Finite Group Databasebeta

← C2×#13081401 #15633440

Subgroups — C2×#13081401 #15633440

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623252C211yesmaximal, characteristic, complemented
2C2×#10623074C211yesmaximal, characteristic
3#13081401C2116yesmaximal, direct product factor
4C2×#10622410C212yesmaximal, complemented
5C2×#10622694C211yesmaximal, characteristic, complemented
6C2×#10622409C212yesmaximal, complemented
7C2×#10622463C211yesmaximal, characteristic, complemented
8C2×#10622775C212yesmaximal
9C2×#10622444C211yesmaximal, characteristic, complemented
10C2×#10622777C212yesmaximal
11C2×C4×#4324C211yesmaximal, characteristic
12C2×C11×#461C211yesmaximal, characteristic
13C22×C11×SD16C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×Q8×Dic11C2212yes—
17C2×#66997C2212yes—
18C2×D4×Dic11C2212yes—
19C22×#4324C2211yescharacteristic
20C22×C4⋊Dic11—21no—
21C2×#66977—21no—
22#10623252—24no—
23#10623252C2218yescomplemented
24#10623074—24no—
25#10623074C2218yes—
26C2×#66943—21no—
27C2×#66943C2212yes—
28C2×#66942—22no—
29C2×#66940—21no—
30C2×#66931—22no—
31C2×#66922C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#461C2218yes—
35C2×C11×C4⋊C8C2211yescharacteristic
36C2×C11×#103C2212yes—
37C2×#66899C2212yes—
38C2×#66899C2212yes—
39C2×#66896C2211yescharacteristic
40#10622777C22116yes—
41#10622775C22116yes—
42C2×#66882C2212yes—
43C2×#66880C2212yes—
44C2×#66879C2212yes—
45C2×Dic11⋊C8C2212yes—
46#10622694C2218yescomplemented
47C4×#4324C2218yes—
48C2×#66874C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622463C2218yescomplemented
52#10622444C2218yescomplemented
53#10622410C22116yescomplemented
54#10622409C22116yescomplemented
55C22×Q8×C11C2312yes—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C23×Dic11—22no—
59C22×Dic22—21no—
60C22×Dic22D411yescharacteristic
61C22×Dic22C2311yescharacteristic
62C2×C11×SD16—28no—
63C2×C11×SD16C2318yes—
64C22×C8×C11C2312yes—
65C11×C4⋊Q8—22no—
66C11×C4⋊Q8C2314yes—
67C4×D4×C11—22no—
68C4×D4×C11C2314yes—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—22no—
75Q8×Dic11—24no—
76Q8×Dic11C2318yes—
77#66997—24no—
78#66997C2318yes—
79D4×Dic11—24no—
80D4×Dic11C2318yes—
81C2×#4324—24no—
82C2×#4324C2314yes—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—28no—
87C2×C4⋊Dic11D411yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2312yes—
90#66977—28no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4—22no—
94C2×Dic11⋊C4—22no—
95C2×Dic11⋊C4D412yes—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11C2312yes—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101#66943—28no—
102#66943—24no—
103#66943C2318yes—
104#66942—216no—
105#66940—28no—
106#66931—216no—
107#66922—22no—
108#66922C2314yes—
109C4×Dic22—22no—
110C4×Dic22D414yes—
111C4×Dic22C2314yes—
112C4×Dic22C2314yes—
113C11×C4⋊C8C2314yes—
