Finite Group Databasebeta

← C2×#13080937 #15630700

Subgroups — C2×#13080937 #15630700

Order 2816.

2426 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623084C211yesmaximal, characteristic, complemented
2#13080937C2116yesmaximal, direct product factor
3C2×#10622701C211yesmaximal, characteristic, complemented
4C2×#10622581C212yesmaximal, complemented
5C2×#10622707C211yesmaximal, characteristic, complemented
6C2×#10622652C212yesmaximal, complemented
7C2×#10622628C211yesmaximal, characteristic, complemented
8C2×#10622650C212yesmaximal, complemented
9C2×C4×#4324C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622579C212yesmaximal, complemented
12C2×C11×#547C211yesmaximal, characteristic, complemented
13C22×C11×#41—21no—
14C22×#4339C2212yes—
15C11×#547—24no—
16C11×#547C2218yescomplemented
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×#123—22no—
19C2×C11×C22⋊Q8—21no—
20C2×C11×#121C2212yes—
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2211yescharacteristic
23C22×C11×C4⋊C4C2212yes—
24C2×#66993—21no—
25C22×#4324C2211yescharacteristic
26C22×#4323C2212yes—
27C2×#66983C2212yes—
28C22×#4318C2212yes—
29#10623084—24no—
30#10623084C2218yescomplemented
31C2×#66946—21no—
32C2×#66937—22no—
33C2×#66927C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622707C2218yescomplemented
38#10622701C2218yescomplemented
39#10622652C22116yescomplemented
40#10622650C22116yescomplemented
41C4×#4324C2218yescomplemented
42#10622628C2218yescomplemented
43#10622625C2218yescomplemented
44C2×#66874C2212yes—
45C2×#66874C2211yescharacteristic
46#10622581C22116yescomplemented
47#10622579C22116yescomplemented
48C2×#66873C2212yes—
49C2×#66873C2212yes—
50C2×#66873C2212yes—
51C2×#66872C2212yes—
52C2×#66872C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C11×#41—28no—
56C2×C11×#41—48no—
57C22×Q8×C11—21no—
58C22×D4×C11—22no—
59C22×D4×C11D411yescharacteristic
60C22×D4×C11C2311yescharacteristic
61C23×C4×C11—22no—
62C23×C4×C11—21no—
63C23×C4×C11C2312yes—
64C22×C22⋊D11—22no—
65C22×C22⋊D11—22no—
66C2×#4339—24no—
67C2×#4339—28no—
68C2×#4339—44no—
69C2×#4339C2318yes—
70C22×D44—21no—
71C22×D44—21no—
72C22×D44C2312yes—
73C22×C4×D11—22no—
74C22×Dic22C2311yescharacteristic
75C11×C4⋊Q8—22no—
76C11×C4⋊Q8C2314yes—
77C11×#123—216no—
78C11×C22⋊Q8—28no—
79C11×#121—24no—
80C11×#121C2318yes—
81C4×D4×C11—22no—
82C4×D4×C11D414yes—
83C4×D4×C11C2314yes—
84C4×D4×C11C2314yes—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4D411yescharacteristic
89C2×C11×C4⋊C4C2311yescharacteristic
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2318yes—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4D412yes—
95C2×C42×C11C2311yescharacteristic
96#66993—28no—
97C2×#4324—24no—
98C2×#4324C2314yes—
99C2×#4323—44no—
100C2×#4323C2318yes—
101#66983—24no—
102#66983C2318yes—
103C2×(C2×D11)⋊C4—22no—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×#4318—44no—
108C2×#4318C2318yes—
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2312yes—
112#66946—28no—
113#66937—216no—
114#66927—22no—
115#66927C2314yes—
116C4×Dic22—22no—
117C4×Dic22C2314yes—
118#66896C2314yes—
119C22⋊(C11⋊C8)C2318yes—
120#66874C2314yes—
121#66874C2318yes—
122#66873C2318yes—
123#66873C2318yes—
124#66873C2318yes—
125#66872C2314yes—
126#66872C2318yes—
127C4⋊(C11⋊C8)C2314yes—
128C4×C11⋊C8C2314yes—
129C2×#3332—111nomaximal, Sylow
