Finite Group Databasebeta

← #15750463

Subgroups — #15750463

Order 3328.

198 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 37 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#13116123C211yesmaximal, characteristic
2#13112749C211yesmaximal, characteristic, complemented
3C13×#1327C211yesmaximal, characteristic, complemented
4#11719453C411yescharacteristic
5C13×#423C2211yescharacteristic
6#11718793—21no—
7C2×#88045—21no—
8#11718585—21no—
9C13×#349—21no—
10#11718152C411yescharacteristic
11C2×#6127—21no—
12C2×C13×M16C2×C411yescharacteristic
13C2×C13×M16D411yescharacteristic
14C2×C42×C13D411yescharacteristic
15C2×#6099—21no—
16C2×#6099—22no—
17#88163—41no—
18#88162—41no—
19#88158—41no—
20C13×M32—41no—
21C13×C4⋊C8—41no—
22#88064—41no—
23#88063—41no—
24#88045—41no—
25#88045—41no—
26C4⋊#1055—41no—
27C4⋊#1055—41no—
28#7414—131nomaximal, Sylow
29C22×C4×C13—21no—
30C22×C4×C13C22⋊C411yescharacteristic
31C2×C22⋊D13—41no—
32#6127—41no—
33#6127—41no—
34#6127—41no—
35#6127—41no—
36C2×D52—21no—
37C2×C4×D13—41no—
38C2×Dic26—21no—
39C13×M16—41no—
40C13×M16—41no—
41C2×C8×C13—21no—
42C2×C8×C13—21no—
43C42×C13—21no—
44C42×C13D811yescharacteristic
45C42×C13SD1611yescharacteristic
46#6099—41no—
47#6099—41no—
48#6099—82no—
49C2×#1055—41no—
50C2×#1055—42no—
51Dic52—41no—
52D104—41no—
53#6095—42no—
54C13×C16—81no—
55#2050—131no—
56#1327D1311yescharacteristic, complemented
57#1309—131no—
58C23×C13#10411yescharacteristic
59C22×D13—41no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—21no—
64C2×C4×C13—41no—
65C2×C4×C13—41no—
66C2×C4×C13#9911yescharacteristic
67C2×C4×C13#10211yescharacteristic
68C22⋊D13—81no—
69C22⋊D13—81no—
70C2×Dic13—41no—
71D52—41no—
72D52—41no—
73C4×D13—81no—
74C4×D13—81no—
75Dic26—41no—
76Dic26—41no—
77C8×C13—41no—
78C8×C13—41no—
79#1055—81no—
80#1055—82no—
81#575—131no—
82#423—261no—
83#423C2×D1311yescharacteristic
84C2×#104—261no—
85#413—261no—
86#349—21no—
87#338—131no—
88C22×C13—21no—
89C22×C13—41no—
90C22×C13#32711yescharacteristic
91C2×D13—81no—
92C2×D13—161no—
93C4×C13—21no—
94C4×C13—21no—
95C4×C13—21no—
96C4×C13—41no—
97C4×C13AΣL(1,𝔽16)11yescharacteristic
98C4×C13#35511yescharacteristic
99Dic13—81no—
100C2×#41—261no—
101#137—521no—
102AGL(1,ℤ/8)—521no—
103#135—521no—
104C2×M16—261no—
105C2×M16—262no—
106C2×M16C4×D1311yescharacteristic
107C2×M16C22⋊D1311yescharacteristic
108C2×C42D5211yescharacteristic
109M32—41no—
110C4⋊C8—41no—
111C4⋊C8—521no—
112C4⋊C8—521no—
113#104—521no—
114#104—521no—
115#101—521no—
116#100—521no—
117C2×C13—21no—
118C2×C13—41no—
119C2×C13#134511yescharacteristic
120D13—161no—
121#41—521no—
122#41—521no—
123#41—521no—
124#41—521no—
125C2×Q8—261no—
126C2×D4—261no—
127C2×D4—521no—
128C22×C4—21no—
129C22×C4—521no—
130C22×C4#610311yescharacteristic
131Q16—521no—
132SD16—522no—
133D8—521no—
134M16—41no—
135M16—41no—
136M16—521no—
137M16—521no—
138M16—1042no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—522no—
142C2×C8—521no—
143C42—21no—
144C42#609511yescharacteristic
145C42D10411yescharacteristic
146C16—81no—
147C13#741411yescharacteristic, complemented, Sylow
148C23—521no—
149C23#8806511yescharacteristic
150Q8—521no—
151Q8—521no—
152D4—521no—
153D4—521no—
154D4—1041no—
155D4—1041no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—521no—
163C2×C4—1041no—
164C2×C4—1041no—
165C2×C4#8804611yescharacteristic
166C2×C4#8806111yescharacteristic
167C8—41no—
168C8—41no—
169C8—1041no—
170C8—1042no—
171C22—21no—
172C22—41no—
173C22—1041no—
174C22—2081no—
175C22#1171806211yescharacteristic
176C4—21no—
177C4—21no—
178C4—21no—
179C4—41no—
180C4—1041no—
181C4#1171806311yescharacteristic
182C4#1171806911yescharacteristic
183C2—21no—
184C2—41no—
185C2—2081no—
186C2#1311284011yescharacteristic
subgroupG/H
centerC2#13112840
commutatorC2×C13×M16C2×C4
Frattini#423C2×D13
FittingC13×#1327C2
socleC2×C13#1345
prime radical#11719453C4
cosocleC13×#423C22
hypercenter#1327D13
hypocenterC13#7414
LCSG ▷ C2×C13×M16 ▷ C22×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #423 ◁ #1327

Complements

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

NH ≅ G/Ntype
2. #13112749C2semidirect
3. C13×#1327C2semidirect
56. #1327D13semidirect
147. C13#7414semidirect

Maximal subgroups

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

subgroupindex
#131161232
#131127492
C13×#13272
#741413