Subgroups — C₂×#15689090 #20251828

Order 6016.

792 conjugacy classes of subgroups.

The subgroup lattice has 192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂³×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689090	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₂²⋊(C₄₇⋊C₈)	C₂	1	4	yes	maximal, complemented
5	C₂²×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#10625329	—	2	4	no	—
7	C₂×#10625329	C₂²	1	4	yes	complemented
8	C₂²×C₄₇⋊C₈	—	2	4	no	—
9	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
10	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
11	C₂²×C₄₇⋊C₈	C₂²	1	4	yes	complemented
12	C₂²⋊(C₄₇⋊C₈)	C₂²	1	16	yes	complemented
13	C₂×#41×C₄₇	—	2	4	no	—
14	C₂×#41×C₄₇	—	2	4	no	—
15	C₂×#41×C₄₇	C₄	1	4	yes	—
16	C₂×#41×C₄₇	C₂²	1	4	yes	—
17	C₂²×Q₈×C₄₇	C₄	1	1	yes	characteristic
18	C₂²×D₄×C₄₇	C₄	1	2	yes	—
19	C₂²×D₄×C₄₇	C₄	1	1	yes	characteristic
20	C₂³×C₄×C₄₇	C₂²	1	2	yes	—
21	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄₇	C₂×C₄	1	2	yes	—
23	C₂⁴×C₄₇	C₂×C₄	1	1	yes	characteristic
24	#41×C₄₇	—	2	16	no	—
25	#41×C₄₇	—	2	8	no	—
26	#41×C₄₇	—	2	8	no	—
27	C₂×Q₈×C₄₇	—	2	4	no	—
28	C₂×Q₈×C₄₇	C₂×C₄	1	4	yes	—
29	C₂×D₄×C₄₇	—	2	8	no	—
30	C₂×D₄×C₄₇	—	2	4	no	—
31	C₂×D₄×C₄₇	C₂×C₄	1	8	yes	—
32	C₂×D₄×C₄₇	C₂×C₄	1	4	yes	—
33	C₂²×C₄×C₄₇	—	2	4	no	—
34	C₂²×C₄×C₄₇	—	2	4	no	—
35	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
36	C₂²×C₄×C₄₇	C₂×C₄	1	4	yes	—
37	C₂²×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
38	C₂²×C₄×C₄₇	C₂×C₄	1	2	yes	—
39	C₂²×C₄×C₄₇	D₄	1	4	yes	—
40	C₂²×C₄×C₄₇	D₄	1	4	yes	—
41	C₂²×C₄×C₄₇	C₂³	1	4	yes	—
42	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
43	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	#10625329	—	2	8	no	—
45	C₂×C₄₇⋊C₈	—	2	4	no	—
46	C₂×C₄₇⋊C₈	—	2	8	no	—
47	C₂×C₄₇⋊C₈	—	2	4	no	—
48	C₂×C₄₇⋊C₈	C₂³	1	4	yes	—
49	C₂×C₄₇⋊C₈	C₂³	1	4	yes	—
50	C₂³×C₄₇	—	2	4	no	—
51	C₂³×C₄₇	—	2	4	no	—
52	C₂³×C₄₇	—	2	8	no	—
53	C₂³×C₄₇	C₂²⋊C₄	1	4	yes	—
54	C₂³×C₄₇	C₂²×C₄	1	4	yes	—
55	C₂³×C₄₇	C₂²×C₄	1	2	yes	—
56	C₂³×C₄₇	C₂²×C₄	1	1	yes	characteristic
57	Q₈×C₄₇	—	2	8	no	—
58	D₄×C₄₇	—	2	16	no	—
59	D₄×C₄₇	—	2	8	no	—
60	C₂×C₄×C₄₇	—	2	4	no	—
61	C₂×C₄×C₄₇	—	2	8	no	—
62	C₂×C₄×C₄₇	—	2	4	no	—
63	C₂×C₄×C₄₇	—	2	4	no	—
64	C₂×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
65	C₂×C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
66	C₂×C₄×C₄₇	C₂²×C₄	1	4	yes	—
67	C₂×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
68	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
69	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
70	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
71	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
72	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
73	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
74	C₄₇⋊C₈	—	2	4	no	—
75	C₄₇⋊C₈	—	2	4	no	—
76	C₂²×C₄₇	—	2	4	no	—
77	C₂²×C₄₇	—	2	8	no	—
78	C₂²×C₄₇	—	2	4	no	—
79	C₂²×C₄₇	—	2	8	no	—
80	C₂²×C₄₇	—	4	8	no	—
81	C₂²×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
82	C₂²×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
83	C₂²×C₄₇	#131	1	4	yes	—
84	C₂²×C₄₇	C₂³×C₄	1	1	yes	characteristic
85	C₄×C₄₇	—	2	4	no	—
86	C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
87	C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
88	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
89	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
90	C₂×#408	—	47	1	no	maximal, Sylow
91	C₂×C₄₇	—	2	4	no	—
92	C₂×C₄₇	—	4	4	no	—
93	C₂×C₄₇	#408	1	4	yes	complemented
94	C₂×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄₇	C₂×#131	1	2	yes	—
