Subgroups — #36542273

Order 22784.

900 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26031377	C₂	1	1	yes	maximal, characteristic, complemented
2	#26031190	C₂	1	1	yes	maximal, characteristic, complemented
3	#26030799	C₂	1	1	yes	maximal, characteristic, complemented
4	#26030705	C₂	1	1	yes	maximal, characteristic
5	C₂×#19151971	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019882	C₂	1	2	yes	maximal, complemented
7	#26019876	C₂	1	2	yes	maximal, complemented
8	#26019842	C₂	1	2	yes	maximal, complemented
9	#26019840	C₂	1	2	yes	maximal, complemented
10	C₈×#13083558	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#3167	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15668037	—	2	2	no	—
13	C₂²×#13083563	—	2	2	no	—
14	C₂×#15668012	C₂²	1	1	yes	characteristic
15	C₂×#15668009	C₂²	1	1	yes	characteristic
16	#19152008	—	2	2	no	—
17	#19152001	C₂²	1	2	yes	complemented
18	#19151994	C₂²	1	2	yes	complemented
19	#19151994	C₂²	1	2	yes	complemented
20	#19151988	—	2	2	no	—
21	#19151974	C₂²	1	2	yes	—
22	#19151972	C₂²	1	2	yes	—
23	#19151972	C₂²	1	2	yes	—
24	#19151971	—	2	2	no	—
25	#19151971	C₂²	1	2	yes	—
26	#19151971	C₂²	1	2	yes	—
27	#19151946	C₂²	1	2	yes	—
28	#19151944	C₂²	1	2	yes	complemented
29	#19151914	—	2	2	no	—
30	#19151888	—	2	2	no	—
31	#19151798	—	2	2	no	—
32	#19151748	—	2	2	no	—
33	#19151651	C₂²	1	1	yes	characteristic
34	#19151641	—	2	2	no	—
35	C₄×#13083558	C₂²	1	1	yes	characteristic
36	#19151320	C₂²	1	2	yes	complemented
37	C₈×#10623494	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	2	no	—
45	C₄×SD₁₆×C₈₉	—	2	2	no	—
46	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂²×Dic₁₇₈	—	2	1	no	—
48	C₂²×D₃₅₆	—	2	1	no	—
49	C₂²×D₃₅₆	—	2	1	no	—
50	C₂²×D₃₅₆	—	2	1	no	—
51	#15668037	—	4	8	no	—
52	C₂×#13083563	—	2	4	no	—
53	C₂×#13083563	—	2	4	no	—
54	C₂×#13083563	—	4	8	no	—
55	C₂×#13083561	—	2	4	no	—
56	C₂×#13083561	—	2	4	no	—
57	C₂×#13083559	—	2	4	no	—
58	C₂×#13083558	D₄	1	2	yes	—
59	#15668012	—	2	1	no	—
60	#15668012	—	2	1	no	—
61	#15668012	—	2	1	no	—
62	#15668012	C₂³	1	2	yes	—
63	#15668009	—	2	1	no	—
64	#15668009	—	2	1	no	—
65	#15668009	—	2	1	no	—
66	#15668009	C₂³	1	2	yes	—
67	C₂×C₄⋊Dic₈₉	—	2	1	no	—
68	C₂×C₄⋊Dic₈₉	—	2	1	no	—
69	#15667945	—	2	4	no	—
70	#15667943	—	2	4	no	—
71	#15667943	—	2	4	no	—
72	C₄⋊#10623494	D₄	1	2	yes	—
73	#15667933	—	2	4	no	—
74	#15667932	—	2	4	no	—
