Subgroups — #15863342

Order 3328.

1086 conjugacy classes of subgroups.

The subgroup lattice has 194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718767	C₂	1	4	yes	maximal
2	#13117243	C₂	1	2	yes	maximal
3	#13115004	C₂	1	8	yes	maximal, complemented
4	C₂²×C₁₃×#97	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₈×C₁₃	C₂²	1	2	yes	—
6	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
7	C₂×#88180	C₂²	1	4	yes	—
8	C₂×C₁₃×#97	C₄	1	8	yes	complemented
9	C₂×C₁₃×#97	C₂²	1	4	yes	—
10	#11718873	—	2	4	no	—
11	#11718767	—	2	16	no	—
12	C₂×#88058	C₂²	1	8	yes	—
13	C₂×#88057	C₂²	1	8	yes	—
14	#11718597	C₂²	1	4	yes	—
15	#11718596	C₂²	1	4	yes	—
16	C₄×C₄⋊Dic₁₃	—	2	4	no	—
17	C₂³×C₄×C₁₃	D₄	1	2	yes	—
18	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
19	C₂²×C₈×C₁₃	C₂×C₄	1	8	yes	—
20	C₂²×C₈×C₁₃	D₄	1	8	yes	—
21	C₂²×C₈×C₁₃	Q₈	1	8	yes	—
22	C₂²×C₈×C₁₃	C₂³	1	4	yes	—
23	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
24	C₂×C₄²×C₁₃	D₄	1	2	yes	—
25	C₂×C₄²×C₁₃	Q₈	1	4	yes	—
26	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
27	C₂×C₂²⋊Dic₁₃	—	2	4	no	—
28	#88180	—	2	16	no	—
29	C₂×C₄⋊Dic₁₃	—	2	8	no	—
30	C₂×C₄⋊Dic₁₃	C₂³	1	8	yes	—
31	C₂×C₄×Dic₁₃	—	2	4	no	—
32	C₁₃×#97	C₂×C₄	1	16	yes	—
33	#88071	—	2	8	no	—
34	#88058	—	2	16	no	—
35	#88057	—	2	16	no	—
36	#20799	—	13	1	no	maximal, Sylow
37	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
38	C₂²×C₄×C₁₃	—	4	4	no	—
39	C₂²×C₄×C₁₃	C₄⋊C₄	1	8	yes	—
40	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
41	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
42	C₂²×C₄×C₁₃	C₂×D₄	1	4	yes	—
43	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
44	C₂²×C₄×C₁₃	C₂×Q₈	1	4	yes	—
45	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
46	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
47	C₂²×Dic₁₃	—	2	8	no	—
48	C₂×C₈×C₁₃	C₄⋊C₄	1	32	yes	complemented
49	C₂×C₈×C₁₃	C₂²×C₄	1	8	yes	—
50	C₂×C₈×C₁₃	C₂×D₄	1	8	yes	—
51	C₂×C₈×C₁₃	C₂×Q₈	1	8	yes	—
52	C₄²×C₁₃	C₄⋊C₄	1	8	yes	—
53	C₄²×C₁₃	C₂²×C₄	1	4	yes	—
54	C₄²×C₁₃	C₂×Q₈	1	4	yes	—
55	C₂²⋊Dic₁₃	—	4	8	no	—
56	C₄⋊Dic₁₃	—	2	16	no	—
57	C₄⋊Dic₁₃	—	4	16	no	—
58	C₄×Dic₁₃	—	4	8	no	—
59	C₂×#427	—	13	4	no	—
60	C₂²×#97	D₁₃	1	1	yes	characteristic
61	#2285	—	13	2	no	—
62	#1847	—	13	8	no	—
63	C₂³×C₁₃	—	2	4	no	—
64	C₂³×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
