Finite Group Databasebeta

← C2×#13079840 #15625898

Subgroups — C2×#13079840 #15625898

Order 2816.

2018 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic, complemented
2C2×#10623155C211yesmaximal, characteristic
3#13079840C2116yesmaximal, direct product factor
4C2×#10622469C212yesmaximal, complemented
5C2×#10622408C212yesmaximal, complemented
6C2×#10622656C211yesmaximal, characteristic, complemented
7C2×#10622349C211yesmaximal, characteristic
8C2×#10622580C211yesmaximal, characteristic
9C2×#10622407C212yesmaximal, complemented
10C2×#10622483C212yesmaximal, complemented
11C2×#10622332C211yesmaximal, characteristic, complemented
12C2×C11×#483C211yesmaximal, characteristic, complemented
13C23×Dic22—21no—
14C2×C11×C22⋊Q8C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C2×#67000C2211yescharacteristic
17C2×Q8×Dic11C2211yescharacteristic
18C2×#66983C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4—21no—
21C22×C4×Dic11C2211yescharacteristic
22#10623155—24no—
23#10623155C2218yes—
24C2×#66951—21no—
25C2×#66946C2211yescharacteristic
26C2×#66945—21no—
27C2×#66943C2211yescharacteristic
28C2×#66941—24no—
29C2×#66941—21no—
30C2×#66941—21no—
31C2×#66941C2212yes—
32C2×#66941C2212yes—
33C2×#66941C2218yescomplemented
34C2×#66939—21no—
35C2×(C22⋊D11)⋊C4—21no—
36C11×#483C2218yescomplemented
37C2×C11×#106C2212yes—
38C2×C11×#103C2212yes—
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×#66899C2212yes—
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×#66885C2212yes—
43C2×#66882C2212yes—
44C2×#66879C2212yes—
45C2×Dic11⋊C8C2212yes—
46#10622656C2218yescomplemented
47#10622580C2218yes—
48C2×#66873C2212yes—
49C2×#66872C2212yes—
50C2×#66871C2212yes—
51#10622483C22116yescomplemented
52#10622469C22116yescomplemented
53#10622408C22116yescomplemented
54#10622407C22116yescomplemented
55#10622349C2218yes—
56#10622332C2218yescomplemented
57C22×Q8×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C23×Dic11D411yescharacteristic
63C23×Dic11D411yescharacteristic
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×Dic22—22no—
67C22×Dic22—22no—
68C22×Dic22—28no—
69C22×Dic22—48no—
70C22×C8×C11C2312yes—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8C2314yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80#67000—22no—
81#67000C2314yes—
82Q8×Dic11—22no—
83Q8×Dic11C2314yes—
84#66983—22no—
85#66983C2314yes—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—22no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11C2312yes—
95C2×C4⋊Dic11C2314yes—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×Dic11⋊C4—28no—
101C2×C4×Dic11—21no—
102C2×C4×Dic11D411yescharacteristic
103C2×C4×Dic11D411yescharacteristic
104C2×C4×Dic11D414yes—
105C2×C4×Dic11C2311yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C2×C4×Dic11C2314yes—
108C22×C11⋊C8C2312yes—
109#66951—28no—
110#66946—22no—
111#66946C2314yes—
112#66945—28no—
113#66943—22no—
114#66943C2314yes—
115#66941—24no—
116#66941—24no—
117#66941—28no—
118#66941—28no—
119#66941C2318yes—
120#66941C2318yes—
121#66939—28no—
122(C22⋊D11)⋊C4—28no—
123C11×#106C2318yes—
124C11×#103C2318yes—
