Finite Group Databasebeta

← C2×#13067692 #14729641

Subgroups — C2×#13067692 #14729641

Order 2816.

1126 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 1126 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×#10623253C211yesmaximal, characteristic, complemented
2C2×#10622688C212yesmaximal
3#13067692C218yesmaximal, direct product factor
4C2×#10622184C211yesmaximal, characteristic, complemented
5C2×#10622094C212yesmaximal, complemented
6C2×C11×#492C211yesmaximal, characteristic
7C22×C11×SD16—22no—
8C2×C11×C4⋊Q8C2211yescharacteristic
9C2×C11×#127C2211yescharacteristic
10C2×#66997—22no—
11C22×#4324—22no—
12#10623253—22no—
13#10623253—24no—
14#10623253C2214yescomplemented
15C2×#66941—22no—
16C2×#66940—22no—
17C2×C4×Dic22C2212yes—
18C11×#492—22no—
19C11×#492C2214yes—
20C2×C4×C8×C11C2211yescharacteristic
21C2×#66896—22no—
22#10622688—24no—
23#10622688C2218yes—
24C2×C4⋊(C11⋊C8)C2212yes—
25#10622184C2214yescomplemented
26#10622094C2218yescomplemented
27C22×Q8×C11D412yes—
28C22×D4×C11—22no—
29C22×D4×C11—21no—
30C22×Dic22—22no—
31C22×Dic22D412yes—
32C2×C11×SD16—28no—
33C2×C11×SD16—48no—
34C22×C8×C11—21no—
35C11×C4⋊Q8—22no—
36C11×C4⋊Q8D412yes—
37C11×C4⋊Q8C2312yes—
38C11×#127—21no—
39C11×#127—22no—
40C11×#127C2312yes—
41C2×C11×C4⋊C4—22no—
42C2×C42×C11C2311yescharacteristic
43#66997—28no—
44#66997—28no—
45C2×#4324—28no—
46C2×#4324—48no—
47C2×C4⋊Dic11D412yes—
48C2×Dic11⋊C4—24no—
49C2×Dic11⋊C4—22no—
50C2×C4×Dic11—22no—
51C2×C4×Dic11—22no—
52C22×C11⋊C8—22no—
53#66941—28no—
54#66941—28no—
55#66940—28no—
56#66940—28no—
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×#1623—111nomaximal, Sylow
67C24×C11—41no—
68C2×Q8×C11—22no—
69C2×Q8×C11—44no—
70C2×Q8×C11C2×D414yes—
71C2×D4×C11—24no—
72C2×D4×C11—22no—
73C2×D4×C11—44no—
74C2×D4×C11—41no—
75C2×D4×C11—42no—
76C2×D4×C11—44no—
77C2×D4×C11—44no—
78C22×C4×C11—22no—
79C22×C4×C11C2×D411yescharacteristic
80C22×C4×C11C2×D412yes—
81C22×Dic11—22no—
82C22×Dic11—22no—
83C2×Dic22—28no—
84C2×Dic22—22no—
85C2×Dic22—24no—
86C2×Dic22—84no—
87C2×Dic22SD1618yescomplemented
88C2×Dic22C2×D414yes—
89C11×SD16—416no—
90C2×C8×C11—24no—
91C2×C8×C11—22no—
92C11×C4⋊C4—24no—
93C11×C4⋊C4—24no—
94C42×C11C2×D412yes—
95C42×C11C2×D411yescharacteristic
96C42×C11C2411yescharacteristic
97#4324—416no—
98C4⋊Dic11—22no—
99C4⋊Dic11C2×D414yes—
100Dic11⋊C4—216no—
101Dic11⋊C4—24no—
102Dic11⋊C4—24no—
103C4×Dic11—28no—
104C4×Dic11—24no—
105C4×Dic11—24no—
106C2×C11⋊C8—24no—
107C2×C11⋊C8—44no—
108C2×Q82—111no—
109C2×#492D1111yescharacteristic
110C2×#460—112no—
111#1623—118no—
112C2×#333—111no—
113C2×Q8⋊C8—112no—
114C23×C11—42no—
115C23×C11—84no—
116C23×C11—82no—
117C23×C11#12011yescharacteristic
118Q8×C11—44no—
119Q8×C11—82no—
120D4×C11—44no—
121D4×C11—44no—
122D4×C11—44no—
123D4×C11—82no—
124D4×C11—84no—
125C2×C4×C11—22no—
126C2×C4×C11—24no—
127C2×C4×C11—44no—
128C2×C4×C11#12011yescharacteristic
129C2×C4×C11#12012yes—
130C2×C4×C11C2×SD1614yes—
131C2×C4×C11#13714yes—
132C2×C4×C11C22×D412yes—
133C2×C4×C11C22×D411yescharacteristic
134C2×Dic11—24no—
135C2×Dic11—28no—
136C2×Dic11—24no—
137C2×Dic11—44no—
138Dic22—24no—
139Dic22—28no—
140Dic22—88no—
141Dic22C2×SD1618yescomplemented
142C8×C11—24no—
143C11⋊C8—44no—
144C22×SD16—22no—
145C22×SD16—222no—
146Q82—114no—
147Q82—224no—
148Q82—222no—
149C2×C4⋊Q8—222no—
150C2×C4⋊Q8—222no—
151C2×C4⋊Q8C2×D1111yescharacteristic
152C2×#127C2×D1111yescharacteristic
153C2×C4×Q8—112no—
154C2×C4×Q8—222no—
155#492—22no—
156#492C2×D1114yes—
157#460—118no—
158#460—224no—
