Finite Group Databasebeta

← C2×#13072885 #14923535

Subgroups — C2×#13072885 #14923535

Order 2816.

4166 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66945C211yesmaximal, characteristic, complemented
2C22×C22⋊C4×D11C211yesmaximal, characteristic
3#13072885C2116yesmaximal, direct product factor
4C2×#10622290C211yesmaximal, characteristic, complemented
5C2×#10622562C211yesmaximal, characteristic, complemented
6C2×#10622606C211yesmaximal, characteristic, complemented
7C2×#10622564C212yesmaximal, complemented
8C2×#10622282C212yesmaximal, complemented
9C2×#10622281C212yesmaximal, complemented
10C2×#10622277C211yesmaximal, characteristic, complemented
11C2×#10622568C212yesmaximal
12C2×C11×#397C211yesmaximal, characteristic, complemented
13C25×D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic, complemented
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2212yes—
27C22×C4⋊Dic11C2211yescharacteristic, complemented
28C22×C4⋊Dic11C2212yescomplemented
29C22×Dic11⋊C4C2212yescomplemented
30C22×C4×Dic11C2212yescomplemented
31C2×#66945—28no—
32C2×#66945C2218yescomplemented
33C2×C22⋊C4×D11—28no—
34C2×C22⋊C4×D11C2218yes—
35C11×#397C2218yescomplemented
36C2×C11×#95C2211yescharacteristic, complemented
37C2×C11×#95C2212yescomplemented
38C2×C11⋊#95C2212yescomplemented
39C2×C11⋊#95C2211yescharacteristic, complemented
40C2×C11⋊#95C2212yescomplemented
41#10622606C2218yescomplemented
42#10622568C22116yes—
43#10622564C22116yescomplemented
44#10622562C2218yescomplemented
45#10622290C2218yescomplemented
46#10622282C22116yescomplemented
47#10622281C22116yescomplemented
48#10622277C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11—24no—
51C24×D11—24no—
52C24×D11—24no—
53C24×D11—28no—
54C24×D11—44no—
55C24×D11C2311yescharacteristic
56C24×D11C2314yes—
57C24×D11C2311yescharacteristic
58C23×C4×C11C2312yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C23×Dic11C2312yes—
63C23×Dic11C2312yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2311yescharacteristic
66C22×C4×D11—28no—
67C22×C4×D11—24no—
68C22×C4×D11—44no—
69C22×C4×D11D418yes—
70C22×C4×D11C2314yes—
71C22×C4×D11C2314yes—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4C2314yescomplemented
74C2×C11×C22⋊C4—28no—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4C2314yes—
77C2×C11×C22⋊C4C2318yes—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—44no—
80C2×C22⋊Dic11C2314yes—
81C2×C22⋊Dic11C2318yes—
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4—28no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—24no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—44no—
88C2×(C2×D11)⋊C4C2314yes—
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×C4⋊Dic11—24no—
95C2×C4⋊Dic11—44no—
96C2×C4⋊Dic11C2314yescomplemented
97C2×C4⋊Dic11C2318yescomplemented
98C2×Dic11⋊C4—44no—
