Finite Group Databasebeta

← C2×#13067630 #14726015

Subgroups — C2×#13067630 #14726015

Order 2816.

1156 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622656C211yesmaximal, characteristic, complemented
2C2×#10622646C211yesmaximal, characteristic, complemented
3C2×#10622566C211yesmaximal, characteristic, complemented
4#13067630C218yesmaximal, direct product factor
5C2×#10622176C211yesmaximal, characteristic, complemented
6C2×#10622175C211yesmaximal, characteristic, complemented
7C2×#10622163C211yesmaximal, characteristic, complemented
8C2×C11×#538C211yesmaximal, characteristic
9C11×#538—22no—
10C11×#538—22no—
11C11×#538—22no—
12C11×#538C2214yes—
13C2×C11×#126—21no—
14C2×C11×#124—21no—
15C2×C11×#123—21no—
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×#121—21no—
18C2×C11×#121C2211yescharacteristic
19C2×C11×#120—21no—
20C2×C4×D4×C11—21no—
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11—21no—
23C22×C4⋊Dic11C2211yescharacteristic
24C2×#66899—21no—
25C2×#66896—21no—
26C2×C11⋊#95—21no—
27C2×C11⋊#95C2211yescharacteristic
28C2×C22⋊(C11⋊C8)C2211yescharacteristic
29C2×C22⋊(C11⋊C8)C2211yescharacteristic
30#10622656—22no—
31#10622656C2214yescomplemented
32#10622646—22no—
33#10622646C2214yescomplemented
34C2×#66872—21no—
35C2×#66871—21no—
36#10622566—22no—
37#10622566C2214yescomplemented
38#10622176C2214yescomplemented
39#10622175C2214yescomplemented
40#10622163C2214yescomplemented
41C25×C11D411yescharacteristic
42C22×Q8×C11D411yescharacteristic
43C22×D4×C11—21no—
44C22×D4×C11—21no—
45C22×D4×C11—21no—
46C22×D4×C11D411yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×Dic11—21no—
51C23×Dic11—21no—
52C11×#126—24no—
53C11×#126—24no—
54C11×#124—24no—
55C11×#124—24no—
56C11×#123—24no—
57C11×#123—24no—
58C11×C22⋊Q8—21no—
59C11×C22⋊Q8—21no—
60C11×C22⋊Q8D412yes—
61C11×C22⋊Q8C2312yes—
62C11×#121—24no—
63C11×#121—24no—
64C11×#121—21no—
65C11×#121—21no—
66C11×#121D412yes—
67C11×#121C2312yes—
68C11×#120—24no—
69C11×#120—24no—
70C4×D4×C11—24no—
71C4×D4×C11—24no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4D411yescharacteristic
75C2×C11×C4⋊C4D411yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C11×C22⋊C4—21no—
80C2×C11×C22⋊C4—21no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4D412yes—
86C2×C11×C22⋊C4C2312yes—
87C2×C42×C11—21no—
88C2×C22⋊Dic11—24no—
89C2×C22⋊Dic11—44no—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11C2312yes—
96C22×C11⋊C8—21no—
97C22×C11⋊C8—21no—
98#66899—24no—
99#66896—24no—
100C11⋊#95—24no—
101C11⋊#95—21no—
102C11⋊#95C2312yes—
103C22⋊(C11⋊C8)—21no—
104C22⋊(C11⋊C8)—21no—
105C22⋊(C11⋊C8)C2312yes—
106C22⋊(C11⋊C8)C2312yes—
107#66872—24no—
108#66871—24no—
109C2×#1612—111nomaximal, Sylow
110C24×C11—21no—
111C24×C11—21no—
112C24×C11—22no—
113C24×C11—21no—
114C24×C11—22no—
115C24×C11—42no—
116C24×C11—42no—
117C24×C11C2×D411yescharacteristic
118C24×C11C2×D412yes—
119C2×Q8×C11—21no—
120C2×Q8×C11—42no—
121C2×Q8×C11C2×D412yes—
122C2×D4×C11—22no—
123C2×D4×C11—22no—
124C2×D4×C11—24no—
125C2×D4×C11—24no—
126C2×D4×C11—21no—
127C2×D4×C11—42no—
128C2×D4×C11—42no—
129C2×D4×C11—42no—
130C2×D4×C11—82no—
131C2×D4×C11—82no—
132C2×D4×C11C2×D412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—24no—
138C22×C4×C11—21no—
139C22×C4×C11—42no—
140C22×C4×C11—42no—
141C22×C4×C11—82no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—42no—
152C22×Dic11—42no—
153C22×Dic11—41no—
154C22×Dic11—41no—
155C22×Dic11—42no—
156C22×Dic11—42no—
157C22×Dic11—42no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—22no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4C2×D412yes—
164C11×C4⋊C4C2×D412yes—
165C11×C22⋊C4—24no—
166C11×C22⋊C4—24no—
167C11×C22⋊C4—24no—
168C11×C22⋊C4—22no—
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—22no—
173C11×C22⋊C4—22no—
174C11×C22⋊C4—22no—
175C11×C22⋊C4—22no—
176C42×C11—24no—
177C22⋊Dic11—48no—
178C4⋊Dic11—22no—
179C4⋊Dic11—22no—
180C4⋊Dic11—41no—
181C4⋊Dic11—41no—
