Finite Group Databasebeta

← C2×#13072229 #14922410

Subgroups — C2×#13072229 #14922410

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×#66936C211yesmaximal, characteristic, complemented
3C22×#66937C212yesmaximal, complemented
4#13072229C2116yesmaximal, direct product factor
5C2×#10622842C211yesmaximal, characteristic, complemented
6C2×#10622285C211yesmaximal, characteristic, complemented
7C2×#10622573C211yesmaximal, characteristic, complemented
8C2×#10622278C212yesmaximal, complemented
9C2×#10622569C212yesmaximal, complemented
10C2×#10622281C212yesmaximal, complemented
11C2×D11×#95C211yesmaximal, characteristic, complemented
12C2×C11×#393C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×C22⋊D11C2212yes—
16C22×#4343—216no—
17C22×#4343—28no—
18C22×#4343C2218yescomplemented
19C23×D44C2211yescharacteristic
20C23×D44C2212yes—
21C23×C4×D11C2212yes—
22C23×C4×D11C2212yes—
23C23×C4×D11C2211yescharacteristic
24C22×C11×C22⋊C4C2212yes—
25C22×C11×C22⋊C4C2211yescharacteristic
26C22×C22⋊Dic11C2211yescharacteristic
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2211yescharacteristic
30C22×(C2×D11)⋊C4C2212yes—
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2212yes—
33C22×Dic11⋊C4C2211yescharacteristic
34C2×#66937—216no—
35C2×#66937C22116yescomplemented
36C2×#66936—28no—
37C2×#66936C2218yescomplemented
38C11×#393C2218yescomplemented
39C2×C11×#95C2211yescharacteristic
40C2×C11×#95C2212yes—
41#10622842C2218yescomplemented
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2212yes—
45#10622573C2218yescomplemented
46#10622569C22116yescomplemented
47#10622285C2218yescomplemented
48#10622281C22116yescomplemented
49#10622278C22116yescomplemented
50D11×#95C2218yescomplemented
51C25×C11C2311yescharacteristic
52C24×D11C2312yes—
53C24×D11C2311yescharacteristic
54C22×Q8×C11—28no—
55C22×Q8×C11—24no—
56C22×Q8×C11C2314yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2312yes—
59C23×C4×C11C2312yes—
60C23×C4×C11C2311yescharacteristic
61C22×C22⋊D11—24no—
62C22×C22⋊D11—28no—
63C22×C22⋊D11—28no—
64C22×C22⋊D11—28no—
65C22×C22⋊D11—44no—
66C22×C22⋊D11C2314yes—
67C22×C22⋊D11C2318yes—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2312yes—
72C2×#4343—2128no—
73C2×#4343—264no—
74C2×#4343—232no—
75C22×D44—28no—
76C22×D44—28no—
77C22×D44—28no—
78C22×D44—24no—
79C22×D44D4116yescomplemented
80C22×D44C2314yes—
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×C22⋊C4—24no—
94C2×C11×C22⋊C4—28no—
95C2×C11×C22⋊C4C2314yes—
96C2×C11×C22⋊C4C2318yes—
97C2×C22⋊Dic11—24no—
98C2×C22⋊Dic11C2314yes—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4—28no—
101C2×(C2×D11)⋊C4—28no—
102C2×(C2×D11)⋊C4—44no—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2318yes—
105C2×(C2×D11)⋊C4C2318yes—
106C2×(C2×D11)⋊C4C2318yes—
