Subgroups — #36537976

Order 22784.

662 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	#26031559	C₂	1	1	yes	maximal, characteristic
2	#26031377	C₂	1	1	yes	maximal, characteristic, complemented
3	#26030646	C₂	1	1	yes	maximal, characteristic, complemented
4	#26019827	C₂	1	2	yes	maximal, complemented
5	#26019785	C₂	1	2	yes	maximal, complemented
6	#26019703	C₂	1	2	yes	maximal, complemented
7	#26019661	C₂	1	2	yes	maximal, complemented
8	#26019004	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#19151346	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018902	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈₉×#2935	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152148	C₂²	1	1	yes	characteristic
13	C₂×#15668012	C₂²	1	1	yes	characteristic
14	#19151994	—	2	1	no	—
15	#19151958	—	2	2	no	—
16	#19151949	C₂²	1	2	yes	—
17	#19151945	C₂²	1	2	yes	—
18	#19151944	—	2	1	no	—
19	#19151914	—	2	2	no	—
20	#19151888	C₂²	1	2	yes	—
21	#19151888	C₂²	1	2	yes	—
22	#19151878	C₂²	1	2	yes	—
23	#19151875	—	2	1	no	—
24	#19151832	—	2	2	no	—
25	#19151793	C₂²	1	2	yes	—
26	#19151790	—	2	1	no	—
27	#19151651	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊#10623494	C₂²	1	1	yes	characteristic
29	#19151600	—	2	1	no	—
30	#19151600	—	2	1	no	—
31	#19151351	C₂²	1	2	yes	—
32	#19151349	C₂²	1	2	yes	—
33	#19151346	C₂²	1	2	yes	—
34	#19151346	C₂²	1	2	yes	—
35	#19151345	C₂²	1	1	yes	characteristic
36	#19151345	C₂²	1	1	yes	characteristic
37	#19151341	C₂²	1	1	yes	characteristic
38	#19151341	C₂²	1	1	yes	characteristic
39	C₂×#131×C₈₉	—	2	1	no	—
40	#532×C₈₉	C₂²	1	1	yes	characteristic
41	#436×C₈₉	C₂²	1	2	yes	—
42	#435×C₈₉	—	2	2	no	—
43	C₈×D₄×C₈₉	C₂²	1	2	yes	—
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	C₂×#13083574	—	2	1	no	—
48	C₂²×Dic₁₇₈	—	2	1	no	—
49	C₂×#13083559	—	2	2	no	—
50	C₂²×#10623494	—	2	1	no	—
51	#15668012	—	2	1	no	—
52	#15668012	—	2	1	no	—
53	#15668012	—	2	1	no	—
54	#15668012	C₂³	1	1	yes	characteristic
55	#15668012	C₂³	1	2	yes	—
56	#15668009	C₂³	1	1	yes	characteristic
57	#15668000	—	2	1	no	—
58	#15667986	—	2	1	no	—
59	#15667986	—	2	1	no	—
60	C₄×D₃₅₆	—	2	1	no	—
61	C₄×D₃₅₆	—	2	1	no	—
62	C₂×C₄⋊Dic₈₉	—	2	1	no	—
63	C₂×C₄⋊Dic₈₉	—	2	1	no	—
64	#15667945	—	2	2	no	—
65	#15667943	—	2	2	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	#15667937	—	2	2	no	—
72	#15667937	—	2	2	no	—
73	#15667934	—	2	2	no	—
74	#15667934	—	2	2	no	—
75	#15667933	—	2	2	no	—
76	#15667933	—	2	2	no	—
77	#15667933	—	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	#13083574	—	4	2	no	—
