Finite Group Databasebeta

← #16779841

Subgroups — #16779841

Order 3328.

1226 conjugacy classes of subgroups; only the 172 normal subgroups are shown.

normal subgroups only

This group has 1226 conjugacy classes of subgroups — too many to draw. Only its 172 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×C4×C22⋊#261C212yesmaximal
2#13129716C214yesmaximal, complemented
3D13×#407C211yesmaximal, characteristic
4C23×C4×D13C2211yescharacteristic
5C22×C22⋊#261—22no—
6C22×C4×#261—22no—
7C2×M16×D13C412yescomplemented
8C4×C22⋊#261—22no—
9C4×C22⋊#261—22no—
10C4×C22⋊#261C414yescomplemented
11C4×C22⋊#261C2214yes—
12C2×(C2×#261)⋊C4C414yescomplemented
13C13×#407C411yescharacteristic, complemented
14#11718868C411yescharacteristic, complemented
15#11718787C2212yes—
16#11718387—22no—
17D13×C22⋊C8—22no—
18C24×D13D411yescharacteristic
19C23×#261—24no—
20C23×C4×C13C2×C411yescharacteristic
21C23×Dic13Q811yescharacteristic
22C22×C4×D13—44no—
23C22×C4×D13C2×C411yescharacteristic
24C22×C4×D13C2×C412yes—
25C22×C4×D13C2×C412yes—
26C22×C4×D13D412yes—
27C22×C4×D13D411yescharacteristic
28C22×C4×D13D412yes—
29C22×C4×D13Q811yescharacteristic
30C22×C4×D13C2311yescharacteristic
31C2×C22⋊#261—216no—
32C2×C22⋊#261—24no—
33C2×C22⋊#261—24no—
34C2×C4×#261—24no—
35C2×C4×#261—24no—
36C2×C4×#261—48no—
37C2×C13×M16C2×C412yescomplemented
38C2×#6099C2×C412yescomplemented
39M16×D13—44no—
40C2×#6094—22no—
41C2×C8×D13—22no—
42(C2×#261)⋊C4—24no—
43(C2×#261)⋊C4C2×C418yescomplemented
44C13×C22⋊C8—22no—
45C22⋊#1055—22no—
46#88060—24no—
47C2×#1297—131nomaximal, Sylow
48C24×C13C4⋊C411yescharacteristic
49C23×D13—28no—
50C23×D13—42no—
51C23×D13C22⋊C412yes—
52C23×D13C22⋊C412yes—
53C23×D13C4⋊C411yescharacteristic
54C23×D13C2×D411yescharacteristic
55C22×#261—216no—
56C22×#261—28no—
57C22×#261—48no—
58C22×#261—48no—
59C22×C4×C13—42no—
60C22×C4×C13C4212yes—
61C22×C4×C13C22⋊C412yes—
62C22×C4×C13C4⋊C411yescharacteristic
63C22×C4×C13C22×C411yescharacteristic
64C22×Dic13—42no—
65C22×Dic13C4⋊C411yescharacteristic
66C22×Dic13C4⋊C412yes—
67C22×Dic13C4⋊C412yes—
68C22×Dic13C2×Q811yescharacteristic
69C2×C4×D13—24no—
70C2×C4×D13—28no—
71C2×C4×D13—44no—
72C2×C4×D13—42no—
73C2×C4×D13—44no—
74C2×C4×D13—42no—
75C2×C4×D13—44no—
76C2×C4×D13—42no—
77C2×C4×D13C4211yescharacteristic
78C2×C4×D13C4211yescharacteristic
79C2×C4×D13C22⋊C412yes—
80C2×C4×D13C22⋊C411yescharacteristic
81C2×C4×D13C22⋊C412yes—
82C2×C4×D13C22⋊C411yescharacteristic
83C2×C4×D13C4⋊C412yes—
84C2×C4×D13C4⋊C412yes—
85C2×C4×D13C22×C412yes—
86C2×C4×D13C2×D412yes—
87C22⋊#261—216no—
88C22⋊#261—216no—
89C4×#261—48no—
90C4×#261—48no—
91C13×M16—42no—
92C2×C8×C13—22no—
93#6099—42no—
94C2×#1055—22no—
95#6094—44no—
96C8×D13—44no—
97C2×#407—131no—
98C2×C4×C22⋊C4—132no—
