Finite Group Databasebeta

← #16785270

Subgroups — #16785270

Order 3328.

1374 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 1374 conjugacy classes of subgroups — too many to draw. Only its 216 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#13131280C212yesmaximal
2C2×#11718267C214yesmaximal, complemented
3C22×M16×D13C211yesmaximal, characteristic
4C23×C4×D13C2211yescharacteristic
5C2×#88237C2214yes—
6C22×C13×M16C411yescharacteristic, complemented
7C22×#6099C411yescharacteristic, complemented
8C2×M16×D13—24no—
9C2×M16×D13—28no—
10C22×#6094C2212yes—
11C22×C8×D13C412yescomplemented
12#11719171—22no—
13#11719136—24no—
14#11719135—22no—
15C4×C22⋊#261C418yescomplemented
16#11718267—28no—
17C24×D13D411yescharacteristic
18C23×C4×C13C2×C411yescharacteristic
19C23×Dic13Q811yescharacteristic
20C22×C4×D13—24no—
21C22×C4×D13—24no—
22C22×C4×D13C2×C411yescharacteristic
23C22×C4×D13C2×C414yes—
24C22×C4×D13D411yescharacteristic
25C22×C4×D13D414yes—
26C22×C4×D13Q811yescharacteristic
27C22×C4×D13C2311yescharacteristic
28C2×C22⋊#261—28no—
29C2×C22⋊#261—24no—
30#88237—28no—
31#88237—28no—
32C2×C4⋊#261—24no—
33C2×C4×#261C2×C418yes—
34C2×C13×M16—22no—
35C2×C13×M16—24no—
36C22×C8×C13C2×C412yes—
37C2×#6099—22no—
38C2×#6099—24no—
39C22×#1055C2×C412yes—
40M16×D13—232no—
41C2×#6094—24no—
42C2×#6094—24no—
43C2×#6094D418yes—
44C2×C8×D13—24no—
45C2×C8×D13—24no—
46C2×C8×D13—24no—
47(C2×#261)⋊C4—28no—
48#10717—131nomaximal, Sylow
49C24×C13C4⋊C411yescharacteristic
50C23×D13—24no—
51C23×D13—44no—
52C23×D13C22⋊C414yes—
53C23×D13C4⋊C411yescharacteristic
54C23×D13C2×D411yescharacteristic
55C22×#261—28no—
56C22×C4×C13—22no—
57C22×C4×C13—22no—
58C22×C4×C13C4212yes—
59C22×C4×C13C22⋊C412yes—
60C22×C4×C13C4⋊C411yescharacteristic
61C22×C4×C13C22×C411yescharacteristic
62C22×Dic13—24no—
63C22×Dic13C4⋊C411yescharacteristic
64C22×Dic13C4⋊C414yes—
65C22×Dic13C2×Q811yescharacteristic
66C2×C4×D13—24no—
67C2×C4×D13—22no—
68C2×C4×D13—22no—
69C2×C4×D13—24no—
70C2×C4×D13—216no—
71C2×C4×D13—28no—
72C2×C4×D13—28no—
73C2×C4×D13C4212yes—
74C2×C4×D13C22⋊C414yes—
75C2×C4×D13C22⋊C412yes—
76C2×C4×D13C4⋊C414yes—
77C2×C4×D13C22×C412yes—
78C2×C4×D13C2×D414yes—
79C2×C4×D13C2×D412yes—
80C2×C4×D13#4114yes—
81C22⋊#261—416no—
82C22⋊#261—48no—
83C4⋊#261—44no—
84C4⋊#261—44no—
85C4×#261—216no—
86C13×M16—28no—
87C2×C8×C13—22no—
88C2×C8×C13—22no—
89C2×C8×C13C22⋊C414yescomplemented
90#6099—28no—
91C2×#1055—22no—
92C2×#1055—22no—
93C2×#1055C22⋊C414yescomplemented
94#6094—216no—
95C8×D13—216no—
96C23×M16—131no—
97#2280—132no—
98C2×H(3,ℤ/4)—134no—
