Finite Group Databasebeta

← #16786854

Subgroups — #16786854

Order 3328.

454 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 108 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)C212yesmaximal, complemented
2#13129773C212yesmaximal, complemented
3#13129756C212yesmaximal, complemented
4C2×C8×C22⋊D13C211yesmaximal, characteristic
5C23×C8×C13C411yescharacteristic
6C2×C4×C22⋊D13C411yescharacteristic
7C22×C8×D13C2211yescharacteristic
8C2×D13⋊C16—22no—
9C2×C22⋊#1055C2211yescharacteristic
10C8×C22⋊D13—22no—
11C8×C22⋊D13—22no—
12C2×#88060C411yescharacteristic
13C2×#88054C2211yescharacteristic
14C2×C8×Dic13C411yescharacteristic
15C22⋊#6092C2214yes—
16#11718259—22no—
17C23×C4×C13C2×C411yescharacteristic
18C22×C22⋊D13C811yescharacteristic
19C22×C4×D13C2×C411yescharacteristic
20C22×C8×C13—21no—
21C22×C8×C13—21no—
22C22×C8×C13—42no—
23C22×C8×C13C2×C411yescharacteristic
24C22×C8×C13C2×C411yescharacteristic
25C2×C22⋊Dic13C811yescharacteristic
26C4×C22⋊D13—22no—
27C4×C22⋊D13—22no—
28C2×#6103C811yescharacteristic
29C2×#6101C811yescharacteristic
30C2×C4×Dic13C2×C411yescharacteristic
31C22×#1055C2×C411yescharacteristic
32C22×#1055C2311yescharacteristic
33C2×C8×D13—42no—
34C2×C8×D13D412yes—
35C2×C8×D13D412yes—
36C2×#6092—24no—
37D13⋊C16—44no—
38C22⋊#1055—22no—
39#88060—22no—
40#88054—22no—
41C8×Dic13—21no—
42C8×Dic13—21no—
43#11465—131nomaximal, Sylow
44C24×C13C2×C811yescharacteristic
45C23×D13C2×C811yescharacteristic
46C22×C4×C13—21no—
47C22×C4×C13—21no—
48C22×C4×C13—41no—
49C22×C4×C13—41no—
50C22×C4×C13C2×C811yescharacteristic
51C22×C4×C13C22×C411yescharacteristic
52C2×C22⋊D13—22no—
53C2×C22⋊D13—22no—
54C2×C22⋊D13C1614yescomplemented
55C22×Dic13C2×C811yescharacteristic
56C22×Dic13C2×C811yescharacteristic
57C22×Dic13C2×C811yescharacteristic
58C2×C4×D13—41no—
59C2×C4×D13—41no—
60C2×C4×D13C22⋊C412yes—
61C2×C4×D13M1612yes—
62C2×C8×C13—22no—
63C2×C8×C13—21no—
64C2×C8×C13—42no—
65C2×C8×C13—42no—
66C2×C8×C13—41no—
67C2×C8×C13C22⋊C411yescharacteristic
68C2×C8×C13C22⋊C411yescharacteristic
69C22⋊Dic13—22no—
70#6103—22no—
71#6101—22no—
72C4×Dic13—21no—
73C4×Dic13—21no—
74C2×#1055—21no—
75C2×#1055—41no—
76C2×#1055—41no—
77C2×#1055C2×D412yes—
78C8×D13—24no—
79C8×D13—42no—
80#6092—44no—
81C2×C8×D4—131no—
82C2×C22⋊C16—132no—
83#1322—132no—
84#1314—132no—
85C23×C13—21no—
86C23×C13—21no—
87C23×C13—41no—
88C23×C13—41no—
89C23×C13C2×C1612yescomplemented
90C23×C13C22×C811yescharacteristic
91C22×D13—41no—
92C22×D13—41no—
93C22×D13C22⋊C812yes—
94C22×D13C2×C1612yes—
95C22×D13M3212yes—
96C2×C4×C13—21no—
97C2×C4×C13—21no—
98C2×C4×C13—21no—
99C2×C4×C13—42no—
100C2×C4×C13—41no—
101C2×C4×C13—41no—
102C2×C4×C13—41no—
103C2×C4×C13C2×C22⋊C411yescharacteristic
104C2×C4×C13C2×M1611yescharacteristic
105C22⋊D13—28no—
106C2×Dic13—21no—
107C2×Dic13—21no—
108C2×Dic13—21no—
109C2×Dic13—41no—
110C2×Dic13—41no—
111C2×Dic13C22⋊C812yes—
112C2×Dic13C2×C1612yescomplemented
113C4×D13—22no—
114C4×D13—22no—
115C4×D13—42no—
116C8×C13—21no—
117C8×C13—41no—
118C8×C13#9912yes—
119#1055—22no—
120#1055—41no—
121C23×C8—131no—
122C23×C8#26111yescharacteristic
123C2×C4×D4—131no—
124C22×C16—262no—
125C8×D4—262no—
126C8×D4—262no—
127C2×C4⋊C8—131no—
128C2×C22⋊C8—131no—
129C2×C22⋊C8—131no—
130C2×C4×C8—131no—
131C22⋊C16—134no—
132C22⋊C16—262no—
133C22×C13—21no—
134C22×C13—21no—
135C22×C13—22no—
136C22×C13—42no—
137C22×C13—42no—
138C22×C13—41no—
139C22×C13—41no—
140C22×C13C2×C22⋊C811yescharacteristic
141C22×C13C22×C1611yescharacteristic
142C22×C13C2×M3211yescharacteristic
