Finite Group Databasebeta

← C2×#13076619 #14959919

Subgroups — C2×#13076619 #14959919

Order 2816.

3322 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66936C211yesmaximal, characteristic, complemented
2C22×#66948C211yesmaximal, characteristic, complemented
3#13076619C2116yesmaximal, direct product factor
4C2×#10622595C211yesmaximal, characteristic, complemented
5C2×#10622607C212yesmaximal, complemented
6C2×#10622285C211yesmaximal, characteristic, complemented
7C2×#10622604C212yesmaximal, complemented
8C2×#10622572C212yesmaximal, complemented
9C2×#10622573C212yesmaximal, complemented
10C2×#10622573C211yesmaximal, characteristic, complemented
11C2×#10622280C211yesmaximal, characteristic, complemented
12C2×C11×#399C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×D44C2212yes—
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2212yes—
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2212yes—
22C22×C22⋊Dic11C2211yescharacteristic
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×(C2×D11)⋊C4C2212yes—
29C22×C4⋊Dic11C2211yescharacteristic
30C22×Dic11⋊C4C2211yescharacteristic
31C22×Dic11⋊C4C2212yes—
32C2×#66948—28no—
33C2×#66948C2218yescomplemented
34C2×#66936—28no—
35C2×#66936C2218yescomplemented
36C11×#399C2218yescomplemented
37C2×C11×#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622607C22116yescomplemented
42#10622604C22116yescomplemented
43#10622595C2218yescomplemented
44#10622573C2218yescomplemented
45#10622573C22116yescomplemented
46#10622572C22116yescomplemented
47#10622285C2218yescomplemented
48#10622280C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2312yes—
51C24×D11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—24no—
57C22×C22⋊D11—44no—
58C22×C22⋊D11—44no—
59C22×C22⋊D11—44no—
60C22×C22⋊D11—44no—
61C22×C22⋊D11C2314yes—
62C22×C22⋊D11C2318yes—
63C23×Dic11C2311yescharacteristic
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2311yescharacteristic
67C22×D44—28no—
68C22×D44—24no—
69C22×D44—44no—
70C22×D44—44no—
71C22×D44—44no—
72C22×D44C2314yes—
73C22×D44C2318yes—
74C22×C4×D11—44no—
75C22×C4×D11D418yescomplemented
76C22×C4×D11C2314yes—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—44no—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2318yes—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—44no—
83C2×C11×C22⋊C4C2314yes—
84C2×C11×C22⋊C4C2318yes—
85C2×C22⋊Dic11—24no—
86C2×C22⋊Dic11C2314yes—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—28no—
89C2×(C2×D11)⋊C4—44no—
90C2×(C2×D11)⋊C4—44no—
91C2×(C2×D11)⋊C4—44no—
92C2×(C2×D11)⋊C4—44no—
93C2×(C2×D11)⋊C4C2314yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×C4⋊Dic11—24no—
100C2×C4⋊Dic11C2314yes—
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4—44no—
103C2×Dic11⋊C4C2314yes—
104C2×Dic11⋊C4C2318yes—
105#66948—232no—
106#66936—232no—
107C11×#95C2314yes—
108C11⋊#95C2314yes—
109C11⋊#95C2318yes—
110C11⋊#95C2318yes—
111C2×#2813—111nomaximal, Sylow
112C24×C11—22no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11C2412yes—
118C24×C11C2411yescharacteristic
119C23×D11—22no—
120C23×D11—24no—
121C23×D11—24no—
122C23×D11—22no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11C2×D414yes—
131C23×D11C2414yes—
132C23×D11C2412yes—