125C11×C22⋊C8C2314yes—
126#66899C2318yes—
127C22⋊(C11⋊C8)C2314yes—
128#66885C2318yes—
129#66882C2318yes—
130#66879C2318yes—
131Dic11⋊C8C2318yes—
132#66873C2318yes—
133#66872C2318yes—
134#66871C2318yes—
135C2×#3238—111nomaximal, Sylow
136C24×C11C2×D411yescharacteristic
137C23×D11—21no—
138C2×Q8×C11—21no—
139C2×Q8×C11—24no—
140C2×Q8×C11C2412yes—
141C22×C4×C11—24no—
142C22×C4×C11—21no—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—21no—
146C22×C4×C11—44no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2411yescharacteristic
151C2×C22⋊D11—24no—
152C2×C22⋊D11—44no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—21no—
156C22×Dic11—24no—
157C22×Dic11—22no—
158C22×Dic11—44no—
159C22×Dic11C2×D414yes—
160C22×Dic11C2×D414yes—
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C2×D44—21no—
166C2×D44—24no—
167C2×D44C2412yes—
168C2×C4×D11—24no—
169C2×C4×D11—44no—
170C2×Dic22—28no—
171C2×Dic22—28no—
172C2×Dic22—48no—
173C2×Dic22—48no—
174C2×Dic22—432no—
175C2×C8×C11—24no—
176C2×C8×C11C2414yes—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—21no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4C2414yes—
182C11×C4⋊C4C2412yes—
183C11×C22⋊C4—24no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—24no—
188C4⋊Dic11—24no—
189C4⋊Dic11—24no—
190C4⋊Dic11—24no—
191C4⋊Dic11—22no—
192C4⋊Dic11—21no—
193C4⋊Dic11C2412yes—
194C4⋊Dic11C2414yes—
195Dic11⋊C4—24no—
196Dic11⋊C4—28no—
197Dic11⋊C4—28no—
198C4×Dic11—24no—
199C4×Dic11C2×D412yes—
200C4×Dic11C2×D414yes—
201C4×Dic11C2×D412yes—
202C4×Dic11C2×D414yes—
203C4×Dic11C2412yes—
204C4×Dic11C2412yes—
205C2×C11⋊C8—24no—
206C2×C11⋊C8C2414yes—
207C22×C4⋊Q8—111no—
208C2×#529—111no—
209#3238—1116no—
210C2×#501—112no—
211C2×#489—112no—
212C2×#483—111no—
213C2×#483D1111yescharacteristic, complemented
214C2×#480—111no—
215C2×#480—111no—
216C2×#477—112no—
217C2×#476—112no—
218C2×#432—111no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11AGL(1,ℤ/8)14yes—
222C23×C11C22×D412yes—
223C23×C11C22×D411yescharacteristic
224C22×D11—22no—
225C22×D11—42no—
226C22×D11—42no—
227C22×D11—42no—
228Q8×C11—24no—
229Q8×C11—42no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—42no—
237C2×C4×C11—48no—
238C2×C4×C11—44no—
239C2×C4×C11—42no—
240C2×C4×C11C22×D412yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C112−1+414yes—
243C2×C4×C11C2511yescharacteristic
244C22⋊D11—48no—
245C2×Dic11—28no—
246C2×Dic11—22no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—28no—
250C2×Dic11—22no—
251C2×Dic11—24no—
252C2×Dic11—48no—
253C2×Dic11—44no—
254C2×Dic11—42no—
255C2×Dic11#13714yes—
256C2×Dic11C22×D412yes—
257C2×Dic11C22×D412yes—
258C2×Dic11C22×D412yes—
259C2×Dic11C22×D412yes—
260D44—24no—
261D44—42no—
262C4×D11—48no—
263Dic22—416no—
264Dic22—416no—
265C8×C11—24no—
266C11⋊C8—24no—
267C23×Q8—221no—
268C2×C4⋊Q8—112no—
269C2×C4⋊Q8—112no—
270C2×C4⋊Q8—118no—
271C2×C4⋊Q8—221no—
272C2×C4⋊Q8—221no—
273C2×C4⋊Q8—224no—
274#529—118no—
275#529—224no—
276C2×#126—221no—
277C2×#125—111no—
278C2×#124—111no—
279C2×#123—221no—
280C2×C22⋊Q8C2×D1111yescharacteristic
281C2×#121—111no—
282C2×C4×Q8—111no—
