Subgroups — #36536697

Order 22784.

694 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	#26030762	C₂	1	1	yes	maximal, characteristic, complemented
2	#26030261	C₂	1	1	yes	maximal, characteristic
3	#26030256	C₂	1	1	yes	maximal, characteristic
4	C₂×#19151663	C₂	1	1	yes	maximal, characteristic
5	#26019650	C₂	1	2	yes	maximal, complemented
6	#26019640	C₂	1	2	yes	maximal, complemented
7	#26019630	C₂	1	2	yes	maximal, complemented
8	#26019626	C₂	1	2	yes	maximal, complemented
9	#26018998	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018910	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#1542	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₈₉	—	2	1	no	—
13	#19152155	C₂²	1	1	yes	characteristic
14	C₂×C₄×D₃₅₆	C₂²	1	1	yes	characteristic
15	#19152001	C₂²	1	1	yes	characteristic, complemented
16	#19152001	C₂²	1	1	yes	characteristic, complemented
17	#19151997	—	2	1	no	—
18	#19151997	—	2	1	no	—
19	#19151994	C₂²	1	1	yes	characteristic, complemented
20	#19151994	C₂²	1	1	yes	characteristic, complemented
21	#19151929	—	2	1	no	—
22	#19151926	—	2	1	no	—
23	#19151889	C₂²	1	2	yes	—
24	#19151885	C₂²	1	2	yes	—
25	#19151804	C₂²	1	2	yes	—
26	#19151800	C₂²	1	2	yes	—
27	#19151751	—	2	1	no	—
28	#19151748	—	2	1	no	—
29	C₄×#13083563	—	2	2	no	—
30	C₄×#13083561	—	2	2	no	—
31	#19151663	—	2	1	no	—
32	#19151663	—	2	1	no	—
33	#19151663	C₂²	1	2	yes	—
34	#19151663	C₂²	1	2	yes	—
35	#19151651	C₂²	1	1	yes	characteristic
36	#19151634	—	2	1	no	—
37	#19151634	—	2	1	no	—
38	C₂×#15667924	—	2	1	no	—
39	C₂×C₄×#10623494	C₂²	1	1	yes	characteristic
40	#19151350	C₂²	1	2	yes	complemented
41	#19151348	C₂²	1	2	yes	complemented
42	#19151346	C₂²	1	2	yes	complemented
43	#19151343	C₂²	1	2	yes	complemented
44	#533×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	#333×C₈₉	C₂²	1	2	yes	complemented
48	#332×C₈₉	C₂²	1	2	yes	complemented
49	C₂²×D₃₅₆	D₄	1	1	yes	characteristic
50	C₂²×C₄×D₈₉	—	2	1	no	—
51	C₂×#13083563	—	2	2	no	—
52	C₂×#13083561	—	2	2	no	—
53	C₂²×#10623494	D₄	1	1	yes	characteristic
54	C₂²×#10623494	D₄	1	1	yes	characteristic
55	C₂×C₈×D₈₉	—	2	2	no	—
56	C₂×C₈×D₈₉	—	2	2	no	—
57	C₂×C₈×D₈₉	—	4	4	no	—
58	#15668012	C₂³	1	1	yes	characteristic
59	#15668012	C₂³	1	1	yes	characteristic
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	C₄×D₃₅₆	—	2	1	no	—
66	C₄×D₃₅₆	—	2	1	no	—
67	C₄×D₃₅₆	D₄	1	2	yes	—
68	C₄×D₃₅₆	C₂³	1	2	yes	—
69	#15667971	—	2	1	no	—
70	C₂×C₄⋊Dic₈₉	D₄	1	1	yes	characteristic
71	C₂×#13083551	—	2	1	no	—
72	#15667945	—	2	1	no	—
73	#15667945	—	2	1	no	—
74	#15667945	—	2	1	no	—
75	#15667945	—	2	1	no	—
76	#15667944	—	2	2	no	—
77	#15667943	—	2	1	no	—
78	#15667943	—	2	1	no	—
79	#15667943	—	2	1	no	—
80	#15667943	—	2	1	no	—
81	#15667943	—	2	2	no	—
82	C₄⋊#10623494	C₂³	1	2	yes	—
83	#15667937	—	2	2	no	—
84	#15667936	—	2	2	no	—
85	#15667934	—	2	2	no	—
