Subgroups — #36524218

Order 22784.

724 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26029219	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#15668037	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151675	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019163	C₂	1	2	yes	maximal, complemented
5	#26019157	C₂	1	2	yes	maximal, complemented
6	#26019139	C₂	1	2	yes	maximal, complemented
7	#26019134	C₂	1	2	yes	maximal, complemented
8	#26019002	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018644	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018533	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1477	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668037	C₄	1	1	yes	characteristic
13	C₂²×#13083557	—	2	1	no	—
14	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
15	#19151729	C₂²	1	1	yes	characteristic, complemented
16	#19151729	C₂²	1	1	yes	characteristic, complemented
17	#19151708	C₄	1	2	yes	—
18	#19151696	C₄	1	2	yes	—
19	C₄×#13083561	C₂²	1	2	yes	—
20	C₄×#13083559	C₂²	1	2	yes	—
21	#19151676	C₂²	1	1	yes	characteristic, complemented
22	#19151676	C₂²	1	1	yes	characteristic, complemented
23	#19151675	—	2	1	no	—
24	#19151675	—	2	1	no	—
25	#19151675	C₂²	1	2	yes	—
26	#19151675	C₂²	1	2	yes	—
27	#19151670	—	2	1	no	—
28	#19151670	—	2	1	no	—
29	#19151651	—	2	1	no	—
30	#19151651	C₂²	1	1	yes	characteristic
31	#19151641	C₄	1	1	yes	characteristic
32	#19151602	C₄	1	1	yes	characteristic
33	#19151599	C₄	1	1	yes	characteristic
34	C₂×#15667924	—	2	1	no	—
35	C₄×#13083558	—	2	1	no	—
36	C₄×#13083558	C₂²	1	1	yes	characteristic
37	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
38	#19151350	C₂²	1	2	yes	complemented
39	#19151348	C₂²	1	2	yes	complemented
40	#19151327	C₂²	1	2	yes	—
41	#19151327	C₂²	1	2	yes	—
42	#19151320	C₂²	1	2	yes	complemented
43	C₈×#10623494	C₂²	1	2	yes	complemented
44	C₄×#41×C₈₉	C₂²	1	1	yes	characteristic
45	#431×C₈₉	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
47	Q₈⋊C₈×C₈₉	C₂²	1	2	yes	complemented
48	D₄⋊C₈×C₈₉	C₂²	1	2	yes	complemented
49	C₂²×D₃₅₆	C₂×C₄	1	1	yes	characteristic
50	C₂²×C₄×D₈₉	—	2	1	no	—
51	#15668037	—	2	4	no	—
52	C₂×#13083561	C₂×C₄	1	2	yes	—
53	C₂×#13083559	C₂×C₄	1	2	yes	—
54	C₂×#13083558	—	2	1	no	—
55	C₂×#13083558	—	2	1	no	—
56	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
57	C₂×#13083558	C₂×C₄	1	1	yes	characteristic
58	C₂×#13083557	—	2	2	no	—
59	C₂×#13083557	—	2	2	no	—
60	C₂×#13083557	—	4	4	no	—
61	C₂²×#10623494	D₄	1	1	yes	characteristic
62	C₂²×#10623494	D₄	1	1	yes	characteristic
63	C₄×D₃₅₆	—	2	1	no	—
64	C₄×D₃₅₆	—	2	1	no	—
65	C₄×D₃₅₆	C₂×C₄	1	2	yes	—
