Finite Group Databasebeta

← #16785097

Subgroups — #16785097

Order 3328.

566 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 106 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
1C4×#88111C211yesmaximal, characteristic
2#13130012C211yesmaximal, characteristic
3#13129709C212yesmaximal
4#13129709C212yesmaximal
5#13123145C211yesmaximal, characteristic
6C2×#88144C411yescharacteristic, complemented
7C2×C42×D13C2211yescharacteristic
8C2×(C2×#261)⋊C4—21no—
9C2×(C2×#261)⋊C4—21no—
10C2×(C2×#261)⋊C4C2212yes—
11C2×#88111C2212yes—
12C2×C4×#1057—21no—
13C13×#389C411yescharacteristic, complemented
14#11718650—21no—
15#11718648C2211yescharacteristic
16#11718648C2211yescharacteristic
17#11718642—21no—
18#11718638C411yescharacteristic, complemented
19#11718589C411yescharacteristic, complemented
20#11718329—21no—
21#11718313—21no—
22#11718290—21no—
23C23×#261—22no—
24C22×C4×D13D411yescharacteristic
25C22×C4×D13D411yescharacteristic
26C22×C4×D13C2311yescharacteristic
27C22×#1057—22no—
28C2×C13×C4⋊C4—21no—
29C2×C13×C4⋊C4C2×C411yescharacteristic
30C2×C13×C4⋊C4C2×C411yescharacteristic
31C2×C42×C13C2×C411yescharacteristic
32C2×#6103—21no—
33C2×#6103—21no—
34C2×C4⋊Dic13—21no—
35C2×C4⋊Dic13C2×C411yescharacteristic
36C2×C4⋊Dic13C2×C411yescharacteristic
37C2×#6101—21no—
38C2×#6101—21no—
39C2×C4×Dic13C2×C411yescharacteristic
40C2×C4×Dic13D411yescharacteristic
41C2×C4×Dic13D411yescharacteristic
42#88144—42no—
43C42×D13—42no—
44(C2×#261)⋊C4—24no—
45(C2×#261)⋊C4—24no—
46(C2×#261)⋊C4—42no—
47#88111—22no—
48#88111Q814yes—
49C4×#1057—42no—
50C13×#95—21no—
51#88071—21no—
52#88071—21no—
53#88071—21no—
54#88071—21no—
55#88071—21no—
56#9886—131nomaximal, Sylow
57C23×D13C2×D411yescharacteristic
58C22×#261—24no—
59C22×#261—42no—
60C22×#261—42no—
61C22×#261—42no—
62C22×#261—42no—
63C22×#261—42no—
64C22×#261—42no—
65C22×C4×C13—21no—
66C22×C4×C13—21no—
67C22×C4×C13C22⋊C411yescharacteristic
68C22×C4×C13C22⋊C411yescharacteristic
69C22×C4×C13C22×C411yescharacteristic
70C22×Dic13—21no—
71C22×Dic13—21no—
72C22×Dic13C22⋊C411yescharacteristic
73C22×Dic13C22⋊C411yescharacteristic
74C22×Dic13C2×D411yescharacteristic
75C2×C4×D13—22no—
76C2×C4×D13—22no—
77C2×C4×D13—22no—
78C2×C4×D13—22no—
79C2×C4×D13—41no—
80C2×C4×D13—41no—
81C2×C4×D13—41no—
82C2×C4×D13—41no—
83C2×C4×D13C2×Q812yes—
84C2×C4×D13#4112yes—
85C2×#1057—24no—
86C2×#1057—42no—
87C2×#1057—42no—
88C13×C4⋊C4—41no—
89C13×C4⋊C4—41no—
90C13×C4⋊C4—42no—
91C42×C13—41no—
92#6103—42no—
93#6103—42no—
94C4⋊Dic13—42no—
95C4⋊Dic13—41no—
96C4⋊Dic13—41no—
97#6101—42no—
98#6101—42no—
99C4×Dic13—22no—
100C4×Dic13—22no—
101C4×Dic13—41no—
102#2851—131no—
103C4×C22⋊C8—131no—
104#1434—131no—
105#1294—132no—
106#1294—132no—
107C23×C13C2×C22⋊C411yescharacteristic
108C22×D13—21no—
109C22×D13—21no—
110C22×D13—21no—
111C22×D13—21no—