159C2×C4⋊C8—112no—
160C2×#102—222no—
161C2×C4×C8C2×D1111yescharacteristic
162#333—114no—
163Q8⋊C8—118no—
164C22×C11—84no—
165C22×C11—82no—
166C22×C11—164no—
167C22×C11#44814yes—
168C22×C11#45312yes—
169C22×C11C2×#12011yescharacteristic
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—44no—
173C4×C11#44814yes—
174C4×C11C22×SD1612yes—
175C4×C11C2×#13712yes—
176Dic11—28no—
177Dic11—44no—
178C22×Q8—112no—
179C22×Q8—222no—
180C22×Q8C22⋊D1112yes—
181C22×D4—22no—
182C22×D4—21no—
183C2×SD16—28no—
184C2×SD16—48no—
185C2×SD16—228no—
186C2×SD16—448no—
187C22×C8—21no—
188C22×C8—222no—
189C4⋊Q8—22no—
190C4⋊Q8—228no—
191C4⋊Q8—228no—
192C4⋊Q8—228no—
193C4⋊Q8—228no—
194C4⋊Q8C22⋊D1112yes—
195C4⋊Q8C22×D1112yes—
196#127—22no—
197#127—21no—
198#127C22×D1112yes—
199C4×Q8—114no—
200C4×Q8—114no—
201C4×Q8—228no—
202C4×Q8—228no—
203C4×Q8—222no—
204C4×Q8—222no—
205C2×C4⋊C4—22no—
206C2×C4⋊C4—112no—
207C2×C4⋊C4—224no—
208C2×C4⋊C4—222no—
209C2×C42—222no—
210C2×C42—222no—
211C2×C42C22×D1111yescharacteristic
212C4⋊C8—114no—
213C4⋊C8—222no—
214#102—228no—
215C4×C8—21no—
216C4×C8C22×D1112yes—
217C2×C11—162no—
218C2×C11#162314yescomplemented
219C2×C11C2×#44812yes—
220C2×C11C2×#45311yescharacteristic
221C24—41no—
222C2×Q8—22no—
223C2×Q8—44no—
224C2×Q8—118no—
225C2×Q8—114no—
226C2×Q8—228no—
227C2×Q8—224no—
228C2×Q8—222no—
229C2×Q8—884no—
230C2×Q8C2×C22⋊D1114yes—
231C2×D4—24no—
232C2×D4—22no—
233C2×D4—44no—
234C2×D4—44no—
235C2×D4—44no—
236C2×D4—41no—
237C2×D4—42no—
238C22×C4—22no—
239C22×C4—222no—
240C22×C4—222no—
241C22×C4D4×D1112yes—
242C22×C4C2×C22⋊D1111yescharacteristic
243SD16—416no—
244SD16—4416no—
245C2×C8—24no—
246C2×C8—22no—
247C2×C8—224no—
248C2×C8—444no—
249C4⋊C4—24no—
250C4⋊C4—24no—
251C4⋊C4—114no—
252C4⋊C4—2216no—
253C4⋊C4—222no—
254C4⋊C4—224no—
255C4⋊C4—224no—
256C42—228no—
257C42—224no—
258C42—224no—
259C42D4×D1112yes—
260C42C2×C22⋊D1111yescharacteristic
261C42C23×D1111yescharacteristic
262C11C2×#162311yescharacteristic, complemented, Sylow
263C23—42no—
264C23—84no—
265C23—82no—
266C23#6699011yescharacteristic
267Q8—44no—
268Q8—82no—
269Q8—118no—
270Q8—224no—
271Q8—228no—
272Q8—888no—
273D4—44no—
274D4—44no—
275D4—44no—
276D4—82no—
277D4—84no—
278C2×C4—22no—
279C2×C4—24no—
280C2×C4—44no—
281C2×C4—228no—
282C2×C4—224no—
283C2×C4—224no—
284C2×C4—444no—
285C2×C4SD16×D1114yes—
286C2×C4#6696814yes—
287C2×C4#6699011yescharacteristic
288C2×C4#6699012yes—
289C2×C4C2×D4×D1112yes—
290C2×C4C22×C22⋊D1111yescharacteristic
291C8—24no—
292C8—444no—
293C22—84no—
294C22—82no—
295C22—164no—
296C22#1062269012yes—
297C22#1062278314yes—
298C22C2×#6699011yescharacteristic
299C4—21no—
300C4—21no—
301C4—44no—
302C4—228no—
303C4—444no—
304C4#1062278314yes—
305C4C2×SD16×D1112yes—
306C4C2×#6696812yes—
307C2—162no—
308C2#1306769214yesdirect product factor
309C2C2×#1062278312yes—
310C2C2×#1062269011yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#492C2
socleC23×C11#120
prime radicalC2×C11×#127C22
hypercenterC2×#492D11
hypocenterC11C2×#1623
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×#10623253C2semidirect
3. #13067692C2direct (N × H)
4. C2×#10622184C2semidirect
5. C2×#10622094C2semidirect
14. #10623253C22semidirect
25. #10622184C22semidirect
26. #10622094C22semidirect
87. C2×Dic22SD16semidirect
141. Dic22C2×SD16semidirect
218. C2×C11#1623semidirect
262. C11C2×#1623semidirect
308. C2#13067692direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232532
C2×#106226882
#130676922
C2×#106221842
C2×#106220942
C2×C11×#4922
C2×#162311