Finite Group Databasebeta

← #16791294

Subgroups — #16791294

Order 3328.

326 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 326 conjugacy classes of subgroups — too many to draw. Only its 60 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#13131109C212yesmaximal
2#13129976C212yesmaximal, complemented
3#13129975C212yesmaximal, complemented
4#13125184C211yesmaximal, characteristic
5C13×#533C411yescharacteristic, complemented
6#11719182C2211yescharacteristic
7#11719116—22no—
8#11718750—22no—
9#11718730C411yescharacteristic, complemented
10#11718730C411yescharacteristic, complemented
11#11718728C2211yescharacteristic
12#11718728C2211yescharacteristic
13#11718663—22no—
14C2×#88043C411yescharacteristic, complemented
15#11718226—22no—
16#11718225C2214yes—
17C2×#6127D412yes—
18#88237—42no—
19C13×C4⋊Q8—21no—
20C13×#125C2×C411yescharacteristic
21C13×#125C2×C411yescharacteristic
22C13×C22⋊Q8—41no—
23C4×Q8×C13—41no—
24C13×#117—21no—
25C2×C42×C13C2×C411yescharacteristic
26#88184—41no—
27C22×#1055—21no—
28#88129D412yes—
29#88128C2311yescharacteristic
30C4×D52—41no—
31#88123C2×C411yescharacteristic
32#88119—42no—
33#88107—24no—
34#88050—22no—
35#88050—22no—
36#88049—22no—
37#88049—22no—
38#88043—21no—
39#88043C2×C411yescharacteristic
40#88043C2×C411yescharacteristic
41#13594—131nomaximal, Sylow
42C2×Q8×C13—41no—
43C22×C4×C13—21no—
44C22×C4×C13C22⋊C411yescharacteristic
45C2×C22⋊D13—22no—
46#6127—42no—
47#6127—42no—
48C2×D52—41no—
49C2×D52C2×D412yes—
50C2×C4×D13—22no—
51C2×Dic26C22⋊C412yes—
52C22⋊#261—44no—
53C4⋊#261—82no—
54C4×#261—82no—
55C13×C4⋊C4—21no—
56C13×C4⋊C4—21no—
57C13×C4⋊C4—41no—
58C13×C4⋊C4—41no—
59C13×C4⋊C4—41no—
60C13×C22⋊C4—41no—
61C42×C13—21no—
62C42×C13—41no—
63C42×C13C22⋊C411yescharacteristic
64C42×C13C22×C411yescharacteristic
65#6103—42no—
66C4⋊Dic13—41no—
67C2×#1055—21no—
68C2×#1055—21no—
69C2×#1055—41no—
70C2×#1055—41no—
71#3135—131no—
72#2126—132no—
73#1412—132no—
74#1412—132no—
75C23×C13#9911yescharacteristic
76C22×D13—22no—
77C2×#261—84no—
78Q8×C13—82no—
79C2×C4×C13—21no—
80C2×C4×C13—21no—
81C2×C4×C13—21no—
82C2×C4×C13—21no—
83C2×C4×C13—41no—
84C2×C4×C13—41no—
85C2×C4×C13—81no—
86C2×C4×C13#9911yescharacteristic
87C2×C4×C13C2×C22⋊C411yescharacteristic
88C22⋊D13—82no—
89C2×Dic13—22no—
90D52—42no—
91D52—82no—
92C4×D13—42no—
93C4×D13—42no—
94Dic26—42no—
95#1055—41no—
96#1055—41no—
97#533#26111yescharacteristic, complemented
98#532—131no—
99#491—131no—
100#491—131no—
101#490—131no—
102#490—131no—
103#489—262no—
104#416—262no—
105#410—262no—
106C2×#97—131no—
107#354—262no—
108#353—134no—
109C22×C13—21no—
110C22×C13—41no—
111C22×C13C2×#9911yescharacteristic
112C2×D13—42no—
113C2×D13—82no—
114#261—164no—
115C4×C13—21no—
116C4×C13—41no—
117C4×C13—41no—
118C4×C13—81no—
119C4×C13—81no—
120C4×C13#35411yescharacteristic
121C4×C13#35411yescharacteristic
122Dic13—42no—
123C2×#41—132no—
124C22×C8—261no—
125C4⋊Q8—21no—
126C4⋊Q8—131no—
127#127—131no—
128#125C2×#26111yescharacteristic
129#125C2×#26111yescharacteristic
130#124—132no—
131C22⋊Q8—41no—
132#121—521no—
133C4×Q8—41no—
134C4×D4—521no—
135#117—21no—
136#117—522no—
137C2×C42C2×#26111yescharacteristic
138#103—262no—
139#103—262no—
140#102—262no—
141#102—262no—
142#99—264no—
143#99—522no—
144#97—131no—
145#97—131no—
146#97—261no—
147C2×C13—21no—
148C2×C13—41no—
149C2×C13C2×#35411yescharacteristic
150D13—82no—
151#41—522no—
152#41—522no—
153C2×Q8—41no—
154C2×Q8—132no—
155C2×D4—132no—
156C2×D4—262no—
157C2×D4—521no—
158C22×C4—21no—
159C22×C4—262no—
160C22×C4C22⋊#26111yescharacteristic
161C2×C8—261no—
162C2×C8—261no—
163C2×C8—521no—
164C2×C8—521no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4—521no—
171C4⋊C4—1042no—
172C22⋊C4—41no—
173C22⋊C4—522no—
174C22⋊C4—524no—
175C42—21no—
176C42—41no—
177C42—1042no—
178C42C22⋊#26111yescharacteristic
179C42C22×#26111yescharacteristic
180C13#1359411yescharacteristic, complemented, Sylow
181C23—262no—
182C23#8811911yescharacteristic
183Q8—82no—
184Q8—522no—
185D4—522no—
186D4—1042no—
187D4—1042no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4—262no—
196C2×C4—522no—
197C2×C4—522no—
198C2×C4—1044no—
199C2×C4#8811911yescharacteristic
200C2×C4C2×C22⋊#26111yescharacteristic
201C8—521no—
202C8—521no—
203C22—21no—
204C22—41no—
205C22—522no—
206C22—1042no—
207C22C2×#8811911yescharacteristic
208C4—21no—
209C4—41no—
210C4—41no—
211C4—81no—
212C4—81no—
213C4—522no—
214C4—2084no—
215C4#1171830011yescharacteristic
216C4#1171830011yescharacteristic
217C2—21no—
218C2—41no—
219C2—1042no—
220C2C2×#1171830011yescharacteristic
subgroupG/H
centerC4#11718300
commutatorC42×C13C22×C4
FrattiniC42C22×#261
FittingC13×#533C4
socleC2×C13C2×#354
prime radical#11719182C22
cosocle#88128C23
hypercenter#533#261
hypocenterC13#13594
LCSG ▷ C42×C13 ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C2×C4 ◁ C22×C4 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
2. #13129976C2semidirect
3. #13129975C2semidirect
5. C13×#533C4semidirect
9. #11718730C4semidirect
10. #11718730C4semidirect
14. C2×#88043C4semidirect
97. #533#261semidirect
180. C13#13594semidirect

Maximal subgroups

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

subgroupindex
#131311092
#131299762
#131299752
#131251842
#1359413