Subgroups — #36520055

Order 22784.

874 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26028883	C₂	1	1	yes	maximal, characteristic
2	#26028880	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×D₈₉	C₂	1	1	yes	maximal, characteristic
4	#26018543	C₂	1	2	yes	maximal, complemented
5	#26018542	C₂	1	1	yes	maximal, characteristic, complemented
6	#26018540	C₂	1	2	yes	maximal, complemented
7	#26018539	C₂	1	1	yes	maximal, characteristic, complemented
8	#26018534	C₂	1	2	yes	maximal, complemented
9	C₈×#13083558	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#13083557	C₂	1	2	yes	maximal, complemented
11	C₈×M₁₆×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₈₉	C₄	1	2	yes	—
13	C₂×C₄²×D₈₉	C₂²	1	1	yes	characteristic
14	#19151654	C₄	1	2	yes	—
15	#19151653	C₄	1	2	yes	—
16	#19151653	C₄	1	2	yes	—
17	#19151652	C₄	1	2	yes	—
18	#19151651	C₂²	1	1	yes	characteristic
19	#19151649	C₂²	1	2	yes	—
20	#19151649	C₂²	1	2	yes	—
21	#19151649	C₂²	1	2	yes	—
22	#19151621	C₄	1	2	yes	—
23	#19151620	C₄	1	2	yes	—
24	#19151561	C₄	1	2	yes	—
25	#19151560	C₄	1	2	yes	—
26	C₄×#13083558	C₂²	1	1	yes	characteristic
27	C₄×#13083557	C₂²	1	2	yes	—
28	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
29	C₂×C₈×Dic₈₉	C₄	1	2	yes	—
30	C₄×C₈×D₈₉	C₄	1	2	yes	—
31	C₄×C₈×D₈₉	C₄	1	2	yes	—
32	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
33	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
34	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
35	C₄×C₈×D₈₉	C₂²	1	1	yes	characteristic
36	#19151320	C₂²	1	2	yes	complemented
37	#19151320	C₂²	1	2	yes	complemented
38	#19151320	C₂²	1	2	yes	complemented
39	#19151320	C₂²	1	2	yes	complemented
40	#19151319	C₂²	1	2	yes	complemented
41	C₈×#10623494	C₂²	1	2	yes	complemented
42	#431×C₈₉	C₂²	1	1	yes	characteristic
43	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
45	#322×C₈₉	C₂²	1	2	yes	complemented
46	C₈²×C₈₉	C₂²	1	2	yes	complemented
47	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₄×D₈₉	C₂×C₄	1	1	yes	characteristic
50	C₂×#13083558	C₂×C₄	1	2	yes	—
51	C₂×#13083557	C₂×C₄	1	4	yes	—
52	C₂²×#10623494	C₂×C₄	1	2	yes	—
53	C₂×C₈×D₈₉	—	2	8	no	—
54	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
55	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
56	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
57	C₂×C₈×D₈₉	C₂×C₄	1	2	yes	—
58	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₈₉	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
62	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
