Finite Group Databasebeta

← #16786926

Subgroups — #16786926

Order 3328.

382 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 82 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#13131073C212yesmaximal, complemented
2#13129785C212yesmaximal, complemented
3#13129768C212yesmaximal, complemented
4#13123530C211yesmaximal, characteristic
5C23×C8×C13C411yescharacteristic
6#11719496C411yescharacteristic
7C2×#88155C2211yescharacteristic
8D13⋊M32—22no—
9#11718868C2211yescharacteristic
10#11718772—22no—
11#11718771C411yescharacteristic
12C8×C22⋊D13—22no—
13#11718763C2211yescharacteristic
14#11718762C411yescharacteristic
15#11718284C2214yes—
16#11718263—22no—
17C23×C4×C13C2×C411yescharacteristic
18C2×#6127C2×C411yescharacteristic
19C22×C8×C13—21no—
20C22×C8×C13—21no—
21C22×C8×C13—41no—
22C22×C8×C13—41no—
23C22×C8×C13C2×C411yescharacteristic
24C22×C8×C13C2×C411yescharacteristic
25#88207C812yes—
26#88184—21no—
27#88183C812yes—
28C4×C22⋊D13—22no—
29#88180C2×C411yescharacteristic
30#88178—21no—
31C2×#6099C2×C411yescharacteristic
32C2×#6099C2311yescharacteristic
33#88155—41no—
34#88155—41no—
35C2×#6094D412yes—
36C2×C8×D13D412yes—
37#88106—24no—
38#88098—42no—
39D13⋊C16—42no—
40C22⋊#1055—22no—
41#88060—22no—
42#88055—21no—
43#88054—22no—
44C8×Dic13—21no—
45#11483—131nomaximal, Sylow
46C24×C13C2×C811yescharacteristic
47C22×C4×C13—21no—
48C22×C4×C13—21no—
49C22×C4×C13—41no—
50C22×C4×C13—41no—
51C22×C4×C13C2×C811yescharacteristic
52C22×C4×C13C22×C411yescharacteristic
53C2×C22⋊D13—22no—
54C2×C22⋊D13C2×C812yes—
55#6127—41no—
56#6127—41no—
57C2×D52M1611yescharacteristic
58C2×C4×D13C22⋊C412yes—
59C2×Dic26M1611yescharacteristic
60C2×C8×C13—21no—
61C2×C8×C13—21no—
62C2×C8×C13—21no—
63C2×C8×C13—42no—
64C2×C8×C13—41no—
65C2×C8×C13—41no—
66C2×C8×C13—41no—
67C2×C8×C13C22⋊C411yescharacteristic
68C2×C8×C13C22⋊C411yescharacteristic
69C22⋊Dic13—22no—
70C22⋊Dic13C2×C812yes—
71#6103—22no—
72C4⋊Dic13—21no—
73#6101—22no—
74C4×Dic13—21no—
75#6099—41no—
76#6099—41no—
77C2×#1055—21no—
78C2×#1055C2×D412yes—
79#6094—42no—
80C8×D13—22no—
81C8×D13—22no—
82#6092—44no—
83#2929—131no—
84#2115—132no—
85#1328—132no—
86#1320—132no—
87C23×C13—21no—
88C23×C13—41no—
89C23×C13—42no—
90C23×C13C22×C811yescharacteristic
91C22×D13C22⋊C812yes—
92C2×C4×C13—21no—
93C2×C4×C13—21no—
94C2×C4×C13—21no—
95C2×C4×C13—42no—
96C2×C4×C13—41no—
97C2×C4×C13—41no—
98C2×C4×C13—41no—
99C2×C4×C13C2×C22⋊C411yescharacteristic
100C2×C4×C13C2×M1611yescharacteristic
101C22⋊D13—42no—
102C22⋊D13—44no—
103C2×Dic13—22no—
104C2×Dic13C22⋊C812yes—
105D52—41no—
106C4×D13—22no—
107C4×D13—22no—
108Dic26—41no—
109C8×C13—21no—
110C8×C13—41no—
111C8×C13#9911yescharacteristic
112C8×C13#9911yescharacteristic
113#1055—22no—
114#1055—41no—
115C2×#131—131no—
116C23×C8#26111yescharacteristic
117#525—131no—
118C2×M32—262no—
119#435—262no—
120C8×D4—262no—
121#424—131no—
122#408—131no—
123#407—131no—
124#405—131no—
125#349—134no—
126#349—262no—
127C22×C13—22no—
128C22×C13—21no—
129C22×C13—41no—
