Subgroups — #21433956

Order 7552.

376 conjugacy classes of subgroups.

The subgroup lattice has 248 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#16838030	C₂	1	1	yes	maximal, characteristic, complemented
2	#16837885	C₂	1	1	yes	maximal, characteristic
3	#16837707	C₂	1	2	yes	maximal, complemented
4	#16837704	C₂	1	2	yes	maximal, complemented
5	#16837690	C₂	1	2	yes	maximal, complemented
6	#16837685	C₂	1	2	yes	maximal, complemented
7	#16837445	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14273659	C₂	1	1	yes	maximal, characteristic, complemented
9	#16837428	C₂	1	1	yes	maximal, characteristic, complemented
10	#16837403	C₂	1	1	yes	maximal, characteristic
11	C₅₉×#416	C₂	1	1	yes	maximal, characteristic
12	C₂×#11745664	C₂²	1	1	yes	characteristic
13	#14273727	—	2	1	no	—
14	#14273726	C₂²	1	2	yes	—
15	#14273719	—	2	1	no	—
16	#14273718	C₂²	1	2	yes	—
17	#14273704	—	2	2	no	—
18	Q₈×Dic₅₉	C₂²	1	2	yes	—
19	D₄×Dic₅₉	—	2	2	no	—
20	D₄×Dic₅₉	C₂²	1	2	yes	—
21	#14273686	—	2	1	no	—
22	#14273686	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊Dic₅₉	—	2	1	no	—
24	C₂×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊Dic₅₉	C₂²	1	1	yes	characteristic
26	#14273660	C₂²	1	2	yes	—
27	#14273659	C₂²	1	2	yes	—
28	#14273659	C₂²	1	2	yes	—
29	#14273658	C₂²	1	2	yes	—
30	Dic₅₉⋊C₈	C₂²	1	2	yes	—
31	Dic₅₉⋊C₈	C₂²	1	2	yes	—
32	#14273651	C₂²	1	2	yes	—
33	#14273648	C₂²	1	2	yes	—
34	C₂×#41×C₅₉	C₂²	1	1	yes	characteristic
35	C₂²×C₈×C₅₉	C₂²	1	1	yes	characteristic
36	#117×C₅₉	C₂²	1	1	yes	characteristic
37	#103×C₅₉	C₂²	1	1	yes	characteristic
38	#103×C₅₉	C₂²	1	1	yes	characteristic
39	#102×C₅₉	C₂²	1	1	yes	characteristic
40	#102×C₅₉	C₂²	1	1	yes	characteristic
41	#41×C₅₉	—	2	2	no	—
42	#41×C₅₉	Q₈	1	4	yes	complemented
43	C₂×Q₈×C₅₉	C₂³	1	1	yes	characteristic
44	C₂×D₄×C₅₉	—	2	1	no	—
45	C₂×D₄×C₅₉	C₂³	1	1	yes	characteristic
46	C₂²×C₄×C₅₉	—	2	1	no	—
47	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
48	C₂²×Dic₅₉	—	2	1	no	—
49	C₂²×Dic₅₉	—	2	1	no	—
50	C₂²×Dic₅₉	—	2	2	no	—
51	C₂×Dic₁₁₈	—	2	2	no	—
52	C₂×C₈×C₅₉	—	2	2	no	—
53	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
54	C₂×C₈×C₅₉	C₂³	1	1	yes	characteristic
55	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
56	C₄⋊C₄×C₅₉	C₂³	1	1	yes	characteristic
57	C₂²⋊C₄×C₅₉	—	2	1	no	—
58	C₄²×C₅₉	—	2	1	no	—
59	C₂²⋊Dic₅₉	—	2	2	no	—
60	C₂²⋊Dic₅₉	D₄	1	2	yes	—
61	C₄⋊Dic₅₉	—	2	1	no	—
62	C₄⋊Dic₅₉	—	2	1	no	—
63	C₄⋊Dic₅₉	—	2	2	no	—
64	C₄⋊Dic₅₉	—	2	2	no	—
65	C₄⋊Dic₅₉	D₄	1	1	yes	characteristic
66	C₄⋊Dic₅₉	D₄	1	1	yes	characteristic
67	C₄⋊Dic₅₉	C₂³	1	2	yes	—
68	C₄⋊Dic₅₉	C₂³	1	2	yes	—
69	Dic₅₉⋊C₄	—	2	2	no	—
70	Dic₅₉⋊C₄	—	2	2	no	—
71	C₄×Dic₅₉	—	2	2	no	—
72	C₄×Dic₅₉	C₂³	1	2	yes	—
