Subgroups — C₂×#13129859 #16788649

Order 3328.

286 conjugacy classes of subgroups.

The subgroup lattice has 168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊#6092	C₂	1	2	yes	maximal
2	#13129859	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₈×#1055	C₂	1	1	yes	maximal, characteristic
4	C₂²×#6092	—	2	2	no	—
5	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂×C₄×#1055	C₄	1	1	yes	characteristic
7	C₂×C₄×#1055	C₂²	1	1	yes	characteristic
8	C₄⋊#6092	—	2	2	no	—
9	C₄⋊#6092	C₂²	1	4	yes	—
10	C₈×#1055	C₄	1	2	yes	—
11	C₈×#1055	C₂²	1	2	yes	—
12	C₂²×C₈×C₁₃	—	2	1	no	—
13	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
14	C₂²×#1055	C₈	1	1	yes	characteristic
15	C₂²×#1055	C₈	1	1	yes	characteristic
16	C₂²×#1055	D₄	1	1	yes	characteristic
17	C₂²×#1055	Q₈	1	1	yes	characteristic
18	C₂×#6092	—	2	4	no	—
19	C₂×#6092	—	4	4	no	—
20	C₄×C₈×C₁₃	—	2	1	no	—
21	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
22	C₄×#1055	C₈	1	2	yes	—
23	C₄×#1055	C₂×C₄	1	1	yes	characteristic
24	C₄×#1055	C₂×C₄	1	2	yes	—
25	C₄×#1055	D₄	1	1	yes	characteristic
26	C₄×#1055	Q₈	1	1	yes	characteristic
27	C₄×#1055	C₂³	1	1	yes	characteristic
28	C₂×#1367	—	13	1	no	maximal, Sylow
29	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
30	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
31	C₂²×C₄×C₁₃	M₁₆	1	1	yes	characteristic
32	C₂×C₈×C₁₃	—	2	4	no	—
33	C₂×C₈×C₁₃	—	2	2	no	—
34	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
35	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
36	C₄²×C₁₃	M₁₆	1	1	yes	characteristic
37	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×#1055	—	2	2	no	—
39	C₂×#1055	—	2	2	no	—
40	C₂×#1055	C₁₆	1	4	yes	complemented
41	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
42	C₂×#1055	C₄⋊C₄	1	1	yes	characteristic
43	C₂×#1055	C₂×C₈	1	2	yes	—
44	C₂×#1055	C₂×C₈	1	2	yes	—
45	C₂×#1055	SD₁₆	1	4	yes	—
46	C₂×#1055	C₂×D₄	1	1	yes	characteristic
47	C₂×#1055	C₂×Q₈	1	1	yes	characteristic
48	#6092	—	4	4	no	—
49	C₂×C₄⋊C₁₆	—	13	2	no	—
50	C₂×C₈²	—	13	1	no	—
51	#1367	—	13	4	no	—
52	C₂³×C₁₃	C₄⋊C₈	1	1	yes	characteristic
53	C₂×C₄×C₁₃	—	2	2	no	—
54	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
55	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
56	C₂×C₄×C₁₃	C₄⋊C₈	1	1	yes	characteristic
57	C₂×C₄×C₁₃	#106	1	2	yes	—
58	C₂×C₄×C₁₃	#108	1	2	yes	—
59	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
60	C₂×C₄×C₁₃	M₃₂	1	2	yes	—
61	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
62	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
63	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
64	C₈×C₁₃	—	2	4	no	—
65	#1055	—	2	1	no	—
66	#1055	—	2	1	no	—
67	#1055	—	2	2	no	—
68	#1055	#106	1	2	yes	—
69	#1055	C₂×C₁₆	1	4	yes	complemented
70	#1055	C₂×SD₁₆	1	2	yes	—
71	C₂²×C₁₆	—	26	2	no	—
72	C₂×C₄×C₈	—	13	1	no	—
73	C₂×C₄×C₈	—	13	1	no	—
74	C₂×C₄×C₈	#261	1	1	yes	characteristic
75	C₄⋊C₁₆	—	13	4	no	—
76	C₄⋊C₁₆	—	26	2	no	—
77	C₈²	—	13	2	no	—
78	C₈²	—	13	2	no	—
79	C₂²×C₁₃	#334	1	2	yes	—
80	C₂²×C₁₃	C₄⋊C₁₆	1	2	yes	—
81	C₂²×C₁₃	#364	1	2	yes	—
82	C₂²×C₁₃	C₂×C₄⋊C₈	1	1	yes	characteristic
83	C₄×C₁₃	—	2	1	no	—
84	C₄×C₁₃	—	2	1	no	—
85	C₄×C₁₃	#334	1	2	yes	—
86	C₄×C₁₃	C₄⋊C₁₆	1	2	yes	—
87	C₄×C₁₃	C₂×#106	1	1	yes	characteristic
