Subgroups — C₄×#14273775 #21437308

Order 7552.

1492 conjugacy classes of subgroups.

The subgroup lattice has 200 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14273775	C₂	1	1	yes	maximal, characteristic
2	#16837884	C₂	1	4	yes	maximal, complemented
3	#16837883	C₂	1	6	yes	maximal, complemented
4	#16837880	C₂	1	1	yes	maximal, characteristic, complemented
5	#16837878	C₂	1	4	yes	maximal, complemented
6	C₄×#11745689	C₂	1	4	yes	maximal, complemented
7	C₄×#11745685	C₂	1	6	yes	maximal, complemented
8	C₄×Q₈×D₅₉	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×Q₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#14273775	C₄	1	16	yes	direct product factor
11	C₂×#11745689	C₂²	1	4	yes	—
12	C₂×#11745685	C₂²	1	6	yes	—
13	C₂×Q₈×D₅₉	C₂²	1	4	yes	—
14	Q₈×Dic₅₉	C₂²	1	4	yes	—
15	Q₈×Dic₅₉	C₂²	1	4	yes	—
16	C₄×Dic₁₁₈	C₂²	1	6	yes	—
17	C₄×Dic₁₁₈	C₂²	1	6	yes	—
18	#14273692	C₂²	1	12	yes	—
19	C₄×D₂₃₆	C₂²	1	6	yes	—
20	C₄×D₂₃₆	C₂²	1	6	yes	—
21	#14273689	C₂²	1	12	yes	—
22	C₄×C₂²⋊D₅₉	C₂²	1	4	yes	—
23	C₄×C₂²⋊D₅₉	C₂²	1	12	yes	—
24	#14273686	C₂²	1	6	yes	—
25	#14273685	C₂²	1	12	yes	—
26	#14273684	C₂²	1	12	yes	—
27	C₄⋊C₄×D₅₉	C₂²	1	12	yes	—
28	C₄²×D₅₉	C₂²	1	12	yes	—
29	C₂²×Q₈×C₅₉	C₂²	1	1	yes	characteristic
30	C₄×Q₈×C₅₉	C₂²	1	4	yes	—
31	C₄×Q₈×C₅₉	C₂²	1	4	yes	—
32	C₂×C₄⋊C₄×C₅₉	C₂²	1	3	yes	—
33	C₂×C₄²×C₅₉	C₂²	1	3	yes	—
34	C₂×Q₈×C₅₉	C₂×C₄	1	8	yes	complemented
35	C₂×Q₈×C₅₉	C₂³	1	4	yes	—
36	C₂²×C₄×C₅₉	C₂³	1	1	yes	characteristic
37	C₂²×C₄×C₅₉	C₂³	1	3	yes	—
38	C₂²×C₄×C₅₉	C₂³	1	3	yes	—
39	C₂×C₂²⋊D₅₉	C₂³	1	4	yes	—
40	#11745689	C₂×C₄	1	32	yes	complemented
41	Q₈×D₅₉	C₂×C₄	1	32	yes	complemented
42	#11745685	C₂×C₄	1	48	yes	complemented
43	C₂×D₂₃₆	C₂³	1	6	yes	—
44	C₂×C₄×D₅₉	C₂³	1	4	yes	—
45	C₂×C₄×D₅₉	C₂³	1	12	yes	—
46	C₂×C₄×D₅₉	C₂³	1	12	yes	—
47	C₂×Dic₁₁₈	C₂³	1	6	yes	—
48	C₄⋊C₄×C₅₉	C₂³	1	12	yes	—
49	C₄²×C₅₉	C₂³	1	6	yes	—
50	C₄²×C₅₉	C₂³	1	6	yes	—
51	C₂²⋊Dic₅₉	C₂³	1	4	yes	—
52	(C₂×D₅₉)⋊C₄	C₂³	1	4	yes	—
53	(C₂×D₅₉)⋊C₄	C₂³	1	12	yes	—
54	C₄⋊Dic₅₉	C₂³	1	6	yes	—
55	C₄⋊Dic₅₉	C₂³	1	6	yes	—
56	Dic₅₉⋊C₄	C₂³	1	12	yes	—
57	Dic₅₉⋊C₄	C₂³	1	4	yes	—
58	C₄×Dic₅₉	C₂³	1	4	yes	—
59	C₄×Dic₅₉	C₂³	1	12	yes	—
60	C₄×Dic₅₉	C₂³	1	12	yes	—
61	C₂³×C₅₉	C₂⁴	1	1	yes	characteristic
62	C₂²×D₅₉	C₂⁴	1	4	yes	—
63	Q₈×C₅₉	C₂²×C₄	1	16	yes	—
64	C₂×C₄×C₅₉	—	2	2	no	—
