Subgroups — #36542295

Order 22784.

848 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	#26031190	C₂	1	1	yes	maximal, characteristic, complemented
2	#26031174	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×#19151945	C₂	1	1	yes	maximal, characteristic, complemented
6	#26019879	C₂	1	2	yes	maximal, complemented
7	#26019877	C₂	1	2	yes	maximal, complemented
8	#26019855	C₂	1	2	yes	maximal, complemented
9	#26019843	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	C₂×#15668012	C₂²	1	1	yes	characteristic
14	C₂×#15668009	C₂²	1	1	yes	characteristic
15	#19152008	—	2	2	no	—
16	#19152001	C₂²	1	2	yes	complemented
17	#19151994	C₂²	1	2	yes	complemented
18	#19151988	—	2	2	no	—
19	#19151974	C₂²	1	2	yes	—
20	#19151972	C₂²	1	2	yes	—
21	#19151972	C₂²	1	2	yes	—
22	#19151970	C₂²	1	2	yes	complemented
23	#19151950	C₂²	1	2	yes	complemented
24	#19151946	C₂²	1	2	yes	—
25	#19151945	—	2	2	no	—
26	#19151945	C₂²	1	2	yes	—
27	#19151945	C₂²	1	2	yes	—
28	#19151803	—	2	2	no	—
29	#19151798	—	2	2	no	—
30	#19151748	—	2	2	no	—
31	#19151736	—	2	2	no	—
32	#19151651	C₂²	1	1	yes	characteristic
33	#19151641	—	2	2	no	—
34	C₂×#15667934	—	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×#13083562	—	2	4	no	—
53	C₂×#13083561	—	2	4	no	—
54	C₂×#13083561	—	2	4	no	—
55	C₂×#13083559	—	2	4	no	—
56	C₂×#13083558	D₄	1	2	yes	—
57	#15668012	—	2	1	no	—
58	#15668012	—	2	1	no	—
59	#15668012	—	2	1	no	—
60	#15668012	C₂³	1	2	yes	—
61	#15668009	—	2	1	no	—
62	#15668009	—	2	1	no	—
63	#15668009	—	2	1	no	—
64	#15668009	C₂³	1	2	yes	—
65	C₂×C₄⋊Dic₈₉	—	2	1	no	—
66	C₂×C₄⋊Dic₈₉	—	2	1	no	—
67	#15667945	—	2	4	no	—
68	#15667943	—	2	4	no	—
69	C₄⋊#10623494	D₄	1	2	yes	—
70	#15667935	—	2	4	no	—
71	#15667934	—	2	4	no	—
72	#15667934	—	2	4	no	—
73	#15667932	—	2	4	no	—
74	C₂²⋊#10623494	D₄	1	2	yes	—
75	#15667923	D₄	1	2	yes	—
76	C₄×#10623494	C₂³	1	2	yes	—
77	C₄×#10623494	C₂³	1	2	yes	—
78	C₂×#41×C₈₉	—	2	1	no	—
79	C₂×SD₁₆×C₈₉	—	2	2	no	—
80	C₂²×C₈×C₈₉	D₄	1	2	yes	—
81	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
82	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
83	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
84	#127×C₈₉	C₂³	1	1	yes	characteristic
85	#125×C₈₉	—	2	1	no	—
86	#124×C₈₉	—	2	1	no	—
87	C₂²⋊Q₈×C₈₉	—	2	1	no	—
88	C₂²⋊Q₈×C₈₉	—	2	1	no	—
89	#121×C₈₉	—	2	1	no	—
90	#121×C₈₉	—	2	1	no	—
91	C₄×Q₈×C₈₉	—	2	1	no	—
92	C₄×Q₈×C₈₉	—	2	1	no	—
93	C₄×D₄×C₈₉	—	2	1	no	—
94	C₄×D₄×C₈₉	—	2	1	no	—
95	#117×C₈₉	—	2	1	no	—
96	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
97	#106×C₈₉	—	2	2	no	—
