Subgroups — #36538429

Order 22784.

712 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030045	C₂	1	1	yes	maximal, characteristic, complemented
2	#26029712	C₂	1	1	yes	maximal, characteristic
3	C₂×#19151677	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019796	C₂	1	2	yes	maximal, complemented
5	#26019782	C₂	1	2	yes	maximal, complemented
6	#26019748	C₂	1	2	yes	maximal, complemented
7	#26019714	C₂	1	2	yes	maximal, complemented
8	#26019011	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018942	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018929	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668037	—	2	1	no	—
13	C₂²×#13083557	—	2	1	no	—
14	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
15	#19151895	—	2	2	no	—
16	#19151885	C₂²	1	2	yes	—
17	#19151875	C₂²	1	2	yes	—
18	#19151810	—	2	2	no	—
19	#19151800	C₂²	1	2	yes	—
20	#19151790	C₂²	1	2	yes	—
21	#19151677	—	2	1	no	—
22	#19151677	—	2	1	no	—
23	#19151677	C₂²	1	2	yes	—
24	#19151677	C₂²	1	2	yes	—
25	#19151641	—	2	1	no	—
26	#19151622	C₂²	1	1	yes	characteristic
27	#19151622	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
29	#19151602	—	2	1	no	—
30	#19151599	—	2	1	no	—
31	C₂×#15667924	—	2	1	no	—
32	#19151351	C₂²	1	2	yes	complemented
33	#19151351	C₂²	1	2	yes	complemented
34	#19151347	C₂²	1	2	yes	complemented
35	#19151344	C₂²	1	2	yes	complemented
36	#19151344	C₂²	1	2	yes	complemented
37	#19151342	C₂²	1	2	yes	complemented
38	#533×C₈₉	C₂²	1	1	yes	characteristic
39	#532×C₈₉	C₂²	1	1	yes	characteristic
40	#498×C₈₉	C₂²	1	1	yes	characteristic, complemented
41	#492×C₈₉	C₂²	1	1	yes	characteristic, complemented
42	#487×C₈₉	C₂²	1	1	yes	characteristic, complemented
43	#486×C₈₉	C₂²	1	1	yes	characteristic, complemented
44	#465×C₈₉	—	2	1	no	—
45	#465×C₈₉	—	2	1	no	—
46	C₄×SD₁₆×C₈₉	—	2	1	no	—
47	C₄×SD₁₆×C₈₉	—	2	1	no	—
48	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂²×D₃₅₆	D₄	1	1	yes	characteristic
50	C₂²×C₄×D₈₉	—	2	1	no	—
51	#15668037	—	4	4	no	—
52	C₂×#13083561	—	2	2	no	—
53	C₂×#13083559	—	2	2	no	—
54	C₂×#13083558	—	2	1	no	—
55	C₂×#13083558	—	2	1	no	—
56	C₂×#13083557	—	2	2	no	—
57	C₂×#13083557	—	2	2	no	—
58	C₂×#13083557	—	4	4	no	—
59	C₂²×#10623494	—	2	1	no	—
60	C₄×D₃₅₆	—	2	1	no	—
61	C₄×D₃₅₆	—	2	1	no	—
62	C₄×D₃₅₆	D₄	1	2	yes	—
63	C₄×D₃₅₆	C₂³	1	2	yes	—
64	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
65	C₂×#13083551	—	2	1	no	—
66	#15667945	—	2	2	no	—
67	#15667943	—	2	2	no	—
68	C₄⋊#10623494	—	2	1	no	—
69	C₄⋊#10623494	—	2	1	no	—
70	C₄⋊#10623494	—	2	1	no	—
71	C₄⋊#10623494	C₂³	1	2	yes	—
72	C₄⋊#10623494	C₂³	1	2	yes	—
73	C₄⋊#10623494	C₂³	1	2	yes	—
