Subgroups — C₂×#14521606 #16859002

Order 3968.

1168 conjugacy classes of subgroups.

The subgroup lattice has 156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521606	C₂	1	16	yes	maximal, direct product factor
2	C₂×#11758446	C₂	1	2	yes	maximal, complemented
3	C₂×#11758447	C₂	1	2	yes	maximal, complemented
4	C₂×#11758501	C₂	1	4	yes	maximal
5	C₂×C₄×Dic₆₂	C₂	1	4	yes	maximal, complemented
6	C₂×#11758503	C₂	1	2	yes	maximal
7	C₂²×C₄²×C₃₁	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₄×C₃₁	C₂²	1	2	yes	—
9	C₂³×C₄×C₃₁	C₂²	1	1	yes	characteristic
10	C₂²×Dic₆₂	C₂²	1	4	yes	—
11	C₂×C₄²×C₃₁	C₂²	1	8	yes	—
12	C₂×C₄²×C₃₁	C₂²	1	2	yes	—
13	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Dic₃₁	C₂²	1	4	yes	—
16	#11758503	C₂²	1	16	yes	—
17	C₂×C₄⋊Dic₃₁	C₂²	1	4	yes	—
18	C₂×C₄⋊Dic₃₁	C₂²	1	4	yes	—
19	#11758501	C₂²	1	32	yes	—
20	C₂×Dic₃₁⋊C₄	C₂²	1	8	yes	—
21	C₂×C₄×Dic₃₁	C₂²	1	4	yes	—
22	#11758447	C₂²	1	16	yes	complemented
23	#11758446	C₂²	1	16	yes	complemented
24	C₄×Dic₆₂	C₂²	1	32	yes	complemented
25	C₂⁴×C₃₁	C₂³	1	1	yes	characteristic
26	C₂²×C₄×C₃₁	—	2	8	no	—
27	C₂²×C₄×C₃₁	Q₈	1	8	yes	complemented
28	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
29	C₂²×C₄×C₃₁	C₂³	1	8	yes	—
30	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
31	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
32	C₂²×C₄×C₃₁	C₂³	1	4	yes	—
33	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
34	C₂²×Dic₃₁	C₂³	1	8	yes	—
35	C₂×Dic₆₂	—	2	16	no	—
36	C₂×Dic₆₂	C₂³	1	16	yes	—
37	C₄²×C₃₁	C₂³	1	8	yes	—
38	C₄²×C₃₁	C₂³	1	4	yes	—
39	C₄²×C₃₁	C₂³	1	4	yes	—
40	C₂²⋊Dic₃₁	C₂³	1	16	yes	—
41	C₄⋊Dic₃₁	C₂³	1	16	yes	—
42	C₄⋊Dic₃₁	C₂³	1	16	yes	—
43	Dic₃₁⋊C₄	C₂³	1	32	yes	—
44	C₄×Dic₃₁	C₂³	1	16	yes	—
45	C₂³×C₃₁	—	2	4	no	—
46	C₂³×C₃₁	C₂×Q₈	1	4	yes	—
47	C₂³×C₃₁	C₂⁴	1	2	yes	—
48	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
49	C₂×C₄×C₃₁	—	2	4	no	—
50	C₂×C₄×C₃₁	—	2	16	no	—
51	C₂×C₄×C₃₁	C₂×Q₈	1	4	yes	—
52	C₂×C₄×C₃₁	C₂×Q₈	1	4	yes	—
53	C₂×C₄×C₃₁	C₂×Q₈	1	16	yes	complemented
54	C₂×C₄×C₃₁	#41	1	8	yes	—
55	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
56	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
57	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
58	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
59	C₂×Dic₃₁	—	2	16	no	—
60	C₂×Dic₃₁	C₂⁴	1	16	yes	—
61	Dic₆₂	—	2	32	no	—
62	C₂×#533	—	31	1	no	maximal, Sylow
63	C₂²×C₃₁	—	2	8	no	—
64	C₂²×C₃₁	—	2	4	no	—
65	C₂²×C₃₁	C₂²×Q₈	1	4	yes	—
66	C₂²×C₃₁	C₂²×Q₈	1	2	yes	—
67	C₂²×C₃₁	C₂×#41	1	4	yes	—
68	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
69	C₄×C₃₁	—	2	4	no	—
70	C₄×C₃₁	C₂²×Q₈	1	4	yes	—
71	C₄×C₃₁	C₂²×Q₈	1	4	yes	—
72	C₄×C₃₁	C₂×#41	1	8	yes	—
73	Dic₃₁	—	2	16	no	—
74	#533	—	31	16	no	—
75	C₂×C₄⋊Q₈	—	31	2	no	—
76	C₂×#125	—	31	2	no	—
77	C₂×C₂²⋊Q₈	—	31	4	no	—
78	C₂×C₄×Q₈	—	31	4	no	—
79	C₂×#117	—	31	2	no	—
80	C₂²×C₄²	D₃₁	1	1	yes	characteristic
81	C₂×C₃₁	—	2	4	no	—
82	C₂×C₃₁	#533	1	4	yes	complemented
83	C₂×C₃₁	C₂³×Q₈	1	1	yes	characteristic
84	C₂×C₃₁	C₂²×#41	1	2	yes	—
85	C₂²×Q₈	—	31	4	no	—
86	C₂³×C₄	C₂×D₃₁	1	2	yes	—
87	C₂³×C₄	C₂×D₃₁	1	1	yes	characteristic
88	C₄⋊Q₈	—	31	16	no	—
