Finite Group Databasebeta

← #16780515

Subgroups — #16780515

Order 3328.

412 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 118 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#13130129C212yesmaximal
2#13130049C211yesmaximal, characteristic, complemented
3C2×#11718251C211yesmaximal, characteristic, complemented
4#13129669C212yesmaximal, complemented
5#13123479C211yesmaximal, characteristic
6#11719227C2211yescharacteristic
7#11719119C2212yes—
8C2×C4×#1057C2212yes—
9C13×#424C411yescharacteristic
10#11718790C411yescharacteristic
11M16×Dic13C2211yescharacteristic
12#11718771C411yescharacteristic
13C2×C8×Dic13C2211yescharacteristic
14#11718660C411yescharacteristic
15#11718501—22no—
16#11718494—22no—
17#1057⋊C8—22no—
18#11718251—22no—
19#11718244C414yes—
20#11718243C414yes—
21C2×#6127C2×C411yescharacteristic
22C22×#1057—22no—
23C2×C13×M16C2×C411yescharacteristic
24C22×C8×C13C2×C411yescharacteristic
25C13×#117C2×C411yescharacteristic
26C2×C4×Dic13C2311yescharacteristic
27C2×#6099C2×C411yescharacteristic
28C22×#1055C2×C411yescharacteristic
29#88147C2×C412yes—
30#88141C2×C412yes—
31#88135—22no—
32#88126—21no—
33C42×D13—21no—
34C22⋊#1057—22no—
35C4⋊#1057C2×C414yes—
36C4×#1057—22no—
37C4×#1057—22no—
38C4×#1057C2×C414yes—
39C13×C4⋊C8—22no—
40#88060—22no—
41#88060—22no—
42#88055—21no—
43C8×Dic13—21no—
44C8×Dic13D412yes—
45C8×Dic13D412yes—
46C4⋊#1055—22no—
47#8188—131nomaximal, Sylow
48C22×C4×C13C22×C411yescharacteristic
49C2×C22⋊D13—21no—
50C22×Dic13#4112yes—
51#6127—22no—
52#6127—22no—
53C2×D52C4211yescharacteristic
54C2×C4×D13—21no—
55C2×C4×D13—22no—
56C2×Dic26C4211yescharacteristic
57C2×#1057—24no—
58C2×#1057—24no—
59C2×#1057—44no—
60C13×M16—22no—
61C2×C8×C13—22no—
62C2×C8×C13—21no—
63C2×C8×C13C22⋊C412yes—
64C13×C4⋊C4C4212yes—
65C13×C22⋊C4—21no—
66C42×C13—21no—
67#6103—22no—
68#6101—22no—
69C4×Dic13—22no—
70C4×Dic13C22×C412yes—
71C4×Dic13C2×D411yescharacteristic
72C4×Dic13C2×D411yescharacteristic
73#6099—22no—
74C2×#1055—22no—
75C2×#1055—21no—
76C2×#1055C22⋊C412yes—
77#2922—131no—
78#1476—132no—
79#1452—131no—
80C2×#322—131no—
81#1278—132no—
82C23×C13#11711yescharacteristic
83C22×D13—21no—
84C2×C4×C13—22no—
85C2×C4×C13C2×C4211yescharacteristic
86C2×C4×C13C2×C22⋊C411yescharacteristic
87C2×C4×C13#13112yes—
88C2×C4×C13#13112yes—
89C22⋊D13—42no—
90C2×Dic13—24no—
91C2×Dic13—21no—
92C2×Dic13C4×D412yes—
93C2×Dic13C4×D412yes—
94D52—22no—
95C4×D13—41no—
96C4×D13—41no—
97C4×D13—44no—
98Dic26—22no—
99#1057—44no—
100#1057—44no—
101C8×C13—22no—
102C8×C13—41no—
103#1055—22no—
104#1055—41no—
105C4×#41—131no—
106#433—262no—
107#431—132no—
108#431—262no—
109#424—131no—
110#424#26111yescharacteristic
111#408—131no—
112#408—131no—