107C2×C4⋊Dic11—24no—
108C2×C4⋊Dic11C2314yes—
109C2×Dic11⋊C4—24no—
110C2×Dic11⋊C4—28no—
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2318yes—
113#66937—264no—
114#66936—232no—
115C11×#95C2314yes—
116C11×#95C2318yes—
117C11⋊#95C2318yes—
118C11⋊#95C2314yes—
119C11⋊#95C2318yes—
120C2×#2430—111nomaximal, Sylow
121C24×C11—22no—
122C24×C11—24no—
123C24×C11—24no—
124C24×C11—22no—
125C24×C11—22no—
126C24×C11C2412yes—
127C24×C11C2411yescharacteristic
128C23×D11—24no—
129C23×D11—22no—
130C23×D11—22no—
131C23×D11—24no—
132C23×D11—24no—
133C23×D11—24no—
134C23×D11—24no—
135C23×D11—24no—
136C23×D11—24no—
137C23×D11C2×D418yes—
138C23×D11C2×D414yes—
139C23×D11C2×D418yes—
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—22no—
149C22×C4×C11—24no—
150C22×C4×C11—24no—
151C22×C4×C11—24no—
152C22×C4×C11—24no—
153C22×C4×C11C2×D418yes—
154C22×C4×C11C2×D414yes—
155C22×C4×C11C2414yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2414yes—
158C22×C4×C11C2412yes—
159C2×C22⋊D11—216no—
160C2×C22⋊D11—28no—
161C2×C22⋊D11—216no—
162C2×C22⋊D11—216no—
163C2×C22⋊D11—48no—
164C2×C22⋊D11—432no—
165C2×C22⋊D11—416no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—24no—
171C22×Dic11—24no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11C2×D414yes—
175C22×Dic11#4118yescomplemented
176C22×Dic11C2412yes—
177C22×Dic11C2412yes—
178C22×Dic11C2412yes—
179C22×Dic11C2414yes—
180#4343—2256no—
181C2×D44—232no—
182C2×D44—264no—
183C2×D44—216no—
184C2×D44—216no—
185C2×D44—216no—
186C2×D44—28no—
187C2×D44C2×D4132yescomplemented
188C2×C4×D11—264no—
189C2×C4×D11—216no—
190C2×C4×D11—216no—
191C2×C4×D11—232no—
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×C22⋊C4—28no—
200C11×C22⋊C4—216no—
201C22⋊Dic11—28no—
202(C2×D11)⋊C4—216no—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—216no—
205(C2×D11)⋊C4—48no—
206C4⋊Dic11—28no—
207Dic11⋊C4—28no—
208Dic11⋊C4—216no—
209C23×#41—111no—
210C22×#123—111no—
211C22×#121—112no—
212#2430—1116no—
213C2×#395—111no—
214C2×#394—111no—
215C2×#393D1111yescharacteristic, complemented
216C2×#392—111no—
217C2×#386—112no—
218C2×#386—112no—
219C2×#385—112no—
220C22×#95—111no—
221C23×C11—22no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—22no—
225C23×C11—22no—
226C23×C11—44no—
227C23×C11—44no—
228C23×C11—44no—
229C23×C11—48no—
230C23×C11—48no—
231C23×C11C22×D412yes—
232C23×C11C22×D414yes—
233C23×C11C2×#4114yes—
234C23×C11H(5,𝔽2)12yes—
235C23×C112−1+412yes—
236C23×C11C2511yescharacteristic
237C22×D11—28no—
238C22×D11—28no—
239C22×D11—216no—
240C22×D11—216no—
241C22×D11—24no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—216no—
245C22×D11—216no—
246C22×D11—216no—
247C22×D11—24no—
248C22×D11—24no—
249C22×D11—24no—
250C22×D11—24no—
251C22×D11—24no—
252C22×D11—24no—
