Finite Group Databasebeta

← C2×#13073512 #14924921

Subgroups — C2×#13073512 #14924921

Order 2816.

4390 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C212yesmaximal, complemented
2C22×D4×Dic11C211yesmaximal, characteristic, complemented
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4#13073512C2116yesmaximal, direct product factor
5C2×#10622287C211yesmaximal, characteristic, complemented
6C2×#10622566C211yesmaximal, characteristic, complemented
7C2×#10622836C211yesmaximal, characteristic, complemented
8C2×#10622833C212yesmaximal, complemented
9C2×#10622569C212yesmaximal, complemented
10C2×#10622263C211yesmaximal, characteristic, complemented
11C2×#10622555C212yesmaximal, complemented
12C2×C11×#392C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2212yes—
15C23×C22⋊D11C2212yes—
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2212yes—
18C24×Dic11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C2×#66992—216no—
26C2×#66992C22116yescomplemented
27C2×D4×Dic11—28no—
28C2×D4×Dic11C2218yescomplemented
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2211yescharacteristic
33C22×Dic11⋊C4C2212yes—
34C22×C4×Dic11C2211yescharacteristic
35C2×(C22⋊D11)⋊C4—28no—
36C2×(C22⋊D11)⋊C4C2218yescomplemented
37C11×#392C2218yescomplemented
38C2×C11×#95C2211yescharacteristic
39#10622836C2218yescomplemented
40#10622833C22116yescomplemented
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2211yescharacteristic
45#10622569C22116yescomplemented
46#10622566C2218yescomplemented
47#10622555C22116yescomplemented
48#10622287C2218yescomplemented
49#10622263C2218yescomplemented
50C25×C11C2311yescharacteristic
51C25×C11C2312yes—
52C24×D11C2311yescharacteristic
53C22×D4×C11—28no—
54C22×D4×C11—28no—
55C22×D4×C11—28no—
56C22×D4×C11—24no—
57C22×D4×C11—44no—
58C22×D4×C11C2314yes—
59C22×D4×C11C2318yes—
60C23×C4×C11C2312yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—28no—
64C22×C22⋊D11—28no—
65C22×C22⋊D11—24no—
66C22×C22⋊D11—24no—
67C22×C22⋊D11—44no—
68C22×C22⋊D11D418yescomplemented
69C22×C22⋊D11C2318yes—
70C22×C22⋊D11C2314yes—
71C23×Dic11—24no—
72C23×Dic11—28no—
73C23×Dic11—28no—
74C23×Dic11—28no—
75C23×Dic11—44no—
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2312yes—
78C23×Dic11C2312yes—
79C23×Dic11C2318yes—
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2314yes—
82C23×Dic11C2311yescharacteristic
83C22×C4×D11—24no—
84C22×C4×D11—44no—
85C22×C4×D11C2314yes—
86C2×C11×C22⋊C4—24no—
87C2×C11×C22⋊C4—44no—
88C2×C11×C22⋊C4C2314yes—
89C2×C11×C22⋊C4C2318yes—
90C2×C22⋊Dic11—28no—
91C2×C22⋊Dic11—28no—
92C2×C22⋊Dic11—44no—
93C2×C22⋊Dic11C2318yes—
94C2×C22⋊Dic11C2318yes—
95C2×C22⋊Dic11C2318yes—
96#66992—264no—
97D4×Dic11—232no—
98C2×(C2×D11)⋊C4—28no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2318yes—
102C2×C4⋊Dic11—24no—
103C2×C4⋊Dic11C2314yes—
