Finite Group Databasebeta

← #15756645

Subgroups — #15756645

Order 3328.

258 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 91 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#13114584C211yesmaximal, characteristic
2#13112680C212yesmaximal
3#13112668C212yesmaximal
4#13112667C211yesmaximal, characteristic
5C13×#1275C211yesmaximal, characteristic
6C13×#431C2212yes—
7C2×C13×#97C2211yescharacteristic
8C42×Dic13C2211yescharacteristic
9#11718586C2212yes—
10C2×#88043C2211yescharacteristic
11#11718142C411yescharacteristic
12#11718142C411yescharacteristic
13#11718142C411yescharacteristic
14#11718142C411yescharacteristic
15C22×C8×C13C2×C411yescharacteristic
16C22×C8×C13C2×C411yescharacteristic
17C2×C42×C13C2311yescharacteristic
18C2×C4×Dic13—21no—
19C2×C4×Dic13—21no—
20C2×C4×Dic13C2×C411yescharacteristic
21C2×C4×Dic13C2×C411yescharacteristic
22C22×#1055C2×C411yescharacteristic
23C22×#1055C2×C411yescharacteristic
24C13×C4⋊C8—22no—
25C13×C22⋊C8—22no—
26C13×#97—22no—
27C4×C8×C13—22no—
28C22⋊#1055—22no—
29C4⋊#1055—22no—
30#88043—22no—
31C4×#1055—22no—
32#8802—131nomaximal, Sylow
33C22×C4×C13C22×C411yescharacteristic
34C22×C4×C13#4111yescharacteristic
35C22×C4×C13#4111yescharacteristic
36C22×Dic13—21no—
37C22×Dic13—21no—
38C2×C8×C13—21no—
39C2×C8×C13—21no—
40C2×C8×C13—21no—
41C2×C8×C13—21no—
42C2×C8×C13—21no—
43C2×C8×C13—21no—
44C2×C8×C13—42no—
45C42×C13#4112yes—
46C42×C13#4112yes—
47C4×Dic13—21no—
48C4×Dic13—21no—
49C4×Dic13—21no—
50C4×Dic13—21no—
51C4×Dic13—42no—
52C4×Dic13—42no—
53C2×#1055—21no—
54C2×#1055—21no—
55C2×#1055—21no—
56C2×#1055—21no—
57C2×#1055—21no—
58C2×#1055—21no—
59C2×#1055—42no—
60#1745—131no—
61#1281—132no—
62#1276—132no—
63#1275—131no—
64#1275D1311yescharacteristic
65C23×C13#11711yescharacteristic
66C2×C4×C13—41no—
67C2×C4×C13—41no—
68C2×C4×C13#11711yescharacteristic
69C2×C4×C13#11711yescharacteristic
70C2×C4×C13#12612yes—
71C2×C4×C13#12612yes—
72C2×C4×C13#13111yescharacteristic
73C2×C4×C13#13111yescharacteristic
74C2×C4×C13#13111yescharacteristic
75C2×C4×C13#13111yescharacteristic
76C2×Dic13—22no—
77C2×Dic13—22no—
78C2×Dic13—41no—
79C2×Dic13—41no—
80C2×Dic13—41no—
81C2×Dic13—41no—
82C8×C13—41no—
83C8×C13—41no—
84C8×C13—82no—
85#1055—41no—
86#1055—41no—
87#1055—82no—
88#431—132no—
89#431C2×D1312yes—
90C2×#97—131no—
91C2×#97C2×D1311yescharacteristic
92C43—131no—
93#336—131no—
94#336—131no—
95#336—131no—
96#336—131no—
97C22×C13—21no—
98C22×C13—21no—
99C22×C13#38311yescharacteristic
100C22×C13#43311yescharacteristic
101C22×C13#43311yescharacteristic
102C4×C13—22no—
103C4×C13—22no—
104C4×C13#43311yescharacteristic
105C4×C13#43311yescharacteristic
106C4×C13#43311yescharacteristic
107C4×C13#43311yescharacteristic
108Dic13—42no—
109Dic13—42no—
110C22×C8—131no—
111C22×C8—131no—
112C22×C8C4×D1311yescharacteristic
113C22×C8C4×D1311yescharacteristic
114C2×C42—131no—
115C2×C42—131no—
116C2×C42—261no—
117C2×C42—261no—
118C2×C42C22×D1311yescharacteristic
119C4⋊C8—22no—
120C4⋊C8—262no—
121C22⋊C8—22no—
122C22⋊C8—262no—
123#97—22no—
124#97—262no—
125C4×C8—22no—
126C4×C8—262no—
127C2×C13—21no—
128C2×C13—21no—
129C2×C13#184011yescharacteristic
130C2×C13#184111yescharacteristic
131C2×C13#184111yescharacteristic
132C22×C4—261no—
133C22×C4—261no—
134C22×C4C2×C4×D1311yescharacteristic
135C22×C4#612911yescharacteristic
136C22×C4#613111yescharacteristic
137C2×C8—21no—
138C2×C8—21no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—21no—
143C2×C8—42no—
144C2×C8—261no—
145C2×C8—261no—
146C2×C8—261no—
147C2×C8—261no—
148C2×C8—261no—
149C2×C8—261no—
150C2×C8—522no—
151C42—261no—
152C42—261no—
153C42—261no—
154C42—261no—
155C42—522no—
156C42—522no—
157C42#612712yes—
158C42#612912yes—
159C13#880211yescharacteristic, complemented, Sylow
160C23#8814611yescharacteristic
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—262no—
164C2×C4—262no—
165C2×C4—521no—
166C2×C4—521no—
167C2×C4—521no—
168C2×C4—521no—
169C2×C4#8812611yescharacteristic
170C2×C4#8813111yescharacteristic
171C2×C4#8813312yes—
172C2×C4#8815212yes—
173C2×C4#8815511yescharacteristic
174C2×C4#8815511yescharacteristic
175C2×C4#8816111yescharacteristic
176C2×C4#8816111yescharacteristic
177C8—41no—
178C8—41no—
179C8—82no—
180C8—521no—
181C8—521no—
182C8—1042no—
183C22—21no—
184C22—21no—
185C22#1171831211yescharacteristic
186C22#1171850111yescharacteristic
187C22#1171850111yescharacteristic
188C4—22no—
189C4—22no—
190C4—522no—
191C4—522no—
192C4#1171835111yescharacteristic
193C4#1171837011yescharacteristic
194C4#1171838111yescharacteristic
195C4#1171838111yescharacteristic
196C2—21no—
197C2—21no—
198C2#1311498011yescharacteristic
199C2#1311498311yescharacteristic
200C2#1311498611yescharacteristic
subgroupG/H
centerC2×C4#88126
commutatorC22×C4×C13C22×C4
FrattiniC2×C42C22×D13
FittingC13×#1275C2
socleC22×C13#383
prime radicalC23×C13#117
cosocleC2×C42×C13C23
hypercenter#1275D13
hypocenterC13#8802
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×#97 ◁ #1275

Complements

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

NH ≅ G/Ntype
159. C13#8802semidirect

Maximal subgroups

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

subgroupindex
#131145842
#131126802
#131126682
#131126672
C13×#12752
#880213