Finite Group Databasebeta

← C2×#13073103 #14923172

Subgroups — C2×#13073103 #14923172

Order 2816.

3438 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic
2C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
3#13073103C2116yesmaximal, direct product factor
4C2×#10622287C211yesmaximal, characteristic, complemented
5C2×#10622606C211yesmaximal, characteristic, complemented
6C2×#10622566C211yesmaximal, characteristic, complemented
7C2×#10622570C212yesmaximal, complemented
8C2×#10622278C212yesmaximal, complemented
9C2×#10622569C212yesmaximal, complemented
10C2×#10622263C212yesmaximal, complemented
11C2×#10622279C211yesmaximal, characteristic, complemented
12C2×C11×#397C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×D44C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C23×C4×D11C2212yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2212yes—
30C2×C4⋊C4×D11—28no—
31C2×C4⋊C4×D11C2218yescomplemented
32C2×#66937—28no—
33C2×#66937C2218yes—
34C11×#397C2218yescomplemented
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622606C2218yescomplemented
42#10622570C22116yescomplemented
43#10622569C22116yescomplemented
44#10622566C2218yescomplemented
45#10622287C2218yescomplemented
46#10622279C2218yescomplemented
47#10622278C22116yescomplemented
48#10622263C22116yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—24no—
57C22×C22⋊D11—28no—
58C22×C22⋊D11—24no—
59C22×C22⋊D11—28no—
60C22×C22⋊D11C2314yes—
61C22×C22⋊D11C2314yes—
62C23×Dic11C2312yes—
63C23×Dic11C2312yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C22×D44—24no—
67C22×D44—28no—
68C22×D44C2314yes—
69C22×C4×D11—28no—
70C22×C4×D11—28no—
71C22×C4×D11—44no—
72C22×C4×D11—44no—
73C22×C4×D11D418yes—
74C22×C4×D11C2314yes—
75C22×C4×D11C2318yes—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4C2314yes—
78C2×C11×C22⋊C4—24no—
79C2×C11×C22⋊C4—44no—
80C2×C11×C22⋊C4C2314yes—
81C2×C11×C22⋊C4C2318yes—
82C2×C22⋊Dic11—44no—
83C2×C22⋊Dic11C2318yes—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—24no—
86C2×(C2×D11)⋊C4—44no—
87C2×(C2×D11)⋊C4—44no—
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×C4⋊Dic11—24no—
93C2×C4⋊Dic11C2314yes—
94C2×Dic11⋊C4—24no—
95C2×Dic11⋊C4—28no—
96C2×Dic11⋊C4C2314yes—
97C2×Dic11⋊C4C2318yes—
98C2×C4×Dic11—28no—
99C2×C4×Dic11C2318yes—
100C4⋊C4×D11—232no—
101#66937—232no—
102C11×#95C2318yes—
103C11×#95C2314yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2314yes—
108C2×#2504—111nomaximal, Sylow
109C24×C11—22no—
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11C2412yes—
115C24×C11C2411yescharacteristic
116C23×D11—24no—
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—22no—
120C23×D11—24no—
121C23×D11—24no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11C2×D414yes—
125C23×D11#4118yes—
126C23×D11C2412yes—
127C23×D11C2412yes—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11C2×D414yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2414yes—
141C22×C4×C11C2412yes—
142C2×C22⋊D11—28no—
143C2×C22⋊D11—216no—
144C2×C22⋊D11—28no—
145C2×C22⋊D11—216no—
146C2×C22⋊D11—416no—
