Finite Group Databasebeta

← #13125995

Subgroups — #13125995

Order 1664.

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

normal subgroups only

This group has 326 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
2#11719175C211yesmaximal, characteristic
3#11718754C211yesmaximal, characteristic, complemented
4#11718754C211yesmaximal, characteristic, complemented
5#11718740C211yesmaximal, characteristic, complemented
6#11718739C211yesmaximal, characteristic, complemented
7#11718724C214yesmaximal, complemented
8#11718657C214yesmaximal
9#11718586C211yesmaximal, characteristic
10C13×C4⋊Q8C2211yescharacteristic
11C13×C4⋊Q8C2211yescharacteristic
12C13×#125C2212yes—
13C13×C22⋊Q8—21no—
14C13×C22⋊Q8—21no—
15C4×Q8×C13—21no—
16C4×Q8×C13—21no—
17C13×#117C2212yes—
18C2×C42×C13C2211yescharacteristic
19#88180—21no—
20#88178—21no—
21#88178C2212yes—
22#88124—21no—
23#88123C2211yescharacteristic
24#88123C2211yescharacteristic
25C4×Dic26—21no—
26C4×Dic26C2212yes—
27C22⋊#1055C2212yes—
28#88050C2214yes—
29#88050C2214yes—
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×Dic26—21no—
41C2×Dic26C2312yes—
42C13×C4⋊C4—22no—
43C13×C4⋊C4—22no—
44C13×C4⋊C4—21no—
45C13×C4⋊C4—21no—
46C13×C4⋊C4C2312yes—
47C13×C4⋊C4C2312yes—
48C13×C22⋊C4—22no—
49C42×C13—22no—
50C42×C13D411yescharacteristic
51C42×C13D411yescharacteristic
52C42×C13C2311yescharacteristic
53C42×C13C2311yescharacteristic
54C22⋊Dic13—22no—
55C4⋊Dic13—21no—
56C4⋊Dic13—21no—
57C4⋊Dic13—21no—
58C4⋊Dic13C2312yes—
59#6101—22no—
60#6101—22no—
61C4×Dic13—22no—
62C2×#1055C2312yes—
63C2×#1055C2312yes—
64#3231—131nomaximal, Sylow
65C23×C13C2×D411yescharacteristic
66Q8×C13—42no—
67Q8×C13—42no—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13—22no—
71C2×C4×C13—22no—
72C2×C4×C13—22no—
73C2×C4×C13C2×D411yescharacteristic
74C2×C4×C13C2×D411yescharacteristic
75C2×C4×C13C2×D411yescharacteristic
76C2×C4×C13C2×D411yescharacteristic
77C2×C4×C13C2×D411yescharacteristic
78C2×C4×C13C2411yescharacteristic
79C2×Dic13—22no—
80C2×Dic13—22no—
81Dic26—24no—
82Dic26—42no—
83#1055—22no—
84#1055—22no—
85#533—131no—
86#533D1311yescharacteristic
87#500—131no—
88#498—131no—
89#487—131no—
90#487—131no—
91#485—134no—
92#479—134no—
93#431—131no—
94C22×C13—21no—
95C22×C13—21no—
96C22×C13—21no—
97C22×C13C22×D411yescharacteristic
98C4×C13—21no—
99C4×C13—21no—
100C4×C13—21no—
101C4×C13—42no—
102C4×C13—42no—
103C4×C13#13512yes—
104C4×C13#13712yes—
105C4×C132−1+412yes—
106Dic13—42no—
107Dic13—42no—
108C4⋊Q8—131no—
109C4⋊Q8—131no—
110C4⋊Q8C2×D1311yescharacteristic
111C4⋊Q8C2×D1311yescharacteristic
112#125—261no—
113#125C2×D1312yes—
114C22⋊Q8—21no—
115C22⋊Q8—21no—
116C22⋊Q8—132no—
117C22⋊Q8—261no—
118C4×Q8—21no—
119C4×Q8—21no—
120C4×Q8—132no—
121C4×Q8—261no—
122#117—261no—
123#117C2×D1312yes—
124C2×C42C2×D1311yescharacteristic
125#107—134no—
126#106—134no—
127C4⋊C8—132no—
128#103—134no—
129#103—134no—
130C22⋊C8—132no—
131C4×C8—131no—
132C4×C8—131no—
133C2×C13—41no—
134C2×C13#53611yescharacteristic
135C2×C13C2×#13511yescharacteristic
136C2×C13C2×#13711yescharacteristic
137C2×Q8—21no—
138C2×Q8—21no—
139C2×Q8—132no—
140C2×Q8—261no—
141C22×C4C22⋊D1311yescharacteristic
142C22×C4C22⋊D1311yescharacteristic
143C22×C4C22×D1311yescharacteristic
144C2×C8—132no—
145C2×C8—132no—
146C4⋊C4—22no—
147C4⋊C4—22no—
148C4⋊C4—21no—
149C4⋊C4—21no—
150C4⋊C4—132no—
151C4⋊C4—261no—
152C4⋊C4—261no—
153C4⋊C4—262no—
154C4⋊C4—262no—
155C4⋊C4—261no—
156C4⋊C4C22×D1312yes—
157C4⋊C4C22×D1312yes—
158C22⋊C4—22no—
159C22⋊C4—262no—
160C42—22no—
161C42—262no—
162C42C22⋊D1311yescharacteristic
163C42C22⋊D1311yescharacteristic
164C42C22×D1311yescharacteristic
165C42C22×D1311yescharacteristic
166C13#323111yescharacteristic, complemented, Sylow
167C23C2×C22⋊D1311yescharacteristic
168Q8—42no—
169Q8—42no—
170Q8—264no—
171Q8—522no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—262no—
178C2×C4—262no—
179C2×C4C2×C22⋊D1311yescharacteristic
180C2×C4C2×C22⋊D1311yescharacteristic
181C2×C4C2×C22⋊D1311yescharacteristic
182C2×C4C2×C22⋊D1311yescharacteristic
183C2×C4C2×C22⋊D1311yescharacteristic
184C2×C4C23×D1311yescharacteristic
185C8—262no—
186C8—262no—
187C22—21no—
188C22—21no—
189C22—21no—
190C22C22×C22⋊D1311yescharacteristic
191C4—21no—
192C4—21no—
193C4—21no—
194C4—42no—
195C4—42no—
196C4—522no—
197C4—522no—
198C4#8820412yes—
199C4#8820512yes—
200C4#8825412yes—
201C2—41no—
202C2#1171952111yescharacteristic
203C2C2×#8820411yescharacteristic
204C2C2×#8820511yescharacteristic
subgroupG/H
centerC22C22×C22⋊D13
commutator, cosocleC2×C4×C13C24
FrattiniC2×C4C23×D13
FittingC13×#533C2
socleC22×C13C22×D4
prime radicalC23×C13C2×D4
hypercenter#533D13
hypocenterC13#3231
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
3. #11718754C2semidirect
4. #11718754C2semidirect
5. #11718740C2semidirect
6. #11718739C2semidirect
7. #11718724C2semidirect
166. C13#3231semidirect

Maximal subgroups

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

subgroupindex
C13×#5332
#117191752
#117187542
#117187402
#117187392
#117187242
#117186572
#117185862
#323113