Finite Group Databasebeta

← C2×#13079164 #15623425

Subgroups — C2×#13079164 #15623425

Order 2816.

1902 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623219C211yesmaximal, characteristic
2C2×D11×#125C211yesmaximal, characteristic
3#13079164C2116yesmaximal, direct product factor
4C2×#10622489C212yesmaximal, complemented
5C2×#10622469C212yesmaximal, complemented
6C2×#10622296C211yesmaximal, characteristic, complemented
7C2×#10622677C211yesmaximal, characteristic, complemented
8C2×#10622677C211yesmaximal, characteristic, complemented
9C2×#10622494C212yesmaximal
10C2×#10622474C212yesmaximal
11C2×C4×#4313C211yesmaximal, characteristic
12C2×C11×#499C211yesmaximal, characteristic, complemented
13C2×C11×#125C2211yescharacteristic
14C2×C11×#125C2211yescharacteristic
15C22×#4313C2211yescharacteristic
16C22×#4313C2211yescharacteristic
17#10623219—24no—
18#10623219C2218yes—
19D11×#125—24no—
20D11×#125C2218yes—
21C2×#66949—22no—
22C2×#66945C2212yes—
23C2×C4⋊C4×D11—22no—
24C2×C4⋊C4×D11C2212yes—
25C2×#66943C2212yes—
26C2×#66942—22no—
27C2×#66941C2212yes—
28C2×#66940—22no—
29C2×C42×D11C2211yescharacteristic
30C2×#66923C2211yescharacteristic
31C2×#66923C2211yescharacteristic
32C11×#499C2218yescomplemented
33C2×C11×#107C2212yes—
34C2×C11×#106C2212yes—
35C2×C4×C8×C11C2211yescharacteristic
36C2×#66882C2212yes—
37C2×#66881C2212yes—
38C2×#66879C2211yescharacteristic
39C2×#66879C2211yescharacteristic
40#10622677C2218yescomplemented
41#10622677C2218yescomplemented
42C2×#66872C2212yes—
43C2×#66872C2212yes—
44C2×#66871C2212yes—
45C2×#66871C2212yes—
46C2×C4×C11⋊C8C2211yescharacteristic
47#10622494C22116yes—
48#10622489C22116yescomplemented
49#10622474C22116yes—
50#10622469C22116yescomplemented
51C4×#4313C2218yes—
52#10622296C2218yescomplemented
53C22×C4×D11—22no—
54C22×C4×D11D412yes—
55C22×C4×D11C2311yescharacteristic
56C22×Dic22—22no—
57C22×C8×C11C2311yescharacteristic
58C22×C8×C11C2311yescharacteristic
59C11×#125—22no—
60C11×#125—22no—
61C11×#125C2314yes—
62C11×#125C2314yes—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—22no—
65C2×C11×C4⋊C4C2312yes—
66C2×C11×C4⋊C4C2312yes—
67C2×C42×C11C2311yescharacteristic
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11C2312yes—
71C2×C4⋊Dic11C2312yes—
72C2×Dic11⋊C4—22no—
73C2×Dic11⋊C4—22no—
74C2×Dic11⋊C4—22no—
75C2×Dic11⋊C4—22no—
76C2×Dic11⋊C4—22no—
77C2×C4×Dic11—22no—
78C2×C4×Dic11D412yes—
79C2×C4×Dic11C2311yescharacteristic
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C2×#4313Q818yescomplemented
83C2×#4313Q818yescomplemented
84C2×#4313C2314yes—
85C2×#4313C2314yes—
86#66949—216no—
87#66945—24no—
88#66945C2318yes—
89C4⋊C4×D11—216no—
90C4⋊C4×D11—24no—
91C4⋊C4×D11C2318yes—
92#66943—24no—
93#66943C2318yes—
94#66942—216no—
95#66941—24no—
96#66941C2318yes—
97#66940—216no—
98C42×D11D414yes—
99C42×D11C2314yes—
100#66923—22no—
101#66923—22no—
102#66923C2314yes—
103#66923C2314yes—
104C11×#107C2318yes—
105C11×#106C2318yes—
106C4×C8×C11C2314yes—
107#66882C2318yes—
108#66881C2318yes—
109#66879C2314yes—
110#66879C2314yes—
111#66872C2318yes—
112#66872C2318yes—
113#66871C2318yes—
114#66871C2318yes—
115C4×C11⋊C8C2314yes—
116C2×#3166—111nomaximal, Sylow
117C23×D11C2×D411yescharacteristic
118C22×C4×C11—22no—
119C22×C4×C11—22no—
120C22×C4×C11C2×D412yes—
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11C2×D412yes—
125C22×Dic11C2×D411yescharacteristic
126C2×C4×D11—28no—
127C2×C4×D11—44no—
128C2×C4×D11—48no—
129C2×C4×D11C2×D418yes—
130C2×C4×D11C2×D412yes—
131C2×C4×D11C2×Q814yes—
132C2×C4×D11C2×Q814yes—
133C2×C4×D11C2412yes—
134C2×Dic22—28no—
135C2×Dic22—48no—
136C2×C8×C11C2×Q814yes—
