Finite Group Databasebeta

← C2×#13067697 #14729653

Subgroups — C2×#13067697 #14729653

Order 2816.

1190 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1190 conjugacy classes of subgroups — too many to draw. Only its 203 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×#10623265C211yesmaximal, characteristic, complemented
2C2×#10622685C212yesmaximal, complemented
3#13067697C218yesmaximal, direct product factor
4C2×#10622184C211yesmaximal, characteristic, complemented
5C2×#10622097C212yesmaximal, complemented
6C2×C11×#492C211yesmaximal, characteristic, complemented
7C22×C11×SD16—22no—
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×#67000—22no—
11C22×#4323—22no—
12#10623265—22no—
13#10623265—24no—
14#10623265C2214yescomplemented
15C2×#66948—22no—
16C2×#66945—22no—
17C2×C4×D44C2212yes—
18C11×#492—22no—
19C11×#492C2214yescomplemented
20C2×C4×C8×C11C2211yescharacteristic
21C2×#66896—22no—
22#10622685—24no—
23#10622685C2218yescomplemented
24C2×C4⋊(C11⋊C8)C2212yes—
25#10622184C2214yescomplemented
26#10622097C2218yescomplemented
27C22×Q8×C11D412yes—
28C22×D4×C11—22no—
29C22×D4×C11—21no—
30C22×D44—22no—
31C22×D44D412yes—
32C22×C4×D11—22no—
33C2×C11×SD16—28no—
34C2×C11×SD16—48no—
35C22×C8×C11—21no—
36C11×C4⋊Q8—22no—
37C11×C4⋊Q8D412yes—
38C11×C4⋊Q8C2312yes—
39C11×#127—21no—
40C11×#127—22no—
41C11×#127C2312yes—
42C2×C11×C4⋊C4—22no—
43C2×C42×C11C2311yescharacteristic
44#67000—28no—
45#67000—28no—
46C2×#4323—28no—
47C2×#4323—48no—
48C2×(C2×D11)⋊C4—24no—
49C2×(C2×D11)⋊C4—22no—
50C2×C4⋊Dic11D412yes—
51C2×C4×Dic11—22no—
52C22×C11⋊C8—22no—
53#66948—28no—
54#66948—28no—
55#66945—28no—
56#66945—28no—
57C4×D44—22no—
58C4×D44—22no—
59C4×D44D414yes—
60C4×D44C2314yes—
61C4×C8×C11—21no—
62C4×C8×C11C2312yes—
63#66896—28no—
64C4⋊(C11⋊C8)—22no—
65C4⋊(C11⋊C8)C2314yes—
66C2×#1624—111nomaximal, Sylow
67C24×C11—41no—
68C23×D11—22no—
69C2×Q8×C11—22no—
70C2×Q8×C11—44no—
71C2×Q8×C11C2×D414yes—
72C2×D4×C11—24no—
73C2×D4×C11—22no—
74C2×D4×C11—44no—
75C2×D4×C11—41no—
76C2×D4×C11—42no—
77C2×D4×C11—44no—
78C2×D4×C11—44no—
79C22×C4×C11—22no—
80C22×C4×C11C2×D411yescharacteristic
81C22×C4×C11C2×D412yes—
82C22×Dic11—22no—
83C2×D44—28no—
84C2×D44—22no—
85C2×D44—24no—
86C2×D44—24no—
87C2×D44—84no—
88C2×D44C2×D414yes—
89C2×C4×D11—24no—
90C2×C4×D11—24no—
91C2×C4×D11—44no—
92C2×C4×D11—44no—
93C11×SD16—416no—
94C2×C8×C11—24no—
95C2×C8×C11—22no—
96C11×C4⋊C4—24no—
97C11×C4⋊C4—24no—
98C42×C11C2×D412yes—
99C42×C11C2×D411yescharacteristic
100C42×C11C2411yescharacteristic
101#4323—416no—
102(C2×D11)⋊C4—216no—
103(C2×D11)⋊C4—24no—