182C2×C11⋊C8—22no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—42no—
185C2×C11⋊C8—42no—
186C2×#538D1111yescharacteristic
187C2×#483—111no—
188C2×#480—111no—
189C2×#397—111no—
190#1612—118no—
191C2×#328—111no—
192C2×#327—111no—
193C2×#323—111no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—22no—
200C23×C11—42no—
201C23×C11—42no—
202C23×C11—48no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11—42no—
209C23×C11—42no—
210C23×C11—81no—
211C23×C11—81no—
212C23×C11—84no—
213C23×C11#12011yescharacteristic
214C23×C11#12011yescharacteristic
215C23×C11#13512yes—
216C23×C11AGL(1,ℤ/8)12yes—
217C23×C11C22×D411yescharacteristic
218Q8×C11—42no—
219Q8×C11—81no—
220D4×C11—42no—
221D4×C11—42no—
222D4×C11—42no—
223D4×C11—44no—
224D4×C11—81no—
225D4×C11—84no—
226D4×C11—84no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—22no—
233C2×C4×C11—41no—
234C2×C4×C11—41no—
235C2×C4×C11—41no—
236C2×C4×C11—41no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—42no—
240C2×C4×C11—42no—
241C2×C4×C11—42no—
242C2×C4×C11—81no—
243C2×C4×C11—84no—
244C2×C4×C11#12011yescharacteristic
245C2×C4×C11#12011yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C22×D411yescharacteristic
248C2×Dic11—42no—
249C2×Dic11—42no—
250C2×Dic11—42no—
251C2×Dic11—42no—
252C2×Dic11—42no—
253C2×Dic11—42no—
254C2×Dic11—84no—
255C2×Dic11—82no—
256C2×Dic11—82no—
257C11⋊C8—42no—
258C11⋊C8—42no—
259#538—22no—
260#538—22no—
261#538—22no—
262#538C2×D1114yes—
263C2×#126—21no—
264C2×#124—21no—
265C2×#123—21no—
266C2×C22⋊Q8C2×D1111yescharacteristic
267C2×#121—21no—
268C2×#121C2×D1111yescharacteristic
269C2×#120—21no—
270C2×C4×D4—21no—
271C22×C4⋊C4—111no—
272C22×C22⋊C4—221no—
273C22×C22⋊C4C2×D1111yescharacteristic
274#483—114no—
275#483—222no—
276#480—114no—
277#480—222no—
278C2×#107—221no—
279C2×#106—221no—
280C2×#103—221no—
281C2×#102—221no—
282C2×C22⋊C8—111no—
283C2×C22⋊C8—111no—
284#397—114no—
285#397—222no—
286C2×#95—111no—
287C2×#95—221no—
288#328—114no—
289#327—114no—
290#323—114no—
291C22×C11—24no—
292C22×C11—24no—
293C22×C11—21no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—44no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—82no—
305C22×C11—84no—
306C22×C11—84no—
307C22×C11—84no—
308C22×C11#44912yes—
309C22×C11#44912yes—
310C22×C11#45512yes—
311C22×C11#45812yes—
312C22×C11C2×#12011yescharacteristic
313C22×C11C2×#13511yescharacteristic
314C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
315C4×C11—21no—
316C4×C11—21no—
317C4×C11—21no—
318C4×C11—21no—
319C4×C11—42no—
320C4×C11—42no—
321C4×C11—42no—
322C4×C11—42no—
323Dic11—82no—
324Dic11—82no—
325C25C22⋊D1111yescharacteristic
326C22×Q8C22⋊D1111yescharacteristic
327C22×D4—21no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4C22⋊D1111yescharacteristic
331C23×C4—21no—
332C23×C4—221no—
333C23×C4—221no—
334C23×C4C22⋊D1111yescharacteristic
335C23×C4C22×D1111yescharacteristic
336C22×C8—221no—
337C22×C8—221no—
338#126—24no—
339#126—24no—
340#124—24no—
341#124—24no—
342#123—24no—
343#123—24no—
344C22⋊Q8—21no—
345C22⋊Q8—21no—
346C22⋊Q8C22⋊D1112yes—
347C22⋊Q8C22×D1112yes—
348#121—24no—
349#121—24no—
350#121—21no—
351#121—21no—
352#121C22⋊D1112yes—
353#121C22×D1112yes—
354#120—24no—
355#120—24no—
356C4×D4—24no—
357C4×D4—24no—
358C2×C4⋊C4—21no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—112no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4C22⋊D1111yescharacteristic
367C2×C4⋊C4C22⋊D1111yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—21no—
370C2×C22⋊C4—21no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4—444no—
379C2×C22⋊C4C22⋊D1112yes—
380C2×C22⋊C4C22×D1112yes—
381C2×C42—21no—
382#107—224no—
383#106—224no—
384#103—224no—
385#102—224no—
386C22⋊C8—112no—
387C22⋊C8—112no—
388C22⋊C8—221no—
389C22⋊C8—221no—
390#95—112no—
391#95—221no—
392#95—224no—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—22no—
396C2×C11—82no—
397C2×C11—82no—
398C2×C11#161214yescomplemented
399C2×C11C2×#44911yescharacteristic
