Subgroups — #36605982

Order 22784.

892 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#26030738	C₂	1	1	yes	maximal, characteristic, complemented
2	#26029983	C₂	1	2	yes	maximal, complemented
3	#26029972	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#19151868	C₂	1	1	yes	maximal, characteristic, complemented
5	#26029170	C₂	1	1	yes	maximal, characteristic, complemented
6	#26021528	C₂	1	2	yes	maximal, complemented
7	#26021304	C₂	1	2	yes	maximal, complemented
8	#26021162	C₂	1	1	yes	maximal, characteristic, complemented
9	#26021042	C₂	1	1	yes	maximal, characteristic, complemented
10	#26020798	C₂	1	2	yes	maximal, complemented
11	C₈₉×#1757	C₂	1	1	yes	maximal, characteristic, complemented
12	#19152396	C₂²	1	2	yes	—
13	C₂×#15668040	C₂²	1	2	yes	—
14	C₂×#15668037	C₂²	1	2	yes	—
15	C₂×#15668034	C₂²	1	1	yes	characteristic
16	C₂²×D₇₁₂	C₂²	1	1	yes	characteristic
17	#19152364	C₂²	1	2	yes	—
18	#19152167	C₂²	1	2	yes	—
19	#19151987	—	2	2	no	—
20	#19151982	—	2	1	no	—
21	#19151975	—	2	1	no	—
22	#19151873	—	2	1	no	—
23	#19151868	—	2	2	no	—
24	#19151868	—	2	2	no	—
25	#19151868	—	2	1	no	—
26	#19151867	—	2	4	no	—
27	#19151864	—	2	4	no	—
28	#19151861	—	2	2	no	—
29	#19151721	—	2	2	no	—
30	#19151716	—	2	2	no	—
31	#19151646	C₂²	1	2	yes	—
32	C₂×#15667948	C₂²	1	1	yes	characteristic
33	C₂×#15667948	C₂²	1	1	yes	characteristic
34	#19151616	C₂²	1	2	yes	—
35	#19151602	C₂²	1	2	yes	—
36	#19151580	C₂²	1	2	yes	—
37	C₂×#15667928	C₂²	1	2	yes	—
38	C₂×#15667928	C₂²	1	2	yes	—
39	#19151368	C₂²	1	2	yes	—
40	C₂×#131×C₈₉	C₂²	1	1	yes	characteristic
41	#413×C₈₉	C₂²	1	1	yes	characteristic
42	#410×C₈₉	C₂²	1	1	yes	characteristic
43	#405×C₈₉	C₂²	1	1	yes	characteristic
44	#405×C₈₉	C₂²	1	1	yes	characteristic
45	#344×C₈₉	C₂²	1	1	yes	characteristic
46	#344×C₈₉	C₂²	1	1	yes	characteristic
47	C₂×#13083574	C₂³	1	2	yes	—
48	C₂²×D₃₅₆	C₂³	1	2	yes	—
49	#15668043	—	2	2	no	—
50	#15668042	—	2	2	no	—
51	#15668040	—	2	4	no	—
52	#15668040	—	4	2	no	—
53	#15668038	—	2	2	no	—
54	#15668037	—	2	2	no	—
55	#15668037	—	2	4	no	—
56	#15668037	—	4	2	no	—
57	#15668034	—	2	1	no	—
58	#15668034	—	2	1	no	—
59	#15668034	—	2	1	no	—
60	#15668034	—	2	1	no	—
61	#15668032	—	4	2	no	—
62	C₂×Dic₃₅₆	D₄	1	1	yes	characteristic
63	C₂×#13083563	—	2	2	no	—