112C22×D13#12411yescharacteristic
113C22×D13C4⋊Q811yescharacteristic
114C22×D13#13512yes—
115C22×D13#13512yes—
116C2×#261—44no—
117C2×#261—44no—
118C2×#261—44no—
119C2×#261—82no—
120C2×#261—82no—
121C2×#261—82no—
122C2×#261—82no—
123C2×C4×C13—21no—
124C2×C4×C13—21no—
125C2×C4×C13—21no—
126C2×C4×C13—21no—
127C2×C4×C13—21no—
128C2×C4×C13—21no—
129C2×C4×C13—21no—
130C2×C4×C13—41no—
131C2×C4×C13—41no—
132C2×C4×C13—41no—
133C2×C4×C13—41no—
134C2×C4×C13—41no—
135C2×C4×C13—41no—
136C2×C4×C13#10412yes—
137C2×C4×C13C4×Q812yes—
138C2×Dic13—21no—
139C2×Dic13—21no—
140C2×Dic13—21no—
141C2×Dic13—21no—
142C2×Dic13—21no—
143C2×Dic13—21no—
144C2×Dic13—21no—
145C2×Dic13—41no—
146C2×Dic13—41no—
147C2×Dic13—41no—
148C2×Dic13—41no—
149C2×Dic13—41no—
150C2×Dic13—41no—
151C2×Dic13#9912yes—
152C2×Dic13C22⋊Q812yes—
153C4×D13—42no—
154C4×D13—42no—
155C4×D13—44no—
156C4×D13—44no—
157#1057—44no—
158C2×#125—131no—
159C22×C42—131no—
160C2×C22⋊C8—132no—
161C2×C4×C8—261no—
162#389—131no—
163#389#26111yescharacteristic, complemented
164#387—261no—
165#387—261no—
166#385—261no—
167#385—261no—
168#382—131no—
169#380—131no—
170#380—131no—
171C2×#95—132no—
172C2×#95—261no—
173C2×#95—261no—
174#336—261no—
175C22×C13#39111yescharacteristic
176C22×C13C2×#9911yescharacteristic
177C22×C13#41011yescharacteristic
178C22×C13#41611yescharacteristic
179C22×C13#41611yescharacteristic
180C22×C13C2×#10411yescharacteristic
181C22×C13#42111yescharacteristic
182C2×D13—21no—
183C2×D13—21no—
184C2×D13—21no—
185C2×D13—21no—
186C2×D13—22no—
187C2×D13—22no—
188C2×D13—22no—
189C2×D13—22no—
190C2×D13#48812yes—
191C2×D13#49912yes—
192#261—84no—
193C4×C13—22no—
194C4×C13—22no—
195C4×C13—41no—
196C4×C13—81no—
197C4×C13—81no—
198Dic13—22no—
199Dic13—22no—
200Dic13—41no—
201Dic13—81no—
202Dic13—81no—
203C23×C4—131no—
204C23×C4—131no—
205C23×C4—131no—
206C23×C4—262no—
207C22×C8—262no—
208#125—522no—
209C2×C4⋊C4—21no—
210C2×C4⋊C4—131no—
211C2×C4⋊C4—131no—
212C2×C4⋊C4—261no—
213C2×C4⋊C4—261no—
214C2×C4⋊C4—261no—
215C2×C4⋊C4C2×#26111yescharacteristic
216C2×C4⋊C4C2×#26111yescharacteristic
217C2×C22⋊C4—261no—
218C2×C22⋊C4—261no—
219C2×C42—131no—
220C2×C42—131no—
221C2×C42—131no—
222C2×C42—522no—
223C2×C42C2×#26111yescharacteristic
224C22⋊C8—134no—
225C22⋊C8—262no—
226C4×C8—522no—
227#95—21no—
228#95—261no—
229#95—261no—
230#95—261no—
231#95—261no—
232#95—264no—
233#95—264no—
234#95—261no—
235#95—522no—
236C2×C13#150011yescharacteristic
237C2×C13#150111yescharacteristic
238C2×C13#151611yescharacteristic
239C2×C13#152111yescharacteristic
240C2×C13#198611yescharacteristic
241C2×C13#199111yescharacteristic
242C2×C13#199611yescharacteristic
243D13—22no—
244D13—22no—
245C24—131no—
246C22×C4—21no—
247C22×C4—21no—
248C22×C4—131no—
249C22×C4—131no—
250C22×C4—132no—
251C22×C4—132no—
252C22×C4—131no—
253C22×C4—262no—
254C22×C4—262no—
