Subgroups — #36537956

Order 22784.

704 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26031568	C₂	1	1	yes	maximal, characteristic, complemented
2	#26031167	C₂	1	1	yes	maximal, characteristic
3	#26030627	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019813	C₂	1	2	yes	maximal, complemented
5	#26019785	C₂	1	2	yes	maximal, complemented
6	#26019689	C₂	1	2	yes	maximal, complemented
7	#26019661	C₂	1	2	yes	maximal, complemented
8	#26019004	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018910	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#19151341	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2935	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152155	C₂²	1	1	yes	characteristic
13	C₂×#15668009	C₂²	1	1	yes	characteristic
14	#19151974	—	2	1	no	—
15	#19151963	—	2	2	no	—
16	#19151946	—	2	1	no	—
17	#19151945	C₂²	1	2	yes	—
18	#19151945	C₂²	1	2	yes	—
19	#19151888	C₂²	1	2	yes	complemented
20	#19151880	—	2	1	no	—
21	#19151825	—	2	2	no	—
22	#19151803	C₂²	1	2	yes	complemented
23	#19151795	—	2	1	no	—
24	#19151793	C₂²	1	2	yes	—
25	#19151793	C₂²	1	2	yes	—
26	#19151731	—	2	2	no	—
27	#19151651	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
29	#19151604	—	2	1	no	—
30	#19151604	—	2	1	no	—
31	#19151351	C₂²	1	2	yes	complemented
32	#19151349	C₂²	1	2	yes	complemented
33	#19151346	C₂²	1	1	yes	characteristic, complemented
34	#19151346	C₂²	1	1	yes	characteristic, complemented
35	#19151343	C₂²	1	1	yes	characteristic, complemented
36	#19151343	C₂²	1	1	yes	characteristic, complemented
37	#19151341	C₂²	1	2	yes	—
38	#19151341	C₂²	1	2	yes	—
39	C₂×#131×C₈₉	—	2	1	no	—
40	#532×C₈₉	C₂²	1	1	yes	characteristic
41	#436×C₈₉	C₂²	1	2	yes	complemented
42	#435×C₈₉	—	2	2	no	—
43	C₈×D₄×C₈₉	C₂²	1	2	yes	complemented
44	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
45	#408×C₈₉	—	2	1	no	—
46	C₄×M₁₆×C₈₉	C₂²	1	1	yes	characteristic
47	C₂²×D₃₅₆	—	2	1	no	—
48	C₂²×D₃₅₆	—	2	1	no	—
49	C₂²×D₃₅₆	—	2	1	no	—
50	C₂×#13083562	—	2	2	no	—
51	C₂×#13083559	—	2	2	no	—
52	C₂×#13083559	—	2	2	no	—
53	C₂²×#10623494	—	2	1	no	—
54	#15668012	C₂³	1	1	yes	characteristic
55	#15668012	C₂³	1	1	yes	characteristic
56	#15668009	—	2	1	no	—
57	#15668009	—	2	1	no	—
58	#15668009	—	2	1	no	—
59	#15668009	C₂³	1	2	yes	—
60	#15668004	—	2	1	no	—
61	#15667991	—	2	1	no	—
62	#15667991	—	2	1	no	—
63	C₄×Dic₁₇₈	—	2	1	no	—
64	C₄×Dic₁₇₈	—	2	1	no	—
65	#15667971	—	2	1	no	—
66	#15667943	—	2	2	no	—
67	C₄⋊#10623494	—	2	1	no	—
68	C₄⋊#10623494	C₂³	1	2	yes	—
69	C₄⋊#10623494	C₂³	1	1	yes	characteristic
70	C₄⋊#10623494	C₂³	1	1	yes	characteristic
71	#15667935	—	2	2	no	—
72	#15667934	—	2	2	no	—
73	#15667934	—	2	2	no	—
74	#15667934	—	2	2	no	—
75	#15667934	—	2	2	no	—
76	#15667933	—	2	2	no	—
77	#15667932	—	2	2	no	—
78	#15667932	—	2	2	no	—
79	C₂²⋊#10623494	—	2	1	no	—
80	C₄×#10623494	—	2	1	no	—
81	C₂×#41×C₈₉	—	2	1	no	—
82	#131×C₈₉	—	4	4	no	—
83	C₂×M₁₆×C₈₉	—	2	2	no	—
