Finite Group Databasebeta

← #15772353

Subgroups — #15772353

Order 3328.

284 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 75 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#13123472C211yesmaximal, characteristic
2#13116648C211yesmaximal, characteristic, complemented
3#13112786C212yesmaximal, complemented
4#13112771C212yesmaximal
5C13×#2165C211yesmaximal, characteristic, complemented
6C2×#88126C411yescharacteristic
7C4×C13×M16C2211yescharacteristic
8#11718787C411yescharacteristic
9#11718787C2211yescharacteristic
10#11718779C411yescharacteristic
11#11718779C2211yescharacteristic
12C4×#6099C411yescharacteristic
13#11718370—21no—
14#11718370—21no—
15#11718351—21no—
16#11718351—21no—
17C13×#364—21no—
18C13×#349C2212yes—
19C13×#347—21no—
20#11718145C2212yes—
21#11718058—21no—
22#11718055—21no—
23C22×C4×D13C2×C411yescharacteristic
24C2×C13×M16C2×C411yescharacteristic
25C2×C13×M16C2311yescharacteristic
26C2×C42×C13C2×C411yescharacteristic
27C2×#6103—21no—
28C2×#6101—21no—
29C2×C4×Dic13C2×C411yescharacteristic
30C2×#6099C2×C411yescharacteristic
31C2×#6099C2×C411yescharacteristic
32#88126—21no—
33#88126—21no—
34#88126—22no—
35C13×M32—22no—
36C13×#97D411yescharacteristic
37C13×#97D411yescharacteristic
38C4×C8×C13D411yescharacteristic
39C4×C8×C13D411yescharacteristic
40#88060—21no—
41#88060—21no—
42#88060—21no—
43#88060—21no—
44#88054—21no—
45#88054—21no—
46#88054—21no—
47#88054—21no—
48#88052—22no—
49#88043—21no—
50C4×#1055—21no—
51#11522—131nomaximal, Sylow
52C23×D13M1611yescharacteristic
53C22×C4×C13—21no—
54C22×C4×C13C22×C411yescharacteristic
55C22×Dic13—21no—
56C22×Dic13M1611yescharacteristic
57C2×C4×D13—21no—
58C2×C4×D13—21no—
59C2×C4×D13—41no—
60C2×C4×D13—41no—
61C13×M16—41no—
62C13×M16—41no—
63C2×C8×C13C22⋊C411yescharacteristic
64C2×C8×C13C22⋊C411yescharacteristic
65C2×C8×C13C2×D411yescharacteristic
66C2×C8×C13C2×D411yescharacteristic
67C42×C13—21no—
68C42×C13C22⋊C411yescharacteristic
69C42×C13C22⋊C411yescharacteristic
70#6103—22no—
71#6103—22no—
72#6101—22no—
73#6101—22no—
74C4×Dic13—21no—
75C4×Dic13M1612yes—
76#6099—41no—
77#6099—41no—
78C2×#1055—21no—
79C2×#1055—21no—
80C13×C16—42no—
81#6090—42no—
82#2921—131no—
83#2165—131no—
84#2165D1311yescharacteristic, complemented
85#1327—132no—
86#1320—132no—
87C23×C13C2×M1611yescharacteristic
88C22×D13—21no—
89C22×D13—41no—
90C22×D13—81no—
91C2×C4×C13—21no—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—81no—
96C2×C4×C13C2×C22⋊C411yescharacteristic
97C2×C4×C13C2×M1611yescharacteristic
98C2×Dic13—22no—
99C2×Dic13—21no—
100C2×Dic13—41no—
101C2×Dic13—81no—
102C4×D13—42no—
103C4×D13—41no—
104C4×D13—41no—
105C8×C13—21no—
106C8×C13—21no—
107C8×C13—21no—
108C8×C13—21no—
109#1055—41no—
110#1055—41no—
111C2×#117—131no—
112#433—261no—
113#433—261no—
114#433—261no—
115#433—261no—
116#423—131no—
117#423—131no—
118#407—131no—
119#407—131no—
120C4×M16—131no—
121C4×M16C2×D1311yescharacteristic