137C2×C8×C11C2×Q814yes—
138C2×C8×C11C2412yes—
139C2×C8×C11C2412yes—
140C11×C4⋊C4—28no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—28no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4C2414yes—
145C11×C4⋊C4C2414yes—
146C42×C11C2×D412yes—
147C42×C11C2412yes—
148(C2×D11)⋊C4—28no—
149C4⋊Dic11—28no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11C2414yes—
153C4⋊Dic11C2414yes—
154Dic11⋊C4—28no—
155Dic11⋊C4—28no—
156Dic11⋊C4—28no—
157Dic11⋊C4—28no—
158Dic11⋊C4—28no—
159C4×Dic11—28no—
160C4×Dic11C2×D412yes—
161C4×Dic11C2×D418yes—
162C4×Dic11C2412yes—
163C2×C11⋊C8C2×Q814yes—
164C2×C11⋊C8C2×Q814yes—
165C2×C11⋊C8C2412yes—
166C2×C11⋊C8C2412yes—
167#4313C2×Q8116yescomplemented
168#4313C2×Q8116yescomplemented
169C2×#533—111no—
170C22×#125—111no—
171#3166—1116no—
172C2×#501—112no—
173C2×#501—112no—
174C2×#499—111no—
175C2×#499—111no—
176C2×#499—111no—
177C2×#499D1111yescharacteristic, complemented
178C2×#428—112no—
179C2×#428—112no—
180C2×C4×M16—111no—
181C23×C11C22×D411yescharacteristic
182C22×D11—24no—
183C22×D11C4⋊Q814yes—
184C22×D11C22×D412yes—
185C2×C4×C11—24no—
186C2×C4×C11—24no—
187C2×C4×C11—24no—
188C2×C4×C11—44no—
189C2×C4×C11—44no—
190C2×C4×C11C22×D414yes—
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C22×Q812yes—
193C2×C4×C11C22×Q812yes—
194C2×C4×C11C2511yescharacteristic
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—44no—
199C2×Dic11—44no—
200C2×Dic11C4⋊Q814yes—
201C2×Dic11C22×D414yes—
202C2×Dic11C22×D412yes—
203C4×D11—48no—
204C4×D11—416no—
205C4×D11C4⋊Q818yes—
206C4×D11C22×Q814yes—
207C4×D11C22×Q814yes—
208Dic22—416no—
209C8×C11C22×Q814yes—
210C8×C11C22×Q814yes—
211C11⋊C8C22×Q814yes—
212C11⋊C8C22×Q814yes—
213C22×M16—111no—
214C22×M16—111no—
215#533—118no—
216#533—224no—
217C2×C4⋊Q8—112no—
218C2×#125—118no—
219C2×#125—112no—
220C2×#125—111no—
221C2×#125—111no—
222C2×#125—222no—
223C2×#125—224no—
224C2×#125C2×D1111yescharacteristic
225C2×#125C2×D1111yescharacteristic
226C2×C22⋊Q8—222no—
227C2×C4×Q8—222no—
228C2×#117—112no—
229C22×C4⋊C4—112no—
230C22×C4⋊C4—222no—
231C22×C42—111no—
232#501—1116no—
233#501—1116no—
234#499—118no—
235#499—118no—
236#499—118no—
237#499C2×D1118yescomplemented
238#428—1116no—
239#428—1116no—
240C2×#107—112no—
241C2×#107—112no—
242C2×#107—112no—
243C2×#107C2×D1112yes—
244C2×#106—112no—
245C2×#106—112no—
246C2×#106—112no—
247C2×#106C2×D1112yes—
248C4×M16—118no—
249C2×#97—111no—
250C2×#97—111no—
251C2×C4×C8—111no—
252C2×C4×C8C2×D1111yescharacteristic
253C22×C11C2×C4⋊Q812yes—
254C22×C11#57514yes—
255C22×C11C23×D411yescharacteristic
256C2×D11—28no—
257C2×D11—24no—
258C2×D11C2×C4⋊Q814yes—
259C4×C11—24no—
260C4×C11—44no—
261C4×C11—44no—
262C4×C11C2×C4⋊Q812yes—
263C4×C11C23×Q811yescharacteristic
264C4×C11C23×Q811yescharacteristic
265Dic11—24no—
266Dic11—44no—
267Dic11—44no—
268Dic11C2×C4⋊Q814yes—
269C22×Q8—222no—
270C23×C4—111no—
271C23×C4—112no—
272C23×C4—222no—
273C2×M16—118no—
274C2×M16—118no—
275C2×M16—114no—
276C2×M16—114no—
277C22×C8—111no—
278C22×C8—111no—
279C22×C8C22×D1111yescharacteristic
280C22×C8C22×D1111yescharacteristic
281C4⋊Q8—118no—
282C4⋊Q8—224no—
283#125—22no—
284#125—22no—
285#125—118no—
286#125—114no—
287#125—114no—
288#125—2216no—
289#125—224no—
290#125—222no—
291#125—222no—
292#125C22×D1114yes—
293#125C22×D1114yes—
294C22⋊Q8—2216no—
295C4×Q8—2216no—
296#117—118no—
297#117—224no—
298C2×C4⋊C4—22no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—112no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—118no—
303C2×C4⋊C4—224no—
304C2×C4⋊C4—2216no—
305C2×C4⋊C4—222no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—222no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4C22×D1112yes—