104C2×Dic11⋊C4—24no—
105C2×Dic11⋊C4—28no—
106C2×Dic11⋊C4C2314yes—
107C2×Dic11⋊C4C2318yes—
108C2×C4×Dic11D418yescomplemented
109C2×C4×Dic11C2314yes—
110(C22⋊D11)⋊C4—232no—
111C11×#95C2314yes—
112C11⋊#95C2314yes—
113C11⋊#95C2318yes—
114C11⋊#95C2318yes—
115C11⋊#95C2318yes—
116C2×#2535—111nomaximal, Sylow
117C24×C11—24no—
118C24×C11—22no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11—22no—
122C24×C11—24no—
123C24×C11—24no—
124C24×C11—24no—
125C24×C11—24no—
126C24×C11—24no—
127C24×C11C2×D414yes—
128C24×C11#4118yes—
129C24×C11C2412yes—
130C24×C11C2414yes—
131C24×C11C2411yescharacteristic
132C23×D11—22no—
133C23×D11—22no—
134C23×D11—24no—
135C23×D11—24no—
136C23×D11C2×D414yes—
137C23×D11C2412yes—
138C2×D4×C11—232no—
139C2×D4×C11—216no—
140C2×D4×C11—216no—
141C2×D4×C11—216no—
142C2×D4×C11—28no—
143C2×D4×C11—48no—
144C2×D4×C11—432no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—22no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11C2×D414yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2412yes—
155C2×C22⋊D11—232no—
156C2×C22⋊D11—28no—
157C2×C22⋊D11—28no—
158C2×C22⋊D11—216no—
159C2×C22⋊D11—216no—
160C2×C22⋊D11—48no—
161C2×C22⋊D11—432no—
162C2×C22⋊D11C2×D4116yescomplemented
163C22×Dic11—28no—
164C22×Dic11—216no—
165C22×Dic11—216no—
166C22×Dic11—216no—
167C22×Dic11—22no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11—24no—
172C22×Dic11—24no—
173C22×Dic11—24no—
174C22×Dic11—24no—
175C22×Dic11—24no—
176C22×Dic11—48no—
177C22×Dic11—416no—
178C22×Dic11—432no—
179C22×Dic11C2×D414yes—
180C22×Dic11C2×D414yes—
181C22×Dic11C2×D414yes—
182C22×Dic11#4114yes—
183C22×Dic11C2414yes—
184C22×Dic11C2412yes—
185C22×Dic11C2414yes—
186C22×Dic11C2412yes—
187C22×Dic11C2412yes—
188C2×C4×D11—28no—
189C2×C4×D11—48no—
190C2×C4×D11—416no—
191C11×C22⋊C4—28no—
192C11×C22⋊C4—48no—
193C22⋊Dic11—216no—
194C22⋊Dic11—216no—
195C22⋊Dic11—48no—
196(C2×D11)⋊C4—216no—
197(C2×D11)⋊C4—28no—
198C4⋊Dic11—28no—
199Dic11⋊C4—28no—
200Dic11⋊C4—216no—
201C4×Dic11C2×D4116yescomplemented
202C22×#121—112no—
203C22×C4×D4—111no—
204C22×C4×D4—111no—
205#2535—1116no—
206C2×#397—111no—
207C2×#397—111no—
208C2×#392—111no—
209C2×#392D1111yescharacteristic, complemented
210C2×#386—112no—
211C2×#386—112no—
212C2×#382—111no—
213C2×#380—112no—
214C23×C11—28no—
215C23×C11—216no—
216C23×C11—216no—
217C23×C11—216no—
218C23×C11—216no—
219C23×C11—24no—
220C23×C11—22no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—22no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—48no—
230C23×C11—44no—
231C23×C11—44no—
232C23×C11—48no—
233C23×C11—48no—
234C23×C11—48no—
235C23×C11—48no—
236C23×C11C22×D414yes—
237C23×C11C22×D412yes—
238C23×C11C22×D412yes—
239C23×C11C2×#4118yes—
240C23×C11C2×#4114yes—
241C23×C11C2×#4112yes—
242C23×C11H(5,𝔽2)14yes—
243C23×C11C2511yescharacteristic
244C22×D11—28no—
