Subgroups — #36520056

Order 22784.

874 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028885	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×#10623494	C₂	1	1	yes	maximal, characteristic
3	#26018545	C₂	1	2	yes	maximal, complemented
4	#26018542	C₂	1	2	yes	maximal, complemented
5	#26018539	C₂	1	2	yes	maximal, complemented
6	#26018536	C₂	1	2	yes	maximal, complemented
7	#26018533	C₂	1	2	yes	maximal, complemented
8	M₁₆×#10623494	C₂	1	2	yes	maximal, complemented
9	C₈₉×#2920	C₂	1	1	yes	maximal, characteristic
10	C₂³×#10623494	C₄	1	2	yes	—
11	#19151655	C₄	1	2	yes	—
12	#19151655	C₄	1	2	yes	—
13	#19151651	C₂²	1	2	yes	—
14	#19151651	C₂²	1	2	yes	—
15	#19151622	C₄	1	2	yes	—
16	#19151562	C₄	1	2	yes	—
17	C₄×#13083558	C₂²	1	2	yes	—
18	C₂×C₄×#10623494	C₄	1	2	yes	—
19	C₂×C₄×#10623494	C₄	1	2	yes	—
20	C₂×C₄×#10623494	C₄	1	2	yes	—
21	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
22	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
23	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
24	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
25	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
26	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
27	#19151320	C₂²	1	4	yes	complemented
28	#19151320	C₂²	1	4	yes	complemented
29	#19151319	C₂²	1	4	yes	complemented
30	C₈×#10623494	C₂²	1	4	yes	complemented
31	C₂²×C₄²×C₈₉	C₂²	1	1	yes	characteristic
32	#432×C₈₉	C₄	1	2	yes	—
33	#432×C₈₉	C₄	1	2	yes	—
34	#431×C₈₉	C₂²	1	2	yes	—
35	#431×C₈₉	C₂²	1	2	yes	—
36	#423×C₈₉	C₄	1	2	yes	—
37	#407×C₈₉	C₄	1	2	yes	—
38	C₄×M₁₆×C₈₉	C₂²	1	2	yes	—
39	C₂×#13083558	C₂×C₄	1	4	yes	—
40	C₂²×#10623494	—	2	8	no	—
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	C₂²×#10623494	C₂×C₄	1	2	yes	—
45	C₂²×#10623494	C₂×C₄	1	2	yes	—
46	C₂²×#10623494	C₂×C₄	1	2	yes	—
47	C₄⋊#10623494	C₂×C₄	1	4	yes	—
48	C₄⋊#10623494	C₂×C₄	1	4	yes	—
49	C₂²⋊#10623494	C₂×C₄	1	4	yes	—
50	C₂²⋊#10623494	C₂×C₄	1	4	yes	—
51	#15667923	C₂×C₄	1	4	yes	—
52	C₄×#10623494	C₂×C₄	1	2	yes	—
53	C₄×#10623494	C₂×C₄	1	2	yes	—
54	C₄×#10623494	C₂×C₄	1	2	yes	—
55	C₄×#10623494	C₂×C₄	1	2	yes	—
56	C₄×#10623494	C₂×C₄	1	2	yes	—
57	C₄×#10623494	C₂×C₄	1	2	yes	—
58	C₄×#10623494	C₂³	1	4	yes	—
59	C₄×#10623494	C₂³	1	1	yes	characteristic
60	C₄×#10623494	C₂³	1	1	yes	characteristic
61	C₄×#10623494	C₂³	1	1	yes	characteristic
62	C₄×#10623494	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
64	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
65	C₂³×C₄×C₈₉	C₂×C₄	1	1	yes	characteristic
66	C₂×M₁₆×C₈₉	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
68	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₈₉	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
80	C₄⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
81	C₂²⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
82	C₂²⋊C₈×C₈₉	C₂×C₄	1	4	yes	—
83	#97×C₈₉	C₂×C₄	1	4	yes	—
84	C₄×C₈×C₈₉	C₂³	1	4	yes	—
85	#13083558	—	2	8	no	—
86	C₂×#10623494	—	2	4	no	—
87	C₂×#10623494	—	2	4	no	—
88	C₂×#10623494	—	2	4	no	—
89	C₂×#10623494	—	2	4	no	—
90	C₂×#10623494	—	2	4	no	—
91	C₂×#10623494	M₁₆	1	8	yes	complemented
92	C₂×#10623494	C₂²×C₄	1	2	yes	—
93	C₂×#10623494	C₂²×C₄	1	2	yes	—
94	C₂×#10623494	C₂²×C₄	1	8	yes	—
95	C₂×#10623494	C₂²×C₄	1	2	yes	—
96	C₂×#10623494	C₂²×C₄	1	2	yes	—
97	C₂⁴×C₈₉	C₄²	1	1	yes	characteristic
98	C₂²×C₄×C₈₉	—	2	4	no	—
99	C₂²×C₄×C₈₉	—	2	4	no	—
100	C₂²×C₄×C₈₉	—	2	4	no	—
101	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
102	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
103	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