98	#103×C₈₉	—	2	2	no	—
99	#102×C₈₉	—	2	2	no	—
100	C₄×C₈×C₈₉	D₄	1	2	yes	—
101	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
103	C₂³×D₈₉	—	4	1	no	—
104	C₂×Dic₁₇₈	—	2	2	no	—
105	C₂×Dic₁₇₈	—	4	1	no	—
106	C₂×Dic₁₇₈	—	8	2	no	—
107	C₂×D₃₅₆	—	2	2	no	—
108	C₂×D₃₅₆	—	2	2	no	—
109	C₂×D₃₅₆	—	2	2	no	—
110	C₂×D₃₅₆	—	4	4	no	—
111	C₂×D₃₅₆	—	4	4	no	—
112	C₂×D₃₅₆	—	4	1	no	—
113	C₂×D₃₅₆	—	4	1	no	—
114	C₂×D₃₅₆	—	4	1	no	—
115	C₂×D₃₅₆	—	8	2	no	—
116	C₂²×Dic₈₉	—	4	1	no	—
117	#13083562	—	8	4	no	—
118	#13083561	—	4	8	no	—
119	#13083561	—	8	4	no	—
120	#13083559	—	4	8	no	—
121	#13083558	SD₁₆	1	8	yes	complemented
122	C₂×#10623494	C₂×D₄	1	4	yes	—
123	C₂×#10623494	C₂×D₄	1	4	yes	—
124	C₄⋊Dic₈₉	—	2	2	no	—
125	C₄⋊Dic₈₉	—	2	2	no	—
126	C₄⋊Dic₈₉	—	4	1	no	—
127	C₄⋊Dic₈₉	—	4	1	no	—
128	#41×C₈₉	—	4	4	no	—
129	C₂×Q₈×C₈₉	—	2	1	no	—
130	C₂×Q₈×C₈₉	—	2	1	no	—
131	C₂×Q₈×C₈₉	—	2	1	no	—
132	C₂×D₄×C₈₉	—	2	1	no	—
133	C₂×D₄×C₈₉	—	2	1	no	—
134	C₂×D₄×C₈₉	—	2	1	no	—
135	C₂×D₄×C₈₉	—	4	1	no	—
136	C₂²×C₄×C₈₉	—	4	1	no	—
137	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
140	SD₁₆×C₈₉	—	4	4	no	—
141	C₂×C₈×C₈₉	—	4	2	no	—
142	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
144	C₄⋊C₄×C₈₉	—	2	1	no	—
145	C₄⋊C₄×C₈₉	—	2	1	no	—
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	—	4	1	no	—
151	C₄⋊C₄×C₈₉	—	4	1	no	—
152	C₂²⋊C₄×C₈₉	—	4	1	no	—
153	C₂²⋊C₄×C₈₉	—	4	1	no	—
154	C₂²⋊C₄×C₈₉	—	4	1	no	—
155	C₄²×C₈₉	—	4	1	no	—
156	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
160	C₂³×C₈₉	—	4	1	no	—
161	C₂³×C₈₉	#127	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	Q₈×C₈₉	—	4	2	no	—
168	Q₈×C₈₉	—	4	2	no	—
169	D₄×C₈₉	—	4	2	no	—
170	D₄×C₈₉	—	4	2	no	—
171	D₄×C₈₉	—	4	2	no	—
172	D₄×C₈₉	—	8	2	no	—
173	C₂×C₄×C₈₉	—	2	2	no	—
174	C₂×C₄×C₈₉	—	2	2	no	—
175	C₂×C₄×C₈₉	—	4	1	no	—
176	C₂×C₄×C₈₉	—	4	1	no	—
177	C₂×C₄×C₈₉	—	4	1	no	—
178	C₂×C₄×C₈₉	—	8	2	no	—
179	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
180	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
181	C₂×C₄×C₈₉	#127	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂×SD₁₆	1	4	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	C₂²×D₄	1	1	yes	characteristic
186	C₂×Dic₈₉	—	4	2	no	—
187	C₂×Dic₈₉	—	8	2	no	—
188	D₃₅₆	—	4	4	no	—
189	D₃₅₆	—	4	4	no	—
190	D₃₅₆	—	4	4	no	—
191	D₃₅₆	—	8	2	no	—
192	D₃₅₆	—	8	2	no	—
193	D₃₅₆	—	8	2	no	—
194	Dic₁₇₈	—	4	4	no	—
195	Dic₁₇₈	—	8	2	no	—
196	C₈×C₈₉	—	2	2	no	—
197	C₈×C₈₉	—	2	2	no	—
198	#10623494	—	2	4	no	—
199	#10623494	C₂×SD₁₆	1	8	yes	—
200	C₂²×C₈₉	—	2	1	no	—
201	C₂²×C₈₉	—	2	1	no	—
202	C₂²×C₈₉	—	8	1	no	—
