Finite Group Databasebeta

← #16777400

Subgroups — #16777400

Order 3328.

292 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 66 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
1D13⋊(C22⋊C16)C211yesmaximal, characteristic
2#13130716C211yesmaximal, characteristic
3#13114860C211yesmaximal, characteristic
4C22×C8×D13C2211yescharacteristic
5#11719127—21no—
6C2×#88104—21no—
7C2×D13⋊C16C412yescomplemented
8#11718648—21no—
9C2×#88048—21no—
10C22⋊#6092—21no—
11#11718268C412yescomplemented
12#11718259—21no—
13C13×#340C411yescharacteristic
14#11718143C411yescharacteristic
15C22×C4×D13D411yescharacteristic
16C2×#6118—22no—
17C22×C8×C13C2×C411yescharacteristic
18C2×C13×C4⋊C4—21no—
19C2×#6103—41no—
20C2×C4⋊Dic13—21no—
21C22×#1055D411yescharacteristic
22C2×C8×D13—42no—
23C2×C8×D13C2×C411yescharacteristic
24C2×C8×D13C2×C411yescharacteristic
25C2×C8×D13D411yescharacteristic
26C2×C8×D13Q811yescharacteristic
27C22⋊#1057—41no—
28#88111—41no—
29C2×#6092—22no—
30#88104—42no—
31D13⋊C16—42no—
32#88071—41no—
33#88048—42no—
34#7232—131nomaximal, Sylow
35C23×D13SD1611yescharacteristic
36C22×C4×C13—41no—
37C22×C4×C13C22⋊C411yescharacteristic
38C22×Dic13—41no—
39C22×Dic13D811yescharacteristic
40C2×C4×D13—41no—
41C2×C4×D13—41no—
42C2×C4×D13C22⋊C411yescharacteristic
43C2×C4×D13C4⋊C411yescharacteristic
44C2×C4×D13SD1611yescharacteristic
45C2×C4×D13Q1611yescharacteristic
46C2×#1057—42no—
47#6118—42no—
48#6118—42no—
49C2×C8×C13—41no—
50C2×C8×C13C4211yescharacteristic
51C2×C8×C13C4⋊C411yescharacteristic
52C13×C4⋊C4—41no—
53C13×C4⋊C4—41no—
54#6103—82no—
55C4⋊Dic13—41no—
56C4⋊Dic13—41no—
57C2×#1055—22no—
58C2×#1055C22⋊C411yescharacteristic
59C2×#1055C4⋊C411yescharacteristic
60C8×D13—22no—
61C8×D13—22no—
62C8×D13—41no—
63C8×D13—41no—
64#6092—42no—
65C2×C22⋊C16—131no—
66#1810—131no—
67#1807—131no—
68C23×C13#10211yescharacteristic
69C22×D13—21no—
70C22×D13—21no—
71C22×D13—22no—
72C22×D13—41no—
73C22×D13#10311yescharacteristic
74C22×D13#10611yescharacteristic
75C2×C4×C13—21no—
76C2×C4×C13—21no—
77C2×C4×C13—81no—
78C2×C4×C13—81no—
79C2×C4×C13—81no—
80C2×C4×C13#9511yescharacteristic
81C2×C4×C13#10311yescharacteristic
82C2×Dic13—41no—
83C2×Dic13—81no—
84C2×Dic13—81no—
85C2×Dic13—81no—
86C2×Dic13#10211yescharacteristic
87C2×Dic13#10711yescharacteristic
88C4×D13—21no—
89C4×D13—21no—
90C4×D13—21no—
91C4×D13—21no—
92C4×D13—41no—
93C4×D13—41no—
94#1057—82no—
95C8×C13—21no—
96C8×C13—21no—
97#1055—21no—
98#1055#9912yes—
99C23×C8—131no—
100C22×C16—132no—
101C2×#108—261no—
102C2×#106—261no—
103#407—261no—
104#380—261no—
105C22⋊C16—261no—
106C22⋊C16—261no—
107#341—132no—
108#340—131no—
109#340#26111yescharacteristic
110C22×C13—21no—
111C22×C13—21no—
112C22×C13#34011yescharacteristic
113C22×C13#35911yescharacteristic
114C22×C13#35911yescharacteristic
115C2×D13—21no—
116C2×D13—21no—
117C2×D13—21no—
118C2×D13—21no—
119C2×D13—21no—
120C2×D13—42no—
121C2×D13—42no—