104	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
105	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
106	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
107	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
108	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
109	C₂²×C₄×C₈₉	C₄²	1	1	yes	characteristic
110	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
117	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
119	M₁₆×C₈₉	—	2	8	no	—
120	C₂×C₈×C₈₉	C₂²×C₄	1	8	yes	—
121	C₄²×C₈₉	C₄²	1	1	yes	characteristic
122	C₄²×C₈₉	C₄²	1	1	yes	characteristic
123	C₄²×C₈₉	C₄²	1	1	yes	characteristic
124	C₄²×C₈₉	C₄²	1	1	yes	characteristic
125	C₄²×C₈₉	C₄²	1	1	yes	characteristic
126	C₄²×C₈₉	C₄²	1	1	yes	characteristic
127	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
129	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
130	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
131	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
135	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
137	C₂³×C₈₉	—	2	2	no	—
138	C₂³×C₈₉	—	2	2	no	—
139	C₂³×C₈₉	—	2	2	no	—
140	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
141	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
142	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
143	C₂×C₄×C₈₉	—	2	2	no	—
144	C₂×C₄×C₈₉	—	2	2	no	—
145	C₂×C₄×C₈₉	—	2	2	no	—
146	C₂×C₄×C₈₉	—	2	2	no	—
147	C₂×C₄×C₈₉	—	2	2	no	—
148	C₂×C₄×C₈₉	—	2	2	no	—
149	C₂×C₄×C₈₉	—	2	2	no	—
150	C₂×C₄×C₈₉	—	2	2	no	—
151	C₂×C₄×C₈₉	—	2	2	no	—
152	C₂×C₄×C₈₉	—	2	2	no	—
153	C₂×C₄×C₈₉	—	2	2	no	—
154	C₂×C₄×C₈₉	—	2	2	no	—
155	C₂×C₄×C₈₉	—	2	2	no	—
156	C₂×C₄×C₈₉	—	2	2	no	—
157	C₂×C₄×C₈₉	—	2	2	no	—
158	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
159	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
161	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
162	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
163	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
164	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
165	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
166	C₂×C₄×C₈₉	C₂×C₄²	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂×M₁₆	1	4	yes	—
168	C₂×C₄×C₈₉	#131	1	4	yes	—
169	C₂×C₄×C₈₉	#131	1	4	yes	—
170	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
171	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
172	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
173	C₈×C₈₉	—	2	8	no	—
174	#10623494	—	2	2	no	—
175	#10623494	—	2	2	no	—
176	#10623494	—	2	8	no	—
177	#10623494	C₂×M₁₆	1	4	yes	—
178	#10623494	C₂×M₁₆	1	4	yes	—
179	C₂²×C₈₉	—	2	8	no	—
180	C₂²×C₈₉	—	2	1	no	—
181	C₂²×C₈₉	—	2	1	no	—
182	C₂²×C₈₉	—	2	1	no	—
183	C₂²×C₈₉	—	2	1	no	—
184	C₂²×C₈₉	—	2	1	no	—
185	C₂²×C₈₉	—	2	1	no	—
186	C₂²×C₈₉	C₄×M₁₆	1	2	yes	—
187	C₂²×C₈₉	#405	1	2	yes	—
188	C₂²×C₈₉	#405	1	2	yes	—
189	C₂²×C₈₉	C₂²×C₄²	1	1	yes	characteristic
190	C₄×C₈₉	—	2	1	no	—
191	C₄×C₈₉	—	2	1	no	—
192	C₄×C₈₉	—	2	1	no	—
193	C₄×C₈₉	—	2	1	no	—
194	C₄×C₈₉	—	2	1	no	—
195	C₄×C₈₉	—	2	1	no	—
196	C₄×C₈₉	C₄×M₁₆	1	2	yes	—
197	C₄×C₈₉	#405	1	2	yes	—
198	C₄×C₈₉	#405	1	2	yes	—
199	C₄×C₈₉	C₂²×M₁₆	1	2	yes	—
200	C₄×C₈₉	C₂×#131	1	2	yes	—
201	C₄×C₈₉	C₂×#131	1	2	yes	—
202	#17323	—	89	1	no	maximal, Sylow
203	C₂×C₈₉	—	2	2	no	—
204	C₂×C₈₉	—	2	2	no	—
205	C₂×C₈₉	—	2	2	no	—
206	C₂×C₈₉	C₂×C₄×M₁₆	1	1	yes	characteristic
207	C₂×C₈₉	C₂×#405	1	1	yes	characteristic
208	C₂×C₈₉	C₂×#405	1	1	yes	characteristic
209	#2920	—	89	1	no	—
210	#2920	D₈₉	1	1	yes	characteristic
211	C₂²×C₄×C₈	—	89	1	no	—
212	#1452	—	89	2	no	—
213	#1451	—	89	2	no	—
214	#1451	—	89	2	no	—
215	#1450	—	89	2	no	—