104	#13083574	—	4	2	no	—
105	C₂×Dic₁₇₈	—	2	1	no	—
106	C₂×Dic₁₇₈	—	2	2	no	—
107	C₂×Dic₁₇₈	—	4	1	no	—
108	C₂×Dic₁₇₈	—	8	2	no	—
109	C₂×D₃₅₆	—	2	1	no	—
110	C₂×D₃₅₆	—	2	1	no	—
111	C₂×D₃₅₆	—	2	1	no	—
112	C₂×C₂²⋊D₈₉	—	4	1	no	—
113	C₂²×Dic₈₉	—	4	1	no	—
114	C₂×C₄×D₈₉	—	4	1	no	—
115	#13083559	—	8	2	no	—
116	C₂×#10623494	—	2	2	no	—
117	C₂×#10623494	—	2	1	no	—
118	C₂×#10623494	—	2	1	no	—
119	C₂×#10623494	—	8	1	no	—
120	C₄⋊Dic₈₉	—	2	1	no	—
121	C₄⋊Dic₈₉	—	2	2	no	—
122	C₄⋊Dic₈₉	—	2	2	no	—
123	C₄⋊Dic₈₉	—	2	1	no	—
124	C₄⋊Dic₈₉	—	4	1	no	—
125	C₄⋊Dic₈₉	—	4	1	no	—
126	#13083551	—	4	1	no	—
127	#13083551	—	4	1	no	—
128	#41×C₈₉	—	4	2	no	—
129	#41×C₈₉	—	4	2	no	—
130	C₂×Q₈×C₈₉	—	2	1	no	—
131	C₂×D₄×C₈₉	—	2	2	no	—
132	C₂×D₄×C₈₉	—	2	1	no	—
133	C₂×D₄×C₈₉	—	2	1	no	—
134	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₈₉	—	2	2	no	—
136	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
139	M₁₆×C₈₉	—	2	2	no	—
140	M₁₆×C₈₉	—	2	2	no	—
141	M₁₆×C₈₉	—	4	4	no	—
142	C₂×C₈×C₈₉	—	2	1	no	—
143	C₂×C₈×C₈₉	—	2	1	no	—
144	C₂×C₈×C₈₉	—	4	4	no	—
145	C₂×C₈×C₈₉	—	4	2	no	—
146	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₈₉	C₂×D₄	1	2	yes	—
148	C₄⋊C₄×C₈₉	—	2	1	no	—
149	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
150	C₂²⋊C₄×C₈₉	—	2	2	no	—
151	C₂²⋊C₄×C₈₉	—	2	2	no	—
152	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
153	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
154	C₄²×C₈₉	#41	1	1	yes	characteristic
155	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
156	C₂³×C₈₉	—	2	2	no	—
157	C₂³×C₈₉	#121	1	1	yes	characteristic
158	C₂²×D₈₉	—	4	1	no	—
159	Q₈×C₈₉	—	4	2	no	—
160	D₄×C₈₉	—	2	2	no	—
161	D₄×C₈₉	—	2	2	no	—
162	D₄×C₈₉	—	4	4	no	—
163	D₄×C₈₉	—	4	2	no	—
164	D₄×C₈₉	—	8	1	no	—
165	C₂×C₄×C₈₉	—	2	1	no	—
166	C₂×C₄×C₈₉	—	2	1	no	—
167	C₂×C₄×C₈₉	—	2	2	no	—
168	C₂×C₄×C₈₉	—	4	1	no	—
169	C₂×C₄×C₈₉	—	4	2	no	—
170	C₂×C₄×C₈₉	—	4	2	no	—
171	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
172	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
173	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
174	C₂×C₄×C₈₉	#135	1	2	yes	—
175	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
176	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
179	C₂²⋊D₈₉	—	8	2	no	—
180	C₂×Dic₈₉	—	4	1	no	—
181	C₂×Dic₈₉	—	4	2	no	—
182	C₂×Dic₈₉	—	8	2	no	—
183	D₃₅₆	—	4	1	no	—
184	D₃₅₆	—	4	1	no	—
185	D₃₅₆	—	4	1	no	—
186	D₃₅₆	—	4	1	no	—
187	D₃₅₆	—	8	1	no	—
188	C₄×D₈₉	—	8	2	no	—
189	Dic₁₇₈	—	4	1	no	—
190	Dic₁₇₈	—	4	1	no	—
191	Dic₁₇₈	—	8	2	no	—
