Finite Group Databasebeta

← #15779201

Subgroups — #15779201

Order 3328.

334 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 79 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#13123483C211yesmaximal, characteristic
2#13114937C212yesmaximal
3#13112964C212yesmaximal
4#13112959C211yesmaximal, characteristic
5C13×#1391C211yesmaximal, characteristic
6#41×Dic13C2211yescharacteristic
7C13×#410C2212yes—
8C13×#408C2211yescharacteristic
9#11718898C2212yes—
10#11718895C2211yescharacteristic
11#11718780C411yescharacteristic, complemented
12M16×Dic13C411yescharacteristic, complemented
13#11718763C411yescharacteristic, complemented
14C2×#88055C411yescharacteristic, complemented
15#11718381—22no—
16#11718380—22no—
17#11718124—22no—
18#11718123—22no—
19C2×C13×#41C2311yescharacteristic
20C2×C13×M16C2×C411yescharacteristic
21C22×C8×C13C2×C411yescharacteristic
22C13×#117—22no—
23Q8×Dic13—21no—
24D4×Dic13—22no—
25D4×Dic13—21no—
26#88180C2×C411yescharacteristic
27#88180D412yes—
28C2×C4×Dic13C2×C411yescharacteristic
29C2×C4×Dic13D412yes—
30C2×#6099—22no—
31C2×#6099C2×C411yescharacteristic
32C22×#1055C2×C411yescharacteristic
33C13×#99—22no—
34C13×#99—22no—
35C13×C22⋊C8—22no—
36#88076—22no—
37#88073—22no—
38C22⋊#1055—22no—
39#88055—21no—
40#88055—21no—
41#88055—21no—
42#88054—22no—
43#88054—22no—
44C8×Dic13—21no—
45#12865—131nomaximal, Sylow
46C13×#41—41no—
47C13×#41—41no—
48C2×Q8×C13#4111yescharacteristic
49C2×D4×C13#4112yes—
50C2×D4×C13#4111yescharacteristic
51C22×C4×C13C22×C411yescharacteristic
52C22×C4×C13C2×D412yes—
53C22×Dic13—21no—
54C22×Dic13—22no—
55C13×M16—41no—
56C2×C8×C13—21no—
57C2×C8×C13—21no—
58C2×C8×C13—41no—
59C13×C4⋊C4—42no—
60C13×C22⋊C4—42no—
61C42×C13—42no—
62C22⋊Dic13—21no—
63C22⋊Dic13—22no—
64C4⋊Dic13—21no—
65C4⋊Dic13—22no—
66C4×Dic13—21no—
67C4×Dic13—22no—
68C4×Dic13C22⋊C411yescharacteristic
69C4×Dic13C22⋊C411yescharacteristic
70C4×Dic13C22⋊C412yes—
71#6099—41no—
72#6099—42no—
73#6099—42no—
74C2×#1055—21no—
75C2×#1055—21no—
76C2×#1055—41no—
77C2×#1055—42no—
78#2923—131no—
79#1827—132no—
80#1395—132no—
81#1392—131no—
82#1391D1311yescharacteristic
83C23×C13#11711yescharacteristic
84C23×C13#12312yes—
85Q8×C13—41no—
86D4×C13—42no—
87D4×C13—41no—
88C2×C4×C13—22no—
89C2×C4×C13—21no—
90C2×C4×C13—22no—
91C2×C4×C13—21no—
92C2×C4×C13—82no—
93C2×C4×C13C2×C22⋊C411yescharacteristic
94C2×C4×C13#11711yescharacteristic
95C2×C4×C13#12312yes—
96C2×Dic13—21no—
97C2×Dic13—21no—
98C2×Dic13—22no—
99C2×Dic13—81no—
100C2×Dic13—82no—
101C8×C13—41no—
102C8×C13—41no—
103#1055—41no—
104#1055—41no—
105#1055—82no—
106C4×#41—131no—
107#433—262no—
108#432—262no—
109#424—131no—
110#424—131no—
111#413—132no—
112#410C2×D1312yes—
113#408—131no—
114#408C2×D1311yescharacteristic
115C4×M16—131no—
116C2×#97—131no—
117#339—262no—