312C2×C4⋊C4C22×D1112yes—
313C2×C22⋊C4—222no—
314C2×C42—112no—
315C2×C42—111no—
316C2×C42—114no—
317C2×C42—114no—
318C2×C42—222no—
319C2×C42C22×D1111yescharacteristic
320#107—118no—
321#107—118no—
322#107—118no—
323#107C22×D1118yes—
324#106—118no—
325#106—118no—
326#106—118no—
327#106C22×D1118yes—
328#97—114no—
329#97—114no—
330C4×C8—114no—
331C4×C8C22×D1114yes—
332C2×C11#316614yescomplemented
333C2×C11C22×C4⋊Q811yescharacteristic
334C2×C11C2×#57512yes—
335D11—24no—
336C24—111no—
337C2×Q8—228no—
338C2×Q8—448no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—111no—
342C22×C4—112no—
343C22×C4—114no—
344C22×C4—114no—
345C22×C4—112no—
346C22×C4—112no—
347C22×C4—118no—
348C22×C4—228no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—444no—
352C22×C4—448no—
353C22×C4D4×D1112yes—
354C22×C4C23×D1111yescharacteristic
355M16—1116no—
356M16—1116no—
357C2×C8—114no—
358C2×C8—114no—
359C2×C8—112no—
360C2×C8—112no—
361C2×C8Q8×D1114yes—
362C2×C8Q8×D1114yes—
363C2×C8C23×D1112yes—
364C2×C8C23×D1112yes—
365C4⋊C4—28no—
366C4⋊C4—28no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—114no—
370C4⋊C4—114no—
371C4⋊C4—228no—
372C4⋊C4—228no—
373C4⋊C4—228no—
374C4⋊C4—228no—
375C4⋊C4—222no—
376C4⋊C4—222no—
377C4⋊C4—228no—
378C4⋊C4—228no—
379C4⋊C4C23×D1114yes—
380C4⋊C4C23×D1114yes—
381C22⋊C4—228no—
382C42—118no—
383C42—112no—
384C42—112no—
385C42—228no—
386C42D4×D1112yes—
387C42C23×D1112yes—
388C11C2×#316611yescharacteristic, complemented, Sylow
389C23—114no—
390C23—112no—
391C23—224no—
392C23C2×D4×D1111yescharacteristic
393Q8—4416no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—24no—
397C2×C4—44no—
398C2×C4—44no—
399C2×C4—114no—
400C2×C4—112no—
401C2×C4—118no—
402C2×C4—114no—
403C2×C4—114no—
404C2×C4—114no—
405C2×C4—224no—
406C2×C4—224no—
407C2×C4—224no—
408C2×C4—448no—
409C2×C4—4416no—
410C2×C4—444no—
411C2×C4—444no—
412C2×C4C2×D4×D1114yes—
413C2×C4C2×D4×D1111yescharacteristic
414C2×C4C2×Q8×D1112yes—
415C2×C4C2×Q8×D1112yes—
416C2×C4C24×D1111yescharacteristic
417C8—114no—
418C8—114no—
419C8C2×Q8×D1114yes—
420C8C2×Q8×D1114yes—
421C22—114no—
422C22—228no—
423C22—224no—
424C22D11×C4⋊Q812yes—
425C22#1062329914yes—
426C22C22×D4×D1111yescharacteristic
427C4—24no—
428C4—44no—
429C4—44no—
430C4—114no—
431C4—224no—
432C4—444no—
433C4—444no—
434C4D11×C4⋊Q812yes—
435C4C22×Q8×D1111yescharacteristic
436C4C22×Q8×D1111yescharacteristic
437C2—224no—
438C2#1307916414yesdirect product factor
439C2C2×D11×C4⋊Q811yescharacteristic
440C2C2×#1062329912yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#499C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#499D11
hypocenterC11C2×#3166
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#499

Complements

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

NH ≅ G/Ntype
3. #13079164C2direct (N × H)
4. C2×#10622489C2semidirect
5. C2×#10622469C2semidirect
6. C2×#10622296C2semidirect
7. C2×#10622677C2semidirect
8. C2×#10622677C2semidirect
12. C2×C11×#499C2semidirect
32. C11×#499C22semidirect
40. #10622677C22semidirect
41. #10622677C22semidirect
48. #10622489C22semidirect
50. #10622469C22semidirect
52. #10622296C22semidirect
82. C2×#4313Q8semidirect
83. C2×#4313Q8semidirect
167. #4313C2×Q8semidirect
168. #4313C2×Q8semidirect
177. C2×#499D11semidirect
237. #499C2×D11semidirect
332. C2×C11#3166semidirect
388. C11C2×#3166semidirect
438. C2#13079164direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232192
C2×D11×#1252
#130791642
C2×#106224892
C2×#106224692
C2×#106222962
C2×#106226772
C2×#106224942
C2×#106224742
C2×C4×#43132
C2×C11×#4992
C2×#316611