Finite Group Databasebeta

← C2×#13074543 #14920206

Subgroups — C2×#13074543 #14920206

Order 2816.

3326 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66950C211yesmaximal, characteristic, complemented
2C22×#66937C211yesmaximal, characteristic
3#13074543C2116yesmaximal, direct product factor
4C2×#10622273C212yesmaximal, complemented
5C2×#10622606C211yesmaximal, characteristic, complemented
6C2×#10622574C212yesmaximal, complemented
7C2×#10622286C211yesmaximal, characteristic, complemented
8C2×#10622560C211yesmaximal, characteristic, complemented
9C2×#10622278C212yesmaximal, complemented
10C2×#10622569C212yesmaximal, complemented
11C2×D11×#95C211yesmaximal, characteristic, complemented
12C2×C11×#397C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×D44C2211yescharacteristic
16C23×C4×D11C2212yes—
17C23×C4×D11C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×C4⋊Dic11C2212yes—
28C22×Dic11⋊C4C2211yescharacteristic
29C2×#66950—28no—
30C2×#66950C2218yescomplemented
31C2×#66937—28no—
32C2×#66937C2218yes—
33C11×#397C2218yescomplemented
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622606C2218yescomplemented
42#10622574C22116yescomplemented
43#10622569C22116yescomplemented
44#10622560C2218yescomplemented
45#10622286C2218yescomplemented
46#10622278C22116yescomplemented
47D11×#95C2218yescomplemented
48#10622273C22116yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—24no—
57C22×C22⋊D11—28no—
58C22×C22⋊D11—24no—
59C22×C22⋊D11—44no—
60C22×C22⋊D11C2314yes—
61C22×C22⋊D11C2314yes—
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2312yes—
64C23×Dic11C2312yes—
65C23×Dic11C2311yescharacteristic
66C22×D44—24no—
67C22×D44—28no—
68C22×D44C2314yes—
69C22×C4×D11—28no—
70C22×C4×D11—44no—
71C22×C4×D11—44no—
72C22×C4×D11—44no—
73C22×C4×D11D418yes—
74C22×C4×D11C2318yes—
75C22×C4×D11C2314yes—
76C22×Dic22—24no—
77C22×Dic22—44no—
78C22×Dic22C2314yes—
79C2×C11×C4⋊C4—24no—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—44no—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2318yes—
85C2×C22⋊Dic11—44no—
86C2×C22⋊Dic11C2318yes—
87C2×(C2×D11)⋊C4—28no—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—44no—
90C2×(C2×D11)⋊C4—44no—
91C2×(C2×D11)⋊C4C2314yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×C4⋊Dic11—28no—
96C2×C4⋊Dic11C2318yes—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4C2314yes—
99#66950—232no—
100#66937—232no—
101C11×#95C2318yes—
102C11×#95C2314yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2314yes—
108C2×#2639—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11C2412yes—
115C24×C11C2411yescharacteristic
116C23×D11—24no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—24no—
121C23×D11—22no—
122C23×D11—24no—
123C23×D11—22no—
124C23×D11C2×D414yes—
125C23×D11#4118yes—
126C23×D11C2412yes—
127C23×D11C2412yes—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2414yes—
141C22×C4×C11C2412yes—
142C2×C22⋊D11—28no—
143C2×C22⋊D11—28no—
144C2×C22⋊D11—216no—
145C2×C22⋊D11—48no—
146C2×C22⋊D11—416no—