99C2×Dic11⋊C4C2318yescomplemented
100C2×C4×Dic11—28no—
101C2×C4×Dic11C2318yescomplemented
102#66945—232no—
103C22⋊C4×D11—232no—
104C11×#95C2314yescomplemented
105C11×#95C2318yescomplemented
106C11⋊#95C2318yescomplemented
107C11⋊#95C2314yescomplemented
108C11⋊#95C2318yescomplemented
109C2×#2482—111nomaximal, Sylow
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11#4114yes—
115C24×C11C2412yes—
116C24×C11C2411yescharacteristic
117C23×D11—22no—
118C23×D11—22no—
119C23×D11—24no—
120C23×D11—232no—
121C23×D11—22no—
122C23×D11—28no—
123C23×D11—22no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—28no—
127C23×D11—28no—
128C23×D11—216no—
129C23×D11—48no—
130C23×D11—432no—
131C23×D11—432no—
132C23×D11—416no—
133C23×D11—416no—
134C23×D11C2×D414yes—
135C23×D11#4114yes—
136C23×D11#4118yes—
137C23×D11C2412yes—
138C23×D11C2412yes—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2414yes—
150C22×C4×C11C2414yes—
151C22×C4×C11C2412yes—
152C22×C4×C11C2412yes—
153C22×Dic11—24no—
154C22×Dic11—22no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11C2×D414yes—
163C22×Dic11C2414yes—
164C22×Dic11C2412yes—
165C22×Dic11C2414yes—
166C22×Dic11C2412yes—
167C2×C4×D11—232no—
168C2×C4×D11—28no—
169C2×C4×D11—216no—
170C2×C4×D11—48no—
171C2×C4×D11—416no—
172C2×C4×D11C2×D4116yes—
173C11×C4⋊C4—28no—
174C11×C22⋊C4—216no—
175C11×C22⋊C4—28no—
176C22⋊Dic11—28no—
177C22⋊Dic11—48no—
178(C2×D11)⋊C4—28no—
179(C2×D11)⋊C4—216no—
180(C2×D11)⋊C4—216no—
181(C2×D11)⋊C4—216no—
182(C2×D11)⋊C4—28no—
183(C2×D11)⋊C4—48no—
184C4⋊Dic11—28no—
185C4⋊Dic11—48no—
186Dic11⋊C4—48no—
187C4×Dic11—216no—
188C22×#117—111no—
189C23×C22⋊C4—111no—
190#2482—1116no—
191C2×#399—111no—
192C2×#399—111no—
193C2×#397—111no—
194C2×#397D1111yescharacteristic, complemented
195C2×#388—112no—
196C2×#388—112no—
197C2×#385—112no—
198C2×#381—111no—
199C2×#379—112no—
200C23×C11—28no—
201C23×C11—216no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—24no—
205C23×C11—24no—
206C23×C11—44no—
207C23×C11—44no—
208C23×C11—48no—
209C23×C11C22×D412yes—
210C23×C11C2×#4114yes—
211C23×C11C2×#4112yes—
212C23×C11C2×#4114yes—
213C23×C11C2×#4112yes—
214C23×C11H(5,𝔽2)14yes—
215C23×C11C2511yescharacteristic
216C22×D11—28no—
217C22×D11—28no—
218C22×D11—216no—
219C22×D11—216no—
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—24no—
223C22×D11—232no—
224C22×D11—28no—
225C22×D11—216no—
226C22×D11—22no—
227C22×D11—22no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—432no—
231C22×D11—432no—
232C22×D11—416no—
233C22×D11—4128no—
234C22×D11—44no—
235C22×D11—44no—
236C22×D11—48no—
237C22×D11—416no—
238C22×D11#123116yes—
239C22×D11C22×D414yes—
240C22×D11C2×#4114yes—
241C22×D11C2×#4118yes—
242C2×C4×C11—28no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—48no—
253C2×C4×C11—44no—
254C2×C4×C11—48no—
255C2×C4×C11C22×D414yes—
256C2×Dic11—28no—
