Finite Group Databasebeta

← C2×#13067735 #14729409

Subgroups — C2×#13067735 #14729409

Order 2816.

1074 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1074 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
2C2×#10622704C212yesmaximal, complemented
3#13067735C218yesmaximal, direct product factor
4C2×#10622182C211yesmaximal, characteristic
5C2×#10622094C212yesmaximal, complemented
6C2×C11×#492C211yesmaximal, characteristic
7C22×C11×SD16—22no—
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×#66989—22no—
11C2×#66988—22no—
12C2×D4×Dic11—22no—
13#10623244—22no—
14#10623244—24no—
15#10623244C2214yes—
16C2×C4×Dic22C2212yes—
17C11×#492—22no—
18C11×#492C2214yes—
19C2×C4×C8×C11C2211yescharacteristic
20#10622704—24no—
21#10622704C2218yescomplemented
22C2×#66874—22no—
23C2×#66871—22no—
24C2×C4⋊(C11⋊C8)C2212yes—
25#10622182C2214yes—
26#10622094C2218yescomplemented
27C22×Q8×C11—21no—
28C22×D4×C11—22no—
29C22×D4×C11D412yes—
30C23×Dic11—22no—
31C22×Dic22D412yes—
32C2×C11×SD16—28no—
33C2×C11×SD16—48no—
34C22×C8×C11—21no—
35C11×C4⋊Q8—22no—
36C11×C4⋊Q8—21no—
37C11×C4⋊Q8C2312yes—
38C11×#127—22no—
39C11×#127D412yes—
40C11×#127C2312yes—
41C2×C11×C4⋊C4—22no—
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×C4⋊Dic11D412yes—
52C2×Dic11⋊C4—22no—
53C2×C4×Dic11—22no—
54C22×C11⋊C8—22no—
55C4×Dic22—22no—
56C4×Dic22—22no—
57C4×Dic22D414yes—
58C4×Dic22C2314yes—
59C4×C8×C11—21no—
60C4×C8×C11C2312yes—
61#66874—28no—
62#66871—28no—
63C4⋊(C11⋊C8)—22no—
64C4⋊(C11⋊C8)C2314yes—
65C2×#1630—111nomaximal, Sylow
66C24×C11—22no—
67C2×Q8×C11—22no—
68C2×Q8×C11—44no—
69C2×Q8×C11—41no—
70C2×D4×C11—24no—
71C2×D4×C11—22no—
72C2×D4×C11—24no—
73C2×D4×C11—44no—
74C2×D4×C11—44no—
75C2×D4×C11—44no—
76C2×D4×C11C2×D414yes—
77C22×C4×C11—41no—
78C22×C4×C11C2×D411yescharacteristic
79C22×C4×C11C2×D412yes—
80C22×Dic11—28no—
81C22×Dic11—22no—
82C22×Dic11—22no—
83C22×Dic11—84no—
84C2×Dic22—22no—
85C2×Dic22—24no—
86C2×Dic22—24no—
87C2×Dic22C2×D414yes—
88C11×SD16—416no—
89C2×C8×C11—24no—
90C2×C8×C11—22no—
91C11×C4⋊C4—24no—
92C11×C4⋊C4—42no—
93C42×C11C2×D412yes—
94C42×C11C2×D411yescharacteristic
95C42×C11C2411yescharacteristic
96C22⋊Dic11—216no—
97C22⋊Dic11—28no—
98C4⋊Dic11—22no—
99C4⋊Dic11C2×D414yes—
100Dic11⋊C4—24no—
101Dic11⋊C4—24no—
102C4×Dic11—24no—
103C4×Dic11—24no—
104C2×C11⋊C8—24no—
105C2×C11⋊C8—44no—
106C2×#559—111no—
107C2×#492D1111yescharacteristic
108C2×#477—112no—
109#1630—118no—
110C2×#331—111no—
111C2×Q8⋊C8—112no—
112C23×C11—24no—
113C23×C11—48no—
114C23×C11—44no—
115C23×C11#12011yescharacteristic
116Q8×C11—44no—
117Q8×C11—82no—
118D4×C11—44no—
119D4×C11—44no—
120D4×C11—44no—
121D4×C11—48no—
122D4×C11—82no—
123C2×C4×C11—22no—
124C2×C4×C11—42no—
125C2×C4×C11—82no—
126C2×C4×C11#12011yescharacteristic
127C2×C4×C11#12012yes—
128C2×C4×C11#13514yes—
129C2×C4×C11#13714yes—
130C2×C4×C11C22×D412yes—
131C2×C4×C11C22×D411yescharacteristic
132C2×Dic11—24no—
133C2×Dic11—24no—
134C2×Dic11—44no—
135C2×Dic11—44no—
136C2×Dic11—88no—
137Dic22—24no—
138Dic22—24no—
139Dic22—44no—
140C8×C11—24no—
141C11⋊C8—44no—
142C22×SD16—22no—
143#559—114no—
144#559—224no—
145#559—222no—
146C2×C4⋊Q8C2×D1111yescharacteristic
147C2×#127C2×D1111yescharacteristic
148C2×#124—222no—
149C2×#123—222no—
150C2×C4×Q8—112no—
151C2×C4×D4—222no—
152#492—22no—
153#492C2×D1114yes—
154#477—118no—
155#477—224no—
156C2×#107—222no—
