Finite Group Databasebeta

← C2×#13072130 #14921648

Subgroups — C2×#13072130 #14921648

Order 2816.

3830 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×#66936C212yesmaximal, complemented
2C22×#66983C211yesmaximal, characteristic
3C22×C4×D44C211yesmaximal, characteristic, complemented
4#13072130C2116yesmaximal, direct product factor
5C2×#10622287C212yesmaximal, complemented
6C2×#10622574C212yesmaximal, complemented
7C2×#10622552C211yesmaximal, characteristic, complemented
8C2×#10622541C211yesmaximal, characteristic, complemented
9C2×#10622281C212yesmaximal, complemented
10C2×#10622548C211yesmaximal, characteristic, complemented
11C2×#10622825C211yesmaximal, characteristic, complemented
12C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×D44C2211yescharacteristic
16C23×C4×D11C2212yes—
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C2×#66983—28no—
23C2×#66983C2218yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2212yes—
32C22×C4⋊Dic11C2212yes—
33C22×Dic11⋊C4C2212yes—
34C2×#66936—216no—
35C2×#66936C22116yescomplemented
36C2×C4×D44—28no—
37C2×C4×D44C2218yescomplemented
38C4×C11×C22⋊C4C2218yescomplemented
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2211yescharacteristic
41#10622825C2218yescomplemented
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44#10622574C22116yescomplemented
45#10622552C2218yescomplemented
46#10622548C2218yescomplemented
47#10622541C2218yescomplemented
48#10622287C22116yescomplemented
49#10622281C22116yescomplemented
50C25×C11C2311yescharacteristic
51C24×D11C2312yes—
52C23×C4×C11—24no—
53C23×C4×C11—24no—
54C23×C4×C11—24no—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2314yes—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2311yescharacteristic
62C22×C22⋊D11—28no—
63C22×C22⋊D11—28no—
64C22×C22⋊D11—44no—
65C22×C22⋊D11C2318yes—
66C23×Dic11C2312yes—
67C23×Dic11C2312yes—
68C23×Dic11C2312yes—
69C22×D44—24no—
70C22×D44—24no—
71C22×D44D418yes—
72C22×D44C2314yes—
73C22×C4×D11—28no—
74C22×C4×D11—28no—
75C22×C4×D11—44no—
76C22×C4×D11C2318yes—
77C2×C11×C22⋊C4—24no—
78C2×C11×C22⋊C4D418yescomplemented
79C2×C11×C22⋊C4C2314yes—
80C2×C11×C22⋊C4C2314yes—
81C2×C42×C11—24no—
82C2×C42×C11—24no—
83C2×C42×C11C2314yes—
84C2×C42×C11C2314yes—
85C2×C22⋊Dic11—28no—
86C2×C22⋊Dic11C2318yes—
87#66983—232no—
88C2×(C2×D11)⋊C4—28no—
89C2×(C2×D11)⋊C4—28no—
90C2×(C2×D11)⋊C4—28no—
91C2×(C2×D11)⋊C4—28no—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×C4⋊Dic11—24no—
97C2×C4⋊Dic11—28no—
98C2×C4⋊Dic11—24no—
99C2×C4⋊Dic11—24no—
100C2×C4⋊Dic11—44no—
101C2×C4⋊Dic11C2314yes—
102C2×C4⋊Dic11C2318yes—
103C2×C4⋊Dic11C2314yes—
104C2×C4⋊Dic11C2314yes—
105C2×C4⋊Dic11C2318yes—
106C2×Dic11⋊C4—28no—
107C2×Dic11⋊C4C2318yes—
108#66936—264no—
109C4×D44—232no—
110C11×#95C2314yes—
