Finite Group Databasebeta

← C2×#13074473 #14920482

Subgroups — C2×#13074473 #14920482

Order 2816.

3670 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66989C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13074473C2116yesmaximal, direct product factor
4C2×#10622565C212yesmaximal, complemented
5C2×#10622286C211yesmaximal, characteristic, complemented
6C2×#10622560C211yesmaximal, characteristic, complemented
7C2×#10622836C211yesmaximal, characteristic, complemented
8C2×#10622836C212yesmaximal, complemented
9C2×#10622833C212yesmaximal, complemented
10C2×#10622569C212yesmaximal, complemented
11C2×#10622264C211yesmaximal, characteristic, complemented
12C2×C11×#392C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2212yes—
15C23×C22⋊D11C2211yescharacteristic
16C23×C22⋊D11C2212yes—
17C24×Dic11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2212yes—
26C2×#66989—28no—
27C2×#66989C2218yescomplemented
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2212yes—
30C22×Dic11⋊C4C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C2×(C22⋊D11)⋊C4—28no—
33C2×(C22⋊D11)⋊C4C2218yescomplemented
34C11×#392C2218yescomplemented
35C2×C11×#95C2211yescharacteristic
36#10622836C2218yescomplemented
37#10622836C22116yescomplemented
38#10622833C22116yescomplemented
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44#10622569C22116yescomplemented
45#10622565C22116yescomplemented
46#10622560C2218yescomplemented
47#10622286C2218yescomplemented
48#10622264C2218yescomplemented
49C25×C11C2312yes—
50C25×C11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C22×D4×C11—28no—
53C22×D4×C11—24no—
54C22×D4×C11—44no—
55C22×D4×C11—44no—
56C22×D4×C11—44no—
57C22×D4×C11C2314yes—
58C22×D4×C11C2318yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—24no—
63C22×C22⋊D11—24no—
64C22×C22⋊D11—28no—
65C22×C22⋊D11—24no—
66C22×C22⋊D11—44no—
67C22×C22⋊D11—44no—
68C22×C22⋊D11C2314yes—
69C22×C22⋊D11C2318yes—
70C23×Dic11—24no—
71C23×Dic11—44no—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2312yes—
74C23×Dic11C2312yes—
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2314yes—
78C22×C4×D11—24no—
79C22×C4×D11—44no—
80C22×C4×D11C2314yes—
81C22×Dic22—24no—
82C22×Dic22—44no—
83C22×Dic22C2314yes—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—44no—
86C2×C11×C22⋊C4C2314yes—
87C2×C11×C22⋊C4C2318yes—
88C2×C22⋊Dic11—28no—
89C2×C22⋊Dic11—28no—
90C2×C22⋊Dic11—44no—
91C2×C22⋊Dic11—44no—
92C2×C22⋊Dic11C2318yes—
93C2×C22⋊Dic11C2318yes—
94C2×C22⋊Dic11C2318yes—
95C2×C22⋊Dic11C2318yes—
96#66989—232no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—44no—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4C2314yes—
103C2×C4×Dic11D418yescomplemented
104C2×C4×Dic11C2314yes—
105(C22⋊D11)⋊C4—232no—
106C11×#95C2314yes—
107C11⋊#95C2314yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C11⋊#95C2318yes—
112C2×#2631—111nomaximal, Sylow
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—24no—
124C24×C11#4114yes—
125C24×C11C2414yes—
126C24×C11C2412yes—
127C24×C11C2411yescharacteristic
128C23×D11—22no—
129C23×D11—22no—
130C23×D11—24no—
131C23×D11—24no—
132C23×D11#4114yes—
133C23×D11C2412yes—
134C2×D4×C11—216no—
135C2×D4×C11—28no—
136C2×D4×C11—48no—