75	C₂²⋊#10623494	D₄	1	2	yes	—
76	#15667923	D₄	1	2	yes	—
77	C₄×#10623494	C₂³	1	2	yes	—
78	C₄×#10623494	C₂³	1	2	yes	—
79	C₂×#41×C₈₉	—	2	1	no	—
80	C₂×SD₁₆×C₈₉	—	2	2	no	—
81	C₂²×C₈×C₈₉	D₄	1	2	yes	—
82	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
83	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
84	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
85	#127×C₈₉	C₂³	1	1	yes	characteristic
86	#125×C₈₉	—	2	1	no	—
87	#124×C₈₉	—	2	1	no	—
88	C₂²⋊Q₈×C₈₉	—	2	1	no	—
89	C₂²⋊Q₈×C₈₉	—	2	1	no	—
90	#121×C₈₉	—	2	1	no	—
91	#121×C₈₉	—	2	1	no	—
92	C₄×Q₈×C₈₉	—	2	1	no	—
93	C₄×Q₈×C₈₉	—	2	1	no	—
94	C₄×D₄×C₈₉	—	2	1	no	—
95	C₄×D₄×C₈₉	—	2	1	no	—
96	#117×C₈₉	—	2	1	no	—
97	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
98	#106×C₈₉	—	2	2	no	—
99	#103×C₈₉	—	2	2	no	—
100	#102×C₈₉	—	2	2	no	—
101	C₄×C₈×C₈₉	D₄	1	2	yes	—
102	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
104	C₂³×D₈₉	—	4	1	no	—
105	C₂×Dic₁₇₈	—	2	2	no	—
106	C₂×Dic₁₇₈	—	4	4	no	—
107	C₂×Dic₁₇₈	—	4	1	no	—
108	C₂×D₃₅₆	—	2	2	no	—
109	C₂×D₃₅₆	—	2	2	no	—
110	C₂×D₃₅₆	—	2	2	no	—
111	C₂×D₃₅₆	—	4	4	no	—
112	C₂×D₃₅₆	—	4	4	no	—
113	C₂×D₃₅₆	—	4	1	no	—
114	C₂×D₃₅₆	—	4	1	no	—
115	C₂×D₃₅₆	—	4	1	no	—
116	C₂×D₃₅₆	—	8	2	no	—
117	C₂²×Dic₈₉	—	4	1	no	—
118	#13083563	—	4	8	no	—
119	#13083563	—	4	8	no	—
120	#13083561	—	4	8	no	—
121	#13083561	—	8	4	no	—
122	#13083559	—	4	8	no	—
123	#13083558	SD₁₆	1	8	yes	complemented
124	C₂×#10623494	C₂×D₄	1	4	yes	—
125	C₂×#10623494	C₂×D₄	1	4	yes	—
126	C₄⋊Dic₈₉	—	2	2	no	—
127	C₄⋊Dic₈₉	—	2	2	no	—
128	C₄⋊Dic₈₉	—	4	1	no	—
129	C₄⋊Dic₈₉	—	4	1	no	—
130	#41×C₈₉	—	4	4	no	—
131	C₂×Q₈×C₈₉	—	2	1	no	—
132	C₂×Q₈×C₈₉	—	2	1	no	—
133	C₂×Q₈×C₈₉	—	2	1	no	—
134	C₂×D₄×C₈₉	—	2	1	no	—
135	C₂×D₄×C₈₉	—	2	1	no	—
136	C₂×D₄×C₈₉	—	2	1	no	—
137	C₂×D₄×C₈₉	—	4	1	no	—
138	C₂²×C₄×C₈₉	—	4	1	no	—
139	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
142	SD₁₆×C₈₉	—	4	4	no	—
143	C₂×C₈×C₈₉	—	2	4	no	—
144	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
145	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
146	C₄⋊C₄×C₈₉	—	2	1	no	—
147	C₄⋊C₄×C₈₉	—	2	1	no	—
148	C₄⋊C₄×C₈₉	—	2	1	no	—
149	C₄⋊C₄×C₈₉	—	2	1	no	—
150	C₄⋊C₄×C₈₉	—	2	1	no	—
151	C₄⋊C₄×C₈₉	—	2	1	no	—
152	C₄⋊C₄×C₈₉	—	4	1	no	—
153	C₄⋊C₄×C₈₉	—	4	1	no	—
154	C₂²⋊C₄×C₈₉	—	4	1	no	—
155	C₂²⋊C₄×C₈₉	—	4	1	no	—
156	C₂²⋊C₄×C₈₉	—	4	1	no	—
157	C₄²×C₈₉	—	4	1	no	—
158	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
