Finite Group Databasebeta

← C2×#13072220 #14922403

Subgroups — C2×#13072220 #14922403

Order 2816.

6042 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66982C211yesmaximal, characteristic, complemented
2C22×#66992C212yesmaximal, complemented
3#13072220C2116yesmaximal, direct product factor
4C2×#10622842C211yesmaximal, characteristic, complemented
5C2×#10622835C211yesmaximal, characteristic, complemented
6C2×#10622844C211yesmaximal, characteristic, complemented
7C2×#10622836C211yesmaximal, characteristic, complemented
8C2×#10622833C212yesmaximal, complemented
9C2×#10622826C212yesmaximal, complemented
10C2×#10622823C212yesmaximal, complemented
11C22×C11⋊#95C211yesmaximal, characteristic, complemented
12C23×C11×#41C211yesmaximal, characteristic, complemented
13C22×C11×#41—216no—
14C22×C11×#41—28no—
15C22×C11×#41C2218yescomplemented
16C23×Q8×C11C2211yescharacteristic
17C23×D4×C11C2211yescharacteristic
18C23×D4×C11C2212yes—
19C24×C4×C11C2212yes—
20C24×C4×C11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2212yes—
23C24×Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2212yes—
28C2×#66992—216no—
29C2×#66992C22116yescomplemented
30C2×#66982—28no—
31C2×#66982C2218yescomplemented
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2212yes—
34C22×(C2×D11)⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2212yes—
37C22×Dic11⋊C4C2211yescharacteristic
38#10622844C2218yescomplemented
39#10622842C2218yescomplemented
40#10622836C2218yescomplemented
41#10622835C2218yescomplemented
42#10622833C22116yescomplemented
43#10622826C22116yescomplemented
44#10622823C22116yescomplemented
45C2×C11⋊#95C2212yes—
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2212yes—
49C2×C11⋊#95C2212yes—
50C2×C11⋊#95C2218yescomplemented
51C25×C11C2312yes—
52C25×C11C2311yescharacteristic
53C24×D11C2311yescharacteristic
54C2×C11×#41—2128no—
55C2×C11×#41—264no—
56C2×C11×#41—232no—
57C22×Q8×C11—28no—
58C22×Q8×C11—24no—
59C22×Q8×C11C2314yes—
60C22×D4×C11—28no—
61C22×D4×C11—28no—
62C22×D4×C11—28no—
63C22×D4×C11—24no—
64C22×D4×C11D4116yescomplemented
65C22×D4×C11C2314yes—
66C22×D4×C11C2318yes—
67C23×C4×C11—28no—
68C23×C4×C11—28no—
69C23×C4×C11—28no—
70C23×C4×C11—28no—
71C23×C4×C11D418yescomplemented
72C23×C4×C11C2318yes—
73C23×C4×C11C2311yescharacteristic
74C23×C4×C11C2312yes—
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2314yes—
77C22×C22⋊D11—24no—
78C22×C22⋊D11—28no—
79C22×C22⋊D11—28no—
80C22×C22⋊D11—28no—
81C22×C22⋊D11—44no—
82C22×C22⋊D11C2314yes—
83C22×C22⋊D11C2318yes—
84C23×Dic11—28no—
85C23×Dic11—28no—
86C23×Dic11—44no—
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2311yescharacteristic
90C23×Dic11C2312yes—
91C23×Dic11C2318yes—
92C23×Dic11C2312yes—
93C2×C22⋊Dic11—24no—
94C2×C22⋊Dic11—28no—
95C2×C22⋊Dic11—28no—
96C2×C22⋊Dic11—44no—
97C2×C22⋊Dic11C2314yes—
98C2×C22⋊Dic11C2318yes—
99C2×C22⋊Dic11C2318yes—
100C2×C22⋊Dic11C2318yes—
101#66992—264no—
102#66982—232no—
103C2×(C2×D11)⋊C4—24no—
104C2×(C2×D11)⋊C4—24no—
105C2×(C2×D11)⋊C4—28no—
106C2×(C2×D11)⋊C4C2314yes—
