Finite Group Databasebeta

← #16777415

Subgroups — #16777415

Order 3328.

376 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 66 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#13130697C212yesmaximal
2#13115630C211yesmaximal, characteristic
3C2×C4×D52C2211yescharacteristic
4#11719136—22no—
5C2×#88107—22no—
6C2×C4×C8×C13C411yescharacteristic, complemented
7C2×#88060—22no—
8C2×C4⋊#1055C411yescharacteristic, complemented
9#11718289C414yescomplemented
10C22×D52D411yescharacteristic
11C22×C4×D13D412yes—
12C2×C22⋊#261—24no—
13C2×C4⋊#261—42no—
14C22×C8×C13—21no—
15C2×C42×C13C2×C411yescharacteristic
16C2×#6103C2×C412yes—
17C2×C4⋊Dic13Q811yescharacteristic
18C22×#1055—21no—
19C4×D52—41no—
20C4×D52—41no—
21(C2×#261)⋊C4—42no—
22#88107—42no—
23#88107—42no—
24C4×C8×C13—41no—
25#88060—44no—
26C4⋊#1055—41no—
27#7237—131nomaximal, Sylow
28C23×D13C22⋊C412yes—
29C22×#261—44no—
30C22×C4×C13C4211yescharacteristic
31C22×C4×C13C22⋊C411yescharacteristic
32C22×C4×C13C4⋊C411yescharacteristic
33C22×Dic13C4⋊C412yes—
34C2×D52—41no—
35C2×D52—41no—
36C2×D52D811yescharacteristic
37C2×D52SD1612yes—
38C2×D52Q1611yescharacteristic
39C2×C4×D13—22no—
40C2×C4×D13—22no—
41C2×C4×D13—42no—
42C2×C4×D13—42no—
43C22⋊#261—44no—
44C22⋊#261—44no—
45C4⋊#261—82no—
46C4⋊#261—82no—
47C2×C8×C13—22no—
48C2×C8×C13—41no—
49C2×C8×C13—41no—
50C42×C13—21no—
51C42×C13—21no—
52#6103—42no—
53C4⋊Dic13—41no—
54C2×#1055—42no—
55C2×#1055—41no—
56#1954—131no—
57#1799—132no—
58C23×C13#9511yescharacteristic
59C22×D13—22no—
60C22×D13—22no—
61C22×D13—42no—
62C22×D13—42no—
63C22×D13#10212yes—
64C22×D13#10312yes—
65C2×#261—84no—
66C2×#261—84no—
67C2×#261—84no—
68C2×C4×C13—21no—
69C2×C4×C13—21no—
70C2×C4×C13—21no—
71C2×C4×C13—21no—
72C2×C4×C13—21no—
73C2×C4×C13—41no—
74C2×C4×C13#9911yescharacteristic
75C2×C4×C13#9911yescharacteristic
76C2×C4×C13#10611yescharacteristic
77C2×C4×C13#10711yescharacteristic
78C2×Dic13—22no—
79C2×Dic13—42no—
80D52—41no—
81D52—42no—
82D52—41no—
83C4×D13—42no—
84C4×D13—42no—
85C4×D13—82no—
86C8×C13—42no—
87#1055—81no—
88C2×C4×D4—131no—
89C2×C4⋊C8—131no—
90C2×#99—262no—
91C2×C22⋊C8—262no—
92C2×C4×C8#26111yescharacteristic, complemented
93#380—262no—
94#342—134no—
95C22×C13—21no—
96C22×C13—21no—
97C22×C13H(3,ℤ/4)11yescharacteristic
98C22×C13#34011yescharacteristic
99C22×C13#34211yescharacteristic
100C2×D13—22no—
101C2×D13—22no—
102C2×D13—42no—
103C2×D13—42no—
104C2×D13—42no—
105C2×D13—42no—
106C2×D13—82no—
107#261—164no—
108C4×C13—21no—
109C4×C13—21no—
110C4×C13—21no—
111C4×C13—41no—
112C4×C13#35311yescharacteristic
113C4×C13#35411yescharacteristic
114Dic13—42no—
115C22×D4—131no—
116C23×C4—132no—
