Finite Group Databasebeta

← #13125969

Subgroups — #13125969

Order 1664.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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, complemented
2#11719421C211yesmaximal, characteristic
3C13×#486C211yesmaximal, characteristic, complemented
4#11718739C211yesmaximal, characteristic, complemented
5#11718731C211yesmaximal, characteristic, complemented
6#11718440C214yesmaximal, complemented
7#11718424C214yesmaximal, complemented
8#11718346C211yesmaximal, characteristic, complemented
9#11718341C211yesmaximal, characteristic, complemented
10C2×#6129—21no—
11C13×C4⋊Q8C2211yescharacteristic
12C13×#127C2211yescharacteristic
13#88200—21no—
14Q8×Dic13—21no—
15#88192—21no—
16#88192C2212yes—
17#88190—21no—
18D4×Dic13—21no—
19D4×Dic13C2212yes—
20#88151—21no—
21#88146C2212yes—
22#88144C2212yes—
23#88141—21no—
24C42×D13C2211yescharacteristic
25#88123C2211yescharacteristic
26#88123C2211yescharacteristic
27C13×#102C2214yes—
28C4×C8×C13C2211yescharacteristic
29#88072C2214yes—
30#88060C2212yes—
31#88057C2214yes—
32#88054C2212yes—
33#88047C2214yes—
34C4×#1055C2211yescharacteristic
35C2×Q8×C13—21no—
36C2×D4×C13—21no—
37C2×D4×C13—21no—
38C2×D4×C13C2312yes—
39C2×C22⋊D13—22no—
40C22×Dic13—22no—
41#6129—44no—
42C2×C4×D13D411yescharacteristic
43C2×C4×D13D411yescharacteristic
44C2×C4×D13C2311yescharacteristic
45C2×Dic26—21no—
46C2×Dic26—21no—
47C2×C8×C13C2312yes—
48C13×C4⋊C4—21no—
49C13×C4⋊C4C2312yes—
50C42×C13C2311yescharacteristic
51C22⋊Dic13—22no—
52C22⋊Dic13—22no—
53#6103—22no—
54C4⋊Dic13—21no—
55C4⋊Dic13—21no—
56C4⋊Dic13—22no—
57C4⋊Dic13C2312yes—
58C4⋊Dic13C2312yes—
59#6101—22no—
60C4×Dic13—22no—
61C4×Dic13D411yescharacteristic
62C4×Dic13D411yescharacteristic
63C4×Dic13C2311yescharacteristic
64C2×#1055C2312yes—
65#3228—131nomaximal, Sylow
66C23×C13—22no—
67C22×D13C2×D411yescharacteristic
68Q8×C13—42no—
69D4×C13—24no—
70D4×C13—42no—
71D4×C13—42no—
72C2×C4×C13—22no—
73C2×C4×C13C2×D411yescharacteristic
74C2×C4×C13C2×D411yescharacteristic
75C2×C4×C13C2411yescharacteristic
76C22⋊D13—44no—
77C2×Dic13—22no—
78C2×Dic13—22no—
79C2×Dic13—44no—
80C2×Dic13C2×D411yescharacteristic
81C2×Dic13C2×D411yescharacteristic
82C2×Dic13C2×D411yescharacteristic
83C4×D13—22no—
84C4×D13—22no—
85C4×D13—22no—
86Dic26—42no—
87Dic26—42no—
88C8×C13—22no—
89#1055—22no—
90#533—131no—
91#532—131no—
92#500—131no—
93#498—131no—
94#486—131no—
95#486D1311yescharacteristic, complemented
96#482—134no—
97#478—134no—
98#431—131no—
99C22×C13—42no—
100C22×C13—42no—
101C22×C13—42no—
102C22×C13C22×D411yescharacteristic
103C2×D13—21no—
104C2×D13—21no—
105C2×D13—21no—
106C4×C13—42no—
107C4×C13#13512yes—
108C4×C13AGL(1,ℤ/8)12yes—
109C4×C132−1+412yes—
110Dic13—21no—
