Subgroups — #21434789

Order 7552.

410 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16837947	C₂	1	1	yes	maximal, characteristic, complemented
2	#16837933	C₂	1	1	yes	maximal, characteristic, complemented
3	#16837810	C₂	1	1	yes	maximal, characteristic, complemented
4	#16837790	C₂	1	1	yes	maximal, characteristic, complemented
5	#16837765	C₂	1	1	yes	maximal, characteristic, complemented
6	#16837760	C₂	1	1	yes	maximal, characteristic, complemented
7	#16837636	C₂	1	1	yes	maximal, characteristic, complemented
8	#16837631	C₂	1	1	yes	maximal, characteristic, complemented
9	#16837629	C₂	1	1	yes	maximal, characteristic, complemented
10	#16837514	C₂	1	1	yes	maximal, characteristic, complemented
11	#16837511	C₂	1	1	yes	maximal, characteristic, complemented
12	#16837501	C₂	1	1	yes	maximal, characteristic, complemented
13	#16837499	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#14273637	C₂	1	1	yes	maximal, characteristic, complemented
15	C₅₉×#466	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#11745687	—	2	1	no	—
17	C₂×#11745660	C₂²	1	1	yes	characteristic
18	C₂×#11745670	C₂²	1	1	yes	characteristic
19	C₂×#11745669	C₂²	1	1	yes	characteristic
20	C₂²×C₅₉⋊C₈	C₂²	1	1	yes	characteristic
21	#14273726	C₂²	1	1	yes	characteristic
22	#14273723	C₂²	1	1	yes	characteristic
23	#14273720	—	2	1	no	—
24	#14273718	C₂²	1	1	yes	characteristic
25	#14273714	C₂²	1	1	yes	characteristic
26	#14273713	—	2	1	no	—
27	#14273708	—	2	1	no	—
28	#14273706	C₂²	1	1	yes	characteristic
29	#14273701	C₂²	1	1	yes	characteristic
30	#14273699	—	2	1	no	—
31	#14273692	C₂²	1	1	yes	characteristic
32	D₄×Dic₅₉	—	2	1	no	—
33	D₄×Dic₅₉	C₂²	1	1	yes	characteristic
34	D₄×Dic₅₉	C₂²	1	1	yes	characteristic
35	#14273689	C₂²	1	1	yes	characteristic
36	(C₂²⋊D₅₉)⋊C₄	—	2	1	no	—
37	#14273683	—	2	1	no	—
38	C₂×C₄×Dic₅₉	C₂²	1	1	yes	characteristic
39	#14273660	C₂²	1	1	yes	characteristic
40	#14273659	C₂²	1	1	yes	characteristic
41	#14273658	C₂²	1	1	yes	characteristic
42	#14273652	C₂²	1	1	yes	characteristic
43	#14273650	C₂²	1	1	yes	characteristic
44	#14273649	C₂²	1	1	yes	characteristic
45	#14273648	C₂²	1	1	yes	characteristic
46	#14273648	C₂²	1	1	yes	characteristic
47	#14273647	C₂²	1	1	yes	characteristic
48	#14273637	C₂²	1	1	yes	characteristic
49	#14273637	C₂²	1	1	yes	characteristic
50	#14273637	C₂²	1	1	yes	characteristic
