Finite Group Databasebeta

← C2×#13072196 #14921919

Subgroups — C2×#13072196 #14921919

Order 2816.

3894 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66999C211yesmaximal, characteristic, complemented
2C22×#66991C211yesmaximal, characteristic
3C22×D4×Dic11C211yesmaximal, characteristic, complemented
4#13072196C2116yesmaximal, direct product factor
5C2×#10622565C212yesmaximal, complemented
6C2×#10622572C212yesmaximal, complemented
7C2×#10622843C211yesmaximal, characteristic, complemented
8C2×#10622541C211yesmaximal, characteristic, complemented
9C2×#10622571C212yesmaximal, complemented
10C2×#10622555C212yesmaximal, complemented
11C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
12C22×C11×#124C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C23×C22⋊D11C2212yes—
16C24×Dic11C2212yes—
17C23×C4×D11C2211yescharacteristic
18C2×C11×#124—28no—
19C2×C11×#124C2218yescomplemented
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2212yes—
22C22×C42×C11C2211yescharacteristic
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C2×#66999—28no—
26C2×#66999C2218yescomplemented
27C2×#66991—28no—
28C2×#66991C2218yes—
29C2×D4×Dic11—28no—
30C2×D4×Dic11C2218yescomplemented
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2212yes—
34C22×C4⋊Dic11C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×Dic11⋊C4C2212yes—
37C22×Dic11⋊C4C2212yes—
38C22×C4×Dic11C2211yescharacteristic
39#10622843C2218yescomplemented
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2212yes—
45#10622572C22116yescomplemented
46#10622571C22116yescomplemented
47#10622565C22116yescomplemented
48#10622555C22116yescomplemented
49C4×(C2×D11)⋊C4C2218yescomplemented
50#10622541C2218yescomplemented
51C25×C11C2312yes—
52C24×D11C2311yescharacteristic
53C22×Q8×C11—24no—
54C22×Q8×C11—24no—
55C22×Q8×C11—24no—
56C22×Q8×C11C2314yes—
57C22×D4×C11—24no—
58C22×D4×C11—24no—
59C22×D4×C11D418yes—
60C22×D4×C11C2314yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2312yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—28no—
66C22×C22⋊D11—28no—
67C22×C22⋊D11—44no—
68C22×C22⋊D11C2318yes—
69C23×Dic11—28no—
70C23×Dic11—28no—
71C23×Dic11—44no—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2312yes—
75C23×Dic11C2318yes—
76C23×Dic11C2312yes—
77C23×Dic11C2311yescharacteristic
78C22×C4×D11—24no—
79C22×C4×D11—24no—
80C22×C4×D11—24no—
81C22×C4×D11C2314yes—
82C11×#124—232no—
83C2×C11×C22⋊C4—28no—
84C2×C11×C22⋊C4—28no—
85C2×C11×C22⋊C4C2318yes—
86C2×C11×C22⋊C4C2318yes—
87C2×C42×C11—24no—
88C2×C42×C11C2314yes—
89C2×C22⋊Dic11—28no—
90C2×C22⋊Dic11—28no—
91C2×C22⋊Dic11C2318yes—
92C2×C22⋊Dic11C2318yes—
93#66999—232no—
94#66991—232no—
95D4×Dic11—232no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—28no—
98C2×(C2×D11)⋊C4—24no—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2318yes—
102C2×C4⋊Dic11—24no—
103C2×C4⋊Dic11D418yescomplemented
104C2×C4⋊Dic11C2314yes—
105C2×C4⋊Dic11C2314yes—