192	Dic₁₇₈	—	8	2	no	—
193	C₈×C₈₉	—	2	2	no	—
194	C₈×C₈₉	—	2	2	no	—
195	C₈×C₈₉	—	4	1	no	—
196	C₈×C₈₉	—	4	1	no	—
197	#10623494	—	4	1	no	—
198	#10623494	—	4	2	no	—
199	#10623494	—	4	1	no	—
200	C₂²×C₈₉	—	2	1	no	—
201	C₂²×C₈₉	—	2	1	no	—
202	C₂²×C₈₉	—	4	2	no	—
203	C₂²×C₈₉	—	4	2	no	—
204	C₂²×C₈₉	—	4	2	no	—
205	C₂²×C₈₉	#463	1	2	yes	—
206	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
207	C₂×D₈₉	—	8	1	no	—
208	C₂×D₈₉	—	8	1	no	—
209	C₂×D₈₉	—	8	1	no	—
210	C₄×C₈₉	—	2	1	no	—
211	C₄×C₈₉	—	2	1	no	—
212	C₄×C₈₉	—	2	1	no	—
213	C₄×C₈₉	—	4	2	no	—
214	C₄×C₈₉	#463	1	2	yes	—
215	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
216	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
217	C₄×C₈₉	#577	1	1	yes	characteristic
218	C₄×C₈₉	#578	1	1	yes	characteristic
219	Dic₈₉	—	8	1	no	—
220	Dic₈₉	—	8	2	no	—
221	#19236	—	89	1	no	maximal, Sylow
222	C₂×C₈₉	—	2	2	no	—
223	C₂×C₈₉	—	8	2	no	—
224	C₂×C₈₉	C₂×#463	1	1	yes	characteristic
225	C₂×C₈₉	#3063	1	1	yes	characteristic
226	C₂×C₈₉	#3068	1	1	yes	characteristic
227	D₈₉	—	16	1	no	—
228	#3245	—	89	1	no	—
229	#3227	—	89	1	no	—
230	#3141	—	89	1	no	—
231	#2935	D₈₉	1	1	yes	characteristic, complemented
232	#1703	—	89	2	no	—
233	#1697	—	89	2	no	—
234	#1683	—	89	2	no	—
235	#1677	—	89	2	no	—
236	#1565	—	89	1	no	—
237	C₂×#333	—	89	1	no	—
238	#1540	—	89	1	no	—
239	C₈₉	#19236	1	1	yes	characteristic, complemented, Sylow
240	C₂×#131	—	2	1	no	—
241	#532	—	89	1	no	—
242	#532	C₂×D₈₉	1	1	yes	characteristic
243	C₂×C₄⋊Q₈	—	89	1	no	—
244	#498	—	178	1	no	—
245	#489	—	178	2	no	—
246	#487	—	89	2	no	—
247	#486	—	89	2	no	—
248	#486	—	178	1	no	—
249	#481	—	178	2	no	—
250	#476	—	89	2	no	—
251	#476	—	89	2	no	—
252	#474	—	89	2	no	—
253	#474	—	178	1	no	—
254	#466	—	178	2	no	—
255	#459	—	89	2	no	—
256	#459	—	178	1	no	—
257	#436	C₂×D₈₉	1	2	yes	—
258	#435	—	2	2	no	—
259	C₈×D₄	C₂×D₈₉	1	2	yes	—
260	#431	—	89	1	no	—
261	C₂×C₄⋊C₈	—	89	1	no	—
262	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
263	#417	—	178	1	no	—
264	#417	—	178	1	no	—
265	#408	—	2	1	no	—
266	C₄×M₁₆	C₂×D₈₉	1	1	yes	characteristic
267	#335	—	89	2	no	—
268	#334	—	89	2	no	—
269	#333	—	89	2	no	—
270	#333	—	89	2	no	—
271	#332	—	89	1	no	—
272	#332	—	89	1	no	—
273	#331	—	89	1	no	—
274	#331	—	89	1	no	—
275	C₂×#41	—	2	1	no	—
276	C₂×#41	—	178	1	no	—
277	C₂²×Q₈	—	178	1	no	—
278	C₂×D₈	—	178	2	no	—
279	#131	—	4	4	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
282	C₂×M₁₆	C₂²⋊D₈₉	1	1	yes	characteristic
283	C₂²×C₈	—	2	1	no	—
284	C₂²×C₈	—	2	2	no	—
285	C₂²×C₈	—	178	1	no	—
