Subgroups — #36459587

Order 22784.

1078 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#15667922	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₈×Dic₈₉	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151353	C₂	1	1	yes	maximal, characteristic
4	C₂×#19151352	C₂	1	1	yes	maximal, characteristic
5	C₂×#19151352	C₂	1	1	yes	maximal, characteristic
6	C₄×#15667919	C₂	1	1	yes	maximal, characteristic
7	C₂²×#97×C₈₉	C₂	1	1	yes	maximal, characteristic
8	C₂³×#10623494	C₂²	1	1	yes	characteristic
9	C₂³×#10623494	C₂²	1	1	yes	characteristic
10	C₂²×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
11	C₂²×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
12	C₂×#15667922	—	2	2	no	—
13	C₂×#15667922	—	2	2	no	—
14	C₂×#15667922	C₄	1	4	yes	complemented
15	C₂×C₈×Dic₈₉	—	2	2	no	—
16	C₂×C₈×Dic₈₉	—	2	2	no	—
17	C₂×C₈×Dic₈₉	C₄	1	4	yes	complemented
18	C₂×#15667919	C₄	1	4	yes	—
19	#19151353	C₄	1	4	yes	complemented
20	#19151352	C₄	1	4	yes	complemented
21	#19151352	C₄	1	4	yes	complemented
22	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
23	C₂³×C₈×C₈₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
25	C₂×#97×C₈₉	—	2	2	no	—
26	C₂×#97×C₈₉	—	2	2	no	—
27	C₂×#97×C₈₉	C₄	1	4	yes	complemented
28	C₂³×Dic₈₉	C₂×C₄	1	2	yes	—
29	C₂³×Dic₈₉	C₂×C₄	1	2	yes	—
30	C₂²×#10623494	—	2	1	no	—
31	C₂²×#10623494	—	2	1	no	—
32	C₂²×#10623494	—	2	1	no	—
33	C₂²×#10623494	—	2	1	no	—
34	C₂²×#10623494	—	2	1	no	—
35	C₂²×#10623494	—	2	1	no	—
36	C₂²×#10623494	—	2	1	no	—
37	C₂²×#10623494	—	2	1	no	—
38	C₂²×#10623494	C₂×C₄	1	2	yes	—
39	C₂²×#10623494	C₂×C₄	1	2	yes	—
40	C₂²×#10623494	C₂×C₄	1	2	yes	—
41	C₂²×#10623494	C₂×C₄	1	2	yes	—
42	C₂²×#10623494	C₂×C₄	1	2	yes	—
43	C₂²×#10623494	C₂×C₄	1	2	yes	—
44	C₂×C₄×Dic₈₉	—	2	1	no	—
45	C₂×C₄×Dic₈₉	—	2	1	no	—
46	C₂×C₄×Dic₈₉	—	2	1	no	—
47	C₂×C₄×Dic₈₉	—	2	1	no	—
48	C₂×C₄×Dic₈₉	—	2	1	no	—
49	C₂×C₄×Dic₈₉	—	2	1	no	—
50	C₂×C₄×Dic₈₉	—	2	1	no	—
51	C₂×C₄×Dic₈₉	—	2	1	no	—
52	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₈₉	C₂×C₄	1	2	yes	—
56	#15667922	—	2	8	no	—
57	C₈×Dic₈₉	—	2	8	no	—
58	#15667919	—	2	8	no	—
59	C₂³×C₄×C₈₉	C₂×C₄	1	2	yes	—
60	C₂³×C₄×C₈₉	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₈₉	—	2	1	no	—
62	C₂²×C₈×C₈₉	—	2	1	no	—
63	C₂²×C₈×C₈₉	—	2	1	no	—
64	C₂²×C₈×C₈₉	—	2	1	no	—
65	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
66	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
67	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
68	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
69	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
70	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
71	C₂²×C₈×C₈₉	D₄	1	2	yes	—
72	C₂²×C₈×C₈₉	D₄	1	2	yes	—
73	C₂²×C₈×C₈₉	D₄	1	2	yes	—
74	C₂²×C₈×C₈₉	Q₈	1	2	yes	—
75	C₂×C₄²×C₈₉	—	2	1	no	—
76	C₂×C₄²×C₈₉	—	2	1	no	—