143C2×D13—22no—
144C2×D13—22no—
145C2×D13—42no—
146C2×D13—42no—
147C2×D13C22⋊C1614yes—
148C4×C13—21no—
149C4×C13—41no—
150C4×C13C2×#9911yescharacteristic
151C4×C13#41311yescharacteristic
152Dic13—22no—
153Dic13—22no—
154Dic13—41no—
155C22×D4—131no—
156C23×C4—131no—
157C23×C4C2×#26111yescharacteristic
158C22×C8—21no—
159C22×C8—21no—
160C22×C8—42no—
161C22×C8—131no—
162C22×C8—132no—
163C22×C8—132no—
164C22×C8—131no—
165C22×C8—522no—
166C22×C8C2×#26111yescharacteristic
167C22×C8C2×#26111yescharacteristic
168C4×D4—262no—
169C4×D4—262no—
170C2×C4⋊C4—131no—
171C2×C22⋊C4—131no—
172C2×C22⋊C4—131no—
173C2×C42—131no—
174C2×C16—264no—
175C2×C16—524no—
176C4⋊C8—262no—
177C22⋊C8—262no—
178C22⋊C8—262no—
179C4×C8—261no—
180C4×C8—261no—
181C2×C13—21no—
182C2×C13—21no—
183C2×C13—42no—
184C2×C13#145911yescharacteristic
185C2×C13C2×C22⋊C1611yescharacteristic
186C2×C13#211511yescharacteristic
187D13—24no—
188C24—131no—
189C24D13⋊C811yescharacteristic
190C2×D4—134no—
191C2×D4—262no—
192C2×D4—262no—
193C22×C4—21no—
194C22×C4—21no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4—131no—
198C22×C4—131no—
199C22×C4—132no—
200C22×C4—132no—
201C22×C4—131no—
202C22×C4—521no—
203C22×C4—521no—
204C22×C4D13⋊C811yescharacteristic
205C22×C4C22×#26111yescharacteristic
206C2×C8—22no—
207C2×C8—21no—
208C2×C8—42no—
209C2×C8—42no—
210C2×C8—41no—
211C2×C8—132no—
212C2×C8—264no—
213C2×C8—261no—
214C2×C8—522no—
215C2×C8—521no—
216C2×C8—521no—
217C2×C8C22⋊#26111yescharacteristic
218C2×C8C22⋊#26111yescharacteristic
219C4⋊C4—262no—
220C22⋊C4—262no—
221C22⋊C4—262no—
222C42—261no—
223C42—261no—
224C16—524no—
225C13#1146511yescharacteristic, complemented, Sylow
226C23—21no—
227C23—21no—
228C23—41no—
229C23—41no—
230C23—132no—
231C23—132no—
232C23—132no—
233C23—521no—
234C23—521no—
235C23D13⋊C1612yescomplemented
236C23C2×D13⋊C811yescharacteristic
237D4—268no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—42no—
242C2×C4—41no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—132no—
246C2×C4—132no—
247C2×C4—261no—
248C2×C4—261no—
249C2×C4—262no—
250C2×C4—262no—
251C2×C4—261no—
252C2×C4—522no—
253C2×C4—521no—
254C2×C4—521no—
255C2×C4D13⋊M1611yescharacteristic
256C2×C4C2×C22⋊#26111yescharacteristic
257C8—21no—
258C8—41no—
259C8—262no—
260C8—521no—
261C8#8811912yes—
262C22—21no—
263C22—21no—
264C22—22no—
265C22—42no—
266C22—42no—
267C22—41no—
268C22—41no—
269C22—134no—
270C22—262no—
271C22—262no—
272C22—522no—
273C22—522no—
274C22C2×D13⋊C1611yescharacteristic
275C22D13⋊M3211yescharacteristic
276C22D13⋊(C22⋊C8)11yescharacteristic
277C4—21no—
278C4—41no—
279C4—262no—
280C4—262no—
281C4—521no—
282C4#1171913211yescharacteristic
283C4C2×#8811911yescharacteristic
284C2—21no—
285C2—21no—
286C2—42no—
287C2—264no—
288C2#1313007111yescharacteristic
289C2D13⋊(C22⋊C16)11yescharacteristic
290C2#1313107311yescharacteristic
subgroupG/H
centerC2×C8C22⋊#261
commutatorC22×C13C22×C16
FrattiniC22×C4C22×#261
FittingC23×C8×C13C4
socleC22×C13C2×C22⋊C8
prime radicalC22×C22⋊D13C8
cosocleC22×#1055C23
hypercenterC23×C8#261
hypocenterC13#11465
LCSG ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
1. D13⋊(C22⋊C16)C2semidirect
2. #13129773C2semidirect
3. #13129756C2semidirect
54. C2×C22⋊D13C16semidirect
89. C23×C13C2×C16semidirect
112. C2×Dic13C2×C16semidirect
225. C13#11465semidirect
235. C23D13⋊C16semidirect

Maximal subgroups

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

subgroupindex
D13⋊(C22⋊C16)2
#131297732
#131297562
C2×C8×C22⋊D132
#1146513