Finite Group Databasebeta

← C2×#13081257 #15633336

Subgroups — C2×#13081257 #15633336

Order 2816.

2058 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623098C211yesmaximal, characteristic, complemented
2C2×#10623258C211yesmaximal, characteristic
3#13081257C2116yesmaximal, direct product factor
4C2×#10622706C211yesmaximal, characteristic, complemented
5C2×#10622405C212yesmaximal, complemented
6C2×#10622467C212yesmaximal, complemented
7C2×#10622454C211yesmaximal, characteristic
8C2×#10622431C212yesmaximal
9C2×#10622443C211yesmaximal, characteristic, complemented
10C2×C4×#4325C211yesmaximal, characteristic
11C2×#10622465C212yesmaximal
12C2×C11×#475C211yesmaximal, characteristic, complemented
13C22×Q8×D11—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×#66999—21no—
17C2×#66997C2212yes—
18C22×#4325C2211yescharacteristic
19C22×#4314C2212yes—
20#10623258—24no—
21#10623258C2218yes—
22#10623098—24no—
23#10623098C2218yescomplemented
24C2×#66949—22no—
25C2×#66946C2212yes—
26C2×#66942—22no—
27C2×#66941C2212yes—
28C2×#66940C2212yes—
29C2×C4×D44C2211yescharacteristic
30C2×#66923—21no—
31C2×#66922C2211yescharacteristic
32C2×C4×Dic22—21no—
33C2×C4×Dic22C2211yescharacteristic
34C11×#475C2218yescomplemented
35C2×C11×#106C2212yes—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#103C2212yes—
38C2×#66899C2211yescharacteristic
39C2×#66880C2212yes—
40C2×Dic11⋊C8C2212yes—
41C2×C8×Dic11C2212yes—
42#10622706C2218yescomplemented
43C4×#4325C2218yes—
44C2×#66874C2212yes—
45C2×#66874C2212yes—
46C2×#66873C2211yescharacteristic
47C2×#66872C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622467C22116yescomplemented
50#10622465C22116yes—
51#10622454C2218yes—
52#10622443C2218yescomplemented
53#10622431C22116yes—
54#10622405C22116yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11C2311yescharacteristic
57C2×Q8×D11—28no—
58C2×Q8×D11—48no—
59C22×D44C2311yescharacteristic
60C22×C4×D11—21no—
61C22×C4×D11—22no—
62C22×Dic22—22no—
63C22×Dic22D411yescharacteristic
64C22×Dic22C2312yes—
65C22×C8×C11C2312yes—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8C2314yes—
68C4×Q8×C11—22no—
69C4×Q8×C11C2314yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2312yes—
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76#66999—28no—
77#66997—24no—
78#66997C2318yes—
79C2×#4325—24no—
80C2×#4325C2314yes—
81C2×(C2×D11)⋊C4—21no—
82C2×(C2×D11)⋊C4—22no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11D411yescharacteristic
86C2×C4⋊Dic11C2311yescharacteristic
87C2×Dic11⋊C4—22no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×Dic11⋊C4D412yes—
92C2×C4×Dic11—22no—
93C2×C4×Dic11C2312yes—
94C22×C11⋊C8C2311yescharacteristic
95C22×C11⋊C8C2311yescharacteristic
96C2×#4314—28no—
97C2×#4314C2318yes—
98#66949—216no—
99#66946—24no—
100#66946C2318yes—
101#66942—216no—
102#66941—24no—
103#66941C2318yes—
104#66940—24no—
105#66940C2318yes—
106C4×D44—22no—
107C4×D44C2314yes—
108#66923—28no—
109#66922—22no—
