Finite Group Databasebeta

← C2×#13071828 #14919966

Subgroups — C2×#13071828 #14919966

Order 2816.

6238 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4341C211yesmaximal, characteristic, complemented
2C22×D4×Dic11C212yesmaximal, complemented
3C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
4#13071828C2116yesmaximal, direct product factor
5C2×#10622269C211yesmaximal, characteristic, complemented
6C2×#10622574C212yesmaximal, complemented
7C2×#10622835C211yesmaximal, characteristic, complemented
8C2×#10622560C211yesmaximal, characteristic, complemented
9C2×#10622836C212yesmaximal, complemented
10C2×C22⋊C4×Dic11C212yesmaximal, complemented
11C2×#10622279C211yesmaximal, characteristic, complemented
12C2×C11×#392C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2212yes—
15C23×C22⋊D11C2212yes—
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C24×Dic11C2212yes—
19C22×#4341—216no—
20C22×#4341—28no—
21C22×#4341C2218yescomplemented
22C23×C4×D11C2211yescharacteristic
23C23×Dic22C2211yescharacteristic
24C22×C11×C22⋊C4C2212yes—
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic11C2212yes—
27C22×C22⋊Dic11C2212yes—
28C22×C22⋊Dic11C2212yes—
29C2×D4×Dic11—216no—
30C2×D4×Dic11C22116yescomplemented
31C22×(C2×D11)⋊C4C2212yes—
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×C4⋊Dic11C2212yes—
34C22×Dic11⋊C4C2211yescharacteristic
35C22×C4×Dic11C2212yes—
36C22×C4×Dic11C2211yescharacteristic
37C2×(C22⋊D11)⋊C4—28no—
38C2×(C22⋊D11)⋊C4C2218yescomplemented
39C11×#392C2218yescomplemented
40C2×C11×#95C2211yescharacteristic
41#10622836C22116yescomplemented
42#10622835C2218yescomplemented
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2212yes—
45C2×C11⋊#95C2212yes—
46#10622574C22116yescomplemented
47#10622560C2218yescomplemented
48C22⋊C4×Dic11C22116yescomplemented
49#10622279C2218yescomplemented
50#10622269C2218yescomplemented
51C25×C11C2312yes—
52C25×C11C2311yescharacteristic
53C24×D11C2311yescharacteristic
54C22×D4×C11—28no—
55C22×D4×C11—28no—
56C22×D4×C11—28no—
57C22×D4×C11—24no—
58C22×D4×C11—28no—
59C22×D4×C11C2318yes—
60C22×D4×C11C2314yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2312yes—
64C22×C22⋊D11—28no—
65C22×C22⋊D11—24no—
66C22×C22⋊D11—24no—
67C22×C22⋊D11—28no—
68C22×C22⋊D11—28no—
69C22×C22⋊D11—24no—
70C22×C22⋊D11C2314yes—
71C22×C22⋊D11C2318yes—
72C23×Dic11—28no—
73C23×Dic11—28no—
74C23×Dic11—24no—
75C23×Dic11—28no—
76C23×Dic11D4116yescomplemented
77C23×Dic11C2314yes—
78C23×Dic11C2312yes—
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2312yes—
81C23×Dic11C2318yes—
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C2×#4341—2128no—
85C2×#4341—264no—
86C2×#4341—232no—
87C22×C4×D11—28no—
88C22×C4×D11D418yescomplemented
89C22×C4×D11C2314yes—
90C22×Dic22—24no—
91C22×Dic22—28no—
92C22×Dic22C2314yes—
93C2×C11×C22⋊C4—24no—
94C2×C11×C22⋊C4—28no—
95C2×C11×C22⋊C4C2314yes—
96C2×C11×C22⋊C4C2318yes—
97C2×C22⋊Dic11—28no—
98C2×C22⋊Dic11—28no—
99C2×C22⋊Dic11—28no—
100C2×C22⋊Dic11C2318yes—
101C2×C22⋊Dic11C2318yes—
102C2×C22⋊Dic11C2318yes—
103D4×Dic11—264no—
104C2×(C2×D11)⋊C4—24no—
