Finite Group Databasebeta

← C2×#13079147 #15623397

Subgroups — C2×#13079147 #15623397

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C212yesmaximal
2#13079147C2116yesmaximal, direct product factor
3C2×#10622315C214yesmaximal, complemented
4C2×#10622296C212yesmaximal, complemented
5C2×#10622293C212yesmaximal, complemented
6C2×#10622734C212yesmaximal
7C2×#10622719C211yesmaximal, characteristic
8C22×#66881C211yesmaximal, characteristic
9C2×C11×#405C211yesmaximal, characteristic
10C22×C11×M16C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×#66979C2212yes—
14C22×C4⋊Dic11C2212yes—
15#10623050—28no—
16#10623050C22116yes—
17C2×#66943—22no—
18C2×#66941—22no—
19C2×#66931—24no—
20C2×#66923C2214yes—
21C2×#66922C2214yes—
22C11×#405C2218yes—
23C2×C11×#97C2212yes—
24C2×C4×C8×C11C2212yes—
25#10622734C22116yes—
26#10622719C2218yes—
27C2×#66882C2214yes—
28C2×#66882C2212yes—
29C2×#66881C2211yescharacteristic
30C2×#66881C2212yes—
31C2×#66881C2214yes—
32C2×#66881C2211yescharacteristic
33C2×#66881C2212yes—
34C2×#66881C2218yes—
35#10622315C22132yescomplemented
36#10622296C22116yescomplemented
37#10622293C22116yescomplemented
38C23×C4×C11C2311yescharacteristic
39C23×Dic11—22no—
40C22×Dic22—24no—
41C2×C11×M16Q818yescomplemented
42C2×C11×M16C2314yes—
43C22×C8×C11Q818yescomplemented
44C22×C8×C11C2311yescharacteristic
45C22×C8×C11C2312yes—
46C22×C8×C11C2311yescharacteristic
47C22×C8×C11C2314yes—
48C11×#117D414yes—
49C11×#117C2314yes—
50C2×C11×C4⋊C4D412yes—
51C2×C11×C22⋊C4D412yes—
52C2×C42×C11C2312yes—
53C2×C22⋊Dic11—22no—
54#66979—24no—
55#66979C2318yes—
56C2×C4⋊Dic11—24no—
57C2×C4⋊Dic11—22no—
58C2×C4⋊Dic11—24no—
59C2×C4⋊Dic11C2318yes—
60C2×C4⋊Dic11C2312yes—
61C2×C4⋊Dic11C2314yes—
62C2×C4⋊Dic11C2312yes—
63C2×Dic11⋊C4—24no—
64C2×Dic11⋊C4—24no—
65C2×C4×Dic11—22no—
66#66943—216no—
67#66941—216no—
68#66931—232no—
69#66923—28no—
70#66923C23116yes—
71#66922—28no—
72#66922C23116yes—
73C11×#97C2318yes—
74C4×C8×C11C2318yes—
75#66882C23116yes—
76#66882C2318yes—
77#66881C23116yes—
78#66881C2314yes—
79#66881C2318yes—
80#66881C2314yes—
81#66881C2318yes—
82C2×#3163—111nomaximal, Sylow
83C24×C11C2×D411yescharacteristic
84C22×C4×C11C2×D414yes—
85C22×C4×C11C2×D411yescharacteristic
86C22×C4×C11C2×D412yes—
87C22×C4×C11C2×Q814yes—
88C22×C4×C11C2×Q814yes—
89C22×C4×C11C2411yescharacteristic
90C22×C4×C11C2412yes—
91C22×Dic11—22no—
92C22×Dic11—22no—
93C22×Dic11—24no—
94C22×Dic11—28no—
95C22×Dic11—84no—
96C2×Dic22—216no—
97C2×Dic22—88no—
98C11×M16C2×Q8116yescomplemented
99C2×C8×C11C2×Q814yes—
100C2×C8×C11C2×Q814yes—
101C2×C8×C11C2×Q818yes—
102C2×C8×C11C2×Q8116yescomplemented
103C2×C8×C11C2412yes—
104C2×C8×C11C2414yes—
105C2×C8×C11C2412yes—
106C11×C4⋊C4C2×D418yes—
107C11×C22⋊C4C2×D418yes—
108C42×C11C2×D414yes—
109C42×C11C2414yes—
110C22⋊Dic11—28no—
