Finite Group Databasebeta

← C2×#13070401 #14906804

Subgroups — C2×#13070401 #14906804

Order 2816.

718 conjugacy classes of subgroups.

The subgroup lattice has 296 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66862C211yesmaximal, characteristic
2C2×#10622493C211yesmaximal, characteristic
3C2×D11×#107C211yesmaximal, characteristic
4#13070401C218yesmaximal, direct product factor
5C2×#10622143C211yesmaximal, characteristic, complemented
6C2×#10622128C211yesmaximal, characteristic, complemented
7C2×#10622127C211yesmaximal, characteristic, complemented
8C2×C11×#366C211yesmaximal, characteristic, complemented
9C22×C8×D11C2211yescharacteristic
10C2×#66945—21no—
11C2×C4⋊C4×D11—21no—
12C22×C11×C16C2211yescharacteristic
13C2×C11×#107C2211yescharacteristic
14C2×C11×#107C2211yescharacteristic
15C2×#66882C2211yescharacteristic
16C2×#66882C2211yescharacteristic
17C22×C11⋊C16C2211yescharacteristic
18C2×#66872—21no—
19C2×#66871—21no—
20C2×#66862C418yescomplemented
21C2×#66862C2214yes—
22#10622493—22no—
23#10622493C2214yes—
24D11×#107—22no—
25D11×#107C2214yes—
26C11×#366C2214yescomplemented
27#10622143C2214yescomplemented
28#10622128C2214yescomplemented
29#10622127C2214yescomplemented
30C22×C4×D11—41no—
31C22×C4×D11D411yescharacteristic
32C22×C8×C11C2311yescharacteristic
33C2×C11×C4⋊C4—21no—
34C2×C11×C4⋊C4—21no—
35C2×(C2×D11)⋊C4—41no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11—21no—
38C2×Dic11⋊C4—41no—
39C2×C4×Dic11—41no—
40C22×C11⋊C8D411yescharacteristic
41C2×C8×D11C2×C414yes—
42C2×C8×D11D412yes—
43C2×C8×D11Q814yes—
44C2×C8×D11C2312yes—
45#66945—24no—
46#66945—42no—
47C4⋊C4×D11—24no—
48C4⋊C4×D11—42no—
49C2×C11×C16C2×C414yescomplemented
50C2×C11×C16C2312yes—
51C11×#107—21no—
52C11×#107—21no—
53C11×#107C2312yes—
54C11×#107C2312yes—
55#66882—21no—
56#66882—21no—
57#66882C2312yes—
58#66882C2312yes—
59C2×C11⋊C16C2×C414yescomplemented
60C2×C11⋊C16C2312yes—
61#66872—24no—
62#66871—24no—
63#66862C2×C4116yescomplemented
64C2×#2159—111nomaximal, Sylow
65C23×D11D811yescharacteristic
66C22×C4×C11—41no—
67C22×C4×C11—41no—
68C22×C4×C11C2×D411yescharacteristic
69C22×Dic11—41no—
70C22×Dic11—41no—
71C22×Dic11D811yescharacteristic
72C2×C4×D11—44no—
73C2×C4×D11—84no—
74C2×C4×D11C4⋊C414yes—
75C2×C4×D11D812yes—
76C2×C4×D11Q1614yes—
77C2×C4×D11C2×D412yes—
78C2×C8×C11C22×C412yes—
79C2×C8×C11C2×D411yescharacteristic
80C2×C8×C11C2×Q812yes—
81C2×C8×C11C2411yescharacteristic
82C11×C4⋊C4—22no—
83C11×C4⋊C4—22no—
84C11×C4⋊C4—41no—
85C11×C4⋊C4—41no—
86(C2×D11)⋊C4—44no—
87C4⋊Dic11—22no—
88C4⋊Dic11—22no—
89C4⋊Dic11—41no—
90C4⋊Dic11—41no—
91Dic11⋊C4—44no—
92C4×Dic11—44no—
93C2×C11⋊C8C4⋊C414yes—
94C2×C11⋊C8C2×D412yes—
95C8×D11C4⋊C418yes—