84	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
85	C₂×M₁₆×C₈₉	D₄	1	1	yes	characteristic
86	C₂²×C₈×C₈₉	—	2	1	no	—
87	C₂²×C₈×C₈₉	—	2	2	no	—
88	C₄⋊Q₈×C₈₉	D₄	1	1	yes	characteristic
89	#127×C₈₉	D₄	1	1	yes	characteristic
90	#124×C₈₉	—	2	1	no	—
91	#121×C₈₉	—	2	1	no	—
92	#121×C₈₉	D₄	1	2	yes	—
93	C₄×D₄×C₈₉	—	2	1	no	—
94	C₄×D₄×C₈₉	C₂³	1	2	yes	—
95	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₈₉	—	2	1	no	—
97	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₈₉	C₂³	1	1	yes	characteristic
99	C₂²⋊C₈×C₈₉	—	2	2	no	—
100	C₂²⋊C₈×C₈₉	—	2	2	no	—
101	#97×C₈₉	D₄	1	2	yes	—
102	C₄×C₈×C₈₉	C₂³	1	2	yes	—
103	C₂³×D₈₉	—	4	1	no	—
104	C₂×Dic₁₇₈	—	2	1	no	—
105	C₂×Dic₁₇₈	—	2	1	no	—
106	C₂×D₃₅₆	—	2	2	no	—
107	C₂×D₃₅₆	—	2	2	no	—
108	C₂×D₃₅₆	—	2	2	no	—
109	C₂×D₃₅₆	—	4	2	no	—
110	C₂×D₃₅₆	—	4	2	no	—
111	C₂×D₃₅₆	—	4	1	no	—
112	C₂×D₃₅₆	—	4	1	no	—
113	C₂×D₃₅₆	—	4	1	no	—
114	C₂×D₃₅₆	—	8	1	no	—
115	C₂×D₃₅₆	—	8	1	no	—
116	C₂×D₃₅₆	—	8	2	no	—
117	#13083562	—	8	2	no	—
118	#13083559	—	8	2	no	—
119	#13083559	—	8	2	no	—
120	C₂×#10623494	—	2	2	no	—
121	C₂×#10623494	—	2	1	no	—
122	C₂×#10623494	—	2	1	no	—
123	C₂×#10623494	—	8	1	no	—
124	C₄⋊Dic₈₉	—	2	1	no	—
125	C₄⋊Dic₈₉	—	2	1	no	—
126	C₄⋊Dic₈₉	—	2	1	no	—
127	C₄⋊Dic₈₉	—	2	1	no	—
128	#13083553	—	4	1	no	—
129	#13083553	—	4	1	no	—
130	C₂²⋊Dic₈₉	—	4	1	no	—
131	C₄×Dic₈₉	—	4	1	no	—
132	#41×C₈₉	—	4	2	no	—
133	#41×C₈₉	—	4	2	no	—
134	C₂×Q₈×C₈₉	—	2	1	no	—
135	C₂×D₄×C₈₉	—	2	2	no	—
136	C₂×D₄×C₈₉	—	2	1	no	—
137	C₂×D₄×C₈₉	—	2	1	no	—
138	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₈₉	—	2	2	no	—
140	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
142	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
143	M₁₆×C₈₉	—	2	2	no	—
144	M₁₆×C₈₉	—	2	2	no	—
145	M₁₆×C₈₉	—	4	4	no	—
146	C₂×C₈×C₈₉	—	2	1	no	—
147	C₂×C₈×C₈₉	—	2	1	no	—
148	C₂×C₈×C₈₉	—	4	4	no	—
149	C₂×C₈×C₈₉	—	4	2	no	—
150	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
151	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
152	C₄⋊C₄×C₈₉	—	2	1	no	—
153	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
154	C₂²⋊C₄×C₈₉	—	2	2	no	—
155	C₂²⋊C₄×C₈₉	—	2	2	no	—
156	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₈₉	#41	1	1	yes	characteristic
159	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
160	C₂³×C₈₉	—	2	2	no	—
161	C₂³×C₈₉	#121	1	1	yes	characteristic
162	C₂²×D₈₉	—	4	2	no	—
163	C₂²×D₈₉	—	8	2	no	—
164	C₂²×D₈₉	—	8	2	no	—
165	C₂²×D₈₉	—	8	2	no	—
166	Q₈×C₈₉	—	4	2	no	—
167	D₄×C₈₉	—	2	2	no	—
168	D₄×C₈₉	—	2	2	no	—
169	D₄×C₈₉	—	4	4	no	—
170	D₄×C₈₉	—	4	2	no	—
171	D₄×C₈₉	—	8	1	no	—
172	C₂×C₄×C₈₉	—	2	1	no	—
173	C₂×C₄×C₈₉	—	2	1	no	—
174	C₂×C₄×C₈₉	—	2	2	no	—
175	C₂×C₄×C₈₉	—	4	1	no	—
176	C₂×C₄×C₈₉	—	4	2	no	—
177	C₂×C₄×C₈₉	—	4	2	no	—
178	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
179	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
180	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
181	C₂×C₄×C₈₉	#135	1	2	yes	—