157C2×C4⋊C8—112no—
158C2×#103—222no—
159C2×C4×C8C2×D1111yescharacteristic
160#331—114no—
161Q8⋊C8—118no—
162C22×C11—48no—
163C22×C11—44no—
164C22×C11—88no—
165C22×C11#45214yes—
166C22×C11#45312yes—
167C22×C11C2×#12011yescharacteristic
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—82no—
171C4×C11#45214yes—
172C4×C11C2×#13512yes—
173C4×C11C2×#13712yes—
174Dic11—44no—
175Dic11—44no—
176C22×Q8—21no—
177C22×Q8—112no—
178C22×D4—22no—
179C22×D4C22⋊D1112yes—
180C23×C4—222no—
181C2×SD16—28no—
182C2×SD16—48no—
183C22×C8—21no—
184C22×C8—222no—
185C4⋊Q8—22no—
186C4⋊Q8—21no—
187C4⋊Q8C22×D1112yes—
188#127—22no—
189#127C22⋊D1112yes—
190#127C22×D1112yes—
191#124—228no—
192#124—228no—
193#123—228no—
194#123—228no—
195C4×Q8—114no—
196C4×Q8—114no—
197C4×Q8—222no—
198C4×Q8—222no—
199C4×D4—228no—
200C4×D4—228no—
201C2×C4⋊C4—22no—
202C2×C4⋊C4—112no—
203C2×C4⋊C4—222no—
204C2×C22⋊C4—224no—
205C2×C22⋊C4—222no—
206C2×C42—222no—
207C2×C42C22×D1111yescharacteristic
208#107—228no—
209C4⋊C8—114no—
210C4⋊C8—222no—
211#103—228no—
212C4×C8—21no—
213C4×C8C22×D1112yes—
214C2×C11—84no—
215C2×C11#163014yescomplemented
216C2×C11C2×#45212yes—
217C2×C11C2×#45311yescharacteristic
218C24—22no—
219C2×Q8—22no—
220C2×Q8—44no—
221C2×Q8—41no—
222C2×Q8—114no—
223C2×Q8—222no—
224C2×Q8—224no—
225C2×Q8—224no—
226C2×D4—24no—
227C2×D4—22no—
228C2×D4—24no—
229C2×D4—44no—
230C2×D4—44no—
231C2×D4—44no—
232C2×D4C2×C22⋊D1114yes—
233C22×C4—41no—
234C22×C4—222no—
235C22×C4—222no—
236C22×C4—228no—
237C22×C4—884no—
238C22×C4D4×D1112yes—
239C22×C4C2×C22⋊D1111yescharacteristic
240SD16—416no—
241C2×C8—24no—
242C2×C8—22no—
243C2×C8—224no—
244C2×C8—444no—
245C4⋊C4—24no—
246C4⋊C4—42no—
247C4⋊C4—114no—
248C4⋊C4—222no—
249C4⋊C4—224no—
250C4⋊C4—224no—
251C22⋊C4—2216no—
252C22⋊C4—228no—
253C42—224no—
254C42—224no—
255C42D4×D1112yes—
256C42C2×C22⋊D1111yescharacteristic
257C42C23×D1111yescharacteristic
258C11C2×#163011yescharacteristic, complemented, Sylow
259C23—24no—
260C23—48no—
261C23—44no—
262C23#6699011yescharacteristic
263Q8—44no—
264Q8—82no—
265Q8—224no—
266Q8—224no—
267Q8—444no—
268D4—44no—
269D4—44no—
270D4—44no—
271D4—48no—
272D4—82no—
273C2×C4—22no—
274C2×C4—42no—
275C2×C4—82no—
276C2×C4—224no—
277C2×C4—224no—
278C2×C4—444no—
279C2×C4—444no—
280C2×C4—888no—
281C2×C4#6696814yes—
282C2×C4#6696914yes—
283C2×C4#6699011yescharacteristic
284C2×C4#6699012yes—
285C2×C4C2×D4×D1112yes—
286C2×C4C22×C22⋊D1111yescharacteristic
287C8—24no—
288C8—444no—
289C22—48no—
290C22—44no—
291C22—88no—
292C22#1062269012yes—
293C22#1062278614yes—
294C22C2×#6699011yescharacteristic
295C4—21no—
296C4—21no—
297C4—82no—
298C4—444no—
299C4—444no—
300C4#1062278614yes—
301C4C2×#6696812yes—
302C4C2×#6696912yes—
303C2—84no—
304C2#1306773514yesdirect product factor
305C2C2×#1062278612yes—
306C2C2×#1062269011yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#492C2
socleC23×C11#120
prime radicalC2×C11×#127C22
hypercenterC2×#492D11
hypocenterC11C2×#1630
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
2. C2×#10622704C2semidirect
3. #13067735C2direct (N × H)
5. C2×#10622094C2semidirect
21. #10622704C22semidirect
26. #10622094C22semidirect
215. C2×C11#1630semidirect
258. C11C2×#1630semidirect
304. C2#13067735direct (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×#106227042
#130677352
C2×#106221822
C2×#106220942
C2×C11×#4922
C2×#163011