Finite Group Databasebeta

← #15772352

Subgroups — #15772352

Order 3328.

284 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 69 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#13123471C211yesmaximal, characteristic
2#13116645C212yesmaximal, complemented
3#13112786C212yesmaximal, complemented
4#13112772C211yesmaximal, characteristic
5C13×#1320C211yesmaximal, characteristic
6C2×#88180C411yescharacteristic
7C13×#407C2211yescharacteristic
8#11718868C411yescharacteristic
9#11718779C411yescharacteristic
10#11718779C2211yescharacteristic
11M16×Dic13C411yescharacteristic
12M16×Dic13C2211yescharacteristic
13#11718381—22no—
14#11718381—22no—
15C13×#349C2212yes—
16#11718145C2212yes—
17#11718104—22no—
18#11718103—22no—
19C23×C4×C13C2×C411yescharacteristic
20C2×C13×M16C2×C411yescharacteristic
21C2×C13×M16C2311yescharacteristic
22C2×C22⋊Dic13—21no—
23#88180—21no—
24#88180—21no—
25#88180—22no—
26C2×C4⋊Dic13—21no—
27C2×C4×Dic13C2×C411yescharacteristic
28C2×C4×Dic13C2×C411yescharacteristic
29C2×#6099C2×C411yescharacteristic
30C2×#6099C2×C411yescharacteristic
31C13×M32—22no—
32C13×C22⋊C8—22no—
33C22⋊#1055—22no—
34#88055—21no—
35#88055D412yes—
36#88054—22no—
37#88054—22no—
38C8×Dic13—21no—
39C8×Dic13D412yes—
40#88052—22no—
41#11522—131nomaximal, Sylow
42C24×C13M1611yescharacteristic
43C22×C4×C13—21no—
44C22×C4×C13—21no—
45C22×C4×C13—41no—
46C22×C4×C13—41no—
47C22×C4×C13M1611yescharacteristic
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13—21no—
50C22×Dic13—21no—
51C13×M16—41no—
52C13×M16—41no—
53C2×C8×C13—21no—
54C2×C8×C13C2×D412yes—
55C22⋊Dic13—22no—
56C22⋊Dic13—22no—
57C4⋊Dic13—22no—
58C4⋊Dic13—22no—
59C4×Dic13—21no—
60C4×Dic13—21no—
61C4×Dic13C22⋊C411yescharacteristic
62C4×Dic13C22⋊C411yescharacteristic
63C4×Dic13M1612yes—
64#6099—41no—
65#6099—41no—
66C2×#1055—21no—
67C2×#1055C22⋊C412yes—
68C13×C16—42no—
69#6090—42no—
70#2921—131no—
71#2165—132no—
72#1327—132no—
73#1320—131no—
74#1320D1311yescharacteristic
75C23×C13—21no—
76C23×C13—41no—
77C23×C13—81no—
78C23×C13C2×M1611yescharacteristic
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—42no—
83C2×C4×C13—41no—
84C2×C4×C13—41no—
85C2×C4×C13—41no—
86C2×C4×C13C2×C22⋊C411yescharacteristic
87C2×C4×C13C2×M1611yescharacteristic
88C2×Dic13—21no—
89C2×Dic13—21no—
90C2×Dic13—22no—
91C2×Dic13—81no—
92C2×Dic13—81no—
93C8×C13—22no—
94C8×C13—41no—
95#1055—22no—
96#1055—41no—
97C2×#117—131no—
98#433—262no—
99#433—262no—
100#423—131no—
101#423—131no—
102#407—131no—
103#407C2×D1311yescharacteristic
104C4×M16—131no—
105C4×M16—131no—
106#364—262no—
107#349—132no—
108#349C2×D1312yes—
109#347—262no—
110C22×C13—21no—
111C22×C13—41no—
112C22×C13—42no—
113C22×C13—41no—
114C22×C13—82no—
115C22×C13#40711yescharacteristic
116C4×C13—21no—
117C4×C13—41no—
118C4×C13#41011yescharacteristic
119C4×C13#41311yescharacteristic
120Dic13—41no—
121Dic13—41no—
122Dic13—42no—
123C23×C4C4×D1311yescharacteristic
124C2×M16—131no—
125C2×M16—131no—
126C2×M16C4×D1311yescharacteristic
127C2×M16C22×D1311yescharacteristic
128#117—262no—
129#117—261no—
130#117—261no—
131C2×C4⋊C4—261no—
132C2×C22⋊C4—261no—
133C2×C42—131no—
134C2×C42—131no—
135M32—22no—
136M32—262no—
137C4⋊C8—262no—
138C4⋊C8—262no—
139C22⋊C8—22no—
140C22⋊C8—262no—
141#97—132no—
142#97—261no—
143C4×C8—132no—
144C4×C8—261no—
145C2×C13—21no—
146C2×C13—41no—
147C2×C13—81no—
148C2×C13#146411yescharacteristic
149C24#609411yescharacteristic
150C22×C4—21no—
151C22×C4—21no—
152C22×C4—41no—
153C22×C4—41no—
154C22×C4—261no—
155C22×C4—261no—
156C22×C4#609411yescharacteristic
157C22×C4C2×C4×D1311yescharacteristic
158M16—41no—
159M16—41no—
160M16—521no—
161M16—521no—
162C2×C8—21no—
163C2×C8—132no—
164C2×C8—261no—
165C2×C8D4×D1312yes—
166C4⋊C4—262no—
167C4⋊C4—262no—
168C22⋊C4—262no—
169C22⋊C4—262no—
170C42—131no—
171C42—131no—
172C42—132no—
173C42—261no—
174C42—261no—
175C16—42no—
176C16—522no—
177C13#1152211yescharacteristic, complemented, Sylow
178C23—21no—
179C23—41no—
180C23—81no—
181C23C2×#609411yescharacteristic
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—42no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—261no—
190C2×C4—261no—
191C2×C4—262no—
192C2×C4—1041no—
193C2×C4—1041no—
194C2×C4C22⋊C4×D1311yescharacteristic
195C2×C4M16×D1311yescharacteristic
196C8—22no—
197C8—41no—
198C8—262no—
199C8—521no—
200C22—21no—
201C22—41no—
202C22—42no—
203C22—41no—
204C22—82no—
205C22#1171838711yescharacteristic
206C4—21no—
207C4—41no—
208C4—521no—
209C4—521no—
210C4—522no—
211C4#1171840111yescharacteristic
212C4#1171840611yescharacteristic
213C2—21no—
214C2—41no—
215C2—81no—
216C2#1311316711yescharacteristic
subgroupG/H
centerC4#11718401
commutatorC22×C4×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#1320C2
socleC2×C13#1464
prime radicalC24×C13M16
cosocleC2×C13×M16C23
hypercenter#1320D13
hypocenterC13#11522
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #13116645C2semidirect
3. #13112786C2semidirect
177. C13#11522semidirect

Maximal subgroups

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

subgroupindex
#131234712
#131166452
#131127862
#131127722
C13×#13202
#1152213