Subgroups — C₄×#11718249 #16791141

Order 3328.

250 conjugacy classes of subgroups.

The subgroup lattice has 138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718249	C₂	1	2	yes	maximal
2	#13129943	C₂	1	2	yes	maximal, complemented
3	C₄×#88036	C₂	1	2	yes	maximal, complemented
4	C₂×C₄×#6090	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic
6	C₂²×#6090	C₄	1	1	yes	characteristic
7	C₂²×#6090	C₂²	1	1	yes	characteristic
8	#11718249	C₄	1	8	yes	direct product factor
9	C₂×#88036	C₂²	1	4	yes	—
10	C₄×#6090	C₄	1	1	yes	characteristic
11	C₄×#6090	C₄	1	1	yes	characteristic
12	C₄×#6090	C₂²	1	1	yes	characteristic
13	C₄×#6090	C₂²	1	1	yes	characteristic
14	C₂²×C₈×C₁₃	C₈	1	1	yes	characteristic
15	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
16	C₂×C₄²×C₁₃	C₈	1	1	yes	characteristic
17	C₄×C₈×C₁₃	C₈	1	1	yes	characteristic
18	C₄×C₈×C₁₃	C₈	1	1	yes	characteristic
19	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
20	C₄×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
21	C₂×#6090	C₈	1	4	yes	—
22	C₂×#6090	C₂×C₄	1	1	yes	characteristic
23	C₂×#6090	C₂×C₄	1	4	yes	—
24	C₂×#6090	C₂×C₄	1	1	yes	characteristic
25	C₂×#6090	C₂×C₄	1	1	yes	characteristic
26	C₂×#6090	C₂³	1	1	yes	characteristic
27	#88036	C₂×C₄	1	8	yes	complemented
28	C₄×M₆₄	—	13	1	no	maximal, Sylow
29	C₂²×C₄×C₁₃	C₁₆	1	2	yes	—
30	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
31	C₂×C₈×C₁₃	C₁₆	1	4	yes	—
32	C₂×C₈×C₁₃	C₄²	1	2	yes	—
33	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
34	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
35	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
36	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
37	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
38	C₄²×C₁₃	C₁₆	1	2	yes	—
39	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
40	C₄²×C₁₃	C₂×C₈	1	1	yes	characteristic
41	#6090	C₄²	1	2	yes	—
42	#6090	C₂×C₈	1	2	yes	—
43	#6090	C₂×C₈	1	2	yes	—
44	#6090	C₂²×C₄	1	2	yes	—
45	C₂×M₆₄	—	13	2	no	—
46	C₂×C₄×C₁₆	—	13	1	no	—
47	#1397	—	13	2	no	—
48	C₄×C₃₂	—	13	2	no	—
49	C₂³×C₁₃	C₂×C₁₆	1	1	yes	characteristic
50	C₂×C₄×C₁₃	—	2	4	no	—
51	C₂×C₄×C₁₃	C₄×C₈	1	2	yes	—
52	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
53	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
54	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
55	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
56	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
57	C₈×C₁₃	C₄×C₈	1	2	yes	—
58	C₈×C₁₃	C₂×C₁₆	1	2	yes	—
59	C₈×C₁₃	C₂×C₁₆	1	2	yes	—
60	C₈×C₁₃	C₂×C₄²	1	1	yes	characteristic
61	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
62	C₂²×C₁₆	—	13	1	no	—
63	C₂²×C₁₆	—	13	1	no	—
64	C₂×C₄×C₈	#261	1	1	yes	characteristic
65	M₆₄	—	13	8	no	—
66	C₂×C₃₂	—	13	4	no	—
67	C₄×C₁₆	—	13	1	no	—
68	C₄×C₁₆	—	13	1	no	—
69	C₄×C₁₆	—	13	1	no	—
70	C₄×C₁₆	—	13	1	no	—
71	C₂²×C₁₃	—	2	2	no	—
72	C₂²×C₁₃	C₄×C₁₆	1	2	yes	—
