Subgroups — #344×Dic₈₉ #36459635

Order 22784.

906 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₁₆×Dic₈₉	C₂	1	1	yes	maximal, characteristic
2	C₂×M₁₆×Dic₈₉	C₂	1	1	yes	maximal, characteristic
3	#117×Dic₈₉	C₂	1	1	yes	maximal, characteristic
4	C₂×#19151370	C₂	1	1	yes	maximal, characteristic
5	C₂×#19151369	C₂	1	1	yes	maximal, characteristic
6	C₂×#19151368	C₂	1	1	yes	maximal, characteristic
7	C₂×#344×C₈₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×#13083558	C₂²	1	1	yes	characteristic
9	C₂²×#13083558	C₂²	1	1	yes	characteristic
10	C₂×#15667971	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
12	M₁₆×Dic₈₉	—	2	2	no	—
13	M₁₆×Dic₈₉	—	2	1	no	—
14	M₁₆×Dic₈₉	—	2	1	no	—
15	M₁₆×Dic₈₉	—	2	1	no	—
16	M₁₆×Dic₈₉	—	2	1	no	—
17	M₁₆×Dic₈₉	C₄	1	4	yes	complemented
18	C₂×#15667922	—	2	1	no	—
19	C₂×#15667922	C₄	1	2	yes	complemented
20	C₂×C₈×Dic₈₉	—	2	1	no	—
21	C₂×C₈×Dic₈₉	C₄	1	2	yes	complemented
22	C₄⋊C₄×Dic₈₉	—	2	2	no	—
23	C₂²⋊C₄×Dic₈₉	C₄	1	4	yes	—
24	#19151444	—	2	1	no	—
25	C₄²×Dic₈₉	—	2	1	no	—
26	#19151370	C₄	1	4	yes	complemented
27	#19151369	C₄	1	4	yes	complemented
28	#19151368	C₄	1	4	yes	complemented
29	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
30	C₂²×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
31	C₂×#117×C₈₉	C₂²	1	1	yes	characteristic
32	#344×C₈₉	C₄	1	4	yes	complemented
33	C₂³×Dic₈₉	C₂×C₄	1	2	yes	—
34	C₂×#13083558	—	2	1	no	—
35	C₂×#13083558	—	2	1	no	—
36	C₂×#13083558	—	2	1	no	—
37	C₂×#13083558	—	2	1	no	—
38	C₂×#13083558	—	2	1	no	—
39	C₂×#13083558	—	2	1	no	—
40	C₂×#13083558	—	2	1	no	—
41	C₂×#13083558	C₂×C₄	1	2	yes	—
42	C₂×#13083558	C₂×C₄	1	2	yes	—
43	C₂×#13083558	C₂×C₄	1	2	yes	—
44	C₂×#13083558	C₂×C₄	1	2	yes	—
45	C₂×#13083558	C₂×C₄	1	2	yes	—
46	C₂²×#10623494	—	2	1	no	—
47	C₂²×#10623494	C₂×C₄	1	2	yes	—
48	#15667971	—	2	1	no	—
49	#15667971	—	2	1	no	—
50	#15667971	C₂×C₄	1	2	yes	—
51	#15667971	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊Dic₈₉	—	2	1	no	—
53	C₂×C₂²⋊Dic₈₉	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₈₉	—	2	4	no	—
55	C₂×C₄×Dic₈₉	—	2	1	no	—
56	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
60	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
61	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
62	C₂×C₄×Dic₈₉	D₄	1	1	yes	characteristic
63	C₂×C₄×Dic₈₉	D₄	1	2	yes	—
64	C₂×C₄×Dic₈₉	Q₈	1	2	yes	—
65	#15667922	—	2	4	no	—
66	#15667922	—	2	2	no	—
67	#15667922	—	2	2	no	—
68	C₈×Dic₈₉	—	2	4	no	—
69	C₈×Dic₈₉	—	2	2	no	—
70	C₈×Dic₈₉	—	2	2	no	—
71	#15667919	—	2	4	no	—
72	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
73	C₂×M₁₆×C₈₉	—	2	1	no	—
74	C₂×M₁₆×C₈₉	—	2	1	no	—
75	C₂×M₁₆×C₈₉	—	2	1	no	—
76	C₂×M₁₆×C₈₉	—	2	1	no	—
77	C₂×M₁₆×C₈₉	—	2	1	no	—
78	C₂×M₁₆×C₈₉	—	2	1	no	—
79	C₂×M₁₆×C₈₉	—	2	1	no	—
80	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
81	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
82	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