255C22×C4—262no—
256C22×C4—262no—
257C22×C4—264no—
258C22×C4—261no—
259C22×C4—261no—
260C22×C4—521no—
261C22×C4—521no—
262C22×C4—521no—
263C22×C4—521no—
264C22×C4—522no—
265C22×C4—522no—
266C22×C4—522no—
267C22×C4—522no—
268C22×C4—522no—
269C22×C4—522no—
270C22×C4C22⋊#26111yescharacteristic
271C22×C4C22⋊#26111yescharacteristic
272C22×C4C22×#26111yescharacteristic
273C2×C8—264no—
274C2×C8—522no—
275C2×C8—522no—
276C4⋊C4—41no—
277C4⋊C4—41no—
278C4⋊C4—42no—
279C4⋊C4—521no—
280C4⋊C4—521no—
281C4⋊C4—522no—
282C4⋊C4—522no—
283C4⋊C4—522no—
284C22⋊C4—522no—
285C22⋊C4—522no—
286C42—41no—
287C42—262no—
288C42—262no—
289C42—521no—
290C13#988611yescharacteristic, complemented, Sylow
291C23—131no—
292C23—131no—
293C23—132no—
294C23—132no—
295C23—261no—
296C23—261no—
297C23—261no—
298C23—261no—
299C23C2×C22⋊#26111yescharacteristic
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—41no—
308C2×C4—41no—
309C2×C4—41no—
310C2×C4—41no—
311C2×C4—41no—
312C2×C4—41no—
313C2×C4—132no—
314C2×C4—132no—
315C2×C4—261no—
316C2×C4—261no—
317C2×C4—261no—
318C2×C4—261no—
319C2×C4—261no—
320C2×C4—261no—
321C2×C4—261no—
322C2×C4—522no—
323C2×C4—522no—
324C2×C4—524no—
325C2×C4—524no—
326C2×C4—524no—
327C2×C4—524no—
328C2×C4—524no—
329C2×C4—521no—
330C2×C4—521no—
331C2×C4—521no—
332C2×C4—521no—
333C2×C4—521no—
334C2×C4—521no—
335C2×C4—1042no—
336C2×C4—1042no—
337C2×C4—1042no—
338C2×C4—1042no—
339C2×C4#8811812yes—
340C2×C4Q8×#26112yes—
341C8—524no—
342C22—132no—
343C22—132no—
344C22—261no—
345C22—261no—
346C22—261no—
347C22—261no—
348C22—262no—
349C22—262no—
350C22—262no—
351C22—262no—
352C22#1171911611yescharacteristic
353C22#1171914011yescharacteristic
354C22D13⋊#9911yescharacteristic
355C22C2×#8811811yescharacteristic
356C22(C2×#261)⋊Q811yescharacteristic
357C22#1171916511yescharacteristic
358C22#1171916511yescharacteristic
359C4—22no—
360C4—22no—
361C4—41no—
362C4—81no—
363C4—81no—
364C4—262no—
365C4—262no—
366C4—521no—
367C4—1044no—
368C4—1041no—
369C4—1041no—
370C2—262no—
371C2—262no—
372C2#1313020911yescharacteristic
373C2#1313021411yescharacteristic
374C2#1313026111yescharacteristic
375C2#1313027811yescharacteristic
376C2#1313101111yescharacteristic
377C2#1313101811yescharacteristic
378C2#1313102711yescharacteristic
subgroupG/H
centerC23C2×C22⋊#261
commutatorC22×C4×C13C22×C4
FrattiniC22×C4C22×#261
FittingC13×#389C4
socleC23×C13C2×C22⋊C4
prime radicalC23×D13C2×D4
cosocleC22×C4×D13C23
hypercenter#389#261
hypocenterC13#9886
LCSG ▷ C22×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
6. C2×#88144C4semidirect
13. C13×#389C4semidirect
18. #11718638C4semidirect
19. #11718589C4semidirect
163. #389#261semidirect
290. C13#9886semidirect

Maximal subgroups

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

subgroupindex
C4×#881112
#131300122
#131297092
#131231452
#988613