Finite Group Databasebeta

← C2×#13071060 #14912113

Subgroups — C2×#13071060 #14912113

Order 2816.

4134 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D44C211yesmaximal, characteristic
2C22×#66925C211yesmaximal, characteristic, complemented
3C22×C42×D11C211yesmaximal, characteristic, complemented
4#13071060C2116yesmaximal, direct product factor
5C2×#10622283C212yesmaximal, complemented
6C2×#10622266C212yesmaximal, complemented
7C2×#10622278C212yesmaximal
8C2×#10622281C212yesmaximal, complemented
9C2×C4×C4⋊Dic11C211yesmaximal, characteristic, complemented
10C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
12C2×C11×#376C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11C2212yes—
15C23×C4×D11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×C4⋊Dic11C2212yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2212yes—
31C2×C4×D44C4116yescomplemented
32C2×C4×D44C2218yes—
33C2×#66925—28no—
34C2×#66925C2218yescomplemented
35C2×C42×D11—28no—
36C2×C42×D11C2218yescomplemented
37C11×#376C2218yescomplemented
38C2×C11×#95C2212yes—
39C2×C11×#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43C4×(C2×D11)⋊C4C2218yescomplemented
44C4×(C2×D11)⋊C4C2218yescomplemented
45C4×C4⋊Dic11C2218yescomplemented
46#10622283C22116yescomplemented
47#10622281C22116yescomplemented
48#10622278C22116yes—
49#10622266C22116yescomplemented
50C24×D11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2312yes—
61C22×D44—28no—
62C22×D44C2×C418yes—
63C22×D44C2314yes—
64C22×C4×D11—28no—
65C22×C4×D11—28no—
66C22×C4×D11—24no—
67C22×C4×D11—24no—
68C22×C4×D11—24no—
69C22×C4×D11—24no—
70C22×C4×D11—28no—
71C22×C4×D11C2×C418yes—
72C22×C4×D11C2×C418yescomplemented
73C22×C4×D11C2318yes—
74C22×C4×D11C2314yes—
75C22×C4×D11C2314yes—
76C2×C42×C11—24no—
77C2×C42×C11C2×C418yescomplemented
78C2×C42×C11D418yescomplemented
79C2×C42×C11C2314yes—
80C2×C42×C11C2314yes—
81C2×C42×C11C2314yes—
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4C2×C418yes—
86C2×(C2×D11)⋊C4C2×C418yescomplemented
87C2×(C2×D11)⋊C4C2318yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2314yes—
91C2×(C2×D11)⋊C4C2314yes—
92C2×C4⋊Dic11—28no—
93C2×C4⋊Dic11C2×C418yescomplemented
94C2×C4⋊Dic11C2318yes—
95C2×C4⋊Dic11C2314yes—
96C2×Dic11⋊C4—28no—
97C2×Dic11⋊C4C2318yes—
98C2×C4×Dic11—28no—
99C2×C4×Dic11—24no—
100C2×C4×Dic11—24no—
101C2×C4×Dic11C2318yes—
102C2×C4×Dic11C2314yes—
103C2×C4×Dic11C2314yes—
104C4×D44C2×C4164yescomplemented
105#66925—232no—
106C42×D11—232no—
107C11×#95C2318yes—
108C11×#95C2318yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C11⋊#95C2318yes—
112C2×#2290—111nomaximal, Sylow
113C24×C11C2411yescharacteristic
