Finite Group Databasebeta

← C2×#13079803 #15625875

Subgroups — C2×#13079803 #15625875

Order 2816.

2050 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623127C211yesmaximal, characteristic
2C22×#66943C211yesmaximal, characteristic, complemented
3#13079803C2116yesmaximal, direct product factor
4C2×#10622489C212yesmaximal, complemented
5C2×#10622377C212yesmaximal, complemented
6C2×#10622348C211yesmaximal, characteristic, complemented
7C2×#10622647C211yesmaximal, characteristic, complemented
8C2×#10622580C211yesmaximal, characteristic, complemented
9C2×#10622504C212yesmaximal, complemented
10C2×#10622376C212yesmaximal, complemented
11C2×#10622332C211yesmaximal, characteristic, complemented
12C2×C11×#480C211yesmaximal, characteristic, complemented
13C22×#4341—21no—
14C2×C11×#121C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C2×#66993C2211yescharacteristic
17C2×#66992—21no—
18C2×D4×Dic11C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C22×C4⋊Dic11—21no—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×Dic11⋊C4—21no—
23C22×C4×Dic11C2211yescharacteristic
24#10623127—24no—
25#10623127C2218yes—
26C2×#66946C2211yescharacteristic
27C2×#66943—24no—
28C2×#66943—21no—
29C2×#66943—21no—
30C2×#66943C2212yes—
31C2×#66943C2212yes—
32C2×#66943C2218yescomplemented
33C2×#66941C2211yescharacteristic
34C2×#66938—21no—
35C2×(C22⋊D11)⋊C4—21no—
36C11×#480C2218yescomplemented
37C2×C11×#107C2212yes—
38C2×C11×#102C2212yes—
39C2×C11×C22⋊C8C2211yescharacteristic
40C2×#66896C2212yes—
41C2×C22⋊(C11⋊C8)C2211yescharacteristic
42C2×#66885C2212yes—
43C2×#66881C2212yes—
44C2×#66879C2212yes—
45C2×Dic11⋊C8C2212yes—
46#10622647C2218yescomplemented
47#10622580C2218yescomplemented
48C2×#66873C2212yes—
49C2×#66872C2212yes—
50C2×#66871C2212yes—
51#10622504C22116yescomplemented
52#10622489C22116yescomplemented
53#10622377C22116yescomplemented
54#10622376C22116yescomplemented
55#10622348C2218yescomplemented
56#10622332C2218yescomplemented
57C22×D4×C11—21no—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—21no—
62C22×C22⋊D11—21no—
63C22×C22⋊D11—21no—
64C23×Dic11—21no—
65C23×Dic11—21no—
66C23×Dic11D411yescharacteristic
67C23×Dic11D411yescharacteristic
68C2×#4341—28no—
69C2×#4341—48no—
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C22×Dic22—21no—
73C22×C8×C11C2312yes—
74C11×#121—22no—
75C11×#121C2314yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C22⋊C4—21no—
82C2×C22⋊Dic11—21no—
83#66993—22no—
84#66993C2314yes—
85#66992—28no—
86D4×Dic11—22no—
87D4×Dic11C2314yes—
88#66983—22no—
89#66983C2314yes—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11—22no—
96C2×C4⋊Dic11—28no—
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2314yes—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—28no—
104C2×C4×Dic11D411yescharacteristic
105C2×C4×Dic11D411yescharacteristic
106C2×C4×Dic11D414yes—
107C2×C4×Dic11C2311yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C2×C4×Dic11C2314yes—
110C22×C11⋊C8C2312yes—
111#66946—22no—
112#66946C2314yes—
113#66943—24no—
114#66943—24no—
115#66943—28no—
116#66943—28no—
117#66943C2318yes—
118#66943C2318yes—
119#66941—22no—
120#66941C2314yes—
121#66938—28no—
122(C22⋊D11)⋊C4—28no—
123C11×#107C2318yes—
124C11×#102C2318yes—
125C11×C22⋊C8C2314yes—
126#66896C2318yes—
127C22⋊(C11⋊C8)C2314yes—
