Finite Group Databasebeta

← C2×#13074508 #14920167

Subgroups — C2×#13074508 #14920167

Order 2816.

3606 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66991C211yesmaximal, characteristic, complemented
2C22×#66946C211yesmaximal, characteristic, complemented
3#13074508C2116yesmaximal, direct product factor
4C2×#10622599C211yesmaximal, characteristic, complemented
5C2×#10622290C211yesmaximal, characteristic, complemented
6C2×#10622574C212yesmaximal, complemented
7C2×#10622573C212yesmaximal, complemented
8C2×#10622836C211yesmaximal, characteristic, complemented
9C2×#10622564C212yesmaximal, complemented
10C2×#10622569C212yesmaximal, complemented
11C2×#10622277C211yesmaximal, characteristic, complemented
12C2×C11×#394C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×C22⋊D11C2212yes—
16C23×D44C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C2×#66991—28no—
25C2×#66991C2218yescomplemented
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2212yes—
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C2×#66946—28no—
34C2×#66946C2218yescomplemented
35C11×#394C2218yescomplemented
36C2×C11×#95C2211yescharacteristic
37#10622836C2218yescomplemented
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622599C2218yescomplemented
43#10622574C22116yescomplemented
44#10622573C22116yescomplemented
45#10622569C22116yescomplemented
46#10622564C22116yescomplemented
47#10622290C2218yescomplemented
48#10622277C2218yescomplemented
49C25×C11C2312yes—
50C24×D11C2311yescharacteristic
51C24×D11C2311yescharacteristic
52C22×D4×C11—24no—
53C22×D4×C11—44no—
54C22×D4×C11C2314yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C22×C22⋊D11—28no—
60C22×C22⋊D11—28no—
61C22×C22⋊D11—44no—
62C22×C22⋊D11—44no—
63C22×C22⋊D11—44no—
64C22×C22⋊D11—44no—
65C22×C22⋊D11C2318yes—
66C22×C22⋊D11C2318yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2312yes—
69C23×Dic11C2312yes—
70C23×Dic11C2311yescharacteristic
71C22×D44—24no—
72C22×D44—24no—
73C22×D44—24no—
74C22×D44C2314yes—
75C22×C4×D11—24no—
76C22×C4×D11—44no—
77C22×C4×D11—44no—
78C22×C4×D11D418yescomplemented
79C22×C4×D11C2314yes—
80C22×C4×D11C2314yes—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4C2314yes—
83C2×C11×C22⋊C4—28no—
84C2×C11×C22⋊C4—44no—
85C2×C11×C22⋊C4C2318yes—
86C2×C11×C22⋊C4C2318yes—
87C2×C22⋊Dic11—28no—
88C2×C22⋊Dic11—44no—
89C2×C22⋊Dic11C2318yes—
90C2×C22⋊Dic11C2318yes—
91#66991—232no—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—44no—
95C2×(C2×D11)⋊C4—44no—
96C2×(C2×D11)⋊C4C2314yes—
97C2×(C2×D11)⋊C4C2314yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×C4⋊Dic11—24no—
101C2×C4⋊Dic11—44no—
102C2×C4⋊Dic11C2314yes—
103C2×C4⋊Dic11C2318yes—
104C2×C4×Dic11—24no—
105C2×C4×Dic11C2314yes—
106#66946—232no—
107C11×#95C2314yes—
108C11⋊#95C2318yes—
109C11⋊#95C2314yes—
110C11⋊#95C2318yes—
111C11⋊#95C2318yes—
112C2×#2635—111nomaximal, Sylow
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11—24no—
118C24×C11—24no—
119C24×C11—24no—
120C24×C11C2414yes—
121C24×C11C2411yescharacteristic
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11C2×D414yes—
131C23×D11#4114yes—
132C23×D11C2412yes—
133C23×D11C2412yes—
134C2×D4×C11—28no—
135C2×D4×C11—48no—
136C2×D4×C11—416no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11—24no—
