Finite Group Databasebeta

← #15765165

Subgroups — #15765165

Order 3328.

542 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 542 conjugacy classes of subgroups — too many to draw. Only its 103 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#13125777C212yesmaximal
2#13125360C211yesmaximal, characteristic, complemented
3#13113399C212yesmaximal, complemented
4#13112681C211yesmaximal, characteristic, complemented
5C13×#1961C211yesmaximal, characteristic
6C2×C13×#127C2211yescharacteristic
7#11719175C2212yes—
8C2×C13×#102—22no—
9C2×C13×#97C2211yescharacteristic
10C13×#382C2211yescharacteristic
11#11718879—24no—
12#11718767—22no—
13#11718737—22no—
14#11718736—24no—
15#11718731—22no—
16#11718586C2212yes—
17#11718363—22no—
18#11718363—22no—
19#11718044—24no—
20C22×D4×C13—21no—
21C22×D4×C13—22no—
22C22×C8×C13D412yes—
23C13×#127—22no—
24C13×#127—21no—
25C13×#127D412yes—
26C2×C13×C4⋊C4—21no—
27C2×C42×C13C2311yescharacteristic
28C2×#6105—28no—
29#88180—22no—
30#88178—22no—
31#88178—22no—
32#88124—22no—
33#88123D412yes—
34#88123D412yes—
35C4×Dic26—22no—
36C4×Dic26—22no—
37C13×#102—44no—
38C13×#97—22no—
39C13×#95—22no—
40#88072—28no—
41C22⋊#1055D414yes—
42#88058—24no—
43#88057—22no—
44#88057—22no—
45C4⋊#1055—22no—
46C4×#1055—22no—
47#10220—131nomaximal, Sylow
48C24×C13—41no—
49C2×D4×C13—24no—
50C2×D4×C13—22no—
51C2×D4×C13—41no—
52C2×D4×C13—42no—
53C2×D4×C13—42no—
54C2×D4×C13—42no—
55C2×D4×C13—84no—
56C22×C4×C13—41no—
57C22×C4×C13C2×D412yes—
58C22×C4×C13C2×D411yescharacteristic
59C2×Dic26—22no—
60C2×Dic26—22no—
61C2×C8×C13—22no—
62C2×C8×C13—22no—
63C2×C8×C13SD1614yescomplemented
64C13×C4⋊C4—42no—
65C42×C13C2×D411yescharacteristic
66C42×C13C2×D412yes—
67C42×C13#4111yescharacteristic
68C22⋊Dic13—42no—
69#6105—88no—
70C4⋊Dic13—22no—
71C4⋊Dic13—22no—
72C4⋊Dic13—22no—
73C4⋊Dic13—22no—
74#6101—42no—
75#6101—42no—
76C4×Dic13—42no—
77C2×#1055—24no—
78#3208—132no—
79#3162—131no—
80#1961D1311yescharacteristic
81#1518—132no—
82#1281—131no—
83C23×C13—42no—
84C23×C13—84no—
85C23×C13—81no—
86C23×C13—81no—
87C23×C13#12711yescharacteristic
88D4×C13—48no—
89D4×C13—44no—
90D4×C13—84no—
91D4×C13—82no—
92C2×C4×C13—42no—
93C2×C4×C13—82no—
94C2×C4×C13—81no—
95C2×C4×C13#12012yes—
96C2×C4×C13#12011yescharacteristic
97C2×C4×C13#12112yes—
98C2×C4×C13#12111yescharacteristic
99C2×C4×C13C2×SD1612yes—
100C2×C4×C13#13712yes—
101C2×Dic13—42no—
102C2×Dic13—42no—
103Dic26—44no—
104Dic26—82no—
105C8×C13—24no—
106#1055—44no—
107#533—132no—
108C2×#127C2×D1311yescharacteristic
109#501—262no—
110#501—262no—
111#492—262no—
112#486—262no—
113#460—264no—
114#450—264no—
115#431—132no—
116#427—262no—
117C2×#102—22no—
118C2×#97C2×D1311yescharacteristic
119#382C2×D1311yescharacteristic
120#328—264no—
121C22×C13—22no—
122C22×C13—84no—
123C22×C13—82no—
124C22×C13—162no—
125C22×C13—162no—