147C2×C22⋊D11—416no—
148C22×Dic11—22no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11C2×D414yes—
158C22×Dic11C2412yes—
159C22×Dic11C2414yes—
160C22×Dic11C2414yes—
161C22×Dic11C2412yes—
162C2×D44—28no—
163C2×D44—216no—
164C2×D44—416no—
165C2×C4×D11—216no—
166C2×C4×D11—416no—
167C2×C4×D11—48no—
168C2×C4×D11—48no—
169C2×C4×D11—48no—
170C2×C4×D11—432no—
171C2×C4×D11C2×D4116yes—
172C2×Dic22—28no—
173C2×Dic22—48no—
174C2×Dic22—416no—
175C11×C4⋊C4—28no—
176C11×C22⋊C4—28no—
177C11×C22⋊C4—48no—
178C22⋊Dic11—48no—
179(C2×D11)⋊C4—216no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—48no—
182(C2×D11)⋊C4—48no—
183C4⋊Dic11—216no—
184Dic11⋊C4—28no—
185C22×C22⋊Q8—111no—
186C22×#121—111no—
187#2639—1116no—
188C2×#400—112no—
189C2×#397—111no—
190C2×#397D1111yescharacteristic, complemented
191C2×#394—112no—
192C2×#393—111no—
193C2×#393—111no—
194C2×#386—112no—
195C2×#386—112no—
196C22×#95—111no—
197C23×C11—22no—
198C23×C11—24no—
199C23×C11—24no—
200C23×C11—22no—
201C23×C11—22no—
202C23×C11—44no—
203C23×C11—44no—
204C23×C11—44no—
205C23×C11—48no—
206C23×C11—48no—
207C23×C11C22×D412yes—
208C23×C11C2×#4114yes—
209C23×C11H(5,𝔽2)12yes—
210C23×C11H(5,𝔽2)14yes—
211C23×C112−1+412yes—
212C23×C11C2511yescharacteristic
213C22×D11—28no—
214C22×D11—28no—
215C22×D11—216no—
216C22×D11—216no—
217C22×D11—22no—
218C22×D11—24no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—24no—
222C22×D11—22no—
223C22×D11—24no—
224C22×D11—22no—
225C22×D11—44no—
226C22×D11—44no—
227C22×D11—44no—
228C22×D11—48no—
229C22×D11—48no—
230C22×D11#124116yes—
231C22×D11C22×D414yes—
232C22×D11C2×#4118yes—
233C2×C4×C11—28no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—24no—
243C2×C4×C11—44no—
244C2×C4×C11—48no—
245C2×C4×C11—48no—
246C2×C4×C11C22×D414yes—
247C22⋊D11—416no—
248C22⋊D11—416no—
249C2×Dic11—28no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—44no—
260C2×Dic11—48no—
261C2×Dic11—48no—
262C2×Dic11C22×D414yes—
263D44—416no—
264C4×D11—416no—
265C4×D11—432no—
266Dic22—416no—
267C23×Q8—111no—
268C23×D4—111no—
269C23×D4—111no—
270C23×D4—111no—
271C24×C4—111no—
272C24×C4—112no—
273C2×C22⋊Q8—118no—
274C2×C22⋊Q8—228no—
275C2×#121—118no—
276C2×#121—228no—
277C22×C4⋊C4—112no—
278C22×C4⋊C4—111no—
279C22×C4⋊C4C2×D1111yescharacteristic
280C22×C22⋊C4—111no—
281C22×C22⋊C4—112no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4—112no—
284C22×C22⋊C4—112no—
285C22×C22⋊C4C2×D1111yescharacteristic
286C22×C22⋊C4C2×D1112yes—
287#400—1116no—
288#397—118no—
289#397C2×D1118yescomplemented
290#394—1116no—
291#393—118no—
292#393—118no—
293#386—1116no—
294#386—1116no—
295C2×#95—111no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95—118no—
301C2×#95C2×D1111yescharacteristic
302C2×#95C2×D1112yes—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—42no—
306C22×C11—44no—
307C22×C11—44no—
308C22×C11—88no—
309C22×C11C2×#12414yes—
310C22×C11#53414yes—
311C22×C11#53714yes—
312C22×C11#53818yes—
313C22×C11#53918yes—
314C22×C11C23×D411yescharacteristic
315C22×C11C22×#4112yes—
