Finite Group Databasebeta

← #13114086

Subgroups — #13114086

Order 1664.

234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.

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

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11719432C211yesmaximal, characteristic
2#11718739C211yesmaximal, characteristic, complemented
3#11718510C211yesmaximal, characteristic, complemented
4#11718507C211yesmaximal, characteristic
5C13×#332C211yesmaximal, characteristic, complemented
6#11718076C211yesmaximal, characteristic, complemented
7#11718075C211yesmaximal, characteristic
8C2×Q8×D13—21no—
9C13×C4⋊Q8C2211yescharacteristic
10#88200—21no—
11C2×Dic52—21no—
12#88150—22no—
13#88147—21no—
14#88142—21no—
15C4×D52C2211yescharacteristic
16#88123C2211yescharacteristic
17C4×Dic26C2211yescharacteristic
18C13×C4⋊C8C2211yescharacteristic
19C13×C4⋊C8C2211yescharacteristic
20#88061—21no—
21#88058—21no—
22#88056—21no—
23#88047—22no—
24C4×#1055C2211yescharacteristic
25C2×Q8×C13—21no—
26Q8×D13—42no—
27Q8×D13—42no—
28C2×D52D411yescharacteristic
29C2×C4×D13—22no—
30C2×C4×D13—21no—
31C2×Dic26—22no—
32C2×Dic26—21no—
33C2×Dic26D411yescharacteristic
34C2×C8×C13—21no—
35C2×C8×C13—21no—
36C13×C4⋊C4—21no—
37C13×C4⋊C4D412yes—
38C42×C13C2311yescharacteristic
39#6103—22no—
40#6103—21no—
41C4⋊Dic13—21no—
42C4⋊Dic13—21no—
43C4⋊Dic13D411yescharacteristic
44C4⋊Dic13D411yescharacteristic
45#6101—22no—
46#6101—21no—
47C4×Dic13—21no—
48C2×#1055—21no—
49Dic52—42no—
50#1649—131nomaximal, Sylow
51C22×D13—21no—
52Q8×C13—41no—
53Q8×C13—41no—
54C2×C4×C13—22no—
55C2×C4×C13C2×D411yescharacteristic
56C2×C4×C13C2×D411yescharacteristic
57C2×C4×C13C2×D411yescharacteristic
58C2×Dic13—21no—
59C2×Dic13—21no—
60C2×Dic13—21no—
61C2×Dic13—41no—
62D52—21no—
63D52Q1612yescomplemented
64C4×D13—44no—
65C4×D13—41no—
66C4×D13—41no—
67Dic26—21no—
68Dic26—44no—
69Dic26—41no—
70Dic26—41no—
71Dic26D812yes—
72C8×C13—41no—
73C8×C13—41no—
74#1055—22no—
75D4×Q8—131no—
76#500—131no—
77#474—131no—
78#462—131no—
79#332D1311yescharacteristic, complemented
80Q8⋊C8—131no—
81D4⋊C8—131no—
82C22×C13#12011yescharacteristic
83C2×D13—22no—
84C2×D13—41no—
85C2×D13—41no—
86C4×C13—21no—
87C4×C13—42no—
88C4×C13C2×D811yescharacteristic
89C4×C13C2×Q1611yescharacteristic
90C4×C13AGL(1,ℤ/8)11yescharacteristic
91C4×C13#13711yescharacteristic
92Dic13—22no—
93Dic13—41no—
94Dic13—41no—
95Dic13—81no—
96C22×Q8—261no—
97C2×Q16—261no—
98C4⋊Q8—131no—
99C4⋊Q8—261no—
100C4⋊Q8C2×D1311yescharacteristic
101C22⋊Q8—261no—
102C22⋊Q8—262no—
103C4×Q8—131no—
104C4×D4—131no—
105C4×D4—261no—
106#107—261no—
107#107—262no—
108C4⋊C8C2×D1311yescharacteristic
109C4⋊C8C2×D1311yescharacteristic
110#103—261no—
111#102—261no—
112C4×C8—131no—
113C2×C13#44711yescharacteristic
114C2×C13#45111yescharacteristic
115C2×C13#45611yescharacteristic
116D13—42no—
117C2×Q8—21no—
118C2×Q8—131no—
119C2×Q8—262no—
120C2×Q8—261no—
121C2×Q8—522no—
122C2×Q8—522no—
123C2×D4—131no—
124C22×C4—262no—
125C22×C4—261no—
126Q16—522no—
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—261no—
130C4⋊C4—21no—
131C4⋊C4—131no—
132C4⋊C4—131no—
133C4⋊C4—262no—
134C4⋊C4—261no—
135C4⋊C4—261no—
136C4⋊C4—261no—
137C4⋊C4D5212yes—
138C22⋊C4—262no—
139C22⋊C4—261no—
140C42—261no—
141C42C22×D1311yescharacteristic
142C13#164911yescharacteristic, complemented, Sylow
143C23—261no—
144Q8—41no—
145Q8—41no—
146Q8—132no—
147Q8—261no—
148Q8—524no—
149Q8—521no—
150Q8—521no—
151D4—132no—
152D4—261no—
153C2×C4—22no—
154C2×C4—261no—
155C2×C4—261no—
156C2×C4—261no—
157C2×C4—524no—
158C2×C4—521no—
159C2×C4—521no—
160C2×C4—521no—
161C2×C4C2×D5211yescharacteristic
162C2×C4D4×D1311yescharacteristic
163C2×C4D4×D1311yescharacteristic
164C8—41no—
165C8—41no—
166C8—262no—
167C22—262no—
168C22—521no—
169C22—521no—
170C22#8813611yescharacteristic
171C4—21no—
172C4—42no—
173C4—262no—
174C4—521no—
175C4—521no—
176C4—1041no—
177C4D8×D1311yescharacteristic
178C4#8816811yescharacteristic
179C4#8816911yescharacteristic
180C4Q16×D1311yescharacteristic
181C2—522no—
182C2#1171841311yescharacteristic
183C2#1171843411yescharacteristic
184C2#1171846911yescharacteristic
subgroupG/H
centerC22#88136
commutator, cosocleC42×C13C23
FrattiniC42C22×D13
FittingC13×#332C2
socleC22×C13#120
prime radicalC2×D52D4
hypercenter#332D13
hypocenterC13#1649
LCSG ▷ C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #11718739C2semidirect
3. #11718510C2semidirect
5. C13×#332C2semidirect
6. #11718076C2semidirect
63. D52Q16semidirect
79. #332D13semidirect
142. C13#1649semidirect

Maximal subgroups

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

subgroupindex
#117194322
#117187392
#117185102
#117185072
C13×#3322
#117180762
#117180752
#164913