Finite Group Databasebeta

← C2×#13074509 #14920175

Subgroups — C2×#13074509 #14920175

Order 2816.

3606 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66948C211yesmaximal, characteristic, complemented
2C22×#66946C211yesmaximal, characteristic, complemented
3#13074509C2116yesmaximal, direct product factor
4C2×#10622605C211yesmaximal, characteristic, complemented
5C2×#10622285C212yesmaximal, complemented
6C2×#10622604C211yesmaximal, characteristic, complemented
7C2×#10622284C211yesmaximal, characteristic, complemented
8C2×#10622284C212yesmaximal, complemented
9C2×#10622282C212yesmaximal, complemented
10C2×#10622278C212yesmaximal, complemented
11C2×#10622277C211yesmaximal, characteristic, complemented
12C2×C11×#400C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×D44C2212yes—
15C23×D44C2211yescharacteristic
16C23×D44C2212yes—
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C2×#66948—28no—
32C2×#66948C2218yescomplemented
33C2×#66946—28no—
34C2×#66946C2218yescomplemented
35C11×#400C2218yescomplemented
36C2×C11×#95C2211yescharacteristic
37C2×C11×#95C2212yes—
38C2×C11×#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2211yescharacteristic
41#10622605C2218yescomplemented
42#10622604C2218yescomplemented
43#10622285C22116yescomplemented
44#10622284C2218yescomplemented
45#10622284C22116yescomplemented
46#10622282C22116yescomplemented
47#10622278C22116yescomplemented
48#10622277C2218yescomplemented
49C24×D11C2312yes—
50C24×D11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C22×D44—24no—
61C22×D44—24no—
62C22×D44—24no—
63C22×D44—28no—
64C22×D44—28no—
65C22×D44—24no—
66C22×D44—44no—
67C22×D44—44no—
68C22×D44—44no—
69C22×D44—44no—
70C22×D44—44no—
71C22×D44C2314yes—
72C22×D44C2318yes—
73C22×D44C2314yes—
74C22×D44C2318yes—
75C22×C4×D11—24no—
76C22×C4×D11—44no—
77C22×C4×D11—44no—
78C22×C4×D11D418yescomplemented
79C22×C4×D11C2314yes—
80C22×C4×D11C2314yes—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2314yes—
85C2×(C2×D11)⋊C4—24no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—28no—
88C2×(C2×D11)⋊C4—28no—
89C2×(C2×D11)⋊C4—44no—
90C2×(C2×D11)⋊C4—44no—
91C2×(C2×D11)⋊C4—44no—
92C2×(C2×D11)⋊C4—44no—
93C2×(C2×D11)⋊C4C2314yes—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×Dic11⋊C4—44no—
102C2×Dic11⋊C4C2318yes—
103C2×C4×Dic11—24no—
104C2×C4×Dic11C2314yes—
105#66948—232no—
106#66946—232no—
107C11×#95C2314yes—
108C11×#95C2318yes—
109C11×#95C2318yes—
110C11⋊#95C2318yes—
111C11⋊#95C2314yes—
112C2×#2635—111nomaximal, Sylow
113C24×C11C2411yescharacteristic
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—22no—
117C23×D11—22no—
118C23×D11—24no—
119C23×D11—24no—
120C23×D11—24no—
121C23×D11—24no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11C2×D414yes—
130C23×D11#4114yes—
131C23×D11C2414yes—
132C23×D11C2412yes—
133C23×D11C2412yes—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11C2×D414yes—
146C22×C4×C11#4114yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2412yes—
151C22×C4×C11C2412yes—
152C22×Dic11—22no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11C2×D414yes—
159C22×Dic11C2414yes—