111C4⋊Dic11—22no—
112C4⋊Dic11—24no—
113C4⋊Dic11—216no—
114C4⋊Dic11—22no—
115C4⋊Dic11—28no—
116C4⋊Dic11C2414yes—
117C4⋊Dic11C2418yes—
118C4⋊Dic11C2414yes—
119Dic11⋊C4—216no—
120Dic11⋊C4—216no—
121C4×Dic11—28no—
122C2×#544—112no—
123#3163—1116no—
124C2×#501—114no—
125C2×#499—112no—
126C2×#498—112no—
127C2×#428—112no—
128C2×#427—111no—
129C22×#106—111no—
130C2×#405D1111yescharacteristic
131C23×C11—24no—
132C23×C11C4⋊Q814yes—
133C23×C11C22×D412yes—
134C23×C11C22×D411yescharacteristic
135C2×C4×C11—28no—
136C2×C4×C11C4⋊Q818yes—
137C2×C4×C11C4⋊Q814yes—
138C2×C4×C11C22×D418yes—
139C2×C4×C11C22×D412yes—
140C2×C4×C11C22×D411yescharacteristic
141C2×C4×C11C22×Q812yes—
142C2×C4×C11C22×Q812yes—
143C2×C4×C11C22×Q814yes—
144C2×C4×C11C22×Q814yes—
145C2×C4×C11C2511yescharacteristic
146C2×Dic11—24no—
147C2×Dic11—24no—
148C2×Dic11—28no—
149C2×Dic11—44no—
150C2×Dic11—48no—
151C2×Dic11—44no—
152C2×Dic11—88no—
153Dic22—816no—
154C8×C11C22×Q814yes—
155C8×C11C22×Q814yes—
156C8×C11C22×Q818yes—
157C22×M16C2×D1111yescharacteristic
158C23×C8C2×D1111yescharacteristic
159#544—1116no—
160#544—228no—
161C2×C4⋊Q8—114no—
162C2×C4⋊Q8—222no—
163C2×#125—114no—
164C2×#125—222no—
165C2×C22⋊Q8—224no—
166C2×#117—112no—
167C2×#117C2×D1111yescharacteristic
168C22×C4⋊C4—112no—
169#501—1132no—
170#499—1116no—
171#498—1116no—
172#428—1116no—
173#427—118no—
174C2×#107—114no—
175C2×#107—112no—
176C2×#106—111no—
177C2×#106—112no—
178C2×#106—114no—
179C2×#106—111no—
180C2×#106—112no—
181C2×#106—118no—
182#405C2×D1118yes—
183C2×#97C2×D1112yes—
184C2×C4×C8C2×D1112yes—
185C22×C11—28no—
186C22×C11—24no—
187C22×C11C2×C4⋊Q814yes—
188C22×C11C2×C4⋊Q812yes—
189C22×C11#57714yes—
190C22×C11C23×D411yescharacteristic
191C4×C11—28no—
192C4×C11C2×C4⋊Q814yes—
193C4×C11C2×C4⋊Q812yes—
194C4×C11C23×Q811yescharacteristic
195C4×C11C23×Q811yescharacteristic
196Dic11—44no—
197Dic11—48no—
198Dic11—44no—
199C22×Q8—224no—
200C23×C4—222no—
201C23×C4C22×D1111yescharacteristic
202C2×M16Dic2218yescomplemented
203C2×M16C22×D1114yes—
204C22×C8Dic2218yescomplemented
205C22×C8C22×D1111yescharacteristic
206C22×C8C22×D1111yescharacteristic
207C22×C8C22×D1112yes—
208C22×C8C22×D1114yes—
209C4⋊Q8—1116no—
210C4⋊Q8—2216no—
211C4⋊Q8—228no—
212#125—1116no—
213#125—2216no—
214#125—228no—
215C22⋊Q8—2232no—
216#117—118no—
217#117—224no—
218#117D4414yes—
219#117C22×D1114yes—
220C2×C4⋊C4—114no—
221C2×C4⋊C4—118no—
222C2×C4⋊C4—112no—
223C2×C4⋊C4—112no—
224C2×C4⋊C4—222no—
225C2×C4⋊C4—224no—
226C2×C4⋊C4—224no—
227C2×C4⋊C4—224no—
228C2×C4⋊C4—224no—
229C2×C4⋊C4D4412yes—
230C2×C22⋊C4—222no—
231C2×C22⋊C4D4412yes—
232C2×C42—222no—
233C2×C42C22×D1112yes—
234#107—118no—
235#107—1116no—
236#106—118no—
237#106—118no—
238#106—114no—
239#106—114no—
240#106—1116no—
241#97C22×D1118yes—
242C4×C8C22×D1118yes—
243C2×C11—24no—