203	C₂²×C₈₉	—	8	1	no	—
204	C₂²×C₈₉	—	8	1	no	—
205	C₂²×C₈₉	#492	1	2	yes	—
206	C₂²×C₈₉	C₂×#127	1	1	yes	characteristic
207	C₂×D₈₉	—	8	2	no	—
208	C₂×D₈₉	—	8	2	no	—
209	C₂×D₈₉	—	8	2	no	—
210	C₂×D₈₉	—	16	4	no	—
211	C₄×C₈₉	—	2	1	no	—
212	C₄×C₈₉	—	2	1	no	—
213	C₄×C₈₉	—	8	1	no	—
214	C₄×C₈₉	—	8	1	no	—
215	C₄×C₈₉	—	8	1	no	—
216	C₄×C₈₉	#492	1	2	yes	—
217	C₄×C₈₉	C₂²×SD₁₆	1	2	yes	—
218	C₄×C₈₉	#575	1	2	yes	—
219	C₄×C₈₉	#576	1	2	yes	—
220	Dic₈₉	—	8	2	no	—
221	#19623	—	89	1	no	maximal, Sylow
222	C₂×C₈₉	—	2	2	no	—
223	C₂×C₈₉	—	16	1	no	—
224	C₂×C₈₉	C₂×#492	1	1	yes	characteristic
225	C₂×C₈₉	#3153	1	1	yes	characteristic
226	C₂×C₈₉	#3155	1	1	yes	characteristic
227	D₈₉	—	16	2	no	—
228	#3208	—	89	1	no	—
229	#3206	—	89	1	no	—
230	#3167	D₈₉	1	1	yes	characteristic, complemented
231	#3165	—	89	1	no	—
232	#3151	—	89	1	no	—
233	C₂×#486	—	89	1	no	—
234	#1715	—	89	2	no	—
235	#1714	—	89	2	no	—
236	#1708	—	89	2	no	—
237	#1706	—	89	2	no	—
238	C₈×M₁₆	—	89	1	no	—
239	C₈₉	#19623	1	1	yes	characteristic, complemented, Sylow
240	C₂×AGL(1,ℤ/8)	—	178	2	no	—
241	#533	C₂×D₈₉	1	1	yes	characteristic
242	#532	C₂×D₈₉	1	1	yes	characteristic
243	C₂×C₄⋊Q₈	—	89	1	no	—
244	C₂×#127	—	89	1	no	—
245	#501	—	178	2	no	—
246	#500	—	89	2	no	—
247	#498	—	89	2	no	—
248	#498	C₂×D₈₉	1	1	yes	characteristic, complemented
249	#496	—	178	2	no	—
250	#493	—	89	2	no	—
251	#492	—	89	2	no	—
252	#492	—	89	2	no	—
253	#492	—	89	2	no	—
254	#492	C₂×D₈₉	1	1	yes	characteristic, complemented
255	#487	—	89	2	no	—
256	#487	C₂×D₈₉	1	1	yes	characteristic, complemented
257	#486	—	89	2	no	—
258	#486	—	89	2	no	—
259	#486	—	89	2	no	—
260	#486	—	178	2	no	—
261	#486	C₂×D₈₉	1	1	yes	characteristic, complemented
262	#465	—	2	2	no	—
263	#461	—	178	2	no	—
264	#460	—	178	2	no	—
265	#450	—	178	2	no	—
266	#448	—	178	2	no	—
267	C₄×SD₁₆	—	2	2	no	—
268	#431	—	89	1	no	—
269	#428	—	178	2	no	—
270	C₂×#102	—	178	2	no	—
271	C₄×M₁₆	—	89	1	no	—
272	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
273	#322	—	89	2	no	—
274	C₈²	—	89	2	no	—
275	C₂×#41	—	2	1	no	—
276	C₂²×Q₈	—	178	1	no	—
277	C₂²×D₄	—	178	1	no	—
278	C₂²×D₄	—	178	1	no	—
279	C₂²×D₄	—	178	1	no	—
280	AGL(1,ℤ/8)	—	356	8	no	—
281	C₂×SD₁₆	—	2	2	no	—
282	C₂×SD₁₆	—	178	4	no	—
283	C₂×SD₁₆	—	178	4	no	—
284	C₂×SD₁₆	—	178	4	no	—
285	C₂×D₈	—	178	4	no	—
286	C₂×M₁₆	—	89	2	no	—
287	C₂²×C₈	C₂²⋊D₈₉	1	2	yes	—
288	C₄⋊Q₈	—	89	2	no	—
289	C₄⋊Q₈	—	178	1	no	—
290	C₄⋊Q₈	—	178	1	no	—
291	C₄⋊Q₈	—	178	1	no	—
292	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
293	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