130C24×C11—21no—
131C24×C11C2×D412yes—
132C23×D11—22no—
133C11×#41—432no—
134C2×Q8×C11—24no—
135C2×Q8×C11—44no—
136C2×D4×C11—28no—
137C2×D4×C11—24no—
138C2×D4×C11—21no—
139C2×D4×C11—22no—
140C2×D4×C11—22no—
141C2×D4×C11—48no—
142C2×D4×C11C2×D414yes—
143C2×D4×C11C2412yes—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—21no—
147C22×C4×C11—22no—
148C22×C4×C11—28no—
149C22×C4×C11—24no—
150C22×C4×C11—48no—
151C22×C4×C11—44no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D414yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2414yes—
157C22×C4×C11C2411yescharacteristic
158C2×C22⋊D11—28no—
159C2×C22⋊D11—28no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—84no—
162C22×Dic11—21no—
163C22×Dic11—21no—
164#4339—216no—
165#4339—48no—
166#4339—416no—
167C2×D44—22no—
168C2×D44—24no—
169C2×D44—24no—
170C2×D44—24no—
171C2×D44—24no—
172C2×D44—44no—
173C2×D44—82no—
174C2×D44C2414yes—
175C2×C4×D11—28no—
176C2×C4×D11—48no—
177C2×Dic22—21no—
178C2×Dic22—22no—
179C2×Dic22#4114yescomplemented
180C2×Dic22C2412yes—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—28no—
184C11×C4⋊C4—24no—
185C11×C4⋊C4C2×D414yes—
186C11×C4⋊C4C2412yes—
187C11×C4⋊C4C2414yes—
188C11×C22⋊C4—24no—
189C11×C22⋊C4—28no—
190C11×C22⋊C4C2×D418yes—
191C42×C11C2×D412yes—
192C42×C11C2412yes—
193#4324—28no—
194#4323—48no—
195(C2×D11)⋊C4—28no—
196C4⋊Dic11—21no—
197C4⋊Dic11C2412yes—
198Dic11⋊C4—24no—
199C4×Dic11—24no—
200#4318—48no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—24no—
204C2×C11⋊C8C2412yes—
205C2×C11⋊C8C2412yes—
206C2×C11⋊C8C2414yes—
207C2×#550—111no—
208C2×#547D1111yescharacteristic, complemented
209#3332—1116no—
210C2×#486—111no—
211C2×#481—112no—
212C2×#475—111no—
213C2×#469—112no—
214C2×#459—111no—
215C2×#449—112no—
216C2×C4×SD16—111no—
217C2×#436—111no—
218C2×#417—112no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—22no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11C22×D414yes—
227C23×C11C22×D411yescharacteristic
228C22×D11—24no—
229C22×D11—44no—
230C22×D11—44no—
231C22×D11—44no—
232Q8×C11—48no—
233D4×C11—28no—
234D4×C11—22no—
235D4×C11—22no—
236D4×C11—416no—
237D4×C11—42no—
238C2×C4×C11—24no—
239C2×C4×C11—22no—
240C2×C4×C11—28no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—416no—
246C2×C4×C11—42no—
247C2×C4×C11—44no—
248C2×C4×C11—48no—
249C2×C4×C11AGL(1,ℤ/8)14yes—
250C2×C4×C11C22×D412yes—
251C2×C4×C11C22×D414yes—
252C2×C4×C11C22×D411yescharacteristic
253C2×C4×C11C22×D412yes—
254C2×C4×C11C2×#4112yes—
255C2×C4×C11H(5,𝔽2)12yes—
256C2×C4×C11C2511yescharacteristic
257C22⋊D11—416no—
258C22⋊D11—88no—
259C2×Dic11—24no—
260C2×Dic11—22no—
261C2×Dic11—22no—
262C2×Dic11—42no—
263D44—24no—
264D44—24no—
265D44—44no—
266D44—48no—
267D44—84no—
268C4×D11—416no—
269Dic22—24no—
270Dic22—22no—
271Dic22C2×#4114yescomplemented
272C11⋊C8—22no—
273C11⋊C8—22no—
274C11⋊C8—24no—
275C22×#41—21no—
276C22×#41—112no—
277C22×SD16—111no—
278C22×D8—112no—
279C22×M16—112no—
280#550—118no—
281#550—224no—
282#547—24no—
283#547C2×D1118yescomplemented
284C2×C4⋊Q8C2×D1111yescharacteristic
285C2×#127—111no—
286C2×#127—221no—
287C2×#123—22no—
288C2×C22⋊Q8—21no—
289C2×#121—112no—
290C2×#121—222no—
291C2×#121C2×D1112yes—
292C2×C4×Q8—111no—
293C2×C4×D4—221no—
294C2×C4×D4C2×D1111yescharacteristic
295C2×C4×D4C2×D1111yescharacteristic
296C22×C4⋊C4C2×D1112yes—
297#486—118no—
298#481—1116no—
