Finite Group Databasebeta

← #13131119

Subgroups — #13131119

Order 1664.

238 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 52 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#11719429C211yesmaximal, characteristic
2#11719156C212yesmaximal
3#11718300C212yesmaximal, complemented
4#11718226C212yesmaximal, complemented
5C2×#6131C2211yescharacteristic
6C2×Q8×D13C411yescharacteristic, complemented
7#88237—22no—
8C13×C4⋊Q8C411yescharacteristic, complemented
9#88201C2211yescharacteristic
10#88198C411yescharacteristic, complemented
11#88150—22no—
12#88148—22no—
13#88129C2211yescharacteristic
14#88126C411yescharacteristic, complemented
15#88107—22no—
16#88107C2214yes—
17C2×Q8×C13C2×C411yescharacteristic
18C2×Q8×C13C2×C411yescharacteristic
19#6131—42no—
20Q8×D13—42no—
21C2×D52D412yes—
22C2×D52C2311yescharacteristic
23C2×C4×D13—21no—
24C2×C4×D13C2×C411yescharacteristic
25C2×C4×D13D412yes—
26C2×Dic26—21no—
27C2×Dic26C2×C411yescharacteristic
28C22⋊#261—24no—
29C4⋊#261—42no—
30C4×#261—42no—
31C13×C4⋊C4—22no—
32C42×C13C2×C411yescharacteristic
33#6103—21no—
34#6103—22no—
35#6103—22no—
36#6101—22no—
37#6101—21no—
38C4×Dic13C2×C411yescharacteristic
39#2129—131nomaximal, Sylow
40C22×D13C22⋊C411yescharacteristic
41C22×D13C2×D412yes—
42C2×#261—44no—
43Q8×C13—41no—
44Q8×C13—41no—
45C2×C4×C13—21no—
46C2×C4×C13—21no—
47C2×C4×C13C22⋊C412yes—
48C2×C4×C13C22×C411yescharacteristic
49C2×Dic13—21no—
50C2×Dic13—21no—
51C2×Dic13C22⋊C411yescharacteristic
52D52—42no—
53D52—41no—
54C4×D13—22no—
55C4×D13—22no—
56C4×D13—22no—
57C4×D13—42no—
58Dic26—42no—
59Dic26—41no—
60#536—131no—
61#410—132no—
62#354—132no—
63#354—132no—
64C22×C13C2×C22⋊C411yescharacteristic
65C2×D13—21no—
66C2×D13—22no—
67C2×D13—41no—
68C2×D13—42no—
69#261—84no—
70C4×C13—21no—
71C4×C13—22no—
72C4×C13—41no—
73C4×C13—41no—
74Dic13—41no—
75Dic13—41no—
76Dic13#9912yes—
77C2×#41—131no—
78C22×Q8—131no—
79C4⋊Q8—131no—
80C4⋊Q8#26111yescharacteristic, complemented
81#124—131no—
82#124—131no—
83#123—262no—
84C22⋊Q8—262no—
85#117—131no—
86#117—262no—
87#99—134no—
88#99—262no—
89C2×C13—21no—
90C2×C13C2×#9911yescharacteristic
91D13—42no—
92D13—41no—
93#41—522no—
94C2×Q8—131no—
95C2×Q8—261no—
96C2×Q8—522no—
97C2×Q8C2×#26111yescharacteristic
98C2×Q8C2×#26111yescharacteristic
99C2×D4—132no—
100C2×D4—131no—
101C22×C4—132no—
102C22×C4—131no—
103C22×C4—261no—
104C4⋊C4—22no—
105C4⋊C4—261no—
106C4⋊C4—262no—
107C4⋊C4—522no—
108C22⋊C4—261no—
109C22⋊C4—262no—
110C22⋊C4—262no—
111C22⋊C4—264no—
112C42—131no—
113C42—522no—
114C42C2×#26111yescharacteristic
115C13#212911yescharacteristic, complemented, Sylow
116C23—132no—
117C23—131no—
118Q8—41no—
119Q8—41no—
120Q8—521no—
121Q8—522no—
122D4—522no—
123D4—521no—
124C2×C4—21no—
125C2×C4—21no—
126C2×C4—131no—
127C2×C4—262no—
128C2×C4—262no—
129C2×C4—262no—
130C2×C4—261no—
131C2×C4—261no—
132C2×C4—522no—
133C2×C4—524no—
134C2×C4C22⋊#26112yes—
135C2×C4C22×#26111yescharacteristic
136C22—262no—
137C22—261no—
138C22—522no—
139C22—521no—
140C22C2×C22⋊#26111yescharacteristic
141C4—22no—
142C4—21no—
143C4—41no—
144C4—41no—
145C4—132no—
146C4—521no—
147C4—521no—
148C4—1044no—
149C2—21no—
150C2—522no—
151C2—521no—
152C2D13⋊#9911yescharacteristic
subgroupG/H
centerC2D13⋊#99
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C4⋊Q8C4
socleC2×C13C2×#99
prime radicalC2×#6131C22
cosocleC2×D52C23
hypercenterC4⋊Q8#261
hypocenterC13#2129
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
3. #11718300C2semidirect
4. #11718226C2semidirect
6. C2×Q8×D13C4semidirect
8. C13×C4⋊Q8C4semidirect
10. #88198C4semidirect
14. #88126C4semidirect
80. C4⋊Q8#261semidirect
115. C13#2129semidirect

Maximal subgroups

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

subgroupindex
#117194292
#117191562
#117183002
#117182262
#212913