Finite Group Databasebeta

← #16785292

Subgroups — #16785292

Order 3328.

1510 conjugacy classes of subgroups; only the 228 normal subgroups are shown.

normal subgroups only

This group has 1510 conjugacy classes of subgroups — too many to draw. Only its 228 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
1C2×#11719135C212yesmaximal
2C2×#11718289C214yesmaximal
3C22×#88126C211yesmaximal, characteristic
4C23×C4×D13C2211yescharacteristic
5C22×C22⋊#261C2214yes—
6C22×C42×C13C411yescharacteristic, complemented
7C22×#6103C2212yes—
8C22×#6101C412yescomplemented
9C22×C4×Dic13C411yescharacteristic, complemented
10C2×#88126—24no—
11C2×#88126—28no—
12#11719135—24no—
13#11719135C418yescomplemented
14C2×(C2×#261)⋊C4—24no—
15#11718289—28no—
16C24×D13C2311yescharacteristic
17C23×#261—24no—
18C23×C4×C13C2×C412yes—
19C23×C4×C13C2×C411yescharacteristic
20C23×Dic13C2×C411yescharacteristic
21C23×Dic13C2×C412yes—
22C22×C4×D13—24no—
23C22×C4×D13—24no—
24C22×C4×D13C2×C414yes—
25C22×C4×D13D412yes—
26C22×C4×D13D414yes—
27C22×C4×D13Q812yes—
28C2×C22⋊#261—28no—
29C2×C22⋊#261—28no—
30C2×C22⋊#261—24no—
31C2×C22⋊#261C2×C418yes—
32C2×C42×C13—24no—
33C2×C42×C13—22no—
34C2×#6103—24no—
35C2×#6103—24no—
36C2×#6103D418yes—
37C2×#6101—24no—
38C2×#6101—24no—
39C2×#6101—24no—
40C2×C4×Dic13—22no—
41C2×C4×Dic13—24no—
42#88126—232no—
43(C2×#261)⋊C4—216no—
44#10726—131nomaximal, Sylow
45C24×C13C22×C411yescharacteristic
46C23×D13—44no—
47C23×D13C22×C412yes—
48C23×D13C2×D412yes—
49C23×D13C2×D411yescharacteristic
50C23×D13C2×D414yes—
51C23×D13C2×Q811yescharacteristic
52C23×D13#4114yes—
53C22×#261—28no—
54C22×#261—416no—
55C22×#261—44no—
56C22×#261—44no—
57C22×C4×C13—22no—
58C22×C4×C13—22no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—44no—
62C22×C4×C13C4212yes—
63C22×C4×C13C22⋊C412yes—
64C22×C4×C13C22⋊C414yes—
65C22×C4×C13C4⋊C412yes—
66C22×Dic13—22no—
67C22×Dic13—22no—
68C22×Dic13—22no—
69C22×Dic13—22no—
70C22×Dic13—44no—
71C22×Dic13C4212yes—
72C22×Dic13C22⋊C412yes—
73C22×Dic13C22⋊C414yes—
74C22×Dic13C4⋊C412yes—
75C2×C4×D13—216no—
76C2×C4×D13—28no—
77C2×C4×D13—28no—
78C2×C4×D13—28no—
79C2×C4×D13—28no—
80C2×C4×D13C22⋊C418yes—
81C2×C4×D13C4⋊C418yes—
82C22⋊#261—216no—
83C22⋊#261—48no—
84C42×C13—28no—
85#6103—216no—
86#6101—216no—
87C4×Dic13—28no—
88C22×#117—131no—
89C2×#381—132no—
90C2×#342—134no—
91C23×C13—24no—
92C23×C13C2×C4211yescharacteristic
93C23×C13C2×C22⋊C412yes—
94C23×C13C2×C22⋊C411yescharacteristic
95C23×C13C2×C4⋊C411yescharacteristic
96C23×C13#11712yes—
97C22×D13—28no—
98C22×D13—44no—
99C22×D13—42no—
100C22×D13—44no—
101C22×D13—44no—
102C22×D13—42no—
103C22×D13—48no—
104C22×D13C2×C22⋊C412yes—
105C22×D13C2×C4⋊C412yes—
106C22×D13C4×D418yes—
107C22×D13#12014yes—
108C22×D13#12114yes—
109C22×D13C22⋊Q814yes—
110C22×D13#12314yes—
111C2×#261—416no—
112C2×#261—48no—
113C2×#261—88no—
114C2×#261—88no—
115C2×C4×C13—24no—
116C2×C4×C13—22no—
117C2×C4×C13—24no—
118C2×C4×C13—22no—
119C2×C4×C13—24no—
120C2×C4×C13—44no—
121C2×C4×C13—44no—
122C2×C4×C13—44no—
123C2×C4×C13#9514yes—
124C2×Dic13—24no—
125C2×Dic13—22no—
126C2×Dic13—24no—
127C2×Dic13—22no—
128C2×Dic13—24no—
129C2×Dic13—44no—
130C2×Dic13—44no—
131C2×Dic13—44no—
132C2×Dic13#9514yes—
133C4×D13—216no—
134C4×D13—216no—
135C24×C4—131no—
136C2×#117—268no—
137C2×#117—264no—
138C22×C4⋊C4—132no—
139C22×C22⋊C4—132no—
140C22×C22⋊C4—134no—
141C22×C42—131no—
142C22×C42#26111yescharacteristic, complemented
143#381—138no—
144#381—264no—
145C2×#95—264no—
146#342—268no—
147C22×C13—24no—
148C22×C13—22no—
149C22×C13—22no—
150C22×C13—22no—
151C22×C13—22no—
152C22×C13C2×#9511yescharacteristic
153C22×C13C4×C22⋊C412yes—
154C22×C13#37911yescharacteristic
155C22×C13#38012yes—
156C22×C13#38111yescharacteristic