77	C₂×C₄²×C₈₉	—	2	1	no	—
78	C₂×C₄²×C₈₉	—	2	1	no	—
79	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
80	C₂×C₄²×C₈₉	C₂×C₄	1	2	yes	—
81	#97×C₈₉	—	2	8	no	—
82	C₂²×Dic₈₉	—	2	2	no	—
83	C₂²×Dic₈₉	—	2	2	no	—
84	C₂²×Dic₈₉	—	2	4	no	—
85	C₂²×Dic₈₉	—	2	2	no	—
86	C₂²×Dic₈₉	—	2	2	no	—
87	C₂²×Dic₈₉	—	2	4	no	—
88	C₂²×Dic₈₉	—	2	4	no	—
89	C₂²×Dic₈₉	C₄²	1	4	yes	—
90	C₂²×Dic₈₉	C₄²	1	4	yes	—
91	C₂²×Dic₈₉	M₁₆	1	8	yes	—
92	C₂×#10623494	—	2	2	no	—
93	C₂×#10623494	—	2	2	no	—
94	C₂×#10623494	—	2	2	no	—
95	C₂×#10623494	—	2	2	no	—
96	C₂×#10623494	—	2	2	no	—
97	C₂×#10623494	—	2	2	no	—
98	C₂×#10623494	—	2	2	no	—
99	C₂×#10623494	—	2	2	no	—
100	C₂×#10623494	—	2	2	no	—
101	C₂×#10623494	—	2	2	no	—
102	C₂×#10623494	—	2	2	no	—
103	C₂×#10623494	—	2	2	no	—
104	C₂×#10623494	C₄²	1	4	yes	—
105	C₂×#10623494	C₄²	1	4	yes	—
106	C₄×Dic₈₉	—	2	2	no	—
107	C₄×Dic₈₉	—	2	2	no	—
108	C₄×Dic₈₉	—	2	2	no	—
109	C₄×Dic₈₉	—	2	2	no	—
110	C₄×Dic₈₉	—	2	2	no	—
111	C₄×Dic₈₉	—	2	2	no	—
112	C₄×Dic₈₉	—	2	2	no	—
113	C₄×Dic₈₉	—	2	2	no	—
114	C₂⁴×C₈₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	—	2	2	no	—
116	C₂²×C₄×C₈₉	—	2	2	no	—
117	C₂²×C₄×C₈₉	—	2	4	no	—
118	C₂²×C₄×C₈₉	—	2	4	no	—
119	C₂²×C₄×C₈₉	C₄²	1	4	yes	—
120	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
122	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
126	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₈₉	C₂×Q₈	1	1	yes	characteristic
130	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
131	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
132	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
133	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
134	C₂×C₈×C₈₉	—	2	2	no	—
135	C₂×C₈×C₈₉	—	2	2	no	—
136	C₂×C₈×C₈₉	—	2	2	no	—
137	C₂×C₈×C₈₉	—	2	2	no	—
138	C₂×C₈×C₈₉	—	2	2	no	—
139	C₂×C₈×C₈₉	—	2	2	no	—
140	C₂×C₈×C₈₉	C₄²	1	4	yes	—
141	C₂×C₈×C₈₉	C₄²	1	4	yes	—
142	C₂×C₈×C₈₉	C₂²⋊C₄	1	4	yes	—
143	C₂×C₈×C₈₉	C₂²⋊C₄	1	4	yes	—
144	C₂×C₈×C₈₉	C₂²⋊C₄	1	4	yes	—
145	C₂×C₈×C₈₉	C₄⋊C₄	1	4	yes	—
146	C₂×C₈×C₈₉	C₄⋊C₄	1	4	yes	—
147	C₂×C₈×C₈₉	C₄⋊C₄	1	4	yes	—
148	C₄²×C₈₉	—	2	2	no	—
149	C₄²×C₈₉	—	2	2	no	—
150	C₄²×C₈₉	—	2	2	no	—
151	C₄²×C₈₉	—	2	2	no	—
152	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
153	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
154	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
155	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
156	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
157	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
158	C₂³×C₈₉	C₄×Q₈	1	1	yes	characteristic
159	C₂³×C₈₉	C₂×M₁₆	1	4	yes	—
160	C₂³×C₈₉	#131	1	4	yes	—
161	C₂×C₄×C₈₉	—	2	4	no	—
162	C₂×C₄×C₈₉	—	2	4	no	—
163	C₂×C₄×C₈₉	—	2	4	no	—
164	C₂×C₄×C₈₉	—	4	4	no	—
165	C₂×C₄×C₈₉	—	4	4	no	—
166	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