145C22×C4×C11C2×D414yes—
146C22×C4×C11#4114yes—
147C22×C4×C11C2412yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2412yes—
151C2×C22⋊D11—216no—
152C2×C22⋊D11—216no—
153C2×C22⋊D11—48no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—48no—
156C2×C22⋊D11—48no—
157C2×C22⋊D11—432no—
158C2×C22⋊D11—432no—
159C22×Dic11—22no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11C2×D414yes—
169C22×Dic11C2414yes—
170C22×Dic11C2414yes—
171C22×Dic11C2412yes—
172C22×Dic11C2412yes—
173C2×D44—232no—
174C2×D44—28no—
175C2×D44—28no—
176C2×D44—28no—
177C2×C4×D11—28no—
178C2×C4×D11—416no—
179C2×C4×D11—48no—
180C2×C4×D11—48no—
181C2×C4×D11—416no—
182C2×C4×D11C2×D4116yescomplemented
183C11×C4⋊C4—28no—
184C11×C22⋊C4—216no—
185C11×C22⋊C4—48no—
186C22⋊Dic11—216no—
187C22⋊Dic11—48no—
188(C2×D11)⋊C4—28no—
189(C2×D11)⋊C4—28no—
190(C2×D11)⋊C4—48no—
191(C2×D11)⋊C4—48no—
192C4⋊Dic11—28no—
193C4⋊Dic11—48no—
194C4×Dic11—28no—
195C22×#121—111no—
196C22×C4×D4—111no—
197#2635—1116no—
198C2×#400—111no—
199C2×#399—111no—
200C2×#394—112no—
201C2×#394D1111yescharacteristic, complemented
202C2×#392—111no—
203C2×#392—112no—
204C2×#388—112no—
205C2×#386—112no—
206C2×#381—111no—
207C23×C11—24no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—48no—
215C23×C11—48no—
216C23×C11—48no—
217C23×C11—48no—
218C23×C11—48no—
219C23×C11—48no—
220C23×C11—48no—
221C23×C11C22×D412yes—
222C23×C11C2×#4112yes—
223C23×C11C2×#4112yes—
224C23×C11H(5,𝔽2)14yes—
225C23×C11H(5,𝔽2)14yes—
226C23×C11C2511yescharacteristic
227C22×D11—28no—
228C22×D11—28no—
229C22×D11—28no—
230C22×D11—28no—
231C22×D11—216no—
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—24no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—24no—
240C22×D11—44no—
241C22×D11—44no—
242C22×D11—48no—
243C22×D11—48no—
244C22×D11—48no—
245C22×D11C22×D414yes—
246C22×D11C2×#4114yes—
247D4×C11—416no—
248C2×C4×C11—28no—
249C2×C4×C11—28no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—44no—
259C2×C4×C11—48no—
260C2×C4×C11C22×D414yes—
261C2×C4×C11C2×#4114yes—
262C22⋊D11—432no—
263C22⋊D11—432no—
264C2×Dic11—28no—
265C2×Dic11—24no—
266C2×Dic11—22no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—44no—
275C2×Dic11—48no—
276C2×Dic11—48no—
277C2×Dic11C22×D414yes—
278D44—232no—
279C4×D11—416no—
280C4×D11—416no—
281C23×D4—112no—
282C23×D4—112no—
283C23×D4—111no—
284C23×D4C2×D1111yescharacteristic
285C24×C4—111no—
286C24×C4—111no—
287C2×#121—118no—
288C2×#121—228no—
289C2×C4×D4—118no—
290C2×C4×D4—228no—
291C22×C4⋊C4—111no—
292C22×C4⋊C4—112no—
293C22×C4⋊C4C2×D1111yescharacteristic
294C22×C22⋊C4—112no—
295C22×C22⋊C4—111no—
296C22×C22⋊C4—111no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4—112no—
300C22×C22⋊C4C2×D1112yes—
301C22×C22⋊C4C2×D1112yes—
302C22×C42—111no—
303#400—118no—
304#399—118no—
305#394—1116no—
306#394C2×D1118yescomplemented
307#392—118no—
308#392—1116no—
309#388—1116no—
310#386—1116no—
311#381—118no—
312C2×#95—111no—
313C2×#95—112no—
314C2×#95—112no—
315C2×#95—112no—
316C2×#95C2×D1111yescharacteristic
317C22×C11—44no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—44no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—816no—
325C22×C11#52514yes—
326C22×C11#53414yes—
327C22×C11#53514yes—
328C22×C11#53818yes—
329C22×C11#54018yes—