137C2×D4×C11—48no—
138C2×D4×C11—48no—
139C2×D4×C11—416no—
140C2×D4×C11—432no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11C2×D414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2412yes—
151C2×C22⋊D11—232no—
152C2×C22⋊D11—28no—
153C2×C22⋊D11—28no—
154C2×C22⋊D11—28no—
155C2×C22⋊D11—216no—
156C2×C22⋊D11—48no—
157C2×C22⋊D11—48no—
158C2×C22⋊D11—432no—
159C22×Dic11—28no—
160C22×Dic11—22no—
161C22×Dic11—24no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11—48no—
172C22×Dic11—416no—
173C22×Dic11C2×D414yes—
174C22×Dic11C2×D414yes—
175C22×Dic11C2414yes—
176C22×Dic11C2412yes—
177C22×Dic11C2414yes—
178C22×Dic11C2412yes—
179C22×Dic11C2412yes—
180C2×C4×D11—28no—
181C2×C4×D11—48no—
182C2×C4×D11—416no—
183C2×Dic22—28no—
184C2×Dic22—48no—
185C2×Dic22—416no—
186C11×C22⋊C4—28no—
187C11×C22⋊C4—48no—
188C22⋊Dic11—216no—
189C22⋊Dic11—216no—
190C22⋊Dic11—48no—
191C22⋊Dic11—48no—
192(C2×D11)⋊C4—28no—
193(C2×D11)⋊C4—48no—
194Dic11⋊C4—28no—
195C4×Dic11C2×D4116yescomplemented
196C22×#124—111no—
197C22×C4×D4—111no—
198#2631—1116no—
199C2×#397—112no—
200C2×#393—111no—
201C2×#393—111no—
202C2×#392—112no—
203C2×#392—111no—
204C2×#392D1111yescharacteristic, complemented
205C2×#386—112no—
206C2×#386—112no—
207C2×#383—111no—
208C23×C11—28no—
209C23×C11—216no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11—48no—
224C23×C11—48no—
225C23×C11—48no—
226C23×C11—48no—
227C23×C11—48no—
228C23×C11—48no—
229C23×C11—48no—
230C23×C11—48no—
231C23×C11C22×D412yes—
232C23×C11C2×#4114yes—
233C23×C11C2×#4112yes—
234C23×C11C2×#4112yes—
235C23×C11H(5,𝔽2)14yes—
236C23×C11H(5,𝔽2)14yes—
237C23×C11C2511yescharacteristic
238C22×D11—28no—
239C22×D11—216no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—24no—
243C22×D11—24no—
244C22×D11—44no—
245C22×D11—44no—
246C22×D11—48no—
247C22×D11C2×#4114yes—
248D4×C11—416no—
249D4×C11—432no—
250C2×C4×C11—28no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—44no—
258C2×C4×C11—48no—
259C2×C4×C11C22×D414yes—
260C22⋊D11—232no—
261C22⋊D11—432no—
262C2×Dic11—28no—
263C2×Dic11—28no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—416no—
276C2×Dic11—48no—
277C2×Dic11—44no—
278C2×Dic11—48no—
279C2×Dic11C22×D414yes—
280C2×Dic11C22×D414yes—
281C4×D11—416no—
282Dic22—416no—
283C23×Q8—111no—
284C23×D4—111no—
285C23×D4—112no—
286C23×D4C2×D1111yescharacteristic
287C23×D4C2×D1112yes—
288C24×C4—111no—
289C24×C4—111no—
290C2×#124—118no—
291C2×#124—228no—
292C2×C4×D4—118no—
293C2×C4×D4—228no—
294C22×C4⋊C4—111no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—111no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4—112no—
300C22×C22⋊C4—112no—
301C22×C22⋊C4C2×D1111yescharacteristic
302C22×C22⋊C4C2×D1112yes—
303C22×C42—111no—
304#397—1116no—
305#393—118no—
306#393—118no—
307#392—118no—
308#392—1116no—
309#392C2×D1118yescomplemented
310#386—1116no—
311#386—1116no—
312#383—118no—
313C2×#95—111no—
314C2×#95—112no—
315C2×#95—112no—
316C2×#95—112no—
317C2×#95—112no—
318C2×#95C2×D1111yescharacteristic
319C22×C11—24no—
320C22×C11—28no—
321C22×C11—416no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—44no—
327C22×C11—44no—
328C22×C11—44no—
329C22×C11—44no—
330C22×C11—44no—
331C22×C11—44no—
332C22×C11—816no—
