Finite Group Databasebeta

← C2×#13080841 #15630596

Subgroups — C2×#13080841 #15630596

Order 2816.

2566 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×D44C211yesmaximal, characteristic
2#13080841C2116yesmaximal, direct product factor
3C2×#10622701C211yesmaximal, characteristic, complemented
4C2×#10622616C212yesmaximal, complemented
5C2×#10622700C211yesmaximal, characteristic, complemented
6C2×#10622662C212yesmaximal, complemented
7C2×#10622640C211yesmaximal, characteristic, complemented
8C2×#10622659C212yesmaximal, complemented
9C2×C4×#4325C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622614C212yesmaximal, complemented
12C2×C11×#556C211yesmaximal, characteristic, complemented
13C22×D4×D11—21no—
14C23×D44C2212yes—
15C11×#556—24no—
16C11×#556C2218yescomplemented
17C2×C11×C4⋊Q8C2211yescharacteristic, complemented
18C2×C11×#126—22no—
19C2×C11×#124—21no—
20C2×C11×C22⋊Q8C2212yescomplemented
21C2×C4×Q8×C11—21no—
22C2×C4×Q8×C11C2211yescharacteristic, complemented
23C2×C4×D4×C11C2211yescharacteristic
24C2×C11×#117C2212yescomplemented
25C22×#4325C2211yescharacteristic
26C22×#4325C2212yescomplemented
27C2×#66983C2212yes—
28C22×#4318C2212yescomplemented
29D4×D44—24no—
30D4×D44C2218yes—
31C2×#66948—21no—
32C2×#66935—22no—
33C2×#66927C2211yescharacteristic
34C2×C4×D44C2211yescharacteristic
35C2×#66899C2211yescharacteristic, complemented
36C2×C22⋊(C11⋊C8)C2212yescomplemented
37#10622701C2218yescomplemented
38#10622700C2218yescomplemented
39#10622662C22116yescomplemented
40#10622659C22116yescomplemented
41#10622640C2218yescomplemented
42C4×#4325C2218yescomplemented
43#10622625C2218yescomplemented
44#10622616C22116yescomplemented
45#10622614C22116yescomplemented
46C2×#66873C2212yes—
47C2×#66873C2211yescharacteristic
48C2×#66873C2212yescomplemented
49C2×#66873C2212yescomplemented
50C2×#66873C2212yescomplemented
51C2×#66872C2211yescharacteristic, complemented
52C2×#66871C2212yescomplemented
53C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
54C2×C4×C11⋊C8C2211yescharacteristic, complemented
55C24×D11—22no—
56C22×Q8×C11—21no—
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11D411yescharacteristic
59C23×C4×C11C2312yes—
60C22×C22⋊D11—22no—
61C2×D4×D11—28no—
62C2×D4×D11—48no—
63C22×D44—28no—
64C22×D44—21no—
65C22×D44—22no—
66C22×D44—24no—
67C22×D44—21no—
68C22×D44—44no—
69C22×D44C2312yes—
70C22×D44C2318yes—
71C22×D44C2311yescharacteristic
72C22×C4×D11—21no—
73C11×C4⋊Q8—22no—
74C11×C4⋊Q8C2314yescomplemented
75C11×#126—216no—
76C11×#124—28no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8C2318yescomplemented
79C4×Q8×C11—28no—
80C4×Q8×C11—22no—
81C4×Q8×C11C2314yescomplemented
82C4×D4×C11D414yes—
83C4×D4×C11C2314yes—
84C11×#117—24no—
85C11×#117C2318yescomplemented
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—21no—
88C2×C11×C4⋊C4—21no—
89C2×C11×C4⋊C4D411yescharacteristic
90C2×C11×C4⋊C4C2312yes—
