Finite Group Databasebeta

← #13130267

Subgroups — #13130267

Order 1664.

264 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 66 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#11719060C211yesmaximal, characteristic, complemented
3#11719049C211yesmaximal, 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#88112—21no—
18#88111C2212yes—
19C4×#1057—21no—
20C22×#261—22no—
21C2×Q8×C13—21no—
22#6131—42no—
23#6131—42no—
24C2×D52—22no—
25C2×D52—21no—
26C2×D52—21no—
27C2×D52C2×C412yes—
28C2×C4×D13—22no—
29C2×C4×D13D411yescharacteristic
30C2×C4×D13D411yescharacteristic
31C2×C4×D13C2311yescharacteristic
32C2×#1057—22no—
33C4⋊#261—42no—
34C13×C4⋊C4—21no—
35C13×C4⋊C4C2×C412yes—
36C42×C13C2×C411yescharacteristic
37#6103—22no—
38#6103—22no—
39C4×Dic13C2×C411yescharacteristic
40C4×Dic13D411yescharacteristic
41C4×Dic13D411yescharacteristic
42#1517—131nomaximal, Sylow
43C22×D13—22no—
44C22×D13C2×D411yescharacteristic
45C2×#261—42no—
46C2×#261—42no—
47C2×#261—42no—
48Q8×C13—42no—
49C2×C4×C13—22no—
50C2×C4×C13C22⋊C411yescharacteristic
51C2×C4×C13C22⋊C411yescharacteristic
52C2×C4×C13C22×C411yescharacteristic
53C2×Dic13C22⋊C411yescharacteristic
54C2×Dic13C22⋊C411yescharacteristic
55C2×Dic13C2×D411yescharacteristic
56D52—42no—
57D52—42no—
58D52—42no—
59D52—42no—
60D52—42no—
61C4×D13—41no—
62C4×D13—41no—
63C4×D13—44no—
64C4×D13D812yes—
65C4×D13SD1612yes—
66#1057—42no—
67#532—131no—
68#431—131no—
69#382—131no—
70#327—134no—
71C22×C13C2×C22⋊C411yescharacteristic
72C2×D13—21no—
73C2×D13—21no—
74C2×D13—42no—
75C2×D13—42no—
76C2×D13—42no—
77C2×D13C2×D811yescharacteristic
78C2×D13C2×SD1611yescharacteristic
79#261—82no—
80C4×C13—21no—
81C4×C13—21no—
82C4×C13—42no—
83C4×C13#10212yes—
84Dic13—21no—
85Dic13—21no—
86Dic13#10212yes—
87C2×#41—261no—
88C4⋊Q8#26111yescharacteristic, complemented
89#127—131no—
90#124—261no—
91#121—132no—
92#121—261no—
93C4×D4—132no—
94C4×D4—261no—
95C2×C4⋊C4—261no—
96C2×C42—131no—
97C4⋊C8—261no—
98C22⋊C8—132no—
99C4×C8—261no—
100#95—132no—
101#95—261no—
102C2×C13#41011yescharacteristic
103C2×C13C2×#10211yescharacteristic
104C2×C13#42111yescharacteristic
105D13—21no—
106D13—21no—
107D13—82no—
108#41—522no—
109#41—522no—
110C2×Q8—21no—
111C2×D4—132no—
112C2×D4—262no—
113C2×D4—261no—
114C2×D4—261no—
115C22×C4—131no—
116C22×C4—131no—
117C22×C4—131no—
118C22×C4—262no—
119C22×C4—262no—
120C2×C8—262no—
121C4⋊C4—21no—
122C4⋊C4—522no—
123C4⋊C4C2×#26112yes—
124C22⋊C4—262no—
125C22⋊C4—262no—
126C42—131no—
127C42—131no—
128C42—131no—
129C42C2×#26111yescharacteristic
130C13#151711yescharacteristic, complemented, Sylow
131C23—131no—
132C23—262no—
133Q8—42no—
134D4—522no—
135D4—522no—
136D4—522no—
137D4—522no—
138D4—522no—
139C2×C4—22no—
140C2×C4—131no—
141C2×C4—132no—
142C2×C4—132no—
143C2×C4—131no—
144C2×C4—131no—
145C2×C4—521no—
146C2×C4—521no—
147C2×C4—524no—
148C2×C4—522no—
149C2×C4—522no—
150C2×C4—522no—
151C2×C4C22⋊#26111yescharacteristic
152C2×C4C22⋊#26111yescharacteristic
153C2×C4C22×#26111yescharacteristic
154C8—522no—
155C22—131no—
156C22—131no—
157C22—261no—
158C22—261no—
159C22—522no—
160C22—522no—
161C22—522no—
162C22C2×C22⋊#26111yescharacteristic
163C4—21no—
164C4—21no—
165C4—42no—
166C4—132no—
167C4—261no—
168C4—261no—
169C4—1042no—
170C4#8811512yes—
171C2—261no—
172C2—261no—
173C2—1042no—
174C2C2×#8811511yescharacteristic
175C2#1171915511yescharacteristic
176C2#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#1517
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. #11719060C2semidirect
3. #11719049C2semidirect
4. #11718240C2semidirect
7. C13×C4⋊Q8C4semidirect
12. #88147C4semidirect
13. #88128C4semidirect
88. C4⋊Q8#261semidirect
130. C13#1517semidirect

Maximal subgroups

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

subgroupindex
#117194302
#117190602
#117190492
#117182402
#151713