Finite Group Databasebeta

← #15783703

Subgroups — #15783703

Order 3328.

220 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 57 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
1C2×#11718041C211yesmaximal, characteristic, complemented
2C2×#11718112C211yesmaximal, characteristic, complemented
3#13117084C211yesmaximal, characteristic
4#13116694C211yesmaximal, characteristic, complemented
5#13113031C211yesmaximal, characteristic, complemented
6#13113013C211yesmaximal, characteristic, complemented
7C13×#1415C211yesmaximal, characteristic, complemented
8C2×C13×D16C2211yescharacteristic
9#11718812—21no—
10C2×#88066—21no—
11C2×Dic104C2211yescharacteristic
12C2×D208C2211yescharacteristic
13#11718534—21no—
14C2×C13×C32C2211yescharacteristic
15C13×#366C2211yescharacteristic
16#11718112—22no—
17C16×Dic13C2211yescharacteristic
18C2×#88034C2211yescharacteristic
19#11718084—21no—
20#11718041—22no—
21C2×C13×D8—21no—
22#88194—41no—
23C2×#6104—41no—
24C2×Dic52—21no—
25C2×D104—21no—
26#88141—41no—
27C13×D16—21no—
28C13×D16—21no—
29C2×C13×C16C2311yescharacteristic
30C13×#107—21no—
31#88066—42no—
32C8×Dic13D411yescharacteristic
33C2×#6090D411yescharacteristic
34#88050—41no—
35Dic104—21no—
36Dic104D412yescomplemented
37D208—21no—
38D208—21no—
39C13×C32—21no—
40#88034—21no—
41#13686—131nomaximal, Sylow
42C2×D4×C13—41no—
43C2×C22⋊D13—81no—
44C2×C22⋊D13—81no—
45C2×D52—41no—
46C2×Dic26—41no—
47C13×D8—41no—
48C13×D8—41no—
49C2×C8×C13C2×D411yescharacteristic
50C13×C4⋊C4—41no—
51#6104—82no—
52#6101—81no—
53C4×Dic13—81no—
54C4×Dic13D811yescharacteristic
55C2×#1055D811yescharacteristic
56Dic52—22no—
57Dic52—41no—
58D104—41no—
59D104—41no—
60C13×C16C2×D411yescharacteristic
61C13×C16#4111yescharacteristic
62#6090—21no—
63C2×SD64—131no—
64C2×SD64—131no—
65#2246—131no—
66C4×Q32—131no—
67C4⋊C32—131no—
68#1415—131no—
69#1415D1311yescharacteristic, complemented
70C23×C13—81no—
71C22×D13—81no—
72D4×C13—81no—
73D4×C13—81no—
74C2×C4×C13—81no—
75C2×C4×C13C2×D811yescharacteristic
76C22⋊D13—162no—
77C22⋊D13—162no—
78C2×Dic13—81no—
79C2×Dic13D1611yescharacteristic
80C2×Dic13D1611yescharacteristic
81D52—81no—
82D52—81no—
83Dic26—42no—
84Dic26—81no—
85C8×C13#12111yescharacteristic
86C8×C13AGL(1,ℤ/8)11yescharacteristic
87#1055—21no—
88C2×Q32—131no—
89C2×D16—131no—
90C2×D16—261no—
91C2×D16C2×D1311yescharacteristic
92#493—261no—
93C4×Q16—261no—
94SD64—262no—
95SD64—262no—
96C2×C32—131no—
97C2×C32C2×D1311yescharacteristic
98#366C2×D1311yescharacteristic
99#358—261no—
100C4×C16—131no—
101C22×C13—161no—
102C22×C13—161no—
103C22×C13—161no—
104C22×C13C2×D1611yescharacteristic
105C2×D13—161no—
106C2×D13—161no—
107C2×D13—161no—
108C4×C13—161no—
109C4×C13#45911yescharacteristic
110C4×C13#50911yescharacteristic
111Dic13—21no—
112Dic13—82no—
113Dic13SD6412yescomplemented
114C2×Q16—261no—
115C2×D8—21no—
116C2×D8—261no—
117C2×D8—521no—
118#127—521no—
119C4×Q8—521no—
120Q32—132no—
121Q32—261no—
122D16—21no—
123D16—21no—
124D16—261no—
125D16—261no—
126D16—522no—
127C2×C16—131no—
128C2×C16C22×D1311yescharacteristic
129#107—21no—
130#103—521no—
131C4×C8—131no—
132C32—21no—
133C32—261no—
134C2×C13—321no—
135C2×C13#220611yescharacteristic
136C2×C13C2×SD6411yescharacteristic
137C2×C13#226311yescharacteristic
138D13—321no—
139C2×Q8—521no—
140C2×D4—41no—
141C2×D4—521no—
142C2×D4—1041no—
143C2×D4—1041no—
144Q16—262no—
145Q16—521no—
146D8—41no—
147D8—41no—
148D8—521no—
149D8—521no—
150D8—1042no—
151C2×C8—131no—
152C2×C8D4×D1311yescharacteristic
153C4⋊C4—41no—
154C4⋊C4—1041no—
155C42—131no—
156C42—1041no—
157C16—261no—
158C16#612711yescharacteristic
159C16D4×D1311yescharacteristic
160C13#1368611yescharacteristic, complemented, Sylow
161C23—81no—
162C23—1041no—
163Q8—522no—
164Q8—1041no—
165D4—81no—
166D4—81no—
167D4—1041no—
168D4—1041no—
169D4—2082no—
170D4—2082no—
171C2×C4—81no—
172C2×C4—131no—
173C2×C4—131no—
174C2×C4—1041no—
175C2×C4D8×D1311yescharacteristic
176C8—261no—
177C8#8813811yescharacteristic
178C8#8816811yescharacteristic
179C22—161no—
180C22—161no—
181C22—161no—
182C22—2081no—
183C22—2081no—
184C22—2081no—
185C22D13×D1611yescharacteristic
186C4—132no—
187C4—161no—
188C4—261no—
189C4—1042no—
190C4#1171844711yescharacteristic
191C4#1171857511yescharacteristic
192C2—321no—
193C2—4161no—
194C2#1311687011yescharacteristic
195C2D13×SD6411yescharacteristic
196C2#1311714711yescharacteristic
subgroupG/H
centerC22D13×D16
commutator, cosocleC2×C13×C16C23
FrattiniC2×C16C22×D13
FittingC13×#1415C2
socleC22×C13C2×D16
prime radical#13117084C2
hypercenter#1415D13
hypocenterC13#13686
LCSG ▷ C2×C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1415

Complements

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

NH ≅ G/Ntype
1. C2×#11718041C2semidirect
2. C2×#11718112C2semidirect
4. #13116694C2semidirect
5. #13113031C2semidirect
6. #13113013C2semidirect
7. C13×#1415C2semidirect
36. Dic104D4semidirect
69. #1415D13semidirect
113. Dic13SD64semidirect
160. C13#13686semidirect

Maximal subgroups

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

subgroupindex
C2×#117180412
C2×#117181122
#131170842
#131166942
#131130312
#131130132
C13×#14152
#1368613