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
131C2×D13—42no—
132C2×D13—41no—
133C2×D13—82no—
134C4×C13—21no—
135C4×C13—41no—
136C4×C13—41no—
137C4×C13#41011yescharacteristic
138C4×C13#41311yescharacteristic
139Dic13—42no—
140Dic13—41no—
141C23×C4—131no—
142C2×M16—131no—
143C2×M16—131no—
144C2×M16C4×D1311yescharacteristic
145C2×M16C22×D1311yescharacteristic
146#117—262no—
147#117—261no—
148#117—261no—
149C2×C4⋊C4—261no—
150C2×C22⋊C4—261no—
151C2×C42—131no—
152C2×C42C4×D1311yescharacteristic
153M32—22no—
154M32—262no—
155C4⋊C8—261no—
156C4⋊C8—261no—
157C4⋊C8—261no—
158C4⋊C8—261no—
159C22⋊C8—261no—
160C22⋊C8—261no—
161C22⋊C8—261no—
162C22⋊C8—261no—
163#97—261no—
164#97D5211yescharacteristic
165#97C22⋊D1311yescharacteristic
166C4×C8—261no—
167C4×C8D5211yescharacteristic
168C4×C8C22⋊D1311yescharacteristic
169C2×C13—21no—
170C2×C13—41no—
171C2×C13#146411yescharacteristic
172D13—81no—
173C24—131no—
174C22×C4—21no—
175C22×C4—131no—
176C22×C4—261no—
177C22×C4—261no—
178C22×C4—261no—
179C22×C4—521no—
180C22×C4—521no—
181C22×C4C2×C4×D1311yescharacteristic
182M16—41no—
183M16—41no—
184M16—521no—
185M16—521no—
186C2×C8—261no—
187C2×C8—261no—
188C2×C8#610311yescharacteristic
189C2×C8#610311yescharacteristic
190C2×C8C2×D5211yescharacteristic
191C2×C8C2×C22⋊D1311yescharacteristic
192C4⋊C4—262no—
193C4⋊C4—262no—
194C22⋊C4—262no—
195C22⋊C4—262no—
196C42—21no—
197C42—132no—
198C42—261no—
199C42#610311yescharacteristic
200C42#610311yescharacteristic
201C16—42no—
202C16—522no—
203C13#1152211yescharacteristic, complemented, Sylow
204C23—261no—
205C23—521no—
206C23—1041no—
207C23M16×D1311yescharacteristic
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—81no—
213C2×C4—262no—
214C2×C4—261no—
215C2×C4—522no—
216C2×C4—521no—
217C2×C4—521no—
218C2×C4—521no—
219C2×C4—1041no—
220C2×C4M16×D1311yescharacteristic
221C2×C4C2×#610311yescharacteristic
222C8—21no—
223C8—21no—
224C8—21no—
225C8—21no—
226C8—521no—
227C8—521no—
228C22—21no—
229C22—41no—
230C22—522no—
231C22—521no—
232C22—1042no—
233C22#1171878711yescharacteristic
234C4—21no—
235C4—41no—
236C4—41no—
237C4—522no—
238C4—521no—
239C4#1171866711yescharacteristic
240C4#1171879311yescharacteristic
241C2—21no—
242C2—41no—
243C2—1041no—
244C2#1311316811yescharacteristic
subgroupG/H
centerC4#11718667
commutatorC22×C4×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#2165C2
socleC2×C13#1464
prime radicalC23×D13M16
cosocleC2×C13×M16C23
hypercenter#2165D13
hypocenterC13#11522
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C42 ◁ C4×M16 ◁ #2165

Complements

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

NH ≅ G/Ntype
2. #13116648C2semidirect
3. #13112786C2semidirect
5. C13×#2165C2semidirect
84. #2165D13semidirect
203. C13#11522semidirect

Maximal subgroups

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

subgroupindex
#131234722
#131166482
#131127862
#131127712
C13×#21652
#1152213