111C11×#95C2314yes—
112C11⋊#95C2318yes—
113C11⋊#95C2318yes—
114C2×#2422—111nomaximal, Sylow
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11C2×D414yes—
122C24×C11C2412yes—
123C24×C11C2411yescharacteristic
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11C2×D418yes—
131C23×D11C2414yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11—22no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—28no—
145C22×C4×C11—28no—
146C22×C4×C11—28no—
147C22×C4×C11—416no—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D414yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11#4114yes—
152C22×C4×C11#4114yes—
153C22×C4×C11#4114yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2412yes—
159C22×C4×C11C2412yes—
160C2×C22⋊D11—216no—
161C2×C22⋊D11—216no—
162C2×C22⋊D11—48no—
163C2×C22⋊D11—432no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11—24no—
172C22×Dic11—24no—
173C22×Dic11C2414yes—
174C22×Dic11C2414yes—
175C22×Dic11C2414yes—
176C2×D44—232no—
177C2×D44—28no—
178C2×D44—28no—
179C2×D44C2×D4116yes—
180C2×C4×D11—216no—
181C2×C4×D11—216no—
182C2×C4×D11—48no—
183C2×C4×D11—432no—
184C11×C22⋊C4—28no—
185C11×C22⋊C4C2×D4116yescomplemented
186C42×C11—28no—
187C42×C11—28no—
188C22⋊Dic11—216no—
189(C2×D11)⋊C4—216no—
190(C2×D11)⋊C4—216no—
191(C2×D11)⋊C4—216no—
192(C2×D11)⋊C4—216no—
193C4⋊Dic11—28no—
194C4⋊Dic11—216no—
195C4⋊Dic11—28no—
196C4⋊Dic11—28no—
197C4⋊Dic11—48no—
198Dic11⋊C4—216no—
199C22×#123—112no—
200C22×#121—111no—
201C22×C4×D4—111no—
202#2422—1116no—
203C2×#397—112no—
204C2×#394—112no—
205C2×#390—111no—
206C2×#389—111no—
207C2×#385—112no—
208C2×#384—111no—
209C2×#380—111no—
210C2×C4×C22⋊C4D1111yescharacteristic, complemented
211C23×C11—28no—
212C23×C11—28no—
213C23×C11—28no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11—44no—
224C23×C11C22×D414yes—
225C23×C11C22×D412yes—
226C23×C11C22×D412yes—
227C23×C11C2×#4112yes—
228C23×C11C2×#4112yes—
229C23×C11C2×#4112yes—
230C23×C11H(5,𝔽2)12yes—
231C23×C112−1+412yes—
232C23×C11C2511yescharacteristic
233C22×D11—216no—
234C22×D11—216no—
235C22×D11—216no—
236C22×D11—24no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—24no—
240C22×D11—24no—
241C22×D11—24no—
242C22×D11—48no—
243C22×D11—48no—
244C22×D11—48no—
245C22×D11—48no—
246C22×D11C22×D418yes—
247C2×C4×C11—28no—
248C2×C4×C11—28no—
249C2×C4×C11—28no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—44no—
263C2×C4×C11—44no—
264C2×C4×C11—416no—
265C2×C4×C11#123116yescomplemented
266C2×C4×C11C22×D414yes—
267C2×C4×C11C22×D414yes—
268C2×C4×C11C22×D414yes—
269C2×C4×C11C2×#4114yes—
270C2×C4×C11C2×#4114yes—
271C2×C4×C11C2×#4114yes—
272C22⋊D11—432no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—48no—
283C2×Dic11—48no—
284C2×Dic11—48no—
285D44—232no—
286C4×D11—432no—
287C23×D4—112no—