283C2×C4×D4—111no—
284C2×C4×D4—221no—
285C2×#117—221no—
286C22×C4⋊C4—111no—
287C22×C4⋊C4—221no—
288C22×C4⋊C4C2×D1111yescharacteristic
289C22×C42—111no—
290#501—1116no—
291#489—1116no—
292#483—118no—
293#483C2×D1118yescomplemented
294#480—118no—
295#480—118no—
296#477—1116no—
297#476—1116no—
298#432—118no—
299C2×#107—112no—
300C2×#107—112no—
301C2×#106—112no—
302C2×#106C2×D1112yes—
303C2×C4⋊C8—112no—
304C2×#103—112no—
305C2×#103C2×D1112yes—
306C2×#102—112no—
307C2×#102—112no—
308C2×C22⋊C8—111no—
309C2×C22⋊C8C2×D1111yescharacteristic
310C2×#97—112no—
311C22×C11—22no—
312C22×C11—28no—
313C22×C11—22no—
314C22×C11#53612yes—
315C22×C11C2×AGL(1,ℤ/8)14yes—
316C22×C11C2×AGL(1,ℤ/8)12yes—
317C22×C11C2×#13712yes—
318C22×C11C23×D411yescharacteristic
319C2×D11—42no—
320C2×D11—42no—
321C2×D11—42no—
322C2×D11—84no—
323C4×C11—22no—
324C4×C11—42no—
325C4×C11—44no—
326C4×C11—42no—
327C4×C11#53612yes—
328C4×C11C2×2−1+412yes—
329Dic11—22no—
330Dic11—22no—
331Dic11—22no—
332Dic11—44no—
333Dic11—42no—
334Dic11C2×#13714yes—
335C22×Q8—228no—
336C22×Q8—222no—
337C22×Q8—222no—
338C22×Q8—448no—
339C22×Q8C22×D1111yescharacteristic
340C22×D4—111no—
341C22×D4—221no—
342C23×C4—21no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—221no—
346C23×C4—221no—
347C23×C4C22×D1111yescharacteristic
348C22×C8—112no—
349C22×C8C22×D1112yes—
350C4⋊Q8—118no—
351C4⋊Q8—118no—
352C4⋊Q8—228no—
353C4⋊Q8—224no—
354C4⋊Q8—224no—
355C4⋊Q8—228no—
356#126—228no—
357#125—114no—
358#125—222no—
359#124—114no—
360#124—222no—
361#123—228no—
362C22⋊Q8—22no—
363C22⋊Q8C22×D1114yes—
364#121—114no—
365#121—222no—
366C4×Q8—114no—
367C4×Q8—222no—
368C4×D4—114no—
369C4×D4—222no—
370C4×D4—228no—
371#117—228no—
372C2×C4⋊C4—22no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—114no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—228no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—222no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C22×D1112yes—
387C2×C4⋊C4C22×D1114yes—
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C22⋊C4—21no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—114no—
397C2×C42—111no—
398C2×C42—111no—
399C2×C42—114no—
400C2×C42—221no—
401#107—118no—
402#107—118no—
403#106—118no—
404#106C22×D1118yes—
405C4⋊C8—118no—
406#103—118no—
407#103C22×D1118yes—
408#102—118no—
409#102—118no—
410C22⋊C8—114no—
411C22⋊C8C22×D1114yes—
412#97—118no—
413C2×C11—24no—
414C2×C11#323814yescomplemented
415C2×C11C2×#53611yescharacteristic
416C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
417C2×C11C22×#13711yescharacteristic
418D11—82no—
419C24—221no—
420C24D4×D1111yescharacteristic
421C2×Q8—21no—
422C2×Q8—24no—
423C2×Q8—228no—
424C2×Q8—228no—
425C2×Q8—4432no—
426C2×Q8—448no—
427C2×Q8—448no—
428C2×Q8C23×D1112yes—
429C2×D4—112no—
430C2×D4—224no—
431C2×D4—221no—
432C2×D4—224no—
433C2×D4—444no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—44no—
440C22×C4—111no—
441C22×C4—114no—
442C22×C4—114no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—111no—
446C22×C4—224no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—224no—
450C22×C4—221no—