107C2×(C2×D11)⋊C4C2314yes—
108C2×(C2×D11)⋊C4C2318yes—
109C2×Dic11⋊C4—24no—
110C2×Dic11⋊C4—24no—
111C2×Dic11⋊C4—28no—
112C2×Dic11⋊C4C2314yes—
113C2×Dic11⋊C4C2314yes—
114C2×Dic11⋊C4C2318yes—
115C11⋊#95C2318yes—
116C11⋊#95C2314yes—
117C11⋊#95C2314yes—
118C11⋊#95C2318yes—
119C11⋊#95C2318yes—
120C2×#2430—111nomaximal, Sylow
121C24×C11—24no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11—24no—
125C24×C11—24no—
126C24×C11—24no—
127C24×C11—24no—
128C24×C11—24no—
129C24×C11—24no—
130C24×C11C2×D418yes—
131C24×C11C2×D414yes—
132C24×C11C2×D418yes—
133C24×C11C2414yes—
134C24×C11C2412yes—
135C24×C11C2411yescharacteristic
136C23×D11—22no—
137C23×D11—24no—
138C23×D11—24no—
139C23×D11—22no—
140C23×D11—22no—
141C23×D11C2412yes—
142C11×#41—2256no—
143C2×Q8×C11—232no—
144C2×Q8×C11—216no—
145C2×Q8×C11—28no—
146C2×D4×C11—232no—
147C2×D4×C11—264no—
148C2×D4×C11—216no—
149C2×D4×C11—216no—
150C2×D4×C11—216no—
151C2×D4×C11—28no—
152C2×D4×C11C2×D4132yescomplemented
153C22×C4×C11—264no—
154C22×C4×C11—232no—
155C22×C4×C11—24no—
156C22×C4×C11—24no—
157C22×C4×C11—24no—
158C22×C4×C11—24no—
159C22×C4×C11—216no—
160C22×C4×C11—216no—
161C22×C4×C11—216no—
162C22×C4×C11—216no—
163C22×C4×C11C2×D414yes—
164C22×C4×C11C2×D418yes—
165C22×C4×C11C2×D414yes—
166C22×C4×C11C2×D4116yescomplemented
167C22×C4×C11C2412yes—
168C22×C4×C11C2414yes—
169C22×C4×C11C2412yes—
170C2×C22⋊D11—216no—
171C2×C22⋊D11—28no—
172C2×C22⋊D11—216no—
173C2×C22⋊D11—216no—
174C2×C22⋊D11—48no—
175C2×C22⋊D11—432no—
176C2×C22⋊D11—416no—
177C22×Dic11—216no—
178C22×Dic11—24no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—24no—
183C22×Dic11—24no—
184C22×Dic11—216no—
185C22×Dic11—24no—
186C22×Dic11—24no—
187C22×Dic11—24no—
188C22×Dic11—22no—
189C22×Dic11—24no—
190C22×Dic11—22no—
191C22×Dic11—48no—
192C22×Dic11—432no—
193C22×Dic11#4118yescomplemented
194C22×Dic11C2414yes—
195C22×Dic11C2412yes—
196C22×Dic11C2412yes—
197C22×Dic11C2412yes—
198C22×Dic11C2414yes—
199C22⋊Dic11—216no—
200C22⋊Dic11—28no—
201C22⋊Dic11—216no—
202C22⋊Dic11—48no—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—28no—
205(C2×D11)⋊C4—216no—
206Dic11⋊C4—28no—
207Dic11⋊C4—28no—
208Dic11⋊C4—216no—
209C23×#41D1111yescharacteristic, complemented
210C22×#123—111no—
211C22×#121—112no—
212#2430—1116no—
213C2×#395—111no—
214C2×#394—111no—
215C2×#393—111no—
216C2×#392—111no—
217C2×#386—112no—
218C2×#386—112no—
219C2×#385—112no—
220C22×#95—111no—
221C23×C11—28no—
222C23×C11—28no—
223C23×C11—216no—
224C23×C11—216no—
225C23×C11—24no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—216no—
229C23×C11—216no—
230C23×C11—216no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—24no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—48no—
238C23×C11—48no—
239C23×C11—48no—
240C23×C11—48no—
241C23×C11#120116yes—
242C23×C11C22×D418yes—
243C23×C11C22×D414yes—
244C23×C11C22×D418yes—
245C23×C11C22×D412yes—
246C23×C11C22×D414yes—
247C23×C11C2×#4114yes—
248C23×C11H(5,𝔽2)12yes—
249C23×C112−1+412yes—
250C23×C11C2511yescharacteristic
251C22×D11—22no—
252C22×D11—24no—