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C22⋊C4—22no—
93C2×C11×C22⋊C4—22no—
94C2×C11×C22⋊C4D412yes—
95C2×C42×C11—22no—
96C2×C42×C11—21no—
97C2×C42×C11C2311yescharacteristic
98C2×#4325—24no—
99C2×#4325—44no—
100C2×#4325C2314yes—
101C2×#4325C2318yescomplemented
102#66983—24no—
103#66983C2318yes—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—22no—
106C2×C4⋊Dic11C2311yescharacteristic
107C2×#4318—44no—
108C2×#4318C2318yescomplemented
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2312yes—
112#66948—28no—
113#66935—216no—
114#66927—22no—
115#66927C2314yes—
116C4×D44—22no—
117C4×D44C2314yes—
118#66899C2314yescomplemented
119C22⋊(C11⋊C8)C2318yescomplemented
120#66873C2314yes—
121#66873C2318yes—
122#66873C2318yescomplemented
123#66873C2318yescomplemented
124#66873C2318yescomplemented
125#66872C2314yescomplemented
126#66871C2318yescomplemented
127C4⋊(C11⋊C8)C2314yescomplemented
128C4×C11⋊C8C2314yescomplemented
129C2×#3324—111nomaximal, Sylow
130C24×C11C2×D412yes—
131C23×D11—21no—
132C23×D11—22no—
133C23×D11—28no—
134C23×D11—48no—
135C23×D11—48no—
136C23×D11—84no—
137C2×Q8×C11—21no—
138C2×Q8×C11—24no—
139C2×Q8×C11—22no—
140C2×Q8×C11—22no—
141C2×Q8×C11—44no—
142C2×Q8×C11C2412yes—
143C2×D4×C11—24no—
144C2×D4×C11C2×D414yes—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2414yes—
155C22×C4×C11C2411yescharacteristic
156C2×C22⋊D11—28no—
157C2×C22⋊D11—48no—
158C22×Dic11—21no—
159D4×D11—432no—
160C2×D44—216no—
161C2×D44—21no—
162C2×D44—22no—
163C2×D44—24no—
164C2×D44—28no—
165C2×D44—24no—
166C2×D44—24no—
167C2×D44—22no—
168C2×D44—24no—
169C2×D44—48no—
170C2×D44—48no—
171C2×D44—416no—
172C2×D44—44no—
173C2×D44—82no—
174C2×D44#4114yes—
175C2×D44C2414yes—
176C2×D44C2412yes—
177C2×C4×D11—24no—
178C2×C4×D11—44no—
179C11×C4⋊C4—28no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4—22no—
184C11×C4⋊C4C2×D414yes—
185C11×C4⋊C4C2414yes—
186C11×C4⋊C4C2412yes—
187C11×C22⋊C4—28no—
188C11×C22⋊C4—28no—
189C11×C22⋊C4C2×D418yes—
190C42×C11—28no—
191C42×C11—24no—
192C42×C11C2×D412yes—
193C42×C11C2412yes—
194#4325—28no—
195#4325—48no—
196(C2×D11)⋊C4—24no—
197(C2×D11)⋊C4—28no—
198C4⋊Dic11—21no—
199C4⋊Dic11C2412yes—
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×#556D1111yescharacteristic, complemented
208C2×D42—111no—
209#3324—1116no—
210C2×#486—111no—
211C2×#482—112no—
212C2×#474—111no—
213C2×#468—112no—
214C2×#460—111no—
215C2×#450—112no—
216C2×C4×SD16—111no—
217C2×#436—111no—
218C2×#418—112no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11C22×D414yes—
223C23×C11C22×D411yescharacteristic
224C22×D11—24no—
225C22×D11—22no—
226C22×D11—24no—
227C22×D11—416no—
228C22×D11—42no—
229C22×D11—42no—
230C22×D11—416no—
231C22×D11—44no—
232C22×D11—44no—
233C22×D11—44no—
234C22×D11—88no—
235C22×D11—832no—
236Q8×C11—22no—
237Q8×C11—22no—
238Q8×C11—42no—
239Q8×C11—48no—
240D4×C11—28no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—28no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—42no—
