Finite Group Databasebeta

← C2×#13074501 #14920166

Subgroups — C2×#13074501 #14920166

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×C4×C22⋊D11C211yesmaximal, characteristic, complemented
2#13074501C2116yesmaximal, direct product factor
3C2×#10622595C211yesmaximal, characteristic, complemented
4C2×#10622605C211yesmaximal, characteristic, complemented
5C2×#10622835C211yesmaximal, characteristic, complemented
6C2×#10622835C212yesmaximal, complemented
7C2×#10622836C211yesmaximal, characteristic, complemented
8C2×#10622836C212yesmaximal, complemented
9C2×#10622557C212yesmaximal, complemented
10C2×#10622569C212yesmaximal, complemented
11C2×#10622824C211yesmaximal, characteristic, complemented
12C22×C11×#121C211yesmaximal, characteristic, complemented
13C23×D4×C11C2212yes—
14C23×D4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C23×C22⋊D11C2211yescharacteristic
17C23×C22⋊D11C2212yes—
18C23×C4×D11C2211yescharacteristic
19C2×C11×#121—28no—
20C2×C11×#121C2218yescomplemented
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2212yes—
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2212yes—
27C22×C22⋊Dic11C2212yes—
28C2×C4×C22⋊D11—28no—
29C2×C4×C22⋊D11C2218yescomplemented
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×(C2×D11)⋊C4C2212yes—
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2212yes—
34C22×C4×Dic11C2211yescharacteristic
35#10622836C22116yescomplemented
36#10622836C2218yescomplemented
37#10622835C2218yescomplemented
38#10622835C22116yescomplemented
39#10622824C2218yescomplemented
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2212yes—
45#10622605C2218yescomplemented
46#10622595C2218yescomplemented
47#10622569C22116yescomplemented
48#10622557C22116yescomplemented
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×C11C2318yes—
58C22×D4×C11C2314yes—
59C23×C4×C11—44no—
60C23×C4×C11D418yescomplemented
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2314yes—
65C22×C22⋊D11—24no—
66C22×C22⋊D11—24no—
67C22×C22⋊D11—28no—
68C22×C22⋊D11—24no—
69C22×C22⋊D11—44no—
70C22×C22⋊D11—44no—
71C22×C22⋊D11C2314yes—
72C22×C22⋊D11C2318yes—
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2312yes—
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2312yes—
77C23×Dic11C2311yescharacteristic
78C22×C4×D11—24no—
79C22×C4×D11—44no—
80C22×C4×D11C2314yes—
81C11×#121—232no—
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C22⋊C4—28no—
85C2×C11×C22⋊C4C2318yes—
86C2×C22⋊Dic11—24no—
87C2×C22⋊Dic11—28no—
88C2×C22⋊Dic11—44no—
89C2×C22⋊Dic11—44no—
90C2×C22⋊Dic11—44no—
91C2×C22⋊Dic11C2314yes—
92C2×C22⋊Dic11C2318yes—
93C2×C22⋊Dic11C2318yes—
94C2×C22⋊Dic11C2318yes—
95C2×C22⋊Dic11C2318yes—
96C4×C22⋊D11—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⋊C4—44no—
103C2×Dic11⋊C4C2314yes—
104C2×Dic11⋊C4C2318yes—
105C2×C4×Dic11—24no—
106C2×C4×Dic11C2314yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2314yes—
110C11⋊#95C2314yes—
111C11⋊#95C2318yes—
112C2×#2635—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×C11C2×D414yes—