160	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
162	C₂³×C₈₉	—	4	1	no	—
163	C₂³×C₈₉	#127	1	1	yes	characteristic
164	C₂²×D₈₉	—	4	2	no	—
165	C₂²×D₈₉	—	8	2	no	—
166	C₂²×D₈₉	—	8	2	no	—
167	C₂²×D₈₉	—	8	2	no	—
168	Q₈×C₈₉	—	4	2	no	—
169	Q₈×C₈₉	—	4	2	no	—
170	Q₈×C₈₉	—	4	2	no	—
171	D₄×C₈₉	—	4	2	no	—
172	D₄×C₈₉	—	4	2	no	—
173	D₄×C₈₉	—	4	2	no	—
174	D₄×C₈₉	—	8	2	no	—
175	C₂×C₄×C₈₉	—	2	2	no	—
176	C₂×C₄×C₈₉	—	2	2	no	—
177	C₂×C₄×C₈₉	—	4	1	no	—
178	C₂×C₄×C₈₉	—	4	1	no	—
179	C₂×C₄×C₈₉	—	4	1	no	—
180	C₂×C₄×C₈₉	—	8	2	no	—
181	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
182	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
183	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
184	C₂×C₄×C₈₉	C₂×SD₁₆	1	4	yes	—
185	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
187	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
188	C₂×Dic₈₉	—	4	2	no	—
189	C₂×Dic₈₉	—	8	2	no	—
190	D₃₅₆	—	4	4	no	—
191	D₃₅₆	—	4	4	no	—
192	D₃₅₆	—	4	4	no	—
193	D₃₅₆	—	8	2	no	—
194	D₃₅₆	—	8	2	no	—
195	D₃₅₆	—	8	2	no	—
196	Dic₁₇₈	—	4	4	no	—
197	Dic₁₇₈	—	8	2	no	—
198	C₈×C₈₉	—	2	2	no	—
199	C₈×C₈₉	AGL(1,ℤ/8)	1	4	yes	complemented
200	#10623494	—	2	4	no	—
201	#10623494	C₂×SD₁₆	1	8	yes	complemented
202	C₂²×C₈₉	—	2	1	no	—
203	C₂²×C₈₉	—	2	1	no	—
204	C₂²×C₈₉	—	8	1	no	—
205	C₂²×C₈₉	—	8	1	no	—
206	C₂²×C₈₉	—	8	1	no	—
207	C₂²×C₈₉	#492	1	2	yes	—
208	C₂²×C₈₉	C₂×#127	1	1	yes	characteristic
209	C₂×D₈₉	—	8	2	no	—
210	C₂×D₈₉	—	8	2	no	—
211	C₂×D₈₉	—	8	2	no	—
212	C₂×D₈₉	—	16	4	no	—
213	C₄×C₈₉	—	2	1	no	—
214	C₄×C₈₉	—	2	1	no	—
215	C₄×C₈₉	—	8	1	no	—
216	C₄×C₈₉	—	8	1	no	—
217	C₄×C₈₉	—	8	1	no	—
218	C₄×C₈₉	#492	1	2	yes	—
219	C₄×C₈₉	C₂²×SD₁₆	1	2	yes	—
220	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	2	yes	—
221	C₄×C₈₉	#577	1	2	yes	—
222	Dic₈₉	—	8	2	no	—
223	#19621	—	89	1	no	maximal, Sylow
224	C₂×C₈₉	—	2	2	no	—
225	C₂×C₈₉	—	16	1	no	—
226	C₂×C₈₉	C₂×#492	1	1	yes	characteristic
227	C₂×C₈₉	#3151	1	1	yes	characteristic
228	C₂×C₈₉	#3154	1	1	yes	characteristic
229	D₈₉	—	16	2	no	—
230	#3227	—	89	1	no	—
231	#3208	—	89	1	no	—
232	#3167	D₈₉	1	1	yes	characteristic, complemented
233	#3165	—	89	1	no	—
234	#3151	—	89	1	no	—
235	C₂×#492	—	89	1	no	—
236	#1715	—	89	2	no	—
237	#1714	—	89	2	no	—
238	#1706	—	89	2	no	—
239	#1705	—	89	2	no	—
240	C₈×M₁₆	—	89	1	no	—
241	C₈₉	#19621	1	1	yes	characteristic, complemented, Sylow