299#475—118no—
300#469—1116no—
301#459—118no—
302#449—1116no—
303C4×SD16—118no—
304#436—118no—
305C2×#106—112no—
306C2×#106—111no—
307C2×C4⋊C8—111no—
308#417—1116no—
309C2×#103—112no—
310C2×#103—111no—
311C2×#102—111no—
312C2×#102—112no—
313C2×#102—112no—
314C2×#102—112no—
315C2×C22⋊C8—112no—
316C2×C4×C8—111no—
317C22×C11—24no—
318C22×C11—24no—
319C22×C11—24no—
320C22×C11—48no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—84no—
325C22×C11#54612yes—
326C22×C11C2×AGL(1,ℤ/8)12yes—
327C22×C11#57712yes—
328C22×C11C23×D411yescharacteristic
329C2×D11—44no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—88no—
333C4×C11—24no—
334C4×C11—22no—
335C4×C11—42no—
336C4×C11—44no—
337C4×C11#54612yes—
338C4×C11C2×AGL(1,ℤ/8)14yes—
339C4×C11C22×#4111yescharacteristic
340C4×C11C2×H(5,𝔽2)11yescharacteristic
341Dic11—24no—
342Dic11—42no—
343C2×#41—28no—
344C2×#41—48no—
345C2×#41—118no—
346C2×#41—228no—
347C2×#41—224no—
348C2×#41—444no—
349C22×Q8—21no—
350C22×Q8—111no—
351C22×D4—22no—
352C22×D4—112no—
353C22×D4—222no—
354C22×D4—222no—
355C22×D4—221no—
356C22×D4—221no—
357C22×D4C22⋊D1111yescharacteristic
358C22×D4C22×D1111yescharacteristic
359C23×C4—22no—
360C23×C4—21no—
361C23×C4—222no—
362C23×C4C22×D1112yes—
363C2×SD16—114no—
364C2×SD16—224no—
365C2×D8—118no—
366C2×D8—444no—
367C2×M16—118no—
368C2×M16—444no—
369C22×C8—111no—
370C22×C8—112no—
371C22×C8—111no—
372C4⋊Q8—22no—
373C4⋊Q8C22×D1114yes—
374#127—114no—
375#127—228no—
376#127—222no—
377#123—216no—
378C22⋊Q8—28no—
379#121—24no—
380#121—118no—
381#121—224no—
382#121—2216no—
383#121C22×D1118yes—
384C4×Q8—114no—
385C4×Q8—222no—
386C4×D4—22no—
387C4×D4—228no—
388C4×D4C22⋊D1114yes—
389C4×D4C22×D1114yes—
390C4×D4C22×D1114yes—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—24no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—111no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4C22⋊D1111yescharacteristic
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C4⋊C4C22×D1112yes—
399C2×C4⋊C4C22×D1118yes—
400C2×C22⋊C4—21no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—222no—
403C2×C22⋊C4C22⋊D1112yes—
404C2×C42—221no—
405C2×C42C22×D1111yescharacteristic
406#106—114no—
407#106—118no—
408C4⋊C8—114no—
409#103—114no—
410#103—118no—
411#102—114no—
412#102—118no—
413#102—118no—
414#102—118no—
415C22⋊C8—118no—
416C4×C8—114no—
417C2×C11—44no—
418C2×C11—82no—
419C2×C11#333214yescomplemented
420C2×C11C2×#54611yescharacteristic
421C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
422C2×C11C2×#57711yescharacteristic
423D11—84no—
424C24—21no—
425C24—222no—
426C24C2×C22⋊D1112yes—
427#41—432no—
428#41—2216no—
429#41—448no—
430#41—4416no—
431C2×Q8—24no—
432C2×Q8—44no—
433C2×Q8—114no—
434C2×Q8—112no—
435C2×Q8—222no—
436C2×Q8—221no—
437C2×D4—28no—
438C2×D4—24no—
439C2×D4—22no—
440C2×D4—22no—
441C2×D4—21no—
442C2×D4—48no—
443C2×D4—114no—
444C2×D4—228no—
445C2×D4—228no—
446C2×D4—224no—
447C2×D4—224no—
448C2×D4—224no—
449C2×D4—222no—
450C2×D4—224no—
451C2×D4—448no—
452C2×D4—444no—
453C2×D4—882no—
454C2×D4—884no—
455C2×D4C2×C22⋊D1114yes—
456C2×D4C23×D1112yes—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—28no—
460C22×C4—21no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—48no—
464C22×C4—44no—
465C22×C4—221no—
466C22×C4—221no—
467C22×C4—228no—
468C22×C4—448no—
469C22×C4C2×C22⋊D1114yes—
