Subgroups — C₂×#20245662 #26371754

Order 12032.

558 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	C₂×#15689527	C₂	1	2	yes	maximal
2	#20245662	C₂	1	8	yes	maximal, direct product factor
3	C₂×#15688949	C₂	1	1	yes	maximal, characteristic
4	C₂×#15688948	C₂	1	2	yes	maximal
5	C₂×C₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄₇×#366	C₂	1	1	yes	maximal, characteristic
7	C₂×#13094023	—	2	2	no	—
8	C₂²×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic
9	#15689527	—	2	4	no	—
10	#15689527	C₂²	1	8	yes	—
11	C₂×#13093958	C₂²	1	2	yes	—
12	C₂×#13093957	—	2	2	no	—
13	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
14	#15688949	C₂²	1	4	yes	—
15	#15688948	C₂²	1	8	yes	—
16	C₁₆×Dic₄₇	C₂²	1	4	yes	—
17	C₂²×C₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#107×C₄₇	C₂²	1	2	yes	—
19	C₄₇×#366	C₂²	1	4	yes	—
20	C₂²×Dic₉₄	—	4	2	no	—
21	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
22	#13094023	—	2	8	no	—
23	#13094023	—	4	4	no	—
24	C₂×C₄⋊Dic₄₇	—	2	2	no	—
25	C₂×Dic₄₇⋊C₄	—	4	2	no	—
26	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
27	C₂×C₄₇⋊C₁₆	Q₈	1	4	yes	complemented
28	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
29	#13093958	—	2	2	no	—
30	#13093958	C₂³	1	4	yes	—
31	#13093957	—	2	8	no	—
32	C₈×Dic₄₇	D₄	1	2	yes	—
33	C₈×Dic₄₇	C₂³	1	2	yes	—
34	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
35	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
36	C₂×C₁₆×C₄₇	Q₈	1	4	yes	complemented
37	C₂×C₁₆×C₄₇	C₂³	1	2	yes	—
38	#107×C₄₇	—	2	2	no	—
39	#107×C₄₇	C₂³	1	4	yes	—
40	C₂²×C₄×C₄₇	—	4	2	no	—
41	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
42	C₂²×Dic₄₇	—	4	2	no	—
43	C₂²×Dic₄₇	D₈	1	1	yes	characteristic
44	C₂²×Dic₄₇	D₈	1	1	yes	characteristic
45	C₂×Dic₉₄	—	4	8	no	—
46	C₂×Dic₉₄	—	8	8	no	—
47	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
48	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
49	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
50	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
51	C₄⋊C₄×C₄₇	—	2	4	no	—
52	C₄⋊C₄×C₄₇	—	4	2	no	—
53	C₄⋊Dic₄₇	—	2	4	no	—
54	C₄⋊Dic₄₇	—	4	2	no	—
55	Dic₄₇⋊C₄	—	4	8	no	—
56	C₄×Dic₄₇	D₈	1	2	yes	—
57	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
58	C₂×C₄₇⋊C₈	Q₁₆	1	4	yes	—
59	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
60	C₁₆×C₄₇	C₂×Q₈	1	4	yes	complemented
61	C₄₇⋊C₁₆	C₂×Q₈	1	4	yes	complemented
62	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
63	C₂×C₄×C₄₇	—	4	4	no	—
64	C₂×C₄×C₄₇	—	8	4	no	—
65	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
66	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
67	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
68	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
69	C₂×Dic₄₇	—	4	4	no	—
70	C₂×Dic₄₇	—	8	4	no	—
71	C₂×Dic₄₇	D₁₆	1	4	yes	—
72	C₂×Dic₄₇	Q₃₂	1	4	yes	—
73	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
74	C₂×Dic₄₇	C₂×D₈	1	2	yes	—
75	Dic₉₄	—	8	16	no	—
76	C₈×C₄₇	C₄⋊Q₈	1	2	yes	—
77	C₈×C₄₇	C₂²×Q₈	1	1	yes	characteristic
78	C₈×C₄₇	C₂²×Q₈	1	1	yes	characteristic
79	C₄₇⋊C₈	C₂×Q₁₆	1	4	yes	—
80	C₂×#2252	—	47	1	no	maximal, Sylow
81	C₂²×C₄₇	#500	1	2	yes	—
82	C₂²×C₄₇	C₂×D₁₆	1	2	yes	—
83	C₂²×C₄₇	C₂×Q₃₂	1	2	yes	—
84	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
85	C₄×C₄₇	—	8	4	no	—
86	C₄×C₄₇	#500	1	2	yes	—
87	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
88	C₄×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
89	Dic₄₇	—	8	4	no	—
90	Dic₄₇	C₂×D₁₆	1	4	yes	—
91	Dic₄₇	C₂×Q₃₂	1	4	yes	—
92	C₂×#500	—	47	2	no	—
93	#2252	—	47	8	no	—
94	C₂×#366	—	47	1	no	—
95	C₂×#366	—	47	2	no	—
96	C₂×#366	D₄₇	1	1	yes	characteristic
97	C₂×C₄×C₁₆	—	47	1	no	—
98	C₂×C₄₇	#2252	1	4	yes	complemented