86	#15667932	—	2	2	no	—
87	C₂²⋊#10623494	—	2	1	no	—
88	#15667924	—	2	2	no	—
89	#15667924	—	2	2	no	—
90	C₄×#10623494	—	2	1	no	—
91	C₄×#10623494	D₄	1	1	yes	characteristic
92	C₄×#10623494	D₄	1	1	yes	characteristic
93	C₄×#10623494	C₂³	1	1	yes	characteristic
94	C₄×#10623494	C₂³	1	1	yes	characteristic
95	C₂²×C₈×C₈₉	—	2	1	no	—
96	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
97	C₄⋊Q₈×C₈₉	C₂³	1	1	yes	characteristic
98	#125×C₈₉	—	2	1	no	—
99	C₂²⋊Q₈×C₈₉	—	2	1	no	—
100	C₂²⋊Q₈×C₈₉	—	2	1	no	—
101	C₄×Q₈×C₈₉	—	2	1	no	—
102	C₄×Q₈×C₈₉	—	2	1	no	—
103	#117×C₈₉	—	2	1	no	—
104	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₈₉	—	2	1	no	—
106	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
107	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
108	C₂²⋊C₈×C₈₉	—	2	1	no	—
109	C₄×C₈×C₈₉	—	2	1	no	—
110	C₂³×D₈₉	—	2	1	no	—
111	C₂×Dic₁₇₈	—	2	1	no	—
112	C₂×Dic₁₇₈	—	2	1	no	—
113	C₂×D₃₅₆	—	2	1	no	—
114	C₂×D₃₅₆	—	2	4	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	#13083563	—	4	4	no	—
122	#13083561	—	4	4	no	—
123	C₂×#10623494	—	2	2	no	—
124	C₂×#10623494	—	2	2	no	—
125	C₂×#10623494	SD₁₆	1	4	yes	complemented
126	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
127	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
128	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
129	C₂×#10623494	C₂×D₄	1	1	yes	characteristic
130	C₈×D₈₉	—	4	4	no	—
131	C₈×D₈₉	—	4	4	no	—
132	C₄⋊Dic₈₉	—	2	1	no	—
133	C₄⋊Dic₈₉	—	2	1	no	—
134	C₄⋊Dic₈₉	—	2	1	no	—
135	C₄⋊Dic₈₉	—	2	1	no	—
136	C₄⋊Dic₈₉	—	2	1	no	—
137	C₄⋊Dic₈₉	C₂×D₄	1	2	yes	—
138	#13083553	—	4	1	no	—
139	#13083553	—	4	1	no	—
140	C₂²⋊Dic₈₉	—	4	1	no	—
141	#13083551	—	2	2	no	—
142	#13083551	—	2	2	no	—
143	C₄×Dic₈₉	—	4	1	no	—
144	C₂×Q₈×C₈₉	—	2	1	no	—
145	C₂×Q₈×C₈₉	—	2	1	no	—
146	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
149	C₂×C₈×C₈₉	—	2	2	no	—
150	C₂×C₈×C₈₉	—	2	2	no	—
151	C₂×C₈×C₈₉	—	4	2	no	—
152	C₄⋊C₄×C₈₉	—	2	1	no	—
153	C₄⋊C₄×C₈₉	—	2	1	no	—
154	C₄⋊C₄×C₈₉	—	2	1	no	—
155	C₄⋊C₄×C₈₉	—	2	1	no	—
156	C₄⋊C₄×C₈₉	—	4	1	no	—
157	C₄⋊C₄×C₈₉	—	4	1	no	—
158	C₂²⋊C₄×C₈₉	—	4	1	no	—
159	C₄²×C₈₉	—	4	1	no	—
160	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
161	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₈₉	#41	1	1	yes	characteristic
163	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
164	C₂³×C₈₉	#121	1	1	yes	characteristic
165	C₂²×D₈₉	—	2	4	no	—
166	C₂²×D₈₉	—	2	2	no	—
167	C₂²×D₈₉	—	4	2	no	—
168	C₂²×D₈₉	—	4	2	no	—
169	Q₈×C₈₉	—	4	2	no	—
170	Q₈×C₈₉	—	8	1	no	—
171	C₂×C₄×C₈₉	—	2	2	no	—
172	C₂×C₄×C₈₉	—	4	1	no	—
173	C₂×C₄×C₈₉	—	4	1	no	—
174	C₂×C₄×C₈₉	—	4	1	no	—
175	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
176	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
177	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂×SD₁₆	1	2	yes	—
