Finite Group Databasebeta

← C2×#13072227 #14922408

Subgroups — C2×#13072227 #14922408

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
1C23×#4343C211yesmaximal, characteristic, complemented
2C22×#66947C211yesmaximal, characteristic, complemented
3C22×#66948C212yesmaximal, complemented
4#13072227C2116yesmaximal, direct product factor
5C2×#10622604C211yesmaximal, characteristic, complemented
6C2×#10622844C211yesmaximal, characteristic, complemented
7C2×#10622284C211yesmaximal, characteristic, complemented
8C2×#10622278C212yesmaximal, complemented
9C2×#10622278C212yesmaximal, complemented
10C2×#10622602C212yesmaximal, complemented
11C2×D11×#95C211yesmaximal, characteristic, complemented
12C2×C11×#395C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C22×#4343—216no—
15C22×#4343—28no—
16C22×#4343C2218yescomplemented
17C23×D44C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×D44C2212yes—
20C23×D44C2212yes—
21C23×C4×D11C2212yes—
22C23×C4×D11C2212yes—
23C23×C4×D11C2211yescharacteristic
24C22×C11×C4⋊C4C2212yes—
25C22×C11×C4⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2212yes—
31C22×(C2×D11)⋊C4C2211yescharacteristic
32C22×(C2×D11)⋊C4C2212yes—
33C22×Dic11⋊C4C2211yescharacteristic
34C2×#66948—216no—
35C2×#66948C22116yescomplemented
36C2×#66947—28no—
37C2×#66947C2218yescomplemented
38C11×#395C2218yescomplemented
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2212yes—
41#10622844C2218yescomplemented
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2212yes—
45#10622604C2218yescomplemented
46#10622602C22116yescomplemented
47#10622284C2218yescomplemented
48#10622278C22116yescomplemented
49#10622278C22116yescomplemented
50D11×#95C2218yescomplemented
51C24×D11C2311yescharacteristic
52C24×D11C2312yes—
53C24×D11C2311yescharacteristic
54C22×Q8×C11—28no—
55C22×Q8×C11—24no—
56C22×Q8×C11C2314yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C23×C4×C11C2312yes—
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2312yes—
64C23×Dic11C2311yescharacteristic
65C2×#4343—2128no—
66C2×#4343—264no—
67C2×#4343—232no—
68C22×D44—28no—
69C22×D44—28no—
70C22×D44—28no—
71C22×D44—24no—
72C22×D44—24no—
73C22×D44—28no—
74C22×D44—28no—
75C22×D44—28no—
76C22×D44—44no—
77C22×D44D4116yescomplemented
78C22×D44C2314yes—
79C22×D44C2314yes—
80C22×D44C2318yes—
81C22×D44C2318yes—
82C22×C4×D11—28no—
83C22×C4×D11—28no—
84C22×C4×D11—28no—
85C22×C4×D11—28no—
86C22×C4×D11—28no—
87C22×C4×D11—28no—
88C22×C4×D11—44no—
89C22×C4×D11D418yescomplemented
90C22×C4×D11C2318yes—
91C22×C4×D11C2318yes—
92C22×C4×D11C2314yes—
93C2×C11×C4⋊C4—24no—
94C2×C11×C4⋊C4—28no—
95C2×C11×C4⋊C4C2314yes—
96C2×C11×C4⋊C4C2318yes—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—28no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4—28no—
101C2×(C2×D11)⋊C4—28no—
102C2×(C2×D11)⋊C4—24no—
103C2×(C2×D11)⋊C4—44no—
104C2×(C2×D11)⋊C4C2314yes—
105C2×(C2×D11)⋊C4C2314yes—