63	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
64	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
65	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
66	C₄²×D₈₉	C₂×C₄	1	1	yes	characteristic
67	C₄²×D₈₉	C₂³	1	1	yes	characteristic
68	C₄²×D₈₉	C₂³	1	1	yes	characteristic
69	C₄⋊#10623494	C₂×C₄	1	2	yes	—
70	#15667941	C₂×C₄	1	4	yes	—
71	#15667941	C₂×C₄	1	4	yes	—
72	#15667941	C₂×C₄	1	4	yes	—
73	C₂²⋊#10623494	C₂×C₄	1	2	yes	—
74	#15667924	C₂×C₄	1	4	yes	—
75	#15667924	C₂×C₄	1	4	yes	—
76	#15667924	C₂×C₄	1	4	yes	—
77	#15667923	C₂×C₄	1	2	yes	—
78	#15667922	C₂×C₄	1	4	yes	—
79	C₄×#10623494	C₂×C₄	1	2	yes	—
80	C₄×#10623494	C₂³	1	2	yes	—
81	C₄×#10623494	C₂³	1	2	yes	—
82	C₄×#10623494	C₂³	1	1	yes	characteristic
83	C₄×#10623494	C₂³	1	1	yes	characteristic
84	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
85	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
86	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
87	C₈×Dic₈₉	C₂×C₄	1	2	yes	—
88	C₂×M₁₆×C₈₉	C₂×C₄	1	2	yes	—
89	C₂²×C₈×C₈₉	C₂×C₄	1	2	yes	—
90	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
92	C₂²⋊C₈×C₈₉	C₂×C₄	1	2	yes	—
93	#97×C₈₉	C₂×C₄	1	2	yes	—
94	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
95	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₈₉	C₂³	1	2	yes	—
97	C₄×C₈×C₈₉	C₂³	1	2	yes	—
98	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₂³×D₈₉	C₄²	1	1	yes	characteristic
100	C₂²×Dic₈₉	C₄²	1	1	yes	characteristic
101	C₂²×Dic₈₉	C₄²	1	1	yes	characteristic
102	C₂²×Dic₈₉	C₄²	1	1	yes	characteristic
103	C₂×C₄×D₈₉	—	2	4	no	—
104	C₂×C₄×D₈₉	—	2	4	no	—
105	C₂×C₄×D₈₉	—	2	4	no	—
106	C₂×C₄×D₈₉	C₄²	1	1	yes	characteristic
107	C₂×C₄×D₈₉	C₄²	1	1	yes	characteristic
108	C₂×C₄×D₈₉	C₄²	1	1	yes	characteristic
109	C₂×C₄×D₈₉	C₄²	1	1	yes	characteristic
110	C₂×C₄×D₈₉	C₄²	1	1	yes	characteristic
111	C₂×C₄×D₈₉	C₄²	1	1	yes	characteristic
112	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₄×D₈₉	C₂²×C₄	1	1	yes	characteristic
118	#13083558	—	2	4	no	—
119	#13083557	—	2	8	no	—
120	C₂×#10623494	—	2	4	no	—
121	C₂×#10623494	C₂²×C₄	1	2	yes	—
122	C₂×#10623494	C₂²×C₄	1	4	yes	—
123	C₂×#10623494	C₂²×C₄	1	4	yes	—
124	C₂×#10623494	C₂²×C₄	1	2	yes	—
125	C₈×D₈₉	—	2	4	no	—
126	C₈×D₈₉	—	2	4	no	—
127	C₈×D₈₉	—	2	4	no	—
128	C₈×D₈₉	M₁₆	1	8	yes	complemented
129	C₄×Dic₈₉	C₄²	1	1	yes	characteristic
130	C₄×Dic₈₉	C₄²	1	1	yes	characteristic
131	C₄×Dic₈₉	C₄²	1	1	yes	characteristic
132	C₄×Dic₈₉	C₄²	1	1	yes	characteristic
