Subgroups — #16015921

Order 3328.

684 conjugacy classes of subgroups.

The subgroup lattice has 182 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13127939	C₂	1	1	yes	maximal, characteristic
2	#131×Dic₁₃	C₂	1	1	yes	maximal, characteristic
3	#13116601	C₂	1	6	yes	maximal, complemented
4	C₂×#11718103	C₂	1	6	yes	maximal, complemented
5	C₁₃×#3407	C₂	1	1	yes	maximal, characteristic
6	C₂×C₁₃×#131	C₂²	1	1	yes	characteristic
7	#41×Dic₁₃	C₄	1	1	yes	characteristic
8	C₂×#88202	C₄	1	1	yes	characteristic
9	C₁₃×#504	—	2	4	no	—
10	C₂×C₁₃×M₃₂	C₂²	1	6	yes	—
11	#11718801	—	2	4	no	—
12	#11718783	C₄	1	3	yes	—
13	M₁₆×Dic₁₃	C₄	1	3	yes	—
14	#11718762	C₂²	1	3	yes	—
15	C₂×C₈×Dic₁₃	C₂²	1	3	yes	—
16	C₂×#88052	C₂²	1	6	yes	—
17	#11718103	C₂²	1	4	yes	—
18	#11718103	C₂²	1	12	yes	—
19	C₂×C₁₃×#41	C₂×C₄	1	1	yes	characteristic
20	C₁₃×#131	D₄	1	4	yes	—
21	C₁₃×#131	Q₈	1	4	yes	—
22	C₂×C₁₃×M₁₆	C₂×C₄	1	3	yes	—
23	C₂²×C₈×C₁₃	C₂³	1	3	yes	—
24	#88202	C₈	1	8	yes	—
25	Q₈×Dic₁₃	—	2	1	no	—
26	D₄×Dic₁₃	—	2	3	no	—
27	#88180	C₂×C₄	1	3	yes	—
28	C₂×C₄×Dic₁₃	C₂×C₄	1	3	yes	—
29	C₂×#6099	C₂×C₄	1	3	yes	—
30	C₂²×#1055	C₂×C₄	1	3	yes	—
31	C₁₃×M₃₂	—	2	6	no	—
32	C₁₃×M₃₂	C₂³	1	4	yes	—
33	C₂×C₁₃×C₁₆	—	2	6	no	—
34	#88055	C₂×C₄	1	6	yes	—
35	C₈×Dic₁₃	C₂×C₄	1	3	yes	—
36	C₈×Dic₁₃	C₂×C₄	1	3	yes	—
37	C₈×Dic₁₃	C₂³	1	1	yes	characteristic
38	C₈×Dic₁₃	C₂³	1	3	yes	—
39	#88052	—	2	6	no	—
40	#88052	C₂³	1	4	yes	—
41	C₂×#6090	—	2	6	no	—
42	#33401	—	13	1	no	maximal, Sylow
43	C₁₃×#41	C₄⋊C₄	1	4	yes	—
44	C₁₃×#41	C₂×C₈	1	4	yes	—
45	C₂×Q₈×C₁₃	M₁₆	1	1	yes	characteristic
46	C₂×D₄×C₁₃	M₁₆	1	3	yes	—
47	C₂²×C₄×C₁₃	C₂²×C₄	1	3	yes	—
48	C₂²×Dic₁₃	—	2	3	no	—
49	C₁₃×M₁₆	C₄⋊C₄	1	12	yes	—
50	C₂×C₈×C₁₃	C₂²×C₄	1	3	yes	—
51	C₂×C₈×C₁₃	C₂×D₄	1	6	yes	—
52	C₂×C₈×C₁₃	C₂×Q₈	1	6	yes	—
53	C₂×C₈×C₁₃	C₂⁴	1	1	yes	characteristic
54	C₂²⋊Dic₁₃	—	2	3	no	—
55	C₄⋊Dic₁₃	—	2	3	no	—
56	C₄×Dic₁₃	—	2	3	no	—
57	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
58	C₄×Dic₁₃	C₂²×C₄	1	3	yes	—
59	#6099	C₂×C₈	1	12	yes	—
60	C₂×#1055	C₂×C₈	1	12	yes	—