182	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
183	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
186	C₂×Dic₈₉	—	4	1	no	—
187	C₂×Dic₈₉	—	4	1	no	—
188	D₃₅₆	—	4	2	no	—
189	D₃₅₆	—	4	2	no	—
190	D₃₅₆	—	4	2	no	—
191	D₃₅₆	—	4	2	no	—
192	D₃₅₆	—	8	2	no	—
193	D₃₅₆	—	8	2	no	—
194	D₃₅₆	—	8	2	no	—
195	D₃₅₆	—	8	2	no	—
196	Dic₁₇₈	—	4	1	no	—
197	Dic₁₇₈	—	4	1	no	—
198	Dic₁₇₈	—	8	1	no	—
199	C₈×C₈₉	—	2	2	no	—
200	C₈×C₈₉	—	2	2	no	—
201	C₈×C₈₉	—	4	1	no	—
202	C₈×C₈₉	—	4	1	no	—
203	#10623494	—	4	2	no	—
204	#10623494	—	4	1	no	—
205	#10623494	—	4	1	no	—
206	C₂²×C₈₉	—	2	1	no	—
207	C₂²×C₈₉	—	2	1	no	—
208	C₂²×C₈₉	—	4	2	no	—
209	C₂²×C₈₉	—	4	2	no	—
210	C₂²×C₈₉	—	4	2	no	—
211	C₂²×C₈₉	#463	1	2	yes	—
212	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
213	C₂×D₈₉	—	8	2	no	—
214	C₂×D₈₉	—	8	2	no	—
215	C₂×D₈₉	—	8	2	no	—
216	C₂×D₈₉	—	16	4	no	—
217	C₄×C₈₉	—	2	1	no	—
218	C₄×C₈₉	—	2	1	no	—
219	C₄×C₈₉	—	2	1	no	—
220	C₄×C₈₉	—	4	2	no	—
221	C₄×C₈₉	#463	1	2	yes	—
222	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
223	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
224	C₄×C₈₉	#576	1	1	yes	characteristic
225	C₄×C₈₉	#577	1	1	yes	characteristic
226	Dic₈₉	—	8	1	no	—
227	Dic₈₉	—	8	1	no	—
228	#19234	—	89	1	no	maximal, Sylow
229	C₂×C₈₉	—	2	2	no	—
230	C₂×C₈₉	—	8	2	no	—
231	C₂×C₈₉	C₂×#463	1	1	yes	characteristic
232	C₂×C₈₉	#3062	1	1	yes	characteristic
233	C₂×C₈₉	#3068	1	1	yes	characteristic
234	D₈₉	—	16	2	no	—
235	#3246	—	89	1	no	—
236	#3205	—	89	1	no	—
237	#3138	—	89	1	no	—
238	#2935	D₈₉	1	1	yes	characteristic, complemented
239	#1701	—	89	2	no	—
240	#1697	—	89	2	no	—
241	#1681	—	89	2	no	—
242	#1677	—	89	2	no	—
243	#1565	—	89	1	no	—
244	#1542	—	89	1	no	—
245	C₂×#331	—	89	1	no	—
246	C₈₉	#19234	1	1	yes	characteristic, complemented, Sylow
247	C₂×#131	—	2	1	no	—
248	#533	—	89	1	no	—
249	#532	C₂×D₈₉	1	1	yes	characteristic
250	C₂×#127	—	89	1	no	—
251	#493	—	178	1	no	—
252	#490	—	178	2	no	—
253	#486	—	89	2	no	—
254	#486	—	89	2	no	—
255	#486	—	178	1	no	—
256	#476	—	89	2	no	—
257	#475	—	178	1	no	—
258	#465	—	178	2	no	—
259	#461	—	89	2	no	—
260	#460	—	178	1	no	—
261	#459	—	89	2	no	—
262	#459	—	89	2	no	—
263	#447	—	178	2	no	—
264	#436	C₂×D₈₉	1	2	yes	complemented
265	#435	—	2	2	no	—
266	C₈×D₄	C₂×D₈₉	1	2	yes	complemented
267	#431	—	89	1	no	—
268	C₂×C₄⋊C₈	—	89	1	no	—
269	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
270	#418	—	178	1	no	—
271	#418	—	178	1	no	—
272	#408	—	2	1	no	—
273	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
274	#335	—	89	2	no	—
275	#334	—	89	2	no	—
276	#333	—	89	1	no	—
277	#333	—	89	1	no	—
278	#332	—	89	1	no	—
279	#332	—	89	1	no	—
280	#331	—	89	2	no	—
281	#331	—	89	2	no	—
282	C₂×#41	—	2	1	no	—
283	C₂²×D₄	—	178	1	no	—
284	C₂²×D₄	—	178	1	no	—
285	C₂²×D₄	—	178	1	no	—
286	C₂×SD₁₆	—	178	2	no	—
287	C₂×D₈	—	178	2	no	—
288	C₂×D₈	—	178	2	no	—
289	#131	—	4	4	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