133C22×C4×C11—24no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—24no—
141C22×C4×C11—24no—
142C22×C4×C11C2×D414yes—
143C22×C4×C11C2414yes—
144C22×C4×C11C2414yes—
145C22×C4×C11C2412yes—
146C22×C4×C11C2412yes—
147C2×C22⋊D11—28no—
148C2×C22⋊D11—48no—
149C2×C22⋊D11—48no—
150C2×C22⋊D11—48no—
151C2×C22⋊D11—48no—
152C2×C22⋊D11—416no—
153C2×C22⋊D11—432no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—22no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—22no—
163C22×Dic11C2×D414yes—
164C22×Dic11C2414yes—
165C22×Dic11C2412yes—
166C22×Dic11C2412yes—
167C22×Dic11C2412yes—
168C2×D44—216no—
169C2×D44—28no—
170C2×D44—48no—
171C2×D44—48no—
172C2×D44—48no—
173C2×D44—416no—
174C2×D44—432no—
175C2×C4×D11—416no—
176C2×C4×D11—48no—
177C2×C4×D11C2×D4116yescomplemented
178C11×C4⋊C4—28no—
179C11×C4⋊C4—48no—
180C11×C22⋊C4—28no—
181C11×C22⋊C4—48no—
182C22⋊Dic11—28no—
183(C2×D11)⋊C4—216no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—48no—
186(C2×D11)⋊C4—48no—
187(C2×D11)⋊C4—48no—
188(C2×D11)⋊C4—48no—
189C4⋊Dic11—28no—
190Dic11⋊C4—28no—
191Dic11⋊C4—48no—
192C22×#123—111no—
193C22×#121—111no—
194#2813—1116no—
195C2×#400—111no—
196C2×#399D1111yescharacteristic, complemented
197C2×#396—112no—
198C2×#394—111no—
199C2×#394—112no—
200C2×#394—112no—
201C2×#392—111no—
202C2×#392—112no—
203C2×#380—111no—
204C23×C11—22no—
205C23×C11—24no—
206C23×C11—24no—
207C23×C11—22no—
208C23×C11—22no—
209C23×C11—44no—
210C23×C11—44no—
211C23×C11—44no—
212C23×C11—48no—
213C23×C11—48no—
214C23×C11C22×D412yes—
215C23×C11H(5,𝔽2)14yes—
216C23×C11H(5,𝔽2)14yes—
217C23×C11H(5,𝔽2)12yes—
218C23×C112−1+412yes—
219C23×C11C2511yescharacteristic
220C22×D11—28no—
221C22×D11—28no—
222C22×D11—28no—
223C22×D11—22no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—22no—
227C22×D11—24no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—48no—
235C22×D11—48no—
236C22×D11—48no—
237C22×D11—48no—
238C22×D11—48no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11C22×D414yes—
244C2×C4×C11—28no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—48no—
255C2×C4×C11—44no—
256C2×C4×C11—48no—
257C2×C4×C11C22×D414yes—
258C22⋊D11—416no—
259C22⋊D11—432no—
260C2×Dic11—28no—
261C2×Dic11—24no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—22no—
270C2×Dic11—44no—
271C2×Dic11—44no—
272C2×Dic11—48no—
273C2×Dic11C22×D414yes—
274D44—416no—
275D44—432no—
276C4×D11—416no—
277C23×D4—111no—
278C23×D4—112no—
279C23×D4—112no—
280C23×D4—111no—
281C24×C4—111no—
282C2×#123—118no—
283C2×#123—228no—
284C2×#121—118no—
285C2×#121—228no—
286C22×C4⋊C4—111no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4—112no—
289C22×C4⋊C4C2×D1111yescharacteristic
290C22×C4⋊C4C2×D1112yes—
291C22×C22⋊C4—111no—
292C22×C22⋊C4—111no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4C2×D1111yescharacteristic
299C22×C22⋊C4C2×D1112yes—
300#400—118no—
301#399C2×D1118yescomplemented
302#396—1116no—
303#394—1116no—
304#394—1116no—
305#394—118no—
306#392—118no—
307#392—1116no—
308#380—118no—
309C2×#95—112no—
310C2×#95—111no—
311C2×#95—112no—
312C2×#95C2×D1111yescharacteristic
313C22×C11—42no—
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—44no—
317C22×C11—44no—
318C22×C11—88no—
319C22×C11#53414yes—
320C22×C11#53514yes—
321C22×C11#53714yes—
322C22×C11#56018yes—
