Finite Group Databasebeta

← #15750131

Subgroups — #15750131

Order 3328.

402 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 75 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
1C4×#88074C212yesmaximal
2C13×#1955C211yesmaximal, characteristic
3C2×C4×D4×C13C2211yescharacteristic
4C2×C13×C4⋊C8C411yescharacteristic, complemented
5C2×C13×C22⋊C8—22no—
6C2×C13×#97C411yescharacteristic, complemented
7C2×#88074—22no—
8C4×C22⋊Dic13—22no—
9#11718118C414yescomplemented
10C22×D4×C13D411yescharacteristic
11C23×C4×C13D412yes—
12C22×C8×C13—21no—
13C22×C8×C13—21no—
14C4×D4×C13—41no—
15C4×D4×C13—41no—
16C2×C13×C4⋊C4Q811yescharacteristic
17C2×C13×C22⋊C4C2×C412yes—
18C2×C42×C13C2×C411yescharacteristic
19C2×C22⋊Dic13—24no—
20C2×C4×Dic13—42no—
21C13×C4⋊C8—41no—
22C13×C22⋊C8—44no—
23C13×#97—41no—
24#88074—28no—
25#88071—42no—
26#7283—131nomaximal, Sylow
27C24×C13C22⋊C412yes—
28C2×D4×C13—24no—
29C2×D4×C13—41no—
30C22×C4×C13—22no—
31C22×C4×C13—22no—
32C22×C4×C13—42no—
33C22×C4×C13—42no—
34C22×C4×C13C4211yescharacteristic
35C22×C4×C13C22⋊C411yescharacteristic
36C22×C4×C13C4⋊C412yes—
37C22×C4×C13C4⋊C411yescharacteristic
38C22×Dic13—44no—
39C2×C8×C13—22no—
40C2×C8×C13—41no—
41C2×C8×C13—41no—
42C2×C8×C13—42no—
43C2×C8×C13—41no—
44C13×C4⋊C4—41no—
45C13×C22⋊C4—42no—
46C42×C13—21no—
47C42×C13—21no—
48C22⋊Dic13—28no—
49C22⋊Dic13—44no—
50C4×Dic13—82no—
51C4×Dic13—82no—
52#1955D1311yescharacteristic
53C4×#99—132no—
54C23×C13—22no—
55C23×C13—22no—
56C23×C13—42no—
57C23×C13—42no—
58C23×C13#9511yescharacteristic
59C23×C13#10414yes—
60D4×C13—44no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—22no—
64C2×C4×C13—21no—
65C2×C4×C13—21no—
66C2×C4×C13—22no—
67C2×C4×C13—42no—
68C2×C4×C13—42no—
69C2×C4×C13—42no—
70C2×C4×C13—41no—
71C2×C4×C13—82no—
72C2×C4×C13#9911yescharacteristic
73C2×C4×C13#9911yescharacteristic
74C2×Dic13—48no—
75C2×Dic13—84no—
76C2×Dic13—84no—
77C8×C13—42no—
78C8×C13—81no—
79C2×C4×D4C2×D1311yescharacteristic
80C2×C4⋊C8Dic1311yescharacteristic, complemented
81C2×#99—262no—
82C2×C22⋊C8—22no—
83C2×#97Dic1311yescharacteristic, complemented
84C4×C22⋊C4—262no—
85#342—134no—
86C22×C13—21no—
87C22×C13—21no—
88C22×C13—24no—
89C22×C13—44no—
90C22×C13—42no—
91C22×C13—42no—
92C22×C13—82no—
93C22×C13#33912yes—
94C22×C13#34211yescharacteristic
95C4×C13—21no—
96C4×C13—41no—
97C4×C13—41no—
98C4×C13—42no—
99C4×C13#35311yescharacteristic
100C4×C13#35411yescharacteristic
101Dic13—88no—
102C22×D4D5211yescharacteristic
103C23×C4C22⋊D1312yes—
104C22×C8—21no—
105C22×C8—21no—
106C4×D4—41no—
107C4×D4—41no—
108C2×C4⋊C4Dic2611yescharacteristic
109C2×C22⋊C4—264no—
110C2×C22⋊C4C4×D1312yes—
111C2×C42—522no—
112C2×C42C2×Dic1311yescharacteristic
113C4⋊C8—41no—
114#99—268no—
115C22⋊C8—44no—
116#97—41no—
117#95—522no—
118C2×C13—22no—
119C2×C13—44no—
120C2×C13#129711yescharacteristic
121C2×C13#139111yescharacteristic
122C2×C13#139311yescharacteristic
123C24#610312yes—
124C2×D4—24no—
125C2×D4—41no—
126C22×C4—22no—
127C22×C4—22no—
128C22×C4—42no—
129C22×C4—42no—
130C22×C4—524no—
131C22×C4C4×Dic1311yescharacteristic
132C22×C4#610112yes—
133C22×C4C4⋊Dic1311yescharacteristic
134C22×C4C22⋊Dic1311yescharacteristic
135C2×C8—22no—
136C2×C8—41no—
137C2×C8—41no—
138C2×C8—42no—
139C2×C8—41no—
140C4⋊C4—41no—
141C22⋊C4—42no—
142C22⋊C4—268no—
143C22⋊C4—524no—
144C42—21no—
145C42—21no—
146C42—1042no—
147C42—1042no—
148C13#728311yescharacteristic, complemented, Sylow
149C23—22no—
150C23—22no—
151C23—42no—
152C23—42no—
153C23#8806514yes—
154C23#8807111yescharacteristic
155D4—44no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—41no—
166C2×C4—82no—
167C2×C4—528no—
168C2×C4—1044no—
169C2×C4—1044no—
170C2×C4#8807411yescharacteristic
171C2×C4#8807411yescharacteristic
172C8—42no—
173C8—81no—
174C22—21no—
175C22—21no—
176C22—24no—
177C22—44no—
178C22—42no—
179C22—42no—
180C22—82no—
181C22#1171811811yescharacteristic
182C22#1171814712yes—
183C4—21no—
184C4—41no—
185C4—42no—
186C4—41no—
187C4—1048no—
188C4#1171813311yescharacteristic
189C4#1171813711yescharacteristic
190C2—22no—
191C2—44no—
192C2#1311272111yescharacteristic
193C2#1311295711yescharacteristic
194C2#1311296111yescharacteristic
subgroupG/H
centerC2×C4#88074
commutatorC22×C4×C13C42
FrattiniC2×C4×D4C2×D13
FittingC13×#1955C2
socleC22×C13#342
prime radicalC22×D4×C13D4
cosocleC2×C4×D4×C13C22
hypercenter#1955D13
hypocenterC13#7283
LCSG ▷ C22×C4×C13 ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1955

Complements

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

NH ≅ G/Ntype
4. C2×C13×C4⋊C8C4semidirect
6. C2×C13×#97C4semidirect
9. #11718118C4semidirect
80. C2×C4⋊C8Dic13semidirect
83. C2×#97Dic13semidirect
148. C13#7283semidirect

Maximal subgroups

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

subgroupindex
C4×#880742
C13×#19552
#728313