Finite Group Databasebeta

← C2×#13079847 #15625906

Subgroups — C2×#13079847 #15625906

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
1C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
2C2×#10623222C211yesmaximal, characteristic
3#13079847C2116yesmaximal, direct product factor
4C2×#10622678C211yesmaximal, characteristic, complemented
5C2×#10622702C211yesmaximal, characteristic, complemented
6C2×#10622327C211yesmaximal, characteristic, complemented
7C2×#10622497C212yesmaximal, complemented
8C2×#10622476C212yesmaximal
9C2×#10622467C212yesmaximal, complemented
10C2×#10622503C212yesmaximal, complemented
11C2×#10622318C211yesmaximal, characteristic, complemented
12C2×C11×#501C211yesmaximal, characteristic, complemented
13C22×Q8×D11—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125C2211yescharacteristic
16C2×#66997—21no—
17D11×C4⋊Q8—24no—
18D11×C4⋊Q8C2218yescomplemented
19#10623222—24no—
20#10623222C2218yes—
21C2×#66951—21no—
22C2×#66950C2211yescharacteristic
23C2×#66948C2211yescharacteristic
24C2×#66947—21no—
25C2×#66946—21no—
26C2×#66946C2211yescharacteristic
27C2×#66945—21no—
28C2×C4⋊C4×D11—21no—
29C2×C4⋊C4×D11C2212yes—
30C2×#66941—21no—
31C2×#66941C2212yes—
32C2×#66940C2211yescharacteristic
33C2×#66928C2211yescharacteristic
34C2×C42×D11C2211yescharacteristic
35C2×#66922C2211yescharacteristic
36C11×#501C2218yescomplemented
37C2×C11×#107C2212yes—
38C2×C11×#106C2212yes—
39C2×C11×#97C2211yescharacteristic
40C2×#66885C2212yes—
41C2×(C2×D11)⋊C8C2212yes—
42C2×#66880C2212yes—
43C2×Dic11⋊C8C2212yes—
44#10622702C2218yescomplemented
45#10622678C2218yescomplemented
46C2×#66874C2212yes—
47C2×#66873C2212yes—
48C2×#66872C2212yes—
49C2×#66871C2212yes—
50C2×#66867C2211yescharacteristic
51#10622503C22116yescomplemented
52#10622497C22116yescomplemented
53#10622476C22116yes—
54#10622467C22116yescomplemented
55#10622327C2218yescomplemented
56#10622318C2218yescomplemented
57C22×Q8×C11—21no—
58C2×Q8×D11—28no—
59C2×Q8×D11—48no—
60C22×D44—21no—
61C22×D44C2311yescharacteristic
62C22×C4×D11—22no—
63C22×C4×D11—21no—
64C22×C4×D11D411yescharacteristic
65C22×C4×D11D411yescharacteristic
66C22×C4×D11C2311yescharacteristic
67C22×Dic22—21no—
68C22×Dic22—22no—
69C22×Dic22C2311yescharacteristic
70C22×C8×C11C2312yes—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8C2314yes—
73C11×#125—22no—
74C11×#125C2314yes—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2312yes—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C42×C11C2311yescharacteristic
82#66997—28no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—21no—
87C2×(C2×D11)⋊C4—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11C2312yes—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—22no—
93C2×Dic11⋊C4—22no—
94C2×C4×Dic11—21no—
95C2×C4×Dic11D411yescharacteristic
96C2×C4×Dic11D411yescharacteristic
97C2×C4×Dic11C2311yescharacteristic
98C22×C11⋊C8C2312yes—
99#66951—28no—
100#66950—22no—
101#66950C2314yes—
102#66948—22no—
103#66948C2314yes—
104#66947—28no—
105#66946—28no—
106#66946—22no—
107#66946C2314yes—
108#66945—28no—
109C4⋊C4×D11—24no—
110C4⋊C4×D11—28no—
111C4⋊C4×D11C2318yes—
112#66941—24no—
113#66941—28no—
114#66941C2318yes—
115#66940—22no—