64	C₂×#13083563	D₄	1	2	yes	—
65	C₂×#13083561	—	2	2	no	—
66	C₂×D₇₁₂	—	2	2	no	—
67	C₂×D₇₁₂	—	2	1	no	—
68	C₂×D₇₁₂	—	2	1	no	—
69	C₂×D₇₁₂	—	2	1	no	—
70	C₂×D₇₁₂	—	2	1	no	—
71	C₂×D₇₁₂	—	2	1	no	—
72	C₂×D₇₁₂	—	2	1	no	—
73	C₂×D₇₁₂	D₄	1	1	yes	characteristic
74	C₂×#13083559	—	2	2	no	—
75	#15668020	—	2	4	no	—
76	#15668018	—	2	4	no	—
77	C₂×#13083558	C₂³	1	2	yes	—
78	C₂×#13083558	C₂³	1	2	yes	—
79	M₁₆×D₈₉	—	4	2	no	—
80	#15668009	—	2	2	no	—
81	#15668000	—	2	2	no	—
82	#15667987	—	4	2	no	—
83	#15667982	—	2	4	no	—
84	#15667948	—	2	1	no	—
85	#15667948	—	2	1	no	—
86	#15667948	D₄	1	2	yes	complemented
87	#15667948	D₄	1	2	yes	complemented
88	#15667947	—	2	4	no	—
89	#15667940	—	2	4	no	—
90	#15667932	—	4	2	no	—
91	#15667930	—	2	2	no	—
92	#15667928	—	2	2	no	—
93	#15667928	—	2	4	no	—
94	#15667928	—	2	4	no	—
95	C₂×#41×C₈₉	C₂³	1	1	yes	characteristic
96	#131×C₈₉	—	2	1	no	—
97	#131×C₈₉	—	2	1	no	—
98	#131×C₈₉	—	2	1	no	—
99	#131×C₈₉	—	2	1	no	—
100	C₂×M₁₆×C₈₉	—	2	1	no	—
101	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
103	C₂×M₁₆×C₈₉	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₈₉	—	2	1	no	—
105	C₂²×C₈×C₈₉	C₂³	1	1	yes	characteristic
106	#117×C₈₉	C₂³	1	1	yes	characteristic
107	#117×C₈₉	C₂³	1	1	yes	characteristic
108	#101×C₈₉	D₄	1	2	yes	complemented
109	#100×C₈₉	D₄	1	2	yes	complemented
110	#99×C₈₉	—	2	2	no	—
111	#97×C₈₉	—	2	1	no	—
112	#97×C₈₉	—	2	1	no	—
113	C₄×C₈×C₈₉	—	2	1	no	—
114	C₄×C₈×C₈₉	—	2	1	no	—
115	C₂³×D₈₉	—	2	2	no	—
116	#13083574	—	2	2	no	—
117	#13083574	—	2	2	no	—
118	#13083574	—	2	2	no	—
119	#13083574	—	2	2	no	—
120	C₂×Dic₁₇₈	C₂×D₄	1	2	yes	—
121	C₂×D₃₅₆	—	2	2	no	—
122	C₂×D₃₅₆	—	2	2	no	—
123	C₂×D₃₅₆	—	2	2	no	—
124	C₂×D₃₅₆	—	2	2	no	—
125	C₂×D₃₅₆	—	2	2	no	—
126	C₂×D₃₅₆	—	2	2	no	—
127	C₂×D₃₅₆	—	4	4	no	—
128	C₂×D₃₅₆	C₂×D₄	1	2	yes	—
129	C₂×C₂²⋊D₈₉	—	2	2	no	—
130	C₂×C₄×D₈₉	—	2	2	no	—
131	Dic₃₅₆	—	2	1	no	—
132	Dic₃₅₆	—	2	1	no	—
133	#13083564	—	4	2	no	—
134	#13083563	—	2	2	no	—
135	#13083563	—	2	2	no	—
136	#13083563	—	4	4	no	—
137	#13083562	—	4	2	no	—
138	#13083561	—	4	4	no	—
139	#13083561	—	4	2	no	—
140	D₇₁₂	—	2	1	no	—
141	D₇₁₂	—	2	1	no	—
142	D₇₁₂	—	4	4	no	—
143	D₇₁₂	—	4	1	no	—
144	D₇₁₂	—	4	1	no	—
145	D₇₁₂	—	4	1	no	—
146	D₇₁₂	—	4	1	no	—
147	#13083559	—	4	4	no	—
148	#13083559	—	4	2	no	—
149	#13083558	—	2	2	no	—