74	#15667936	—	2	2	no	—
75	#15667933	—	2	2	no	—
76	#15667932	—	2	2	no	—
77	#15667932	—	2	2	no	—
78	#15667924	—	2	2	no	—
79	#15667924	—	2	2	no	—
80	C₂×#41×C₈₉	—	2	1	no	—
81	C₂×SD₁₆×C₈₉	—	2	1	no	—
82	C₂×SD₁₆×C₈₉	—	2	1	no	—
83	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
84	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
85	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
86	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
87	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
88	#127×C₈₉	C₂³	1	1	yes	characteristic
89	#125×C₈₉	—	2	1	no	—
90	#124×C₈₉	—	2	1	no	—
91	C₂²⋊Q₈×C₈₉	—	2	1	no	—
92	C₂²⋊Q₈×C₈₉	—	2	1	no	—
93	#121×C₈₉	—	2	1	no	—
94	#121×C₈₉	—	2	1	no	—
95	C₄×Q₈×C₈₉	—	2	1	no	—
96	C₄×Q₈×C₈₉	—	2	1	no	—
97	C₄×D₄×C₈₉	—	2	1	no	—
98	C₄×D₄×C₈₉	—	2	1	no	—
99	#117×C₈₉	—	2	1	no	—
100	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
101	#106×C₈₉	—	2	1	no	—
102	#106×C₈₉	—	2	1	no	—
103	#103×C₈₉	—	2	1	no	—
104	#103×C₈₉	—	2	1	no	—
105	#102×C₈₉	—	2	1	no	—
106	#102×C₈₉	—	2	1	no	—
107	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
108	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
109	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
111	C₂³×D₈₉	—	2	1	no	—
112	C₂×D₃₅₆	—	2	2	no	—
113	C₂×D₃₅₆	—	2	2	no	—
114	C₂×D₃₅₆	—	2	1	no	—
115	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
116	C₂²×Dic₈₉	—	2	1	no	—
117	C₂×C₄×D₈₉	—	2	2	no	—
118	C₂×C₄×D₈₉	—	2	2	no	—
119	C₂×C₄×D₈₉	—	4	2	no	—
120	C₂×C₄×D₈₉	—	4	2	no	—
121	#13083561	—	4	4	no	—
122	#13083559	—	4	4	no	—
123	#13083558	—	4	2	no	—
124	#13083558	—	4	2	no	—
125	#13083557	—	4	4	no	—
126	#13083557	—	4	4	no	—
127	C₂×#10623494	—	2	2	no	—
128	C₂×#10623494	—	2	2	no	—
129	C₂×#10623494	—	2	2	no	—
130	C₂×#10623494	—	4	2	no	—
131	C₄⋊Dic₈₉	—	2	1	no	—
132	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
133	#13083551	—	2	2	no	—
134	#13083551	—	2	2	no	—
135	#41×C₈₉	—	4	2	no	—
136	#41×C₈₉	—	4	2	no	—
137	C₂×Q₈×C₈₉	—	2	1	no	—
138	C₂×Q₈×C₈₉	—	2	1	no	—
139	C₂×Q₈×C₈₉	—	2	1	no	—
140	C₂×D₄×C₈₉	—	2	1	no	—
141	C₂×D₄×C₈₉	—	2	1	no	—
142	C₂×D₄×C₈₉	—	2	1	no	—
143	C₂×D₄×C₈₉	—	4	1	no	—
144	C₂²×C₄×C₈₉	—	4	1	no	—
145	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
148	SD₁₆×C₈₉	—	4	2	no	—
149	SD₁₆×C₈₉	—	4	2	no	—
150	C₂×C₈×C₈₉	—	2	2	no	—
151	C₂×C₈×C₈₉	—	4	1	no	—
152	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₄⋊C₄×C₈₉	—	2	1	no	—
157	C₄⋊C₄×C₈₉	—	2	1	no	—
158	C₄⋊C₄×C₈₉	—	2	1	no	—
159	C₄⋊C₄×C₈₉	—	2	1	no	—
160	C₄⋊C₄×C₈₉	—	2	1	no	—
161	C₄⋊C₄×C₈₉	—	2	1	no	—
162	C₄⋊C₄×C₈₉	—	4	1	no	—
163	C₄⋊C₄×C₈₉	—	4	1	no	—
164	C₂²⋊C₄×C₈₉	—	4	1	no	—
165	C₂²⋊C₄×C₈₉	—	4	1	no	—
