Finite Group Databasebeta

← #13130270

Subgroups — #13130270

Order 1664.

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

normal subgroups only

This group has 220 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#11719433C211yesmaximal, characteristic
2#11719060C211yesmaximal, characteristic
3#11719049C211yesmaximal, characteristic
4#11718298C214yesmaximal
5C2×C4⋊#261—21no—
6C13×C4⋊Q8C411yescharacteristic, complemented
7#88200C2212yes—
8Q8×Dic13C412yescomplemented
9#88151—21no—
10#88146—21no—
11#88144—21no—
12#88141—21no—
13C42×D13C2211yescharacteristic
14#88123C411yescharacteristic, complemented
15(C2×#261)⋊C4—21no—
16(C2×#261)⋊C4C2212yes—
17#88112—21no—
18#88111C2212yes—
19C4×#1057—21no—
20C22×#261—22no—
21C2×Q8×C13C2×C412yes—
22C2×C4×D13D411yescharacteristic
23C2×C4×D13D411yescharacteristic
24C2×C4×D13C2311yescharacteristic
25C2×Dic26—21no—
26C2×#1057—22no—
27C4⋊#261—42no—
28C13×C4⋊C4—21no—
29C13×C4⋊C4—21no—
30C42×C13C2×C411yescharacteristic
31#6103—22no—
32C4⋊Dic13—21no—
33C4⋊Dic13—22no—
34C4⋊Dic13C2×C412yes—
35#6101—22no—
36C4×Dic13—22no—
37C4×Dic13C2×C411yescharacteristic
38C4×Dic13D411yescharacteristic
39C4×Dic13D411yescharacteristic
40#1518—131nomaximal, Sylow
41C22×D13C2×D411yescharacteristic
42C2×#261—42no—
43C2×#261—42no—
44C2×#261—42no—
45Q8×C13—42no—
46C2×C4×C13—22no—
47C2×C4×C13C22⋊C411yescharacteristic
48C2×C4×C13C22⋊C411yescharacteristic
49C2×C4×C13C22×C411yescharacteristic
50C2×Dic13—22no—
51C2×Dic13C22⋊C411yescharacteristic
52C2×Dic13C22⋊C411yescharacteristic
53C2×Dic13C2×D411yescharacteristic
54C4×D13—41no—
55C4×D13—41no—
56C4×D13SD1612yes—
57C4×D13Q1612yes—
58Dic26—42no—
59#1057—42no—
60#533—131no—
61#431—131no—
62#382—131no—
63#328—134no—
64C22×C13C2×C22⋊C411yescharacteristic
65C2×D13—21no—
66C2×D13—21no—
67C2×D13C2×SD1611yescharacteristic
68C2×D13C2×Q1611yescharacteristic
69#261—82no—
70C4×C13—21no—
71C4×C13—21no—
72C4×C13—42no—
73C4×C13#10312yes—
74Dic13—21no—
75Dic13—21no—
76Dic13—42no—
77Dic13#10312yes—
78C4⋊Q8—131no—
79C4⋊Q8#26111yescharacteristic, complemented
80#125—261no—
81C22⋊Q8—132no—
82C22⋊Q8—261no—
83C4×Q8—132no—
84C4×Q8—261no—
85#117—261no—
86C2×C4⋊C4—261no—
87C2×C42—131no—
88C4⋊C8—261no—
89C22⋊C8—132no—
90C4×C8—261no—
91#95—132no—
92#95—261no—
93C2×C13#41011yescharacteristic
94C2×C13C2×#10311yescharacteristic
95C2×C13#42111yescharacteristic
96D13—21no—
97D13—21no—
98C2×Q8—261no—
99C2×Q8C2×#26112yes—
100C22×C4—131no—
101C22×C4—131no—
102C22×C4—131no—
103C22×C4—262no—
104C2×C8—262no—
105C4⋊C4—21no—
106C4⋊C4—21no—
107C4⋊C4—132no—
108C4⋊C4—262no—
109C4⋊C4—262no—
110C4⋊C4—261no—
111C4⋊C4—522no—
112C22⋊C4—262no—
113C42—131no—
114C42—131no—
115C42—131no—
116C42—262no—
117C42C2×#26111yescharacteristic
118C13#151811yescharacteristic, complemented, Sylow
119C23—131no—
120Q8—42no—
121Q8—522no—
122C2×C4—22no—
123C2×C4—131no—
124C2×C4—132no—
125C2×C4—132no—
126C2×C4—131no—
127C2×C4—131no—
128C2×C4—262no—
129C2×C4—521no—
130C2×C4—521no—
131C2×C4—522no—
132C2×C4—522no—
133C2×C4—522no—
134C2×C4C22⋊#26111yescharacteristic
135C2×C4C22⋊#26111yescharacteristic
136C2×C4C22×#26111yescharacteristic
137C8—522no—
138C22—131no—
139C22—131no—
140C22—261no—
141C22—261no—
142C22C2×C22⋊#26111yescharacteristic
143C4—21no—
144C4—21no—
145C4—42no—
146C4—132no—
147C4—261no—
148C4—261no—
149C4—522no—
150C4—1042no—
151C4#8811712yes—
152C2—261no—
153C2—261no—
154C2#1171914211yescharacteristic
155C2C2×#8811711yescharacteristic
156C2#1171915511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C4⋊Q8C4
socleC22×C13C2×C22⋊C4
prime radicalC22×D13C2×D4
cosocleC2×C4×D13C23
hypercenterC4⋊Q8#261
hypocenterC13#1518
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
6. C13×C4⋊Q8C4semidirect
8. Q8×Dic13C4semidirect
14. #88123C4semidirect
79. C4⋊Q8#261semidirect
118. C13#1518semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117190602
#117190492
#117182982
#151813