128#66885C2318yes—
129#66881C2318yes—
130#66879C2318yes—
131Dic11⋊C8C2318yes—
132#66873C2318yes—
133#66872C2318yes—
134#66871C2318yes—
135C2×#3234—111nomaximal, Sylow
136C24×C11—21no—
137C24×C11C2×D411yescharacteristic
138C23×D11—21no—
139C2×D4×C11—24no—
140C2×D4×C11—21no—
141C2×D4×C11—24no—
142C2×D4×C11—44no—
143C2×D4×C11C2412yes—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—44no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2411yescharacteristic
153C2×C22⋊D11—24no—
154C2×C22⋊D11—24no—
155C2×C22⋊D11—24no—
156C2×C22⋊D11—44no—
157C2×C22⋊D11—44no—
158C2×C22⋊D11—44no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—22no—
163C22×Dic11—21no—
164C22×Dic11—42no—
165C22×Dic11—44no—
166C22×Dic11—44no—
167C22×Dic11C2×D411yescharacteristic
168C22×Dic11C2×D411yescharacteristic
169C22×Dic11C2×D414yes—
170C22×Dic11C2×D411yescharacteristic
171C22×Dic11C2×D411yescharacteristic
172C22×Dic11C2×D414yes—
173#4341—432no—
174C2×D44—21no—
175C2×D44—24no—
176C2×D44C2412yes—
177C2×C4×D11—24no—
178C2×C4×D11—44no—
179C2×Dic22—24no—
180C2×Dic22—44no—
181C2×C8×C11—24no—
182C2×C8×C11C2414yes—
183C11×C4⋊C4—21no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4—22no—
186C11×C4⋊C4C2414yes—
187C11×C4⋊C4C2412yes—
188C11×C22⋊C4—24no—
189C22⋊Dic11—24no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192C4⋊Dic11—28no—
193C4⋊Dic11—28no—
194C4⋊Dic11—21no—
195C4⋊Dic11—24no—
196C4⋊Dic11—22no—
197C4⋊Dic11C2412yes—
198C4⋊Dic11C2414yes—
199Dic11⋊C4—24no—
200Dic11⋊C4—28no—
201Dic11⋊C4—28no—
202C4×Dic11C2×D414yes—
203C4×Dic11C2×D414yes—
204C4×Dic11C2×D412yes—
205C4×Dic11C2×D412yes—
206C4×Dic11C2412yes—
207C4×Dic11C2412yes—
208C2×C11⋊C8—24no—
209C2×C11⋊C8C2414yes—
210C2×#532—111no—
211C22×#125—111no—
212#3234—1116no—
213C2×#501—112no—
214C2×#490—112no—
215C2×#481—111no—
216C2×#481—111no—
217C2×#480—111no—
218C2×#480D1111yescharacteristic, complemented
219C2×#478—112no—
220C2×#478—112no—
221C2×#432—111no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—22no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11AGL(1,ℤ/8)14yes—
229C23×C11C22×D412yes—
230C23×C11C22×D411yescharacteristic
231C22×D11—22no—
232C22×D11—42no—
233C22×D11—42no—
234C22×D11—42no—
235D4×C11—24no—
236D4×C11—48no—
237D4×C11—42no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—42no—
244C2×C4×C11—48no—
245C2×C4×C11—44no—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C112−1+414yes—
249C2×C4×C11C2511yescharacteristic
250C22⋊D11—48no—
251C22⋊D11—48no—
252C22⋊D11—48no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—28no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—22no—
260C2×Dic11—44no—
261C2×Dic11—48no—
262C2×Dic11—48no—
263C2×Dic11—42no—
264C2×Dic11—44no—
265C2×Dic11C22×D412yes—
266C2×Dic11C22×D412yes—
267C2×Dic11C22×D412yes—
268C2×Dic11C22×D412yes—
269D44—24no—
270D44—42no—
271C4×D11—48no—
272Dic22—48no—
273C8×C11—24no—
274C11⋊C8—24no—
275C22×#41—221no—
276#532—118no—
277#532—224no—
278C2×C4⋊Q8—111no—
279C2×#127—111no—
280C2×#125—112no—
281C2×#125—112no—
282C2×#125—118no—
283C2×#125—221no—
284C2×#125—221no—
285C2×#125—224no—
286C2×#124—221no—
287C2×#121—111no—
288C2×#121—221no—
289C2×#121C2×D1111yescharacteristic
290C2×C4×D4—111no—
291C2×C4×D4—111no—
292C2×C4×D4—221no—
293C22×C4⋊C4—111no—
294C22×C4⋊C4—221no—