106C2×Dic11⋊C4—28no—
107C2×Dic11⋊C4—44no—
108C2×Dic11⋊C4C2318yes—
109C2×Dic11⋊C4C2318yes—
110C2×C4×Dic11—24no—
111C2×C4×Dic11C2314yes—
112C11⋊#95C2318yes—
113C11⋊#95C2314yes—
114C11⋊#95C2314yes—
115C11⋊#95C2318yes—
116C11⋊#95C2318yes—
117C2×#2427—111nomaximal, Sylow
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—24no—
124C24×C11C2×D418yes—
125C24×C11C2414yes—
126C24×C11C2411yescharacteristic
127C23×D11—22no—
128C23×D11—22no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11—22no—
132C23×D11—22no—
133C23×D11#4114yes—
134C23×D11C2412yes—
135C2×Q8×C11—28no—
136C2×Q8×C11—28no—
137C2×Q8×C11—28no—
138C2×Q8×C11—416no—
139C2×D4×C11—232no—
140C2×D4×C11—28no—
141C2×D4×C11—28no—
142C2×D4×C11C2×D4116yes—
143C22×C4×C11—24no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—24no—
147C22×C4×C11—22no—
148C22×C4×C11—22no—
149C22×C4×C11—24no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11C2×D414yes—
153C22×C4×C11C2×D414yes—
154C22×C4×C11#4114yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2414yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2412yes—
159C2×C22⋊D11—216no—
160C2×C22⋊D11—216no—
161C2×C22⋊D11—48no—
162C2×C22⋊D11—432no—
163C22×Dic11—216no—
164C22×Dic11—216no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—22no—
168C22×Dic11—24no—
169C22×Dic11—22no—
170C22×Dic11—24no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—24no—
174C22×Dic11—24no—
175C22×Dic11—22no—
176C22×Dic11—24no—
177C22×Dic11—22no—
178C22×Dic11—48no—
179C22×Dic11—432no—
180C22×Dic11C2×D418yes—
181C22×Dic11#4114yes—
182C22×Dic11C2412yes—
183C22×Dic11C2414yes—
184C22×Dic11C2412yes—
185C22×Dic11C2414yes—
186C22×Dic11C2412yes—
187C2×C4×D11—28no—
188C2×C4×D11—28no—
189C2×C4×D11—28no—
190C2×C4×D11—416no—
191C11×C22⋊C4—216no—
192C11×C22⋊C4—216no—
193C42×C11—28no—
194C22⋊Dic11—216no—
195C22⋊Dic11—216no—
196(C2×D11)⋊C4—216no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—28no—
199C4⋊Dic11—28no—
200C4⋊Dic11C2×D4116yescomplemented
201Dic11⋊C4—216no—
202Dic11⋊C4—48no—
203C4×Dic11—28no—
204C22×#124D1111yescharacteristic, complemented
205C22×C22⋊Q8—111no—
206C22×#121—111no—
207C22×C4×D4—111no—
208#2427—1116no—
209C2×#397—112no—
210C2×#394—112no—
211C2×#391—111no—
212C2×#389—111no—
213C2×#386—112no—
214C2×#380—112no—
215C2×C4×C22⋊C4—111no—
216C23×C11—216no—
217C23×C11—216no—
218C23×C11—216no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—48no—
226C23×C11—48no—
227C23×C11—48no—
228C23×C11—48no—
229C23×C11C22×D412yes—
230C23×C11C22×D418yes—
231C23×C11C22×D412yes—
232C23×C11C2×#4112yes—
233C23×C11C2×#4112yes—
234C23×C11C2×#4112yes—
235C23×C11H(5,𝔽2)12yes—
236C23×C112−1+412yes—
237C23×C11C2511yescharacteristic
238C22×D11—28no—
239C22×D11—28no—
240C22×D11—28no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—44no—
248C22×D11—44no—
249C22×D11—44no—
250C22×D11—44no—
251C22×D11C2×#4114yes—
252Q8×C11—416no—
253D4×C11—232no—
254C2×C4×C11—24no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—48no—
