Finite Group Databasebeta

← #16782171

Subgroups — #16782171

Order 3328.

588 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 588 conjugacy classes of subgroups — too many to draw. Only its 110 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#13130728C211yesmaximal, characteristic
2#13130012C211yesmaximal, characteristic
3#13129709C214yesmaximal
4#13117241C211yesmaximal, characteristic
5C2×#88146—21no—
6C2×C42×D13C2211yescharacteristic
7C2×(C2×#261)⋊C4—21no—
8C2×(C2×#261)⋊C4—21no—
9C2×(C2×#261)⋊C4C2212yes—
10C2×#88111C2212yes—
11C13×#384C411yescharacteristic, complemented
12#11718648—21no—
13#11718648C2212yes—
14#11718638—21no—
15C4⋊C4×Dic13—21no—
16C4⋊C4×Dic13C412yescomplemented
17#11718596C411yescharacteristic, complemented
18#11718290—21no—
19#11718290—21no—
20C23×#261—22no—
21C22×C4×D13D411yescharacteristic
22C22×C4×D13D411yescharacteristic
23C22×C4×D13C2311yescharacteristic
24C22×#1057—22no—
25C2×C13×C4⋊C4—21no—
26C2×C13×C4⋊C4—21no—
27C2×C13×C4⋊C4C2×C412yes—
28C2×C42×C13C2×C411yescharacteristic
29C2×#6103—22no—
30C2×C4⋊Dic13—21no—
31C2×C4⋊Dic13—21no—
32C2×C4⋊Dic13C2×C412yes—
33C2×C4×Dic13—22no—
34C2×C4×Dic13C2×C411yescharacteristic
35C2×C4×Dic13D411yescharacteristic
36C2×C4×Dic13D411yescharacteristic
37#88146—44no—
38C42×D13—24no—
39(C2×#261)⋊C4—24no—
40(C2×#261)⋊C4—24no—
41(C2×#261)⋊C4—42no—
42#88111—24no—
43#88071—22no—
44#88071—22no—
45#8717—131nomaximal, Sylow
46C23×D13C2×D411yescharacteristic
47C22×#261—24no—
48C22×#261—42no—
49C22×#261—42no—
50C22×#261—42no—
51C22×#261—42no—
52C22×#261—42no—
53C22×#261—42no—
54C22×C4×C13—22no—
55C22×C4×C13C22⋊C411yescharacteristic
56C22×C4×C13C22⋊C411yescharacteristic
57C22×C4×C13C22×C411yescharacteristic
58C22×Dic13—22no—
59C22×Dic13C22⋊C411yescharacteristic
60C22×Dic13C22⋊C411yescharacteristic
61C22×Dic13C2×D411yescharacteristic
62C2×C4×D13—22no—
63C2×C4×D13—22no—
64C2×C4×D13—22no—
65C2×C4×D13—22no—
66C2×C4×D13—41no—
67C2×C4×D13—41no—
68C2×C4×D13—41no—
69C2×C4×D13SD1612yes—
70C2×C4×D13Q1612yes—
71C2×C4×D13#4114yes—
72C2×#1057—42no—
73C2×#1057—42no—
74C2×#1057—42no—
75C13×C4⋊C4—42no—
76C13×C4⋊C4—42no—
77C13×C4⋊C4—42no—
78C42×C13—22no—
79#6103—44no—
80C4⋊Dic13—42no—
81C4⋊Dic13—42no—
82C4⋊Dic13—42no—
83C4×Dic13—22no—
84C4×Dic13—22no—
85C4×Dic13—22no—
86C4×Dic13—44no—
87#2285—131no—
88#1817—131no—
89#1434—131no—
90#1294—134no—
91C23×C13C2×C22⋊C411yescharacteristic
92C22×D13—21no—
93C22×D13—21no—
94C22×D13—21no—
95C22×D13—21no—
96C22×D13#12312yes—
97C22×D13C2×SD1611yescharacteristic
98C22×D13C2×Q1611yescharacteristic
99C22×D13AGL(1,ℤ/8)12yes—
100C2×#261—44no—
101C2×#261—44no—
102C2×#261—44no—
103C2×#261—82no—
104C2×#261—82no—
105C2×#261—82no—
106C2×#261—82no—
107C2×C4×C13—21no—
108C2×C4×C13—21no—
109C2×C4×C13—21no—
110C2×C4×C13—21no—
111C2×C4×C13—21no—
112C2×C4×C13—21no—
113C2×C4×C13—42no—
114C2×C4×C13—42no—
115C2×C4×C13—42no—
116C2×C4×C13#10312yes—
117C2×C4×C13#10412yes—
118C2×C4×C13#11712yes—
119C2×Dic13—21no—
120C2×Dic13—21no—
121C2×Dic13—21no—
122C2×Dic13—21no—
123C2×Dic13—21no—
124C2×Dic13—21no—
125C2×Dic13—21no—
126C2×Dic13—42no—
127C2×Dic13—42no—
128C2×Dic13—42no—
129C2×Dic13#10312yes—
130C2×Dic13#12312yes—
131C4×D13—24no—
132C4×D13—24no—
133C4×D13—44no—
134C4×D13—44no—
135#1057—82no—
136C2×#117—261no—
137C22×C42—131no—
138C2×C22⋊C8—132no—
139#384—131no—
140#384#26111yescharacteristic, complemented
141#382—261no—
142#380—132no—
143#380—261no—
144C4×C4⋊C4—132no—
145C4×C4⋊C4—261no—
146C2×#95—132no—
147C2×#95—261no—
148C2×#95—261no—
149#336—261no—
150#336—261no—
151C22×C13#38111yescharacteristic
152C22×C13#41011yescharacteristic
153C22×C13#41011yescharacteristic
154C22×C13C2×#10311yescharacteristic
155C22×C13#41811yescharacteristic
156C22×C13C2×#10411yescharacteristic
157C22×C13#42111yescharacteristic
