Finite Group Databasebeta

← C2×#13079149 #15623400

Subgroups — C2×#13079149 #15623400

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623260C212yesmaximal
2#13079149C2116yesmaximal, direct product factor
3C2×#10622489C212yesmaximal, complemented
4C2×#10622693C212yesmaximal, complemented
5C2×#10622487C211yesmaximal, characteristic, complemented
6C2×#10622296C211yesmaximal, characteristic, complemented
7C2×#10622491C211yesmaximal, characteristic, complemented
8C2×#10622494C212yesmaximal
9C2×#10622493C211yesmaximal, characteristic
10C2×D11×#107C211yesmaximal, characteristic
11C2×#10622302C211yesmaximal, characteristic
12C2×C11×#500C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2212yes—
14C2×#66999—22no—
15C2×#66997—22no—
16C22×#4313C2211yescharacteristic
17C22×C8×D11C2211yescharacteristic
18#10623260—28no—
19#10623260C22116yes—
20C2×#66949—22no—
21C2×#66945C2212yes—
22C2×C4⋊C4×D11C2212yes—
23C2×#66943C2212yes—
24C2×#66942—22no—
25C2×#66941C2212yes—
26C2×#66925C2211yescharacteristic
27C2×#66923C2212yes—
28C11×#500C2218yescomplemented
29C2×C11×#107C2211yescharacteristic
30C2×C11×#107C2211yescharacteristic
31C2×C11×#107C2212yes—
32C2×C4×C8×C11C2211yescharacteristic
33C2×#66882C2211yescharacteristic
34C2×#66882C2211yescharacteristic
35C2×#66881C2212yes—
36C2×#66879C2211yescharacteristic
37C2×C8×Dic11C2211yescharacteristic
38#10622693C22116yescomplemented
39C2×#66872C2212yes—
40C2×#66872C2212yes—
41C2×#66871C2212yes—
42C2×#66871C2212yes—
43C2×#66867C2211yescharacteristic
44#10622494C22116yes—
45#10622493C2218yes—
46D11×#107C2218yes—
47#10622491C2218yescomplemented
48#10622489C22116yescomplemented
49#10622487C2218yescomplemented
50#10622302C2218yes—
51#10622296C2218yescomplemented
52C22×Q8×C11—22no—
53C22×C4×D11—22no—
54C22×C4×D11C2311yescharacteristic
55C22×Dic22—22no—
56C22×C8×C11C2311yescharacteristic
57C22×C8×C11C2311yescharacteristic
58C11×C4⋊Q8—24no—
59C11×C4⋊Q8C2318yes—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C42×C11C2311yescharacteristic
64#66999—216no—
65#66997—216no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4D411yescharacteristic
68C2×(C2×D11)⋊C4D411yescharacteristic
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×Dic11⋊C4D411yescharacteristic
78C2×Dic11⋊C4D411yescharacteristic
79C2×C4×Dic11—22no—
80C2×C4×Dic11C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C22×C11⋊C8C2311yescharacteristic
83C2×#4313Q818yescomplemented
84C2×#4313C2314yes—
85C2×C8×D11Q818yescomplemented
86C2×C8×D11C2314yes—
87#66949—216no—
88#66945—24no—
89#66945C2318yes—
90C4⋊C4×D11—24no—
91C4⋊C4×D11C2318yes—
92#66943—24no—
93#66943C2318yes—
94#66942—216no—
95#66941—24no—
96#66941C2318yes—
97#66925D414yes—
98#66925C2314yes—
99#66923—24no—
100#66923C2318yes—
101C11×#107C2314yes—
102C11×#107C2318yes—