83	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
84	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
85	C₂²×C₈×C₈₉	—	2	1	no	—
86	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
87	#117×C₈₉	—	2	1	no	—
88	#117×C₈₉	—	2	1	no	—
89	#117×C₈₉	C₂×C₄	1	2	yes	—
90	#117×C₈₉	C₂×C₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₈₉	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₈₉	C₂×C₄	1	2	yes	—
93	C₂×C₄²×C₈₉	—	2	1	no	—
94	C₂²×Dic₈₉	—	2	2	no	—
95	C₂²×Dic₈₉	—	4	4	no	—
96	C₂²×Dic₈₉	C₄²	1	2	yes	—
97	C₂²×Dic₈₉	C₄²	1	2	yes	—
98	C₂²×Dic₈₉	C₂²⋊C₄	1	2	yes	—
99	C₂²×Dic₈₉	C₂²⋊C₄	1	2	yes	—
100	C₂²×Dic₈₉	C₄⋊C₄	1	2	yes	—
101	C₂²×Dic₈₉	C₄⋊C₄	1	2	yes	—
102	#13083558	—	2	2	no	—
103	#13083558	—	2	2	no	—
104	#13083558	—	2	2	no	—
105	#13083558	—	2	2	no	—
106	#13083558	—	2	2	no	—
107	#13083558	—	2	2	no	—
108	#13083558	—	2	2	no	—
109	#13083558	C₄²	1	4	yes	complemented
110	C₂×#10623494	—	2	2	no	—
111	C₂×#10623494	—	2	2	no	—
112	C₂×#10623494	—	2	2	no	—
113	C₂×#10623494	—	2	2	no	—
114	C₂×#10623494	—	2	2	no	—
115	C₂×#10623494	C₄²	1	4	yes	complemented
116	C₄⋊Dic₈₉	—	2	2	no	—
117	C₄⋊Dic₈₉	—	2	2	no	—
118	C₂²⋊Dic₈₉	—	2	2	no	—
119	C₂²⋊Dic₈₉	C₄²	1	4	yes	—
120	C₄×Dic₈₉	—	2	2	no	—
121	C₄×Dic₈₉	—	2	2	no	—
122	C₄×Dic₈₉	—	4	8	no	—
123	C₄×Dic₈₉	C₂²⋊C₄	1	1	yes	characteristic
124	C₄×Dic₈₉	C₂²⋊C₄	1	2	yes	—
125	C₄×Dic₈₉	C₂²⋊C₄	1	1	yes	characteristic
126	C₄×Dic₈₉	C₂²⋊C₄	1	2	yes	—
127	C₄×Dic₈₉	C₂²⋊C₄	1	1	yes	characteristic
128	C₄×Dic₈₉	C₂²⋊C₄	1	1	yes	characteristic
129	C₄×Dic₈₉	C₄⋊C₄	1	2	yes	—
130	C₄×Dic₈₉	C₄⋊C₄	1	2	yes	—
131	C₄×Dic₈₉	C₄⋊C₄	1	2	yes	—
132	C₄×Dic₈₉	C₄⋊C₄	1	2	yes	—
133	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₈₉	—	2	2	no	—
135	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
143	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
144	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
145	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
146	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
149	M₁₆×C₈₉	—	2	2	no	—
150	M₁₆×C₈₉	—	2	2	no	—
151	M₁₆×C₈₉	—	2	2	no	—
152	M₁₆×C₈₉	—	2	2	no	—
153	M₁₆×C₈₉	—	2	2	no	—
154	M₁₆×C₈₉	—	2	2	no	—
155	M₁₆×C₈₉	—	2	2	no	—
156	M₁₆×C₈₉	C₄²	1	4	yes	complemented
157	C₂×C₈×C₈₉	—	2	2	no	—
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	2	no	—
162	C₂×C₈×C₈₉	C₄²	1	4	yes	complemented
163	C₄⋊C₄×C₈₉	—	2	2	no	—
164	C₄⋊C₄×C₈₉	—	2	2	no	—
165	C₂²⋊C₄×C₈₉	—	2	2	no	—
166	C₂²⋊C₄×C₈₉	C₄²	1	4	yes	—
167	C₄²×C₈₉	—	2	2	no	—
168	C₄²×C₈₉	—	2	2	no	—
169	C₂³×C₈₉	—	4	2	no	—
170	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
171	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
172	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
173	C₂³×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
174	C₂³×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂³×C₈₉	#117	1	1	yes	characteristic
176	C₂³×C₈₉	#117	1	1	yes	characteristic
177	C₂×C₄×C₈₉	—	2	4	no	—
178	C₂×C₄×C₈₉	—	4	4	no	—
