Finite Group Databasebeta

← C2×#13067733 #14729384

Subgroups — C2×#13067733 #14729384

Order 2816.

1722 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 1722 conjugacy classes of subgroups — too many to draw. Only its 219 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×#10623248C211yesmaximal, characteristic
2C2×#10622689C211yesmaximal, characteristic, complemented
3C2×#10622455C212yesmaximal, complemented
4#13067733C218yesmaximal, direct product factor
5C2×#10622121C212yesmaximal, complemented
6C2×C11×#331C211yesmaximal, characteristic, complemented
7C22×D4×D11—22no—
8C2×C11×#127C2211yescharacteristic
9C2×#66991—22no—
10C2×#66990—22no—
11C22×#4324—22no—
12#10623248—22no—
13#10623248—24no—
14#10623248C2214yes—
15C2×C4×D44C2212yes—
16C2×#66922C2211yescharacteristic, complemented
17C2×C11×C4⋊C8C2212yescomplemented
18C2×#66885—22no—
19C2×#66881—22no—
20#10622689—22no—
21#10622689C2214yescomplemented
22C2×C4×C11⋊C8C2211yescharacteristic, complemented
23#10622455—24no—
24#10622455C2218yescomplemented
25C11×#331C2214yescomplemented
26#10622121C2218yescomplemented
27C24×D11—22no—
28C22×D4×C11—22no—
29C22×D4×C11D412yes—
30C22×C22⋊D11—24no—
31C2×D4×D11—28no—
32C2×D4×D11—28no—
33C2×D4×D11—48no—
34C2×D4×D11—48no—
35C22×D44D412yes—
36C22×C4×D11—22no—
37C22×Dic22—21no—
38C22×C8×C11—22no—
39C11×#127—22no—
40C11×#127D412yes—
41C11×#127C2312yes—
42C2×C42×C11C2311yescharacteristic
43C2×C22⋊Dic11—22no—
44#66991—28no—
45#66991—28no—
46#66990—28no—
47#66990—28no—
48C2×#4324—28no—
49C2×#4324—48no—
50C2×(C2×D11)⋊C4—22no—
51C2×C4⋊Dic11—22no—
52C2×C4⋊Dic11D412yes—
53C22×C11⋊C8—21no—
54C4×D44—22no—
55C4×D44—22no—
56C4×D44D414yes—
57C4×D44C2314yes—
58#66922—22no—
59#66922—21no—
60#66922C2312yescomplemented
61C11×C4⋊C8—22no—
62C11×C4⋊C8C2314yescomplemented
63#66885—28no—
64#66881—28no—
65C4×C11⋊C8—21no—
66C4×C11⋊C8C2312yescomplemented
67C2×#1629—111nomaximal, Sylow
68C24×C11—22no—
69C23×D11—22no—
70C23×D11—28no—
71C23×D11—416no—
72C23×D11—84no—
73C2×D4×C11—24no—
74C2×D4×C11—22no—
75C2×D4×C11—24no—
76C2×D4×C11—44no—
77C2×D4×C11—44no—
78C2×D4×C11—44no—
79C2×D4×C11C2×D414yes—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D412yes—
82C2×C22⋊D11—216no—
83C2×C22⋊D11—416no—
84C22×Dic11—22no—
85C22×Dic11—41no—
86D4×D11—416no—
87D4×D11—432no—
88D4×D11—416no—
89C2×D44—22no—
90C2×D44—24no—
91C2×D44SD1618yescomplemented
92C2×D44C2×D414yes—
93C2×C4×D11—24no—
94C2×C4×D11—24no—
95C2×C4×D11—44no—
96C2×C4×D11—44no—
97C2×Dic22—22no—
98C2×Dic22—44no—
99C2×Dic22—41no—
100C2×C8×C11—24no—
101C2×C8×C11—44no—
102C42×C11C2×D411yescharacteristic
103C42×C11C2×D412yes—
104C42×C11C2411yescharacteristic
105C22⋊Dic11—28no—
106#4324—416no—
107(C2×D11)⋊C4—24no—
108(C2×D11)⋊C4—24no—
109C4⋊Dic11—22no—
110C4⋊Dic11—24no—
111C4⋊Dic11—42no—