333C22×C11#52514yes—
334C22×C11#53514yes—
335C22×C11#53514yes—
336C22×C11#53818yes—
337C22×C11#53818yes—
338C22×C11C23×D411yescharacteristic
339C22×C11C22×#4111yescharacteristic
340C22×C11C22×#4111yescharacteristic
341C22×C11C2×H(5,𝔽2)12yes—
342C22×C11C2×H(5,𝔽2)12yes—
343C2×D11—24no—
344C2×D11—28no—
345C2×D11—416no—
346C2×D11—42no—
347C2×D11—42no—
348C2×D11—44no—
349C4×C11—24no—
350C4×C11—42no—
351C4×C11—44no—
352Dic11—24no—
353Dic11—24no—
354Dic11—44no—
355Dic11—42no—
356Dic11—44no—
357C25—111no—
358C25C22×D1112yes—
359C25C22×D1111yescharacteristic
360C22×Q8—114no—
361C22×Q8—224no—
362C22×Q8—444no—
363C22×D4—28no—
364C22×D4—24no—
365C22×D4—44no—
366C22×D4—44no—
367C22×D4—44no—
368C22×D4—114no—
369C22×D4—118no—
370C22×D4—224no—
371C22×D4—224no—
372C22×D4—224no—
373C22×D4—228no—
374C22×D4—444no—
375C22×D4—444no—
376C22×D4C22×D1114yes—
377C22×D4C22×D1118yes—
378C23×C4—111no—
379C23×C4—111no—
380C23×C4—112no—
381C23×C4—111no—
382C23×C4—112no—
383C23×C4—114no—
384C23×C4—114no—
385C23×C4—224no—
386C23×C4—224no—
387C23×C4—444no—
388C23×C4—444no—
389C23×C4C22×D1112yes—
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1111yescharacteristic
392#124—2232no—
393C4×D4—2232no—
394C2×C4⋊C4—114no—
395C2×C4⋊C4—224no—
396C2×C22⋊C4—24no—
397C2×C22⋊C4—44no—
398C2×C22⋊C4—118no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—114no—
401C2×C22⋊C4—118no—
402C2×C22⋊C4—118no—
403C2×C22⋊C4—118no—
404C2×C22⋊C4—228no—
405C2×C22⋊C4—228no—
406C2×C22⋊C4—224no—
407C2×C22⋊C4—444no—
408C2×C22⋊C4—444no—
409C2×C22⋊C4—444no—
410C2×C22⋊C4C22×D1114yes—
411C2×C22⋊C4C22×D1118yes—
412C2×C42—118no—
413C2×C42—114no—
414#95—118no—
415#95—114no—
416#95—118no—
417#95—118no—
418#95—118no—
419#95C22×D1114yes—
420C2×C11—44no—
421C2×C11—84no—
422C2×C11#263118yescomplemented
423C2×C11C2×#52511yescharacteristic
424C2×C11C2×#53511yescharacteristic
425C2×C11C2×#53511yescharacteristic
426C2×C11C2×#53812yes—
427C2×C11C2×#53812yes—
428D11—44no—
429C24—22no—
430C24—24no—
431C24—24no—
432C24—22no—
433C24—24no—
434C24—24no—
435C24—24no—
436C24—24no—
437C24—24no—
438C24—24no—
439C24—24no—
440C24—114no—
441C24—112no—
442C24—222no—
443C24—222no—
444C24—224no—
445C24—224no—
446C24#434114yes—
447C24C23×D1114yes—
448C24C23×D1112yes—
449C24C23×D1111yescharacteristic
450C2×Q8—228no—
451C2×Q8—448no—
452C2×Q8—4416no—
453C2×D4—216no—
454C2×D4—28no—
455C2×D4—48no—
456C2×D4—48no—
457C2×D4—48no—
458C2×D4—416no—
459C2×D4—432no—
460C2×D4—228no—
461C2×D4—228no—
462C2×D4—2232no—
463C2×D4—228no—
464C2×D4—2216no—
465C2×D4—448no—
466C2×D4—448no—
467C2×D4—4432no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—114no—
475C22×C4—114no—
476C22×C4—112no—
477C22×C4—112no—
478C22×C4—114no—
479C22×C4—114no—
480C22×C4—112no—
481C22×C4—228no—
482C22×C4—228no—
483C22×C4—222no—
484C22×C4—224no—
485C22×C4—222no—
486C22×C4—224no—
487C22×C4—222no—
488C22×C4—224no—
489C22×C4—224no—
490C22×C4—224no—
491C22×C4—224no—
492C22×C4—224no—
493C22×C4—224no—
494C22×C4—448no—
495C22×C4—4416no—
496C22×C4—448no—
497C22×C4—4416no—
498C22×C4D4×D1114yes—
499C22×C4C23×D1114yes—
500C22×C4C23×D1112yes—
501C22×C4C23×D1112yes—
502C4⋊C4—228no—
503C22⋊C4—28no—
504C22⋊C4—48no—
505C22⋊C4—2216no—
506C22⋊C4—2216no—
507C22⋊C4—228no—