106C2×(C2×D11)⋊C4C2314yes—
107C2×(C2×D11)⋊C4C2318yes—
108C2×(C2×D11)⋊C4C2318yes—
109C2×(C2×D11)⋊C4C2318yes—
110C2×(C2×D11)⋊C4C2318yes—
111C2×Dic11⋊C4—24no—
112C2×Dic11⋊C4C2314yes—
113#66948—264no—
114#66947—232no—
115C11×#95C2314yes—
116C11×#95C2318yes—
117C11⋊#95C2318yes—
118C11⋊#95C2314yes—
119C11⋊#95C2318yes—
120C2×#2430—111nomaximal, Sylow
121C24×C11C2411yescharacteristic
122C23×D11—24no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—24no—
131C23×D11—22no—
132C23×D11—24no—
133C23×D11—24no—
134C23×D11—22no—
135C23×D11—22no—
136C23×D11C2×D418yes—
137C23×D11C2×D414yes—
138C23×D11C2×D418yes—
139C23×D11C2412yes—
140C23×D11C2414yes—
141C23×D11C2412yes—
142C2×Q8×C11—232no—
143C2×Q8×C11—216no—
144C2×Q8×C11—28no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—24no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11C2×D418yes—
156C22×C4×C11C2×D414yes—
157C22×C4×C11#4118yescomplemented
158C22×C4×C11C2412yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2414yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2414yes—
163C22×Dic11—24no—
164C22×Dic11—22no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11C2×D414yes—
170C22×Dic11C2414yes—
171C22×Dic11C2412yes—
172C22×Dic11C2412yes—
173#4343—2256no—
174C2×D44—232no—
175C2×D44—264no—
176C2×D44—216no—
177C2×D44—216no—
178C2×D44—216no—
179C2×D44—28no—
180C2×D44—216no—
181C2×D44—216no—
182C2×D44—28no—
183C2×D44—216no—
184C2×D44—48no—
185C2×D44—432no—
186C2×D44—416no—
187C2×D44C2×D4132yescomplemented
188C2×C4×D11—264no—
189C2×C4×D11—216no—
190C2×C4×D11—232no—
191C2×C4×D11—216no—
192C2×C4×D11—216no—
193C2×C4×D11—216no—
194C2×C4×D11—216no—
195C2×C4×D11—216no—
196C2×C4×D11—48no—
197C2×C4×D11—432no—
198C2×C4×D11C2×D4116yescomplemented
199C11×C4⋊C4—28no—
200C11×C4⋊C4—216no—
201(C2×D11)⋊C4—28no—
202(C2×D11)⋊C4—28no—
203(C2×D11)⋊C4—216no—
204(C2×D11)⋊C4—28no—
205(C2×D11)⋊C4—216no—
206(C2×D11)⋊C4—216no—
207(C2×D11)⋊C4—48no—
208Dic11⋊C4—28no—
209C23×#41—111no—
210C22×#123—111no—
211C22×#121—112no—
212#2430—1116no—
213C2×#395D1111yescharacteristic, complemented
214C2×#394—111no—
215C2×#393—111no—
216C2×#392—111no—
217C2×#386—112no—
218C2×#386—112no—
219C2×#385—112no—
220C22×#95—111no—
221C23×C11C22×D412yes—
222C23×C11C22×D414yes—
223C23×C11C2×#4114yes—
224C23×C11H(5,𝔽2)12yes—
225C23×C112−1+412yes—
226C23×C11C2511yescharacteristic
227C22×D11—28no—
228C22×D11—28no—
229C22×D11—216no—
230C22×D11—216no—
231C22×D11—24no—
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—216no—
235C22×D11—216no—
236C22×D11—216no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—24no—
240C22×D11—24no—
241C22×D11—24no—
242C22×D11—24no—
243C22×D11—22no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—48no—
249C22×D11—48no—
250C22×D11—48no—
251C22×D11—48no—
252C22×D11—44no—
253C22×D11—44no—
254C22×D11—44no—
255C22×D11—48no—
256C22×D11—48no—
257C22×D11#120116yes—
258C22×D11C22×D418yes—
259C22×D11C22×D414yes—