250C2×C4×C11—44no—
251C2×C4×C11—42no—
252C2×C4×C11AGL(1,ℤ/8)14yes—
253C2×C4×C11C22×D414yes—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D411yescharacteristic
256C2×C4×C11C22×D412yes—
257C2×C4×C11C2×#4112yes—
258C2×C4×C11H(5,𝔽2)12yes—
259C2×C4×C11C2511yescharacteristic
260C22⋊D11—416no—
261C2×Dic11—22no—
262C2×Dic11—42no—
263D44—24no—
264D44—24no—
265D44—22no—
266D44—24no—
267D44—416no—
268D44—44no—
269D44—48no—
270D44—84no—
271D44C2×#4114yes—
272C4×D11—48no—
273C11⋊C8—22no—
274C11⋊C8—22no—
275C11⋊C8—24no—
276C23×D4—112no—
277C23×D4—221no—
278C22×SD16—111no—
279C22×SD16—112no—
280C22×M16—112no—
281#556—24no—
282#556C2×D1118yescomplemented
283D42—118no—
284D42—224no—
285C2×C4⋊Q8C2×D1111yescharacteristic, complemented
286C2×#127—111no—
287C2×#126—22no—
288C2×#124—21no—
289C2×C22⋊Q8C2×D1112yescomplemented
290C2×#121—112no—
291C2×#121—221no—
292C2×#120—222no—
293C2×C4×Q8—21no—
294C2×C4×Q8C2×D1111yescharacteristic, complemented
295C2×C4×D4—111no—
296C2×C4×D4C2×D1111yescharacteristic
297C2×#117C2×D1112yescomplemented
298#486—118no—
299#482—1116no—
300#474—118no—
301#468—1116no—
302#460—118no—
303#450—1116no—
304C4×SD16—118no—
305#436—118no—
306C2×#107—112no—
307C2×#106—111no—
308C2×C4⋊C8—111no—
309#418—1116no—
310C2×#103—111no—
311C2×#102—112no—
312C2×#102—112no—
313C2×#102—112no—
314C2×#102—111no—
315C2×#102—112no—
316C2×C22⋊C8—112no—
317C2×C4×C8—111no—
318C22×C11—24no—
319C22×C11—24no—
320C22×C11—24no—
321C22×C11—48no—
322C22×C11#54612yes—
323C22×C11C2×AGL(1,ℤ/8)12yes—
324C22×C11#57712yes—
325C22×C11C23×D411yescharacteristic
326C2×D11—24no—
327C2×D11—42no—
328C2×D11—48no—
329C2×D11—42no—
330C2×D11—44no—
331C2×D11—44no—
332C2×D11—44no—
333C2×D11—832no—
334C2×D11—88no—
335C4×C11—24no—
336C4×C11—22no—
337C4×C11—42no—
338C4×C11—44no—
339C4×C11—42no—
340C4×C11#54612yes—
341C4×C11C2×AGL(1,ℤ/8)14yes—
342C4×C11C22×#4111yescharacteristic
343C4×C11C2×H(5,𝔽2)11yescharacteristic
344Dic11—42no—
345C25—222no—
346C22×Q8—21no—
347C22×Q8C22×D1111yescharacteristic
348C22×D4—111no—
349C22×D4—112no—
350C22×D4—118no—
351C22×D4—228no—
352C22×D4—222no—
353C22×D4—228no—
354C22×D4—222no—
355C22×D4—221no—
356C22×D4—224no—
357C22×D4—221no—
358C22×D4—444no—
359C22×D4—448no—
360C22×D4C22⋊D1111yescharacteristic
361C23×C4—221no—
362C23×C4C22×D1112yes—
363C2×SD16—114no—
364C2×SD16—118no—
365C2×SD16—224no—
366C2×SD16—444no—
367C2×M16—118no—
368C2×M16—444no—
369C22×C8—111no—
370C22×C8—112no—
371C22×C8—111no—
372C4⋊Q8—22no—
373C4⋊Q8C22×D1114yescomplemented
374#127—114no—
375#127—222no—
376#126—216no—
377#124—28no—
378C22⋊Q8—24no—
379C22⋊Q8C22×D1118yescomplemented
380#121—118no—
381#121—224no—
382#121—228no—
383#120—2216no—
384C4×Q8—28no—
385C4×Q8—22no—
386C4×Q8C22×D1114yescomplemented
387C4×D4—114no—
388C4×D4—222no—
389C4×D4C22⋊D1114yes—
390C4×D4C22×D1114yes—
391#117—24no—
392#117C22×D1118yescomplemented
