Finite Group Databasebeta

← #16781925

Subgroups — #16781925

Order 3328.

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

normal subgroups only

This group has 486 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
1#13130700C212yesmaximal
2#13130393C212yesmaximal, complemented
3#13129706C212yesmaximal, complemented
4C2×C8×C22⋊D13C211yesmaximal, characteristic
5C23×C8×C13C411yescharacteristic
6C2×C4×C22⋊D13C2211yescharacteristic
7C22×C8×D13C411yescharacteristic
8C2×#88121—22no—
9#11719129C2214yes—
10C2×C22⋊#1055C411yescharacteristic
11C8×C22⋊D13—22no—
12C8×C22⋊D13—22no—
13C2×#88060C411yescharacteristic
14C2×#88054C2211yescharacteristic
15C2×C8×Dic13C2211yescharacteristic
16#11718291—22no—
17#11718256—22no—
18#11718254—22no—
19C23×C4×C13C2×C411yescharacteristic
20C22×C22⋊D13D411yescharacteristic
21C22×C4×D13C2×C411yescharacteristic
22C2×#6122—24no—
23C22×C8×C13—21no—
24C22×C8×C13—21no—
25C22×C8×C13—42no—
26C22×C8×C13C2×C411yescharacteristic
27C22×C8×C13C2×C411yescharacteristic
28C2×C22⋊Dic13Q811yescharacteristic
29C4×C22⋊D13—22no—
30C4×C22⋊D13—22no—
31C2×#6103Q811yescharacteristic
32C2×#6101D411yescharacteristic
33C2×C4×Dic13C2311yescharacteristic
34C22×#1055C2×C411yescharacteristic
35C22×#1055C2×C411yescharacteristic
36C2×C8×D13—21no—
37C2×C8×D13—21no—
38C2×C8×D13—42no—
39#88121—44no—
40#88112—24no—
41C4⋊#1057—24no—
42C22⋊#1055—22no—
43#88060—22no—
44#88054—22no—
45C8×Dic13D412yes—
46C8×Dic13D412yes—
47#8616—131nomaximal, Sylow
48C24×C13C4⋊C411yescharacteristic
49C23×D13C4⋊C411yescharacteristic
50C22×C4×C13—21no—
51C22×C4×C13—21no—
52C22×C4×C13—41no—
53C22×C4×C13—41no—
54C22×C4×C13C4⋊C411yescharacteristic
55C22×C4×C13C22×C411yescharacteristic
56C2×C22⋊D13—22no—
57C2×C22⋊D13—22no—
58C2×C22⋊D13D812yes—
59C2×C22⋊D13Q1612yes—
60C22×Dic13C4⋊C411yescharacteristic
61C22×Dic13C2×D411yescharacteristic
62C22×Dic13C2×Q811yescharacteristic
63C2×C4×D13—21no—
64C2×C4×D13—21no—
65C2×C4×D13—41no—
66C2×C4×D13—41no—
67#6122—44no—
68#6122—44no—
69C2×#1057—44no—
70C2×C8×C13—22no—
71C2×C8×C13—21no—
72C2×C8×C13—42no—
73C2×C8×C13—42no—
74C2×C8×C13—41no—
75C2×C8×C13C22⋊C411yescharacteristic
76C2×C8×C13C22⋊C411yescharacteristic
77C22⋊Dic13—22no—
78#6103—22no—
79#6101—22no—
80C4×Dic13C2×D412yes—
81C4×Dic13#4112yes—
82C2×#1055—21no—
83C2×#1055—41no—
84C2×#1055—41no—
85C2×#1055C22⋊C412yes—
86C8×D13—42no—
87C8×D13—42no—
88C2×C8×D4—131no—
89#1800—132no—
90#1567—132no—
91#1292—132no—
92C23×C13—21no—
93C23×C13—21no—
94C23×C13—41no—
95C23×C13—41no—
96C23×C13#10712yes—
97C23×C13C2×C4⋊C411yescharacteristic
98C22×D13—21no—
99C22×D13—21no—
100C22×D13—41no—
101C22×D13—41no—
102C22×D13#10712yes—
103C2×C4×C13—21no—
104C2×C4×C13—21no—
105C2×C4×C13—21no—
106C2×C4×C13—42no—
107C2×C4×C13—41no—
108C2×C4×C13—41no—
109C2×C4×C13—41no—
110C2×C4×C13C2×C22⋊C411yescharacteristic
111C2×C4×C13#11711yescharacteristic
112C22⋊D13—24no—
113C22⋊D13—24no—
114C2×Dic13—21no—
115C2×Dic13—41no—
116C2×Dic13—41no—
117C2×Dic13#12112yes—
118C2×Dic13C22⋊Q812yes—
119C2×Dic13C2×D811yescharacteristic
120C2×Dic13C2×Q1611yescharacteristic
121C2×Dic13#13512yes—
122C4×D13—42no—
123C4×D13—41no—
124C4×D13—41no—
125#1057—84no—
126C8×C13—21no—
127C8×C13—41no—
128C8×C13#10012yescomplemented
129#1055—22no—
130#1055—41no—
131C23×C8—131no—
132C23×C8#26111yescharacteristic
133C2×C4×D4—131no—
134C8×D4—262no—
135C8×D4—262no—
136#423—134no—
137C2×C4⋊C8—131no—
138C2×#100—262no—
139C2×C22⋊C8—131no—
140C2×C22⋊C8—131no—
141C2×C4×C8—131no—
142#343—262no—
143#335—262no—
144#335—262no—
145C22×C13—21no—
146C22×C13—21no—
147C22×C13—22no—
148C22×C13—42no—
149C22×C13—42no—
150C22×C13—41no—
151C22×C13—41no—
152C22×C13#38011yescharacteristic