113C4×M16—131no—
114C2×C4×C8—131no—
115C2×C4×C8—132no—
116Q8⋊C8—134no—
117D4⋊C8—134no—
118#322—262no—
119#322—262no—
120C22×C13—22no—
121C22×C13C4×C22⋊C411yescharacteristic
122C22×C13#43312yes—
123C2×D13—41no—
124C2×D13—42no—
125C4×C13—42no—
126C4×C13#40512yes—
127C4×C13#40811yescharacteristic
128C4×C13#40811yescharacteristic
129Dic13—22no—
130Dic13—41no—
131Dic13#44414yes—
132C2×#41—131no—
133C2×M16—131no—
134C2×M16C2×#26111yescharacteristic
135C22×C8—131no—
136C22×C8—262no—
137C22×C8C2×#26111yescharacteristic
138C4×Q8—132no—
139C4×D4—132no—
140C4×D4—262no—
141#117—261no—
142#117C2×#26111yescharacteristic
143C2×C42—131no—
144C2×C42—261no—
145C4⋊C8—22no—
146C4⋊C8—134no—
147C4⋊C8—262no—
148C22⋊C8—262no—
149C22⋊C8—262no—
150C22⋊C8—262no—
151#97—261no—
152C4×C8—132no—
153C4×C8—132no—
154C4×C8—134no—
155C4×C8—261no—
156C4×C8—262no—
157C4×C8—262no—
158C2×C13—22no—
159C2×C13#175011yescharacteristic
160C2×C13#176512yes—
161D13—81no—
162#41—262no—
163#41—262no—
164C2×Q8—131no—
165C2×D4—131no—
166C2×D4—261no—
167C22×C4—132no—
168C22×C4—262no—
169C22×C4—261no—
170C22×C4C22×#26111yescharacteristic
171M16—22no—
172M16—262no—
173C2×C8—22no—
174C2×C8—21no—
175C2×C8—132no—
176C2×C8—262no—
177C2×C8—264no—
178C2×C8—264no—
179C2×C8—261no—
180C2×C8—524no—
181C2×C8C22⋊#26112yes—
182C4⋊C4—262no—
183C4⋊C4C4×#26112yes—
184C22⋊C4—21no—
185C22⋊C4—262no—
186C42—21no—
187C42—132no—
188C42—131no—
189C42—131no—
190C42—262no—
191C13#818811yescharacteristic, complemented, Sylow
192C23—261no—
193C23#8823711yescharacteristic
194Q8—262no—
195D4—262no—
196D4—522no—
197C2×C4—22no—
198C2×C4—132no—
199C2×C4—132no—
200C2×C4—264no—
201C2×C4—261no—
202C2×C4—524no—
203C2×C4—521no—
204C2×C4—521no—
205C2×C4C2×C4×#26111yescharacteristic
206C2×C4#8823812yes—
207C2×C4#8824012yes—
208C2×C4C2×C22⋊#26111yescharacteristic
209C8—22no—
210C8—41no—
211C8—262no—
212C8—524no—
213C8—524no—
214C8—521no—
215C22—22no—
216C22—521no—
217C22—522no—
218C22#1171907712yes—
219C22C4×C22⋊#26111yescharacteristic
220C4—42no—
221C4—134no—
222C4—262no—
223C4—521no—
224C4#1171907212yes—
225C4#1171914611yescharacteristic
226C4#1171915911yescharacteristic
227C2—22no—
228C2—1041no—
229C2#1313056511yescharacteristic
230C2#1313061412yes—
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#424C4
socleC22×C13C4×C22⋊C4
prime radicalC2×#6127C2×C4
cosocleC2×C4×Dic13C23
hypercenter#424#261
hypocenterC13#8188
LCSG ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #13130049C2semidirect
3. C2×#11718251C2semidirect
4. #13129669C2semidirect
191. C13#8188semidirect

Maximal subgroups

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

subgroupindex
#131301292
#131300492
C2×#117182512
#131296692
#131234792
#818813