169	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
170	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
173	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
174	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
175	C₂×C₄×C₈₉	C₂×C₄⋊C₄	1	1	yes	characteristic
176	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
177	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
178	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
179	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
180	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
181	C₂×C₄×C₈₉	#117	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
183	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
189	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
190	C₂×C₄×C₈₉	C₄×D₄	1	1	yes	characteristic
191	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
192	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
193	C₂×C₄×C₈₉	C₄×Q₈	1	1	yes	characteristic
194	C₂×Dic₈₉	—	2	4	no	—
195	C₂×Dic₈₉	—	2	4	no	—
196	C₂×Dic₈₉	—	2	8	no	—
197	C₂×Dic₈₉	—	2	8	no	—
198	C₂×Dic₈₉	—	2	4	no	—
199	C₂×Dic₈₉	—	2	4	no	—
200	C₂×Dic₈₉	—	2	4	no	—
201	C₂×Dic₈₉	—	4	4	no	—
202	C₂×Dic₈₉	—	4	4	no	—
203	C₂×Dic₈₉	#97	1	8	yes	complemented
204	C₈×C₈₉	—	2	4	no	—
205	C₈×C₈₉	#95	1	8	yes	complemented
206	#10623494	—	2	4	no	—
207	#10623494	—	2	4	no	—
208	C₂²×C₈₉	C₄³	1	1	yes	characteristic
209	C₂²×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
210	C₂²×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
212	C₂²×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
213	C₂²×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
214	C₂²×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
215	C₂²×C₈₉	C₂×#97	1	2	yes	—
216	C₂²×C₈₉	C₄×M₁₆	1	2	yes	—
217	C₂²×C₈₉	C₄×M₁₆	1	2	yes	—
218	C₂²×C₈₉	#405	1	2	yes	—
219	C₂²×C₈₉	#405	1	2	yes	—
220	C₂²×C₈₉	#405	1	2	yes	—
221	C₂²×C₈₉	#435	1	4	yes	—
222	C₂²×C₈₉	#435	1	4	yes	—
223	C₂²×C₈₉	#436	1	4	yes	—
224	C₂²×C₈₉	#446	1	4	yes	—
225	C₄×C₈₉	—	4	4	no	—
226	C₄×C₈₉	C₂×#95	1	1	yes	characteristic
227	C₄×C₈₉	#376	1	1	yes	characteristic
228	C₄×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
229	C₄×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
230	C₄×C₈₉	C₄×C₂²⋊C₄	1	1	yes	characteristic
231	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
232	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
233	C₄×C₈₉	C₄×C₄⋊C₄	1	1	yes	characteristic
234	Dic₈₉	—	2	8	no	—
235	Dic₈₉	—	4	4	no	—
236	#10696	—	89	1	no	maximal, Sylow
237	C₂×C₈₉	C₄×#95	1	1	yes	characteristic
238	C₂×C₈₉	C₄×#97	1	1	yes	characteristic
239	C₂×C₈₉	#1726	1	1	yes	characteristic
240	C₂×C₈₉	#1752	1	2	yes	—
241	C₂×C₈₉	#1753	1	2	yes	—
242	C₂×C₈₉	#1753	1	2	yes	—
243	C₂×C₈₉	#1770	1	2	yes	—
244	C₂×C₈₉	#1771	1	2	yes	—
245	C₂×C₈₉	#1771	1	2	yes	—
246	C₂²×#97	—	89	1	no	—