99	C₂×C₄₇	C₂×#500	1	1	yes	characteristic
100	C₂×C₄₇	C₂²×D₁₆	1	1	yes	characteristic
101	C₂×C₄₇	C₂²×Q₃₂	1	1	yes	characteristic
102	C₂×C₄⋊Q₈	—	94	2	no	—
103	C₂²×C₁₆	—	47	1	no	—
104	C₂²×C₁₆	C₂×D₄₇	1	1	yes	characteristic
105	#500	—	47	8	no	—
106	#500	—	94	4	no	—
107	C₂×#107	—	47	2	no	—
108	C₂×#107	—	94	2	no	—
109	C₂×#107	C₂×D₄₇	1	2	yes	—
110	C₂×C₄×C₈	—	47	1	no	—
111	#366	—	47	4	no	—
112	#366	—	47	8	no	—
113	#366	C₂×D₄₇	1	4	yes	—
114	C₄×C₁₆	—	47	4	no	—
115	C₄₇	C₂×#2252	1	1	yes	characteristic, complemented, Sylow
116	C₂²×Q₈	—	188	2	no	—
117	C₂²×C₈	—	47	1	no	—
118	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
119	C₄⋊Q₈	—	94	8	no	—
120	C₄⋊Q₈	—	188	4	no	—
121	C₂×C₄⋊C₄	—	2	2	no	—
122	C₂×C₄⋊C₄	—	94	2	no	—
123	C₂×C₄⋊C₄	—	188	2	no	—
124	C₂×C₄²	—	47	1	no	—
125	C₂×C₁₆	—	47	4	no	—
126	C₂×C₁₆	—	47	2	no	—
127	C₂×C₁₆	Dic₉₄	1	4	yes	complemented
128	C₂×C₁₆	C₂²×D₄₇	1	2	yes	—
129	#107	—	2	2	no	—
130	#107	—	47	4	no	—
131	#107	—	94	8	no	—
132	#107	—	94	2	no	—
133	#107	C₂²×D₄₇	1	4	yes	—
134	C₄×C₈	—	47	2	no	—
135	C₄×C₈	—	47	2	no	—
136	C₂×Q₈	—	376	8	no	—
137	C₂×Q₈	—	188	8	no	—
138	C₂²×C₄	—	4	2	no	—
139	C₂²×C₄	—	47	1	no	—
140	C₂²×C₄	—	47	1	no	—
141	C₂²×C₄	—	188	2	no	—
142	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
143	C₂×C₈	—	47	4	no	—
144	C₂×C₈	—	47	2	no	—
145	C₂×C₈	C₂×Dic₉₄	1	2	yes	—
146	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
147	C₂×C₈	Q₈×D₄₇	1	2	yes	—
148	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
149	C₄⋊C₄	—	2	4	no	—
150	C₄⋊C₄	—	4	2	no	—
151	C₄⋊C₄	—	94	4	no	—
152	C₄⋊C₄	—	188	8	no	—
153	C₄⋊C₄	—	188	2	no	—
154	C₄²	—	47	2	no	—
155	C₄²	—	47	2	no	—
156	C₁₆	—	47	4	no	—
157	C₁₆	C₂×Dic₉₄	1	4	yes	complemented
158	C₂³	D₈×D₄₇	1	1	yes	characteristic
159	Q₈	—	376	16	no	—
160	C₂×C₄	—	4	4	no	—
161	C₂×C₄	—	8	4	no	—
162	C₂×C₄	—	47	4	no	—
163	C₂×C₄	—	47	4	no	—
164	C₂×C₄	—	47	2	no	—
165	C₂×C₄	—	47	2	no	—
166	C₂×C₄	—	376	4	no	—
167	C₂×C₄	—	188	4	no	—
168	C₂×C₄	#13094023	1	2	yes	—
169	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
170	C₂×C₄	Q₁₆×D₄₇	1	2	yes	—
171	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
172	C₈	—	47	4	no	—
173	C₈	#13094023	1	2	yes	—
174	C₈	C₂×Q₈×D₄₇	1	1	yes	characteristic
175	C₈	C₂²×Dic₉₄	1	1	yes	characteristic
176	C₂²	#15689527	1	2	yes	—
177	C₂²	D₁₆×D₄₇	1	2	yes	—
178	C₂²	Q₃₂×D₄₇	1	2	yes	—
179	C₂²	C₂×D₈×D₄₇	1	1	yes	characteristic
180	C₄	—	8	4	no	—
181	C₄	—	47	4	no	—
182	C₄	—	47	4	no	—
183	C₄	—	376	4	no	—
184	C₄	#15689527	1	2	yes	—
185	C₄	C₂×#13094023	1	1	yes	characteristic
186	C₄	C₂×Q₁₆×D₄₇	1	1	yes	characteristic
187	C₂	#20245662	1	4	yes	direct product factor
188	C₂	C₂×#15689527	1	1	yes	characteristic
189	C₂	C₂×D₁₆×D₄₇	1	1	yes	characteristic
190	C₂	C₂×Q₃₂×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₈×D₄₇
commutator, cosocle	C₂×C₈×C₄₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₄₇
Fitting	C₂×C₄₇×#366	C₂
socle, prime radical	C₂³×C₄₇	C₂×D₈
hypercenter	C₂×#366	D₄₇
hypocenter	C₄₇	C₂×#2252
LCS	G ▷ C₂×C₈×C₄₇ ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂×#366

Complements

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

N	H ≅ G/N	type
2. #20245662	C₂	direct (N × H)
27. C₂×C₄₇⋊C₁₆	Q₈	semidirect
36. C₂×C₁₆×C₄₇	Q₈	semidirect
60. C₁₆×C₄₇	C₂×Q₈	semidirect
61. C₄₇⋊C₁₆	C₂×Q₈	semidirect
98. C₂×C₄₇	#2252	semidirect
115. C₄₇	C₂×#2252	semidirect
127. C₂×C₁₆	Dic₉₄	semidirect
157. C₁₆	C₂×Dic₉₄	semidirect
187. C₂	#20245662	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#15689527	2
#20245662	2
C₂×#15688949	2
C₂×#15688948	2
C₂×C₁₆×Dic₄₇	2
C₂×C₄₇×#366	2
C₂×#2252	47

Subgroups — C2×#20245662 #26371754

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20245662 #26371754