160C22×Dic11C2412yes—
161C22×Dic11C2412yes—
162C2×D44—232no—
163C2×D44—28no—
164C2×D44—216no—
165C2×D44—28no—
166C2×D44—216no—
167C2×D44—28no—
168C2×D44—28no—
169C2×D44—48no—
170C2×D44—48no—
171C2×D44—48no—
172C2×D44—48no—
173C2×D44—48no—
174C2×D44—416no—
175C2×D44—432no—
176C2×D44—432no—
177C2×C4×D11—28no—
178C2×C4×D11—416no—
179C2×C4×D11—48no—
180C2×C4×D11—48no—
181C2×C4×D11—416no—
182C2×C4×D11C2×D4116yescomplemented
183C11×C4⋊C4—28no—
184C11×C4⋊C4—28no—
185(C2×D11)⋊C4—216no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—216no—
189(C2×D11)⋊C4—48no—
190(C2×D11)⋊C4—48no—
191(C2×D11)⋊C4—48no—
192(C2×D11)⋊C4—48no—
193Dic11⋊C4—48no—
194C4×Dic11—28no—
195C22×#121—111no—
196C22×C4×D4—111no—
197#2635—1116no—
198C2×#400D1111yescharacteristic, complemented
199C2×#399—111no—
200C2×#394—112no—
201C2×#394—111no—
202C2×#392—112no—
203C2×#392—111no—
204C2×#388—112no—
205C2×#386—112no—
206C2×#381—111no—
207C23×C11C22×D412yes—
208C23×C11C2×#4112yes—
209C23×C11C2×#4112yes—
210C23×C11H(5,𝔽2)14yes—
211C23×C11H(5,𝔽2)14yes—
212C23×C11C2511yescharacteristic
213C22×D11—28no—
214C22×D11—28no—
215C22×D11—28no—
216C22×D11—28no—
217C22×D11—216no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—24no—
223C22×D11—24no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—44no—
234C22×D11—44no—
235C22×D11—48no—
236C22×D11—48no—
237C22×D11—48no—
238C22×D11—48no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11—48no—
244C22×D11—48no—
245C22×D11C22×D414yes—
246C22×D11C2×#4114yes—
247C2×C4×C11—28no—
248C2×C4×C11—28no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
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—24no—
258C2×C4×C11—24no—
259C2×C4×C11—24no—
260C2×C4×C11—44no—
261C2×C4×C11—48no—
262C2×C4×C11—48no—
263C2×C4×C11C22×D414yes—
264C2×C4×C11C2×#4114yes—
265C2×Dic11—28no—
266C2×Dic11—24no—
267C2×Dic11—22no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—44no—
273C2×Dic11—48no—
274C2×Dic11C22×D414yes—
275D44—232no—
276D44—416no—
277D44—432no—
278D44—432no—
279C4×D11—416no—
280C4×D11—416no—
281C23×D4—111no—
282C23×D4—112no—
283C23×D4—112no—
284C23×D4—111no—
285C24×C4—111no—
286C24×C4—111no—
287C2×#121—118no—
288C2×#121—228no—
289C2×C4×D4—118no—
290C2×C4×D4—228no—
291C22×C4⋊C4—112no—
292C22×C4⋊C4C2×D1111yescharacteristic
293C22×C4⋊C4C2×D1111yescharacteristic
294C22×C22⋊C4—112no—
295C22×C22⋊C4—111no—
296C22×C22⋊C4—111no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4—112no—
300C22×C22⋊C4—112no—
301C22×C22⋊C4—112no—
302C22×C42—111no—
303#400C2×D1118yescomplemented
304#399—118no—
305#394—118no—
306#394—1116no—
307#392—118no—
308#392—1116no—
309#388—1116no—
310#386—1116no—
311#381—118no—
312C2×#95—111no—
313C2×#95—112no—
314C2×#95C2×D1111yescharacteristic
315C2×#95C2×D1112yes—
316C2×#95C2×D1112yes—
317C22×C11#52514yes—
318C22×C11#53414yes—
319C22×C11#53514yes—
320C22×C11#53818yes—
321C22×C11#54018yes—
322C22×C11C23×D411yescharacteristic
323C22×C11C22×#4111yescharacteristic
324C22×C11C22×#4111yescharacteristic
325C22×C11C2×H(5,𝔽2)12yes—
326C22×C11C2×H(5,𝔽2)12yes—
327C2×D11—24no—
328C2×D11—24no—
329C2×D11—24no—
330C2×D11—24no—
331C2×D11—28no—