66	C₄×D₃₅₆	C₂³	1	2	yes	—
67	C₂×C₄⋊Dic₈₉	C₂×C₄	1	1	yes	characteristic
68	C₂×#13083551	—	2	1	no	—
69	#15667945	C₂×C₄	1	2	yes	—
70	#15667943	C₂×C₄	1	2	yes	—
71	C₄⋊#10623494	—	2	1	no	—
72	C₄⋊#10623494	—	2	1	no	—
73	C₄⋊#10623494	C₂³	1	1	yes	characteristic
74	C₄⋊#10623494	C₂³	1	1	yes	characteristic
75	#15667936	C₂×C₄	1	2	yes	—
76	#15667933	C₂×C₄	1	2	yes	—
77	#15667932	C₂×C₄	1	2	yes	—
78	#15667932	C₂×C₄	1	2	yes	—
79	C₂²⋊#10623494	—	2	1	no	—
80	C₂²⋊#10623494	—	2	1	no	—
81	C₂²⋊#10623494	—	2	1	no	—
82	#15667924	—	2	2	no	—
83	#15667924	—	2	2	no	—
84	#15667923	—	2	1	no	—
85	#15667923	—	2	1	no	—
86	#15667923	C₂×C₄	1	2	yes	—
87	C₄×#10623494	—	2	1	no	—
88	C₄×#10623494	D₄	1	1	yes	characteristic
89	C₄×#10623494	D₄	1	1	yes	characteristic
90	C₄×#10623494	C₂³	1	2	yes	—
91	C₄×#10623494	C₂³	1	1	yes	characteristic
92	C₄×#10623494	C₂³	1	1	yes	characteristic
93	C₂×#41×C₈₉	C₂×C₄	1	1	yes	characteristic
94	C₂²×C₈×C₈₉	—	2	1	no	—
95	C₄×Q₈×C₈₉	C₂×C₄	1	1	yes	characteristic
96	C₄×Q₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₈₉	—	2	1	no	—
98	C₄×D₄×C₈₉	—	2	1	no	—
99	C₄×D₄×C₈₉	C₂×C₄	1	1	yes	characteristic
100	C₄×D₄×C₈₉	C₂³	1	1	yes	characteristic
101	#117×C₈₉	—	2	1	no	—
102	#117×C₈₉	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₈₉	—	2	1	no	—
104	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₈₉	—	2	1	no	—
106	C₄⋊C₈×C₈₉	—	2	1	no	—
107	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
108	C₂²⋊C₈×C₈₉	—	2	1	no	—
109	C₄×C₈×C₈₉	C₂³	1	2	yes	—
110	C₂³×D₈₉	—	2	1	no	—
111	C₂×D₃₅₆	—	2	2	no	—
112	C₂×D₃₅₆	—	2	2	no	—
113	C₂×D₃₅₆	—	2	1	no	—
114	C₂×D₃₅₆	C₂²×C₄	1	2	yes	—
115	C₂²×Dic₈₉	—	2	1	no	—
116	C₂×C₄×D₈₉	—	2	2	no	—
117	C₂×C₄×D₈₉	—	2	2	no	—
118	C₂×C₄×D₈₉	—	4	2	no	—
119	C₂×C₄×D₈₉	—	4	2	no	—
120	#13083561	—	2	4	no	—
121	#13083559	—	2	4	no	—
122	#13083558	—	2	2	no	—
123	#13083558	—	4	2	no	—
124	#13083558	—	4	2	no	—
125	#13083558	M₁₆	1	4	yes	complemented
126	#13083557	—	4	4	no	—
127	#13083557	—	4	4	no	—
128	C₂×#10623494	—	2	2	no	—
129	C₂×#10623494	—	2	1	no	—
130	C₂×#10623494	—	2	1	no	—
131	C₂×#10623494	—	4	1	no	—
132	C₂×#10623494	C₂²×C₄	1	2	yes	—
133	C₂×#10623494	C₂²×C₄	1	2	yes	—
134	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
135	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
136	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
137	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
138	C₄⋊Dic₈₉	—	2	1	no	—
139	C₄⋊Dic₈₉	C₂²×C₄	1	2	yes	—
140	#13083551	—	2	2	no	—
141	#13083551	—	2	2	no	—
142	#41×C₈₉	—	2	2	no	—
143	#41×C₈₉	—	2	2	no	—
144	C₂×Q₈×C₈₉	C₂²×C₄	1	1	yes	characteristic
145	C₂×D₄×C₈₉	—	2	1	no	—
146	C₂×D₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	—	2	1	no	—