105C2×(C2×D11)⋊C4—28no—
106C2×(C2×D11)⋊C4C2314yes—
107C2×(C2×D11)⋊C4C2318yes—
108C2×C4⋊Dic11—28no—
109C2×C4⋊Dic11C2318yes—
110C2×Dic11⋊C4—24no—
111C2×Dic11⋊C4C2314yes—
112C2×C4×Dic11—24no—
113C2×C4×Dic11—28no—
114C2×C4×Dic11C2314yes—
115C2×C4×Dic11C2318yes—
116(C22⋊D11)⋊C4—232no—
117C11×#95C2314yes—
118C11⋊#95C2318yes—
119C11⋊#95C2314yes—
120C11⋊#95C2318yes—
121C2×#2388—111nomaximal, Sylow
122C24×C11—24no—
123C24×C11—22no—
124C24×C11—24no—
125C24×C11—24no—
126C24×C11—24no—
127C24×C11—24no—
128C24×C11—22no—
129C24×C11—24no—
130C24×C11—24no—
131C24×C11—24no—
132C24×C11C2×D418yes—
133C24×C11#4114yescomplemented
134C24×C11C2414yes—
135C24×C11C2412yes—
136C24×C11C2411yescharacteristic
137C23×D11—24no—
138C23×D11—24no—
139C23×D11—22no—
140C23×D11—22no—
141C23×D11C2×D414yes—
142C23×D11C2412yes—
143C2×D4×C11—232no—
144C2×D4×C11—264no—
145C2×D4×C11—216no—
146C2×D4×C11—216no—
147C2×D4×C11—216no—
148C2×D4×C11—28no—
149C2×D4×C11—216no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—24no—
153C22×C4×C11—22no—
154C22×C4×C11—24no—
155C22×C4×C11C2×D414yes—
156C22×C4×C11#4118yescomplemented
157C22×C4×C11C2412yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2414yes—
160C2×C22⋊D11—264no—
161C2×C22⋊D11—232no—
162C2×C22⋊D11—216no—
163C2×C22⋊D11—28no—
164C2×C22⋊D11—216no—
165C2×C22⋊D11—28no—
166C2×C22⋊D11—28no—
167C2×C22⋊D11—216no—
168C22×Dic11—264no—
169C22×Dic11—216no—
170C22×Dic11—216no—
171C22×Dic11—28no—
172C22×Dic11—216no—
173C22×Dic11—22no—
174C22×Dic11—24no—
175C22×Dic11—24no—
176C22×Dic11—24no—
177C22×Dic11—22no—
178C22×Dic11—24no—
179C22×Dic11—22no—
180C22×Dic11—24no—
181C22×Dic11—24no—
182C22×Dic11—416no—
183C22×Dic11C2×D418yes—
184C22×Dic11C2×D418yes—
185C22×Dic11C2×D414yes—
186C22×Dic11C2×D4132yescomplemented
187C22×Dic11#4114yescomplemented
188C22×Dic11C2414yes—
189C22×Dic11C2412yes—
190C22×Dic11C2414yes—
191C22×Dic11C2412yes—
192C22×Dic11C2412yes—
193#4341—2256no—
194C2×C4×D11—232no—
195C2×C4×D11—216no—
196C2×C4×D11C2×D4116yescomplemented
197C2×Dic22—232no—
198C2×Dic22—216no—
199C2×Dic22—28no—
200C11×C22⋊C4—28no—
201C11×C22⋊C4—216no—
202C22⋊Dic11—216no—
203C22⋊Dic11—216no—
204C22⋊Dic11—216no—
205(C2×D11)⋊C4—28no—
206(C2×D11)⋊C4—216no—
207C4⋊Dic11—216no—
208Dic11⋊C4—28no—
209C4×Dic11—28no—
210C4×Dic11—216no—
211C23×#41—111no—
212C22×C4×D4—112no—
213C22×C4×D4—111no—
214#2388—1116no—
215C2×#395—111no—
216C2×#394—111no—
217C2×#394—112no—
218C2×#393—111no—
219C2×#392—112no—
220C2×#392D1111yescharacteristic, complemented
221C2×C4×C22⋊C4—111no—
222C2×C4×C22⋊C4—112no—
223C23×C11—216no—
224C23×C11—28no—
225C23×C11—216no—
226C23×C11—216no—
227C23×C11—216no—
228C23×C11—24no—
229C23×C11—22no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—22no—
235C23×C11—24no—
236C23×C11—24no—
237C23×C11—24no—
238C23×C11—44no—
239C23×C11—48no—
240C23×C11—48no—
241C23×C11—44no—
242C23×C11—48no—
243C23×C11—48no—
244C23×C11—48no—
245C23×C11C22×D418yes—
246C23×C11C22×D412yes—
247C23×C11C22×D414yes—
248C23×C11C2×#4112yes—
249C23×C11C2×#4114yes—
250C23×C11C2×#4112yes—
251C23×C11C2×#4114yescomplemented
252C23×C11C2511yescharacteristic