288C23×D4—111no—
289C24×C4—112no—
290C24×C4C2×D1111yescharacteristic
291C2×#123—1116no—
292C2×#123—2216no—
293C2×#121—118no—
294C2×#121—228no—
295C2×C4×D4—118no—
296C2×C4×D4—228no—
297C22×C4⋊C4—112no—
298C22×C4⋊C4—112no—
299C22×C4⋊C4—111no—
300C22×C4⋊C4—111no—
301C22×C4⋊C4—111no—
302C22×C4⋊C4—112no—
303C22×C22⋊C4—112no—
304C22×C22⋊C4—112no—
305C22×C22⋊C4—112no—
306C22×C22⋊C4—112no—
307C22×C22⋊C4—112no—
308C22×C22⋊C4C2×D1111yescharacteristic
309C22×C22⋊C4C2×D1111yescharacteristic
310C22×C42C2×D1111yescharacteristic
311C22×C42C2×D1111yescharacteristic
312#397—1116no—
313#394—1116no—
314#390—118no—
315#389—118no—
316#385—1116no—
317#384—118no—
318#380—118no—
319C4×C22⋊C4C2×D1118yescomplemented
320C2×#95—112no—
321C2×#95—112no—
322C2×#95C2×D1111yescharacteristic
323C2×#95C2×D1111yescharacteristic
324C22×C11—24no—
325C22×C11—24no—
326C22×C11—24no—
327C22×C11—42no—
328C22×C11—416no—
329C22×C11—42no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11C2×#12314yes—
333C22×C11#53214yes—
334C22×C11#54214yes—
335C22×C11D4214yes—
336C22×C11#54714yes—
337C22×C11#54714yes—
338C22×C11#55314yes—
339C22×C11C23×D411yescharacteristic
340C22×C11C23×D411yescharacteristic
341C22×C11C22×#4111yescharacteristic
342C22×C11C22×#4111yescharacteristic
343C22×C11C22×#4111yescharacteristic
344C22×C11C2×H(5,𝔽2)11yescharacteristic
345C22×C11C2×2−1+411yescharacteristic
346C2×D11—28no—
347C2×D11—28no—
348C2×D11—28no—
349C2×D11—44no—
350C2×D11—432no—
351C2×D11—44no—
352C2×D11—44no—
353C2×D11—44no—
354C4×C11—24no—
355C4×C11—24no—
356C4×C11—24no—
357C4×C11—42no—
358C4×C11—42no—
359C4×C11C2×#12318yescomplemented
360Dic11—44no—
361Dic11—44no—
362Dic11—44no—
363C25—112no—
364C25C22×D1111yescharacteristic
365C22×D4—118no—
366C22×D4—118no—
367C22×D4—114no—
368C22×D4—228no—
369C22×D4—228no—
370C22×D4—224no—
371C22×D4—224no—
372C22×D4—444no—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—112no—
377C23×C4—112no—
378C23×C4—112no—
379C23×C4—118no—
380C23×C4—228no—
381C23×C4—228no—
382C23×C4—444no—
383C23×C4C22×D1114yes—
384C23×C4C22×D1111yescharacteristic
385C23×C4C22×D1111yescharacteristic
386C23×C4C22×D1111yescharacteristic
387C23×C4C22×D1111yescharacteristic
388C23×C4C22×D1111yescharacteristic
389C23×C4C22×D1111yescharacteristic
390#123—2264no—
391#121—2232no—
392C4×D4—2232no—
393C2×C4⋊C4—114no—
394C2×C4⋊C4—114no—
395C2×C4⋊C4—118no—
396C2×C4⋊C4—118no—
397C2×C4⋊C4—114no—
398C2×C4⋊C4—118no—
399C2×C4⋊C4—228no—
400C2×C4⋊C4—228no—
401C2×C4⋊C4—224no—
402C2×C4⋊C4—224no—
403C2×C4⋊C4—224no—
404C2×C4⋊C4—444no—
405C2×C22⋊C4—24no—
406C2×C22⋊C4—118no—
407C2×C22⋊C4—118no—
408C2×C22⋊C4—118no—
409C2×C22⋊C4—118no—
410C2×C22⋊C4—118no—
411C2×C22⋊C4—228no—
412C2×C22⋊C4—228no—
413C2×C22⋊C4—228no—
414C2×C22⋊C4—228no—
415C2×C22⋊C4—228no—