148	C₂²×C₄×C₈₉	—	2	1	no	—
149	C₂²×C₄×C₈₉	—	2	1	no	—
150	C₂²×C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
153	C₂×C₈×C₈₉	—	2	2	no	—
154	C₂×C₈×C₈₉	—	2	2	no	—
155	C₂×C₈×C₈₉	—	4	2	no	—
156	C₄⋊C₄×C₈₉	—	2	1	no	—
157	C₄⋊C₄×C₈₉	—	2	1	no	—
158	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
159	C₄⋊C₄×C₈₉	C₂²×C₄	1	1	yes	characteristic
160	C₂²⋊C₄×C₈₉	—	2	1	no	—
161	C₂²⋊C₄×C₈₉	—	2	1	no	—
162	C₂²⋊C₄×C₈₉	—	2	1	no	—
163	C₄²×C₈₉	—	2	1	no	—
164	C₄²×C₈₉	—	2	1	no	—
165	C₄²×C₈₉	—	2	1	no	—
166	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
167	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₈₉	#41	1	1	yes	characteristic
169	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
170	C₂³×C₈₉	—	2	1	no	—
171	C₂³×C₈₉	C₄×D₄	1	1	yes	characteristic
172	C₂²×D₈₉	—	2	2	no	—
173	C₂²×D₈₉	—	4	2	no	—
174	C₂²×D₈₉	—	4	2	no	—
175	C₂²×D₈₉	—	4	2	no	—
176	Q₈×C₈₉	—	2	1	no	—
177	Q₈×C₈₉	—	2	1	no	—
178	D₄×C₈₉	—	2	1	no	—
179	D₄×C₈₉	—	2	1	no	—
180	D₄×C₈₉	—	4	2	no	—
181	C₂×C₄×C₈₉	—	2	1	no	—
182	C₂×C₄×C₈₉	—	2	1	no	—
183	C₂×C₄×C₈₉	—	2	1	no	—
184	C₂×C₄×C₈₉	—	2	1	no	—
185	C₂×C₄×C₈₉	—	2	1	no	—
186	C₂×C₄×C₈₉	—	4	1	no	—
187	C₂×C₄×C₈₉	—	4	2	no	—
188	C₂×C₄×C₈₉	—	4	1	no	—
189	C₂×C₄×C₈₉	—	4	1	no	—
190	C₂×C₄×C₈₉	—	4	2	no	—
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	C₂×M₁₆	1	2	yes	—
195	C₂×C₄×C₈₉	#131	1	2	yes	—
196	C₂×C₄×C₈₉	C₂³×C₄	1	1	yes	characteristic
197	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
199	C₂×Dic₈₉	—	2	2	no	—
200	C₂×Dic₈₉	—	4	2	no	—
201	D₃₅₆	—	2	2	no	—
202	D₃₅₆	—	2	2	no	—
203	D₃₅₆	—	4	2	no	—
204	C₄×D₈₉	—	4	4	no	—
205	C₄×D₈₉	—	4	2	no	—
206	C₄×D₈₉	—	4	2	no	—
207	C₈×C₈₉	—	4	2	no	—
208	C₈×C₈₉	—	4	2	no	—
209	#10623494	—	2	2	no	—
210	#10623494	—	2	1	no	—
211	#10623494	—	2	1	no	—
212	#10623494	—	2	1	no	—
213	#10623494	—	4	1	no	—
214	#10623494	—	4	1	no	—
215	#10623494	C₂×M₁₆	1	4	yes	complemented
216	#10623494	AGL(1,ℤ/8)	1	2	yes	complemented
217	C₂²×C₈₉	—	2	1	no	—
218	C₂²×C₈₉	—	2	1	no	—
219	C₂²×C₈₉	—	4	1	no	—
220	C₂²×C₈₉	—	4	1	no	—
221	C₂²×C₈₉	—	4	1	no	—
222	C₂²×C₈₉	#436	1	2	yes	—
223	C₂²×C₈₉	C₂×C₄×D₄	1	1	yes	characteristic
224	C₂×D₈₉	—	4	2	no	—
225	C₂×D₈₉	—	4	2	no	—
226	C₂×D₈₉	—	4	2	no	—
227	C₂×D₈₉	—	8	4	no	—
228	C₄×C₈₉	—	2	1	no	—
229	C₄×C₈₉	—	2	1	no	—
230	C₄×C₈₉	—	2	1	no	—
231	C₄×C₈₉	—	4	1	no	—
232	C₄×C₈₉	—	4	1	no	—
233	C₄×C₈₉	—	4	1	no	—
234	C₄×C₈₉	#436	1	2	yes	—
235	C₄×C₈₉	C₂²×M₁₆	1	1	yes	characteristic
236	C₄×C₈₉	C₂×#131	1	1	yes	characteristic
237	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
238	C₄×C₈₉	#575	1	1	yes	characteristic
239	Dic₈₉	—	4	2	no	—
240	#17891	—	89	1	no	maximal, Sylow
241	C₂×C₈₉	—	2	2	no	—