51	#14273637	C₂²	1	1	yes	characteristic
52	C₂×D₈×C₅₉	C₂²	1	1	yes	characteristic
53	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
54	#121×C₅₉	C₂²	1	1	yes	characteristic
55	#121×C₅₉	C₂²	1	1	yes	characteristic
56	#107×C₅₉	C₂²	1	1	yes	characteristic
57	#102×C₅₉	C₂²	1	1	yes	characteristic
58	#102×C₅₉	C₂²	1	1	yes	characteristic
59	C₂×D₄×C₅₉	—	2	1	no	—
60	C₂×D₄×C₅₉	—	2	1	no	—
61	C₂×D₄×C₅₉	C₂³	1	1	yes	characteristic
62	C₂×D₄×C₅₉	C₂³	1	1	yes	characteristic
63	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊D₅₉	—	2	1	no	—
65	C₂×C₂²⋊D₅₉	—	2	1	no	—
66	C₂×C₂²⋊D₅₉	—	2	1	no	—
67	C₂²×Dic₅₉	—	2	1	no	—
68	C₂²×Dic₅₉	—	2	1	no	—
69	C₂²×Dic₅₉	D₄	1	1	yes	characteristic
70	C₂²×Dic₅₉	D₄	1	1	yes	characteristic
71	#11745687	—	4	4	no	—
72	C₂×D₂₃₆	C₂³	1	1	yes	characteristic
73	C₂×C₄×D₅₉	—	2	1	no	—
74	C₂×Dic₁₁₈	—	2	1	no	—
75	C₂×Dic₁₁₈	C₂³	1	1	yes	characteristic
76	D₈×C₅₉	—	2	2	no	—
77	C₂×C₈×C₅₉	—	2	2	no	—
78	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
79	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
80	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
81	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
82	C₂²⋊C₄×C₅₉	—	2	1	no	—
83	C₂²⋊C₄×C₅₉	—	2	1	no	—
84	C₂²⋊Dic₅₉	—	2	1	no	—
85	C₂²⋊Dic₅₉	—	2	1	no	—
86	C₂²⋊Dic₅₉	—	2	1	no	—
87	C₂²⋊Dic₅₉	—	2	1	no	—
88	C₂²⋊Dic₅₉	—	2	1	no	—
89	#11745670	—	2	2	no	—
90	#11745669	—	2	2	no	—
91	(C₂×D₅₉)⋊C₄	—	2	1	no	—
92	(C₂×D₅₉)⋊C₄	—	2	1	no	—
93	C₄⋊Dic₅₉	—	2	1	no	—
94	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
95	C₄⋊Dic₅₉	C₂³	1	1	yes	characteristic
96	Dic₅₉⋊C₄	—	2	1	no	—
97	Dic₅₉⋊C₄	—	2	1	no	—
98	Dic₅₉⋊C₄	—	2	1	no	—
99	Dic₅₉⋊C₄	—	2	1	no	—
100	C₄×Dic₅₉	—	2	1	no	—
101	C₄×Dic₅₉	D₄	1	1	yes	characteristic
102	C₄×Dic₅₉	D₄	1	1	yes	characteristic
103	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
104	C₄×Dic₅₉	C₂³	1	1	yes	characteristic
105	C₂×C₅₉⋊C₈	—	2	2	no	—
106	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
107	C₂×C₅₉⋊C₈	C₂³	1	1	yes	characteristic
108	#11745660	—	2	2	no	—
109	C₂³×C₅₉	—	2	1	no	—
110	C₂³×C₅₉	—	2	1	no	—
111	C₂³×C₅₉	C₂×D₄	1	1	yes	characteristic
112	C₂²×D₅₉	—	2	1	no	—
113	D₄×C₅₉	—	2	1	no	—
114	D₄×C₅₉	—	2	1	no	—
115	D₄×C₅₉	—	2	1	no	—
116	D₄×C₅₉	—	2	1	no	—
117	D₄×C₅₉	—	4	2	no	—
118	D₄×C₅₉	—	4	2	no	—
119	C₂×C₄×C₅₉	—	2	1	no	—
120	C₂×C₄×C₅₉	—	2	1	no	—
121	C₂×C₄×C₅₉	—	2	1	no	—
122	C₂×C₄×C₅₉	—	2	1	no	—