118H(3,ℤ/4)—262no—
119C22×C13—22no—
120C22×C13—21no—
121C22×C13—41no—
122C22×C13—42no—
123C22×C13#38111yescharacteristic
124C4×C13—22no—
125C4×C13—21no—
126C4×C13—162no—
127C4×C13#41011yescharacteristic
128C4×C13#41011yescharacteristic
129Dic13—41no—
130Dic13—42no—
131Dic13—41no—
132C2×#41C22×D1311yescharacteristic
133C2×M16—131no—
134C2×M16—262no—
135C2×M16C4×D1311yescharacteristic
136C22×C8—131no—
137C22×C8C4×D1311yescharacteristic
138C4×Q8—261no—
139C4×D4—262no—
140C4×D4—261no—
141#117—22no—
142#117—131no—
143#117—132no—
144C2×C42—131no—
145C2×C42—132no—
146C4⋊C8—262no—
147C4⋊C8—262no—
148#101—262no—
149#100—262no—
150#99—22no—
151#99—22no—
152C22⋊C8—22no—
153C22⋊C8—262no—
154#97—261no—
155#97—261no—
156#97—261no—
157C4×C8—261no—
158C2×C13—21no—
159C2×C13—42no—
160C2×C13—41no—
161C2×C13#182011yescharacteristic
162#41—41no—
163#41—41no—
164C2×Q8#613111yescharacteristic
165C2×D4#612712yes—
166C2×D4#612911yescharacteristic
167C22×C4—261no—
168C22×C4—262no—
169C22×C4C2×C4×D1311yescharacteristic
170C22×C4D4×D1312yes—
171M16—41no—
172M16—521no—
173M16—522no—
174M16—522no—
175C2×C8—21no—
176C2×C8—21no—
177C2×C8—41no—
178C2×C8—261no—
179C2×C8—261no—
180C2×C8—521no—
181C2×C8—522no—
182C4⋊C4—42no—
183C4⋊C4—261no—
184C4⋊C4—262no—
185C22⋊C4—42no—
186C22⋊C4—261no—
187C22⋊C4—262no—
188C42—42no—
189C42—131no—
190C42—131no—
191C42—132no—
192C42—261no—
193C42—262no—
194C13#1286511yescharacteristic, complemented, Sylow
195C23#8812611yescharacteristic
196C23#8813712yes—
197Q8—41no—
198D4—42no—
199D4—41no—
200C2×C4—22no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—82no—
205C2×C4—261no—
206C2×C4—261no—
207C2×C4—262no—
208C2×C4—1041no—
209C2×C4—1042no—
210C2×C4C22⋊C4×D1311yescharacteristic
211C2×C4#8814611yescharacteristic
212C2×C4#8814812yes—
213C8—41no—
214C8—41no—
215C8—521no—
216C8—521no—
217C8—1042no—
218C22—22no—
219C22—21no—
220C22—41no—
221C22—42no—
222C22#1171832511yescharacteristic
223C4—22no—
224C4—21no—
225C4—162no—
226C4—521no—
227C4—522no—
228C4—521no—
229C4#1171840111yescharacteristic
230C4#1171840111yescharacteristic
231C2—21no—
232C2—42no—
233C2—41no—
234C2#1311491211yescharacteristic
subgroupG/H
centerC4#11718401
commutatorC22×C4×C13C22×C4
FrattiniC2×#41C22×D13
FittingC13×#1391C2
socleC2×C13#1820
prime radical, cosocleC2×C13×#41C23
hypercenter#1391D13
hypocenterC13#12865
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #1391

Complements

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

NH ≅ G/Ntype
11. #11718780C4semidirect
12. M16×Dic13C4semidirect
13. #11718763C4semidirect
14. C2×#88055C4semidirect
194. C13#12865semidirect

Maximal subgroups

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

subgroupindex
#131234832
#131149372
#131129642
#131129592
C13×#13912
#1286513