114C11×#103C2318yes—
115#66899C2318yes—
116#66899C2318yes—
117#66896C2314yes—
118#66882C2318yes—
119#66880C2318yes—
120#66879C2318yes—
121Dic11⋊C8C2318yes—
122#66874C2314yes—
123#66872C2314yes—
124C4×C11⋊C8C2314yes—
125C2×#3372—111nomaximal, Sylow
126C24×C11—21no—
127C2×Q8×C11—22no—
128C2×Q8×C11—24no—
129C2×Q8×C11—24no—
130C2×Q8×C11C2414yes—
131C2×D4×C11—21no—
132C2×D4×C11—22no—
133C2×D4×C11#4114yes—
134C2×D4×C11C2412yes—
135C22×C4×C11—22no—
136C22×C4×C11—21no—
137C22×C4×C11—24no—
138C22×C4×C11—44no—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2411yescharacteristic
142C22×Dic11—28no—
143C22×Dic11—21no—
144C22×Dic11—21no—
145C22×Dic11—22no—
146C22×Dic11—84no—
147C22×Dic11C2×D412yes—
148C22×Dic11C2×D412yes—
149C2×Dic22—24no—
150C2×Dic22—21no—
151C2×Dic22—24no—
152C2×Dic22—22no—
153C2×Dic22—22no—
154C2×Dic22—82no—
155C2×Dic22C2×D414yes—
156C2×Dic22C2412yes—
157C11×SD16—216no—
158C2×C8×C11—24no—
159C2×C8×C11C2414yes—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4C2412yes—
164C11×C22⋊C4—24no—
165C42×C11C2×D412yes—
166C42×C11C2412yes—
167C22⋊Dic11—28no—
168#4324—28no—
169C4⋊Dic11—28no—
170C4⋊Dic11—28no—
171C4⋊Dic11—21no—
172C4⋊Dic11—22no—
173C4⋊Dic11—24no—
174C4⋊Dic11C2×D414yes—
175C4⋊Dic11C2412yes—
176C4⋊Dic11C2414yes—
177Dic11⋊C4—28no—
178Dic11⋊C4—28no—
179Dic11⋊C4—28no—
180Dic11⋊C4—24no—
181Dic11⋊C4C2×D418yes—
182C4×Dic11—28no—
183C4×Dic11—24no—
184C4×Dic11C2×D414yes—
185C4×Dic11C2414yes—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8C2412yes—
189C2×C11⋊C8C2412yes—
190C2×#557—111no—
191C2×#554—111no—
192#3372—1116no—
193C2×#491—112no—
194C2×#487—111no—
195C2×#479—112no—
196C2×#477—111no—
197C2×#461—112no—
198C2×#461D1111yescharacteristic
199C2×#446—111no—
200C2×#440—112no—
201C2×C4×SD16—111no—
202C23×C11—24no—
203C23×C11—22no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11C22×D411yescharacteristic
207Q8×C11—24no—
208Q8×C11—24no—
209Q8×C11—44no—
210D4×C11—24no—
211D4×C11—22no—
212D4×C11C2×#4114yes—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—44no—
217C2×C4×C11—42no—
218C2×C4×C11—48no—
219C2×C4×C11#13714yes—
220C2×C4×C11C22×D412yes—
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D412yes—
223C2×C4×C11C2×#4112yes—
224C2×C4×C112−1+412yes—
225C2×C4×C11C2511yescharacteristic
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—42no—
232C2×Dic11—44no—
233C2×Dic11—42no—
234C2×Dic11—88no—
235C2×Dic11C22×D414yes—
236C2×Dic11C22×D414yes—
237Dic22—28no—
238Dic22—22no—
239Dic22—22no—
240Dic22—42no—
241Dic22—84no—
242C8×C11—24no—
243C11⋊C8—22no—
244C11⋊C8—22no—
245C22×SD16—111no—
246C22×SD16C2×D1112yes—
247#557—118no—
248#557—224no—
249#554—118no—
250#554—224no—
251C2×C4⋊Q8—112no—
252C2×C4⋊Q8—111no—
253C2×C4⋊Q8C2×D1111yescharacteristic
254C2×#125—112no—
255C2×#125—222no—
256C2×#125—221no—
257C2×C22⋊Q8—222no—
