Finite Group Databasebeta

← C2×#13074095 #14924290

Subgroups — C2×#13074095 #14924290

Order 2816.

3438 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C211yesmaximal, characteristic
2C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
3#13074095C2116yesmaximal, direct product factor
4C2×#10622271C212yesmaximal, complemented
5C2×#10622572C212yesmaximal, complemented
6C2×#10622282C212yesmaximal, complemented
7C2×#10622557C212yesmaximal, complemented
8C2×#10622833C211yesmaximal, characteristic, complemented
9C2×#10622826C211yesmaximal, characteristic, complemented
10C2×#10622571C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
12C2×C11×#386C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2211yescharacteristic
24C2×#66992—28no—
25C2×#66992C2218yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2212yes—
29C22×Dic11⋊C4—28no—
30C22×Dic11⋊C4C2212yes—
31C22×Dic11⋊C4C2212yes—
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2218yescomplemented
34C22×C4×Dic11C2212yes—
35C11×#386C2218yescomplemented
36C2×C11×#95C2212yes—
37#10622833C2218yescomplemented
38#10622826C2218yescomplemented
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622572C22116yescomplemented
44#10622571C2218yescomplemented
45#10622557C22116yescomplemented
46C22⋊C4×Dic11C2218yescomplemented
47#10622282C22116yescomplemented
48#10622271C22116yescomplemented
49C25×C11C2311yescharacteristic
50C25×C11C2311yescharacteristic
51C24×D11C2311yescharacteristic
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×C11C2312yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2314yes—
62C22×C22⋊D11—24no—
63C22×C22⋊D11—24no—
64C22×C22⋊D11—24no—
65C22×C22⋊D11—24no—
66C22×C22⋊D11—44no—
67C22×C22⋊D11C2314yes—
68C22×C22⋊D11C2314yes—
69C23×Dic11—24no—
70C23×Dic11—28no—
71C23×Dic11—44no—
72C23×Dic11D418yes—
73C23×Dic11C2312yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2314yes—
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2312yes—
79C23×Dic11C2314yes—
80C2×C11×C22⋊C4—24no—
81C2×C11×C22⋊C4—44no—
82C2×C11×C22⋊C4C2314yes—
83C2×C11×C22⋊C4C2318yes—
84C2×C22⋊Dic11—24no—
85C2×C22⋊Dic11—24no—
86C2×C22⋊Dic11—28no—
87C2×C22⋊Dic11C2314yes—
88C2×C22⋊Dic11C2314yes—
89C2×C22⋊Dic11C2318yes—
90#66992—232no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—28no—
93C2×(C2×D11)⋊C4—44no—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×Dic11⋊C4—28no—
98C2×Dic11⋊C4—28no—
99C2×Dic11⋊C4—232no—
100C2×Dic11⋊C4—24no—
101C2×Dic11⋊C4C2314yes—
102C2×Dic11⋊C4C2318yes—
103C2×Dic11⋊C4C2318yes—
104C2×C4×Dic11—44no—
105C2×C4×Dic11C2318yes—
106C11×#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C2×#2591—111nomaximal, Sylow
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—22no—
115C24×C11—24no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—24no—
119C24×C11C2×D414yes—
120C24×C11#4114yes—
121C24×C11#4114yes—
122C24×C11C2412yes—
123C24×C11C2412yes—
124C24×C11C2411yescharacteristic
125C23×D11—22no—
126C23×D11—24no—
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—24no—
130C23×D11C2412yes—
131C2×D4×C11—28no—
132C2×D4×C11—28no—
133C2×D4×C11—28no—
134C2×D4×C11—416no—
135C22×C4×C11—28no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—48no—