332C2×D11—416no—
333C2×D11—416no—
334C2×D11—42no—
335C2×D11—42no—
336C2×D11—44no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—816no—
347C4×C11—24no—
348C4×C11—24no—
349C4×C11—42no—
350C4×C11—44no—
351C4×C11—44no—
352Dic11—24no—
353Dic11—42no—
354Dic11—44no—
355C25—111no—
356C25—111no—
357C25—112no—
358C22×D4—114no—
359C22×D4—118no—
360C22×D4—114no—
361C22×D4—118no—
362C22×D4—224no—
363C22×D4—224no—
364C22×D4—228no—
365C22×D4—228no—
366C22×D4—224no—
367C22×D4—224no—
368C22×D4—444no—
369C22×D4—444no—
370C22×D4—444no—
371C22×D4—444no—
372C22×D4—444no—
373C23×C4—111no—
374C23×C4—118no—
375C23×C4—114no—
376C23×C4—111no—
377C23×C4—112no—
378C23×C4—114no—
379C23×C4—224no—
380C23×C4—444no—
381C23×C4—444no—
382C23×C4C22×D1111yescharacteristic
383C23×C4C22×D1112yes—
384C23×C4C22×D1112yes—
385C23×C4C22×D1111yescharacteristic
386C23×C4C22×D1111yescharacteristic
387#121—2232no—
388C4×D4—2232no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—24no—
391C2×C4⋊C4—118no—
392C2×C4⋊C4—444no—
393C2×C4⋊C4C22×D1114yes—
394C2×C4⋊C4C22×D1114yes—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—114no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—118no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—118no—
401C2×C22⋊C4—118no—
402C2×C22⋊C4—118no—
403C2×C22⋊C4—228no—
404C2×C22⋊C4—224no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—228no—
407C2×C22⋊C4—444no—
408C2×C22⋊C4—444no—
409C2×C22⋊C4—444no—
410C2×C22⋊C4—444no—
411C2×C42—114no—
412C2×C42—224no—
413#95—118no—
414#95—114no—
415#95C22×D1114yes—
416#95C22×D1118yes—
417#95C22×D1118yes—
418C2×C11#263518yescomplemented
419C2×C11C2×#52511yescharacteristic
420C2×C11C2×#53411yescharacteristic
421C2×C11C2×#53511yescharacteristic
422C2×C11C2×#53812yes—
423C2×C11C2×#54012yes—
424D11—44no—
425D11—44no—
426D11—84no—
427C24—114no—
428C24—114no—
429C24—112no—
430C24—112no—
431C24—114no—
432C24—222no—
433C24—222no—
434C24—222no—
435C24—222no—
436C24—224no—
437C24—224no—
438C24—224no—
439C24—224no—
440C24—224no—
441C24—224no—
442C24—224no—
443C24—224no—
444C24—224no—
445C24—224no—
446C24—224no—
447C24C23×D1111yescharacteristic
448C2×D4—228no—
449C2×D4—228no—
450C2×D4—2232no—
451C2×D4—2216no—
452C2×D4—2216no—
453C2×D4—228no—
454C2×D4—228no—
455C2×D4—448no—
456C2×D4—448no—
457C2×D4—448no—
458C2×D4—448no—
459C2×D4—448no—
460C2×D4—4416no—
461C2×D4—4432no—
462C2×D4—4432no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—24no—
473C22×C4—24no—
474C22×C4—114no—
475C22×C4—112no—
476C22×C4—1116no—
477C22×C4—114no—
478C22×C4—112no—
479C22×C4—228no—
480C22×C4—224no—
481C22×C4—222no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—4416no—
487C22×C4—448no—
488C22×C4—448no—
489C22×C4—4416no—
490C22×C4D4×D1114yes—
491C22×C4#434314yes—
492C22×C4C23×D1114yes—
493C22×C4C23×D1112yes—
494C22×C4C23×D1114yes—
495C22×C4C23×D1112yes—
496C22×C4C23×D1112yes—
497C4⋊C4—28no—
498C4⋊C4—28no—
499C4⋊C4—448no—
500C22⋊C4—2216no—
501C22⋊C4—228no—
502C22⋊C4—228no—
503C22⋊C4—2216no—
504C22⋊C4—448no—
505C22⋊C4—448no—
506C22⋊C4—448no—
507C22⋊C4—448no—
508C42—228no—
509C11C2×#263511yescharacteristic, complemented, Sylow
510C23—114no—