96C8×D11C22×C414yes—
97C8×D11C2×Q814yes—
98C11×C16C22×C414yescomplemented
99C11⋊C16C22×C414yescomplemented
100C22×M32—111no—
101C2×#427—111no—
102C22×#107—111no—
103#2159—118no—
104C2×#367—111no—
105C2×#367—111no—
106C2×#366—111no—
107C2×#366D1111yescharacteristic, complemented
108C23×C11C2×D811yescharacteristic
109C22×D11—22no—
110C22×D11—22no—
111C22×D11#10714yes—
112C22×D11C2×D812yes—
113C2×C4×C11—42no—
114C2×C4×C11—42no—
115C2×C4×C11—82no—
116C2×C4×C11—82no—
117C2×C4×C11C2×C4⋊C412yes—
118C2×C4×C11C2×D811yescharacteristic
119C2×C4×C11C2×Q1612yes—
120C2×C4×C11C22×D411yescharacteristic
121C2×Dic11—42no—
122C2×Dic11—42no—
123C2×Dic11—82no—
124C2×Dic11—82no—
125C2×Dic11#10714yes—
126C2×Dic11C2×D812yes—
127C4×D11—88no—
128C4×D11#10718yes—
129C4×D11C2×C4⋊C414yes—
130C4×D11C2×Q1614yes—
131C8×C11C2×C4⋊C412yes—
132C8×C11C23×C411yescharacteristic
133C8×C11C22×Q811yescharacteristic
134C11⋊C8C2×C4⋊C414yes—
135C23×C8—111no—
136C2×#117—221no—
137C22×C4⋊C4—221no—
138C2×M32—114no—
139C2×M32—118no—
140C22×C16—111no—
141C22×C16C2×D1111yescharacteristic
142#427—114no—
143#427—222no—
144C2×#107—111no—
145C2×#107—111no—
146C2×#107—114no—
147C2×#107—222no—
148C2×#107—221no—
149C2×#107C2×D1111yescharacteristic
150C2×#107C2×D1111yescharacteristic
151C2×#106—221no—
152#367—114no—
153#367—114no—
154#366—114no—
155#366C2×D1114yescomplemented
156C22×C11C2×#10712yes—
157C22×C11#50912yes—
158C22×C11#51012yes—
159C22×C11C22×D811yescharacteristic
160C2×D11—22no—
161C2×D11—22no—
162C2×D11—28no—
163C2×D11C2×#10714yes—
164C4×C11—82no—
165C4×C11—82no—
166C4×C11C2×#10712yes—
167C4×C11C22×C4⋊C411yescharacteristic
168C4×C11C22×Q1611yescharacteristic
169Dic11—82no—
170Dic11—82no—
171Dic11C2×#10714yes—
172C23×C4—111no—
173C23×C4—441no—
174C22×C8—111no—
175C22×C8—114no—
176C22×C8—112no—
177C22×C8—114no—
178C22×C8—112no—
179C22×C8C22×D1111yescharacteristic
180#117—224no—
181#117—442no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—224no—
185C2×C4⋊C4—221no—
186C2×C4⋊C4—221no—
187C2×C4⋊C4—442no—
188C2×C4⋊C4—441no—
189C2×C22⋊C4—441no—
190C2×C42—441no—
191M32—1116no—
192C2×C16—114no—
193C2×C16—112no—
194C2×C16C4×D1114yescomplemented
195C2×C16C22×D1112yes—
196#107—21no—
197#107—21no—
198#107—112no—
199#107—112no—
200#107—224no—
201#107—221no—
202#107—221no—
203#107C22×D1112yes—
204#107C22×D1112yes—
205#106—224no—
206C2×C11#215914yescomplemented
207C2×C11C22×#10711yescharacteristic
208C2×C11C2×#50911yescharacteristic
209C2×C11C2×#51011yescharacteristic
210D11—24no—
211C24—111no—
212C22×C4—41no—
213C22×C4—41no—
214C22×C4—111no—
215C22×C4—114no—
216C22×C4—112no—
217C22×C4—114no—
218C22×C4—112no—
219C22×C4—444no—
220C22×C4—441no—
221C22×C4—441no—
