Finite Group Databasebeta

← C2×#13071079 #14912133

Subgroups — C2×#13071079 #14912133

Order 2816.

3790 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D11C211yesmaximal, characteristic
2C22×#66979C211yesmaximal, characteristic, complemented
3C22×#66925C211yesmaximal, characteristic, complemented
4#13071079C2116yesmaximal, direct product factor
5C2×#10622570C212yesmaximal
6C2×#10622260C212yesmaximal, complemented
7C2×#10622283C212yesmaximal, complemented
8C2×#10622557C212yesmaximal, complemented
9C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
10C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
11C2×C42×Dic11C211yesmaximal, characteristic, complemented
12C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C2×C4×C22⋊D11C4116yescomplemented
22C2×C4×C22⋊D11C2218yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C2×#66979—28no—
27C2×#66979C2218yescomplemented
28C22×C4⋊Dic11C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2212yes—
31C22×Dic11⋊C4C2211yescharacteristic
32C22×C4×Dic11C2212yes—
33C22×C4×Dic11C2212yes—
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2211yescharacteristic
36C22×C4×Dic11C2211yescharacteristic
37C2×#66925—28no—
38C2×#66925C2218yescomplemented
39C4×C11×C22⋊C4C2218yescomplemented
40C2×C11×#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622570C22116yes—
44#10622557C22116yescomplemented
45C4×(C2×D11)⋊C4C2218yescomplemented
46C4×Dic11⋊C4C2218yescomplemented
47C42×Dic11C2218yescomplemented
48#10622283C22116yescomplemented
49#10622260C22116yescomplemented
50C25×C11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C23×C4×C11—24no—
53C23×C4×C11—24no—
54C23×C4×C11C2×C418yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2314yes—
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C22×C22⋊D11—28no—
61C22×C22⋊D11C2×C418yes—
62C22×C22⋊D11C2314yes—
63C23×Dic11C2312yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C22×C4×D11—24no—
69C22×C4×D11—24no—
70C22×C4×D11C2×C418yes—
71C22×C4×D11C2314yes—
72C2×C11×C22⋊C4—28no—
73C2×C11×C22⋊C4C2318yes—
74C2×C42×C11—24no—
75C2×C42×C11—24no—
76C2×C42×C11C2314yes—
77C2×C42×C11C2314yes—
78C2×C22⋊Dic11—28no—
79C2×C22⋊Dic11C2×C418yes—
80C2×C22⋊Dic11C2318yes—
81C2×C22⋊Dic11C2314yes—
82C4×C22⋊D11C2×C4164yescomplemented
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4C2×C418yes—
86C2×(C2×D11)⋊C4C2318yes—
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2314yes—
89#66979—232no—
90C2×C4⋊Dic11—28no—
91C2×C4⋊Dic11C2318yes—
92C2×Dic11⋊C4—28no—
93C2×Dic11⋊C4—28no—
94C2×Dic11⋊C4C2×C418yes—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2318yes—
97C2×Dic11⋊C4C2314yes—
98C2×C4×Dic11—24no—
99C2×C4×Dic11—28no—
100C2×C4×Dic11—28no—
101C2×C4×Dic11C2×C418yes—
102C2×C4×Dic11D418yescomplemented
103C2×C4×Dic11C2318yes—
104C2×C4×Dic11C2318yes—
105C2×C4×Dic11C2314yes—
106C2×C4×Dic11C2314yes—
107C2×C4×Dic11C2314yes—
108#66925—232no—
109C11×#95C2318yes—
110C11⋊#95C2318yes—
111C11⋊#95C2318yes—
112C2×#2293—111nomaximal, Sylow
113C24×C11—22no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—22no—
117C24×C11C22×C414yes—
118C24×C11C2412yes—
119C24×C11C2411yescharacteristic
120C23×D11—22no—
121C23×D11—24no—
122C23×D11—22no—
123C23×D11—24no—
124C23×D11C22×C414yes—
125C23×D11C2412yes—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—22no—