242	C₂×C₈₉	—	8	1	no	—
243	C₂×C₈₉	C₂×#436	1	1	yes	characteristic
244	C₂×C₈₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
245	C₂×C₈₉	#2955	1	1	yes	characteristic
246	D₈₉	—	8	2	no	—
247	#2965	—	89	1	no	—
248	C₄×AGL(1,ℤ/8)	—	89	1	no	—
249	C₂×#436	—	89	1	no	—
250	#1594	—	89	2	no	—
251	#1592	—	89	2	no	—
252	#1590	—	89	2	no	—
253	#1589	—	89	2	no	—
254	#1565	—	89	1	no	—
255	#1478	—	89	1	no	—
256	#1477	D₈₉	1	1	yes	characteristic, complemented
257	C₈×M₁₆	—	89	1	no	—
258	C₈₉	#17891	1	1	yes	characteristic, complemented, Sylow
259	C₂×AGL(1,ℤ/8)	—	89	1	no	—
260	C₂²×M₁₆	—	178	1	no	—
261	C₄×#41	C₂×D₈₉	1	1	yes	characteristic
262	C₂×C₄×D₄	—	89	1	no	—
263	#446	—	89	1	no	—
264	#446	—	89	1	no	—
265	#442	—	89	2	no	—
266	#440	—	89	2	no	—
267	C₄×SD₁₆	—	89	2	no	—
268	C₄×D₈	—	89	2	no	—
269	#436	—	89	1	no	—
270	#436	—	89	1	no	—
271	#436	—	89	2	no	—
272	#436	—	89	2	no	—
273	#436	—	178	1	no	—
274	#436	—	178	1	no	—
275	#435	—	178	1	no	—
276	#435	—	178	1	no	—
277	#431	—	89	1	no	—
278	#431	—	178	1	no	—
279	#431	C₂×D₈₉	1	1	yes	characteristic
280	#428	—	89	1	no	—
281	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
282	#418	—	89	1	no	—
283	#417	—	89	1	no	—
284	C₂×C₂²⋊C₈	—	178	1	no	—
285	C₄×M₁₆	—	89	1	no	—
286	C₄×M₁₆	—	178	1	no	—
287	C₂×C₄×C₈	—	89	1	no	—
288	#335	—	89	2	no	—
289	#334	—	89	2	no	—
290	Q₈⋊C₈	C₂×D₈₉	1	2	yes	complemented
291	D₄⋊C₈	—	89	2	no	—
292	D₄⋊C₈	—	89	2	no	—
293	D₄⋊C₈	C₂×D₈₉	1	2	yes	complemented
294	#322	—	89	2	no	—
295	C₈²	—	89	2	no	—
296	C₂×#41	C₄×D₈₉	1	1	yes	characteristic
297	C₂²×D₄	—	89	1	no	—
298	C₂³×C₄	—	178	1	no	—
299	AGL(1,ℤ/8)	—	178	4	no	—
300	C₂×SD₁₆	—	89	2	no	—
301	C₂×D₈	—	89	2	no	—
302	C₂×M₁₆	—	89	1	no	—
303	C₂×M₁₆	—	89	1	no	—
304	C₂×M₁₆	—	356	4	no	—
305	C₂×M₁₆	—	178	2	no	—
306	C₂×M₁₆	—	178	2	no	—
307	C₂×M₁₆	—	178	1	no	—
308	C₂×M₁₆	—	178	1	no	—
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	—	89	1	no	—
311	C₂²×C₈	—	89	1	no	—
312	C₄×Q₈	C₄×D₈₉	1	1	yes	characteristic
313	C₄×Q₈	C₂²×D₈₉	1	1	yes	characteristic
314	C₄×D₄	—	2	1	no	—
315	C₄×D₄	—	2	1	no	—
316	C₄×D₄	—	89	2	no	—
317	C₄×D₄	—	89	2	no	—
318	C₄×D₄	—	178	1	no	—
319	C₄×D₄	—	178	1	no	—
320	C₄×D₄	C₄×D₈₉	1	1	yes	characteristic
321	C₄×D₄	C₂²×D₈₉	1	1	yes	characteristic
322	#117	—	2	1	no	—
323	#117	C₄×D₈₉	1	1	yes	characteristic
324	C₂×C₄⋊C₄	—	89	1	no	—
325	C₂×C₂²⋊C₄	—	178	1	no	—
326	C₂×C₄²	—	2	1	no	—
327	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
328	#107	—	89	2	no	—
329	#106	—	89	2	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	2	1	no	—
332	C₄⋊C₈	—	89	1	no	—
333	C₄⋊C₈	—	89	1	no	—
334	C₄⋊C₈	—	178	1	no	—
335	C₄⋊C₈	—	178	1	no	—
