Subgroups — #36537010

Order 22784.

684 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030575	C₂	1	1	yes	maximal, characteristic, complemented
2	#26030260	C₂	1	1	yes	maximal, characteristic, complemented
3	#26030252	C₂	1	1	yes	maximal, characteristic
4	#26019827	C₂	1	2	yes	maximal, complemented
5	#26019813	C₂	1	2	yes	maximal, complemented
6	#26019799	C₂	1	2	yes	maximal, complemented
7	#26019785	C₂	1	2	yes	maximal, complemented
8	#26019000	C₂	1	1	yes	maximal, characteristic, complemented
9	#26018910	C₂	1	1	yes	maximal, characteristic, complemented
10	#26018902	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#436×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152155	C₂²	1	1	yes	characteristic
13	#19152148	C₂²	1	1	yes	characteristic
14	#19151953	—	2	1	no	—
15	#19151953	—	2	1	no	—
16	#19151949	C₂²	1	1	yes	characteristic, complemented
17	#19151949	C₂²	1	1	yes	characteristic, complemented
18	#19151945	C₂²	1	1	yes	characteristic, complemented
19	#19151945	C₂²	1	1	yes	characteristic, complemented
20	#19151928	—	2	1	no	—
21	#19151911	—	2	1	no	—
22	#19151888	C₂²	1	2	yes	—
23	#19151878	C₂²	1	2	yes	—
24	#19151803	C₂²	1	2	yes	—
25	#19151793	C₂²	1	2	yes	—
26	#19151749	—	2	1	no	—
27	#19151732	—	2	1	no	—
28	C₄×#13083562	—	2	2	no	—
29	C₄×#13083559	—	2	2	no	—
30	#19151651	C₂²	1	1	yes	characteristic
31	#19151651	C₂²	1	1	yes	characteristic
32	#19151595	—	2	1	no	—
33	#19151595	—	2	1	no	—
34	#19151351	C₂²	1	2	yes	complemented
35	#19151349	C₂²	1	2	yes	complemented
36	#19151346	C₂²	1	2	yes	complemented
37	#19151345	C₂²	1	2	yes	complemented
38	#19151343	C₂²	1	2	yes	complemented
39	#19151341	C₂²	1	2	yes	complemented
40	C₂²×M₁₆×C₈₉	—	2	1	no	—
41	C₂×C₄×D₄×C₈₉	C₂²	1	1	yes	characteristic
42	#436×C₈₉	—	2	1	no	—
43	#436×C₈₉	—	2	1	no	—
44	#436×C₈₉	C₂²	1	2	yes	—
45	#436×C₈₉	C₂²	1	2	yes	—
46	C₂×C₄⋊C₈×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊C₈×C₈₉	—	2	1	no	—
48	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
49	C₂×#13083574	—	2	1	no	—
50	C₂×#13083562	—	2	2	no	—
51	C₂×#13083559	—	2	2	no	—
52	#15668012	C₂³	1	1	yes	characteristic
53	#15668012	C₂³	1	1	yes	characteristic
54	#15668012	C₂³	1	1	yes	characteristic
55	#15668009	C₂³	1	1	yes	characteristic
56	#15668004	—	2	1	no	—
57	#15668000	—	2	1	no	—
58	#15667991	—	2	1	no	—
59	#15667991	—	2	1	no	—
60	#15667986	—	2	1	no	—
61	#15667986	—	2	1	no	—
62	C₄×Dic₁₇₈	—	2	1	no	—
63	C₄×Dic₁₇₈	—	2	1	no	—
64	C₄×D₃₅₆	—	2	1	no	—
