Finite Group Databasebeta

← #16785293

Subgroups — #16785293

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×#88146C211yesmaximal, characteristic
4C23×C4×D13C2211yescharacteristic
5C22×C22⋊#261C2214yes—
6C22×C13×C4⋊C4C411yescharacteristic, complemented
7C22×#6103C2212yes—
8C22×C4⋊Dic13C411yescharacteristic, complemented
9C22×C4×Dic13C412yescomplemented
10C2×#88146—24no—
11C2×#88146—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×C13×C4⋊C4—24no—
33C2×C13×C4⋊C4—22no—
34C2×#6103—24no—
35C2×#6103—24no—
36C2×#6103D418yes—
37C2×C4⋊Dic13—22no—
38C2×C4⋊Dic13—24no—
39C2×C4×Dic13—24no—
40C2×C4×Dic13—24no—
41C2×C4×Dic13—24no—
42#88146—232no—
43(C2×#261)⋊C4—216no—
44#10726—131nomaximal, Sylow
45C24×C13C22×C411yescharacteristic
46C23×D13—42no—
47C23×D13—42no—
48C23×D13C22×C412yes—
49C23×D13C2×D412yes—
50C23×D13C2×D411yescharacteristic
51C23×D13C2×D414yes—
52C23×D13C2×Q811yescharacteristic
53C23×D13#4114yes—
54C22×#261—28no—
55C22×#261—48no—
56C22×#261—48no—
57C22×#261—44no—
58C22×#261—44no—
59C22×C4×C13—22no—
60C22×C4×C13—22no—
61C22×C4×C13—22no—
62C22×C4×C13—22no—
63C22×C4×C13—44no—
64C22×C4×C13C4212yes—
65C22×C4×C13C22⋊C412yes—
66C22×C4×C13C22⋊C414yes—
67C22×C4×C13C4⋊C412yes—
68C22×Dic13—22no—
69C22×Dic13—22no—
70C22×Dic13—22no—
71C22×Dic13—22no—
72C22×Dic13—44no—
73C22×Dic13C4212yes—
74C22×Dic13C22⋊C412yes—
75C22×Dic13C22⋊C414yes—
76C22×Dic13C4⋊C412yes—
77C2×C4×D13—216no—
78C2×C4×D13—28no—
79C2×C4×D13—28no—
80C2×C4×D13—28no—
81C2×C4×D13—28no—
82C2×C4×D13C22⋊C418yes—
83C2×C4×D13C4⋊C418yes—
84C22⋊#261—216no—
85C22⋊#261—48no—
86C13×C4⋊C4—28no—
87#6103—216no—
88C4⋊Dic13—28no—
89C4×Dic13—216no—
90C22×#117—131no—
91C2×#381—132no—
92C2×#342—134no—
93C23×C13—22no—
94C23×C13—22no—
95C23×C13C2×C4211yescharacteristic
96C23×C13C2×C22⋊C412yes—
97C23×C13C2×C22⋊C411yescharacteristic
98C23×C13C2×C4⋊C411yescharacteristic
99C23×C13#11712yes—
100C22×D13—24no—
101C22×D13—24no—
102C22×D13—44no—
103C22×D13—42no—
104C22×D13—44no—
105C22×D13—44no—
106C22×D13—42no—
107C22×D13—48no—
108C22×D13C2×C22⋊C412yes—
109C22×D13C2×C4⋊C412yes—
110C22×D13C4×D418yes—
111C22×D13#12014yes—
112C22×D13#12114yes—
113C22×D13C22⋊Q814yes—
114C22×D13#12314yes—
115C2×#261—416no—
116C2×#261—48no—
117C2×#261—88no—
118C2×#261—84no—
119C2×#261—84no—
120C2×C4×C13—24no—
121C2×C4×C13—22no—
122C2×C4×C13—24no—
123C2×C4×C13—22no—
124C2×C4×C13—24no—
125C2×C4×C13—44no—
126C2×C4×C13—44no—
127C2×C4×C13—44no—
128C2×C4×C13#9514yes—
129C2×Dic13—24no—
130C2×Dic13—22no—
131C2×Dic13—24no—
132C2×Dic13—22no—
133C2×Dic13—24no—
134C2×Dic13—44no—
135C2×Dic13—44no—
136C2×Dic13—44no—
137C2×Dic13#9514yes—
138C4×D13—216no—
139C4×D13—216no—
140C24×C4—131no—
141C2×#117—268no—
142C2×#117—264no—
143C22×C4⋊C4—131no—
144C22×C4⋊C4#26111yescharacteristic, complemented
145C22×C22⋊C4—132no—
146C22×C22⋊C4—134no—
147C22×C42—132no—
148#381—138no—
149#381—264no—
150C2×#95—264no—
151#342—268no—
152C22×C13—24no—
153C22×C13—22no—
154C22×C13—22no—
155C22×C13—22no—
156C22×C13—22no—
157C22×C13C2×#9511yescharacteristic
158C22×C13C4×C22⋊C412yes—
159C22×C13#37911yescharacteristic
160C22×C13#38012yes—
161C22×C13#38111yescharacteristic
162C22×C13#41012yes—
163C22×C13#41012yes—
164C2×D13—28no—
165C2×D13—24no—
166C2×D13—24no—
167C2×D13—24no—
168C2×D13—24no—
169C2×D13—48no—
170C2×D13—44no—
171C2×D13—44no—
172C2×D13#38514yes—
173C2×D13#38614yes—
174#261—88no—
175C4×C13—24no—
176C4×C13—44no—
177Dic13—24no—
178Dic13—44no—
179C25—131no—
180C23×C4—131no—
181C23×C4—134no—
182C23×C4—132no—
183C23×C4—132no—
184C23×C4—134no—
185C23×C4—132no—