253C22×D11—24no—
254C22×D11—22no—
255C22×D11—22no—
256C22×D11—44no—
257C22×D11—44no—
258C22×D11—44no—
259C22×D11—48no—
260C22×D11—48no—
261Q8×C11—232no—
262D4×C11—232no—
263D4×C11—264no—
264C2×C4×C11—264no—
265C2×C4×C11—28no—
266C2×C4×C11—216no—
267C2×C4×C11—28no—
268C2×C4×C11—232no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11C22×D414yes—
274C2×C4×C11C22×D418yes—
275C2×C4×C11C22×D414yes—
276C22⋊D11—432no—
277C22⋊D11—416no—
278C2×Dic11—216no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—22no—
284C2×Dic11—24no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—22no—
289C2×Dic11—24no—
290C2×Dic11—22no—
291C2×Dic11—432no—
292C2×Dic11—44no—
293C2×Dic11—44no—
294C2×Dic11—44no—
295C2×Dic11—48no—
296C2×Dic11C2×#4118yescomplemented
297C22×#41—216no—
298C22×#41—28no—
299C22×#41C2×D1118yescomplemented
300C23×Q8C2×D1111yescharacteristic
301C23×D4—111no—
302C23×D4—112no—
303C23×D4C2×D1111yescharacteristic
304C23×D4C2×D1112yes—
305C24×C4—112no—
306C24×C4C2×D1112yes—
307C24×C4C2×D1111yescharacteristic
308C2×#123—118no—
309C2×#123—228no—
310C2×#121—1116no—
311C2×#121—2216no—
312C22×C4⋊C4—111no—
313C22×C4⋊C4—112no—
314C22×C4⋊C4—111no—
315C22×C22⋊C4—112no—
316C22×C22⋊C4—112no—
317C22×C22⋊C4—111no—
318C22×C22⋊C4—111no—
319C22×C22⋊C4—112no—
320C22×C22⋊C4—111no—
321C22×C22⋊C4—112no—
322#395—118no—
323#394—118no—
324#393—118no—
325#392—118no—
326#386—1116no—
327#386—1116no—
328#385—1116no—
329C2×#95—111no—
330C2×#95—111no—
331C2×#95—112no—
332C2×#95—112no—
333C2×#95—112no—
334C2×#95—118no—
335C22×C11—24no—
336C22×C11—24no—
337C22×C11—232no—
338C22×C11—28no—
339C22×C11—28no—
340C22×C11—28no—
341C22×C11—28no—
342C22×C11—28no—
343C22×C11—44no—
344C22×C11—44no—
345C22×C11—432no—
346C22×C11—44no—
347C22×C11—44no—
348C22×C11C2×#12018yes—
349C22×C11C2×#12014yes—
350C22×C11#53214yes—
351C22×C11#53714yes—
352C22×C11#54618yes—
353C22×C11#54718yes—
354C22×C11C23×D411yescharacteristic
355C22×C11C23×D412yes—
356C22×C11C22×#4112yes—
357C22×C11C2×H(5,𝔽2)11yescharacteristic
358C22×C11C2×2−1+411yescharacteristic
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—42no—
362C2×D11—44no—
363C2×D11—44no—
364C2×D11—88no—
365C4×C11—24no—
366C4×C11—28no—
367C4×C11—24no—
368Dic11—28no—
369Dic11—42no—
370Dic11—42no—
371Dic11—42no—
372Dic11—44no—
373C25—111no—
374C25C22×D1112yes—
375C25C22×D1111yescharacteristic
376C2×#41—2128no—
377C2×#41—264no—
378C2×#41—232no—
379C22×Q8—28no—
380C22×Q8—24no—
381C22×Q8C22×D1114yes—
382C22×D4—28no—
383C22×D4—28no—
384C22×D4—28no—
385C22×D4—24no—
386C22×D4—114no—
387C22×D4—118no—
388C22×D4—228no—
389C22×D4—228no—
390C22×D4—228no—
391C22×D4—224no—
392C22×D4—444no—
393C22×D4C22⋊D11116yescomplemented
394C22×D4C22×D1114yes—
395C22×D4C22×D1118yes—
396C23×C4—28no—
397C23×C4—28no—
398C23×C4—28no—
399C23×C4—28no—
400C23×C4—112no—
401C23×C4—111no—
402C23×C4—111no—
403C23×C4—112no—
404C23×C4—111no—
405C23×C4—118no—
406C23×C4—228no—
407C23×C4—228no—
408C23×C4—444no—
409C23×C4C22⋊D1118yescomplemented
410C23×C4C22×D1118yes—
411C23×C4C22×D1111yescharacteristic
