Subgroups — C₂×#15689119 #20251884

Order 6016.

792 conjugacy classes of subgroups.

The subgroup lattice has 216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689119	C₂	1	8	yes	maximal, direct product factor
4	C₂×#13093948	C₂	1	2	yes	maximal, complemented
5	C₂×#13093945	C₂	1	2	yes	maximal, complemented
6	C₂²×#41×C₄₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄₇⋊C₈	—	2	4	no	—
8	C₂²×C₄₇⋊C₈	C₂²	1	2	yes	—
9	C₂²×C₄₇⋊C₈	C₂²	1	4	yes	complemented
10	#13093983	—	2	2	no	—
11	#13093983	C₂²	1	4	yes	complemented
12	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
13	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
14	C₂×C₄×Dic₄₇	—	2	1	no	—
15	#13093948	C₂²	1	8	yes	complemented
16	#13093945	C₂²	1	8	yes	complemented
17	C₂×#41×C₄₇	—	2	4	no	—
18	C₂×#41×C₄₇	—	2	2	no	—
19	C₂×#41×C₄₇	C₄	1	8	yes	complemented
20	C₂×#41×C₄₇	C₂²	1	4	yes	—
21	C₂²×Q₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₂²×D₄×C₄₇	—	2	1	no	—
23	C₂²×D₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂³×C₄×C₄₇	—	2	1	no	—
25	C₂³×C₄×C₄₇	C₂²	1	1	yes	characteristic
26	C₂⁴×C₄₇	—	2	1	no	—
27	C₂⁴×C₄₇	D₄	1	1	yes	characteristic
28	#41×C₄₇	—	2	16	no	—
29	#41×C₄₇	—	2	8	no	—
30	#41×C₄₇	C₂×C₄	1	16	yes	complemented
31	C₂×Q₈×C₄₇	—	2	2	no	—
32	C₂×Q₈×C₄₇	—	2	1	no	—
33	C₂×Q₈×C₄₇	C₂×C₄	1	4	yes	—
34	C₂×Q₈×C₄₇	C₂³	1	2	yes	—
35	C₂×D₄×C₄₇	—	2	8	no	—
36	C₂×D₄×C₄₇	—	2	4	no	—
37	C₂×D₄×C₄₇	—	2	1	no	—
38	C₂×D₄×C₄₇	—	2	2	no	—
39	C₂×D₄×C₄₇	C₂×C₄	1	4	yes	—
40	C₂×D₄×C₄₇	C₂³	1	2	yes	—
41	C₂²×C₄×C₄₇	—	2	1	no	—
42	C₂²×C₄×C₄₇	—	2	8	no	—
43	C₂²×C₄×C₄₇	—	2	4	no	—
44	C₂²×C₄×C₄₇	C₂×C₄	1	4	yes	—
45	C₂²×C₄×C₄₇	D₄	1	2	yes	—
46	C₂²×C₄×C₄₇	D₄	1	1	yes	characteristic
47	C₂²×C₄×C₄₇	D₄	1	4	yes	—
48	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
49	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
50	C₂²×Dic₄₇	—	2	2	no	—
51	C₂²⋊Dic₄₇	—	2	4	no	—
52	C₄⋊Dic₄₇	—	2	2	no	—
53	C₄⋊Dic₄₇	C₂³	1	4	yes	—
54	C₄×Dic₄₇	—	2	4	no	—
55	C₂×C₄₇⋊C₈	—	2	4	no	—
56	C₂×C₄₇⋊C₈	—	2	8	no	—
57	C₂×C₄₇⋊C₈	C₂³	1	4	yes	—
58	C₂³×C₄₇	—	2	4	no	—
59	C₂³×C₄₇	—	2	4	no	—
60	C₂³×C₄₇	—	2	2	no	—
61	C₂³×C₄₇	—	4	4	no	—
62	C₂³×C₄₇	C₂²⋊C₄	1	4	yes	—
63	C₂³×C₄₇	C₂×D₄	1	2	yes	—
64	C₂³×C₄₇	C₂×D₄	1	1	yes	characteristic
65	Q₈×C₄₇	—	2	4	no	—
66	Q₈×C₄₇	—	2	2	no	—
67	Q₈×C₄₇	C₂²×C₄	1	4	yes	—
68	D₄×C₄₇	—	2	16	no	—
69	D₄×C₄₇	—	2	4	no	—
70	D₄×C₄₇	—	2	2	no	—
71	D₄×C₄₇	C₂²×C₄	1	4	yes	—
72	C₂×C₄×C₄₇	—	2	4	no	—
73	C₂×C₄×C₄₇	—	2	2	no	—
74	C₂×C₄×C₄₇	—	2	16	no	—
75	C₂×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
76	C₂×C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
77	C₂×C₄×C₄₇	C₂²×C₄	1	2	yes	—