245C22×D11—216no—
246C22×D11—22no—
247C22×D11—24no—
248C22×D11—22no—
249C22×D11—24no—
250C22×D11—44no—
251C22×D11—44no—
252C22×D11—48no—
253C22×D11C22×D414yes—
254D4×C11—232no—
255D4×C11—432no—
256C2×C4×C11—28no—
257C2×C4×C11—24no—
258C2×C4×C11—24no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—24no—
263C2×C4×C11—44no—
264C2×C4×C11—48no—
265C2×C4×C11C22×D414yes—
266C22⋊D11—232no—
267C22⋊D11—432no—
268C2×Dic11—28no—
269C2×Dic11—24no—
270C2×Dic11—22no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—416no—
279C2×Dic11—48no—
280C2×Dic11—44no—
281C2×Dic11—48no—
282C2×Dic11—432no—
283C2×Dic11#121116yes—
284C2×Dic11C22×D414yes—
285C2×Dic11C22×D414yes—
286C2×Dic11C22×D414yes—
287C2×Dic11C2×#4114yes—
288C4×D11—416no—
289C23×D4—111no—
290C23×D4—112no—
291C23×D4C2×D1111yescharacteristic
292C23×D4C2×D1112yes—
293C24×C4—112no—
294C24×C4—111no—
295C24×C4—111no—
296C2×#121—1116no—
297C2×#121—2216no—
298C2×C4×D4—118no—
299C2×C4×D4—118no—
300C2×C4×D4—228no—
301C2×C4×D4—228no—
302C22×C4⋊C4—111no—
303C22×C4⋊C4—112no—
304C22×C4⋊C4—111no—
305C22×C22⋊C4—112no—
306C22×C22⋊C4—112no—
307C22×C22⋊C4—111no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4C2×D1111yescharacteristic
311C22×C22⋊C4C2×D1112yes—
312C22×C42—111no—
313#397—118no—
314#397—118no—
315#392—118no—
316#392C2×D1118yescomplemented
317#386—1116no—
318#386—1116no—
319#382—118no—
320#380—1116no—
321C2×#95—111no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95C2×D1111yescharacteristic
326C22×C11—24no—
327C22×C11—28no—
328C22×C11—28no—
329C22×C11—28no—
330C22×C11—28no—
331C22×C11—44no—
332C22×C11—42no—
333C22×C11—44no—
334C22×C11—42no—
335C22×C11—44no—
336C22×C11—44no—
337C22×C11—44no—
338C22×C11—416no—
339C22×C11—432no—
340C22×C11C2×#12114yes—
341C22×C11#52514yes—
342C22×C11#53514yes—
343C22×C11#54618yes—
344C22×C11#55318yes—
345C22×C11C23×D411yescharacteristic
346C22×C11C23×D411yescharacteristic
347C22×C11C22×#4112yes—
348C22×C11C22×#4111yescharacteristic
349C22×C11C2×H(5,𝔽2)12yes—
350C2×D11—24no—
351C2×D11—28no—
352C2×D11—42no—
353C2×D11—42no—
354C2×D11—44no—
355C2×D11—416no—
356C4×C11—24no—
357C4×C11—42no—
358C4×C11—44no—
359Dic11—24no—
360Dic11—44no—
361Dic11—42no—
362Dic11—44no—
363Dic11C2×#12118yes—
364C25—111no—
365C25C22×D1111yescharacteristic
366C25C22×D1112yes—
367C22×D4—28no—
368C22×D4—28no—
369C22×D4—28no—
370C22×D4—24no—
371C22×D4—44no—
372C22×D4—118no—
373C22×D4—114no—
374C22×D4—118no—
375C22×D4—224no—
376C22×D4—224no—
377C22×D4—228no—
378C22×D4—228no—
379C22×D4—444no—
380C22×D4C22×D1114yes—
381C22×D4C22×D1118yes—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—118no—
385C23×C4—112no—
386C23×C4—111no—
387C23×C4—112no—
388C23×C4—114no—
389C23×C4—114no—
390C23×C4—224no—
391C23×C4—228no—
392C23×C4—224no—
393C23×C4—228no—
394C23×C4—228no—
395C23×C4—444no—
396C23×C4—444no—
