Finite Group Databasebeta

← C2×#13074500 #14920172

Subgroups — C2×#13074500 #14920172

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×#66983C211yesmaximal, characteristic, complemented
2#13074500C2116yesmaximal, direct product factor
3C2×#10622599C211yesmaximal, characteristic, complemented
4C2×#10622562C211yesmaximal, characteristic, complemented
5C2×#10622604C211yesmaximal, characteristic, complemented
6C2×#10622572C212yesmaximal, complemented
7C2×#10622573C211yesmaximal, characteristic, complemented
8C2×#10622836C212yesmaximal, complemented
9C2×#10622553C212yesmaximal, complemented
10C2×#10622826C212yesmaximal, complemented
11C2×#10622824C211yesmaximal, characteristic, complemented
12C22×C4×D4×C11C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C23×C22⋊D11C2212yes—
17C23×C22⋊D11C2212yes—
18C23×D44C2211yescharacteristic
19C2×C4×D4×C11—28no—
20C2×C4×D4×C11C2218yescomplemented
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2212yes—
27C2×#66983—28no—
28C2×#66983C2218yescomplemented
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2212yes—
31C22×(C2×D11)⋊C4C2212yes—
32C22×(C2×D11)⋊C4C2212yes—
33C22×C4⋊Dic11C2211yescharacteristic
34C22×Dic11⋊C4C2212yes—
35#10622836C22116yescomplemented
36#10622826C22116yescomplemented
37#10622824C2218yescomplemented
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622604C2218yescomplemented
44#10622599C2218yescomplemented
45#10622573C2218yescomplemented
46#10622572C22116yescomplemented
47#10622562C2218yescomplemented
48#10622553C22116yescomplemented
49C25×C11C2311yescharacteristic
50C25×C11C2311yescharacteristic
51C24×D11C2312yes—
52C22×D4×C11—24no—
53C22×D4×C11—24no—
54C22×D4×C11—24no—
55C22×D4×C11C2314yes—
56C23×C4×C11—24no—
57C23×C4×C11—44no—
58C23×C4×C11—44no—
59C23×C4×C11D418yescomplemented
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2314yes—
66C23×C4×C11C2314yes—
67C22×C22⋊D11—28no—
68C22×C22⋊D11—28no—
69C22×C22⋊D11—44no—
70C22×C22⋊D11—44no—
71C22×C22⋊D11—44no—
72C22×C22⋊D11—44no—
73C22×C22⋊D11C2318yes—
74C22×C22⋊D11C2318yes—
75C23×Dic11C2312yes—
76C23×Dic11C2312yes—
77C23×Dic11C2312yes—
78C22×D44—24no—
79C22×D44—44no—
80C22×D44C2314yes—
81C4×D4×C11—232no—
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—24no—
86C2×C11×C22⋊C4C2314yes—
87C2×C11×C22⋊C4C2314yes—
88C2×C42×C11—24no—
89C2×C42×C11C2314yes—
90C2×C22⋊Dic11—44no—
91C2×C22⋊Dic11—44no—
92C2×C22⋊Dic11C2318yes—
93C2×C22⋊Dic11C2318yes—
94#66983—232no—
95C2×(C2×D11)⋊C4—28no—
96C2×(C2×D11)⋊C4—28no—
97C2×(C2×D11)⋊C4—44no—
98C2×(C2×D11)⋊C4—44no—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×(C2×D11)⋊C4C2318yes—
102C2×(C2×D11)⋊C4C2318yes—
103C2×C4⋊Dic11—24no—
104C2×C4⋊Dic11C2314yes—
105C2×Dic11⋊C4—44no—
106C2×Dic11⋊C4C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2314yes—
110C11⋊#95C2314yes—
111C11⋊#95C2318yes—
112C2×#2635—111nomaximal, Sylow
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—24no—
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11C2×D414yes—
122C24×C11#4114yes—
123C24×C11C2412yes—
124C24×C11C2412yes—
125C24×C11C2411yescharacteristic
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—24no—
131C23×D11—24no—
132C23×D11—24no—
133C23×D11C2414yes—
