Finite Group Databasebeta

← C2×#13074506 #14920173

Subgroups — C2×#13074506 #14920173

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×#66948C211yesmaximal, characteristic, complemented
2C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
3#13074506C2116yesmaximal, direct product factor
4C2×#10622595C211yesmaximal, characteristic, complemented
5C2×#10622285C211yesmaximal, characteristic, complemented
6C2×#10622604C212yesmaximal, complemented
7C2×#10622573C212yesmaximal, complemented
8C2×#10622573C211yesmaximal, characteristic, complemented
9C2×#10622603C212yesmaximal, complemented
10C2×#10622571C212yesmaximal, complemented
11C2×#10622277C211yesmaximal, characteristic, complemented
12C2×C11×#399C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C24×Dic11C2211yescharacteristic
16C23×D44C2212yes—
17C23×D44C2211yescharacteristic
18C23×C4×D11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C4⋊C4C2212yes—
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2212yes—
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×Dic11⋊C4C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×#66948—28no—
32C2×#66948C2218yescomplemented
33C2×(C22⋊D11)⋊C4—28no—
34C2×(C22⋊D11)⋊C4C2218yescomplemented
35C11×#399C2218yescomplemented
36C2×C11×#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622604C22116yescomplemented
42#10622603C22116yescomplemented
43#10622595C2218yescomplemented
44#10622573C2218yescomplemented
45#10622573C22116yescomplemented
46#10622571C22116yescomplemented
47#10622285C2218yescomplemented
48#10622277C2218yescomplemented
49C25×C11C2311yescharacteristic
50C24×D11C2312yes—
51C24×D11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C22×C22⋊D11—24no—
57C22×C22⋊D11—24no—
58C22×C22⋊D11—28no—
59C22×C22⋊D11—24no—
60C22×C22⋊D11—44no—
61C22×C22⋊D11—44no—
62C22×C22⋊D11C2314yes—
63C22×C22⋊D11C2318yes—
64C23×Dic11—24no—
65C23×Dic11—44no—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2312yes—
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C23×Dic11C2314yes—
71C22×D44—28no—
72C22×D44—24no—
73C22×D44—44no—
74C22×D44—44no—
75C22×D44—44no—
76C22×D44C2314yes—
77C22×D44C2318yes—
78C22×C4×D11—44no—
79C22×C4×D11D418yescomplemented
80C22×C4×D11C2314yes—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4—44no—
83C2×C11×C4⋊C4C2314yes—
84C2×C11×C4⋊C4C2318yes—
85C2×C11×C22⋊C4—24no—
86C2×C11×C22⋊C4—44no—
87C2×C11×C22⋊C4C2314yes—
88C2×C11×C22⋊C4C2318yes—
89C2×(C2×D11)⋊C4—24no—
90C2×(C2×D11)⋊C4—28no—
91C2×(C2×D11)⋊C4—28no—
92C2×(C2×D11)⋊C4—44no—
93C2×(C2×D11)⋊C4—44no—
94C2×(C2×D11)⋊C4—44no—
95C2×(C2×D11)⋊C4C2314yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×(C2×D11)⋊C4C2318yes—
99C2×(C2×D11)⋊C4C2318yes—
100C2×(C2×D11)⋊C4C2318yes—
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4C2314yes—
103C2×C4×Dic11—24no—
104C2×C4×Dic11C2314yes—
105#66948—232no—
106(C22⋊D11)⋊C4—232no—
107C11×#95C2314yes—
108C11⋊#95C2318yes—
109C11⋊#95C2314yes—
110C11⋊#95C2318yes—
111C11⋊#95C2318yes—
112C2×#2635—111nomaximal, Sylow
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11#4114yes—
118C24×C11C2412yes—
119C24×C11C2411yescharacteristic
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—24no—
131C23×D11C2×D414yes—
132C23×D11C2414yes—
133C23×D11C2412yes—