253C22×D11—48no—
254C22×D11—48no—
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—24no—
265C2×C4×C11—24no—
266C2×C4×C11—24no—
267C2×C4×C11—22no—
268C2×C4×C11—24no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—24no—
272C2×C4×C11—44no—
273C2×C4×C11—48no—
274C2×C4×C11C22×D418yes—
275C2×C4×C11C22×D414yes—
276C22⋊D11—432no—
277C22⋊D11—416no—
278C2×Dic11—28no—
279C2×Dic11—216no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—24no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—24no—
286C2×Dic11—22no—
287C2×Dic11—22no—
288C2×Dic11—44no—
289C2×Dic11—44no—
290C2×Dic11C22×D414yes—
291C2×Dic11C2×#4118yescomplemented
292D44—232no—
293D44—264no—
294C4×D11—264no—
295C4×D11—232no—
296C4×D11—432no—
297C22×#41—118no—
298C22×#41—228no—
299C22×#41—2216no—
300C23×Q8C2×D1111yescharacteristic
301C23×D4—111no—
302C23×D4—112no—
303C23×D4—112no—
304C23×D4—111no—
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⋊C4—112no—
314C22×C4⋊C4—111no—
315C22×C22⋊C4—111no—
316C22×C22⋊C4—112no—
317C22×C22⋊C4—112no—
318C22×C22⋊C4—111no—
319C22×C22⋊C4—112no—
320C22×C22⋊C4C2×D1111yescharacteristic
321C22×C22⋊C4C2×D1112yes—
322#395—118no—
323#394—118no—
324#393C2×D1118yescomplemented
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×C11—42no—
336C22×C11—42no—
337C22×C11—42no—
338C22×C11—44no—
339C22×C11—44no—
340C22×C11—88no—
341C22×C11C2×#12014yes—
342C22×C11#53214yes—
343C22×C11#53714yes—
344C22×C11#54618yes—
345C22×C11#54718yes—
346C22×C11C23×D411yescharacteristic
347C22×C11C23×D412yes—
348C22×C11C22×#4112yes—
349C22×C11C2×H(5,𝔽2)11yescharacteristic
350C22×C11C2×2−1+411yescharacteristic
351C2×D11—24no—
352C2×D11—24no—
353C2×D11—232no—
354C2×D11—28no—
355C2×D11—28no—
356C2×D11—28no—
357C2×D11—28no—
358C2×D11—28no—
359C2×D11—44no—
360C2×D11—44no—
361C2×D11—432no—
362C2×D11—44no—
363C2×D11—44no—
364C2×D11C2×#12018yes—
365C4×C11—28no—
366C4×C11—24no—
367C4×C11—42no—
368C4×C11—44no—
369Dic11—24no—
370Dic11—28no—
371Dic11—42no—
372Dic11—42no—
373C25—111no—
374C25—112no—
375C25C22×D1111yescharacteristic
376C2×#41—2232no—
377C2×#41—2264no—
378C2×#41—22128no—
379C22×Q8—24no—
380C22×Q8—28no—
381C22×Q8C22×D1114yes—
382C22×D4—114no—
383C22×D4—118no—
384C22×D4—1116no—
385C22×D4—118no—
386C22×D4—114no—
387C22×D4—228no—
388C22×D4—228no—
389C22×D4—228no—
390C22×D4—228no—
391C22×D4—228no—
392C22×D4—228no—
393C22×D4—224no—
394C22×D4—224no—
395C22×D4—444no—
396C23×C4—111no—
397C23×C4—112no—
398C23×C4—118no—
399C23×C4—114no—
400C23×C4—111no—
401C23×C4—111no—
402C23×C4—118no—
403C23×C4—118no—
404C23×C4—228no—
405C23×C4—228no—
406C23×C4—228no—
407C23×C4—228no—
408C23×C4—228no—
409C23×C4—228no—
410C23×C4—444no—
411C23×C4C22×D1111yescharacteristic
412C23×C4C22×D1112yes—
413C23×C4C22×D1111yescharacteristic
414C23×C4C22×D1112yes—