123	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
124	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
125	C₂²⋊D₅₉	—	4	2	no	—
126	C₂²⋊D₅₉	—	4	2	no	—
127	C₂²⋊D₅₉	—	4	2	no	—
128	C₂×Dic₅₉	—	2	2	no	—
129	C₂×Dic₅₉	—	2	1	no	—
130	C₂×Dic₅₉	—	2	1	no	—
131	C₂×Dic₅₉	—	2	1	no	—
132	C₂×Dic₅₉	—	4	1	no	—
133	C₂×Dic₅₉	—	4	2	no	—
134	C₂×Dic₅₉	—	4	2	no	—
135	C₂×Dic₅₉	C₂×D₄	1	1	yes	characteristic
136	C₂×Dic₅₉	C₂×D₄	1	1	yes	characteristic
137	C₂×Dic₅₉	C₂×D₄	1	1	yes	characteristic
138	C₂×Dic₅₉	C₂×D₄	1	1	yes	characteristic
139	D₂₃₆	—	2	1	no	—
140	D₂₃₆	—	2	1	no	—
141	C₄×D₅₉	—	4	2	no	—
142	Dic₁₁₈	—	2	1	no	—
143	Dic₁₁₈	—	2	1	no	—
144	Dic₁₁₈	—	4	2	no	—
145	C₈×C₅₉	—	2	1	no	—
146	C₈×C₅₉	#41	1	2	yes	complemented
147	C₅₉⋊C₈	—	2	1	no	—
148	C₅₉⋊C₈	#41	1	2	yes	complemented
149	C₂²×C₅₉	—	2	1	no	—
150	C₂²×C₅₉	—	2	1	no	—
151	C₂²×C₅₉	—	4	1	no	—
152	C₂²×C₅₉	—	4	1	no	—
153	C₂²×C₅₉	—	4	1	no	—
154	C₂²×C₅₉	—	4	1	no	—
155	C₂²×C₅₉	—	4	1	no	—
156	C₂²×C₅₉	—	4	1	no	—
157	C₂²×C₅₉	AGL(1,ℤ/8)	1	2	yes	—
158	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
159	C₂×D₅₉	—	4	1	no	—
160	C₂×D₅₉	—	4	1	no	—
161	C₂×D₅₉	—	4	1	no	—
162	C₄×C₅₉	—	2	1	no	—
163	C₄×C₅₉	—	4	1	no	—
164	C₄×C₅₉	—	4	1	no	—
165	C₄×C₅₉	C₂×#41	1	1	yes	characteristic
166	C₄×C₅₉	C₂×#41	1	1	yes	characteristic
167	Dic₅₉	—	2	1	no	—
168	Dic₅₉	—	2	1	no	—
169	Dic₅₉	—	2	1	no	—
170	Dic₅₉	—	2	1	no	—
171	Dic₅₉	—	4	1	no	—
172	Dic₅₉	—	4	1	no	—
173	Dic₅₉	—	4	1	no	—
174	#3180	—	59	1	no	maximal, Sylow
175	C₂×C₅₉	—	2	2	no	—
176	C₂×C₅₉	—	8	1	no	—
177	C₂×C₅₉	—	8	1	no	—
178	C₂×C₅₉	#532	1	1	yes	characteristic
179	C₂×C₅₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
180	C₂×C₅₉	#575	1	1	yes	characteristic
181	D₅₉	—	8	1	no	—
182	#532	—	59	1	no	—
183	#529	—	59	1	no	—
184	#501	—	59	1	no	—
185	#496	—	59	1	no	—
186	#490	—	59	1	no	—
187	#489	—	59	1	no	—
188	#466	—	59	1	no	—
189	#466	D₅₉	1	1	yes	characteristic, complemented
190	#465	—	59	1	no	—
191	#465	—	59	1	no	—
192	#442	—	59	1	no	—
193	#442	—	59	1	no	—
194	#440	—	59	1	no	—
195	#440	—	59	1	no	—
196	C₂×#97	—	59	1	no	—
197	C₅₉	#3180	1	1	yes	characteristic, complemented, Sylow
198	C₂×#41	—	118	1	no	—
199	C₂×SD₁₆	—	59	1	no	—
200	C₂×SD₁₆	—	59	1	no	—
201	C₂×D₈	—	59	1	no	—
202	C₂×D₈	C₂×D₅₉	1	1	yes	characteristic
203	C₂²×C₈	—	59	1	no	—
204	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
205	C₄⋊Q₈	—	59	1	no	—
206	#127	—	59	1	no	—
207	#126	—	118	1	no	—