247	C₂²×#97	D₈₉	1	1	yes	characteristic
248	C₂²×C₄×C₈	—	89	1	no	—
249	C₂×#336	—	89	1	no	—
250	C₂×#336	—	89	1	no	—
251	C₂×#336	—	89	1	no	—
252	C₄×#95	—	89	1	no	—
253	C₈₉	#10696	1	1	yes	characteristic, complemented, Sylow
254	C₂³×C₈	—	89	1	no	—
255	C₂³×C₈	—	89	1	no	—
256	C₂³×C₈	C₂×D₈₉	1	1	yes	characteristic
257	C₂³×C₈	C₂×D₈₉	1	1	yes	characteristic
258	C₂²×C₄²	—	89	1	no	—
259	C₂²×C₄²	—	89	1	no	—
260	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
261	C₂×#97	—	2	2	no	—
262	C₂×#97	—	2	2	no	—
263	C₂×#97	—	89	4	no	—
264	C₂×#97	—	178	2	no	—
265	C₂×#97	—	178	2	no	—
266	C₂×#97	Dic₈₉	1	4	yes	complemented
267	C₂×C₄×C₈	—	89	4	no	—
268	C₂×C₄×C₈	—	178	2	no	—
269	C₂×C₄×C₈	—	178	2	no	—
270	C₂×#95	—	89	4	no	—
271	#336	—	89	4	no	—
272	#336	—	89	4	no	—
273	#336	—	89	4	no	—
274	C₂³×C₄	—	89	2	no	—
275	C₂³×C₄	—	89	2	no	—
276	C₂³×C₄	C₄×D₈₉	1	2	yes	—
277	C₂³×C₄	C₂²×D₈₉	1	1	yes	characteristic
278	C₂²×C₈	—	2	1	no	—
279	C₂²×C₈	—	2	1	no	—
280	C₂²×C₈	—	2	1	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	89	2	no	—
283	C₂²×C₈	—	89	2	no	—
284	C₂²×C₈	—	89	2	no	—
285	C₂²×C₈	—	89	2	no	—
286	C₂²×C₈	—	89	2	no	—
287	C₂²×C₈	—	89	2	no	—
288	C₂²×C₈	—	178	1	no	—
289	C₂²×C₈	—	178	1	no	—
290	C₂²×C₈	—	178	1	no	—
291	C₂²×C₈	—	178	1	no	—
292	C₂²×C₈	—	178	1	no	—
293	C₂²×C₈	—	178	1	no	—
294	C₂²×C₈	—	178	1	no	—
295	C₂²×C₈	—	178	1	no	—
296	C₂²×C₈	Dic₁₇₈	1	2	yes	—
297	C₂²×C₈	C₄×D₈₉	1	2	yes	—
298	C₂²×C₈	C₄×D₈₉	1	2	yes	—
299	C₂²×C₈	C₄×D₈₉	1	2	yes	—
300	C₂²×C₈	C₄×D₈₉	1	2	yes	—
301	C₂²×C₈	D₃₅₆	1	2	yes	—
302	C₂²×C₈	C₂×Dic₈₉	1	2	yes	—
303	C₂²×C₈	C₂×Dic₈₉	1	2	yes	—
304	C₂²×C₈	C₂²⋊D₈₉	1	2	yes	—
305	C₂²×C₈	C₂²⋊D₈₉	1	2	yes	—
306	C₂×C₄²	—	2	1	no	—
307	C₂×C₄²	—	2	1	no	—
308	C₂×C₄²	—	2	1	no	—
309	C₂×C₄²	—	2	1	no	—
310	C₂×C₄²	—	89	2	no	—
311	C₂×C₄²	—	89	2	no	—
312	C₂×C₄²	—	89	2	no	—
313	C₂×C₄²	—	89	2	no	—
314	C₂×C₄²	—	178	1	no	—
315	C₂×C₄²	—	178	1	no	—
316	C₂×C₄²	—	178	1	no	—
317	C₂×C₄²	—	178	1	no	—
318	C₂×C₄²	—	178	1	no	—
319	C₂×C₄²	—	178	1	no	—
320	C₂×C₄²	—	178	1	no	—
321	C₂×C₄²	—	178	1	no	—
322	C₂×C₄²	C₄×D₈₉	1	2	yes	—
323	C₂×C₄²	C₂×Dic₈₉	1	2	yes	—
324	#97	—	2	8	no	—
325	#97	—	178	8	no	—
326	C₄×C₈	—	178	8	no	—
327	#95	—	178	8	no	—
328	C₂⁴	C₂×C₄×D₈₉	1	1	yes	characteristic
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	4	no	—
332	C₂²×C₄	—	2	4	no	—
333	C₂²×C₄	—	89	8	no	—
334	C₂²×C₄	—	89	4	no	—
335	C₂²×C₄	—	89	4	no	—
336	C₂²×C₄	—	178	2	no	—
337	C₂²×C₄	—	178	2	no	—
338	C₂²×C₄	—	178	4	no	—
339	C₂²×C₄	—	178	4	no	—
340	C₂²×C₄	—	178	2	no	—
341	C₂²×C₄	—	178	2	no	—
342	C₂²×C₄	—	178	4	no	—
343	C₂²×C₄	C₄×Dic₈₉	1	4	yes	—
344	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
345	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
348	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
349	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