61	C₂×#1055	C₂²×C₄	1	1	yes	characteristic
62	C₂×#1055	C₂²×C₄	1	3	yes	—
63	C₁₃×C₁₆	—	2	4	no	—
64	#6090	—	2	4	no	—
65	#3407	—	13	1	no	—
66	#3407	D₁₃	1	1	yes	characteristic
67	C₄×#131	—	13	1	no	—
68	#2153	—	13	6	no	—
69	C₂×#364	—	13	6	no	—
70	C₂³×C₁₃	C₂×M₁₆	1	3	yes	—
71	Q₈×C₁₃	C₄⋊C₈	1	4	yes	—
72	D₄×C₁₃	C₄⋊C₈	1	12	yes	—
73	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	6	yes	—
74	C₂×C₄×C₁₃	C₂²×C₈	1	6	yes	—
75	C₂×C₄×C₁₃	C₂×M₁₆	1	3	yes	—
76	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
77	C₂×Dic₁₃	—	2	1	no	—
78	C₂×Dic₁₃	—	2	3	no	—
79	C₂×Dic₁₃	—	4	6	no	—
80	C₈×C₁₃	C₂×C₄⋊C₄	1	6	yes	—
81	C₈×C₁₃	C₂²×D₄	1	1	yes	characteristic
82	C₈×C₁₃	C₂²×Q₈	1	1	yes	characteristic
83	#1055	C₂²×C₈	1	2	yes	—
84	#1055	C₂²×C₈	1	6	yes	—
85	C₂×#131	—	13	1	no	—
86	C₂×#131	C₂×D₁₃	1	1	yes	characteristic
87	C₄×#41	—	13	1	no	—
88	#504	—	2	4	no	—
89	#504	—	26	4	no	—
90	C₂×M₃₂	—	13	6	no	—
91	C₂×M₃₂	C₂×D₁₃	1	6	yes	—
92	#405	—	13	3	no	—
93	#405	—	13	3	no	—
94	C₄×M₁₆	—	13	3	no	—
95	C₂×C₄×C₈	—	13	3	no	—
96	#364	—	13	4	no	—
97	#364	—	13	12	no	—
98	C₂²×C₁₃	—	4	3	no	—
99	C₂²×C₁₃	C₂×C₄⋊C₈	1	6	yes	—
100	C₂²×C₁₃	C₂²×M₁₆	1	1	yes	characteristic
101	C₄×C₁₃	C₂×C₄⋊C₈	1	6	yes	—
102	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
103	C₄×C₁₃	C₂³×C₈	1	1	yes	characteristic
104	Dic₁₃	—	2	2	no	—
105	Dic₁₃	—	4	3	no	—
106	C₂×#41	C₄×D₁₃	1	1	yes	characteristic
107	#131	—	13	8	no	—
108	#131	Dic₂₆	1	4	yes	—
109	#131	C₂²⋊D₁₃	1	4	yes	—
110	C₂×M₁₆	—	13	3	no	—
111	C₂×M₁₆	C₄×D₁₃	1	3	yes	—
112	C₂²×C₈	—	13	3	no	—
113	C₂²×C₈	C₂²×D₁₃	1	3	yes	—
114	C₄×Q₈	—	26	1	no	—
115	C₄×D₄	—	26	3	no	—
116	#117	—	13	3	no	—
117	C₂×C₄²	—	13	3	no	—
118	M₃₂	—	2	6	no	—
119	M₃₂	—	13	4	no	—
120	M₃₂	—	26	6	no	—
121	M₃₂	C₂²×D₁₃	1	4	yes	—
122	C₂×C₁₆	—	2	6	no	—
123	C₂×C₁₆	—	26	6	no	—
124	#97	—	13	6	no	—
125	C₄×C₈	—	13	3	no	—
126	C₄×C₈	—	13	3	no	—
127	C₄×C₈	—	13	1	no	—
128	C₄×C₈	—	13	3	no	—
129	C₂×C₁₃	—	2	1	no	—
130	C₂×C₁₃	—	2	6	no	—
131	C₂×C₁₃	C₂²×C₄⋊C₈	1	1	yes	characteristic
132	#41	C₈×D₁₃	1	4	yes	—