242	C₂×AGL(1,ℤ/8)	—	178	2	no	—
243	C₂²×SD₁₆	—	178	2	no	—
244	#533	C₂×D₈₉	1	1	yes	characteristic
245	#532	C₂×D₈₉	1	1	yes	characteristic
246	C₂×C₄⋊Q₈	—	89	1	no	—
247	C₂×#127	—	89	1	no	—
248	#501	—	178	2	no	—
249	#500	—	89	2	no	—
250	#498	—	89	2	no	—
251	#498	—	89	2	no	—
252	#498	C₂×D₈₉	1	1	yes	characteristic, complemented
253	#496	—	178	2	no	—
254	#493	—	89	2	no	—
255	#492	—	89	2	no	—
256	#492	—	89	2	no	—
257	#492	—	89	2	no	—
258	#492	—	89	2	no	—
259	#492	—	178	2	no	—
260	#492	C₂×D₈₉	1	1	yes	characteristic, complemented
261	#487	C₂×D₈₉	1	1	yes	characteristic, complemented
262	#486	—	89	2	no	—
263	#486	—	89	2	no	—
264	#486	C₂×D₈₉	1	1	yes	characteristic, complemented
265	#481	—	178	2	no	—
266	#476	—	178	2	no	—
267	#465	—	2	2	no	—
268	#460	—	178	2	no	—
269	#450	—	178	2	no	—
270	C₄×SD₁₆	—	2	2	no	—
271	#431	—	89	1	no	—
272	#428	—	178	2	no	—
273	C₄×M₁₆	—	89	1	no	—
274	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
275	#322	—	89	2	no	—
276	C₈²	—	89	2	no	—
277	C₂×#41	—	2	1	no	—
278	C₂²×Q₈	—	178	1	no	—
279	C₂²×D₄	—	178	1	no	—
280	C₂²×D₄	—	178	1	no	—
281	C₂²×D₄	—	178	1	no	—
282	AGL(1,ℤ/8)	—	356	8	no	—
283	C₂×SD₁₆	—	2	2	no	—
284	C₂×SD₁₆	—	356	8	no	—
285	C₂×SD₁₆	—	178	4	no	—
286	C₂×SD₁₆	—	178	4	no	—
287	C₂×SD₁₆	—	178	4	no	—
288	C₂×SD₁₆	—	178	4	no	—
289	C₂×D₈	—	178	4	no	—
290	C₂×M₁₆	—	89	2	no	—
291	C₂²×C₈	C₂²⋊D₈₉	1	2	yes	—
292	C₄⋊Q₈	—	89	2	no	—
293	C₄⋊Q₈	—	178	1	no	—
294	C₄⋊Q₈	—	178	1	no	—
295	C₄⋊Q₈	—	178	1	no	—
296	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
297	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
298	C₄⋊Q₈	C₂²×D₈₉	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	C₂²×D₈₉	1	1	yes	characteristic
304	#125	—	2	1	no	—
305	#124	—	2	1	no	—
306	C₂²⋊Q₈	—	2	1	no	—
307	C₂²⋊Q₈	—	2	1	no	—
308	#121	—	2	1	no	—
309	#121	—	2	1	no	—
310	C₄×Q₈	—	2	1	no	—
311	C₄×Q₈	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	2	1	no	—
314	#117	—	2	1	no	—
315	C₂×C₄⋊C₄	—	178	1	no	—
316	C₂×C₄⋊C₄	—	178	1	no	—
317	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
318	#107	—	178	4	no	—
319	#106	—	2	2	no	—
320	#106	—	178	4	no	—
321	#106	—	178	4	no	—
322	C₄⋊C₈	—	89	2	no	—
323	#103	—	2	2	no	—
324	#102	—	2	2	no	—
325	#102	—	178	4	no	—
326	#102	—	178	4	no	—
327	C₂²⋊C₈	—	89	2	no	—
328	#97	—	89	2	no	—
329	C₄×C₈	—	89	2	no	—
330	C₄×C₈	—	89	2	no	—
331	C₄×C₈	C₂²⋊D₈₉	1	2	yes	—
