Finite Group Databasebeta

← #16782267

Subgroups — #16782267

Order 3328.

398 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 72 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#13130735C212yesmaximal
2#13129739C214yesmaximal
3#13117436C211yesmaximal, characteristic
4C22×#6101C2211yescharacteristic
5#11719169C2214yes—
6C4×C13×C22⋊C4C411yescharacteristic
7C4×C22⋊Dic13C411yescharacteristic
8#11718604C2212yes—
9#11718603C412yes—
10#11718594—22no—
11#11718313—22no—
12#11718291—22no—
13#11718291—22no—
14C23×C4×C13C2×C411yescharacteristic
15C23×Dic13C2×C411yescharacteristic
16C23×Dic13C2311yescharacteristic
17C2×#6122—24no—
18C2×C13×C22⋊C4C2×C412yes—
19C2×C42×C13—21no—
20C2×C22⋊Dic13C2×C412yes—
21C2×#6101—24no—
22C2×#6101—22no—
23C2×#6101D412yes—
24C2×#6101D412yes—
25C2×C4×Dic13—21no—
26C22⋊#1057—28no—
27C13×#95—21no—
28#88071—21no—
29#88071—22no—
30#88071—24no—
31#8755—131nomaximal, Sylow
32C24×C13C22×C411yescharacteristic
33C22×C4×C13—22no—
34C22×C4×C13—22no—
35C22×C4×C13—81no—
36C22×C4×C13C22⋊C411yescharacteristic
37C22×C4×C13C22⋊C411yescharacteristic
38C22×Dic13—22no—
39C22×Dic13—22no—
40C22×Dic13—42no—
41C22×Dic13—81no—
42C22×Dic13C22⋊C412yes—
43C22×Dic13C2×D412yes—
44C22×Dic13#4114yes—
45#6122—48no—
46C2×#1057—44no—
47C13×C22⋊C4—42no—
48C42×C13—81no—
49C22⋊Dic13—42no—
50#6101—24no—
51#6101—24no—
52#6101—82no—
53C4×Dic13—81no—
54#2313—131no—
55#1821—132no—
56#1306—134no—
57C23×C13—22no—
58C23×C13—41no—
59C23×C13—41no—
60C23×C13C2×C22⋊C411yescharacteristic
61C23×C13#11712yes—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—41no—
65C2×C4×C13—41no—
66C2×C4×C13—42no—
67C2×C4×C13—42no—
68C2×C4×C13—42no—
69C2×C4×C13—82no—
70C2×Dic13—24no—
71C2×Dic13—22no—
72C2×Dic13—44no—
73C2×Dic13—42no—
74C2×Dic13—42no—
75C2×Dic13—42no—
76C2×Dic13—42no—
77C2×Dic13—82no—
78C2×Dic13#12314yes—
79#1057—84no—
80C22×C4⋊C4—131no—
81#407—134no—
82#387—262no—
83#387—262no—
84#381—132no—
85#380—132no—
86C4×C22⋊C4—131no—
87C4×C22⋊C4#26111yescharacteristic
88#343—262no—
89#343—262no—
90C22×C13—21no—
91C22×C13—21no—
92C22×C13—22no—
93C22×C13—22no—
94C22×C13—22no—
95C22×C13—44no—
96C22×C13#38111yescharacteristic
97C22×C13#41012yes—
98C4×C13—41no—
99C4×C13—41no—
100C4×C13—82no—
101Dic13—24no—
102Dic13—42no—
103Dic13—82no—
104C23×C4—131no—
105C23×C4—131no—
106C23×C4C2×#26111yescharacteristic
107C2×M16—264no—
108C2×C4⋊C4—132no—
109C2×C4⋊C4—132no—
110C2×C4⋊C4—264no—
111C2×C4⋊C4—262no—
112C2×C22⋊C4—132no—
113C2×C22⋊C4C2×#26112yes—
114C2×C42—21no—
115C2×C42—261no—
116C22⋊C8—268no—
117#95—21no—
118#95—262no—
119#95—264no—
120#95—261no—
121C2×C13—22no—
122C2×C13—42no—
123C2×C13#182011yescharacteristic
124C2×C13#182911yescharacteristic
125C2×C13#183011yescharacteristic
126C24C22×#26111yescharacteristic
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—81no—
130C22×C4—132no—
131C22×C4—134no—
132C22×C4—132no—
133C22×C4—262no—
134C22×C4—262no—
135C22×C4—522no—
136C22×C4—1041no—
137C22×C4C22⋊#26111yescharacteristic
138C22×C4C22⋊#26111yescharacteristic
139M16—528no—
140C2×C8—524no—
141C4⋊C4—264no—
142C4⋊C4—264no—
143C4⋊C4—1042no—
144C22⋊C4—42no—
145C22⋊C4—522no—
146C42—81no—
147C42—1041no—
148C13#875511yescharacteristic, complemented, Sylow
149C23—22no—
150C23—41no—
151C23—41no—
152C23#8823712yes—
153C23C2×C22⋊#26111yescharacteristic
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—82no—
162C2×C4—134no—
163C2×C4—264no—
164C2×C4—262no—
165C2×C4—524no—
166C2×C4—522no—
167C2×C4—522no—
168C2×C4—522no—
169C2×C4—522no—
170C2×C4—1042no—
171C8—1044no—
172C22—21no—
173C22—21no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—44no—
178C22#1171911612yes—
179C22#1171913511yescharacteristic
180C4—41no—
181C4—41no—
182C4—82no—
183C4—264no—
184C4—522no—
185C4—1042no—
186C2—22no—
187C2—42no—
188C2#1313073311yescharacteristic
189C2#1313074911yescharacteristic
190C2#1313075011yescharacteristic
subgroupG/H
centerC22#11719135
commutator, prime radicalC24×C13C22×C4
FrattiniC24C22×#261
FittingC4×C13×C22⋊C4C4
socleC22×C13#381
cosocleC23×Dic13C23
hypercenterC4×C22⋊C4#261
hypocenterC13#8755
LCSG ▷ C24×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C24 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
148. C13#8755semidirect

Maximal subgroups

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

subgroupindex
#131307352
#131297392
#131174362
#875513