146C22×C4×C11—416no—
147C22×C4×C11C2412yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2414yes—
150C2×C22⋊D11—28no—
151C2×C22⋊D11—28no—
152C2×C22⋊D11—28no—
153C2×C22⋊D11—28no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—416no—
156C2×C22⋊D11—416no—
157C22×Dic11—232no—
158C22×Dic11—216no—
159C22×Dic11—28no—
160C22×Dic11—24no—
161C22×Dic11—22no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—416no—
171C22×Dic11—48no—
172C22×Dic11C2×D414yes—
173C22×Dic11C2×D414yes—
174C22×Dic11C2×D4116yes—
175C22×Dic11#4118yes—
176C22×Dic11C2412yes—
177C22×Dic11C2414yes—
178C22×Dic11C2412yes—
179C22×Dic11C2412yes—
180C22×Dic11C2414yes—
181C11×C22⋊C4—28no—
182C11×C22⋊C4—48no—
183C22⋊Dic11—28no—
184C22⋊Dic11—216no—
185C22⋊Dic11—28no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—216no—
188(C2×D11)⋊C4—48no—
189Dic11⋊C4—216no—
190Dic11⋊C4—216no—
191Dic11⋊C4—28no—
192C4×Dic11—48no—
193C22×#121—111no—
194C23×C4⋊C4—111no—
195#2591—1116no—
196C2×#400—112no—
197C2×#394—112no—
198C2×#388—112no—
199C2×#388—112no—
200C2×#386—111no—
201C2×#386—111no—
202C2×#386—111no—
203C2×#386D1111yescharacteristic, complemented
204C2×C4×C22⋊C4—111no—
205C23×C11—28no—
206C23×C11—28no—
207C23×C11—216no—
208C23×C11—216no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—22no—
212C23×C11—24no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—24no—
216C23×C11—44no—
217C23×C11—44no—
218C23×C11—44no—
219C23×C11—48no—
220C23×C11—48no—
221C23×C11#124116yes—
222C23×C11C22×D414yes—
223C23×C11C22×D412yes—
224C23×C11C2×#4114yes—
225C23×C11C2×#4112yes—
226C23×C11C2×#4114yes—
227C23×C11C2×#4112yes—
228C23×C11C2×#4114yes—
229C23×C11H(5,𝔽2)14yes—
230C23×C11C2511yescharacteristic
231C22×D11—22no—
232C22×D11—24no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—24no—
236C22×D11—44no—
237C22×D11—44no—
238C22×D11—44no—
239C22×D11—48no—
240C22×D11—48no—
241D4×C11—416no—
242C2×C4×C11—24no—
243C2×C4×C11—22no—
244C2×C4×C11—24no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—416no—
252C2×C4×C11—44no—
253C2×C4×C11—48no—
254C2×C4×C11—48no—
255C22⋊D11—416no—
256C22⋊D11—416no—
257C2×Dic11—232no—
258C2×Dic11—216no—
259C2×Dic11—28no—
260C2×Dic11—28no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—24no—
271C2×Dic11—416no—
272C2×Dic11—44no—
273C2×Dic11—48no—
274C2×Dic11C22×D414yes—
275C2×Dic11C22×D414yes—
276C2×Dic11C2×#4118yes—
277C23×D4—111no—
278C23×D4—111no—
279C23×D4C2×D1111yescharacteristic
280C24×C4—111no—
281C24×C4—111no—
282C24×C4C2×D1111yescharacteristic
283C2×#121—118no—
284C2×#121—228no—
285C22×C4⋊C4—118no—
286C22×C4⋊C4—112no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4—112no—
289C22×C4⋊C4—228no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—111no—
292C22×C22⋊C4—111no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—111no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4C2×D1111yescharacteristic
297C22×C22⋊C4C2×D1112yes—
298C22×C42—112no—
299#400—1116no—
300#394—1116no—
301#388—1116no—
302#388—1116no—
303#386—118no—
304#386—118no—
305#386—118no—
306#386C2×D1118yescomplemented
307C4×C22⋊C4—118no—
308C2×#95—112no—
309C2×#95—112no—
310C2×#95—112no—
311C2×#95—112no—
312C2×#95C2×D1112yes—
