Finite Group Databasebeta

← #16780430

Subgroups — #16780430

Order 3328.

518 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 518 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C4×#88121C211yesmaximal, characteristic
2#13130075C211yesmaximal, characteristic
3#13130045C212yesmaximal, complemented
4#13129681C212yesmaximal, complemented
5C2×#11718386C211yesmaximal, characteristic
6C2×C4×C22⋊D13C2211yescharacteristic
7C23×#1055C411yescharacteristic
8C22×C8×D13C411yescharacteristic
9C2×#88121C412yes—
10#11719125C2212yes—
11C4×#6122C2212yes—
12C2×C13×C22⋊C8C411yescharacteristic
13C2×#88060C411yescharacteristic
14C2×#88054C2211yescharacteristic
15C2×C8×Dic13C2211yescharacteristic
16#11718386—22no—
17#11718386—22no—
18#11718305C412yes—
19#11718291C412yes—
20#11718287C412yes—
21#1057⋊C8—22no—
22#11718251—22no—
23C23×C4×C13C2×C411yescharacteristic
24C22×C22⋊D13C2×C411yescharacteristic
25C22×C4×D13C2×C411yescharacteristic
26C2×#6122C2×C414yes—
27C22×C8×C13C2×C411yescharacteristic
28C22×C8×C13C2×C411yescharacteristic
29C2×C22⋊Dic13C2×C411yescharacteristic
30C4×C22⋊D13—22no—
31C4×C22⋊D13—22no—
32C2×#6103C2×C411yescharacteristic
33C2×#6101C2×C411yescharacteristic
34C2×C4×Dic13C2311yescharacteristic
35C22×#1055—21no—
36C22×#1055—21no—
37C22×#1055—42no—
38C22×#1055C2×C411yescharacteristic
39C22×#1055C2×C411yescharacteristic
40C2×C8×D13—21no—
41C2×C8×D13—21no—
42C2×C8×D13—42no—
43#88121—24no—
44C22⋊#1057C2×C414yes—
45#88112—22no—
46#88110—22no—
47C4×#1057—22no—
48C4×#1057—22no—
49C13×C22⋊C8—22no—
50#88060—22no—
51#88054—22no—
52C8×Dic13D412yes—
53C8×Dic13D412yes—
54#8164—131nomaximal, Sylow
55C24×C13C4211yescharacteristic
56C23×D13C4211yescharacteristic
57C22×C4×C13—21no—
58C22×C4×C13—21no—
59C22×C4×C13—41no—
60C22×C4×C13—41no—
61C22×C4×C13C4211yescharacteristic
62C22×C4×C13C22×C411yescharacteristic
63C2×C22⋊D13—22no—
64C2×C22⋊D13—22no—
65C2×C22⋊D13M1614yes—
66C22×Dic13C4211yescharacteristic
67C22×Dic13C22×C411yescharacteristic
68C22×Dic13C22×C411yescharacteristic
69C2×C4×D13—21no—
70C2×C4×D13—21no—
71C2×C4×D13—41no—
72C2×C4×D13—41no—
73#6122—24no—
74#6122—24no—
75C2×#1057—24no—
76C2×#1057—24no—
77C2×C8×C13—21no—
78C2×C8×C13—41no—
79C2×C8×C13—41no—
80C2×C8×C13C22⋊C412yes—
81C22⋊Dic13—22no—
82#6103—22no—
83#6101—22no—
84C4×Dic13C2×D412yes—
85C4×Dic13#4112yes—
86C2×#1055—22no—
87C2×#1055—21no—
88C2×#1055—42no—
89C2×#1055—42no—
90C2×#1055—41no—
91C2×#1055C22⋊C411yescharacteristic
92C2×#1055C22⋊C411yescharacteristic
93C8×D13—42no—
94C8×D13—42no—
95C2×C8×D4—131no—
96C4×#100—131no—
97#1460—131no—
98#1451—132no—
99#1283—132no—
100C23×C13—21no—
101C23×C13—21no—
102C23×C13—41no—
103C23×C13—41no—
104C23×C13#9712yes—
105C23×C13C2×C4211yescharacteristic
106C22×D13—21no—
107C22×D13—21no—
108C22×D13—41no—
109C22×D13—41no—
110C22×D13#9712yes—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—21no—
114C2×C4×C13—42no—
115C2×C4×C13—41no—
116C2×C4×C13—41no—
117C2×C4×C13—41no—
118C2×C4×C13C2×C22⋊C411yescharacteristic
119C2×C4×C13#11711yescharacteristic
120C22⋊D13—28no—
121C2×Dic13—21no—
122C2×Dic13—41no—
123C2×Dic13—41no—
124C2×Dic13C4×D412yes—
125C2×Dic13C4×D412yes—
126C2×Dic13C2×M1612yes—
127C2×Dic13#13112yes—
128C4×D13—42no—
129C4×D13—41no—
130C4×D13—41no—
131#1057—44no—
132#1057—44no—
133C8×C13—22no—
134C8×C13—41no—
135#1055—21no—
136#1055—41no—
137#1055#10012yescomplemented
138C23×C8—131no—
139C23×C8—131no—
140C2×C4×D4—131no—
141C8×D4—262no—
142C8×D4—262no—
143#431—132no—
144C2×C4⋊C8—131no—
145C2×#100—132no—
146C2×C22⋊C8—131no—
147C2×C22⋊C8#26111yescharacteristic
148C4×M16—132no—
149C2×C4×C8—131no—
150#343—132no—
151#323—132no—
152#323—132no—
153#322—262no—
154#322—262no—
155C22×C13—21no—