73	#11745664	—	2	2	no	—
74	C₂×C₅₉⋊C₈	C₂³	1	2	yes	—
75	C₂³×C₅₉	—	2	1	no	—
76	C₂³×C₅₉	C₂×D₄	1	1	yes	characteristic
77	Q₈×C₅₉	—	2	1	no	—
78	Q₈×C₅₉	C₂×Q₈	1	2	yes	—
79	D₄×C₅₉	—	2	4	no	—
80	D₄×C₅₉	—	2	1	no	—
81	D₄×C₅₉	C₂×Q₈	1	2	yes	—
82	C₂×C₄×C₅₉	—	2	1	no	—
83	C₂×C₄×C₅₉	—	2	4	no	—
84	C₂×C₄×C₅₉	—	2	1	no	—
85	C₂×C₄×C₅₉	—	2	1	no	—
86	C₂×C₄×C₅₉	C₂×D₄	1	1	yes	characteristic
87	C₂×C₄×C₅₉	C₂×Q₈	1	2	yes	—
88	C₂×C₄×C₅₉	#41	1	2	yes	—
89	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
90	C₂×Dic₅₉	—	2	2	no	—
91	C₂×Dic₅₉	—	2	2	no	—
92	C₂×Dic₅₉	—	8	2	no	—
93	C₂×Dic₅₉	—	8	1	no	—
94	C₂×Dic₅₉	—	8	1	no	—
95	C₂×Dic₅₉	C₂×D₄	1	2	yes	—
96	C₂×Dic₅₉	C₂×D₄	1	2	yes	—
97	Dic₁₁₈	—	8	2	no	—
98	C₈×C₅₉	—	2	1	no	—
99	C₈×C₅₉	—	2	1	no	—
100	C₅₉⋊C₈	—	2	2	no	—
101	C₂²×C₅₉	—	2	1	no	—
102	C₂²×C₅₉	—	2	1	no	—
103	C₂²×C₅₉	—	2	2	no	—
104	C₂²×C₅₉	—	4	1	no	—
105	C₂²×C₅₉	—	4	1	no	—
106	C₂²×C₅₉	C₂²⋊Q₈	1	2	yes	—
107	C₂²×C₅₉	C₂²×D₄	1	1	yes	characteristic
108	C₄×C₅₉	—	2	2	no	—
109	C₄×C₅₉	—	4	1	no	—
110	C₄×C₅₉	—	4	1	no	—
111	C₄×C₅₉	C₂²⋊Q₈	1	2	yes	—
112	C₄×C₅₉	C₂²×Q₈	1	1	yes	characteristic
113	C₄×C₅₉	C₂×#41	1	1	yes	characteristic
114	Dic₅₉	—	2	2	no	—
115	Dic₅₉	—	2	2	no	—
116	Dic₅₉	—	4	2	no	—
117	Dic₅₉	—	4	2	no	—
118	#3084	—	59	1	no	maximal, Sylow
119	C₂×C₅₉	—	2	2	no	—
120	C₂×C₅₉	—	4	2	no	—
121	C₂×C₅₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
122	C₂×C₅₉	#577	1	1	yes	characteristic
123	C₂×C₅₉	#577	1	1	yes	characteristic
124	#544	—	59	1	no	—
125	#520	—	59	1	no	—
126	#479	—	59	2	no	—
127	#478	—	59	2	no	—
128	#476	—	59	2	no	—
129	#475	—	59	2	no	—
130	#428	—	59	1	no	—
131	C₂×#106	—	59	1	no	—
132	#424	—	59	1	no	—
133	#417	—	59	1	no	—
134	#416	D₅₉	1	1	yes	characteristic
135	C₅₉	#3084	1	1	yes	characteristic, complemented, Sylow
136	C₂×#41	C₂×D₅₉	1	1	yes	characteristic
137	C₂×M₁₆	—	59	1	no	—
138	C₂²×C₈	C₂×D₅₉	1	1	yes	characteristic
139	C₄⋊Q₈	—	59	2	no	—
140	C₄⋊Q₈	—	118	1	no	—
141	#125	—	59	2	no	—
142	#125	—	118	1	no	—
143	C₂²⋊Q₈	—	118	2	no	—
144	C₄×Q₈	—	59	2	no	—
145	C₄×D₄	—	59	2	no	—
146	C₄×D₄	—	118	2	no	—
147	#117	—	59	1	no	—
148	#117	—	118	1	no	—
149	#117	C₂×D₅₉	1	1	yes	characteristic
150	C₂×C₄⋊C₄	—	59	1	no	—
151	C₂×C₄⋊C₄	—	59	1	no	—
152	C₂×C₄⋊C₄	—	118	1	no	—
153	#107	—	59	2	no	—
154	#106	—	59	2	no	—
155	#106	—	59	2	no	—
156	#106	—	59	2	no	—
157	C₄⋊C₈	—	59	2	no	—
158	C₄⋊C₈	—	59	2	no	—
159	#103	—	59	2	no	—
160	#103	C₂×D₅₉	1	1	yes	characteristic
161	#103	C₂×D₅₉	1	1	yes	characteristic
162	#102	—	59	2	no	—
163	#102	C₂×D₅₉	1	1	yes	characteristic
164	#102	C₂×D₅₉	1	1	yes	characteristic
165	#41	—	2	2	no	—
166	#41	Dic₁₁₈	1	4	yes	complemented
167	C₂×Q₈	—	118	2	no	—
168	C₂×Q₈	C₂²×D₅₉	1	1	yes	characteristic
169	C₂×D₄	—	2	1	no	—
170	C₂×D₄	C₂²×D₅₉	1	1	yes	characteristic