323C22×C11#56218yes—
324C22×C11C23×D411yescharacteristic
325C22×C11C2×H(5,𝔽2)12yes—
326C22×C11C2×H(5,𝔽2)12yes—
327C22×C11C2×H(5,𝔽2)11yescharacteristic
328C22×C11C2×2−1+411yescharacteristic
329C2×D11—24no—
330C2×D11—24no—
331C2×D11—24no—
332C2×D11—44no—
333C2×D11—44no—
334C2×D11—416no—
335C2×D11—44no—
336C2×D11—44no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—816no—
343C4×C11—24no—
344C4×C11—42no—
345C4×C11—44no—
346C4×C11—44no—
347Dic11—24no—
348Dic11—42no—
349Dic11—42no—
350Dic11—44no—
351C25—111no—
352C25—112no—
353C25C22×D1111yescharacteristic
354C22×D4—114no—
355C22×D4—118no—
356C22×D4—118no—
357C22×D4—114no—
358C22×D4—228no—
359C22×D4—224no—
360C22×D4—224no—
361C22×D4—444no—
362C22×D4—444no—
363C22×D4—444no—
364C22×D4—444no—
365C22×D4—444no—
366C22×D4—444no—
367C22×D4—444no—
368C23×C4—111no—
369C23×C4—118no—
370C23×C4—114no—
371C23×C4—111no—
372C23×C4—111no—
373C23×C4—112no—
374C23×C4—444no—
375C23×C4C22×D1111yescharacteristic
376C23×C4C22×D1112yes—
377C23×C4C22×D1112yes—
378C23×C4C22×D1111yescharacteristic
379#123—2232no—
380#121—2232no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—44no—
383C2×C4⋊C4—114no—
384C2×C4⋊C4—114no—
385C2×C4⋊C4—118no—
386C2×C4⋊C4—224no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4—444no—
389C2×C4⋊C4C22×D1114yes—
390C2×C4⋊C4C22×D1118yes—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—44no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—118no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—228no—
401C2×C22⋊C4—224no—
402C2×C22⋊C4—224no—
403C2×C22⋊C4—444no—
404C2×C22⋊C4—444no—
405C2×C22⋊C4—444no—
406C2×C22⋊C4—444no—
407C2×C22⋊C4C22×D1114yes—
408C2×C22⋊C4C22×D1118yes—
409#95—114no—
410#95—118no—
411#95—118no—
412#95C22×D1114yes—
413C2×C11—82no—
414C2×C11#281318yescomplemented
415C2×C11C2×#53411yescharacteristic
416C2×C11C2×#53511yescharacteristic
417C2×C11C2×#53711yescharacteristic
418C2×C11C2×#56012yes—
419C2×C11C2×#56212yes—
420D11—44no—
421D11—84no—
422C24—22no—
423C24—24no—
424C24—22no—
425C24—22no—
426C24—24no—
427C24—114no—
428C24—112no—
429C24—114no—
430C24—224no—
431C24—222no—
432C24—222no—
433C24—224no—
434C24—224no—
435C24—224no—
436C24—224no—
437C24—224no—
438C24—224no—
439C24—224no—
440C24—224no—
441C24C23×D1112yes—
442C24C23×D1111yescharacteristic
443C2×D4—2216no—
444C2×D4—228no—
445C2×D4—228no—
446C2×D4—448no—
447C2×D4—448no—
448C2×D4—448no—
449C2×D4—4416no—
450C2×D4—4432no—
451C2×D4—448no—
452C2×D4—448no—
453C2×D4—448no—
454C2×D4—448no—
455C2×D4—4416no—
456C2×D4—4432no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—24no—
464C22×C4—24no—
465C22×C4—24no—
466C22×C4—114no—
467C22×C4—112no—
468C22×C4—1116no—
469C22×C4—114no—
470C22×C4—112no—
471C22×C4—112no—
472C22×C4—224no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—224no—
476C22×C4—222no—
477C22×C4—222no—
478C22×C4—224no—
479C22×C4—224no—
480C22×C4—224no—
481C22×C4—4416no—
482C22×C4—448no—
483C22×C4D4×D1114yes—
484C22×C4C23×D1114yes—
485C22×C4C23×D1114yes—
486C22×C4C23×D1112yes—
487C22×C4C23×D1112yes—
488C4⋊C4—28no—
489C4⋊C4—48no—
490C4⋊C4—228no—
491C4⋊C4—228no—
492C4⋊C4—448no—
493C22⋊C4—28no—
494C22⋊C4—48no—
495C22⋊C4—2216no—
496C22⋊C4—228no—
497C22⋊C4—228no—
498C22⋊C4—448no—
499C22⋊C4—448no—
500C22⋊C4—448no—
