Finite Group Databasebeta

← #15772428

Subgroups — #15772428

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#13123773C211yesmaximal, characteristic
2#13116649C212yesmaximal
3#13112788C212yesmaximal
4#13112787C211yesmaximal, characteristic
5C13×#1327C211yesmaximal, characteristic
6#11719175C411yescharacteristic
7C13×#423C2211yescharacteristic
8#11718783C411yescharacteristic
9#11718783C2211yescharacteristic
10#11718780C411yescharacteristic
11#11718780C2211yescharacteristic
12C2×#88043C411yescharacteristic
13#11718489—22no—
14#11718489—22no—
15C13×#349C2212yes—
16#11718145C2212yes—
17#11718104—22no—
18#11718103—22no—
19C2×C13×M16C2×C411yescharacteristic
20C2×C13×M16C2311yescharacteristic
21C2×C42×C13C2×C411yescharacteristic
22#88180C2×C411yescharacteristic
23#88180C2×C411yescharacteristic
24#88178—22no—
25C22×#1055C2×C411yescharacteristic
26C22×#1055C2×C411yescharacteristic
27#88124—21no—
28#88123—21no—
29C4×Dic26—22no—
30C13×M32—22no—
31C13×C4⋊C8—22no—
32#88055—21no—
33#88055D412yes—
34#88054—22no—
35#88054—22no—
36C8×Dic13—21no—
37C8×Dic13D412yes—
38#88052—22no—
39#88043—21no—
40#88043—21no—
41#11540—131nomaximal, Sylow
42C22×C4×C13—21no—
43C22×C4×C13C22×C411yescharacteristic
44C2×Dic26—22no—
45C13×M16—41no—
46C13×M16—41no—
47C2×C8×C13—21no—
48C2×C8×C13C2×D412yes—
49C42×C13—21no—
50C42×C13M1611yescharacteristic
51C42×C13M1611yescharacteristic
52C22⋊Dic13—21no—
53C22⋊Dic13M1612yes—
54C4⋊Dic13—22no—
55C4⋊Dic13—21no—
56C4⋊Dic13—21no—
57#6101—24no—
58C4×Dic13—21no—
59C4×Dic13C22⋊C412yes—
60C2×#1055—22no—
61C2×#1055—21no—
62C2×#1055—41no—
63C2×#1055C22⋊C411yescharacteristic
64C2×#1055C22⋊C411yescharacteristic
65C13×C16—42no—
66#6090—42no—
67#2961—131no—
68#2166—132no—
69#1328—132no—
70#1327—131no—
71#1327D1311yescharacteristic
72C23×C13C2×M1611yescharacteristic
73C2×C4×C13—21no—
74C2×C4×C13—21no—
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—81no—
78C2×C4×C13C2×C22⋊C411yescharacteristic
79C2×C4×C13C2×M1611yescharacteristic
80C2×Dic13—22no—
81C2×Dic13—22no—
82Dic26—82no—
83C8×C13—22no—
84C8×C13—41no—
85#1055—21no—
86#1055—41no—
87#1055#10112yes—
88#533—131no—
89#446—262no—
90#446—262no—
91#424—131no—
92#424—131no—
93#423C2×D1311yescharacteristic
94#405—131no—
95#405—131no—
96C2×#97—131no—
97#364—262no—
98#349—132no—
99#349C2×D1312yes—
100#347—262no—
101C22×C13—21no—
102C22×C13—41no—
103C22×C13#40711yescharacteristic
104C4×C13—21no—
105C4×C13—41no—
106C4×C13—41no—
107C4×C13#41011yescharacteristic
108C4×C13C2×#10111yescharacteristic
109Dic13—42no—
110Dic13—42no—
111C2×M16C4×D1311yescharacteristic
112C2×M16C22×D1311yescharacteristic
113C22×C8—131no—
114C22×C8—131no—
115C4⋊Q8—261no—
116#125—261no—
117C22⋊Q8—262no—
118C4×Q8—262no—
119#117—131no—
120#117—131no—
121C2×C42C4×D1311yescharacteristic
122M32—22no—
123M32—262no—
124C4⋊C8—22no—
125C4⋊C8—262no—
126C4⋊C8—262no—
127#97—132no—
128#97—261no—
129#97—261no—
130#97—261no—
131C4×C8—132no—
132C4×C8—261no—
133C2×C13—21no—
134C2×C13—41no—
135C2×C13#146711yescharacteristic
136C2×Q8—262no—
137C22×C4—21no—
138C22×C4C2×C4×D1311yescharacteristic
139M16—41no—
140M16—41no—
141C2×C8—21no—
142C2×C8—131no—
143C2×C8—131no—
144C2×C8—262no—
145C2×C8—261no—
146C2×C8—521no—
147C2×C8D4×D1312yes—
148C4⋊C4—264no—
149C4⋊C4—262no—
150C4⋊C4—261no—
151C4⋊C4—261no—
152C22⋊C4—132no—
153C22⋊C4—261no—
154C42—21no—
155C42—132no—
156C42—261no—
157C42#609411yescharacteristic
158C42#609411yescharacteristic
159C16—42no—
160C16—522no—
161C13#1154011yescharacteristic, complemented, Sylow
162C23M16×D1311yescharacteristic
163Q8—1042no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—81no—
169C2×C4—262no—
170C2×C4—262no—
171C2×C4C22⋊C4×D1311yescharacteristic
172C2×C4C2×#609411yescharacteristic
173C8—22no—
174C8—41no—
175C8—132no—
176C8—261no—
177C8—521no—
178C22—21no—
179C22—41no—
180C22#1171838711yescharacteristic
181C4—21no—
182C4—41no—
183C4—41no—
184C4—522no—
185C4—522no—
186C4#1171840111yescharacteristic
187C4D13×#10111yescharacteristic
188C2—21no—
189C2—41no—
190C2#1311317811yescharacteristic
subgroupG/H
centerC4#11718401
commutatorC22×C4×C13C22×C4
FrattiniC2×M16C22×D13
FittingC13×#1327C2
socleC2×C13#1467
prime radicalC23×C13C2×M16
cosocleC2×C13×M16C23
hypercenter#1327D13
hypocenterC13#11540
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
161. C13#11540semidirect

Maximal subgroups

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

subgroupindex
#131237732
#131166492
#131127882
#131127872
C13×#13272
#1154013