222C22×C4—884no—
223C22×C4D4×D1111yescharacteristic
224C2×C8—114no—
225C2×C8—112no—
226C2×C8—118no—
227C2×C8—114no—
228C2×C8—114no—
229C2×C8C2×C4×D1112yes—
230C2×C8D4×D1111yescharacteristic
231C2×C8Q8×D1112yes—
232C2×C8C23×D1111yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—22no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—222no—
238C4⋊C4—222no—
239C4⋊C4—444no—
240C4⋊C4—441no—
241C4⋊C4—441no—
242C22⋊C4—444no—
243C42—444no—
244C16—114no—
245C16C2×C4×D1114yescomplemented
246C11C2×#215911yescharacteristic, complemented, Sylow
247C23—114no—
248C23—112no—
249C23—222no—
250C23—222no—
251C23D8×D1111yescharacteristic
252C2×C4—42no—
253C2×C4—42no—
254C2×C4—82no—
255C2×C4—82no—
256C2×C4—114no—
257C2×C4—112no—
258C2×C4—118no—
259C2×C4—114no—
260C2×C4—114no—
261C2×C4—442no—
262C2×C4—442no—
263C2×C4—888no—
264C2×C4—882no—
265C2×C4—882no—
266C2×C4C4⋊C4×D1112yes—
267C2×C4D8×D1111yescharacteristic
268C2×C4Q16×D1112yes—
269C2×C4C2×D4×D1111yescharacteristic
270C8—114no—
271C8C4⋊C4×D1112yes—
272C8C22×C4×D1111yescharacteristic
273C8C2×Q8×D1111yescharacteristic
274C22—114no—
275C22—228no—
276C22—222no—
277C22—222no—
278C22D11×#10712yes—
279C22#1062252412yes—
280C22#1062253112yes—
281C22C2×D8×D1111yescharacteristic
282C4—82no—
283C4—82no—
284C4—114no—
285C4—882no—
286C4—882no—
287C4D11×#10712yes—
288C4C2×C4⋊C4×D1111yescharacteristic
289C4C2×Q16×D1111yescharacteristic
290C2—224no—
291C2#1307040114yesdirect product factor
292C2C2×D11×#10711yescharacteristic
293C2C2×#1062252411yescharacteristic
294C2C2×#1062253111yescharacteristic
subgroupG/H
centerC23D8×D11
commutatorC8×C11C23×C4
FrattiniC2×C8C23×D11
FittingC2×C11×#366C2
socleC23×C11C2×D8
prime radicalC23×D11D8
cosocleC2×C8×C11C24
hypercenterC2×#366D11
hypocenterC11C2×#2159
LCSG ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#366

Complements

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

NH ≅ G/Ntype
4. #13070401C2direct (N × H)
5. C2×#10622143C2semidirect
6. C2×#10622128C2semidirect
7. C2×#10622127C2semidirect
8. C2×C11×#366C2semidirect
20. C2×#66862C4semidirect
26. C11×#366C22semidirect
27. #10622143C22semidirect
28. #10622128C22semidirect
29. #10622127C22semidirect
49. C2×C11×C16C2×C4semidirect
59. C2×C11⋊C16C2×C4semidirect
63. #66862C2×C4semidirect
98. C11×C16C22×C4semidirect
99. C11⋊C16C22×C4semidirect
107. C2×#366D11semidirect
155. #366C2×D11semidirect
194. C2×C16C4×D11semidirect
206. C2×C11#2159semidirect
245. C16C2×C4×D11semidirect
246. C11C2×#2159semidirect
291. C2#13070401direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668622
C2×#106224932
C2×D11×#1072
#130704012
C2×#106221432
C2×#106221282
C2×#106221272
C2×C11×#3662
C2×#215911