65	C₂×C₄×C₅₉	—	4	3	no	—
66	C₂×C₄×C₅₉	C₂²×C₄	1	12	yes	—
67	C₂×C₄×C₅₉	C₂⁴	1	6	yes	—
68	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
69	C₂×C₄×C₅₉	C₂⁴	1	6	yes	—
70	C₂×C₄×C₅₉	C₂⁴	1	1	yes	characteristic
71	C₂²⋊D₅₉	C₂²×C₄	1	16	yes	—
72	C₂×Dic₅₉	C₂⁴	1	4	yes	—
73	C₂×Dic₅₉	C₂⁴	1	4	yes	—
74	C₂×Dic₅₉	C₂⁴	1	4	yes	—
75	D₂₃₆	C₂²×C₄	1	24	yes	—
76	C₄×D₅₉	—	2	8	no	—
77	C₄×D₅₉	—	4	12	no	—
78	C₄×D₅₉	C₂²×C₄	1	48	yes	—
79	Dic₁₁₈	C₂²×C₄	1	24	yes	—
80	C₂²×C₅₉	—	2	1	no	—
81	C₂²×C₅₉	—	2	1	no	—
82	C₂²×C₅₉	C₂³×C₄	1	2	yes	—
83	C₂²×C₅₉	C₂⁵	1	1	yes	characteristic
84	C₂×D₅₉	—	2	4	no	—
85	C₂×D₅₉	—	2	4	no	—
86	C₂×D₅₉	C₂³×C₄	1	8	yes	—
87	C₄×C₅₉	—	2	1	no	—
88	C₄×C₅₉	—	2	6	no	—
89	C₄×C₅₉	C₂³×C₄	1	12	yes	—
90	C₄×C₅₉	2₋¹⁺⁴	1	2	yes	complemented
91	Dic₅₉	—	2	4	no	—
92	Dic₅₉	—	2	4	no	—
93	Dic₅₉	C₂³×C₄	1	8	yes	—
94	C₄×2₋¹⁺⁴	—	59	1	no	maximal, Sylow
95	C₂×C₅₉	—	2	2	no	—
96	C₂×C₅₉	C₂⁴×C₄	1	1	yes	characteristic
97	C₂×C₅₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
98	C₂×C₅₉	#585	1	1	yes	characteristic
99	D₅₉	—	2	8	no	—
100	C₂×2₋¹⁺⁴	—	59	1	no	—
101	#520	—	59	4	no	—
102	#520	—	59	6	no	—
103	#519	—	59	1	no	—
104	#519	—	59	4	no	—
105	C₄×#41	—	59	4	no	—
106	C₄×#41	—	59	6	no	—
107	C₂×C₄×Q₈	—	59	4	no	—
108	C₂×C₄×Q₈	D₅₉	1	1	yes	characteristic, complemented
109	C₅₉	C₄×2₋¹⁺⁴	1	1	yes	characteristic, complemented, Sylow
110	2₋¹⁺⁴	—	59	16	no	—
111	C₂×#41	—	59	4	no	—
112	C₂×#41	—	59	6	no	—
113	C₂²×Q₈	—	59	4	no	—
114	C₂²×Q₈	C₂×D₅₉	1	1	yes	characteristic
115	C₄×Q₈	—	59	4	no	—
116	C₄×Q₈	—	59	4	no	—
117	C₄×Q₈	—	59	12	no	—
118	C₄×Q₈	—	59	6	no	—
119	C₄×Q₈	—	59	6	no	—
120	C₄×Q₈	C₂×D₅₉	1	4	yes	—
121	C₄×Q₈	C₂×D₅₉	1	4	yes	—
122	C₄×D₄	—	59	4	no	—
123	C₄×D₄	—	59	12	no	—
124	C₄×D₄	—	59	12	no	—
125	C₄×D₄	—	59	6	no	—
126	C₄×D₄	—	59	6	no	—
127	#117	—	59	6	no	—
128	#117	—	59	12	no	—
129	#117	—	59	12	no	—
130	C₂×C₄⋊C₄	—	59	12	no	—
131	C₂×C₄⋊C₄	C₂×D₅₉	1	3	yes	—
132	C₂×C₄²	—	59	12	no	—
133	C₂×C₄²	C₂×D₅₉	1	3	yes	—
134	#41	—	59	32	no	—
135	#41	—	59	48	no	—
136	C₂×Q₈	—	59	32	no	—
137	C₂×Q₈	—	59	6	no	—
138	C₂×Q₈	C₄×D₅₉	1	8	yes	complemented
139	C₂×Q₈	C₂²×D₅₉	1	4	yes	—
140	C₂×D₄	—	59	4	no	—
141	C₂×D₄	—	59	6	no	—
142	C₂²×C₄	—	59	12	no	—
143	C₂²×C₄	—	59	4	no	—
144	C₂²×C₄	—	59	12	no	—
145	C₂²×C₄	C₂²×D₅₉	1	1	yes	characteristic
146	C₂²×C₄	C₂²×D₅₉	1	3	yes	—