253C22×D11—28no—
254C22×D11—28no—
255C22×D11—28no—
256C22×D11—24no—
257C22×D11—24no—
258C22×D11—22no—
259C22×D11—22no—
260C22×D11—48no—
261C22×D11—48no—
262C22×D11C22×D414yes—
263D4×C11—232no—
264D4×C11—264no—
265C2×C4×C11—28no—
266C2×C4×C11—216no—
267C2×C4×C11—24no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—22no—
271C2×C4×C11—24no—
272C2×C4×C11—44no—
273C2×C4×C11C22×D414yes—
274C2×C4×C11C2×#4118yescomplemented
275C22⋊D11—264no—
276C22⋊D11—232no—
277C2×Dic11—216no—
278C2×Dic11—28no—
279C2×Dic11—22no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—264no—
284C2×Dic11—24no—
285C2×Dic11—22no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—24no—
289C2×Dic11—44no—
290C2×Dic11—48no—
291C2×Dic11—416no—
292C2×Dic11#120116yes—
293C2×Dic11C22×D418yes—
294C2×Dic11C22×D418yes—
295C2×Dic11C22×D414yes—
296C2×Dic11C2×#4114yescomplemented
297C4×D11—232no—
298Dic22—232no—
299C22×#41—118no—
300C22×#41—2216no—
301C22×#41—228no—
302C23×Q8—111no—
303C23×D4—112no—
304C23×D4—111no—
305C23×D4C2×D1111yescharacteristic
306C23×D4C2×D1112yes—
307C24×C4—112no—
308C24×C4—111no—
309C24×C4—111no—
310C2×C4×D4—1116no—
311C2×C4×D4—118no—
312C2×C4×D4—228no—
313C2×C4×D4—2216no—
314C22×C4⋊C4—111no—
315C22×C4⋊C4—112no—
316C22×C22⋊C4—112no—
317C22×C22⋊C4—112no—
318C22×C22⋊C4—112no—
319C22×C22⋊C4—112no—
320C22×C22⋊C4—111no—
321C22×C22⋊C4C2×D1111yescharacteristic
322C22×C22⋊C4C2×D1112yes—
323C22×C42—111no—
324C22×C42—112no—
325#395—118no—
326#394—118no—
327#394—1116no—
328#393—118no—
329#392—1116no—
330#392C2×D1118yescomplemented
331C4×C22⋊C4—1116no—
332C4×C22⋊C4—118no—
333C2×#95—112no—
334C2×#95—112no—
335C2×#95—111no—
336C2×#95C2×D1111yescharacteristic
337C22×C11—28no—
338C22×C11—28no—
339C22×C11—28no—
340C22×C11—24no—
341C22×C11—28no—
342C22×C11—432no—
343C22×C11—416no—
344C22×C11—42no—
345C22×C11—44no—
346C22×C11—44no—
347C22×C11—44no—
348C22×C11—44no—
349C22×C11—42no—
350C22×C11—44no—
351C22×C11C2×#12014yes—
352C22×C11#52518yes—
353C22×C11#52514yes—
354C22×C11#53214yes—
355C22×C11#53218yes—
356C22×C11C23×D412yes—
357C22×C11C23×D411yescharacteristic
358C22×C11C22×#4111yescharacteristic
359C22×C11C22×#4112yes—
360C22×C11C22×#4111yescharacteristic
361C2×D11—24no—
362C2×D11—24no—
363C2×D11—24no—
364C2×D11—416no—
365C2×D11—44no—
366C2×D11—44no—
367C4×C11—24no—
368C4×C11—28no—
369C4×C11—42no—
370Dic11—28no—
371Dic11—24no—
372Dic11—42no—
373Dic11—44no—
374Dic11C2×#12018yes—
375C25—111no—
376C25C22×D1112yes—
377C25C22×D1111yescharacteristic
378C2×#41—2264no—
379C2×#41—2232no—
380C2×#41—22128no—
381C22×Q8—114no—
382C22×Q8—228no—
383C22×Q8—224no—
384C22×D4—28no—
385C22×D4—28no—
386C22×D4—28no—
387C22×D4—24no—
388C22×D4—28no—
389C22×D4—114no—
390C22×D4—118no—
391C22×D4—228no—
392C22×D4—224no—
393C22×D4—224no—
394C22×D4—228no—
395C22×D4—228no—
396C22×D4—224no—
397C22×D4C22×D1118yes—
398C22×D4C22×D1114yes—
399C23×C4—111no—
400C23×C4—1116no—
401C23×C4—118no—
402C23×C4—111no—
403C23×C4—112no—
404C23×C4—118no—
405C23×C4—114no—
406C23×C4—114no—
407C23×C4—112no—
408C23×C4—111no—
409C23×C4—228no—
410C23×C4—228no—
411C23×C4—228no—