294	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
295	#127	—	89	2	no	—
296	#127	—	178	1	no	—
297	#127	—	178	1	no	—
298	#127	—	178	1	no	—
299	#127	C₂²×D₈₉	1	1	yes	characteristic
300	#125	—	2	1	no	—
301	#124	—	2	1	no	—
302	C₂²⋊Q₈	—	2	1	no	—
303	C₂²⋊Q₈	—	2	1	no	—
304	#121	—	2	1	no	—
305	#121	—	2	1	no	—
306	C₄×Q₈	—	2	1	no	—
307	C₄×Q₈	—	2	1	no	—
308	C₄×D₄	—	2	1	no	—
309	C₄×D₄	—	2	1	no	—
310	#117	—	2	1	no	—
311	C₂×C₄⋊C₄	—	178	1	no	—
312	C₂×C₄⋊C₄	—	178	1	no	—
313	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
314	#107	—	178	4	no	—
315	#106	—	2	2	no	—
316	#106	—	178	4	no	—
317	C₄⋊C₈	—	89	2	no	—
318	#103	—	2	2	no	—
319	#103	—	178	4	no	—
320	#102	—	2	2	no	—
321	#102	—	178	4	no	—
322	#102	—	178	4	no	—
323	#102	—	178	4	no	—
324	C₂²⋊C₈	—	89	2	no	—
325	#97	—	89	2	no	—
326	C₄×C₈	—	89	2	no	—
327	C₄×C₈	—	89	2	no	—
328	C₄×C₈	C₂²⋊D₈₉	1	2	yes	—
329	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
330	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
331	C₂⁴	—	356	1	no	—
332	#41	—	4	4	no	—
333	C₂×Q₈	—	2	1	no	—
334	C₂×Q₈	—	2	1	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	356	1	no	—
337	C₂×Q₈	—	178	2	no	—
338	C₂×Q₈	—	712	2	no	—
339	C₂×D₄	—	2	1	no	—
340	C₂×D₄	—	2	1	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂×D₄	—	356	4	no	—
344	C₂×D₄	—	356	1	no	—
345	C₂×D₄	—	356	1	no	—
346	C₂×D₄	—	356	1	no	—
347	C₂×D₄	—	356	4	no	—
348	C₂×D₄	—	178	2	no	—
349	C₂×D₄	—	178	2	no	—
350	C₂×D₄	—	178	2	no	—
351	C₂×D₄	—	712	2	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	—	356	1	no	—
354	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
355	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
356	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
357	SD₁₆	—	4	4	no	—
358	SD₁₆	—	356	8	no	—
359	SD₁₆	—	712	4	no	—
360	SD₁₆	—	712	4	no	—
361	D₈	—	356	8	no	—
362	M₁₆	—	89	8	no	—
363	C₂×C₈	—	4	2	no	—
364	C₂×C₈	—	89	4	no	—
365	C₂×C₈	—	89	4	no	—
366	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
367	C₂×C₈	C₂×C₂²⋊D₈₉	1	2	yes	—
368	C₄⋊C₄	—	2	1	no	—
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	2	1	no	—
371	C₄⋊C₄	—	2	1	no	—
372	C₄⋊C₄	—	2	1	no	—
373	C₄⋊C₄	—	2	1	no	—
374	C₄⋊C₄	—	4	1	no	—
375	C₄⋊C₄	—	4	1	no	—
376	C₄⋊C₄	—	356	1	no	—
377	C₄⋊C₄	—	356	1	no	—
378	C₄⋊C₄	—	178	2	no	—
379	C₄⋊C₄	—	178	2	no	—
380	C₂²⋊C₄	—	4	1	no	—
381	C₂²⋊C₄	—	4	1	no	—
382	C₂²⋊C₄	—	4	1	no	—
383	C₄²	—	4	1	no	—
384	C₄²	D₄×D₈₉	1	1	yes	characteristic
385	C₄²	D₄×D₈₉	1	1	yes	characteristic
386	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
387	C₄²	C₂³×D₈₉	1	1	yes	characteristic