157C22×C13#41014yes—
158C2×D13—28no—
159C2×D13—24no—
160C2×D13—24no—
161C2×D13—28no—
162C2×D13—48no—
163C2×D13—44no—
164C2×D13—44no—
165C2×D13#38514yes—
166C2×D13#38614yes—
167#261—88no—
168C4×C13—24no—
169C4×C13—44no—
170Dic13—24no—
171Dic13—44no—
172C25—131no—
173C23×C4—131no—
174C23×C4—134no—
175C23×C4—132no—
176C23×C4—132no—
177C23×C4—134no—
178C23×C4—132no—
179C23×C4—264no—
180C23×C4—264no—
181C23×C4—264no—
182C23×C4C2×#26112yes—
183C23×C4C2×#26111yescharacteristic
184#117—2632no—
185C2×C4⋊C4—264no—
186C2×C4⋊C4—264no—
187C2×C4⋊C4—264no—
188C2×C22⋊C4—138no—
189C2×C22⋊C4—138no—
190C2×C22⋊C4—264no—
191C2×C22⋊C4—264no—
192C2×C22⋊C4—268no—
193C2×C22⋊C4—268no—
194C2×C22⋊C4—264no—
195C2×C42—24no—
196C2×C42—22no—
197C2×C42—264no—
198C2×C42—262no—
199#95—2616no—
200C2×C13—22no—
201C2×C13—22no—
202C2×C13C22⋊#9511yescharacteristic
203C2×C13#174012yes—
204C2×C13#178212yes—
205C2×C13#182012yes—
206D13—24no—
207D13—24no—
208C24—132no—
209C24—132no—
210C24—131no—
211C24—131no—
212C24—134no—
213C24—134no—
214C24—524no—
215C24C22×#26111yescharacteristic
216C22×C4—22no—
217C22×C4—22no—
218C22×C4—22no—
219C22×C4—22no—
220C22×C4—44no—
221C22×C4—132no—
222C22×C4—132no—
223C22×C4—132no—
224C22×C4—138no—
225C22×C4—138no—
226C22×C4—134no—
227C22×C4—268no—
228C22×C4—2616no—
229C22×C4—268no—
230C22×C4—268no—
231C22×C4—268no—
232C22×C4—262no—
233C22×C4—262no—
234C22×C4—262no—
235C22×C4—262no—
236C22×C4—268no—
237C22×C4—524no—
238C22×C4—524no—
239C22×C4—524no—
240C22×C4—5216no—
241C22×C4C4×#26112yes—
242C22×C4C4⋊#26112yes—
243C22×C4C22⋊#26112yes—
244C22×C4C22⋊#26114yes—
245C4⋊C4—2616no—
246C22⋊C4—2616no—
247C22⋊C4—2616no—
248C22⋊C4—528no—
249C42—28no—
250C42—268no—
251C13#1072611yescharacteristic, complemented, Sylow
252C23—24no—
253C23—134no—
254C23—132no—
255C23—132no—
256C23—134no—
257C23—138no—
258C23—134no—
259C23—134no—
260C23—268no—
261C23—524no—
262C23—522no—
263C23—522no—
264C23—524no—
265C23—524no—
266C23—528no—
267C23C2×C4×#26111yescharacteristic
268C23C2×C4⋊#26111yescharacteristic
269C23#8823712yes—
270C23C2×C22⋊#26112yes—
271C23C2×C22⋊#26111yescharacteristic
272C2×C4—22no—
273C2×C4—24no—
274C2×C4—22no—
275C2×C4—24no—
276C2×C4—24no—
277C2×C4—44no—
278C2×C4—44no—
279C2×C4—44no—
280C2×C4—134no—
281C2×C4—2616no—
282C2×C4—2616no—
283C2×C4—262no—
284C2×C4—264no—
285C2×C4—262no—
286C2×C4—264no—
287C2×C4—264no—
288C2×C4—524no—
289C2×C4—524no—
290C2×C4—524no—
291C2×C4—528no—
292C2×C4—5216no—
293C2×C4—1048no—
294C2×C4—1048no—
295C2×C4(C2×#261)⋊C414yes—
296C22—22no—
297C22—22no—
298C22—22no—
299C22—22no—
300C22—24no—
301C22—134no—
302C22—134no—
303C22—264no—
304C22—264no—
305C22—268no—
306C22—268no—
307C22—528no—
308C22—524no—
309C22—524no—
310C22#1171911614yes—
311C22C2×(C2×#261)⋊C411yescharacteristic
312C22C4×C22⋊#26112yes—
313C22#1171913511yescharacteristic
314C22#1171913612yes—
315C22#1171917111yescharacteristic
316C4—24no—
317C4—44no—
318C4—264no—
319C4—524no—
320C4—1048no—
321C2—22no—
322C2—22no—
323C2—264no—
324C2—264no—
325C2#1313001011yescharacteristic
326C2#1313053512yes—
327C2#1313066512yes—
328C2#1313073312yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C2×C42
FrattiniC24C22×#261
FittingC22×C42×C13C4
socleC23×C13C2×C22⋊C4
prime radical, cosocleC24×D13C23
hypercenterC22×C42#261
hypocenterC13#10726
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C42

Complements

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

NH ≅ G/Ntype
6. C22×C42×C13C4semidirect
8. C22×#6101C4semidirect
9. C22×C4×Dic13C4semidirect
13. #11719135C4semidirect
142. C22×C42#261semidirect
251. C13#10726semidirect

Maximal subgroups

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

subgroupindex
C2×#117191352
C2×#117182892
C22×#881262
#1072613