150	#13083558	—	2	2	no	—
151	#13083558	—	2	2	no	—
152	#13083558	C₂×D₄	1	4	yes	—
153	#13083557	—	4	4	no	—
154	C₂×#10623494	—	2	2	no	—
155	C₂×#10623494	—	2	2	no	—
156	C₈×D₈₉	—	4	4	no	—
157	#13083551	—	4	4	no	—
158	#41×C₈₉	—	2	1	no	—
159	#41×C₈₉	—	2	1	no	—
160	#41×C₈₉	—	2	1	no	—
161	#41×C₈₉	—	2	1	no	—
162	C₂×Q₈×C₈₉	C₂×D₄	1	1	yes	characteristic
163	C₂×D₄×C₈₉	—	2	1	no	—
164	C₂×D₄×C₈₉	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₈₉	—	2	1	no	—
166	C₂²×C₄×C₈₉	C₂⁴	1	1	yes	characteristic
167	M₁₆×C₈₉	—	2	1	no	—
168	M₁₆×C₈₉	—	2	1	no	—
169	M₁₆×C₈₉	—	2	1	no	—
170	M₁₆×C₈₉	—	2	1	no	—
171	M₁₆×C₈₉	—	4	1	no	—
172	M₁₆×C₈₉	—	4	1	no	—
173	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
174	M₁₆×C₈₉	C₂×D₄	1	2	yes	—
175	C₂×C₈×C₈₉	—	2	1	no	—
176	C₂×C₈×C₈₉	—	2	1	no	—
177	C₂×C₈×C₈₉	—	2	1	no	—
178	C₂×C₈×C₈₉	—	4	1	no	—
179	C₂×C₈×C₈₉	—	4	1	no	—
180	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
181	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
182	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
183	C₂×C₈×C₈₉	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
185	C₂×C₈×C₈₉	#41	1	1	yes	characteristic
186	C₄⋊C₄×C₈₉	—	2	1	no	—
187	C₄⋊C₄×C₈₉	—	2	1	no	—
188	C₂²⋊C₄×C₈₉	—	2	1	no	—
189	C₂²⋊C₄×C₈₉	#41	1	2	yes	—
190	C₄²×C₈₉	—	2	1	no	—
191	C₄²×C₈₉	—	2	1	no	—
192	C₂³×C₈₉	—	2	1	no	—
193	C₂³×C₈₉	C₂×#41	1	1	yes	characteristic
194	C₂²×D₈₉	—	2	2	no	—
195	C₂²×D₈₉	—	4	2	no	—
196	C₂²×D₈₉	—	4	2	no	—
197	C₂²×D₈₉	—	4	2	no	—
198	C₂²×D₈₉	—	16	2	no	—
199	Q₈×C₈₉	—	2	1	no	—
200	Q₈×C₈₉	—	2	1	no	—
201	D₄×C₈₉	—	2	1	no	—
202	D₄×C₈₉	—	2	1	no	—
203	D₄×C₈₉	—	4	1	no	—
204	D₄×C₈₉	—	4	1	no	—
205	C₂×C₄×C₈₉	—	2	1	no	—
206	C₂×C₄×C₈₉	—	2	2	no	—
207	C₂×C₄×C₈₉	—	4	1	no	—
208	C₂×C₄×C₈₉	—	4	1	no	—
209	C₂×C₄×C₈₉	—	4	1	no	—
210	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₈₉	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₈₉	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
215	C₂×C₄×C₈₉	H(5,𝔽₂)	1	1	yes	characteristic
216	C₂²⋊D₈₉	—	4	2	no	—
217	C₂²⋊D₈₉	—	4	2	no	—
218	C₂×Dic₈₉	—	2	2	no	—
219	D₃₅₆	—	2	2	no	—
220	D₃₅₆	—	2	2	no	—
221	D₃₅₆	—	4	2	no	—
222	D₃₅₆	—	4	2	no	—
223	D₃₅₆	—	4	2	no	—
224	D₃₅₆	—	4	2	no	—
225	D₃₅₆	—	16	4	no	—
226	C₄×D₈₉	—	4	2	no	—
227	C₄×D₈₉	—	4	2	no	—
228	Dic₁₇₈	—	2	2	no	—