147C2×C22⋊D11—416no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11C2×D414yes—
157C22×Dic11#4118yes—
158C22×Dic11C2412yes—
159C22×Dic11C2414yes—
160C22×Dic11C2414yes—
161C22×Dic11C2412yes—
162C2×D44—28no—
163C2×D44—216no—
164C2×D44—416no—
165C2×C4×D11—232no—
166C2×C4×D11—216no—
167C2×C4×D11—216no—
168C2×C4×D11—48no—
169C2×C4×D11—48no—
170C2×C4×D11—432no—
171C2×C4×D11C2×D4116yes—
172C11×C4⋊C4—28no—
173C11×C22⋊C4—28no—
174C11×C22⋊C4—48no—
175C22⋊Dic11—48no—
176(C2×D11)⋊C4—216no—
177(C2×D11)⋊C4—28no—
178(C2×D11)⋊C4—48no—
179(C2×D11)⋊C4—48no—
180C4⋊Dic11—28no—
181Dic11⋊C4—28no—
182Dic11⋊C4—216no—
183C4×Dic11—216no—
184C22×#121—111no—
185C23×C4⋊C4—111no—
186#2504—1116no—
187C2×#397—111no—
188C2×#397—111no—
189C2×#397—111no—
190C2×#397D1111yescharacteristic, complemented
191C2×#390—112no—
192C2×#386—112no—
193C2×#386—112no—
194C2×#382—112no—
195C2×C4×C22⋊C4—111no—
196C23×C11—22no—
197C23×C11—24no—
198C23×C11—24no—
199C23×C11—22no—
200C23×C11—22no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11—44no—
204C23×C11—48no—
205C23×C11—48no—
206C23×C11C22×D412yes—
207C23×C11C2×#4114yes—
208C23×C11C2×#4114yes—
209C23×C11H(5,𝔽2)12yes—
210C23×C11H(5,𝔽2)12yes—
211C23×C11C2511yescharacteristic
212C22×D11—28no—
213C22×D11—28no—
214C22×D11—216no—
215C22×D11—216no—
216C22×D11—24no—
217C22×D11—22no—
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—24no—
221C22×D11—24no—
222C22×D11—22no—
223C22×D11—22no—
224C22×D11—44no—
225C22×D11—44no—
226C22×D11—44no—
227C22×D11—48no—
228C22×D11—48no—
229C22×D11#124116yes—
230C22×D11C22×D414yes—
231C22×D11C2×#4118yes—
232C2×C4×C11—28no—
233C2×C4×C11—24no—
234C2×C4×C11—22no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—24no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—24no—
242C2×C4×C11—44no—
243C2×C4×C11—48no—
244C2×C4×C11—48no—
245C2×C4×C11C22×D414yes—
246C22⋊D11—416no—
247C22⋊D11—416no—
248C2×Dic11—24no—
249C2×Dic11—22no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—44no—
257C2×Dic11—48no—
258C2×Dic11—48no—
259C2×Dic11#123116yes—
260C2×Dic11C22×D414yes—
261C2×Dic11C2×#4118yes—
262D44—416no—
263C4×D11—232no—
264C4×D11—432no—
265C23×D4—111no—
266C23×D4—111no—
267C23×D4—111no—
268C24×C4—111no—
269C24×C4—112no—
270C2×#121—118no—
271C2×#121—228no—
272C22×C4⋊C4—112no—
273C22×C4⋊C4—111no—
274C22×C4⋊C4—111no—
275C22×C4⋊C4—118no—
276C22×C4⋊C4—228no—
277C22×C4⋊C4C2×D1111yescharacteristic
278C22×C22⋊C4—111no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4—112no—
282C22×C22⋊C4—112no—
283C22×C22⋊C4C2×D1111yescharacteristic
284C22×C22⋊C4C2×D1112yes—
285C22×C42—112no—
286#397—118no—
287#397—118no—
288#397—118no—
289#397C2×D1118yescomplemented
290#390—1116no—
291#386—1116no—
292#386—1116no—
293#382—1116no—
294C4×C22⋊C4—118no—
295C2×#95—111no—
296C2×#95—112no—
297C2×#95—112no—
298C2×#95—112no—
299C2×#95C2×D1111yescharacteristic
300C2×#95C2×D1112yes—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—44no—
305C22×C11—44no—
306C22×C11—88no—
307C22×C11C2×#12314yes—
308C22×C11C2×#12414yes—
309C22×C11#53514yes—
310C22×C11#55318yes—
311C22×C11#55318yes—
312C22×C11C23×D411yescharacteristic