99#1297—134no—
100C23×C13—24no—
101C23×C13—41no—
102C23×C13#9512yes—
103C23×C13C2×C4⋊C411yescharacteristic
104C22×D13—24no—
105C22×D13—24no—
106C22×D13—24no—
107C22×D13—24no—
108C22×D13—22no—
109C22×D13—24no—
110C22×D13—24no—
111C22×D13—42no—
112C22×D13—41no—
113C22×D13—416no—
114C22×D13#9511yescharacteristic
115C22×D13#9511yescharacteristic
116C22×D13#10418yes—
117C22×D13C2×C22⋊C412yes—
118C2×#261—216no—
119C2×#261—48no—
120C2×#261—432no—
121C2×#261—48no—
122C2×C4×C13—22no—
123C2×C4×C13—24no—
124C2×C4×C13—42no—
125C2×C4×C13—41no—
126C2×C4×C13#9512yes—
127C2×C4×C13C2×C4211yescharacteristic
128C2×C4×C13C2×C22⋊C411yescharacteristic
129C2×Dic13—22no—
130C2×Dic13—24no—
131C2×Dic13—42no—
132C2×Dic13—41no—
133C2×Dic13#9511yescharacteristic
134C2×Dic13#9511yescharacteristic
135C2×Dic13C2×C4⋊C412yes—
136C4×D13—22no—
137C4×D13—24no—
138C4×D13—22no—
139C4×D13—24no—
140C4×D13—24no—
141C4×D13—22no—
142C4×D13—42no—
143C4×D13—42no—
144C4×D13—42no—
145C4×D13#9914yes—
146C8×C13—42no—
147#1055—42no—
148C24×C4—131no—
149C22×M16—132no—
150C22×C22⋊C4—262no—
151C22×C42—262no—
152#407—131no—
153#407—132no—
154#407—262no—
155#407#26111yescharacteristic, complemented
156C2×C22⋊C8—262no—
157C4×C22⋊C4—134no—
158C4×C22⋊C4—134no—
159C4×C22⋊C4—262no—
160C4×C22⋊C4—262no—
161C2×#95—134no—
162C22×C13—22no—
163C22×C13—22no—
164C22×C13—22no—
165C22×C13—21no—
166C22×C13—44no—
167C22×C13#33914yes—
168C22×C13C2×#9511yescharacteristic
169C2×D13—22no—
170C2×D13—22no—
171C2×D13—216no—
172C2×D13—22no—
173C2×D13—21no—
174C2×D13—44no—
175C2×D13—48no—
176C2×D13—44no—
177C2×D13#33914yes—
178C2×D13#34212yes—
179C2×D13C2×#10414yes—
180#261—416no—
181C4×C13—22no—
182C4×C13—21no—
183C4×C13C2×#9912yes—
184Dic13—21no—
185Dic13—22no—
186Dic13#34212yes—
187C25—131no—
188C23×C4—131no—
189C23×C4—132no—
190C23×C4—131no—
191C23×C4—132no—
192C23×C4—132no—
193C23×C4—131no—
194C23×C4—131no—
195C23×C4—132no—
196C23×C4—131no—
197C23×C4—264no—
198C23×C4—524no—
199C23×C4C2×#26111yescharacteristic
200C2×M16—132no—
201C2×M16—262no—
202C2×M16—524no—
203C2×M16C2×#26112yescomplemented
204C22×C8—262no—
205C2×C22⋊C4—264no—
206C2×C22⋊C4—264no—
207C2×C22⋊C4—2616no—
208C2×C42—264no—
209C2×C42—264no—
210C2×C42—528no—
211C22⋊C8—22no—
212C22⋊C8—264no—
213C22⋊C8—262no—
214#95—138no—
215#95—264no—
216C2×C13—24no—
217C2×C13—41no—
218C2×C13C2×#33912yes—
219C2×C13C2×#34211yescharacteristic
220D13—24no—
221D13—41no—
222D13#129714yescomplemented
223C24—132no—
224C24—131no—
225C24—132no—
226C24—131no—
227C24—268no—
228C24—522no—
229C24C4⋊#26111yescharacteristic
230C22×C4—42no—
231C22×C4—131no—
232C22×C4—132no—
233C22×C4—131no—
234C22×C4—132no—
235C22×C4—131no—
236C22×C4—132no—
237C22×C4—132no—
238C22×C4—131no—
239C22×C4—131no—
240C22×C4—132no—