110#66922C2314yes—
111C4×Dic22—28no—
112C4×Dic22D414yes—
113C4×Dic22C2314yes—
114C11×#106C2318yes—
115C11×C4⋊C8C2314yes—
116C11×#103C2318yes—
117#66899C2314yes—
118#66880C2318yes—
119Dic11⋊C8C2318yes—
120C8×Dic11C2318yes—
121#66874C2318yes—
122#66874C2318yes—
123#66873C2314yes—
124#66872C2314yes—
125C4×C11⋊C8C2314yes—
126C2×#3359—111nomaximal, Sylow
127C23×D11—21no—
128C2×Q8×C11—21no—
129C2×Q8×C11—24no—
130C2×Q8×C11—22no—
131C2×Q8×C11—22no—
132C2×Q8×C11—44no—
133C2×Q8×C11C2412yes—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—22no—
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2411yescharacteristic
140C22×Dic11—22no—
141C22×Dic11—21no—
142C22×Dic11C2×D412yes—
143C22×Dic11C2×D412yes—
144Q8×D11—432no—
145C2×D44—21no—
146C2×D44—22no—
147C2×D44#4114yes—
148C2×D44C2412yes—
149C2×C4×D11—28no—
150C2×C4×D11—24no—
151C2×C4×D11—48no—
152C2×C4×D11—44no—
153C2×Dic22—28no—
154C2×Dic22—22no—
155C2×Dic22—24no—
156C2×Dic22—24no—
157C2×Dic22—48no—
158C2×Dic22SD1618yescomplemented
159C2×Dic22C2×D414yes—
160C2×Dic22C2414yes—
161C2×C8×C11—24no—
162C2×C8×C11C2414yes—
163C11×C4⋊C4—21no—
164C11×C4⋊C4—22no—
165C11×C4⋊C4—24no—
166C11×C4⋊C4—24no—
167C11×C4⋊C4C2412yes—
168C11×C4⋊C4C2414yes—
169C42×C11—24no—
170C42×C11C2×D412yes—
171C42×C11C2412yes—
172#4325—28no—
173(C2×D11)⋊C4—28no—
174(C2×D11)⋊C4—24no—
175C4⋊Dic11—24no—
176C4⋊Dic11—24no—
177C4⋊Dic11—21no—
178C4⋊Dic11C2×D414yes—
179C4⋊Dic11C2412yes—
180Dic11⋊C4—28no—
181Dic11⋊C4—28no—
182Dic11⋊C4—28no—
183Dic11⋊C4—28no—
184Dic11⋊C4C2×D418yes—
185C4×Dic11—28no—
186C4×Dic11C2×D414yes—
187C4×Dic11C2414yes—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8C2412yes—
191C2×C11⋊C8C2412yes—
192#4314—216no—
193C2×#557—111no—
194C2×D4×Q8—111no—
195#3359—1116no—
196C2×#487—112no—
197C2×#487—111no—
198C2×#475—112no—
199C2×#475D1111yescharacteristic, complemented
200C2×#461—111no—
201C2×#461—112no—
202C2×C8×Q8—111no—
203C2×C4×SD16—112no—
204C2×C4×SD16—111no—
205C23×C11C22×D411yescharacteristic
206C22×D11—24no—
207C22×D11—22no—
208C22×D11—42no—
209C22×D11—42no—
210Q8×C11—22no—
211Q8×C11—22no—
212Q8×C11—42no—
213Q8×C11—48no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—42no—
219C2×C4×C11—44no—
220C2×C4×C11—42no—
221C2×C4×C11C2×SD1614yes—
222C2×C4×C11C22×D412yes—
223C2×C4×C11C22×D411yescharacteristic
224C2×C4×C11C22×D412yes—
225C2×C4×C11C2×#4112yes—
226C2×C4×C112−1+412yes—
227C2×C4×C11C2511yescharacteristic
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—22no—
231C2×Dic11—44no—
232C2×Dic11—42no—
233C2×Dic11C2×SD1618yes—
234C2×Dic11C22×D414yes—
235C2×Dic11C22×D414yes—
236D44—24no—
237D44—22no—
238D44C2×#4114yes—
239C4×D11—48no—
240C4×D11—416no—
241Dic22—24no—
242Dic22—24no—
243Dic22—44no—
244Dic22—416no—
245Dic22C2×SD16116yescomplemented
246C8×C11—24no—
247C11⋊C8—22no—
248C11⋊C8—22no—
249C23×Q8—221no—
250C22×SD16—111no—
251C22×SD16—112no—
252#557—118no—
253#557—224no—
254D4×Q8—118no—
255D4×Q8—224no—
256C2×C4⋊Q8—112no—
257C2×C4⋊Q8—112no—
