—	2	1	no	—
231	C₂×C₄×C₈₉	—	2	1	no	—
232	C₂×C₄×C₈₉	—	2	1	no	—
233	C₂×C₄×C₈₉	—	4	1	no	—
234	C₂×C₄×C₈₉	—	4	1	no	—
235	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
236	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
238	C₂²⋊D₈₉	—	2	4	no	—
239	C₂×Dic₈₉	—	2	1	no	—
240	C₂×Dic₈₉	—	2	1	no	—
241	C₂×Dic₈₉	—	2	1	no	—
242	C₂×Dic₈₉	—	4	2	no	—
243	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
244	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
245	C₂×Dic₈₉	C₄×D₄	1	1	yes	characteristic
246	D₃₅₆	—	2	1	no	—
247	D₃₅₆	C₂²×C₈	1	2	yes	—
248	C₄×D₈₉	—	2	4	no	—
249	C₄×D₈₉	—	2	2	no	—
250	C₄×D₈₉	—	4	2	no	—
251	C₄×D₈₉	—	4	2	no	—
252	C₄×D₈₉	—	4	1	no	—
253	C₄×D₈₉	—	4	1	no	—
254	C₄×D₈₉	—	4	2	no	—
255	C₄×D₈₉	C₂²×C₈	1	2	yes	—
256	C₄×D₈₉	#131	1	2	yes	—
257	C₄×D₈₉	C₂×SD₁₆	1	2	yes	—
258	C₄×D₈₉	#135	1	2	yes	—
259	Dic₁₇₈	—	2	1	no	—
260	Dic₁₇₈	—	2	4	no	—
261	Dic₁₇₈	C₂²×C₈	1	2	yes	complemented
262	C₈×C₈₉	—	2	2	no	—
263	C₈×C₈₉	—	2	1	no	—
264	C₈×C₈₉	—	2	1	no	—
265	C₈×C₈₉	—	4	1	no	—
266	C₈×C₈₉	—	4	1	no	—
267	C₈×C₈₉	C₂²×C₈	1	2	yes	complemented
268	C₈×C₈₉	C₂×SD₁₆	1	2	yes	complemented
269	#10623494	—	2	2	no	—
270	#10623494	—	2	1	no	—
271	#10623494	—	2	1	no	—
272	#10623494	—	4	1	no	—
273	#10623494	—	4	1	no	—
274	#10623494	C₂²×C₈	1	2	yes	complemented
275	#10623494	C₂×SD₁₆	1	2	yes	complemented
276	C₂²×C₈₉	—	2	2	no	—
277	C₂²×C₈₉	—	4	1	no	—
278	C₂²×C₈₉	—	4	1	no	—
279	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
280	C₂×D₈₉	—	2	2	no	—
281	C₂×D₈₉	—	4	1	no	—
282	C₂×D₈₉	—	4	1	no	—
283	C₂×D₈₉	—	4	8	no	—
284	C₂×D₈₉	C₈×D₄	1	2	yes	—
285	C₂×D₈₉	C₄×SD₁₆	1	2	yes	—
286	C₂×D₈₉	#443	1	2	yes	—
287	C₄×C₈₉	—	2	2	no	—
288	C₄×C₈₉	—	2	1	no	—
289	C₄×C₈₉	—	4	1	no	—
290	C₄×C₈₉	—	4	1	no	—
291	C₄×C₈₉	C₂³×C₈	1	1	yes	characteristic
292	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
293	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
294	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
295	Dic₈₉	—	2	2	no	—
296	Dic₈₉	—	2	1	no	—
297	Dic₈₉	—	4	1	no	—
298	Dic₈₉	—	4	1	no	—
299	Dic₈₉	C₈×D₄	1	2	yes	—
300	Dic₈₉	C₄×SD₁₆	1	2	yes	—
301	C₂×C₈×SD₁₆	—	89	1	no	maximal, Sylow
302	C₂×C₈₉	—	4	2	no	—
303	C₂×C₈₉	C₂×C₈×D₄	1	1	yes	characteristic
304	C₂×C₈₉	C₂×C₄×SD₁₆	1	1	yes	characteristic
305	C₂×C₈₉	C₂×#443	1	1	yes	characteristic
306	D₈₉	—	4	2	no	—
307	D₈₉	C₈×SD₁₆	1	4	yes	direct product factor
308	C₂×C₈×Q₈	—	89	1	no	—
309	C₂×C₄×SD₁₆	—	89	1	no	—
310	C₂×C₈×D₄	—	89	1	no	—
311	C₈×SD₁₆	—	89	1	no	—
312	C₈×SD₁₆	—	89	1	no	—
313	C₈×SD₁₆	—	89	1	no	—
314	C₈×SD₁₆	—	89	1	no	—
315	C₈×SD₁₆	—	89	1	no	—