65	C₄×D₃₅₆	—	2	1	no	—
66	#15667971	—	2	1	no	—
67	#15667945	—	2	2	no	—
68	#15667943	—	2	2	no	—
69	C₄⋊#10623494	C₂³	1	2	yes	—
70	C₄⋊#10623494	C₂³	1	2	yes	—
71	#15667937	—	2	1	no	—
72	#15667937	—	2	1	no	—
73	#15667937	—	2	1	no	—
74	#15667937	—	2	1	no	—
75	#15667935	—	2	2	no	—
76	#15667934	—	2	1	no	—
77	#15667934	—	2	1	no	—
78	#15667934	—	2	1	no	—
79	#15667934	—	2	1	no	—
80	#15667933	—	2	2	no	—
81	#15667933	—	2	2	no	—
82	#15667932	—	2	2	no	—
83	C₂²⋊#10623494	—	2	1	no	—
84	C₂²⋊#10623494	—	2	1	no	—
85	C₄×#10623494	—	2	1	no	—
86	C₄×#10623494	—	2	1	no	—
87	C₂²×D₄×C₈₉	D₄	1	1	yes	characteristic
88	C₂³×C₄×C₈₉	—	2	1	no	—
89	C₂×M₁₆×C₈₉	—	2	2	no	—
90	C₂×M₁₆×C₈₉	—	2	2	no	—
91	C₂×M₁₆×C₈₉	—	4	4	no	—
92	C₂²×C₈×C₈₉	—	2	1	no	—
93	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
94	C₂²×C₈×C₈₉	D₄	1	1	yes	characteristic
95	C₄×D₄×C₈₉	—	2	1	no	—
96	C₄×D₄×C₈₉	—	2	1	no	—
97	C₄×D₄×C₈₉	D₄	1	2	yes	—
98	C₄×D₄×C₈₉	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₈₉	D₄	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₈₉	—	2	1	no	—
101	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₈₉	—	2	1	no	—
103	C₄⋊C₈×C₈₉	C₂³	1	2	yes	—
104	C₂²⋊C₈×C₈₉	—	2	2	no	—
105	C₂²⋊C₈×C₈₉	—	2	2	no	—
106	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
107	C₄×C₈×C₈₉	D₄	1	1	yes	characteristic
108	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₈₉	C₂³	1	1	yes	characteristic
110	#13083574	—	4	2	no	—
111	#13083574	—	4	2	no	—
112	C₂×Dic₁₇₈	—	2	1	no	—
113	C₂×Dic₁₇₈	—	2	1	no	—
114	C₂×Dic₁₇₈	—	2	1	no	—
115	C₂×D₃₅₆	—	2	1	no	—
116	C₂×D₃₅₆	—	2	1	no	—
117	C₂×D₃₅₆	—	2	1	no	—
118	C₂×C₂²⋊D₈₉	—	4	1	no	—
119	C₂×C₄×D₈₉	—	4	1	no	—
120	#13083562	—	4	4	no	—
121	#13083559	—	4	4	no	—
122	C₂×#10623494	—	2	2	no	—
123	C₂×#10623494	—	2	2	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	C₄⋊Dic₈₉	—	2	1	no	—
129	C₄⋊Dic₈₉	—	2	1	no	—
130	#13083553	—	4	1	no	—
131	#13083553	—	4	1	no	—
132	C₂²⋊Dic₈₉	—	4	1	no	—
133	#13083551	—	4	1	no	—
134	#13083551	—	4	1	no	—
135	C₄×Dic₈₉	—	4	1	no	—
136	C₂⁴×C₈₉	—	2	1	no	—
137	C₂×D₄×C₈₉	—	2	1	no	—
138	C₂×D₄×C₈₉	—	4	2	no	—
139	C₂×D₄×C₈₉	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₈₉	—	2	1	no	—
141	C₂²×C₄×C₈₉	—	2	2	no	—
142	C₂²×C₄×C₈₉	—	2	2	no	—
143	C₂²×C₄×C₈₉	—	4	2	no	—
144	C₂²×C₄×C₈₉	—	4	2	no	—
145	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₈₉	#41	1	1	yes	characteristic
148	M₁₆×C₈₉	—	4	4	no	—
149	M₁₆×C₈₉	—	4	4	no	—
150	C₂×C₈×C₈₉	—	2	2	no	—
151	C₂×C₈×C₈₉	—	2	2	no	—