179	C₂×C₄×C₈₉	#137	1	2	yes	—
180	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
181	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
182	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
183	C₂×Dic₈₉	—	2	2	no	—
184	C₂×Dic₈₉	—	4	2	no	—
185	C₂×Dic₈₉	—	4	1	no	—
186	C₂×Dic₈₉	—	4	1	no	—
187	D₃₅₆	—	2	4	no	—
188	D₃₅₆	—	2	2	no	—
189	D₃₅₆	#135	1	4	yes	—
190	C₄×D₈₉	—	4	2	no	—
191	C₄×D₈₉	—	4	2	no	—
192	C₄×D₈₉	—	4	4	no	—
193	Dic₁₇₈	—	4	2	no	—
194	Dic₁₇₈	—	8	1	no	—
195	C₈×C₈₉	—	4	2	no	—
196	C₈×C₈₉	—	4	2	no	—
197	#10623494	—	2	1	no	—
198	#10623494	—	2	1	no	—
199	#10623494	—	4	2	no	—
200	#10623494	C₂×SD₁₆	1	2	yes	—
201	#10623494	C₂×SD₁₆	1	2	yes	—
202	C₂²×C₈₉	—	2	1	no	—
203	C₂²×C₈₉	—	2	1	no	—
204	C₂²×C₈₉	#461	1	2	yes	—
205	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
206	C₂×D₈₉	—	2	4	no	—
207	C₂×D₈₉	—	4	8	no	—
208	C₂×D₈₉	—	4	2	no	—
209	C₂×D₈₉	—	4	2	no	—
210	C₄×C₈₉	—	2	1	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	#461	1	2	yes	—
216	C₄×C₈₉	C₂²×SD₁₆	1	1	yes	characteristic
217	C₄×C₈₉	C₂×#135	1	2	yes	—
218	C₄×C₈₉	C₂×#137	1	1	yes	characteristic
219	Dic₈₉	—	4	2	no	—
220	Dic₈₉	—	8	1	no	—
221	Dic₈₉	—	8	1	no	—
222	#19105	—	89	1	no	maximal, Sylow
223	C₂×C₈₉	—	2	2	no	—
224	C₂×C₈₉	C₂×#461	1	1	yes	characteristic
225	C₂×C₈₉	#3050	1	1	yes	characteristic
226	C₂×C₈₉	#3067	1	1	yes	characteristic
227	D₈₉	—	4	4	no	—
228	#3160	—	89	1	no	—
229	#3101	—	89	1	no	—
230	#3101	—	89	1	no	—
231	C₂×C₈×D₄	—	89	1	no	—
232	#1675	—	89	2	no	—
233	#1673	—	89	2	no	—
234	#1671	—	89	2	no	—
235	#1671	—	89	2	no	—
236	#1564	—	89	1	no	—
237	#1542	—	89	1	no	—
238	#1542	D₈₉	1	1	yes	characteristic, complemented
239	C₈₉	#19105	1	1	yes	characteristic, complemented, Sylow
240	C₂³×C₈	—	178	1	no	—
241	#533	—	89	1	no	—
242	#533	C₂×D₈₉	1	1	yes	characteristic
243	C₂×C₄×D₄	—	89	1	no	—
244	#500	—	89	1	no	—
245	#500	—	89	1	no	—
246	#499	—	178	1	no	—
247	#499	—	178	1	no	—
248	#498	—	89	1	no	—
249	#498	—	89	1	no	—
250	#483	—	178	1	no	—
251	#483	—	178	1	no	—
252	#476	—	89	2	no	—
253	#476	—	89	2	no	—
254	#461	—	89	2	no	—
255	#461	—	89	2	no	—
256	#450	—	178	1	no	—
257	#450	—	178	1	no	—
258	C₄×SD₁₆	—	178	2	no	—
259	C₄×SD₁₆	—	178	2	no	—
260	C₈×D₄	—	89	2	no	—
261	C₈×D₄	—	89	2	no	—
262	C₈×D₄	—	178	1	no	—
263	C₈×D₄	—	178	1	no	—
264	#431	—	89	1	no	—
265	#431	C₂×D₈₉	1	1	yes	characteristic
266	#427	—	178	1	no	—
267	#427	—	178	1	no	—
268	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
269	C₂×C₂²⋊C₈	—	178	1	no	—
270	C₂×C₄×C₈	—	89	1	no	—
271	#335	—	89	2	no	—
272	#334	—	89	2	no	—
273	#333	—	89	2	no	—
274	#333	C₂×D₈₉	1	2	yes	complemented
275	#332	—	89	2	no	—
276	#332	C₂×D₈₉	1	2	yes	complemented
277	C₂²×D₄	—	89	1	no	—
278	C₂³×C₄	—	178	1	no	—
279	C₂×SD₁₆	—	178	2	no	—
280	C₂×SD₁₆	—	178	2	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	89	1	no	—