313C22×C11—232no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—28no—
317C22×C11—28no—
318C22×C11—42no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—88no—
324C22×C11#52514yes—
325C22×C11C2×#12418yes—
326C22×C11C2×#12414yes—
327C22×C11#53414yes—
328C22×C11#55318yes—
329C22×C11#55318yes—
330C22×C11C23×D411yescharacteristic
331C22×C11C22×#4111yescharacteristic
332C22×C11C22×#4111yescharacteristic
333C22×C11C22×#4112yes—
334C22×C11C2×H(5,𝔽2)12yes—
335C2×D11—42no—
336C2×D11—42no—
337C2×D11—42no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—88no—
341C4×C11—42no—
342C4×C11—44no—
343C4×C11—44no—
344Dic11—28no—
345Dic11—24no—
346Dic11—24no—
347Dic11—42no—
348Dic11—44no—
349C25—111no—
350C25C22×D1111yescharacteristic
351C25C22×D1111yescharacteristic
352C22×D4—24no—
353C22×D4—24no—
354C22×D4—24no—
355C22×D4—114no—
356C22×D4—114no—
357C22×D4—224no—
358C22×D4—224no—
359C22×D4—224no—
360C22×D4—224no—
361C22×D4—444no—
362C22×D4C22×D1114yes—
363C23×C4—24no—
364C23×C4—44no—
365C23×C4—112no—
366C23×C4—111no—
367C23×C4—111no—
368C23×C4—118no—
369C23×C4—114no—
370C23×C4—114no—
371C23×C4—112no—
372C23×C4—111no—
373C23×C4—228no—
374C23×C4—224no—
375C23×C4—444no—
376C23×C4C22×D1112yes—
377C23×C4C22×D1112yes—
378C23×C4C22×D1111yescharacteristic
379C23×C4C22×D1114yes—
380#121—2232no—
381C2×C4⋊C4—118no—
382C2×C4⋊C4—118no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—228no—
385C2×C4⋊C4—228no—
386C2×C4⋊C4—2232no—
387C2×C4⋊C4—224no—
388C2×C22⋊C4—24no—
389C2×C22⋊C4—44no—
390C2×C22⋊C4—114no—
391C2×C22⋊C4—114no—
392C2×C22⋊C4—118no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—224no—
397C2×C22⋊C4—228no—
398C2×C22⋊C4—224no—
399C2×C22⋊C4—228no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—444no—
402C2×C22⋊C4C22×D1114yes—
403C2×C22⋊C4C22×D1118yes—
404C2×C42—118no—
405C2×C42—444no—
406#95—118no—
407#95—118no—
408#95—118no—
409#95—118no—
410#95C22×D1118yes—
411C2×C11—28no—
412C2×C11—82no—
413C2×C11#259118yescomplemented
414C2×C11C2×#52511yescharacteristic
415C2×C11C22×#12411yescharacteristic
416C2×C11C2×#53411yescharacteristic
417C2×C11C2×#55312yes—
418C2×C11C2×#55312yes—
419D11—82no—
420C24—24no—
421C24—24no—
422C24—22no—
423C24—22no—
424C24—22no—
425C24—24no—
426C24—24no—
427C24—112no—
428C24—222no—
429C24—222no—
430C24—222no—
431C24—224no—
432C24—224no—
433C24#433914yes—
434C24D4×D1114yes—
435C24#434114yes—
436C24C23×D1112yes—
437C24C23×D1112yes—
438C24C23×D1111yescharacteristic
439C2×D4—28no—
440C2×D4—28no—
441C2×D4—28no—
442C2×D4—416no—
443C2×D4—228no—
444C2×D4—228no—
445C2×D4—228no—
446C2×D4—228no—
447C2×D4—448no—
448C2×D4—4416no—
449C2×D4—4416no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—28no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—48no—
461C22×C4—416no—
462C22×C4—114no—
463C22×C4—114no—
464C22×C4—118no—
465C22×C4—114no—
466C22×C4—112no—
467C22×C4—112no—
468C22×C4—1116no—
469C22×C4—112no—
470C22×C4—114no—
471C22×C4—2216no—
472C22×C4—2232no—
473C22×C4—228no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—224no—
479C22×C4—222no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—4416no—
485C22×C4—448no—
486C22×C4C23×D1112yes—
487C22×C4C23×D1114yes—
488C22×C4C23×D1114yes—