152	C₂×C₈×C₈₉	—	2	2	no	—
153	C₂×C₈×C₈₉	—	4	2	no	—
154	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
155	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
156	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
157	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
158	C₄⋊C₄×C₈₉	—	2	1	no	—
159	C₄⋊C₄×C₈₉	C₂×D₄	1	2	yes	—
160	C₂²⋊C₄×C₈₉	—	2	2	no	—
161	C₂²⋊C₄×C₈₉	—	2	2	no	—
162	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₈₉	#41	1	1	yes	characteristic
165	C₄²×C₈₉	C₂⁴	1	1	yes	characteristic
166	C₂³×C₈₉	—	2	2	no	—
167	C₂³×C₈₉	—	4	2	no	—
168	C₂³×C₈₉	—	4	2	no	—
169	C₂³×C₈₉	—	4	2	no	—
170	C₂³×C₈₉	#121	1	1	yes	characteristic
171	C₂²×D₈₉	—	4	1	no	—
172	D₄×C₈₉	—	2	2	no	—
173	D₄×C₈₉	—	2	2	no	—
174	D₄×C₈₉	—	4	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	2	no	—
179	C₂×C₄×C₈₉	—	4	2	no	—
180	C₂×C₄×C₈₉	—	4	2	no	—
181	C₂×C₄×C₈₉	—	4	4	no	—
182	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
183	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
184	C₂×C₄×C₈₉	#121	1	1	yes	characteristic
185	C₂×C₄×C₈₉	#135	1	2	yes	—
186	C₂×C₄×C₈₉	AGL(1,ℤ/8)	1	2	yes	—
187	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
190	C₂²⋊D₈₉	—	8	2	no	—
191	C₂×Dic₈₉	—	4	1	no	—
192	C₂×Dic₈₉	—	4	1	no	—
193	C₂×Dic₈₉	—	4	1	no	—
194	D₃₅₆	—	4	1	no	—
195	D₃₅₆	—	4	1	no	—
196	D₃₅₆	—	4	2	no	—
197	D₃₅₆	—	8	1	no	—
198	C₄×D₈₉	—	8	2	no	—
199	Dic₁₇₈	—	4	1	no	—
200	Dic₁₇₈	—	4	1	no	—
201	Dic₁₇₈	—	4	2	no	—
202	Dic₁₇₈	—	8	1	no	—
203	C₈×C₈₉	—	2	1	no	—
204	C₈×C₈₉	—	2	1	no	—
205	C₈×C₈₉	—	2	1	no	—
206	C₈×C₈₉	—	2	1	no	—
207	C₈×C₈₉	—	4	2	no	—
208	#10623494	—	4	2	no	—
209	#10623494	—	4	2	no	—
210	C₂²×C₈₉	—	2	1	no	—
211	C₂²×C₈₉	—	2	1	no	—
212	C₂²×C₈₉	—	4	2	no	—
213	C₂²×C₈₉	—	4	2	no	—
214	C₂²×C₈₉	—	4	2	no	—
215	C₂²×C₈₉	—	8	4	no	—
216	C₂²×C₈₉	#463	1	2	yes	—
217	C₂²×C₈₉	C₂×#121	1	1	yes	characteristic
218	C₂×D₈₉	—	8	1	no	—
219	C₂×D₈₉	—	8	1	no	—
220	C₂×D₈₉	—	8	1	no	—
221	C₄×C₈₉	—	2	1	no	—
222	C₄×C₈₉	—	2	1	no	—
223	C₄×C₈₉	—	2	1	no	—
224	C₄×C₈₉	—	4	2	no	—
225	C₄×C₈₉	#463	1	2	yes	—
226	C₄×C₈₉	C₂×#135	1	1	yes	characteristic
227	C₄×C₈₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
228	C₄×C₈₉	#575	1	2	yes	—
229	Dic₈₉	—	8	1	no	—
230	Dic₈₉	—	8	1	no	—
231	Dic₈₉	—	8	1	no	—
232	#19142	—	89	1	no	maximal, Sylow
233	C₂×C₈₉	—	2	2	no	—
234	C₂×C₈₉	—	8	2	no	—
235	C₂×C₈₉	C₂×#463	1	1	yes	characteristic
236	C₂×C₈₉	#3054	1	1	yes	characteristic
237	C₂×C₈₉	#3067	1	1	yes	characteristic
238	D₈₉	—	16	1	no	—
239	#3131	—	89	1	no	—
