Finite Group Databasebeta

← C2×#13073564 #14925549

Subgroups — C2×#13073564 #14925549

Order 2816.

4006 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66941C211yesmaximal, characteristic, complemented
2C22×#66949C212yesmaximal, complemented
3C22×#66931C212yesmaximal, complemented
4C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
5#13073564C2116yesmaximal, direct product factor
6C2×#10622290C211yesmaximal, characteristic, complemented
7C2×#10622562C211yesmaximal, characteristic, complemented
8C2×#10622605C211yesmaximal, characteristic, complemented
9C2×#10622570C212yesmaximal
10C2×#10622589C212yesmaximal, complemented
11C2×#10622262C211yesmaximal, characteristic, complemented
12C2×C11×#399C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C23×Dic22C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2212yes—
27C22×Dic11⋊C4C2212yes—
28C22×Dic11⋊C4C2211yescharacteristic
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2212yes—
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2212yes—
33C22×C4×Dic11C2211yescharacteristic
34C2×#66949—216no—
35C2×#66949C22116yescomplemented
36C2×#66941—28no—
37C2×#66941C2218yescomplemented
38C2×(C22⋊D11)⋊C4—28no—
39C2×(C22⋊D11)⋊C4C2218yes—
40C2×#66931—216no—
41C2×#66931C22116yescomplemented
42C11×#399C2218yescomplemented
43C2×C11×#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45#10622605C2218yescomplemented
46#10622589C22116yescomplemented
47#10622570C22116yes—
48#10622562C2218yescomplemented
49#10622290C2218yescomplemented
50#10622262C2218yescomplemented
51C25×C11C2311yescharacteristic
52C24×D11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2312yes—
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—24no—
58C22×C22⋊D11—24no—
59C22×C22⋊D11Q818yescomplemented
60C22×C22⋊D11C2314yes—
61C23×Dic11—28no—
62C23×Dic11—24no—
63C23×Dic11C2314yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C22×C4×D11—24no—
70C22×C4×D11—28no—
71C22×C4×D11C2314yes—
72C22×Dic22—28no—
73C22×Dic22—28no—
74C22×Dic22—28no—
75C22×Dic22C2318yes—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4—28no—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C4⋊C4C2318yes—
80C2×C11×C22⋊C4—28no—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4C2318yes—
83C2×C11×C22⋊C4C2314yes—
84C2×C22⋊Dic11—28no—
85C2×C22⋊Dic11C2318yes—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—28no—
88C2×(C2×D11)⋊C4—28no—
89C2×(C2×D11)⋊C4C2314yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×(C2×D11)⋊C4C2318yes—
92C2×C4⋊Dic11—28no—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11C2318yes—
95C2×C4⋊Dic11C2314yes—
96C2×Dic11⋊C4—28no—
97C2×Dic11⋊C4—24no—
98C2×Dic11⋊C4—28no—
99C2×Dic11⋊C4—28no—
100C2×Dic11⋊C4D4116yescomplemented
101C2×Dic11⋊C4C2318yes—
102C2×Dic11⋊C4C2314yes—
103C2×Dic11⋊C4C2318yes—
104C2×Dic11⋊C4C2318yes—
105C2×Dic11⋊C4C2318yes—
106C2×C4×Dic11—28no—
107C2×C4×Dic11D418yes—
108C2×C4×Dic11C2318yes—
109C2×C4×Dic11C2314yes—
110#66949—264no—
111#66941—232no—
112(C22⋊D11)⋊C4—232no—
113#66931—264no—
114C11×#95C2314yes—
115C11⋊#95C2314yes—
116C2×#2542—111nomaximal, Sylow
117C24×C11—24no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—24no—
121C24×C11C2×Q814yes—
122C24×C11C2412yes—
123C24×C11C2411yescharacteristic
124C23×D11—24no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11—24no—
128C23×D11C2×Q814yes—
129C23×D11C2412yes—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11—24no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11C2×D414yes—