258C2×C4⋊Q8—111no—
259C2×C4⋊Q8C2×D1111yescharacteristic
260C2×#125—221no—
261C2×#125—222no—
262C2×C22⋊Q8—222no—
263C2×C22⋊Q8—221no—
264C2×C4×Q8—111no—
265C2×C4×Q8—112no—
266C2×C4×Q8—221no—
267C2×C4×Q8C2×D1111yescharacteristic
268C2×C4×D4—112no—
269C2×C4×D4—111no—
270#487—118no—
271#487—1116no—
272#475—1116no—
273#475C2×D1118yescomplemented
274#461—118no—
275#461—1116no—
276C8×Q8—118no—
277C4×SD16—118no—
278C4×SD16—1116no—
279C2×#106—111no—
280C2×#106C2×D1112yes—
281C2×C4⋊C8—112no—
282C2×C4⋊C8C2×D1111yescharacteristic
283C2×#103—111no—
284C2×#103—112no—
285C2×#103—112no—
286C2×#103—112no—
287C2×#103C2×D1112yes—
288C2×#102—111no—
289C2×C4×C8—112no—
290C2×C4×C8—111no—
291C22×C11#54812yes—
292C22×C11C22×SD1612yes—
293C22×C11#57812yes—
294C22×C11C23×D411yescharacteristic
295C2×D11—24no—
296C2×D11—48no—
297C2×D11—42no—
298C2×D11—42no—
299C4×C11—22no—
300C4×C11—42no—
301C4×C11—44no—
302C4×C11—42no—
303C4×C11#54812yes—
304C4×C11C22×SD1614yes—
305C4×C11C22×#4111yescharacteristic
306C4×C11C2×2−1+411yescharacteristic
307Dic11—24no—
308Dic11—44no—
309Dic11—42no—
310Dic11C22×SD1618yes—
311C22×Q8—21no—
312C22×Q8—111no—
313C22×Q8—112no—
314C22×Q8—222no—
315C22×Q8—228no—
316C22×Q8—448no—
317C22×Q8C22×D1111yescharacteristic
318C22×D4—111no—
319C23×C4—222no—
320C23×C4—221no—
321C2×SD16—114no—
322C2×SD16—118no—
323C2×SD16—228no—
324C2×SD16—224no—
325C22×C8—111no—
326C22×C8—111no—
327C22×C8C22×D1112yes—
328C4⋊Q8—22no—
329C4⋊Q8—118no—
330C4⋊Q8—118no—
331C4⋊Q8—114no—
332C4⋊Q8—224no—
333C4⋊Q8—224no—
334C4⋊Q8—222no—
335C4⋊Q8C22×D1114yes—
336#125—228no—
337#125—2216no—
338C22⋊Q8—2216no—
339C22⋊Q8—228no—
340C4×Q8—22no—
341C4×Q8—114no—
342C4×Q8—114no—
343C4×Q8—118no—
344C4×Q8—228no—
345C4×Q8—224no—
346C4×Q8C22×D1114yes—
347C4×D4—118no—
348C4×D4—114no—
349C4×D4—224no—
350C4×D4—222no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—112no—
354C2×C4⋊C4—111no—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—222no—
358C2×C4⋊C4—222no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4C22×D1112yes—
363C2×C4⋊C4C22×D1111yescharacteristic
364C2×C22⋊C4—222no—
365C2×C22⋊C4—221no—
366C2×C42—21no—
367C2×C42—112no—
368C2×C42—222no—
369C2×C42C22×D1111yescharacteristic
370#106—114no—
371#106C22×D1118yes—
372C4⋊C8—118no—
373C4⋊C8C22×D1114yes—
374#103—114no—
375#103—118no—
376#103—118no—
377#103—118no—
378#103C22×D1118yes—
379#102—114no—
380C4×C8—118no—
381C4×C8—114no—
382C2×C11#335914yescomplemented
383C2×C11C2×#54811yescharacteristic
384C2×C11C23×SD1611yescharacteristic
385C2×C11C2×#57811yescharacteristic
386D11—44no—
387C24—221no—
388C2×Q8—21no—
389C2×Q8—24no—
390C2×Q8—22no—
391C2×Q8—22no—
392C2×Q8—44no—
393C2×Q8—118no—
394C2×Q8—114no—
395C2×Q8—114no—
396C2×Q8—228no—
397C2×Q8—222no—
398C2×Q8—224no—
399C2×Q8—224no—
400C2×Q8—448no—
401C2×Q8—4432no—
402C2×Q8C23×D1112yes—
403C2×D4—114no—
404C2×D4—112no—
405C2×D4—221no—
406C2×D4—222no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—112no—
411C22×C4—112no—