332	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
333	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
334	C₂⁴	—	356	1	no	—
335	#41	—	4	4	no	—
336	C₂×Q₈	—	2	1	no	—
337	C₂×Q₈	—	2	1	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	356	4	no	—
340	C₂×Q₈	—	356	1	no	—
341	C₂×Q₈	—	178	2	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	2	1	no	—
344	C₂×D₄	—	2	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	356	4	no	—
347	C₂×D₄	—	356	1	no	—
348	C₂×D₄	—	356	1	no	—
349	C₂×D₄	—	356	1	no	—
350	C₂×D₄	—	356	4	no	—
351	C₂×D₄	—	178	2	no	—
352	C₂×D₄	—	178	2	no	—
353	C₂×D₄	—	178	2	no	—
354	C₂×D₄	—	712	2	no	—
355	C₂²×C₄	—	4	1	no	—
356	C₂²×C₄	—	356	1	no	—
357	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
358	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
359	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
360	SD₁₆	—	4	4	no	—
361	SD₁₆	—	356	8	no	—
362	SD₁₆	—	356	8	no	—
363	SD₁₆	—	356	8	no	—
364	SD₁₆	—	712	4	no	—
365	D₈	—	356	8	no	—
366	M₁₆	—	89	8	no	—
367	C₂×C₈	—	2	4	no	—
368	C₂×C₈	—	89	4	no	—
369	C₂×C₈	—	89	4	no	—
370	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
371	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	2	1	no	—
375	C₄⋊C₄	—	2	1	no	—
376	C₄⋊C₄	—	2	1	no	—
377	C₄⋊C₄	—	2	1	no	—
378	C₄⋊C₄	—	4	1	no	—
379	C₄⋊C₄	—	4	1	no	—
380	C₄⋊C₄	—	356	1	no	—
381	C₄⋊C₄	—	356	1	no	—
382	C₄⋊C₄	—	178	2	no	—
383	C₄⋊C₄	—	178	2	no	—
384	C₂²⋊C₄	—	4	1	no	—
385	C₂²⋊C₄	—	4	1	no	—
386	C₂²⋊C₄	—	4	1	no	—
387	C₄²	—	4	1	no	—
388	C₄²	D₄×D₈₉	1	1	yes	characteristic
389	C₄²	D₄×D₈₉	1	1	yes	characteristic
390	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
391	C₄²	C₂³×D₈₉	1	1	yes	characteristic
392	C₂³	—	4	1	no	—
393	C₂³	—	356	2	no	—
394	C₂³	—	712	2	no	—
395	C₂³	—	712	2	no	—
396	C₂³	—	712	2	no	—
397	C₂³	#15668008	1	1	yes	characteristic
398	Q₈	—	4	2	no	—
399	Q₈	—	4	2	no	—
400	Q₈	—	4	2	no	—
401	Q₈	—	356	4	no	—
402	Q₈	—	712	2	no	—
403	D₄	—	4	2	no	—
404	D₄	—	4	2	no	—
405	D₄	—	4	2	no	—
406	D₄	—	8	2	no	—
407	D₄	—	356	4	no	—
408	D₄	—	356	4	no	—
409	D₄	—	356	4	no	—
410	D₄	—	712	2	no	—
411	D₄	—	712	2	no	—
412	D₄	—	712	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	1	no	—
417	C₂×C₄	—	4	1	no	—
418	C₂×C₄	—	8	2	no	—
419	C₂×C₄	—	356	2	no	—
420	C₂×C₄	—	712	2	no	—
421	C₂×C₄	#15668008	1	1	yes	characteristic
422	C₂×C₄	#15668008	1	1	yes	characteristic
423	C₂×C₄	#15668008	1	1	yes	characteristic