179	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
180	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
188	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
189	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
190	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
191	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
192	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
193	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
194	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
195	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
196	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
197	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
201	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
202	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
203	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
204	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
205	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
206	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
207	C₂×Dic₈₉	—	2	4	no	—
208	C₂×Dic₈₉	—	2	4	no	—
209	C₂×Dic₈₉	—	2	4	no	—
210	C₂×Dic₈₉	—	2	4	no	—
211	C₂×Dic₈₉	—	4	2	no	—
212	C₂×Dic₈₉	—	4	2	no	—
213	C₂×Dic₈₉	—	4	2	no	—
214	C₂×Dic₈₉	—	4	4	no	—
215	C₂×Dic₈₉	#95	1	2	yes	—
216	C₂×Dic₈₉	#95	1	2	yes	—
217	C₂×Dic₈₉	#95	1	2	yes	—
218	C₂×Dic₈₉	#95	1	2	yes	—
219	C₈×C₈₉	—	2	4	no	—
220	C₈×C₈₉	—	2	4	no	—
221	#10623494	—	2	4	no	—
222	#10623494	—	2	4	no	—
223	C₂²×C₈₉	—	2	2	no	—
224	C₂²×C₈₉	—	2	2	no	—
225	C₂²×C₈₉	—	2	2	no	—
226	C₂²×C₈₉	—	4	1	no	—
227	C₂²×C₈₉	—	4	1	no	—
228	C₂²×C₈₉	—	4	1	no	—
229	C₂²×C₈₉	—	4	1	no	—
230	C₂²×C₈₉	C₄³	1	1	yes	characteristic
231	C₂²×C₈₉	C₂×#95	1	1	yes	characteristic
232	C₂²×C₈₉	#376	1	1	yes	characteristic
233	C₂²×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
234	C₂²×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
235	C₂²×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
236	C₂²×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
237	C₄×C₈₉	—	4	4	no	—
238	C₄×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
239	C₄×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
240	C₄×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
241	C₄×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
242	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
243	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
244	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
245	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
246	Dic₈₉	—	2	2	no	—
247	Dic₈₉	—	2	2	no	—
248	Dic₈₉	—	2	2	no	—
249	Dic₈₉	—	4	4	no	—
250	Dic₈₉	#344	1	4	yes	direct product factor
251	C₄×#344	—	89	1	no	maximal, Sylow
252	C₂×C₈₉	—	2	1	no	—
253	C₂×C₈₉	—	2	1	no	—
254	C₂×C₈₉	—	2	1	no	—
255	C₂×C₈₉	—	2	1	no	—
256	C₂×C₈₉	—	2	1	no	—
257	C₂×C₈₉	—	2	1	no	—
258	C₂×C₈₉	C₄×#95	1	1	yes	characteristic
259	C₂×C₈₉	C₂×#344	1	2	yes	—
260	C₂×C₄×M₁₆	—	89	1	no	—
