Finite Group Databasebeta

← #13131024

Subgroups — #13131024

Order 1664.

244 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 70 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#11719433C211yesmaximal, characteristic
2#11719057C211yesmaximal, characteristic
3#11719053C211yesmaximal, characteristic
4#11718247C214yesmaximal
5C2×C4×#261C2212yes—
6C2×#6118C2212yes—
7C13×C4⋊Q8C411yescharacteristic, complemented
8#88200—21no—
9Q8×Dic13—21no—
10#88151—21no—
11#88146C2212yes—
12#88144C412yescomplemented
13#88141—21no—
14C42×D13C2211yescharacteristic
15#88123C411yescharacteristic, complemented
16(C2×#261)⋊C4—21no—
17(C2×#261)⋊C4—21no—
18#88112—21no—
19#88112—21no—
20C22×#261—22no—
21C2×Q8×C13—21no—
22C2×C4×D13D411yescharacteristic
23C2×C4×D13D411yescharacteristic
24C2×C4×D13C2311yescharacteristic
25C2×Dic26—21no—
26C2×#1057—22no—
27C4×#261—22no—
28C4×#261Q814yescomplemented
29#6118—24no—
30C13×C4⋊C4—21no—
31C13×C4⋊C4C2×C412yes—
32C42×C13C2×C411yescharacteristic
33#6103—22no—
34C4⋊Dic13—21no—
35C4⋊Dic13—22no—
36C4⋊Dic13C2×C412yes—
37#6101—22no—
38C4×Dic13—22no—
39C4×Dic13C2×C411yescharacteristic
40C4×Dic13D411yescharacteristic
41C4×Dic13D411yescharacteristic
42#1995—131nomaximal, Sylow
43C22×D13C2×D411yescharacteristic
44C2×#261—24no—
45C2×#261—42no—
46C2×#261—42no—
47Q8×C13—42no—
48C2×C4×C13—22no—
49C2×C4×C13C22⋊C411yescharacteristic
50C2×C4×C13C22⋊C411yescharacteristic
51C2×C4×C13C22×C411yescharacteristic
52C2×Dic13—22no—
53C2×Dic13C22⋊C411yescharacteristic
54C2×Dic13C22⋊C411yescharacteristic
55C2×Dic13C2×D411yescharacteristic
56C4×D13—41no—
57C4×D13—41no—
58C4×D13C2×Q812yes—
59C4×D13#4112yes—
60Dic26—42no—
61#1057—42no—
62#533—131no—
63#423—131no—
64#376—131no—
65#339—134no—
66C22×C13C2×C22⋊C411yescharacteristic
67C2×D13—21no—
68C2×D13—21no—
69C2×D13C22⋊Q812yes—
70#261—44no—
71C4×C13—21no—
72C4×C13—21no—
73C4×C13—42no—
74C4×C13C4×Q812yes—
75Dic13—21no—
76Dic13—21no—
77Dic13—42no—
78Dic13#12411yescharacteristic
79Dic13C4⋊Q811yescharacteristic
80C2×M16—132no—
81C4⋊Q8—131no—
82C4⋊Q8#26111yescharacteristic, complemented
83#125—132no—
84C22⋊Q8—261no—
85C22⋊Q8—261no—
86C4×Q8—261no—
87C4×Q8—261no—
88#117—132no—
89C2×C42—131no—
90C2×C42—132no—
91C4⋊C8—261no—
92C4⋊C8—261no—
93#95—261no—
94#95—261no—
95C2×C13#39111yescharacteristic
96C2×C13#42111yescharacteristic
97C2×C13#42111yescharacteristic
98D13—22no—
99C2×Q8—21no—
100C2×Q8—261no—
101C22×C4—131no—
102C22×C4—131no—
103C22×C4—131no—
104C22×C4—262no—
105M16—264no—
106C2×C8—262no—
107C4⋊C4—21no—
108C4⋊C4—132no—
109C4⋊C4—262no—
110C4⋊C4—262no—
111C4⋊C4—261no—
112C4⋊C4C2×#26112yes—
113C22⋊C4—262no—
114C42—131no—
115C42—131no—
116C42—131no—
117C42—134no—
118C42—262no—
119C42—262no—
120C42C2×#26111yescharacteristic
121C13#199511yescharacteristic, complemented, Sylow
122C23—131no—
123Q8—42no—
124Q8—522no—
125C2×C4—22no—
126C2×C4—131no—
127C2×C4—132no—
128C2×C4—132no—
129C2×C4—131no—
130C2×C4—131no—
131C2×C4—264no—
132C2×C4—262no—
133C2×C4—521no—
134C2×C4—521no—
135C2×C4—522no—
136C2×C4—522no—
137C2×C4C22⋊#26111yescharacteristic
138C2×C4C22⋊#26111yescharacteristic
139C2×C4C22×#26111yescharacteristic
140C8—522no—
141C22—132no—
142C22—261no—
143C22—261no—
144C22C2×C22⋊#26111yescharacteristic
145C4—21no—
146C4—21no—
147C4—42no—
148C4—131no—
149C4—131no—
150C4—261no—
151C4—261no—
152C4—524no—
153C4—522no—
154C4Q8×#26112yes—
155C2—262no—
156C2#1171914011yescharacteristic
157C2#1171915511yescharacteristic
158C2(C2×#261)⋊Q811yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C4⋊Q8C4
socleC22×C13C2×C22⋊C4
prime radicalC22×D13C2×D4
cosocleC2×C4×D13C23
hypercenterC4⋊Q8#261
hypocenterC13#1995
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
7. C13×C4⋊Q8C4semidirect
12. #88144C4semidirect
15. #88123C4semidirect
28. C4×#261Q8semidirect
82. C4⋊Q8#261semidirect
121. C13#1995semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117190572
#117190532
#117182472
#199513