134C22×C4×C11—24no—
135C22×C4×C11—22no—
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×C11—24no—
143C22×C4×C11C2×D414yes—
144C22×C4×C11C2414yes—
145C22×C4×C11C2414yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2412yes—
148C2×C22⋊D11—232no—
149C2×C22⋊D11—28no—
150C2×C22⋊D11—28no—
151C2×C22⋊D11—216no—
152C2×C22⋊D11—28no—
153C2×C22⋊D11—48no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—432no—
156C22×Dic11—28no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—48no—
166C22×Dic11—416no—
167C22×Dic11C2×D414yes—
168C22×Dic11#4114yes—
169C22×Dic11C2414yes—
170C22×Dic11C2412yes—
171C22×Dic11C2412yes—
172C22×Dic11C2412yes—
173C2×D44—216no—
174C2×D44—28no—
175C2×D44—48no—
176C2×D44—48no—
177C2×D44—48no—
178C2×D44—416no—
179C2×D44—432no—
180C2×C4×D11—416no—
181C2×C4×D11—48no—
182C2×C4×D11C2×D4116yescomplemented
183C11×C4⋊C4—28no—
184C11×C4⋊C4—48no—
185C11×C22⋊C4—28no—
186C11×C22⋊C4—48no—
187(C2×D11)⋊C4—216no—
188(C2×D11)⋊C4—216no—
189(C2×D11)⋊C4—28no—
190(C2×D11)⋊C4—48no—
191(C2×D11)⋊C4—48no—
192(C2×D11)⋊C4—48no—
193Dic11⋊C4—28no—
194C4×Dic11—28no—
195C22×#121—111no—
196C22×C4×D4—111no—
197#2635—1116no—
198C2×#400—111no—
199C2×#399D1111yescharacteristic, complemented
200C2×#394—111no—
201C2×#394—112no—
202C2×#392—112no—
203C2×#392—111no—
204C2×#388—112no—
205C2×#386—112no—
206C2×#381—111no—
207C23×C11—28no—
208C23×C11—216no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—44no—
214C23×C11—44no—
215C23×C11—48no—
216C23×C11C22×D412yes—
217C23×C11C2×#4114yes—
218C23×C11C2×#4112yes—
219C23×C11C2×#4112yes—
220C23×C11H(5,𝔽2)14yes—
221C23×C11H(5,𝔽2)14yes—
222C23×C11C2511yescharacteristic
223C22×D11—28no—
224C22×D11—28no—
225C22×D11—28no—
226C22×D11—22no—
227C22×D11—22no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—24no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11—48no—
238C22×D11—48no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11—48no—
244C22×D11—48no—
245C22×D11—48no—
246C22×D11C22×D414yes—
247C2×C4×C11—28no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—48no—
258C2×C4×C11—44no—
259C2×C4×C11—48no—
260C2×C4×C11C22×D414yes—
261C22⋊D11—232no—
262C22⋊D11—432no—
263C2×Dic11—28no—
264C2×Dic11—28no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—24no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—416no—
274C2×Dic11—44no—
275C2×Dic11—48no—
276C2×Dic11C22×D414yes—
277C2×Dic11C2×#4114yes—
278D44—416no—
279D44—432no—
280C4×D11—416no—
281C23×D4—111no—
282C23×D4—112no—
283C23×D4—112no—
284C23×D4—111no—
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⋊C4C2×D1111yescharacteristic
293C22×C4⋊C4C2×D1112yes—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—111no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4—112no—
300C22×C22⋊C4C2×D1111yescharacteristic
301C22×C22⋊C4C2×D1112yes—
302C22×C42—111no—
303#400—118no—
304#399C2×D1118yescomplemented
305#394—1116no—
306#394—118no—
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—24no—
318C22×C11—28no—
319C22×C11—416no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—44no—
323C22×C11#52514yes—
324C22×C11#53414yes—
325C22×C11#53514yes—
326C22×C11#53818yes—
327C22×C11#54018yes—
328C22×C11C23×D411yescharacteristic
329C22×C11C22×#4111yescharacteristic
330C22×C11C22×#4111yescharacteristic