126C22×C13#39211yescharacteristic
127C22×C13#49211yescharacteristic
128C22×C13#49711yescharacteristic
129C4×C13—22no—
130C4×C13—22no—
131C4×C13—161no—
132C4×C13#44812yes—
133C4×C13#46112yes—
134Dic13—82no—
135Dic13—82no—
136C22×D4—22no—
137C22×D4—21no—
138C2×SD16—268no—
139C22×C8C22⋊D1312yes—
140C4⋊Q8—132no—
141C4⋊Q8—132no—
142#127—21no—
143#127—22no—
144#127D5212yes—
145#125—262no—
146C22⋊Q8—262no—
147C22⋊Q8—262no—
148C4×Q8—262no—
149C4×Q8—262no—
150#117—262no—
151C2×C4⋊C4—21no—
152C2×C42C22×D1311yescharacteristic
153#107—264no—
154#106—262no—
155#106—262no—
156C4⋊C8—262no—
157#102—44no—
158#102—268no—
159C22⋊C8—134no—
160#97—22no—
161C4×C8—262no—
162#95—22no—
163C2×C13—21no—
164C2×C13—21no—
165C2×C13—162no—
166C2×C13#200812yes—
167C2×C13#201311yescharacteristic
168C24—41no—
169C2×Q8—262no—
170C2×Q8—262no—
171C2×D4—24no—
172C2×D4—22no—
173C2×D4—42no—
174C2×D4—42no—
175C2×D4—41no—
176C2×D4—42no—
177C2×D4—84no—
178C22×C4—41no—
179C22×C4D4×D1312yes—
180C22×C4C2×C22⋊D1311yescharacteristic
181SD16—1048no—
182C2×C8—22no—
183C2×C8—22no—
184C2×C8—264no—
185C2×C8#610514yescomplemented
186C4⋊C4—42no—
187C4⋊C4—262no—
188C4⋊C4—262no—
189C4⋊C4—262no—
190C4⋊C4—262no—
191C4⋊C4—522no—
192C4⋊C4—522no—
193C22⋊C4—522no—
194C42—522no—
195C42C2×D5211yescharacteristic
196C42#612711yescharacteristic
197C42D4×D1312yes—
198C13#1022011yescharacteristic, complemented, Sylow
199C23—42no—
200C23—84no—
201C23—81no—
202C23—81no—
203C23#8819411yescharacteristic
204Q8—524no—
205Q8—1042no—
206D4—48no—
207D4—44no—
208D4—84no—
209D4—82no—
210C2×C4—42no—
211C2×C4—82no—
212C2×C4—81no—
213C2×C4—522no—
214C2×C4—522no—
215C2×C4#8813612yes—
216C2×C4#8813812yes—
217C2×C4#8818411yescharacteristic
218C2×C4C2×#610512yes—
219C2×C4#8819111yescharacteristic
220C2×C4#8820512yes—
221C8—24no—
222C8—524no—
223C22—22no—
224C22—82no—
225C22—84no—
226C22—162no—
227C22—162no—
228C22#1171862111yescharacteristic
229C22#1171872111yescharacteristic
230C22#1171873711yescharacteristic
231C4—22no—
232C4—22no—
233C4—161no—
234C4—1042no—
235C4—1042no—
236C4#1171868012yes—
237C4#1171870112yes—
238C2—21no—
239C2—21no—
240C2—162no—
241C2#1311589112yes—
242C2#1311591811yescharacteristic
subgroupG/H
centerC22#11718621
commutator, cosocleC2×C42×C13C23
FrattiniC2×C42C22×D13
FittingC13×#1961C2
socleC22×C13#392
prime radicalC2×C13×#127C22
hypercenter#1961D13
hypocenterC13#10220
LCSG ▷ C2×C42×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1961

Complements

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

NH ≅ G/Ntype
2. #13125360C2semidirect
3. #13113399C2semidirect
4. #13112681C2semidirect
63. C2×C8×C13SD16semidirect
185. C2×C8#6105semidirect
198. C13#10220semidirect

Maximal subgroups

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

subgroupindex
#131257772
#131253602
#131133992
#131126812
C13×#19612
#1022013