88	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
89	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
90	C₄×C₁₃	C₂×M₃₂	1	1	yes	characteristic
91	C₂²×C₈	—	2	1	no	—
92	C₂²×C₈	—	13	1	no	—
93	C₂²×C₈	—	13	1	no	—
94	C₂²×C₈	—	13	1	no	—
95	C₂²×C₈	—	13	1	no	—
96	C₂×C₄²	C₂×#261	1	1	yes	characteristic
97	C₂×C₁₆	—	26	4	no	—
98	C₂×C₁₆	—	52	4	no	—
99	C₄×C₈	—	2	1	no	—
100	C₄×C₈	—	13	2	no	—
101	C₄×C₈	—	13	1	no	—
102	C₄×C₈	—	13	1	no	—
103	C₄×C₈	—	13	1	no	—
104	C₄×C₈	—	13	2	no	—
105	C₄×C₈	—	13	1	no	—
106	C₄×C₈	C₂×#261	1	2	yes	—
107	C₂×C₁₃	#1367	1	4	yes	complemented
108	C₂×C₁₃	C₂×#334	1	1	yes	characteristic
109	C₂×C₁₃	C₂×C₄⋊C₁₆	1	1	yes	characteristic
110	C₂×C₁₃	C₂×#364	1	1	yes	characteristic
111	C₂²×C₄	D₁₃⋊C₈	1	1	yes	characteristic
112	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
113	C₂²×C₄	#6122	1	1	yes	characteristic
114	C₂×C₈	—	2	4	no	—
115	C₂×C₈	—	2	2	no	—
116	C₂×C₈	—	13	4	no	—
117	C₂×C₈	—	13	4	no	—
118	C₂×C₈	—	13	2	no	—
119	C₂×C₈	—	13	1	no	—
120	C₂×C₈	—	13	1	no	—
121	C₂×C₈	—	13	2	no	—
122	C₂×C₈	—	13	1	no	—
123	C₂×C₈	—	13	1	no	—
124	C₂×C₈	—	26	2	no	—
125	C₂×C₈	—	26	2	no	—
126	C₄²	D₁₃⋊C₈	1	1	yes	characteristic
127	C₄²	C₄⋊#261	1	1	yes	characteristic
128	C₄²	#6122	1	1	yes	characteristic
129	C₄²	C₂²×#261	1	1	yes	characteristic
130	C₁₆	—	52	4	no	—
131	C₁₃	C₂×#1367	1	1	yes	characteristic, complemented, Sylow
132	C₂³	#88112	1	1	yes	characteristic
133	C₂×C₄	—	2	2	no	—
134	C₂×C₄	D₁₃⋊C₁₆	1	2	yes	—
135	C₂×C₄	#88098	1	2	yes	—
136	C₂×C₄	#88101	1	2	yes	—
137	C₂×C₄	#88104	1	2	yes	—
138	C₂×C₄	#88112	1	1	yes	characteristic
139	C₂×C₄	#88112	1	1	yes	characteristic
140	C₂×C₄	#88112	1	1	yes	characteristic
141	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
142	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
143	C₂×C₄	C₂×#6122	1	1	yes	characteristic
144	C₈	—	2	4	no	—
145	C₈	—	13	4	no	—
146	C₈	—	13	2	no	—
147	C₈	—	13	2	no	—
148	C₈	—	26	2	no	—
149	C₈	—	26	1	no	—
150	C₈	—	26	1	no	—
151	C₂²	#11718233	1	2	yes	—
152	C₂²	#11718255	1	2	yes	—
153	C₂²	#11718260	1	2	yes	—
154	C₂²	C₂×#88112	1	1	yes	characteristic
155	C₄	—	2	1	no	—
156	C₄	—	2	1	no	—
157	C₄	#11718255	1	2	yes	—
158	C₄	#11718260	1	2	yes	—
159	C₄	C₂×D₁₃⋊C₁₆	1	1	yes	characteristic
160	C₄	C₂×#88098	1	1	yes	characteristic
161	C₄	C₂×#88101	1	1	yes	characteristic
162	C₄	C₂×#88104	1	1	yes	characteristic
163	C₂	#13129859	1	4	yes	direct product factor
164	C₂	C₂×#11718255	1	1	yes	characteristic
165	C₂	C₂×#11718260	1	1	yes	characteristic
166	C₂	C₂×#11718233	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₄⋊#261
commutator	C₄×C₁₃	C₂²×C₁₆
Frattini	C₄²	C₂²×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle, prime radical	C₂³×C₁₃	C₄⋊C₈
cosocle	C₄×#1055	C₂³
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₂×#1367
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13129859	C₂	direct (N × H)
40. C₂×#1055	C₁₆	semidirect
69. #1055	C₂×C₁₆	semidirect
107. C₂×C₁₃	#1367	semidirect
131. C₁₃	C₂×#1367	semidirect
163. C₂	#13129859	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×C₄⋊#6092	2
#13129859	2
C₂×C₈×#1055	2
C₂×#1367	13

Subgroups — C2×#13129859 #16788649

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129859 #16788649