260C22×D11C22×D418yes—
261Q8×C11—232no—
262C2×C4×C11—216no—
263C2×C4×C11—28no—
264C2×C4×C11—216no—
265C2×C4×C11—24no—
266C2×C4×C11—24no—
267C2×C4×C11—24no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—22no—
271C2×C4×C11—22no—
272C2×C4×C11—24no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—44no—
276C2×C4×C11—44no—
277C2×C4×C11C22×D418yes—
278C2×C4×C11C22×D414yes—
279C2×C4×C11C2×#4118yescomplemented
280C2×Dic11—28no—
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—24no—
284C2×Dic11—24no—
285C2×Dic11—24no—
286C2×Dic11—24no—
287C2×Dic11—44no—
288C2×Dic11—48no—
289C2×Dic11C22×D414yes—
290D44—232no—
291D44—264no—
292D44—432no—
293D44—416no—
294C4×D11—264no—
295C4×D11—232no—
296C4×D11—432no—
297C22×#41—118no—
298C22×#41—228no—
299C22×#41—2216no—
300C23×Q8C2×D1111yescharacteristic
301C23×D4—112no—
302C23×D4—111no—
303C23×D4—111no—
304C23×D4—112no—
305C24×C4—111no—
306C24×C4—112no—
307C24×C4—112no—
308C2×#123—118no—
309C2×#123—228no—
310C2×#121—1116no—
311C2×#121—2216no—
312C22×C4⋊C4—111no—
313C22×C4⋊C4C2×D1111yescharacteristic
314C22×C4⋊C4C2×D1112yes—
315C22×C22⋊C4—111no—
316C22×C22⋊C4—112no—
317C22×C22⋊C4—112no—
318C22×C22⋊C4—112no—
319C22×C22⋊C4—111no—
320C22×C22⋊C4—111no—
321C22×C22⋊C4—112no—
322#395C2×D1118yescomplemented
323#394—118no—
324#393—118no—
325#392—118no—
326#386—1116no—
327#386—1116no—
328#385—1116no—
329C2×#95—111no—
330C2×#95—112no—
331C2×#95—112no—
332C2×#95—118no—
333C2×#95C2×D1111yescharacteristic
334C2×#95C2×D1112yes—
335C22×C11C2×#12014yes—
336C22×C11#53214yes—
337C22×C11#53714yes—
338C22×C11#54618yes—
339C22×C11#54718yes—
340C22×C11C23×D411yescharacteristic
341C22×C11C23×D412yes—
342C22×C11C22×#4112yes—
343C22×C11C2×H(5,𝔽2)11yescharacteristic
344C22×C11C2×2−1+411yescharacteristic
345C2×D11—24no—
346C2×D11—24no—
347C2×D11—232no—
348C2×D11—28no—
349C2×D11—28no—
350C2×D11—28no—
351C2×D11—28no—
352C2×D11—28no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—432no—
356C2×D11—44no—
357C2×D11—44no—
358C2×D11—42no—
359C2×D11—42no—
360C2×D11—42no—
361C2×D11—44no—
362C2×D11—44no—
363C2×D11—88no—
364C2×D11C2×#12018yes—
365C4×C11—28no—
366C4×C11—24no—
367C4×C11—28no—
368C4×C11—42no—
369C4×C11—42no—
370Dic11—24no—
371Dic11—42no—
372Dic11—44no—
373C25—111no—
374C25—112no—
375C25—111no—
376C2×#41—2232no—
377C2×#41—2264no—
378C2×#41—22128no—
379C22×Q8—24no—
380C22×Q8—28no—
381C22×Q8C22×D1114yes—
382C22×D4—1116no—
383C22×D4—118no—
384C22×D4—114no—
385C22×D4—114no—
386C22×D4—118no—
387C22×D4—228no—
388C22×D4—228no—
389C22×D4—228no—
390C22×D4—228no—
391C22×D4—228no—
392C22×D4—224no—
393C22×D4—224no—
394C22×D4—228no—
395C22×D4—444no—
396C23×C4—111no—
397C23×C4—118no—
398C23×C4—114no—
399C23×C4—111no—
400C23×C4—112no—
401C23×C4—118no—
402C23×C4—118no—
403C23×C4—228no—
404C23×C4—228no—
405C23×C4—228no—
406C23×C4—228no—
407C23×C4—228no—
408C23×C4—228no—
409C23×C4—444no—
410C23×C4C22×D1111yescharacteristic
411C23×C4C22×D1111yescharacteristic
