Finite Group Databasebeta

← #13130189

Subgroups — #13130189

Order 1664.

230 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 64 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#11719329C211yesmaximal, characteristic
2#11719130C211yesmaximal, characteristic, complemented
3C2×C4×#1057C211yesmaximal, characteristic, complemented
4Q8⋊#1057C212yesmaximal, complemented
5#11718243C212yesmaximal, complemented
6C22×#1057—21no—
7C13×C22⋊Q8C411yescharacteristic
8#88201C411yescharacteristic
9Q8×Dic13C2211yescharacteristic
10#88184C411yescharacteristic
11C2×C4×Dic13C2211yescharacteristic
12#88152—21no—
13#88147C2211yescharacteristic
14#88146—21no—
15#88144C411yescharacteristic
16#88140—21no—
17#88135—21no—
18C22⋊#1057—21no—
19#88110—21no—
20C4⋊#1057C2212yes—
21C4×#1057—21no—
22C4×#1057C2212yes—
23C2×Q8×C13C2×C411yescharacteristic
24C22×C4×C13C2×C411yescharacteristic
25C2×C22⋊D13—21no—
26C22×Dic13D411yescharacteristic
27C22×Dic13D411yescharacteristic
28C2×D52C2×C411yescharacteristic
29C2×C4×D13—21no—
30C2×#1057—24no—
31C2×#1057—22no—
32C2×#1057—22no—
33C13×C4⋊C4—21no—
34C13×C4⋊C4C2×C411yescharacteristic
35C13×C22⋊C4—21no—
36#6103—21no—
37#6103—21no—
38#6103—21no—
39#6103—21no—
40C4⋊Dic13—21no—
41C4⋊Dic13—21no—
42C4⋊Dic13C2×C411yescharacteristic
43#6101—21no—
44C4×Dic13—21no—
45C4×Dic13C2×C411yescharacteristic
46C4×Dic13D411yescharacteristic
47C4×Dic13D411yescharacteristic
48C4×Dic13C2311yescharacteristic
49#1494—131nomaximal, Sylow
50C23×C13C22⋊C411yescharacteristic
51C22×D13—21no—
52Q8×C13—22no—
53C2×C4×C13—22no—
54C2×C4×C13—21no—
55C2×C4×C13—21no—
56C2×C4×C13C22⋊C411yescharacteristic
57C2×C4×C13C22×C411yescharacteristic
58C22⋊D13—42no—
59C2×Dic13—22no—
60C2×Dic13—22no—
61C2×Dic13—21no—
62C2×Dic13C22⋊C411yescharacteristic
63C2×Dic13C22⋊C411yescharacteristic
64C2×Dic13C2×D411yescharacteristic
65C2×Dic13C2×D411yescharacteristic
66D52—22no—
67C4×D13—42no—
68#1057—24no—
69#1057—42no—
70#529—131no—
71#432—131no—
72C2×C4×C8—131no—
73Q8⋊C8—132no—
74D4⋊C8—132no—
75C22×C13—21no—
76C22×C13—21no—
77C22×C13#10412yes—
78C22×C13C2×C22⋊C411yescharacteristic
79C2×D13—41no—
80C2×D13—41no—
81C2×D13—41no—
82C4×C13—21no—
83C4×C13—41no—
84C4×C13—41no—
85C4×C13#13112yes—
86Dic13—21no—
87Dic13—21no—
88Dic13—21no—
89Dic13—41no—
90Dic13#13512yes—
91C22×C8—261no—
92#126—261no—
93#125—131no—
94#124—131no—
95#123—261no—
96C22⋊Q8#26111yescharacteristic
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—22no—
109C2×C13#40811yescharacteristic
110C2×C13#41611yescharacteristic
111C2×C13C2×#10411yescharacteristic
112D13—81no—
113C2×Q8C2×#26111yescharacteristic
114C2×D4—131no—
115C2×D4—261no—
116C22×C4—131no—
117C22×C4—131no—
118C22×C4—261no—
119C22×C4C2×#26111yescharacteristic
120C2×C8—262no—
121C2×C8—264no—
122C2×C8—262no—
123C4⋊C4—21no—
124C4⋊C4—131no—
125C4⋊C4—261no—
126C4⋊C4—261no—
127C4⋊C4—261no—
128C4⋊C4C2×#26111yescharacteristic
129C22⋊C4—21no—
130C22⋊C4—261no—
131C22⋊C4—261no—
132C22⋊C4—261no—
133C22⋊C4—261no—
134C42—131no—
135C42—131no—
136C42—131no—
137C42—131no—
138C42—261no—
139C13#149411yescharacteristic, complemented, Sylow
140C23—261no—
141C23C22⋊#26111yescharacteristic
142Q8—22no—
143D4—262no—
144D4—522no—
145C2×C4—22no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—131no—
149C2×C4—131no—
150C2×C4—131no—
151C2×C4—131no—
152C2×C4—262no—
153C2×C4—262no—
154C2×C4—261no—
155C2×C4—522no—
156C2×C4C22⋊#26111yescharacteristic
157C2×C4C22×#26111yescharacteristic
158C8—264no—
159C8—522no—
160C22—21no—
161C22—21no—
162C22—521no—
163C22—521no—
164C22—521no—
165C22#8811812yes—
166C22C2×C22⋊#26111yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—132no—
171C4—261no—
172C4—261no—
173C4—261no—
174C4—521no—
175C4#8823812yes—
176C2—22no—
177C2—1041no—
178C2#1171914611yescharacteristic
179C2C2×#8811811yescharacteristic
180C2#1171916511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C22⋊Q8C4
socleC22×C13C2×C22⋊C4
prime radical#88184C4
cosocleC4×Dic13C23
hypercenterC22⋊Q8#261
hypocenterC13#1494
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #11719130C2semidirect
3. C2×C4×#1057C2semidirect
4. Q8⋊#1057C2semidirect
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
#117193292
#117191302
C2×C4×#10572
Q8⋊#10572
#117182432
#149413