166	C₂²⋊C₄×C₈₉	—	4	1	no	—
167	C₄²×C₈₉	—	4	1	no	—
168	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
170	C₄²×C₈₉	#41	1	1	yes	characteristic
171	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
172	C₂³×C₈₉	—	4	1	no	—
173	C₂³×C₈₉	#121	1	1	yes	characteristic
174	C₂²×D₈₉	—	2	2	no	—
175	C₂²×D₈₉	—	4	2	no	—
176	C₂²×D₈₉	—	4	2	no	—
177	C₂²×D₈₉	—	4	2	no	—
178	Q₈×C₈₉	—	4	1	no	—
179	Q₈×C₈₉	—	4	1	no	—
180	Q₈×C₈₉	—	4	1	no	—
181	Q₈×C₈₉	—	4	1	no	—
182	Q₈×C₈₉	—	8	1	no	—
183	D₄×C₈₉	—	4	1	no	—
184	D₄×C₈₉	—	4	1	no	—
185	D₄×C₈₉	—	4	1	no	—
186	D₄×C₈₉	—	4	1	no	—
187	D₄×C₈₉	—	8	1	no	—
188	D₄×C₈₉	—	8	2	no	—
189	C₂×C₄×C₈₉	—	2	1	no	—
190	C₂×C₄×C₈₉	—	2	1	no	—
191	C₂×C₄×C₈₉	—	4	1	no	—
192	C₂×C₄×C₈₉	—	4	1	no	—
193	C₂×C₄×C₈₉	—	4	1	no	—
194	C₂×C₄×C₈₉	—	4	1	no	—
195	C₂×C₄×C₈₉	—	8	2	no	—
196	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
197	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
198	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
199	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
200	C₂×C₄×C₈₉	#137	1	2	yes	—
201	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
203	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
204	C₂×Dic₈₉	—	2	2	no	—
205	C₂×Dic₈₉	—	4	2	no	—
206	D₃₅₆	—	2	2	no	—
207	D₃₅₆	—	2	2	no	—
208	D₃₅₆	—	4	2	no	—
209	C₄×D₈₉	—	4	4	no	—
210	C₄×D₈₉	—	4	2	no	—
211	C₄×D₈₉	—	4	2	no	—
212	C₈×C₈₉	—	2	1	no	—
213	C₈×C₈₉	—	2	1	no	—
214	C₈×C₈₉	—	2	1	no	—
215	C₈×C₈₉	AGL(1,ℤ/8)	1	2	yes	complemented
216	#10623494	—	4	2	no	—
217	#10623494	—	4	2	no	—
218	#10623494	—	4	2	no	—
219	C₂²×C₈₉	—	2	1	no	—
220	C₂²×C₈₉	—	2	1	no	—
221	C₂²×C₈₉	—	8	1	no	—
222	C₂²×C₈₉	—	8	1	no	—
223	C₂²×C₈₉	—	8	1	no	—
224	C₂²×C₈₉	#468	1	2	yes	—
225	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
226	C₂×D₈₉	—	4	2	no	—
227	C₂×D₈₉	—	4	2	no	—
228	C₂×D₈₉	—	4	2	no	—
229	C₂×D₈₉	—	8	4	no	—
230	C₄×C₈₉	—	2	1	no	—
231	C₄×C₈₉	—	2	1	no	—
232	C₄×C₈₉	—	2	1	no	—
233	C₄×C₈₉	—	8	1	no	—
234	C₄×C₈₉	—	8	1	no	—
235	C₄×C₈₉	—	8	1	no	—
236	C₄×C₈₉	#468	1	2	yes	—
237	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
238	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
239	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
240	C₄×C₈₉	#575	1	1	yes	characteristic
241	Dic₈₉	—	4	2	no	—
242	#19279	—	89	1	no	maximal, Sylow
243	C₂×C₈₉	—	2	2	no	—
244	C₂×C₈₉	—	16	1	no	—
245	C₂×C₈₉	#3036	1	1	yes	characteristic
246	C₂×C₈₉	C₂×#468	1	1	yes	characteristic
247	C₂×C₈₉	#3067	1	1	yes	characteristic
248	D₈₉	—	8	2	no	—
249	#3167	D₈₉	1	1	yes	characteristic, complemented
250	#3077	—	89	1	no	—
251	#3036	—	89	1	no	—
252	C₂×#436	—	89	1	no	—
253	#1699	—	89	2	no	—