313C22×C11C22×#4112yes—
314C22×C11C22×#4112yes—
315C22×C11C2×H(5,𝔽2)11yescharacteristic
316C22×C11C2×H(5,𝔽2)11yescharacteristic
317C2×D11—24no—
318C2×D11—24no—
319C2×D11—28no—
320C2×D11—28no—
321C2×D11—232no—
322C2×D11—42no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—44no—
326C2×D11—44no—
327C2×D11—88no—
328C2×D11C2×#12418yes—
329C4×C11—24no—
330C4×C11—42no—
331C4×C11—44no—
332C4×C11—44no—
333Dic11—42no—
334Dic11—44no—
335Dic11—44no—
336Dic11C2×#12318yes—
337C25—111no—
338C25—111no—
339C25C22×D1111yescharacteristic
340C22×D4—114no—
341C22×D4—114no—
342C22×D4—114no—
343C22×D4—224no—
344C22×D4—228no—
345C22×D4—224no—
346C22×D4—228no—
347C22×D4—224no—
348C22×D4—228no—
349C23×C4—111no—
350C23×C4—118no—
351C23×C4—114no—
352C23×C4—112no—
353C23×C4—112no—
354C23×C4—111no—
355C23×C4—118no—
356C23×C4—228no—
357C23×C4—228no—
358C23×C4—444no—
359C23×C4—444no—
360C23×C4C22×D1112yes—
361C23×C4C22×D1112yes—
362C23×C4C22×D1111yescharacteristic
363C23×C4C22×D1111yescharacteristic
364#121—2232no—
365C2×C4⋊C4—24no—
366C2×C4⋊C4—118no—
367C2×C4⋊C4—114no—
368C2×C4⋊C4—114no—
369C2×C4⋊C4—2232no—
370C2×C4⋊C4—228no—
371C2×C4⋊C4—224no—
372C2×C4⋊C4—224no—
373C2×C4⋊C4C22×D1114yes—
374C2×C22⋊C4—24no—
375C2×C22⋊C4—44no—
376C2×C22⋊C4—114no—
377C2×C22⋊C4—118no—
378C2×C22⋊C4—118no—
379C2×C22⋊C4—118no—
380C2×C22⋊C4—118no—
381C2×C22⋊C4—228no—
382C2×C22⋊C4—224no—
383C2×C22⋊C4—444no—
384C2×C22⋊C4—444no—
385C2×C22⋊C4—444no—
386C2×C22⋊C4C22×D1114yes—
387C2×C22⋊C4C22×D1118yes—
388C2×C42—118no—
389C2×C42—228no—
390#95—114no—
391#95—118no—
392#95—118no—
393#95—118no—
394#95C22×D1114yes—
395#95C22×D1118yes—
396C2×C11—82no—
397C2×C11#250418yescomplemented
398C2×C11C22×#12311yescharacteristic
399C2×C11C22×#12411yescharacteristic
400C2×C11C2×#53511yescharacteristic
401C2×C11C2×#55312yes—
402C2×C11C2×#55312yes—
403D11—28no—
404D11—82no—
405C24—22no—
406C24—22no—
407C24—24no—
408C24—24no—
409C24—22no—
410C24—114no—
411C24—118no—
412C24—112no—
413C24—112no—
414C24—222no—
415C24—224no—
416C24—222no—
417C24—222no—
418C24—222no—
419C24—224no—
420C24—224no—
421C24—222no—
422C24C23×D1112yes—
423C24C23×D1111yescharacteristic
424C2×D4—228no—
425C2×D4—2216no—
426C2×D4—228no—
427C2×D4—2216no—
428C2×D4—228no—
429C2×D4—2216no—
430C2×D4—4416no—
431C2×D4—4416no—
432C2×D4—4416no—
433C22×C4—24no—
434C22×C4—22no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—24no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—114no—
443C22×C4—118no—
444C22×C4—112no—
445C22×C4—1116no—
446C22×C4—112no—
447C22×C4—114no—
448C22×C4—114no—
449C22×C4—2232no—
450C22×C4—2216no—
451C22×C4—2216no—
452C22×C4—222no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—224no—
456C22×C4—224no—
457C22×C4—224no—
458C22×C4—224no—
459C22×C4—224no—
460C22×C4—448no—
461C22×C4—448no—
462C22×C4—4432no—
463C22×C4D4×D1114yes—
464C22×C4C23×D1112yes—
465C22×C4C23×D1114yes—
466C22×C4C23×D1114yes—
467C22×C4C23×D1112yes—
468C4⋊C4—28no—
469C4⋊C4—2216no—
470C4⋊C4—228no—
471C4⋊C4—228no—
472C22⋊C4—28no—
473C22⋊C4—48no—
474C22⋊C4—2216no—
475C22⋊C4—228no—
476C22⋊C4—448no—
477C22⋊C4—448no—
478C22⋊C4—448no—