130C22×C13—41no—
131C22×C13—42no—
132C22×C13—42no—
133C22×C13—41no—
134C22×C13C2×C22⋊C811yescharacteristic
135C2×D13—22no—
136C2×D13—42no—
137C4×C13—21no—
138C4×C13—41no—
139C4×C13C2×#9911yescharacteristic
140C4×C13#41311yescharacteristic
141Dic13—22no—
142Dic13—42no—
143C2×#41—131no—
144C23×C4C2×#26111yescharacteristic
145#131—521no—
146#131—521no—
147C2×M16—131no—
148C2×M16—132no—
149C2×M16—131no—
150C22×C8—21no—
151C22×C8—21no—
152C22×C8—41no—
153C22×C8—41no—
154C22×C8—132no—
155C22×C8C2×#26111yescharacteristic
156C22×C8C2×#26111yescharacteristic
157#123—132no—
158C22⋊Q8—261no—
159#121—261no—
160#120—132no—
161C4×D4—262no—
162#117—131no—
163M32—264no—
164M32—522no—
165C2×C16—522no—
166C4⋊C8—262no—
167C22⋊C8—262no—
168C22⋊C8—262no—
169#97—261no—
170C4×C8—261no—
171C2×C13—21no—
172C2×C13—42no—
173C2×C13—41no—
174C2×C13#145911yescharacteristic
175D13—42no—
176C24D13⋊C811yescharacteristic
177#41—521no—
178#41—521no—
179C2×Q8—131no—
180C2×D4—132no—
181C2×D4—131no—
182C2×D4—262no—
183C22×C4—21no—
184C22×C4—21no—
185C22×C4—41no—
186C22×C4—41no—
187C22×C4—132no—
188C22×C4D13⋊C811yescharacteristic
189C22×C4C22×#26111yescharacteristic
190M16—522no—
191M16—521no—
192M16—521no—
193C2×C8—21no—
194C2×C8—21no—
195C2×C8—21no—
196C2×C8—42no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8—132no—
201C2×C8—262no—
202C2×C8—262no—
203C2×C8—261no—
204C2×C8C22⋊#26111yescharacteristic
205C2×C8C22⋊#26111yescharacteristic
206C4⋊C4—262no—
207C4⋊C4—261no—
208C22⋊C4—132no—
209C22⋊C4—262no—
210C22⋊C4—262no—
211C42—261no—
212C16—524no—
213C13#1148311yescharacteristic, complemented, Sylow
214C23—21no—
215C23—41no—
216C23—42no—
217C23—132no—
218C23C2×D13⋊C811yescharacteristic
219Q8—521no—
220D4—521no—
221D4—522no—
222D4—524no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—132no—
231C2×C4—262no—
232C2×C4—262no—
233C2×C4—262no—
234C2×C4D13⋊M1611yescharacteristic
235C2×C4C2×C22⋊#26111yescharacteristic
236C8—21no—
237C8—41no—
238C8—262no—
239C8—521no—
240C8#8811911yescharacteristic
241C8#8811911yescharacteristic
242C22—22no—
243C22—21no—
244C22—41no—
245C22—41no—
246C22—42no—
247C22—42no—
248C22—41no—
249C22—262no—
250C22—522no—
251C22D13⋊(C22⋊C8)11yescharacteristic
252C4—21no—
253C4—41no—
254C4—262no—
255C4—522no—
256C4#1171913211yescharacteristic
257C4C2×#8811911yescharacteristic
258C2—21no—
259C2—42no—
260C2—41no—
261C2—522no—
262C2#1313007111yescharacteristic
subgroupG/H
centerC8#88119
commutatorC23×C13C22×C8
FrattiniC22×C4C22×#261
FittingC23×C8×C13C4
socleC2×C13#1459
prime radical#11719496C4
cosocleC2×#6099C23
hypercenterC23×C8#261
hypocenterC13#11483
LCSG ▷ C23×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C8 ◁ C2×C8 ◁ C22×C8 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. #13131073C2semidirect
2. #13129785C2semidirect
3. #13129768C2semidirect
213. C13#11483semidirect

Maximal subgroups

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

subgroupindex
#131310732
#131297852
#131297682
#131235302
#1148313