229	Dic₁₇₈	—	2	2	no	—
230	C₈×C₈₉	—	2	2	no	—
231	C₈×C₈₉	—	2	2	no	—
232	C₈×C₈₉	—	4	1	no	—
233	C₈×C₈₉	#121	1	1	yes	characteristic
234	C₈×C₈₉	#121	1	1	yes	characteristic
235	C₈×C₈₉	#121	1	1	yes	characteristic
236	C₈×C₈₉	#121	1	1	yes	characteristic
237	#10623494	—	2	4	no	—
238	#10623494	—	4	2	no	—
239	C₂²×C₈₉	—	4	1	no	—
240	C₂²×C₈₉	—	4	1	no	—
241	C₂²×C₈₉	—	8	1	no	—
242	C₂²×C₈₉	#532	1	1	yes	characteristic
243	C₂²×C₈₉	#546	1	1	yes	characteristic
244	C₂²×C₈₉	#550	1	1	yes	characteristic
245	C₂×D₈₉	—	4	2	no	—
246	C₂×D₈₉	—	8	2	no	—
247	C₂×D₈₉	—	8	4	no	—
248	C₂×D₈₉	—	8	2	no	—
249	C₂×D₈₉	—	16	2	no	—
250	C₂×D₈₉	—	16	2	no	—
251	C₄×C₈₉	—	4	2	no	—
252	C₄×C₈₉	—	4	1	no	—
253	C₄×C₈₉	—	8	1	no	—
254	C₄×C₈₉	C₂×#121	1	1	yes	characteristic
255	C₄×C₈₉	#540	1	1	yes	characteristic
256	C₄×C₈₉	D₄²	1	1	yes	characteristic
257	C₄×C₈₉	D₄²	1	1	yes	characteristic
258	Dic₈₉	—	4	2	no	—
259	#25447	—	89	1	no	maximal, Sylow
260	C₂×C₈₉	—	2	1	no	—
261	C₂×C₈₉	—	2	1	no	—
262	C₂×C₈₉	—	2	1	no	—
263	C₂×C₈₉	—	8	1	no	—
264	C₂×C₈₉	#2428	1	1	yes	characteristic
265	D₈₉	—	8	2	no	—
266	D₈₉	—	16	2	no	—
267	#3155	—	89	1	no	—
268	#3068	—	89	2	no	—
269	#3067	—	89	1	no	—
270	C₂×#472	—	89	1	no	—
271	#2957	—	89	1	no	—
272	#2048	—	89	2	no	—
273	#2008	—	89	2	no	—
274	#1978	—	89	1	no	—
275	#1953	—	89	1	no	—
276	#1914	—	89	2	no	—
277	#1757	D₈₉	1	1	yes	characteristic, complemented
278	C₈₉	#25447	1	1	yes	characteristic, complemented, Sylow
279	#575	—	89	2	no	—
280	C₂×AGL(1,ℤ/8)	—	89	2	no	—
281	C₂×AGL(1,ℤ/8)	—	89	2	no	—
282	C₂×#135	—	89	1	no	—
283	C₂²×D₈	—	89	1	no	—
284	#568	—	89	2	no	—
285	C₂×#131	C₂×D₈₉	1	1	yes	characteristic
286	#535	—	89	2	no	—
287	#496	—	178	2	no	—
288	#495	—	178	1	no	—
289	#493	—	178	1	no	—
290	#473	—	178	1	no	—
291	#472	—	178	2	no	—
292	#472	—	178	2	no	—
293	#472	—	178	1	no	—
294	#472	—	178	4	no	—
295	#471	—	178	2	no	—
296	#471	—	178	4	no	—
297	#444	—	178	2	no	—
298	#443	—	178	2	no	—
299	#430	—	89	2	no	—
300	C₂×#108	—	89	1	no	—
301	C₂×#108	—	89	1	no	—
302	#421	—	89	2	no	—
303	#418	—	89	2	no	—
304	#413	—	89	2	no	—
305	#413	C₂×D₈₉	1	1	yes	characteristic
306	C₂×#100	—	89	2	no	—
307	C₂×#100	—	89	2	no	—
308	#410	C₂×D₈₉	1	1	yes	characteristic
309	#405	C₂×D₈₉	1	1	yes	characteristic
310	#405	C₂×D₈₉	1	1	yes	characteristic
311	#344	—	89	2	no	—