479C42—2216no—
480C11C2×#250411yescharacteristic, complemented, Sylow
481C23—22no—
482C23—22no—
483C23—24no—
484C23—24no—
485C23—22no—
486C23—48no—
487C23—44no—
488C23—44no—
489C23—48no—
490C23—44no—
491C23—114no—
492C23—118no—
493C23—1116no—
494C23—2216no—
495C23—228no—
496C23—228no—
497C23—222no—
498C23—2216no—
499C23—224no—
500C23—222no—
501C23—222no—
502C23—222no—
503C23—224no—
504C23—224no—
505C23—222no—
506C23—448no—
507C23—444no—
508C23—444no—
509C23—448no—
510C23—444no—
511C23C2×D4×D1112yes—
512C23#6703712yes—
513C23#41×D1114yes—
514C23#41×D1114yes—
515C23#6704212yes—
516C23C24×D1111yescharacteristic
517D4—4416no—
518D4—4416no—
519D4—4416no—
520C2×C4—28no—
521C2×C4—24no—
522C2×C4—22no—
523C2×C4—24no—
524C2×C4—24no—
525C2×C4—24no—
526C2×C4—24no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—48no—
531C2×C4—48no—
532C2×C4—44no—
533C2×C4—1116no—
534C2×C4—114no—
535C2×C4—118no—
536C2×C4—2232no—
537C2×C4—222no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—224no—
543C2×C4—224no—
544C2×C4—224no—
545C2×C4—4432no—
546C2×C4—448no—
547C2×C4—448no—
548C2×C4—444no—
549C2×C4C2×D4×D1114yes—
550C22—42no—
551C22—44no—
552C22—44no—
553C22—42no—
554C22—42no—
555C22—88no—
556C22—118no—
557C22—228no—
558C22—228no—
559C22—224no—
560C22—2232no—
561C22—224no—
562C22—442no—
563C22—444no—
564C22—444no—
565C22—442no—
566C22—442no—
567C22—888no—
568C22#1062313814yes—
569C22D11×#12314yes—
570C22#1062319218yes—
571C22D11×#12414yes—
572C22#1062324018yes—
573C22C22×D4×D1111yescharacteristic
574C22C2×#6703711yescharacteristic
575C22C2×#41×D1112yes—
576C22C2×#41×D1112yes—
577C22C2×#6704211yescharacteristic
578C4—24no—
579C4—42no—
580C4—44no—
581C4—44no—
582C4—118no—
583C4—442no—
584C4—444no—
585C4—444no—
586C2—82no—
587C2—228no—
588C2—882no—
589C2#1307310318yesdirect product factor
590C2C2×D11×#12311yescharacteristic
591C2C2×D11×#12411yescharacteristic
592C2C2×#1062313811yescharacteristic
593C2C2×#1062319212yes—
594C2C2×#1062324012yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
prime radicalC22×#66937C2
hypercenterC2×#397D11
hypocenterC11C2×#2504
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
2. C22×C4⋊C4×D11C2semidirect
3. #13073103C2direct (N × H)
4. C2×#10622287C2semidirect
5. C2×#10622606C2semidirect
6. C2×#10622566C2semidirect
7. C2×#10622570C2semidirect
8. C2×#10622278C2semidirect
9. C2×#10622569C2semidirect
10. C2×#10622263C2semidirect
11. C2×#10622279C2semidirect
12. C2×C11×#397C2semidirect
31. C2×C4⋊C4×D11C22semidirect
34. C11×#397C22semidirect
41. #10622606C22semidirect
42. #10622570C22semidirect
43. #10622569C22semidirect
44. #10622566C22semidirect
45. #10622287C22semidirect
46. #10622279C22semidirect
47. #10622278C22semidirect
48. #10622263C22semidirect
190. C2×#397D11semidirect
289. #397C2×D11semidirect
397. C2×C11#2504semidirect
480. C11C2×#2504semidirect
589. C2#13073103direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669372
C22×C4⋊C4×D112
#130731032
C2×#106222872
C2×#106226062
C2×#106225662
C2×#106225702
C2×#106222782
C2×#106225692
C2×#106222632
C2×#106222792
C2×C11×#3972
C2×#250411