336	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
337	#103	—	89	2	no	—
338	#102	—	89	2	no	—
339	#102	—	89	2	no	—
340	#102	—	89	2	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	178	2	no	—
343	C₂²⋊C₈	—	178	2	no	—
344	C₂²⋊C₈	—	178	1	no	—
345	C₂²⋊C₈	—	178	1	no	—
346	C₂²⋊C₈	—	178	1	no	—
347	#97	—	89	2	no	—
348	#97	—	178	1	no	—
349	#97	—	178	1	no	—
350	C₄×C₈	—	89	1	no	—
351	C₄×C₈	—	89	1	no	—
352	C₄×C₈	—	89	1	no	—
353	C₄×C₈	—	89	2	no	—
354	C₄×C₈	—	89	1	no	—
355	C₄×C₈	—	178	1	no	—
356	C₄×C₈	C₂²×D₈₉	1	2	yes	—
357	C₂⁴	—	178	1	no	—
358	#41	—	2	2	no	—
359	#41	—	2	2	no	—
360	C₂×Q₈	C₂×C₄×D₈₉	1	1	yes	characteristic
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	89	2	no	—
363	C₂×D₄	—	178	1	no	—
364	C₂×D₄	—	178	2	no	—
365	C₂×D₄	—	178	2	no	—
366	C₂×D₄	C₂×C₄×D₈₉	1	1	yes	characteristic
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	356	2	no	—
371	C₂²×C₄	—	356	2	no	—
372	C₂²×C₄	—	178	1	no	—
373	C₂²×C₄	—	178	2	no	—
374	C₂²×C₄	—	178	2	no	—
375	C₂²×C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
376	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
377	C₂²×C₄	#13083573	1	1	yes	characteristic
378	SD₁₆	—	178	4	no	—
379	D₈	—	178	4	no	—
380	M₁₆	—	89	4	no	—
381	M₁₆	—	356	4	no	—
382	M₁₆	—	356	4	no	—
383	M₁₆	—	356	2	no	—
384	M₁₆	—	356	2	no	—
385	M₁₆	—	178	2	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	2	2	no	—
388	C₂×C₈	—	4	2	no	—
389	C₂×C₈	—	89	2	no	—
390	C₂×C₈	—	89	1	no	—
391	C₂×C₈	—	89	2	no	—
392	C₂×C₈	—	89	1	no	—
393	C₂×C₈	—	89	1	no	—
394	C₂×C₈	—	89	1	no	—
395	C₂×C₈	—	356	1	no	—
396	C₂×C₈	—	178	2	no	—
397	C₂×C₈	—	178	1	no	—
398	C₂×C₈	—	178	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	89	2	no	—
402	C₄⋊C₄	—	178	1	no	—
403	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
404	C₄⋊C₄	C₂×C₄×D₈₉	1	1	yes	characteristic
405	C₂²⋊C₄	—	2	1	no	—
406	C₂²⋊C₄	—	2	1	no	—
407	C₂²⋊C₄	—	2	1	no	—
408	C₂²⋊C₄	—	178	2	no	—
409	C₂²⋊C₄	—	178	2	no	—
410	C₄²	—	2	1	no	—
411	C₄²	—	2	1	no	—
412	C₄²	—	2	1	no	—
413	C₄²	C₂×C₄×D₈₉	1	1	yes	characteristic
414	C₄²	D₄×D₈₉	1	1	yes	characteristic
415	C₄²	#13083573	1	1	yes	characteristic
416	C₄²	C₂³×D₈₉	1	1	yes	characteristic
417	C₂³	—	2	1	no	—
418	C₂³	—	356	2	no	—
419	C₂³	—	356	2	no	—
420	C₂³	—	356	2	no	—
421	C₂³	—	178	2	no	—
422	C₂³	#15667972	1	1	yes	characteristic
423	Q₈	—	2	1	no	—
424	Q₈	—	2	1	no	—
425	D₄	—	2	1	no	—
426	D₄	—	2	1	no	—
427	D₄	—	4	2	no	—
428	D₄	—	356	2	no	—
429	D₄	—	178	2	no	—
430	D₄	—	178	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	356	4	no	—
442	C₂×C₄	—	356	2	no	—
443	C₂×C₄	—	356	2	no	—
444	C₂×C₄	—	356	2	no	—
445	C₂×C₄	—	178	2	no	—
446	C₂×C₄	#15667972	1	1	yes	characteristic