65	C₂³×C₁₃	#127	1	2	yes	—
66	C₂³×C₁₃	C₄⋊Q₈	1	2	yes	—
67	C₂³×C₁₃	C₂²×D₄	1	1	yes	characteristic
68	C₂×C₄×C₁₃	—	2	8	no	—
69	C₂×C₄×C₁₃	—	4	8	no	—
70	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
71	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	8	yes	—
72	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
73	C₂×C₄×C₁₃	#127	1	2	yes	—
74	C₂×C₄×C₁₃	C₄⋊Q₈	1	8	yes	—
75	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
76	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
77	C₂×C₄×C₁₃	C₂²×D₄	1	2	yes	—
78	C₂×C₄×C₁₃	C₂²×Q₈	1	2	yes	—
79	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
80	C₂×Dic₁₃	—	4	8	no	—
81	C₂×Dic₁₃	—	4	16	no	—
82	C₈×C₁₃	C₂×C₄⋊C₄	1	16	yes	—
83	C₂³×C₈	C₂×D₁₃	1	2	yes	—
84	C₂×#117	—	13	4	no	—
85	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
86	#427	—	26	16	no	—
87	C₂×#107	—	13	8	no	—
88	C₂×#106	—	13	8	no	—
89	C₂×#97	Dic₁₃	1	8	yes	complemented
90	C₂×#97	C₂×D₁₃	1	4	yes	—
91	#384	—	13	4	no	—
92	#382	—	13	4	no	—
93	#380	—	26	4	no	—
94	C₄×C₄⋊C₄	—	26	4	no	—
95	C₂²×C₁₃	—	2	4	no	—
96	C₂²×C₁₃	—	2	4	no	—
97	C₂²×C₁₃	—	2	4	no	—
98	C₂²×C₁₃	#384	1	4	yes	—
99	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
100	C₂²×C₁₃	C₂×#127	1	1	yes	characteristic
101	C₂²×C₁₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
102	C₂²×C₁₃	#575	1	4	yes	—
103	C₄×C₁₃	—	2	8	no	—
104	C₄×C₁₃	#384	1	4	yes	—
105	C₄×C₁₃	C₂²×C₄⋊C₄	1	2	yes	—
106	C₄×C₁₃	C₂×C₄⋊Q₈	1	2	yes	—
107	Dic₁₃	—	8	8	no	—
108	C₂³×C₄	D₅₂	1	2	yes	—
109	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
110	C₂²×C₈	Dic₂₆	1	8	yes	—
111	C₂²×C₈	D₅₂	1	8	yes	—
112	C₂²×C₈	C₂×Dic₁₃	1	8	yes	—
113	C₂²×C₈	C₂²×D₁₃	1	4	yes	—
114	#117	—	26	16	no	—
115	C₂×C₄⋊C₄	—	13	8	no	—
116	C₂×C₄⋊C₄	—	26	8	no	—
117	C₂×C₂²⋊C₄	—	26	4	no	—
118	C₂×C₄²	—	26	4	no	—
119	C₂×C₄²	Dic₂₆	1	4	yes	—
120	C₂×C₄²	D₅₂	1	2	yes	—
121	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
122	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
123	#107	—	26	16	no	—
124	#106	—	26	16	no	—
125	#97	C₂×Dic₁₃	1	16	yes	—
126	#95	—	26	8	no	—
127	C₂×C₁₃	—	2	4	no	—
128	C₂×C₁₃	C₂×#384	1	1	yes	characteristic
129	C₂×C₁₃	#2911	1	2	yes	—
130	C₂×C₁₃	#3150	1	2	yes	—
131	C₂×C₁₃	#3162	1	2	yes	—
132	C₂⁴	C₂×D₅₂	1	1	yes	characteristic
133	C₂²×C₄	—	4	4	no	—
134	C₂²×C₄	—	26	8	no	—
135	C₂²×C₄	C₄⋊Dic₁₃	1	8	yes	—
136	C₂²×C₄	C₂×Dic₂₆	1	2	yes	—