133	C₄×Dic₈₉	C₄²	1	1	yes	characteristic
134	C₄×Dic₈₉	C₄²	1	1	yes	characteristic
135	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
137	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
138	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
139	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
140	C₄×Dic₈₉	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
144	M₁₆×C₈₉	—	2	4	no	—
145	C₂×C₈×C₈₉	—	2	4	no	—
146	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
147	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
148	C₂×C₈×C₈₉	C₂²×C₄	1	4	yes	—
149	C₂×C₈×C₈₉	C₂²×C₄	1	2	yes	—
150	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
152	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
153	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
154	C₂³×C₈₉	C₂×C₄²	1	1	yes	characteristic
155	C₂²×D₈₉	—	2	2	no	—
156	C₂²×D₈₉	—	2	2	no	—
157	C₂²×D₈₉	—	2	2	no	—
158	C₂²×D₈₉	C₂×C₄²	1	1	yes	characteristic
159	C₂²×D₈₉	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₈₉	—	2	2	no	—
161	C₂×C₄×C₈₉	—	2	2	no	—
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	#131	1	4	yes	—
166	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
168	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
169	C₂×Dic₈₉	—	2	2	no	—
170	C₂×Dic₈₉	—	2	2	no	—
171	C₂×Dic₈₉	—	2	2	no	—
172	C₂×Dic₈₉	C₂×C₄²	1	1	yes	characteristic
173	C₂×Dic₈₉	C₂×C₄²	1	1	yes	characteristic
174	C₂×Dic₈₉	C₂×C₄²	1	1	yes	characteristic
175	C₂×Dic₈₉	C₂×C₄²	1	1	yes	characteristic
176	C₂×Dic₈₉	C₂×C₄²	1	1	yes	characteristic
177	C₂×Dic₈₉	C₂×C₄²	1	1	yes	characteristic
178	C₄×D₈₉	—	2	2	no	—
179	C₄×D₈₉	—	2	2	no	—
180	C₄×D₈₉	—	2	2	no	—
181	C₄×D₈₉	—	2	2	no	—
182	C₄×D₈₉	—	2	2	no	—
183	C₄×D₈₉	—	2	2	no	—
184	C₄×D₈₉	—	2	2	no	—
185	C₄×D₈₉	—	2	2	no	—
186	C₄×D₈₉	—	2	2	no	—
187	C₄×D₈₉	—	2	2	no	—
188	C₄×D₈₉	C₂×M₁₆	1	4	yes	—
189	C₄×D₈₉	#131	1	4	yes	—
190	C₈×C₈₉	—	2	2	no	—
191	C₈×C₈₉	—	2	4	no	—
192	C₈×C₈₉	—	2	4	no	—
193	C₈×C₈₉	C₂×M₁₆	1	4	yes	—
194	#10623494	—	2	2	no	—
195	#10623494	—	2	4	no	—
196	#10623494	—	2	4	no	—
197	#10623494	C₂×M₁₆	1	4	yes	—
198	C₂²×C₈₉	—	2	1	no	—
199	C₂²×C₈₉	—	2	1	no	—
200	C₂²×C₈₉	#405	1	2	yes	—
201	C₂²×C₈₉	C₂²×C₄²	1	1	yes	characteristic
202	C₂×D₈₉	—	2	8	no	—
203	C₂×D₈₉	—	2	1	no	—
204	C₂×D₈₉	—	2	1	no	—
205	C₂×D₈₉	—	2	1	no	—
206	C₂×D₈₉	—	2	1	no	—
207	C₂×D₈₉	C₄×M₁₆	1	2	yes	—
208	C₂×D₈₉	#405	1	2	yes	—
209	C₄×C₈₉	—	2	1	no	—
210	C₄×C₈₉	—	2	1	no	—
211	C₄×C₈₉	#405	1	2	yes	—
212	C₄×C₈₉	C₂²×M₁₆	1	2	yes	—
213	C₄×C₈₉	C₂×#131	1	2	yes	—
214	C₄×C₈₉	C₂×#131	1	2	yes	—
