Subgroups — D₁₃×#2868 #16069014

Order 3328.

3774 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₁₃×C₄⋊Q₈	C₂	1	6	yes	maximal
2	#13123234	C₂	1	1	yes	maximal, characteristic, complemented
3	#13123233	C₂	1	8	yes	maximal, complemented
4	#13123232	C₂	1	6	yes	maximal, complemented
5	D₁₃×#384	C₂	1	8	yes	maximal
6	C₄³×D₁₃	C₂	1	1	yes	maximal, characteristic
7	C₁₃×#2868	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×Q₈×D₁₃	C₂²	1	4	yes	—
9	C₂×C₁₃×C₄⋊Q₈	C₂²	1	6	yes	—
10	C₂×#88198	C₂²	1	12	yes	—
11	D₁₃×C₄⋊Q₈	—	2	48	no	—
12	C₂×C₄⋊C₄×D₁₃	C₂²	1	24	yes	—
13	C₂×#88142	C₂²	1	24	yes	—
14	C₂×C₄²×D₁₃	C₂²	1	3	yes	—
15	C₂×C₄²×D₁₃	C₂²	1	4	yes	—
16	C₂×#88123	C₂²	1	6	yes	—
17	C₁₃×#384	C₂²	1	8	yes	—
18	C₄³×C₁₃	C₂²	1	1	yes	characteristic
19	#11718637	C₂²	1	48	yes	—
20	#11718596	C₂²	1	8	yes	—
21	C₄²×Dic₁₃	C₂²	1	3	yes	—
22	C₄²×Dic₁₃	C₂²	1	4	yes	—
23	C₂²×Q₈×C₁₃	C₂³	1	4	yes	—
24	C₂×Q₈×D₁₃	—	2	48	no	—
25	C₂²×C₄×D₁₃	C₂³	1	8	yes	—
26	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
27	C₂²×C₄×D₁₃	C₂³	1	6	yes	—
28	C₂²×Dic₂₆	C₂³	1	4	yes	—
29	C₂²×Dic₂₆	C₂³	1	8	yes	—
30	C₁₃×C₄⋊Q₈	—	2	24	no	—
31	C₂×C₁₃×C₄⋊C₄	C₂³	1	24	yes	—
32	C₂×C₄²×C₁₃	C₂³	1	3	yes	—
33	C₂×C₄²×C₁₃	C₂³	1	4	yes	—
34	#88198	—	2	48	no	—
35	C₂×C₄⋊Dic₁₃	C₂³	1	24	yes	—
36	C₂×#6101	C₂³	1	48	yes	—
37	C₂×C₄×Dic₁₃	C₂³	1	6	yes	—
38	C₂×C₄×Dic₁₃	C₂³	1	3	yes	—
39	C₂×C₄×Dic₁₃	C₂³	1	12	yes	—
40	C₄⋊C₄×D₁₃	—	2	96	no	—
41	#88142	—	2	96	no	—
42	C₄²×D₁₃	D₄	1	24	yes	—
43	C₄²×D₁₃	Q₈	1	32	yes	complemented
44	#88123	—	2	24	no	—
45	C₂×#2868	—	13	1	no	maximal, Sylow
46	C₂³×D₁₃	C₂⁴	1	1	yes	characteristic
47	C₂×Q₈×C₁₃	—	2	24	no	—
48	C₂²×C₄×C₁₃	C₂⁴	1	8	yes	—
49	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
50	C₂²×C₄×C₁₃	C₂⁴	1	6	yes	—
51	C₂²×Dic₁₃	C₂⁴	1	8	yes	—
52	C₂²×Dic₁₃	C₂⁴	1	1	yes	characteristic
53	C₂²×Dic₁₃	C₂⁴	1	6	yes	—
54	Q₈×D₁₃	—	4	64	no	—
55	C₂×C₄×D₁₃	—	2	48	no	—
56	C₂×C₄×D₁₃	C₂×D₄	1	12	yes	—
57	C₂×C₄×D₁₃	C₂×D₄	1	24	yes	—
58	C₂×C₄×D₁₃	C₂×Q₈	1	48	yes	—
59	C₂×Dic₂₆	—	2	24	no	—
60	C₂×Dic₂₆	—	2	48	no	—
61	C₁₃×C₄⋊C₄	—	2	48	no	—
62	C₄²×C₁₃	C₂×D₄	1	12	yes	—
63	C₄²×C₁₃	C₂×Q₈	1	16	yes	complemented
64	C₄⋊Dic₁₃	—	2	48	no	—
65	#6101	—	2	96	no	—
66	C₄×Dic₁₃	C₂×D₄	1	24	yes	—
67	C₄×Dic₁₃	C₂×D₄	1	12	yes	—
68	C₄×Dic₁₃	C₂×Q₈	1	48	yes	complemented
