Finite Group Databasebeta

← D13⋊#1832 #16798150

Subgroups — D13⋊#1832 #16798150

Order 3328.

1006 conjugacy classes of subgroups; only the 320 normal subgroups are shown.

normal subgroups only

This group has 1006 conjugacy classes of subgroups — too many to draw. Only its 320 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
1C2×D13⋊(C4⋊C8)C212yesmaximal
2#13130754C218yesmaximal, complemented
3#13130497C214yesmaximal
4D13×#376C211yesmaximal, characteristic
5C22×D13⋊C8C2214yes—
6C2×C42×D13C2212yes—
7C2×C42×D13C2211yescharacteristic
8C2×#88112C2214yes—
9C2×C4⋊#1057C2214yes—
10D13⋊(C4⋊C8)—28no—
11C13×#376C411yescharacteristic
12#11718593C411yescharacteristic
13#11718593C412yes—
14D13×#95C414yes—
15#11718309C2214yes—
16#11718290C22116yes—
17C22×C4×D13C2×C414yes—
18C22×C4×D13C2×C412yes—
19C22×C4×D13C2311yescharacteristic
20C22×#1057C2318yes—
21C2×D13⋊C8—28no—
22C2×D13⋊C8—216no—
23C2×C42×C13C2×C412yes—
24C2×C42×C13C2×C411yescharacteristic
25C2×C4×Dic13C2×C412yes—
26C2×C4×Dic13C2×C411yescharacteristic
27C2×C4×Dic13C2314yes—
28C2×C4×Dic13C2312yes—
29C42×D13—28no—
30C42×D13D414yes—
31C42×D13Q814yes—
32#88112—28no—
33C4⋊#1057—28no—
34C13×#95C2×C414yes—
35#88071C2×C414yes—
36#88071C2×C418yes—
37C2×#1832—131nomaximal, Sylow
38C23×D13C22×C411yescharacteristic
39C22×C4×C13C22×C414yes—
40C22×C4×C13C22×C412yes—
41C22×C4×C13C22×C411yescharacteristic
42C22×Dic13C22×C414yes—
43C22×Dic13C22×C412yes—
44C22×Dic13C2411yescharacteristic
45C2×C4×D13—28no—
46C2×C4×D13—28no—
47C2×C4×D13—216no—
48C2×C4×D13C4⋊C418yes—
49C2×C4×D13C2×D412yes—
50C2×C4×D13C2×Q812yes—
51C2×C4×D13#4118yes—
52C2×#1057—28no—
53C2×#1057—216no—
54D13⋊C8—416no—
55C42×C13—24no—
56C42×C13C4⋊C414yes—
57C4×Dic13—24no—
58C4×Dic13—28no—
59C4×Dic13C4⋊C414yes—
60C4×Dic13C2×D414yes—
61C4×Dic13C2×Q814yes—
62C22×C4⋊C8—132no—
63C2×#376—131no—
64#1832—138no—
65C2×#336—134no—
66C23×C13C23×C411yescharacteristic
67C22×D13C2×C4⋊C412yes—
68C22×D13#11714yes—
69C22×D13#13118yes—
70C2×C4×C13—24no—
71C2×C4×C13—24no—
72C2×C4×C13—28no—
73C2×C4×C13C2×C4⋊C414yes—
74C2×C4×C13C2×C4⋊C412yes—
75C2×C4×C13#11714yes—
76C2×Dic13—24no—
77C2×Dic13—24no—
78C2×Dic13—28no—
79C2×Dic13C2×C4⋊C414yes—
80C2×Dic13C22×D411yescharacteristic
81C2×Dic13C22×Q811yescharacteristic
82C2×Dic13C2×#4114yes—
83C4×D13—216no—
84C4×D13—416no—
85C4×D13#12418yes—
86C4×D13#12518yes—
87#1057—48no—
88C23×C8—134no—
89C22×C42—131no—
90C22×C42—132no—
91C2×C4⋊C8—134no—
92C2×C4⋊C8—134no—
93C2×C4⋊C8—268no—
94#376—132no—
95#376—131no—
96#376—134no—
