Subgroups — C₂×#14521777 #16859283

Order 3968.

1048 conjugacy classes of subgroups.

The subgroup lattice has 196 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14521777	C₂	1	16	yes	maximal, direct product factor
2	C₂×#11758446	C₂	1	1	yes	maximal, characteristic
3	C₂×#11758521	C₂	1	2	yes	maximal
4	C₂×#11758447	C₂	1	2	yes	maximal
5	C₂×#11758466	C₂	1	4	yes	maximal
6	C₂×C₄×Dic₆₂	C₂	1	2	yes	maximal
7	C₂×C₄×Dic₆₂	C₂	1	1	yes	maximal, characteristic
8	C₂×#11758464	C₂	1	2	yes	maximal
9	C₂×C₄×Q₈×C₃₁	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₈×C₃₁	C₂²	1	1	yes	characteristic
11	C₂²×Dic₆₂	C₂²	1	2	yes	—
12	C₂²×Dic₆₂	C₂²	1	1	yes	characteristic
13	C₄×Q₈×C₃₁	C₂²	1	8	yes	—
14	C₂×C₄⋊C₄×C₃₁	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×C₃₁	C₂²	1	2	yes	—
16	C₂×C₄²×C₃₁	C₂²	1	2	yes	—
17	C₂×C₄²×C₃₁	C₂²	1	1	yes	characteristic
18	#11758521	C₂²	1	16	yes	—
19	C₂×C₄⋊Dic₃₁	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊Dic₃₁	C₂²	1	2	yes	—
21	C₂×C₄⋊Dic₃₁	C₂²	1	2	yes	—
22	C₂×Dic₃₁⋊C₄	C₂²	1	4	yes	—
23	C₂×Dic₃₁⋊C₄	C₂²	1	2	yes	—
24	C₂×Dic₃₁⋊C₄	C₂²	1	4	yes	—
25	C₂×Dic₃₁⋊C₄	C₂²	1	4	yes	—
26	C₂×C₄×Dic₃₁	C₂²	1	4	yes	—
27	C₂×C₄×Dic₃₁	C₂²	1	2	yes	—
28	#11758466	C₂²	1	32	yes	—
29	#11758464	C₂²	1	16	yes	—
30	#11758447	C₂²	1	16	yes	—
31	#11758446	C₂²	1	8	yes	—
32	C₄×Dic₆₂	C₂²	1	16	yes	—
33	C₄×Dic₆₂	C₂²	1	8	yes	—
34	C₂×Q₈×C₃₁	—	2	4	no	—
35	C₂×Q₈×C₃₁	C₂³	1	4	yes	—
36	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
37	C₂²×C₄×C₃₁	C₂³	1	2	yes	—
38	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
39	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
40	C₂²×C₄×C₃₁	C₂³	1	1	yes	characteristic
41	C₂²×Dic₃₁	C₂³	1	2	yes	—
42	C₂²×Dic₃₁	C₂³	1	4	yes	—
43	C₂²×Dic₃₁	C₂³	1	2	yes	—
44	C₂×Dic₆₂	—	2	8	no	—
45	C₂×Dic₆₂	Q₈	1	8	yes	complemented
46	C₂×Dic₆₂	C₂³	1	8	yes	—
47	C₂×Dic₆₂	C₂³	1	4	yes	—
48	C₄⋊C₄×C₃₁	C₂³	1	4	yes	—
49	C₄⋊C₄×C₃₁	C₂³	1	8	yes	—
50	C₄²×C₃₁	C₂³	1	4	yes	—
51	C₄²×C₃₁	C₂³	1	8	yes	—
52	C₄⋊Dic₃₁	C₂³	1	8	yes	—
53	C₄⋊Dic₃₁	C₂³	1	4	yes	—
54	C₄⋊Dic₃₁	C₂³	1	8	yes	—
55	Dic₃₁⋊C₄	C₂³	1	8	yes	—
56	Dic₃₁⋊C₄	C₂³	1	16	yes	—
57	Dic₃₁⋊C₄	C₂³	1	16	yes	—
58	Dic₃₁⋊C₄	C₂³	1	16	yes	—
59	C₄×Dic₃₁	C₂³	1	16	yes	—
60	C₄×Dic₃₁	C₂³	1	8	yes	—
61	C₂³×C₃₁	C₂⁴	1	1	yes	characteristic
62	Q₈×C₃₁	—	2	8	no	—