316	C₈×SD₁₆	—	89	1	no	—
317	C₈×SD₁₆	—	89	1	no	—
318	C₈×SD₁₆	D₈₉	1	1	yes	characteristic, direct product factor
319	C₂×#334	—	89	1	no	—
320	C₂×Q₈⋊C₈	—	89	1	no	—
321	C₂×D₄⋊C₈	—	89	1	no	—
322	C₂×C₈²	—	89	1	no	—
323	C₈₉	C₂×C₈×SD₁₆	1	1	yes	characteristic, complemented, Sylow
324	C₂²×SD₁₆	—	89	1	no	—
325	C₂³×C₈	—	178	1	no	—
326	C₂×C₄×Q₈	—	89	1	no	—
327	C₂×C₄×D₄	—	89	1	no	—
328	C₈×Q₈	—	89	1	no	—
329	C₈×Q₈	—	89	1	no	—
330	C₈×Q₈	—	89	1	no	—
331	C₈×Q₈	—	178	1	no	—
332	C₈×Q₈	—	178	1	no	—
333	C₈×Q₈	C₂×D₈₉	1	1	yes	characteristic, complemented
334	C₄×SD₁₆	—	89	1	no	—
335	C₄×SD₁₆	—	89	1	no	—
336	C₄×SD₁₆	—	89	1	no	—
337	C₄×SD₁₆	—	89	1	no	—
338	C₄×SD₁₆	—	89	1	no	—
339	C₄×SD₁₆	—	89	1	no	—
340	C₄×SD₁₆	—	89	1	no	—
341	C₄×SD₁₆	C₂×D₈₉	1	1	yes	characteristic
342	C₈×D₄	—	89	1	no	—
343	C₈×D₄	—	89	1	no	—
344	C₈×D₄	—	89	1	no	—
345	C₈×D₄	—	178	1	no	—
346	C₈×D₄	—	178	1	no	—
347	C₈×D₄	C₂×D₈₉	1	1	yes	characteristic
348	C₂×#106	—	89	1	no	—
349	C₂×C₄⋊C₈	—	89	1	no	—
350	C₂×C₄⋊C₈	—	89	1	no	—
351	C₂×C₄⋊C₈	—	178	1	no	—
352	C₂×#103	—	89	1	no	—
353	C₂×#102	—	89	1	no	—
354	C₂×C₂²⋊C₈	—	178	1	no	—
355	C₂×C₄×C₈	—	89	1	no	—
356	C₂×C₄×C₈	—	89	1	no	—
357	C₂×C₄×C₈	—	89	1	no	—
358	C₂×C₄×C₈	—	178	1	no	—
359	#334	—	89	1	no	—
360	#334	—	89	1	no	—
361	#334	—	89	1	no	—
362	#334	C₂×D₈₉	1	1	yes	characteristic, complemented
363	Q₈⋊C₈	—	89	1	no	—
364	Q₈⋊C₈	—	89	1	no	—
365	Q₈⋊C₈	—	89	1	no	—
366	Q₈⋊C₈	C₂×D₈₉	1	1	yes	characteristic, complemented
367	D₄⋊C₈	—	89	1	no	—
368	D₄⋊C₈	—	89	1	no	—
369	D₄⋊C₈	—	89	1	no	—
370	D₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
371	C₈²	—	89	1	no	—
372	C₈²	—	89	1	no	—
373	C₈²	—	89	1	no	—
374	C₈²	C₂×D₈₉	1	1	yes	characteristic, complemented
375	C₂²×Q₈	—	89	1	no	—
376	C₂²×D₄	—	89	1	no	—
377	C₂³×C₄	—	178	1	no	—
378	C₂×SD₁₆	—	89	1	no	—
379	C₂×SD₁₆	—	89	1	no	—
380	C₂×SD₁₆	—	89	8	no	—
381	C₂×SD₁₆	—	89	1	no	—
382	C₂×SD₁₆	C₄×D₈₉	1	1	yes	characteristic
383	C₂²×C₈	—	2	1	no	—
384	C₂²×C₈	—	89	1	no	—
385	C₂²×C₈	—	89	1	no	—
386	C₂²×C₈	—	89	1	no	—
387	C₂²×C₈	—	89	1	no	—
388	C₂²×C₈	—	356	4	no	—
389	C₂²×C₈	—	178	1	no	—
390	C₂²×C₈	—	178	1	no	—
391	C₂²×C₈	—	178	1	no	—
392	C₂²×C₈	—	178	1	no	—
393	C₂²×C₈	—	178	1	no	—
394	C₂²×C₈	—	178	1	no	—
395	C₄×Q₈	—	89	1	no	—
396	C₄×Q₈	—	89	1	no	—
397	C₄×Q₈	—	89	1	no	—
398	C₄×Q₈	—	178	1	no	—
399	C₄×Q₈	—	178	1	no	—
400	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
401	C₄×D₄	—	89	1	no	—
402	C₄×D₄	—	89	1	no	—
403	C₄×D₄	—	89	1	no	—
404	C₄×D₄	—	178	1	no	—
405	C₄×D₄	—	178	1	no	—
406	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
407	C₂×C₄⋊C₄	—	89	1	no	—
