Finite Group Databasebeta

← #15767692

Subgroups — #15767692

Order 3328.

292 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 95 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#13114990C211yesmaximal, characteristic
2#13113493C212yesmaximal
3#13112731C212yesmaximal
4#13112665C211yesmaximal, characteristic
5C13×#1995C211yesmaximal, characteristic
6C13×#533C2211yescharacteristic
7C13×#423C2211yescharacteristic
8C13×#376C2211yescharacteristic
9#11718586C2212yes—
10C2×C4⋊#1055—21no—
11C2×C4⋊#1055—21no—
12C2×C4⋊#1055C2212yes—
13C13×#339—21no—
14C13×#339—21no—
15#11718139—22no—
16#11718138—22no—
17C2×C13×M16—21no—
18C13×C4⋊Q8D412yes—
19C13×#125—21no—
20C13×C22⋊Q8—22no—
21C4×Q8×C13—22no—
22C13×#117—21no—
23C2×C42×C13D411yescharacteristic
24C2×C42×C13D411yescharacteristic
25C2×C42×C13C2311yescharacteristic
26C22×#1055—22no—
27C13×C4⋊C8—22no—
28C13×#95—22no—
29C22⋊#1055—22no—
30C4⋊#1055—22no—
31C4⋊#1055—22no—
32C4⋊#1055—22no—
33C4⋊#1055—42no—
34C4⋊#1055—42no—
35C4×#1055—22no—
36#10628—131nomaximal, Sylow
37C2×Q8×C13—22no—
38C22×C4×C13—21no—
39C22×C4×C13—21no—
40C22×C4×C13C2×D411yescharacteristic
41C22×C4×C13#4112yes—
42C13×M16—41no—
43C13×M16—41no—
44C2×C8×C13—41no—
45C13×C4⋊C4—22no—
46C13×C4⋊C4—22no—
47C13×C4⋊C4—42no—
48C13×C22⋊C4—41no—
49C42×C13—21no—
50C42×C13—21no—
51C42×C13—41no—
52C42×C13SD1612yes—
53C42×C13Q1612yes—
54C42×C13C2×D411yescharacteristic
55C42×C13#4111yescharacteristic
56C42×C13#4112yes—
57C2×#1055—42no—
58C2×#1055—42no—
59C2×#1055—42no—
60C2×#1055—42no—
61#1995D1311yescharacteristic
62#1843—131no—
63#1542—132no—
64#1301—132no—
65#1274—131no—
66C23×C13#12311yescharacteristic
67Q8×C13—82no—
68C2×C4×C13—22no—
69C2×C4×C13—22no—
70C2×C4×C13—42no—
71C2×C4×C13—42no—
72C2×C4×C13—42no—
73C2×C4×C13—42no—
74C2×C4×C13#12111yescharacteristic
75C2×C4×C13#12312yes—
76C2×C4×C13#12411yescharacteristic
77C2×C4×C13#12612yes—
78C2×C4×C13C2×SD1611yescharacteristic
79C2×C4×C13C2×Q1611yescharacteristic
80C2×C4×C13AGL(1,ℤ/8)11yescharacteristic
81C2×C4×C13#13711yescharacteristic
82C8×C13—81no—
83#1055—82no—
84#1055—82no—
85#533C2×D1311yescharacteristic
86#431—132no—
87#423C2×D1311yescharacteristic
88C2×C4⋊C8—132no—
89C2×C4⋊C8—261no—
90C2×C4⋊C8—261no—
91#376C2×D1311yescharacteristic
92#339—21no—
93#339—21no—
94#333—262no—
95#332—262no—
96C22×C13—22no—
97C22×C13#39711yescharacteristic
98C22×C13#48311yescharacteristic
99C22×C13#48411yescharacteristic
100C4×C13—22no—
101C4×C13—22no—
102C4×C13—42no—
103C4×C13—42no—
104C4×C13—82no—
105C4×C13#46011yescharacteristic
106C4×C13#46211yescharacteristic
107C4×C13#48711yescharacteristic
108C4×C13#48911yescharacteristic
109C2×M16—21no—
110C22×C8—262no—
111C4⋊Q8D5212yes—
112#125—21no—
113C22⋊Q8—22no—
114C4×Q8—22no—
115#117—21no—
116C2×C42C22⋊D1311yescharacteristic
117C2×C42C22⋊D1311yescharacteristic
118C2×C42C22×D1311yescharacteristic
119C4⋊C8—22no—
120C4⋊C8—262no—
121C4⋊C8—262no—
122C4⋊C8—262no—
123C4⋊C8—522no—
124C4⋊C8—522no—
125C22⋊C8—262no—
126C4×C8—262no—
127#95—22no—
128C2×C13—21no—
129C2×C13—21no—
130C2×C13#207211yescharacteristic
131C2×C13#208012yes—
132C2×Q8—22no—
133C22×C4—21no—
134C22×C4—21no—
135C22×C4#612912yes—
136C22×C4C2×C22⋊D1311yescharacteristic
137M16—41no—
138M16—41no—
139C2×C8—41no—
140C2×C8—522no—
141C2×C8—522no—
142C2×C8—522no—
143C2×C8—522no—
144C4⋊C4—22no—
145C4⋊C4—22no—
146C4⋊C4—42no—
147C22⋊C4—41no—
148C42—21no—
149C42—21no—
150C42—41no—
151C42#610612yes—
152C42#610712yes—
153C42C2×D5211yescharacteristic
154C42#612711yescharacteristic
155C42#612912yes—
156C13#1062811yescharacteristic, complemented, Sylow
157C23#8818911yescharacteristic
158Q8—82no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4#8813312yes—
166C2×C4#8814012yes—
167C2×C4#8818411yescharacteristic
168C2×C4#8819011yescharacteristic
169C2×C4C2×#610611yescharacteristic
170C2×C4C2×#610711yescharacteristic
171C2×C4#8820311yescharacteristic
172C2×C4#8820511yescharacteristic
173C8—81no—
174C8—1042no—
175C8—1042no—
176C22—22no—
177C22#1171861411yescharacteristic
178C22#1171870411yescharacteristic
179C22#1171870511yescharacteristic
180C4—22no—
181C4—22no—
182C4—42no—
183C4—42no—
184C4—82no—
185C4#1171868811yescharacteristic
186C4#1171869211yescharacteristic
187C4#1171871611yescharacteristic
188C4#1171874211yescharacteristic
189C2—21no—
190C2—21no—
191C2#1311624411yescharacteristic
192C2#1311628612yes—
subgroupG/H
centerC2×C4#88190
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1995C2
socleC22×C13#397
prime radicalC23×C13#123
hypercenter#1995D13
hypocenterC13#10628
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
156. C13#10628semidirect

Maximal subgroups

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

subgroupindex
#131149902
#131134932
#131127312
#131126652
C13×#19952
#1062813