Finite Group Databasebeta

← #15777696

Subgroups — #15777696

Order 3328.

284 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 79 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#13117088C211yesmaximal, characteristic, complemented
3#13117065C211yesmaximal, characteristic, complemented
4#13117061C211yesmaximal, characteristic
5#13114442C211yesmaximal, characteristic
6#13112754C211yesmaximal, characteristic, complemented
7C13×#1707C211yesmaximal, characteristic, complemented
8C13×#500C2211yescharacteristic
9C13×#498—21no—
10C13×#494C2211yescharacteristic
11C13×#487—21no—
12C2×#88069—22no—
13C2×#88068—22no—
14#11718360C2211yescharacteristic
15#11718356C2211yescharacteristic
16#11718355—21no—
17#11718355—21no—
18C82×C13C2211yescharacteristic
19#11718084—22no—
20#11718083—22no—
21C4×#6090C2211yescharacteristic
22C4×#6090C2211yescharacteristic
23C2×C13×Q16—21no—
24C2×C13×Q16—21no—
25C13×C4⋊Q8—21no—
26C13×C4⋊Q8—21no—
27C2×Dic52—21no—
28C2×Dic52—21no—
29C2×D104—21no—
30C2×D104—21no—
31#88128—21no—
32#88123—21no—
33C13×#107—21no—
34C13×#107—21no—
35C13×#106—42no—
36C13×#103—42no—
37C4×C8×C13D411yescharacteristic
38C4×C8×C13D411yescharacteristic
39C4×C8×C13C2311yescharacteristic
40#88069—44no—
41#88068—44no—
42#88061—42no—
43#88061—42no—
44C2×#6090D412yes—
45C2×#6090D412yes—
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—
55C2×C8×C13D812yes—
56C2×C8×C13D812yes—
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—
66Dic52—42no—
67Dic52—42no—
68D104—42no—
69D104—42no—
70#6090—22no—
71#6090—22no—
72#2248—131no—
73#2247—131no—
74#2241—131no—
75#2240—131no—
76#1709—131no—
77#1707D1311yescharacteristic, complemented
78#1312—131no—
79C22×D13—81no—
80Q8×C13—81no—
81Q8×C13—81no—
82Q8×C13—82no—
83C2×C4×C13—81no—
84C2×C4×C13—81no—
85C2×C4×C13#12711yescharacteristic
86C2×C4×C13C2×D811yescharacteristic
87C2×C4×C13C2×D811yescharacteristic
88C2×Dic13—81no—
89D52—81no—
90D52—81no—
91D52—82no—
92D52—82no—
93Dic26—81no—
94Dic26—81no—
95C8×C13—22no—
96C8×C13—22no—
97C8×C13AGL(1,ℤ/8)12yes—
98C8×C13AGL(1,ℤ/8)12yes—
99C2×Q32—262no—
100C2×SD32—262no—
101#500C2×D1311yescharacteristic
102#498—21no—
103#494—131no—
104#494C2×D1311yescharacteristic
105#493—131no—
106#487—21no—
107#486—261no—
108#486—261no—
109#358—262no—
110#357—262no—
111C4×C16—131no—
112C4×C16—131no—
113C82C2×D1311yescharacteristic
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—261no—
128C2×Q16—261no—
129C2×D8—261no—
130C2×D8—261no—
131C4⋊Q8—21no—
132C4⋊Q8—21no—
133C4⋊Q8—261no—
134#127—261no—
135Q32—524no—
136SD32—524no—
137C2×C16—132no—
138C2×C16—132no—
139#107—21no—
140#107—21no—
141#106—42no—
142#103—42no—
143#102—522no—
144#102—522no—
145C4×C8C22⋊D1311yescharacteristic
146C4×C8C22⋊D1311yescharacteristic
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—522no—
161Q16—522no—
162D8—522no—
163D8—522no—
164C2×C8#610412yes—
165C2×C8#610412yes—
166C2×C8D4×D1311yescharacteristic
167C2×C8D4×D1311yescharacteristic
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—41no—
171C4⋊C4—41no—
172C4⋊C4—521no—
173C4⋊C4—521no—
174C42C2×C22⋊D1311yescharacteristic
175C16—262no—
176C16—262no—
177C13#1253011yescharacteristic, complemented, Sylow
178C23—1041no—
179Q8—81no—
180Q8—81no—
181Q8—82no—
182Q8—1041no—
183Q8—1041no—
184D4—1041no—
185D4—1041no—
186D4—1042no—
187D4—1042no—
188C2×C4—81no—
189C2×C4—81no—
190C2×C4—1041no—
191C2×C4C2×#610411yescharacteristic
192C2×C4C2×#610411yescharacteristic
193C2×C4#8819411yescharacteristic
194C8—22no—
195C8—22no—
196C8#8816812yes—
197C8#8816812yes—
198C22—2081no—
199C22—2081no—
200C22—2081no—
201C22#1171873411yescharacteristic
202C4—161no—
203C4—161no—
204C4—2081no—
205C4#1171883711yescharacteristic
206C4#1171883711yescharacteristic
207C4#1171884012yes—
208C4#1171885512yes—
209C2—4161no—
210C2#1311450011yescharacteristic
211C2#1311709511yescharacteristic
212C2#1311710511yescharacteristic
subgroupG/H
centerC22#11718734
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1707C2
socleC22×C13#493
prime radical#11718356C22
hypercenter#1707D13
hypocenterC13#12530
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1707

Complements

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

NH ≅ G/Ntype
2. #13117088C2semidirect
3. #13117065C2semidirect
6. #13112754C2semidirect
7. C13×#1707C2semidirect
77. #1707D13semidirect
177. C13#12530semidirect

Maximal subgroups

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

subgroupindex
#131170932
#131170882
#131170652
#131170612
#131144422
#131127542
C13×#17072
#1253013