415#123—2232no—
416#121—2264no—
417C2×C4⋊C4—118no—
418C2×C4⋊C4—114no—
419C2×C4⋊C4—114no—
420C2×C4⋊C4—224no—
421C2×C4⋊C4—228no—
422C2×C4⋊C4—224no—
423C2×C22⋊C4—28no—
424C2×C22⋊C4—24no—
425C2×C22⋊C4—114no—
426C2×C22⋊C4—118no—
427C2×C22⋊C4—114no—
428C2×C22⋊C4—118no—
429C2×C22⋊C4—118no—
430C2×C22⋊C4—228no—
431C2×C22⋊C4—228no—
432C2×C22⋊C4—224no—
433C2×C22⋊C4—224no—
434C2×C22⋊C4—444no—
435C2×C22⋊C4C22×D1118yes—
436C2×C22⋊C4C22×D1114yes—
437#95—118no—
438#95—114no—
439#95—118no—
440#95C22×D1114yes—
441#95C22×D1118yes—
442C2×C11—82no—
443C2×C11#243018yescomplemented
444C2×C11C22×#12011yescharacteristic
445C2×C11C2×#53211yescharacteristic
446C2×C11C2×#53711yescharacteristic
447C2×C11C2×#54612yes—
448C2×C11C2×#54712yes—
449D11—28no—
450D11—48no—
451C24—22no—
452C24—24no—
453C24—22no—
454C24—24no—
455C24—22no—
456C24—114no—
457C24—118no—
458C24—112no—
459C24—118no—
460C24—114no—
461C24—222no—
462C24—224no—
463C24—222no—
464C24—224no—
465C24—224no—
466C24—224no—
467C24—224no—
468C24—224no—
469C24—224no—
470C24C23×D1112yes—
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—2216no—
485C2×D4—228no—
486C2×D4—228no—
487C2×D4—448no—
488C2×D4—4432no—
489C2×D4—4416no—
490C22×C4—24no—
491C22×C4—24no—
492C22×C4—24no—
493C22×C4—22no—
494C22×C4—24no—
495C22×C4—24no—
496C22×C4—24no—
497C22×C4—24no—
498C22×C4—114no—
499C22×C4—118no—
500C22×C4—114no—
501C22×C4—112no—
502C22×C4—1116no—
503C22×C4—112no—
504C22×C4—112no—
505C22×C4—2216no—
506C22×C4—2216no—
507C22×C4—2232no—
508C22×C4—2216no—
509C22×C4—2216no—
510C22×C4—2264no—
511C22×C4—2216no—
512C22×C4—224no—
513C22×C4—224no—
514C22×C4—224no—
515C22×C4—2216no—
516C22×C4—222no—
517C22×C4—224no—
518C22×C4—222no—
519C22×C4—222no—
520C22×C4—222no—
521C22×C4—448no—
522C22×C4—4432no—
523C22×C4D4×D1114yes—
524C22×C4D4×D1118yes—
525C22×C4C23×D1114yes—
526C22×C4C23×D1112yes—
527C22×C4C23×D1112yes—
528C22×C4C23×D1114yes—
529C4⋊C4—228no—
530C4⋊C4—2216no—
531C4⋊C4—228no—
532C22⋊C4—216no—
533C22⋊C4—28no—
534C22⋊C4—2216no—
535C22⋊C4—2216no—
536C22⋊C4—228no—
537C22⋊C4—228no—
538C22⋊C4—448no—
539C11C2×#243011yescharacteristic, complemented, Sylow
540C23—22no—
541C23—24no—
542C23—22no—
543C23—24no—
544C23—22no—
545C23—44no—
546C23—44no—
547C23—48no—
548C23—44no—
549C23—48no—
550C23—1116no—
551C23—114no—
552C23—118no—
553C23—118no—
554C23—228no—
555C23—2216no—
556C23—222no—
557C23—224no—
558C23—222no—
559C23—228no—
560C23—2216no—
561C23—2216no—
562C23—2216no—
563C23—224no—
564C23—224no—
565C23—224no—
566C23—224no—
567C23—224no—
568C23—224no—
569C23—2216no—
570C23—448no—
571C23—448no—
572C23—448no—
573C23—448no—
574C23C2×D4×D1112yes—
575C23C2×D4×D1114yes—
576C23#6704012yes—
577C23#41×D1114yes—
578C23#6704212yes—
579C23C24×D1111yescharacteristic
580Q8—232no—
581D4—2264no—