412C22×C4—228no—
413C22×C4—222no—
414C22×C4—221no—
415C22×C4—224no—
416C22×C4—448no—
417C22×C4—444no—
418C22×C4D4×D1111yescharacteristic
419C22×C4D4×D1111yescharacteristic
420C22×C4C23×D1111yescharacteristic
421SD16—2216no—
422SD16—228no—
423C2×C8—24no—
424C2×C8—112no—
425C2×C8—112no—
426C2×C8—222no—
427C2×C8—222no—
428C2×C8C23×D1114yes—
429C4⋊C4—24no—
430C4⋊C4—24no—
431C4⋊C4—22no—
432C4⋊C4—21no—
433C4⋊C4—118no—
434C4⋊C4—114no—
435C4⋊C4—112no—
436C4⋊C4—228no—
437C4⋊C4—228no—
438C4⋊C4—228no—
439C4⋊C4—228no—
440C4⋊C4—221no—
441C4⋊C4—224no—
442C4⋊C4—224no—
443C4⋊C4C23×D1112yes—
444C4⋊C4C23×D1114yes—
445C22⋊C4—228no—
446C22⋊C4—224no—
447C42—24no—
448C42—114no—
449C42—114no—
450C42—228no—
451C42D4×D1112yes—
452C42C23×D1112yes—
453C11C2×#335911yescharacteristic, complemented, Sylow
454C23—224no—
455C23—222no—
456C23—442no—
457C23—442no—
458C23C2×D4×D1111yescharacteristic
459Q8—22no—
460Q8—22no—
461Q8—48no—
462Q8—42no—
463Q8—1116no—
464Q8—224no—
465Q8—224no—
466Q8—4416no—
467Q8—444no—
468D4—114no—
469D4—224no—
470D4—222no—
471C2×C4—22no—
472C2×C4—22no—
473C2×C4—22no—
474C2×C4—24no—
475C2×C4—44no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—118no—
479C2×C4—114no—
480C2×C4—114no—
481C2×C4—224no—
482C2×C4—224no—
483C2×C4—222no—
484C2×C4—4416no—
485C2×C4—442no—
486C2×C4—444no—
487C2×C4—448no—
488C2×C4SD16×D1114yes—
489C2×C4C2×D4×D1112yes—
490C2×C4C2×D4×D1112yes—
491C2×C4C2×D4×D1111yescharacteristic
492C2×C4#6704012yes—
493C2×C4#41×D1112yes—
494C2×C4C24×D1111yescharacteristic
495C8—24no—
496C8—222no—
497C8—222no—
498C22—224no—
499C22—448no—
500C22—442no—
501C22—442no—
502C22#1062316412yes—
503C22C2×SD16×D1112yes—
504C22#1062331012yes—
505C22C22×D4×D1111yescharacteristic
506C4—22no—
507C4—44no—
508C4—42no—
509C4—42no—
510C4—118no—
511C4—224no—
512C4—442no—
513C4—444no—
514C4#1062316412yes—
515C4C2×SD16×D1114yes—
516C4C2×#6704011yescharacteristic
517C4C2×#41×D1111yescharacteristic
518C2—444no—
519C2#1308125714yesdirect product factor
520C2C2×#1062316411yescharacteristic
521C2C22×SD16×D1111yescharacteristic
522C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#475D11
hypocenterC11C2×#3359
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#10623098C2semidirect
3. #13081257C2direct (N × H)
4. C2×#10622706C2semidirect
5. C2×#10622405C2semidirect
6. C2×#10622467C2semidirect
9. C2×#10622443C2semidirect
12. C2×C11×#475C2semidirect
23. #10623098C22semidirect
34. C11×#475C22semidirect
42. #10622706C22semidirect
49. #10622467C22semidirect
52. #10622443C22semidirect
54. #10622405C22semidirect
158. C2×Dic22SD16semidirect
199. C2×#475D11semidirect
245. Dic22C2×SD16semidirect
273. #475C2×D11semidirect
382. C2×C11#3359semidirect
453. C11C2×#3359semidirect
519. C2#13081257direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230982
C2×#106232582
#130812572
C2×#106227062
C2×#106224052
C2×#106224672
C2×#106224542
C2×#106224312
C2×#106224432
C2×C4×#43252
C2×#106224652
C2×C11×#4752
C2×#335911