Finite Group Databasebeta

← #13130198

Subgroups — #13130198

Order 1664.

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

normal subgroups only

This group has 202 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#11719327C211yesmaximal, characteristic
2#11719130C211yesmaximal, characteristic
3#11719119C211yesmaximal, characteristic
4Q8⋊#1057C212yesmaximal, complemented
5#11718244C212yesmaximal, complemented
6C13×C22⋊Q8C411yescharacteristic
7Q8×Dic13C2211yescharacteristic
8#88198C411yescharacteristic
9#88178C411yescharacteristic
10C2×C4×Dic13C2211yescharacteristic
11#88143—21no—
12#88142C411yescharacteristic
13#88141—21no—
14#88141C2211yescharacteristic
15#88132—21no—
16#88131—21no—
17C22⋊#1057—21no—
18C22⋊#1057—21no—
19#88110—21no—
20C4⋊#1057—21no—
21C4⋊#1057C2212yes—
22C4×#1057C2212yes—
23C2×Q8×C13C2×C411yescharacteristic
24C22×C4×C13C2×C411yescharacteristic
25C22×Dic13D411yescharacteristic
26C22×Dic13D411yescharacteristic
27C2×Dic26—21no—
28C2×Dic26C2×C411yescharacteristic
29C2×#1057—22no—
30C2×#1057—22no—
31C13×C4⋊C4—21no—
32C13×C4⋊C4C2×C411yescharacteristic
33C13×C22⋊C4—21no—
34C22⋊Dic13—21no—
35C4⋊Dic13—21no—
36C4⋊Dic13C2×C411yescharacteristic
37#6101—21no—
38#6101—21no—
39#6101—21no—
40#6101—21no—
41#6101—21no—
42C4×Dic13—21no—
43C4×Dic13—21no—
44C4×Dic13C2×C411yescharacteristic
45C4×Dic13D411yescharacteristic
46C4×Dic13D411yescharacteristic
47C4×Dic13C2311yescharacteristic
48#1497—131nomaximal, Sylow
49C23×C13C22⋊C411yescharacteristic
50Q8×C13—22no—
51C2×C4×C13—22no—
52C2×C4×C13—21no—
53C2×C4×C13—21no—
54C2×C4×C13C22⋊C411yescharacteristic
55C2×C4×C13C22×C411yescharacteristic
56C2×Dic13—22no—
57C2×Dic13—21no—
58C2×Dic13—21no—
59C2×Dic13—41no—
60C2×Dic13C22⋊C411yescharacteristic
61C2×Dic13C22⋊C411yescharacteristic
62C2×Dic13C2×D411yescharacteristic
63C2×Dic13C2×D411yescharacteristic
64Dic26—22no—
65Dic26—42no—
66#1057—42no—
67#1057—42no—
68#533—131no—
69#432—131no—
70#431—131no—
71Q8⋊C8—132no—
72Q8⋊C8—132no—
73C22×C13—21no—
74C22×C13—21no—
75C22×C13—21no—
76C22×C13C2×C22⋊C411yescharacteristic
77C4×C13—21no—
78C4×C13—41no—
79C4×C13—41no—
80C4×C13#13112yes—
81Dic13—21no—
82Dic13—21no—
83Dic13—21no—
84Dic13—41no—
85Dic13—41no—
86Dic13#13712yes—
87C4⋊Q8—131no—
88C4⋊Q8—131no—
89#125—261no—
90C22⋊Q8—131no—
91C22⋊Q8—261no—
92C22⋊Q8#26111yescharacteristic
93C4×Q8—131no—
94C4×Q8—131no—
95C4×Q8—261no—
96#117—261no—
97C2×C42—131no—
98C4⋊C8—132no—
99C4⋊C8—261no—
100C22⋊C8—261no—
101C22⋊C8—261no—
102#97—261no—
103C4×C8—132no—
104C2×C13—41no—
105C2×C13#40811yescharacteristic
106C2×C13#41911yescharacteristic
107C2×C13#42111yescharacteristic
108C2×Q8—131no—
109C2×Q8—261no—
110C2×Q8C2×#26111yescharacteristic
111C22×C4—131no—
112C22×C4—131no—
113C22×C4C2×#26111yescharacteristic
114C2×C8—262no—
115C2×C8—262no—
116C4⋊C4—21no—
117C4⋊C4—131no—
118C4⋊C4—261no—
119C4⋊C4—261no—
120C4⋊C4—261no—
121C4⋊C4—261no—
122C4⋊C4—261no—
123C4⋊C4—261no—
124C4⋊C4C2×#26111yescharacteristic
125C22⋊C4—21no—
126C22⋊C4—261no—
127C42—131no—
128C42—131no—
129C42—131no—
130C42—131no—
131C42—261no—
132C42—261no—
133C13#149711yescharacteristic, complemented, Sylow
134C23C22⋊#26111yescharacteristic
135Q8—22no—
136Q8—262no—
137Q8—522no—
138C2×C4—22no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—131no—
142C2×C4—131no—
143C2×C4—131no—
144C2×C4—131no—
145C2×C4—262no—
146C2×C4—261no—
147C2×C4—261no—
148C2×C4—521no—
149C2×C4C22⋊#26111yescharacteristic
150C2×C4C22×#26111yescharacteristic
151C8—522no—
152C8—522no—
153C22—21no—
154C22—21no—
155C22—21no—
156C22C2×C22⋊#26111yescharacteristic
157C4—21no—
158C4—41no—
159C4—41no—
160C4—132no—
161C4—261no—
162C4—261no—
163C4—261no—
164C4—521no—
165C4—521no—
166C4#8823812yes—
167C2—41no—
168C2#1171914611yescharacteristic
169C2#1171915311yescharacteristic
170C2#1171916611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C22⋊Q8C4
socleC22×C13C2×C22⋊C4
prime radicalC23×C13C22⋊C4
cosocleC4×Dic13C23
hypercenterC22⋊Q8#261
hypocenterC13#1497
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
4. Q8⋊#1057C2semidirect
5. #11718244C2semidirect
133. C13#1497semidirect

Maximal subgroups

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

subgroupindex
#117193272
#117191302
#117191192
Q8⋊#10572
#117182442
#149713