130C22×C4×C11—232no—
131C22×C4×C11—28no—
132C22×C4×C11—28no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11C22×C414yes—
137C22×C4×C11C22×C4116yes—
138C22×C4×C11C22×C414yes—
139C22×C4×C11C2×D414yes—
140C22×C4×C11#4118yes—
141C22×C4×C11#4114yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2412yes—
144C22×C4×C11C2414yes—
145C22×C4×C11C2412yes—
146C2×C22⋊D11—232no—
147C2×C22⋊D11—216no—
148C2×C22⋊D11C22×C4116yes—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11C22×C414yes—
158C22×Dic11C22×C414yes—
159C22×Dic11C22×C414yes—
160C22×Dic11C2×D418yes—
161C22×Dic11#4118yes—
162C22×Dic11C2414yes—
163C22×Dic11C2412yes—
164C22×Dic11C2412yes—
165C22×Dic11C2414yes—
166C22×Dic11C2412yes—
167C2×C4×D11—232no—
168C2×C4×D11—28no—
169C2×C4×D11—28no—
170C2×C4×D11C22×C4116yes—
171C11×C22⋊C4—216no—
172C42×C11—28no—
173C42×C11—28no—
174C22⋊Dic11—216no—
175C22⋊Dic11C22×C4116yes—
176(C2×D11)⋊C4—216no—
177(C2×D11)⋊C4—216no—
178(C2×D11)⋊C4C22×C4116yes—
179C4⋊Dic11—216no—
180Dic11⋊C4—216no—
181Dic11⋊C4—216no—
182Dic11⋊C4C22×C4116yes—
183C4×Dic11—216no—
184C4×Dic11—28no—
185C4×Dic11—216no—
186C4×Dic11C22×C4116yes—
187C4×Dic11C2×D4116yescomplemented
188C22×C4×D4—111no—
189C22×#117—111no—
190C22×#117—111no—
191#2293—1116no—
192C2×#390—112no—
193C2×#389—112no—
194C2×#388—112no—
195C2×#388—112no—
196C2×C4×C4⋊C4—111no—
197C2×C4×C22⋊C4—111no—
198C2×C4×C22⋊C4D1111yescharacteristic, complemented
199C2×C43—111no—
200C23×C11—28no—
201C23×C11—28no—
202C23×C11—28no—
203C23×C11—22no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—22no—
207C23×C11—48no—
208C23×C11—48no—
209C23×C11C23×C414yes—
210C23×C11C23×C412yes—
211C23×C11C22×D412yes—
212C23×C11C2×#4114yes—
213C23×C11C2×#4112yes—
214C23×C11C2×#4114yes—
215C23×C11C2511yescharacteristic
216C22×D11—28no—
217C22×D11—28no—
218C22×D11—28no—
219C22×D11—22no—
220C22×D11—24no—
221C22×D11—22no—
222C22×D11—24no—
223C22×D11—48no—
224C22×D11—48no—
225C22×D11C23×C414yes—
226C2×C4×C11—28no—
227C2×C4×C11—216no—
228C2×C4×C11—22no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—232no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—48no—
237C2×C4×C11C4×D4116yes—
238C2×C4×C11C23×C414yes—
239C2×C4×C11C23×C414yes—
240C2×C4×C11C22×D414yes—
241C2×C4×C11C2×#4118yes—
242C2×C4×C11C2×#4114yes—
243C22⋊D11—232no—
244C2×Dic11—28no—
245C2×Dic11—28no—
246C2×Dic11—216no—
247C2×Dic11—22no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—48no—
256C2×Dic11#117116yescomplemented
257C2×Dic11C23×C414yes—
258C2×Dic11C23×C414yes—
259C2×Dic11C23×C414yes—
260C2×Dic11C22×D418yes—
261C2×Dic11C2×#4118yes—
262C4×D11—232no—
263C23×D4—111no—
264C24×C4—111no—
265C24×C4C2×D1111yescharacteristic
266C2×C4×D4—118no—
267C2×C4×D4—1116no—
268C2×#117—118no—
269C2×#117—118no—
270C2×#117—228no—
271C2×#117—228no—
272C22×C4⋊C4—111no—
273C22×C4⋊C4—112no—
274C22×C4⋊C4—112no—
275C22×C4⋊C4—112no—
276C22×C22⋊C4—111no—
277C22×C22⋊C4—111no—
278C22×C22⋊C4—112no—
279C22×C22⋊C4—112no—
280C22×C22⋊C4—112no—
281C22×C22⋊C4C2×D1112yes—
282C22×C42—111no—
283C22×C42—111no—
284C22×C42—112no—
285C22×C42—112no—
286C22×C42—111no—
287C22×C42C2×D1111yescharacteristic
288C22×C42C2×D1111yescharacteristic
289#390—1116no—
290#389—1116no—
291#388—1116no—
292#388—1116no—
293C4×C4⋊C4—118no—
294C4×C22⋊C4—118no—
295C4×C22⋊C4C2×D1118yescomplemented
296C2×#95—112no—