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1112yes—
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C23×D1114yes—
474C22×C4C23×D1111yescharacteristic
475SD16—228no—
476D8—448no—
477M16—448no—
478C2×C8—112no—
479C2×C8—112no—
480C2×C8—114no—
481C2×C8—222no—
482C2×C8—222no—
483C2×C8—224no—
484C4⋊C4—21no—
485C4⋊C4—22no—
486C4⋊C4—28no—
487C4⋊C4—24no—
488C4⋊C4—112no—
489C4⋊C4—221no—
490C4⋊C4—224no—
491C4⋊C4C2×C22⋊D1114yes—
492C4⋊C4C23×D1112yes—
493C4⋊C4C23×D1114yes—
494C22⋊C4—24no—
495C22⋊C4—28no—
496C22⋊C4—228no—
497C22⋊C4C2×C22⋊D1118yes—
498C42—224no—
499C42C2×C22⋊D1112yes—
500C42C23×D1112yes—
501C11C2×#333211yescharacteristic, complemented, Sylow
502C23—24no—
503C23—24no—
504C23—24no—
505C23—22no—
506C23—42no—
507C23—42no—
508C23—42no—
509C23—224no—
510C23—444no—
511C23—444no—
512C23—444no—
513C23C22×C22⋊D1114yes—
514C23C22×C22⋊D1111yescharacteristic
515Q8—48no—
516Q8—114no—
517Q8—224no—
518Q8—222no—
519D4—28no—
520D4—22no—
521D4—22no—
522D4—416no—
523D4—42no—
524D4—224no—
525D4—224no—
526D4—4416no—
527D4—448no—
528D4—444no—
529D4—884no—
530D4—888no—
531C2×C4—24no—
532C2×C4—22no—
533C2×C4—28no—
534C2×C4—24no—
535C2×C4—24no—
536C2×C4—22no—
537C2×C4—24no—
538C2×C4—416no—
539C2×C4—42no—
540C2×C4—44no—
541C2×C4—48no—
542C2×C4—224no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—4416no—
546C2×C4—442no—
547C2×C4#6698514yes—
548C2×C4#41×D1112yes—
549C2×C4#6704212yes—
550C2×C4C22×C22⋊D1112yes—
551C2×C4C22×C22⋊D1114yes—
552C2×C4C22×C22⋊D1112yes—
553C2×C4C22×C22⋊D1111yescharacteristic
554C2×C4C24×D1111yescharacteristic
555C8—222no—
556C8—222no—
557C8—224no—
558C22—24no—
559C22—24no—
560C22—24no—
561C22—48no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—84no—
566C22—444no—
567C22—444no—
568C22—444no—
569C22—888no—
570C22C2×#6698512yes—
571C22#1062336012yes—
572C22#1062336812yes—
573C22C23×C22⋊D1111yescharacteristic
574C4—24no—
575C4—22no—
576C4—42no—
577C4—44no—
578C4—224no—
579C4—442no—
580C4C2×#6698514yes—
581C4#1062336012yes—
582C4C2×#41×D1111yescharacteristic
583C4C2×#6704211yescharacteristic
584C2—44no—
585C2—82no—
586C2—884no—
587C2#1308093714yesdirect product factor
588C2C2×#1062336011yescharacteristic
589C2C22×#6698511yescharacteristic
590C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11C2×#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10623084C2semidirect
2. #13080937C2direct (N × H)
3. C2×#10622701C2semidirect
4. C2×#10622581C2semidirect
5. C2×#10622707C2semidirect
6. C2×#10622652C2semidirect
7. C2×#10622628C2semidirect
8. C2×#10622650C2semidirect
9. C2×C4×#4324C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622579C2semidirect
12. C2×C11×#547C2semidirect
16. C11×#547C22semidirect
30. #10623084C22semidirect
37. #10622707C22semidirect
38. #10622701C22semidirect
39. #10622652C22semidirect
40. #10622650C22semidirect
41. C4×#4324C22semidirect
42. #10622628C22semidirect
43. #10622625C22semidirect
46. #10622581C22semidirect
47. #10622579C22semidirect
179. C2×Dic22#41semidirect
208. C2×#547D11semidirect
271. Dic22C2×#41semidirect
283. #547C2×D11semidirect
419. C2×C11#3332semidirect
501. C11C2×#3332semidirect
587. C2#13080937direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230842
#130809372
C2×#106227012
C2×#106225812
C2×#106227072
C2×#106226522
C2×#106226282
C2×#106226502
C2×C4×#43242
C2×#106226252
C2×#106225792
C2×C11×#5472
C2×#333211