Finite Group Databasebeta

← #16790175

Subgroups — #16790175

Order 3328.

342 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 342 conjugacy classes of subgroups — too many to draw. Only its 68 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#13130745C212yesmaximal
2#13129937C212yesmaximal
3#13129928C211yesmaximal, characteristic
4#13129925C211yesmaximal, characteristic
5#13123481C211yesmaximal, characteristic
6C4×#6127C2211yescharacteristic
7#11719132C2212yes—
8#11719116C2212yes—
9C4×C13×M16C411yescharacteristic, complemented
10#11718790C2211yescharacteristic
11#11718790C2211yescharacteristic
12#11718780C411yescharacteristic, complemented
13#11718780C411yescharacteristic, complemented
14C2×C4×#1055C411yescharacteristic, complemented
15#11718370—22no—
16#11718346—22no—
17#11718235—22no—
18#11718234—22no—
19C2×#6127C2311yescharacteristic
20#88237—22no—
21D13⋊M16—22no—
22C2×C13×M16C2×C411yescharacteristic
23C2×C13×M16C2×C411yescharacteristic
24C2×C42×C13C2×C411yescharacteristic
25C4×C22⋊D13—22no—
26#88180C2×C411yescharacteristic
27C22×#1055C2×C411yescharacteristic
28C22×#1055C2×C411yescharacteristic
29C4×D52—21no—
30#88126D412yes—
31C42×D13D412yes—
32C4×Dic26—21no—
33#88121—22no—
34#88119—22no—
35#88113—22no—
36#88107—22no—
37C13×#97—21no—
38C4×C8×C13—21no—
39#88060—22no—
40#88060—22no—
41#88054—22no—
42#88054—22no—
43C4×#1055—21no—
44C4×#1055—21no—
45#12864—131nomaximal, Sylow
46C22×C4×C13—21no—
47C22×C4×C13C22×C411yescharacteristic
48C2×C22⋊D13#4112yes—
49#6127—41no—
50#6127—41no—
51C2×D52#4111yescharacteristic
52C2×C4×D13—22no—
53C2×C4×D13C2×D412yes—
54C2×Dic26#4111yescharacteristic
55C22⋊#261—42no—
56#6122—42no—
57C4⋊#261—42no—
58C4×#261—42no—
59#6118—42no—
60D13⋊C8—42no—
61C13×M16—41no—
62C13×M16—41no—
63C2×C8×C13—21no—
64C2×C8×C13—21no—
65C42×C13—21no—
66C42×C13C22⋊C411yescharacteristic
67C42×C13C22⋊C411yescharacteristic
68C22⋊Dic13—21no—
69#6103—22no—
70C4⋊Dic13—21no—
71#6101—22no—
72C4×Dic13—22no—
73C4×Dic13C22⋊C412yes—
74C2×#1055—21no—
75C2×#1055—21no—
76C2×#1055—41no—
77C2×#1055—41no—
78#2922—131no—
79#1827—132no—
80#1395—132no—
81#1392—131no—
82#1391—131no—
83C23×C13#11711yescharacteristic
84C22×D13#12312yes—
85C2×#261—82no—
86C2×C4×C13—21no—
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—42no—
91C2×C4×C13C2×C22⋊C411yescharacteristic
92C2×C4×C13#11711yescharacteristic
93C22⋊D13—42no—
94C2×Dic13—22no—
95C2×Dic13#12312yes—
96D52—41no—
97C4×D13—22no—
98C4×D13—22no—
99C4×D13—44no—
100Dic26—41no—
101#1057—82no—
102C8×C13—41no—
103C8×C13—41no—
104#1055—41no—
105#1055—41no—
106C4×#41—131no—
107#433—262no—
108#431—262no—
109#424—131no—
110#424—131no—
111#413—132no—
112#410—132no—
113#408—131no—
114#408—131no—
115C4×M16#26111yescharacteristic, complemented
116C2×C4×C8—131no—
117#339—262no—
118H(3,ℤ/4)—262no—
119C22×C13—21no—
120C22×C13—41no—
121C22×C13#38111yescharacteristic
122C2×D13—22no—
123C2×D13—42no—
124#261—162no—
125C4×C13—22no—
126C4×C13—21no—
127C4×C13—41no—
128C4×C13#41011yescharacteristic
129C4×C13#41011yescharacteristic
130Dic13—22no—
131Dic13—42no—
132C2×#41—131no—
133C2×M16—262no—
134C2×M16C2×#26111yescharacteristic
135C2×M16C2×#26111yescharacteristic
136C22×C8—131no—
137C22×C8—131no—
138C4×Q8—261no—
139C4×D4—261no—
140C4×D4—262no—
141#117—131no—
142#117—132no—
143#117—262no—
144C2×C42—132no—
145C2×C42C2×#26111yescharacteristic
146C4⋊C8—262no—
147C4⋊C8—262no—
148#101—262no—
149#100—262no—
150#99—262no—
151#99—262no—
152C22⋊C8—262no—
153C22⋊C8—262no—
154#97—21no—
155C4×C8—21no—
156C4×C8—261no—
157C4×C8—261no—
158C2×C13—21no—
159C2×C13—41no—
160C2×C13#182011yescharacteristic
161D13—42no—
162#41—521no—
163#41—521no—
164C2×Q8—131no—
165C2×D4—132no—
166C2×D4—131no—
167C22×C4—21no—
168C22×C4—132no—
169C22×C4—262no—
170C22×C4C22×#26111yescharacteristic
171M16—41no—
172M16—41no—
173M16—522no—
174M16—522no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—261no—
178C2×C8—261no—
179C2×C8—521no—
180C2×C8—521no—
181C2×C8—522no—
182C4⋊C4—262no—
183C4⋊C4—261no—
184C4⋊C4—522no—
185C22⋊C4—262no—
186C22⋊C4—261no—
187C22⋊C4—522no—
188C42—21no—
189C42—132no—
190C42—262no—
191C42—522no—
192C42C22⋊#26111yescharacteristic
193C42C22⋊#26111yescharacteristic
194C13#1286411yescharacteristic, complemented, Sylow
195C23—132no—
196C23#8823711yescharacteristic
197Q8—521no—
198D4—521no—
199D4—522no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—42no—
205C2×C4—132no—
206C2×C4—262no—
207C2×C4—262no—
208C2×C4—262no—
209C2×C4—524no—
210C2×C4—1042no—
211C2×C4#8823711yescharacteristic
212C2×C4C2×C22⋊#26111yescharacteristic
213C8—41no—
214C8—41no—
215C8—521no—
216C8—521no—
217C8—1042no—
218C22—21no—
219C22—41no—
220C22—262no—
221C22—522no—
222C22#1171913511yescharacteristic
223C4—22no—
224C4—21no—
225C4—41no—
226C4—262no—
227C4—522no—
228C4—2082no—
229C4#1171911611yescharacteristic
230C4#1171911611yescharacteristic
231C2—21no—
232C2—41no—
233C2—522no—
234C2#1313073311yescharacteristic
subgroupG/H
centerC4#11719116
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC4×C13×M16C4
socleC2×C13#1820
prime radical, cosocleC2×#6127C23
hypercenterC4×M16#261
hypocenterC13#12864
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C42 ◁ C2×C42 ◁ C4×M16

Complements

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

NH ≅ G/Ntype
9. C4×C13×M16C4semidirect
12. #11718780C4semidirect
13. #11718780C4semidirect
14. C2×C4×#1055C4semidirect
115. C4×M16#261semidirect
194. C13#12864semidirect

Maximal subgroups

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

subgroupindex
#131307452
#131299372
#131299282
#131299252
#131234812
#1286413