295C22×C4⋊C4—221no—
296C22×C4⋊C4C2×D1111yescharacteristic
297C22×C42—111no—
298#501—1116no—
299#490—1116no—
300#481—118no—
301#481—118no—
302#480—118no—
303#480C2×D1118yescomplemented
304#478—1116no—
305#478—1116no—
306#432—118no—
307C2×#107—112no—
308C2×#107C2×D1112yes—
309C2×#106—112no—
310C2×#106—112no—
311C2×C4⋊C8—112no—
312C2×#102—112no—
313C2×#102—112no—
314C2×#102—112no—
315C2×#102C2×D1112yes—
316C2×C22⋊C8—111no—
317C2×C22⋊C8C2×D1111yescharacteristic
318C2×#97—112no—
319C22×C11—22no—
320C22×C11—28no—
321C22×C11—22no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—84no—
326C22×C11#53612yes—
327C22×C11C2×AGL(1,ℤ/8)14yes—
328C22×C11C2×AGL(1,ℤ/8)12yes—
329C22×C11#57512yes—
330C22×C11C23×D411yescharacteristic
331C2×D11—42no—
332C2×D11—42no—
333C2×D11—42no—
334C2×D11—84no—
335C4×C11—22no—
336C4×C11—44no—
337C4×C11—42no—
338C4×C11#53612yes—
339C4×C11C2×2−1+412yes—
340Dic11—22no—
341Dic11—22no—
342Dic11—22no—
343Dic11—22no—
344Dic11—42no—
345Dic11—44no—
346C2×#41—228no—
347C2×#41—448no—
348C22×Q8—221no—
349C22×D4—21no—
350C22×D4—111no—
351C22×D4—221no—
352C22×D4—221no—
353C22×D4—221no—
354C22×D4C22×D1111yescharacteristic
355C23×C4—21no—
356C23×C4—111no—
357C23×C4—111no—
358C23×C4—221no—
359C23×C4—221no—
360C23×C4—221no—
361C23×C4C22×D1111yescharacteristic
362C22×C8—112no—
363C22×C8C22×D1112yes—
364C4⋊Q8—114no—
365C4⋊Q8—222no—
366#127—114no—
367#127—222no—
368#125—118no—
369#125—118no—
370#125—224no—
371#125—228no—
372#125—228no—
373#125—224no—
374#124—228no—
375#121—22no—
376#121—114no—
377#121—228no—
378#121—222no—
379#121C22×D1114yes—
380C4×D4—114no—
381C4×D4—114no—
382C4×D4—228no—
383C4×D4—222no—
384C4×D4—222no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—21no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—114no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—228no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4—228no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—221no—
399C2×C4⋊C4C22×D1112yes—
400C2×C4⋊C4C22×D1114yes—
401C2×C4⋊C4C22×D1111yescharacteristic
402C2×C22⋊C4—21no—
403C2×C22⋊C4—221no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C42—111no—
407C2×C42—111no—
408C2×C42—114no—
409C2×C42—111no—
410C2×C42—111no—
411C2×C42—114no—
412#107—118no—
413#107C22×D1118yes—
414#106—118no—
415#106—118no—
416C4⋊C8—118no—
417#102—118no—
418#102—118no—
419#102—118no—
420#102C22×D1118yes—
421C22⋊C8—114no—
422C22⋊C8C22×D1114yes—
423#97—118no—
424C2×C11—24no—
425C2×C11—82no—
426C2×C11#323414yescomplemented
427C2×C11C2×#53611yescharacteristic
428C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
429C2×C11C2×#57511yescharacteristic
430D11—82no—
431C24—21no—
432C24—221no—
433C24D4×D1111yescharacteristic
434#41—4432no—
435C2×Q8—224no—
436C2×Q8—444no—
437C2×D4—24no—
438C2×D4—21no—
439C2×D4—24no—
440C2×D4—44no—
441C2×D4—112no—
442C2×D4—224no—
443C2×D4—224no—
444C2×D4—224no—
445C2×D4—221no—
446C2×D4—224no—
447C2×D4—444no—
448C2×D4—444no—
449C2×D4—444no—
450C2×D4C23×D1112yes—
451C22×C4—24no—
452C22×C4—24no—
453C22×C4—21no—
454C22×C4—22no—
455C22×C4—44no—
456C22×C4—114no—
457C22×C4—111no—
458C22×C4—111no—
459C22×C4—111no—
460C22×C4—111no—
461C22×C4—114no—
462C22×C4—224no—
463C22×C4—224no—
464C22×C4—224no—
465C22×C4—224no—
466C22×C4—221no—
467C22×C4—222no—
468C22×C4—444no—