116#66940C2314yes—
117#66928—22no—
118#66928C2314yes—
119C42×D11D414yes—
120C42×D11C2314yes—
121#66922—22no—
122#66922C2314yes—
123C11×#107C2318yes—
124C11×#106C2318yes—
125C11×#97C2314yes—
126#66885C2318yes—
127(C2×D11)⋊C8C2318yes—
128#66880C2318yes—
129Dic11⋊C8C2318yes—
130#66874C2318yes—
131#66873C2318yes—
132#66872C2318yes—
133#66871C2318yes—
134#66867C2314yes—
135C2×#3239—111nomaximal, Sylow
136C23×D11—21no—
137C23×D11C2×D411yescharacteristic
138C2×Q8×C11—24no—
139C2×Q8×C11—44no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—22no—
148C22×Dic11C2×D411yescharacteristic
149C22×Dic11C2×D411yescharacteristic
150C22×Dic11C2×D411yescharacteristic
151Q8×D11—432no—
152C2×D44—24no—
153C2×D44—21no—
154C2×D44—24no—
155C2×D44—44no—
156C2×D44C2412yes—
157C2×C4×D11—24no—
158C2×C4×D11—24no—
159C2×C4×D11—24no—
160C2×C4×D11—28no—
161C2×C4×D11—24no—
162C2×C4×D11—48no—
163C2×C4×D11—44no—
164C2×C4×D11C2×D412yes—
165C2×C4×D11C2×D414yes—
166C2×C4×D11C2×D414yes—
167C2×C4×D11C2412yes—
168C2×Dic22—28no—
169C2×Dic22—24no—
170C2×Dic22—21no—
171C2×Dic22—24no—
172C2×Dic22—44no—
173C2×Dic22—48no—
174C2×Dic22C2412yes—
175C2×C8×C11—24no—
176C2×C8×C11C2414yes—
177C11×C4⋊C4—21no—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4C2412yes—
184C11×C4⋊C4C2412yes—
185C11×C4⋊C4C2414yes—
186C42×C11C2×D412yes—
187C42×C11C2412yes—
188(C2×D11)⋊C4—24no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—24no—
193C4⋊Dic11—24no—
194C4⋊Dic11—22no—
195C4⋊Dic11—24no—
196C4⋊Dic11C2414yes—
197Dic11⋊C4—24no—
198Dic11⋊C4—28no—
199Dic11⋊C4—28no—
200C4×Dic11—24no—
201C4×Dic11C2×D412yes—
202C4×Dic11C2×D414yes—
203C4×Dic11C2×D414yes—
204C4×Dic11C2412yes—
205C2×C11⋊C8—24no—
206C2×C11⋊C8C2414yes—
207C22×C4⋊Q8—111no—
208C2×#529—111no—
209#3239—1116no—
210C2×#501—111no—
211C2×#501D1111yescharacteristic, complemented
212C2×#489—111no—
213C2×#489—111no—
214C2×#484—112no—
215C2×#481—112no—
216C2×#475—112no—
217C2×#474—112no—
218C2×#432—111no—
219C23×C11C22×D411yescharacteristic
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—22no—
223C22×D11—42no—
224C22×D11—42no—
225C22×D11—42no—
226C22×D11#13714yes—
227C22×D11C22×D412yes—
228Q8×C11—48no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—44no—
235C2×C4×C11—42no—
236C2×C4×C11—42no—
237C2×C4×C11C22×D412yes—
238C2×C4×C11C22×D412yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C112−1+414yes—
241C2×C4×C11C2511yescharacteristic
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—42no—
247C2×Dic11—44no—
248C2×Dic11AGL(1,ℤ/8)14yes—
249C2×Dic11C22×D412yes—
250C2×Dic11C22×D412yes—
251C2×Dic11C22×D412yes—
252D44—24no—
253D44—48no—
254D44—42no—
255C4×D11—28no—
256C4×D11—24no—
257C4×D11—24no—
258C4×D11—28no—
259C4×D11—416no—
260C4×D11—48no—
261Dic22—24no—
262Dic22—48no—
263Dic22—42no—
264Dic22—416no—
265C8×C11—24no—
266C11⋊C8—24no—
267C23×Q8—221no—
268C2×C4⋊Q8—118no—
269C2×C4⋊Q8—112no—
270C2×C4⋊Q8—111no—
271C2×C4⋊Q8—221no—
272C2×C4⋊Q8—224no—
273C2×C4⋊Q8—221no—
274C2×C4⋊Q8C2×D1111yescharacteristic
275#529—118no—
276#529—224no—
277C2×#126—221no—
278C2×#125C2×D1111yescharacteristic
279C2×#124—111no—
280C2×#123—221no—
281C2×C22⋊Q8—111no—
282C2×#121—111no—
283C2×C4×Q8—111no—
284C2×C4×D4—111no—
285C2×C4×D4—221no—