147	C₂²×C₄	C₂²×D₅₉	1	3	yes	—
148	C₄⋊C₄	—	59	12	no	—
149	C₄⋊C₄	—	59	6	no	—
150	C₄⋊C₄	—	59	4	no	—
151	C₄⋊C₄	—	59	6	no	—
152	C₄⋊C₄	C₂²×D₅₉	1	12	yes	—
153	C₂²⋊C₄	—	59	4	no	—
154	C₂²⋊C₄	—	59	12	no	—
155	C₂²⋊C₄	—	59	4	no	—
156	C₄²	—	59	12	no	—
157	C₄²	—	59	12	no	—
158	C₄²	—	59	4	no	—
159	C₄²	C₂²×D₅₉	1	6	yes	—
160	C₄²	C₂²×D₅₉	1	6	yes	—
161	C₂³	—	59	4	no	—
162	C₂³	C₂³×D₅₉	1	1	yes	characteristic
163	Q₈	—	59	24	no	—
164	Q₈	C₂×C₄×D₅₉	1	16	yes	—
165	D₄	—	59	16	no	—
166	D₄	—	59	24	no	—
167	C₂×C₄	—	2	2	no	—
168	C₂×C₄	—	4	3	no	—
169	C₂×C₄	—	59	4	no	—
170	C₂×C₄	—	59	48	no	—
171	C₂×C₄	—	59	4	no	—
172	C₂×C₄	—	59	4	no	—
173	C₂×C₄	—	118	8	no	—
174	C₂×C₄	—	236	12	no	—
175	C₂×C₄	C₂×C₄×D₅₉	1	12	yes	—
176	C₂×C₄	C₂³×D₅₉	1	6	yes	—
177	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
178	C₂×C₄	C₂³×D₅₉	1	6	yes	—
179	C₂×C₄	C₂³×D₅₉	1	1	yes	characteristic
180	C₂²	—	2	1	no	—
181	C₂²	—	2	1	no	—
182	C₂²	—	59	8	no	—
183	C₂²	—	118	4	no	—
184	C₂²	—	118	4	no	—
185	C₂²	C₂²×C₄×D₅₉	1	2	yes	—
186	C₂²	C₂⁴×D₅₉	1	1	yes	characteristic
187	C₄	—	2	1	no	—
188	C₄	—	2	6	no	—
189	C₄	—	59	8	no	—
190	C₄	—	118	4	no	—
191	C₄	—	118	4	no	—
192	C₄	C₂²×C₄×D₅₉	1	12	yes	—
193	C₄	#14273775	1	2	yes	direct product factor
194	C₂	—	2	2	no	—
195	C₂	—	118	8	no	—
196	C₂	C₂³×C₄×D₅₉	1	1	yes	characteristic
197	C₂	C₂×#14273775	1	1	yes	characteristic
198	C₂	#16838238	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₅₉
commutator	C₂×C₅₉	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₅₉
Fitting	C₂×C₄×Q₈×C₅₉	C₂
socle	C₂²×C₅₉	C₂⁵
hypercenter	C₂×C₄×Q₈	D₅₉
hypocenter	C₅₉	C₄×2₋¹⁺⁴
LCS	G ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
2. #16837884	C₂	semidirect
3. #16837883	C₂	semidirect
4. #16837880	C₂	semidirect
5. #16837878	C₂	semidirect
6. C₄×#11745689	C₂	semidirect
7. C₄×#11745685	C₂	semidirect
8. C₄×Q₈×D₅₉	C₂	semidirect
9. C₂×C₄×Q₈×C₅₉	C₂	semidirect
10. #14273775	C₄	direct (N × H)
34. C₂×Q₈×C₅₉	C₂×C₄	semidirect
40. #11745689	C₂×C₄	semidirect
41. Q₈×D₅₉	C₂×C₄	semidirect
42. #11745685	C₂×C₄	semidirect
90. C₄×C₅₉	2₋¹⁺⁴	semidirect
108. C₂×C₄×Q₈	D₅₉	semidirect
109. C₅₉	C₄×2₋¹⁺⁴	semidirect
138. C₂×Q₈	C₄×D₅₉	semidirect
193. C₄	#14273775	direct (N × H)

Subgroups — C4×#14273775 #21437308

Conjugacy classes of subgroups

Complements

Subgroups — C₄×#14273775 #21437308