Finite Group Databasebeta

← #15765166

Subgroups — #15765166

Order 3328.

542 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 105 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#13125774C212yesmaximal
2#13115660C211yesmaximal, characteristic
3#13113400C212yesmaximal, complemented
4#13112681C211yesmaximal, characteristic, complemented
5C13×#3162C211yesmaximal, characteristic, complemented
6C13×#533C2212yes—
7C2×#88128C2211yescharacteristic
8C13×#501—22no—
9C13×#501—22no—
10C13×#427—22no—
11C2×C13×#97C2211yescharacteristic
12C2×#88061—22no—
13#11718749—22no—
14#11718746—22no—
15#11718707—24no—
16#11718688—24no—
17#11718597C2211yescharacteristic
18#11718586C2212yes—
19#11718130—24no—
20C22×D52—21no—
21C22×D52—22no—
22C22×C8×C13D412yes—
23C13×C4⋊Q8D412yes—
24C13×C4⋊Q8D412yes—
25C13×#125—22no—
26C13×C22⋊Q8—22no—
27C13×C22⋊Q8—22no—
28C4×Q8×C13—22no—
29C4×Q8×C13—22no—
30C13×#117—22no—
31C2×C42×C13C2311yescharacteristic
32C2×#6106—28no—
33C2×C4⋊Dic13—21no—
34#88128—22no—
35#88128—21no—
36#88128D412yes—
37C13×#107—24no—
38C13×#106—22no—
39C13×#106—22no—
40C13×#97—22no—
41#88071—22no—
42C22⋊#1055D414yes—
43#88061—44no—
44#88049—28no—
45C4⋊#1055—22no—
46C4×#1055—22no—
47#10220—131nomaximal, Sylow
48C23×D13—41no—
49C2×Q8×C13—22no—
50C2×Q8×C13—22no—
51C22×C4×C13C2×D412yes—
52C22×C4×C13C2×D411yescharacteristic
53C22×Dic13—41no—
54C2×D52—24no—
55C2×D52—22no—
56C2×D52—42no—
57C2×D52—42no—
58C2×D52—41no—
59C2×D52—42no—
60C2×D52—84no—
61C2×C8×C13—22no—
62C2×C8×C13—22no—
63C2×C8×C13SD1614yescomplemented
64C13×C4⋊C4—22no—
65C13×C4⋊C4—22no—
66C13×C4⋊C4—22no—
67C13×C4⋊C4—22no—
68C13×C4⋊C4—42no—
69C13×C4⋊C4—42no—
70C13×C22⋊C4—42no—
71C42×C13—42no—
72C42×C13C2×D411yescharacteristic
73C42×C13C2×D412yes—
74C42×C13#4111yescharacteristic
75#6106—88no—
76C4⋊Dic13—42no—
77C2×#1055—24no—
78#3208—132no—
79#3162D1311yescharacteristic, complemented
80#1961—131no—
81#1518—132no—
82#1281—131no—
83C23×C13#12711yescharacteristic
84C22×D13—42no—
85C22×D13—84no—
86C22×D13—81no—
87C22×D13—81no—
88Q8×C13—44no—
89Q8×C13—82no—
90C2×C4×C13—42no—
91C2×C4×C13—42no—
92C2×C4×C13—42no—
93C2×C4×C13#12012yes—
94C2×C4×C13#12011yescharacteristic
95C2×C4×C13#12112yes—
96C2×C4×C13#12111yescharacteristic
97C2×C4×C13C2×SD1612yes—
98C2×C4×C13#13712yes—
99C2×Dic13—82no—
100C2×Dic13—81no—
101D52—48no—
102D52—44no—
103D52—84no—
104D52—82no—
105C8×C13—24no—
106#1055—44no—
107#533C2×D1312yes—
108C2×#127—131no—
109#501—22no—
110#501—22no—
111#492—262no—
112#486—262no—
113#460—264no—
114#450—264no—
115#431—132no—
116#427—22no—
117C2×#102—262no—
118C2×#97C2×D1311yescharacteristic
119#382—131no—
120#328—264no—
121C22×C13—22no—
122C22×C13#39211yescharacteristic
123C22×C13#49211yescharacteristic
124C22×C13#49711yescharacteristic
125C2×D13—84no—
126C2×D13—82no—
127C2×D13—162no—