63	C₂×C₄×C₃₁	—	2	4	no	—
64	C₂×C₄×C₃₁	—	2	4	no	—
65	C₂×C₄×C₃₁	—	2	2	no	—
66	C₂×C₄×C₃₁	C₂×Q₈	1	4	yes	—
67	C₂×C₄×C₃₁	#41	1	4	yes	—
68	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
69	C₂×C₄×C₃₁	C₂⁴	1	4	yes	—
70	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
71	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
72	C₂×C₄×C₃₁	C₂⁴	1	2	yes	—
73	C₂×Dic₃₁	—	2	8	no	—
74	C₂×Dic₃₁	—	2	4	no	—
75	C₂×Dic₃₁	C₂×Q₈	1	8	yes	—
76	C₂×Dic₃₁	C₂⁴	1	4	yes	—
77	C₂×Dic₃₁	C₂⁴	1	8	yes	—
78	C₂×Dic₃₁	C₂⁴	1	4	yes	—
79	Dic₆₂	—	2	16	no	—
80	Dic₆₂	C₂×Q₈	1	16	yes	complemented
81	C₂×#557	—	31	1	no	maximal, Sylow
82	C₂²×C₃₁	C₂²×Q₈	1	2	yes	—
83	C₂²×C₃₁	C₂×#41	1	2	yes	—
84	C₂²×C₃₁	2₋¹⁺⁴	1	2	yes	—
85	C₂²×C₃₁	C₂⁵	1	1	yes	characteristic
86	C₄×C₃₁	—	2	4	no	—
87	C₄×C₃₁	—	2	4	no	—
88	C₄×C₃₁	—	2	2	no	—
89	C₄×C₃₁	C₂²×Q₈	1	4	yes	—
90	C₄×C₃₁	C₂×#41	1	4	yes	—
91	Dic₃₁	—	2	8	no	—
92	Dic₃₁	—	2	4	no	—
93	Dic₃₁	C₂²×Q₈	1	8	yes	—
94	#557	—	31	16	no	—
95	C₂×C₄⋊Q₈	—	31	2	no	—
96	C₂×C₄⋊Q₈	—	31	1	no	—
97	C₂×#125	—	31	4	no	—
98	C₂×#125	—	31	2	no	—
99	C₂×C₄×Q₈	—	31	2	no	—
100	C₂×C₄×Q₈	—	31	2	no	—
101	C₂×C₄×Q₈	—	31	1	no	—
102	C₂×C₄×Q₈	D₃₁	1	1	yes	characteristic
103	C₂×C₃₁	#557	1	4	yes	complemented
104	C₂×C₃₁	C₂³×Q₈	1	1	yes	characteristic
105	C₂×C₃₁	C₂²×#41	1	1	yes	characteristic
106	C₂×C₃₁	C₂×2₋¹⁺⁴	1	1	yes	characteristic
107	C₂²×Q₈	—	31	1	no	—
108	C₂²×Q₈	—	31	2	no	—
109	C₂²×Q₈	C₂×D₃₁	1	1	yes	characteristic
110	C₄⋊Q₈	—	31	16	no	—
111	C₄⋊Q₈	—	31	8	no	—
112	#125	—	31	32	no	—
113	#125	—	31	16	no	—
114	C₄×Q₈	—	31	16	no	—
115	C₄×Q₈	—	31	16	no	—
116	C₄×Q₈	—	31	8	no	—
117	C₄×Q₈	C₂×D₃₁	1	8	yes	—
118	C₂×C₄⋊C₄	—	31	2	no	—
119	C₂×C₄⋊C₄	—	31	4	no	—
120	C₂×C₄⋊C₄	—	31	1	no	—
121	C₂×C₄⋊C₄	—	31	4	no	—
122	C₂×C₄⋊C₄	—	31	2	no	—
123	C₂×C₄⋊C₄	—	31	4	no	—
124	C₂×C₄⋊C₄	—	31	2	no	—
125	C₂×C₄⋊C₄	C₂×D₃₁	1	1	yes	characteristic
126	C₂×C₄⋊C₄	C₂×D₃₁	1	2	yes	—
127	C₂×C₄²	—	31	4	no	—
128	C₂×C₄²	—	31	2	no	—
129	C₂×C₄²	C₂×D₃₁	1	2	yes	—
130	C₂×C₄²	C₂×D₃₁	1	1	yes	characteristic
131	C₃₁	C₂×#557	1	1	yes	characteristic, complemented, Sylow
132	C₂×Q₈	—	2	4	no	—
133	C₂×Q₈	—	31	8	no	—
134	C₂×Q₈	—	31	4	no	—
135	C₂×Q₈	—	31	8	no	—
136	C₂×Q₈	—	62	8	no	—
137	C₂×Q₈	C₂²×D₃₁	1	4	yes	—
138	C₂²×C₄	—	31	2	no	—
139	C₂²×C₄	—	31	2	no	—
140	C₂²×C₄	—	31	4	no	—
141	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
