Finite Group Databasebeta

Subgroups — #13130952

Order 1664.

200 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 72 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	C₂×#88104	C₂	1	1	yes	maximal, characteristic
2	C₂×#88103	C₂	1	1	yes	maximal, characteristic
3	#11719053	C₂	1	1	yes	maximal, characteristic
4	C₄×#6118	C₂	1	1	yes	maximal, characteristic
5	D₁₃×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	#11718268	C₂	1	1	yes	maximal, characteristic
7	#11718268	C₂	1	1	yes	maximal, characteristic
8	C₂×#6118	C₂²	1	1	yes	characteristic
9	C₂×#6118	C₂²	1	1	yes	characteristic
10	C₂×#6118	C₂²	1	1	yes	characteristic
11	C₂×#6118	C₂²	1	1	yes	characteristic
12	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
13	C₂×C₈×D₁₃	C₂²	1	1	yes	characteristic
14	C₄²×D₁₃	C₂²	1	1	yes	characteristic
15	#88112	—	2	1	no	—
16	#88112	—	2	1	no	—
17	#88110	—	2	1	no	—
18	C₄×#1057	—	2	1	no	—
19	#88104	—	2	2	no	—
20	#88103	—	2	2	no	—
21	C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
22	#88054	C₄	1	1	yes	characteristic
23	#88054	C₄	1	1	yes	characteristic
24	C₄⋊#1055	C₄	1	1	yes	characteristic
25	C₂×C₄×D₁₃	Q₈	1	1	yes	characteristic
26	C₂×C₄×D₁₃	Q₈	1	1	yes	characteristic
27	C₂×C₄×D₁₃	C₂³	1	1	yes	characteristic
28	C₂×#1057	—	2	1	no	—
29	C₂×#1057	—	2	1	no	—
30	C₂×#1057	—	2	1	no	—
31	C₂×#1057	—	2	1	no	—
32	#6118	—	2	1	no	—
33	#6118	—	2	1	no	—
34	#6118	—	2	1	no	—
35	#6118	—	2	1	no	—
36	#6118	—	2	1	no	—
37	#6118	—	2	1	no	—
38	#6118	D₄	1	2	yes	—
39	#6118	Q₈	1	2	yes	—
40	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
43	C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
44	C₄×Dic₁₃	D₄	1	1	yes	characteristic
45	C₄×Dic₁₃	D₄	1	1	yes	characteristic
46	C₂×#1055	C₂×C₄	1	1	yes	characteristic
47	C₂×#1055	C₂×C₄	1	1	yes	characteristic
48	C₈×D₁₃	—	2	1	no	—
49	C₈×D₁₃	—	2	1	no	—
50	C₈×D₁₃	—	2	1	no	—
51	C₈×D₁₃	—	2	1	no	—
52	#1950	—	13	1	no	maximal, Sylow
53	C₂²×D₁₃	C₂×Q₈	1	1	yes	characteristic
54	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
55	C₂×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
56	C₂×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
57	C₂×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
58	C₂×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
59	C₂×Dic₁₃	C₂×D₄	1	1	yes	characteristic
60	C₄×D₁₃	—	2	2	no	—
61	C₄×D₁₃	—	4	1	no	—
62	C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
63	C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
64	C₄×D₁₃	#41	1	1	yes	characteristic
65	C₄×D₁₃	#41	1	1	yes	characteristic
66	#1057	—	2	2	no	—
67	#1057	—	2	2	no	—
68	#1057	—	4	1	no	—
69	#1057	—	4	1	no	—
70	C₈×C₁₃	—	2	1	no	—
71	C₈×C₁₃	—	2	1	no	—
72	#1055	—	2	1	no	—
73	#1055	—	2	1	no	—
74	C₂×#108	—	13	1	no	—
75	C₂×#108	—	13	1	no	—
76	#423	—	13	1	no	—
77	C₂×C₄⋊C₈	—	13	1	no	—
78	C₄×M₁₆	—	13	1	no	—
79	#341	—	13	1	no	—
80	#341	—	13	1	no	—
81	C₂²×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
82	C₂×D₁₃	—	2	1	no	—
83	C₂×D₁₃	—	2	1	no	—
84	C₂×D₁₃	#125	1	1	yes	characteristic
85	C₂×D₁₃	C₄⋊Q₈	1	1	yes	characteristic
86	C₄×C₁₃	—	2	1	no	—
87	C₄×C₁₃	—	2	1	no	—