331C22×C11C2×H(5,𝔽2)12yes—
332C22×C11C2×H(5,𝔽2)12yes—
333C2×D11—24no—
334C2×D11—24no—
335C2×D11—24no—
336C2×D11—416no—
337C2×D11—44no—
338C2×D11—44no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—44no—
342C2×D11—44no—
343C2×D11—44no—
344C2×D11—44no—
345C2×D11—44no—
346C2×D11—816no—
347C4×C11—24no—
348C4×C11—42no—
349C4×C11—44no—
350C4×C11—44no—
351Dic11—24no—
352Dic11—24no—
353Dic11—42no—
354Dic11—44no—
355C25—111no—
356C25—112no—
357C25C22×D1111yescharacteristic
358C22×D4—114no—
359C22×D4—118no—
360C22×D4—118no—
361C22×D4—114no—
362C22×D4—228no—
363C22×D4—224no—
364C22×D4—224no—
365C22×D4—224no—
366C22×D4—228no—
367C22×D4—224no—
368C22×D4—444no—
369C22×D4—444no—
370C22×D4—444no—
371C22×D4—444no—
372C22×D4—444no—
373C23×C4—111no—
374C23×C4—111no—
375C23×C4—118no—
376C23×C4—114no—
377C23×C4—111no—
378C23×C4—112no—
379C23×C4—114no—
380C23×C4—224no—
381C23×C4—444no—
382C23×C4—444no—
383C23×C4C22×D1111yescharacteristic
384C23×C4C22×D1112yes—
385C23×C4C22×D1112yes—
386C23×C4C22×D1111yescharacteristic
387#121—2232no—
388C4×D4—2232no—
389C2×C4⋊C4—24no—
390C2×C4⋊C4—44no—
391C2×C4⋊C4—114no—
392C2×C4⋊C4—224no—
393C2×C4⋊C4C22×D1114yes—
394C2×C4⋊C4C22×D1118yes—
395C2×C22⋊C4—24no—
396C2×C22⋊C4—44no—
397C2×C22⋊C4—114no—
398C2×C22⋊C4—118no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—118no—
401C2×C22⋊C4—118no—
402C2×C22⋊C4—118no—
403C2×C22⋊C4—228no—
404C2×C22⋊C4—228no—
405C2×C22⋊C4—224no—
406C2×C22⋊C4—444no—
407C2×C22⋊C4—444no—
408C2×C22⋊C4—444no—
409C2×C22⋊C4C22×D1114yes—
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—44no—
419C2×C11#263518yescomplemented
420C2×C11C2×#52511yescharacteristic
421C2×C11C2×#53411yescharacteristic
422C2×C11C2×#53511yescharacteristic
423C2×C11C2×#53812yes—
424C2×C11C2×#54012yes—
425D11—44no—
426D11—84no—
427C24—22no—
428C24—24no—
429C24—22no—
430C24—24no—
431C24—114no—
432C24—112no—
433C24—114no—
434C24—224no—
435C24—222no—
436C24—222no—
437C24—224no—
438C24—224no—
439C24—224no—
440C24—224no—
441C24—224no—
442C24—224no—
443C24—224no—
444C24—224no—
445C24#434314yes—
446C24C23×D1112yes—
447C24C23×D1111yescharacteristic
448C2×D4—2216no—
449C2×D4—228no—
450C2×D4—228no—
451C2×D4—2232no—
452C2×D4—228no—
453C2×D4—2216no—
454C2×D4—228no—
455C2×D4—448no—
456C2×D4—448no—
457C2×D4—448no—
458C2×D4—4416no—
459C2×D4—4432no—
460C2×D4—448no—
461C2×D4—448no—
462C2×D4—4432no—
463C22×C4—24no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—24no—
467C22×C4—24no—
468C22×C4—24no—
469C22×C4—24no—
470C22×C4—24no—
471C22×C4—24no—
472C22×C4—114no—
473C22×C4—114no—
474C22×C4—112no—
475C22×C4—112no—
476C22×C4—1116no—
477C22×C4—114no—
478C22×C4—112no—
479C22×C4—228no—
480C22×C4—222no—
481C22×C4—222no—
482C22×C4—224no—
483C22×C4—222no—
484C22×C4—224no—
485C22×C4—224no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—4416no—
489C22×C4—448no—
490C22×C4—448no—
491C22×C4—4416no—
492C22×C4D4×D1114yes—
493C22×C4C23×D1114yes—
494C22×C4C23×D1114yes—
495C22×C4C23×D1112yes—
496C22×C4C23×D1112yes—
497C4⋊C4—28no—
498C4⋊C4—48no—
499C4⋊C4—228no—
500C22⋊C4—28no—
501C22⋊C4—48no—
502C22⋊C4—2216no—
503C22⋊C4—2216no—
504C22⋊C4—228no—
505C22⋊C4—448no—
506C22⋊C4—448no—
507C22⋊C4—448no—
508C42—228no—
509C11C2×#263511yescharacteristic, complemented, Sylow