254	#1697	—	89	2	no	—
255	#1691	—	89	2	no	—
256	#1685	—	89	2	no	—
257	#1567	—	89	1	no	—
258	#1550	—	89	1	no	—
259	#1547	—	89	1	no	—
260	C₈₉	#19279	1	1	yes	characteristic, complemented, Sylow
261	C₂×AGL(1,ℤ/8)	—	178	1	no	—
262	C₂²×M₁₆	—	178	1	no	—
263	#533	C₂×D₈₉	1	1	yes	characteristic
264	#532	C₂×D₈₉	1	1	yes	characteristic
265	C₂×C₄×D₄	—	89	1	no	—
266	#498	C₂×D₈₉	1	1	yes	characteristic, complemented
267	#492	C₂×D₈₉	1	1	yes	characteristic, complemented
268	#487	C₂×D₈₉	1	1	yes	characteristic, complemented
269	#486	C₂×D₈₉	1	1	yes	characteristic, complemented
270	#478	—	178	2	no	—
271	#476	—	89	2	no	—
272	#474	—	89	2	no	—
273	#465	—	2	1	no	—
274	#465	—	2	1	no	—
275	#463	—	178	2	no	—
276	#461	—	89	2	no	—
277	#459	—	89	2	no	—
278	C₄×SD₁₆	—	2	1	no	—
279	C₄×SD₁₆	—	2	1	no	—
280	#436	—	89	2	no	—
281	#436	—	89	2	no	—
282	#436	—	178	1	no	—
283	#436	—	178	1	no	—
284	#428	—	178	1	no	—
285	#423	—	89	1	no	—
286	#423	—	89	1	no	—
287	C₂×C₄⋊C₈	—	89	1	no	—
288	#418	—	178	1	no	—
289	#417	—	178	1	no	—
290	C₂×C₂²⋊C₈	—	178	1	no	—
291	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
292	#335	—	89	2	no	—
293	#335	—	89	2	no	—
294	#333	—	89	2	no	—
295	#332	—	89	2	no	—
296	#332	—	89	2	no	—
297	#331	—	89	2	no	—
298	C₂×#41	—	2	1	no	—
299	C₂²×D₄	—	89	1	no	—
300	C₂³×C₄	—	178	1	no	—
301	AGL(1,ℤ/8)	—	356	4	no	—
302	C₂×SD₁₆	—	2	1	no	—
303	C₂×SD₁₆	—	2	1	no	—
304	C₂×SD₁₆	—	178	2	no	—
305	C₂×D₈	—	178	2	no	—
306	C₂×M₁₆	—	356	4	no	—
307	C₂×M₁₆	—	178	1	no	—
308	C₂×M₁₆	—	178	1	no	—
309	C₂×M₁₆	—	178	2	no	—
310	C₂×M₁₆	—	178	2	no	—
311	C₂²×C₈	—	178	1	no	—
312	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
313	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
314	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
315	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
316	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
317	#127	C₂²×D₈₉	1	1	yes	characteristic
318	#125	—	2	1	no	—
319	#124	—	2	1	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	#121	—	2	1	no	—
323	#121	—	2	1	no	—
324	C₄×Q₈	—	2	1	no	—
325	C₄×Q₈	—	2	1	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	—	89	2	no	—
329	C₄×D₄	—	89	2	no	—
330	C₄×D₄	—	178	1	no	—
331	C₄×D₄	—	178	1	no	—
332	#117	—	2	1	no	—
333	C₂×C₄⋊C₄	—	89	1	no	—
334	C₂×C₂²⋊C₄	—	178	1	no	—
335	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
336	#107	—	178	2	no	—
337	#106	—	2	1	no	—
338	#106	—	2	1	no	—
339	#106	—	178	2	no	—
340	C₄⋊C₈	—	89	2	no	—
341	C₄⋊C₈	—	89	2	no	—
342	C₄⋊C₈	—	89	2	no	—
343	C₄⋊C₈	—	178	1	no	—
344	C₄⋊C₈	—	178	1	no	—
345	C₄⋊C₈	—	178	1	no	—
346	#103	—	2	1	no	—
347	#103	—	2	1	no	—
348	#103	—	178	2	no	—
