Finite Group Databasebeta

← #15765580

Subgroups — #15765580

Order 3328.

542 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 111 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#13125961C212yesmaximal
2#13123214C211yesmaximal, characteristic, complemented
3#13113522C212yesmaximal, complemented
4#13112669C211yesmaximal, characteristic, complemented
5C13×#1962C211yesmaximal, characteristic
6C13×#532C2211yescharacteristic
7C2×#88123C2212yes—
8C13×#423C2211yescharacteristic
9C2×C13×#104—22no—
10C43×C13C2211yescharacteristic
11#11718740—22no—
12#11718731—22no—
13#11718695—24no—
14#11718669—24no—
15#11718597—22no—
16#11718590—24no—
17#11718586C2212yes—
18#11718078—24no—
19C2×C13×#41—21no—
20C22×Dic26—22no—
21C2×C13×M16—21no—
22C13×C4⋊Q8D411yescharacteristic
23C13×#127D411yescharacteristic
24C13×#124—21no—
25C13×#121—22no—
26C4×D4×C13—22no—
27C2×C42×C13—22no—
28C2×C42×C13D412yes—
29C2×C42×C13C2311yescharacteristic
30C2×C4⋊Dic13—22no—
31C2×C4⋊Dic13D414yes—
32#88123—22no—
33#88123—22no—
34#88123—22no—
35#88123—22no—
36C13×C4⋊C8—22no—
37C13×#104—44no—
38#88072—28no—
39#88071—28no—
40C22⋊#1055—22no—
41#88048—28no—
42C4⋊#1055D414yes—
43C4×#1055—22no—
44#10285—131nomaximal, Sylow
45C13×#41—42no—
46C13×#41—42no—
47C2×Q8×C13—21no—
48C2×D4×C13—22no—
49C2×D4×C13—21no—
50C2×D4×C13—41no—
51C22×C4×C13—22no—
52C22×C4×C13—41no—
53C22×C4×C13C2×D412yes—
54C22×C4×C13C2×D411yescharacteristic
55C22×Dic13—24no—
56C2×Dic26—48no—
57C2×Dic26—42no—
58C2×Dic26—42no—
59C13×M16—42no—
60C2×C8×C13—41no—
61C13×C4⋊C4—22no—
62C13×C22⋊C4—42no—
63C42×C13—22no—
64C42×C13—44no—
65C42×C13SD1614yes—
66C42×C13C2×D411yescharacteristic
67C42×C13C2×D412yes—
68C42×C13#4111yescharacteristic
69C4⋊Dic13—24no—
70C4⋊Dic13—24no—
71C4⋊Dic13—42no—
72C4⋊Dic13—42no—
73C2×#1055—24no—
74#3227—132no—
75#2862—131no—
76#1962D1311yescharacteristic
77#1549—132no—
78#1276—131no—
79C23×C13—41no—
80C23×C13#12011yescharacteristic
81Q8×C13—42no—
82D4×C13—44no—
83D4×C13—42no—
84D4×C13—82no—
85C2×C4×C13—24no—
86C2×C4×C13—24no—
87C2×C4×C13—44no—
88C2×C4×C13—41no—
89C2×C4×C13—81no—
90C2×C4×C13—81no—
91C2×C4×C13#12012yes—
92C2×C4×C13#12112yes—
93C2×C4×C13#12111yescharacteristic
94C2×C4×C13#12711yescharacteristic
95C2×C4×C13C2×SD1612yes—
96C2×C4×C13#13712yes—
97C2×Dic13—48no—
98C2×Dic13—44no—
99Dic26—84no—
100Dic26—84no—
101C8×C13—81no—
102#1055—44no—
103#532C2×D1311yescharacteristic
104C2×C4⋊Q8—132no—
105#498—262no—
106#486—262no—
107#481—264no—
108#476—264no—
109#431—132no—
110#423C2×D1311yescharacteristic
111C2×#104—22no—
112#391—264no—
113#382—262no—
114C43C2×D1311yescharacteristic
115#332—264no—
116C22×C13—22no—
117C22×C13—82no—
118C22×C13—81no—