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—22no—
260C2×Dic11—24no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—44no—
267C2×Dic11—48no—
268C2×Dic11—48no—
269C2×Dic11C22×D414yes—
270C4×D11—232no—
271C4×D11—416no—
272C26—111no—
273C24×C4—111no—
274C24×C4—111no—
275C2×#117—118no—
276C2×#117—228no—
277C22×C4⋊C4—111no—
278C22×C4⋊C4—112no—
279C22×C4⋊C4—112no—
280C22×C4⋊C4C2×D1111yescharacteristic, complemented
281C22×C22⋊C4—111no—
282C22×C22⋊C4—111no—
283C22×C22⋊C4—112no—
284C22×C22⋊C4—111no—
285C22×C22⋊C4—112no—
286C22×C22⋊C4—112no—
287C22×C22⋊C4—112no—
288C22×C22⋊C4—112no—
289C22×C22⋊C4—118no—
290C22×C22⋊C4—228no—
291C22×C22⋊C4C2×D1111yescharacteristic
292C22×C22⋊C4C2×D1112yes—
293C22×C42—112no—
294#399—118no—
295#399—118no—
296#397—118no—
297#397C2×D1118yescomplemented
298#388—1116no—
299#388—1116no—
300#385—1116no—
301#381—118no—
302#379—1116no—
303C2×#95—111no—
304C2×#95—112no—
305C2×#95—112no—
306C2×#95C2×D1111yescharacteristic, complemented
307C2×#95C2×D1112yescomplemented
308C22×C11—24no—
309C22×C11—28no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—44no—
313C22×C11—416no—
314C22×C11C2×#12314yes—
315C22×C11#52514yes—
316C22×C11#53514yes—
317C22×C11#55118yes—
318C22×C11#55118yes—
319C22×C11C23×D411yescharacteristic
320C22×C11C22×#4111yescharacteristic
321C22×C11C22×#4112yes—
322C22×C11C22×#4111yescharacteristic
323C22×C11C2×H(5,𝔽2)12yes—
324C2×D11—24no—
325C2×D11—24no—
326C2×D11—28no—
327C2×D11—28no—
328C2×D11—232no—
329C2×D11—24no—
330C2×D11—28no—
331C2×D11—464no—
332C2×D11—42no—
333C2×D11—42no—
334C2×D11—44no—
335C2×D11—416no—
336C2×D11C2×#12318yes—
337C4×C11—24no—
338C4×C11—44no—
339C4×C11—42no—
340C4×C11—44no—
341Dic11—24no—
342Dic11—42no—
343Dic11—44no—
344Dic11—44no—
345C25—111no—
346C25—111no—
347C25—114no—
348C25—224no—
349C25—224no—
350C25—228no—
351C25—224no—
352C25—444no—
353C25C22×D1111yescharacteristic
354C23×C4—111no—
355C23×C4—118no—
356C23×C4—114no—
357C23×C4—112no—
358C23×C4—112no—
359C23×C4—111no—
360C23×C4—114no—
361C23×C4—228no—
362C23×C4—224no—
363C23×C4—444no—
364C23×C4C22×D1112yes—
365C23×C4C22×D1112yes—
366C23×C4C22×D1111yescharacteristic
367C23×C4C22×D1111yescharacteristic
368#117—2232no—
369C2×C4⋊C4—24no—
370C2×C4⋊C4—114no—
371C2×C4⋊C4—118no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4—444no—
375C2×C4⋊C4—444no—
376C2×C4⋊C4C22×D1114yescomplemented
377C2×C22⋊C4—28no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—114no—
380C2×C22⋊C4—114no—
381C2×C22⋊C4—114no—
382C2×C22⋊C4—118no—
383C2×C22⋊C4—118no—
384C2×C22⋊C4—118no—
385C2×C22⋊C4—118no—
386C2×C22⋊C4—118no—
387C2×C22⋊C4—2232no—
388C2×C22⋊C4—224no—
389C2×C22⋊C4—228no—
390C2×C22⋊C4—228no—
391C2×C22⋊C4—228no—
392C2×C22⋊C4—224no—
393C2×C22⋊C4—224no—
394C2×C22⋊C4—444no—
395C2×C22⋊C4—444no—
396C2×C22⋊C4C22×D1114yes—
397C2×C22⋊C4C22×D1118yes—
