Finite Group Databasebeta

← #13130148

Subgroups — #13130148

Order 1664.

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

normal subgroups only

This group has 212 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#11719385C211yesmaximal, characteristic
2#11719051C211yesmaximal, characteristic, complemented
3#11719051C211yesmaximal, characteristic, complemented
4Q8⋊#1057C212yesmaximal, complemented
5D4⋊#1057C212yesmaximal, complemented
6C13×#124C411yescharacteristic
7#88200C411yescharacteristic
8Q8×Dic13C2211yescharacteristic
9#88192C411yescharacteristic
10D4×Dic13C2211yescharacteristic
11#88137—21no—
12#88135—21no—
13#88133—21no—
14#88131—21no—
15C42×D13C2211yescharacteristic
16#88124C411yescharacteristic
17#88111—21no—
18#88111—21no—
19C4⋊#1057—21no—
20C4⋊#1057C2212yes—
21C4×#1057—21no—
22C4×#1057C2212yes—
23C2×Q8×C13C2×C411yescharacteristic
24C2×D4×C13C2×C411yescharacteristic
25C2×C22⋊D13—21no—
26C22×Dic13—21no—
27C2×C4×D13C2×C411yescharacteristic
28C2×C4×D13D411yescharacteristic
29C2×C4×D13D411yescharacteristic
30C2×#1057—22no—
31C2×#1057—22no—
32C13×C22⋊C4—21no—
33C13×C22⋊C4—21no—
34C42×C13C2×C411yescharacteristic
35C22⋊Dic13—21no—
36C22⋊Dic13—21no—
37#6103—21no—
38C4⋊Dic13—21no—
39C4⋊Dic13C2×C411yescharacteristic
40C4⋊Dic13C2×C411yescharacteristic
41#6101—21no—
42#6101—21no—
43#6101—21no—
44C4×Dic13—21no—
45C4×Dic13D411yescharacteristic
46C4×Dic13D411yescharacteristic
47C4×Dic13C2311yescharacteristic
48#1482—131nomaximal, Sylow
49C23×C13—21no—
50C22×D13C22⋊C411yescharacteristic
51Q8×C13—22no—
52D4×C13—22no—
53C2×C4×C13—21no—
54C2×C4×C13C22⋊C411yescharacteristic
55C2×C4×C13C22⋊C411yescharacteristic
56C2×C4×C13C22×C411yescharacteristic
57C22⋊D13—42no—
58C2×Dic13—21no—
59C2×Dic13—21no—
60C2×Dic13—42no—
61C2×Dic13C22⋊C411yescharacteristic
62C2×Dic13C2×D411yescharacteristic
63C2×Dic13C2×D411yescharacteristic
64C4×D13—22no—
65C4×D13—22no—
66C4×D13—41no—
67#1057—42no—
68#1057—42no—
69#529—131no—
70#431—131no—
71#431—131no—
72Q8⋊C8—132no—
73D4⋊C8—132no—
74C22×C13—41no—
75C22×C13—41no—
76C22×C13—41no—
77C22×C13C2×C22⋊C411yescharacteristic
78C2×D13—21no—
79C2×D13—21no—
80C2×D13—21no—
81C4×C13—21no—
82C4×C13—21no—
83C4×C13—41no—
84C4×C13#13112yes—
85Dic13—21no—
86Dic13—21no—
87Dic13—41no—
88Dic13—41no—
89Dic13#13512yes—
90#126—261no—
91#125—131no—
92#124#26111yescharacteristic
93#123—261no—
94C22⋊Q8—131no—
95#121—131no—
96C4×Q8—131no—
97C4×D4—131no—
98C4×D4—261no—
99#117—261no—
100C2×C42—131no—
101C4⋊C8—132no—
102C4⋊C8—261no—
103C22⋊C8—261no—
104C22⋊C8—261no—
105C4×C8—132no—
106C4×C8—261no—
107C2×C13—81no—
108C2×C13#40811yescharacteristic
109C2×C13#41611yescharacteristic
110C2×C13#42111yescharacteristic
111D13—41no—
112C2×Q8C2×#26111yescharacteristic
113C2×D4—261no—
114C2×D4C2×#26111yescharacteristic
115C22×C4—131no—
116C22×C4—131no—
117C22×C4—131no—
118C22×C4—261no—
119C2×C8—262no—
120C2×C8—262no—
121C4⋊C4—131no—
122C4⋊C4—131no—
123C4⋊C4—261no—
124C4⋊C4—261no—
125C4⋊C4—261no—
126C4⋊C4—261no—
127C22⋊C4—21no—
128C22⋊C4—21no—
129C22⋊C4—261no—
130C22⋊C4—261no—
131C22⋊C4—261no—
132C42—131no—
133C42—131no—
134C42—131no—
135C42—261no—
136C42C2×#26111yescharacteristic
137C13#148211yescharacteristic, complemented, Sylow
138C23—21no—
139C23—131no—
140Q8—22no—
141D4—22no—
142D4—522no—
143C2×C4—21no—
144C2×C4—131no—
145C2×C4—131no—
146C2×C4—131no—
147C2×C4—262no—
148C2×C4—262no—
149C2×C4—261no—
150C2×C4—261no—
151C2×C4—521no—
152C2×C4—522no—
153C2×C4C22⋊#26111yescharacteristic
154C2×C4C22⋊#26111yescharacteristic
155C2×C4C22×#26111yescharacteristic
156C8—522no—
157C8—522no—
158C22—41no—
159C22—41no—
160C22—41no—
161C22—261no—
162C22—261no—
163C22—261no—
164C22C2×C22⋊#26111yescharacteristic
165C4—21no—
166C4—21no—
167C4—41no—
168C4—132no—
169C4—261no—
170C4—261no—
171C4—521no—
172C4—521no—
173C4#8823812yes—
174C2—81no—
175C2—521no—
176C2#1171914711yescharacteristic
177C2#1171916511yescharacteristic
178C2#1171916611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#124C4
socleC22×C13C2×C22⋊C4
prime radical#88192C4
cosocleC4×Dic13C23
hypercenter#124#261
hypocenterC13#1482
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. #11719051C2semidirect
3. #11719051C2semidirect
4. Q8⋊#1057C2semidirect
5. D4⋊#1057C2semidirect
137. C13#1482semidirect

Maximal subgroups

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

subgroupindex
#117193852
#117190512
Q8⋊#10572
D4⋊#10572
#148213