Finite Group Databasebeta

← #13131001

Subgroups — #13131001

Order 1664.

336 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 336 conjugacy classes of subgroups — too many to draw. Only its 72 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#11719373C211yesmaximal, characteristic
2C2×#88118C212yesmaximal, complemented
3C2×#88116C212yesmaximal, complemented
4C4×C4⋊#261C211yesmaximal, characteristic, complemented
5C4×#6118C211yesmaximal, characteristic, complemented
6C2×#6131C2211yescharacteristic
7C2×#6129C2211yescharacteristic
8C2×C4⋊#261—21no—
9C2×C4×#261C2212yes—
10C2×#6118C2212yes—
11C13×#124C411yescharacteristic, complemented
12#88198C411yescharacteristic, complemented
13#88194C411yescharacteristic, complemented
14#88138—21no—
15#88138—21no—
16#88135—21no—
17#88135—21no—
18#88129C411yescharacteristic, complemented
19C42×D13C2211yescharacteristic
20#88118—24no—
21#88116—24no—
22(C2×#261)⋊C4—21no—
23#88110—21no—
24C4×#1057—21no—
25C22×#261—22no—
26C2×Q8×C13C2×C411yescharacteristic
27C2×D4×C13C2×C411yescharacteristic
28C2×C22⋊D13—21no—
29C2×C22⋊D13—21no—
30C2×C22⋊D13—21no—
31C22×Dic13—21no—
32#6131—22no—
33#6131—22no—
34#6129—22no—
35#6129—22no—
36C2×D52—21no—
37C2×D52C2×C411yescharacteristic
38C2×C4×D13—21no—
39C2×C4×D13D411yescharacteristic
40C2×C4×D13D411yescharacteristic
41C2×C4×D13C2311yescharacteristic
42C2×Dic26C2×C411yescharacteristic
43C2×#1057—22no—
44C4⋊#261—24no—
45C4×#261—22no—
46C4×#261—22no—
47#6118—22no—
48#6118D414yescomplemented
49C13×C22⋊C4—21no—
50C13×C22⋊C4—21no—
51C42×C13C2×C411yescharacteristic
52#6103—21no—
53#6103—21no—
54#6101—21no—
55#6101—21no—
56C4×Dic13C2×C411yescharacteristic
57C4×Dic13D411yescharacteristic
58C4×Dic13D411yescharacteristic
59#1980—131nomaximal, Sylow
60C23×C13—21no—
61C22×D13—21no—
62C22×D13C2×D411yescharacteristic
63C2×#261—24no—
64C2×#261—42no—
65C2×#261—42no—
66Q8×C13—22no—
67D4×C13—22no—
68C2×C4×C13—21no—
69C2×C4×C13C22⋊C411yescharacteristic
70C2×C4×C13C22⋊C411yescharacteristic
71C2×C4×C13C22×C411yescharacteristic
72C22⋊D13—42no—
73C22⋊D13—41no—
74C22⋊D13—41no—
75C22⋊D13—42no—
76C2×Dic13—21no—
77C2×Dic13—42no—
78C2×Dic13C22⋊C411yescharacteristic
79C2×Dic13C22⋊C411yescharacteristic
80C2×Dic13C2×D411yescharacteristic
81D52—22no—
82D52—41no—
83D52—41no—
84C4×D13—22no—
85C4×D13—41no—
86C4×D13—42no—
87C4×D13C2×D412yes—
88C4×D13#4112yes—
89Dic26—22no—
90#1057—24no—
91#532—131no—
92C2×#104—132no—
93C2×#104—132no—
94C4×M16—131no—
95C4×C4⋊C4—131no—
96C22×C13—41no—
97C22×C13—41no—
98C22×C13—41no—
99C22×C13C2×C22⋊C411yescharacteristic
100C2×D13—21no—
101C2×D13—21no—
102C2×D13—41no—
103C2×D13—41no—
104C2×D13—41no—
105C2×D13#12411yescharacteristic
106C2×D13#12711yescharacteristic
107#261—44no—
108C4×C13—21no—
109C4×C13—21no—
110C4×C13—41no—
111C4×C13C4×D412yes—
112Dic13—21no—
113Dic13—41no—
114Dic13#10412yescomplemented
