Finite Group Databasebeta

← C2×#13067673 #14729403

Subgroups — C2×#13067673 #14729403

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×#10623244C211yesmaximal, characteristic, complemented
2C2×#10622688C212yesmaximal, complemented
3#13067673C218yesmaximal, direct product factor
4C2×#10622182C211yesmaximal, characteristic, complemented
5C2×#10622094C212yesmaximal, complemented
6C2×C11×#493C211yesmaximal, characteristic
7C22×C11×D8—22no—
8C2×C11×#127C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×#66989—22no—
11C2×#66988—22no—
12C2×D4×Dic11—22no—
13C22×#4324—22no—
14#10623244—22no—
15#10623244—24no—
16#10623244C2214yescomplemented
17C2×C4×Dic22C2212yes—
18C11×#493—22no—
19C11×#493C2214yes—
20C2×C4×C8×C11C2211yescharacteristic
21C2×#66896—22no—
22#10622688—24no—
23#10622688C2218yescomplemented
24C2×C4⋊(C11⋊C8)C2212yes—
25#10622182C2214yescomplemented
26#10622094C2218yescomplemented
27C22×D4×C11—22no—
28C22×D4×C11—22no—
29C22×D4×C11—21no—
30C22×D4×C11D412yes—
31C23×Dic11—22no—
32C22×Dic22D412yes—
33C2×C11×D8—28no—
34C2×C11×D8—48no—
35C22×C8×C11—21no—
36C11×#127—22no—
37C11×#127—21no—
38C11×#127—22no—
39C11×#127D412yes—
40C11×#127C2312yes—
41C11×#127C2312yes—
42C2×C42×C11C2311yescharacteristic
43C2×C22⋊Dic11—24no—
44C2×C22⋊Dic11—22no—
45#66989—28no—
46#66989—28no—
47#66988—28no—
48#66988—28no—
49D4×Dic11—28no—
50D4×Dic11—28no—
51C2×#4324—28no—
52C2×#4324—48no—
53C2×C4⋊Dic11D412yes—
54C2×Dic11⋊C4—22no—
55C2×C4×Dic11—22no—
56C22×C11⋊C8—22no—
57C4×Dic22—22no—
58C4×Dic22—22no—
59C4×Dic22D414yes—
60C4×Dic22C2314yes—
61C4×C8×C11—21no—
62C4×C8×C11C2312yes—
63#66896—28no—
64C4⋊(C11⋊C8)—22no—
65C4⋊(C11⋊C8)C2314yes—
66C2×#1620—111nomaximal, Sylow
67C24×C11—22no—
68C24×C11—41no—
69C2×D4×C11—24no—
70C2×D4×C11—22no—
71C2×D4×C11—24no—
72C2×D4×C11—24no—
73C2×D4×C11—22no—
74C2×D4×C11—44no—
75C2×D4×C11—44no—
76C2×D4×C11—41no—
77C2×D4×C11—42no—
78C2×D4×C11—44no—
79C2×D4×C11—44no—
80C2×D4×C11—44no—
81C2×D4×C11—44no—
82C2×D4×C11C2×D414yes—
83C22×C4×C11C2×D411yescharacteristic
84C22×C4×C11C2×D412yes—
85C22×Dic11—28no—
86C22×Dic11—22no—
87C22×Dic11—22no—
88C22×Dic11—84no—
89C2×Dic22—22no—
90C2×Dic22—24no—
91C2×Dic22—24no—
92C2×Dic22C2×D414yes—
93C11×D8—416no—
94C2×C8×C11—24no—
95C2×C8×C11—22no—
96C42×C11C2×D412yes—
97C42×C11C2×D411yescharacteristic
98C42×C11C2411yescharacteristic
99C22⋊Dic11—216no—
100C22⋊Dic11—28no—
101#4324—416no—
102C4⋊Dic11—22no—
103C4⋊Dic11C2×D414yes—
104Dic11⋊C4—24no—
105Dic11⋊C4—24no—
106C4×Dic11—24no—
107C4×Dic11—24no—
108C2×C11⋊C8—24no—
109C2×C11⋊C8—44no—
110C2×#559—111no—
111C2×#493D1111yescharacteristic
112C2×#460—112no—
113#1620—118no—
114C2×#331—111no—
115C2×Q8⋊C8—112no—
116C23×C11—24no—
117C23×C11—48no—
118C23×C11—44no—
119C23×C11—42no—
120C23×C11—84no—
121C23×C11—82no—
122C23×C11#12011yescharacteristic
123D4×C11—44no—
124D4×C11—44no—
125D4×C11—44no—
126D4×C11—44no—
127D4×C11—44no—
128D4×C11—44no—
129D4×C11—48no—
130D4×C11—82no—
131D4×C11—82no—
132D4×C11—84no—
133C2×C4×C11—22no—
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—24no—
142C2×Dic11—44no—
143C2×Dic11—44no—
144C2×Dic11—88no—
145Dic22—24no—
146Dic22—24no—
147Dic22—44no—
148C8×C11—24no—
149C11⋊C8—44no—
150C22×SD16—222no—
151C22×D8—22no—
152#559—114no—
153#559—224no—
154#559—222no—
155C2×#127C2×D1111yescharacteristic
156C2×#127C2×D1111yescharacteristic
157C2×#124—222no—
158C2×#123—222no—
159C2×C4×Q8—112no—
160C2×C4×D4—222no—
161#493—22no—
162#493C2×D1114yes—
163#460—118no—
164#460—224no—
165C2×C4⋊C8—112no—
166C2×#102—222no—
167C2×C4×C8C2×D1111yescharacteristic
168#331—114no—
169Q8⋊C8—118no—
170C22×C11—48no—
171C22×C11—44no—