73	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
74	C₄×C₁₃	—	2	2	no	—
75	C₄×C₁₃	C₄×C₁₆	1	2	yes	—
76	C₄×C₁₃	M₆₄	1	4	yes	complemented
77	C₄×C₁₃	C₂×C₄×C₈	1	1	yes	characteristic
78	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
79	C₂²×C₈	#1057	1	1	yes	characteristic
80	C₂²×C₈	C₂×#261	1	1	yes	characteristic
81	C₂×C₄²	#1057	1	1	yes	characteristic
82	C₂×C₁₆	—	13	4	no	—
83	C₂×C₁₆	—	13	4	no	—
84	C₂×C₁₆	—	13	1	no	—
85	C₂×C₁₆	—	13	1	no	—
86	C₂×C₁₆	—	13	1	no	—
87	C₂×C₁₆	—	13	1	no	—
88	C₄×C₈	#1057	1	1	yes	characteristic
89	C₄×C₈	#1057	1	1	yes	characteristic
90	C₄×C₈	C₂×#261	1	1	yes	characteristic
91	C₄×C₈	C₂×#261	1	1	yes	characteristic
92	C₃₂	—	13	8	no	—
93	C₂×C₁₃	—	2	2	no	—
94	C₂×C₁₃	C₂×C₄×C₁₆	1	1	yes	characteristic
95	C₂×C₁₃	C₂×M₆₄	1	2	yes	—
96	C₂²×C₄	#6092	1	2	yes	—
97	C₂²×C₄	C₂×#1057	1	1	yes	characteristic
98	C₂×C₈	#6092	1	4	yes	—
99	C₂×C₈	D₁₃⋊C₈	1	2	yes	—
100	C₂×C₈	C₄×#261	1	2	yes	—
101	C₂×C₈	C₂×#1057	1	1	yes	characteristic
102	C₂×C₈	C₂×#1057	1	1	yes	characteristic
103	C₂×C₈	C₂×#1057	1	1	yes	characteristic
104	C₂×C₈	C₂²×#261	1	1	yes	characteristic
105	C₄²	#6092	1	2	yes	—
106	C₄²	C₂×#1057	1	1	yes	characteristic
107	C₄²	C₂×#1057	1	1	yes	characteristic
108	C₁₆	—	13	2	no	—
109	C₁₆	—	13	2	no	—
110	C₁₆	—	13	2	no	—
111	C₁₆	—	13	2	no	—
112	C₁₃	C₄×M₆₄	1	1	yes	characteristic, complemented, Sylow
113	C₂³	C₂×#6092	1	1	yes	characteristic
114	C₂×C₄	—	2	4	no	—
115	C₂×C₄	C₂×#6092	1	2	yes	—
116	C₂×C₄	C₂×#6092	1	1	yes	characteristic
117	C₂×C₄	C₂×#6092	1	2	yes	—
118	C₂×C₄	C₂×#6092	1	2	yes	—
119	C₂×C₄	C₄×#1057	1	2	yes	—
120	C₂×C₄	C₂²×#1057	1	1	yes	characteristic
121	C₈	C₂×#6092	1	2	yes	—
122	C₈	C₂×#6092	1	2	yes	—
123	C₈	C₄×#1057	1	2	yes	—
124	C₈	C₂×D₁₃⋊C₈	1	1	yes	characteristic
125	C₈	C₂×C₄×#261	1	1	yes	characteristic
126	C₂²	—	2	2	no	—
127	C₂²	C₄×#6092	1	2	yes	—
128	C₂²	C₂²×#6092	1	1	yes	characteristic
129	C₄	—	2	2	no	—
130	C₄	C₄×#6092	1	2	yes	—
131	C₄	#11718249	1	4	yes	direct product factor
132	C₄	C₂²×#6092	1	1	yes	characteristic
133	C₄	C₂×C₄×#1057	1	1	yes	characteristic
134	C₂	—	2	2	no	—
135	C₂	C₂×C₄×#6092	1	1	yes	characteristic
136	C₂	C₂×#11718249	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂×#261
commutator	C₂×C₁₃	C₂×C₄×C₁₆
Frattini	C₂×C₈	C₂²×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂²×C₁₃	C₂²×C₁₆
prime radical	C₂³×C₁₃	C₂×C₁₆
cosocle	C₂×#6090	C₂³
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₄×M₆₄
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₄×C₈ ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
2. #13129943	C₂	semidirect
3. C₄×#88036	C₂	semidirect
8. #11718249	C₄	direct (N × H)
27. #88036	C₂×C₄	semidirect
76. C₄×C₁₃	M₆₄	semidirect
112. C₁₃	C₄×M₆₄	semidirect
131. C₄	#11718249	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×#11718249	2
#13129943	2
C₄×#88036	2
C₂×C₄×#6090	2
C₄×M₆₄	13

Subgroups — C4×#11718249 #16791141

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11718249 #16791141