Finite Group Databasebeta

← #15783698

Subgroups — #15783698

Order 3328.

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

normal subgroups only

This group has 232 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×D416C211yesmaximal, characteristic, complemented
2C2×#11718111C211yesmaximal, characteristic, complemented
3#13117084C211yesmaximal, characteristic, complemented
4#13116682C211yesmaximal, characteristic, complemented
5#13113031C211yesmaximal, characteristic, complemented
6#13113013C211yesmaximal, characteristic, complemented
7C13×#1415C211yesmaximal, characteristic, complemented
8C2×C13×D16C2211yescharacteristic
9#11718812—21no—
10C2×#88066—21no—
11C2×D208C2211yescharacteristic
12C2×D208C2211yescharacteristic
13#11718533—21no—
14C2×C13×C32C2211yescharacteristic
15C13×#366C2211yescharacteristic
16#11718111—22no—
17C16×Dic13C2211yescharacteristic
18C2×#88034C2211yescharacteristic
19#11718083—21no—
20D416—22no—
21C2×C13×D8—21no—
22#88194—41no—
23C2×#6104—41no—
24C2×D104—21no—
25C2×D104—21no—
26#88147—41no—
27C13×D16—21no—
28C13×D16—21no—
29C2×C13×C16C2311yescharacteristic
30C13×#107—21no—
31#88066—42no—
32C8×Dic13D411yescharacteristic
33C2×#6090D411yescharacteristic
34#88049—41no—
35D208—21no—
36D208—21no—
37D208—21no—
38D208D412yescomplemented
39C13×C32—21no—
40#88034—21no—
41#13685—131nomaximal, Sylow
42C2×D4×C13—41no—
43C2×C22⋊D13—81no—
44C2×C22⋊D13—81no—
45C2×D52—41no—
46C2×D52—41no—
47C2×C4×D13—81no—
48C13×D8—41no—
49C13×D8—41no—
50C2×C8×C13C2×D411yescharacteristic
51C13×C4⋊C4—41no—
52#6104—82no—
53#6103—81no—
54C4×Dic13D811yescharacteristic
55C2×#1055D811yescharacteristic
56D104—22no—
57D104—41no—
58D104—41no—
59D104—41no—
60C13×C16C2×D411yescharacteristic
61C13×C16#4111yescharacteristic
62#6090—21no—
63C2×D32—131no—
64C2×D32—131no—
65#2246—131no—
66C4×D16—131no—
67C4⋊C32—131no—
68#1415—131no—
69#1415D1311yescharacteristic, complemented
70C23×C13—81no—
71C22×D13—81no—
72C22×D13—81no—
73D4×C13—81no—
74D4×C13—81no—
75C2×C4×C13—81no—
76C2×C4×C13C2×D811yescharacteristic
77C22⋊D13—162no—
78C22⋊D13—162no—
79C2×Dic13D1611yescharacteristic
80C2×Dic13D1611yescharacteristic
81D52—42no—
82D52—81no—
83D52—81no—
84D52—81no—
85C4×D13—162no—
86C8×C13#12111yescharacteristic
87C8×C13AGL(1,ℤ/8)11yescharacteristic
88#1055—21no—
89C2×D16—131no—
90C2×D16—131no—
91C2×D16—261no—
92C2×D16C2×D1311yescharacteristic
93#493—261no—
94C4×D8—261no—
95D32—262no—
96D32—262no—
97C2×C32—131no—
98C2×C32C2×D1311yescharacteristic
99#366C2×D1311yescharacteristic
100#357—261no—
101C4×C16—131no—
102C22×C13—161no—
103C22×C13—161no—
104C22×C13—161no—
105C22×C13C2×D1611yescharacteristic
106C2×D13—82no—
107C2×D13—161no—
108C2×D13—161no—
109C2×D13—161no—
110C2×D13—161no—
111C2×D13—161no—
112C4×C13—161no—
113C4×C13#45911yescharacteristic
114C4×C13#50911yescharacteristic
115Dic13—21no—
116Dic13D3212yescomplemented
117C2×D8—21no—
118C2×D8—261no—
119C2×D8—261no—
120C2×D8—521no—
121#127—521no—
122C4×D4—521no—
123D16—21no—
124D16—21no—
125D16—132no—
126D16—261no—
127D16—261no—
128D16—261no—
129D16—522no—
130C2×C16—131no—
131C2×C16C22×D1311yescharacteristic
132#107—21no—
133#102—521no—
134C4×C8—131no—
135C32—21no—
136C32—261no—
137C2×C13—321no—
138C2×C13#220611yescharacteristic
139C2×C13C2×D3211yescharacteristic
140C2×C13#226311yescharacteristic
141D13—162no—
142D13—321no—
143C2×D4—41no—
144C2×D4—521no—
145C2×D4—521no—
146C2×D4—1041no—
147C2×D4—1041no—
148C22×C4—1041no—
149D8—41no—
150D8—41no—
151D8—262no—
152D8—521no—
153D8—521no—
154D8—521no—
155D8—1042no—
156C2×C8—131no—
157C2×C8D4×D1311yescharacteristic
158C4⋊C4—41no—
159C22⋊C4—1041no—
160C42—131no—
161C16—261no—
162C16#612711yescharacteristic
163C16D4×D1311yescharacteristic
164C13#1368511yescharacteristic, complemented, Sylow
165C23—81no—
166C23—1041no—
167C23—1041no—
168D4—81no—
169D4—81no—
170D4—522no—
171D4—1041no—
172D4—1041no—
173D4—1041no—
174D4—2082no—
175D4—2082no—
176C2×C4—81no—
177C2×C4—131no—
178C2×C4—131no—
179C2×C4—2082no—
180C2×C4D8×D1311yescharacteristic
181C8—261no—
182C8#8813811yescharacteristic
183C8#8816811yescharacteristic
184C22—161no—
185C22—161no—
186C22—161no—
187C22—1042no—
188C22—2081no—
189C22—2081no—
190C22—2081no—
191C22—2081no—
192C22—2081no—
193C22D13×D1611yescharacteristic
194C4—132no—
195C4—161no—
196C4—261no—
197C4#1171844711yescharacteristic
198C4#1171857511yescharacteristic
199C2—321no—
200C2—4161no—
201C2—2082no—
202C2#1311687011yescharacteristic
203C2D13×D3211yescharacteristic
204C2#1311715011yescharacteristic
subgroupG/H
centerC22D13×D16
commutator, cosocleC2×C13×C16C23
FrattiniC2×C16C22×D13
FittingC13×#1415C2
socleC22×C13C2×D16
hypercenter#1415D13
hypocenterC13#13685
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×D416C2semidirect
2. C2×#11718111C2semidirect
3. #13117084C2semidirect
4. #13116682C2semidirect
5. #13113031C2semidirect
6. #13113013C2semidirect
7. C13×#1415C2semidirect
38. D208D4semidirect
69. #1415D13semidirect
116. Dic13D32semidirect
164. C13#13685semidirect

Maximal subgroups

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

subgroupindex
C2×D4162
C2×#117181112
#131170842
#131166822
#131130312
#131130132
C13×#14152
#1368513