349	#102	—	2	1	no	—
350	#102	—	2	1	no	—
351	#102	—	178	2	no	—
352	#102	—	178	2	no	—
353	#102	—	178	2	no	—
354	C₂²⋊C₈	—	178	2	no	—
355	C₂²⋊C₈	—	178	2	no	—
356	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
357	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
358	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
359	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
360	C₂⁴	—	178	1	no	—
361	#41	—	4	2	no	—
362	#41	—	4	2	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	—	2	1	no	—
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	1	no	—
368	C₂×D₄	—	2	1	no	—
369	C₂×D₄	—	4	1	no	—
370	C₂×D₄	—	89	2	no	—
371	C₂×D₄	—	178	1	no	—
372	C₂×D₄	—	178	2	no	—
373	C₂×D₄	—	178	2	no	—
374	C₂²×C₄	—	4	1	no	—
375	C₂²×C₄	—	356	2	no	—
376	C₂²×C₄	—	356	2	no	—
377	C₂²×C₄	—	178	1	no	—
378	C₂²×C₄	—	178	2	no	—
379	C₂²×C₄	—	178	2	no	—
380	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
382	C₂²×C₄	#13083573	1	1	yes	characteristic
383	SD₁₆	—	4	2	no	—
384	SD₁₆	—	4	2	no	—
385	SD₁₆	—	356	4	no	—
386	D₈	—	356	4	no	—
387	M₁₆	—	356	4	no	—
388	M₁₆	—	356	2	no	—
389	M₁₆	—	356	2	no	—
390	M₁₆	—	356	4	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	4	1	no	—
393	C₂×C₈	—	356	2	no	—
394	C₂×C₈	—	178	2	no	—
395	C₂×C₈	—	178	2	no	—
396	C₂×C₈	—	178	2	no	—
397	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
398	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
399	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
400	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	4	1	no	—
408	C₄⋊C₄	—	4	1	no	—
409	C₄⋊C₄	—	89	2	no	—
410	C₄⋊C₄	—	178	1	no	—
411	C₂²⋊C₄	—	4	1	no	—
412	C₂²⋊C₄	—	4	1	no	—
413	C₂²⋊C₄	—	4	1	no	—
414	C₂²⋊C₄	—	178	2	no	—
415	C₂²⋊C₄	—	178	2	no	—
416	C₄²	—	4	1	no	—
417	C₄²	D₄×D₈₉	1	1	yes	characteristic
418	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
419	C₄²	#13083573	1	1	yes	characteristic
420	C₄²	C₂³×D₈₉	1	1	yes	characteristic
421	C₂³	—	4	1	no	—
422	C₂³	—	356	2	no	—
423	C₂³	—	356	2	no	—
424	C₂³	—	356	2	no	—
425	C₂³	—	178	2	no	—
426	C₂³	#15667983	1	1	yes	characteristic
427	Q₈	—	4	1	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	4	1	no	—
430	Q₈	—	4	1	no	—
431	Q₈	—	8	1	no	—
432	D₄	—	4	1	no	—
433	D₄	—	4	1	no	—
434	D₄	—	4	1	no	—
435	D₄	—	4	1	no	—
436	D₄	—	8	1	no	—
437	D₄	—	8	2	no	—
438	D₄	—	356	2	no	—
439	D₄	—	178	2	no	—
440	D₄	—	178	2	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	8	2	no	—
448	C₂×C₄	—	356	4	no	—
449	C₂×C₄	—	356	2	no	—
450	C₂×C₄	—	356	2	no	—
451	C₂×C₄	—	356	2	no	—
452	C₂×C₄	—	178	2	no	—
453	C₂×C₄	#15667983	1	1	yes	characteristic
454	C₂×C₄	#15667983	1	1	yes	characteristic