128C2×D13—162no—
129C4×C13—22no—
130C4×C13—22no—
131C4×C13—82no—
132C4×C13—82no—
133C4×C13#44812yes—
134C4×C13#46112yes—
135Dic13—161no—
136C22×D4—262no—
137C22×D4—261no—
138C2×SD16—268no—
139C22×C8C22⋊D1312yes—
140C4⋊Q8C22⋊D1312yes—
141C4⋊Q8C22⋊D1312yes—
142#127—132no—
143#127—261no—
144#127—262no—
145#125—22no—
146C22⋊Q8—22no—
147C22⋊Q8—22no—
148C4×Q8—22no—
149C4×Q8—22no—
150#117—22no—
151C2×C4⋊C4—261no—
152C2×C42C22×D1311yescharacteristic
153#107—24no—
154#106—22no—
155#106—22no—
156C4⋊C8—262no—
157#102—268no—
158#102—524no—
159C22⋊C8—134no—
160#97—22no—
161C4×C8—262no—
162#95—262no—
163C2×C13—21no—
164C2×C13—21no—
165C2×C13#200812yes—
166C2×C13#201311yescharacteristic
167D13—162no—
168C24—521no—
169C2×Q8—22no—
170C2×Q8—22no—
171C2×D4—264no—
172C2×D4—262no—
173C2×D4—522no—
174C2×D4—522no—
175C2×D4—522no—
176C2×D4—521no—
177C2×D4—1044no—
178C22×C4—521no—
179C22×C4D4×D1312yes—
180C22×C4C2×C22⋊D1311yescharacteristic
181SD16—1048no—
182C2×C8—22no—
183C2×C8—22no—
184C2×C8—264no—
185C2×C8#610614yescomplemented
186C4⋊C4—22no—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C4⋊C4—22no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—522no—
193C22⋊C4—42no—
194C42—42no—
195C42D4×D1311yescharacteristic
196C42#612911yescharacteristic
197C42C2×C22⋊D1312yes—
198C13#1022011yescharacteristic, complemented, Sylow
199C23—522no—
200C23—1044no—
201C23—1041no—
202C23—1041no—
203C23#8819411yescharacteristic
204Q8—44no—
205Q8—82no—
206D4—528no—
207D4—524no—
208D4—1044no—
209D4—1042no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—1042no—
214C2×C4—1041no—
215C2×C4#8819112yes—
216C2×C4#8819211yescharacteristic
217C2×C4#8819312yes—
218C2×C4C2×#610612yes—
219C2×C4#8819612yes—
220C2×C4#8820711yescharacteristic
221C8—24no—
222C8—524no—
223C22—22no—
224C22—1042no—
225C22—1044no—
226C22—2082no—
227C22—2082no—
228C22#1171874611yescharacteristic
229C22#1171874711yescharacteristic
230C22#1171888411yescharacteristic
231C4—22no—
232C4—22no—
233C4—82no—
234C4—82no—
235C4—2081no—
236C4#1171874412yes—
237C4#1171888812yes—
238C2—21no—
239C2—21no—
240C2—2082no—
241C2#1311588612yes—
242C2#1311591911yescharacteristic
subgroupG/H
centerC22#11718884
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#3162C2
socleC22×C13#392
prime radicalC2×#88128C22
hypercenter#3162D13
hypocenterC13#10220
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3162

Complements

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

NH ≅ G/Ntype
3. #13113400C2semidirect
4. #13112681C2semidirect
5. C13×#3162C2semidirect
63. C2×C8×C13SD16semidirect
79. #3162D13semidirect
185. C2×C8#6106semidirect
198. C13#10220semidirect

Maximal subgroups

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

subgroupindex
#131257742
#131156602
#131134002
#131126812
C13×#31622
#1022013