264C2×C4×C11—44no—
265C2×C4×C11—44no—
266C2×C4×C11#121116yes—
267C2×C4×C11C22×D414yes—
268C2×C4×C11C22×D414yes—
269C2×C4×C11C2×#4114yes—
270C22⋊D11—432no—
271C2×Dic11—28no—
272C2×Dic11—216no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—22no—
279C2×Dic11—24no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—22no—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—22no—
286C2×Dic11—432no—
287C2×Dic11—44no—
288C2×Dic11—48no—
289C2×Dic11—44no—
290C2×Dic11C22×D418yes—
291C2×Dic11C2×#4114yes—
292C4×D11—416no—
293C23×Q8C2×D1111yescharacteristic
294C23×D4—112no—
295C23×D4C2×D1111yescharacteristic
296C24×C4—112no—
297C24×C4—111no—
298C2×#124—28no—
299C2×#124C2×D1118yescomplemented
300C2×C22⋊Q8—118no—
301C2×C22⋊Q8—228no—
302C2×#121—118no—
303C2×#121—228no—
304C2×C4×D4—118no—
305C2×C4×D4—228no—
306C22×C4⋊C4—111no—
307C22×C4⋊C4—112no—
308C22×C4⋊C4—111no—
309C22×C4⋊C4—112no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4—112no—
312C22×C22⋊C4—111no—
313C22×C22⋊C4—112no—
314C22×C22⋊C4—111no—
315C22×C22⋊C4C2×D1112yes—
316C22×C22⋊C4C2×D1112yes—
317C22×C42—111no—
318C22×C42C2×D1111yescharacteristic
319#397—1116no—
320#394—1116no—
321#391—118no—
322#389—118no—
323#386—1116no—
324#380—1116no—
325C4×C22⋊C4—118no—
326C2×#95—112no—
327C2×#95—111no—
328C2×#95—112no—
329C2×#95—111no—
330C2×#95—112no—
331C22×C11—28no—
332C22×C11—28no—
333C22×C11—28no—
334C22×C11—44no—
335C22×C11—432no—
336C22×C11—44no—
337C22×C11—44no—
338C22×C11—44no—
339C22×C11C2×#12114yes—
340C22×C11#52914yes—
341C22×C11#54214yes—
342C22×C11#54614yes—
343C22×C11#54614yes—
344C22×C11#54714yes—
345C22×C11#54814yes—
346C22×C11C23×D411yescharacteristic
347C22×C11C23×D411yescharacteristic
348C22×C11C22×#4111yescharacteristic
349C22×C11C22×#4111yescharacteristic
350C22×C11C22×#4111yescharacteristic
351C22×C11C2×H(5,𝔽2)11yescharacteristic
352C22×C11C2×2−1+411yescharacteristic
353C2×D11—24no—
354C2×D11—24no—
355C2×D11—24no—
356C2×D11—42no—
357C2×D11—416no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C4×C11—44no—
362C4×C11—42no—
363C4×C11—42no—
364C4×C11C2×#12118yes—
365Dic11—24no—
366Dic11—28no—
367Dic11—42no—
368Dic11—44no—
369Dic11—42no—
370C25—111no—
371C25C22×D1112yes—
372C22×Q8—24no—
373C22×Q8—24no—
374C22×Q8—24no—
375C22×Q8C22×D1114yes—
376C22×D4—24no—
377C22×D4—24no—
378C22×D4—118no—
379C22×D4—228no—
380C22×D4—228no—
381C22×D4—444no—
382C22×D4C22⋊D1118yes—
383C22×D4C22×D1114yes—
384C23×C4—112no—
385C23×C4—111no—
386C23×C4—111no—
387C23×C4—111no—
388C23×C4—112no—
389C23×C4—118no—
390C23×C4—114no—
391C23×C4—228no—
392C23×C4—228no—
393C23×C4—224no—
394C23×C4—224no—
395C23×C4—224no—
396C23×C4—444no—
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1112yes—
399C23×C4C22×D1111yescharacteristic
400C23×C4C22×D1111yescharacteristic
401#124—232no—
402C22⋊Q8—2232no—
403#121—2232no—
404C4×D4—2232no—
405C2×C4⋊C4—118no—
406C2×C4⋊C4—114no—
407C2×C4⋊C4—114no—