172C22×C11—88no—
173C22×C11—84no—
174C22×C11—82no—
175C22×C11—164no—
176C22×C11#44914yes—
177C22×C11#45312yes—
178C22×C11C2×#12011yescharacteristic
179C4×C11—21no—
180C4×C11—21no—
181C4×C11#44914yes—
182C4×C11C2×#13512yes—
183C4×C11C2×AGL(1,ℤ/8)12yes—
184Dic11—44no—
185Dic11—44no—
186C22×Q8—112no—
187C22×D4—22no—
188C22×D4—22no—
189C22×D4—21no—
190C22×D4C22⋊D1112yes—
191C23×C4—222no—
192C2×SD16—228no—
193C2×SD16—448no—
194C2×D8—28no—
195C2×D8—48no—
196C22×C8—21no—
197C22×C8—222no—
198#127—22no—
199#127—22no—
200#127—21no—
201#127C22⋊D1112yes—
202#127C22×D1112yes—
203#127C22×D1112yes—
204#124—228no—
205#124—228no—
206#123—228no—
207#123—228no—
208C4×Q8—114no—
209C4×Q8—114no—
210C4×Q8—222no—
211C4×Q8—222no—
212C4×D4—228no—
213C4×D4—228no—
214C2×C4⋊C4—112no—
215C2×C4⋊C4—222no—
216C2×C22⋊C4—224no—
217C2×C22⋊C4—222no—
218C2×C42—222no—
219C2×C42C22×D1111yescharacteristic
220C4⋊C8—114no—
221C4⋊C8—222no—
222#102—228no—
223C4×C8—21no—
224C4×C8C22×D1112yes—
225C2×C11—84no—
226C2×C11—162no—
227C2×C11#162014yescomplemented
228C2×C11C2×#44912yes—
229C2×C11C2×#45311yescharacteristic
230C24—22no—
231C24—41no—
232C2×Q8—114no—
233C2×Q8—222no—
234C2×Q8—224no—
235C2×Q8—224no—
236C2×D4—24no—
237C2×D4—22no—
238C2×D4—24no—
239C2×D4—24no—
240C2×D4—22no—
241C2×D4—44no—
242C2×D4—44no—
243C2×D4—44no—
244C2×D4—44no—
245C2×D4—44no—
246C2×D4—44no—
247C2×D4—41no—
248C2×D4—42no—
249C2×D4C2×C22⋊D1114yes—
250C22×C4—222no—
251C22×C4—222no—
252C22×C4—228no—
253C22×C4—884no—
254C22×C4D4×D1112yes—
255C22×C4C2×C22⋊D1111yescharacteristic
256SD16—4416no—
257D8—416no—
258C2×C8—24no—
259C2×C8—22no—
260C2×C8—224no—
261C2×C8—444no—
262C4⋊C4—114no—
263C4⋊C4—222no—
264C4⋊C4—224no—
265C4⋊C4—224no—
266C22⋊C4—2216no—
267C22⋊C4—228no—
268C42—224no—
269C42—224no—
270C42D4×D1112yes—
271C42C2×C22⋊D1111yescharacteristic
272C42C23×D1111yescharacteristic
273C11C2×#162011yescharacteristic, complemented, Sylow
274C23—24no—
275C23—48no—
276C23—44no—
277C23—42no—
278C23—84no—
279C23—82no—
280C23#6699011yescharacteristic
281Q8—224no—
282Q8—224no—
283Q8—444no—
284D4—44no—
285D4—44no—
286D4—48no—
287D4—44no—
288D4—44no—
289D4—44no—
290D4—44no—
291D4—82no—
292D4—82no—
293D4—84no—
294C2×C4—22no—
295C2×C4—224no—
296C2×C4—224no—
297C2×C4—444no—
298C2×C4—444no—
299C2×C4—888no—
300C2×C4#6696414yes—
301C2×C4#6696514yes—
302C2×C4#6699011yescharacteristic
303C2×C4#6699012yes—
304C2×C4C2×D4×D1112yes—
305C2×C4C22×C22⋊D1111yescharacteristic
306C8—24no—
307C8—444no—
308C22—48no—
309C22—44no—
310C22—88no—
311C22—84no—
312C22—82no—
313C22—164no—
314C22#1062269012yes—
315C22#1062277114yes—
316C22C2×#6699011yescharacteristic
317C4—21no—
318C4—21no—
319C4—444no—
320C4—444no—
321C4#1062277114yes—
322C4C2×#6696412yes—
323C4C2×#6696512yes—
324C2—84no—
325C2—162no—
326C2#1306767314yesdirect product factor
327C2C2×#1062277112yes—
328C2C2×#1062269011yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
Fitting, prime radicalC2×C11×#493C2
socleC23×C11#120
hypercenterC2×#493D11
hypocenterC11C2×#1620
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#493

Complements

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

NH ≅ G/Ntype
1. C2×#10623244C2semidirect
2. C2×#10622688C2semidirect
3. #13067673C2direct (N × H)
4. C2×#10622182C2semidirect
5. C2×#10622094C2semidirect
16. #10623244C22semidirect
23. #10622688C22semidirect
25. #10622182C22semidirect
26. #10622094C22semidirect
227. C2×C11#1620semidirect
273. C11C2×#1620semidirect
326. C2#13067673direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232442
C2×#106226882
#130676732
C2×#106221822
C2×#106220942
C2×C11×#4932
C2×#162011