261	C₂×C₄×M₁₆	—	89	1	no	—
262	C₄×#117	—	89	1	no	—
263	C₂×#344	—	89	1	no	—
264	C₂×#344	—	89	1	no	—
265	C₂×#344	—	89	1	no	—
266	C₂×#344	D₈₉	1	1	yes	characteristic
267	C₈₉	C₄×#344	1	1	yes	characteristic, complemented, Sylow
268	C₂²×M₁₆	—	89	1	no	—
269	C₂²×M₁₆	—	89	1	no	—
270	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
271	C₂²×M₁₆	C₂×D₈₉	1	1	yes	characteristic
272	C₂×#117	—	89	1	no	—
273	C₂×#117	C₂×D₈₉	1	1	yes	characteristic
274	C₂²×C₄²	—	89	1	no	—
275	C₄×M₁₆	—	89	4	no	—
276	C₄×M₁₆	—	178	1	no	—
277	C₄×M₁₆	—	178	1	no	—
278	C₄×M₁₆	—	178	1	no	—
279	C₄×M₁₆	—	178	1	no	—
280	C₄×M₁₆	—	178	2	no	—
281	C₂×#97	—	89	2	no	—
282	C₂×#97	—	178	1	no	—
283	C₂×C₄×C₈	—	89	2	no	—
284	C₂×C₄×C₈	—	178	1	no	—
285	C₄×C₄⋊C₄	—	178	2	no	—
286	C₄×C₂²⋊C₄	—	89	4	no	—
287	#376	—	178	1	no	—
288	C₄³	—	178	1	no	—
289	#344	—	89	4	no	—
290	#344	—	89	4	no	—
291	#344	—	89	4	no	—
292	#344	Dic₈₉	1	4	yes	direct product factor
293	C₂³×C₄	—	89	2	no	—
294	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
295	C₂×M₁₆	—	2	1	no	—
296	C₂×M₁₆	—	2	1	no	—
297	C₂×M₁₆	—	2	1	no	—
298	C₂×M₁₆	—	2	1	no	—
299	C₂×M₁₆	—	2	1	no	—
300	C₂×M₁₆	—	2	1	no	—
301	C₂×M₁₆	—	2	1	no	—
302	C₂×M₁₆	—	89	2	no	—
303	C₂×M₁₆	—	89	2	no	—
304	C₂×M₁₆	—	89	2	no	—
305	C₂×M₁₆	—	89	2	no	—
306	C₂×M₁₆	—	89	2	no	—
307	C₂×M₁₆	—	178	1	no	—
308	C₂×M₁₆	—	178	1	no	—
309	C₂×M₁₆	—	178	1	no	—
310	C₂×M₁₆	—	178	1	no	—
311	C₂×M₁₆	—	178	1	no	—
312	C₂×M₁₆	—	178	1	no	—
313	C₂×M₁₆	—	178	1	no	—
314	C₂×M₁₆	C₄×D₈₉	1	2	yes	—
315	C₂×M₁₆	C₄×D₈₉	1	2	yes	—
316	C₂×M₁₆	C₄×D₈₉	1	2	yes	—
317	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
318	C₂×M₁₆	C₂×Dic₈₉	1	2	yes	—
319	C₂²×C₈	—	2	1	no	—
320	C₂²×C₈	—	89	2	no	—
321	C₂²×C₈	—	178	1	no	—
322	C₂²×C₈	C₄×D₈₉	1	2	yes	—
323	#117	—	2	1	no	—
324	#117	—	2	1	no	—
325	#117	—	89	2	no	—
326	#117	—	89	2	no	—
327	#117	—	178	1	no	—
328	#117	—	178	1	no	—
329	#117	C₄×D₈₉	1	2	yes	—
330	#117	C₂×Dic₈₉	1	2	yes	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	178	1	no	—
333	C₂×C₂²⋊C₄	—	89	2	no	—
334	C₂×C₂²⋊C₄	C₄×D₈₉	1	2	yes	—
335	C₂×C₄²	—	2	1	no	—
336	C₂×C₄²	—	89	1	no	—
337	C₂×C₄²	—	89	1	no	—
338	C₂×C₄²	—	89	2	no	—
339	C₂×C₄²	—	89	1	no	—
340	C₂×C₄²	—	89	1	no	—
341	C₂×C₄²	—	89	2	no	—
342	C₂×C₄²	—	89	1	no	—
343	C₂×C₄²	—	89	1	no	—
344	C₂×C₄²	—	89	2	no	—
345	C₂×C₄²	—	178	4	no	—
346	C₂×C₄²	—	178	1	no	—
347	#97	—	178	2	no	—
348	#97	—	178	2	no	—
349	#97	—	178	4	no	—
350	C₄×C₈	—	178	2	no	—
351	C₄×C₈	—	178	2	no	—
352	C₄×C₈	—	178	4	no	—
353	#95	—	178	4	no	—
354	C₂⁴	C₂×C₄×D₈₉	1	1	yes	characteristic
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	89	2	no	—
357	C₂²×C₄	—	89	2	no	—
358	C₂²×C₄	—	89	2	no	—
359	C₂²×C₄	—	89	2	no	—
360	C₂²×C₄	—	89	2	no	—
361	C₂²×C₄	—	89	2	no	—
362	C₂²×C₄	—	356	4	no	—
363	C₂²×C₄	—	178	2	no	—
364	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
369	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
370	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