114C23×D11—22no—
115C23×D11—22no—
116C23×D11—24no—
117C23×D11—22no—
118C23×D11—24no—
119C23×D11—22no—
120C23×D11—24no—
121C23×D11C22×C414yes—
122C23×D11C22×C414yes—
123C23×D11#4118yes—
124C23×D11C2412yes—
125C23×D11C2412yes—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11C22×C414yes—
134C22×C4×C11C22×C414yes—
135C22×C4×C11C22×C414yes—
136C22×C4×C11C2×D418yes—
137C22×C4×C11C2×D414yes—
138C22×C4×C11#4114yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2412yes—
142C22×C4×C11C2414yes—
143C22×C4×C11C2412yes—
144C22×Dic11—22no—
145C22×Dic11—24no—
146C22×Dic11—22no—
147C22×Dic11—24no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11C22×C414yes—
154C22×Dic11C22×C414yes—
155C22×Dic11#4118yes—
156C22×Dic11C2414yes—
157C22×Dic11C2412yes—
158C22×Dic11C2412yes—
159C22×Dic11C2414yes—
160C2×D44—232no—
161C2×D44—216no—
162C2×D44C22×C4116yes—
163C2×C4×D11—264no—
164C2×C4×D11—216no—
165C2×C4×D11—216no—
166C2×C4×D11—232no—
167C2×C4×D11—232no—
168C2×C4×D11—216no—
169C2×C4×D11—28no—
170C2×C4×D11—28no—
171C2×C4×D11—28no—
172C2×C4×D11—28no—
173C2×C4×D11C22×C4116yes—
174C2×C4×D11C22×C4116yescomplemented
175C42×C11—28no—
176C42×C11C22×C4116yescomplemented
177C42×C11C2×D4116yescomplemented
178(C2×D11)⋊C4—216no—
179(C2×D11)⋊C4—216no—
180(C2×D11)⋊C4—216no—
181(C2×D11)⋊C4C22×C4116yes—
182(C2×D11)⋊C4C22×C4116yescomplemented
183C4⋊Dic11—216no—
184C4⋊Dic11C22×C4116yescomplemented
185Dic11⋊C4—216no—
186C4×Dic11—216no—
187C4×Dic11—28no—
188C4×Dic11—28no—
189C22×C4×D4—111no—
190C22×#117—111no—
191C23×C42—111no—
192#2290—1116no—
193C2×#388—112no—
194C2×#387—112no—
195C2×#386—112no—
196C2×#385—112no—
197C2×C4×C4⋊C4—111no—
198C2×C4×C22⋊C4—111no—
199C2×C4×C22⋊C4—111no—
200C2×#376D1111yescharacteristic, complemented
201C23×C11C23×C412yes—
202C23×C11C22×D412yes—
203C23×C11C2×#4112yes—
204C23×C11C2×#4114yes—
205C23×C11C2×#4114yes—
206C23×C11C2511yescharacteristic
207C22×D11—28no—
208C22×D11—28no—
209C22×D11—216no—
210C22×D11—216no—
211C22×D11—22no—
212C22×D11—22no—
213C22×D11—24no—
214C22×D11—28no—
215C22×D11—28no—
216C22×D11—28no—
217C22×D11—22no—
218C22×D11—24no—
219C22×D11—22no—
220C22×D11—24no—
221C22×D11—48no—
222C22×D11—48no—
223C22×D11#117116yescomplemented
224C22×D11C23×C414yes—
225C22×D11C23×C414yes—
226C22×D11C2×#4118yes—
227C2×C4×C11—28no—
228C2×C4×C11—28no—
229C2×C4×C11—216no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—48no—
238C2×C4×C11C4×D4116yes—
239C2×C4×C11C23×C414yes—
240C2×C4×C11C23×C414yes—
241C2×C4×C11C23×C414yes—
242C2×C4×C11C22×D418yes—
243C2×C4×C11C22×D414yes—
244C2×C4×C11C2×#4114yes—
245C2×Dic11—28no—
246C2×Dic11—28no—
247C2×Dic11—216no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—24no—
