Finite Group Databasebeta

← #15777697

Subgroups — #15777697

Order 3328.

284 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 75 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#13117093C211yesmaximal, characteristic
2#13117063C211yesmaximal, characteristic, complemented
3#13117060C211yesmaximal, characteristic
4#13114443C211yesmaximal, characteristic
5#13114430C211yesmaximal, characteristic, complemented
6#13112755C211yesmaximal, characteristic, complemented
7C13×#2247C211yesmaximal, characteristic, complemented
8C2×C13×Q32—22no—
9C13×#494C2211yescharacteristic
10C13×#494C2211yescharacteristic
11C2×#88068—22no—
12#11718754—21no—
13#11718749—21no—
14#11718749—21no—
15#11718740—21no—
16#11718356C2211yescharacteristic
17#11718343C2211yescharacteristic
18C4×C13×C16C2211yescharacteristic
19#11718156—22no—
20#11718101—22no—
21C4×#6090C2211yescharacteristic
22C8×#1055C2211yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C2×C13×Q16—21no—
26C2×C13×Q16—21no—
27C13×C4⋊Q8—21no—
28C13×C4⋊Q8—21no—
29C2×D104—21no—
30C2×D104—21no—
31#88128—21no—
32#88123—21no—
33C13×Q32—44no—
34C2×C13×C16D412yes—
35C4×C8×C13C2311yescharacteristic
36#88068—44no—
37#88058—21no—
38#88058—21no—
39C2×#6090D412yes—
40#88050—42no—
41#88049—42no—
42#88049—42no—
43#88048—42no—
44C4×#1055D411yescharacteristic
45C4×#1055D411yescharacteristic
46#12530—131nomaximal, Sylow
47C2×Q8×C13—41no—
48C2×Q8×C13—41no—
49C2×D52—41no—
50C2×D52—41no—
51C2×D52—41no—
52C2×Dic26—41no—
53C13×Q16—42no—
54C13×Q16—42no—
55C13×Q16—42no—
56C13×Q16—42no—
57C2×C8×C13C2×D411yescharacteristic
58C2×C8×C13C2×D411yescharacteristic
59C13×C4⋊C4—41no—
60C13×C4⋊C4—41no—
61C13×C4⋊C4—41no—
62C13×C4⋊C4—41no—
63C42×C13C2×D411yescharacteristic
64C4⋊Dic13—41no—
65C4⋊Dic13—41no—
66C2×#1055D812yes—
67C2×#1055D812yes—
68D104—42no—
69D104—42no—
70C13×C16—22no—
71#6090—22no—
72#2248—131no—
73#2247D1311yescharacteristic, complemented
74#2241—131no—
75#2240—131no—
76#1709—131no—
77#1707—131no—
78#1312—131no—
79C22×D13—81no—
80Q8×C13—81no—
81Q8×C13—81no—
82Q8×C13—81no—
83Q8×C13—81no—
84C2×C4×C13—81no—
85C2×C4×C13—81no—
86C2×C4×C13#12711yescharacteristic
87C2×C4×C13C2×D811yescharacteristic
88C2×C4×C13C2×D811yescharacteristic
89C2×Dic13—81no—
90D52—81no—
91D52—81no—
92D52—82no—
93D52—82no—
94Dic26—82no—
95C8×C13AGL(1,ℤ/8)12yes—
96C8×C13AGL(1,ℤ/8)12yes—
97#1055—22no—
98#1055—22no—
99C2×Q32—22no—
100C2×SD32—262no—
101#500—131no—
102#498—261no—
103#494C2×D1311yescharacteristic
104#494C2×D1311yescharacteristic
105#493—131no—
106#487—261no—
107#486—261no—
108#486—261no—
109#358—262no—
110#357—262no—
111C4×C16—131no—
112C4×C16C2×D1311yescharacteristic
113C82—131no—
114C22×C13#49311yescharacteristic
115C2×D13—161no—
116C2×D13—161no—
117C2×D13—161no—
118C4×C13—161no—
119C4×C13—161no—
120C4×C13#49611yescharacteristic
121C4×C13#49611yescharacteristic
122C4×C13#50812yes—
123C4×C13#51012yes—
124Dic13—161no—
125C2×Q16—21no—
126C2×Q16—21no—
127C2×Q16—21no—
128C2×Q16—21no—
129C2×D8—261no—
130C2×D8—261no—
131C4⋊Q8—21no—
132C4⋊Q8—21no—
133C4⋊Q8—261no—
134#127—261no—
135Q32—44no—
136SD32—524no—
137C2×C16—132no—
138C2×C16C22⋊D1312yes—
139#107—261no—
140#107—261no—
141#106—522no—
142#103—522no—
143#102—522no—
144#102—522no—
145C4×C8—131no—
146C4×C8—131no—
147C4×C8C22×D1311yescharacteristic
148C2×C13#172111yescharacteristic
149C2×C13#224911yescharacteristic
150C2×C13#225111yescharacteristic
151D13—321no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8—521no—
155C2×D4—521no—
156C2×D4—521no—
157C2×D4—521no—
158Q16—42no—
159Q16—42no—
160Q16—42no—
161Q16—42no—
162D8—522no—
163D8—522no—
164C2×C8—132no—
165C2×C8—132no—
166C2×C8D4×D1311yescharacteristic
167C2×C8C2×C22⋊D1311yescharacteristic
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—521no—
173C4⋊C4—521no—
174C42D4×D1311yescharacteristic
175C16—22no—
176C16—262no—
177C13#1253011yescharacteristic, complemented, Sylow
178C23—1041no—
179Q8—81no—
180Q8—81no—
181Q8—81no—
182Q8—81no—
183Q8—1042no—
184D4—1041no—
185D4—1041no—
186D4—1042no—
187D4—1042no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—1041no—
191C2×C4D8×D1311yescharacteristic
192C2×C4D8×D1311yescharacteristic
193C2×C4#8819411yescharacteristic
194C8—262no—
195C8—262no—
196C8#8816512yes—
197C8#8818612yes—
198C22—2081no—
199C22—2081no—
200C22—2081no—
201C22#1171881211yescharacteristic
202C4—161no—
203C4—161no—
204C4—2081no—
205C4#1171857912yes—
206C4#1171858012yes—
207C4#1171873511yescharacteristic
208C4#1171881511yescharacteristic
209C2—4161no—
210C2#1311450111yescharacteristic
211C2#1311709811yescharacteristic
212C2#1311710411yescharacteristic
subgroupG/H
centerC22#11718812
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#2247C2
socleC22×C13#493
prime radical#11718356C22
hypercenter#2247D13
hypocenterC13#12530
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2247

Complements

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

NH ≅ G/Ntype
2. #13117063C2semidirect
5. #13114430C2semidirect
6. #13112755C2semidirect
7. C13×#2247C2semidirect
73. #2247D13semidirect
177. C13#12530semidirect

Maximal subgroups

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

subgroupindex
#131170932
#131170632
#131170602
#131144432
#131144302
#131127552
C13×#22472
#1253013