412C23×C4C22×D1111yescharacteristic
413C23×C4C22×D1112yes—
414C23×C4C22×D1112yes—
415#123—2232no—
416#121—2264no—
417C2×C4⋊C4—28no—
418C2×C4⋊C4—24no—
419C2×C4⋊C4—114no—
420C2×C4⋊C4—224no—
421C2×C4⋊C4C22×D1118yes—
422C2×C4⋊C4C22×D1114yes—
423C2×C22⋊C4—118no—
424C2×C22⋊C4—118no—
425C2×C22⋊C4—114no—
426C2×C22⋊C4—114no—
427C2×C22⋊C4—114no—
428C2×C22⋊C4—118no—
429C2×C22⋊C4—118no—
430C2×C22⋊C4—224no—
431C2×C22⋊C4—228no—
432C2×C22⋊C4—224no—
433C2×C22⋊C4—228no—
434C2×C22⋊C4—224no—
435C2×C22⋊C4—228no—
436C2×C22⋊C4—444no—
437#95—118no—
438#95—114no—
439#95—118no—
440#95C22×D1114yes—
441#95C22×D1118yes—
442C2×C11#243018yescomplemented
443C2×C11C22×#12011yescharacteristic
444C2×C11C2×#53211yescharacteristic
445C2×C11C2×#53711yescharacteristic
446C2×C11C2×#54612yes—
447C2×C11C2×#54712yes—
448D11—28no—
449D11—48no—
450D11—82no—
451C24—114no—
452C24—118no—
453C24—112no—
454C24—118no—
455C24—114no—
456C24—112no—
457C24—224no—
458C24—222no—
459C24—222no—
460C24—224no—
461C24—224no—
462C24—224no—
463C24—224no—
464C24—224no—
465C24—224no—
466C24—222no—
467C24—224no—
468C24—224no—
469C24—222no—
470C24—222no—
471C24C23×D1111yescharacteristic
472#41—22256no—
473C2×Q8—232no—
474C2×Q8—28no—
475C2×Q8—216no—
476C2×D4—1132no—
477C2×D4—2264no—
478C2×D4—2216no—
479C2×D4—2216no—
480C2×D4—2216no—
481C2×D4—2232no—
482C2×D4—2216no—
483C2×D4—2216no—
484C2×D4—228no—
485C2×D4—228no—
486C2×D4—2216no—
487C2×D4—448no—
488C2×D4—4432no—
489C2×D4—4416no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—24no—
494C22×C4—24no—
495C22×C4—22no—
496C22×C4—24no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—114no—
501C22×C4—112no—
502C22×C4—1116no—
503C22×C4—114no—
504C22×C4—112no—
505C22×C4—2216no—
506C22×C4—2232no—
507C22×C4—2216no—
508C22×C4—2216no—
509C22×C4—2264no—
510C22×C4—2216no—
511C22×C4—224no—
512C22×C4—2216no—
513C22×C4—222no—
514C22×C4—224no—
515C22×C4—224no—
516C22×C4—224no—
517C22×C4—224no—
518C22×C4—2216no—
519C22×C4—448no—
520C22×C4—4432no—
521C22×C4D4×D1114yes—
522C22×C4D4×D1118yes—
523C22×C4#434318yescomplemented
524C22×C4C23×D1112yes—
525C22×C4C23×D1112yes—
526C22×C4C23×D1112yes—
527C22×C4C23×D1114yes—
528C22×C4C23×D1114yes—
529C4⋊C4—216no—
530C4⋊C4—28no—
531C4⋊C4—228no—
532C22⋊C4—228no—
533C22⋊C4—2216no—
534C22⋊C4—228no—
535C22⋊C4—2216no—
536C22⋊C4—228no—
537C22⋊C4—2216no—
538C22⋊C4—448no—
539C11C2×#243011yescharacteristic, complemented, Sylow
540C23—1116no—
541C23—114no—
542C23—118no—
543C23—118no—
544C23—228no—
545C23—2216no—
546C23—228no—
547C23—2216no—
548C23—224no—
549C23—222no—
550C23—222no—
551C23—2216no—
552C23—2216no—
553C23—2216no—
554C23—224no—
555C23—224no—
556C23—224no—
557C23—224no—
558C23—224no—
559C23—224no—
560C23—222no—
561C23—224no—
562C23—224no—
563C23—222no—
564C23—222no—
565C23—448no—
566C23—448no—
567C23—448no—
568C23—448no—
569C23—444no—
570C23—448no—
571C23—444no—
572C23—444no—
573C23—448no—
574C23C2×D4×D1112yes—
