Finite Group Databasebeta

← #15774457

Subgroups — #15774457

Order 3328.

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

normal subgroups only

This group has 258 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#13125388C211yesmaximal, characteristic
2#13116648C211yesmaximal, characteristic
3#13112898C212yesmaximal, complemented
4#13112896C212yesmaximal, complemented
5C13×#2165C211yesmaximal, characteristic
6#11719175C411yescharacteristic
7C2×#88124C411yescharacteristic
8C4×C13×M16C2211yescharacteristic
9#11718782—21no—
10#11718782—21no—
11#11718363—21no—
12#11718363—21no—
13#11718344C411yescharacteristic
14#11718344C411yescharacteristic
15#11718344C2211yescharacteristic
16#11718344C2211yescharacteristic
17C13×#364C2212yes—
18C13×#349—21no—
19C13×#347—21no—
20#11718145—21no—
21#11718058—21no—
22#11718055C2212yes—
23C2×C13×M16D411yescharacteristic
24C2×C13×M16D411yescharacteristic
25C2×C42×C13C2×C411yescharacteristic
26#88180—21no—
27C2×C4⋊Dic13—21no—
28#88178—41no—
29C2×#6101—41no—
30#88124—21no—
31#88124—41no—
32#88124C2×C411yescharacteristic
33#88124C2×C411yescharacteristic
34#88124C2×C411yescharacteristic
35#88124C2×C411yescharacteristic
36#88123—21no—
37C4×Dic26—41no—
38C13×M32—22no—
39C13×#97D411yescharacteristic
40C13×#97D411yescharacteristic
41C4×C8×C13C2×C411yescharacteristic
42C4×C8×C13C2311yescharacteristic
43#88058—21no—
44#88058—21no—
45#88058—21no—
46#88058—21no—
47#88057—21no—
48#88057—21no—
49#88057—21no—
50#88057—21no—
51#88052—22no—
52#11994—131nomaximal, Sylow
53C22×C4×C13—21no—
54C22×C4×C13C22⋊C411yescharacteristic
55C22×Dic13—41no—
56C2×Dic26—41no—
57C13×M16—22no—
58C13×M16—22no—
59C2×C8×C13C22⋊C411yescharacteristic
60C2×C8×C13C22⋊C411yescharacteristic
61C2×C8×C13C2×D411yescharacteristic
62C2×C8×C13C2×D411yescharacteristic
63C42×C13—21no—
64C42×C13C22⋊C411yescharacteristic
65C42×C13C22×C411yescharacteristic
66C22⋊Dic13—41no—
67C4⋊Dic13—21no—
68C4⋊Dic13—21no—
69C4⋊Dic13—21no—
70C4⋊Dic13—21no—
71C4⋊Dic13—41no—
72C4⋊Dic13—41no—
73#6101—42no—
74#6101—41no—
75#6101—41no—
76#6101—41no—
77#6101—41no—
78C4×Dic13—41no—
79C13×C16—42no—
80#6090—42no—
81#3166—131no—
82#2165—131no—
83#2165D1311yescharacteristic
84#1366—132no—
85#1366—132no—
86C23×C13#10011yescharacteristic
87C2×C4×C13—21no—
88C2×C4×C13—21no—
89C2×C4×C13—21no—
90C2×C4×C13—21no—
91C2×C4×C13—81no—
92C2×C4×C13#10011yescharacteristic
93C2×C4×C13C2×C22⋊C411yescharacteristic
94C2×Dic13—41no—
95C2×Dic13—41no—
96C2×Dic13—41no—
97C2×Dic13—41no—
98C2×Dic13—82no—
99Dic26—82no—
100C8×C13—21no—
101C8×C13—21no—
102C8×C13#13712yes—
103C8×C13#13712yes—
104#533—131no—
105C2×#125—131no—
106#501—261no—
107#501—261no—
108#499—131no—
109#499—131no—
110#499—131no—
111#499—131no—
112#428—261no—