371	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
372	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
373	C₂²×C₄	Q₈×D₈₉	1	1	yes	characteristic
374	C₂²×C₄	#13083573	1	1	yes	characteristic
375	C₂²×C₄	#13083573	1	1	yes	characteristic
376	C₂²×C₄	#13083573	1	1	yes	characteristic
377	C₂²×C₄	#13083575	1	1	yes	characteristic
378	M₁₆	—	2	2	no	—
379	M₁₆	—	2	2	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	2	2	no	—
382	M₁₆	—	2	2	no	—
383	M₁₆	—	2	2	no	—
384	M₁₆	—	2	2	no	—
385	M₁₆	—	89	4	no	—
386	M₁₆	—	178	2	no	—
387	M₁₆	—	178	2	no	—
388	M₁₆	—	178	2	no	—
389	M₁₆	—	178	2	no	—
390	M₁₆	—	178	2	no	—
391	M₁₆	—	178	2	no	—
392	M₁₆	—	178	2	no	—
393	M₁₆	C₄×Dic₈₉	1	4	yes	complemented
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	2	2	no	—
396	C₂×C₈	—	2	2	no	—
397	C₂×C₈	—	2	2	no	—
398	C₂×C₈	—	2	2	no	—
399	C₂×C₈	—	89	4	no	—
400	C₂×C₈	—	178	2	no	—
401	C₂×C₈	—	178	2	no	—
402	C₂×C₈	—	178	2	no	—
403	C₂×C₈	—	178	2	no	—
404	C₂×C₈	—	178	2	no	—
405	C₂×C₈	C₄×Dic₈₉	1	4	yes	complemented
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	178	2	no	—
409	C₄⋊C₄	—	178	2	no	—
410	C₂²⋊C₄	—	2	2	no	—
411	C₂²⋊C₄	—	89	4	no	—
412	C₂²⋊C₄	—	178	2	no	—
413	C₂²⋊C₄	C₄×Dic₈₉	1	4	yes	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	89	2	no	—
417	C₄²	—	89	2	no	—
418	C₄²	—	89	1	no	—
419	C₄²	—	89	1	no	—
420	C₄²	—	89	1	no	—
421	C₄²	—	89	1	no	—
422	C₄²	—	89	2	no	—
423	C₄²	—	89	2	no	—
424	C₄²	—	89	2	no	—
425	C₄²	—	89	2	no	—
426	C₄²	—	356	8	no	—
427	C₄²	—	178	2	no	—
428	C₄²	—	178	2	no	—
429	C₂³	—	4	2	no	—
430	C₂³	C₄²×D₈₉	1	1	yes	characteristic
431	C₂³	C₄²×D₈₉	1	1	yes	characteristic
432	C₂³	C₂×C₄×Dic₈₉	1	1	yes	characteristic
433	C₂³	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
434	C₂³	C₄⋊C₄×D₈₉	1	1	yes	characteristic
435	C₂³	#15667968	1	1	yes	characteristic
436	C₂³	#15667970	1	1	yes	characteristic
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	89	2	no	—
440	C₂×C₄	—	89	2	no	—
441	C₂×C₄	—	89	2	no	—
442	C₂×C₄	—	89	2	no	—
443	C₂×C₄	—	356	4	no	—
444	C₂×C₄	—	356	2	no	—
445	C₂×C₄	—	356	2	no	—
446	C₂×C₄	—	356	2	no	—
447	C₂×C₄	—	178	4	no	—
448	C₂×C₄	—	178	4	no	—
449	C₂×C₄	—	178	4	no	—
450	C₂×C₄	—	178	4	no	—
451	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
452	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
453	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
454	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
455	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
456	C₂×C₄	C₂²⋊C₄×D₈₉	1	1	yes	characteristic
457	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
458	C₂×C₄	C₄⋊C₄×D₈₉	1	1	yes	characteristic
459	C₂×C₄	#15667968	1	1	yes	characteristic
460	C₂×C₄	#15667968	1	1	yes	characteristic
461	C₂×C₄	#15667970	1	1	yes	characteristic
462	C₂×C₄	#15667970	1	1	yes	characteristic
463	C₂×C₄	#15667972	1	1	yes	characteristic
464	C₂×C₄	#15667972	1	1	yes	characteristic
465	C₂×C₄	#15667972	1	1	yes	characteristic
