Subgroups — #20246257

Order 6016.

604 conjugacy classes of subgroups.

The subgroup lattice has 202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13093983	C₂	1	2	yes	maximal
2	#15689022	C₂	1	2	yes	maximal, complemented
3	#15689009	C₂	1	4	yes	maximal, complemented
4	#15688986	C₂	1	2	yes	maximal
5	#15688983	C₂	1	1	yes	maximal, characteristic
6	C₄⋊C₄×Dic₄₇	C₂	1	2	yes	maximal, complemented
7	C₄×C₂²⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
9	#13093983	—	2	8	no	—
10	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
11	C₂×C₄⋊Dic₄₇	C₂²	1	4	yes	—
12	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
14	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
16	C₂×C₄×Dic₄₇	C₂²	1	4	yes	—
17	C₄₇⋊#95	C₂²	1	2	yes	—
18	C₄₇⋊#95	C₂²	1	4	yes	—
19	C₄₇⋊#95	C₂²	1	2	yes	—
20	C₄₇⋊#95	C₂²	1	4	yes	—
21	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₂³×C₄×C₄₇	C₂²	1	2	yes	—
23	C₂×C₄⋊C₄×C₄₇	C₄	1	8	yes	complemented
24	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
26	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
27	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
28	C₂²×C₄×C₄₇	—	2	4	no	—
29	C₂²×C₄×C₄₇	—	2	4	no	—
30	C₂²×C₄×C₄₇	—	2	4	no	—
31	C₂²×C₄×C₄₇	C₂×C₄	1	8	yes	—
32	C₂²×C₄×C₄₇	C₂×C₄	1	4	yes	—
33	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
34	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
35	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
36	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
37	C₂²×Dic₄₇	C₂³	1	2	yes	—
38	C₂²×Dic₄₇	C₂³	1	4	yes	—
39	C₂²×Dic₄₇	C₂³	1	2	yes	—
40	C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	—
41	C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
42	C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
43	C₂²⋊Dic₄₇	—	2	4	no	—
44	C₂²⋊Dic₄₇	—	2	2	no	—
45	C₂²⋊Dic₄₇	D₄	1	4	yes	—
46	C₄⋊Dic₄₇	—	2	4	no	—
47	C₄⋊Dic₄₇	—	2	8	no	—
48	C₄×Dic₄₇	—	2	4	no	—
49	C₄×Dic₄₇	—	2	8	no	—
50	C₂³×C₄₇	—	2	2	no	—
51	C₂³×C₄₇	—	2	2	no	—
52	C₂³×C₄₇	C₂²×C₄	1	2	yes	—
53	C₂³×C₄₇	C₂×D₄	1	2	yes	—
54	C₂³×C₄₇	#41	1	2	yes	—
55	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
56	C₂×C₄×C₄₇	—	2	16	no	—
57	C₂×C₄×C₄₇	—	2	2	no	—
58	C₂×C₄×C₄₇	—	2	2	no	—
59	C₂×C₄×C₄₇	—	2	2	no	—
60	C₂×C₄×C₄₇	—	2	2	no	—
61	C₂×C₄×C₄₇	—	2	2	no	—
62	C₂×C₄×C₄₇	—	2	8	no	—
63	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
64	C₂×C₄×C₄₇	C₂²×C₄	1	4	yes	—
65	C₂×C₄×C₄₇	C₂²×C₄	1	4	yes	—
66	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
67	C₂×C₄×C₄₇	#41	1	4	yes	—
68	C₂×Dic₄₇	—	2	2	no	—
69	C₂×Dic₄₇	—	2	2	no	—
70	C₂×Dic₄₇	—	2	4	no	—
71	C₂×Dic₄₇	—	2	2	no	—
72	C₂×Dic₄₇	—	2	4	no	—
73	C₂×Dic₄₇	—	2	2	no	—
74	C₂×Dic₄₇	—	2	4	no	—
75	C₂×Dic₄₇	—	2	2	no	—
76	C₂×Dic₄₇	C₂×D₄	1	4	yes	—
77	C₂²×C₄₇	—	2	2	no	—
78	C₂²×C₄₇	—	2	2	no	—
79	C₂²×C₄₇	—	2	4	no	—
80	C₂²×C₄₇	—	2	4	no	—
81	C₂²×C₄₇	C₄×D₄	1	4	yes	—
82	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
83	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
84	C₂²×C₄₇	C₂×#41	1	1	yes	characteristic
85	C₂²×C₄₇	C₂×#41	1	2	yes	—
86	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
87	C₄×C₄₇	—	2	2	no	—
88	C₄×C₄₇	—	2	4	no	—
89	C₄×C₄₇	—	2	4	no	—
90	C₄×C₄₇	#117	1	4	yes	complemented
91	Dic₄₇	—	2	4	no	—
92	Dic₄₇	—	4	4	no	—
93	Dic₄₇	—	4	2	no	—
94	#2344	—	47	1	no	maximal, Sylow
95	C₂×C₄₇	—	2	4	no	—
96	C₂×C₄₇	C₂×#117	1	1	yes	characteristic
97	C₂×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
98	C₂×C₄₇	#519	1	1	yes	characteristic
99	C₂×C₄₇	#547	1	2	yes	—