113#428—261no—
114C4×M16C2×D1311yescharacteristic
115#364—132no—
116#364C2×D1312yes—
117#349—21no—
118#349—261no—
119#347—21no—
120#347—261no—
121C22×C13—21no—
122C22×C13—41no—
123C22×C13C2×#10011yescharacteristic
124C4×C13—21no—
125C4×C13—41no—
126C4×C13—41no—
127C4×C13#41911yescharacteristic
128C4×C13#41911yescharacteristic
129Dic13—81no—
130Dic13—81no—
131Dic13—81no—
132Dic13—81no—
133C2×M16D5211yescharacteristic
134C2×M16C22⋊D1311yescharacteristic
135C4⋊Q8—261no—
136#125—131no—
137#125—131no—
138#125—131no—
139#125—131no—
140#125—261no—
141#125—521no—
142C22⋊Q8—521no—
143C4×Q8—521no—
144#117—261no—
145C2×C4⋊C4—261no—
146C2×C4⋊C4—521no—
147C2×C42C4×D1311yescharacteristic
148M32—22no—
149M32—262no—
150#107—261no—
151#107—261no—
152#107—261no—
153#107—261no—
154#106—261no—
155#106—261no—
156#106—261no—
157#106—261no—
158#97D5211yescharacteristic
159#97C22⋊D1311yescharacteristic
160C4×C8C4×D1311yescharacteristic
161C4×C8C22×D1311yescharacteristic
162C2×C13—21no—
163C2×C13—41no—
164C2×C13#155811yescharacteristic
165C2×Q8—521no—
166C22×C4—21no—
167C22×C4—521no—
168C22×C4#610311yescharacteristic
169M16—22no—
170M16—22no—
171C2×C8#610311yescharacteristic
172C2×C8#610311yescharacteristic
173C2×C8C2×D5211yescharacteristic
174C2×C8C2×C22⋊D1311yescharacteristic
175C4⋊C4—261no—
176C4⋊C4—261no—
177C4⋊C4—261no—
178C4⋊C4—261no—
179C4⋊C4—521no—
180C4⋊C4—521no—
181C4⋊C4—521no—
182C4⋊C4—521no—
183C4⋊C4—522no—
184C4⋊C4—521no—
185C4⋊C4—521no—
186C22⋊C4—521no—
187C42—21no—
188C42—521no—
189C42#610311yescharacteristic
190C42C2×C4×D1311yescharacteristic
191C16—42no—
192C16—522no—
193C13#1199411yescharacteristic, complemented, Sylow
194C23#8806311yescharacteristic
195Q8—1042no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—81no—
201C2×C4—521no—
202C2×C4—521no—
203C2×C4—521no—
204C2×C4—521no—
205C2×C4—1042no—
206C2×C4#8806311yescharacteristic
207C2×C4C2×#610311yescharacteristic
208C8—21no—
209C8—21no—
210C8#8816312yes—
211C8#8820512yes—
212C22—21no—
213C22—41no—
214C22C2×#8806311yescharacteristic
215C4—21no—
216C4—41no—
217C4—41no—
218C4—1041no—
219C4—1041no—
220C4—1041no—
221C4—1041no—
222C4#1171866511yescharacteristic
223C4#1171878111yescharacteristic
224C2—21no—
225C2—41no—
226C2#1311356111yescharacteristic
subgroupG/H
centerC2#13113561
commutatorC42×C13C22×C4
FrattiniC4×C8C22×D13
FittingC13×#2165C2
socleC2×C13#1558
prime radicalC23×C13#100
cosocleC4×C8×C13C23
hypercenter#2165D13
hypocenterC13#11994
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
3. #13112898C2semidirect
4. #13112896C2semidirect
193. C13#11994semidirect

Maximal subgroups

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

subgroupindex
#131253882
#131166482
#131128982
#131128962
C13×#21652
#1199413