139C22×C4×C11C2×D418yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2414yes—
142C22×C4×C11C2412yes—
143C22×C4×C11C2414yes—
144C2×C22⋊D11—232no—
145C2×C22⋊D11—28no—
146C2×C22⋊D11—28no—
147C2×C22⋊D11C2×Q8116yescomplemented
148C22×Dic11—216no—
149C22×Dic11—28no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—22no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—24no—
157C22×Dic11—416no—
158C22×Dic11C2×D418yes—
159C22×Dic11C2×D414yes—
160C22×Dic11C2×D414yes—
161C22×Dic11C2×D418yes—
162C22×Dic11C2×Q814yes—
163C22×Dic11#4114yes—
164C22×Dic11C2412yes—
165C22×Dic11C2414yes—
166C22×Dic11C2414yes—
167C22×Dic11C2412yes—
168C22×Dic11C2412yes—
169C2×C4×D11—28no—
170C2×C4×D11—216no—
171C2×C4×D11—416no—
172C2×Dic22—216no—
173C2×Dic22—216no—
174C2×Dic22—216no—
175C2×Dic22—432no—
176C11×C4⋊C4—28no—
177C11×C4⋊C4—216no—
178C11×C22⋊C4—216no—
179C11×C22⋊C4—28no—
180C22⋊Dic11—216no—
181(C2×D11)⋊C4—216no—
182(C2×D11)⋊C4—28no—
183(C2×D11)⋊C4—216no—
184C4⋊Dic11—216no—
185C4⋊Dic11—28no—
186Dic11⋊C4—216no—
187Dic11⋊C4—28no—
188Dic11⋊C4—216no—
189Dic11⋊C4—216no—
190Dic11⋊C4C2×D4132yescomplemented
191C4×Dic11—216no—
192C4×Dic11C2×D4116yes—
193C22×C4⋊Q8—111no—
194C22×C22⋊Q8—112no—
195C22×C22⋊Q8—112no—
196C22×C4×D4—111no—
197#2542—1116no—
198C2×#399—111no—
199C2×#399—111no—
200C2×#399—111no—
201C2×#399D1111yescharacteristic, complemented
202C2×#390—112no—
203C2×#384—112no—
204C2×C4×C4⋊C4—111no—
205C23×C11—28no—
206C23×C11—216no—
207C23×C11—24no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—24no—
211C23×C11—44no—
212C23×C11—44no—
213C23×C11—48no—
214C23×C11C22×D412yes—
215C23×C11C22×D414yes—
216C23×C11C22×Q814yes—
217C23×C11C22×Q812yes—
218C23×C11C2×#4112yes—
219C23×C112−1+414yes—
220C23×C11C2511yescharacteristic
221C22×D11—28no—
222C22×D11—216no—
223C22×D11—24no—
224C22×D11—22no—
225C22×D11—22no—
226C22×D11—24no—
227C22×D11—44no—
228C22×D11—44no—
229C22×D11—48no—
230C22×D11C22×Q814yes—
231C2×C4×C11—28no—
232C2×C4×C11—216no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—24no—
240C2×C4×C11—24no—
241C2×C4×C11—48no—
242C2×C4×C11—44no—
243C2×C4×C11C22×D414yes—
244C2×C4×C11C22×D418yes—
245C22⋊D11—232no—
246C2×Dic11—216no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—24no—
252C2×Dic11—22no—
253C2×Dic11—24no—
254C2×Dic11—48no—
255C2×Dic11—44no—
256C2×Dic11—416no—
257C2×Dic11C22⋊Q8116yescomplemented
258C2×Dic11#127116yes—
259C2×Dic11C22×D418yes—
260C2×Dic11C22×D414yes—
261C2×Dic11C22×D414yes—
262C2×Dic11C22×D418yes—
263C2×Dic11C22×Q814yes—
264C2×Dic11C2×#4114yes—
265C4×D11—416no—
266Dic22—432no—
267C23×Q8—112no—
268C23×D4—111no—
269C24×C4—111no—
270C24×C4—111no—
271C2×C4⋊Q8—118no—
272C2×C4⋊Q8—228no—
273C2×C22⋊Q8—1116no—
274C2×C22⋊Q8—1116no—
275C2×C22⋊Q8—2216no—
276C2×C22⋊Q8—2216no—
277C2×C4×D4—118no—
278C2×C4×D4—228no—
279C22×C4⋊C4—112no—
280C22×C4⋊C4—112no—
281C22×C4⋊C4—112no—
282C22×C4⋊C4—111no—
283C22×C4⋊C4—112no—
284C22×C4⋊C4—111no—
285C22×C4⋊C4—112no—
286C22×C4⋊C4C2×D1111yescharacteristic
287C22×C4⋊C4C2×D1112yes—
288C22×C22⋊C4—112no—
289C22×C22⋊C4—111no—
290C22×C22⋊C4—112no—
291C22×C22⋊C4—112no—
292C22×C22⋊C4C2×D1111yescharacteristic
293C22×C22⋊C4C2×D1112yes—
294C22×C42—111no—
295C22×C42—112no—
296#399—118no—
297#399—118no—
298#399—118no—
299#399C2×D1118yescomplemented
300#390—1116no—
301#384—1116no—
302C4×C4⋊C4—118no—
303C2×#95—111no—
304C2×#95C2×D1111yescharacteristic
305C22×C11—24no—