78	C₂×C₄×C₄₇	C₂²×C₄	1	4	yes	—
79	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
80	C₂×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂×C₄×C₄₇	C₂×D₄	1	2	yes	—
82	C₂×C₄×C₄₇	C₂×D₄	1	4	yes	—
83	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
84	C₂×Dic₄₇	—	2	4	no	—
85	C₂×Dic₄₇	—	4	4	no	—
86	C₄₇⋊C₈	—	2	4	no	—
87	C₂²×C₄₇	—	2	4	no	—
88	C₂²×C₄₇	—	2	8	no	—
89	C₂²×C₄₇	—	2	4	no	—
90	C₂²×C₄₇	—	4	4	no	—
91	C₂²×C₄₇	—	4	8	no	—
92	C₂²×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
93	C₂²×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
94	C₂²×C₄₇	#135	1	4	yes	—
95	C₂²×C₄₇	C₂²×D₄	1	1	yes	characteristic
96	C₄×C₄₇	—	2	4	no	—
97	C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
98	C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
99	C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
100	C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
101	Dic₄₇	—	4	4	no	—
102	C₂×#416	—	47	1	no	maximal, Sylow
103	C₂×C₄₇	—	2	4	no	—
104	C₂×C₄₇	—	4	4	no	—
105	C₂×C₄₇	#416	1	4	yes	complemented
106	C₂×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₄₇	C₂×#135	1	2	yes	—
108	C₂²×#41	D₄₇	1	1	yes	characteristic
109	C₂³×C₈	—	47	1	no	—
110	C₂×#117	—	47	1	no	—
111	#416	—	47	8	no	—
112	C₂×#103	—	47	2	no	—
113	C₂×#102	—	47	2	no	—
114	C₄₇	C₂×#416	1	1	yes	characteristic, complemented, Sylow
115	C₂×#41	—	2	4	no	—
116	C₂×#41	—	2	2	no	—
117	C₂×#41	Dic₄₇	1	8	yes	complemented
118	C₂×#41	C₂×D₄₇	1	4	yes	—
119	C₂²×Q₈	C₂×D₄₇	1	1	yes	characteristic
120	C₂²×D₄	—	2	1	no	—
121	C₂²×D₄	C₂×D₄₇	1	1	yes	characteristic
122	C₂³×C₄	—	2	1	no	—
123	C₂³×C₄	C₂×D₄₇	1	1	yes	characteristic
124	C₂²×C₈	—	47	2	no	—
125	C₂²×C₈	—	47	4	no	—
126	C₂²×C₈	—	94	4	no	—
127	#117	—	47	4	no	—
128	#117	—	94	2	no	—
129	C₂×C₄⋊C₄	—	47	2	no	—
130	C₂×C₂²⋊C₄	—	94	1	no	—
131	C₂×C₄²	—	94	1	no	—
132	#103	—	47	8	no	—
133	#102	—	47	8	no	—
134	C₂⁴	—	2	1	no	—
135	C₂⁴	C₂²⋊D₄₇	1	1	yes	characteristic
136	#41	—	2	16	no	—
137	#41	—	2	8	no	—
138	#41	C₂×Dic₄₇	1	16	yes	complemented
139	C₂×Q₈	—	2	2	no	—
140	C₂×Q₈	—	2	1	no	—
141	C₂×Q₈	C₂×Dic₄₇	1	4	yes	—
142	C₂×Q₈	C₂²×D₄₇	1	2	yes	—
143	C₂×D₄	—	2	8	no	—
144	C₂×D₄	—	2	4	no	—
145	C₂×D₄	—	2	1	no	—
146	C₂×D₄	—	2	2	no	—
147	C₂×D₄	C₂×Dic₄₇	1	4	yes	—
148	C₂×D₄	C₂²×D₄₇	1	2	yes	—
149	C₂²×C₄	—	2	1	no	—
150	C₂²×C₄	—	2	8	no	—
151	C₂²×C₄	—	2	4	no	—
152	C₂²×C₄	—	94	2	no	—
153	C₂²×C₄	C₂×Dic₄₇	1	4	yes	—
154	C₂²×C₄	C₂²⋊D₄₇	1	2	yes	—
155	C₂²×C₄	C₂²⋊D₄₇	1	4	yes	—
156	C₂²×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
157	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