283	C₂²×C₈	—	89	1	no	—
284	C₂²×C₈	—	356	4	no	—
285	C₂²×C₈	—	178	2	no	—
286	C₂²×C₈	—	178	2	no	—
287	C₄⋊Q₈	—	89	1	no	—
288	C₄⋊Q₈	—	89	1	no	—
289	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
290	C₄⋊Q₈	C₂²×D₈₉	1	1	yes	characteristic
291	#125	—	2	1	no	—
292	#125	—	178	1	no	—
293	C₂²⋊Q₈	—	2	1	no	—
294	C₂²⋊Q₈	—	2	1	no	—
295	C₂²⋊Q₈	—	178	1	no	—
296	C₂²⋊Q₈	—	178	1	no	—
297	C₄×Q₈	—	2	1	no	—
298	C₄×Q₈	—	2	1	no	—
299	C₄×Q₈	—	178	1	no	—
300	C₄×Q₈	—	178	1	no	—
301	C₄×D₄	—	89	2	no	—
302	C₄×D₄	—	89	2	no	—
303	C₄×D₄	—	178	1	no	—
304	C₄×D₄	—	178	1	no	—
305	#117	—	2	1	no	—
306	#117	—	178	1	no	—
307	C₂×C₄⋊C₄	—	89	1	no	—
308	C₂×C₂²⋊C₄	—	178	1	no	—
309	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
310	#107	—	178	1	no	—
311	#107	—	178	1	no	—
312	#107	—	178	1	no	—
313	#107	—	178	1	no	—
314	#106	—	178	2	no	—
315	#106	—	178	1	no	—
316	#106	—	178	1	no	—
317	#106	—	178	1	no	—
318	#106	—	178	1	no	—
319	#106	—	178	2	no	—
320	C₄⋊C₈	—	2	1	no	—
321	C₄⋊C₈	—	89	2	no	—
322	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
323	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
324	#103	—	178	2	no	—
325	#103	—	178	2	no	—
326	#102	—	178	2	no	—
327	#102	—	178	2	no	—
328	C₂²⋊C₈	—	2	1	no	—
329	C₂²⋊C₈	—	178	2	no	—
330	C₂²⋊C₈	—	178	2	no	—
331	C₂²⋊C₈	—	178	1	no	—
332	C₄×C₈	—	2	1	no	—
333	C₄×C₈	—	89	1	no	—
334	C₄×C₈	—	89	1	no	—
335	C₄×C₈	—	89	1	no	—
336	C₄×C₈	—	89	1	no	—
337	C₄×C₈	—	178	1	no	—
338	C₂⁴	—	178	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	178	1	no	—
342	C₂×Q₈	—	178	1	no	—
343	C₂×D₄	—	89	2	no	—
344	C₂×D₄	—	178	4	no	—
345	C₂×D₄	—	178	1	no	—
346	C₂²×C₄	—	356	2	no	—
347	C₂²×C₄	—	356	2	no	—
348	C₂²×C₄	—	178	1	no	—
349	C₂²×C₄	—	178	2	no	—
350	C₂²×C₄	—	178	2	no	—
351	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
352	C₂²×C₄	D₄×D₈₉	1	1	yes	characteristic
353	C₂²×C₄	#13083574	1	1	yes	characteristic
354	SD₁₆	—	356	4	no	—
355	SD₁₆	—	356	4	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	4	2	no	—
359	C₂×C₈	—	89	4	no	—
360	C₂×C₈	—	89	1	no	—
361	C₂×C₈	—	89	1	no	—
362	C₂×C₈	—	89	1	no	—
363	C₂×C₈	—	89	1	no	—
364	C₂×C₈	—	356	4	no	—
365	C₂×C₈	—	356	4	no	—
366	C₂×C₈	—	178	2	no	—
367	C₂×C₈	—	178	2	no	—
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	—	4	1	no	—
373	C₄⋊C₄	—	4	1	no	—
374	C₄⋊C₄	—	89	2	no	—
375	C₄⋊C₄	—	356	1	no	—
376	C₄⋊C₄	—	356	1	no	—
377	C₄⋊C₄	—	178	1	no	—
378	C₄⋊C₄	—	178	1	no	—
379	C₄⋊C₄	—	178	1	no	—
380	C₄⋊C₄	—	178	1	no	—
381	C₄⋊C₄	—	178	1	no	—
382	C₂²⋊C₄	—	4	1	no	—
383	C₂²⋊C₄	—	356	1	no	—
384	C₂²⋊C₄	—	178	2	no	—
385	C₂²⋊C₄	—	178	2	no	—
386	C₄²	—	4	1	no	—
387	C₄²	—	356	1	no	—
388	C₄²	D₄×D₈₉	1	1	yes	characteristic
389	C₄²	D₄×D₈₉	1	1	yes	characteristic
390	C₄²	#13083574	1	1	yes	characteristic
391	C₄²	C₂³×D₈₉	1	1	yes	characteristic
392	C₂³	—	356	2	no	—
393	C₂³	—	356	2	no	—
394	C₂³	—	178	4	no	—