316C22×C11C2×H(5,𝔽2)11yescharacteristic
317C22×C11C2×H(5,𝔽2)12yes—
318C22×C11C2×2−1+411yescharacteristic
319C2×D11—232no—
320C2×D11—24no—
321C2×D11—24no—
322C2×D11—28no—
323C2×D11—28no—
324C2×D11—42no—
325C2×D11—42no—
326C2×D11—42no—
327C2×D11—44no—
328C2×D11—44no—
329C2×D11—88no—
330C2×D11C2×#12418yes—
331C4×C11—24no—
332C4×C11—42no—
333C4×C11—44no—
334C4×C11—44no—
335Dic11—24no—
336Dic11—42no—
337Dic11—44no—
338Dic11—44no—
339C25—111no—
340C25—111no—
341C25C22×D1111yescharacteristic
342C22×Q8—114no—
343C22×Q8—224no—
344C22×Q8—444no—
345C22×D4—114no—
346C22×D4—114no—
347C22×D4—114no—
348C22×D4—224no—
349C22×D4—228no—
350C22×D4—224no—
351C22×D4—224no—
352C22×D4—228no—
353C22×D4—444no—
354C23×C4—111no—
355C23×C4—118no—
356C23×C4—114no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4—111no—
360C23×C4—118no—
361C23×C4—228no—
362C23×C4—444no—
363C23×C4—444no—
364C23×C4—444no—
365C23×C4C22×D1112yes—
366C23×C4C22×D1112yes—
367C23×C4C22×D1111yescharacteristic
368C23×C4C22×D1111yescharacteristic
369C22⋊Q8—2232no—
370#121—2232no—
371C2×C4⋊C4—24no—
372C2×C4⋊C4—114no—
373C2×C4⋊C4—118no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—228no—
376C2×C4⋊C4C22×D1114yes—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—44no—
379C2×C22⋊C4—114no—
380C2×C22⋊C4—118no—
381C2×C22⋊C4—118no—
382C2×C22⋊C4—118no—
383C2×C22⋊C4—118no—
384C2×C22⋊C4—228no—
385C2×C22⋊C4—224no—
386C2×C22⋊C4—444no—
387C2×C22⋊C4—444no—
388C2×C22⋊C4—444no—
389C2×C22⋊C4C22×D1114yes—
390C2×C22⋊C4C22×D1118yes—
391#95—114no—
392#95—118no—
393#95—118no—
394#95—118no—
395#95—118no—
396#95C22×D1114yes—
397#95C22×D1118yes—
398C2×C11—82no—
399C2×C11#263918yescomplemented
400C2×C11C22×#12411yescharacteristic
401C2×C11C2×#53411yescharacteristic
402C2×C11C2×#53711yescharacteristic
403C2×C11C2×#53812yes—
404C2×C11C2×#53912yes—
405D11—28no—
406D11—82no—
407C24—22no—
408C24—22no—
409C24—24no—
410C24—24no—
411C24—22no—
412C24—114no—
413C24—118no—
414C24—112no—
415C24—112no—
416C24—222no—
417C24—224no—
418C24—222no—
419C24—222no—
420C24—222no—
421C24—224no—
422C24—224no—
423C24—222no—
424C24C23×D1112yes—
425C24C23×D1111yescharacteristic
426C2×Q8—228no—
427C2×Q8—448no—
428C2×Q8—4416no—
429C2×D4—228no—
430C2×D4—2216no—
431C2×D4—228no—
432C2×D4—228no—
433C2×D4—2216no—
434C2×D4—4416no—
435C2×D4—448no—
436C2×D4—4416no—
437C2×D4—4416no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—114no—
448C22×C4—112no—
449C22×C4—1116no—
450C22×C4—114no—
451C22×C4—112no—
452C22×C4—114no—
453C22×C4—2216no—
454C22×C4—224no—
455C22×C4—222no—
456C22×C4—224no—
457C22×C4—224no—
458C22×C4—224no—
459C22×C4—224no—
460C22×C4—224no—
461C22×C4—224no—
462C22×C4—224no—
463C22×C4—4416no—
464C22×C4—448no—
465C22×C4—448no—
466C22×C4—448no—
467C22×C4—4432no—
468C22×C4D4×D1114yes—
469C22×C4C23×D1114yes—
470C22×C4C23×D1112yes—
471C22×C4C23×D1114yes—
472C22×C4C23×D1112yes—
473C4⋊C4—28no—
474C4⋊C4—228no—
475C4⋊C4—2216no—
476C22⋊C4—28no—
477C22⋊C4—48no—
478C22⋊C4—2216no—
479C22⋊C4—228no—
480C22⋊C4—448no—
481C22⋊C4—448no—
482C22⋊C4—448no—