412C23×C4—224no—
413C23×C4—228no—
414C23×C4C22×D1111yescharacteristic
415C23×C4C22×D1111yescharacteristic
416C23×C4C22×D1112yes—
417C4×D4—2232no—
418C4×D4—2264no—
419C2×C4⋊C4—114no—
420C2×C4⋊C4—118no—
421C2×C4⋊C4—228no—
422C2×C4⋊C4—224no—
423C2×C22⋊C4—24no—
424C2×C22⋊C4—28no—
425C2×C22⋊C4—118no—
426C2×C22⋊C4—118no—
427C2×C22⋊C4—118no—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—118no—
430C2×C22⋊C4—224no—
431C2×C22⋊C4—228no—
432C2×C22⋊C4—228no—
433C2×C22⋊C4—228no—
434C2×C22⋊C4—228no—
435C2×C22⋊C4C22×D1114yes—
436C2×C22⋊C4C22×D1118yes—
437C2×C42—114no—
438C2×C42—118no—
439C2×C42—228no—
440C2×C42—224no—
441#95—118no—
442#95—118no—
443#95—114no—
444#95C22×D1114yes—
445C2×C11—48no—
446C2×C11—44no—
447C2×C11#238818yescomplemented
448C2×C11C22×#12011yescharacteristic
449C2×C11C2×#52511yescharacteristic
450C2×C11C2×#52512yes—
451C2×C11C2×#53212yes—
452C2×C11C2×#53211yescharacteristic
453D11—44no—
454C24—22no—
455C24—24no—
456C24—24no—
457C24—24no—
458C24—24no—
459C24—24no—
460C24—24no—
461C24—24no—
462C24—24no—
463C24—22no—
464C24—114no—
465C24—112no—
466C24—224no—
467C24—224no—
468C24—222no—
469C24—222no—
470C24D4×D1118yes—
471C24#434114yescomplemented
472C24C23×D1114yes—
473C24C23×D1112yes—
474C24C23×D1111yescharacteristic
475#41—22256no—
476C2×Q8—2216no—
477C2×Q8—2232no—
478C2×Q8—228no—
479C2×D4—232no—
480C2×D4—264no—
481C2×D4—216no—
482C2×D4—216no—
483C2×D4—216no—
484C2×D4—28no—
485C2×D4—216no—
486C2×D4—2216no—
487C2×D4—228no—
488C2×D4—228no—
489C2×D4—2216no—
490C2×D4—2264no—
491C2×D4—2232no—
492C2×D4—2216no—
493C2×D4—228no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—24no—
499C22×C4—114no—
500C22×C4—118no—
501C22×C4—112no—
502C22×C4—118no—
503C22×C4—1132no—
504C22×C4—114no—
505C22×C4—112no—
506C22×C4—114no—
507C22×C4—1116no—
508C22×C4—114no—
509C22×C4—112no—
510C22×C4—2232no—
511C22×C4—2216no—
512C22×C4—2264no—
513C22×C4—2216no—
514C22×C4—2216no—
515C22×C4—228no—
516C22×C4—2216no—
517C22×C4—222no—
518C22×C4—224no—
519C22×C4—224no—
520C22×C4—222no—
521C22×C4—224no—
522C22×C4—222no—
523C22×C4—224no—
524C22×C4—224no—
525C22×C4—224no—
526C22×C4—4416no—
527C22×C4D4×D1114yes—
528C22×C4#434118yescomplemented
529C22×C4C23×D1112yes—
530C22×C4C23×D1112yes—
531C22×C4C23×D1114yes—
532C4⋊C4—2216no—
533C4⋊C4—228no—
534C22⋊C4—28no—
535C22⋊C4—216no—
536C22⋊C4—228no—
537C22⋊C4—2216no—
538C22⋊C4—2216no—
539C22⋊C4—2216no—
540C22⋊C4—2216no—
541C42—2216no—
542C42—228no—
543C11C2×#238811yescharacteristic, complemented, Sylow
544C23—216no—
545C23—216no—
546C23—216no—
547C23—216no—
548C23—28no—
549C23—22no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—24no—
554C23—24no—
555C23—24no—
556C23—24no—
557C23—24no—
558C23—22no—
559C23—44no—
560C23—48no—
561C23—48no—
562C23—44no—
563C23—48no—
564C23—48no—
565C23—48no—
566C23—114no—
567C23—228no—
568C23—228no—
569C23—228no—
570C23—224no—
571C23—224no—
572C23—222no—
573C23—222no—
574C23—448no—
575C23—448no—
576C23C2×D4×D1118yes—
577C23C2×D4×D1112yes—
578C23C2×D4×D1114yes—
579C23C2×#434114yes—
580C23C2×#434112yes—
581C23C2×#434114yescomplemented
582C23#41×D1112yes—