398C2×C42—118no—
399C2×C42—228no—
400#95—118no—
401#95—114no—
402#95—118no—
403#95C22×D1114yescomplemented
404#95C22×D1118yescomplemented
405C2×C11—44no—
406C2×C11#248218yescomplemented
407C2×C11C22×#12311yescharacteristic
408C2×C11C2×#52511yescharacteristic
409C2×C11C2×#53511yescharacteristic
410C2×C11C2×#55112yes—
411C2×C11C2×#55112yes—
412D11—28no—
413D11—44no—
414C24—22no—
415C24—22no—
416C24—24no—
417C24—24no—
418C24—114no—
419C24—118no—
420C24—112no—
421C24—114no—
422C24—112no—
423C24—228no—
424C24—228no—
425C24—2216no—
426C24—2232no—
427C24—222no—
428C24—222no—
429C24—224no—
430C24—222no—
431C24—228no—
432C24—222no—
433C24—224no—
434C24—224no—
435C24—448no—
436C24—4432no—
437C24—4416no—
438C24—4432no—
439C24—4416no—
440C24#434114yes—
441C24C23×D1112yes—
442C24C23×D1111yescharacteristic
443C22×C4—24no—
444C22×C4—24no—
445C22×C4—22no—
446C22×C4—24no—
447C22×C4—24no—
448C22×C4—24no—
449C22×C4—24no—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—114no—
453C22×C4—112no—
454C22×C4—1116no—
455C22×C4—114no—
456C22×C4—112no—
457C22×C4—114no—
458C22×C4—2232no—
459C22×C4—2216no—
460C22×C4—228no—
461C22×C4—224no—
462C22×C4—224no—
463C22×C4—222no—
464C22×C4—224no—
465C22×C4—224no—
466C22×C4—224no—
467C22×C4—224no—
468C22×C4—224no—
469C22×C4—224no—
470C22×C4—448no—
471C22×C4—4416no—
472C22×C4D4×D1114yes—
473C22×C4C23×D1114yes—
474C22×C4C23×D1114yes—
475C22×C4C23×D1112yes—
476C22×C4C23×D1112yes—
477C4⋊C4—28no—
478C4⋊C4—228no—
479C4⋊C4—448no—
480C4⋊C4—448no—
481C22⋊C4—216no—
482C22⋊C4—28no—
483C22⋊C4—228no—
484C22⋊C4—2216no—
485C22⋊C4—2216no—
486C22⋊C4—2216no—
487C22⋊C4—228no—
488C22⋊C4—228no—
489C22⋊C4—448no—
490C22⋊C4—448no—
491C42—2216no—
492C11C2×#248211yescharacteristic, complemented, Sylow
493C23—28no—
494C23—22no—
495C23—216no—
496C23—22no—
497C23—24no—
498C23—24no—
499C23—48no—
500C23—44no—
501C23—44no—
502C23—1116no—
503C23—114no—
504C23—118no—
505C23—114no—
506C23—2232no—
507C23—2216no—
508C23—228no—
509C23—2216no—
510C23—222no—
511C23—222no—
512C23—224no—
513C23—228no—
514C23—2216no—
515C23—228no—
516C23—222no—
517C23—222no—
518C23—224no—
519C23—224no—
520C23—4432no—
521C23—4416no—
522C23—4432no—
523C23—4416no—
524C23—44128no—
525C23—444no—
526C23—448no—
527C23—444no—
528C23C2×D4×D1112yes—
529C23C2×#434114yes—
530C23C2×#434112yes—
531C23#41×D1112yes—
532C23#41×D1114yes—
533C23#6704214yes—
534C23C24×D1111yescharacteristic
535C2×C4—28no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—24no—
540C2×C4—24no—
541C2×C4—24no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—24no—
545C2×C4—48no—
546C2×C4—48no—
547C2×C4—44no—
548C2×C4—114no—
549C2×C4—2232no—
550C2×C4—228no—
551C2×C4—224no—
552C2×C4—224no—
553C2×C4—222no—
554C2×C4—224no—
555C2×C4—224no—
556C2×C4—224no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—4416no—
561C2×C4—448no—