312	#344	C₂×D₈₉	1	1	yes	characteristic
313	#344	C₂×D₈₉	1	1	yes	characteristic
314	C₂×#41	—	89	2	no	—
315	C₂×#41	C₂²×D₈₉	1	1	yes	characteristic
316	C₂²×D₄	—	89	2	no	—
317	#137	—	178	2	no	—
318	#137	—	178	2	no	—
319	AGL(1,ℤ/8)	—	356	2	no	—
320	AGL(1,ℤ/8)	—	356	2	no	—
321	AGL(1,ℤ/8)	—	178	4	no	—
322	AGL(1,ℤ/8)	—	178	2	no	—
323	AGL(1,ℤ/8)	—	178	2	no	—
324	AGL(1,ℤ/8)	—	178	4	no	—
325	#135	—	356	2	no	—
326	#135	—	178	1	no	—
327	#135	—	178	1	no	—
328	#135	—	178	1	no	—
329	#135	—	178	1	no	—
330	C₂×Q₁₆	—	89	1	no	—
331	C₂×SD₁₆	—	89	2	no	—
332	C₂×SD₁₆	—	178	2	no	—
333	C₂×SD₁₆	—	178	2	no	—
334	C₂×D₈	—	89	1	no	—
335	C₂×D₈	—	178	2	no	—
336	C₂×D₈	—	178	2	no	—
337	C₂×D₈	—	178	1	no	—
338	C₂×D₈	—	178	1	no	—
339	C₂×D₈	—	178	1	no	—
340	C₂×D₈	—	178	1	no	—
341	C₂×D₈	—	178	1	no	—
342	C₂×D₈	—	178	1	no	—
343	#131	—	2	1	no	—
344	#131	—	2	1	no	—
345	#131	—	2	1	no	—
346	#131	—	2	1	no	—
347	#131	—	178	4	no	—
348	#131	—	178	4	no	—
349	C₂×M₁₆	—	2	1	no	—
350	C₂×M₁₆	—	89	2	no	—
351	C₂×M₁₆	—	89	2	no	—
352	C₂×M₁₆	—	356	2	no	—
353	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
354	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
355	C₂×M₁₆	C₂²×D₈₉	1	1	yes	characteristic
356	C₂²×C₈	—	2	1	no	—
357	C₂²×C₈	C₂²×D₈₉	1	1	yes	characteristic
358	#127	—	178	2	no	—
359	#124	—	178	2	no	—
360	#121	—	356	2	no	—
361	#120	—	178	4	no	—
362	#117	C₂²×D₈₉	1	1	yes	characteristic
363	#117	C₂²×D₈₉	1	1	yes	characteristic
364	#108	—	89	2	no	—
365	#108	—	89	2	no	—
366	#108	—	178	4	no	—
367	#108	—	178	1	no	—
368	#108	—	178	1	no	—
369	#104	—	178	4	no	—
370	#102	—	356	2	no	—
371	#101	—	178	2	no	—
372	#101	D₃₅₆	1	2	yes	complemented
373	#100	—	178	4	no	—
374	#100	—	178	2	no	—
375	#100	—	178	4	no	—
376	#100	D₃₅₆	1	2	yes	complemented
377	#99	—	2	2	no	—
378	#97	—	2	1	no	—
379	#97	—	2	1	no	—
380	C₄×C₈	—	2	1	no	—
381	C₄×C₈	—	2	1	no	—
382	C₂⁴	—	178	2	no	—
383	#41	—	2	1	no	—
384	#41	—	2	1	no	—
385	#41	—	2	1	no	—
386	#41	—	2	1	no	—
387	#41	—	178	2	no	—
388	#41	—	178	2	no	—
389	#41	—	178	2	no	—
390	#41	—	178	2	no	—
391	C₂×Q₈	—	89	2	no	—
392	C₂×Q₈	C₂×D₃₅₆	1	1	yes	characteristic
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	89	2	no	—
395	C₂×D₄	—	356	4	no	—
396	C₂×D₄	—	178	2	no	—
397	C₂×D₄	—	178	2	no	—
398	C₂×D₄	—	178	2	no	—
