Finite Group Databasebeta

← #15783543

Subgroups — #15783543

Order 3328.

194 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 59 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#13117151C211yesmaximal, characteristic
2#13116721C211yesmaximal, characteristic, complemented
3#13116711C211yesmaximal, characteristic, complemented
4#13113025C211yesmaximal, characteristic, complemented
5#13113022C211yesmaximal, characteristic, complemented
6#13112971C211yesmaximal, characteristic, complemented
7C13×#1426C211yesmaximal, characteristic, complemented
8#11718565C2211yescharacteristic
9C2×D208C2211yescharacteristic
10#11718556—21no—
11#11718533—21no—
12C13×M64C2211yescharacteristic
13C13×#368C2211yescharacteristic
14C13×#367C2211yescharacteristic
15#11718094C2211yescharacteristic
16#11718091C2211yescharacteristic
17#11718089—21no—
18#11718083—21no—
19#11718041C412yescomplemented
20D416C412yescomplemented
21#88161—41no—
22#88158—21no—
23C2×D104—21no—
24#88147—41no—
25C2×C13×C16C2311yescharacteristic
26C13×#108—21no—
27C13×#107—21no—
28#88065—41no—
29C8×Dic13D411yescharacteristic
30C2×#6090D411yescharacteristic
31#88049—41no—
32Dic104C2×C411yescharacteristic, complemented
33#88040—21no—
34D208—21no—
35D208C2×C412yes—
36D208C2×C411yescharacteristic, complemented
37C13×C32C2×C412yescomplemented
38#88034—21no—
39#13658—131nomaximal, Sylow
40#6127—41no—
41C2×D52—41no—
42C2×C4×D13—81no—
43C13×M16—41no—
44C2×C8×C13C2×D411yescharacteristic
45C13×C4⋊C4—41no—
46#6103—81no—
47C4×Dic13D811yescharacteristic
48C2×#1055D811yescharacteristic
49Dic52—21no—
50D104—22no—
51D104—21no—
52D104—41no—
53#6095—41no—
54#6094—81no—
55C8×D13—81no—
56C13×C16C22×C411yescharacteristic
57C13×C16#4111yescharacteristic
58#6090—21no—
59#2263—131no—
60#2179—131no—
61#2177—131no—
62#1426D1311yescharacteristic, complemented
63#1419—131no—
64#1418—131no—
65#1398—131no—
66C22×D13—81no—
67C2×C4×C13—81no—
68C2×C4×C13C2×D811yescharacteristic
69C22⋊D13—81no—
70C2×Dic13—21no—
71D52—41no—
72D52—42no—
73D52—81no—
74C4×D13—81no—
75C4×D13—162no—
76Dic26—41no—
77C8×C13—81no—
78C8×C13C4×D411yescharacteristic
79C8×C13#13511yescharacteristic
80#1055—21no—
81#508—131no—
82C2×D16—131no—
83#443—261no—
84C4×D8—261no—
85SD64—132no—
86D32—132no—
87M64—131no—
88M64C2×D1311yescharacteristic
89#368C2×D1311yescharacteristic
90#367C2×D1311yescharacteristic
91#359—261no—
92#357—261no—
93#346—131no—
94C22×C13#50911yescharacteristic
95C2×D13—81no—
96C2×D13—82no—
97C2×D13—161no—
98C2×D13—161no—
99C4×C13—161no—
100C4×C13C4×D811yescharacteristic
101C4×C13#50911yescharacteristic
102Dic13—41no—
103Dic13—81no—
104#135—261no—
105C2×D8—261no—
106#131—521no—
107C4×D4—521no—
108Q32—131no—
109SD32—261no—
110D16—131no—
111D16—132no—
112D16—261no—
113C2×C16—131no—
114C2×C16C22×D1311yescharacteristic
115#108—21no—
116#107—21no—
117#104—521no—
118#102—521no—
119C4×C8—131no—
120C32—261no—
121C32C4×D1312yescomplemented
122C2×C13—21no—
123C2×C13#217711yescharacteristic
124D13—161no—
125D13—162no—
126#41—521no—
127C2×D4—521no—
128C22×C4—1041no—
129Q16—261no—
130SD16—521no—
131D8—262no—
132D8—261no—
133D8—521no—
134M16—41no—
135M16—1041no—
136C2×C8—131no—
137C2×C8—1041no—
138C2×C8D4×D1311yescharacteristic
139C4⋊C4—41no—
140C22⋊C4—1041no—
141C42—131no—
142C16—261no—
143C16C2×C4×D1311yescharacteristic
144C16#613111yescharacteristic
145C13#1365811yescharacteristic, complemented, Sylow
146C23—1041no—
147Q8—521no—
148D4—522no—
149D4—521no—
150D4—1041no—
151D4—1041no—
152C2×C4—81no—
153C2×C4—261no—
154C2×C4—1041no—
155C2×C4—2082no—
156C2×C4D8×D1311yescharacteristic
157C8—81no—
158C8—261no—
159C8#8814711yescharacteristic
160C8#8817311yescharacteristic
161C22—1041no—
162C22—1042no—
163C22—2081no—
164C22—2081no—
165C22#1171857511yescharacteristic
166C4—161no—
167C4—521no—
168C4—1041no—
169C4#1171853311yescharacteristic
170C4#1171857511yescharacteristic
171C2—21no—
172C2—2082no—
173C2—2081no—
174C2#1311671111yescharacteristic
subgroupG/H
centerC2#13116711
commutatorC13×C16C22×C4
FrattiniC2×C16C22×D13
FittingC13×#1426C2
socleC2×C13#2177
prime radical#13117151C2
cosocleC2×C13×C16C23
hypercenter#1426D13
hypocenterC13#13658
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1426

Complements

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

NH ≅ G/Ntype
2. #13116721C2semidirect
3. #13116711C2semidirect
4. #13113025C2semidirect
5. #13113022C2semidirect
6. #13112971C2semidirect
7. C13×#1426C2semidirect
19. #11718041C4semidirect
20. D416C4semidirect
32. Dic104C2×C4semidirect
36. D208C2×C4semidirect
37. C13×C32C2×C4semidirect
62. #1426D13semidirect
121. C32C4×D13semidirect
145. C13#13658semidirect

Maximal subgroups

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

subgroupindex
#131171512
#131167212
#131167112
#131130252
#131130222
#131129712
C13×#14262
#1365813