Finite Group Databasebeta

← #16777933

Subgroups — #16777933

Order 3328.

194 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 36 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#13129933C211yesmaximal, characteristic
2#13129767C211yesmaximal, characteristic
3#13116380C211yesmaximal, characteristic
4C2×#88113—21no—
5C13×#384C411yescharacteristic
6C2×#88050—21no—
7C2×#88048—21no—
8#11718590C2211yescharacteristic
9#11718285—21no—
10#11718116C411yescharacteristic
11C22×Dic26D411yescharacteristic
12C2×#6122—41no—
13C2×C13×C4⋊C4—21no—
14C2×C13×C4⋊C4—41no—
15C2×C42×C13C2×C411yescharacteristic
16C2×C4⋊Dic13D411yescharacteristic
17C22×#1055—21no—
18C22⋊#1057—41no—
19#88113—22no—
20#88113—41no—
21#88071—41no—
22#88050—42no—
23#88048—42no—
24#7437—131nomaximal, Sylow
25C22×C4×C13—21no—
26C22×C4×C13—41no—
27C22×C4×C13C22⋊C411yescharacteristic
28C22×Dic13—21no—
29C22×Dic13—21no—
30C2×Dic26—21no—
31C2×Dic26—41no—
32C2×Dic26—41no—
33C2×Dic26SD1611yescharacteristic
34C2×Dic26Q1611yescharacteristic
35#6122—42no—
36#6122—81no—
37C2×#1057—81no—
38C2×#1057—81no—
39C13×C4⋊C4—41no—
40C13×C4⋊C4—41no—
41C13×C4⋊C4—82no—
42C42×C13—41no—
43C4⋊Dic13—41no—
44C2×#1055—22no—
45C2×#1055—41no—
46C2×#1055—41no—
47#2096—131no—
48#1394—131no—
49#1319—131no—
50C23×C13#9911yescharacteristic
51C2×C4×C13—21no—
52C2×C4×C13—21no—
53C2×C4×C13—22no—
54C2×C4×C13—41no—
55C2×C4×C13—41no—
56C2×C4×C13—82no—
57C2×C4×C13—81no—
58C2×C4×C13#10311yescharacteristic
59C2×C4×C13#10411yescharacteristic
60C2×Dic13—21no—
61C2×Dic13—21no—
62C2×Dic13—41no—
63C2×Dic13—41no—
64C2×Dic13—41no—
65C2×Dic13—81no—
66Dic26—41no—
67Dic26—41no—
68Dic26—81no—
69#1057—82no—
70#1057—161no—
71#1055—42no—
72C2×#106—261no—
73C2×#103—261no—
74C2×#101—261no—
75#391—131no—
76#384#26111yescharacteristic
77#336—131no—
78#324—261no—
79C22×C13—21no—
80C22×C13—21no—
81C22×C13#32811yescharacteristic
82C22×C13#35211yescharacteristic
83C22×C13#35311yescharacteristic
84C4×C13—21no—
85C4×C13—21no—
86C4×C13—42no—
87C4×C13—161no—
88Dic13—41no—
89Dic13—41no—
90Dic13—81no—
91C22×Q8—131no—
92C2×M16—521no—
93C22×C8—261no—
94C2×C4⋊C4—21no—
95C2×C4⋊C4—41no—
96C2×C4⋊C4—131no—
97C2×C42C2×#26111yescharacteristic
98#106—522no—
99#103—522no—
100#101—262no—
101#101—521no—
102C22⋊C8—521no—
103#95—521no—
104C2×C13—21no—
105C2×C13—21no—
106C2×C13#135211yescharacteristic
107C2×C13#140711yescharacteristic
108C2×C13#141011yescharacteristic
109C2×Q8—131no—
110C2×Q8—131no—
111C2×Q8—261no—
112C2×Q8—521no—
113C2×Q8—521no—
114C22×C4—21no—
115C22×C4—41no—
116C22×C4—261no—
117C22×C4—261no—
118C22×C4C22⋊#26111yescharacteristic
119M16—522no—
120M16—1041no—
121C2×C8—262no—
122C2×C8—521no—
123C2×C8—521no—
124C2×C8—1041no—
125C2×C8—1041no—
126C4⋊C4—41no—
127C4⋊C4—41no—
128C4⋊C4—82no—
129C4⋊C4—521no—
130C42—41no—
131C13#743711yescharacteristic, complemented, Sylow
132C23#8811911yescharacteristic
133Q8—521no—
134Q8—521no—
135Q8—1041no—
136C2×C4—21no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—41no—
140C2×C4—41no—
141C2×C4—82no—
142C2×C4—81no—
143C2×C4—261no—
144C2×C4—261no—
145C2×C4—521no—
146C2×C4—521no—
147C2×C4—521no—
148C2×C4—1041no—
149C2×C4#8811711yescharacteristic
150C2×C4#8811811yescharacteristic
151C8—522no—
152C8—1042no—
153C8—2081no—
154C22—21no—
155C22—21no—
156C22#1171828811yescharacteristic
157C22#1171829411yescharacteristic
158C22#1171829811yescharacteristic
159C4—21no—
160C4—21no—
161C4—42no—
162C4—161no—
163C4—521no—
164C4—521no—
165C4—1041no—
166C2—21no—
167C2—21no—
168C2#1312983311yescharacteristic
169C2#1312996511yescharacteristic
170C2#1312997111yescharacteristic
subgroupG/H
centerC22#11718294
commutatorC2×C42×C13C2×C4
FrattiniC2×C42C2×#261
FittingC13×#384C4
socleC22×C13#353
prime radicalC23×C13#99
cosocle#11718590C22
hypercenter#384#261
hypocenterC13#7437
LCSG ▷ C2×C42×C13 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
131. C13#7437semidirect

Maximal subgroups

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

subgroupindex
#131299332
#131297672
#131163802
#743713