100	C₂×C₄₇	#552	1	2	yes	—
101	C₂×#117	—	47	2	no	—
102	C₂²×C₄⋊C₄	D₄₇	1	1	yes	characteristic
103	#389	—	47	2	no	—
104	#387	—	47	4	no	—
105	#381	—	47	2	no	—
106	#380	—	47	1	no	—
107	C₄×C₄⋊C₄	—	47	2	no	—
108	C₄×C₂²⋊C₄	—	47	1	no	—
109	C₄₇	#2344	1	1	yes	characteristic, complemented, Sylow
110	C₂³×C₄	C₂×D₄₇	1	2	yes	—
111	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
112	#117	—	94	8	no	—
113	C₂×C₄⋊C₄	—	47	4	no	—
114	C₂×C₄⋊C₄	—	47	2	no	—
115	C₂×C₄⋊C₄	Dic₄₇	1	8	yes	complemented
116	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
117	C₂×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
118	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
119	C₂×C₂²⋊C₄	—	47	1	no	—
120	C₂×C₂²⋊C₄	—	47	2	no	—
121	C₂×C₂²⋊C₄	—	47	1	no	—
122	C₂×C₄²	—	47	4	no	—
123	C₂×C₄²	—	47	2	no	—
124	#95	—	47	2	no	—
125	#95	—	47	4	no	—
126	#95	—	47	2	no	—
127	#95	—	47	4	no	—
128	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
129	C₂²×C₄	—	2	4	no	—
130	C₂²×C₄	—	2	4	no	—
131	C₂²×C₄	—	2	4	no	—
132	C₂²×C₄	—	47	2	no	—
133	C₂²×C₄	—	47	2	no	—
134	C₂²×C₄	—	47	4	no	—
135	C₂²×C₄	C₂×Dic₄₇	1	8	yes	—
136	C₂²×C₄	C₂×Dic₄₇	1	4	yes	—
137	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
138	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
139	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
140	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
141	C₄⋊C₄	—	94	8	no	—
142	C₄⋊C₄	—	94	4	no	—
143	C₄⋊C₄	C₂×Dic₄₇	1	8	yes	—
144	C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
145	C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
146	C₂²⋊C₄	—	47	4	no	—
147	C₂²⋊C₄	—	94	4	no	—
148	C₂²⋊C₄	—	94	2	no	—
149	C₄²	—	94	8	no	—
150	C₄²	—	94	4	no	—
151	C₂³	—	2	2	no	—
152	C₂³	—	2	2	no	—
153	C₂³	D₄×D₄₇	1	2	yes	—
154	C₂³	#10625352	1	2	yes	—
155	C₂³	C₂²×Dic₄₇	1	2	yes	—
156	C₂³	C₂³×D₄₇	1	1	yes	characteristic
157	C₂×C₄	—	2	16	no	—
158	C₂×C₄	—	2	2	no	—
159	C₂×C₄	—	2	2	no	—
160	C₂×C₄	—	2	2	no	—
161	C₂×C₄	—	2	2	no	—
162	C₂×C₄	—	2	2	no	—
163	C₂×C₄	—	2	8	no	—
164	C₂×C₄	—	47	4	no	—
165	C₂×C₄	—	94	2	no	—
166	C₂×C₄	—	94	2	no	—
167	C₂×C₄	—	94	4	no	—
168	C₂×C₄	—	94	2	no	—
169	C₂×C₄	—	94	2	no	—
170	C₂×C₄	—	94	4	no	—
171	C₂×C₄	—	94	4	no	—
172	C₂×C₄	—	94	2	no	—
173	C₂×C₄	#10625350	1	4	yes	—
174	C₂×C₄	C₂²×Dic₄₇	1	2	yes	—
175	C₂×C₄	C₂²×Dic₄₇	1	4	yes	—
176	C₂×C₄	C₂²×Dic₄₇	1	4	yes	—
177	C₂×C₄	C₂²×Dic₄₇	1	2	yes	—
178	C₂²	—	2	4	no	—
179	C₂²	—	2	4	no	—
180	C₂²	—	2	2	no	—
181	C₂²	—	2	2	no	—
182	C₂²	D₄×Dic₄₇	1	4	yes	—
183	C₂²	C₂³×Dic₄₇	1	1	yes	characteristic
184	C₂²	C₂×D₄×D₄₇	1	1	yes	characteristic
185	C₂²	C₂×#10625352	1	1	yes	characteristic
186	C₂²	C₂×#10625350	1	2	yes	—
187	C₂²	#13094072	1	2	yes	—
188	C₄	—	2	2	no	—
189	C₄	—	2	4	no	—
190	C₄	—	2	4	no	—
191	C₄	—	94	4	no	—
192	C₄	—	188	4	no	—
193	C₄	—	188	2	no	—
194	C₄	#13093983	1	4	yes	complemented
195	C₂	—	2	4	no	—
196	C₂	C₂×#13093983	1	1	yes	characteristic
197	C₂	C₂×D₄×Dic₄₇	1	1	yes	characteristic
198	C₂	#15689601	1	1	yes	characteristic
199	C₂	#15689774	1	2	yes	—
200	C₂	#15689808	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₄
Fitting	C₂²×C₄⋊C₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂⁴
hypercenter	C₂²×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#2344
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. #15689022	C₂	semidirect
3. #15689009	C₂	semidirect
6. C₄⋊C₄×Dic₄₇	C₂	semidirect
23. C₂×C₄⋊C₄×C₄₇	C₄	semidirect
90. C₄×C₄₇	#117	semidirect
109. C₄₇	#2344	semidirect
115. C₂×C₄⋊C₄	Dic₄₇	semidirect
194. C₄	#13093983	semidirect