Finite Group Databasebeta

← #15750466

Subgroups — #15750466

Order 3328.

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

normal subgroups only

This group has 190 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#13112747C211yesmaximal, characteristic, complemented
3C13×#1327C211yesmaximal, characteristic, complemented
4#11719453C411yescharacteristic
5C13×#423C2211yescharacteristic
6#11718793—21no—
7C2×#88045—21no—
8#11718587—21no—
9C13×#349—21no—
10#11718152C411yescharacteristic
11C2×#6127—21no—
12C2×C13×M16C2×C411yescharacteristic
13C2×C13×M16D411yescharacteristic
14C2×C42×C13D411yescharacteristic
15C2×#6099—21no—
16#88163—41no—
17#88162—41no—
18#88158—41no—
19C13×M32—41no—
20C13×C4⋊C8—41no—
21C22⋊#1055—22no—
22#88064—41no—
23#88063—41no—
24#88045—41no—
25#88045—41no—
26C4⋊#1055—41no—
27#88043—41no—
28#7415—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—
48C2×#1055—42no—
49C2×#1055—41no—
50Dic52—41no—
51D104—41no—
52#6095—42no—
53C13×C16—81no—
54#2050—131no—
55#1327D1311yescharacteristic, complemented
56#1307—131no—
57C23×C13#10411yescharacteristic
58C22×D13—41no—
59C2×C4×C13—21no—
60C2×C4×C13—21no—
61C2×C4×C13—21no—
62C2×C4×C13—21no—
63C2×C4×C13—81no—
64C2×C4×C13#9911yescharacteristic
65C2×C4×C13#10211yescharacteristic
66C22⋊D13—81no—
67C22⋊D13—81no—
68C2×Dic13—41no—
69D52—41no—
70D52—41no—
71C4×D13—81no—
72C4×D13—81no—
73Dic26—41no—
74Dic26—41no—
75C8×C13—41no—
76C8×C13—41no—
77#1055—81no—
78#1055—82no—
79#575—131no—
80#432—261no—
81#423C2×D1311yescharacteristic
82C2×#104—261no—
83#413—261no—
84#349—21no—
85#338—131no—
86C22×C13—21no—
87C22×C13—41no—
88C22×C13#32711yescharacteristic
89C2×D13—81no—
90C2×D13—161no—
91C4×C13—21no—
92C4×C13—41no—
93C4×C13—41no—
94C4×C13AΣL(1,𝔽16)11yescharacteristic
95C4×C13#35511yescharacteristic
96Dic13—81no—
97C2×#41—261no—
98#137—521no—
99AGL(1,ℤ/8)—521no—
100#135—521no—
101C2×M16—261no—
102C2×M16C4×D1311yescharacteristic
103C2×M16C22⋊D1311yescharacteristic
104C2×C42D5211yescharacteristic
105M32—41no—
106C4⋊C8—41no—
107C4⋊C8—521no—
108#104—521no—
109#104—521no—
110#101—521no—
111#100—521no—
112C22⋊C8—262no—
113#97—521no—
114C2×C13—21no—
115C2×C13—41no—
116C2×C13#134511yescharacteristic
117D13—161no—
118#41—521no—
119#41—521no—
120#41—521no—
121#41—521no—
122C2×Q8—261no—
123C2×D4—261no—
124C2×D4—521no—
125C22×C4—21no—
126C22×C4—521no—
127C22×C4#610311yescharacteristic
128Q16—521no—
129SD16—522no—
130D8—521no—
131M16—41no—
132M16—41no—
133M16—521no—
134M16—521no—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—522no—
138C2×C8—521no—
139C42—21no—
140C42#609511yescharacteristic
141C42D10411yescharacteristic
142C16—81no—
143C13#741511yescharacteristic, complemented, Sylow
144C23—521no—
145C23#8806511yescharacteristic
146Q8—521no—
147Q8—521no—
148D4—521no—
149D4—521no—
150D4—1041no—
151D4—1041no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—81no—
157C2×C4—521no—
158C2×C4—1041no—
159C2×C4—1041no—
160C2×C4#8804611yescharacteristic
161C2×C4#8806111yescharacteristic
162C8—41no—
163C8—41no—
164C8—1041no—
165C8—1042no—
166C22—21no—
167C22—41no—
168C22—1041no—
169C22—2081no—
170C22#1171806211yescharacteristic
171C4—21no—
172C4—41no—
173C4—41no—
174C4—1041no—
175C4#1171806311yescharacteristic
176C4#1171806911yescharacteristic
177C2—21no—
178C2—41no—
179C2—2081no—
180C2#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#7415
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. #13112747C2semidirect
3. C13×#1327C2semidirect
55. #1327D13semidirect
143. C13#7415semidirect

Maximal subgroups

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

subgroupindex
#131161232
#131127472
C13×#13272
#741513