412C23×C4C22×D1112yes—
413C23×C4C22×D1111yescharacteristic
414C23×C4C22×D1114yes—
415#123—2232no—
416#121—2264no—
417C2×C4⋊C4—118no—
418C2×C4⋊C4—114no—
419C2×C4⋊C4—114no—
420C2×C4⋊C4—228no—
421C2×C4⋊C4—224no—
422C2×C4⋊C4—224no—
423C2×C22⋊C4—118no—
424C2×C22⋊C4—114no—
425C2×C22⋊C4—118no—
426C2×C22⋊C4—118no—
427C2×C22⋊C4—114no—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—118no—
430C2×C22⋊C4—228no—
431C2×C22⋊C4—228no—
432C2×C22⋊C4—224no—
433C2×C22⋊C4—228no—
434C2×C22⋊C4—224no—
435C2×C22⋊C4—224no—
436C2×C22⋊C4—444no—
437#95—118no—
438#95—114no—
439#95—114no—
440#95—118no—
441#95—118no—
442C2×C11—28no—
443C2×C11—48no—
444C2×C11#243018yescomplemented
445C2×C11C22×#12011yescharacteristic
446C2×C11C2×#53211yescharacteristic
447C2×C11C2×#53711yescharacteristic
448C2×C11C2×#54612yes—
449C2×C11C2×#54712yes—
450D11—82no—
451C24—24no—
452C24—22no—
453C24—22no—
454C24—24no—
455C24—24no—
456C24—24no—
457C24—24no—
458C24—24no—
459C24—24no—
460C24—112no—
461C24—224no—
462C24—222no—
463C24—222no—
464C24—222no—
465C24—224no—
466C24C2×C22⋊D1118yes—
467C24C2×C22⋊D1114yes—
468C24C2×C22⋊D1118yes—
469C24C23×D1114yes—
470C24C23×D1112yes—
471C24C23×D1111yescharacteristic
472#41—2256no—
473C2×Q8—232no—
474C2×Q8—216no—
475C2×Q8—28no—
476C2×D4—232no—
477C2×D4—264no—
478C2×D4—216no—
479C2×D4—216no—
480C2×D4—216no—
481C2×D4—28no—
482C2×D4—2216no—
483C2×D4—2216no—
484C2×D4—2216no—
485C2×D4—228no—
486C2×D4—448no—
487C2×D4—4432no—
488C2×D4—4416no—
489C2×D4C2×C22⋊D11132yescomplemented
490C22×C4—264no—
491C22×C4—232no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—216no—
497C22×C4—216no—
498C22×C4—216no—
499C22×C4—216no—
500C22×C4—118no—
501C22×C4—114no—
502C22×C4—114no—
503C22×C4—112no—
504C22×C4—112no—
505C22×C4—112no—
506C22×C4—2216no—
507C22×C4—224no—
508C22×C4—224no—
509C22×C4—224no—
510C22×C4—224no—
511C22×C4—222no—
512C22×C4—224no—
513C22×C4—222no—
514C22×C4—222no—
515C22×C4—222no—
516C22×C4—224no—
517C22×C4—224no—
518C22×C4—222no—
519C22×C4—2216no—
520C22×C4—448no—
521C22×C4—4432no—
522C22×C4C2×C22⋊D1114yes—
523C22×C4C2×C22⋊D1118yes—
524C22×C4C2×C22⋊D1114yes—
525C22×C4C2×C22⋊D11116yescomplemented
526C22×C4C23×D1112yes—
527C22×C4C23×D1114yes—
528C22×C4C23×D1112yes—
529C4⋊C4—2216no—
530C4⋊C4—228no—
531C4⋊C4—228no—
532C22⋊C4—2216no—
533C22⋊C4—2216no—
534C22⋊C4—228no—
535C22⋊C4—2216no—
536C22⋊C4—228no—
537C22⋊C4—228no—
538C22⋊C4—448no—
539C11C2×#243011yescharacteristic, complemented, Sylow
540C23—216no—
541C23—216no—
542C23—28no—
543C23—28no—
544C23—24no—
545C23—22no—
546C23—22no—
547C23—216no—
548C23—216no—
549C23—216no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—48no—
557C23—48no—
558C23—48no—
559C23—48no—
560C23—224no—
561C23—222no—
562C23—222no—
563C23—222no—
564C23—224no—
565C23—448no—
566C23—448no—
567C23—444no—
568C23—444no—
569C23—444no—
570C23#67006116yes—
571C23#41×D1114yes—
572C23#6704212yes—
573C23#6704312yes—
574C23C22×C22⋊D1118yes—
575C23C22×C22⋊D1114yes—
576C23C22×C22⋊D1118yes—
577C23C22×C22⋊D1114yes—
578C23C22×C22⋊D1112yes—