466	C₂×C₄	#15667972	1	1	yes	characteristic
467	C₂×C₄	#15667972	1	1	yes	characteristic
468	C₂×C₄	#15667972	1	1	yes	characteristic
469	C₂×C₄	#15667974	1	1	yes	characteristic
470	C₂×C₄	#15667974	1	1	yes	characteristic
471	C₂×C₄	#15667974	1	1	yes	characteristic
472	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
473	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
474	C₂×C₄	D₄×Dic₈₉	1	1	yes	characteristic
475	C₂×C₄	#15667977	1	1	yes	characteristic
476	C₂×C₄	#15667977	1	1	yes	characteristic
477	C₂×C₄	#15667977	1	1	yes	characteristic
478	C₂×C₄	Q₈×Dic₈₉	1	1	yes	characteristic
479	C₈	—	2	4	no	—
480	C₈	—	2	4	no	—
481	C₈	—	178	4	no	—
482	C₈	—	178	4	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	4	1	no	—
487	C₂²	—	4	1	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	4	1	no	—
490	C₂²	C₄²×Dic₈₉	1	1	yes	characteristic
491	C₂²	#95×D₈₉	1	1	yes	characteristic
492	C₂²	#19151443	1	1	yes	characteristic
493	C₂²	#19151445	1	1	yes	characteristic
494	C₂²	C₂²⋊C₄×Dic₈₉	1	1	yes	characteristic
495	C₂²	#19151449	1	1	yes	characteristic
496	C₂²	C₄⋊C₄×Dic₈₉	1	1	yes	characteristic
497	C₄	—	4	4	no	—
498	C₄	—	89	4	no	—
499	C₄	—	356	4	no	—
500	C₄	—	178	2	no	—
501	C₄	—	178	2	no	—
502	C₄	—	178	2	no	—
503	C₄	#19151445	1	1	yes	characteristic
504	C₄	#19151445	1	1	yes	characteristic
505	C₄	C₂²⋊C₄×Dic₈₉	1	1	yes	characteristic
506	C₄	C₂²⋊C₄×Dic₈₉	1	1	yes	characteristic
507	C₄	#19151449	1	1	yes	characteristic
508	C₄	#19151449	1	1	yes	characteristic
509	C₄	C₄⋊C₄×Dic₈₉	1	1	yes	characteristic
510	C₄	C₄⋊C₄×Dic₈₉	1	1	yes	characteristic
511	C₂	—	2	1	no	—
512	C₂	—	2	1	no	—
513	C₂	—	2	1	no	—
514	C₂	—	2	1	no	—
515	C₂	—	2	1	no	—
516	C₂	—	2	1	no	—
517	C₂	#95×Dic₈₉	1	1	yes	characteristic
518	C₂	#344×D₈₉	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₈₉
commutator	C₂²×C₈₉	C₄³
Frattini	C₂³×C₄	C₂²×D₈₉
Fitting	C₂×#344×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#95
prime radical	C₂⁴×C₈₉	C₂²×C₄
cosocle	C₂³×C₄×C₈₉	C₂³
hypercenter	C₂×#344	D₈₉
hypocenter	C₈₉	C₄×#344
LCS	G ▷ C₂²×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#344

Complements

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

N	H ≅ G/N	type
17. M₁₆×Dic₈₉	C₄	semidirect
19. C₂×#15667922	C₄	semidirect
21. C₂×C₈×Dic₈₉	C₄	semidirect
26. #19151370	C₄	semidirect
27. #19151369	C₄	semidirect
28. #19151368	C₄	semidirect
32. #344×C₈₉	C₄	semidirect
109. #13083558	C₄²	semidirect
115. C₂×#10623494	C₄²	semidirect
156. M₁₆×C₈₉	C₄²	semidirect
162. C₂×C₈×C₈₉	C₄²	semidirect
250. Dic₈₉	#344	direct (N × H)
267. C₈₉	C₄×#344	semidirect
292. #344	Dic₈₉	direct (N × H)
393. M₁₆	C₄×Dic₈₉	semidirect
405. C₂×C₈	C₄×Dic₈₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₁₆×Dic₈₉	2
#117×Dic₈₉	2
C₂×#19151370	2
C₂×#19151369	2
C₂×#19151368	2
C₂×#344×C₈₉	2
C₄×#344	89

Subgroups — #344×Dic89 #36459635

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #344×Dic₈₉ #36459635