Finite Group Databasebeta

← #15772425

Subgroups — #15772425

Order 3328.

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

normal subgroups only

This group has 270 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#13123768C211yesmaximal, characteristic
2#13116652C211yesmaximal, characteristic
3#13112788C212yesmaximal
4#13112786C212yesmaximal
5C13×#2166C211yesmaximal, characteristic
6#11719222C411yescharacteristic
7C13×#405C2211yescharacteristic
8#11718780C2211yescharacteristic
9#11718779C2211yescharacteristic
10#11718762C411yescharacteristic
11C2×C8×Dic13C411yescharacteristic
12#11718660C411yescharacteristic
13#11718362—21no—
14#11718362—21no—
15C8×Dic26—21no—
16C8×Dic26—21no—
17C13×#364—21no—
18C13×#349C2212yes—
19C13×#347—21no—
20#11718145C2212yes—
21#11718058—21no—
22#11718055—21no—
23C2×C13×M16C2311yescharacteristic
24C22×C8×C13C2×C411yescharacteristic
25C13×#117C2×C411yescharacteristic
26#88180C2×C411yescharacteristic
27C2×C4×Dic13C2×C411yescharacteristic
28C2×#6099C2×C411yescharacteristic
29C22×#1055C2×C411yescharacteristic
30#88144—21no—
31#88142—21no—
32#88132—21no—
33#88132—21no—
34C4×Dic26—21no—
35C4×Dic26—21no—
36C13×M32—22no—
37C13×#97D411yescharacteristic
38C13×#97D411yescharacteristic
39C4×C8×C13D411yescharacteristic
40C4×C8×C13D411yescharacteristic
41#88055—21no—
42#88054—21no—
43#88054—21no—
44#88054—21no—
45#88054—21no—
46C8×Dic13—21no—
47C8×Dic13—21no—
48C8×Dic13—21no—
49#88052—22no—
50C4⋊#1055—21no—
51C4⋊#1055—21no—
52#11539—131nomaximal, Sylow
53C22×C4×C13C22×C411yescharacteristic
54C22×Dic13—21no—
55C2×Dic26—21no—
56C2×Dic26—21no—
57C13×M16—41no—
58C2×C8×C13—22no—
59C2×C8×C13C22⋊C411yescharacteristic
60C2×C8×C13C22⋊C411yescharacteristic
61C2×C8×C13C2×D411yescharacteristic
62C2×C8×C13C2×D411yescharacteristic
63C13×C4⋊C4—21no—
64C13×C22⋊C4—21no—
65C42×C13C22⋊C411yescharacteristic
66C42×C13C22⋊C411yescharacteristic
67C22⋊Dic13M1611yescharacteristic
68C22⋊Dic13M1611yescharacteristic
69C4⋊Dic13—21no—
70C4⋊Dic13—21no—
71C4⋊Dic13—21no—
72#6101—21no—
73#6101—21no—
74#6101—21no—
75#6101—21no—
76C4×Dic13—21no—
77C4×Dic13—21no—
78C4×Dic13M1611yescharacteristic
79C4×Dic13M1611yescharacteristic
80#6099—41no—
81C2×#1055—21no—
82C2×#1055—21no—
83C2×#1055—41no—
84C13×C16—42no—
85#6090—42no—
86#2960—131no—
87#2166—131no—
88#2166D1311yescharacteristic
89#1328—132no—
90#1327—132no—
91C23×C13C2×M1611yescharacteristic
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—21no—
96C2×C4×C13C2×C22⋊C411yescharacteristic
97C2×C4×C13C2×M1611yescharacteristic
98C2×Dic13—21no—
99C2×Dic13—21no—
100C2×Dic13—21no—
101C2×Dic13—21no—
102C2×Dic13—42no—
103Dic26—42no—
104Dic26—42no—
105C8×C13—21no—
106C8×C13—21no—
107C8×C13—21no—
108C8×C13#10112yes—
109#1055—41no—
110#1055—41no—
111#533—131no—
112#446—261no—
113#446—261no—
114C8×Q8—261no—
115C8×Q8—261no—
116#424—131no—
117#424—131no—
118#423—131no—