408	C₂×C₄⋊C₄	—	89	1	no	—
409	C₂×C₄⋊C₄	—	178	1	no	—
410	C₂×C₂²⋊C₄	—	178	1	no	—
411	C₂×C₄²	—	89	1	no	—
412	C₂×C₄²	—	178	1	no	—
413	#106	—	89	1	no	—
414	#106	—	89	1	no	—
415	#106	—	89	1	no	—
416	#106	C₄×D₈₉	1	1	yes	characteristic
417	C₄⋊C₈	—	2	1	no	—
418	C₄⋊C₈	—	89	1	no	—
419	C₄⋊C₈	—	89	1	no	—
420	C₄⋊C₈	—	178	1	no	—
421	C₄⋊C₈	—	178	1	no	—
422	C₄⋊C₈	—	178	1	no	—
423	C₄⋊C₈	—	178	1	no	—
424	C₄⋊C₈	—	178	1	no	—
425	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
426	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
427	#103	—	89	1	no	—
428	#103	—	89	1	no	—
429	#103	—	89	1	no	—
430	#103	C₄×D₈₉	1	1	yes	characteristic
431	#102	—	89	1	no	—
432	#102	—	89	1	no	—
433	#102	—	89	1	no	—
434	#102	C₄×D₈₉	1	1	yes	characteristic
435	C₂²⋊C₈	—	2	1	no	—
436	C₂²⋊C₈	—	178	1	no	—
437	C₂²⋊C₈	—	178	1	no	—
438	C₂²⋊C₈	—	178	1	no	—
439	C₄×C₈	—	2	1	no	—
440	C₄×C₈	—	89	1	no	—
441	C₄×C₈	—	89	1	no	—
442	C₄×C₈	—	89	1	no	—
443	C₄×C₈	—	89	1	no	—
444	C₄×C₈	—	89	1	no	—
445	C₄×C₈	—	89	1	no	—
446	C₄×C₈	—	89	1	no	—
447	C₄×C₈	—	178	1	no	—
448	C₄×C₈	—	178	1	no	—
449	C₄×C₈	—	178	1	no	—
450	C₄×C₈	—	178	1	no	—
451	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
452	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
453	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
454	C₂⁴	—	178	1	no	—
455	C₂×Q₈	—	89	4	no	—
456	C₂×Q₈	—	89	1	no	—
457	C₂×Q₈	—	178	1	no	—
458	C₂×Q₈	—	178	2	no	—
459	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
460	C₂×D₄	—	89	4	no	—
461	C₂×D₄	—	89	1	no	—
462	C₂×D₄	—	178	2	no	—
463	C₂×D₄	—	178	1	no	—
464	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	89	1	no	—
467	C₂²×C₄	—	89	1	no	—
468	C₂²×C₄	—	89	1	no	—
469	C₂²×C₄	—	356	2	no	—
470	C₂²×C₄	—	356	2	no	—
471	C₂²×C₄	—	178	1	no	—
472	C₂²×C₄	—	178	1	no	—
473	C₂²×C₄	—	178	1	no	—
474	C₂²×C₄	—	178	1	no	—
475	C₂²×C₄	—	178	1	no	—
476	C₂²×C₄	—	178	1	no	—
477	SD₁₆	—	89	4	no	—
478	SD₁₆	—	89	4	no	—
479	SD₁₆	—	89	4	no	—
480	SD₁₆	C₈×D₈₉	1	4	yes	direct product factor
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	4	2	no	—
485	C₂×C₈	—	89	1	no	—
486	C₂×C₈	—	89	1	no	—
487	C₂×C₈	—	89	4	no	—
488	C₂×C₈	—	89	4	no	—
489	C₂×C₈	—	89	1	no	—
490	C₂×C₈	—	89	1	no	—
491	C₂×C₈	—	356	2	no	—
492	C₂×C₈	—	356	2	no	—
493	C₂×C₈	—	356	2	no	—
494	C₂×C₈	—	356	2	no	—
495	C₂×C₈	—	356	2	no	—
496	C₂×C₈	—	178	2	no	—
497	C₂×C₈	—	178	2	no	—
498	C₂×C₈	—	178	4	no	—
499	C₂×C₈	—	178	1	no	—
500	C₂×C₈	—	178	1	no	—
501	C₂×C₈	—	178	1	no	—
502	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
503	C₂×C₈	C₂×C₄×D₈₉	1	1	yes	characteristic