137	C₂²×C₄	C₂×Dic₂₆	1	4	yes	—
138	C₂²×C₄	C₂×D₅₂	1	4	yes	—
139	C₂²×C₄	C₂×D₅₂	1	4	yes	—
140	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
141	C₂²×C₄	C₂²×Dic₁₃	1	2	yes	—
142	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
143	C₂×C₈	C₄⋊Dic₁₃	1	32	yes	complemented
144	C₂×C₈	C₂×Dic₂₆	1	8	yes	—
145	C₂×C₈	C₂×D₅₂	1	8	yes	—
146	C₂×C₈	C₂²×Dic₁₃	1	8	yes	—
147	C₄⋊C₄	—	26	16	no	—
148	C₄⋊C₄	—	52	16	no	—
149	C₂²⋊C₄	—	52	8	no	—
150	C₄²	—	52	8	no	—
151	C₄²	C₄⋊Dic₁₃	1	8	yes	—
152	C₄²	C₂×Dic₂₆	1	4	yes	—
153	C₄²	C₂²×Dic₁₃	1	4	yes	—
154	C₁₃	#20799	1	1	yes	characteristic, complemented, Sylow
155	C₂³	—	2	4	no	—
156	C₂³	#88123	1	2	yes	—
157	C₂³	#88128	1	2	yes	—
158	C₂³	C₂×C₄⋊Dic₁₃	1	2	yes	—
159	C₂³	C₂²×D₅₂	1	1	yes	characteristic
160	C₂×C₄	—	2	8	no	—
161	C₂×C₄	—	4	8	no	—
162	C₂×C₄	—	52	8	no	—
163	C₂×C₄	—	52	16	no	—
164	C₂×C₄	#88123	1	8	yes	—
165	C₂×C₄	#88123	1	2	yes	—
166	C₂×C₄	#88128	1	2	yes	—
167	C₂×C₄	C₂×C₄⋊Dic₁₃	1	8	yes	—
168	C₂×C₄	C₂×C₄⋊Dic₁₃	1	8	yes	—
169	C₂×C₄	C₂×C₄⋊Dic₁₃	1	2	yes	—
170	C₂×C₄	C₂²×Dic₂₆	1	1	yes	characteristic
171	C₂×C₄	C₂²×Dic₂₆	1	2	yes	—
172	C₂×C₄	C₂²×D₅₂	1	2	yes	—
173	C₂×C₄	C₂³×Dic₁₃	1	1	yes	characteristic
174	C₈	C₂×C₄⋊Dic₁₃	1	16	yes	—
175	C₂²	—	2	4	no	—
176	C₂²	—	2	4	no	—
177	C₂²	—	2	4	no	—
178	C₂²	#11718596	1	4	yes	—
179	C₂²	C₂×#88123	1	1	yes	characteristic
180	C₂²	C₂×#88128	1	1	yes	characteristic
181	C₂²	#11719453	1	4	yes	—
182	C₂²	C₂²×C₄⋊Dic₁₃	1	1	yes	characteristic
183	C₄	—	2	8	no	—
184	C₄	—	104	8	no	—
185	C₄	#11718596	1	4	yes	—
186	C₄	C₂×#88123	1	2	yes	—
187	C₄	C₂²×C₄⋊Dic₁₃	1	2	yes	—
188	C₂	—	2	4	no	—
189	C₂	C₂×#11718596	1	1	yes	characteristic
190	C₂	#13123426	1	2	yes	—
191	C₂	#13125282	1	2	yes	—
192	C₂	#13125360	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₃
Fitting	C₂²×C₁₃×#97	C₂
socle	C₂³×C₁₃	C₂²×D₄
prime radical	C₂⁴×C₁₃	C₂×D₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂²×#97	D₁₃
hypocenter	C₁₃	#20799
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×#97

Complements

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

N	H ≅ G/N	type
3. #13115004	C₂	semidirect
8. C₂×C₁₃×#97	C₄	semidirect
48. C₂×C₈×C₁₃	C₄⋊C₄	semidirect
89. C₂×#97	Dic₁₃	semidirect
143. C₂×C₈	C₄⋊Dic₁₃	semidirect
154. C₁₃	#20799	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718767	2
#13117243	2
#13115004	2
C₂²×C₁₃×#97	2
#20799	13