397C23×C4C22×D1112yes—
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1111yescharacteristic
400#121—2264no—
401C4×D4—2232no—
402C4×D4—2232no—
403C2×C4⋊C4—114no—
404C2×C4⋊C4—114no—
405C2×C4⋊C4—118no—
406C2×C4⋊C4—224no—
407C2×C4⋊C4—228no—
408C2×C4⋊C4—224no—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—44no—
411C2×C22⋊C4—118no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4—114no—
414C2×C22⋊C4—118no—
415C2×C22⋊C4—118no—
416C2×C22⋊C4—228no—
417C2×C22⋊C4—228no—
418C2×C22⋊C4—228no—
419C2×C22⋊C4—224no—
420C2×C22⋊C4—444no—
421C2×C22⋊C4C22×D1114yes—
422C2×C22⋊C4C22×D1118yes—
423C2×C42—118no—
424C2×C42—114no—
425#95—118no—
426#95—118no—
427#95—118no—
428#95—114no—
429#95C22×D1114yes—
430C2×C11—44no—
431C2×C11—48no—
432C2×C11#253518yescomplemented
433C2×C11C22×#12111yescharacteristic
434C2×C11C2×#52511yescharacteristic
435C2×C11C2×#53511yescharacteristic
436C2×C11C2×#54612yes—
437C2×C11C2×#55312yes—
438D11—44no—
439C24—22no—
440C24—24no—
441C24—24no—
442C24—24no—
443C24—24no—
444C24—24no—
445C24—24no—
446C24—24no—
447C24—24no—
448C24—22no—
449C24—114no—
450C24—112no—
451C24—222no—
452C24—224no—
453C24—224no—
454C24—222no—
455C24D4×D1114yes—
456C24#434118yes—
457C24C23×D1112yes—
458C24C23×D1114yes—
459C24C23×D1111yescharacteristic
460C2×D4—232no—
461C2×D4—216no—
462C2×D4—216no—
463C2×D4—216no—
464C2×D4—28no—
465C2×D4—48no—
466C2×D4—432no—
467C2×D4—1116no—
468C2×D4—228no—
469C2×D4—2232no—
470C2×D4—228no—
471C2×D4—2216no—
472C2×D4—2216no—
473C2×D4—448no—
474C2×D4—4432no—
475C22×C4—24no—
476C22×C4—22no—
477C22×C4—24no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—114no—
482C22×C4—114no—
483C22×C4—114no—
484C22×C4—112no—
485C22×C4—114no—
486C22×C4—112no—
487C22×C4—114no—
488C22×C4—114no—
489C22×C4—112no—
490C22×C4—228no—
491C22×C4—2216no—
492C22×C4—228no—
493C22×C4—2216no—
494C22×C4—2216no—
495C22×C4—224no—
496C22×C4—224no—
497C22×C4—222no—
498C22×C4—224no—
499C22×C4—224no—
500C22×C4—224no—
501C22×C4—224no—
502C22×C4—224no—
503C22×C4—224no—
504C22×C4—448no—
505C22×C4—4416no—
506C22×C4—4432no—
507C22×C4—448no—
508C22×C4—4416no—
509C22×C4D4×D1114yes—
510C22×C4C23×D1114yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1112yes—
513C4⋊C4—228no—
514C4⋊C4—2216no—
515C4⋊C4—228no—
516C22⋊C4—28no—
517C22⋊C4—48no—
518C22⋊C4—2216no—
519C22⋊C4—2216no—
520C22⋊C4—2216no—
521C22⋊C4—228no—
522C22⋊C4—448no—
523C42—1116no—
524C11C2×#253511yescharacteristic, complemented, Sylow
525C23—216no—
526C23—216no—
527C23—216no—
528C23—216no—
529C23—28no—
530C23—22no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—24no—
535C23—24no—
536C23—24no—
537C23—24no—
538C23—24no—
539C23—22no—
540C23—44no—
541C23—48no—
542C23—44no—
543C23—48no—
544C23—48no—
545C23—48no—
546C23—48no—
547C23—114no—
548C23—2216no—
549C23—228no—
550C23—222no—
551C23—224no—
552C23—224no—