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—24no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—416no—
147C22×C4×C11—48no—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D414yes—
150C22×C4×C11C2×D4116yescomplemented
151C22×C4×C11C2414yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2412yes—
154C2×C22⋊D11—232no—
155C2×C22⋊D11—28no—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—28no—
158C2×C22⋊D11—216no—
159C2×C22⋊D11—48no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—432no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11—24no—
172C22×Dic11—24no—
173C22×Dic11—24no—
174C22×Dic11#4114yes—
175C22×Dic11C2414yes—
176C22×Dic11C2414yes—
177C22×Dic11C2412yes—
178C22×Dic11C2412yes—
179C22×Dic11C2412yes—
180C2×C4×D11—28no—
181C2×C4×D11—48no—
182C2×C4×D11—416no—
183C11×C4⋊C4—28no—
184C11×C22⋊C4—216no—
185C22⋊Dic11—216no—
186C22⋊Dic11—28no—
187C22⋊Dic11—48no—
188C22⋊Dic11—48no—
189C22⋊Dic11—48no—
190(C2×D11)⋊C4—28no—
191(C2×D11)⋊C4—48no—
192Dic11⋊C4—28no—
193Dic11⋊C4—48no—
194C4×Dic11—28no—
195C22×#121D1111yescharacteristic, complemented
196C22×C4×D4—111no—
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—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—48no—
222C23×C11—48no—
223C23×C11—48no—
224C23×C11—48no—
225C23×C11—48no—
226C23×C11—48no—
227C23×C11—48no—
228C23×C11—48no—
229C23×C11—48no—
230C23×C11C22×D414yes—
231C23×C11C22×D412yes—
232C23×C11C2×#4112yes—
233C23×C11C2×#4112yes—
234C23×C11H(5,𝔽2)14yes—
235C23×C11H(5,𝔽2)14yes—
236C23×C11C2511yescharacteristic
237C22×D11—28no—
238C22×D11—216no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—24no—
242C22×D11—24no—
243C22×D11—44no—
244C22×D11—44no—
245C22×D11—48no—
246C22×D11C2×#4114yes—
247D4×C11—416no—
248D4×C11—432no—
249C2×C4×C11—28no—
250C2×C4×C11—28no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—416no—
257C2×C4×C11—48no—
258C2×C4×C11C22×D414yes—
259C2×C4×C11C22×D414yes—
260C22⋊D11—232no—
261C22⋊D11—432no—
262C2×Dic11—28no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—44no—
276C2×Dic11—44no—
277C2×Dic11—48no—
278C2×Dic11—48no—
279C2×Dic11C2×#4114yes—
280C4×D11—416no—
281C23×D4—111no—
282C23×D4—112no—
283C23×D4C2×D1112yes—
284C23×D4C2×D1111yescharacteristic
285C24×C4—111no—
286C24×C4C2×D1111yescharacteristic
287C2×#121—28no—
288C2×#121C2×D1118yescomplemented
289C2×C4×D4—118no—
290C2×C4×D4—228no—
291C22×C4⋊C4—111no—
292C22×C4⋊C4—112no—
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⋊C4C2×D1112yes—
302C22×C42—111no—
303#400—118no—
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×#95—111no—
315C2×#95—112no—
316C2×#95—112no—
317C22×C11—24no—
318C22×C11—24no—
319C22×C11—24no—
320C22×C11—416no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11—44no—
326C22×C11—44no—
327C22×C11—44no—
328C22×C11—44no—
329C22×C11—44no—
330C22×C11—816no—
331C22×C11#52514yes—
332C22×C11#53414yes—
333C22×C11#53514yes—
334C22×C11#53818yes—
335C22×C11#54018yes—
336C22×C11C23×D411yescharacteristic
337C22×C11C22×#4111yescharacteristic
338C22×C11C22×#4111yescharacteristic