112C4⋊Dic11C2×D414yes—
113C2×C11⋊C8—24no—
114C2×C11⋊C8—22no—
115C2×D42—111no—
116C2×#492—111no—
117C2×#476—112no—
118#1629—118no—
119C2×#331D1111yescharacteristic, complemented
120C2×D4⋊C8—112no—
121C23×C11—24no—
122C23×C11—48no—
123C23×C11—44no—
124C23×C11#12011yescharacteristic
125C22×D11—24no—
126C22×D11—28no—
127C22×D11—432no—
128C22×D11—44no—
129C22×D11—44no—
130C22×D11—88no—
131C22×D11—832no—
132D4×C11—44no—
133D4×C11—44no—
134D4×C11—44no—
135D4×C11—48no—
136D4×C11—82no—
137C2×C4×C11—22no—
138C2×C4×C11#12011yescharacteristic
139C2×C4×C11#12012yes—
140C2×C4×C11C2×SD1614yes—
141C2×C4×C11AGL(1,ℤ/8)14yes—
142C2×C4×C11C22×D411yescharacteristic
143C2×C4×C11C22×D412yes—
144C22⋊D11—432no—
145C2×Dic11—24no—
146C2×Dic11—44no—
147C2×Dic11—42no—
148C2×Dic11—82no—
149D44—24no—
150D44—28no—
151D44C2×SD1618yescomplemented
152C4×D11—44no—
153C4×D11—44no—
154C4×D11—48no—
155Dic22—44no—
156Dic22—82no—
157C8×C11—44no—
158C11⋊C8—24no—
159C23×D4—222no—
160C22×SD16—222no—
161D42—114no—
162D42—224no—
163D42—222no—
164C2×C4⋊Q8—111no—
165C2×#127C2×D1111yescharacteristic
166C2×#121—222no—
167C2×#120—222no—
168C2×C4×D4—112no—
169#492—114no—
170#492—222no—
171#476—118no—
172#476—224no—
173C2×#106—222no—
174C2×C4⋊C8C2×D1112yescomplemented
175C2×#102—222no—
176C2×C4×C8—111no—
177#331C2×D1114yescomplemented
178D4⋊C8—118no—
179C22×C11—48no—
180C22×C11—44no—
181C22×C11—88no—
182C22×C11#45014yes—
183C22×C11#45312yes—
184C22×C11C2×#12011yescharacteristic
185C2×D11—28no—
186C2×D11—416no—
187C2×D11—44no—
188C2×D11—44no—
189C2×D11—832no—
190C4×C11—21no—
191C4×C11—21no—
192C4×C11#45014yes—
193C4×C11C22×SD1612yes—
194C4×C11C2×AGL(1,ℤ/8)12yes—
195Dic11—44no—
196Dic11—82no—
197C25—222no—
198C22×Q8—221no—
199C22×D4—22no—
200C22×D4—112no—
201C22×D4—228no—
202C22×D4—228no—
203C22×D4—224no—
204C22×D4—448no—
205C22×D4—448no—
206C22×D4D4412yes—
207C23×C4—222no—
208C2×SD16—228no—
209C2×SD16—448no—
210C22×C8—22no—
211C22×C8—221no—
212C4⋊Q8—112no—
213C4⋊Q8—221no—
214C4⋊Q8—222no—
215#127—22no—
216#127D4412yes—
217#127C22×D1112yes—
218#121—228no—
219#121—228no—
220#120—228no—
221#120—228no—
222C4×D4—114no—
223C4×D4—114no—
224C4×D4—222no—
225C4×D4—222no—
226C2×C4⋊C4—112no—
227C2×C4⋊C4—222no—
228C2×C22⋊C4—222no—
229C2×C22⋊C4—222no—
230C2×C42C22×D1111yescharacteristic
231#106—228no—
232C4⋊C8—22no—
233C4⋊C8C22×D1114yescomplemented
234#102—228no—
235C4×C8—112no—
236C4×C8—221no—
237C2×C11—84no—
238C2×C11#162914yescomplemented
239C2×C11C2×#45012yes—
240C2×C11C2×#45311yescharacteristic
241D11—48no—
242C24—22no—
243C24—228no—
244C24—222no—
245C24—4416no—
246C24—884no—
247C2×Q8—222no—
248C2×Q8—444no—
249C2×Q8—441no—
250C2×D4—24no—
251C2×D4—22no—
252C2×D4—24no—
253C2×D4—44no—
254C2×D4—44no—
255C2×D4—44no—
256C2×D4—118no—
257C2×D4—114no—