88	C₄×C₁₃	C₄×D₄	1	1	yes	characteristic
89	C₄×C₁₃	C₄×Q₈	1	1	yes	characteristic
90	Dic₁₃	—	2	1	no	—
91	Dic₁₃	#108	1	2	yes	complemented
92	Dic₁₃	#121	1	1	yes	characteristic
93	Dic₁₃	C₂²⋊Q₈	1	1	yes	characteristic
94	C₂×M₁₆	—	13	1	no	—
95	C₂×M₁₆	—	13	1	no	—
96	C₂×M₁₆	—	13	1	no	—
97	C₂×M₁₆	—	13	1	no	—
98	C₂²×C₈	—	13	1	no	—
99	C₂²×C₈	—	13	1	no	—
100	C₂×C₄²	—	13	1	no	—
101	#108	—	26	2	no	—
102	#108	—	26	2	no	—
103	C₄⋊C₈	—	13	1	no	—
104	C₄⋊C₈	—	13	1	no	—
105	C₄⋊C₈	—	13	1	no	—
106	C₄⋊C₈	—	26	1	no	—
107	C₄⋊C₈	—	26	1	no	—
108	C₄⋊C₈	#261	1	1	yes	characteristic
109	#97	—	26	1	no	—
110	C₄×C₈	—	26	1	no	—
111	C₂×C₁₃	#389	1	1	yes	characteristic
112	C₂×C₁₃	C₂×#108	1	1	yes	characteristic
113	C₂×C₁₃	#430	1	1	yes	characteristic
114	D₁₃	—	2	1	no	—
115	D₁₃	—	2	1	no	—
116	C₂²×C₄	—	13	1	no	—
117	C₂²×C₄	—	13	1	no	—
118	C₂²×C₄	—	13	1	no	—
119	M₁₆	—	13	2	no	—
120	M₁₆	—	13	2	no	—
121	M₁₆	—	26	1	no	—
122	M₁₆	—	26	1	no	—
123	M₁₆	—	26	1	no	—
124	M₁₆	—	26	1	no	—
125	M₁₆	—	26	1	no	—
126	M₁₆	—	26	1	no	—
127	C₂×C₈	—	13	1	no	—
128	C₂×C₈	—	13	1	no	—
129	C₂×C₈	—	26	1	no	—
130	C₂×C₈	—	26	1	no	—
131	C₂×C₈	—	26	1	no	—
132	C₂×C₈	—	26	1	no	—
133	C₂×C₈	—	26	1	no	—
134	C₂×C₈	—	26	1	no	—
135	C₂×C₈	—	26	1	no	—
136	C₂×C₈	—	26	1	no	—
137	C₂×C₈	C₂×#261	1	1	yes	characteristic
138	C₂×C₈	C₂×#261	1	1	yes	characteristic
139	C₄²	—	13	1	no	—
140	C₄²	—	13	1	no	—
141	C₄²	—	13	1	no	—
142	C₄²	C₂×#261	1	1	yes	characteristic
143	C₁₃	#1950	1	1	yes	characteristic, complemented, Sylow
144	C₂³	—	13	1	no	—
145	C₂×C₄	—	13	1	no	—
146	C₂×C₄	—	13	1	no	—
147	C₂×C₄	—	13	1	no	—
148	C₂×C₄	—	13	1	no	—
149	C₂×C₄	—	13	1	no	—
150	C₂×C₄	—	13	1	no	—
151	C₂×C₄	—	13	1	no	—
152	C₂×C₄	—	26	2	no	—
153	C₂×C₄	—	52	1	no	—
154	C₂×C₄	C₄⋊#261	1	1	yes	characteristic
155	C₂×C₄	C₄⋊#261	1	1	yes	characteristic
156	C₂×C₄	C₂²×#261	1	1	yes	characteristic
157	C₈	—	2	1	no	—
158	C₈	—	2	1	no	—
159	C₈	—	26	2	no	—
160	C₈	—	26	2	no	—
161	C₈	—	26	1	no	—
162	C₈	—	26	1	no	—
163	C₈	—	52	1	no	—
164	C₈	—	52	1	no	—
165	C₂²	—	13	1	no	—
166	C₂²	—	13	1	no	—
167	C₂²	—	26	1	no	—
168	C₂²	—	26	1	no	—
169	C₂²	C₂×C₄⋊#261	1	1	yes	characteristic
170	C₄	—	2	1	no	—
171	C₄	—	2	1	no	—
172	C₄	—	13	1	no	—
173	C₄	—	13	1	no	—
174	C₄	—	13	2	no	—
175	C₄	—	26	1	no	—
176	C₄	D₄×#261	1	1	yes	characteristic
177	C₄	Q₈×#261	1	1	yes	characteristic
178	C₂	—	26	1	no	—
179	C₂	—	26	1	no	—
180	C₂	#11719083	1	1	yes	characteristic
181	C₂	D₁₃⋊#108	1	1	yes	characteristic
182	C₂	#11719100	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊#261
commutator	C₂×C₄×C₁₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#261
Fitting	C₁₃×C₄⋊C₈	C₄
socle	C₂²×C₁₃	C₂×C₄⋊C₄
prime radical	C₂²×D₁₃	C₂×Q₈
cosocle	C₂×C₄×D₁₃	C₂³
hypercenter	C₄⋊C₈	#261
hypocenter	C₁₃	#1950
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄⋊C₈

Complements

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

N	H ≅ G/N	type
91. Dic₁₃	#108	semidirect
143. C₁₃	#1950	semidirect

Maximal subgroups

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

subgroup	index
C₂×#88104	2
C₂×#88103	2
#11719053	2
C₄×#6118	2
D₁₃×C₄⋊C₈	2
#11718268	2
#1950	13