111Dic13—21no—
112Dic13—21no—
113Dic13—42no—
114Dic13—42no—
115C2×#41—261no—
116C4⋊Q8—131no—
117C4⋊Q8—131no—
118C4⋊Q8C2×D1311yescharacteristic
119#127C2×D1311yescharacteristic
120#125—132no—
121#124—261no—
122C22⋊Q8—261no—
123C22⋊Q8—261no—
124#121—132no—
125#121—261no—
126C4×Q8—261no—
127C4×Q8—261no—
128C4×D4—132no—
129C4×D4—261no—
130#117—132no—
131C2×C42—131no—
132#107—134no—
133#106—134no—
134C4⋊C8—132no—
135#102—134no—
136#102C2×D1314yes—
137C22⋊C8—132no—
138C4×C8—131no—
139C4×C8C2×D1311yescharacteristic
140C2×C13—82no—
141C2×C13#53611yescharacteristic
142C2×C13C2×#13511yescharacteristic
143C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
144D13—41no—
145#41—524no—
146C2×Q8—21no—
147C2×Q8—261no—
148C2×Q8—261no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4—262no—
152C2×D4C22×D1312yes—
153C22×C4—131no—
154C22×C4—131no—
155C22×C4—131no—
156C22×C4—262no—
157C2×C8—132no—
158C2×C8C22×D1312yes—
159C4⋊C4—21no—
160C4⋊C4—132no—
161C4⋊C4—132no—
162C4⋊C4—262no—
163C4⋊C4—262no—
164C4⋊C4—261no—
165C4⋊C4—261no—
166C4⋊C4C22×D1312yes—
167C22⋊C4—262no—
168C22⋊C4—262no—
169C22⋊C4—262no—
170C42—131no—
171C42—131no—
172C42—131no—
173C42—262no—
174C42C22×D1311yescharacteristic
175C13#322811yescharacteristic, complemented, Sylow
176C23—22no—
177C23—131no—
178Q8—42no—
179Q8—522no—
180Q8—522no—
181D4—24no—
182D4—42no—
183D4—42no—
184D4—524no—
185C2×C4—22no—
186C2×C4—131no—
187C2×C4—131no—
188C2×C4—131no—
189C2×C4—262no—
190C2×C4—262no—
191C2×C4—262no—
192C2×C4—262no—
193C2×C4—262no—
194C2×C4—524no—
195C2×C4D4×D1311yescharacteristic
196C2×C4D4×D1311yescharacteristic
197C2×C4C23×D1311yescharacteristic
198C8—22no—
199C8—262no—
200C22—42no—
201C22—42no—
202C22—42no—
203C22—261no—
204C22—261no—
205C22—261no—
206C22C2×D4×D1311yescharacteristic
207C4—42no—
208C4—261no—
209C4—261no—
210C4—261no—
211C4—522no—
212C4—522no—
213C4#8816512yes—
214C4#8817012yes—
215C4#8825712yes—
216C2—82no—
217C2—521no—
218C2#1171938011yescharacteristic
219C2C2×#8816511yescharacteristic
220C2C2×#8817011yescharacteristic
subgroupG/H
centerC22C2×D4×D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#486C2
socleC22×C13C22×D4
prime radical#11719421C2
hypercenter#486D13
hypocenterC13#3228
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #11719433C2semidirect
3. C13×#486C2semidirect
4. #11718739C2semidirect
5. #11718731C2semidirect
6. #11718440C2semidirect
7. #11718424C2semidirect
8. #11718346C2semidirect
9. #11718341C2semidirect
95. #486D13semidirect
175. C13#3228semidirect

Maximal subgroups

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

subgroupindex
#117194332
#117194212
C13×#4862
#117187392
#117187312
#117184402
#117184242
#117183462
#117183412
#322813