393C2×C4⋊C4—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—21no—
396C2×C4⋊C4—111no—
397C2×C4⋊C4C22⋊D1111yescharacteristic
398C2×C4⋊C4C22×D1111yescharacteristic
399C2×C4⋊C4C22×D1112yes—
400C2×C22⋊C4—22no—
401C2×C22⋊C4—22no—
402C2×C22⋊C4—221no—
403C2×C22⋊C4—222no—
404C2×C22⋊C4C22⋊D1112yes—
405C2×C42—22no—
406C2×C42—21no—
407C2×C42C22×D1111yescharacteristic
408#107—118no—
409#106—114no—
410C4⋊C8—114no—
411#103—114no—
412#102—114no—
413#102—118no—
414#102—118no—
415#102—118no—
416#102—118no—
417C22⋊C8—118no—
418C4×C8—114no—
419C2×C11—44no—
420C2×C11#332414yescomplemented
421C2×C11C2×#54611yescharacteristic
422C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
423C2×C11C2×#57711yescharacteristic
424D11—44no—
425D11—84no—
426C24—221no—
427C24—222no—
428C24—228no—
429C24—448no—
430C24—448no—
431C24—884no—
432C24C2×C22⋊D1112yes—
433C2×Q8—21no—
434C2×Q8—24no—
435C2×Q8—22no—
436C2×Q8—22no—
437C2×Q8—44no—
438C2×Q8C23×D1112yes—
439C2×D4—24no—
440C2×D4—114no—
441C2×D4—112no—
442C2×D4—114no—
443C2×D4—2216no—
444C2×D4—228no—
445C2×D4—224no—
446C2×D4—222no—
447C2×D4—224no—
448C2×D4—221no—
449C2×D4—228no—
450C2×D4—224no—
451C2×D4—222no—
452C2×D4—224no—
453C2×D4—448no—
454C2×D4—4416no—
455C2×D4—448no—
456C2×D4—4432no—
457C2×D4—448no—
458C2×D4—444no—
459C2×D4—882no—
460C2×D4C2×C22⋊D1114yes—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—221no—
467C22×C4—224no—
468C22×C4—444no—
469C22×C4C2×C22⋊D1114yes—
470C22×C4C2×C22⋊D1112yes—
471C22×C4C2×C22⋊D1111yescharacteristic
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C23×D1114yes—
474C22×C4C23×D1111yescharacteristic
475SD16—228no—
476SD16—448no—
477M16—448no—
478C2×C8—112no—
479C2×C8—112no—
480C2×C8—114no—
481C2×C8—222no—
482C2×C8—222no—
483C2×C8—224no—
484C4⋊C4—28no—
485C4⋊C4—24no—
486C4⋊C4—24no—
487C4⋊C4—21no—
488C4⋊C4—22no—
489C4⋊C4—112no—
490C4⋊C4—221no—
491C4⋊C4C2×C22⋊D1114yes—
492C4⋊C4C23×D1112yes—
493C4⋊C4C23×D1114yes—
494C22⋊C4—28no—
495C22⋊C4—28no—
496C22⋊C4—224no—
497C22⋊C4—228no—
498C22⋊C4C2×C22⋊D1118yes—
499C42—28no—
500C42—24no—
501C42C2×C22⋊D1112yes—
502C42C23×D1112yes—
503C11C2×#332411yescharacteristic, complemented, Sylow
504C23—24no—
505C23—24no—
506C23—24no—
507C23—224no—
508C23—222no—
509C23—224no—
510C23—4416no—
511C23—4416no—
512C23—442no—
513C23—442no—
514C23—444no—
515C23—444no—
516C23—444no—
517C23—888no—
518C23—8832no—
519C23C22×C22⋊D1114yes—
520C23C22×C22⋊D1111yescharacteristic
521Q8—22no—
522Q8—22no—
523Q8—48no—
524Q8—42no—
525D4—28no—
526D4—114no—
527D4—224no—
528D4—224no—
529D4—222no—
530D4—224no—
531D4—4416no—
532D4—4416no—
533D4—448no—
534D4—444no—
535D4—884no—
536C2×C4—24no—
537C2×C4—22no—
538C2×C4—28no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—44no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—222no—
548C2×C4—442no—
549C2×C4—448no—
550C2×C4#6700214yes—
551C2×C4#41×D1112yes—
552C2×C4#6704212yes—
553C2×C4C22×C22⋊D1114yes—
554C2×C4C22×C22⋊D1112yes—
555C2×C4C22×C22⋊D1112yes—