553C23—222no—
554C23—444no—
555C23—444no—
556C23—448no—
557C23C2×D4×D1114yes—
558C23C2×D4×D1112yes—
559C23C2×D4×D1112yes—
560C23C2×#434118yes—
561C23C2×#434114yes—
562C23#6703714yes—
563C23#41×D1112yes—
564C23C24×D1111yescharacteristic
565D4—232no—
566D4—432no—
567D4—2232no—
568D4—4432no—
569C2×C4—28no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—44no—
577C2×C4—48no—
578C2×C4—1116no—
579C2×C4—114no—
580C2×C4—114no—
581C2×C4—114no—
582C2×C4—114no—
583C2×C4—228no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—222no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—4416no—
594C2×C4—4432no—
595C2×C4—4416no—
596C2×C4—444no—
597C2×C4—448no—
598C2×C4—448no—
599C2×C4C2×D4×D1114yes—
600C22—28no—
601C22—28no—
602C22—28no—
603C22—24no—
604C22—28no—
605C22—44no—
606C22—44no—
607C22—42no—
608C22—44no—
609C22—432no—
610C22—416no—
611C22—44no—
612C22—44no—
613C22—42no—
614C22—228no—
615C22—224no—
616C22—444no—
617C22—442no—
618C22—4416no—
619C22—442no—
620C22#1062311714yes—
621C22#1062312218yes—
622C22#1062313218yes—
623C22D11×#12114yes—
624C22#1062324614yes—
625C22C22×D4×D1111yescharacteristic
626C22C22×D4×D1111yescharacteristic
627C22C22×#434112yes—
628C22C2×#6703712yes—
629C22C2×#41×D1111yescharacteristic
630C4—24no—
631C4—42no—
632C4—44no—
633C4—118no—
634C4—224no—
635C4—442no—
636C4—444no—
637C4—444no—
638C2—48no—
639C2—44no—
640C2—444no—
641C2#1307351218yesdirect product factor
642C2C2×D11×#12111yescharacteristic
643C2C2×#1062311711yescharacteristic
644C2C2×#1062324611yescharacteristic
645C2C2×#1062312212yes—
646C2C2×#1062313212yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2535
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C22×#66992C2semidirect
2. C22×D4×Dic11C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. #13073512C2direct (N × H)
5. C2×#10622287C2semidirect
6. C2×#10622566C2semidirect
7. C2×#10622836C2semidirect
8. C2×#10622833C2semidirect
9. C2×#10622569C2semidirect
10. C2×#10622263C2semidirect
11. C2×#10622555C2semidirect
12. C2×C11×#392C2semidirect
26. C2×#66992C22semidirect
28. C2×D4×Dic11C22semidirect
36. C2×(C22⋊D11)⋊C4C22semidirect
37. C11×#392C22semidirect
39. #10622836C22semidirect
40. #10622833C22semidirect
45. #10622569C22semidirect
46. #10622566C22semidirect
47. #10622555C22semidirect
48. #10622287C22semidirect
49. #10622263C22semidirect
68. C22×C22⋊D11D4semidirect
108. C2×C4×Dic11D4semidirect
162. C2×C22⋊D11C2×D4semidirect
201. C4×Dic11C2×D4semidirect
209. C2×#392D11semidirect
316. #392C2×D11semidirect
432. C2×C11#2535semidirect
524. C11C2×#2535semidirect
641. C2#13073512direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669922
C22×D4×Dic112
C22×(C22⋊D11)⋊C42
#130735122
C2×#106222872
C2×#106225662
C2×#106228362
C2×#106228332
C2×#106225692
C2×#106222632
C2×#106225552
C2×C11×#3922
C2×#253511