511C23—114no—
512C23—2216no—
513C23—228no—
514C23—228no—
515C23—228no—
516C23—222no—
517C23—222no—
518C23—222no—
519C23—222no—
520C23—224no—
521C23—224no—
522C23—224no—
523C23—224no—
524C23—228no—
525C23—224no—
526C23—224no—
527C23—224no—
528C23—224no—
529C23—224no—
530C23—224no—
531C23—224no—
532C23—448no—
533C23—444no—
534C23—444no—
535C23—448no—
536C23—448no—
537C23—448no—
538C23—448no—
539C23—448no—
540C23—448no—
541C23—448no—
542C23—448no—
543C23—448no—
544C23C2×D4×D1112yes—
545C23C2×#434312yes—
546C23#41×D1112yes—
547C23#6704214yes—
548C23#6704214yes—
549C23C24×D1111yescharacteristic
550D4—2232no—
551D4—4416no—
552D4—4432no—
553D4—4432no—
554C2×C4—28no—
555C2×C4—28no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—24no—
566C2×C4—24no—
567C2×C4—48no—
568C2×C4—44no—
569C2×C4—48no—
570C2×C4—114no—
571C2×C4—228no—
572C2×C4—224no—
573C2×C4—222no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—4416no—
579C2×C4—4416no—
580C2×C4—444no—
581C2×C4—448no—
582C2×C4C2×D4×D1114yes—
583C2×C4C2×#434314yes—
584C22—224no—
585C22—224no—
586C22—224no—
587C22—224no—
588C22—228no—
589C22—442no—
590C22—442no—
591C22—4416no—
592C22—4416no—
593C22—444no—
594C22—444no—
595C22—444no—
596C22—444no—
597C22—444no—
598C22—444no—
599C22—444no—
600C22—444no—
601C22—444no—
602C22—444no—
603C22—8816no—
604C22#1062315814yes—
605C22#1062318414yes—
606C22#1062320514yes—
607C22#1062322918yes—
608C22#1062323518yes—
609C22C22×D4×D1111yescharacteristic
610C22C22×#434311yescharacteristic
611C22C2×#41×D1111yescharacteristic
612C22C2×#6704212yes—
613C22C2×#6704212yes—
614C4—24no—
615C4—24no—
616C4—42no—
617C4—44no—
618C4—44no—
619C4—224no—
620C4—442no—
621C4—444no—
622C2—444no—
623C2—444no—
624C2—884no—
625C2#1307450918yesdirect product factor
626C2C2×#1062315811yescharacteristic
627C2C2×#1062318411yescharacteristic
628C2C2×#1062320511yescharacteristic
629C2C2×#1062323512yes—
630C2C2×#1062322912yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#400C2
socleC24×C11C24
hypercenterC2×#400D11
hypocenterC11C2×#2635
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C22×#66948C2semidirect
2. C22×#66946C2semidirect
3. #13074509C2direct (N × H)
4. C2×#10622605C2semidirect
5. C2×#10622285C2semidirect
6. C2×#10622604C2semidirect
7. C2×#10622284C2semidirect
8. C2×#10622284C2semidirect
9. C2×#10622282C2semidirect
10. C2×#10622278C2semidirect
11. C2×#10622277C2semidirect
12. C2×C11×#400C2semidirect
32. C2×#66948C22semidirect
34. C2×#66946C22semidirect
35. C11×#400C22semidirect
41. #10622605C22semidirect
42. #10622604C22semidirect
43. #10622285C22semidirect
44. #10622284C22semidirect
45. #10622284C22semidirect
46. #10622282C22semidirect
47. #10622278C22semidirect
48. #10622277C22semidirect
78. C22×C4×D11D4semidirect
182. C2×C4×D11C2×D4semidirect
198. C2×#400D11semidirect
303. #400C2×D11semidirect
418. C2×C11#2635semidirect
509. C11C2×#2635semidirect
625. C2#13074509direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669482
C22×#669462
#130745092
C2×#106226052
C2×#106222852
C2×#106226042
C2×#106222842
C2×#106222822
C2×#106222782
C2×#106222772
C2×C11×#4002
C2×#263511