451C22×C4—222no—
452C22×C4—444no—
453C22×C4—444no—
454C22×C4D4×D1112yes—
455C22×C4D4×D1111yescharacteristic
456C22×C4C23×D1112yes—
457C22×C4C23×D1111yescharacteristic
458C2×C8—24no—
459C2×C8—114no—
460C2×C8—224no—
461C2×C8C23×D1114yes—
462C4⋊C4—24no—
463C4⋊C4—22no—
464C4⋊C4—24no—
465C4⋊C4—21no—
466C4⋊C4—114no—
467C4⋊C4—112no—
468C4⋊C4—228no—
469C4⋊C4—228no—
470C4⋊C4—224no—
471C4⋊C4—224no—
472C4⋊C4—224no—
473C4⋊C4—224no—
474C4⋊C4—222no—
475C4⋊C4—221no—
476C4⋊C4C23×D1114yes—
477C4⋊C4C23×D1112yes—
478C22⋊C4—24no—
479C22⋊C4—224no—
480C22⋊C4—224no—
481C22⋊C4—224no—
482C22⋊C4—224no—
483C42—114no—
484C42—112no—
485C42—112no—
486C42—114no—
487C42—112no—
488C42—112no—
489C42—224no—
490C11C2×#323811yescharacteristic, complemented, Sylow
491C23—22no—
492C23—22no—
493C23—222no—
494C23—442no—
495C23—442no—
496C23—442no—
497C23#6696714yes—
498C23C2×D4×D1112yes—
499C23C2×D4×D1111yescharacteristic
500Q8—24no—
501Q8—42no—
502Q8—4416no—
503Q8—4416no—
504D4—224no—
505D4—448no—
506D4—442no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—48no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—114no—
518C2×C4—112no—
519C2×C4—112no—
520C2×C4—112no—
521C2×C4—112no—
522C2×C4—228no—
523C2×C4—228no—
524C2×C4—222no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—224no—
529C2×C4—448no—
530C2×C4—448no—
531C2×C4—444no—
532C2×C4—442no—
533C2×C4C2×D4×D1112yes—
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4#6704314yes—
536C2×C4C24×D1111yescharacteristic
537C8—24no—
538C8—224no—
539C22—28no—
540C22—22no—
541C22—22no—
542C22—442no—
543C22—442no—
544C22—442no—
545C22—884no—
546C22#1062317912yes—
547C22C2×#6696714yes—
548C22C2×#6696712yes—
549C22D11×#13712yes—
550C22C22×D4×D1111yescharacteristic
551C4—22no—
552C4—42no—
553C4—44no—
554C4—42no—
555C4—114no—
556C4—222no—
557C4—222no—
558C4—222no—
559C4—444no—
560C4—442no—
561C4#1062317912yes—
562C4C2×#6704312yes—
563C2—24no—
564C2—882no—
565C2#1307984014yesdirect product factor
566C2C2×#1062317911yescharacteristic
567C2C22×#6696711yescharacteristic
568C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#483C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenterC2×#483D11
hypocenterC11C2×#3238
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#483

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
3. #13079840C2direct (N × H)
4. C2×#10622469C2semidirect
5. C2×#10622408C2semidirect
6. C2×#10622656C2semidirect
9. C2×#10622407C2semidirect
10. C2×#10622483C2semidirect
11. C2×#10622332C2semidirect
12. C2×C11×#483C2semidirect
33. C2×#66941C22semidirect
36. C11×#483C22semidirect
46. #10622656C22semidirect
51. #10622483C22semidirect
52. #10622469C22semidirect
53. #10622408C22semidirect
54. #10622407C22semidirect
56. #10622332C22semidirect
213. C2×#483D11semidirect
293. #483C2×D11semidirect
414. C2×C11#3238semidirect
490. C11C2×#3238semidirect
565. C2#13079840direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669412
C2×#106231552
#130798402
C2×#106224692
C2×#106224082
C2×#106226562
C2×#106223492
C2×#106225802
C2×#106224072
C2×#106224832
C2×#106223322
C2×C11×#4832
C2×#323811