469C22×C4—442no—
470C22×C4—444no—
471C22×C4—444no—
472C22×C4D4×D1112yes—
473C22×C4D4×D1111yescharacteristic
474C22×C4C23×D1112yes—
475C22×C4C23×D1111yescharacteristic
476C2×C8—24no—
477C2×C8—114no—
478C2×C8—224no—
479C2×C8C23×D1114yes—
480C4⋊C4—24no—
481C4⋊C4—22no—
482C4⋊C4—21no—
483C4⋊C4—114no—
484C4⋊C4—112no—
485C4⋊C4—228no—
486C4⋊C4—228no—
487C4⋊C4—228no—
488C4⋊C4—228no—
489C4⋊C4—224no—
490C4⋊C4—224no—
491C4⋊C4—222no—
492C4⋊C4—221no—
493C4⋊C4C23×D1114yes—
494C4⋊C4C23×D1112yes—
495C22⋊C4—24no—
496C22⋊C4—224no—
497C22⋊C4—224no—
498C22⋊C4—224no—
499C42—112no—
500C42—114no—
501C42—114no—
502C42—112no—
503C42—112no—
504C42—112no—
505C11C2×#323411yescharacteristic, complemented, Sylow
506C23—22no—
507C23—22no—
508C23—22no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—222no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23#6696414yes—
517C23C2×D4×D1112yes—
518C23C2×D4×D1111yescharacteristic
519Q8—448no—
520D4—24no—
521D4—48no—
522D4—42no—
523D4—224no—
524D4—448no—
525D4—448no—
526D4—448no—
527D4—442no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—48no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—112no—
537C2×C4—112no—
538C2×C4—112no—
539C2×C4—112no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—228no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—224no—
547C2×C4—448no—
548C2×C4—444no—
549C2×C4—448no—
550C2×C4—448no—
551C2×C4—442no—
552C2×C4—444no—
553C2×C4C2×D4×D1112yes—
554C2×C4C2×D4×D1111yescharacteristic
555C2×C4#6704314yes—
556C2×C4C24×D1111yescharacteristic
557C8—24no—
558C8—224no—
559C22—22no—
560C22—22no—
561C22—28no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—84no—
566C22—442no—
567C22—442no—
568C22—442no—
569C22—884no—
570C22#1062317912yes—
571C22C2×#6696414yes—
572C22C2×#6696412yes—
573C22#1062330812yes—
574C22C22×D4×D1111yescharacteristic
575C4—22no—
576C4—44no—
577C4—42no—
578C4—222no—
579C4—222no—
580C4—222no—
581C4—222no—
582C4—442no—
583C4—444no—
584C4#1062317912yes—
585C4C2×#6704312yes—
586C2—24no—
587C2—82no—
588C2—882no—
589C2#1307980314yesdirect product factor
590C2C2×#1062317911yescharacteristic
591C2C22×#6696411yescharacteristic
592C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#480C2
socleC23×C11C22×D4
prime radicalC2×#10623127C2
hypercenterC2×#480D11
hypocenterC11C2×#3234
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C22×#66943C2semidirect
3. #13079803C2direct (N × H)
4. C2×#10622489C2semidirect
5. C2×#10622377C2semidirect
6. C2×#10622348C2semidirect
7. C2×#10622647C2semidirect
8. C2×#10622580C2semidirect
9. C2×#10622504C2semidirect
10. C2×#10622376C2semidirect
11. C2×#10622332C2semidirect
12. C2×C11×#480C2semidirect
32. C2×#66943C22semidirect
36. C11×#480C22semidirect
46. #10622647C22semidirect
47. #10622580C22semidirect
51. #10622504C22semidirect
52. #10622489C22semidirect
53. #10622377C22semidirect
54. #10622376C22semidirect
55. #10622348C22semidirect
56. #10622332C22semidirect
218. C2×#480D11semidirect
303. #480C2×D11semidirect
426. C2×C11#3234semidirect
505. C11C2×#3234semidirect
589. C2#13079803direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231272
C22×#669432
#130798032
C2×#106224892
C2×#106223772
C2×#106223482
C2×#106226472
C2×#106225802
C2×#106225042
C2×#106223762
C2×#106223322
C2×C11×#4802
C2×#323411