575C23C2×D4×D1114yes—
576C23C2×#434314yes—
577C23#6704012yes—
578C23#6704212yes—
579C23C24×D1111yescharacteristic
580Q8—232no—
581D4—2264no—
582D4—2232no—
583D4—4432no—
584D4—4416no—
585C2×C4—28no—
586C2×C4—216no—
587C2×C4—216no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—22no—
594C2×C4—24no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—44no—
599C2×C4—44no—
600C2×C4—114no—
601C2×C4—2232no—
602C2×C4—2264no—
603C2×C4—228no—
604C2×C4—224no—
605C2×C4—222no—
606C2×C4—224no—
607C2×C4—224no—
608C2×C4—224no—
609C2×C4—224no—
610C2×C4—4432no—
611C2×C4—444no—
612C2×C4—448no—
613C2×C4C2×D4×D1114yes—
614C2×C4C2×D4×D1118yes—
615C2×C4C2×#434318yescomplemented
616C22—118no—
617C22—224no—
618C22—224no—
619C22—2232no—
620C22—228no—
621C22—228no—
622C22—228no—
623C22—228no—
624C22—228no—
625C22—444no—
626C22—444no—
627C22—4432no—
628C22—444no—
629C22—444no—
630C22—442no—
631C22—442no—
632C22—444no—
633C22—444no—
634C22—442no—
635C22—888no—
636C22D11×#12014yes—
637C22#1062316014yes—
638C22#1062316118yes—
639C22#1062325614yes—
640C22#1062325718yes—
641C22C22×D4×D1111yescharacteristic
642C22C22×D4×D1112yes—
643C22C22×#434312yes—
644C22C2×#6704011yescharacteristic
645C22C2×#6704211yescharacteristic
646C4—28no—
647C4—24no—
648C4—28no—
649C4—42no—
650C4—42no—
651C4—224no—
652C4—442no—
653C4—444no—
654C2—228no—
655C2—448no—
656C2—882no—
657C2#1307222718yesdirect product factor
658C2C2×D11×#12011yescharacteristic
659C2C2×#1062325611yescharacteristic
660C2C2×#1062316011yescharacteristic
661C2C2×#1062316112yes—
662C2C2×#1062325712yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#395C2
socleC24×C11C24
hypercenterC2×#395D11
hypocenterC11C2×#2430
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
1. C23×#4343C2semidirect
2. C22×#66947C2semidirect
3. C22×#66948C2semidirect
4. #13072227C2direct (N × H)
5. C2×#10622604C2semidirect
6. C2×#10622844C2semidirect
7. C2×#10622284C2semidirect
8. C2×#10622278C2semidirect
9. C2×#10622278C2semidirect
10. C2×#10622602C2semidirect
11. C2×D11×#95C2semidirect
12. C2×C11×#395C2semidirect
16. C22×#4343C22semidirect
35. C2×#66948C22semidirect
37. C2×#66947C22semidirect
38. C11×#395C22semidirect
41. #10622844C22semidirect
45. #10622604C22semidirect
46. #10622602C22semidirect
47. #10622284C22semidirect
48. #10622278C22semidirect
49. #10622278C22semidirect
50. D11×#95C22semidirect
77. C22×D44D4semidirect
89. C22×C4×D11D4semidirect
157. C22×C4×C11#41semidirect
187. C2×D44C2×D4semidirect
198. C2×C4×D11C2×D4semidirect
213. C2×#395D11semidirect
279. C2×C4×C11C2×#41semidirect
322. #395C2×D11semidirect
442. C2×C11#2430semidirect
523. C22×C4#4343semidirect
539. C11C2×#2430semidirect
615. C2×C4C2×#4343semidirect
657. C2#13072227direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43432
C22×#669472
C22×#669482
#130722272
C2×#106226042
C2×#106228442
C2×#106222842
C2×#106222782
C2×#106226022
C2×D11×#952
C2×C11×#3952
C2×#243011