240	#3101	—	89	1	no	—
241	#3100	—	89	1	no	—
242	C₂×#436	D₈₉	1	1	yes	characteristic, complemented
243	#1703	—	89	2	no	—
244	#1701	—	89	2	no	—
245	#1699	—	89	2	no	—
246	#1697	—	89	2	no	—
247	#1564	—	89	1	no	—
248	#1542	—	89	1	no	—
249	#1540	—	89	1	no	—
250	C₈₉	#19142	1	1	yes	characteristic, complemented, Sylow
251	C₂²×M₁₆	—	2	1	no	—
252	#533	—	89	1	no	—
253	#532	—	89	1	no	—
254	C₂×C₄×D₄	C₂×D₈₉	1	1	yes	characteristic
255	#488	—	178	1	no	—
256	#488	—	178	1	no	—
257	#487	—	89	1	no	—
258	#487	—	89	1	no	—
259	#486	—	89	1	no	—
260	#486	—	89	1	no	—
261	#483	—	178	1	no	—
262	#480	—	178	1	no	—
263	#476	—	89	2	no	—
264	#474	—	89	2	no	—
265	#461	—	89	2	no	—
266	#459	—	89	2	no	—
267	#450	—	178	1	no	—
268	#447	—	178	1	no	—
269	C₄×SD₁₆	—	178	2	no	—
270	C₄×D₈	—	178	2	no	—
271	#436	—	2	1	no	—
272	#436	—	2	1	no	—
273	#436	C₂×D₈₉	1	2	yes	—
274	#436	C₂×D₈₉	1	2	yes	—
275	#431	—	89	1	no	—
276	#431	—	89	1	no	—
277	C₂×C₄⋊C₈	C₂×D₈₉	1	1	yes	characteristic
278	#416	—	178	1	no	—
279	#416	—	178	1	no	—
280	C₂×C₂²⋊C₈	—	2	1	no	—
281	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
282	#335	—	89	2	no	—
283	#334	—	89	2	no	—
284	#333	—	89	2	no	—
285	#332	—	89	2	no	—
286	#332	—	89	2	no	—
287	#331	—	89	2	no	—
288	C₂×#41	—	178	1	no	—
289	C₂²×D₄	D₃₅₆	1	1	yes	characteristic
290	C₂³×C₄	—	2	1	no	—
291	C₂×SD₁₆	—	178	2	no	—
292	C₂×D₈	—	178	2	no	—
293	C₂×M₁₆	—	2	2	no	—
294	C₂×M₁₆	—	2	2	no	—
295	C₂×M₁₆	—	4	4	no	—
296	C₂²×C₈	—	2	1	no	—
297	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
298	C₂²×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
299	C₄⋊Q₈	—	89	1	no	—
300	C₄⋊Q₈	—	89	1	no	—
301	C₄⋊Q₈	—	89	1	no	—
302	#127	—	89	1	no	—
303	#125	—	178	1	no	—
304	#124	—	178	1	no	—
305	C₂²⋊Q₈	—	178	1	no	—
306	C₂²⋊Q₈	—	178	1	no	—
307	#121	—	178	1	no	—
308	#121	—	178	1	no	—
309	C₄×Q₈	—	178	1	no	—
310	C₄×Q₈	—	178	1	no	—
311	C₄×D₄	—	2	1	no	—
312	C₄×D₄	—	2	1	no	—
313	C₄×D₄	—	178	1	no	—
314	C₄×D₄	—	178	1	no	—
315	C₄×D₄	D₃₅₆	1	2	yes	—
316	C₄×D₄	C₂²×D₈₉	1	2	yes	—
317	#117	—	178	1	no	—
318	C₂×C₄⋊C₄	D₃₅₆	1	1	yes	characteristic
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
321	#107	—	178	2	no	—
322	#106	—	178	2	no	—
323	C₄⋊C₈	—	2	1	no	—
324	C₄⋊C₈	—	89	2	no	—
325	C₄⋊C₈	—	89	2	no	—
326	C₄⋊C₈	C₂²×D₈₉	1	2	yes	—
327	#103	—	178	1	no	—
328	#103	—	178	1	no	—
329	#103	—	178	1	no	—
330	#103	—	178	1	no	—
331	#103	—	178	2	no	—
332	#102	—	178	2	no	—
333	#102	—	178	2	no	—
334	#102	—	178	1	no	—
335	#102	—	178	1	no	—
