Subgroups — #16807439

Order 3328.

462 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	#13131260	C₂	1	8	yes	maximal, complemented
2	D₁₃⋊M₆₄	C₂	1	4	yes	maximal, complemented
3	C₂×#11718249	C₂	1	2	yes	maximal, complemented
4	C₂×#11718568	C₂	1	1	yes	maximal, characteristic
5	C₂×#88155	C₄	1	1	yes	characteristic
6	C₂×C₁₃×M₃₂	C₄	1	1	yes	characteristic
7	C₂²×#6090	C₂²	1	1	yes	characteristic
8	#11718568	C₄	1	4	yes	—
9	#11718568	C₂²	1	4	yes	—
10	C₂×#88038	C₄	1	2	yes	—
11	C₂×C₁₆×D₁₃	C₂²	1	2	yes	—
12	#11718249	C₂²	1	4	yes	—
13	#11718249	C₂²	1	4	yes	complemented
14	C₂×#88036	C₂²	1	4	yes	complemented
15	#11718214	C₂²	1	8	yes	complemented
16	D₁₃⋊C₃₂	C₂²	1	8	yes	complemented
17	C₂×#6127	C₈	1	1	yes	characteristic
18	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
19	C₂×#6099	C₈	1	1	yes	characteristic
20	#88155	C₈	1	4	yes	—
21	#88155	C₂×C₄	1	4	yes	—
22	C₂×#6094	C₈	1	2	yes	—
23	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
24	C₁₃×M₃₂	C₂×C₄	1	4	yes	—
25	C₂×C₁₃×C₁₆	C₂×C₄	1	2	yes	—
26	C₂×#6090	C₂×C₄	1	1	yes	characteristic
27	C₂×#6090	C₂×C₄	1	2	yes	—
28	C₂×#6090	C₂³	1	2	yes	—
29	C₂×#6090	C₂³	1	1	yes	characteristic
30	#88038	C₂×C₄	1	8	yes	—
31	C₁₆×D₁₃	C₂×C₄	1	4	yes	—
32	C₁₆×D₁₃	C₂³	1	4	yes	—
33	#88036	C₂³	1	8	yes	—
34	#33974	—	13	1	no	maximal, Sylow
35	C₂²×C₄×C₁₃	C₂×C₈	1	1	yes	characteristic
36	C₂×C₂²⋊D₁₃	C₁₆	1	2	yes	—
37	#6127	C₁₆	1	4	yes	—
38	#6127	C₂×C₈	1	4	yes	—
39	C₂×D₅₂	C₁₆	1	1	yes	characteristic
40	C₂×C₄×D₁₃	C₂×C₈	1	2	yes	—
41	C₂×Dic₂₆	C₁₆	1	1	yes	characteristic
42	C₂×C₈×C₁₃	C₂×C₈	1	1	yes	characteristic
43	C₂×C₈×C₁₃	C₂×C₈	1	2	yes	—
44	C₂×C₈×C₁₃	C₂²×C₄	1	1	yes	characteristic
45	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
46	#6099	C₂×C₈	1	4	yes	—
47	C₂×#1055	C₂×C₈	1	2	yes	—
48	#6094	C₂×C₈	1	8	yes	—
49	C₈×D₁₃	C₂×C₈	1	4	yes	—
50	C₈×D₁₃	C₂²×C₄	1	4	yes	—
51	C₁₃×C₁₆	C₂²×C₄	1	4	yes	—
52	#6090	C₂²×C₄	1	1	yes	characteristic
53	#6090	C₂²×C₄	1	2	yes	—
54	#6090	C₂⁴	1	1	yes	characteristic
55	C₂×#504	—	13	1	no	—
56	#2258	—	13	8	no	—
57	C₂×M₆₄	—	13	2	no	—
58	C₂×M₆₄	—	13	4	no	—
59	C₂³×C₁₃	C₂×C₁₆	1	1	yes	characteristic
60	C₂²×D₁₃	C₂×C₁₆	1	2	yes	—
61	C₂×C₄×C₁₃	C₂×C₁₆	1	1	yes	characteristic
62	C₂×C₄×C₁₃	C₂×C₁₆	1	2	yes	—
63	C₂×C₄×C₁₃	C₂²×C₈	1	1	yes	characteristic
64	C₂×C₄×C₁₃	C₂²×C₈	1	2	yes	—
65	C₂²⋊D₁₃	C₂×C₁₆	1	8	yes	—
66	C₂×Dic₁₃	C₂×C₁₆	1	2	yes	—
67	D₅₂	C₂×C₁₆	1	4	yes	—
68	C₄×D₁₃	C₂×C₁₆	1	4	yes	—
69	C₄×D₁₃	C₂²×C₈	1	4	yes	—
70	Dic₂₆	C₂×C₁₆	1	4	yes	—
71	C₈×C₁₃	C₂²×C₈	1	1	yes	characteristic
72	C₈×C₁₃	C₂²×C₈	1	2	yes	—
73	C₈×C₁₃	C₂³×C₄	1	1	yes	characteristic
74	#1055	C₂²×C₈	1	4	yes	—
75	C₂×#131	—	13	1	no	—
76	#504	—	13	4	no	—
77	#504	—	13	4	no	—
78	C₂×M₃₂	—	13	2	no	—
79	C₂×M₃₂	#261	1	1	yes	characteristic
80	C₂²×C₁₆	—	13	1	no	—
81	C₂²×C₁₆	—	13	2	no	—
82	M₆₄	—	13	8	no	—
83	M₆₄	—	13	4	no	—
84	M₆₄	—	13	4	no	—
85	C₂×C₃₂	—	13	8	no	—
86	C₂×C₃₂	—	13	4	no	—
87	C₂²×C₁₃	—	4	1	no	—
