Subgroups — C₄×#11718104 #15777746

Order 3328.

418 conjugacy classes of subgroups.

The subgroup lattice has 164 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718104	C₂	1	4	yes	maximal
2	C₄×#88052	C₂	1	1	yes	maximal, characteristic
3	C₄×#88055	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₃×M₃₂	C₂	1	1	yes	maximal, characteristic
5	C₂×C₁₃×M₃₂	C₂²	1	2	yes	—
6	C₂×C₄×C₈×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×#88055	C₄	1	2	yes	—
8	C₂×#88055	C₂²	1	2	yes	—
9	C₂×#88052	C₂²	1	2	yes	—
10	C₄²×Dic₁₃	C₄	1	1	yes	characteristic
11	C₂×C₄×#1055	C₄	1	1	yes	characteristic
12	C₁₃×#346	C₄	1	2	yes	complemented
13	C₄×C₁₃×C₁₆	C₄	1	2	yes	complemented
14	#11718104	C₄	1	16	yes	direct product factor
15	#11718053	C₄	1	2	yes	complemented
16	C₄×#6090	C₄	1	2	yes	complemented
17	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂³	1	1	yes	characteristic
19	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₃	—	2	2	no	—
21	C₂×C₄×Dic₁₃	C₂×C₄	1	2	yes	—
22	C₂²×#1055	C₂×C₄	1	2	yes	—
23	C₁₃×M₃₂	C₂×C₄	1	8	yes	—
24	C₂×C₁₃×C₁₆	C₂×C₄	1	4	yes	—
25	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
26	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
27	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
28	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
29	#88055	—	2	4	no	—
30	#88055	C₂×C₄	1	8	yes	—
31	#88052	C₂×C₄	1	8	yes	—
32	C₂×#6090	C₂×C₄	1	4	yes	—
33	C₄×#1055	—	2	2	no	—
34	C₄×#347	—	13	1	no	maximal, Sylow
35	C₂²×C₄×C₁₃	M₁₆	1	2	yes	—
36	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
37	C₂²×Dic₁₃	—	2	2	no	—
38	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
39	C₂×C₈×C₁₃	C₄²	1	1	yes	characteristic
40	C₂×C₈×C₁₃	M₁₆	1	4	yes	—
41	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₂²×C₄	1	4	yes	—
43	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
44	C₄²×C₁₃	C₄²	1	1	yes	characteristic
45	C₄²×C₁₃	C₄²	1	1	yes	characteristic
46	C₄²×C₁₃	M₁₆	1	2	yes	—
47	C₄×Dic₁₃	—	2	2	no	—
48	C₄×Dic₁₃	—	4	4	no	—
49	C₄×Dic₁₃	C₄²	1	4	yes	—
50	C₂×#1055	—	2	2	no	—
51	C₂×#1055	—	2	2	no	—
52	C₂×#1055	C₄²	1	4	yes	—
53	C₁₃×C₁₆	C₄²	1	8	yes	complemented
54	#6090	C₄²	1	8	yes	complemented
55	C₂×#347	—	13	4	no	—
56	C₄×M₃₂	—	13	1	no	—
57	C₄×M₃₂	D₁₃	1	1	yes	characteristic
58	C₄×#97	—	13	1	no	—
59	C₂³×C₁₃	C₂×M₁₆	1	1	yes	characteristic
60	C₂×C₄×C₁₃	—	2	4	no	—
61	C₂×C₄×C₁₃	#97	1	2	yes	—
62	C₂×C₄×C₁₃	#97	1	2	yes	—
63	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
64	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
65	C₂×C₄×C₁₃	C₂×M₁₆	1	2	yes	—
66	C₂×C₄×C₁₃	C₂×M₁₆	1	1	yes	characteristic
67	C₂×Dic₁₃	—	2	4	no	—
68	C₂×Dic₁₃	—	4	4	no	—
69	C₈×C₁₃	#97	1	2	yes	—
70	C₈×C₁₃	#97	1	2	yes	—
71	C₈×C₁₃	C₂×C₄²	1	2	yes	—
72	C₈×C₁₃	C₂×C₄²	1	2	yes	—
73	#1055	—	2	4	no	—
74	C₂×M₃₂	—	13	2	no	—
75	C₂×M₃₂	C₂×D₁₃	1	2	yes	—
76	C₂×#97	—	13	2	no	—
77	C₂×#97	—	13	2	no	—
78	C₂×C₄×C₈	—	13	1	no	—
79	C₂×C₄×C₈	C₂×D₁₃	1	1	yes	characteristic
80	C₄³	—	13	1	no	—
81	#347	—	13	16	no	—
82	#346	—	13	2	no	—
83	#346	Dic₁₃	1	2	yes	complemented
84	C₄×C₁₆	—	13	2	no	—
85	C₄×C₁₆	Dic₁₃	1	2	yes	complemented
86	C₂²×C₁₃	—	2	2	no	—
87	C₂²×C₁₃	C₂×#97	1	1	yes	characteristic
88	C₂²×C₁₃	C₄×M₁₆	1	2	yes	—
89	C₄×C₁₃	—	2	2	no	—
90	C₄×C₁₃	#347	1	4	yes	complemented
91	C₄×C₁₃	C₄³	1	1	yes	characteristic
92	C₄×C₁₃	C₂×#97	1	1	yes	characteristic
93	C₄×C₁₃	C₄×M₁₆	1	2	yes	—
94	Dic₁₃	—	4	4	no	—
95	C₂²×C₈	—	13	2	no	—
96	C₂²×C₈	C₄×D₁₃	1	1	yes	characteristic
97	C₂²×C₈	C₂²×D₁₃	1	1	yes	characteristic
98	C₂×C₄²	—	13	2	no	—
99	C₂×C₄²	—	26	2	no	—
100	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
101	M₃₂	—	13	8	no	—
102	M₃₂	C₄×D₁₃	1	8	yes	—
103	C₂×C₁₆	—	13	4	no	—
104	C₂×C₁₆	C₂×Dic₁₃	1	4	yes	—
105	#97	—	13	8	no	—
106	#97	—	26	4	no	—
107	C₄×C₈	—	26	2	no	—
108	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
109	C₄×C₈	C₄×D₁₃	1	1	yes	characteristic
110	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
111	C₄×C₈	C₂×Dic₁₃	1	1	yes	characteristic
112	C₂×C₁₃	—	2	2	no	—
113	C₂×C₁₃	C₄×#97	1	1	yes	characteristic
114	C₂×C₁₃	C₂×#347	1	2	yes	—
115	C₂²×C₄	—	26	2	no	—
116	C₂²×C₄	#6094	1	2	yes	—
117	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
118	C₂×C₈	—	13	4	no	—
119	C₂×C₈	—	26	2	no	—
120	C₂×C₈	—	26	2	no	—
121	C₂×C₈	#6094	1	4	yes	—
122	C₂×C₈	C₄×Dic₁₃	1	1	yes	characteristic
123	C₂×C₈	C₄×Dic₁₃	1	1	yes	characteristic
124	C₂×C₈	C₂×C₄×D₁₃	1	1	yes	characteristic
125	C₂×C₈	C₂×C₄×D₁₃	1	4	yes	—
126	C₂×C₈	C₂²×Dic₁₃	1	1	yes	characteristic
127	C₄²	—	13	4	no	—
128	C₄²	—	26	2	no	—
129	C₄²	—	52	4	no	—
130	C₄²	#6094	1	2	yes	—
131	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
132	C₄²	C₄×Dic₁₃	1	1	yes	characteristic
133	C₁₆	—	13	8	no	—
134	C₁₆	C₄×Dic₁₃	1	8	yes	complemented
135	C₁₃	C₄×#347	1	1	yes	characteristic, complemented, Sylow
136	C₂³	C₂×#6094	1	1	yes	characteristic
137	C₂×C₄	—	2	4	no	—
138	C₂×C₄	—	26	4	no	—
139	C₂×C₄	—	52	4	no	—
140	C₂×C₄	#88055	1	2	yes	—
141	C₂×C₄	#88055	1	2	yes	—
142	C₂×C₄	C₄²×D₁₃	1	2	yes	—
143	C₂×C₄	C₂×#6094	1	2	yes	—
144	C₂×C₄	C₂×#6094	1	1	yes	characteristic
145	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
146	C₈	—	26	4	no	—
147	C₈	#88055	1	2	yes	—
148	C₈	#88055	1	2	yes	—
149	C₈	C₄²×D₁₃	1	2	yes	—
150	C₈	C₂×C₄×Dic₁₃	1	2	yes	—
151	C₂²	—	2	2	no	—
152	C₂²	C₄×#6094	1	2	yes	—
153	C₂²	C₂×#88055	1	1	yes	characteristic
154	C₄	—	2	2	no	—
155	C₄	—	52	4	no	—
156	C₄	#11718104	1	4	yes	direct product factor
157	C₄	C₄×#6094	1	2	yes	—
158	C₄	C₄²×Dic₁₃	1	1	yes	characteristic
159	C₄	C₂×#88055	1	1	yes	characteristic
160	C₂	—	2	2	no	—
161	C₂	C₄×#88055	1	1	yes	characteristic
162	C₂	C₂×#11718104	1	2	yes	—