216	C₈×M₁₆	—	89	2	no	—
217	C₈×M₁₆	—	89	2	no	—
218	C₈₉	#17323	1	1	yes	characteristic, complemented, Sylow
219	C₂³×C₈	—	89	2	no	—
220	C₂²×C₄²	C₂×D₈₉	1	1	yes	characteristic
221	#432	—	89	2	no	—
222	#432	—	89	2	no	—
223	#432	Dic₈₉	1	2	yes	—
224	#432	Dic₈₉	1	2	yes	—
225	#431	—	89	2	no	—
226	#431	—	89	2	no	—
227	#431	C₂×D₈₉	1	2	yes	—
228	#431	C₂×D₈₉	1	2	yes	—
229	#423	—	89	2	no	—
230	#423	Dic₈₉	1	2	yes	—
231	#407	—	89	2	no	—
232	#407	Dic₈₉	1	2	yes	—
233	C₄×M₁₆	—	89	2	no	—
234	C₄×M₁₆	C₂×D₈₉	1	2	yes	—
235	C₂×C₄×C₈	—	89	2	no	—
236	C₂×C₄×C₈	—	89	2	no	—
237	C₂×C₄×C₈	—	89	2	no	—
238	C₂×C₄×C₈	—	89	1	no	—
239	C₂×C₄×C₈	—	89	1	no	—
240	C₂×C₄×C₈	—	89	1	no	—
241	C₂×C₄×C₈	—	89	1	no	—
242	C₂×C₄×C₈	—	89	1	no	—
243	C₂×C₄×C₈	—	89	1	no	—
244	#322	—	89	4	no	—
245	#322	—	89	4	no	—
246	#322	—	89	4	no	—
247	C₈²	—	89	4	no	—
248	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
249	C₂³×C₄	C₄×D₈₉	1	1	yes	characteristic
250	C₂³×C₄	C₂×Dic₈₉	1	1	yes	characteristic
251	C₂×M₁₆	—	89	4	no	—
252	C₂×M₁₆	C₂×Dic₈₉	1	4	yes	—
253	C₂²×C₈	—	89	2	no	—
254	C₂²×C₈	—	89	2	no	—
255	C₂²×C₈	—	89	2	no	—
256	C₂²×C₈	—	89	2	no	—
257	C₂²×C₈	—	89	2	no	—
258	C₂²×C₈	—	89	2	no	—
259	C₂²×C₈	—	178	8	no	—
260	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
261	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
262	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
263	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
264	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
265	C₂×C₄²	C₄×D₈₉	1	1	yes	characteristic
266	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
267	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
268	C₂×C₄²	C₂×Dic₈₉	1	1	yes	characteristic
269	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
270	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
271	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
272	C₄⋊C₈	—	89	4	no	—
273	C₄⋊C₈	—	89	4	no	—
274	C₄⋊C₈	C₂×Dic₈₉	1	4	yes	—
275	C₄⋊C₈	C₂×Dic₈₉	1	4	yes	—
276	C₂²⋊C₈	—	89	4	no	—
277	C₂²⋊C₈	—	89	4	no	—
278	C₂²⋊C₈	C₂×Dic₈₉	1	4	yes	—
279	C₂²⋊C₈	C₂×Dic₈₉	1	4	yes	—
280	#97	—	89	4	no	—
281	#97	C₂×Dic₈₉	1	4	yes	—
282	C₄×C₈	—	89	2	no	—
283	C₄×C₈	—	89	2	no	—
284	C₄×C₈	—	89	2	no	—
285	C₄×C₈	—	89	2	no	—
286	C₄×C₈	—	89	2	no	—
287	C₄×C₈	—	89	2	no	—
288	C₄×C₈	—	89	1	no	—
289	C₄×C₈	—	89	4	no	—
290	C₄×C₈	—	89	1	no	—
291	C₄×C₈	—	89	1	no	—
292	C₄×C₈	—	89	1	no	—
293	C₄×C₈	C₂²×D₈₉	1	4	yes	—
294	C₂⁴	C₄×Dic₈₉	1	1	yes	characteristic
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	4	no	—
297	C₂²×C₄	—	2	4	no	—
298	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
299	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
300	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
301	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
302	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
303	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
304	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
305	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
306	C₂²×C₄	C₄×Dic₈₉	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
312	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
313	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
314	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
315	C₂²×C₄	C₂²×Dic₈₉	1	1	yes	characteristic
316	M₁₆	—	2	8	no	—
317	M₁₆	—	178	8	no	—
318	C₂×C₈	—	89	8	no	—
319	C₂×C₈	—	89	2	no	—
320	C₂×C₈	—	89	2	no	—
321	C₂×C₈	—	89	2	no	—
322	C₂×C₈	—	89	2	no	—
323	C₂×C₈	—	89	8	no	—
324	C₂×C₈	—	178	4	no	—
325	C₂×C₈	—	178	4	no	—
326	C₂×C₈	—	178	4	no	—
327	C₂×C₈	—	178	4	no	—
328	C₂×C₈	—	178	4	no	—