69	C₂²×C₄⋊Q₈	—	13	6	no	—
70	#2868	—	13	8	no	—
71	#2868	—	13	1	no	—
72	#2868	—	13	6	no	—
73	#2868	D₁₃	1	1	yes	characteristic, direct product factor
74	C₂×#384	—	13	8	no	—
75	C₂×C₄³	—	13	1	no	—
76	C₂³×C₁₃	C₂⁵	1	1	yes	characteristic
77	C₂²×D₁₃	C₂²×D₄	1	6	yes	—
78	C₂²×D₁₃	C₂²×Q₈	1	8	yes	—
79	Q₈×C₁₃	—	4	16	no	—
80	C₂×C₄×C₁₃	—	2	24	no	—
81	C₂×C₄×C₁₃	C₂²×D₄	1	6	yes	—
82	C₂×C₄×C₁₃	C₂²×D₄	1	12	yes	—
83	C₂×C₄×C₁₃	C₂²×Q₈	1	24	yes	—
84	C₂×Dic₁₃	—	2	24	no	—
85	C₂×Dic₁₃	C₂²×D₄	1	6	yes	—
86	C₂×Dic₁₃	C₂²×D₄	1	12	yes	—
87	C₂×Dic₁₃	C₂²×Q₈	1	24	yes	—
88	C₄×D₁₃	—	4	32	no	—
89	C₄×D₁₃	#127	1	16	yes	—
90	C₄×D₁₃	C₄⋊Q₈	1	96	yes	complemented
91	Dic₂₆	—	4	16	no	—
92	Dic₂₆	—	4	32	no	—
93	C₂³×Q₈	—	13	4	no	—
94	C₂×C₄⋊Q₈	—	13	12	no	—
95	C₂×C₄⋊Q₈	—	13	24	no	—
96	C₂×C₄⋊Q₈	—	13	6	no	—
97	C₂×C₄⋊Q₈	—	26	48	no	—
98	C₂×C₄⋊Q₈	C₂×D₁₃	1	6	yes	—
99	C₂²×C₄⋊C₄	—	13	24	no	—
100	C₂²×C₄²	—	13	3	no	—
101	C₂²×C₄²	—	13	4	no	—
102	#384	—	13	48	no	—
103	#384	—	13	8	no	—
104	#384	C₂×D₁₃	1	8	yes	—
105	C₄³	—	13	4	no	—
106	C₄³	—	13	3	no	—
107	C₄³	C₂×D₁₃	1	1	yes	characteristic
108	C₂²×C₁₃	C₂³×D₄	1	3	yes	—
109	C₂²×C₁₃	C₂³×Q₈	1	4	yes	—
110	C₂×D₁₃	C₂×#127	1	4	yes	—
111	C₂×D₁₃	C₂×C₄⋊Q₈	1	24	yes	—
112	C₄×C₁₃	—	4	8	no	—
113	C₄×C₁₃	C₂×#127	1	4	yes	—
114	C₄×C₁₃	C₂×C₄⋊Q₈	1	24	yes	complemented
115	Dic₁₃	—	4	8	no	—
116	Dic₁₃	C₂×#127	1	4	yes	—
117	Dic₁₃	C₂×C₄⋊Q₈	1	24	yes	complemented
118	C₂²×Q₈	—	13	8	no	—
119	C₂²×Q₈	—	13	4	no	—
120	C₂²×Q₈	—	26	48	no	—
121	C₂²×Q₈	C₂²×D₁₃	1	4	yes	—
122	C₂³×C₄	—	13	6	no	—
123	C₂³×C₄	—	13	1	no	—
124	C₂³×C₄	—	13	8	no	—
125	C₄⋊Q₈	—	2	24	no	—
126	C₄⋊Q₈	—	26	96	no	—
127	C₄⋊Q₈	—	26	48	no	—
128	C₄⋊Q₈	—	26	24	no	—
129	C₂×C₄⋊C₄	—	13	48	no	—
130	C₂×C₄⋊C₄	—	13	24	no	—
131	C₂×C₄⋊C₄	—	26	96	no	—
132	C₂×C₄⋊C₄	C₂²×D₁₃	1	24	yes	—
133	C₂×C₄²	—	13	3	no	—
134	C₂×C₄²	—	13	6	no	—
135	C₂×C₄²	—	13	12	no	—
136	C₂×C₄²	—	13	24	no	—
137	C₂×C₄²	—	13	32	no	—
138	C₂×C₄²	C₂²×D₁₃	1	3	yes	—
139	C₂×C₄²	C₂²×D₁₃	1	4	yes	—
140	C₂×C₁₃	C₂²×#127	1	1	yes	characteristic
141	C₂×C₁₃	C₂²×C₄⋊Q₈	1	6	yes	—
142	D₁₃	#2868	1	8	yes	direct product factor
143	C₂⁴	—	13	1	no	—
144	C₂×Q₈	—	2	24	no	—
145	C₂×Q₈	—	26	48	no	—
146	C₂×Q₈	—	26	24	no	—
147	C₂×Q₈	—	52	64	no	—
148	C₂²×C₄	—	13	6	no	—
149	C₂²×C₄	—	13	1	no	—
150	C₂²×C₄	—	13	24	no	—
151	C₂²×C₄	—	13	12	no	—