99C23×C13—22no—
100C23×C13—42no—
101C23×C13#9512yes—
102C23×C13C2×C4⋊C411yescharacteristic
103C22×D13—22no—
104C22×D13—24no—
105C22×D13—28no—
106C22×D13—28no—
107C22×D13—44no—
108C22×D13—42no—
109C22×D13—416no—
110C22×D13#9512yes—
111C22×D13C2×C22⋊C412yes—
112C22×D13#12114yes—
113C2×#261—416no—
114C2×#261—48no—
115C2×C4×C13—22no—
116C2×C4×C13—24no—
117C2×C4×C13—22no—
118C2×C4×C13—22no—
119C2×C4×C13#9512yes—
120C2×C4×C13C2×C4211yescharacteristic
121C2×C4×C13C2×C22⋊C412yes—
122C2×C4×C13C2×C22⋊C411yescharacteristic
123C2×C4×C13#11712yes—
124C2×Dic13—22no—
125C2×Dic13—28no—
126C2×Dic13#9512yes—
127C2×Dic13C2×C4⋊C412yes—
128C2×Dic13C22⋊Q814yes—
129C4×D13—28no—
130C4×D13—24no—
131C4×D13—22no—
132C4×D13—22no—
133C4×D13—28no—
134C4×D13C4×D418yes—
135C4×D13#12014yes—
136C4×D13#12314yes—
137C8×C13—24no—
138#1055—24no—
139C24×C4—131no—
140C22×M16—131no—
141C22×M16—132no—
142C22×M16—268no—
143C22×M16—264no—
144C22×M16#26111yescharacteristic, complemented
145C23×C8—132no—
146C2×#117—134no—
147#381—262no—
148#380—264no—
149#379—262no—
150C4×C22⋊C4—138no—
151H(3,ℤ/4)—268no—
152C22×C13—22no—
153C22×C13—22no—
154C22×C13—24no—
155C22×C13—44no—
156C22×C13C2×#9511yescharacteristic
157C22×C13#38012yes—
158C2×D13—28no—
159C2×D13—22no—
160C2×D13—24no—
161C2×D13—22no—
162C2×D13—44no—
163C2×D13—416no—
164C2×D13H(3,ℤ/4)14yescomplemented
165C2×D13#38614yes—
166#261—88no—
167C4×C13—22no—
168C4×C13C4×C22⋊C412yes—
169C4×C13#37911yescharacteristic
170C4×C13#38111yescharacteristic
171Dic13—22no—
172Dic13#38514yes—
173C25—131no—
174C23×C4—131no—
175C23×C4—131no—
176C23×C4—134no—
177C23×C4—131no—
178C23×C4—131no—
179C23×C4—134no—
180C23×C4—131no—
181C23×C4—264no—
182C23×C4—264no—
183C23×C4C2×#26111yescharacteristic
184C2×M16—22no—
185C2×M16—24no—
186C2×M16—138no—
187C2×M16—264no—
188C2×M16—264no—
189C2×M16—264no—
190C2×M16—2632no—
191C2×M16—262no—
192C22×C8—132no—
193C22×C8—264no—
194C22×C8—264no—
195C22×C8—264no—
196C22×C8C2×#26112yes—
197#117—268no—
198#117—268no—
199C2×C4⋊C4—264no—
200C2×C22⋊C4—264no—
201C2×C22⋊C4—268no—
202C2×C42—138no—
203#95—268no—
204C2×C13—22no—
205C2×C13—42no—
206C2×C13C22⋊#9511yescharacteristic
207C2×C13C2×H(3,ℤ/4)12yes—
208D13—24no—
209D13—24no—
210C24—131no—
211C24—131no—
212C24—134no—
213C24—264no—
214C24—524no—
215C24C4⋊#26111yescharacteristic
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—131no—
219C22×C4—132no—
220C22×C4—134no—
221C22×C4—132no—
222C22×C4—134no—
223C22×C4—134no—
224C22×C4—131no—
225C22×C4—134no—
226C22×C4—134no—
227C22×C4—132no—
228C22×C4—132no—
229C22×C4—268no—
230C22×C4—264no—