134C2×D4×C11—232no—
135C2×D4×C11—28no—
136C2×D4×C11—28no—
137C2×D4×C11—28no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—28no—
147C22×C4×C11—416no—
148C22×C4×C11—48no—
149C22×C4×C11—48no—
150C22×C4×C11—416no—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D4116yescomplemented
154C22×C4×C11#4114yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2412yes—
160C2×C22⋊D11—216no—
161C2×C22⋊D11—216no—
162C2×C22⋊D11—48no—
163C2×C22⋊D11—48no—
164C2×C22⋊D11—48no—
165C2×C22⋊D11—48no—
166C2×C22⋊D11—432no—
167C2×C22⋊D11—432no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11—24no—
172C22×Dic11—24no—
173C22×Dic11—24no—
174C22×Dic11—24no—
175C22×Dic11—24no—
176C22×Dic11—24no—
177C22×Dic11C2414yes—
178C22×Dic11C2414yes—
179C22×Dic11C2414yes—
180C2×D44—28no—
181C2×D44—48no—
182C2×D44—416no—
183C11×C4⋊C4—28no—
184C11×C22⋊C4—28no—
185C11×C22⋊C4—28no—
186C42×C11—28no—
187C22⋊Dic11—48no—
188C22⋊Dic11—48no—
189(C2×D11)⋊C4—216no—
190(C2×D11)⋊C4—216no—
191(C2×D11)⋊C4—48no—
192(C2×D11)⋊C4—48no—
193C4⋊Dic11—28no—
194Dic11⋊C4—48no—
195C22×#121—111no—
196C22×C4×D4D1111yescharacteristic, complemented
197#2635—1116no—
198C2×#400—111no—
199C2×#399—111no—
200C2×#394—111no—
201C2×#394—112no—
202C2×#392—112no—
203C2×#392—111no—
204C2×#388—112no—
205C2×#386—112no—
206C2×#381—111no—
207C23×C11—28no—
208C23×C11—28no—
209C23×C11—28no—
210C23×C11—28no—
211C23×C11—216no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—24no—
217C23×C11—24no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11—48no—
223C23×C11—48no—
224C23×C11—48no—
225C23×C11C22×D414yes—
226C23×C11C22×D412yes—
227C23×C11C2×#4114yes—
228C23×C11C2×#4112yes—
229C23×C11C2×#4112yes—
230C23×C11H(5,𝔽2)14yes—
231C23×C11H(5,𝔽2)14yes—
232C23×C11C2511yescharacteristic
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—24no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11—48no—
244C22×D11—48no—
245C22×D11—48no—
246C22×D11—48no—
247D4×C11—232no—
248C2×C4×C11—28no—
249C2×C4×C11—28no—
250C2×C4×C11—28no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—416no—
260C2×C4×C11—416no—
261C2×C4×C11—44no—
262C2×C4×C11—44no—
263C2×C4×C11C22×D414yes—
264C2×C4×C11C22×D414yes—
265C2×C4×C11C2×#4114yes—
266C22⋊D11—432no—
267C22⋊D11—432no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—48no—
278C2×Dic11—48no—
279C2×Dic11—48no—
280D44—416no—
281C23×D4—112no—
282C23×D4—112no—
283C23×D4—111no—
284C23×D4C2×D1111yescharacteristic
285C24×C4C2×D1111yescharacteristic
286C24×C4C2×D1111yescharacteristic
287C2×#121—118no—
288C2×#121—228no—
289C2×C4×D4—28no—
290C2×C4×D4C2×D1118yescomplemented
291C22×C4⋊C4—111no—
292C22×C4⋊C4—112no—
293C22×C4⋊C4C2×D1111yescharacteristic
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4—112no—
300C22×C22⋊C4C2×D1111yescharacteristic
301C22×C22⋊C4C2×D1111yescharacteristic
302C22×C42C2×D1111yescharacteristic
303#400—118no—
304#399—118no—
305#394—118no—
306#394—1116no—
307#392—1116no—
308#392—118no—
309#388—1116no—
310#386—1116no—
311#381—118no—
312C2×#95—111no—
313C2×#95—112no—
314C2×#95—111no—
315C2×#95—112no—
316C2×#95—112no—
317C22×C11—24no—
318C22×C11—24no—
319C22×C11—24no—
320C22×C11—24no—
321C22×C11—28no—
322C22×C11—416no—
