Subgroups — C₄×#11718096 #15778318

Order 3328.

366 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	C₂×#11718096	C₂	1	2	yes	maximal
2	C₄×#88058	C₂	1	2	yes	maximal
3	#13112928	C₂	1	2	yes	maximal
4	C₂×C₄×C₁₃×C₁₆	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
6	C₂²×C₁₃×C₁₆	C₂²	1	1	yes	characteristic
7	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88058	C₂²	1	4	yes	—
9	C₄×C₄⋊Dic₁₃	—	2	2	no	—
10	C₄×C₁₃×C₁₆	C₄	1	4	yes	complemented
11	#11718143	—	2	2	no	—
12	#11718096	C₄	1	8	yes	direct product factor
13	C₂²×C₈×C₁₃	D₄	1	1	yes	characteristic
14	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
15	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
16	C₂×C₄⋊Dic₁₃	—	2	4	no	—
17	C₂×C₄×Dic₁₃	—	4	2	no	—
18	C₂×C₁₃×C₁₆	—	2	2	no	—
19	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
20	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
21	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
22	C₄×C₈×C₁₃	C₂×C₄	1	2	yes	—
23	C₄×C₈×C₁₃	Q₈	1	2	yes	—
24	#88071	—	4	2	no	—
25	#88058	—	2	4	no	—
26	#88058	C₂×C₄	1	8	yes	—
27	C₄×#366	—	13	1	no	maximal, Sylow
28	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
29	C₂²×C₄×C₁₃	D₈	1	1	yes	characteristic
30	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
31	C₂²×Dic₁₃	—	4	4	no	—
32	C₂×C₈×C₁₃	—	2	2	no	—
33	C₂×C₈×C₁₃	C₄⋊C₄	1	2	yes	—
34	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
36	C₂×C₈×C₁₃	C₂×Q₈	1	1	yes	characteristic
37	C₂×C₈×C₁₃	#41	1	2	yes	—
38	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
39	C₄²×C₁₃	Q₁₆	1	2	yes	—
40	C₄⋊Dic₁₃	—	2	8	no	—
41	C₄⋊Dic₁₃	—	4	4	no	—
42	C₄×Dic₁₃	—	8	4	no	—
43	C₁₃×C₁₆	—	2	2	no	—
44	C₁₃×C₁₆	C₄²	1	4	yes	complemented
45	C₂×#366	—	13	2	no	—
46	C₂×C₄×C₁₆	D₁₃	1	1	yes	characteristic
47	C₄×#107	—	13	2	no	—
48	#1380	—	13	2	no	—
49	C₂³×C₁₃	C₂×D₈	1	1	yes	characteristic
50	C₂×C₄×C₁₃	—	2	2	no	—
51	C₂×C₄×C₁₃	#107	1	2	yes	—
52	C₂×C₄×C₁₃	#107	1	2	yes	—
53	C₂×C₄×C₁₃	D₁₆	1	2	yes	—
54	C₂×C₄×C₁₃	Q₃₂	1	2	yes	—
55	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
57	C₂×C₄×C₁₃	C₂×Q₁₆	1	1	yes	characteristic
58	C₂×C₄×C₁₃	#135	1	2	yes	—
59	C₂×Dic₁₃	—	4	8	no	—
60	C₂×Dic₁₃	—	8	4	no	—
61	C₂×Dic₁₃	—	8	4	no	—
62	C₈×C₁₃	—	2	2	no	—
63	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
64	C₈×C₁₃	#117	1	1	yes	characteristic
65	C₈×C₁₃	C₄×Q₈	1	2	yes	—
66	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
67	C₂²×C₁₆	C₂×D₁₃	1	1	yes	characteristic
68	C₂×#107	—	13	4	no	—
69	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
70	C₄×C₄⋊C₄	—	26	2	no	—
71	#366	—	13	8	no	—
72	C₄×C₁₆	Dic₁₃	1	4	yes	complemented
73	#340	—	26	2	no	—
74	C₂²×C₁₃	C₂×#107	1	1	yes	characteristic
75	C₂²×C₁₃	C₄×D₈	1	2	yes	—
76	C₂²×C₁₃	C₂×D₁₆	1	1	yes	characteristic
77	C₂²×C₁₃	C₂×Q₃₂	1	1	yes	characteristic
78	C₂²×C₁₃	#508	1	2	yes	—
79	C₄×C₁₃	—	2	2	no	—
80	C₄×C₁₃	#366	1	4	yes	complemented
81	C₄×C₁₃	C₄×C₄⋊C₄	1	1	yes	characteristic
82	C₄×C₁₃	#427	1	1	yes	characteristic
83	C₄×C₁₃	C₄×Q₁₆	1	2	yes	—
84	Dic₁₃	—	8	8	no	—
85	C₂²×C₈	D₅₂	1	1	yes	characteristic
86	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
87	C₂×C₄⋊C₄	—	26	4	no	—
