Finite Group Databasebeta

Subgroups — #15783843

Order 3328.

186 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 55 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#13116919	C₂	1	1	yes	maximal, characteristic
2	D₁₃×#366	C₂	1	1	yes	maximal, characteristic, complemented
3	#13113036	C₂	1	1	yes	maximal, characteristic, complemented
4	#13113035	C₂	1	1	yes	maximal, characteristic, complemented
5	#13113014	C₂	1	1	yes	maximal, characteristic, complemented
6	#13112973	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₃×#1415	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₃×D₁₆	C₂²	1	1	yes	characteristic
9	#11718818	—	2	1	no	—
10	C₂×C₁₆×D₁₃	C₂²	1	1	yes	characteristic
11	D₁₃×#107	—	2	1	no	—
12	C₂×C₁₃×C₃₂	C₂²	1	1	yes	characteristic
13	C₁₃×#366	C₂²	1	1	yes	characteristic
14	#11718154	—	2	1	no	—
15	#11718096	C₂²	1	1	yes	characteristic
16	#11718096	C₂²	1	1	yes	characteristic
17	C₂×#88034	C₂²	1	1	yes	characteristic
18	#11718081	—	2	1	no	—
19	C₂×C₁₃×D₈	—	2	1	no	—
20	#88192	—	4	1	no	—
21	C₂×C₈×D₁₃	D₄	1	1	yes	characteristic
22	C₄⋊C₄×D₁₃	—	4	1	no	—
23	C₁₃×D₁₆	—	2	1	no	—
24	C₁₃×D₁₆	—	2	1	no	—
25	C₂×C₁₃×C₁₆	C₂³	1	1	yes	characteristic
26	C₁₃×#107	—	2	1	no	—
27	#88072	—	4	1	no	—
28	#88058	—	2	1	no	—
29	#88058	—	2	1	no	—
30	C₂×#6090	D₄	1	1	yes	characteristic
31	#88047	—	4	1	no	—
32	C₁₆×D₁₃	—	2	1	no	—
33	C₁₆×D₁₃	—	2	1	no	—
34	C₁₃×C₃₂	—	2	1	no	—
35	#88034	—	2	1	no	—
36	#13711	—	13	1	no	maximal, Sylow
37	C₂×D₄×C₁₃	—	4	1	no	—
38	C₂×C₂²⋊D₁₃	—	8	1	no	—
39	C₂×C₄×D₁₃	—	8	1	no	—
40	C₂×C₄×D₁₃	D₈	1	1	yes	characteristic
41	C₁₃×D₈	—	4	1	no	—
42	C₁₃×D₈	—	4	1	no	—
43	C₂×C₈×C₁₃	C₂×D₄	1	1	yes	characteristic
44	C₁₃×C₄⋊C₄	—	4	1	no	—
45	C₂²⋊Dic₁₃	—	8	1	no	—
46	C₄⋊Dic₁₃	—	4	1	no	—
47	C₄⋊Dic₁₃	—	4	1	no	—
48	#6101	—	8	1	no	—
49	C₂×#1055	D₈	1	1	yes	characteristic
50	C₈×D₁₃	—	2	1	no	—
51	C₈×D₁₃	—	2	1	no	—
52	C₁₃×C₁₆	#41	1	1	yes	characteristic
53	C₁₃×C₁₆	#41	1	1	yes	characteristic
54	#6090	—	2	1	no	—
55	#2215	—	13	1	no	—
56	C₂×#366	—	13	1	no	—
57	#1423	—	13	1	no	—
58	#1423	—	13	1	no	—
59	#1415	—	13	1	no	—
60	#1415	D₁₃	1	1	yes	characteristic, complemented
61	C₂²⋊C₃₂	—	13	1	no	—
62	C₂³×C₁₃	—	8	1	no	—
63	C₂²×D₁₃	D₁₆	1	1	yes	characteristic
64	D₄×C₁₃	—	8	1	no	—
65	D₄×C₁₃	—	8	1	no	—
66	C₂×C₄×C₁₃	—	8	1	no	—
67	C₂×C₄×C₁₃	C₂×D₈	1	1	yes	characteristic
68	C₂²⋊D₁₃	—	16	2	no	—
69	C₂×Dic₁₃	—	8	1	no	—
70	C₂×Dic₁₃	—	8	1	no	—
71	C₂×Dic₁₃	D₁₆	1	1	yes	characteristic
72	C₄×D₁₃	—	2	1	no	—
73	C₄×D₁₃	—	2	1	no	—
74	C₄×D₁₃	—	16	2	no	—
75	C₈×C₁₃	#123	1	1	yes	characteristic
76	C₈×C₁₃	#137	1	1	yes	characteristic
77	#1055	—	2	1	no	—
78	C₂×D₁₆	C₂×D₁₃	1	1	yes	characteristic
79	C₂²×C₁₆	—	13	1	no	—
80	#466	—	26	1	no	—
81	C₂×#107	—	26	1	no	—
82	C₂×C₃₂	—	13	1	no	—
83	C₂×C₃₂	C₂×D₁₃	1	1	yes	characteristic
84	#366	—	13	1	no	—
85	#366	—	13	1	no	—
86	#366	—	26	1	no	—
87	#366	C₂×D₁₃	1	1	yes	characteristic
88	#357	—	26	1	no	—
89	C₂²×C₁₃	—	16	1	no	—
90	C₂²×C₁₃	—	16	1	no	—
91	C₂²×C₁₃	—	16	1	no	—
92	C₂²×C₁₃	C₂×D₁₆	1	1	yes	characteristic
