Finite Group Databasebeta

← #13130190

Subgroups — #13130190

Order 1664.

230 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 62 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#11719396C211yesmaximal, characteristic
2#11719054C211yesmaximal, characteristic, complemented
3C4×D13⋊C8C211yesmaximal, characteristic, complemented
4#11718244C212yesmaximal, complemented
5#11718243C212yesmaximal, complemented
6C2×D13⋊C8—21no—
7C13×#125C411yescharacteristic
8#88152—21no—
9#88151C411yescharacteristic
10#88149C411yescharacteristic
11#88148—21no—
12#88147—21no—
13#88147C2211yescharacteristic
14#88146—21no—
15#88141C2211yescharacteristic
16#88129C411yescharacteristic
17C42×D13C2211yescharacteristic
18#88111—21no—
19#88110—21no—
20C4⋊#1057C2212yes—
21C4×#1057—21no—
22C4×#1057C2212yes—
23C2×D52—21no—
24C2×D52C2×C411yescharacteristic
25C2×C4×D13—21no—
26C2×C4×D13C2×C411yescharacteristic
27C2×C4×D13D411yescharacteristic
28C2×C4×D13D411yescharacteristic
29C2×Dic26C2×C411yescharacteristic
30C2×#1057—22no—
31C2×#1057—22no—
32D13⋊C8—24no—
33C13×C4⋊C4—21no—
34C13×C4⋊C4—21no—
35C13×C4⋊C4C2×C411yescharacteristic
36C13×C4⋊C4C2×C411yescharacteristic
37C42×C13C2×C411yescharacteristic
38#6103—21no—
39#6103—21no—
40#6103—21no—
41#6103—21no—
42#6103—21no—
43C4⋊Dic13—21no—
44#6101—21no—
45C4×Dic13—21no—
46C4×Dic13D411yescharacteristic
47C4×Dic13D411yescharacteristic
48C4×Dic13C2311yescharacteristic
49#1494—131nomaximal, Sylow
50C22×D13—21no—
51C22×D13C22⋊C411yescharacteristic
52C2×C4×C13—21no—
53C2×C4×C13—21no—
54C2×C4×C13C22⋊C411yescharacteristic
55C2×C4×C13C22⋊C411yescharacteristic
56C2×C4×C13C22×C411yescharacteristic
57C2×Dic13—21no—
58C2×Dic13C22⋊C411yescharacteristic
59C2×Dic13C2×D411yescharacteristic
60C2×Dic13C2×D411yescharacteristic
61D52—22no—
62D52—42no—
63C4×D13—22no—
64C4×D13—22no—
65C4×D13—22no—
66C4×D13—42no—
67Dic26—22no—
68#1057—24no—
69#1057—42no—
70#529—131no—
71#432—131no—
72C2×C4×C8—131no—
73Q8⋊C8—132no—
74D4⋊C8—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—41no—
85C4×C13—41no—
86C4×C13#13112yes—
87Dic13—21no—
88Dic13—21no—
89Dic13—41no—
90Dic13#13512yes—
91C22×C8—261no—
92#126—261no—
93#125#26111yescharacteristic
94#124—131no—
95#123—261no—
96C22⋊Q8—131no—
97#121—131no—
98C4×Q8—131no—
99C4×D4—131no—
100C4×D4—261no—
101#117—261no—
102C2×C42—131no—
103C4⋊C8—132no—
104C22⋊C8—261no—
105#97—261no—
106C4×C8—132no—
107C4×C8—261no—
108C2×C13#40811yescharacteristic
109C2×C13#41611yescharacteristic
110C2×C13C2×#10411yescharacteristic
111D13—22no—
112D13—81no—
113C2×Q8—131no—
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—21no—
125C4⋊C4—261no—
126C4⋊C4—261no—
127C4⋊C4C2×#26111yescharacteristic
128C4⋊C4C2×#26111yescharacteristic
129C22⋊C4—261no—
130C22⋊C4—261no—
131C22⋊C4—261no—
132C22⋊C4—261no—
133C22⋊C4—261no—
134C42—131no—
135C42—131no—
136C42—131no—
137C42—261no—
138C42C2×#26111yescharacteristic
139C13#149411yescharacteristic, complemented, Sylow
140C23—131no—
141C23—261no—
142Q8—262no—
143D4—262no—
144D4—522no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—131no—
148C2×C4—131no—
149C2×C4—131no—
150C2×C4—262no—
151C2×C4—262no—
152C2×C4—262no—
153C2×C4—261no—
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—41no—
170C4—41no—
171C4—132no—
172C4—261no—
173C4—261no—
174C4—521no—
175C4#8824012yes—
176C2—262no—
177C2—1041no—
178C2#1171915911yescharacteristic
179C2D13⋊#10411yescharacteristic
180C2#1171916511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#125C4
socleC22×C13C2×C22⋊C4
prime radical#88149C4
cosocleC4×Dic13C23
hypercenter#125#261
hypocenterC13#1494
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
2. #11719054C2semidirect
3. C4×D13⋊C8C2semidirect
4. #11718244C2semidirect
5. #11718243C2semidirect
139. C13#1494semidirect

Maximal subgroups

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

subgroupindex
#117193962
#117190542
C4×D13⋊C82
#117182442
#117182432
#149413