455	C₂×C₄	#15667983	1	1	yes	characteristic
456	C₂×C₄	#15668039	1	2	yes	—
457	C₂×C₄	#15668041	1	2	yes	—
458	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
459	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
460	C₂×C₄	C₂×#13083573	1	1	yes	characteristic
461	C₈	—	2	1	no	—
462	C₈	—	2	1	no	—
463	C₈	—	2	1	no	—
464	C₈	—	356	2	no	—
465	C₈	—	356	2	no	—
466	C₈	—	356	2	no	—
467	C₈	#15668037	1	2	yes	complemented
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	8	1	no	—
471	C₂²	—	8	1	no	—
472	C₂²	—	8	1	no	—
473	C₂²	—	356	2	no	—
474	C₂²	—	356	2	no	—
475	C₂²	—	356	2	no	—
476	C₂²	—	712	4	no	—
477	C₂²	#19151841	1	2	yes	—
478	C₂²	C₂×#15667983	1	1	yes	characteristic
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	2	1	no	—
482	C₄	—	8	1	no	—
483	C₄	—	8	1	no	—
484	C₄	—	8	1	no	—
485	C₄	—	356	2	no	—
486	C₄	#19151841	1	2	yes	—
487	C₄	C₂×#15668037	1	1	yes	characteristic
488	C₄	C₂×#15668039	1	1	yes	characteristic
489	C₄	C₂×#15668041	1	1	yes	characteristic
490	C₄	#19152396	1	1	yes	characteristic
491	C₂	—	2	2	no	—
492	C₂	—	16	1	no	—
493	C₂	—	712	2	no	—
494	C₂	#26029712	1	1	yes	characteristic
495	C₂	C₂×#19151841	1	1	yes	characteristic
496	C₂	#26029968	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667983
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#3167	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#26029712	C₂
hypercenter	#3167	D₈₉
hypocenter	C₈₉	#19279
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3167

Complements

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

N	H ≅ G/N	type
1. #26030045	C₂	semidirect
3. C₂×#19151677	C₂	semidirect
4. #26019796	C₂	semidirect
5. #26019782	C₂	semidirect
6. #26019748	C₂	semidirect
7. #26019714	C₂	semidirect
8. #26019011	C₂	semidirect
9. #26018942	C₂	semidirect
10. #26018929	C₂	semidirect
11. C₈₉×#3167	C₂	semidirect
32. #19151351	C₂²	semidirect
33. #19151351	C₂²	semidirect
34. #19151347	C₂²	semidirect
35. #19151344	C₂²	semidirect
36. #19151344	C₂²	semidirect
37. #19151342	C₂²	semidirect
40. #498×C₈₉	C₂²	semidirect
41. #492×C₈₉	C₂²	semidirect
42. #487×C₈₉	C₂²	semidirect
43. #486×C₈₉	C₂²	semidirect
215. C₈×C₈₉	AGL(1,ℤ/8)	semidirect
249. #3167	D₈₉	semidirect
260. C₈₉	#19279	semidirect
266. #498	C₂×D₈₉	semidirect
267. #492	C₂×D₈₉	semidirect
268. #487	C₂×D₈₉	semidirect
269. #486	C₂×D₈₉	semidirect
467. C₈	#15668037	semidirect

Maximal subgroups

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

subgroup	index
#26030045	2
#26029712	2
C₂×#19151677	2
#26019796	2
#26019782	2
#26019748	2
#26019714	2
#26019011	2
#26018942	2
#26018929	2
C₈₉×#3167	2
#19279	89