286C2×#117—221no—
287C22×C4⋊C4—112no—
288C22×C4⋊C4—221no—
289C22×C42—111no—
290#501—118no—
291#501C2×D1118yescomplemented
292#489—118no—
293#489—118no—
294#484—1116no—
295#481—1116no—
296#475—1116no—
297#474—1116no—
298#432—118no—
299C2×#107—112no—
300C2×#107C2×D1112yes—
301C2×#106—112no—
302C2×#106C2×D1112yes—
303C2×C4⋊C8—112no—
304C2×#103—112no—
305C2×#103—112no—
306C2×#102—112no—
307C2×#102—112no—
308C2×C22⋊C8—112no—
309C2×#97—111no—
310C2×#97C2×D1111yescharacteristic
311C22×C11#53612yes—
312C22×C11C2×AGL(1,ℤ/8)12yes—
313C22×C11C2×#13712yes—
314C22×C11C23×D411yescharacteristic
315C2×D11—22no—
316C2×D11—28no—
317C2×D11—22no—
318C2×D11—42no—
319C2×D11—42no—
320C2×D11—42no—
321C2×D11—84no—
322C2×D11C2×#13714yes—
323C4×C11—22no—
324C4×C11—22no—
325C4×C11—44no—
326C4×C11—42no—
327C4×C11—42no—
328C4×C11#53612yes—
329C4×C11C2×2−1+412yes—
330Dic11—22no—
331Dic11—22no—
332Dic11—42no—
333Dic11—44no—
334Dic11C2×AGL(1,ℤ/8)14yes—
335C22×Q8—21no—
336C22×Q8—111no—
337C22×Q8—222no—
338C22×Q8—228no—
339C22×Q8—221no—
340C22×Q8—448no—
341C22×D4—111no—
342C22×D4—221no—
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—221no—
347C23×C4—222no—
348C22×C8—112no—
349C22×C8C22×D1112yes—
350C4⋊Q8—22no—
351C4⋊Q8—118no—
352C4⋊Q8—114no—
353C4⋊Q8—228no—
354C4⋊Q8—224no—
355C4⋊Q8—228no—
356C4⋊Q8—222no—
357C4⋊Q8C22×D1114yes—
358#126—228no—
359#125—22no—
360#125C22×D1114yes—
361#124—114no—
362#124—222no—
363#123—228no—
364C22⋊Q8—114no—
365C22⋊Q8—222no—
366#121—114no—
367#121—222no—
368C4×Q8—114no—
369C4×Q8—222no—
370C4×D4—114no—
371C4×D4—222no—
372C4×D4—228no—
373#117—228no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—118no—
379C2×C4⋊C4—224no—
380C2×C4⋊C4—228no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4—222no—
383C2×C4⋊C4—221no—
384C2×C4⋊C4—221no—
385C2×C4⋊C4—221no—
386C2×C4⋊C4C22×D1112yes—
387C2×C4⋊C4C22×D1111yescharacteristic
388C2×C4⋊C4C22×D1111yescharacteristic
389C2×C22⋊C4—221no—
390C2×C22⋊C4—221no—
391C2×C22⋊C4—221no—
392C2×C22⋊C4—221no—
393C2×C22⋊C4—221no—
394C2×C42—111no—
395C2×C42—111no—
396C2×C42—111no—
397C2×C42—114no—
398C2×C42—114no—
399C2×C42—221no—
400C2×C42C22×D1111yescharacteristic
401#107—118no—
402#107C22×D1118yes—
403#106—118no—
404#106C22×D1118yes—
405C4⋊C8—118no—
406#103—118no—
407#103—118no—
408#102—118no—
409#102—118no—
410C22⋊C8—118no—
411#97—114no—
412#97C22×D1114yes—
413C2×C11#323914yescomplemented
414C2×C11C2×#53611yescharacteristic
415C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
416C2×C11C22×#13711yescharacteristic
417D11—24no—
418D11—82no—
419C24—111no—
420C24—221no—
421C2×Q8—24no—
422C2×Q8—44no—
423C2×Q8—112no—
424C2×Q8—228no—
425C2×Q8—221no—
426C2×Q8—224no—
427C2×Q8—224no—
428C2×Q8—444no—
429C2×Q8—448no—
430C2×Q8—4432no—
431C2×D4—112no—
432C2×D4—224no—
433C2×D4—221no—
434C2×D4—224no—
435C2×D4—444no—
436C22×C4—21no—
437C22×C4—21no—
438C22×C4—22no—
439C22×C4—111no—
440C22×C4—111no—
441C22×C4—111no—
442C22×C4—112no—
443C22×C4—114no—
444C22×C4—114no—
445C22×C4—112no—
446C22×C4—224no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4—228no—
450C22×C4—224no—
451C22×C4—221no—
452C22×C4—222no—
453C22×C4—444no—
454C22×C4—448no—
455C22×C4D4×D1111yescharacteristic