395	C₂³	—	178	2	no	—
396	C₂³	#15667985	1	1	yes	characteristic
397	Q₈	—	4	2	no	—
398	Q₈	—	8	1	no	—
399	Q₈	—	356	2	no	—
400	Q₈	—	712	1	no	—
401	D₄	—	89	4	no	—
402	D₄	—	178	4	no	—
403	D₄	—	178	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	1	no	—
408	C₂×C₄	—	356	2	no	—
409	C₂×C₄	—	356	2	no	—
410	C₂×C₄	—	356	4	no	—
411	C₂×C₄	—	356	2	no	—
412	C₂×C₄	—	356	1	no	—
413	C₂×C₄	—	356	1	no	—
414	C₂×C₄	—	178	2	no	—
415	C₂×C₄	#15667985	1	1	yes	characteristic
416	C₂×C₄	#15667985	1	1	yes	characteristic
417	C₂×C₄	#15667985	1	1	yes	characteristic
418	C₂×C₄	SD₁₆×D₈₉	1	2	yes	—
419	C₂×C₄	#15668044	1	2	yes	—
420	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
421	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
422	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
423	C₈	—	4	2	no	—
424	C₈	—	4	2	no	—
425	C₈	—	89	2	no	—
426	C₈	—	89	2	no	—
427	C₈	—	356	2	no	—
428	C₈	—	178	1	no	—
429	C₈	—	178	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	356	8	no	—
433	C₂²	—	356	2	no	—
434	C₂²	—	356	2	no	—
435	C₂²	—	178	4	no	—
436	C₂²	#19151802	1	2	yes	—
437	C₂²	C₂×#15667985	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	8	1	no	—
442	C₄	—	8	1	no	—
443	C₄	—	356	2	no	—
444	C₄	—	712	1	no	—
445	C₄	—	712	1	no	—
446	C₄	#19151802	1	2	yes	—
447	C₄	C₂×SD₁₆×D₈₉	1	1	yes	characteristic
448	C₄	#135×D₈₉	1	2	yes	—
449	C₄	C₂×#15668044	1	1	yes	characteristic
450	C₂	—	2	2	no	—
451	C₂	—	356	4	no	—
452	C₂	C₂×#19151802	1	1	yes	characteristic
453	C₂	#26029832	1	1	yes	characteristic
454	C₂	#26029971	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#15667985
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₈₉×#1542	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	C₂²×D₃₅₆	D₄
hypercenter	#1542	D₈₉
hypocenter	C₈₉	#19105
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1542

Complements

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

N	H ≅ G/N	type
1. #26030762	C₂	semidirect
5. #26019650	C₂	semidirect
6. #26019640	C₂	semidirect
7. #26019630	C₂	semidirect
8. #26019626	C₂	semidirect
9. #26018998	C₂	semidirect
10. #26018910	C₂	semidirect
11. C₈₉×#1542	C₂	semidirect
15. #19152001	C₂²	semidirect
16. #19152001	C₂²	semidirect
19. #19151994	C₂²	semidirect
20. #19151994	C₂²	semidirect
40. #19151350	C₂²	semidirect
41. #19151348	C₂²	semidirect
42. #19151346	C₂²	semidirect
43. #19151343	C₂²	semidirect
47. #333×C₈₉	C₂²	semidirect
48. #332×C₈₉	C₂²	semidirect
125. C₂×#10623494	SD₁₆	semidirect
238. #1542	D₈₉	semidirect
239. C₈₉	#19105	semidirect
274. #333	C₂×D₈₉	semidirect
276. #332	C₂×D₈₉	semidirect

Maximal subgroups

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

subgroup	index
#26030762	2
#26030261	2
#26030256	2
C₂×#19151663	2
#26019650	2
#26019640	2
#26019630	2
#26019626	2
#26018998	2
#26018910	2
C₈₉×#1542	2
#19105	89