Finite Group Databasebeta

← #13130313

Subgroups — #13130313

Order 1664.

218 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 56 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#11719285C211yesmaximal, characteristic
2#11719055C211yesmaximal, characteristic, complemented
3#11719047C211yesmaximal, characteristic, complemented
4#11718299C212yesmaximal, complemented
5#11718242C212yesmaximal, complemented
6C2×D13⋊C8—21no—
7C4×Q8×C13C411yescharacteristic
8#88201C2211yescharacteristic
9#88200C411yescharacteristic
10#88152—21no—
11#88149C411yescharacteristic
12#88148—21no—
13#88144C2211yescharacteristic
14C4×D52—21no—
15C4×D52C411yescharacteristic
16#88126—21no—
17C42×D13C2211yescharacteristic
18#88112—21no—
19#88111—21no—
20#88110—21no—
21#88110C2212yes—
22#88110C2212yes—
23C2×Q8×C13C2×C411yescharacteristic
24C2×D52—21no—
25C2×D52C2×C411yescharacteristic
26C2×C4×D13—21no—
27C2×C4×D13C2×C411yescharacteristic
28C2×C4×D13D411yescharacteristic
29C2×C4×D13D411yescharacteristic
30C2×#1057—22no—
31C2×#1057—22no—
32D13⋊C8—24no—
33C13×C4⋊C4—21no—
34C13×C4⋊C4C2×C411yescharacteristic
35C42×C13—21no—
36C42×C13C2×C411yescharacteristic
37#6103—21no—
38#6103—21no—
39#6103—21no—
40#6103—21no—
41#6103—21no—
42C4⋊Dic13—21no—
43C4⋊Dic13C2×C411yescharacteristic
44#6101—21no—
45#6101—21no—
46C4×Dic13D411yescharacteristic
47C4×Dic13D411yescharacteristic
48C4×Dic13C2311yescharacteristic
49#1532—131nomaximal, Sylow
50C22×D13—21no—
51C22×D13C22⋊C411yescharacteristic
52Q8×C13—41no—
53C2×C4×C13—21no—
54C2×C4×C13—21no—
55C2×C4×C13C22⋊C411yescharacteristic
56C2×C4×C13C22⋊C411yescharacteristic
57C2×C4×C13C22×C411yescharacteristic
58C2×Dic13—21no—
59C2×Dic13C22⋊C411yescharacteristic
60C2×Dic13C2×D411yescharacteristic
61C2×Dic13C2×D411yescharacteristic
62D52—41no—
63D52—42no—
64C4×D13—22no—
65C4×D13—41no—
66C4×D13—41no—
67C4×D13—42no—
68#1057—24no—
69#1057—42no—
70#529—131no—
71#432—131no—
72C2×#97—131no—
73#330—132no—
74#329—132no—
75C22×C13C2×C22⋊C411yescharacteristic
76C2×D13—21no—
77C2×D13—21no—
78C2×D13—41no—
79C2×D13—41no—
80C2×D13—41no—
81C2×D13#10412yes—
82C4×C13—21no—
83C4×C13—21no—
84C4×C13—21no—
85C4×C13—41no—
86C4×C13—41no—
87Dic13—21no—
88Dic13—21no—
89Dic13—21no—
90Dic13—41no—
91C22×C8—261no—
92#126—261no—
93#125—131no—
94#124—131no—
95#123—261no—
96C22⋊Q8—131no—
97#121—131no—
98C4×Q8#26111yescharacteristic
99C4×D4—131no—
100C4×D4—261no—
101#117—261no—
102C2×C42—131no—
103C4⋊C8—261no—
104C22⋊C8—261no—
105#97—132no—
106#97—132no—
107#97—261no—
108C2×C13#41311yescharacteristic
109C2×C13C2×#10411yescharacteristic
110C2×C13#42111yescharacteristic
111D13—22no—
112D13—81no—
113C2×Q8C2×#26111yescharacteristic
114C2×D4—131no—
115C2×D4—261no—
116C22×C4—131no—
117C22×C4—131no—
118C22×C4—131no—
119C22×C4—261no—
120C2×C8—262no—
121C2×C8—264no—
122C2×C8—262no—
123C4⋊C4—21no—
124C4⋊C4—131no—
125C4⋊C4—261no—
126C4⋊C4—261no—
127C4⋊C4—261no—
128C4⋊C4C2×#26111yescharacteristic
129C22⋊C4—261no—
130C22⋊C4—261no—
131C22⋊C4—261no—
132C22⋊C4—261no—
133C22⋊C4—261no—
134C42—21no—
135C42—131no—
136C42—131no—
137C42—131no—
138C42C2×#26111yescharacteristic
139C13#153211yescharacteristic, complemented, Sylow
140C23—131no—
141C23—261no—
142Q8—41no—
143D4—521no—
144D4—522no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—131no—
148C2×C4—131no—
149C2×C4—131no—
150C2×C4—262no—
151C2×C4—261no—
152C2×C4—521no—
153C2×C4—521no—
154C2×C4—522no—
155C2×C4C22⋊#26111yescharacteristic
156C2×C4C22⋊#26111yescharacteristic
157C2×C4C22×#26111yescharacteristic
158C8—264no—
159C8—522no—
160C22—132no—
161C22—261no—
162C22—261no—
163C22—521no—
164C22—521no—
165C22—521no—
166C22C2×C22⋊#26111yescharacteristic
167C4—21no—
168C4—21no—
169C4—21no—
170C4—41no—
171C4—41no—
172C4—261no—
173C4—261no—
174C4—261no—
175C4—521no—
176C2—262no—
177C2—1041no—
178C2#1171913211yescharacteristic
179C2#1171915511yescharacteristic
180C2D13⋊#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC4×Q8×C13C4
socleC22×C13C2×C22⋊C4
prime radical#88149C4
cosocleC4×Dic13C23
hypercenterC4×Q8#261
hypocenterC13#1532
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. #11719055C2semidirect
3. #11719047C2semidirect
4. #11718299C2semidirect
5. #11718242C2semidirect
139. C13#1532semidirect

Maximal subgroups

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

subgroupindex
#117192852
#117190552
#117190472
#117182992
#117182422
#153213