Finite Group Databasebeta

← D13×#393 #13118034

Subgroups — D13×#393 #13118034

Order 1664.

1036 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 203 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
1C22×Q8×D13C211yesmaximal, characteristic, complemented
2C2×C22⋊C4×D13C213yesmaximal
3C13×#393C211yesmaximal, characteristic, complemented
4#11718892C211yesmaximal, characteristic, complemented
5#11718608C213yesmaximal, complemented
6#11718334C213yesmaximal, complemented
7D13×#95C213yesmaximal, complemented
8C24×D13C2211yescharacteristic
9C22×Q8×C13C2211yescharacteristic, complemented
10C2×Q8×D13—212no—
11C22×C4×D13C2213yes—
12C22×C4×D13C2213yes—
13C22×Dic26C2213yescomplemented
14C2×C13×C22⋊C4C2213yes—
15C2×C22⋊Dic13C2213yes—
16C2×#6103C2213yes—
17C2×#6103C2213yes—
18C22⋊C4×D13—212no—
19C13×#95C2213yescomplemented
20#88071C2216yescomplemented
21#88071C2213yescomplemented
22C24×C13C2311yescharacteristic
23C23×D13—26no—
24C23×D13—26no—
25C23×D13Q814yescomplemented
26C23×D13C2311yescharacteristic
27C23×D13C2311yescharacteristic
28C2×Q8×C13—26no—
29C22×C4×C13C2313yes—
30C22×C4×C13C2313yes—
31C22×Dic13C2313yes—
32C22×Dic13C2313yes—
33Q8×D13—232no—
34C2×C4×D13—212no—
35C2×C4×D13—26no—
36C2×C4×D13—212no—
37C2×C4×D13D4112yes—
38C2×Dic26—26no—
39C2×Dic26—212no—
40C13×C22⋊C4—26no—
41C22⋊Dic13—26no—
42#6103—26no—
43#6103—26no—
44C2×#393—131nomaximal, Sylow
45C23×C13—23no—
46C23×C13—23no—
47C23×C13C2×Q812yescomplemented
48C23×C13C2411yescharacteristic
49C22×D13—23no—
50C22×D13—23no—
51C22×D13—224no—
52C22×D13—44no—
53C22×D13—412no—
54C22×D13C2×D416yes—
55C22×D13C2×Q812yes—
56C22×D13C2×Q812yescomplemented
57C22×D13#4116yes—
58Q8×C13—28no—
59C2×C4×C13—26no—
60C2×C4×C13—23no—
61C2×C4×C13—26no—
62C2×C4×C13C2×D416yes—
63C2×Dic13—26no—
64C2×Dic13—23no—
65C2×Dic13—26no—
66C2×Dic13C2×D416yes—
67C4×D13—224no—
68C4×D13—412no—
69Dic26—224no—
70C23×Q8—131no—
71C22×C22⋊C4—133no—
72#393—131no—
73#393—133no—
74#393—133no—
75#393D1311yescharacteristic, direct product factor
76C2×#95—133no—
77C22×C13—26no—
78C22×C13—41no—
79C22×C13—43no—
80C22×C13C22×D413yes—
81C22×C13C22×Q811yescharacteristic
82C22×C13C2×#4113yes—
83C2×D13—26no—
84C2×D13—41no—
85C2×D13—43no—
86C2×D13—416no—
87C2×D13#12014yes—
88C2×D13C22⋊Q8112yes—
89C2×D13#124112yes—
90C4×C13—26no—
91C4×C13—43no—
92Dic13—26no—
93Dic13—43no—
94C25—131no—
95C22×Q8—133no—
96C22×Q8—2612no—
97C22×Q8C2×D1311yescharacteristic, complemented
98C23×C4—133no—
99C23×C4—133no—
100C2×C22⋊C4—133no—
101C2×C22⋊C4—133no—
102C2×C22⋊C4—133no—
103C2×C22⋊C4—2612no—
104C2×C22⋊C4C2×D1313yes—
105#95—136no—
106#95—133no—
107#95C2×D1313yescomplemented
108C2×C13—42no—
109C2×C13C2×#12011yescharacteristic
110C2×C13C2×C22⋊Q813yes—
111C2×C13C2×#12413yes—
112D13—42no—
113D13#39318yesdirect product factor
114C24—131no—
115C24—134no—
116C24—131no—
117C24—266no—
118C24—266no—
119C24C22×D1311yescharacteristic
120C2×Q8—26no—
121C2×Q8—2612no—
122C2×Q8—2632no—
123C2×Q8—266no—
124C22×C4—133no—
125C22×C4—1312no—
126C22×C4—133no—
127C22×C4—2612no—
128C22×C4—266no—
129C22×C4—2612no—
130C22×C4C22×D1313yes—
131C22×C4C22×D1313yes—
132C22⋊C4—26no—
133C22⋊C4—266no—
134C22⋊C4—266no—
135C22⋊C4—266no—
136C13C2×#39311yescharacteristic, complemented, Sylow
137C23—23no—
138C23—23no—
139C23—136no—
140C23—132no—
141C23—136no—
142C23—132no—
143C23—2624no—
144C23—263no—
145C23—263no—
146C23—524no—
147C23—5212no—
148C23Q8×D1312yescomplemented
149C23C23×D1311yescharacteristic
150Q8—28no—
151Q8—2624no—
152C2×C4—26no—
153C2×C4—23no—
154C2×C4—26no—
155C2×C4—136no—
156C2×C4—2624no—
157C2×C4—266no—
158C2×C4—263no—
159C2×C4—266no—
160C2×C4—5212no—
161C2×C4D4×D1316yes—
162C22—26no—
163C22—41no—
164C22—43no—
165C22—134no—
166C22—1312no—
167C22—1312no—
168C22—266no—
169C22—5216no—
170C22—521no—
171C22—523no—
172C22C2×D4×D1313yes—
173C22C2×Q8×D1311yescharacteristic
174C22#41×D1313yes—
175C4—26no—
176C4—43no—
177C4—266no—
178C4—523no—
179C2—42no—
180C2—138no—
181C2—522no—
182C2D13×#12011yescharacteristic
183C2D13×C22⋊Q813yes—
184C2D13×#12413yes—
subgroupG/H
center, FrattiniC23C23×D13
commutator, socle, cosocleC23×C13C24
FittingC13×#393C2
prime radicalC24×D13C22
hypercenter#393D13
hypocenterC13C2×#393
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C22×Q8×D13C2semidirect
3. C13×#393C2semidirect
4. #11718892C2semidirect
5. #11718608C2semidirect
6. #11718334C2semidirect
7. D13×#95C2semidirect
9. C22×Q8×C13C22semidirect
13. C22×Dic26C22semidirect
19. C13×#95C22semidirect
20. #88071C22semidirect
21. #88071C22semidirect
25. C23×D13Q8semidirect
47. C23×C13C2×Q8semidirect
56. C22×D13C2×Q8semidirect
75. #393D13direct (N × H)
97. C22×Q8C2×D13semidirect
107. #95C2×D13semidirect
113. D13#393direct (N × H)
136. C13C2×#393semidirect
148. C23Q8×D13semidirect

Maximal subgroups

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

subgroupindex
C22×Q8×D132
C2×C22⋊C4×D132
C13×#3932
#117188922
#117186082
#117183342
D13×#952
C2×#39313