Finite Group Databasebeta

← #15772356

Subgroups — #15772356

Order 3328.

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

normal subgroups only

This group has 280 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#13123483C211yesmaximal, characteristic
2#13116645C212yesmaximal, complemented
3#13112788C212yesmaximal, complemented
4#13112774C211yesmaximal, characteristic
5C13×#1321C211yesmaximal, characteristic
6#41×Dic13C411yescharacteristic
7C13×#408C2211yescharacteristic
8#11718895C411yescharacteristic
9#11718780C2211yescharacteristic
10M16×Dic13C2211yescharacteristic
11#11718763C411yescharacteristic
12C2×#88055C411yescharacteristic
13#11718381—22no—
14#11718380—22no—
15C13×#349C2212yes—
16#11718145C2212yes—
17#11718104—22no—
18#11718103—22no—
19C2×C13×#41C2×C411yescharacteristic
20C2×C13×M16C2311yescharacteristic
21C22×C8×C13C2×C411yescharacteristic
22Q8×Dic13—21no—
23D4×Dic13—21no—
24D4×Dic13—22no—
25#88180—21no—
26#88180C2×C411yescharacteristic
27C2×C4×Dic13—21no—
28C2×C4×Dic13C2×C411yescharacteristic
29C2×#6099C2×C411yescharacteristic
30C22×#1055C2×C411yescharacteristic
31C13×M32—22no—
32C13×C22⋊C8—22no—
33C22⋊#1055—22no—
34#88055—21no—
35#88055—21no—
36#88055D412yes—
37#88054—22no—
38#88054—22no—
39C8×Dic13D412yes—
40#88052—22no—
41#11523—131nomaximal, Sylow
42C13×#41—41no—
43C13×#41—41no—
44C2×Q8×C13M1611yescharacteristic
45C2×D4×C13—21no—
46C2×D4×C13M1611yescharacteristic
47C22×C4×C13—21no—
48C22×C4×C13C22×C411yescharacteristic
49C22×Dic13—22no—
50C22×Dic13—21no—
51C13×M16—41no—
52C2×C8×C13—21no—
53C2×C8×C13—41no—
54C2×C8×C13C2×D412yes—
55C22⋊Dic13—22no—
56C22⋊Dic13M1612yes—
57C4⋊Dic13—22no—
58C4⋊Dic13—21no—
59C4×Dic13—22no—
60C4×Dic13—21no—
61C4×Dic13—21no—
62C4×Dic13C22⋊C411yescharacteristic
63C4×Dic13C22⋊C411yescharacteristic
64#6099—41no—
65C2×#1055—21no—
66C2×#1055—41no—
67C2×#1055C22⋊C412yes—
68C13×C16—42no—
69#6090—42no—
70#2923—131no—
71#2165—132no—
72#1328—132no—
73#1321—131no—
74#1321D1311yescharacteristic
75C23×C13—21no—
76C23×C13C2×M1611yescharacteristic
77Q8×C13—41no—
78D4×C13—41no—
79D4×C13—42no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—41no—
84C2×C4×C13—41no—
85C2×C4×C13C2×C22⋊C411yescharacteristic
86C2×C4×C13C2×M1611yescharacteristic
87C2×Dic13—21no—
88C2×Dic13—22no—
89C2×Dic13—21no—
90C2×Dic13—81no—
91C2×Dic13—82no—
92C8×C13—22no—
93C8×C13—41no—
94#1055—22no—
95#1055—41no—
96C4×#41—131no—
97#433—262no—
98#432—262no—
99#424—131no—
100#424—131no—
101#408—131no—
102#408C2×D1311yescharacteristic
103C4×M16—131no—
104C2×#97—131no—
105#364—262no—
106#349—132no—
107#349C2×D1312yes—
108#347—262no—
109C22×C13—21no—
110C22×C13—41no—
111C22×C13—42no—
112C22×C13—41no—
113C22×C13#40711yescharacteristic
114C4×C13—21no—
115C4×C13—41no—
116C4×C13#41011yescharacteristic
117C4×C13#41311yescharacteristic
118Dic13—42no—
119Dic13—41no—
120Dic13—41no—
121C2×#41C4×D1311yescharacteristic
122C2×M16—131no—
123C2×M16C22×D1311yescharacteristic
124C22×C8—131no—
125C22×C8C4×D1311yescharacteristic
126C4×Q8—261no—
127C4×D4—262no—
128C4×D4—261no—
129#117—131no—
130#117—261no—
131C2×C42—131no—
132C2×C42—261no—
133M32—22no—
134M32—262no—
135C4⋊C8—262no—
136C4⋊C8—262no—
137C22⋊C8—22no—
138C22⋊C8—262no—
139#97—132no—
140#97—261no—
141#97—261no—
142C4×C8—132no—
143C2×C13—21no—
144C2×C13—41no—
145C2×C13—81no—
146C2×C13#146411yescharacteristic
147#41—41no—
148#41—41no—
149C2×Q8#609411yescharacteristic
150C2×D4—21no—
151C2×D4#609411yescharacteristic
152C22×C4—21no—
153C22×C4—262no—
154C22×C4—261no—
155C22×C4C2×C4×D1311yescharacteristic
156M16—41no—
157M16—521no—
158C2×C8—21no—
159C2×C8—41no—
160C2×C8—132no—
161C2×C8—261no—
162C2×C8—521no—
163C2×C8D4×D1312yes—
164C4⋊C4—262no—
165C4⋊C4—261no—
166C22⋊C4—132no—
167C22⋊C4—262no—
168C42—131no—
169C42—131no—
170C42—262no—
171C42—261no—
172C42—261no—
173C16—42no—
174C16—522no—
175C13#1152311yescharacteristic, complemented, Sylow
176C23—21no—
177C23M16×D1311yescharacteristic
178Q8—41no—
179D4—41no—
180D4—42no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—261no—
187C2×C4—261no—
188C2×C4—262no—
189C2×C4—1041no—
190C2×C4—1042no—
191C2×C4C22⋊C4×D1311yescharacteristic
192C2×C4C2×#609411yescharacteristic
193C8—22no—
194C8—41no—
195C8—262no—
196C8—521no—
197C22—21no—
198C22—41no—
199C22—42no—
200C22—41no—
201C22#1171838711yescharacteristic
202C4—21no—
203C4—41no—
204C4—521no—
205C4—522no—
206C4—521no—
207C4#1171840111yescharacteristic
208C4#1171840611yescharacteristic
209C2—21no—
210C2—41no—
211C2—81no—
212C2#1311316711yescharacteristic
subgroupG/H
centerC4#11718401
commutatorC22×C4×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#1321C2
socleC2×C13#1464
prime radicalC2×C13×#41C2×C4
cosocleC2×C13×M16C23
hypercenter#1321D13
hypocenterC13#11523
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1321

Complements

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

NH ≅ G/Ntype
2. #13116645C2semidirect
3. #13112788C2semidirect
175. C13#11523semidirect

Maximal subgroups

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

subgroupindex
#131234832
#131166452
#131127882
#131127742
C13×#13212
#1152313