158	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
159	C₂×C₈	—	47	4	no	—
160	C₂×C₈	—	94	4	no	—
161	C₂×C₈	—	94	8	no	—
162	C₄⋊C₄	—	47	4	no	—
163	C₄⋊C₄	—	94	2	no	—
164	C₂²⋊C₄	—	94	4	no	—
165	C₄²	—	94	4	no	—
166	C₂³	—	2	4	no	—
167	C₂³	—	2	4	no	—
168	C₂³	—	2	2	no	—
169	C₂³	—	4	4	no	—
170	C₂³	C₂²⋊Dic₄₇	1	4	yes	—
171	C₂³	C₂×C₂²⋊D₄₇	1	2	yes	—
172	C₂³	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
173	Q₈	—	2	4	no	—
174	Q₈	—	2	2	no	—
175	Q₈	C₂²×Dic₄₇	1	4	yes	—
176	D₄	—	2	16	no	—
177	D₄	—	2	4	no	—
178	D₄	—	2	2	no	—
179	D₄	C₂²×Dic₄₇	1	4	yes	—
180	C₂×C₄	—	2	4	no	—
181	C₂×C₄	—	2	2	no	—
182	C₂×C₄	—	2	16	no	—
183	C₂×C₄	—	94	4	no	—
184	C₂×C₄	—	188	4	no	—
185	C₂×C₄	C₂²⋊Dic₄₇	1	4	yes	—
186	C₂×C₄	C₂²⋊Dic₄₇	1	8	yes	—
187	C₂×C₄	C₂²×Dic₄₇	1	2	yes	—
188	C₂×C₄	C₂²×Dic₄₇	1	4	yes	—
189	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
190	C₂×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
191	C₂×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
192	C₂×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
193	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
194	C₈	—	94	4	no	—
195	C₂²	—	2	8	no	—
196	C₂²	—	2	4	no	—
197	C₂²	—	2	4	no	—
198	C₂²	—	4	8	no	—
199	C₂²	—	4	4	no	—
200	C₂²	C₂×C₂²⋊Dic₄₇	1	4	yes	—
201	C₂²	C₂×C₂²⋊Dic₄₇	1	2	yes	—
202	C₂²	#13094044	1	4	yes	—
203	C₂²	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
204	C₄	—	2	4	no	—
205	C₄	—	188	4	no	—
206	C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
207	C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
208	C₄	C₂³×Dic₄₇	1	1	yes	characteristic
209	C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
210	C₂	—	2	4	no	—
211	C₂	—	4	4	no	—
212	C₂	#15689119	1	4	yes	direct product factor
213	C₂	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
214	C₂	C₂×#13094044	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₄₇
Fitting	C₂²×#41×C₄₇	C₂
socle	C₂³×C₄₇	C₂×D₄
hypercenter	C₂²×#41	D₄₇
hypocenter	C₄₇	C₂×#416
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. C₂³×C₄₇⋊C₈	C₂	semidirect
2. C₂×#13093983	C₂	semidirect
3. #15689119	C₂	direct (N × H)
4. C₂×#13093948	C₂	semidirect
5. C₂×#13093945	C₂	semidirect
9. C₂²×C₄₇⋊C₈	C₂²	semidirect
11. #13093983	C₂²	semidirect
15. #13093948	C₂²	semidirect
16. #13093945	C₂²	semidirect
19. C₂×#41×C₄₇	C₄	semidirect
30. #41×C₄₇	C₂×C₄	semidirect
105. C₂×C₄₇	#416	semidirect
114. C₄₇	C₂×#416	semidirect
117. C₂×#41	Dic₄₇	semidirect
138. #41	C₂×Dic₄₇	semidirect
212. C₂	#15689119	direct (N × H)

Subgroups — C2×#15689119 #20251884

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#15689119 #20251884