399	C₂×D₄	—	178	2	no	—
400	C₂×D₄	—	178	2	no	—
401	C₂×D₄	—	178	2	no	—
402	C₂×D₄	—	178	2	no	—
403	C₂×D₄	C₂×D₃₅₆	1	1	yes	characteristic
404	C₂²×C₄	—	2	1	no	—
405	C₂²×C₄	—	178	2	no	—
406	C₂²×C₄	C₂³×D₈₉	1	1	yes	characteristic
407	Q₁₆	—	356	2	no	—
408	Q₁₆	—	178	1	no	—
409	Q₁₆	—	178	1	no	—
410	SD₁₆	—	356	4	no	—
411	SD₁₆	—	356	2	no	—
412	SD₁₆	—	356	2	no	—
413	SD₁₆	—	356	4	no	—
414	SD₁₆	—	178	2	no	—
415	SD₁₆	—	178	2	no	—
416	D₈	—	356	4	no	—
417	D₈	—	356	2	no	—
418	D₈	—	356	4	no	—
419	D₈	—	356	1	no	—
420	D₈	—	356	1	no	—
421	D₈	—	356	1	no	—
422	D₈	—	356	1	no	—
423	D₈	—	178	1	no	—
424	D₈	—	178	1	no	—
425	M₁₆	—	2	1	no	—
426	M₁₆	—	2	1	no	—
427	M₁₆	—	2	1	no	—
428	M₁₆	—	2	1	no	—
429	M₁₆	—	4	1	no	—
430	M₁₆	—	4	1	no	—
431	M₁₆	—	89	4	no	—
432	M₁₆	—	356	4	no	—
433	M₁₆	—	178	2	no	—
434	M₁₆	—	178	2	no	—
435	M₁₆	—	178	2	no	—
436	M₁₆	C₂×D₃₅₆	1	2	yes	—
437	M₁₆	C₂×D₃₅₆	1	2	yes	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	4	1	no	—
442	C₂×C₈	—	4	1	no	—
443	C₂×C₈	—	356	4	no	—
444	C₂×C₈	—	178	2	no	—
445	C₂×C₈	—	178	2	no	—
446	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
447	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
448	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
449	C₂×C₈	D₄×D₈₉	1	1	yes	characteristic
450	C₂×C₈	#13083574	1	1	yes	characteristic
451	C₂×C₈	#13083574	1	1	yes	characteristic
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	—	2	1	no	—
455	C₂²⋊C₄	—	356	4	no	—
456	C₂²⋊C₄	#13083574	1	2	yes	—
457	C₄²	—	2	1	no	—
458	C₄²	—	2	1	no	—
459	C₂³	—	2	1	no	—
460	C₂³	—	356	2	no	—
461	C₂³	—	356	2	no	—
462	C₂³	—	356	2	no	—
463	C₂³	—	1424	2	no	—
464	C₂³	—	178	2	no	—
465	C₂³	C₂×#13083574	1	1	yes	characteristic
466	Q₈	—	2	1	no	—
467	Q₈	—	2	1	no	—
468	Q₈	—	178	2	no	—
469	Q₈	—	178	2	no	—
470	D₄	—	2	1	no	—
471	D₄	—	2	1	no	—
472	D₄	—	4	1	no	—
473	D₄	—	4	1	no	—
474	D₄	—	356	2	no	—
475	D₄	—	356	2	no	—
476	D₄	—	356	2	no	—
477	D₄	—	356	2	no	—
478	D₄	—	356	2	no	—
479	D₄	—	356	2	no	—
480	D₄	—	1424	4	no	—
481	D₄	—	178	2	no	—
482	D₄	—	178	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	356	2	no	—
489	C₂×C₄	—	356	2	no	—
490	C₂×C₄	—	178	2	no	—
491	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
492	C₂×C₄	C₂×D₄×D₈₉	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₃₅₆	1	1	yes	characteristic