424	C₂×C₄	SD₁₆×D₈₉	1	4	yes	—
425	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
426	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
427	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
428	C₈	—	2	2	no	—
429	C₈	—	89	8	no	—
430	C₈	—	178	4	no	—
431	C₈	#15668037	1	4	yes	complemented
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	8	1	no	—
435	C₂²	—	8	1	no	—
436	C₂²	—	8	1	no	—
437	C₂²	—	1424	4	no	—
438	C₂²	—	712	2	no	—
439	C₂²	—	712	2	no	—
440	C₂²	—	712	2	no	—
441	C₂²	#19151969	1	2	yes	—
442	C₂²	C₂×#15668008	1	1	yes	characteristic
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	8	1	no	—
446	C₄	—	8	1	no	—
447	C₄	—	8	1	no	—
448	C₄	—	712	2	no	—
449	C₄	#19151969	1	2	yes	—
450	C₄	C₂×SD₁₆×D₈₉	1	2	yes	—
451	C₄	C₂×#15668037	1	2	yes	—
452	C₄	#19152405	1	2	yes	—
453	C₂	—	2	2	no	—
454	C₂	—	16	1	no	—
455	C₂	—	1424	2	no	—
456	C₂	C₂×#19151969	1	1	yes	characteristic
457	C₂	#26030705	1	1	yes	characteristic
458	C₂	#26030729	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#15668008
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#3167	C₂
socle	C₂²×C₈₉	C₂×#127
prime radical	#26030705	C₂
hypercenter	#3167	D₈₉
hypocenter	C₈₉	#19621
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. #26031377	C₂	semidirect
2. #26031190	C₂	semidirect
3. #26030799	C₂	semidirect
5. C₂×#19151971	C₂	semidirect
6. #26019882	C₂	semidirect
7. #26019876	C₂	semidirect
8. #26019842	C₂	semidirect
9. #26019840	C₂	semidirect
10. C₈×#13083558	C₂	semidirect
11. C₈₉×#3167	C₂	semidirect
17. #19152001	C₂²	semidirect
18. #19151994	C₂²	semidirect
19. #19151994	C₂²	semidirect
28. #19151944	C₂²	semidirect
36. #19151320	C₂²	semidirect
37. C₈×#10623494	C₂²	semidirect
40. #498×C₈₉	C₂²	semidirect
41. #492×C₈₉	C₂²	semidirect
42. #487×C₈₉	C₂²	semidirect
43. #486×C₈₉	C₂²	semidirect
123. #13083558	SD₁₆	semidirect
199. C₈×C₈₉	AGL(1,ℤ/8)	semidirect
201. #10623494	C₂×SD₁₆	semidirect
232. #3167	D₈₉	semidirect
241. C₈₉	#19621	semidirect
252. #498	C₂×D₈₉	semidirect
260. #492	C₂×D₈₉	semidirect
261. #487	C₂×D₈₉	semidirect
264. #486	C₂×D₈₉	semidirect
431. C₈	#15668037	semidirect

Maximal subgroups

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

subgroup	index
#26031377	2
#26031190	2
#26030799	2
#26030705	2
C₂×#19151971	2
#26019882	2
#26019876	2
#26019842	2
#26019840	2
C₈×#13083558	2
C₈₉×#3167	2
#19621	89