215	Dic₈₉	—	2	1	no	—
216	Dic₈₉	—	2	1	no	—
217	Dic₈₉	—	2	1	no	—
218	Dic₈₉	—	2	1	no	—
219	Dic₈₉	C₄×M₁₆	1	2	yes	—
220	Dic₈₉	#405	1	2	yes	—
221	#17323	—	89	1	no	maximal, Sylow
222	C₂×C₈₉	—	2	2	no	—
223	C₂×C₈₉	C₂×C₄×M₁₆	1	1	yes	characteristic
224	C₂×C₈₉	C₂×#405	1	1	yes	characteristic
225	C₂×C₈₉	C₂×#405	1	1	yes	characteristic
226	D₈₉	—	2	2	no	—
227	D₈₉	—	2	2	no	—
228	#2920	—	89	1	no	—
229	#2920	—	89	1	no	—
230	C₂²×C₄×C₈	—	89	1	no	—
231	#1452	—	89	2	no	—
232	#1451	—	89	1	no	—
233	#1451	—	89	1	no	—
234	#1451	—	89	2	no	—
235	#1450	—	89	2	no	—
236	C₈×M₁₆	—	89	1	no	—
237	C₈×M₁₆	—	89	2	no	—
238	C₈×M₁₆	D₈₉	1	1	yes	characteristic, complemented
239	C₈₉	#17323	1	1	yes	characteristic, complemented, Sylow
240	C₂³×C₈	—	89	2	no	—
241	C₂²×C₄²	—	89	1	no	—
242	#432	—	89	2	no	—
243	#432	—	89	2	no	—
244	#432	—	89	2	no	—
245	#432	—	89	2	no	—
246	#431	—	89	1	no	—
247	#431	—	89	2	no	—
248	#431	—	89	2	no	—
249	#431	—	89	2	no	—
250	#431	C₂×D₈₉	1	1	yes	characteristic
251	#423	—	89	2	no	—
252	#423	—	89	2	no	—
253	#407	—	89	2	no	—
254	#407	—	89	2	no	—
255	C₄×M₁₆	—	89	1	no	—
256	C₄×M₁₆	—	89	2	no	—
257	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
258	C₂×C₄×C₈	—	89	2	no	—
259	C₂×C₄×C₈	—	89	1	no	—
260	C₂×C₄×C₈	—	89	2	no	—
261	C₂×C₄×C₈	—	89	2	no	—
262	C₂×C₄×C₈	—	89	1	no	—
263	C₂×C₄×C₈	—	89	1	no	—
264	C₂×C₄×C₈	—	89	1	no	—
265	C₂×C₄×C₈	—	89	1	no	—
266	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
267	#322	—	89	2	no	—
268	#322	—	89	2	no	—
269	#322	—	89	2	no	—
270	#322	—	89	2	no	—
271	#322	—	89	2	no	—
272	#322	C₂×D₈₉	1	2	yes	complemented
273	C₈²	—	89	2	no	—
274	C₈²	C₂×D₈₉	1	2	yes	complemented
275	C₂³×C₄	—	89	1	no	—
276	C₂³×C₄	—	89	1	no	—
277	C₂³×C₄	—	89	1	no	—
278	C₂×M₁₆	—	89	2	no	—
279	C₂×M₁₆	—	89	4	no	—
280	C₂×M₁₆	C₄×D₈₉	1	2	yes	—
281	C₂²×C₈	—	89	2	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	—	178	8	no	—
287	C₂²×C₈	C₄×D₈₉	1	2	yes	—
288	C₂×C₄²	—	89	1	no	—
289	C₂×C₄²	—	89	1	no	—
290	C₂×C₄²	—	89	1	no	—
291	C₂×C₄²	—	89	1	no	—
292	C₂×C₄²	—	89	1	no	—
293	C₂×C₄²	—	89	1	no	—
294	C₂×C₄²	—	89	1	no	—
295	C₂×C₄²	—	89	1	no	—
296	C₂×C₄²	—	89	1	no	—
297	C₂×C₄²	—	89	1	no	—
298	C₂×C₄²	—	89	1	no	—
299	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
300	C₄⋊C₈	—	89	4	no	—
301	C₄⋊C₈	—	89	4	no	—
302	C₄⋊C₈	—	89	4	no	—
303	C₄⋊C₈	—	89	2	no	—
304	C₄⋊C₈	C₄×D₈₉	1	2	yes	—
305	C₂²⋊C₈	—	89	2	no	—
306	C₂²⋊C₈	—	89	4	no	—
307	C₂²⋊C₈	—	89	4	no	—
308	C₂²⋊C₈	—	89	4	no	—
309	C₂²⋊C₈	C₄×D₈₉	1	2	yes	—
310	#97	—	89	4	no	—