88	C₂²×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
89	C₂²×C₁₃	C₂²×C₁₆	1	2	yes	—
90	C₂×D₁₃	—	4	2	no	—
91	C₂×D₁₃	C₂²×C₁₆	1	4	yes	—
92	C₄×C₁₃	C₂²×C₁₆	1	2	yes	—
93	C₄×C₁₃	C₂²×C₁₆	1	1	yes	characteristic
94	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
95	Dic₁₃	C₂²×C₁₆	1	4	yes	—
96	C₂×#41	—	13	1	no	—
97	#131	—	13	4	no	—
98	#131	—	13	4	no	—
99	C₂×M₁₆	—	13	1	no	—
100	C₂×M₁₆	—	13	2	no	—
101	C₂²×C₈	—	13	2	no	—
102	C₂²×C₈	C₂×#261	1	1	yes	characteristic
103	M₃₂	—	13	8	no	—
104	M₃₂	C₂×#261	1	4	yes	—
105	C₂×C₁₆	—	13	2	no	—
106	C₂×C₁₆	—	13	1	no	—
107	C₂×C₁₆	—	13	1	no	—
108	C₂×C₁₆	—	13	2	no	—
109	C₂×C₁₆	—	13	4	no	—
110	C₂×C₁₆	—	13	4	no	—
111	C₂×C₁₆	C₂×#261	1	2	yes	—
112	C₃₂	—	13	8	no	—
113	C₂×C₁₃	—	2	1	no	—
114	C₂×C₁₃	—	2	2	no	—
115	C₂×C₁₃	C₂³×C₁₆	1	1	yes	characteristic
116	D₁₃	—	2	4	no	—
117	#41	—	13	4	no	—
118	#41	—	13	4	no	—
119	C₂×Q₈	—	13	1	no	—
120	C₂×D₄	—	13	2	no	—
121	C₂×D₄	—	13	1	no	—
122	C₂²×C₄	—	13	2	no	—
123	C₂²×C₄	D₁₃⋊C₈	1	1	yes	characteristic
124	M₁₆	—	13	4	no	—
125	M₁₆	—	13	8	no	—
126	C₂×C₈	—	13	2	no	—
127	C₂×C₈	—	13	4	no	—
128	C₂×C₈	—	13	4	no	—
129	C₂×C₈	D₁₃⋊C₈	1	1	yes	characteristic
130	C₂×C₈	D₁₃⋊C₈	1	2	yes	—
131	C₂×C₈	C₂²×#261	1	1	yes	characteristic
132	C₂×C₈	C₂²×#261	1	2	yes	—
133	C₁₆	—	13	1	no	—
134	C₁₆	—	13	1	no	—
135	C₁₆	—	13	2	no	—
136	C₁₆	C₂²×#261	1	4	yes	—
137	C₁₃	#33974	1	1	yes	characteristic, complemented, Sylow
138	C₂³	—	13	2	no	—
139	C₂³	D₁₃⋊C₁₆	1	1	yes	characteristic
140	Q₈	—	13	4	no	—
141	D₄	—	13	8	no	—
142	D₄	—	13	4	no	—
143	C₂×C₄	—	13	2	no	—
144	C₂×C₄	—	13	4	no	—
145	C₂×C₄	—	13	4	no	—
146	C₂×C₄	D₁₃⋊C₁₆	1	1	yes	characteristic
147	C₂×C₄	D₁₃⋊C₁₆	1	2	yes	—
148	C₂×C₄	C₂×D₁₃⋊C₈	1	1	yes	characteristic
149	C₂×C₄	C₂×D₁₃⋊C₈	1	2	yes	—
150	C₈	—	13	4	no	—
151	C₈	C₂×D₁₃⋊C₈	1	1	yes	characteristic
152	C₈	C₂×D₁₃⋊C₈	1	2	yes	—
153	C₈	C₂³×#261	1	1	yes	characteristic
154	C₂²	—	4	1	no	—
155	C₂²	—	13	4	no	—
156	C₂²	—	52	2	no	—
157	C₂²	C₂×D₁₃⋊C₁₆	1	1	yes	characteristic
158	C₂²	C₂×D₁₃⋊C₁₆	1	2	yes	—
159	C₄	—	13	4	no	—
160	C₄	C₂×D₁₃⋊C₁₆	1	1	yes	characteristic
161	C₄	C₂×D₁₃⋊C₁₆	1	2	yes	—
162	C₄	C₂²×D₁₃⋊C₈	1	1	yes	characteristic
163	C₂	—	2	1	no	—
164	C₂	—	2	2	no	—
165	C₂	—	26	4	no	—
166	C₂	C₂²×D₁₃⋊C₁₆	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂³×#261
commutator, socle	C₂×C₁₃	C₂³×C₁₆
Fitting	C₂×C₁₃×M₃₂	C₄
prime radical	C₂×#6127	C₈
cosocle	#6090	C₂⁴
hypercenter	C₂×M₃₂	#261
hypocenter	C₁₃	#33974
LCS	G ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂×M₃₂

Complements

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

N	H ≅ G/N	type
1. #13131260	C₂	semidirect
2. D₁₃⋊M₆₄	C₂	semidirect
3. C₂×#11718249	C₂	semidirect
13. #11718249	C₂²	semidirect
14. C₂×#88036	C₂²	semidirect
15. #11718214	C₂²	semidirect
16. D₁₃⋊C₃₂	C₂²	semidirect
137. C₁₃	#33974	semidirect

Maximal subgroups

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

subgroup	index
#13131260	2
D₁₃⋊M₆₄	2
C₂×#11718249	2
C₂×#11718568	2
#33974	13