255C2×Dic11—24no—
256C2×Dic11—24no—
257C2×Dic11—48no—
258C2×Dic11C23×C414yes—
259C2×Dic11C23×C414yes—
260C2×Dic11C2×#4118yes—
261D44—232no—
262C4×D11—264no—
263C4×D11—232no—
264C4×D11—232no—
265C23×D4—111no—
266C24×C4—111no—
267C24×C4—111no—
268C24×C4—112no—
269C2×C4×D4—118no—
270C2×C4×D4—1116no—
271C2×#117—118no—
272C2×#117—228no—
273C22×C4⋊C4—111no—
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×C42—112no—
282C22×C42—111no—
283C22×C42—111no—
284C22×C42—118no—
285C22×C42—228no—
286C22×C42C2×D1111yescharacteristic
287C22×C42C2×D1111yescharacteristic
288C22×C42C2×D1111yescharacteristic
289#388—1116no—
290#387—1116no—
291#386—1116no—
292#385—1116no—
293C4×C4⋊C4—118no—
294C4×C22⋊C4—118no—
295C4×C22⋊C4—118no—
296#376C2×D1118yescomplemented
297C2×#95—112no—
298C2×#95—112no—
299C2×#95—112no—
300C2×#95C2×D1112yes—
301C2×#95C2×D1112yes—
302C22×C11C2×#11714yes—
303C22×C11C2×C4×D414yes—
304C22×C11C4×#4114yes—
305C22×C11#52518yes—
306C22×C11#52918yes—
307C22×C11C24×C411yescharacteristic
308C22×C11C23×D411yescharacteristic
309C22×C11C22×#4111yescharacteristic
310C22×C11C22×#4112yes—
311C22×C11C22×#4112yes—
312C2×D11—24no—
313C2×D11—24no—
314C2×D11—28no—
315C2×D11—28no—
316C2×D11—232no—
317C2×D11—24no—
318C2×D11—24no—
319C2×D11—24no—
320C2×D11—44no—
321C2×D11—44no—
322C2×D11—416no—
323C2×D11C2×#11718yescomplemented
324C4×C11—24no—
325C4×C11—24no—
326C4×C11—28no—
327C4×C11—44no—
328C4×C11C2×C4×D418yes—
329Dic11—24no—
330Dic11—24no—
331Dic11—28no—
332Dic11—44no—
333C25—111no—
334C25—111no—
335C22×D4—118no—
336C22×D4—114no—
337C22×D4—228no—
338C23×C4—111no—
339C23×C4—111no—
340C23×C4—112no—
341C23×C4—118no—
342C23×C4—118no—
343C23×C4—114no—
344C23×C4—114no—
345C23×C4—112no—
346C23×C4—118no—
347C23×C4—228no—
348C23×C4—228no—
349C23×C4—224no—
350C23×C4—228no—
351C23×C4—224no—
352C23×C4—224no—
353C23×C4—224no—
354C23×C4C22×D1112yes—
355C23×C4C22×D1111yescharacteristic
356C23×C4C22×D1111yescharacteristic
357C23×C4C22×D1112yes—
358C23×C4C22×D1111yescharacteristic
359C4×D4—1164no—
360#117—2232no—
361C2×C4⋊C4—118no—
362C2×C4⋊C4—114no—
363C2×C4⋊C4—118no—
364C2×C4⋊C4—118no—
365C2×C4⋊C4—228no—
366C2×C4⋊C4—228no—
367C2×C22⋊C4—118no—
368C2×C22⋊C4—118no—
369C2×C22⋊C4—114no—
370C2×C22⋊C4—114no—
371C2×C22⋊C4—118no—
372C2×C22⋊C4—118no—
373C2×C22⋊C4—118no—
374C2×C22⋊C4—228no—
375C2×C22⋊C4—228no—
376C2×C22⋊C4—228no—
377C2×C42—24no—
378C2×C42—114no—
379C2×C42—114no—
380C2×C42—118no—
381C2×C42—224no—
382C2×C42—228no—
383C2×C42—224no—
384C2×C42—2232no—
385C2×C42C4×D1118yescomplemented
386C2×C42D4418yescomplemented
387C2×C42C22×D1114yes—
388C2×C42C22×D1114yes—
389C2×C42C22×D1114yes—
390#95—118no—