103C11×#107C2314yes—
104C4×C8×C11C2314yes—
105#66882C2314yes—
106#66882C2314yes—
107#66881C2318yes—
108#66879C2314yes—
109C8×Dic11C2314yes—
110#66872C2318yes—
111#66872C2318yes—
112#66871C2318yes—
113#66871C2318yes—
114#66867C2314yes—
115C2×#3164—111nomaximal, Sylow
116C23×D11C2×D411yescharacteristic
117C2×Q8×C11—28no—
118C2×Q8×C11—84no—
119C22×C4×C11—22no—
120C22×C4×C11—22no—
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D411yescharacteristic
123C22×C4×C11C2411yescharacteristic
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11C2×D411yescharacteristic
127C22×Dic11C2×D411yescharacteristic
128C22×Dic11C2×D411yescharacteristic
129C2×C4×D11—28no—
130C2×C4×D11—84no—
131C2×C4×D11C2×D412yes—
132C2×C4×D11C2×Q814yes—
133C2×C4×D11C2×Q814yes—
134C2×C4×D11C2412yes—
135C2×Dic22—28no—
136C2×Dic22—84no—
137C2×C8×C11C2×Q814yes—
138C2×C8×C11C2×Q814yes—
139C2×C8×C11C2412yes—
140C2×C8×C11C2412yes—
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—
149(C2×D11)⋊C4C2×D414yes—
150(C2×D11)⋊C4C2×D414yes—
151C4⋊Dic11—28no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11C2414yes—
155C4⋊Dic11C2414yes—
156Dic11⋊C4—28no—
157Dic11⋊C4—28no—
158Dic11⋊C4—28no—
159Dic11⋊C4—28no—
160Dic11⋊C4—28no—
161Dic11⋊C4C2×D414yes—
162Dic11⋊C4C2×D414yes—
163C4×Dic11—28no—
164C4×Dic11C2×D412yes—
165C4×Dic11C2412yes—
166C2×C11⋊C8C2×Q814yes—
167C2×C11⋊C8C2×Q814yes—
168C2×C11⋊C8C2412yes—
169C2×C11⋊C8C2412yes—
170#4313C2×Q8116yescomplemented
171C8×D11C2×Q8116yescomplemented
172C2×#544—112no—
173#3164—1116no—
174C2×#501—112no—
175C2×#501—112no—
176C2×#500—111no—
177C2×#500D1111yescharacteristic, complemented
178C2×#499—111no—
179C2×#499—111no—
180C2×#428—112no—
181C2×#427—111no—
182C22×#107—111no—
183C2×#405—111no—
184C23×C11C22×D411yescharacteristic
185C22×D11—22no—
186C22×D11—22no—
187C22×D11C4⋊Q814yes—
188C22×D11C22×D412yes—
189Q8×C11—88no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—44no—
195C2×C4×C11—44no—
196C2×C4×C11C22×D412yes—
197C2×C4×C11C22×D412yes—
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C22×Q812yes—
200C2×C4×C11C22×Q812yes—
201C2×C4×C11C2511yescharacteristic
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—24no—
205C2×Dic11—24no—
206C2×Dic11—44no—
207C2×Dic11—44no—
208C2×Dic11C4⋊Q814yes—
209C2×Dic11C22×D412yes—
210C2×Dic11C22×D412yes—
211C2×Dic11C22×D412yes—
212C4×D11—88no—
213C4×D11C4⋊Q818yes—
214C4×D11C22×Q814yes—
215C4×D11C22×Q814yes—
216Dic22—88no—
217C8×C11C22×Q814yes—
218C8×C11C22×Q814yes—
219C11⋊C8C22×Q814yes—
220C11⋊C8C22×Q814yes—
221C22×M16—111no—
222C23×C8—111no—
223#544—1116no—
224#544—228no—
225C2×C4⋊Q8—112no—
226C2×C4⋊Q8—222no—
227C2×C4⋊Q8C2×D1112yes—
228C2×#125—112no—
229C2×#125—112no—
230C2×#125—222no—
231C2×C22⋊Q8—222no—
232C2×C22⋊Q8—222no—
233C2×#117—111no—
234C2×#117—112no—