88	C₂×C₄²	—	52	2	no	—
89	C₂×C₄²	D₅₂	1	1	yes	characteristic
90	C₂×C₁₆	—	2	2	no	—
91	C₂×C₁₆	C₄×D₁₃	1	4	yes	—
92	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
93	C₂×C₁₆	C₂×Dic₁₃	1	2	yes	—
94	#107	—	13	8	no	—
95	#107	—	26	4	no	—
96	C₄×C₈	Dic₂₆	1	2	yes	—
97	C₄×C₈	C₂×Dic₁₃	1	2	yes	—
98	#95	—	52	2	no	—
99	C₂×C₁₃	C₄×#107	1	1	yes	characteristic
100	C₂×C₁₃	C₂×#366	1	1	yes	characteristic
101	C₂×C₁₃	#2158	1	1	yes	characteristic
102	C₂×C₁₃	C₄×D₁₆	1	2	yes	—
103	C₂×C₁₃	C₄×Q₃₂	1	2	yes	—
104	C₂²×C₄	—	52	4	no	—
105	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
106	C₂²×C₄	D₁₀₄	1	1	yes	characteristic
107	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
108	C₂×C₈	—	2	2	no	—
109	C₂×C₈	C₄⋊Dic₁₃	1	2	yes	—
110	C₂×C₈	C₂×Dic₂₆	1	1	yes	characteristic
111	C₂×C₈	C₂×C₄×D₁₃	1	2	yes	—
112	C₂×C₈	#6127	1	2	yes	—
113	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
114	C₄⋊C₄	—	26	8	no	—
115	C₄⋊C₄	—	52	4	no	—
116	C₄²	—	104	4	no	—
117	C₄²	Dic₅₂	1	2	yes	—
118	C₄²	C₄⋊Dic₁₃	1	2	yes	—
119	C₁₆	—	2	2	no	—
120	C₁₆	C₄×Dic₁₃	1	4	yes	complemented
121	C₁₃	C₄×#366	1	1	yes	characteristic, complemented, Sylow
122	C₂³	C₂×D₁₀₄	1	1	yes	characteristic
123	C₂×C₄	—	2	2	no	—
124	C₂×C₄	—	52	8	no	—
125	C₂×C₄	—	104	4	no	—
126	C₂×C₄	—	104	4	no	—
127	C₂×C₄	D₂₀₈	1	2	yes	—
128	C₂×C₄	Dic₁₀₄	1	2	yes	—
129	C₂×C₄	#88058	1	2	yes	—
130	C₂×C₄	#88058	1	2	yes	—
131	C₂×C₄	C₄×D₅₂	1	2	yes	—
132	C₂×C₄	#88158	1	2	yes	—
133	C₂×C₄	C₂×Dic₅₂	1	1	yes	characteristic
134	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
135	C₈	—	2	2	no	—
136	C₈	C₄×Dic₂₆	1	2	yes	—
137	C₈	C₂×C₄×Dic₁₃	1	1	yes	characteristic
138	C₈	#88180	1	1	yes	characteristic
139	C₂²	C₄×D₁₀₄	1	2	yes	—
140	C₂²	C₂×D₂₀₈	1	1	yes	characteristic
141	C₂²	#11718565	1	2	yes	—
142	C₂²	C₂×Dic₁₀₄	1	1	yes	characteristic
143	C₂²	C₂×#88058	1	1	yes	characteristic
144	C₄	—	2	2	no	—
145	C₄	—	104	8	no	—
146	C₄	#11718096	1	4	yes	direct product factor
147	C₄	C₄×Dic₅₂	1	2	yes	—
148	C₄	C₄×C₄⋊Dic₁₃	1	1	yes	characteristic
149	C₄	#11718767	1	1	yes	characteristic
150	C₂	C₄×#88058	1	1	yes	characteristic
151	C₂	C₂×#11718096	1	1	yes	characteristic
152	C₂	#13116620	1	1	yes	characteristic
153	C₂	C₄×D₂₀₈	1	2	yes	—
154	C₂	C₄×Dic₁₀₄	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	D₁₀₄
commutator	C₈×C₁₃	C₂×C₄²
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×C₁₆	C₂
socle, prime radical	C₂³×C₁₃	C₂×D₈
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₂×C₄×C₁₆	D₁₃
hypocenter	C₁₃	C₄×#366
LCS	G ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×C₁₆

Complements

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

N	H ≅ G/N	type
10. C₄×C₁₃×C₁₆	C₄	semidirect
12. #11718096	C₄	direct (N × H)
44. C₁₃×C₁₆	C₄²	semidirect
72. C₄×C₁₆	Dic₁₃	semidirect
80. C₄×C₁₃	#366	semidirect
120. C₁₆	C₄×Dic₁₃	semidirect
121. C₁₃	C₄×#366	semidirect
146. C₄	#11718096	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×#11718096	2
C₄×#88058	2
#13112928	2
C₂×C₄×C₁₃×C₁₆	2
C₄×#366	13

Subgroups — C4×#11718096 #15778318

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718096 #15778318