Finite Group Databasebeta

← C2×#13067757 #14729650

Subgroups — C2×#13067757 #14729650

Order 2816.

1010 conjugacy classes of subgroups; only the 219 normal subgroups are shown.

normal subgroups only

This group has 1010 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
2C2×#10622705C211yesmaximal, characteristic
3C2×#10622463C212yesmaximal
4#13067757C218yesmaximal, direct product factor
5C2×#10622122C212yesmaximal
6C2×C11×#333C211yesmaximal, characteristic
7C2×C11×C4⋊Q8C2211yescharacteristic
8C2×#66997—22no—
9C22×#4326—22no—
10#10623253—22no—
11#10623253—24no—
12#10623253C2214yes—
13C2×#66941—22no—
14C2×#66940—22no—
15C2×#66922C2211yescharacteristic
16C2×C4×Dic22C2212yes—
17C2×C11×C4⋊C8C2212yes—
18C2×#66882—22no—
19C2×#66880—22no—
20#10622705—22no—
21#10622705C2214yes—
22C2×C4×C11⋊C8C2211yescharacteristic
23#10622463—24no—
24#10622463C2218yes—
25C11×#333C2214yes—
26#10622122C2218yes—
27C22×Q8×C11D412yes—
28C22×Dic22—22no—
29C22×Dic22—21no—
30C22×Dic22D412yes—
31C22×C8×C11—22no—
32C11×C4⋊Q8—22no—
33C11×C4⋊Q8D412yes—
34C11×C4⋊Q8C2312yes—
35C2×C11×C4⋊C4—22no—
36C2×C42×C11C2311yescharacteristic
37#66997—28no—
38#66997—28no—
39C2×#4326—28no—
40C2×#4326—48no—
41C2×C4⋊Dic11—22no—
42C2×C4⋊Dic11D412yes—
43C2×Dic11⋊C4—24no—
44C2×Dic11⋊C4—22no—
45C2×C4×Dic11—22no—
46C2×C4×Dic11—22no—
47C22×C11⋊C8—21no—
48#66941—28no—
49#66941—28no—
50#66940—28no—
51#66940—28no—
52#66922—22no—
53#66922—21no—
54#66922C2312yes—
55C4×Dic22—22no—
56C4×Dic22—22no—
57C4×Dic22D414yes—
58C4×Dic22C2314yes—
59C11×C4⋊C8—22no—
60C11×C4⋊C8C2314yes—
61#66882—28no—
62#66880—28no—
63C4×C11⋊C8—21no—
64C4×C11⋊C8C2312yes—
65C2×#1633—111nomaximal, Sylow
66C2×Q8×C11—22no—
67C2×Q8×C11—44no—
68C2×Q8×C11C2×D414yes—
69C22×C4×C11—22no—
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11C2×D412yes—
72C22×Dic11—22no—
73C22×Dic11—22no—
74C22×Dic11—41no—
75C2×Dic22—28no—
76C2×Dic22—22no—
77C2×Dic22—24no—
78C2×Dic22—22no—
79C2×Dic22—44no—
80C2×Dic22—41no—
81C2×Dic22—84no—
82C2×Dic22Q1618yescomplemented
83C2×Dic22C2×D414yes—
84C2×C8×C11—24no—
85C2×C8×C11—44no—
86C11×C4⋊C4—24no—
87C11×C4⋊C4—24no—
88C42×C11C2×D411yescharacteristic
89C42×C11C2×D412yes—
90C42×C11C2411yescharacteristic
91#4326—416no—
92C4⋊Dic11—22no—
93C4⋊Dic11—24no—
94C4⋊Dic11—42no—
95C4⋊Dic11C2×D414yes—
96Dic11⋊C4—216no—
97Dic11⋊C4—24no—
98Dic11⋊C4—24no—
99C4×Dic11—28no—
100C4×Dic11—24no—
101C4×Dic11—24no—
102C2×C11⋊C8—24no—
103C2×C11⋊C8—22no—
104C2×Q82—111no—
105C2×#494—111no—
106C2×#477—112no—
107#1633—118no—
108C2×#333D1111yescharacteristic
109C2×Q8⋊C8—112no—
110C23×C11#12011yescharacteristic
111Q8×C11—44no—
112Q8×C11—82no—
113C2×C4×C11—22no—
114C2×C4×C11—24no—
115C2×C4×C11—44no—
116C2×C4×C11#12011yescharacteristic
117C2×C4×C11#12012yes—
118C2×C4×C11C2×Q1614yes—
119C2×C4×C11#13714yes—
120C2×C4×C11C22×D411yescharacteristic
121C2×C4×C11C22×D412yes—
122C2×Dic11—24no—
123C2×Dic11—28no—
124C2×Dic11—24no—
125C2×Dic11—44no—
126C2×Dic11—42no—
127C2×Dic11—82no—
128Dic22—24no—
129Dic22—28no—
130Dic22—44no—
131Dic22—88no—
132Dic22—82no—
133Dic22C2×Q1618yescomplemented
134C8×C11—44no—
135C11⋊C8—24no—
136C22×Q16—222no—
137Q82—114no—
138Q82—224no—
139Q82—222no—
140C2×C4⋊Q8—111no—
141C2×C4⋊Q8—222no—
142C2×C4⋊Q8—222no—
143C2×C4⋊Q8C2×D1111yescharacteristic
144C2×C4×Q8—112no—