504	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
505	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	89	1	no	—
508	C₄⋊C₄	—	89	1	no	—
509	C₄⋊C₄	—	178	1	no	—
510	C₄⋊C₄	—	178	1	no	—
511	C₄⋊C₄	—	178	1	no	—
512	C₄⋊C₄	—	178	1	no	—
513	C₄⋊C₄	—	178	1	no	—
514	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
515	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
516	C₂²⋊C₄	—	2	1	no	—
517	C₂²⋊C₄	—	178	1	no	—
518	C₂²⋊C₄	—	178	1	no	—
519	C₂²⋊C₄	—	178	1	no	—
520	C₄²	—	2	1	no	—
521	C₄²	—	89	1	no	—
522	C₄²	—	89	1	no	—
523	C₄²	—	89	1	no	—
524	C₄²	—	178	1	no	—
525	C₄²	—	178	1	no	—
526	C₄²	—	178	1	no	—
527	C₄²	C₂³×D₈₉	1	1	yes	characteristic
528	C₂³	—	2	1	no	—
529	C₂³	—	89	1	no	—
530	C₂³	—	356	2	no	—
531	C₂³	—	356	2	no	—
532	C₂³	—	178	4	no	—
533	C₂³	—	178	1	no	—
534	Q₈	—	2	1	no	—
535	Q₈	—	89	2	no	—
536	Q₈	—	178	4	no	—
537	Q₈	—	178	1	no	—
538	Q₈	C₂×C₈×D₈₉	1	2	yes	complemented
539	D₄	—	2	1	no	—
540	D₄	—	89	2	no	—
541	D₄	—	178	4	no	—
542	D₄	—	178	1	no	—
543	D₄	C₂×C₈×D₈₉	1	2	yes	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	89	1	no	—
550	C₂×C₄	—	89	1	no	—
551	C₂×C₄	—	89	2	no	—
552	C₂×C₄	—	89	2	no	—
553	C₂×C₄	—	89	2	no	—
554	C₂×C₄	—	89	2	no	—
555	C₂×C₄	—	89	1	no	—
556	C₂×C₄	—	356	2	no	—
557	C₂×C₄	—	356	2	no	—
558	C₂×C₄	—	356	2	no	—
559	C₂×C₄	—	356	2	no	—
560	C₂×C₄	—	356	1	no	—
561	C₂×C₄	—	356	1	no	—
562	C₂×C₄	—	178	2	no	—
563	C₂×C₄	—	178	4	no	—
564	C₂×C₄	—	178	1	no	—
565	C₂×C₄	—	178	1	no	—
566	C₂×C₄	—	178	1	no	—
567	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
568	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
569	C₂×C₄	#41×D₈₉	1	1	yes	characteristic
570	C₈	—	2	2	no	—
571	C₈	—	2	1	no	—
572	C₈	—	2	1	no	—
573	C₈	—	4	1	no	—
574	C₈	—	4	1	no	—
575	C₈	—	89	2	no	—
576	C₈	—	89	2	no	—
577	C₈	—	356	1	no	—
578	C₈	—	356	1	no	—
579	C₈	—	178	2	no	—
580	C₈	—	178	1	no	—
581	C₈	—	178	1	no	—
582	C₈	C₂×C₈×D₈₉	1	2	yes	complemented
583	C₈	SD₁₆×D₈₉	1	2	yes	direct product factor
584	C₂²	—	2	2	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	1	no	—
587	C₂²	—	89	2	no	—
588	C₂²	—	89	2	no	—
589	C₂²	—	89	2	no	—
590	C₂²	—	356	8	no	—
591	C₂²	—	356	1	no	—
592	C₂²	—	356	1	no	—
593	C₂²	—	178	2	no	—
594	C₂²	C₄×D₄×D₈₉	1	1	yes	characteristic
595	C₄	—	2	1	no	—
596	C₄	—	2	2	no	—
597	C₄	—	4	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	89	2	no	—
600	C₄	—	89	2	no	—
601	C₄	—	356	1	no	—
602	C₄	—	356	1	no	—
603	C₄	—	178	1	no	—
604	C₄	—	178	2	no	—
605	C₄	C₂²×C₈×D₈₉	1	1	yes	characteristic
606	C₄	#131×D₈₉	1	1	yes	characteristic
607	C₄	C₂×SD₁₆×D₈₉	1	1	yes	characteristic