311	#97	—	89	2	no	—
312	#97	C₄×D₈₉	1	2	yes	—
313	C₄×C₈	—	89	2	no	—
314	C₄×C₈	—	89	2	no	—
315	C₄×C₈	—	89	2	no	—
316	C₄×C₈	—	89	2	no	—
317	C₄×C₈	—	89	2	no	—
318	C₄×C₈	—	89	2	no	—
319	C₄×C₈	—	89	2	no	—
320	C₄×C₈	—	89	1	no	—
321	C₄×C₈	—	89	1	no	—
322	C₄×C₈	C₄×D₈₉	1	2	yes	—
323	C₄×C₈	C₂²×D₈₉	1	2	yes	—
324	C₄×C₈	C₂²×D₈₉	1	2	yes	—
325	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
326	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
327	C₂⁴	—	89	1	no	—
328	C₂²×C₄	—	89	1	no	—
329	C₂²×C₄	—	89	1	no	—
330	C₂²×C₄	—	89	1	no	—
331	C₂²×C₄	—	89	1	no	—
332	C₂²×C₄	—	89	1	no	—
333	C₂²×C₄	—	89	1	no	—
334	C₂²×C₄	—	89	1	no	—
335	C₂²×C₄	—	89	1	no	—
336	C₂²×C₄	—	89	1	no	—
337	C₂²×C₄	—	89	1	no	—
338	C₂²×C₄	—	89	1	no	—
339	C₂²×C₄	—	89	1	no	—
340	C₂²×C₄	—	89	1	no	—
341	C₂²×C₄	—	89	1	no	—
342	C₂²×C₄	—	89	1	no	—
343	C₂²×C₄	—	178	4	no	—
344	C₂²×C₄	—	178	4	no	—
345	C₂²×C₄	—	178	4	no	—
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	M₁₆	—	2	4	no	—
350	M₁₆	—	178	8	no	—
351	M₁₆	—	178	4	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	89	2	no	—
354	C₂×C₈	—	89	8	no	—
355	C₂×C₈	—	89	2	no	—
356	C₂×C₈	—	89	4	no	—
357	C₂×C₈	—	89	4	no	—
358	C₂×C₈	—	178	4	no	—
359	C₂×C₈	—	178	4	no	—
360	C₂×C₈	—	178	4	no	—
361	C₂×C₈	—	178	4	no	—
362	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
363	C₂×C₈	C₂×C₄×D₈₉	1	4	yes	—
364	C₂×C₈	C₂×C₄×D₈₉	1	4	yes	—
365	C₂×C₈	C₂×C₄×D₈₉	1	2	yes	—
366	C₄²	—	89	1	no	—
367	C₄²	—	89	1	no	—
368	C₄²	—	89	1	no	—
369	C₄²	—	89	1	no	—
370	C₄²	—	89	1	no	—
371	C₄²	—	89	1	no	—
372	C₄²	—	89	1	no	—
373	C₄²	—	89	1	no	—
374	C₄²	—	89	1	no	—
375	C₄²	—	89	1	no	—
376	C₄²	—	89	1	no	—
377	C₄²	—	89	1	no	—
378	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
379	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
380	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
381	C₄²	C₂³×D₈₉	1	1	yes	characteristic
382	C₂³	—	89	1	no	—
383	C₂³	—	89	1	no	—
384	C₂³	—	178	2	no	—
385	C₂³	—	178	2	no	—
386	C₂³	—	178	2	no	—
387	C₂³	C₄²×D₈₉	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	89	1	no	—
391	C₂×C₄	—	89	1	no	—
392	C₂×C₄	—	89	4	no	—
393	C₂×C₄	—	89	4	no	—
394	C₂×C₄	—	89	1	no	—
395	C₂×C₄	—	89	1	no	—
396	C₂×C₄	—	89	1	no	—
397	C₂×C₄	—	89	1	no	—
398	C₂×C₄	—	178	2	no	—
399	C₂×C₄	—	178	2	no	—
400	C₂×C₄	—	178	2	no	—
401	C₂×C₄	—	178	2	no	—
402	C₂×C₄	—	178	2	no	—
403	C₂×C₄	—	178	2	no	—
404	C₂×C₄	—	178	2	no	—
405	C₂×C₄	—	178	2	no	—
406	C₂×C₄	—	178	2	no	—
407	C₂×C₄	—	178	2	no	—
408	C₂×C₄	—	178	2	no	—
409	C₂×C₄	—	178	2	no	—