582D4—2232no—
583D4—4432no—
584D4—4416no—
585C2×C4—28no—
586C2×C4—216no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—24no—
590C2×C4—22no—
591C2×C4—24no—
592C2×C4—24no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—44no—
596C2×C4—48no—
597C2×C4—114no—
598C2×C4—118no—
599C2×C4—2232no—
600C2×C4—2264no—
601C2×C4—228no—
602C2×C4—224no—
603C2×C4—224no—
604C2×C4—224no—
605C2×C4—2216no—
606C2×C4—222no—
607C2×C4—224no—
608C2×C4—222no—
609C2×C4—222no—
610C2×C4—222no—
611C2×C4—4432no—
612C2×C4—444no—
613C2×C4—444no—
614C2×C4C2×D4×D1114yes—
615C2×C4C2×D4×D1118yes—
616C22—42no—
617C22—42no—
618C22—44no—
619C22—44no—
620C22—42no—
621C22—88no—
622C22—118no—
623C22—224no—
624C22—224no—
625C22—2232no—
626C22—228no—
627C22—228no—
628C22—228no—
629C22—228no—
630C22—228no—
631C22—444no—
632C22—444no—
633C22—4432no—
634C22—444no—
635C22—444no—
636C22D11×#12014yes—
637C22#1062316014yes—
638C22#1062316218yes—
639C22#1062319914yes—
640C22#1062320718yes—
641C22C22×D4×D1111yescharacteristic
642C22C22×D4×D1112yes—
643C22C2×#6704011yescharacteristic
644C22C2×#41×D1112yes—
645C22C2×#6704211yescharacteristic
646C4—24no—
647C4—28no—
648C4—42no—
649C4—44no—
650C4—228no—
651C4—224no—
652C4—442no—
653C4—442no—
654C2—82no—
655C2—228no—
656C2—448no—
657C2#1307222918yesdirect product factor
658C2C2×D11×#12011yescharacteristic
659C2C2×#1062319911yescharacteristic
660C2C2×#1062316011yescharacteristic
661C2C2×#1062320712yes—
662C2C2×#1062316212yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#393C2
socleC24×C11C24
hypercenterC2×#393D11
hypocenterC11C2×#2430
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
1. C23×#4343C2semidirect
2. C22×#66936C2semidirect
3. C22×#66937C2semidirect
4. #13072229C2direct (N × H)
5. C2×#10622842C2semidirect
6. C2×#10622285C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622278C2semidirect
9. C2×#10622569C2semidirect
10. C2×#10622281C2semidirect
11. C2×D11×#95C2semidirect
12. C2×C11×#393C2semidirect
18. C22×#4343C22semidirect
35. C2×#66937C22semidirect
37. C2×#66936C22semidirect
38. C11×#393C22semidirect
41. #10622842C22semidirect
45. #10622573C22semidirect
46. #10622569C22semidirect
47. #10622285C22semidirect
48. #10622281C22semidirect
49. #10622278C22semidirect
50. D11×#95C22semidirect
79. C22×D44D4semidirect
89. C22×C4×D11D4semidirect
175. C22×Dic11#41semidirect
187. C2×D44C2×D4semidirect
198. C2×C4×D11C2×D4semidirect
215. C2×#393D11semidirect
291. C2×Dic11C2×#41semidirect
324. #393C2×D11semidirect
443. C2×C11#2430semidirect
539. C11C2×#2430semidirect
657. C2#13072229direct (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×#669362
C22×#669372
#130722292
C2×#106228422
C2×#106222852
C2×#106225732
C2×#106222782
C2×#106225692
C2×#106222812
C2×D11×#952
C2×C11×#3932
C2×#243011