156C22×C13—21no—
157C22×C13—22no—
158C22×C13—42no—
159C22×C13—42no—
160C22×C13—41no—
161C22×C13—41no—
162C22×C13C4×C22⋊C411yescharacteristic
163C22×C13C2×#9711yescharacteristic
164C22×C13#40511yescharacteristic
165C2×D13—22no—
166C2×D13—42no—
167C2×D13—41no—
168C2×D13—41no—
169C2×D13—42no—
170C4×C13—21no—
171C4×C13—41no—
172C4×C13C2×#10011yescharacteristic
173C4×C13#41311yescharacteristic
174Dic13—22no—
175Dic13—41no—
176Dic13#43514yes—
177C22×D4—131no—
178C23×C4—131no—
179C23×C4C2×#26111yescharacteristic
180C2×M16—134no—
181C22×C8—131no—
182C22×C8—131no—
183C22×C8—261no—
184C22×C8—261no—
185C22×C8—261no—
186C22×C8—261no—
187C22×C8—522no—
188C22×C8—522no—
189C22×C8C2×#26111yescharacteristic
190C22×C8C2×#26111yescharacteristic
191C4×D4—262no—
192C4×D4—262no—
193C2×C4⋊C4—131no—
194C2×C22⋊C4—131no—
195C2×C22⋊C4—131no—
196C2×C42—131no—
197C4⋊C8—262no—
198C4⋊C8—262no—
199#100—264no—
200C22⋊C8—22no—
201C22⋊C8—134no—
202C22⋊C8—262no—
203#97—262no—
204C4×C8—132no—
205C4×C8—132no—
206C4×C8—262no—
207C4×C8—262no—
208C2×C13—21no—
209C2×C13—21no—
210C2×C13—42no—
211C2×C13#175211yescharacteristic
212C2×C13C4×#10011yescharacteristic
213C2×C13#175711yescharacteristic
214D13—42no—
215C24—131no—
216C24C4×#26111yescharacteristic
217C2×D4—134no—
218C2×D4—262no—
219C2×D4—262no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—41no—
223C22×C4—41no—
224C22×C4—131no—
225C22×C4—131no—
226C22×C4—131no—
227C22×C4—261no—
228C22×C4—261no—
229C22×C4—521no—
230C22×C4—521no—
231C22×C4C4×#26111yescharacteristic
232C22×C4C22×#26111yescharacteristic
233M16—264no—
234M16—264no—
235C2×C8—21no—
236C2×C8—41no—
237C2×C8—41no—
238C2×C8—131no—
239C2×C8—131no—
240C2×C8—262no—
241C2×C8—264no—
242C2×C8—264no—
243C2×C8—261no—
244C2×C8—522no—
245C2×C8—522no—
246C2×C8—522no—
247C2×C8—522no—
248C2×C8—521no—
249C2×C8C22⋊#26112yes—
250C4⋊C4—262no—
251C22⋊C4—262no—
252C22⋊C4—262no—
253C42—132no—
254C42—132no—
255C13#816411yescharacteristic, complemented, Sylow
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23—132no—
261C23—261no—
262C23—261no—
263C23—521no—
264C23—521no—
265C23#8810012yes—
266C23C2×C4×#26111yescharacteristic
267D4—268no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—42no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—132no—
276C2×C4—132no—
277C2×C4—132no—
278C2×C4—132no—
279C2×C4—261no—
280C2×C4—522no—
281C2×C4—521no—
282C2×C4—521no—
283C2×C4—521no—
284C2×C4—521no—
285C2×C4#8823711yescharacteristic
286C2×C4C2×C22⋊#26111yescharacteristic
287C8—22no—
288C8—41no—
289C8—132no—
290C8—261no—
291C8—524no—
292C8—524no—
293C8—521no—
294C22—21no—
295C22—21no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—41no—
300C22—41no—
301C22—262no—
302C22—522no—
303C22—522no—
304C22—521no—
305C22—521no—
306C22C2×#8810011yescharacteristic
307C22#1171908911yescharacteristic
308C22C4×C22⋊#26111yescharacteristic
309C4—21no—
310C4—41no—
311C4—134no—
312C4—262no—
313C4—521no—
314C4#1171914811yescharacteristic
315C4D13⋊#10011yescharacteristic
316C2—21no—
317C2—21no—
318C2—42no—
319C2—522no—
320C2#1313057211yescharacteristic
321C2#1313058611yescharacteristic
322C2#1313059211yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC23×C13C2×C42
FrattiniC22×C4C22×#261
FittingC2×C13×C22⋊C8C4
socleC22×C13C4×C22⋊C4
prime radicalC22×C22⋊D13C2×C4
cosocleC2×C4×Dic13C23
hypercenterC2×C22⋊C8#261
hypocenterC13#8164
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
3. #13130045C2semidirect
4. #13129681C2semidirect
137. #1055#100semidirect
255. C13#8164semidirect

Maximal subgroups

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

subgroupindex
C4×#881212
#131300752
#131300452
#131296812
C2×#117183862
#816413