235C22×C4⋊C4—112no—
236#501—1116no—
237#501—1116no—
238#500—118no—
239#500C2×D1118yescomplemented
240#499—118no—
241#499—118no—
242#428—1116no—
243#427—118no—
244C2×#107—111no—
245C2×#107—111no—
246C2×#107—112no—
247C2×#107—112no—
248C2×#107—118no—
249C2×#107C2×D1111yescharacteristic
250C2×#107C2×D1111yescharacteristic
251C2×#107C2×D1112yes—
252C2×#106—112no—
253C2×#106—112no—
254C2×#106—112no—
255#405—118no—
256C2×#97—111no—
257C2×#97—111no—
258C2×C4×C8—111no—
259C2×C4×C8C2×D1111yescharacteristic
260C22×C11C2×C4⋊Q812yes—
261C22×C11#57612yes—
262C22×C11#57812yes—
263C22×C11C23×D411yescharacteristic
264C2×D11—28no—
265C2×D11—22no—
266C2×D11—22no—
267C2×D11C2×C4⋊Q814yes—
268C4×C11—22no—
269C4×C11—22no—
270C4×C11—44no—
271C4×C11—44no—
272C4×C11C2×C4⋊Q812yes—
273C4×C11C23×Q811yescharacteristic
274C4×C11C23×Q811yescharacteristic
275Dic11—22no—
276Dic11—22no—
277Dic11—44no—
278Dic11—44no—
279Dic11C2×C4⋊Q814yes—
280C22×Q8—22no—
281C22×Q8—222no—
282C23×C4—111no—
283C23×C4—222no—
284C2×M16—118no—
285C2×M16—114no—
286C22×C8—111no—
287C22×C8—111no—
288C22×C8—118no—
289C22×C8—114no—
290C22×C8C22×D1111yescharacteristic
291C22×C8C22×D1111yescharacteristic
292C4⋊Q8—24no—
293C4⋊Q8—118no—
294C4⋊Q8—224no—
295C4⋊Q8—2216no—
296C4⋊Q8C22×D1118yes—
297#125—118no—
298#125—118no—
299#125—224no—
300#125—2216no—
301#125—224no—
302C22⋊Q8—2216no—
303C22⋊Q8—2216no—
304#117—114no—
305#117—114no—
306#117—118no—
307#117—224no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—112no—
312C2×C4⋊C4—112no—
313C2×C4⋊C4—118no—
314C2×C4⋊C4—224no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—222no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4—222no—
321C2×C4⋊C4C22×D1112yes—
322C2×C4⋊C4C22×D1112yes—
323C2×C22⋊C4—111no—
324C2×C22⋊C4—111no—
325C2×C22⋊C4—222no—
326C2×C42—111no—
327C2×C42—222no—
328C2×C42C22×D1111yescharacteristic
329#107—114no—
330#107—114no—
331#107—118no—
332#107—118no—
333#107C22×D1114yes—
334#107C22×D1114yes—
335#107C22×D1118yes—
336#106—118no—
337#106—118no—
338#106—118no—
339#97—114no—
340#97—114no—
341C4×C8—114no—
342C4×C8C22×D1114yes—
343C2×C11#316414yescomplemented
344C2×C11C22×C4⋊Q811yescharacteristic
345C2×C11C2×#57611yescharacteristic
346C2×C11C2×#57811yescharacteristic
347D11—24no—
348C24—111no—
349C2×Q8—28no—
350C2×Q8—84no—
351C2×Q8—228no—
352C2×Q8—884no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—111no—
356C22×C4—112no—
357C22×C4—114no—
358C22×C4—114no—
359C22×C4—112no—
360C22×C4—111no—
361C22×C4—111no—
362C22×C4—228no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—884no—
366C22×C4D4×D1111yescharacteristic
367C22×C4D4×D1111yescharacteristic
368C22×C4C23×D1111yescharacteristic
369M16—1116no—
370C2×C8—114no—
371C2×C8—114no—
372C2×C8—112no—
373C2×C8—112no—
374C2×C8—1116no—
375C2×C8Q8×D1114yes—