391#95—118no—
392#95—118no—
393#95C22×D1118yes—
394#95C22×D1118yes—
395C2×C11#229018yescomplemented
396C2×C11C22×#11711yescharacteristic
397C2×C11C22×C4×D411yescharacteristic
398C2×C11C2×C4×#4111yescharacteristic
399C2×C11C2×#52512yes—
400C2×C11C2×#52912yes—
401D11—28no—
402D11—44no—
403C24—114no—
404C24—118no—
405C24—112no—
406C24—114no—
407C24—112no—
408C24—222no—
409C24—222no—
410C24—224no—
411C24—222no—
412C24—222no—
413C24—224no—
414C24—224no—
415C24C23×D1111yescharacteristic
416C2×D4—1116no—
417C2×D4—2232no—
418C2×D4—2216no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—24no—
423C22×C4—24no—
424C22×C4—24no—
425C22×C4—24no—
426C22×C4—114no—
427C22×C4—114no—
428C22×C4—118no—
429C22×C4—112no—
430C22×C4—114no—
431C22×C4—112no—
432C22×C4—1116no—
433C22×C4—1116no—
434C22×C4—114no—
435C22×C4—2216no—
436C22×C4—2216no—
437C22×C4—2264no—
438C22×C4—222no—
439C22×C4—224no—
440C22×C4—222no—
441C22×C4—222no—
442C22×C4—222no—
443C22×C4—224no—
444C22×C4—2232no—
445C22×C4—2232no—
446C22×C4—2216no—
447C22×C4—228no—
448C22×C4—228no—
449C22×C4—228no—
450C22×C4—228no—
451C22×C4—224no—
452C22×C4—224no—
453C22×C4—224no—
454C22×C4C2×C4×D1114yes—
455C22×C4C2×C4×D1114yes—
456C22×C4C2×C4×D1114yes—
457C22×C4C2×D4418yes—
458C22×C4C2×D4414yes—
459C22×C4#433914yes—
460C22×C4C23×D1114yes—
461C22×C4C23×D1112yes—
462C22×C4C23×D1112yes—
463C22×C4C23×D1114yes—
464C22×C4C23×D1112yes—
465C4⋊C4—1116no—
466C4⋊C4—2216no—
467C4⋊C4—2216no—
468C22⋊C4—1116no—
469C22⋊C4—1116no—
470C22⋊C4—2216no—
471C22⋊C4—2216no—
472C22⋊C4—2216no—
473C42—28no—
474C42—2216no—
475C42—228no—
476C42—228no—
477C42C2×C4×D11116yescomplemented
478C42C2×D44116yescomplemented
479C11C2×#229011yescharacteristic, complemented, Sylow
480C23—1116no—
481C23—114no—
482C23—118no—
483C23—114no—
484C23—228no—
485C23—228no—
486C23—2216no—
487C23—2216no—
488C23—222no—
489C23—222no—
490C23—224no—
491C23—228no—
492C23—228no—
493C23—228no—
494C23—222no—
495C23—222no—
496C23—224no—
497C23—224no—
498C23—448no—
499C23—448no—
500C23C22×C4×D1112yes—
501C23C22×D4412yes—
502C23C2×#433912yes—
503C23#41×D1114yes—
504C23#41×D1114yes—
505C23C24×D1111yescharacteristic
506D4—2232no—
507C2×C4—28no—
508C2×C4—28no—
509C2×C4—216no—
510C2×C4—24no—
511C2×C4—24no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—24no—
517C2×C4—48no—
518C2×C4—114no—
519C2×C4—114no—
520C2×C4—118no—
521C2×C4—2264no—
522C2×C4—228no—
523C2×C4—228no—
524C2×C4—2216no—
525C2×C4—224no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—224no—
531C2×C4—2232no—
532C2×C4—2232no—
533C2×C4—224no—
534C2×C4—224no—
535C2×C4—224no—
536C2×C4—448no—
537C2×C4C4×D44116yes—
538C2×C4C22×C4×D1114yes—