483C11C2×#263911yescharacteristic, complemented, Sylow
484C23—22no—
485C23—22no—
486C23—24no—
487C23—24no—
488C23—22no—
489C23—48no—
490C23—44no—
491C23—44no—
492C23—48no—
493C23—44no—
494C23—114no—
495C23—118no—
496C23—1116no—
497C23—2216no—
498C23—228no—
499C23—228no—
500C23—2216no—
501C23—222no—
502C23—224no—
503C23—222no—
504C23—222no—
505C23—222no—
506C23—224no—
507C23—224no—
508C23—222no—
509C23—448no—
510C23—444no—
511C23—444no—
512C23—448no—
513C23—444no—
514C23C2×D4×D1112yes—
515C23#6703712yes—
516C23#41×D1114yes—
517C23#6704214yes—
518C23#6704312yes—
519C23C24×D1111yescharacteristic
520Q8—4416no—
521D4—4416no—
522D4—4416no—
523D4—4416no—
524C2×C4—28no—
525C2×C4—24no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—24no—
534C2×C4—48no—
535C2×C4—48no—
536C2×C4—44no—
537C2×C4—114no—
538C2×C4—228no—
539C2×C4—224no—
540C2×C4—222no—
541C2×C4—224no—
542C2×C4—224no—
543C2×C4—224no—
544C2×C4—224no—
545C2×C4—224no—
546C2×C4—224no—
547C2×C4—224no—
548C2×C4—4416no—
549C2×C4—4432no—
550C2×C4—448no—
551C2×C4—448no—
552C2×C4—444no—
553C2×C4C2×D4×D1114yes—
554C22—42no—
555C22—42no—
556C22—42no—
557C22—44no—
558C22—44no—
559C22—88no—
560C22—118no—
561C22—224no—
562C22—224no—
563C22—228no—
564C22—228no—
565C22—2232no—
566C22—442no—
567C22—442no—
568C22—442no—
569C22—444no—
570C22—444no—
571C22—888no—
572C22#1062313914yes—
573C22#1062318414yes—
574C22#1062318818yes—
575C22D11×#12414yes—
576C22#1062323818yes—
577C22C22×D4×D1111yescharacteristic
578C22C2×#6703711yescharacteristic
579C22C2×#41×D1112yes—
580C22C2×#6704212yes—
581C22C2×#6704311yescharacteristic
582C4—24no—
583C4—42no—
584C4—44no—
585C4—44no—
586C4—224no—
587C4—442no—
588C4—444no—
589C4—444no—
590C2—82no—
591C2—228no—
592C2—882no—
593C2#1307454318yesdirect product factor
594C2C2×D11×#12411yescharacteristic
595C2C2×#1062318411yescharacteristic
596C2C2×#1062313911yescharacteristic
597C2C2×#1062318812yes—
598C2C2×#1062323812yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
prime radicalC22×#66937C2
hypercenterC2×#397D11
hypocenterC11C2×#2639
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#66950C2semidirect
3. #13074543C2direct (N × H)
4. C2×#10622273C2semidirect
5. C2×#10622606C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622286C2semidirect
8. C2×#10622560C2semidirect
9. C2×#10622278C2semidirect
10. C2×#10622569C2semidirect
11. C2×D11×#95C2semidirect
12. C2×C11×#397C2semidirect
30. C2×#66950C22semidirect
33. C11×#397C22semidirect
41. #10622606C22semidirect
42. #10622574C22semidirect
43. #10622569C22semidirect
44. #10622560C22semidirect
45. #10622286C22semidirect
46. #10622278C22semidirect
47. D11×#95C22semidirect
48. #10622273C22semidirect
190. C2×#397D11semidirect
289. #397C2×D11semidirect
399. C2×C11#2639semidirect
483. C11C2×#2639semidirect
593. C2#13074543direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669502
C22×#669372
#130745432
C2×#106222732
C2×#106226062
C2×#106225742
C2×#106222862
C2×#106225602
C2×#106222782
C2×#106225692
C2×D11×#952
C2×C11×#3972
C2×#263911