562C2×C4—444no—
563C2×C4—448no—
564C2×C4C2×D4×D1114yes—
565C22—24no—
566C22—28no—
567C22—44no—
568C22—42no—
569C22—416no—
570C22—42no—
571C22—118no—
572C22—228no—
573C22—224no—
574C22—224no—
575C22—2232no—
576C22—228no—
577C22—228no—
578C22—224no—
579C22—4464no—
580C22—442no—
581C22—4416no—
582C22—442no—
583C22—444no—
584C22#1062313714yes—
585C22D11×#12314yes—
586C22#1062318918yes—
587C22#1062320514yes—
588C22#1062323618yes—
589C22C22×D4×D1111yescharacteristic
590C22C22×#434111yescharacteristic
591C22C2×#41×D1111yescharacteristic
592C22C2×#41×D1112yes—
593C22C2×#6704212yes—
594C4—24no—
595C4—44no—
596C4—42no—
597C4—44no—
598C4—224no—
599C4—444no—
600C4—442no—
601C4—444no—
602C2—44no—
603C2—228no—
604C2—444no—
605C2#1307288518yesdirect product factor
606C2C2×D11×#12311yescharacteristic
607C2C2×#1062313711yescharacteristic
608C2C2×#1062320511yescharacteristic
609C2C2×#1062318912yes—
610C2C2×#1062323612yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#397C2
socleC24×C11C24
prime radicalC25×D11C22
hypercenterC2×#397D11
hypocenterC11C2×#2482
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#397

Complements

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

NH ≅ G/Ntype
1. C22×#66945C2semidirect
3. #13072885C2direct (N × H)
4. C2×#10622290C2semidirect
5. C2×#10622562C2semidirect
6. C2×#10622606C2semidirect
7. C2×#10622564C2semidirect
8. C2×#10622282C2semidirect
9. C2×#10622281C2semidirect
10. C2×#10622277C2semidirect
12. C2×C11×#397C2semidirect
16. C22×C11×C4⋊C4C22semidirect
27. C22×C4⋊Dic11C22semidirect
28. C22×C4⋊Dic11C22semidirect
29. C22×Dic11⋊C4C22semidirect
30. C22×C4×Dic11C22semidirect
32. C2×#66945C22semidirect
35. C11×#397C22semidirect
36. C2×C11×#95C22semidirect
37. C2×C11×#95C22semidirect
38. C2×C11⋊#95C22semidirect
39. C2×C11⋊#95C22semidirect
40. C2×C11⋊#95C22semidirect
41. #10622606C22semidirect
43. #10622564C22semidirect
44. #10622562C22semidirect
45. #10622290C22semidirect
46. #10622282C22semidirect
47. #10622281C22semidirect
48. #10622277C22semidirect
73. C2×C11×C4⋊C4C23semidirect
96. C2×C4⋊Dic11C23semidirect
97. C2×C4⋊Dic11C23semidirect
99. C2×Dic11⋊C4C23semidirect
101. C2×C4×Dic11C23semidirect
104. C11×#95C23semidirect
105. C11×#95C23semidirect
106. C11⋊#95C23semidirect
107. C11⋊#95C23semidirect
108. C11⋊#95C23semidirect
194. C2×#397D11semidirect
280. C22×C4⋊C4C2×D11semidirect
297. #397C2×D11semidirect
306. C2×#95C2×D11semidirect
307. C2×#95C2×D11semidirect
376. C2×C4⋊C4C22×D11semidirect
403. #95C22×D11semidirect
404. #95C22×D11semidirect
406. C2×C11#2482semidirect
492. C11C2×#2482semidirect
605. C2#13072885direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669452
C22×C22⋊C4×D112
#130728852
C2×#106222902
C2×#106225622
C2×#106226062
C2×#106225642
C2×#106222822
C2×#106222812
C2×#106222772
C2×#106225682
C2×C11×#3972
C2×#248211