297C2×#95—112no—
298C2×#95C2×D1112yes—
299C43—118no—
300C22×C11—24no—
301C22×C11—24no—
302C22×C11—24no—
303C22×C11—44no—
304C22×C11—44no—
305C22×C11—416no—
306C22×C11C2×#11714yes—
307C22×C11C2×C4×D414yes—
308C22×C11C4×#4114yes—
309C22×C11#52918yes—
310C22×C11#53218yes—
311C22×C11C24×C411yescharacteristic
312C22×C11C23×D411yescharacteristic
313C22×C11C22×#4112yes—
314C22×C11C22×#4111yescharacteristic
315C22×C11C22×#4112yes—
316C2×D11—24no—
317C2×D11—24no—
318C2×D11—24no—
319C2×D11—44no—
320C2×D11—44no—
321C2×D11—416no—
322C4×C11—24no—
323C4×C11—28no—
324C4×C11—44no—
325C4×C11C2×C4×D418yes—
326Dic11—24no—
327Dic11—24no—
328Dic11—28no—
329Dic11—44no—
330Dic11C2×#11718yescomplemented
331C25—111no—
332C25C22×D1111yescharacteristic
333C22×D4—118no—
334C22×D4—114no—
335C22×D4—228no—
336C23×C4—24no—
337C23×C4—24no—
338C23×C4—111no—
339C23×C4—112no—
340C23×C4—111no—
341C23×C4—111no—
342C23×C4—118no—
343C23×C4—114no—
344C23×C4—112no—
345C23×C4—224no—
346C23×C4—224no—
347C23×C4C4×D1118yes—
348C23×C4C22×D1112yes—
349C23×C4C22×D1111yescharacteristic
350C23×C4C22×D1114yes—
351C23×C4C22×D1112yes—
352C23×C4C22×D1111yescharacteristic
353C4×D4—1164no—
354#117—2232no—
355#117—2232no—
356C2×C4⋊C4—118no—
357C2×C4⋊C4—114no—
358C2×C4⋊C4—118no—
359C2×C4⋊C4—118no—
360C2×C4⋊C4—118no—
361C2×C4⋊C4—228no—
362C2×C4⋊C4—228no—
363C2×C4⋊C4—228no—
364C2×C22⋊C4—28no—
365C2×C22⋊C4—118no—
366C2×C22⋊C4—114no—
367C2×C22⋊C4—118no—
368C2×C22⋊C4—114no—
369C2×C22⋊C4—118no—
370C2×C22⋊C4—118no—
371C2×C22⋊C4—118no—
372C2×C22⋊C4—228no—
373C2×C22⋊C4—228no—
374C2×C22⋊C4—228no—
375C2×C22⋊C4C22×D1118yes—
376C2×C42—24no—
377C2×C42—24no—
378C2×C42—118no—
379C2×C42—118no—
380C2×C42—114no—
381C2×C42—114no—
382C2×C42—114no—
383C2×C42—118no—
384C2×C42—118no—
385C2×C42—228no—
386C2×C42—228no—
387C2×C42—224no—
388C2×C42C22×D1114yes—
389C2×C42C22×D1114yes—
390#95—118no—
391#95—118no—
392#95C22×D1118yes—
393C2×C11—44no—
394C2×C11#229318yescomplemented
395C2×C11C22×#11711yescharacteristic
396C2×C11C22×C4×D411yescharacteristic
397C2×C11C2×C4×#4111yescharacteristic
398C2×C11C2×#52912yes—
399C2×C11C2×#53212yes—
400D11—44no—
401C24—24no—
402C24—22no—
403C24—22no—
404C24—24no—
405C24—114no—
406C24—112no—
407C24—224no—
408C24—222no—
409C24—222no—
410C24—224no—
411C24C2×C4×D1114yes—
412C24C23×D1112yes—
413C24C23×D1111yescharacteristic
414C2×D4—1116no—
415C2×D4—2232no—
416C2×D4—2216no—
417C22×C4—22no—
418C22×C4—24no—
419C22×C4—22no—
420C22×C4—24no—
421C22×C4—232no—
422C22×C4—28no—
423C22×C4—28no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—24no—
427C22×C4—114no—
428C22×C4—118no—
429C22×C4—112no—
430C22×C4—114no—
431C22×C4—114no—
432C22×C4—118no—
433C22×C4—112no—
434C22×C4—112no—
435C22×C4—114no—
436C22×C4—1116no—
437C22×C4—114no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—224no—
443C22×C4—2232no—
444C22×C4—228no—
445C22×C4—228no—
446C22×C4—224no—
447C22×C4—224no—
448C22×C4—224no—
449C22×C4C2×C4×D1114yes—
450C22×C4C2×C4×D11116yes—
451C22×C4C2×C4×D1114yes—
452C22×C4#433918yes—
453C22×C4D4×D1114yes—
454C22×C4#434114yes—
455C22×C4C23×D1114yes—
456C22×C4C23×D1112yes—
457C22×C4C23×D1114yes—
458C22×C4C23×D1112yes—
459C4⋊C4—1116no—
460C4⋊C4—2216no—
461C4⋊C4—2216no—
462C4⋊C4—2216no—
463C22⋊C4—216no—
464C22⋊C4—1116no—
465C22⋊C4—1116no—
466C22⋊C4—2216no—
467C22⋊C4—2216no—
468C22⋊C4—2216no—