489C4⋊C4—2216no—
490C4⋊C4—2216no—
491C4⋊C4—228no—
492C22⋊C4—28no—
493C22⋊C4—48no—
494C22⋊C4—228no—
495C22⋊C4—2216no—
496C22⋊C4—228no—
497C22⋊C4—2216no—
498C22⋊C4—228no—
499C22⋊C4—448no—
500C42—448no—
501C11C2×#259111yescharacteristic, complemented, Sylow
502C23—216no—
503C23—28no—
504C23—216no—
505C23—28no—
506C23—24no—
507C23—24no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—24no—
512C23—24no—
513C23—44no—
514C23—48no—
515C23—44no—
516C23—48no—
517C23—44no—
518C23—222no—
519C23—222no—
520C23—222no—
521C23—224no—
522C23—224no—
523C23—444no—
524C23—448no—
525C23—444no—
526C23—448no—
527C23—444no—
528C23#66938116yes—
529C23C2×#433914yes—
530C23C2×#433912yes—
531C23C2×D4×D1114yes—
532C23C2×D4×D1112yes—
533C23C2×#434114yes—
534C23C2×#434112yes—
535C23#6703714yes—
536C23#41×D1114yes—
537C23C24×D1111yescharacteristic
538D4—416no—
539D4—4416no—
540D4—4416no—
541C2×C4—22no—
542C2×C4—22no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—416no—
551C2×C4—44no—
552C2×C4—48no—
553C2×C4—48no—
554C2×C4—114no—
555C2×C4—114no—
556C2×C4—118no—
557C2×C4—2232no—
558C2×C4—228no—
559C2×C4—228no—
560C2×C4—2216no—
561C2×C4—224no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—4416no—
572C2×C4—444no—
573C2×C4—448no—
574C22—28no—
575C22—28no—
576C22—24no—
577C22—232no—
578C22—24no—
579C22—42no—
580C22—44no—
581C22—44no—
582C22—42no—
583C22—42no—
584C22—88no—
585C22—442no—
586C22—444no—
587C22—444no—
588C22—442no—
589C22—442no—
590C22—888no—
591C22C2×#6693818yes—
592C22C2×#6693814yes—
593C22#1062307118yes—
594C22#1062312014yes—
595C22#1062313218yes—
596C22#1062318714yes—
597C22C22×#433911yescharacteristic
598C22C22×D4×D1111yescharacteristic
599C22C22×#434111yescharacteristic
600C22C2×#6703712yes—
601C22C2×#41×D1112yes—
602C4—42no—
603C4—44no—
604C4—44no—
605C4—224no—
606C4—224no—
607C4—228no—
608C4—442no—
609C4—444no—
610C2—28no—
611C2—82no—
612C2—882no—
613C2#1307409518yesdirect product factor
614C2C2×#1062318711yescharacteristic
615C2C22×#6693811yescharacteristic
616C2C2×#1062312011yescharacteristic
617C2C2×#1062313212yes—
618C2C2×#1062307112yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC22×#66992C2
hypercenterC2×#386D11
hypocenterC11C2×#2591
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C23×Dic11⋊C4C2semidirect
3. #13074095C2direct (N × H)
4. C2×#10622271C2semidirect
5. C2×#10622572C2semidirect
6. C2×#10622282C2semidirect
7. C2×#10622557C2semidirect
8. C2×#10622833C2semidirect
9. C2×#10622826C2semidirect
10. C2×#10622571C2semidirect
11. C2×C22⋊C4×Dic11C2semidirect
12. C2×C11×#386C2semidirect
33. C22×Dic11⋊C4C22semidirect
35. C11×#386C22semidirect
37. #10622833C22semidirect
38. #10622826C22semidirect
43. #10622572C22semidirect
44. #10622571C22semidirect
45. #10622557C22semidirect
46. C22⋊C4×Dic11C22semidirect
47. #10622282C22semidirect
48. #10622271C22semidirect
203. C2×#386D11semidirect
306. #386C2×D11semidirect
413. C2×C11#2591semidirect
501. C11C2×#2591semidirect
613. C2#13074095direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669922
C23×Dic11⋊C42
#130740952
C2×#106222712
C2×#106225722
C2×#106222822
C2×#106225572
C2×#106228332
C2×#106228262
C2×#106225712
C2×C22⋊C4×Dic112
C2×C11×#3862
C2×#259111