447	C₂×C₄	#15667972	1	1	yes	characteristic
448	C₂×C₄	#15667972	1	1	yes	characteristic
449	C₂×C₄	M₁₆×D₈₉	1	2	yes	—
450	C₂×C₄	#15668018	1	2	yes	—
451	C₂×C₄	C₂²×C₄×D₈₉	1	1	yes	characteristic
452	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
453	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
454	C₈	—	4	2	no	—
455	C₈	—	4	2	no	—
456	C₈	—	89	4	no	—
457	C₈	—	89	2	no	—
458	C₈	—	356	1	no	—
459	C₈	—	356	1	no	—
460	C₈	—	178	1	no	—
461	C₈	—	178	1	no	—
462	C₈	—	178	2	no	—
463	C₈	—	178	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	4	1	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	356	2	no	—
470	C₂²	—	356	2	no	—
471	C₂²	—	356	2	no	—
472	C₂²	—	712	4	no	—
473	C₂²	#19151673	1	2	yes	—
474	C₂²	C₂×#15667972	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	4	1	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	356	2	no	—
482	C₄	#19151673	1	2	yes	—
483	C₄	C₂×M₁₆×D₈₉	1	1	yes	characteristic
484	C₄	C₂×#15668018	1	1	yes	characteristic
485	C₄	AGL(1,ℤ/8)×D₈₉	1	1	yes	characteristic
486	C₄	#19152397	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	8	1	no	—
489	C₂	—	712	2	no	—
490	C₂	C₂×#19151673	1	1	yes	characteristic
491	C₂	#26029065	1	1	yes	characteristic
492	C₂	#26029151	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₈₉
commutator	C₂×C₄×C₈₉	C₂³×C₄
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1477	C₂
socle	C₂²×C₈₉	C₂×C₄×D₄
prime radical	C₂×#15668037	C₄
cosocle	C₄²×C₈₉	C₂⁴
hypercenter	#1477	D₈₉
hypocenter	C₈₉	#17891
LCS	G ▷ C₂×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1477

Complements

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

N	H ≅ G/N	type
1. #26029219	C₂	semidirect
3. C₂×#19151675	C₂	semidirect
4. #26019163	C₂	semidirect
5. #26019157	C₂	semidirect
6. #26019139	C₂	semidirect
7. #26019134	C₂	semidirect
8. #26019002	C₂	semidirect
9. #26018644	C₂	semidirect
10. #26018533	C₂	semidirect
11. C₈₉×#1477	C₂	semidirect
15. #19151729	C₂²	semidirect
16. #19151729	C₂²	semidirect
21. #19151676	C₂²	semidirect
22. #19151676	C₂²	semidirect
38. #19151350	C₂²	semidirect
39. #19151348	C₂²	semidirect
42. #19151320	C₂²	semidirect
43. C₈×#10623494	C₂²	semidirect
47. Q₈⋊C₈×C₈₉	C₂²	semidirect
48. D₄⋊C₈×C₈₉	C₂²	semidirect
125. #13083558	M₁₆	semidirect
215. #10623494	C₂×M₁₆	semidirect
216. #10623494	AGL(1,ℤ/8)	semidirect
256. #1477	D₈₉	semidirect
258. C₈₉	#17891	semidirect
290. Q₈⋊C₈	C₂×D₈₉	semidirect
293. D₄⋊C₈	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26029219	2
C₄×#15668037	2
C₂×#19151675	2
#26019163	2
#26019157	2
#26019139	2
#26019134	2
#26019002	2
#26018644	2
#26018533	2
C₈₉×#1477	2
#17891	89