119C22×C13#39211yescharacteristic
120C22×C13#44812yes—
121C4×C13—22no—
122C4×C13—44no—
123C4×C13—81no—
124C4×C13#45414yes—
125C4×C13#46112yes—
126C4×C13#49211yescharacteristic
127C4×C13#49711yescharacteristic
128Dic13—84no—
129C2×#41—21no—
130C22×Q8—262no—
131C2×M16—21no—
132C4⋊Q8—262no—
133C4⋊Q8—262no—
134C4⋊Q8—262no—
135C4⋊Q8—262no—
136C4⋊Q8D5211yescharacteristic
137#127D5211yescharacteristic
138#124—21no—
139#121—22no—
140C4×D4—22no—
141C2×C4⋊C4—134no—
142C2×C4⋊C4—262no—
143C2×C42—22no—
144C2×C42C22⋊D1312yes—
145C2×C42C22×D1311yescharacteristic
146#106—268no—
147C4⋊C8—22no—
148C4⋊C8—134no—
149#104—44no—
150#102—268no—
151C22⋊C8—262no—
152C4×C8—262no—
153#95—268no—
154C2×C13—22no—
155C2×C13—161no—
156C2×C13#200312yes—
157C2×C13#201311yescharacteristic
158#41—42no—
159#41—42no—
160C2×Q8—21no—
161C2×Q8—528no—
162C2×Q8—522no—
163C2×Q8—522no—
164C2×D4—22no—
165C2×D4—21no—
166C2×D4—41no—
167C22×C4—22no—
168C22×C4—41no—
169C22×C4—264no—
170C22×C4D4×D1312yes—
171C22×C4C2×C22⋊D1311yescharacteristic
172M16—42no—
173C2×C8—41no—
174C2×C8—264no—
175C4⋊C4—22no—
176C4⋊C4—264no—
177C4⋊C4—264no—
178C4⋊C4—522no—
179C4⋊C4—522no—
180C22⋊C4—42no—
181C42—22no—
182C42—44no—
183C42#610514yes—
184C42C2×D5211yescharacteristic
185C42#612711yescharacteristic
186C42D4×D1312yes—
187C13#1028511yescharacteristic, complemented, Sylow
188C23—41no—
189C23#8819111yescharacteristic
190Q8—42no—
191Q8—1044no—
192Q8—1044no—
193D4—42no—
194D4—44no—
195D4—82no—
196C2×C4—24no—
197C2×C4—24no—
198C2×C4—44no—
199C2×C4—41no—
200C2×C4—81no—
201C2×C4—81no—
202C2×C4—528no—
203C2×C4—524no—
204C2×C4#8813612yes—
205C2×C4#8813812yes—
206C2×C4#8818411yescharacteristic
207C2×C4C2×#610512yes—
208C2×C4#8819411yescharacteristic
209C2×C4#8820512yes—
210C8—81no—
211C8—524no—
212C22—22no—
213C22—81no—
214C22—82no—
215C22#1171862111yescharacteristic
216C22#1171870112yes—
217C4—22no—
218C4—44no—
219C4—81no—
220C4—1044no—
221C4#1171848814yes—
222C4#1171868012yes—
223C4#1171872111yescharacteristic
224C4#1171873711yescharacteristic
225C2—22no—
226C2—161no—
227C2#1311585712yes—
228C2#1311591811yescharacteristic
subgroupG/H
centerC22#11718621
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1962C2
socleC22×C13#392
prime radicalC13×#532C22
hypercenter#1962D13
hypocenterC13#10285
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1962

Complements

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

NH ≅ G/Ntype
2. #13123214C2semidirect
3. #13113522C2semidirect
4. #13112669C2semidirect
187. C13#10285semidirect

Maximal subgroups

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

subgroupindex
#131259612
#131232142
#131135222
#131126692
C13×#19622
#1028513