93	C₂×D₁₃	—	2	1	no	—
94	C₂×D₁₃	—	2	1	no	—
95	C₂×D₁₃	D₃₂	1	2	yes	—
96	C₄×C₁₃	—	16	1	no	—
97	C₄×C₁₃	#480	1	1	yes	characteristic
98	C₄×C₁₃	#510	1	1	yes	characteristic
99	Dic₁₃	—	2	1	no	—
100	Dic₁₃	—	16	1	no	—
101	Dic₁₃	—	16	1	no	—
102	C₂×D₈	—	2	1	no	—
103	C₂²×C₈	—	13	1	no	—
104	#121	—	52	1	no	—
105	C₂×C₄⋊C₄	—	52	1	no	—
106	D₁₆	—	2	1	no	—
107	D₁₆	—	2	1	no	—
108	C₂×C₁₆	—	13	1	no	—
109	C₂×C₁₆	—	26	1	no	—
110	C₂×C₁₆	—	26	1	no	—
111	C₂×C₁₆	C₂²×D₁₃	1	1	yes	characteristic
112	#107	—	2	1	no	—
113	#107	—	26	1	no	—
114	#107	—	26	1	no	—
115	#107	—	52	1	no	—
116	#102	—	52	1	no	—
117	C₃₂	—	2	1	no	—
118	C₃₂	—	26	1	no	—
119	C₂×C₁₃	—	32	1	no	—
120	C₂×C₁₃	#2232	1	1	yes	characteristic
121	C₂×C₁₃	C₂×D₃₂	1	1	yes	characteristic
122	C₂×C₁₃	#2264	1	1	yes	characteristic
123	D₁₃	—	2	2	no	—
124	C₂×D₄	—	4	1	no	—
125	C₂×D₄	—	104	1	no	—
126	C₂²×C₄	—	13	1	no	—
127	C₂²×C₄	—	104	1	no	—
128	D₈	—	4	1	no	—
129	D₈	—	4	1	no	—
130	C₂×C₈	—	13	1	no	—
131	C₂×C₈	—	26	1	no	—
132	C₂×C₈	—	26	1	no	—
133	C₂×C₈	D₄×D₁₃	1	1	yes	characteristic
134	C₄⋊C₄	—	4	1	no	—
135	C₄⋊C₄	—	52	1	no	—
136	C₄⋊C₄	—	52	1	no	—
137	C₄⋊C₄	—	104	1	no	—
138	C₂²⋊C₄	—	104	1	no	—
139	C₁₆	—	26	1	no	—
140	C₁₆	#6127	1	1	yes	characteristic
141	C₁₆	#6129	1	1	yes	characteristic
142	C₁₃	#13711	1	1	yes	characteristic, complemented, Sylow
143	C₂³	—	8	1	no	—
144	C₂³	—	13	1	no	—
145	D₄	—	8	1	no	—
146	D₄	—	8	1	no	—
147	D₄	—	208	2	no	—
148	C₂×C₄	—	8	1	no	—
149	C₂×C₄	—	13	1	no	—
150	C₂×C₄	—	26	1	no	—
151	C₂×C₄	—	26	1	no	—
152	C₂×C₄	—	104	1	no	—
153	C₂×C₄	—	104	1	no	—
154	C₂×C₄	—	208	2	no	—
155	C₂×C₄	D₈×D₁₃	1	1	yes	characteristic
156	C₈	—	26	1	no	—
157	C₈	#88137	1	1	yes	characteristic
158	C₈	#88169	1	1	yes	characteristic
159	C₂²	—	13	2	no	—
160	C₂²	—	16	1	no	—
161	C₂²	—	16	1	no	—
162	C₂²	—	16	1	no	—
163	C₂²	—	26	1	no	—
164	C₂²	—	26	1	no	—
165	C₂²	D₁₃×D₁₆	1	1	yes	characteristic
166	C₄	—	16	1	no	—
167	C₄	—	26	1	no	—
168	C₄	—	208	1	no	—
169	C₄	—	208	1	no	—
170	C₄	#11718435	1	1	yes	characteristic
171	C₄	#11718576	1	1	yes	characteristic
172	C₂	—	26	2	no	—
173	C₂	—	32	1	no	—
174	C₂	#13117015	1	1	yes	characteristic
175	C₂	D₁₃×D₃₂	1	1	yes	characteristic
176	C₂	#13117152	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₃×D₁₆
commutator, cosocle	C₂×C₁₃×C₁₆	C₂³
Frattini	C₂×C₁₆	C₂²×D₁₃
Fitting	C₁₃×#1415	C₂
socle	C₂²×C₁₃	C₂×D₁₆
prime radical	#13116919	C₂
hypercenter	#1415	D₁₃
hypocenter	C₁₃	#13711
LCS	G ▷ C₂×C₁₃×C₁₆ ▷ C₈×C₁₃ ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ #1415

Complements

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

N	H ≅ G/N	type
2. D₁₃×#366	C₂	semidirect
3. #13113036	C₂	semidirect
4. #13113035	C₂	semidirect
5. #13113014	C₂	semidirect
6. #13112973	C₂	semidirect
7. C₁₃×#1415	C₂	semidirect
60. #1415	D₁₃	semidirect
142. C₁₃	#13711	semidirect

Maximal subgroups

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

subgroup	index
#13116919	2
D₁₃×#366	2
#13113036	2
#13113035	2
#13113014	2
#13112973	2
C₁₃×#1415	2
#13711	13