Finite Group Databasebeta

← #13130195

Subgroups — #13130195

Order 1664.

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

normal subgroups only

This group has 246 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#11719301C211yesmaximal, characteristic
2#11719130C211yesmaximal, characteristic, complemented
3#11719119C211yesmaximal, characteristic, complemented
4D4⋊#1057C212yesmaximal, complemented
5#11718243C212yesmaximal, complemented
6C2×#6129—21no—
7C13×#121C411yescharacteristic
8#88194C411yescharacteristic
9#88193—21no—
10D4×Dic13C2211yescharacteristic
11#88184C411yescharacteristic
12C2×C4×Dic13C2211yescharacteristic
13#88147C2211yescharacteristic
14#88142C411yescharacteristic
15#88139—21no—
16#88135—21no—
17C22⋊#1057—21no—
18C22⋊#1057—21no—
19#88110—21no—
20C4⋊#1057—21no—
21C4⋊#1057C2212yes—
22C4×#1057C2212yes—
23C2×D4×C13—21no—
24C2×D4×C13C2×C411yescharacteristic
25C22×C4×C13C2×C411yescharacteristic
26C2×C22⋊D13—21no—
27C2×C22⋊D13—21no—
28C2×C22⋊D13—21no—
29C22×Dic13—21no—
30C22×Dic13D411yescharacteristic
31C22×Dic13D411yescharacteristic
32#6129—44no—
33C2×D52C2×C411yescharacteristic
34C2×C4×D13—21no—
35C2×Dic26—21no—
36C2×#1057—22no—
37C2×#1057—22no—
38C13×C4⋊C4C2×C411yescharacteristic
39C13×C22⋊C4—21no—
40C22⋊Dic13—21no—
41#6103—21no—
42#6103—21no—
43C4⋊Dic13C2×C411yescharacteristic
44#6101—21no—
45C4×Dic13C2×C411yescharacteristic
46C4×Dic13D411yescharacteristic
47C4×Dic13D411yescharacteristic
48C4×Dic13C2311yescharacteristic
49#1496—131nomaximal, Sylow
50C23×C13—21no—
51C23×C13C22⋊C411yescharacteristic
52C22×D13—21no—
53D4×C13—22no—
54D4×C13—42no—
55C2×C4×C13—22no—
56C2×C4×C13—21no—
57C2×C4×C13C22⋊C411yescharacteristic
58C2×C4×C13C22×C411yescharacteristic
59C22⋊D13—42no—
60C22⋊D13—42no—
61C22⋊D13—42no—
62C2×Dic13—22no—
63C2×Dic13—21no—
64C2×Dic13—41no—
65C2×Dic13—42no—
66C2×Dic13C22⋊C411yescharacteristic
67C2×Dic13C22⋊C411yescharacteristic
68C2×Dic13C2×D411yescharacteristic
69C2×Dic13C2×D411yescharacteristic
70D52—22no—
71C4×D13—42no—
72Dic26—42no—
73#1057—42no—
74#1057—42no—
75#532—131no—
76#432—131no—
77#431—131no—
78D4⋊C8—132no—
79D4⋊C8—132no—
80C22×C13—21no—
81C22×C13—21no—
82C22×C13—21no—
83C22×C13—41no—
84C22×C13—41no—
85C22×C13—41no—
86C22×C13C2×C22⋊C411yescharacteristic
87C2×D13—41no—
88C2×D13—41no—
89C2×D13—41no—
90C4×C13—21no—
91C4×C13—41no—
92C4×C13#13112yes—
93Dic13—21no—
94Dic13—21no—
95Dic13—21no—
96Dic13—41no—
97Dic13AGL(1,ℤ/8)12yes—
98C2×#41—261no—
99C4⋊Q8—131no—
100#127—131no—
101#124—261no—
102#121—131no—
103#121—261no—
104#121#26111yescharacteristic
105C4×D4—131no—
106C4×D4—131no—
107C4×D4—261no—
108C2×C42—131no—
109C4⋊C8—132no—
110C4⋊C8—261no—
111C22⋊C8—261no—
112C22⋊C8—261no—
113#97—261no—
114C4×C8—132no—
115C2×C13—41no—
116C2×C13—81no—
117C2×C13#40811yescharacteristic
118C2×C13#41811yescharacteristic
119C2×C13#42111yescharacteristic
120D13—81no—
121#41—524no—
122C2×Q8—261no—
123C2×D4—21no—
124C2×D4—131no—
125C2×D4—261no—
126C2×D4—261no—
127C2×D4—261no—
128C2×D4C2×#26111yescharacteristic
129C22×C4—131no—
130C22×C4—131no—
131C22×C4—261no—
132C22×C4—261no—
133C22×C4C2×#26111yescharacteristic
134C2×C8—262no—
135C2×C8—262no—
136C4⋊C4—131no—
137C4⋊C4—261no—
138C4⋊C4C2×#26111yescharacteristic
139C22⋊C4—21no—
140C22⋊C4—261no—
141C22⋊C4—261no—
142C22⋊C4—261no—
143C42—131no—
144C42—131no—
145C42—131no—
146C42—131no—
147C13#149611yescharacteristic, complemented, Sylow
148C23—21no—
149C23—261no—
150C23C22⋊#26111yescharacteristic
151Q8—522no—
152D4—22no—
153D4—42no—
154D4—262no—
155D4—522no—
156D4—522no—
157D4—522no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—131no—
161C2×C4—131no—
162C2×C4—131no—
163C2×C4—131no—
164C2×C4—262no—
165C2×C4—261no—
166C2×C4—522no—
167C2×C4—522no—
168C2×C4—521no—
169C2×C4C22⋊#26111yescharacteristic
170C2×C4C22×#26111yescharacteristic
171C8—522no—
172C8—522no—
173C22—21no—
174C22—21no—
175C22—21no—
176C22—41no—
177C22—41no—
178C22—41no—
179C22—521no—
180C22—521no—
181C22—521no—
182C22C2×C22⋊#26111yescharacteristic
183C4—21no—
184C4—41no—
185C4—132no—
186C4—261no—
187C4—261no—
188C4—261no—
189C4—521no—
190C4#8823812yes—
191C2—41no—
192C2—81no—
193C2—1041no—
194C2#1171913811yescharacteristic
195C2#1171914611yescharacteristic
196C2#1171916611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#121C4
socleC22×C13C2×C22⋊C4
prime radical#11719301C2
cosocleC4×Dic13C23
hypercenter#121#261
hypocenterC13#1496
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #121

Complements

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

NH ≅ G/Ntype
2. #11719130C2semidirect
3. #11719119C2semidirect
4. D4⋊#1057C2semidirect
5. #11718243C2semidirect
147. C13#1496semidirect

Maximal subgroups

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

subgroupindex
#117193012
#117191302
#117191192
D4⋊#10572
#117182432
#149613