142	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
143	C₂²×C₄	C₂²×D₃₁	1	2	yes	—
144	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
145	C₂²×C₄	C₂²×D₃₁	1	1	yes	characteristic
146	C₄⋊C₄	—	31	8	no	—
147	C₄⋊C₄	—	31	16	no	—
148	C₄⋊C₄	—	31	16	no	—
149	C₄⋊C₄	—	31	16	no	—
150	C₄⋊C₄	—	31	4	no	—
151	C₄⋊C₄	—	31	8	no	—
152	C₄⋊C₄	—	31	8	no	—
153	C₄⋊C₄	C₂²×D₃₁	1	4	yes	—
154	C₄⋊C₄	C₂²×D₃₁	1	8	yes	—
155	C₄²	—	31	16	no	—
156	C₄²	—	31	8	no	—
157	C₄²	C₂²×D₃₁	1	8	yes	—
158	C₄²	C₂²×D₃₁	1	4	yes	—
159	C₂³	C₂³×D₃₁	1	1	yes	characteristic
160	Q₈	—	2	8	no	—
161	Q₈	—	31	16	no	—
162	Q₈	—	62	16	no	—
163	C₂×C₄	—	2	4	no	—
164	C₂×C₄	—	2	4	no	—
165	C₂×C₄	—	2	2	no	—
166	C₂×C₄	—	31	8	no	—
167	C₂×C₄	—	31	4	no	—
168	C₂×C₄	—	31	4	no	—
169	C₂×C₄	—	31	8	no	—
170	C₂×C₄	—	62	8	no	—
171	C₂×C₄	—	62	4	no	—
172	C₂×C₄	#92495	1	4	yes	—
173	C₂×C₄	Q₈×D₃₁	1	4	yes	—
174	C₂×C₄	C₂³×D₃₁	1	4	yes	—
175	C₂×C₄	C₂³×D₃₁	1	2	yes	—
176	C₂×C₄	C₂³×D₃₁	1	4	yes	—
177	C₂×C₄	C₂³×D₃₁	1	2	yes	—
178	C₂×C₄	C₂³×D₃₁	1	2	yes	—
179	C₂²	C₂×#92495	1	2	yes	—
180	C₂²	C₂×Q₈×D₃₁	1	2	yes	—
181	C₂²	#11758567	1	2	yes	—
182	C₂²	C₂⁴×D₃₁	1	1	yes	characteristic
183	C₄	—	2	4	no	—
184	C₄	—	2	4	no	—
185	C₄	—	2	2	no	—
186	C₄	—	31	8	no	—
187	C₄	—	62	8	no	—
188	C₄	—	62	4	no	—
189	C₄	C₂×#92495	1	4	yes	—
190	C₄	C₂×Q₈×D₃₁	1	4	yes	—
191	C₂	#14521777	1	4	yes	direct product factor
192	C₂	C₂²×Q₈×D₃₁	1	1	yes	characteristic
193	C₂	C₂²×#92495	1	1	yes	characteristic
194	C₂	C₂×#11758567	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₃₁
commutator, cosocle	C₂²×C₃₁	C₂⁵
Frattini	C₂²	C₂⁴×D₃₁
Fitting	C₂×C₄×Q₈×C₃₁	C₂
socle, prime radical	C₂³×C₃₁	C₂⁴
hypercenter	C₂×C₄×Q₈	D₃₁
hypocenter	C₃₁	C₂×#557
LCS	G ▷ C₂²×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. #14521777	C₂	direct (N × H)
45. C₂×Dic₆₂	Q₈	semidirect
80. Dic₆₂	C₂×Q₈	semidirect
103. C₂×C₃₁	#557	semidirect
131. C₃₁	C₂×#557	semidirect
191. C₂	#14521777	direct (N × H)

Maximal subgroups

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

subgroup	index
#14521777	2
C₂×#11758446	2
C₂×#11758521	2
C₂×#11758447	2
C₂×#11758466	2
C₂×C₄×Dic₆₂	2
C₂×#11758464	2
C₂×C₄×Q₈×C₃₁	2
C₂×#557	31

Subgroups — C2×#14521777 #16859283

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14521777 #16859283