350	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
351	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
353	C₂²×C₄	C₂×Dic₁₇₈	1	1	yes	characteristic
354	C₂²×C₄	#13083574	1	1	yes	characteristic
355	C₂²×C₄	#13083574	1	1	yes	characteristic
356	C₂²×C₄	#13083574	1	1	yes	characteristic
357	C₂²×C₄	#13083574	1	1	yes	characteristic
358	C₂×C₈	—	2	2	no	—
359	C₂×C₈	—	2	2	no	—
360	C₂×C₈	—	2	2	no	—
361	C₂×C₈	—	2	2	no	—
362	C₂×C₈	—	2	2	no	—
363	C₂×C₈	—	2	2	no	—
364	C₂×C₈	—	89	4	no	—
365	C₂×C₈	—	89	4	no	—
366	C₂×C₈	—	178	2	no	—
367	C₂×C₈	—	178	2	no	—
368	C₂×C₈	—	178	2	no	—
369	C₂×C₈	—	178	2	no	—
370	C₂×C₈	—	178	2	no	—
371	C₂×C₈	—	178	2	no	—
372	C₂×C₈	—	178	2	no	—
373	C₂×C₈	—	178	2	no	—
374	C₂×C₈	—	178	2	no	—
375	C₂×C₈	—	178	2	no	—
376	C₂×C₈	—	178	2	no	—
377	C₂×C₈	—	178	2	no	—
378	C₂×C₈	C₄×Dic₈₉	1	4	yes	—
379	C₂×C₈	C₄×Dic₈₉	1	4	yes	—
380	C₂×C₈	#13083551	1	4	yes	—
381	C₂×C₈	#13083551	1	4	yes	—
382	C₂×C₈	C₂²⋊Dic₈₉	1	4	yes	—
383	C₂×C₈	#13083553	1	4	yes	—
384	C₂×C₈	#13083553	1	4	yes	—
385	C₂×C₈	C₄⋊Dic₈₉	1	4	yes	—
386	C₄²	—	2	2	no	—
387	C₄²	—	2	2	no	—
388	C₄²	—	2	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	178	2	no	—
391	C₄²	—	178	2	no	—
392	C₄²	—	178	2	no	—
393	C₄²	—	178	2	no	—
394	C₄²	—	178	2	no	—
395	C₄²	—	178	2	no	—
396	C₄²	—	178	2	no	—
397	C₄²	—	178	2	no	—
398	C₂³	C₄²×D₈₉	1	1	yes	characteristic
399	C₂³	C₄²×D₈₉	1	1	yes	characteristic
400	C₂³	C₂×C₄×Dic₈₉	1	1	yes	characteristic
401	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
402	C₂³	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
403	C₂³	C₄×D₃₅₆	1	1	yes	characteristic
404	C₂³	C₄×Dic₁₇₈	1	1	yes	characteristic
405	C₂³	M₁₆×D₈₉	1	4	yes	—
406	C₂³	#15668020	1	4	yes	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	—	4	4	no	—
412	C₂×C₄	—	89	8	no	—
413	C₂×C₄	—	356	4	no	—
414	C₂×C₄	—	356	4	no	—
415	C₂×C₄	—	178	4	no	—
416	C₂×C₄	—	178	4	no	—
417	C₂×C₄	—	178	4	no	—
418	C₂×C₄	—	178	8	no	—
419	C₂×C₄	—	178	8	no	—
420	C₂×C₄	—	178	4	no	—
421	C₂×C₄	—	178	4	no	—
422	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
423	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
424	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
425	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
426	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
427	C₂×C₄	C₂×#13083551	1	1	yes	characteristic
428	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
429	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
430	C₂×C₄	C₂×#13083553	1	1	yes	characteristic
431	C₂×C₄	C₂×C₄⋊Dic₈₉	1	1	yes	characteristic
432	C₂×C₄	#15667969	1	1	yes	characteristic
433	C₂×C₄	#15667969	1	1	yes	characteristic
434	C₂×C₄	#15667969	1	1	yes	characteristic
435	C₂×C₄	#15667969	1	1	yes	characteristic
436	C₂×C₄	#15667971	1	1	yes	characteristic