376C2×C8Q8×D1114yes—
377C2×C8C23×D1112yes—
378C2×C8C23×D1112yes—
379C4⋊C4—28no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—114no—
383C4⋊C4—114no—
384C4⋊C4—114no—
385C4⋊C4—114no—
386C4⋊C4—228no—
387C4⋊C4—228no—
388C4⋊C4—228no—
389C4⋊C4—228no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C4⋊C4—228no—
393C4⋊C4—228no—
394C4⋊C4C23×D1114yes—
395C4⋊C4C23×D1114yes—
396C22⋊C4—114no—
397C22⋊C4—114no—
398C22⋊C4—228no—
399C42—112no—
400C42—112no—
401C42—228no—
402C42D4×D1112yes—
403C42C23×D1112yes—
404C11C2×#316411yescharacteristic, complemented, Sylow
405C23—114no—
406C23—112no—
407C23—222no—
408C23—222no—
409C23C2×D4×D1111yescharacteristic
410Q8—88no—
411Q8—888no—
412C2×C4—22no—
413C2×C4—22no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—44no—
417C2×C4—44no—
418C2×C4—114no—
419C2×C4—112no—
420C2×C4—118no—
421C2×C4—114no—
422C2×C4—114no—
423C2×C4—112no—
424C2×C4—112no—
425C2×C4—222no—
426C2×C4—222no—
427C2×C4—224no—
428C2×C4—224no—
429C2×C4—444no—
430C2×C4—444no—
431C2×C4—888no—
432C2×C4C2×D4×D1112yes—
433C2×C4C2×D4×D1112yes—
434C2×C4C2×D4×D1111yescharacteristic
435C2×C4C2×Q8×D1112yes—
436C2×C4C2×Q8×D1112yes—
437C2×C4C24×D1111yescharacteristic
438C8—114no—
439C8—114no—
440C8C2×Q8×D1114yes—
441C8C2×Q8×D1114yes—
442C22—114no—
443C22—228no—
444C22—222no—
445C22—222no—
446C22D11×C4⋊Q812yes—
447C22#1062328812yes—
448C22#1062329712yes—
449C22C22×D4×D1111yescharacteristic
450C4—22no—
451C4—22no—
452C4—44no—
453C4—44no—
454C4—114no—
455C4—222no—
456C4—222no—
457C4—444no—
458C4—444no—
459C4D11×C4⋊Q812yes—
460C4C22×Q8×D1111yescharacteristic
461C4C22×Q8×D1111yescharacteristic
462C2—224no—
463C2#1307914914yesdirect product factor
464C2C2×D11×C4⋊Q811yescharacteristic
465C2C2×#1062328811yescharacteristic
466C2C2×#1062329711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#500C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#500D11
hypocenterC11C2×#3164
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
2. #13079149C2direct (N × H)
3. C2×#10622489C2semidirect
4. C2×#10622693C2semidirect
5. C2×#10622487C2semidirect
6. C2×#10622296C2semidirect
7. C2×#10622491C2semidirect
12. C2×C11×#500C2semidirect
28. C11×#500C22semidirect
38. #10622693C22semidirect
47. #10622491C22semidirect
48. #10622489C22semidirect
49. #10622487C22semidirect
51. #10622296C22semidirect
83. C2×#4313Q8semidirect
85. C2×C8×D11Q8semidirect
170. #4313C2×Q8semidirect
171. C8×D11C2×Q8semidirect
177. C2×#500D11semidirect
239. #500C2×D11semidirect
343. C2×C11#3164semidirect
404. C11C2×#3164semidirect
463. C2#13079149direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232602
#130791492
C2×#106224892
C2×#106226932
C2×#106224872
C2×#106222962
C2×#106224912
C2×#106224942
C2×#106224932
C2×D11×#1072
C2×#106223022
C2×C11×#5002
C2×#316411