339C22×C11C2×H(5,𝔽2)12yes—
340C22×C11C2×H(5,𝔽2)12yes—
341C2×D11—24no—
342C2×D11—28no—
343C2×D11—416no—
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—44no—
347C4×C11—24no—
348C4×C11—24no—
349C4×C11—44no—
350Dic11—24no—
351Dic11—42no—
352Dic11—42no—
353Dic11—44no—
354Dic11—44no—
355C25—111no—
356C25C22×D1112yes—
357C25C22×D1111yescharacteristic
358C22×D4—28no—
359C22×D4—24no—
360C22×D4—44no—
361C22×D4—44no—
362C22×D4—44no—
363C22×D4—114no—
364C22×D4—118no—
365C22×D4—224no—
366C22×D4—224no—
367C22×D4—224no—
368C22×D4—228no—
369C22×D4—444no—
370C22×D4—444no—
371C22×D4C22×D1118yes—
372C22×D4C22×D1114yes—
373C23×C4—44no—
374C23×C4—111no—
375C23×C4—111no—
376C23×C4—112no—
377C23×C4—111no—
378C23×C4—112no—
379C23×C4—114no—
380C23×C4—224no—
381C23×C4—444no—
382C23×C4C22⋊D1118yescomplemented
383C23×C4C22×D1112yes—
384C23×C4C22×D1111yescharacteristic
385C23×C4C22×D1111yescharacteristic
386C23×C4C22×D1114yes—
387#121—232no—
388C4×D4—2232no—
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—28no—
396C2×C22⋊C4—114no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—114no—
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—444no—
407C2×C22⋊C4—444no—
408C2×C22⋊C4—444no—
409C2×C22⋊C4—444no—
410C2×C22⋊C4C22×D1118yes—
411C2×C42—114no—
412C2×C42—224no—
413#95—118no—
414#95—114no—
415#95—114no—
416#95—118no—
417#95—118no—
418C2×C11—44no—
419C2×C11—84no—
420C2×C11#263518yescomplemented
421C2×C11C2×#52511yescharacteristic
422C2×C11C2×#53411yescharacteristic
423C2×C11C2×#53511yescharacteristic
424C2×C11C2×#53812yes—
425C2×C11C2×#54012yes—
426D11—44no—
427C24—24no—
428C24—24no—
429C24—22no—
430C24—22no—
431C24—24no—
432C24—24no—
433C24—24no—
434C24—24no—
435C24—24no—
436C24—24no—
437C24—24no—
438C24—114no—
439C24—112no—
440C24—224no—
441C24—224no—
442C24—222no—
443C24—222no—
444C24C2×C22⋊D1114yes—
445C24C23×D1114yes—
446C24C23×D1112yes—
447C24C23×D1111yescharacteristic
448C2×D4—216no—
449C2×D4—28no—
450C2×D4—48no—
451C2×D4—48no—
452C2×D4—48no—
453C2×D4—416no—
454C2×D4—432no—
455C2×D4—228no—
456C2×D4—228no—
457C2×D4—2232no—
458C2×D4—228no—
459C2×D4—2216no—
460C2×D4—448no—
461C2×D4—448no—
462C2×D4—4432no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—48no—
469C22×C4—416no—
470C22×C4—114no—
471C22×C4—112no—
472C22×C4—114no—
473C22×C4—114no—
474C22×C4—112no—
475C22×C4—112no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—224no—
479C22×C4—224no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—228no—
489C22×C4—448no—
490C22×C4—4416no—
491C22×C4C2×C22⋊D1114yes—
492C22×C4C2×C22⋊D1114yes—
493C22×C4C2×C22⋊D11116yescomplemented
494C22×C4C23×D1114yes—
495C22×C4C23×D1112yes—
496C22×C4C23×D1112yes—
497C4⋊C4—28no—
498C4⋊C4—228no—
499C4⋊C4—448no—
500C22⋊C4—216no—
501C22⋊C4—2216no—
502C22⋊C4—228no—
503C22⋊C4—228no—
504C22⋊C4—448no—
505C22⋊C4—448no—
506C22⋊C4—448no—
507C22⋊C4—448no—
508C42—228no—
509C11C2×#263511yescharacteristic, complemented, Sylow
510C23—28no—
511C23—28no—
512C23—28no—
513C23—24no—
514C23—24no—
515C23—22no—
516C23—22no—