608	C₄	#135×D₈₉	1	1	yes	characteristic
609	C₂	—	4	2	no	—
610	C₂	—	89	4	no	—
611	C₂	—	356	2	no	—
612	C₂	C₈×D₄×D₈₉	1	1	yes	characteristic
613	C₂	C₄×SD₁₆×D₈₉	1	1	yes	characteristic
614	C₂	#443×D₈₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₈₉
commutator	C₄×C₈₉	C₂³×C₈
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×SD₁₆×C₈₉	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×D₄×D₈₉	C₂×C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₈×SD₁₆	D₈₉
hypocenter	C₈₉	C₂×C₈×SD₁₆
LCS	G ▷ C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₈×Q₈×D₈₉	C₂	semidirect
4. #26019055	C₂	semidirect
5. C₈×#13083563	C₂	semidirect
6. SD₁₆×#10623494	C₂	semidirect
7. C₈×#13083561	C₂	semidirect
8. #26019051	C₂	semidirect
9. C₈×#13083562	C₂	semidirect
10. #26019049	C₂	semidirect
11. #334×D₈₉	C₂	semidirect
12. Q₈⋊C₈×D₈₉	C₂	semidirect
14. C₈²×D₈₉	C₂	semidirect
15. C₈×SD₁₆×C₈₉	C₂	semidirect
20. Q₈×#10623494	C₂²	semidirect
22. C₈×Dic₁₇₈	C₂²	semidirect
24. #19151722	C₂²	semidirect
48. #19151349	C₂²	semidirect
49. #19151348	C₂²	semidirect
50. #19151348	C₂²	semidirect
51. #19151330	C₂²	semidirect
52. Q₈⋊#10623494	C₂²	semidirect
53. #19151328	C₂²	semidirect
57. C₈×#10623494	C₂²	semidirect
58. C₈×#10623494	C₂²	semidirect
59. C₈×#10623494	C₂²	semidirect
60. C₈×Q₈×C₈₉	C₂²	semidirect
63. #334×C₈₉	C₂²	semidirect
64. Q₈⋊C₈×C₈₉	C₂²	semidirect
66. C₈²×C₈₉	C₂²	semidirect
73. SD₁₆×D₈₉	C₈	direct (N × H)
150. Q₈×D₈₉	C₂×C₈	semidirect
166. #13083563	C₂×C₈	semidirect
167. #13083562	C₂×C₈	semidirect
168. #13083561	C₂×C₈	semidirect
184. C₈×D₈₉	C₂×C₈	semidirect
185. C₈×D₈₉	SD₁₆	direct (N × H)
205. SD₁₆×C₈₉	C₂×C₈	semidirect
227. Q₈×C₈₉	C₂²×C₈	semidirect
261. Dic₁₇₈	C₂²×C₈	semidirect
267. C₈×C₈₉	C₂²×C₈	semidirect
268. C₈×C₈₉	C₂×SD₁₆	semidirect
274. #10623494	C₂²×C₈	semidirect
275. #10623494	C₂×SD₁₆	semidirect
307. D₈₉	C₈×SD₁₆	direct (N × H)
318. C₈×SD₁₆	D₈₉	direct (N × H)
323. C₈₉	C₂×C₈×SD₁₆	semidirect
333. C₈×Q₈	C₂×D₈₉	semidirect
362. #334	C₂×D₈₉	semidirect
366. Q₈⋊C₈	C₂×D₈₉	semidirect
374. C₈²	C₂×D₈₉	semidirect
480. SD₁₆	C₈×D₈₉	direct (N × H)
538. Q₈	C₂×C₈×D₈₉	semidirect
582. C₈	C₂×C₈×D₈₉	semidirect
583. C₈	SD₁₆×D₈₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×Q₈×D₈₉	2
C₄×SD₁₆×D₈₉	2
C₈×D₄×D₈₉	2
#26019055	2
C₈×#13083563	2
SD₁₆×#10623494	2
C₈×#13083561	2
#26019051	2
C₈×#13083562	2
#26019049	2
#334×D₈₉	2
Q₈⋊C₈×D₈₉	2
D₄⋊C₈×D₈₉	2
C₈²×D₈₉	2
C₈×SD₁₆×C₈₉	2
C₂×C₈×SD₁₆	89

Subgroups — C8×SD16×D89 #36523787

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×SD₁₆×D₈₉ #36523787