336	#102	—	178	1	no	—
337	#102	—	178	1	no	—
338	#102	—	178	2	no	—
339	C₂²⋊C₈	—	2	2	no	—
340	C₂²⋊C₈	—	2	2	no	—
341	C₂²⋊C₈	—	178	1	no	—
342	C₂²⋊C₈	—	178	1	no	—
343	C₄×C₈	—	178	1	no	—
344	C₄×C₈	—	178	1	no	—
345	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
346	C₄×C₈	C₂²⋊D₈₉	1	1	yes	characteristic
347	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
348	C₄×C₈	C₂²×D₈₉	1	1	yes	characteristic
349	C₂⁴	—	2	1	no	—
350	#41	—	356	2	no	—
351	#41	—	356	2	no	—
352	C₂×Q₈	—	178	1	no	—
353	C₂×Q₈	—	178	1	no	—
354	C₂×Q₈	—	178	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	4	2	no	—
357	C₂×D₄	—	356	1	no	—
358	C₂×D₄	—	178	1	no	—
359	C₂×D₄	—	178	1	no	—
360	C₂×D₄	—	178	1	no	—
361	C₂×D₄	C₂×D₃₅₆	1	2	yes	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	—	356	1	no	—
368	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₃₅₆	1	1	yes	characteristic
370	C₂²×C₄	#13083574	1	1	yes	characteristic
371	SD₁₆	—	356	4	no	—
372	D₈	—	356	4	no	—
373	M₁₆	—	4	4	no	—
374	M₁₆	—	4	4	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	4	2	no	—
379	C₂×C₈	—	178	2	no	—
380	C₂×C₈	—	178	2	no	—
381	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
382	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
383	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
384	C₂×C₈	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
385	C₄⋊C₄	—	2	1	no	—
386	C₄⋊C₄	—	356	1	no	—
387	C₄⋊C₄	—	356	1	no	—
388	C₄⋊C₄	—	178	1	no	—
389	C₄⋊C₄	—	178	1	no	—
390	C₄⋊C₄	—	178	1	no	—
391	C₄⋊C₄	—	178	1	no	—
392	C₄⋊C₄	—	178	1	no	—
393	C₄⋊C₄	—	178	1	no	—
394	C₄⋊C₄	C₂×D₃₅₆	1	2	yes	—
395	C₂²⋊C₄	—	2	2	no	—
396	C₂²⋊C₄	—	2	2	no	—
397	C₂²⋊C₄	—	356	1	no	—
398	C₂²⋊C₄	—	356	1	no	—
399	C₂²⋊C₄	—	356	1	no	—
400	C₄²	—	356	1	no	—
401	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
402	C₄²	C₂×D₃₅₆	1	1	yes	characteristic
403	C₄²	#13083574	1	1	yes	characteristic
404	C₄²	C₂³×D₈₉	1	1	yes	characteristic
405	C₂³	—	2	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	356	1	no	—
410	C₂³	#15667986	1	1	yes	characteristic
411	Q₈	—	356	1	no	—
412	Q₈	—	356	2	no	—
413	Q₈	—	356	1	no	—
414	Q₈	—	712	1	no	—
415	D₄	—	2	2	no	—
416	D₄	—	2	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	356	1	no	—
419	D₄	—	356	2	no	—
420	D₄	—	356	1	no	—
421	D₄	—	712	1	no	—
422	D₄	—	712	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	4	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	356	1	no	—
431	C₂×C₄	—	356	1	no	—
432	C₂×C₄	—	356	1	no	—