400C2×C11C2×#45511yescharacteristic
401C2×C11C2×#45811yescharacteristic
402C24—22no—
403C24—21no—
404C24—21no—
405C24—22no—
406C24—21no—
407C24—42no—
408C24—42no—
409C24C2×C22⋊D1111yescharacteristic
410C24C2×C22⋊D1112yes—
411C2×Q8—21no—
412C2×Q8—42no—
413C2×Q8C2×C22⋊D1112yes—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—24no—
417C2×D4—24no—
418C2×D4—21no—
419C2×D4—42no—
420C2×D4—42no—
421C2×D4—42no—
422C2×D4—82no—
423C2×D4—82no—
424C2×D4C2×C22⋊D1112yes—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—24no—
430C22×C4—21no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—82no—
434C22×C4—222no—
435C22×C4—222no—
436C22×C4—442no—
437C22×C4—442no—
438C22×C4—442no—
439C22×C4—442no—
440C22×C4—442no—
441C22×C4—441no—
442C22×C4—441no—
443C22×C4C2×C22⋊D1111yescharacteristic
444C22×C4C2×C22⋊D1111yescharacteristic
445C22×C4C2×C22⋊D1112yes—
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C2×C22⋊D1111yescharacteristic
448C22×C4C2×C22⋊D1111yescharacteristic
449C22×C4C23×D1111yescharacteristic
450C2×C8—222no—
451C2×C8—222no—
452C2×C8—442no—
453C2×C8—442no—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—22no—
459C4⋊C4—222no—
460C4⋊C4—222no—
461C4⋊C4—441no—
462C4⋊C4—441no—
463C4⋊C4C2×C22⋊D1112yes—
464C4⋊C4C2×C22⋊D1112yes—
465C22⋊C4—24no—
466C22⋊C4—24no—
467C22⋊C4—24no—
468C22⋊C4—22no—
469C22⋊C4—22no—
470C22⋊C4—22no—
471C22⋊C4—22no—
472C22⋊C4—22no—
473C22⋊C4—22no—
474C22⋊C4—22no—
475C22⋊C4—22no—
476C22⋊C4—448no—
477C42—24no—
478C11C2×#161211yescharacteristic, complemented, Sylow
479C23—22no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—22no—
484C23—22no—
485C23—42no—
486C23—42no—
487C23—48no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—42no—
495C23—81no—
496C23—81no—
497C23—84no—
498C23#6700212yes—
499C23#6700312yes—
500C23#6700611yescharacteristic
501C23#6700611yescharacteristic
502C23C22×C22⋊D1111yescharacteristic
503Q8—42no—
504Q8—81no—
505D4—42no—
506D4—42no—
507D4—42no—
508D4—44no—
509D4—81no—
510D4—84no—
511D4—84no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—81no—
528C2×C4—84no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—442no—
535C2×C4—884no—
536C2×C4—882no—
537C2×C4—882no—
538C2×C4#6700611yescharacteristic
539C2×C4#6700611yescharacteristic
540C2×C4C22×C22⋊D1111yescharacteristic
541C2×C4C22×C22⋊D1111yescharacteristic
542C8—442no—
543C8—442no—
544C22—24no—
545C22—24no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—44no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—82no—
558C22—84no—
559C22—84no—
560C22—84no—
561C22#1062285112yes—
562C22#1062285112yes—
563C22#1062285512yes—
564C22#1062285612yes—
565C22C2×#6700211yescharacteristic
566C22C2×#6700311yescharacteristic
567C22C2×#6700611yescharacteristic
568C4—21no—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—42no—
573C4—42no—
574C4—42no—
575C4—42no—
576C4—882no—
577C4—882no—
578C2—21no—
579C2—21no—
580C2—22no—
581C2—82no—
582C2—82no—
583C2#1306763014yesdirect product factor
584C2C2×#1062285111yescharacteristic
585C2C2×#1062285511yescharacteristic
586C2C2×#1062285611yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#538C2
socleC23×C11#120
hypercenterC2×#538D11
hypocenterC11C2×#1612
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#538

Complements

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

NH ≅ G/Ntype
1. C2×#10622656C2semidirect
2. C2×#10622646C2semidirect
3. C2×#10622566C2semidirect
4. #13067630C2direct (N × H)
5. C2×#10622176C2semidirect
6. C2×#10622175C2semidirect
7. C2×#10622163C2semidirect
31. #10622656C22semidirect
33. #10622646C22semidirect
37. #10622566C22semidirect
38. #10622176C22semidirect
39. #10622175C22semidirect
40. #10622163C22semidirect
398. C2×C11#1612semidirect
478. C11C2×#1612semidirect
583. C2#13067630direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226562
C2×#106226462
C2×#106225662
#130676302
C2×#106221762
C2×#106221752
C2×#106221632
C2×C11×#5382
C2×#161211