186C23×C4—264no—
187C23×C4—264no—
188C23×C4—264no—
189C23×C4C2×#26112yes—
190C23×C4C2×#26111yescharacteristic
191#117—2632no—
192C2×C4⋊C4—24no—
193C2×C4⋊C4—22no—
194C2×C4⋊C4—264no—
195C2×C4⋊C4—262no—
196C2×C22⋊C4—138no—
197C2×C22⋊C4—138no—
198C2×C22⋊C4—264no—
199C2×C22⋊C4—264no—
200C2×C22⋊C4—268no—
201C2×C22⋊C4—268no—
202C2×C22⋊C4—264no—
203C2×C42—264no—
204C2×C42—264no—
205C2×C42—264no—
206#95—2616no—
207C2×C13—22no—
208C2×C13—22no—
209C2×C13C22⋊#9511yescharacteristic
210C2×C13#174012yes—
211C2×C13#178211yescharacteristic
212C2×C13#178211yescharacteristic
213C2×C13#182012yes—
214D13—24no—
215D13—24no—
216C24—132no—
217C24—132no—
218C24—131no—
219C24—131no—
220C24—134no—
221C24—134no—
222C24—522no—
223C24—522no—
224C24C22×#26111yescharacteristic
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—22no—
228C22×C4—22no—
229C22×C4—44no—
230C22×C4—132no—
231C22×C4—132no—
232C22×C4—132no—
233C22×C4—138no—
234C22×C4—138no—
235C22×C4—134no—
236C22×C4—268no—
237C22×C4—2616no—
238C22×C4—268no—
239C22×C4—268no—
240C22×C4—268no—
241C22×C4—262no—
242C22×C4—262no—
243C22×C4—262no—
244C22×C4—262no—
245C22×C4—268no—
246C22×C4—524no—
247C22×C4—524no—
248C22×C4—524no—
249C22×C4—528no—
250C22×C4—528no—
251C22×C4C4×#26112yes—
252C22×C4C4⋊#26112yes—
253C22×C4C22⋊#26112yes—
254C22×C4C22⋊#26114yes—
255C4⋊C4—28no—
256C4⋊C4—268no—
257C22⋊C4—2616no—
258C22⋊C4—2616no—
259C22⋊C4—528no—
260C42—2616no—
261C13#1072611yescharacteristic, complemented, Sylow
262C23—22no—
263C23—22no—
264C23—134no—
265C23—132no—
266C23—132no—
267C23—134no—
268C23—138no—
269C23—134no—
270C23—134no—
271C23—264no—
272C23—264no—
273C23—524no—
274C23—522no—
275C23—522no—
276C23—524no—
277C23—524no—
278C23—528no—
279C23C2×C4×#26111yescharacteristic
280C23C2×C4⋊#26111yescharacteristic
281C23#8823712yes—
282C23C2×C22⋊#26112yes—
283C23C2×C22⋊#26111yescharacteristic
284C2×C4—22no—
285C2×C4—24no—
286C2×C4—22no—
287C2×C4—24no—
288C2×C4—24no—
289C2×C4—44no—
290C2×C4—44no—
291C2×C4—44no—
292C2×C4—134no—
293C2×C4—2616no—
294C2×C4—2616no—
295C2×C4—262no—
296C2×C4—264no—
297C2×C4—262no—
298C2×C4—264no—
299C2×C4—264no—
300C2×C4—524no—
301C2×C4—524no—
302C2×C4—524no—
303C2×C4—528no—
304C2×C4—5216no—
305C2×C4—1044no—
306C2×C4—1044no—
307C2×C4—1048no—
308C2×C4(C2×#261)⋊C414yes—
309C22—22no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—24no—
314C22—134no—
315C22—134no—
316C22—264no—
317C22—264no—
318C22—264no—
319C22—264no—
320C22—268no—
321C22—528no—
322C22—524no—
323C22—524no—
324C22C2×(C2×#261)⋊C411yescharacteristic
325C22C4×C22⋊#26112yes—
326C22#1171913511yescharacteristic
327C22#1171913612yes—
328C22#1171914212yes—
329C22#1171915612yes—
330C22#1171917111yescharacteristic
331C4—24no—
332C4—44no—
333C4—264no—
334C4—524no—
335C4—1048no—
336C2—22no—
337C2—22no—
338C2—264no—
339C2—264no—
340C2#1313001011yescharacteristic
341C2#1313053612yes—
342C2#1313066611yescharacteristic
343C2#1313066711yescharacteristic
344C2#1313073412yes—
subgroupG/H
centerC23C2×C22⋊#261
commutatorC23×C13C2×C42
FrattiniC24C22×#261
FittingC22×C13×C4⋊C4C4
socleC23×C13C2×C22⋊C4
prime radical, cosocleC24×D13C23
hypercenterC22×C4⋊C4#261
hypocenterC13#10726
LCSG ▷ C23×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊C4

Complements

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

NH ≅ G/Ntype
6. C22×C13×C4⋊C4C4semidirect
8. C22×C4⋊Dic13C4semidirect
9. C22×C4×Dic13C4semidirect
13. #11719135C4semidirect
144. C22×C4⋊C4#261semidirect
261. 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×#881462
#1072613