133	#41	#6101	1	4	yes	—
134	C₂×Q₈	#6094	1	1	yes	characteristic
135	C₂×D₄	#6094	1	3	yes	—
136	C₂²×C₄	—	26	3	no	—
137	C₂²×C₄	C₂×C₄×D₁₃	1	3	yes	—
138	M₁₆	—	13	12	no	—
139	M₁₆	#6101	1	12	yes	—
140	C₂×C₈	—	13	12	no	—
141	C₂×C₈	—	13	1	no	—
142	C₂×C₈	—	13	3	no	—
143	C₂×C₈	C₂×Dic₂₆	1	6	yes	—
144	C₂×C₈	C₂×C₄×D₁₃	1	3	yes	—
145	C₂×C₈	C₂×C₂²⋊D₁₃	1	6	yes	—
146	C₂×C₈	C₂³×D₁₃	1	1	yes	characteristic
147	C₄⋊C₄	—	26	3	no	—
148	C₂²⋊C₄	—	26	3	no	—
149	C₄²	—	13	1	no	—
150	C₄²	—	13	3	no	—
151	C₄²	—	26	3	no	—
152	C₁₆	—	2	4	no	—
153	C₁₆	—	26	4	no	—
154	C₁₃	#33401	1	1	yes	characteristic, complemented, Sylow
155	C₂³	C₂×#6094	1	3	yes	—
156	Q₈	#88054	1	4	yes	—
157	D₄	#88054	1	12	yes	—
158	C₂×C₄	—	26	1	no	—
159	C₂×C₄	—	26	3	no	—
160	C₂×C₄	—	52	6	no	—
161	C₂×C₄	C₂×C₈×D₁₃	1	6	yes	—
162	C₂×C₄	C₂×#6094	1	3	yes	—
163	C₂×C₄	C₂×#6101	1	6	yes	—
164	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
165	C₈	—	13	2	no	—
166	C₈	—	13	6	no	—
167	C₈	C₂×#6101	1	6	yes	—
168	C₈	C₂²×Dic₂₆	1	1	yes	characteristic
169	C₈	C₂²×C₂²⋊D₁₃	1	1	yes	characteristic
170	C₂²	—	4	3	no	—
171	C₂²	C₂×#88054	1	6	yes	—
172	C₂²	C₂²×#6094	1	1	yes	characteristic
173	C₄	—	26	2	no	—
174	C₄	—	52	3	no	—
175	C₄	C₂×#88054	1	6	yes	—
176	C₄	C₂²×C₈×D₁₃	1	1	yes	characteristic
177	C₄	C₂²×#6101	1	1	yes	characteristic
178	C₂	—	2	1	no	—
179	C₂	—	2	6	no	—
180	C₂	C₂²×#88054	1	1	yes	characteristic

	subgroup	G/H
center	C₈	C₂²×C₂²⋊D₁₃
commutator	C₄×C₁₃	C₂³×C₈
Frattini	C₂×C₈	C₂³×D₁₃
Fitting	C₁₃×#3407	C₂
socle	C₂×C₁₃	C₂²×C₄⋊C₈
prime radical	C₂×C₁₃×#41	C₂×C₄
cosocle	C₂×C₈×C₁₃	C₂⁴
hypercenter	#3407	D₁₃
hypocenter	C₁₃	#33401
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₈ ◁ C₂×#131 ◁ #3407

Complements

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

N	H ≅ G/N	type
3. #13116601	C₂	semidirect
4. C₂×#11718103	C₂	semidirect
154. C₁₃	#33401	semidirect

Maximal subgroups

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

subgroup	index
#13127939	2
#131×Dic₁₃	2
#13116601	2
C₂×#11718103	2
C₁₃×#3407	2
#33401	13