104(C2×D11)⋊C4—24no—
105C4⋊Dic11—22no—
106C4⋊Dic11C2×D414yes—
107C4×Dic11—28no—
108C2×C11⋊C8—24no—
109C2×C11⋊C8—44no—
110C2×#555—111no—
111C2×#492D1111yescharacteristic, complemented
112C2×#459—112no—
113#1624—118no—
114C2×#333—111no—
115C2×D4⋊C8—112no—
116C23×C11—42no—
117C23×C11—84no—
118C23×C11—82no—
119C23×C11#12011yescharacteristic
120C22×D11—24no—
121C22×D11—44no—
122C22×D11—44no—
123C22×D11—44no—
124Q8×C11—44no—
125Q8×C11—82no—
126D4×C11—44no—
127D4×C11—44no—
128D4×C11—44no—
129D4×C11—82no—
130D4×C11—84no—
131C2×C4×C11—22no—
132C2×C4×C11—24no—
133C2×C4×C11—44no—
134C2×C4×C11#12011yescharacteristic
135C2×C4×C11#12012yes—
136C2×C4×C11#13514yes—
137C2×C4×C11AGL(1,ℤ/8)14yes—
138C2×C4×C11C22×D412yes—
139C2×C4×C11C22×D411yescharacteristic
140C2×Dic11—24no—
141C2×Dic11—44no—
142D44—24no—
143D44—24no—
144D44—44no—
145D44—88no—
146C4×D11—44no—
147C4×D11—44no—
148C4×D11—48no—
149C8×C11—24no—
150C11⋊C8—44no—
151C22×SD16—22no—
152C22×D8—222no—
153#555—114no—
154#555—224no—
155#555—222no—
156C2×C4⋊Q8C2×D1111yescharacteristic
157C2×#127C2×D1111yescharacteristic
158C2×#124—222no—
159C2×#121—222no—
160C2×C4×D4—112no—
161C2×#117—222no—
162#492—22no—
163#492C2×D1114yescomplemented
164#459—118no—
165#459—224no—
166C2×C4⋊C8—112no—
167C2×#102—222no—
168C2×C4×C8C2×D1111yescharacteristic
169#333—114no—
170D4⋊C8—118no—
171C22×C11—84no—
172C22×C11—82no—
173C22×C11—164no—
174C22×C11#44914yes—
175C22×C11#45312yes—
176C22×C11C2×#12011yescharacteristic
177C2×D11—44no—
178C2×D11—44no—
179C2×D11—44no—
180C2×D11—88no—
181C4×C11—21no—
182C4×C11—21no—
183C4×C11—44no—
184C4×C11#44914yes—
185C4×C11C2×#13512yes—
186C4×C11C2×AGL(1,ℤ/8)12yes—
187Dic11—44no—
188C22×Q8C22⋊D1112yes—
189C22×D4—22no—
190C22×D4—21no—
191C22×D4—112no—
192C22×D4—222no—
193C23×C4—222no—
194C2×SD16—28no—
195C2×SD16—48no—
196C2×D8—228no—
197C2×D8—448no—
198C22×C8—21no—
199C22×C8—222no—
200C4⋊Q8—22no—
201C4⋊Q8C22⋊D1112yes—
202C4⋊Q8C22×D1112yes—
203#127—22no—
204#127—21no—
205#127C22×D1112yes—
206#124—228no—
207#124—228no—
208#121—228no—
209#121—228no—
210C4×D4—114no—
211C4×D4—114no—
212C4×D4—222no—
213C4×D4—222no—
214#117—228no—
215#117—228no—
216C2×C4⋊C4—22no—
217C2×C4⋊C4—112no—
218C2×C22⋊C4—224no—
219C2×C22⋊C4—222no—
220C2×C42—222no—
221C2×C42C22×D1111yescharacteristic
222C4⋊C8—114no—
223C4⋊C8—222no—
224#102—228no—
225C4×C8—21no—
226C4×C8C22×D1112yes—
227C2×C11—162no—
228C2×C11#162414yescomplemented
229C2×C11C2×#44912yes—
230C2×C11C2×#45311yescharacteristic
231D11—84no—
232C24—41no—
233C24—222no—
234C2×Q8—22no—
235C2×Q8—44no—
236C2×Q8C2×C22⋊D1114yes—