323C22×C11—416no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—44no—
327C22×C11—44no—
328C22×C11—44no—
329C22×C11#52514yes—
330C22×C11#53414yes—
331C22×C11#53514yes—
332C22×C11#53818yes—
333C22×C11#54018yes—
334C22×C11C23×D411yescharacteristic
335C22×C11C22×#4111yescharacteristic
336C22×C11C22×#4111yescharacteristic
337C22×C11C2×H(5,𝔽2)12yes—
338C22×C11C2×H(5,𝔽2)12yes—
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—24no—
350C4×C11—42no—
351C4×C11—42no—
352Dic11—44no—
353Dic11—44no—
354Dic11—44no—
355C25—112no—
356C25C22×D1111yescharacteristic
357C25C22×D1111yescharacteristic
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—24no—
361C22×D4—118no—
362C22×D4—118no—
363C22×D4—114no—
364C22×D4—228no—
365C22×D4—228no—
366C22×D4—224no—
367C22×D4—444no—
368C22×D4—444no—
369C22×D4—444no—
370C22×D4—444no—
371C22×D4—444no—
372C22×D4C22×D1114yes—
373C23×C4—24no—
374C23×C4—44no—
375C23×C4—44no—
376C23×C4—112no—
377C23×C4—112no—
378C23×C4—112no—
379C23×C4C22⋊D1118yescomplemented
380C23×C4C22×D1111yescharacteristic
381C23×C4C22×D1111yescharacteristic
382C23×C4C22×D1111yescharacteristic
383C23×C4C22×D1111yescharacteristic
384C23×C4C22×D1111yescharacteristic
385C23×C4C22×D1114yes—
386C23×C4C22×D1114yes—
387#121—2232no—
388C4×D4—232no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—114no—
391C2×C4⋊C4—118no—
392C2×C4⋊C4—224no—
393C2×C4⋊C4—444no—
394C2×C4⋊C4C22×D1114yes—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—24no—
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—228no—
405C2×C22⋊C4—444no—
406C2×C22⋊C4—444no—
407C2×C22⋊C4—444no—
408C2×C22⋊C4—444no—
409C2×C22⋊C4C22×D1114yes—
410C2×C22⋊C4C22×D1114yes—
411C2×C42—24no—
412C2×C42C22×D1114yes—
413#95—118no—
414#95—114no—
415#95—114no—
416#95—118no—
417#95—118no—
418C2×C11—44no—
419C2×C11—44no—
420C2×C11#263518yescomplemented
421C2×C11C2×#52511yescharacteristic
422C2×C11C2×#53411yescharacteristic
423C2×C11C2×#53511yescharacteristic
424C2×C11C2×#53812yes—
425C2×C11C2×#54012yes—
426D11—84no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—24no—
431C24—24no—
432C24—24no—
433C24—24no—
434C24—22no—
435C24—114no—
436C24—224no—
437C24—224no—
438C24—224no—
439C24—224no—
440C24—224no—
441C24—224no—
442C24—224no—
443C24#433914yes—
444C24C2×C22⋊D1114yes—
445C24C23×D1112yes—
446C24C23×D1112yes—
447C24C23×D1111yescharacteristic
448C2×D4—232no—
449C2×D4—28no—
450C2×D4—28no—
451C2×D4—28no—
452C2×D4—2216no—
453C2×D4—2216no—
454C2×D4—228no—
455C2×D4—448no—
456C2×D4—4416no—
457C2×D4—448no—
458C2×D4—448no—
459C2×D4—448no—
460C2×D4—448no—
461C2×D4—4432no—
462C2×D4—4432no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—28no—
472C22×C4—48no—
473C22×C4—48no—
474C22×C4—416no—
475C22×C4—416no—
476C22×C4—114no—
477C22×C4—114no—
478C22×C4—114no—
479C22×C4—224no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4#433914yes—
489C22×C4C2×C22⋊D1114yes—
490C22×C4C2×C22⋊D1114yes—
491C22×C4C2×C22⋊D11116yescomplemented
492C22×C4C23×D1112yes—
493C22×C4C23×D1112yes—
494C22×C4C23×D1112yes—
495C22×C4C23×D1112yes—
496C22×C4C23×D1112yes—
497C4⋊C4—28no—
498C4⋊C4—228no—
499C4⋊C4—448no—
500C22⋊C4—28no—
501C22⋊C4—28no—
502C22⋊C4—2216no—
503C22⋊C4—2216no—
504C22⋊C4—448no—
505C22⋊C4—448no—
506C22⋊C4—448no—