410	C₂×C₄	—	178	2	no	—
411	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
412	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
413	C₂×C₄	C₄²×D₈₉	1	1	yes	characteristic
414	C₂×C₄	#15668018	1	4	yes	—
415	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
416	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
417	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
418	C₈	—	2	2	no	—
419	C₈	—	2	4	no	—
420	C₈	—	2	4	no	—
421	C₈	—	89	4	no	—
422	C₈	—	178	2	no	—
423	C₈	—	178	4	no	—
424	C₈	—	178	4	no	—
425	C₈	M₁₆×D₈₉	1	4	yes	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	89	2	no	—
429	C₂²	—	89	2	no	—
430	C₂²	—	178	8	no	—
431	C₂²	—	178	1	no	—
432	C₂²	—	178	1	no	—
433	C₂²	—	178	1	no	—
434	C₂²	—	178	1	no	—
435	C₂²	#19151552	1	2	yes	—
436	C₂²	C₂×C₄²×D₈₉	1	1	yes	characteristic
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	89	2	no	—
440	C₄	—	89	2	no	—
441	C₄	—	178	1	no	—
442	C₄	—	178	1	no	—
443	C₄	—	178	1	no	—
444	C₄	—	178	1	no	—
445	C₄	#19151552	1	2	yes	—
446	C₄	C₂×M₁₆×D₈₉	1	2	yes	—
447	C₄	#131×D₈₉	1	2	yes	—
448	C₄	C₂×#15668018	1	2	yes	—
449	C₂	—	2	2	no	—
450	C₂	—	178	2	no	—
451	C₂	—	178	2	no	—
452	C₂	C₄×M₁₆×D₈₉	1	1	yes	characteristic
453	C₂	#405×D₈₉	1	1	yes	characteristic
454	C₂	C₂×#19151552	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₈	C₂²×D₈₉
commutator, socle	C₂²×C₈₉	C₂²×C₄²
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈×M₁₆×C₈₉	C₂
prime radical	C₂³×D₈₉	C₄²
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	C₈×M₁₆	D₈₉
hypocenter	C₈₉	#17323
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₄×C₈ ◁ C₈×M₁₆

Complements

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

N	H ≅ G/N	type
4. #26018543	C₂	semidirect
5. #26018542	C₂	semidirect
6. #26018540	C₂	semidirect
7. #26018539	C₂	semidirect
8. #26018534	C₂	semidirect
9. C₈×#13083558	C₂	semidirect
10. C₈×#13083557	C₂	semidirect
11. C₈×M₁₆×C₈₉	C₂	semidirect
36. #19151320	C₂²	semidirect
37. #19151320	C₂²	semidirect
38. #19151320	C₂²	semidirect
39. #19151320	C₂²	semidirect
40. #19151319	C₂²	semidirect
41. C₈×#10623494	C₂²	semidirect
45. #322×C₈₉	C₂²	semidirect
46. C₈²×C₈₉	C₂²	semidirect
128. C₈×D₈₉	M₁₆	semidirect
238. C₈×M₁₆	D₈₉	semidirect
239. C₈₉	#17323	semidirect
272. #322	C₂×D₈₉	semidirect
274. C₈²	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26028883	2
#26028880	2
C₂×C₄×C₈×D₈₉	2
#26018543	2
#26018542	2
#26018540	2
#26018539	2
#26018534	2
C₈×#13083558	2
C₈×#13083557	2
C₈×M₁₆×C₈₉	2
#17323	89