330C22×C11C23×D411yescharacteristic
331C22×C11C22×#4111yescharacteristic
332C22×C11C22×#4111yescharacteristic
333C22×C11C2×H(5,𝔽2)12yes—
334C22×C11C2×H(5,𝔽2)12yes—
335C2×D11—24no—
336C2×D11—24no—
337C2×D11—24no—
338C2×D11—24no—
339C2×D11—28no—
340C2×D11—416no—
341C2×D11—416no—
342C2×D11—42no—
343C2×D11—42no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—44no—
347C4×C11—24no—
348C4×C11—24no—
349C4×C11—42no—
350C4×C11—44no—
351Dic11—24no—
352Dic11—42no—
353Dic11—44no—
354Dic11—44no—
355C25—111no—
356C25—111no—
357C25C22×D1112yes—
358C22×D4—24no—
359C22×D4—44no—
360C22×D4—118no—
361C22×D4—118no—
362C22×D4—114no—
363C22×D4—224no—
364C22×D4—224no—
365C22×D4—228no—
366C22×D4—228no—
367C22×D4—224no—
368C22×D4—444no—
369C22×D4—444no—
370C22×D4—444no—
371C22×D4—444no—
372C22×D4C22×D1114yes—
373C23×C4—111no—
374C23×C4—118no—
375C23×C4—114no—
376C23×C4—111no—
377C23×C4—112no—
378C23×C4—112no—
379C23×C4—114no—
380C23×C4—224no—
381C23×C4—444no—
382C23×C4—444no—
383C23×C4C22×D1112yes—
384C23×C4C22×D1111yescharacteristic
385C23×C4C22×D1111yescharacteristic
386C23×C4C22×D1111yescharacteristic
387#121—2232no—
388C4×D4—2232no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—114no—
391C2×C4⋊C4—118no—
392C2×C4⋊C4—224no—
393C2×C4⋊C4—444no—
394C2×C4⋊C4C22×D1114yes—
395C2×C22⋊C4—28no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—114no—
399C2×C22⋊C4—114no—
400C2×C22⋊C4—118no—
401C2×C22⋊C4—118no—
402C2×C22⋊C4—118no—
403C2×C22⋊C4—224no—
404C2×C22⋊C4—228no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—444no—
407C2×C22⋊C4—444no—
408C2×C22⋊C4—444no—
409C2×C22⋊C4C22×D1118yes—
410C2×C22⋊C4C22×D1118yes—
411C2×C42—114no—
412C2×C42—224no—
413#95—118no—
414#95—114no—
415#95—118no—
416#95—118no—
417#95C22×D1114yes—
418C2×C11—84no—
419C2×C11#263518yescomplemented
420C2×C11C2×#52511yescharacteristic
421C2×C11C2×#53411yescharacteristic
422C2×C11C2×#53511yescharacteristic
423C2×C11C2×#53812yes—
424C2×C11C2×#54012yes—
425D11—44no—
426D11—44no—
427C24—24no—
428C24—24no—
429C24—24no—
430C24—24no—
431C24—24no—
432C24—24no—
433C24—24no—
434C24—114no—
435C24—114no—
436C24—112no—
437C24—112no—
438C24—222no—
439C24—222no—
440C24—222no—
441C24—224no—
442C24—224no—
443C24—222no—
444C24—224no—
445C24—224no—
446C24C23×D1114yes—
447C24C23×D1111yescharacteristic
448C2×D4—28no—
449C2×D4—48no—
450C2×D4—416no—
451C2×D4—228no—
452C2×D4—228no—
453C2×D4—2232no—
454C2×D4—2216no—
455C2×D4—2216no—
456C2×D4—228no—
457C2×D4—448no—
458C2×D4—448no—
459C2×D4—448no—
460C2×D4—448no—
461C2×D4—4432no—
462C2×D4—4432no—
463C22×C4—22no—
464C22×C4—24no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—114no—
472C22×C4—112no—
473C22×C4—1116no—
474C22×C4—114no—
475C22×C4—114no—
476C22×C4—112no—
477C22×C4—228no—
478C22×C4—224no—
479C22×C4—222no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—224no—
483C22×C4—224no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—4416no—
488C22×C4—448no—
489C22×C4—448no—
490C22×C4—4416no—
491C22×C4D4×D1114yes—
492C22×C4#434114yes—
493C22×C4C23×D1112yes—
494C22×C4C23×D1114yes—
495C22×C4C23×D1112yes—
496C22×C4C23×D1112yes—
497C4⋊C4—28no—
498C4⋊C4—228no—
499C4⋊C4—448no—
500C22⋊C4—216no—
501C22⋊C4—48no—
502C22⋊C4—228no—
503C22⋊C4—2216no—
504C22⋊C4—228no—
505C22⋊C4—448no—
506C22⋊C4—448no—