286	C₄⋊Q₈	—	89	2	no	—
287	C₄⋊Q₈	—	89	1	no	—
288	C₄⋊Q₈	—	178	1	no	—
289	C₄⋊Q₈	—	178	1	no	—
290	C₄⋊Q₈	—	178	1	no	—
291	C₄⋊Q₈	D₃₅₆	1	1	yes	characteristic
292	#127	—	89	1	no	—
293	#127	D₃₅₆	1	1	yes	characteristic
294	#124	—	2	1	no	—
295	#124	—	178	1	no	—
296	#121	—	2	1	no	—
297	#121	—	178	1	no	—
298	#121	—	178	1	no	—
299	#121	D₃₅₆	1	2	yes	—
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	178	1	no	—
302	C₄×D₄	—	178	1	no	—
303	C₄×D₄	C₂²×D₈₉	1	2	yes	—
304	C₂×C₄⋊C₄	—	178	1	no	—
305	C₂×C₄⋊C₄	—	178	1	no	—
306	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
307	#107	—	178	2	no	—
308	#106	—	178	2	no	—
309	#106	—	178	2	no	—
310	C₄⋊C₈	—	2	1	no	—
311	C₄⋊C₈	—	89	1	no	—
312	C₄⋊C₈	—	89	1	no	—
313	C₄⋊C₈	—	89	2	no	—
314	C₄⋊C₈	—	178	1	no	—
315	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
316	C₄⋊C₈	C₂²×D₈₉	1	1	yes	characteristic
317	#103	—	178	2	no	—
318	#103	—	178	2	no	—
319	#102	—	178	2	no	—
320	#102	—	178	2	no	—
321	#102	—	178	2	no	—
322	#102	—	178	2	no	—
323	#102	—	178	2	no	—
324	#102	—	178	2	no	—
325	C₂²⋊C₈	—	2	2	no	—
326	C₂²⋊C₈	—	2	2	no	—
327	C₂²⋊C₈	—	178	1	no	—
328	#97	C₂²⋊D₈₉	1	2	yes	—
329	C₄×C₈	—	178	1	no	—
330	C₄×C₈	C₂²×D₈₉	1	2	yes	—
331	#41	—	4	2	no	—
332	#41	—	4	2	no	—
333	#41	—	356	2	no	—
334	#41	—	356	2	no	—
335	C₂×Q₈	—	2	1	no	—
336	C₂×Q₈	—	356	1	no	—
337	C₂×Q₈	—	178	1	no	—
338	C₂×Q₈	—	178	2	no	—
339	C₂×Q₈	—	712	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	1	no	—
342	C₂×D₄	—	2	1	no	—
343	C₂×D₄	—	356	1	no	—
344	C₂×D₄	—	178	1	no	—
345	C₂×D₄	—	178	1	no	—
346	C₂×D₄	—	178	1	no	—
347	C₂×D₄	C₂×D₃₅₆	1	2	yes	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	356	1	no	—
350	C₂²×C₄	—	356	1	no	—
351	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
352	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
353	C₂²×C₄	#13083574	1	1	yes	characteristic
354	D₈	—	712	2	no	—
355	M₁₆	—	2	2	no	—
356	M₁₆	—	2	2	no	—
357	M₁₆	—	4	4	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	4	4	no	—
361	C₂×C₈	—	4	2	no	—
362	C₂×C₈	—	178	1	no	—
363	C₂×C₈	—	178	1	no	—
364	C₂×C₈	—	178	2	no	—
365	C₂×C₈	—	712	1	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	—	356	1	no	—
370	C₄⋊C₄	—	356	1	no	—
371	C₄⋊C₄	—	178	2	no	—
372	C₄⋊C₄	—	178	2	no	—
373	C₄⋊C₄	—	178	1	no	—
374	C₄⋊C₄	—	178	1	no	—
375	C₄⋊C₄	C₂×D₃₅₆	1	2	yes	—
376	C₂²⋊C₄	—	2	2	no	—
377	C₂²⋊C₄	—	2	2	no	—
378	C₂²⋊C₄	—	356	1	no	—
379	C₂²⋊C₄	—	356	1	no	—
380	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
381	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