539C2×C4C22×C4×D1114yes—
540C2×C4C22×C4×D1114yes—
541C2×C4C22×D4418yes—
542C2×C4C22×D4414yes—
543C2×C4C2×#433914yes—
544C22—118no—
545C22—228no—
546C22—228no—
547C22—224no—
548C22—224no—
549C22—2232no—
550C22—224no—
551C22—224no—
552C22—224no—
553C22—444no—
554C22—444no—
555C22—4416no—
556C22C2×C4×D4414yes—
557C22D11×#11714yes—
558C22#1062305314yes—
559C22#1062305518yes—
560C22#1062305918yes—
561C22C23×C4×D1111yescharacteristic
562C22C23×D4411yescharacteristic
563C22C22×#433911yescharacteristic
564C22C2×#41×D1112yes—
565C22C2×#41×D1112yes—
566C4—28no—
567C4—24no—
568C4—24no—
569C4—44no—
570C4—228no—
571C4—224no—
572C4—224no—
573C4—444no—
574C4C2×C4×D4418yes—
575C2—228no—
576C2—444no—
577C2#1307106018yesdirect product factor
578C2C2×D11×#11711yescharacteristic
579C2C22×C4×D4411yescharacteristic
580C2C2×#1062305311yescharacteristic
581C2C2×#1062305512yes—
582C2C2×#1062305912yes—
subgroupG/H
centerC23×C4C22×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC2×C11×#376C2
socleC24×C11C24
prime radicalC23×D44C22
cosocleC23×C11C25
hypercenterC2×#376D11
hypocenterC11C2×#2290
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C2×#376

Complements

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

NH ≅ G/Ntype
2. C22×#66925C2semidirect
3. C22×C42×D11C2semidirect
4. #13071060C2direct (N × H)
5. C2×#10622283C2semidirect
6. C2×#10622266C2semidirect
8. C2×#10622281C2semidirect
9. C2×C4×C4⋊Dic11C2semidirect
10. C2×C4×(C2×D11)⋊C4C2semidirect
11. C2×C4×(C2×D11)⋊C4C2semidirect
12. C2×C11×#376C2semidirect
31. C2×C4×D44C4semidirect
34. C2×#66925C22semidirect
36. C2×C42×D11C22semidirect
37. C11×#376C22semidirect
43. C4×(C2×D11)⋊C4C22semidirect
44. C4×(C2×D11)⋊C4C22semidirect
45. C4×C4⋊Dic11C22semidirect
46. #10622283C22semidirect
47. #10622281C22semidirect
49. #10622266C22semidirect
72. C22×C4×D11C2×C4semidirect
77. C2×C42×C11C2×C4semidirect
78. C2×C42×C11D4semidirect
86. C2×(C2×D11)⋊C4C2×C4semidirect
93. C2×C4⋊Dic11C2×C4semidirect
104. C4×D44C2×C4semidirect
174. C2×C4×D11C22×C4semidirect
176. C42×C11C22×C4semidirect
177. C42×C11C2×D4semidirect
182. (C2×D11)⋊C4C22×C4semidirect
184. C4⋊Dic11C22×C4semidirect
200. C2×#376D11semidirect
223. C22×D11#117semidirect
296. #376C2×D11semidirect
323. C2×D11C2×#117semidirect
385. C2×C42C4×D11semidirect
386. C2×C42D44semidirect
395. C2×C11#2290semidirect
477. C42C2×C4×D11semidirect
478. C42C2×D44semidirect
479. C11C2×#2290semidirect
577. C2#13071060direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D442
C22×#669252
C22×C42×D112
#130710602
C2×#106222832
C2×#106222662
C2×#106222782
C2×#106222812
C2×C4×C4⋊Dic112
C2×C4×(C2×D11)⋊C42
C2×C11×#3762
C2×#229011