508C22⋊C4—448no—
509C22⋊C4—448no—
510C22⋊C4—448no—
511C42—1116no—
512C11C2×#263111yescharacteristic, complemented, Sylow
513C23—216no—
514C23—28no—
515C23—22no—
516C23—24no—
517C23—24no—
518C23—22no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—24no—
525C23—24no—
526C23—44no—
527C23—44no—
528C23—48no—
529C23—48no—
530C23—48no—
531C23—48no—
532C23—48no—
533C23—48no—
534C23—48no—
535C23—48no—
536C23—114no—
537C23—228no—
538C23—2216no—
539C23—222no—
540C23—222no—
541C23—224no—
542C23—224no—
543C23—444no—
544C23—444no—
545C23—448no—
546C23C2×D4×D1112yes—
547C23C2×#434114yes—
548C23C2×#434112yes—
549C23#6703714yes—
550C23#6703714yes—
551C23#41×D1112yes—
552C23C24×D1111yescharacteristic
553Q8—4416no—
554D4—416no—
555D4—432no—
556D4—2232no—
557D4—4432no—
558C2×C4—28no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—44no—
566C2×C4—48no—
567C2×C4—114no—
568C2×C4—114no—
569C2×C4—228no—
570C2×C4—228no—
571C2×C4—222no—
572C2×C4—224no—
573C2×C4—222no—
574C2×C4—224no—
575C2×C4—222no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—4416no—
583C2×C4—4416no—
584C2×C4—444no—
585C2×C4—448no—
586C2×C4—448no—
587C2×C4C2×D4×D1114yes—
588C22—24no—
589C22—28no—
590C22—416no—
591C22—42no—
592C22—42no—
593C22—44no—
594C22—44no—
595C22—44no—
596C22—44no—
597C22—44no—
598C22—44no—
599C22—44no—
600C22—44no—
601C22—816no—
602C22—224no—
603C22—228no—
604C22—4416no—
605C22—442no—
606C22—442no—
607C22—444no—
608C22#1062312314yes—
609C22#1062312418yes—
610C22#1062313714yes—
611C22#1062314418yes—
612C22#1062324614yes—
613C22C22×D4×D1111yescharacteristic
614C22C22×#434111yescharacteristic
615C22C2×#6703712yes—
616C22C2×#6703712yes—
617C22C2×#41×D1111yescharacteristic
618C4—24no—
619C4—42no—
620C4—44no—
621C4—224no—
622C4—224no—
623C4—442no—
624C4—444no—
625C4—444no—
626C2—44no—
627C2—84no—
628C2—444no—
629C2#1307447318yesdirect product factor
630C2C2×#1062313711yescharacteristic
631C2C2×#1062324611yescharacteristic
632C2C2×#1062312311yescharacteristic
633C2C2×#1062314412yes—
634C2C2×#1062312412yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2631
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66989C2semidirect
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13074473C2direct (N × H)
4. C2×#10622565C2semidirect
5. C2×#10622286C2semidirect
6. C2×#10622560C2semidirect
7. C2×#10622836C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622833C2semidirect
10. C2×#10622569C2semidirect
11. C2×#10622264C2semidirect
12. C2×C11×#392C2semidirect
27. C2×#66989C22semidirect
33. C2×(C22⋊D11)⋊C4C22semidirect
34. C11×#392C22semidirect
36. #10622836C22semidirect
37. #10622836C22semidirect
38. #10622833C22semidirect
44. #10622569C22semidirect
45. #10622565C22semidirect
46. #10622560C22semidirect
47. #10622286C22semidirect
48. #10622264C22semidirect
103. C2×C4×Dic11D4semidirect
195. C4×Dic11C2×D4semidirect
204. C2×#392D11semidirect
309. #392C2×D11semidirect
422. C2×C11#2631semidirect
512. C11C2×#2631semidirect
629. C2#13074473direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669892
C22×(C22⋊D11)⋊C42
#130744732
C2×#106225652
C2×#106222862
C2×#106225602
C2×#106228362
C2×#106228332
C2×#106225692
C2×#106222642
C2×C11×#3922
C2×#263111