96	C₂²×#41	D₄₇	1	1	yes	characteristic
97	C₂²×M₁₆	—	47	1	no	—
98	C₂³×C₈	—	47	1	no	—
99	#408	—	47	8	no	—
100	C₂×C₂²⋊C₈	—	47	4	no	—
101	C₄₇	C₂×#408	1	1	yes	characteristic, complemented, Sylow
102	C₂×#41	—	2	4	no	—
103	C₂×#41	—	2	4	no	—
104	C₂×#41	Dic₄₇	1	4	yes	—
105	C₂×#41	C₂×D₄₇	1	4	yes	—
106	C₂²×Q₈	Dic₄₇	1	1	yes	characteristic
107	C₂²×D₄	Dic₄₇	1	2	yes	—
108	C₂²×D₄	Dic₄₇	1	1	yes	characteristic
109	C₂³×C₄	C₂×D₄₇	1	2	yes	—
110	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
111	C₂×M₁₆	—	47	4	no	—
112	C₂×M₁₆	—	94	4	no	—
113	C₂²×C₈	—	47	4	no	—
114	C₂²×C₈	—	47	2	no	—
115	C₂²×C₈	—	47	2	no	—
116	C₂²×C₈	—	94	4	no	—
117	C₂²⋊C₈	—	47	16	no	—
118	C₂⁴	C₂×Dic₄₇	1	2	yes	—
119	C₂⁴	C₂×Dic₄₇	1	1	yes	characteristic
120	#41	—	2	16	no	—
121	#41	—	2	8	no	—
122	#41	—	2	8	no	—
123	C₂×Q₈	—	2	4	no	—
124	C₂×Q₈	C₂×Dic₄₇	1	4	yes	—
125	C₂×D₄	—	2	8	no	—
126	C₂×D₄	—	2	4	no	—
127	C₂×D₄	C₂×Dic₄₇	1	8	yes	—
128	C₂×D₄	C₂×Dic₄₇	1	4	yes	—
129	C₂²×C₄	—	2	4	no	—
130	C₂²×C₄	—	2	4	no	—
131	C₂²×C₄	C₂×Dic₄₇	1	2	yes	—
132	C₂²×C₄	C₂×Dic₄₇	1	4	yes	—
133	C₂²×C₄	C₂×Dic₄₇	1	1	yes	characteristic
134	C₂²×C₄	C₂×Dic₄₇	1	2	yes	—
135	C₂²×C₄	C₂²⋊D₄₇	1	4	yes	—
136	C₂²×C₄	C₂²⋊D₄₇	1	4	yes	—
137	C₂²×C₄	C₂²×D₄₇	1	4	yes	—
138	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
139	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
140	M₁₆	—	94	8	no	—
141	C₂×C₈	—	47	4	no	—
142	C₂×C₈	—	47	4	no	—
143	C₂×C₈	—	94	4	no	—
144	C₂×C₈	—	94	8	no	—
145	C₂×C₈	—	94	4	no	—
146	C₂³	—	2	4	no	—
147	C₂³	—	2	4	no	—
148	C₂³	—	2	8	no	—
149	C₂³	C₂²⋊Dic₄₇	1	4	yes	—
150	C₂³	C₂²×Dic₄₇	1	4	yes	—
151	C₂³	C₂²×Dic₄₇	1	2	yes	—
152	C₂³	C₂²×Dic₄₇	1	1	yes	characteristic
153	Q₈	—	2	8	no	—
154	D₄	—	2	16	no	—
155	D₄	—	2	8	no	—
156	C₂×C₄	—	2	4	no	—
157	C₂×C₄	—	2	8	no	—
158	C₂×C₄	—	2	4	no	—
159	C₂×C₄	—	2	4	no	—
160	C₂×C₄	C₂²⋊Dic₄₇	1	4	yes	—
161	C₂×C₄	C₂²⋊Dic₄₇	1	8	yes	—
162	C₂×C₄	C₂²×Dic₄₇	1	4	yes	—
163	C₂×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
164	C₂×C₄	C₂²×Dic₄₇	1	2	yes	—
165	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
166	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
167	C₂×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
168	C₂×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
169	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
170	C₈	—	94	4	no	—
171	C₈	—	94	4	no	—
172	C₂²	—	2	8	no	—
173	C₂²	—	2	4	no	—
174	C₂²	—	2	4	no	—
175	C₂²	—	2	8	no	—
176	C₂²	—	4	8	no	—
177	C₂²	C₂×C₂²⋊Dic₄₇	1	4	yes	—
178	C₂²	C₂×C₂²⋊Dic₄₇	1	2	yes	—
179	C₂²	#13094031	1	4	yes	—
180	C₂²	C₂³×Dic₄₇	1	1	yes	characteristic
181	C₄	—	2	4	no	—
182	C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
183	C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
184	C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
185	C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
186	C₂	—	2	4	no	—
187	C₂	—	4	4	no	—
188	C₂	#15689090	1	4	yes	direct product factor
189	C₂	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
190	C₂	C₂×#13094031	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₂²×#41×C₄₇	C₂
socle	C₂³×C₄₇	C₂²×C₄
hypercenter	C₂²×#41	D₄₇
hypocenter	C₄₇	C₂×#408
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×#10625329	C₂	semidirect
2. C₂³×C₄₇⋊C₈	C₂	semidirect
3. #15689090	C₂	direct (N × H)
4. C₂×C₂²⋊(C₄₇⋊C₈)	C₂	semidirect
7. C₂×#10625329	C₂²	semidirect
11. C₂²×C₄₇⋊C₈	C₂²	semidirect
12. C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
93. C₂×C₄₇	#408	semidirect
101. C₄₇	C₂×#408	semidirect
188. C₂	#15689090	direct (N × H)

Subgroups — C2×#15689090 #20251828

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689090 #20251828