510C23—28no—
511C23—216no—
512C23—22no—
513C23—24no—
514C23—22no—
515C23—24no—
516C23—44no—
517C23—44no—
518C23—48no—
519C23—114no—
520C23—228no—
521C23—228no—
522C23—228no—
523C23—224no—
524C23—222no—
525C23—222no—
526C23—224no—
527C23—224no—
528C23—224no—
529C23—224no—
530C23—224no—
531C23—224no—
532C23—224no—
533C23—224no—
534C23—448no—
535C23—448no—
536C23—448no—
537C23—448no—
538C23—448no—
539C23—448no—
540C23—448no—
541C23—448no—
542C23—448no—
543C23C2×D4×D1112yes—
544C23#6703714yes—
545C23C2×#434314yes—
546C23C2×#434312yes—
547C23#41×D1112yes—
548C23#6704214yes—
549C23C24×D1111yescharacteristic
550D4—2232no—
551D4—4416no—
552D4—4432no—
553D4—4432no—
554C2×C4—28no—
555C2×C4—24no—
556C2×C4—22no—
557C2×C4—24no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—24no—
561C2×C4—24no—
562C2×C4—24no—
563C2×C4—24no—
564C2×C4—44no—
565C2×C4—48no—
566C2×C4—48no—
567C2×C4—114no—
568C2×C4—114no—
569C2×C4—228no—
570C2×C4—228no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—224no—
574C2×C4—222no—
575C2×C4—224no—
576C2×C4—224no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—4416no—
580C2×C4—4416no—
581C2×C4—448no—
582C2×C4—444no—
583C2×C4C2×D4×D1114yes—
584C22—24no—
585C22—28no—
586C22—42no—
587C22—42no—
588C22—416no—
589C22—44no—
590C22—224no—
591C22—224no—
592C22—224no—
593C22—4416no—
594C22—444no—
595C22—444no—
596C22—444no—
597C22—444no—
598C22—444no—
599C22—444no—
600C22—444no—
601C22—444no—
602C22—444no—
603C22—8816no—
604C22#1062315814yes—
605C22#1062317518yes—
606C22#1062318414yes—
607C22#1062319418yes—
608C22#1062324614yes—
609C22C22×D4×D1111yescharacteristic
610C22C2×#6703712yes—
611C22C22×#434311yescharacteristic
612C22C2×#41×D1111yescharacteristic
613C22C2×#6704212yes—
614C4—24no—
615C4—44no—
616C4—42no—
617C4—44no—
618C4—224no—
619C4—224no—
620C4—442no—
621C4—444no—
622C2—44no—
623C2—444no—
624C2—884no—
625C2#1307450618yesdirect product factor
626C2C2×#1062315811yescharacteristic
627C2C2×#1062318411yescharacteristic
628C2C2×#1062324611yescharacteristic
629C2C2×#1062317512yes—
630C2C2×#1062319412yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#399C2
socleC24×C11C24
hypercenterC2×#399D11
hypocenterC11C2×#2635
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#66948C2semidirect
2. C22×(C22⋊D11)⋊C4C2semidirect
3. #13074506C2direct (N × H)
4. C2×#10622595C2semidirect
5. C2×#10622285C2semidirect
6. C2×#10622604C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622603C2semidirect
10. C2×#10622571C2semidirect
11. C2×#10622277C2semidirect
12. C2×C11×#399C2semidirect
32. C2×#66948C22semidirect
34. C2×(C22⋊D11)⋊C4C22semidirect
35. C11×#399C22semidirect
41. #10622604C22semidirect
42. #10622603C22semidirect
43. #10622595C22semidirect
44. #10622573C22semidirect
45. #10622573C22semidirect
46. #10622571C22semidirect
47. #10622285C22semidirect
48. #10622277C22semidirect
79. C22×C4×D11D4semidirect
182. C2×C4×D11C2×D4semidirect
199. C2×#399D11semidirect
304. #399C2×D11semidirect
419. C2×C11#2635semidirect
509. C11C2×#2635semidirect
625. C2#13074506direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669482
C22×(C22⋊D11)⋊C42
#130745062
C2×#106225952
C2×#106222852
C2×#106226042
C2×#106225732
C2×#106226032
C2×#106225712
C2×#106222772
C2×C11×#3992
C2×#263511