Finite Group Databasebeta

← #16782275

Subgroups — #16782275

Order 3328.

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

normal subgroups only

This group has 394 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#13130086C212yesmaximal
2#13129737C214yesmaximal
3#13117436C211yesmaximal, characteristic
4C22×#6101C2211yescharacteristic
5#11719169C2214yes—
6C4×C13×C22⋊C4C411yescharacteristic
7C4×C22⋊Dic13C411yescharacteristic
8#11718604C412yes—
9#11718603C2212yes—
10#11718594—22no—
11#11718313—22no—
12#11718286—22no—
13#11718286—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—24no—
27C22⋊#1057—24no—
28C13×#95—21no—
29#88071—21no—
30#88071—24no—
31#88071—22no—
32#8758—131nomaximal, Sylow
33C24×C13C22×C411yescharacteristic
34C22×C4×C13—22no—
35C22×C4×C13—22no—
36C22×C4×C13—81no—
37C22×C4×C13C22⋊C411yescharacteristic
38C22×C4×C13C22⋊C411yescharacteristic
39C22×Dic13—22no—
40C22×Dic13—22no—
41C22×Dic13—42no—
42C22×Dic13—81no—
43C22×Dic13C22⋊C412yes—
44C22×Dic13C2×D412yes—
45C22×Dic13#4114yes—
46#6122—84no—
47C2×#1057—44no—
48C13×C22⋊C4—42no—
49C42×C13—81no—
50C22⋊Dic13—42no—
51#6101—24no—
52#6101—24no—
53#6101—82no—
54C4×Dic13—81no—
55#2313—131no—
56#1463—132no—
57#1305—134no—
58C23×C13—22no—
59C23×C13—41no—
60C23×C13—41no—
61C23×C13C2×C22⋊C411yescharacteristic
62C23×C13#11712yes—
63C2×C4×C13—21no—
64C2×C4×C13—21no—
65C2×C4×C13—41no—
66C2×C4×C13—41no—
67C2×C4×C13—42no—
68C2×C4×C13—42no—
69C2×C4×C13—42no—
70C2×C4×C13—82no—
71C2×Dic13—22no—
72C2×Dic13—24no—
73C2×Dic13—42no—
74C2×Dic13—44no—
75C2×Dic13—44no—
76C2×Dic13—42no—
77C2×Dic13—42no—
78C2×Dic13—42no—
79C2×Dic13#12314yes—
80#1057—84no—
81C22×C4⋊C4—131no—
82#407—134no—
83#387—262no—
84#387—262no—
85#381—132no—
86#380—132no—
87C4×C22⋊C4—131no—
88C4×C22⋊C4#26111yescharacteristic
89#324—262no—
90#324—262no—
91C22×C13—21no—
92C22×C13—21no—
93C22×C13—22no—
94C22×C13—22no—
95C22×C13—22no—
96C22×C13—44no—
97C22×C13#38111yescharacteristic
98C22×C13#41312yes—
99C4×C13—41no—
100C4×C13—41no—
101C4×C13—82no—
102Dic13—24no—
103Dic13—42no—
104Dic13—82no—
105C23×C4—131no—
106C23×C4—131no—
107C23×C4C2×#26111yescharacteristic
108C2×M16—264no—
109C2×C4⋊C4—132no—
110C2×C4⋊C4—132no—
111C2×C4⋊C4—264no—
112C2×C4⋊C4—262no—
113C2×C22⋊C4—132no—
114C2×C22⋊C4C2×#26112yes—
115C2×C42—21no—
116C2×C42—261no—
117C22⋊C8—264no—
118C22⋊C8—264no—
119#95—21no—
120#95—262no—
121#95—264no—
122#95—261no—
123C2×C13—22no—
124C2×C13—42no—
125C2×C13#182211yescharacteristic
126C2×C13#182811yescharacteristic
127C2×C13#183011yescharacteristic
128C24C22×#26111yescharacteristic
129C22×C4—22no—
130C22×C4—22no—
131C22×C4—81no—
132C22×C4—134no—
133C22×C4—132no—
134C22×C4—132no—
135C22×C4—262no—
136C22×C4—262no—
137C22×C4—522no—
138C22×C4—1041no—
139C22×C4C22⋊#26111yescharacteristic
140C22×C4C22⋊#26111yescharacteristic
141M16—1044no—
142C2×C8—524no—
143C4⋊C4—264no—
144C4⋊C4—264no—
145C4⋊C4—1042no—
146C22⋊C4—42no—
147C22⋊C4—522no—
148C42—81no—
149C42—1041no—
150C13#875811yescharacteristic, complemented, Sylow
151C23—22no—
152C23—41no—
153C23—41no—
154C23#8823712yes—
155C23C2×C22⋊#26111yescharacteristic
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—42no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—82no—
164C2×C4—134no—
165C2×C4—264no—
166C2×C4—262no—
167C2×C4—522no—
168C2×C4—524no—
169C2×C4—524no—
170C2×C4—522no—
171C2×C4—522no—
172C2×C4—522no—
173C8—1044no—
174C22—21no—
175C22—21no—
176C22—22no—
177C22—22no—
178C22—22no—
179C22—44no—
180C22#1171913212yes—
181C22#1171913511yescharacteristic
182C4—41no—
183C4—41no—
184C4—82no—
185C4—264no—
186C4—522no—
187C4—1042no—
188C2—22no—
189C2—42no—
190C2#1313073711yescharacteristic
191C2#1313074711yescharacteristic
192C2#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#8758
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
150. C13#8758semidirect

Maximal subgroups

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

subgroupindex
#131300862
#131297372
#131174362
#875813