241C22×C4—131no—
242C22×C4—132no—
243C22×C4—132no—
244C22×C4—132no—
245C22×C4—268no—
246C22×C4—264no—
247C22×C4—268no—
248C22×C4—2616no—
249C22×C4—522no—
250C22×C4—524no—
251C22×C4—524no—
252C22×C4—522no—
253C22×C4—524no—
254C22×C4—522no—
255C22×C4—522no—
256C22×C4—528no—
257C22×C4—528no—
258C22×C4C4×#26112yes—
259C22×C4C4⋊#26111yescharacteristic
260C22×C4C22⋊#26112yes—
261C22×C4C22×#26111yescharacteristic
262M16—42no—
263M16—524no—
264M16—522no—
265C2×C8—22no—
266C2×C8—262no—
267C2×C8—524no—
268C22⋊C4—2616no—
269C22⋊C4—2616no—
270C42—528no—
271C42—528no—
272C13C2×#129711yescharacteristic, complemented, Sylow
273C23—24no—
274C23—41no—
275C23—131no—
276C23—138no—
277C23—132no—
278C23—131no—
279C23—264no—
280C23—264no—
281C23—264no—
282C23—262no—
283C23—264no—
284C23—264no—
285C23—264no—
286C23—522no—
287C23—521no—
288C23—5216no—
289C23(C2×#261)⋊C412yes—
290C23C2×C4⋊#26111yescharacteristic
291C2×C4—22no—
292C2×C4—24no—
293C2×C4—42no—
294C2×C4—41no—
295C2×C4—131no—
296C2×C4—134no—
297C2×C4—131no—
298C2×C4—132no—
299C2×C4—264no—
300C2×C4—262no—
301C2×C4—264no—
302C2×C4—262no—
303C2×C4—264no—
304C2×C4—262no—
305C2×C4—264no—
306C2×C4—262no—
307C2×C4—2616no—
308C2×C4—522no—
309C2×C4—522no—
310C2×C4—522no—
311C2×C4—522no—
312C2×C4—521no—
313C2×C4—528no—
314C2×C4—528no—
315C2×C4—5232no—
316C2×C4(C2×#261)⋊C412yes—
317C2×C4C2×C4×#26111yescharacteristic
318C2×C4C2×C22⋊#26111yescharacteristic
319C8—42no—
320C8—522no—
321C22—22no—
322C22—22no—
323C22—22no—
324C22—21no—
325C22—44no—
326C22—134no—
327C22—132no—
328C22—134no—
329C22—2616no—
330C22—262no—
331C22—262no—
332C22—262no—
333C22—261no—
334C22—528no—
335C22—524no—
336C22—524no—
337C22#1171827214yes—
338C22C2×(C2×#261)⋊C411yescharacteristic
339C4—22no—
340C4—21no—
341C4—132no—
342C4—261no—
343C4—262no—
344C4—5216no—
345C4D13⋊#9912yes—
346C2—24no—
347C2—41no—
348C2—134no—
349C2—264no—
350C2—521no—
351C2C2×#1171827212yes—
352C2#1313053311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#261
commutatorC2×C4×C13C2×C42
FrattiniC22×C4C22×#261
FittingC13×#407C4
socleC22×C13C2×#95
prime radicalC24×D13D4
cosocleC22×C4×D13C23
hypercenter#407#261
hypocenterC13C2×#1297
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #407

Complements

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

NH ≅ G/Ntype
2. #13129716C2semidirect
7. C2×M16×D13C4semidirect
10. C4×C22⋊#261C4semidirect
12. C2×(C2×#261)⋊C4C4semidirect
13. C13×#407C4semidirect
14. #11718868C4semidirect
37. C2×C13×M16C2×C4semidirect
38. C2×#6099C2×C4semidirect
43. (C2×#261)⋊C4C2×C4semidirect
155. #407#261semidirect
203. C2×M16C2×#261semidirect
222. D13#1297semidirect
272. C13C2×#1297semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊#2612
#131297162
D13×#4072
C2×#129713