408C2×C4⋊C4—118no—
409C2×C4⋊C4—118no—
410C2×C4⋊C4—228no—
411C2×C4⋊C4—224no—
412C2×C4⋊C4—444no—
413C2×C22⋊C4—28no—
414C2×C22⋊C4—28no—
415C2×C22⋊C4—118no—
416C2×C22⋊C4—118no—
417C2×C22⋊C4—118no—
418C2×C22⋊C4—114no—
419C2×C22⋊C4—114no—
420C2×C22⋊C4—228no—
421C2×C22⋊C4—224no—
422C2×C22⋊C4—224no—
423C2×C22⋊C4—228no—
424C2×C22⋊C4—228no—
425C2×C22⋊C4C22×D1118yes—
426C2×C22⋊C4C22×D1118yes—
427C2×C42—24no—
428C2×C42—114no—
429C2×C42—224no—
430C2×C42C22×D1114yes—
431#95—114no—
432#95—114no—
433#95—118no—
434#95—118no—
435#95—118no—
436C2×C11—48no—
437C2×C11#242718yescomplemented
438C2×C11C22×#12111yescharacteristic
439C2×C11C2×#52911yescharacteristic
440C2×C11C2×#54211yescharacteristic
441C2×C11C2×#54611yescharacteristic
442C2×C11C2×#54611yescharacteristic
443C2×C11C2×#54711yescharacteristic
444C2×C11C2×#54811yescharacteristic
445D11—44no—
446C24—24no—
447C24—24no—
448C24—24no—
449C24—24no—
450C24—24no—
451C24—24no—
452C24—114no—
453C24—112no—
454C24—222no—
455C24—222no—
456C24—222no—
457C24—222no—
458C24—222no—
459C24—222no—
460C24C2×C22⋊D1118yes—
461C24C23×D1114yes—
462C24C23×D1111yescharacteristic
463C2×Q8—28no—
464C2×Q8—28no—
465C2×Q8—28no—
466C2×Q8—416no—
467C2×D4—232no—
468C2×D4—28no—
469C2×D4—28no—
470C2×D4—2216no—
471C2×D4—2216no—
472C2×D4—448no—
473C2×D4—4432no—
474C2×D4C2×C22⋊D11116yes—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—24no—
484C22×C4—118no—
485C22×C4—114no—
486C22×C4—112no—
487C22×C4—114no—
488C22×C4—112no—
489C22×C4—114no—
490C22×C4—112no—
491C22×C4—2216no—
492C22×C4—2216no—
493C22×C4—222no—
494C22×C4—224no—
495C22×C4—224no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—222no—
499C22×C4—222no—
500C22×C4—222no—
501C22×C4—224no—
502C22×C4—224no—
503C22×C4—222no—
504C22×C4—222no—
505C22×C4—224no—
506C22×C4—228no—
507C22×C4—228no—
508C22×C4—228no—
509C22×C4—448no—
510C22×C4—4432no—
511C22×C4—4416no—
512C22×C4D4×D1114yes—
513C22×C4#434114yes—
514C22×C4C2×C22⋊D1114yes—
515C22×C4C23×D1112yes—
516C22×C4C23×D1114yes—
517C22×C4C23×D1112yes—
518C22×C4C23×D1112yes—
519C4⋊C4—1116no—
520C4⋊C4—2216no—
521C4⋊C4—228no—
522C4⋊C4—448no—
523C22⋊C4—216no—
524C22⋊C4—216no—
525C22⋊C4—2216no—
526C22⋊C4—228no—
527C22⋊C4—228no—
528C22⋊C4—2216no—
529C22⋊C4—2216no—
530C42—28no—
531C42—228no—
532C11C2×#242711yescharacteristic, complemented, Sylow
533C23—216no—
534C23—216no—
535C23—216no—
536C23—24no—
537C23—24no—
538C23—24no—
539C23—24no—
540C23—24no—
541C23—24no—
542C23—48no—
543C23—48no—
544C23—48no—
545C23—48no—
546C23—114no—
547C23—228no—
548C23—222no—
549C23—222no—
550C23—222no—
551C23—222no—
552C23—222no—
553C23—222no—
554C23—228no—
555C23—228no—
556C23—444no—
557C23—444no—
558C23—444no—
559C23—444no—
560C23C2×D4×D1112yes—
561C23C2×#434112yes—
562C23#41×D1112yes—
563C23#41×D1112yes—
564C23#6704212yes—
565C23#6704312yes—
566C23C22×C22⋊D1118yes—
567C23C22×C22⋊D1112yes—
568C23C24×D1111yescharacteristic
569Q8—416no—
570D4—232no—