89	#125	—	31	16	no	—
90	C₂²⋊Q₈	—	31	32	no	—
91	C₄×Q₈	—	31	32	no	—
92	#117	—	31	16	no	—
93	C₂×C₄⋊C₄	—	31	4	no	—
94	C₂×C₄⋊C₄	—	31	8	no	—
95	C₂×C₄⋊C₄	—	31	4	no	—
96	C₂×C₂²⋊C₄	—	31	4	no	—
97	C₂×C₄²	—	31	4	no	—
98	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
99	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
100	C₂×C₄²	C₂×D₃₁	1	8	yes	—
101	C₂×C₄²	C₂×D₃₁	1	2	yes	—
102	C₃₁	C₂×#533	1	1	yes	characteristic, complemented, Sylow
103	C₂⁴	C₂²×D₃₁	1	1	yes	characteristic
104	C₂×Q₈	—	31	16	no	—
105	C₂×Q₈	—	62	16	no	—
106	C₂²×C₄	—	2	8	no	—
107	C₂²×C₄	—	31	8	no	—
108	C₂²×C₄	Dic₆₂	1	8	yes	complemented
109	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
110	C₂²×C₄	C₂²×D₃₁	1	8	yes	—
111	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
112	C₂²×C₄	C₂²×D₃₁	1	4	yes	—
113	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
114	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
115	C₄⋊C₄	—	31	32	no	—
116	C₄⋊C₄	—	31	16	no	—
117	C₄⋊C₄	—	31	16	no	—
118	C₂²⋊C₄	—	31	16	no	—
119	C₄²	—	31	16	no	—
120	C₄²	C₂²×D₃₁	1	8	yes	—
121	C₄²	C₂²×D₃₁	1	4	yes	—
122	C₄²	C₂²×D₃₁	1	4	yes	—
123	C₂³	—	2	4	no	—
124	C₂³	C₂×Dic₆₂	1	4	yes	—
125	C₂³	C₂³×D₃₁	1	2	yes	—
126	C₂³	C₂³×D₃₁	1	1	yes	characteristic
127	Q₈	—	62	32	no	—
128	C₂×C₄	—	2	4	no	—
129	C₂×C₄	—	2	16	no	—
130	C₂×C₄	—	31	16	no	—
131	C₂×C₄	—	62	16	no	—
132	C₂×C₄	C₂×Dic₆₂	1	4	yes	—
133	C₂×C₄	C₂×Dic₆₂	1	4	yes	—
134	C₂×C₄	C₂×Dic₆₂	1	16	yes	complemented
135	C₂×C₄	#92495	1	8	yes	—
136	C₂×C₄	C₂³×D₃₁	1	4	yes	—
137	C₂×C₄	C₂³×D₃₁	1	2	yes	—
138	C₂×C₄	C₂³×D₃₁	1	2	yes	—
139	C₂×C₄	C₂³×D₃₁	1	4	yes	—
140	C₂²	—	2	8	no	—
141	C₂²	—	2	4	no	—
142	C₂²	C₂²×Dic₆₂	1	4	yes	—
143	C₂²	C₂²×Dic₆₂	1	2	yes	—
144	C₂²	C₂×#92495	1	4	yes	—
145	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
146	C₄	—	2	4	no	—
147	C₄	—	62	16	no	—
148	C₄	C₂²×Dic₆₂	1	4	yes	—
149	C₄	C₂²×Dic₆₂	1	4	yes	—
150	C₄	C₂×#92495	1	8	yes	—
151	C₂	—	2	4	no	—
152	C₂	#14521606	1	4	yes	direct product factor
153	C₂	C₂³×Dic₆₂	1	1	yes	characteristic
154	C₂	C₂²×#92495	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂²×D₃₁
commutator, cosocle	C₂²×C₃₁	C₂⁵
Frattini	C₂²	C₂⁴×D₃₁
Fitting	C₂²×C₄²×C₃₁	C₂
socle	C₂³×C₃₁	C₂⁴
prime radical	C₂⁴×C₃₁	C₂³
hypercenter	C₂²×C₄²	D₃₁
hypocenter	C₃₁	C₂×#533
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄²

Complements

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

N	H ≅ G/N	type
1. #14521606	C₂	direct (N × H)
2. C₂×#11758446	C₂	semidirect
3. C₂×#11758447	C₂	semidirect
5. C₂×C₄×Dic₆₂	C₂	semidirect
22. #11758447	C₂²	semidirect
23. #11758446	C₂²	semidirect
24. C₄×Dic₆₂	C₂²	semidirect
27. C₂²×C₄×C₃₁	Q₈	semidirect
53. C₂×C₄×C₃₁	C₂×Q₈	semidirect
82. C₂×C₃₁	#533	semidirect
102. C₃₁	C₂×#533	semidirect
108. C₂²×C₄	Dic₆₂	semidirect
134. C₂×C₄	C₂×Dic₆₂	semidirect
152. C₂	#14521606	direct (N × H)

Maximal subgroups

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

subgroup	index
#14521606	2
C₂×#11758446	2
C₂×#11758447	2
C₂×#11758501	2
C₂×C₄×Dic₆₂	2
C₂×#11758503	2
C₂²×C₄²×C₃₁	2
C₂×#533	31

Subgroups — C2×#14521606 #16859002

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14521606 #16859002