117C22×C8—21no—
118C22×C8—261no—
119C4×D4—521no—
120C4×D4—521no—
121C2×C4⋊C4—131no—
122C2×C4⋊C4—522no—
123C2×C22⋊C4—132no—
124C2×C22⋊C4—264no—
125C2×C42C2×#26111yescharacteristic
126C4⋊C8—521no—
127#99—522no—
128#99—522no—
129C22⋊C8—524no—
130C4×C8—41no—
131#95—522no—
132C2×C13—21no—
133C2×C13—21no—
134C2×C13#128911yescharacteristic
135C2×C13#139111yescharacteristic
136C2×C13#139311yescharacteristic
137D13—42no—
138D13—42no—
139C24—132no—
140C2×D4—132no—
141C2×D4—131no—
142C2×D4—131no—
143C2×D4—521no—
144C2×D4—521no—
145C22×C4—132no—
146C22×C4—262no—
147C22×C4—262no—
148C22×C4—522no—
149C22×C4—522no—
150C22×C4—524no—
151C22×C4C4×#26111yescharacteristic
152C22×C4C4⋊#26111yescharacteristic
153C22×C4C22⋊#26111yescharacteristic
154C2×C8—22no—
155C2×C8—41no—
156C2×C8—41no—
157C2×C8—522no—
158C2×C8—521no—
159C4⋊C4—521no—
160C4⋊C4—1042no—
161C4⋊C4—1042no—
162C22⋊C4—522no—
163C22⋊C4—524no—
164C22⋊C4—524no—
165C42—21no—
166C42—21no—
167C13#723711yescharacteristic, complemented, Sylow
168C23—132no—
169C23—132no—
170C23—262no—
171C23—262no—
172C23—522no—
173C23—522no—
174C23(C2×#261)⋊C411yescharacteristic
175D4—522no—
176D4—521no—
177D4—521no—
178C2×C4—21no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—262no—
185C2×C4—522no—
186C2×C4—522no—
187C2×C4—522no—
188C2×C4—1042no—
189C2×C4—1044no—
190C2×C4—1044no—
191C2×C4—1044no—
192C2×C4#8810111yescharacteristic
193C2×C4#8810211yescharacteristic
194C2×C4#8810711yescharacteristic
195C2×C4#8811911yescharacteristic
196C8—42no—
197C8—1041no—
198C22—21no—
199C22—21no—
200C22—262no—
201C22—262no—
202C22—522no—
203C22—522no—
204C22—522no—
205C22—522no—
206C22—1042no—
207C22#1171826511yescharacteristic
208C22#1171826711yescharacteristic
209C22#1171828911yescharacteristic
210C4—21no—
211C4—21no—
212C4—21no—
213C4—41no—
214C4—522no—
215C4—2084no—
216C4#1171822511yescharacteristic
217C4#1171822611yescharacteristic
218C2—21no—
219C2—21no—
220C2—522no—
221C2—522no—
222C2#1312969911yescharacteristic
223C2#1312992411yescharacteristic
224C2#1312993011yescharacteristic
subgroupG/H
centerC22#11718289
commutatorC22×C4×C13C42
FrattiniC2×C42C2×#261
FittingC2×C4×C8×C13C4
socleC22×C13#342
prime radicalC22×D52D4
cosocleC2×C4×D52C22
hypercenterC2×C4×C8#261
hypocenterC13#7237
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×C8

Complements

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

NH ≅ G/Ntype
6. C2×C4×C8×C13C4semidirect
8. C2×C4⋊#1055C4semidirect
9. #11718289C4semidirect
92. C2×C4×C8#261semidirect
167. C13#7237semidirect

Maximal subgroups

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

subgroupindex
#131306972
#131156302
#723713