583C23C24×D1111yescharacteristic
584Q8—2232no—
585D4—264no—
586D4—232no—
587D4—2264no—
588D4—2232no—
589C2×C4—216no—
590C2×C4—28no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—22no—
595C2×C4—24no—
596C2×C4—44no—
597C2×C4—1116no—
598C2×C4—114no—
599C2×C4—118no—
600C2×C4—118no—
601C2×C4—114no—
602C2×C4—2232no—
603C2×C4—2264no—
604C2×C4—2216no—
605C2×C4—228no—
606C2×C4—222no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—222no—
610C2×C4—224no—
611C2×C4—222no—
612C2×C4—224no—
613C2×C4—224no—
614C2×C4—224no—
615C2×C4—4416no—
616C2×C4—444no—
617C2×C4—448no—
618C2×C4C2×D4×D1114yes—
619C2×C4C2×#434118yescomplemented
620C22—24no—
621C22—28no—
622C22—28no—
623C22—28no—
624C22—28no—
625C22—44no—
626C22—44no—
627C22—44no—
628C22—42no—
629C22—44no—
630C22—432no—
631C22—416no—
632C22—42no—
633C22—44no—
634C22—224no—
635C22—224no—
636C22—224no—
637C22—444no—
638C22—4416no—
639C22—444no—
640C22#1062311718yes—
641C22D11×#12014yes—
642C22#1062312718yes—
643C22#1062313714yes—
644C22#1062324714yes—
645C22C22×D4×D1111yescharacteristic
646C22C22×D4×D1112yes—
647C22C22×#434111yescharacteristic
648C22C22×#434112yes—
649C22C2×#41×D1111yescharacteristic
650C4—24no—
651C4—28no—
652C4—42no—
653C4—118no—
654C4—224no—
655C4—228no—
656C4—444no—
657C4—442no—
658C2—44no—
659C2—48no—
660C2—444no—
661C2#1307182818yesdirect product factor
662C2C2×D11×#12011yescharacteristic
663C2C2×#1062311712yes—
664C2C2×#1062313711yescharacteristic
665C2C2×#1062312712yes—
666C2C2×#1062324711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#392C2
socleC24×C11C24
hypercenterC2×#392D11
hypocenterC11C2×#2388
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C23×#4341C2semidirect
2. C22×D4×Dic11C2semidirect
3. C22×(C22⋊D11)⋊C4C2semidirect
4. #13071828C2direct (N × H)
5. C2×#10622269C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622835C2semidirect
8. C2×#10622560C2semidirect
9. C2×#10622836C2semidirect
10. C2×C22⋊C4×Dic11C2semidirect
11. C2×#10622279C2semidirect
12. C2×C11×#392C2semidirect
21. C22×#4341C22semidirect
30. C2×D4×Dic11C22semidirect
38. C2×(C22⋊D11)⋊C4C22semidirect
39. C11×#392C22semidirect
41. #10622836C22semidirect
42. #10622835C22semidirect
46. #10622574C22semidirect
47. #10622560C22semidirect
48. C22⋊C4×Dic11C22semidirect
49. #10622279C22semidirect
50. #10622269C22semidirect
76. C23×Dic11D4semidirect
88. C22×C4×D11D4semidirect
133. C24×C11#41semidirect
156. C22×C4×C11#41semidirect
186. C22×Dic11C2×D4semidirect
187. C22×Dic11#41semidirect
196. C2×C4×D11C2×D4semidirect
220. C2×#392D11semidirect
251. C23×C11C2×#41semidirect
274. C2×C4×C11C2×#41semidirect
296. C2×Dic11C2×#41semidirect
330. #392C2×D11semidirect
447. C2×C11#2388semidirect
471. C24#4341semidirect
528. C22×C4#4341semidirect
543. C11C2×#2388semidirect
581. C23C2×#4341semidirect
619. C2×C4C2×#4341semidirect
661. C2#13071828direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43412
C22×D4×Dic112
C22×(C22⋊D11)⋊C42
#130718282
C2×#106222692
C2×#106225742
C2×#106228352
C2×#106225602
C2×#106228362
C2×C22⋊C4×Dic112
C2×#106222792
C2×C11×#3922
C2×#238811