437	C₂×C₄	#15667971	1	1	yes	characteristic
438	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
439	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
440	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
441	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
442	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
443	C₂×C₄	C₄×C₂²⋊D₈₉	1	1	yes	characteristic
444	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
445	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
446	C₂×C₄	C₄×D₃₅₆	1	1	yes	characteristic
447	C₂×C₄	C₄×Dic₁₇₈	1	1	yes	characteristic
448	C₂×C₄	C₄×Dic₁₇₈	1	1	yes	characteristic
449	C₂×C₄	C₄×Dic₁₇₈	1	1	yes	characteristic
450	C₈	—	2	4	no	—
451	C₈	—	178	4	no	—
452	C₈	—	178	4	no	—
453	C₈	#15667919	1	8	yes	complemented
454	C₂²	C₄²×Dic₈₉	1	1	yes	characteristic
455	C₂²	C₄×C₂²⋊Dic₈₉	1	1	yes	characteristic
456	C₂²	C₄×#13083551	1	1	yes	characteristic
457	C₂²	C₄×#13083551	1	1	yes	characteristic
458	C₂²	C₄×C₄⋊Dic₈₉	1	1	yes	characteristic
459	C₂²	C₄×#13083553	1	1	yes	characteristic
460	C₂²	C₄×#13083553	1	1	yes	characteristic
461	C₂²	#97×D₈₉	1	2	yes	—
462	C₂²	M₁₆×Dic₈₉	1	2	yes	—
463	C₂²	#19151550	1	2	yes	—
464	C₂²	#19151555	1	2	yes	—
465	C₂²	#19151555	1	2	yes	—
466	C₂²	#19151556	1	2	yes	—
467	C₂²	#19151667	1	4	yes	—
468	C₂²	#19151671	1	4	yes	—
469	C₂²	#19151674	1	4	yes	—
470	C₂²	#19151726	1	4	yes	—
471	C₄	—	4	4	no	—
472	C₄	—	356	4	no	—
473	C₄	—	178	8	no	—
474	C₄	C₂×#15667919	1	1	yes	characteristic
475	C₄	#19151444	1	1	yes	characteristic
476	C₄	C₄×C₂²⋊Dic₈₉	1	1	yes	characteristic
477	C₄	C₄×#13083551	1	1	yes	characteristic
478	C₄	C₄×#13083551	1	1	yes	characteristic
479	C₄	C₄×C₄⋊Dic₈₉	1	1	yes	characteristic
480	C₄	C₄×#13083553	1	1	yes	characteristic
481	C₄	C₄×#13083553	1	1	yes	characteristic
482	C₂	C₄×#15667919	1	1	yes	characteristic
483	C₂	#97×Dic₈₉	1	1	yes	characteristic
484	C₂	#26019940	1	1	yes	characteristic
485	C₂	#26020029	1	2	yes	—
486	C₂	#26020033	1	2	yes	—
487	C₂	#26020037	1	2	yes	—
488	C₂	#26020120	1	2	yes	—
489	C₂	#26020124	1	2	yes	—
490	C₂	#26020128	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³×C₄	C₂²×D₈₉
commutator	C₂²×C₈₉	C₄³
Fitting	C₂²×#97×C₈₉	C₂
socle, prime radical	C₂⁴×C₈₉	C₂²×C₄
cosocle	C₂³×C₄×C₈₉	C₂³
hypercenter	C₂²×#97	D₈₉
hypocenter	C₈₉	#10696
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
14. C₂×#15667922	C₄	semidirect
17. C₂×C₈×Dic₈₉	C₄	semidirect
19. #19151353	C₄	semidirect
20. #19151352	C₄	semidirect
21. #19151352	C₄	semidirect
27. C₂×#97×C₈₉	C₄	semidirect
203. C₂×Dic₈₉	#97	semidirect
205. C₈×C₈₉	#95	semidirect
253. C₈₉	#10696	semidirect
266. C₂×#97	Dic₈₉	semidirect
453. C₈	#15667919	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#15667922	2
C₂²×C₈×Dic₈₉	2
C₂×#19151353	2
C₂×#19151352	2
C₄×#15667919	2
C₂²×#97×C₈₉	2
#10696	89