Finite Group Databasebeta

← #15783542

Subgroups — #15783542

Order 3328.

194 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 63 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#13117149C211yesmaximal, characteristic
2#13116723C211yesmaximal, characteristic, complemented
3#13113041C211yesmaximal, characteristic, complemented
4#13113026C211yesmaximal, characteristic, complemented
5#13113022C211yesmaximal, characteristic, complemented
6#13112972C211yesmaximal, characteristic, complemented
7C13×#2177C211yesmaximal, characteristic, complemented
8C2×C13×D16C2211yescharacteristic
9C4×C13×D8—21no—
10#11718565C2211yescharacteristic
11#11718361—21no—
12C13×#367C2211yescharacteristic
13C13×#357—21no—
14C13×#346C2211yescharacteristic
15#11718112C412yescomplemented
16#11718111C412yescomplemented
17#11718102—21no—
18#11718098C2211yescharacteristic
19#11718091C2211yescharacteristic
20#11718091C2211yescharacteristic
21C2×C13×D8—21no—
22C4×D4×C13—41no—
23#88158—21no—
24#88155—41no—
25C13×D16—21no—
26C13×D16C2×C412yes—
27C2×C13×C16D411yescharacteristic
28C2×C13×C16C2311yescharacteristic
29C13×#107—21no—
30C13×#102—41no—
31C4×C8×C13D411yescharacteristic
32#88059—21no—
33#88045—41no—
34Dic104C2×C411yescharacteristic, complemented
35#88040—21no—
36D208C2×C411yescharacteristic, complemented
37#88034—21no—
38#88034C2×C412yescomplemented
39#13658—131nomaximal, Sylow
40C2×D4×C13—41no—
41C22×C4×C13—81no—
42#6127—41no—
43C13×D8—22no—
44C13×D8—41no—
45C2×C8×C13D811yescharacteristic
46C2×C8×C13C2×D411yescharacteristic
47C13×C4⋊C4—41no—
48C13×C22⋊C4—81no—
49C42×C13D811yescharacteristic
50#6099—41no—
51Dic52—21no—
52D104—21no—
53#6095—41no—
54#6094—81no—
55C8×D13—81no—
56C13×C16—21no—
57C13×C16C22×C411yescharacteristic
58C13×C16#4111yescharacteristic
59#2263—131no—
60#2179—131no—
61#2177D1311yescharacteristic, complemented
62#1426—131no—
63#1419—131no—
64#1418—131no—
65#1398—131no—
66C23×C13—81no—
67D4×C13—42no—
68D4×C13—81no—
69C2×C4×C13—21no—
70C2×C4×C13—81no—
71C2×C4×C13—162no—
72C2×C4×C13C2×D811yescharacteristic
73C22⋊D13—81no—
74D52—41no—
75C4×D13—81no—
76Dic26—41no—
77C8×C13—21no—
78C8×C13C4×D411yescharacteristic
79C8×C13#13511yescharacteristic
80#1055—81no—
81#508—131no—
82C2×D16C2×D1311yescharacteristic
83#443—261no—
84C4×D8—21no—
85SD64—132no—
86D32—132no—
87M64—131no—
88M64—131no—
89#368—131no—
90#367C2×D1311yescharacteristic
91#359—261no—
92#357—21no—
93#346C2×D1311yescharacteristic
94C22×C13—82no—
95C22×C13—161no—
96C22×C13—161no—
97C22×C13#50911yescharacteristic
98C2×D13—81no—
99C4×C13—41no—
100C4×C13—161no—
101C4×C13C4×D811yescharacteristic
102C4×C13#50911yescharacteristic
103Dic13—81no—
104#135—261no—
105C2×D8—21no—
106#131—521no—
107C4×D4—41no—
108Q32—131no—
109SD32—261no—
110D16—21no—
111D16—131no—
112D16C4×D1312yes—
113C2×C16C22⋊D1311yescharacteristic
114C2×C16C22×D1311yescharacteristic
115#108—261no—
116#107—21no—
117#104—521no—
118#102—41no—
119C4×C8C22⋊D1311yescharacteristic
120C32—132no—
121C32—261no—
122C2×C13—21no—
123C2×C13—162no—
124C2×C13#217711yescharacteristic
125D13—161no—
126#41—521no—
127C2×D4—41no—
128C22×C4—81no—
129Q16—261no—
130SD16—521no—
131D8—22no—
132D8—41no—
133D8—261no—
134M16—521no—
135M16—1041no—
136C2×C8—1041no—
137C2×C8#610411yescharacteristic
138C2×C8C2×C22⋊D1311yescharacteristic
139C4⋊C4—41no—
140C22⋊C4—81no—
141C42#610411yescharacteristic
142C16—21no—
143C16C2×C4×D1311yescharacteristic
144C16#612711yescharacteristic
145C13#1365811yescharacteristic, complemented, Sylow
146C23—81no—
147Q8—521no—
148D4—42no—
149D4—81no—
150D4—521no—
151D4—1041no—
152C2×C4—21no—
153C2×C4—81no—
154C2×C4—162no—
155C2×C4—1041no—
156C2×C4C2×#610411yescharacteristic
157C8—21no—
158C8—1041no—
159C8C4×C22⋊D1311yescharacteristic
160C8#8820411yescharacteristic
161C22—82no—
162C22—161no—
163C22—161no—
164C22—1041no—
165C22#1171880811yescharacteristic
166C4—41no—
167C4—161no—
168C4—1041no—
169C4C4×#610411yescharacteristic
170C4#1171885411yescharacteristic
171C2—21no—
172C2—162no—
173C2—2081no—
174C2#1311671011yescharacteristic
subgroupG/H
centerC2#13116710
commutatorC13×C16C22×C4
FrattiniC2×C16C22×D13
FittingC13×#2177C2
socleC2×C13#2177
prime radical#13117149C2
cosocleC2×C13×C16C23
hypercenter#2177D13
hypocenterC13#13658
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #346 ◁ #2177

Complements

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

NH ≅ G/Ntype
2. #13116723C2semidirect
3. #13113041C2semidirect
4. #13113026C2semidirect
5. #13113022C2semidirect
6. #13112972C2semidirect
7. C13×#2177C2semidirect
15. #11718112C4semidirect
16. #11718111C4semidirect
34. Dic104C2×C4semidirect
36. D208C2×C4semidirect
38. #88034C2×C4semidirect
61. #2177D13semidirect
145. C13#13658semidirect

Maximal subgroups

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

subgroupindex
#131171492
#131167232
#131130412
#131130262
#131130222
#131129722
C13×#21772
#1365813