388	C₂³	—	4	1	no	—
389	C₂³	—	356	2	no	—
390	C₂³	—	712	2	no	—
391	C₂³	—	712	2	no	—
392	C₂³	—	712	2	no	—
393	C₂³	#15668008	1	1	yes	characteristic
394	Q₈	—	4	2	no	—
395	Q₈	—	4	2	no	—
396	Q₈	—	4	2	no	—
397	Q₈	—	356	4	no	—
398	Q₈	—	712	2	no	—
399	D₄	—	4	2	no	—
400	D₄	—	4	2	no	—
401	D₄	—	4	2	no	—
402	D₄	—	8	2	no	—
403	D₄	—	356	4	no	—
404	D₄	—	356	4	no	—
405	D₄	—	356	4	no	—
406	D₄	—	712	2	no	—
407	D₄	—	712	2	no	—
408	D₄	—	712	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	8	2	no	—
415	C₂×C₄	—	356	2	no	—
416	C₂×C₄	—	712	2	no	—
417	C₂×C₄	#15668008	1	1	yes	characteristic
418	C₂×C₄	#15668008	1	1	yes	characteristic
419	C₂×C₄	#15668008	1	1	yes	characteristic
420	C₂×C₄	SD₁₆×D₈₉	1	4	yes	—
421	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
422	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
423	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
424	C₈	—	2	2	no	—
425	C₈	—	2	2	no	—
426	C₈	—	89	8	no	—
427	C₈	—	178	4	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	8	1	no	—
431	C₂²	—	8	1	no	—
432	C₂²	—	8	1	no	—
433	C₂²	—	1424	4	no	—
434	C₂²	—	712	2	no	—
435	C₂²	—	712	2	no	—
436	C₂²	—	712	2	no	—
437	C₂²	#19151969	1	2	yes	—
438	C₂²	C₂×#15668008	1	1	yes	characteristic
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	1	no	—
443	C₄	—	8	1	no	—
444	C₄	—	712	2	no	—
445	C₄	#19151969	1	2	yes	—
446	C₄	C₂×SD₁₆×D₈₉	1	2	yes	—
447	C₄	#19152396	1	2	yes	—
448	C₄	#19152400	1	2	yes	—
449	C₂	—	2	2	no	—
450	C₂	—	16	1	no	—
451	C₂	—	1424	2	no	—
452	C₂	C₂×#19151969	1	1	yes	characteristic
453	C₂	#26030720	1	1	yes	characteristic
454	C₂	#26030739	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	#19623
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. #26031190	C₂	semidirect
2. #26031174	C₂	semidirect
3. #26030799	C₂	semidirect
5. C₂×#19151945	C₂	semidirect
6. #26019879	C₂	semidirect
7. #26019877	C₂	semidirect
8. #26019855	C₂	semidirect
9. #26019843	C₂	semidirect
10. C₈×#13083558	C₂	semidirect
11. C₈₉×#3167	C₂	semidirect
16. #19152001	C₂²	semidirect
17. #19151994	C₂²	semidirect
22. #19151970	C₂²	semidirect
23. #19151950	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
121. #13083558	SD₁₆	semidirect
230. #3167	D₈₉	semidirect
239. C₈₉	#19623	semidirect
248. #498	C₂×D₈₉	semidirect
254. #492	C₂×D₈₉	semidirect
256. #487	C₂×D₈₉	semidirect
261. #486	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26031190	2
#26031174	2
#26030799	2
#26030705	2
C₂×#19151945	2
#26019879	2
#26019877	2
#26019855	2
#26019843	2
C₈×#13083558	2
C₈₉×#3167	2
#19623	89