97#376#26111yescharacteristic
98C2×#95—134no—
99#336—1316no—
100C22×C13C22×C4⋊C411yescharacteristic
101C22×C13C2×#11712yes—
102C22×C13C2×#13114yes—
103C2×D13#38214yes—
104C2×D13#42418yes—
105C2×D13#433116yes—
106C4×C13—24no—
107C4×C13—44no—
108C4×C13#38214yes—
109Dic13—24no—
110Dic13—44no—
111Dic13C2×#12412yes—
112Dic13C2×#12512yes—
113C23×C4—131no—
114C23×C4—132no—
115C23×C4—134no—
116C22×C8—138no—
117C22×C8—268no—
118C22×C8—2616no—
119C2×C42—132no—
120C2×C42—131no—
121C2×C42—134no—
122C2×C42—134no—
123C2×C42—134no—
124C2×C42—132no—
125C2×C42—268no—
126C2×C42C2×#26112yes—
127C2×C42C2×#26111yescharacteristic
128C4⋊C8—268no—
129C4⋊C8—268no—
130#95—138no—
131#95—134no—
132#95C2×#26114yes—
133C2×C13C2×#38211yescharacteristic
134C2×C13C2×#42412yes—
135C2×C13C2×#43314yes—
136D13#183218yescomplemented
137C24—131no—
138C22×C4—131no—
139C22×C4—132no—
140C22×C4—132no—
141C22×C4—138no—
142C22×C4—132no—
143C22×C4—138no—
144C22×C4—134no—
145C22×C4—268no—
146C22×C4—268no—
147C22×C4—2616no—
148C22×C4C22×#26114yes—
149C22×C4C22×#26112yes—
150C22×C4C22×#26111yescharacteristic
151C2×C8—268no—
152C2×C8—2616no—
153C2×C8—5216no—
154C42—24no—
155C42—134no—
156C42—134no—
157C42—134no—
158C42—268no—
159C42—264no—
160C42C4⋊#26114yes—
161C13C2×#183211yescharacteristic, complemented, Sylow
162C23—132no—
163C23—134no—
164C23—138no—
165C23C23×#26111yescharacteristic
166C2×C4—24no—
167C2×C4—24no—
168C2×C4—28no—
169C2×C4—131no—
170C2×C4—131no—
171C2×C4—134no—
172C2×C4—138no—
173C2×C4—138no—
174C2×C4—134no—
175C2×C4—2616no—
176C2×C4—264no—
177C2×C4—264no—
178C2×C4—268no—
179C2×C4—5216no—
180C2×C4C2×C4⋊#26114yes—
181C2×C4C2×C4⋊#26112yes—
182C2×C4#8823714yes—
183C8—528no—
184C22—134no—
185C22—138no—
186C22—1316no—
187C22C22×C4⋊#26111yescharacteristic
188C22C2×#8823712yes—
189C22D13⋊#13114yes—
190C4—24no—
191C4—44no—
192C4—132no—
193C4—132no—
194C4—264no—
195C4—524no—
196C4#1171906014yes—
197C2—138no—
198C2C2×#1171906011yescharacteristic
199C2D13⋊#42412yes—
200C2D13⋊#43314yes—
subgroupG/H
centerC22×C4C22×#261
commutator, socleC23×C13C23×C4
FrattiniC23C23×#261
FittingC13×#376C4
prime radicalC23×D13C22×C4
cosocleC22×Dic13C24
hypercenter#376#261
hypocenterC13C2×#1832
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C22×C4 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #13130754C2semidirect
136. D13#1832semidirect
161. C13C2×#1832semidirect

Maximal subgroups

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

subgroupindex
C2×D13⋊(C4⋊C8)2
#131307542
#131304972
D13×#3762
C2×#183213