416C2×C22⋊C4D4418yescomplemented
417C2×C22⋊C4C22×D1114yes—
418C2×C22⋊C4C22×D1114yes—
419C2×C42—24no—
420C2×C42—24no—
421C2×C42C22×D1114yes—
422C2×C42C22×D1114yes—
423#95—118no—
424#95—118no—
425#95C22×D1114yes—
426#95C22×D1114yes—
427C2×C11—44no—
428C2×C11#242218yescomplemented
429C2×C11C22×#12311yescharacteristic
430C2×C11C2×#53211yescharacteristic
431C2×C11C2×#54211yescharacteristic
432C2×C11C2×D4211yescharacteristic
433C2×C11C2×#54711yescharacteristic
434C2×C11C2×#54711yescharacteristic
435C2×C11C2×#55311yescharacteristic
436D11—48no—
437C24—22no—
438C24—22no—
439C24—22no—
440C24—22no—
441C24—22no—
442C24—22no—
443C24—118no—
444C24—114no—
445C24—224no—
446C24—224no—
447C24—224no—
448C24—224no—
449C24—224no—
450C24—224no—
451C24C2×D4414yes—
452C24C23×D1112yes—
453C24C23×D1111yescharacteristic
454C2×D4—1116no—
455C2×D4—2216no—
456C2×D4—2216no—
457C2×D4—2232no—
458C2×D4—228no—
459C2×D4—228no—
460C2×D4—448no—
461C2×D4—4432no—
462C22×C4—22no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—22no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—28no—
475C22×C4—28no—
476C22×C4—28no—
477C22×C4—416no—
478C22×C4—114no—
479C22×C4—114no—
480C22×C4—114no—
481C22×C4—2216no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—224no—
489C22×C4—224no—
490C22×C4—224no—
491C22×C4—2216no—
492C22×C4—448no—
493C22×C4—4432no—
494C22×C4C2×D4414yes—
495C22×C4C2×D4414yes—
496C22×C4#433914yes—
497C22×C4#433914yes—
498C22×C4D4×D1114yes—
499C22×C4#434114yes—
500C22×C4C23×D1112yes—
501C22×C4C23×D1112yes—
502C22×C4C23×D1112yes—
503C22×C4C23×D1112yes—
504C22×C4C23×D1112yes—
505C22×C4C23×D1112yes—
506C4⋊C4—2216no—
507C4⋊C4—2216no—
508C4⋊C4—228no—
509C4⋊C4—228no—
510C4⋊C4—228no—
511C4⋊C4—448no—
512C22⋊C4—28no—
513C22⋊C4—2216no—
514C22⋊C4—2216no—
515C22⋊C4—2216no—
516C22⋊C4—2216no—
517C22⋊C4—2216no—
518C22⋊C4C2×D44116yescomplemented
519C42—28no—
520C42—28no—
521C11C2×#242211yescharacteristic, complemented, Sylow
522C23—28no—
523C23—28no—
524C23—28no—
525C23—22no—
526C23—22no—
527C23—22no—
528C23—22no—
529C23—22no—
530C23—22no—
531C23—44no—
532C23—44no—
533C23—44no—
534C23—44no—
535C23—118no—
536C23—2216no—
537C23—2216no—
538C23—2216no—
539C23—224no—
540C23—224no—
541C23—224no—
542C23—224no—
543C23—224no—
544C23—224no—
545C23—448no—
546C23—448no—
547C23—448no—
548C23—448no—
549C23C22×D4414yes—
550C23C22×D4412yes—
551C23C2×#433912yes—
552C23C2×#433912yes—
553C23C2×D4×D1112yes—
554C23C2×#434112yes—
555C23#6704212yes—
556C23#6704312yes—
557C23C24×D1111yescharacteristic
558D4—2232no—
559D4—4432no—
560C2×C4—28no—
561C2×C4—28no—
562C2×C4—28no—
563C2×C4—22no—
564C2×C4—22no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—22no—
568C2×C4—22no—
569C2×C4—22no—
570C2×C4—22no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—44no—