469C42—28no—
470C42—28no—
471C42—1116no—
472C42—1116no—
473C42—2216no—
474C42—2216no—
475C42—228no—
476C11C2×#229311yescharacteristic, complemented, Sylow
477C23—28no—
478C23—28no—
479C23—28no—
480C23—24no—
481C23—22no—
482C23—22no—
483C23—24no—
484C23—48no—
485C23—48no—
486C23—114no—
487C23—228no—
488C23—228no—
489C23—228no—
490C23—224no—
491C23—222no—
492C23—222no—
493C23—224no—
494C23—448no—
495C23—448no—
496C23C22×C4×D1114yes—
497C23C22×C4×D1112yes—
498C23C2×#433914yes—
499C23C2×D4×D1112yes—
500C23C2×#434112yes—
501C23#41×D1114yes—
502C23C24×D1111yescharacteristic
503D4—2232no—
504C2×C4—28no—
505C2×C4—216no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—232no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—48no—
515C2×C4—1116no—
516C2×C4—114no—
517C2×C4—118no—
518C2×C4—114no—
519C2×C4—114no—
520C2×C4—118no—
521C2×C4—228no—
522C2×C4—228no—
523C2×C4—2216no—
524C2×C4—224no—
525C2×C4—224no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—224no—
529C2×C4—2232no—
530C2×C4—224no—
531C2×C4—224no—
532C2×C4—224no—
533C2×C4—448no—
534C2×C4(C22⋊D11)⋊C4116yes—
535C2×C4C22×C4×D1114yes—
536C2×C4C22×C4×D1114yes—
537C2×C4C2×#433918yes—
538C2×C4C2×D4×D1114yes—
539C2×C4C2×#434114yes—
540C22—24no—
541C22—24no—
542C22—24no—
543C22—44no—
544C22—44no—
545C22—416no—
546C22—224no—
547C22—224no—
548C22—224no—
549C22—444no—
550C22—444no—
551C22—4416no—
552C22C4×#433914yes—
553C22C2×(C22⋊D11)⋊C414yes—
554C22D11×#11714yes—
555C22#1062306918yes—
556C22#1062307918yes—
557C22C23×C4×D1111yescharacteristic
558C22C22×#433912yes—
559C22C22×D4×D1111yescharacteristic
560C22C22×#434111yescharacteristic
561C22C2×#41×D1112yes—
562C4—28no—
563C4—24no—
564C4—44no—
565C4—118no—
566C4—228no—
567C4—224no—
568C4—224no—
569C4—444no—
570C4C2×(C22⋊D11)⋊C418yes—
571C2—44no—
572C2—444no—
573C2#1307107918yesdirect product factor
574C2C2×D11×#11711yescharacteristic
575C2C22×(C22⋊D11)⋊C411yescharacteristic
576C2C2×C4×#433911yescharacteristic
577C2C2×#1062306912yes—
578C2C2×#1062307912yes—
subgroupG/H
centerC23×C4C22×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
cosocleC23×C11C25
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2293
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×#66979C2semidirect
3. C22×#66925C2semidirect
4. #13071079C2direct (N × H)
6. C2×#10622260C2semidirect
7. C2×#10622283C2semidirect
8. C2×#10622557C2semidirect
9. C2×C4×Dic11⋊C4C2semidirect
10. C2×C4×(C2×D11)⋊C4C2semidirect
11. C2×C42×Dic11C2semidirect
12. C2×C4×C11×C22⋊C4C2semidirect
21. C2×C4×C22⋊D11C4semidirect
27. C2×#66979C22semidirect
38. C2×#66925C22semidirect
39. C4×C11×C22⋊C4C22semidirect
44. #10622557C22semidirect
45. C4×(C2×D11)⋊C4C22semidirect
46. C4×Dic11⋊C4C22semidirect
47. C42×Dic11C22semidirect
48. #10622283C22semidirect
49. #10622260C22semidirect
82. C4×C22⋊D11C2×C4semidirect
102. C2×C4×Dic11D4semidirect
187. C4×Dic11C2×D4semidirect
198. C2×C4×C22⋊C4D11semidirect
256. C2×Dic11#117semidirect
295. C4×C22⋊C4C2×D11semidirect
330. Dic11C2×#117semidirect
394. C2×C11#2293semidirect
476. C11C2×#2293semidirect
573. C2#13071079direct (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
C22×#669792
C22×#669252
#130710792
C2×#106225702
C2×#106222602
C2×#106222832
C2×#106225572
C2×C4×Dic11⋊C42
C2×C4×(C2×D11)⋊C42
C2×C42×Dic112
C2×C4×C11×C22⋊C42
C2×#229311