119#405—131no—
120#405C2×D1311yescharacteristic
121C2×C4×C8—131no—
122#364—21no—
123#364—261no—
124#349—132no—
125#349C2×D1312yes—
126#347—21no—
127#347—261no—
128C22×C13—21no—
129C22×C13—41no—
130C22×C13#40711yescharacteristic
131C4×C13—21no—
132C4×C13—41no—
133C4×C13—41no—
134C4×C13#41011yescharacteristic
135C4×C13C2×#10111yescharacteristic
136Dic13—22no—
137Dic13—41no—
138Dic13—41no—
139Dic13—41no—
140C2×M16—131no—
141C2×M16C22×D1311yescharacteristic
142C22×C8—131no—
143C22×C8C4×D1311yescharacteristic
144C4⋊Q8—261no—
145#125—261no—
146C22⋊Q8—261no—
147C22⋊Q8—261no—
148C4×Q8—261no—
149C4×Q8—261no—
150#117—131no—
151#117C4×D1311yescharacteristic
152C2×C42—131no—
153M32—22no—
154M32—262no—
155C4⋊C8—261no—
156C4⋊C8—261no—
157C4⋊C8—261no—
158C4⋊C8—261no—
159C4⋊C8—261no—
160C4⋊C8—261no—
161#97—261no—
162#97D5211yescharacteristic
163#97C22⋊D1311yescharacteristic
164C4×C8—261no—
165C4×C8—261no—
166C4×C8—261no—
167C4×C8D5211yescharacteristic
168C4×C8C22⋊D1311yescharacteristic
169C2×C13—21no—
170C2×C13—41no—
171C2×C13#146711yescharacteristic
172C2×Q8—261no—
173C2×Q8—261no—
174C22×C4—261no—
175C22×C4C2×C4×D1311yescharacteristic
176M16—41no—
177M16—521no—
178C2×C8—22no—
179C2×C8—261no—
180C2×C8—261no—
181C2×C8—521no—
182C2×C8#610311yescharacteristic
183C2×C8#610311yescharacteristic
184C2×C8C2×D5211yescharacteristic
185C2×C8C2×C22⋊D1311yescharacteristic
186C4⋊C4—21no—
187C4⋊C4—261no—
188C4⋊C4—261no—
189C4⋊C4—261no—
190C4⋊C4—261no—
191C4⋊C4—261no—
192C4⋊C4—261no—
193C4⋊C4—261no—
194C22⋊C4—21no—
195C22⋊C4—131no—
196C22⋊C4—131no—
197C42—131no—
198C42—131no—
199C42—261no—
200C42—261no—
201C42#610311yescharacteristic
202C42#610311yescharacteristic
203C16—42no—
204C16—522no—
205C13#1153911yescharacteristic, complemented, Sylow
206C23M16×D1311yescharacteristic
207Q8—522no—
208Q8—522no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—261no—
214C2×C4—261no—
215C2×C4—261no—
216C2×C4—261no—
217C2×C4—522no—
218C2×C4M16×D1311yescharacteristic
219C2×C4C2×#610311yescharacteristic
220C8—21no—
221C8—21no—
222C8—21no—
223C8—521no—
224C8—521no—
225C8#8806412yes—
226C22—21no—
227C22—41no—
228C22#1171878711yescharacteristic
229C4—21no—
230C4—41no—
231C4—41no—
232C4—262no—
233C4—521no—
234C4—521no—
235C4—521no—
236C4#1171866711yescharacteristic
237C4C2×#8806411yescharacteristic
238C2—21no—
239C2—41no—
240C2#1311317911yescharacteristic
subgroupG/H
centerC4#11718667
commutatorC22×C4×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#2166C2
socleC2×C13#1467
prime radicalC23×C13C2×M16
cosocleC2×C13×M16C23
hypercenter#2166D13
hypocenterC13#11539
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C8 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
205. C13#11539semidirect

Maximal subgroups

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

subgroupindex
#131237682
#131166522
#131127882
#131127862
C13×#21662
#1153913