576C2×C4—44no—
577C2×C4—416no—
578C2×C4—224no—
579C2×C4—224no—
580C2×C4—224no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—4432no—
588C2×C4—448no—
589C2×C4—448no—
590C2×C4—448no—
591C2×C4#66936116yescomplemented
592C2×C4C22×D4414yes—
593C2×C4C22×D4414yes—
594C2×C4C2×#433914yes—
595C2×C4C2×#433914yes—
596C2×C4C2×D4×D1114yes—
597C2×C4C2×#434114yes—
598C22—24no—
599C22—24no—
600C22—24no—
601C22—416no—
602C22—42no—
603C22—42no—
604C22—42no—
605C22—42no—
606C22—228no—
607C22—228no—
608C22—228no—
609C22—4432no—
610C22—444no—
611C22—444no—
612C22—444no—
613C22—444no—
614C22#1062300814yes—
615C22C2×#6693614yes—
616C22#1062306514yes—
617C22D4×D4414yes—
618C22#1062308214yes—
619C22#1062308614yes—
620C22#1062309614yes—
621C22C23×D4411yescharacteristic
622C22C22×#433911yescharacteristic
623C22C22×#433911yescharacteristic
624C22C22×D4×D1111yescharacteristic
625C22C22×#434111yescharacteristic
626C22C2×#6704211yescharacteristic
627C22C2×#6704311yescharacteristic
628C4—24no—
629C4—24no—
630C4—24no—
631C4—42no—
632C4—42no—
633C4—444no—
634C4—444no—
635C4—444no—
636C4C2×#6693618yescomplemented
637C2—44no—
638C2—448no—
639C2#1307213018yesdirect product factor
640C2C22×#6693611yescharacteristic
641C2C2×#1062300811yescharacteristic
642C2C2×#1062306511yescharacteristic
643C2C2×D4×D4411yescharacteristic
644C2C2×#1062308611yescharacteristic
645C2C2×#1062308211yescharacteristic
646C2C2×#1062309611yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC22×#66983C2
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2422
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#66936C2semidirect
3. C22×C4×D44C2semidirect
4. #13072130C2direct (N × H)
5. C2×#10622287C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622552C2semidirect
8. C2×#10622541C2semidirect
9. C2×#10622281C2semidirect
10. C2×#10622548C2semidirect
11. C2×#10622825C2semidirect
12. C2×C4×C11×C22⋊C4C2semidirect
35. C2×#66936C22semidirect
37. C2×C4×D44C22semidirect
38. C4×C11×C22⋊C4C22semidirect
41. #10622825C22semidirect
44. #10622574C22semidirect
45. #10622552C22semidirect
46. #10622548C22semidirect
47. #10622541C22semidirect
48. #10622287C22semidirect
49. #10622281C22semidirect
78. C2×C11×C22⋊C4D4semidirect
185. C11×C22⋊C4C2×D4semidirect
210. C2×C4×C22⋊C4D11semidirect
265. C2×C4×C11#123semidirect
319. C4×C22⋊C4C2×D11semidirect
359. C4×C11C2×#123semidirect
416. C2×C22⋊C4D44semidirect
428. C2×C11#2422semidirect
518. C22⋊C4C2×D44semidirect
521. C11C2×#2422semidirect
591. C2×C4#66936semidirect
636. C4C2×#66936semidirect
639. C2#13072130direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669362
C22×#669832
C22×C4×D442
#130721302
C2×#106222872
C2×#106225742
C2×#106225522
C2×#106225412
C2×#106222812
C2×#106225482
C2×#106228252
C2×C4×C11×C22⋊C42
C2×#242211