517C23—24no—
518C23—24no—
519C23—24no—
520C23—24no—
521C23—24no—
522C23—24no—
523C23—24no—
524C23—48no—
525C23—48no—
526C23—48no—
527C23—48no—
528C23—48no—
529C23—48no—
530C23—48no—
531C23—48no—
532C23—48no—
533C23—114no—
534C23—228no—
535C23—2216no—
536C23—224no—
537C23—224no—
538C23—222no—
539C23—222no—
540C23—444no—
541C23—444no—
542C23—448no—
543C23#6703714yes—
544C23#6703714yes—
545C23#41×D1112yes—
546C23#41×D1112yes—
547C23C22×C22⋊D1114yes—
548C23C22×C22⋊D1112yes—
549C23C24×D1111yescharacteristic
550D4—416no—
551D4—432no—
552D4—2232no—
553D4—4432no—
554C2×C4—28no—
555C2×C4—28no—
556C2×C4—24no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—416no—
562C2×C4—48no—
563C2×C4—114no—
564C2×C4—228no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—4416no—
578C2×C4—444no—
579C2×C4—444no—
580C2×C4—448no—
581C2×C4—448no—
582C2×C4C22×C22⋊D1114yes—
583C2×C4C22×C22⋊D1114yes—
584C22—24no—
585C22—24no—
586C22—24no—
587C22—416no—
588C22—44no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—44no—
594C22—44no—
595C22—44no—
596C22—44no—
597C22—816no—
598C22—228no—
599C22—224no—
600C22—442no—
601C22—4416no—
602C22—442no—
603C22—444no—
604C22#1062314418yes—
605C22#1062314618yes—
606C22#1062333514yes—
607C22#1062333614yes—
608C22#1062335914yes—
609C22C2×#6703712yes—
610C22C2×#6703712yes—
611C22C2×#41×D1111yescharacteristic
612C22C2×#41×D1111yescharacteristic
613C22C23×C22⋊D1111yescharacteristic
614C4—24no—
615C4—24no—
616C4—44no—
617C4—224no—
618C4—442no—
619C4—442no—
620C4—444no—
621C4—444no—
622C2—44no—
623C2—84no—
624C2—444no—
625C2#1307450118yesdirect product factor
626C2C2×#1062335911yescharacteristic
627C2C2×#1062333511yescharacteristic
628C2C2×#1062333611yescharacteristic
629C2C2×#1062314412yes—
630C2C2×#1062314612yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#121C2
socleC24×C11C24
hypercenterC22×#121D11
hypocenterC11C2×#2635
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×C4×C22⋊D11C2semidirect
2. #13074501C2direct (N × H)
3. C2×#10622595C2semidirect
4. C2×#10622605C2semidirect
5. C2×#10622835C2semidirect
6. C2×#10622835C2semidirect
7. C2×#10622836C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622557C2semidirect
10. C2×#10622569C2semidirect
11. C2×#10622824C2semidirect
12. C22×C11×#121C2semidirect
20. C2×C11×#121C22semidirect
29. C2×C4×C22⋊D11C22semidirect
35. #10622836C22semidirect
36. #10622836C22semidirect
37. #10622835C22semidirect
38. #10622835C22semidirect
39. #10622824C22semidirect
45. #10622605C22semidirect
46. #10622595C22semidirect
47. #10622569C22semidirect
48. #10622557C22semidirect
60. C23×C4×C11D4semidirect
150. C22×C4×C11C2×D4semidirect
195. C22×#121D11semidirect
288. C2×#121C2×D11semidirect
382. C23×C4C22⋊D11semidirect
420. C2×C11#2635semidirect
493. C22×C4C2×C22⋊D11semidirect
509. C11C2×#2635semidirect
625. C2#13074501direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
#130745012
C2×#106225952
C2×#106226052
C2×#106228352
C2×#106228362
C2×#106225572
C2×#106225692
C2×#106228242
C22×C11×#1212
C2×#263511