501C22⋊C4—448no—
502C11C2×#281311yescharacteristic, complemented, Sylow
503C23—22no—
504C23—24no—
505C23—22no—
506C23—24no—
507C23—22no—
508C23—44no—
509C23—44no—
510C23—48no—
511C23—44no—
512C23—48no—
513C23—114no—
514C23—228no—
515C23—228no—
516C23—228no—
517C23—224no—
518C23—222no—
519C23—222no—
520C23—224no—
521C23—224no—
522C23—224no—
523C23—224no—
524C23—224no—
525C23—224no—
526C23—224no—
527C23—224no—
528C23—448no—
529C23—448no—
530C23—448no—
531C23—448no—
532C23—448no—
533C23—448no—
534C23—448no—
535C23—448no—
536C23—448no—
537C23C2×D4×D1112yes—
538C23#6703714yes—
539C23#6704012yes—
540C23#6704212yes—
541C23#6704214yes—
542C23C24×D1111yescharacteristic
543D4—4416no—
544D4—4432no—
545D4—4416no—
546D4—4432no—
547C2×C4—28no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—24no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—44no—
558C2×C4—48no—
559C2×C4—48no—
560C2×C4—114no—
561C2×C4—228no—
562C2×C4—224no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—224no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—224no—
569C2×C4—224no—
570C2×C4—224no—
571C2×C4—4416no—
572C2×C4—444no—
573C2×C4—444no—
574C2×C4—448no—
575C2×C4C2×D4×D1114yes—
576C22—42no—
577C22—42no—
578C22—42no—
579C22—44no—
580C22—44no—
581C22—88no—
582C22—224no—
583C22—224no—
584C22—224no—
585C22—444no—
586C22—444no—
587C22—4416no—
588C22—444no—
589C22—444no—
590C22—444no—
591C22—444no—
592C22—444no—
593C22—444no—
594C22—444no—
595C22—8816no—
596C22#1062316014yes—
597C22#1062317818yes—
598C22#1062318414yes—
599C22#1062319718yes—
600C22#1062324614yes—
601C22C22×D4×D1111yescharacteristic
602C22C2×#6703712yes—
603C22C2×#6704011yescharacteristic
604C22C2×#6704212yes—
605C22C2×#6704211yescharacteristic
606C4—24no—
607C4—44no—
608C4—42no—
609C4—44no—
610C4—224no—
611C4—442no—
612C4—442no—
613C4—444no—
614C2—82no—
615C2—444no—
616C2—884no—
617C2#1307661918yesdirect product factor
618C2C2×#1062318411yescharacteristic
619C2C2×#1062324611yescharacteristic
620C2C2×#1062316011yescharacteristic
621C2C2×#1062319712yes—
622C2C2×#1062317812yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#399C2
socleC24×C11C24
hypercenterC2×#399D11
hypocenterC11C2×#2813
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#66936C2semidirect
2. C22×#66948C2semidirect
3. #13076619C2direct (N × H)
4. C2×#10622595C2semidirect
5. C2×#10622607C2semidirect
6. C2×#10622285C2semidirect
7. C2×#10622604C2semidirect
8. C2×#10622572C2semidirect
9. C2×#10622573C2semidirect
10. C2×#10622573C2semidirect
11. C2×#10622280C2semidirect
12. C2×C11×#399C2semidirect
33. C2×#66948C22semidirect
35. C2×#66936C22semidirect
36. C11×#399C22semidirect
41. #10622607C22semidirect
42. #10622604C22semidirect
43. #10622595C22semidirect
44. #10622573C22semidirect
45. #10622573C22semidirect
46. #10622572C22semidirect
47. #10622285C22semidirect
48. #10622280C22semidirect
75. C22×C4×D11D4semidirect
177. C2×C4×D11C2×D4semidirect
196. C2×#399D11semidirect
301. #399C2×D11semidirect
414. C2×C11#2813semidirect
502. C11C2×#2813semidirect
617. C2#13076619direct (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×#669482
#130766192
C2×#106225952
C2×#106226072
C2×#106222852
C2×#106226042
C2×#106225722
C2×#106225732
C2×#106222802
C2×C11×#3992
C2×#281311