	subgroup	G/H
center	C₄²	C₄×Dic₁₃
commutator	C₄×C₁₃	C₄³
Frattini	C₂²×C₈	C₂²×D₁₃
Fitting	C₄×C₁₃×M₃₂	C₂
socle	C₂²×C₁₃	C₂×#97
prime radical	C₂³×C₁₃	C₂×M₁₆
cosocle	C₂²×C₈×C₁₃	C₂³
hypercenter	C₄×M₃₂	D₁₃
hypocenter	C₁₃	C₄×#347
LCS	G ▷ C₄×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄² ◁ C₄×M₃₂

Complements

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

N	H ≅ G/N	type
12. C₁₃×#346	C₄	semidirect
13. C₄×C₁₃×C₁₆	C₄	semidirect
14. #11718104	C₄	direct (N × H)
15. #11718053	C₄	semidirect
16. C₄×#6090	C₄	semidirect
53. C₁₃×C₁₆	C₄²	semidirect
54. #6090	C₄²	semidirect
83. #346	Dic₁₃	semidirect
85. C₄×C₁₆	Dic₁₃	semidirect
90. C₄×C₁₃	#347	semidirect
134. C₁₆	C₄×Dic₁₃	semidirect
135. C₁₃	C₄×#347	semidirect
156. C₄	#11718104	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×#11718104	2
C₄×#88052	2
C₄×#88055	2
C₄×C₁₃×M₃₂	2
C₄×#347	13

Subgroups — C4×#11718104 #15777746

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718104 #15777746