237C2×D4—24no—
238C2×D4—22no—
239C2×D4—44no—
240C2×D4—44no—
241C2×D4—44no—
242C2×D4—41no—
243C2×D4—42no—
244C2×D4—114no—
245C2×D4—228no—
246C2×D4—224no—
247C2×D4—224no—
248C2×D4—222no—
249C2×D4—884no—
250C22×C4—22no—
251C22×C4—222no—
252C22×C4—224no—
253C22×C4—224no—
254C22×C4—444no—
255C22×C4—444no—
256C22×C4D4×D1112yes—
257C22×C4C2×C22⋊D1111yescharacteristic
258SD16—416no—
259D8—4416no—
260C2×C8—24no—
261C2×C8—22no—
262C2×C8—224no—
263C2×C8—444no—
264C4⋊C4—24no—
265C4⋊C4—24no—
266C4⋊C4—114no—
267C4⋊C4—222no—
268C22⋊C4—2216no—
269C22⋊C4—224no—
270C22⋊C4—224no—
271C42—228no—
272C42D4×D1112yes—
273C42C2×C22⋊D1111yescharacteristic
274C42C23×D1111yescharacteristic
275C11C2×#162411yescharacteristic, complemented, Sylow
276C23—42no—
277C23—84no—
278C23—82no—
279C23—224no—
280C23—444no—
281C23—444no—
282C23—444no—
283C23#6699011yescharacteristic
284Q8—44no—
285Q8—82no—
286D4—44no—
287D4—44no—
288D4—44no—
289D4—82no—
290D4—84no—
291D4—224no—
292D4—224no—
293D4—444no—
294D4—888no—
295C2×C4—22no—
296C2×C4—24no—
297C2×C4—44no—
298C2×C4—224no—
299C2×C4—444no—
300C2×C4—444no—
301C2×C4—444no—
302C2×C4—448no—
303C2×C4#6696714yes—
304C2×C4#6696914yes—
305C2×C4#6699011yescharacteristic
306C2×C4#6699012yes—
307C2×C4C2×D4×D1112yes—
308C2×C4C22×C22⋊D1111yescharacteristic
309C8—24no—
310C8—444no—
311C22—84no—
312C22—82no—
313C22—164no—
314C22—444no—
315C22—444no—
316C22—444no—
317C22—888no—
318C22#1062269012yes—
319C22#1062278514yes—
320C22C2×#6699011yescharacteristic
321C4—21no—
322C4—21no—
323C4—44no—
324C4—444no—
325C4#1062278514yes—
326C4C2×#6696712yes—
327C4C2×#6696912yes—
328C2—162no—
329C2—884no—
330C2#1306769714yesdirect product factor
331C2C2×#1062278512yes—
332C2C2×#1062269011yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#492C2
socleC23×C11#120
hypercenterC2×#492D11
hypocenterC11C2×#1624
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#492

Complements

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

NH ≅ G/Ntype
1. C2×#10623265C2semidirect
2. C2×#10622685C2semidirect
3. #13067697C2direct (N × H)
4. C2×#10622184C2semidirect
5. C2×#10622097C2semidirect
6. C2×C11×#492C2semidirect
14. #10623265C22semidirect
19. C11×#492C22semidirect
23. #10622685C22semidirect
25. #10622184C22semidirect
26. #10622097C22semidirect
111. C2×#492D11semidirect
163. #492C2×D11semidirect
228. C2×C11#1624semidirect
275. C11C2×#1624semidirect
330. C2#13067697direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232652
C2×#106226852
#130676972
C2×#106221842
C2×#106220972
C2×C11×#4922
C2×#162411