258C2×C22⋊Q8—221no—
259C2×C4×Q8—111no—
260C2×C4×Q8—112no—
261C2×C4×Q8—111no—
262C2×C4×Q8—221no—
263C2×C4×D4—112no—
264C2×C4×D4C2×D1111yescharacteristic
265C22×C4⋊C4—221no—
266#491—1116no—
267#487—118no—
268#479—1116no—
269#477—118no—
270#461—1116no—
271#461C2×D1118yes—
272#446—118no—
273#440—1116no—
274C4×SD16—118no—
275C2×#107—112no—
276C2×#106—111no—
277C2×C4⋊C8—112no—
278C2×C4⋊C8C2×D1111yescharacteristic
279C2×#103—112no—
280C2×#103—112no—
281C2×#103—112no—
282C2×#103—111no—
283C2×#103C2×D1112yes—
284C2×#102—111no—
285C2×#97—112no—
286C2×C4×C8—111no—
287C22×C11—24no—
288C22×C11—48no—
289C22×C11—42no—
290C22×C11—42no—
291C22×C11#54812yes—
292C22×C11C2×#13712yes—
293C22×C11#57712yes—
294C22×C11C23×D411yescharacteristic
295C4×C11—22no—
296C4×C11—44no—
297C4×C11—42no—
298C4×C11#54812yes—
299C4×C11C2×#13714yes—
300C4×C11C22×#4111yescharacteristic
301C4×C11C2×2−1+411yescharacteristic
302Dic11—24no—
303Dic11—24no—
304Dic11—42no—
305Dic11—44no—
306Dic11—42no—
307C22×Q8—111no—
308C22×Q8—111no—
309C22×Q8—221no—
310C22×Q8C22×D1112yes—
311C22×D4C22×D1111yescharacteristic
312C23×C4—21no—
313C23×C4—222no—
314C2×SD16—28no—
315C2×SD16—114no—
316C2×SD16—224no—
317C2×SD16C22×D1118yes—
318C22×C8—111no—
319C22×C8—111no—
320C22×C8C22×D1112yes—
321C4⋊Q8—22no—
322C4⋊Q8—118no—
323C4⋊Q8—114no—
324C4⋊Q8—224no—
325C4⋊Q8—222no—
326C4⋊Q8C22×D1114yes—
327#125—118no—
328#125—224no—
329#125—2216no—
330#125—228no—
331C22⋊Q8—2216no—
332C22⋊Q8—228no—
333C4×Q8—114no—
334C4×Q8—114no—
335C4×Q8—118no—
336C4×Q8—114no—
337C4×Q8—224no—
338C4×Q8—228no—
339C4×Q8—222no—
340C4×D4—22no—
341C4×D4—118no—
342C4×D4—224no—
343C4×D4C22×D1114yes—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—112no—
348C2×C4⋊C4—112no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—228no—
351C2×C4⋊C4—222no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—221no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4C22×D1111yescharacteristic
359C2×C22⋊C4—21no—
360C2×C22⋊C4—222no—
361C2×C42—112no—
362C2×C42—222no—
363C2×C42—221no—
364C2×C42C22×D1111yescharacteristic
365#107—118no—
366#106—114no—
367C4⋊C8—118no—
368C4⋊C8C22×D1114yes—
369#103—118no—
370#103—118no—
371#103—118no—
372#103—114no—
373#103C22×D1118yes—
374#102—114no—
375#97—118no—
376C4×C8—114no—
377C2×C11—44no—
378C2×C11#337214yescomplemented
379C2×C11C2×#54811yescharacteristic
380C2×C11C22×#13711yescharacteristic
381C2×C11C2×#57711yescharacteristic
382C24—21no—
383C2×Q8—22no—
384C2×Q8—24no—
385C2×Q8—24no—
386C2×Q8—114no—
387C2×Q8—112no—
388C2×Q8—224no—
389C2×Q8—221no—
390C2×Q8—224no—
391C2×Q8—222no—
392C2×Q8—222no—
393C2×Q8—882no—
394C2×Q8C23×D1114yes—
395C2×D4—21no—
396C2×D4—22no—
397C2×D4#434114yes—
398C2×D4C23×D1112yes—
399C22×C4—22no—
400C22×C4—21no—
401C22×C4—24no—
402C22×C4—44no—
403C22×C4—112no—
404C22×C4—112no—
405C22×C4—228no—