329	C₂×C₈	C₂²×Dic₈₉	1	8	yes	—
330	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
331	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
332	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
333	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
334	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
335	C₄²	C₄×Dic₈₉	1	1	yes	characteristic
336	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
337	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
338	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
339	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
340	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
341	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
342	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
343	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
344	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
345	C₄²	C₂³×D₈₉	1	1	yes	characteristic
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	2	no	—
349	C₂³	C₂×C₄×Dic₈₉	1	1	yes	characteristic
350	C₂³	C₂×C₄×Dic₈₉	1	1	yes	characteristic
351	C₂³	C₂×C₄×Dic₈₉	1	1	yes	characteristic
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
368	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
369	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
370	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
371	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
372	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
374	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
375	C₂×C₄	C₂×C₄×Dic₈₉	1	1	yes	characteristic
376	C₂×C₄	M₁₆×D₈₉	1	4	yes	—
377	C₂×C₄	#15668019	1	4	yes	—
378	C₂×C₄	#15668020	1	4	yes	—
379	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
381	C₂×C₄	C₂³×Dic₈₉	1	1	yes	characteristic
382	C₈	—	2	8	no	—
383	C₈	—	89	4	no	—
384	C₈	—	89	4	no	—
385	C₈	—	178	2	no	—
386	C₈	—	178	2	no	—
387	C₈	—	178	8	no	—
388	C₂²	—	2	8	no	—
389	C₂²	—	2	1	no	—
390	C₂²	—	2	1	no	—
391	C₂²	—	2	1	no	—
392	C₂²	—	2	1	no	—
393	C₂²	—	2	1	no	—
394	C₂²	—	2	1	no	—
395	C₂²	M₁₆×Dic₈₉	1	2	yes	—
396	C₂²	#19151554	1	2	yes	—
397	C₂²	#19151556	1	2	yes	—
398	C₂²	C₂²×C₄×Dic₈₉	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	2	1	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	1	no	—
404	C₄	—	2	1	no	—
405	C₄	M₁₆×Dic₈₉	1	2	yes	—
406	C₄	#19151554	1	2	yes	—
407	C₄	#19151556	1	2	yes	—
408	C₄	C₂×M₁₆×D₈₉	1	2	yes	—
409	C₄	C₂×#15668019	1	2	yes	—
410	C₄	C₂×#15668020	1	2	yes	—
411	C₂	—	2	2	no	—
412	C₂	—	2	2	no	—
413	C₂	—	2	2	no	—
414	C₂	C₂×M₁₆×Dic₈₉	1	1	yes	characteristic
415	C₂	C₂×#19151554	1	1	yes	characteristic
416	C₂	C₂×#19151556	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₄²	C₂³×D₈₉
commutator, socle	C₂²×C₈₉	C₂²×C₄²
Fitting	C₈₉×#2920	C₂
prime radical	C₂⁴×C₈₉	C₄²
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#2920	D₈₉
hypocenter	C₈₉	#17323
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄² ◁ #2920

Complements

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

N	H ≅ G/N	type
3. #26018545	C₂	semidirect
4. #26018542	C₂	semidirect
5. #26018539	C₂	semidirect
6. #26018536	C₂	semidirect
7. #26018533	C₂	semidirect
8. M₁₆×#10623494	C₂	semidirect
27. #19151320	C₂²	semidirect
28. #19151320	C₂²	semidirect
29. #19151319	C₂²	semidirect
30. C₈×#10623494	C₂²	semidirect
91. C₂×#10623494	M₁₆	semidirect
218. C₈₉	#17323	semidirect

Maximal subgroups

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

subgroup	index
#26028885	2
C₂²×C₄×#10623494	2
#26018545	2
#26018542	2
#26018539	2
#26018536	2
#26018533	2
M₁₆×#10623494	2
C₈₉×#2920	2
#17323	89