152	C₂²×C₄	—	13	48	no	—
153	C₂²×C₄	—	13	8	no	—
154	C₂²×C₄	—	26	48	no	—
155	C₂²×C₄	C₂³×D₁₃	1	8	yes	—
156	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
157	C₂²×C₄	C₂³×D₁₃	1	6	yes	—
158	C₄⋊C₄	—	2	48	no	—
159	C₄⋊C₄	—	26	96	no	—
160	C₄⋊C₄	—	26	48	no	—
161	C₄²	—	13	12	no	—
162	C₄²	—	13	24	no	—
163	C₄²	—	13	48	no	—
164	C₄²	D₄×D₁₃	1	12	yes	—
165	C₄²	Q₈×D₁₃	1	16	yes	complemented
166	C₁₃	C₂×#2868	1	1	yes	characteristic, complemented, Sylow
167	C₂³	—	13	6	no	—
168	C₂³	—	13	8	no	—
169	C₂³	C₂⁴×D₁₃	1	1	yes	characteristic
170	Q₈	—	4	16	no	—
171	Q₈	—	52	32	no	—
172	Q₈	—	52	16	no	—
173	C₂×C₄	—	2	24	no	—
174	C₂×C₄	—	13	12	no	—
175	C₂×C₄	—	13	6	no	—
176	C₂×C₄	—	13	24	no	—
177	C₂×C₄	—	13	96	no	—
178	C₂×C₄	—	13	16	no	—
179	C₂×C₄	—	26	24	no	—
180	C₂×C₄	—	52	32	no	—
181	C₂×C₄	C₂×D₄×D₁₃	1	12	yes	—
182	C₂×C₄	C₂×D₄×D₁₃	1	6	yes	—
183	C₂×C₄	C₂×Q₈×D₁₃	1	24	yes	—
184	C₂²	—	13	4	no	—
185	C₂²	—	13	24	no	—
186	C₂²	C₂²×D₄×D₁₃	1	3	yes	—
187	C₂²	C₂²×Q₈×D₁₃	1	4	yes	—
188	C₄	—	4	8	no	—
189	C₄	—	13	4	no	—
190	C₄	—	13	24	no	—
191	C₄	—	52	8	no	—
192	C₄	D₁₃×#127	1	4	yes	—
193	C₄	D₁₃×C₄⋊Q₈	1	24	yes	complemented
194	C₂	—	13	8	no	—
195	C₂	C₂×D₁₃×#127	1	1	yes	characteristic
196	C₂	C₂×D₁₃×C₄⋊Q₈	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₁₃
commutator, socle, cosocle	C₂³×C₁₃	C₂⁵
Fitting	C₁₃×#2868	C₂
prime radical	C₂³×D₁₃	C₂⁴
hypercenter	#2868	D₁₃
hypocenter	C₁₃	C₂×#2868
LCS	G ▷ C₂³×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ #2868

Complements

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

N	H ≅ G/N	type
2. #13123234	C₂	semidirect
3. #13123233	C₂	semidirect
4. #13123232	C₂	semidirect
7. C₁₃×#2868	C₂	semidirect
43. C₄²×D₁₃	Q₈	semidirect
63. C₄²×C₁₃	C₂×Q₈	semidirect
68. C₄×Dic₁₃	C₂×Q₈	semidirect
73. #2868	D₁₃	direct (N × H)
90. C₄×D₁₃	C₄⋊Q₈	semidirect
114. C₄×C₁₃	C₂×C₄⋊Q₈	semidirect
117. Dic₁₃	C₂×C₄⋊Q₈	semidirect
142. D₁₃	#2868	direct (N × H)
165. C₄²	Q₈×D₁₃	semidirect
166. C₁₃	C₂×#2868	semidirect
193. C₄	D₁₃×C₄⋊Q₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₁₃×C₄⋊Q₈	2
#13123234	2
#13123233	2
#13123232	2
D₁₃×#384	2
C₄³×D₁₃	2
C₁₃×#2868	2
C₂×#2868	13

Subgroups — D13×#2868 #16069014

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₁₃×#2868 #16069014