382	C₄²	#13083574	1	1	yes	characteristic
383	C₄²	C₂³×D₈₉	1	1	yes	characteristic
384	C₂³	—	2	2	no	—
385	C₂³	—	356	1	no	—
386	C₂³	#15667986	1	1	yes	characteristic
387	Q₈	—	4	2	no	—
388	Q₈	—	356	1	no	—
389	Q₈	—	356	1	no	—
390	Q₈	—	712	2	no	—
391	Q₈	—	712	2	no	—
392	D₄	—	2	2	no	—
393	D₄	—	2	2	no	—
394	D₄	—	4	4	no	—
395	D₄	—	4	2	no	—
396	D₄	—	8	1	no	—
397	D₄	—	356	1	no	—
398	D₄	—	356	1	no	—
399	D₄	—	356	1	no	—
400	D₄	—	356	1	no	—
401	D₄	—	712	1	no	—
402	D₄	—	712	2	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	4	1	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	356	1	no	—
410	C₂×C₄	—	356	2	no	—
411	C₂×C₄	—	712	2	no	—
412	C₂×C₄	—	712	2	no	—
413	C₂×C₄	#15667986	1	1	yes	characteristic
414	C₂×C₄	#15667986	1	1	yes	characteristic
415	C₂×C₄	#15667986	1	1	yes	characteristic
416	C₂×C₄	#15668032	1	2	yes	—
417	C₂×C₄	#15668038	1	2	yes	—
418	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
420	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
421	C₈	—	2	2	no	—
422	C₈	—	2	2	no	—
423	C₈	—	4	1	no	—
424	C₈	—	4	1	no	—
425	C₈	—	356	1	no	—
426	C₈	—	356	2	no	—
427	C₈	—	356	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	2	no	—
432	C₂²	—	4	2	no	—
433	C₂²	—	712	1	no	—
434	C₂²	—	712	1	no	—
435	C₂²	—	712	1	no	—
436	C₂²	#19151813	1	2	yes	—
437	C₂²	C₂×#15667986	1	1	yes	characteristic
438	C₄	—	2	1	no	—
439	C₄	—	2	1	no	—
440	C₄	—	2	1	no	—
441	C₄	—	4	2	no	—
442	C₄	—	712	1	no	—
443	C₄	—	712	2	no	—
444	C₄	#19151813	1	2	yes	—
445	C₄	C₂×#15668032	1	1	yes	characteristic
446	C₄	C₂×#15668038	1	1	yes	characteristic
447	C₄	#19152410	1	1	yes	characteristic
448	C₄	#19152415	1	1	yes	characteristic
449	C₂	—	2	2	no	—
450	C₂	—	8	2	no	—
451	C₂	—	1424	1	no	—
452	C₂	C₂×#19151813	1	1	yes	characteristic
453	C₂	#26029943	1	1	yes	characteristic
454	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	#26031559	C₂
hypercenter	#2935	D₈₉
hypocenter	C₈₉	#19236
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
2. #26031377	C₂	semidirect
3. #26030646	C₂	semidirect
4. #26019827	C₂	semidirect
5. #26019785	C₂	semidirect
6. #26019703	C₂	semidirect
7. #26019661	C₂	semidirect
8. #26019004	C₂	semidirect
9. C₂×#19151346	C₂	semidirect
10. #26018902	C₂	semidirect
11. C₈₉×#2935	C₂	semidirect
231. #2935	D₈₉	semidirect
239. C₈₉	#19236	semidirect

Maximal subgroups

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

subgroup	index
#26031559	2
#26031377	2
#26030646	2
#26019827	2
#26019785	2
#26019703	2
#26019661	2
#26019004	2
C₂×#19151346	2
#26018902	2
C₈₉×#2935	2
#19236	89