153C22×C13C2×#10711yescharacteristic
154C22×C13#42711yescharacteristic
155C2×D13—22no—
156C2×D13—42no—
157C2×D13—41no—
158C2×D13—41no—
159C2×D13—42no—
160C4×C13—21no—
161C4×C13—41no—
162C4×C13C2×#10011yescharacteristic
163C4×C13#41311yescharacteristic
164Dic13—22no—
165Dic13—41no—
166Dic13#46612yes—
167Dic13#46712yes—
168C22×D4—131no—
169C23×C4—131no—
170C23×C4C2×#26111yescharacteristic
171C2×M16—264no—
172C22×C8—21no—
173C22×C8—21no—
174C22×C8—42no—
175C22×C8—131no—
176C22×C8—131no—
177C22×C8—261no—
178C22×C8—261no—
179C22×C8—522no—
180C22×C8C2×#26111yescharacteristic
181C22×C8C2×#26111yescharacteristic
182C4×D4—262no—
183C4×D4—262no—
184C2×C4⋊C4—131no—
185C2×C22⋊C4—131no—
186C2×C22⋊C4—131no—
187C2×C42—131no—
188C4⋊C8—262no—
189C4⋊C8—264no—
190C4⋊C8—264no—
191#100—524no—
192C22⋊C8—262no—
193C22⋊C8—262no—
194C4×C8—132no—
195C4×C8—132no—
196C2×C13—21no—
197C2×C13—21no—
198C2×C13—42no—
199C2×C13#180011yescharacteristic
200C2×C13#180811yescharacteristic
201C2×C13#181311yescharacteristic
202D13—42no—
203C24—131no—
204C24C4⋊#26111yescharacteristic
205C2×D4—132no—
206C2×D4—132no—
207C2×D4—262no—
208C2×D4—262no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4—41no—
212C22×C4—41no—
213C22×C4—131no—
214C22×C4—131no—
215C22×C4—131no—
216C22×C4—261no—
217C22×C4—261no—
218C22×C4—521no—
219C22×C4—521no—
220C22×C4C4⋊#26111yescharacteristic
221C22×C4C22×#26111yescharacteristic
222M16—524no—
223M16—524no—
224C2×C8—22no—
225C2×C8—21no—
226C2×C8—42no—
227C2×C8—42no—
228C2×C8—41no—
229C2×C8—132no—
230C2×C8—261no—
231C2×C8—522no—
232C2×C8—521no—
233C2×C8—522no—
234C2×C8—521no—
235C2×C8—524no—
236C2×C8C22⋊#26111yescharacteristic
237C2×C8C22⋊#26111yescharacteristic
238C4⋊C4—262no—
239C22⋊C4—262no—
240C22⋊C4—262no—
241C42—132no—
242C42—132no—
243C13#861611yescharacteristic, complemented, Sylow
244C23—21no—
245C23—21no—
246C23—41no—
247C23—41no—
248C23—132no—
249C23—261no—
250C23—261no—
251C23—521no—
252C23—521no—
253C23#8810212yes—
254C23C2×C4⋊#26111yescharacteristic
255D4—264no—
256D4—264no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—42no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—131no—
265C2×C4—131no—
266C2×C4—132no—
267C2×C4—132no—
268C2×C4—132no—
269C2×C4—261no—
270C2×C4—522no—
271C2×C4—521no—
272C2×C4—521no—
273C2×C4—521no—
274C2×C4—521no—
275C2×C4#8823711yescharacteristic
276C2×C4C2×C22⋊#26111yescharacteristic
277C8—21no—
278C8—41no—
279C8—262no—
280C8—521no—
281C8—1044no—
282C8#8812112yescomplemented
283C22—21no—
284C22—21no—
285C22—22no—
286C22—42no—
287C22—42no—
288C22—41no—
289C22—41no—
290C22—262no—
291C22—522no—
292C22—522no—
293C22—521no—
294C22—521no—
295C22C2×#8810211yescharacteristic
296C22#1171909211yescharacteristic
297C22#1171913611yescharacteristic
298C4—21no—
299C4—41no—
300C4—132no—
301C4—132no—
302C4—262no—
303C4—521no—
304C4#1171913211yescharacteristic
305C4C2×#8812111yescharacteristic
306C2—21no—
307C2—21no—
308C2—42no—
309C2—522no—
310C2#1313070011yescharacteristic
311C2#1313071311yescharacteristic
312C2#1313072011yescharacteristic
subgroupG/H
centerC22#11719136
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC23×C8×C13C4
socleC22×C13#380
prime radicalC22×C22⋊D13D4
cosocleC2×C4×Dic13C23
hypercenterC23×C8#261
hypocenterC13#8616
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C8

Complements

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

NH ≅ G/Ntype
2. #13130393C2semidirect
3. #13129706C2semidirect
128. C8×C13#100semidirect
243. C13#8616semidirect
282. C8#88121semidirect

Maximal subgroups

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

subgroupindex
#131307002
#131303932
#131297062
C2×C8×C22⋊D132
#861613