579C23C24×D1111yescharacteristic
580Q8—232no—
581D4—232no—
582D4—264no—
583D4—4432no—
584D4—4416no—
585C2×C4—264no—
586C2×C4—28no—
587C2×C4—216no—
588C2×C4—28no—
589C2×C4—232no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—118no—
595C2×C4—2216no—
596C2×C4—224no—
597C2×C4—224no—
598C2×C4—224no—
599C2×C4—224no—
600C2×C4—222no—
601C2×C4—224no—
602C2×C4—222no—
603C2×C4—222no—
604C2×C4—222no—
605C2×C4—224no—
606C2×C4—224no—
607C2×C4—222no—
608C2×C4—4432no—
609C2×C4—448no—
610C2×C4—444no—
611C2×C4—444no—
612C2×C4—444no—
613C2×C4C22×C22⋊D1114yes—
614C2×C4C22×C22⋊D1118yes—
615C2×C4C22×C22⋊D1114yes—
616C22—24no—
617C22—24no—
618C22—232no—
619C22—28no—
620C22—28no—
621C22—28no—
622C22—28no—
623C22—28no—
624C22—44no—
625C22—44no—
626C22—432no—
627C22—44no—
628C22—44no—
629C22—442no—
630C22—442no—
631C22—444no—
632C22—444no—
633C22—442no—
634C22—888no—
635C22#1062335518yes—
636C22#1062336018yes—
637C22#1062336314yes—
638C22#1062336414yes—
639C22C2×#6700618yes—
640C22C2×#6700614yes—
641C22C2×#41×D1112yes—
642C22C2×#6704211yescharacteristic
643C22C2×#6704311yescharacteristic
644C22C23×C22⋊D1111yescharacteristic
645C22C23×C22⋊D1112yes—
646C4—24no—
647C4—28no—
648C4—24no—
649C4—228no—
650C4—442no—
651C4—442no—
652C4—444no—
653C4—442no—
654C2—28no—
655C2—48no—
656C2—882no—
657C2#1307222018yesdirect product factor
658C2C22×#6700611yescharacteristic
659C2C2×#1062336311yescharacteristic
660C2C2×#1062336411yescharacteristic
661C2C2×#1062336012yes—
662C2C2×#1062335512yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC23×C11×#41C2
socleC24×C11C24
hypercenterC23×#41D11
hypocenterC11C2×#2430
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×#41

Complements

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

NH ≅ G/Ntype
1. C22×#66982C2semidirect
2. C22×#66992C2semidirect
3. #13072220C2direct (N × H)
4. C2×#10622842C2semidirect
5. C2×#10622835C2semidirect
6. C2×#10622844C2semidirect
7. C2×#10622836C2semidirect
8. C2×#10622833C2semidirect
9. C2×#10622826C2semidirect
10. C2×#10622823C2semidirect
11. C22×C11⋊#95C2semidirect
12. C23×C11×#41C2semidirect
15. C22×C11×#41C22semidirect
29. C2×#66992C22semidirect
31. C2×#66982C22semidirect
38. #10622844C22semidirect
39. #10622842C22semidirect
40. #10622836C22semidirect
41. #10622835C22semidirect
42. #10622833C22semidirect
43. #10622826C22semidirect
44. #10622823C22semidirect
50. C2×C11⋊#95C22semidirect
64. C22×D4×C11D4semidirect
71. C23×C4×C11D4semidirect
152. C2×D4×C11C2×D4semidirect
166. C22×C4×C11C2×D4semidirect
193. C22×Dic11#41semidirect
209. C23×#41D11semidirect
296. C2×Dic11C2×#41semidirect
299. C22×#41C2×D11semidirect
393. C22×D4C22⋊D11semidirect
409. C23×C4C22⋊D11semidirect
444. C2×C11#2430semidirect
489. C2×D4C2×C22⋊D11semidirect
525. C22×C4C2×C22⋊D11semidirect
539. C11C2×#2430semidirect
657. C2#13072220direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669822
C22×#669922
#130722202
C2×#106228422
C2×#106228352
C2×#106228442
C2×#106228362
C2×#106228332
C2×#106228262
C2×#106228232
C22×C11⋊#952
C23×C11×#412
C2×#243011