292	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	2	2	no	—
295	C₂²×C₈	—	178	1	no	—
296	C₄⋊Q₈	—	89	1	no	—
297	C₄⋊Q₈	—	89	1	no	—
298	C₄⋊Q₈	D₃₅₆	1	1	yes	characteristic
299	#127	—	89	2	no	—
300	#127	—	178	1	no	—
301	#127	—	178	1	no	—
302	#127	—	178	1	no	—
303	#127	D₃₅₆	1	1	yes	characteristic
304	#125	—	178	1	no	—
305	#124	—	2	1	no	—
306	C₂²⋊Q₈	—	178	1	no	—
307	C₂²⋊Q₈	—	178	1	no	—
308	#121	—	2	1	no	—
309	#121	D₃₅₆	1	2	yes	—
310	C₄×Q₈	—	178	1	no	—
311	C₄×Q₈	—	178	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	C₂²×D₈₉	1	2	yes	—
314	#117	—	178	1	no	—
315	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
316	#106	—	178	2	no	—
317	C₄⋊C₈	—	2	1	no	—
318	C₄⋊C₈	—	89	2	no	—
319	C₄⋊C₈	—	89	1	no	—
320	C₄⋊C₈	—	89	1	no	—
321	C₄⋊C₈	—	178	1	no	—
322	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
323	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
324	#103	—	178	2	no	—
325	#102	—	178	2	no	—
326	#102	—	178	2	no	—
327	#102	—	178	2	no	—
328	#102	—	178	2	no	—
329	#102	—	178	2	no	—
330	#102	—	178	2	no	—
331	#102	—	178	2	no	—
332	C₂²⋊C₈	—	2	2	no	—
333	C₂²⋊C₈	—	2	2	no	—
334	C₂²⋊C₈	—	178	1	no	—
335	#97	C₂²⋊D₈₉	1	2	yes	—
336	C₄×C₈	—	178	1	no	—
337	C₄×C₈	C₂²×D₈₉	1	2	yes	—
338	C₂⁴	—	356	1	no	—
339	#41	—	4	2	no	—
340	#41	—	4	2	no	—
341	C₂×Q₈	—	2	1	no	—
342	C₂×Q₈	—	178	1	no	—
343	C₂×Q₈	—	178	1	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	356	1	no	—
348	C₂×D₄	—	356	1	no	—
349	C₂×D₄	—	356	1	no	—
350	C₂×D₄	—	356	2	no	—
351	C₂×D₄	—	356	2	no	—
352	C₂×D₄	—	178	2	no	—
353	C₂×D₄	—	178	2	no	—
354	C₂×D₄	—	178	2	no	—
355	C₂×D₄	—	712	1	no	—
356	C₂×D₄	—	712	1	no	—
357	C₂×D₄	—	712	2	no	—
358	C₂×D₄	C₂×D₃₅₆	1	2	yes	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
361	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
362	C₂²×C₄	#13083574	1	1	yes	characteristic
363	SD₁₆	—	712	2	no	—
364	D₈	—	712	2	no	—
365	D₈	—	712	2	no	—
366	M₁₆	—	2	2	no	—
367	M₁₆	—	2	2	no	—
368	M₁₆	—	4	4	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	4	4	no	—
372	C₂×C₈	—	4	2	no	—
373	C₂×C₈	—	178	1	no	—
374	C₂×C₈	—	178	1	no	—
375	C₂×C₈	—	178	2	no	—
376	C₂×C₈	—	712	1	no	—
377	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
378	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
379	C₄⋊C₄	—	2	1	no	—
380	C₄⋊C₄	—	356	1	no	—
381	C₄⋊C₄	—	356	1	no	—
382	C₄⋊C₄	—	178	1	no	—
383	C₄⋊C₄	—	178	1	no	—
384	C₄⋊C₄	—	178	1	no	—
385	C₄⋊C₄	—	178	1	no	—
386	C₄⋊C₄	C₂×D₃₅₆	1	2	yes	—
387	C₂²⋊C₄	—	2	2	no	—
388	C₂²⋊C₄	—	2	2	no	—
389	C₂²⋊C₄	—	356	1	no	—
390	C₄²	—	356	1	no	—
391	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
392	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
393	C₄²	#13083574	1	1	yes	characteristic
394	C₄²	C₂³×D₈₉	1	1	yes	characteristic
395	C₂³	—	2	2	no	—
396	C₂³	—	356	2	no	—
397	C₂³	—	712	2	no	—
398	C₂³	—	712	2	no	—
399	C₂³	—	712	2	no	—
400	C₂³	#15667986	1	1	yes	characteristic
401	Q₈	—	4	2	no	—
402	Q₈	—	356	1	no	—