494	C₂×C₄	C₂×#13083574	1	1	yes	characteristic
495	C₂×C₄	#15668058	1	1	yes	characteristic
496	C₂×C₄	#15668058	1	1	yes	characteristic
497	C₈	—	2	2	no	—
498	C₈	—	2	2	no	—
499	C₈	—	4	1	no	—
500	C₈	—	356	2	no	—
501	C₈	—	178	4	no	—
502	C₈	#15667985	1	1	yes	characteristic
503	C₈	#15667985	1	1	yes	characteristic
504	C₈	#15667985	1	1	yes	characteristic
505	C₈	#15667985	1	1	yes	characteristic
506	C₂²	—	4	1	no	—
507	C₂²	—	4	1	no	—
508	C₂²	—	8	1	no	—
509	C₂²	—	356	2	no	—
510	C₂²	—	1424	2	no	—
511	C₂²	—	1424	2	no	—
512	C₂²	—	712	4	no	—
513	C₂²	—	712	2	no	—
514	C₂²	—	712	2	no	—
515	C₂²	#19152148	1	1	yes	characteristic
516	C₂²	#19152244	1	1	yes	characteristic
517	C₂²	#19152269	1	1	yes	characteristic
518	C₄	—	4	2	no	—
519	C₄	—	4	1	no	—
520	C₄	—	8	1	no	—
521	C₄	—	356	2	no	—
522	C₄	C₂×#15667985	1	1	yes	characteristic
523	C₄	#19152203	1	1	yes	characteristic
524	C₄	D₄×D₃₅₆	1	1	yes	characteristic
525	C₄	D₄×D₃₅₆	1	1	yes	characteristic
526	C₂	—	2	1	no	—
527	C₂	—	2	1	no	—
528	C₂	—	2	1	no	—
529	C₂	—	8	1	no	—
530	C₂	—	1424	2	no	—
531	C₂	—	712	2	no	—
532	C₂	#26023840	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#26023840
commutator, cosocle	C₂²×C₄×C₈₉	C₂⁴
Frattini	C₂²×C₄	C₂³×D₈₉
Fitting	C₈₉×#1757	C₂
socle	C₂×C₈₉	#2428
hypercenter	#1757	D₈₉
hypocenter	C₈₉	#25447
LCS	G ▷ C₂²×C₄×C₈₉ ▷ C₂×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂ ◁ C₂²×C₄ ◁ #1757

Complements

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

N	H ≅ G/N	type
1. #26030738	C₂	semidirect
2. #26029983	C₂	semidirect
3. #26029972	C₂	semidirect
4. C₂×#19151868	C₂	semidirect
5. #26029170	C₂	semidirect
6. #26021528	C₂	semidirect
7. #26021304	C₂	semidirect
8. #26021162	C₂	semidirect
9. #26021042	C₂	semidirect
10. #26020798	C₂	semidirect
11. C₈₉×#1757	C₂	semidirect
86. #15667948	D₄	semidirect
87. #15667948	D₄	semidirect
108. #101×C₈₉	D₄	semidirect
109. #100×C₈₉	D₄	semidirect
277. #1757	D₈₉	semidirect
278. C₈₉	#25447	semidirect
372. #101	D₃₅₆	semidirect
376. #100	D₃₅₆	semidirect

Maximal subgroups

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

subgroup	index
#26030738	2
#26029983	2
#26029972	2
C₂×#19151868	2
#26029170	2
#26021528	2
#26021304	2
#26021162	2
#26021042	2
#26020798	2
C₈₉×#1757	2
#25447	89