433	C₂×C₄	—	712	2	no	—
434	C₂×C₄	#15667986	1	1	yes	characteristic
435	C₂×C₄	#15667986	1	1	yes	characteristic
436	C₂×C₄	#15667986	1	1	yes	characteristic
437	C₂×C₄	#15668032	1	2	yes	—
438	C₂×C₄	#15668038	1	2	yes	—
439	C₂×C₄	C₂²×C₂²⋊D₈₉	1	1	yes	characteristic
440	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
441	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
442	C₈	—	2	1	no	—
443	C₈	—	2	1	no	—
444	C₈	—	2	1	no	—
445	C₈	—	2	1	no	—
446	C₈	—	4	2	no	—
447	C₈	—	356	2	no	—
448	C₈	—	356	2	no	—
449	C₂²	—	2	1	no	—
450	C₂²	—	2	1	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	8	4	no	—
455	C₂²	—	712	1	no	—
456	C₂²	—	712	1	no	—
457	C₂²	—	712	1	no	—
458	C₂²	#19151813	1	2	yes	—
459	C₂²	C₂×#15667986	1	1	yes	characteristic
460	C₄	—	2	1	no	—
461	C₄	—	2	1	no	—
462	C₄	—	2	1	no	—
463	C₄	—	4	2	no	—
464	C₄	—	712	1	no	—
465	C₄	—	712	1	no	—
466	C₄	—	712	1	no	—
467	C₄	#19151813	1	2	yes	—
468	C₄	C₂×#15668032	1	1	yes	characteristic
469	C₄	C₂×#15668038	1	1	yes	characteristic
470	C₄	#19152398	1	2	yes	—
471	C₂	—	2	2	no	—
472	C₂	—	8	2	no	—
473	C₂	—	1424	1	no	—
474	C₂	C₂×#19151813	1	1	yes	characteristic
475	C₂	#26029861	1	1	yes	characteristic
476	C₂	#26029972	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#15667986
commutator, cosocle	C₄²×C₈₉	C₂⁴
Frattini	C₄²	C₂³×D₈₉
Fitting	C₂×#436×C₈₉	C₂
socle	C₂²×C₈₉	C₂×#121
prime radical	#26030252	C₂
hypercenter	C₂×#436	D₈₉
hypocenter	C₈₉	#19142
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×#436

Complements

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

N	H ≅ G/N	type
1. #26030575	C₂	semidirect
2. #26030260	C₂	semidirect
4. #26019827	C₂	semidirect
5. #26019813	C₂	semidirect
6. #26019799	C₂	semidirect
7. #26019785	C₂	semidirect
8. #26019000	C₂	semidirect
9. #26018910	C₂	semidirect
10. #26018902	C₂	semidirect
11. C₂×#436×C₈₉	C₂	semidirect
16. #19151949	C₂²	semidirect
17. #19151949	C₂²	semidirect
18. #19151945	C₂²	semidirect
19. #19151945	C₂²	semidirect
34. #19151351	C₂²	semidirect
35. #19151349	C₂²	semidirect
36. #19151346	C₂²	semidirect
37. #19151345	C₂²	semidirect
38. #19151343	C₂²	semidirect
39. #19151341	C₂²	semidirect
242. C₂×#436	D₈₉	semidirect
250. C₈₉	#19142	semidirect

Maximal subgroups

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

subgroup	index
#26030575	2
#26030260	2
#26030252	2
#26019827	2
#26019813	2
#26019799	2
#26019785	2
#26019000	2
#26018910	2
#26018902	2
C₂×#436×C₈₉	2
#19142	89