158C2×D13—22no—
159C2×D13—22no—
160C2×D13—21no—
161C2×D13—21no—
162C2×D13—22no—
163C2×D13—22no—
164C2×D13—21no—
165C2×D13—21no—
166C2×D13#48112yes—
167C2×D13#48412yes—
168#261—84no—
169C4×C13—22no—
170C4×C13—22no—
171C4×C13—22no—
172C4×C13—82no—
173Dic13—22no—
174Dic13—22no—
175Dic13—41no—
176Dic13—82no—
177C23×C4—131no—
178C23×C4—131no—
179C23×C4—131no—
180C23×C4—262no—
181C22×C8—262no—
182#117—524no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4—132no—
186C2×C4⋊C4—261no—
187C2×C4⋊C4—261no—
188C2×C4⋊C4C2×#26112yes—
189C2×C22⋊C4—262no—
190C2×C42—131no—
191C2×C42—131no—
192C2×C42—131no—
193C2×C42—264no—
194C2×C42—262no—
195C2×C42C2×#26111yescharacteristic
196C22⋊C8—264no—
197#95—262no—
198#95—262no—
199#95—264no—
200#95—264no—
201#95—522no—
202C2×C13#150311yescharacteristic
203C2×C13#150511yescharacteristic
204C2×C13#151411yescharacteristic
205C2×C13#151811yescharacteristic
206C2×C13#182011yescharacteristic
207C2×C13#182411yescharacteristic
208C2×C13#182611yescharacteristic
209D13—22no—
210D13—22no—
211C24—131no—
212C22×C4—22no—
213C22×C4—131no—
214C22×C4—131no—
215C22×C4—132no—
216C22×C4—132no—
217C22×C4—134no—
218C22×C4—131no—
219C22×C4—262no—
220C22×C4—262no—
221C22×C4—262no—
222C22×C4—262no—
223C22×C4—264no—
224C22×C4—262no—
225C22×C4—521no—
226C22×C4—521no—
227C22×C4—521no—
228C22×C4—522no—
229C22×C4—522no—
230C22×C4—522no—
231C22×C4—522no—
232C22×C4—522no—
233C22×C4—522no—
234C22×C4C22⋊#26111yescharacteristic
235C22×C4C22⋊#26111yescharacteristic
236C22×C4C22×#26111yescharacteristic
237C2×C8—522no—
238C2×C8—522no—
239C2×C8—522no—
240C4⋊C4—42no—
241C4⋊C4—42no—
242C4⋊C4—42no—
243C4⋊C4—522no—
244C4⋊C4—522no—
245C4⋊C4—522no—
246C22⋊C4—524no—
247C42—22no—
248C42—262no—
249C42—262no—
250C42—262no—
251C42—524no—
252C13#871711yescharacteristic, complemented, Sylow
253C23—132no—
254C23—132no—
255C23—131no—
256C23—131no—
257C23—261no—
258C23—261no—
259C23—261no—
260C23—261no—
261C23C2×C22⋊#26111yescharacteristic
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—42no—
269C2×C4—42no—
270C2×C4—42no—
271C2×C4—132no—
272C2×C4—132no—
273C2×C4—264no—
274C2×C4—264no—
275C2×C4—261no—
276C2×C4—261no—
277C2×C4—261no—
278C2×C4—261no—
279C2×C4—261no—
280C2×C4—261no—
281C2×C4—261no—
282C2×C4—524no—
283C2×C4—524no—
284C2×C4—524no—
285C2×C4—524no—
286C2×C4—524no—
287C2×C4—522no—
288C2×C4—522no—
289C2×C4—522no—
290C2×C4—1042no—
291C2×C4—1042no—
292C2×C4—1042no—
293C2×C4—1042no—
294C2×C4#8811612yes—
295C2×C4#8811712yes—
296C2×C4#8823712yes—
297C8—1042no—
298C22—132no—
299C22—132no—
300C22—262no—
301C22—261no—
302C22—261no—
303C22—261no—
304C22—261no—
305C22—262no—
306C22—262no—
307C22—262no—
308C22#1171913511yescharacteristic
309C22#1171913811yescharacteristic
310C22C2×#8811611yescharacteristic
311C22#1171914211yescharacteristic
312C22C2×#8811711yescharacteristic
313C22#1171915511yescharacteristic
314C22#1171915611yescharacteristic
315C4—22no—
316C4—22no—
317C4—22no—
318C4—82no—
319C4—262no—
320C4—262no—
321C4—521no—
322C4—1044no—
323C4—1042no—
324C2—262no—
325C2—262no—
326C2#1313021911yescharacteristic
327C2#1313022511yescharacteristic
328C2#1313025711yescharacteristic
329C2#1313027011yescharacteristic
330C2#1313073411yescharacteristic
331C2#1313074011yescharacteristic
332C2#1313074211yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#384C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C2×D4
cosocleC22×C4×D13C23
hypercenter#384#261
hypocenterC13#8717
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
11. C13×#384C4semidirect
16. C4⋊C4×Dic13C4semidirect
17. #11718596C4semidirect
140. #384#261semidirect
252. C13#8717semidirect

Maximal subgroups

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

subgroupindex
#131307282
#131300122
#131297092
#131172412
#871713