406C22×C4—221no—
407C22×C4—221no—
408C22×C4—222no—
409C22×C4—884no—
410C22×C4D4×D1111yescharacteristic
411C22×C4D4×D1111yescharacteristic
412C22×C4C23×D1111yescharacteristic
413SD16—216no—
414SD16—228no—
415C2×C8—24no—
416C2×C8—112no—
417C2×C8—112no—
418C2×C8—222no—
419C2×C8—222no—
420C2×C8C23×D1114yes—
421C4⋊C4—24no—
422C4⋊C4—24no—
423C4⋊C4—21no—
424C4⋊C4—114no—
425C4⋊C4—118no—
426C4⋊C4—112no—
427C4⋊C4—114no—
428C4⋊C4—228no—
429C4⋊C4—228no—
430C4⋊C4—228no—
431C4⋊C4—228no—
432C4⋊C4—228no—
433C4⋊C4—222no—
434C4⋊C4—221no—
435C4⋊C4—224no—
436C4⋊C4—224no—
437C4⋊C4C23×D1112yes—
438C22⋊C4—24no—
439C22⋊C4—228no—
440C42—114no—
441C42—114no—
442C42—228no—
443C42—224no—
444C42D4×D1112yes—
445C42C23×D1112yes—
446C11C2×#337211yescharacteristic, complemented, Sylow
447C23—24no—
448C23—22no—
449C23—42no—
450C23—42no—
451C23C2×D4×D1111yescharacteristic
452Q8—24no—
453Q8—24no—
454Q8—44no—
455Q8—228no—
456Q8—222no—
457Q8—222no—
458Q8—442no—
459Q8—884no—
460D4—24no—
461D4—22no—
462D4C2×#434114yes—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—42no—
467C2×C4—44no—
468C2×C4—48no—
469C2×C4—114no—
470C2×C4—114no—
471C2×C4—224no—
472C2×C4—224no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—224no—
476C2×C4—444no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—888no—
480C2×C4#6696814yes—
481C2×C4C2×D4×D1112yes—
482C2×C4C2×D4×D1112yes—
483C2×C4C2×D4×D1111yescharacteristic
484C2×C4C2×#434112yes—
485C2×C4#6704312yes—
486C2×C4C24×D1111yescharacteristic
487C8—24no—
488C8—222no—
489C8—222no—
490C22—24no—
491C22—48no—
492C22—42no—
493C22—42no—
494C22#1062312912yes—
495C22C2×#6696812yes—
496C22#1062330912yes—
497C22C22×D4×D1111yescharacteristic
498C4—22no—
499C4—42no—
500C4—44no—
501C4—224no—
502C4—224no—
503C4—442no—
504C4—444no—
505C4—442no—
506C4#1062312912yes—
507C4C2×#6696814yes—
508C4C22×#434111yescharacteristic
509C4C2×#6704311yescharacteristic
510C2—44no—
511C2#1308140114yesdirect product factor
512C2C2×#1062312911yescharacteristic
513C2C22×#6696811yescharacteristic
514C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#461D11
hypocenterC11C2×#3372
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#10623252C2semidirect
3. #13081401C2direct (N × H)
4. C2×#10622410C2semidirect
5. C2×#10622694C2semidirect
6. C2×#10622409C2semidirect
7. C2×#10622463C2semidirect
9. C2×#10622444C2semidirect
23. #10623252C22semidirect
46. #10622694C22semidirect
51. #10622463C22semidirect
52. #10622444C22semidirect
53. #10622410C22semidirect
54. #10622409C22semidirect
378. C2×C11#3372semidirect
446. C11C2×#3372semidirect
511. C2#13081401direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232522
C2×#106230742
#130814012
C2×#106224102
C2×#106226942
C2×#106224092
C2×#106224632
C2×#106227752
C2×#106224442
C2×#106227772
C2×C4×#43242
C2×C11×#4612
C2×#337211