456C22×C4D4×D1111yescharacteristic
457C22×C4C23×D1111yescharacteristic
458C2×C8—24no—
459C2×C8—114no—
460C2×C8—224no—
461C2×C8C23×D1114yes—
462C4⋊C4—24no—
463C4⋊C4—24no—
464C4⋊C4—24no—
465C4⋊C4—22no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—114no—
469C4⋊C4—228no—
470C4⋊C4—228no—
471C4⋊C4—224no—
472C4⋊C4—224no—
473C4⋊C4—222no—
474C4⋊C4—224no—
475C4⋊C4C23×D1114yes—
476C4⋊C4C23×D1112yes—
477C4⋊C4C23×D1112yes—
478C22⋊C4—224no—
479C22⋊C4—224no—
480C22⋊C4—224no—
481C22⋊C4—224no—
482C22⋊C4—224no—
483C42—114no—
484C42—112no—
485C42—114no—
486C42—112no—
487C42—224no—
488C42D4×D1112yes—
489C42C23×D1112yes—
490C11C2×#323911yescharacteristic, complemented, Sylow
491C23—114no—
492C23—112no—
493C23—222no—
494C23—222no—
495C23—222no—
496C23—442no—
497C23—442no—
498C23—442no—
499C23C2×D4×D1111yescharacteristic
500Q8—48no—
501Q8—224no—
502Q8—448no—
503Q8—4416no—
504Q8—442no—
505D4—224no—
506D4—448no—
507D4—442no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—24no—
513C2×C4—42no—
514C2×C4—44no—
515C2×C4—42no—
516C2×C4—114no—
517C2×C4—112no—
518C2×C4—112no—
519C2×C4—112no—
520C2×C4—228no—
521C2×C4—228no—
522C2×C4—222no—
523C2×C4—222no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—222no—
527C2×C4—224no—
528C2×C4—448no—
529C2×C4—4416no—
530C2×C4—442no—
531C2×C4—444no—
532C2×C4C2×D4×D1112yes—
533C2×C4C2×D4×D1112yes—
534C2×C4C2×D4×D1111yescharacteristic
535C2×C4#6704014yes—
536C2×C4C24×D1111yescharacteristic
537C8—24no—
538C8—224no—
539C22—114no—
540C22—228no—
541C22—222no—
542C22—222no—
543C22—442no—
544C22—442no—
545C22—442no—
546C22—884no—
547C22#1062325512yes—
548C22D11×AGL(1,ℤ/8)12yes—
549C22D11×#13712yes—
550C22C22×D4×D1111yescharacteristic
551C4—22no—
552C4—22no—
553C4—44no—
554C4—42no—
555C4—42no—
556C4—114no—
557C4—222no—
558C4—222no—
559C4—442no—
560C4—444no—
561C4#1062325512yes—
562C4C2×#6704012yes—
563C2—224no—
564C2—882no—
565C2#1307984714yesdirect product factor
566C2C2×#1062325511yescharacteristic
567C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
568C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#501C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenterC2×#501D11
hypocenterC11C2×#3239
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#501

Complements

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

NH ≅ G/Ntype
1. C2×D11×C4⋊Q8C2semidirect
3. #13079847C2direct (N × H)
4. C2×#10622678C2semidirect
5. C2×#10622702C2semidirect
6. C2×#10622327C2semidirect
7. C2×#10622497C2semidirect
9. C2×#10622467C2semidirect
10. C2×#10622503C2semidirect
11. C2×#10622318C2semidirect
12. C2×C11×#501C2semidirect
18. D11×C4⋊Q8C22semidirect
36. C11×#501C22semidirect
44. #10622702C22semidirect
45. #10622678C22semidirect
51. #10622503C22semidirect
52. #10622497C22semidirect
54. #10622467C22semidirect
55. #10622327C22semidirect
56. #10622318C22semidirect
211. C2×#501D11semidirect
291. #501C2×D11semidirect
413. C2×C11#3239semidirect
490. C11C2×#3239semidirect
565. C2#13079847direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D11×C4⋊Q82
C2×#106232222
#130798472
C2×#106226782
C2×#106227022
C2×#106223272
C2×#106224972
C2×#106224762
C2×#106224672
C2×#106225032
C2×#106223182
C2×C11×#5012
C2×#323911