403	Q₈	—	356	1	no	—
404	Q₈	—	712	1	no	—
405	D₄	—	2	2	no	—
406	D₄	—	2	2	no	—
407	D₄	—	4	4	no	—
408	D₄	—	4	2	no	—
409	D₄	—	8	1	no	—
410	D₄	—	356	2	no	—
411	D₄	—	356	2	no	—
412	D₄	—	356	2	no	—
413	D₄	—	356	2	no	—
414	D₄	—	712	2	no	—
415	D₄	—	712	2	no	—
416	D₄	—	712	2	no	—
417	D₄	—	712	2	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	4	1	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	356	1	no	—
425	C₂×C₄	—	356	1	no	—
426	C₂×C₄	#15667986	1	1	yes	characteristic
427	C₂×C₄	#15667986	1	1	yes	characteristic
428	C₂×C₄	#15667986	1	1	yes	characteristic
429	C₂×C₄	#15668032	1	2	yes	—
430	C₂×C₄	#15668038	1	2	yes	—
431	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
432	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
433	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
434	C₈	—	2	2	no	—
435	C₈	—	2	2	no	—
436	C₈	—	4	1	no	—
437	C₈	—	4	1	no	—
438	C₈	—	356	2	no	—
439	C₈	—	356	1	no	—
440	C₈	—	356	1	no	—
441	C₂²	—	2	1	no	—
442	C₂²	—	2	1	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	1424	4	no	—
447	C₂²	—	712	2	no	—
448	C₂²	—	712	2	no	—
449	C₂²	—	712	2	no	—
450	C₂²	#19151813	1	2	yes	—
451	C₂²	C₂×#15667986	1	1	yes	characteristic
452	C₄	—	2	1	no	—
453	C₄	—	2	1	no	—
454	C₄	—	2	1	no	—
455	C₄	—	4	2	no	—
456	C₄	—	712	1	no	—
457	C₄	—	712	1	no	—
458	C₄	#19151813	1	2	yes	—
459	C₄	C₂×#15668032	1	1	yes	characteristic
460	C₄	C₂×#15668038	1	1	yes	characteristic
461	C₄	#19152403	1	1	yes	characteristic
462	C₄	#19152410	1	1	yes	characteristic
463	C₂	—	2	2	no	—
464	C₂	—	8	2	no	—
465	C₂	—	1424	2	no	—
466	C₂	C₂×#19151813	1	1	yes	characteristic
467	C₂	#26029932	1	1	yes	characteristic
468	C₂	#26029980	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15667986
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#2935	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#26031167	C₂
hypercenter	#2935	D₈₉
hypocenter	C₈₉	#19234
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #2935

Complements

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

N	H ≅ G/N	type
1. #26031568	C₂	semidirect
3. #26030627	C₂	semidirect
4. #26019813	C₂	semidirect
5. #26019785	C₂	semidirect
6. #26019689	C₂	semidirect
7. #26019661	C₂	semidirect
8. #26019004	C₂	semidirect
9. #26018910	C₂	semidirect
10. C₂×#19151341	C₂	semidirect
11. C₈₉×#2935	C₂	semidirect
19. #19151888	C₂²	semidirect
22. #19151803	C₂²	semidirect
31. #19151351	C₂²	semidirect
32. #19151349	C₂²	semidirect
33. #19151346	C₂²	semidirect
34. #19151346	C₂²	semidirect
35. #19151343	C₂²	semidirect
36. #19151343	C₂²	semidirect
41. #436×C₈₉	C₂²	semidirect
43. C₈×D₄×C₈₉	C₂²	semidirect
238. #2935	D₈₉	semidirect
246. C₈₉	#19234	semidirect
264. #436	C₂×D₈₉	semidirect
266. C₈×D₄	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26031568	2
#26031167	2
#26030627	2
#26019813	2
#26019785	2
#26019689	2
#26019661	2
#26019004	2
#26018910	2
C₂×#19151341	2
C₈₉×#2935	2
#19234	89