507C22⋊C4—448no—
508C42—228no—
509C11C2×#263511yescharacteristic, complemented, Sylow
510C23—24no—
511C23—24no—
512C23—24no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—48no—
518C23—48no—
519C23—48no—
520C23—48no—
521C23—48no—
522C23—48no—
523C23—48no—
524C23—114no—
525C23—114no—
526C23—228no—
527C23—228no—
528C23—228no—
529C23—2216no—
530C23—222no—
531C23—222no—
532C23—222no—
533C23—224no—
534C23—224no—
535C23—222no—
536C23—224no—
537C23—224no—
538C23—228no—
539C23—444no—
540C23—448no—
541C23—448no—
542C23—448no—
543C23—444no—
544C23C2×D4×D1112yes—
545C23C2×#434112yes—
546C23#6703714yes—
547C23#41×D1112yes—
548C23#6704214yes—
549C23C24×D1111yescharacteristic
550D4—416no—
551D4—2232no—
552D4—4432no—
553D4—4432no—
554C2×C4—28no—
555C2×C4—28no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—44no—
565C2×C4—48no—
566C2×C4—114no—
567C2×C4—228no—
568C2×C4—224no—
569C2×C4—222no—
570C2×C4—224no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—224no—
574C2×C4—224no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—4416no—
578C2×C4—4416no—
579C2×C4—448no—
580C2×C4—448no—
581C2×C4—444no—
582C2×C4C2×D4×D1114yes—
583C2×C4C2×#434114yes—
584C22—44no—
585C22—44no—
586C22—44no—
587C22—44no—
588C22—44no—
589C22—44no—
590C22—44no—
591C22—816no—
592C22—224no—
593C22—224no—
594C22—224no—
595C22—224no—
596C22—228no—
597C22—442no—
598C22—442no—
599C22—4416no—
600C22—4416no—
601C22—444no—
602C22—444no—
603C22—444no—
604C22#1062312014yes—
605C22#1062313714yes—
606C22#1062315018yes—
607C22#1062318818yes—
608C22#1062320514yes—
609C22C22×D4×D1111yescharacteristic
610C22C22×#434111yescharacteristic
611C22C2×#6703712yes—
612C22C2×#41×D1111yescharacteristic
613C22C2×#6704212yes—
614C4—24no—
615C4—24no—
616C4—42no—
617C4—44no—
618C4—224no—
619C4—444no—
620C4—442no—
621C4—444no—
622C2—84no—
623C2—444no—
624C2—444no—
625C2#1307450818yesdirect product factor
626C2C2×#1062313711yescharacteristic
627C2C2×#1062312011yescharacteristic
628C2C2×#1062320511yescharacteristic
629C2C2×#1062318812yes—
630C2C2×#1062315012yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#394C2
socleC24×C11C24
hypercenterC2×#394D11
hypocenterC11C2×#2635
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#66991C2semidirect
2. C22×#66946C2semidirect
3. #13074508C2direct (N × H)
4. C2×#10622599C2semidirect
5. C2×#10622290C2semidirect
6. C2×#10622574C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622836C2semidirect
9. C2×#10622564C2semidirect
10. C2×#10622569C2semidirect
11. C2×#10622277C2semidirect
12. C2×C11×#394C2semidirect
25. C2×#66991C22semidirect
34. C2×#66946C22semidirect
35. C11×#394C22semidirect
37. #10622836C22semidirect
42. #10622599C22semidirect
43. #10622574C22semidirect
44. #10622573C22semidirect
45. #10622569C22semidirect
46. #10622564C22semidirect
47. #10622290C22semidirect
48. #10622277C22semidirect
78. C22×C4×D11D4semidirect
182. C2×C4×D11C2×D4semidirect
201. C2×#394D11semidirect
306. #394C2×D11semidirect
419. C2×C11#2635semidirect
509. C11C2×#2635semidirect
625. C2#13074508direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669912
C22×#669462
#130745082
C2×#106225992
C2×#106222902
C2×#106225742
C2×#106225732
C2×#106228362
C2×#106225642
C2×#106225692
C2×#106222772
C2×C11×#3942
C2×#263511