Finite Group Databasebeta

← #13125972

Subgroups — #13125972

Order 1664.

370 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C13×#533C211yesmaximal, characteristic, complemented
2#11719182C211yesmaximal, characteristic
3#11718749C211yesmaximal, characteristic, complemented
4#11718749C211yesmaximal, characteristic, complemented
5#11718740C211yesmaximal, characteristic, complemented
6#11718739C211yesmaximal, characteristic, complemented
7#11718727C214yesmaximal, complemented
8#11718664C214yesmaximal, complemented
9#11718586C211yesmaximal, characteristic, complemented
10C2×#6127—21no—
11C13×C4⋊Q8C2211yescharacteristic
12C13×C4⋊Q8C2211yescharacteristic
13C13×#125C2212yes—
14C13×C22⋊Q8—21no—
15C13×C22⋊Q8—21no—
16C4×Q8×C13—21no—
17C4×Q8×C13—21no—
18C13×#117C2212yes—
19C2×C42×C13C2211yescharacteristic
20#88184—21no—
21#88184C2212yes—
22#88129—21no—
23#88128C2211yescharacteristic
24C4×D52—21no—
25C4×D52C2212yes—
26#88123C2211yescharacteristic
27C22⋊#1055C2212yes—
28#88049C2214yes—
29#88049C2214yes—
30#88048C2214yes—
31#88047C2214yes—
32C4⋊#1055C2212yes—
33C4×#1055C2211yescharacteristic
34C4×#1055C2211yescharacteristic
35C2×Q8×C13—21no—
36C2×Q8×C13—21no—
37C22×C4×C13D411yescharacteristic
38C22×C4×C13D411yescharacteristic
39C22×C4×C13C2311yescharacteristic
40C2×C22⋊D13—22no—
41#6127—44no—
42C2×D52—21no—
43C2×D52—21no—
44C2×D52C2312yes—
45C2×C4×D13—22no—
46C2×Dic26—21no—
47C13×C4⋊C4—22no—
48C13×C4⋊C4—22no—
49C13×C4⋊C4—21no—
50C13×C4⋊C4—21no—
51C13×C4⋊C4C2312yes—
52C13×C4⋊C4C2312yes—
53C13×C22⋊C4—22no—
54C42×C13—22no—
55C42×C13D411yescharacteristic
56C42×C13D411yescharacteristic
57C42×C13C2311yescharacteristic
58C42×C13C2311yescharacteristic
59#6103—22no—
60#6103—22no—
61C4⋊Dic13—21no—
62C4⋊Dic13C2312yes—
63C2×#1055C2312yes—
64C2×#1055C2312yes—
65#3228—131nomaximal, Sylow
66C23×C13C2×D411yescharacteristic
67C22×D13—22no—
68Q8×C13—42no—
69Q8×C13—42no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13—22no—
74C2×C4×C13—22no—
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2×D411yescharacteristic
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2×D411yescharacteristic
79C2×C4×C13C2×D411yescharacteristic
80C2×C4×C13C2411yescharacteristic
81C22⋊D13—44no—
82C2×Dic13—22no—
83D52—24no—
84D52—42no—
85D52—42no—
86C4×D13—44no—
87Dic26—42no—
88#1055—22no—
89#1055—22no—
90#533D1311yescharacteristic, complemented
91#532—131no—
92#500—131no—
93#498—131no—
94#486—131no—
95#486—131no—
96#482—134no—
97#478—134no—
98#431—131no—
99C22×C13—21no—
100C22×C13—21no—
101C22×C13—21no—
102C22×C13C22×D411yescharacteristic
103C2×D13—42no—
104C2×D13—42no—
105C2×D13—42no—
106C4×C13—21no—
107C4×C13—21no—
108C4×C13—21no—
109C4×C13—42no—
110C4×C13—42no—
111C4×C13#13512yes—
112C4×C13AGL(1,ℤ/8)12yes—
113C4×C132−1+412yes—
114Dic13—42no—
115C2×#41—261no—
116C4⋊Q8—131no—
117C4⋊Q8C2×D1311yescharacteristic
118C4⋊Q8C2×D1311yescharacteristic
119#127—131no—
120#125C2×D1312yes—
121#124—261no—
122C22⋊Q8—21no—
123C22⋊Q8—21no—
124#121—132no—
125#121—261no—
126C4×Q8—21no—
127C4×Q8—21no—
128C4×D4—132no—
129C4×D4—261no—
130#117C2×D1312yes—
131C2×C42C2×D1311yescharacteristic
132#107—134no—
133#106—134no—
134C4⋊C8—132no—
135#102—134no—
136#102—134no—
137C22⋊C8—132no—
138C4×C8—131no—
139C4×C8—131no—
140C2×C13—41no—
141C2×C13#53611yescharacteristic
142C2×C13C2×#13511yescharacteristic
143C2×C13C2×AGL(1,ℤ/8)11yescharacteristic
144D13—82no—
145#41—524no—
146C2×Q8—21no—
147C2×Q8—21no—
148C2×Q8—261no—
149C2×D4—132no—
150C2×D4—262no—
151C2×D4—261no—
152C2×D4—261no—
153C22×C4—262no—
154C22×C4C22⋊D1311yescharacteristic
155C22×C4C22⋊D1311yescharacteristic
156C22×C4C22×D1311yescharacteristic
157C2×C8—132no—
158C2×C8—132no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—132no—
164C4⋊C4—261no—
165C4⋊C4C22×D1312yes—
166C4⋊C4C22×D1312yes—
167C22⋊C4—22no—
168C22⋊C4—262no—
169C22⋊C4—262no—
170C42—22no—
171C42C22⋊D1311yescharacteristic
172C42C22⋊D1311yescharacteristic
173C42C22×D1311yescharacteristic
174C42C22×D1311yescharacteristic
175C13#322811yescharacteristic, complemented, Sylow
176C23—262no—
177C23C2×C22⋊D1311yescharacteristic
178Q8—42no—
179Q8—42no—
180Q8—522no—
181D4—264no—
182D4—524no—
183D4—522no—
184D4—522no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—262no—
191C2×C4—524no—
192C2×C4C2×C22⋊D1311yescharacteristic
193C2×C4C2×C22⋊D1311yescharacteristic
194C2×C4C2×C22⋊D1311yescharacteristic
195C2×C4C2×C22⋊D1311yescharacteristic
196C2×C4C2×C22⋊D1311yescharacteristic
197C2×C4C23×D1311yescharacteristic
198C8—262no—
199C8—262no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—522no—
204C22—522no—
205C22—522no—
206C22C22×C22⋊D1311yescharacteristic
207C4—21no—
208C4—21no—
209C4—21no—
210C4—42no—
211C4—42no—
212C4—522no—
213C4#8820312yes—
214C4#8820412yes—
215C4#8825412yes—
216C2—41no—
217C2—1042no—
218C2#1171952111yescharacteristic
219C2C2×#8820311yescharacteristic
220C2C2×#8820411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#533C2
socleC22×C13C22×D4
prime radical#11719182C2
hypercenter#533D13
hypocenterC13#3228
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C13×#533C2semidirect
3. #11718749C2semidirect
4. #11718749C2semidirect
5. #11718740C2semidirect
6. #11718739C2semidirect
7. #11718727C2semidirect
8. #11718664C2semidirect
9. #11718586C2semidirect
90. #533D13semidirect
175. C13#3228semidirect

Maximal subgroups

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

subgroupindex
C13×#5332
#117191822
#117187492
#117187402
#117187392
#117187272
#117186642
#117185862
#322813