115Dic13#12112yes—
116C2×#41—131no—
117C2×#41—131no—
118C2×M16—132no—
119C4⋊Q8—131no—
120#127—131no—
121#124—131no—
122#124#26111yescharacteristic, complemented
123#121—261no—
124#121—261no—
125C4×D4—261no—
126C4×D4—261no—
127C2×C4⋊C4—261no—
128C2×C42—131no—
129C2×C42—132no—
130#104—264no—
131#104—264no—
132#97—261no—
133C4×C8—261no—
134#95—261no—
135C2×C13—81no—
136C2×C13#39011yescharacteristic
137C2×C13C2×#10411yescharacteristic
138C2×C13#42111yescharacteristic
139D13—21no—
140D13—21no—
141D13—81no—
142#41—262no—
143#41—262no—
144#41—262no—
145#41—262no—
146C2×Q8—131no—
147C2×Q8C2×#26111yescharacteristic
148C2×D4—131no—
149C2×D4—261no—
150C2×D4—261no—
151C2×D4—261no—
152C2×D4—261no—
153C2×D4C2×#26111yescharacteristic
154C22×C4—131no—
155C22×C4—131no—
156C22×C4—131no—
157C22×C4—261no—
158C22×C4—261no—
159C22×C4—262no—
160M16—134no—
161M16—262no—
162C2×C8—262no—
163C4⋊C4—261no—
164C4⋊C4—261no—
165C4⋊C4—264no—
166C22⋊C4—21no—
167C22⋊C4—21no—
168C22⋊C4—261no—
169C22⋊C4—261no—
170C42—131no—
171C42—131no—
172C42—131no—
173C42—262no—
174C42—262no—
175C42C2×#26111yescharacteristic
176C13#198011yescharacteristic, complemented, Sylow
177C23—21no—
178C23—131no—
179C23—261no—
180Q8—22no—
181Q8—262no—
182D4—22no—
183D4—262no—
184D4—521no—
185D4—521no—
186D4—522no—
187D4—522no—
188D4—521no—
189D4—521no—
190C2×C4—21no—
191C2×C4—131no—
192C2×C4—131no—
193C2×C4—132no—
194C2×C4—132no—
195C2×C4—131no—
196C2×C4—262no—
197C2×C4—264no—
198C2×C4—261no—
199C2×C4—521no—
200C2×C4—522no—
201C2×C4—522no—
202C2×C4—522no—
203C2×C4—522no—
204C2×C4C22⋊#26111yescharacteristic
205C2×C4C22⋊#26111yescharacteristic
206C2×C4C22×#26111yescharacteristic
207C8—264no—
208C22—41no—
209C22—41no—
210C22—41no—
211C22—131no—
212C22—131no—
213C22—261no—
214C22—261no—
215C22—521no—
216C22—521no—
217C22—521no—
218C22C2×C22⋊#26111yescharacteristic
219C4—21no—
220C4—21no—
221C4—41no—
222C4—132no—
223C4—132no—
224C4—261no—
225C4—524no—
226C4—521no—
227C4D4×#26112yes—
228C2—81no—
229C2—261no—
230C2—261no—
231C2—1041no—
232C2#1171915111yescharacteristic
233C2D13⋊#10411yescharacteristic
234C2#1171916611yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#124C4
socleC22×C13C2×C22⋊C4
prime radical#11719373C2
cosocleC2×C4×D13C23
hypercenter#124#261
hypocenterC13#1980
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ #124

Complements

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

NH ≅ G/Ntype
2. C2×#88118C2semidirect
3. C2×#88116C2semidirect
4. C4×C4⋊#261C2semidirect
5. C4×#6118C2semidirect
11. C13×#124C4semidirect
12. #88198C4semidirect
13. #88194C4semidirect
18. #88129C4semidirect
48. #6118D4semidirect
114. Dic13#104semidirect
122. #124#261semidirect
176. C13#1980semidirect

Maximal subgroups

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

subgroupindex
#117193732
C2×#881182
C2×#881162
C4×C4⋊#2612
C4×#61182
#198013