208	#125	—	59	1	no	—
209	#124	—	59	1	no	—
210	#124	—	118	1	no	—
211	#123	—	118	1	no	—
212	C₂²⋊Q₈	—	59	1	no	—
213	#121	—	59	1	no	—
214	#121	—	118	1	no	—
215	#121	C₂×D₅₉	1	1	yes	characteristic
216	#121	C₂×D₅₉	1	1	yes	characteristic
217	C₄×Q₈	—	59	1	no	—
218	C₄×D₄	—	59	1	no	—
219	C₄×D₄	—	59	1	no	—
220	C₄×D₄	—	59	1	no	—
221	C₄×D₄	—	118	1	no	—
222	C₄×D₄	—	118	1	no	—
223	#117	—	118	1	no	—
224	C₂×C₄²	—	59	1	no	—
225	#107	—	59	1	no	—
226	#107	C₂×D₅₉	1	1	yes	characteristic
227	#106	—	59	1	no	—
228	#106	—	59	1	no	—
229	#103	—	59	1	no	—
230	#103	—	59	1	no	—
231	#102	—	59	1	no	—
232	#102	—	59	1	no	—
233	#102	—	59	1	no	—
234	#102	—	59	1	no	—
235	#102	C₂×D₅₉	1	1	yes	characteristic
236	#102	C₂×D₅₉	1	1	yes	characteristic
237	#97	—	59	1	no	—
238	#97	—	59	1	no	—
239	#97	—	59	1	no	—
240	#97	—	59	1	no	—
241	#41	—	236	4	no	—
242	C₂×Q₈	—	59	1	no	—
243	C₂×Q₈	—	118	1	no	—
244	C₂×D₄	—	2	1	no	—
245	C₂×D₄	—	2	1	no	—
246	C₂×D₄	—	59	1	no	—
247	C₂×D₄	—	118	1	no	—
248	C₂×D₄	—	118	1	no	—
249	C₂×D₄	—	118	1	no	—
250	C₂×D₄	C₂²×D₅₉	1	1	yes	characteristic
251	C₂×D₄	C₂²×D₅₉	1	1	yes	characteristic
252	C₂²×C₄	—	59	1	no	—
253	C₂²×C₄	—	59	1	no	—
254	C₂²×C₄	—	118	1	no	—
255	C₂²×C₄	—	118	1	no	—
256	C₂²×C₄	—	118	1	no	—
257	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
258	SD₁₆	—	118	2	no	—
259	SD₁₆	—	118	2	no	—
260	D₈	—	2	2	no	—
261	D₈	—	118	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	59	1	no	—
264	C₂×C₈	—	59	1	no	—
265	C₂×C₈	—	118	2	no	—
266	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
267	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
268	C₄⋊C₄	—	59	1	no	—
269	C₄⋊C₄	—	59	1	no	—
270	C₄⋊C₄	—	118	1	no	—
271	C₄⋊C₄	—	118	1	no	—
272	C₄⋊C₄	—	118	1	no	—
273	C₄⋊C₄	—	118	1	no	—
274	C₄⋊C₄	—	118	1	no	—
275	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
276	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
277	C₂²⋊C₄	—	2	1	no	—
278	C₂²⋊C₄	—	2	1	no	—
279	C₂²⋊C₄	—	118	1	no	—
280	C₂²⋊C₄	—	118	1	no	—
281	C₂²⋊C₄	—	118	1	no	—
282	C₂²⋊C₄	—	118	1	no	—
283	C₂²⋊C₄	—	118	1	no	—
284	C₂²⋊C₄	—	118	1	no	—
285	C₂²⋊C₄	—	118	1	no	—
286	C₄²	—	59	1	no	—
287	C₄²	—	59	1	no	—
288	C₄²	—	59	1	no	—
289	C₄²	—	59	1	no	—
290	C₄²	—	118	1	no	—
291	C₂³	—	2	1	no	—
292	C₂³	—	2	1	no	—
293	C₂³	—	118	1	no	—
294	C₂³	D₄×D₅₉	1	1	yes	characteristic
295	Q₈	—	118	1	no	—
296	Q₈	—	118	1	no	—
297	Q₈	—	236	2	no	—