258C2×D4—2216no—
259C2×D4—222no—
260C2×D4—224no—
261C2×D4—4416no—
262C2×D4—4416no—
263C2×D4—4432no—
264C2×D4—4416no—
265C2×D4C2×D4414yes—
266C22×C4—222no—
267C22×C4—224no—
268C22×C4—224no—
269C22×C4—444no—
270C22×C4—444no—
271C22×C4—441no—
272C22×C4C2×D4411yescharacteristic
273C22×C4D4×D1112yes—
274SD16—4416no—
275C2×C8—24no—
276C2×C8—44no—
277C2×C8—224no—
278C2×C8—222no—
279C4⋊C4—114no—
280C4⋊C4—222no—
281C4⋊C4—224no—
282C4⋊C4—442no—
283C22⋊C4—228no—
284C22⋊C4—224no—
285C22⋊C4—224no—
286C42C2×D4411yescharacteristic
287C42D4×D1112yes—
288C42C23×D1111yescharacteristic
289C11C2×#162911yescharacteristic, complemented, Sylow
290C23—24no—
291C23—44no—
292C23—48no—
293C23—224no—
294C23—228no—
295C23—4432no—
296C23—444no—
297C23—444no—
298C23—888no—
299C23—8832no—
300C23#6693511yescharacteristic
301Q8—444no—
302Q8—882no—
303D4—44no—
304D4—44no—
305D4—44no—
306D4—48no—
307D4—82no—
308D4—118no—
309D4—224no—
310D4—228no—
311D4—4432no—
312C2×C4—22no—
313C2×C4—224no—
314C2×C4—444no—
315C2×C4—444no—
316C2×C4—444no—
317C2×C4—448no—
318C2×C4—442no—
319C2×C4—882no—
320C2×C4#6693511yescharacteristic
321C2×C4#6693512yes—
322C2×C4#6696414yes—
323C2×C4SD16×D1114yes—
324C2×C4C22×D4411yescharacteristic
325C2×C4C2×D4×D1112yes—
326C8—44no—
327C8—224no—
328C22—48no—
329C22—44no—
330C22—88no—
331C22—228no—
332C22—444no—
333C22—444no—
334C22—4416no—
335C22—8832no—
336C22#1062236012yes—
337C22#1062238914yes—
338C22C2×#6693511yescharacteristic
339C4—21no—
340C4—21no—
341C4—444no—
342C4—882no—
343C4#1062238914yes—
344C4C2×#6696412yes—
345C4C2×SD16×D1112yes—
346C2—84no—
347C2—448no—
348C2#1306773314yesdirect product factor
349C2C2×#1062238912yes—
350C2C2×#1062236011yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#331C2
socleC23×C11#120
prime radicalC2×#10623248C2
hypercenterC2×#331D11
hypocenterC11C2×#1629
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#331

Complements

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

NH ≅ G/Ntype
2. C2×#10622689C2semidirect
3. C2×#10622455C2semidirect
4. #13067733C2direct (N × H)
5. C2×#10622121C2semidirect
6. C2×C11×#331C2semidirect
16. C2×#66922C22semidirect
17. C2×C11×C4⋊C8C22semidirect
21. #10622689C22semidirect
22. C2×C4×C11⋊C8C22semidirect
24. #10622455C22semidirect
25. C11×#331C22semidirect
26. #10622121C22semidirect
60. #66922C23semidirect
62. C11×C4⋊C8C23semidirect
66. C4×C11⋊C8C23semidirect
91. C2×D44SD16semidirect
119. C2×#331D11semidirect
151. D44C2×SD16semidirect
174. C2×C4⋊C8C2×D11semidirect
177. #331C2×D11semidirect
233. C4⋊C8C22×D11semidirect
238. C2×C11#1629semidirect
289. C11C2×#1629semidirect
348. C2#13067733direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232482
C2×#106226892
C2×#106224552
#130677332
C2×#106221212
C2×C11×#3312
C2×#162911