507C22⋊C4—448no—
508C42—28no—
509C11C2×#263511yescharacteristic, complemented, Sylow
510C23—28no—
511C23—28no—
512C23—28no—
513C23—216no—
514C23—28no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—24no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—22no—
523C23—44no—
524C23—48no—
525C23—48no—
526C23—48no—
527C23—44no—
528C23—224no—
529C23—224no—
530C23—224no—
531C23—224no—
532C23—224no—
533C23—224no—
534C23—224no—
535C23—448no—
536C23—448no—
537C23—448no—
538C23—448no—
539C23—448no—
540C23—448no—
541C23—448no—
542C23C2×#433914yes—
543C23C2×#433912yes—
544C23C2×#433912yes—
545C23#6703714yes—
546C23#6704214yes—
547C23C22×C22⋊D1114yes—
548C23C22×C22⋊D1112yes—
549C23C24×D1111yescharacteristic
550D4—232no—
551D4—4416no—
552D4—4432no—
553D4—4432no—
554C2×C4—28no—
555C2×C4—28no—
556C2×C4—28no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—416no—
566C2×C4—416no—
567C2×C4—44no—
568C2×C4—44no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—448no—
579C2×C4—448no—
580C2×C4—448no—
581C2×C4C2×#433914yes—
582C2×C4C22×C22⋊D1114yes—
583C2×C4C22×C22⋊D1114yes—
584C22—24no—
585C22—24no—
586C22—24no—
587C22—24no—
588C22—28no—
589C22—42no—
590C22—42no—
591C22—416no—
592C22—416no—
593C22—44no—
594C22—44no—
595C22—44no—
596C22—444no—
597C22—444no—
598C22—444no—
599C22—444no—
600C22—444no—
601C22—444no—
602C22—444no—
603C22—8816no—
604C22#1062309118yes—
605C22#1062309318yes—
606C22#1062332214yes—
607C22#1062333514yes—
608C22#1062336114yes—
609C22C22×#433911yescharacteristic
610C22C22×#433911yescharacteristic
611C22C2×#6703712yes—
612C22C2×#6704212yes—
613C22C23×C22⋊D1111yescharacteristic
614C4—24no—
615C4—24no—
616C4—24no—
617C4—42no—
618C4—42no—
619C4—444no—
620C4—444no—
621C4—444no—
622C2—44no—
623C2—44no—
624C2—884no—
625C2#1307450018yesdirect product factor
626C2C2×#1062332211yescharacteristic
627C2C2×#1062333511yescharacteristic
628C2C2×#1062336111yescharacteristic
629C2C2×#1062309112yes—
630C2C2×#1062309312yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
hypercenterC22×C4×D4D11
hypocenterC11C2×#2635
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66983C2semidirect
2. #13074500C2direct (N × H)
3. C2×#10622599C2semidirect
4. C2×#10622562C2semidirect
5. C2×#10622604C2semidirect
6. C2×#10622572C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622553C2semidirect
10. C2×#10622826C2semidirect
11. C2×#10622824C2semidirect
12. C22×C4×D4×C11C2semidirect
20. C2×C4×D4×C11C22semidirect
28. C2×#66983C22semidirect
35. #10622836C22semidirect
36. #10622826C22semidirect
37. #10622824C22semidirect
43. #10622604C22semidirect
44. #10622599C22semidirect
45. #10622573C22semidirect
46. #10622572C22semidirect
47. #10622562C22semidirect
48. #10622553C22semidirect
59. C23×C4×C11D4semidirect
153. C22×C4×C11C2×D4semidirect
196. C22×C4×D4D11semidirect
290. C2×C4×D4C2×D11semidirect
379. C23×C4C22⋊D11semidirect
420. C2×C11#2635semidirect
491. C22×C4C2×C22⋊D11semidirect
509. C11C2×#2635semidirect
625. C2#13074500direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669832
#130745002
C2×#106225992
C2×#106225622
C2×#106226042
C2×#106225722
C2×#106225732
C2×#106228362
C2×#106225532
C2×#106228262
C2×#106228242
C22×C4×D4×C112
C2×#263511