122C2×D13#36512yes—
123C4×C13—21no—
124C4×C13—161no—
125C4×C13H(3,ℤ/4)11yescharacteristic
126C4×C13#34211yescharacteristic
127Dic13—21no—
128Dic13—21no—
129Dic13—161no—
130C23×C4—131no—
131C2×M16—262no—
132C22×C8—131no—
133C22×C8—131no—
134C22×C8—131no—
135C22×C8—131no—
136C22×C8—131no—
137C22×C8—522no—
138C22×C8C2×#26111yescharacteristic
139C2×C4⋊C4—21no—
140C2×C4⋊C4—261no—
141C2×C22⋊C4—521no—
142C2×C16—262no—
143C2×C16—522no—
144#108—522no—
145#106—522no—
146C22⋊C8—521no—
147C22⋊C8—521no—
148#95—521no—
149C2×C13—21no—
150C2×C13—21no—
151C2×C13#128911yescharacteristic
152C2×C13#138211yescharacteristic
153C2×C13#138311yescharacteristic
154D13—22no—
155D13—41no—
156C24—131no—
157C22×C4—41no—
158C22×C4—131no—
159C22×C4—131no—
160C22×C4—131no—
161C22×C4—131no—
162C22×C4—131no—
163C22×C4—521no—
164C22×C4—521no—
165C22×C4—521no—
166C22×C4C22⋊#26111yescharacteristic
167M16—522no—
168M16—522no—
169C2×C8—41no—
170C2×C8—131no—
171C2×C8—131no—
172C2×C8—262no—
173C2×C8—262no—
174C2×C8—262no—
175C2×C8—521no—
176C2×C8—521no—
177C2×C8—522no—
178C2×C8C4×#26111yescharacteristic
179C2×C8C4⋊#26111yescharacteristic
180C4⋊C4—41no—
181C4⋊C4—41no—
182C4⋊C4—521no—
183C4⋊C4—521no—
184C22⋊C4—1042no—
185C16—522no—
186C13#723211yescharacteristic, complemented, Sylow
187C23—131no—
188C23—131no—
189C23—262no—
190C23—261no—
191C23—261no—
192C23—521no—
193C23#8811511yescharacteristic
194C2×C4—21no—
195C2×C4—21no—
196C2×C4—81no—
197C2×C4—81no—
198C2×C4—81no—
199C2×C4—131no—
200C2×C4—131no—
201C2×C4—261no—
202C2×C4—261no—
203C2×C4—261no—
204C2×C4—261no—
205C2×C4—521no—
206C2×C4—521no—
207C2×C4—521no—
208C2×C4—1041no—
209C2×C4—1041no—
210C2×C4—1041no—
211C2×C4(C2×#261)⋊C411yescharacteristic
212C2×C4#8811711yescharacteristic
213C8—21no—
214C8—21no—
215C8—132no—
216C8—261no—
217C8—1042no—
218C22—21no—
219C22—21no—
220C22—132no—
221C22—261no—
222C22—261no—
223C22—261no—
224C22—261no—
225C22—261no—
226C22—522no—
227C22—522no—
228C22#1171824611yescharacteristic
229C22#1171827711yescharacteristic
230C22#1171828111yescharacteristic
231C4—21no—
232C4—161no—
233C4—261no—
234C4—261no—
235C4—2081no—
236C4#1171823511yescharacteristic
237C4#1171823811yescharacteristic
238C2—21no—
239C2—21no—
240C2—262no—
241C2—521no—
242C2#1312969811yescharacteristic
243C2#1312989711yescharacteristic
244C2#1312990011yescharacteristic
subgroupG/H
centerC22#11718246
commutatorC2×C8×C13C42
FrattiniC22×C8C2×#261
FittingC13×#340C4
socleC22×C13#340
prime radicalC23×D13SD16
cosocleC22×C8×D13C22
hypercenter#340#261
hypocenterC13#7232
LCSG ▷ C2×C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #340

Complements

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

NH ≅ G/Ntype
7. C2×D13⋊C16C4semidirect
11. #11718268C4semidirect
186. C13#7232semidirect

Maximal subgroups

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

subgroupindex
D13⋊(C22⋊C16)2
#131307162
#131148602
#723213