571D4—4432no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—48no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—118no—
585C2×C4—114no—
586C2×C4—222no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—222no—
590C2×C4—228no—
591C2×C4—2216no—
592C2×C4—222no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—222no—
596C2×C4—224no—
597C2×C4—224no—
598C2×C4—222no—
599C2×C4—222no—
600C2×C4—224no—
601C2×C4—4432no—
602C2×C4—444no—
603C2×C4—448no—
604C2×C4—444no—
605C2×C4—4416no—
606C2×C4#66992116yes—
607C2×C4C2×D4×D1114yes—
608C2×C4C2×#434114yes—
609C2×C4C22×C22⋊D1114yes—
610C22—28no—
611C22—28no—
612C22—28no—
613C22—44no—
614C22—432no—
615C22—44no—
616C22—44no—
617C22—44no—
618C22—224no—
619C22—224no—
620C22—224no—
621C22—4416no—
622C22—442no—
623C22—442no—
624C22—442no—
625C22—442no—
626C22#1062320714yes—
627C22#1062320814yes—
628C22#1062321114yes—
629C22#1062321314yes—
630C22C2×#6699214yes—
631C22#1062335514yes—
632C22#1062336014yes—
633C22C22×D4×D1111yescharacteristic
634C22C22×#434111yescharacteristic
635C22C2×#41×D1111yescharacteristic
636C22C2×#41×D1111yescharacteristic
637C22C2×#6704211yescharacteristic
638C22C2×#6704311yescharacteristic
639C22C23×C22⋊D1111yescharacteristic
640C4—42no—
641C4—42no—
642C4—44no—
643C4—224no—
644C4—228no—
645C4—444no—
646C4—442no—
647C4—442no—
648C4C2×#6699218yes—
649C2—48no—
650C2—444no—
651C2#1307219618yesdirect product factor
652C2C22×#6699211yescharacteristic
653C2C2×#1062321111yescharacteristic
654C2C2×#1062321311yescharacteristic
655C2C2×#1062336011yescharacteristic
656C2C2×#1062320711yescharacteristic
657C2C2×#1062335511yescharacteristic
658C2C2×#1062320811yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#124C2
socleC24×C11C24
prime radicalC22×#66991C2
hypercenterC22×#124D11
hypocenterC11C2×#2427
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#124

Complements

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

NH ≅ G/Ntype
1. C22×#66999C2semidirect
3. C22×D4×Dic11C2semidirect
4. #13072196C2direct (N × H)
5. C2×#10622565C2semidirect
6. C2×#10622572C2semidirect
7. C2×#10622843C2semidirect
8. C2×#10622541C2semidirect
9. C2×#10622571C2semidirect
10. C2×#10622555C2semidirect
11. C2×C4×(C2×D11)⋊C4C2semidirect
12. C22×C11×#124C2semidirect
19. C2×C11×#124C22semidirect
26. C2×#66999C22semidirect
30. C2×D4×Dic11C22semidirect
39. #10622843C22semidirect
45. #10622572C22semidirect
46. #10622571C22semidirect
47. #10622565C22semidirect
48. #10622555C22semidirect
49. C4×(C2×D11)⋊C4C22semidirect
50. #10622541C22semidirect
103. C2×C4⋊Dic11D4semidirect
200. C4⋊Dic11C2×D4semidirect
204. C22×#124D11semidirect
299. C2×#124C2×D11semidirect
437. C2×C11#2427semidirect
532. C11C2×#2427semidirect
651. C2#13072196direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669992
C22×#669912
C22×D4×Dic112
#130721962
C2×#106225652
C2×#106225722
C2×#106228432
C2×#106225412
C2×#106225712
C2×#106225552
C2×C4×(C2×D11)⋊C42
C22×C11×#1242
C2×#242711