298	D₄	—	2	1	no	—
299	D₄	—	2	1	no	—
300	D₄	—	2	1	no	—
301	D₄	—	2	1	no	—
302	D₄	—	4	2	no	—
303	D₄	—	4	2	no	—
304	D₄	—	118	1	no	—
305	D₄	—	118	1	no	—
306	D₄	—	236	2	no	—
307	D₄	—	236	2	no	—
308	D₄	—	236	2	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	2	1	no	—
312	C₂×C₄	—	2	1	no	—
313	C₂×C₄	—	59	1	no	—
314	C₂×C₄	—	59	1	no	—
315	C₂×C₄	—	59	1	no	—
316	C₂×C₄	—	59	1	no	—
317	C₂×C₄	—	118	2	no	—
318	C₂×C₄	—	118	1	no	—
319	C₂×C₄	—	118	1	no	—
320	C₂×C₄	—	118	1	no	—
321	C₂×C₄	—	236	2	no	—
322	C₂×C₄	—	236	1	no	—
323	C₂×C₄	—	236	2	no	—
324	C₂×C₄	—	236	2	no	—
325	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
326	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
327	C₈	—	2	1	no	—
328	C₈	—	59	2	no	—
329	C₈	—	118	1	no	—
330	C₈	#11745687	1	2	yes	complemented
331	C₂²	—	2	1	no	—
332	C₂²	—	2	1	no	—
333	C₂²	—	4	1	no	—
334	C₂²	—	4	1	no	—
335	C₂²	—	4	1	no	—
336	C₂²	—	4	1	no	—
337	C₂²	—	4	1	no	—
338	C₂²	—	4	1	no	—
339	C₂²	—	236	1	no	—
340	C₂²	—	236	1	no	—
341	C₂²	—	236	1	no	—
342	C₂²	#14273751	1	2	yes	—
343	C₂²	C₂×D₄×D₅₉	1	1	yes	characteristic
344	C₄	—	2	1	no	—
345	C₄	—	4	1	no	—
346	C₄	—	4	1	no	—
347	C₄	—	118	1	no	—
348	C₄	—	118	1	no	—
349	C₄	—	118	1	no	—
350	C₄	—	118	1	no	—
351	C₄	—	236	1	no	—
352	C₄	—	236	1	no	—
353	C₄	—	236	1	no	—
354	C₄	#41×D₅₉	1	1	yes	characteristic
355	C₄	C₂×#11745687	1	1	yes	characteristic
356	C₂	—	2	2	no	—
357	C₂	—	8	1	no	—
358	C₂	—	8	1	no	—
359	C₂	—	472	1	no	—
360	C₂	#16837947	1	1	yes	characteristic
361	C₂	C₂×#14273751	1	1	yes	characteristic
362	C₂	#16838199	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₅₉×#466	C₂
socle	C₂²×C₅₉	C₂²×D₄
hypercenter	#466	D₅₉
hypocenter	C₅₉	#3180
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #466

Complements

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

N	H ≅ G/N	type
1. #16837947	C₂	semidirect
2. #16837933	C₂	semidirect
3. #16837810	C₂	semidirect
4. #16837790	C₂	semidirect
5. #16837765	C₂	semidirect
6. #16837760	C₂	semidirect
7. #16837636	C₂	semidirect
8. #16837631	C₂	semidirect
9. #16837629	C₂	semidirect
10. #16837514	C₂	semidirect
11. #16837511	C₂	semidirect
12. #16837501	C₂	semidirect
13. #16837499	C₂	semidirect
14. C₂×#14273637	C₂	semidirect
15. C₅₉×#466	C₂	semidirect
146. C₈×C₅₉	#41	semidirect
148. C₅₉⋊C₈	#41	semidirect
189. #466	D₅₉	semidirect
197. C₅₉	#3180	semidirect
330. C₈	#11745687	semidirect