171	C₂²×C₄	—	2	1	no	—
172	C₂²×C₄	—	118	2	no	—
173	C₂²×C₄	—	118	1	no	—
174	C₂²×C₄	—	118	1	no	—
175	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
176	M₁₆	—	118	2	no	—
177	C₂×C₈	—	2	2	no	—
178	C₂×C₈	—	59	2	no	—
179	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
180	C₂×C₈	C₂²×D₅₉	1	1	yes	characteristic
181	C₄⋊C₄	—	59	1	no	—
182	C₄⋊C₄	—	59	1	no	—
183	C₄⋊C₄	—	59	2	no	—
184	C₄⋊C₄	—	59	2	no	—
185	C₄⋊C₄	—	118	2	no	—
186	C₄⋊C₄	—	118	2	no	—
187	C₄⋊C₄	—	118	2	no	—
188	C₄⋊C₄	—	118	2	no	—
189	C₄⋊C₄	—	118	1	no	—
190	C₄⋊C₄	—	118	1	no	—
191	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
192	C₄⋊C₄	C₂²×D₅₉	1	1	yes	characteristic
193	C₂²⋊C₄	—	2	1	no	—
194	C₂²⋊C₄	—	59	2	no	—
195	C₂²⋊C₄	—	118	2	no	—
196	C₄²	—	2	1	no	—
197	C₄²	—	59	2	no	—
198	C₄²	—	118	2	no	—
199	C₂³	—	2	1	no	—
200	C₂³	D₄×D₅₉	1	1	yes	characteristic
201	Q₈	—	2	1	no	—
202	Q₈	—	472	2	no	—
203	Q₈	C₂×Dic₁₁₈	1	2	yes	—
204	D₄	—	2	4	no	—
205	D₄	—	2	1	no	—
206	D₄	C₂×Dic₁₁₈	1	2	yes	—
207	C₂×C₄	—	2	1	no	—
208	C₂×C₄	—	2	4	no	—
209	C₂×C₄	—	2	1	no	—
210	C₂×C₄	—	2	1	no	—
211	C₂×C₄	—	59	2	no	—
212	C₂×C₄	—	59	2	no	—
213	C₂×C₄	—	118	2	no	—
214	C₂×C₄	—	118	2	no	—
215	C₂×C₄	—	472	2	no	—
216	C₂×C₄	—	472	1	no	—
217	C₂×C₄	—	472	1	no	—
218	C₂×C₄	C₂×Dic₁₁₈	1	2	yes	—
219	C₂×C₄	D₄×D₅₉	1	1	yes	characteristic
220	C₂×C₄	#11745687	1	2	yes	—
221	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
222	C₈	—	2	1	no	—
223	C₈	—	2	1	no	—
224	C₈	—	118	2	no	—
225	C₂²	—	2	1	no	—
226	C₂²	—	2	1	no	—
227	C₂²	—	2	2	no	—
228	C₂²	—	4	1	no	—
229	C₂²	—	4	1	no	—
230	C₂²	#14273704	1	2	yes	—
231	C₂²	C₂×D₄×D₅₉	1	1	yes	characteristic
232	C₄	—	2	2	no	—
233	C₄	—	4	1	no	—
234	C₄	—	4	1	no	—
235	C₄	—	118	2	no	—
236	C₄	—	118	2	no	—
237	C₄	—	236	2	no	—
238	C₄	—	236	2	no	—
239	C₄	#14273704	1	2	yes	—
240	C₄	C₂²×Dic₁₁₈	1	1	yes	characteristic
241	C₄	C₂×#11745687	1	1	yes	characteristic
242	C₂	—	2	2	no	—
243	C₂	—	4	2	no	—
244	C₂	C₂×#14273704	1	1	yes	characteristic
245	C₂	#16838209	1	1	yes	characteristic
246	C₂	#16838209	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₅₉
commutator	C₂×C₄×C₅₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₅₉
Fitting	C₅₉×#416	C₂
socle	C₂²×C₅₉	C₂²×D₄
hypercenter	#416	D₅₉
hypocenter	C₅₉	#3084
LCS	G ▷ C₂×C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #416

Complements

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

N	H ≅ G/N	type
1. #16838030	C₂	semidirect
3. #16837707	C₂	semidirect
4. #16837704	C₂	semidirect
5. #16837690	C₂	semidirect
6. #16837685	C₂	semidirect
7. #16837445	C₂	semidirect
8. C₂×#14273659	C₂	semidirect
9. #16837428	C₂	semidirect
42. #41×C₅₉	Q₈	semidirect
135. C₅₉	#3084	semidirect
166. #41	Dic₁₁₈	semidirect