Finite Group Databasebeta

← #15772430

Subgroups — #15772430

Order 3328.

262 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 71 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#13123775C211yesmaximal, characteristic
2#13116649C212yesmaximal
3#13112789C211yesmaximal, characteristic
4#13112786C212yesmaximal
5C13×#1328C211yesmaximal, characteristic
6#11719222C411yescharacteristic
7C13×#424C2211yescharacteristic
8#11718783C2211yescharacteristic
9#11718779C2211yescharacteristic
10#11718763C411yescharacteristic
11C2×#88055C411yescharacteristic
12#11718658C411yescharacteristic
13#11718492—22no—
14#11718489—22no—
15C13×#349C2212yes—
16#11718145C2212yes—
17#11718104—22no—
18#11718103—22no—
19C2×C13×M16C2311yescharacteristic
20C22×C8×C13C2×C411yescharacteristic
21C13×#117C2×C411yescharacteristic
22#88180C2×C411yescharacteristic
23C2×C4×Dic13C2×C411yescharacteristic
24C2×#6099C2×C411yescharacteristic
25C22×#1055C2×C411yescharacteristic
26#88144—21no—
27#88142—21no—
28#88132—22no—
29C4×Dic26—22no—
30C13×M32—22no—
31C13×C4⋊C8—22no—
32#88055—21no—
33#88055—21no—
34#88055D412yes—
35#88054—22no—
36#88054—22no—
37C8×Dic13D412yes—
38#88052—22no—
39#88043—21no—
40C4×#1055—21no—
41#11540—131nomaximal, Sylow
42C22×C4×C13C22×C411yescharacteristic
43C22×Dic13—21no—
44C2×Dic26—22no—
45C13×M16—41no—
46C2×C8×C13—21no—
47C2×C8×C13—41no—
48C2×C8×C13C2×D412yes—
49C13×C4⋊C4—21no—
50C13×C22⋊C4M1612yes—
51C42×C13—21no—
52C22⋊Dic13—21no—
53C4⋊Dic13—22no—
54C4⋊Dic13—21no—
55#6101—22no—
56#6101—22no—
57C4×Dic13—21no—
58C4×Dic13C22⋊C412yes—
59C4×Dic13M1611yescharacteristic
60C4×Dic13M1611yescharacteristic
61#6099—41no—
62C2×#1055—22no—
63C2×#1055—21no—
64C2×#1055C22⋊C411yescharacteristic
65C2×#1055C22⋊C411yescharacteristic
66C13×C16—42no—
67#6090—42no—
68#2961—131no—
69#2166—132no—
70#1328—131no—
71#1328D1311yescharacteristic
72#1327—132no—
73C23×C13C2×M1611yescharacteristic
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—22no—
77C2×C4×C13C2×C22⋊C411yescharacteristic
78C2×C4×C13C2×M1611yescharacteristic
79C2×Dic13—21no—
80C2×Dic13—21no—
81C2×Dic13—22no—
82C2×Dic13—81no—
83Dic26—82no—
84C8×C13—22no—
85C8×C13—41no—
86#1055—21no—
87#1055—41no—
88#1055#10112yes—
89#533—131no—
90#446—262no—
91#446—262no—
92#424—131no—
93#424C2×D1311yescharacteristic
94#423—131no—
95#405—131no—
96#405—131no—
97C2×#97—131no—
98#364—262no—
99#349—132no—
100#349C2×D1312yes—
101#347—262no—
102C22×C13—21no—
103C22×C13—41no—
104C22×C13#40711yescharacteristic
105C4×C13—21no—
106C4×C13—42no—
107C4×C13#41011yescharacteristic
108C4×C13C2×#10111yescharacteristic
109Dic13—41no—
110Dic13—42no—
111Dic13—41no—
112C2×M16—131no—
113C2×M16C22×D1311yescharacteristic
114C22×C8—131no—
115C22×C8C4×D1311yescharacteristic
116C4⋊Q8—261no—
117#125—261no—
118C22⋊Q8—262no—
119C4×Q8—262no—
120#117—131no—
121#117C4×D1311yescharacteristic
122C2×C42—131no—
123M32—22no—
124M32—262no—
125C4⋊C8—22no—
126C4⋊C8—262no—
127C4⋊C8—262no—
128#97—132no—
129#97—261no—
130#97—261no—
131#97—261no—
132C4×C8—132no—
133C4×C8—261no—
134C2×C13—21no—
135C2×C13—41no—
136C2×C13#146711yescharacteristic
137C2×Q8—262no—
138C22×C4—261no—
139C22×C4C2×C4×D1311yescharacteristic
140M16—41no—
141M16—521no—
142C2×C8—21no—
143C2×C8—41no—
144C2×C8—131no—
145C2×C8—131no—
146C2×C8—262no—
147C2×C8—261no—
148C2×C8D4×D1312yes—
149C4⋊C4—21no—
150C4⋊C4—262no—
151C4⋊C4—262no—
152C4⋊C4—262no—
153C4⋊C4—261no—
154C22⋊C4—261no—
155C22⋊C4#609412yes—
156C42—21no—
157C42—132no—
158C42—131no—
159C42—131no—
160C42—261no—
161C16—42no—
162C16—522no—
163C13#1154011yescharacteristic, complemented, Sylow
164C23C2×#609411yescharacteristic
165Q8—1042no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—261no—
170C2×C4—261no—
171C2×C4—262no—
172C2×C4—1041no—
173C2×C4C22⋊C4×D1311yescharacteristic
174C2×C4M16×D1311yescharacteristic
175C8—22no—
176C8—41no—
177C8—132no—
178C8—261no—
179C8—521no—
180C22—21no—
181C22—41no—
182C22#1171838711yescharacteristic
183C4—21no—
184C4—42no—
185C4—521no—
186C4—521no—
187C4—522no—
188C4#1171840111yescharacteristic
189C4D13×#10111yescharacteristic
190C2—21no—
191C2—41no—
192C2#1311317811yescharacteristic
subgroupG/H
centerC4#11718401
commutatorC22×C4×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#1328C2
socleC2×C13#1467
prime radicalC23×C13C2×M16
cosocleC2×C13×M16C23
hypercenter#1328D13
hypocenterC13#11540
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1328

Complements

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

NH ≅ G/Ntype
163. C13#11540semidirect

Maximal subgroups

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

subgroupindex
#131237752
#131166492
#131127892
#131127862
C13×#13282
#1154013