145C2×C4×Q8—222no—
146#494—114no—
147#494—222no—
148#477—118no—
149#477—224no—
150C2×#107—222no—
151C2×C4⋊C8C2×D1112yes—
152C2×#103—222no—
153C2×C4×C8—111no—
154#333C2×D1114yes—
155Q8⋊C8—118no—
156C22×C11#45114yes—
157C22×C11#45312yes—
158C22×C11C2×#12011yescharacteristic
159C4×C11—21no—
160C4×C11—21no—
161C4×C11—44no—
162C4×C11#45114yes—
163C4×C11C22×Q1612yes—
164C4×C11C2×#13712yes—
165Dic11—28no—
166Dic11—44no—
167Dic11—82no—
168C22×Q8—112no—
169C22×Q8—222no—
170C22×Q8—221no—
171C22×Q8D4412yes—
172C2×Q16—228no—
173C2×Q16—448no—
174C22×C8—22no—
175C22×C8—221no—
176C4⋊Q8—22no—
177C4⋊Q8—112no—
178C4⋊Q8—228no—
179C4⋊Q8—228no—
180C4⋊Q8—228no—
181C4⋊Q8—228no—
182C4⋊Q8—221no—
183C4⋊Q8—222no—
184C4⋊Q8D4412yes—
185C4⋊Q8C22×D1112yes—
186C4×Q8—114no—
187C4×Q8—114no—
188C4×Q8—228no—
189C4×Q8—228no—
190C4×Q8—222no—
191C4×Q8—222no—
192C2×C4⋊C4—22no—
193C2×C4⋊C4—112no—
194C2×C4⋊C4—224no—
195C2×C4⋊C4—222no—
196C2×C4⋊C4—222no—
197C2×C42—222no—
198C2×C42—222no—
199C2×C42C22×D1111yescharacteristic
200#107—228no—
201C4⋊C8—22no—
202C4⋊C8C22×D1114yes—
203#103—228no—
204C4×C8—112no—
205C4×C8—221no—
206C2×C11#163314yescomplemented
207C2×C11C2×#45112yes—
208C2×C11C2×#45311yescharacteristic
209C2×Q8—22no—
210C2×Q8—44no—
211C2×Q8—118no—
212C2×Q8—114no—
213C2×Q8—228no—
214C2×Q8—222no—
215C2×Q8—224no—
216C2×Q8—222no—
217C2×Q8—444no—
218C2×Q8—441no—
219C2×Q8—884no—
220C2×Q8C2×D4414yes—
221C22×C4—22no—
222C22×C4—222no—
223C22×C4—222no—
224C22×C4—441no—
225C22×C4C2×D4411yescharacteristic
226C22×C4D4×D1112yes—
227Q16—4416no—
228C2×C8—24no—
229C2×C8—44no—
230C2×C8—224no—
231C2×C8—222no—
232C4⋊C4—24no—
233C4⋊C4—24no—
234C4⋊C4—114no—
235C4⋊C4—2216no—
236C4⋊C4—222no—
237C4⋊C4—224no—
238C4⋊C4—224no—
239C4⋊C4—224no—
240C4⋊C4—442no—
241C42—228no—
242C42—224no—
243C42—224no—
244C42C2×D4411yescharacteristic
245C42D4×D1112yes—
246C42C23×D1111yescharacteristic
247C11C2×#163311yescharacteristic, complemented, Sylow
248C23#6693511yescharacteristic
249Q8—44no—
250Q8—82no—
251Q8—118no—
252Q8—224no—
253Q8—228no—
254Q8—444no—
255Q8—882no—
256Q8—888no—
257C2×C4—22no—
258C2×C4—24no—
259C2×C4—44no—
260C2×C4—224no—
261C2×C4—228no—
262C2×C4—224no—
263C2×C4—444no—
264C2×C4—442no—
265C2×C4—882no—
266C2×C4#6693511yescharacteristic
267C2×C4#6693512yes—
268C2×C4#6696814yes—
269C2×C4Q16×D1114yes—
270C2×C4C22×D4411yescharacteristic
271C2×C4C2×D4×D1112yes—
272C8—44no—
273C8—224no—
274C22#1062236012yes—
275C22#1062242114yes—
276C22C2×#6693511yescharacteristic
277C4—21no—
278C4—21no—
279C4—44no—
280C4—228no—
281C4—444no—
282C4—882no—
283C4#1062242114yes—
284C4C2×#6696812yes—
285C4C2×Q16×D1112yes—
286C2#1306775714yesdirect product factor
287C2C2×#1062242112yes—
288C2C2×#1062236011yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#333C2
socle, prime radicalC23×C11#120
hypercenterC2×#333D11
hypocenterC11C2×#1633
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#333

Complements

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

NH ≅ G/Ntype
4. #13067757C2direct (N × H)
82. C2×Dic22Q16semidirect
133. Dic22C2×Q16semidirect
206. C2×C11#1633semidirect
247. C11C2×#1633semidirect
286. C2#13067757direct (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×#106227052
C2×#106224632
#130677572
C2×#106221222
C2×C11×#3332
C2×#163311