244C2×C11#316314yescomplemented
245C2×C11C22×C4⋊Q811yescharacteristic
246C2×C11C2×#57712yes—
247C24C2×D4411yescharacteristic
248C2×Q8—2216no—
249C2×Q8—888no—
250C22×C4—222no—
251C22×C4—222no—
252C22×C4—224no—
253C22×C4—228no—
254C22×C4—884no—
255C22×C4C2×Dic2214yes—
256C22×C4C2×Dic2214yes—
257C22×C4C2×D4414yes—
258C22×C4C2×D4412yes—
259C22×C4C2×D4411yescharacteristic
260C22×C4C23×D1112yes—
261C22×C4C23×D1111yescharacteristic
262M16C2×Dic22116yescomplemented
263C2×C8C2×Dic2214yes—
264C2×C8C2×Dic2214yes—
265C2×C8C2×Dic2218yes—
266C2×C8C2×Dic22116yescomplemented
267C2×C8C23×D1112yes—
268C2×C8C23×D1114yes—
269C2×C8C23×D1112yes—
270C4⋊C4—118no—
271C4⋊C4—114no—
272C4⋊C4—114no—
273C4⋊C4—228no—
274C4⋊C4—224no—
275C4⋊C4—222no—
276C4⋊C4—222no—
277C4⋊C4—2216no—
278C4⋊C4—2216no—
279C4⋊C4—2216no—
280C4⋊C4C2×D4418yes—
281C22⋊C4—228no—
282C22⋊C4C2×D4418yes—
283C42—228no—
284C42C2×D4414yes—
285C42C23×D1114yes—
286C11C2×#316311yescharacteristic, complemented, Sylow
287C23—24no—
288C23#6692214yes—
289C23C22×D4412yes—
290C23C22×D4411yescharacteristic
291Q8—8816no—
292C2×C4—28no—
293C2×C4—224no—
294C2×C4—224no—
295C2×C4—228no—
296C2×C4—448no—
297C2×C4—444no—
298C2×C4—444no—
299C2×C4—888no—
300C2×C4#6692218yes—
301C2×C4#6692214yes—
302C2×C4C22×Dic2212yes—
303C2×C4C22×Dic2212yes—
304C2×C4C22×Dic2214yes—
305C2×C4C22×Dic2214yes—
306C2×C4C22×D4418yes—
307C2×C4C22×D4412yes—
308C2×C4C22×D4411yescharacteristic
309C2×C4C24×D1111yescharacteristic
310C8C22×Dic2214yes—
311C8C22×Dic2214yes—
312C8C22×Dic2218yes—
313C22—28no—
314C22—24no—
315C22C2×#6692214yes—
316C22C2×#6692212yes—
317C22#1062328214yes—
318C22C23×D4411yescharacteristic
319C4—28no—
320C4—448no—
321C4—444no—
322C4—444no—
323C4C2×#6692212yes—
324C4C2×#6692214yes—
325C4C23×Dic2211yescharacteristic
326C4C23×Dic2211yescharacteristic
327C2—24no—
328C2#1307914714yesdirect product factor
329C2C22×#6692211yescharacteristic
330C2C2×#1062328212yes—
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#405C2
socleC23×C11C22×D4
prime radicalC24×C11C2×D4
hypercenterC2×#405D11
hypocenterC11C2×#3163
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
2. #13079147C2direct (N × H)
3. C2×#10622315C2semidirect
4. C2×#10622296C2semidirect
5. C2×#10622293C2semidirect
35. #10622315C22semidirect
36. #10622296C22semidirect
37. #10622293C22semidirect
41. C2×C11×M16Q8semidirect
43. C22×C8×C11Q8semidirect
98. C11×M16C2×Q8semidirect
102. C2×C8×C11C2×Q8semidirect
202. C2×M16Dic22semidirect
204. C22×C8Dic22semidirect
244. C2×C11#3163semidirect
262. M16C2×Dic22semidirect
266. C2×C8C2×Dic22semidirect
286. C11C2×#3163semidirect
328. C2#13079147direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230502
#130791472
C2×#106223152
C2×#106222962
C2×#106222932
C2×#106227342
C2×#106227192
C22×#668812
C2×C11×#4052
C2×#316311