556C2×C4C22×C22⋊D1111yescharacteristic
557C2×C4C24×D1111yescharacteristic
558C8—222no—
559C8—222no—
560C8—224no—
561C22—24no—
562C22—24no—
563C22—24no—
564C22—48no—
565C22—224no—
566C22—448no—
567C22—442no—
568C22—442no—
569C22—444no—
570C22—444no—
571C22—444no—
572C22—8832no—
573C22—888no—
574C22C2×#6700212yes—
575C22#1062336012yes—
576C22#1062336812yes—
577C22C23×C22⋊D1111yescharacteristic
578C4—24no—
579C4—22no—
580C4—42no—
581C4—44no—
582C4—42no—
583C4—442no—
584C4C2×#6700214yes—
585C4#1062336012yes—
586C4C2×#41×D1111yescharacteristic
587C4C2×#6704211yescharacteristic
588C2—44no—
589C2—444no—
590C2—884no—
591C2#1308084114yesdirect product factor
592C2C2×#1062336011yescharacteristic
593C2C22×#6700211yescharacteristic
594C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC2×D4×D44C2
hypercenterC2×#556D11
hypocenterC11C2×#3324
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
2. #13080841C2direct (N × H)
3. C2×#10622701C2semidirect
4. C2×#10622616C2semidirect
5. C2×#10622700C2semidirect
6. C2×#10622662C2semidirect
7. C2×#10622640C2semidirect
8. C2×#10622659C2semidirect
9. C2×C4×#4325C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622614C2semidirect
12. C2×C11×#556C2semidirect
16. C11×#556C22semidirect
17. C2×C11×C4⋊Q8C22semidirect
20. C2×C11×C22⋊Q8C22semidirect
22. C2×C4×Q8×C11C22semidirect
24. C2×C11×#117C22semidirect
26. C22×#4325C22semidirect
28. C22×#4318C22semidirect
35. C2×#66899C22semidirect
36. C2×C22⋊(C11⋊C8)C22semidirect
37. #10622701C22semidirect
38. #10622700C22semidirect
39. #10622662C22semidirect
40. #10622659C22semidirect
41. #10622640C22semidirect
42. C4×#4325C22semidirect
43. #10622625C22semidirect
44. #10622616C22semidirect
45. #10622614C22semidirect
48. C2×#66873C22semidirect
49. C2×#66873C22semidirect
50. C2×#66873C22semidirect
51. C2×#66872C22semidirect
52. C2×#66871C22semidirect
53. C2×C4⋊(C11⋊C8)C22semidirect
54. C2×C4×C11⋊C8C22semidirect
74. C11×C4⋊Q8C23semidirect
78. C11×C22⋊Q8C23semidirect
81. C4×Q8×C11C23semidirect
85. C11×#117C23semidirect
101. C2×#4325C23semidirect
108. C2×#4318C23semidirect
118. #66899C23semidirect
119. C22⋊(C11⋊C8)C23semidirect
122. #66873C23semidirect
123. #66873C23semidirect
124. #66873C23semidirect
125. #66872C23semidirect
126. #66871C23semidirect
127. C4⋊(C11⋊C8)C23semidirect
128. C4×C11⋊C8C23semidirect
207. C2×#556D11semidirect
282. #556C2×D11semidirect
285. C2×C4⋊Q8C2×D11semidirect
289. C2×C22⋊Q8C2×D11semidirect
294. C2×C4×Q8C2×D11semidirect
297. C2×#117C2×D11semidirect
373. C4⋊Q8C22×D11semidirect
379. C22⋊Q8C22×D11semidirect
386. C4×Q8C22×D11semidirect
392. #117C22×D11semidirect
420. C2×C11#3324semidirect
503. C11C2×#3324semidirect
591. C2#13080841direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×D442
#130808412
C2×#106227012
C2×#106226162
C2×#106227002
C2×#106226622
C2×#106226402
C2×#106226592
C2×C4×#43252
C2×#106226252
C2×#106226142
C2×C11×#5562
C2×#332411