231C22×C4—2616no—
232C22×C4—268no—
233C22×C4—264no—
234C22×C4—264no—
235C22×C4—262no—
236C22×C4—262no—
237C22×C4—268no—
238C22×C4C4×#26112yes—
239C22×C4C4⋊#26111yescharacteristic
240C22×C4C22⋊#26112yes—
241C22×C4C22×#26111yescharacteristic
242M16—28no—
243M16—2616no—
244M16—268no—
245C2×C8—22no—
246C2×C8—22no—
247C2×C8—134no—
248C2×C8—2616no—
249C2×C8—262no—
250C2×C8—262no—
251C2×C8C22⋊#26114yescomplemented
252C4⋊C4—524no—
253C4⋊C4—524no—
254C22⋊C4—528no—
255C22⋊C4—5216no—
256C42—2616no—
257C13#1071711yescharacteristic, complemented, Sylow
258C23—22no—
259C23—42no—
260C23—132no—
261C23—132no—
262C23—134no—
263C23—264no—
264C23—268no—
265C23—268no—
266C23—262no—
267C23—522no—
268C23—524no—
269C23—5216no—
270C23(C2×#261)⋊C412yes—
271C23C2×C4⋊#26111yescharacteristic
272C2×C4—22no—
273C2×C4—22no—
274C2×C4—24no—
275C2×C4—22no—
276C2×C4—132no—
277C2×C4—134no—
278C2×C4—134no—
279C2×C4—138no—
280C2×C4—134no—
281C2×C4—132no—
282C2×C4—268no—
283C2×C4—268no—
284C2×C4—268no—
285C2×C4—262no—
286C2×C4—262no—
287C2×C4—264no—
288C2×C4—262no—
289C2×C4—528no—
290C2×C4—5216no—
291C2×C4(C2×#261)⋊C412yes—
292C2×C4C2×C4×#26111yescharacteristic
293C2×C4#8823712yes—
294C2×C4C2×C22⋊#26112yes—
295C2×C4C2×C22⋊#26111yescharacteristic
296C8—24no—
297C8—264no—
298C22—22no—
299C22—24no—
300C22—22no—
301C22—44no—
302C22—134no—
303C22—134no—
304C22—268no—
305C22—264no—
306C22—262no—
307C22—262no—
308C22—524no—
309C22—5216no—
310C22C2×(C2×#261)⋊C411yescharacteristic
311C22#1171913612yes—
312C4—22no—
313C4—134no—
314C4—262no—
315C4—1048no—
316C4C4×C22⋊#26112yes—
317C4#1171913511yescharacteristic
318C4#1171917111yescharacteristic
319C2—22no—
320C2—42no—
321C2—264no—
322C2—264no—
323C2#1313001011yescharacteristic
324C2#1313050812yes—
subgroupG/H
centerC2×C4C2×C4×#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC22×C13×M16C4
socleC22×C13C2×#95
prime radicalC24×D13D4
cosocleC22×C4×D13C23
hypercenterC22×M16#261
hypocenterC13#10717
LCSG ▷ C2×C4×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C22×M16

Complements

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

NH ≅ G/Ntype
2. C2×#11718267C2semidirect
6. C22×C13×M16C4semidirect
7. C22×#6099C4semidirect
11. C22×C8×D13C4semidirect
15. C4×C22⋊#261C4semidirect
89. C2×C8×C13C22⋊C4semidirect
93. C2×#1055C22⋊C4semidirect
144. C22×M16#261semidirect
164. C2×D13H(3,ℤ/4)semidirect
251. C2×C8C22⋊#261semidirect
257. C13#10717semidirect

Maximal subgroups

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

subgroupindex
#131312802
C2×#117182672
C22×M16×D132
#1071713