Finite Group Databasebeta

← #13130227

Subgroups — #13130227

Order 1664.

272 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 60 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#11719430C211yesmaximal, characteristic
2#11719057C211yesmaximal, characteristic, complemented
3#11719054C211yesmaximal, characteristic, complemented
4#11718240C214yesmaximal, complemented
5C2×#6131—21no—
6C2×C4×#261—21no—
7C13×C4⋊Q8C411yescharacteristic, complemented
8#88201—21no—
9#88149—21no—
10#88149C2212yes—
11#88147—21no—
12#88147C412yescomplemented
13#88128C411yescharacteristic, complemented
14C42×D13C2211yescharacteristic
15(C2×#261)⋊C4—21no—
16(C2×#261)⋊C4C2212yes—
17#88111C2212yes—
18#88110—21no—
19C4⋊#1057—21no—
20C22×#261—22no—
21C2×Q8×C13—21no—
22#6131—44no—
23C2×D52—22no—
24C2×D52—21no—
25C2×D52—21no—
26C2×D52C2×C412yes—
27C2×C4×D13—22no—
28C2×C4×D13D411yescharacteristic
29C2×C4×D13D411yescharacteristic
30C2×C4×D13C2311yescharacteristic
31C2×#1057—22no—
32C4×#261—24no—
33C13×C4⋊C4—21no—
34C13×C4⋊C4C2×C412yes—
35C42×C13C2×C411yescharacteristic
36#6103—22no—
37#6103—22no—
38C4×Dic13C2×C411yescharacteristic
39C4×Dic13D411yescharacteristic
40C4×Dic13D411yescharacteristic
41#1505—131nomaximal, Sylow
42C22×D13—22no—
43C22×D13C2×D411yescharacteristic
44C2×#261—24no—
45C2×#261—42no—
46C2×#261—42no—
47Q8×C13—42no—
48C2×C4×C13—22no—
49C2×C4×C13C22⋊C411yescharacteristic
50C2×C4×C13C22⋊C411yescharacteristic
51C2×C4×C13C22×C411yescharacteristic
52C2×Dic13C22⋊C411yescharacteristic
53C2×Dic13C22⋊C411yescharacteristic
54C2×Dic13C2×D411yescharacteristic
55D52—42no—
56D52—42no—
57D52—44no—
58D52—42no—
59C4×D13—22no—
60C4×D13—22no—
61C4×D13—41no—
62C4×D13—44no—
63#1057—42no—
64#532—131no—
65#432—131no—
66#376—131no—
67#327—134no—
68C22×C13C2×C22⋊C411yescharacteristic
69C2×D13—21no—
70C2×D13—21no—
71C2×D13—42no—
72C2×D13—42no—
73C2×D13—42no—
74C2×D13AGL(1,ℤ/8)12yes—
75#261—44no—
76C4×C13—21no—
77C4×C13—21no—
78C4×C13—42no—
79C4×C13#10412yes—
80Dic13—21no—
81Dic13—21no—
82Dic13—21no—
83C2×#41—261no—
84C4⋊Q8#26111yescharacteristic, complemented
85#127—131no—
86#124—261no—
87#121—132no—
88#121—261no—
89C4×D4—132no—
90C4×D4—261no—
91C2×C42—131no—
92C2×C42—261no—
93C4⋊C8—261no—
94C22⋊C8—132no—
95#97—261no—
96#95—132no—
97#95—261no—
98C2×C13#41011yescharacteristic
99C2×C13#41811yescharacteristic
100C2×C13C2×#10411yescharacteristic
101D13—22no—
102D13—82no—
103#41—524no—
104C2×Q8—21no—
105C2×D4—132no—
106C2×D4—262no—
107C2×D4—261no—
108C2×D4—261no—
109C22×C4—131no—
110C22×C4—131no—
111C22×C4—131no—
112C22×C4—262no—
113C22×C4—262no—
114C2×C8—262no—
115C4⋊C4—21no—
116C4⋊C4C2×#26112yes—
117C22⋊C4—262no—
118C22⋊C4—262no—
119C42—131no—
120C42—131no—
121C42—131no—
122C42—264no—
123C42C2×#26111yescharacteristic
124C13#150511yescharacteristic, complemented, Sylow
125C23—131no—
126C23—262no—
127Q8—42no—
128D4—522no—
129D4—522no—
130D4—524no—
131D4—522no—
132C2×C4—22no—
133C2×C4—131no—
134C2×C4—131no—
135C2×C4—131no—
136C2×C4—262no—
137C2×C4—262no—
138C2×C4—264no—
139C2×C4—521no—
140C2×C4—524no—
141C2×C4—522no—
142C2×C4—522no—
143C2×C4C22⋊#26111yescharacteristic
144C2×C4C22⋊#26111yescharacteristic
145C2×C4C22×#26111yescharacteristic
146C8—522no—
147C22—132no—
148C22—261no—
149C22—261no—
150C22—522no—
151C22—522no—
152C22—522no—
153C22C2×C22⋊#26111yescharacteristic
154C4—21no—
155C4—21no—
156C4—42no—
157C4—261no—
158C4—261no—
159C4—261no—
160C4—524no—
161C4#8811812yes—
162C2—262no—
163C2—1042no—
164C2#1171913811yescharacteristic
165C2C2×#8811811yescharacteristic
166C2#1171915611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C4⋊Q8C4
socleC22×C13C2×C22⋊C4
prime radical#11719430C2
cosocleC2×C4×D13C23
hypercenterC4⋊Q8#261
hypocenterC13#1505
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11719057C2semidirect
3. #11719054C2semidirect
4. #11718240C2semidirect
7. C13×C4⋊Q8C4semidirect
12. #88147C4semidirect
13. #88128C4semidirect
84. C4⋊Q8#261semidirect
124. C13#1505semidirect

Maximal subgroups

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

subgroupindex
#117194302
#117190572
#117190542
#117182402
#150513