306C22×C11—28no—
307C22×C11—42no—
308C22×C11—42no—
309C22×C11—44no—
310C22×C11—416no—
311C22×C11C2×C22⋊Q814yes—
312C22×C11C2×#12714yes—
313C22×C11#53614yes—
314C22×C11#54718yes—
315C22×C11D4×Q818yes—
316C22×C11C23×D411yescharacteristic
317C22×C11C23×D412yes—
318C22×C11C23×Q811yescharacteristic
319C22×C11C22×#4111yescharacteristic
320C22×C11C2×2−1+412yes—
321C2×D11—24no—
322C2×D11—28no—
323C2×D11—42no—
324C2×D11—42no—
325C2×D11—44no—
326C2×D11—416no—
327C4×C11—24no—
328C4×C11—28no—
329C4×C11—44no—
330C4×C11—42no—
331Dic11—28no—
332Dic11—44no—
333Dic11—42no—
334Dic11C2×C22⋊Q818yescomplemented
335Dic11C2×#12718yes—
336C25—111no—
337C25C22×D1111yescharacteristic
338C22×Q8—118no—
339C22×Q8—228no—
340C22×Q8—228no—
341C22×Q8—228no—
342C22×D4—118no—
343C22×D4—114no—
344C22×D4—224no—
345C22×D4—224no—
346C23×C4—111no—
347C23×C4—111no—
348C23×C4—112no—
349C23×C4—114no—
350C23×C4—112no—
351C23×C4—111no—
352C23×C4—114no—
353C23×C4—224no—
354C23×C4—228no—
355C23×C4—224no—
356C23×C4—228no—
357C23×C4C22×D1112yes—
358C23×C4C22×D1111yescharacteristic
359C23×C4C22×D1112yes—
360C23×C4C22×D1111yescharacteristic
361C4⋊Q8—2232no—
362C22⋊Q8—2264no—
363C22⋊Q8—2264no—
364C4×D4—2232no—
365C2×C4⋊C4—28no—
366C2×C4⋊C4—24no—
367C2×C4⋊C4—1116no—
368C2×C4⋊C4—118no—
369C2×C4⋊C4—114no—
370C2×C4⋊C4—118no—
371C2×C4⋊C4—118no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—118no—
374C2×C4⋊C4—114no—
375C2×C4⋊C4—224no—
376C2×C4⋊C4—228no—
377C2×C4⋊C4—228no—
378C2×C4⋊C4—228no—
379C2×C4⋊C4—228no—
380C2×C4⋊C4—224no—
381C2×C4⋊C4C22×D1118yes—
382C2×C4⋊C4C22×D1114yes—
383C2×C22⋊C4—24no—
384C2×C22⋊C4—28no—
385C2×C22⋊C4—118no—
386C2×C22⋊C4—114no—
387C2×C22⋊C4—118no—
388C2×C22⋊C4—118no—
389C2×C22⋊C4—228no—
390C2×C22⋊C4—228no—
391C2×C22⋊C4—224no—
392C2×C22⋊C4—228no—
393C2×C22⋊C4C22×D1114yes—
394C2×C22⋊C4C22×D1118yes—
395C2×C42—118no—
396C2×C42—114no—
397C2×C42—118no—
398C2×C42—228no—
399#95—114no—
400#95C22×D1114yes—
401C2×C11—44no—
402C2×C11#254218yescomplemented
403C2×C11C22×C22⋊Q811yescharacteristic
404C2×C11C22×#12711yescharacteristic
405C2×C11C2×#53611yescharacteristic
406C2×C11C2×#54712yes—
407C2×C11C2×D4×Q812yes—
408D11—44no—
409C24—24no—
410C24—22no—
411C24—22no—
412C24—24no—
413C24—114no—
414C24—112no—
415C24—224no—
416C24—222no—
417C24—222no—
418C24—224no—
419C24Q8×D1114yes—
420C24C23×D1112yes—
421C24C23×D1111yescharacteristic
422C2×Q8—2216no—
423C2×Q8—2216no—
424C2×Q8—2216no—
425C2×Q8—4432no—
426C2×D4—1116no—
427C2×D4—228no—
428C2×D4—2232no—
429C2×D4—228no—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—24no—
436C22×C4—24no—
437C22×C4—24no—
438C22×C4—114no—
439C22×C4—114no—
440C22×C4—118no—
441C22×C4—114no—
442C22×C4—114no—
443C22×C4—112no—
444C22×C4—112no—
445C22×C4—118no—
446C22×C4—114no—
447C22×C4—114no—
448C22×C4—112no—
449C22×C4—228no—
450C22×C4—2216no—
451C22×C4—228no—
452C22×C4—2216no—
453C22×C4—224no—
454C22×C4—224no—
455C22×C4—222no—
456C22×C4—224no—
457C22×C4—224no—
458C22×C4—224no—
459C22×C4—224no—
460C22×C4—4416no—
461C22×C4—4416no—
462C22×C4D4×D1114yes—
463C22×C4D4×D1118yes—
464C22×C4C23×D1114yes—
465C22×C4C23×D1112yes—
466C22×C4C23×D1112yes—
467C22×C4C23×D1114yes—
468C4⋊C4—216no—
469C4⋊C4—28no—
470C4⋊C4—1132no—
471C4⋊C4—228no—
472C4⋊C4—2216no—
473C4⋊C4—2216no—
474C4⋊C4—2216no—
475C4⋊C4—2216no—
476C4⋊C4—228no—
477C22⋊C4—28no—
478C22⋊C4—216no—
479C22⋊C4—2216no—
480C22⋊C4—2216no—
481C22⋊C4—228no—
482C22⋊C4—2216no—
483C42—1116no—
484C42—2216no—
485C11C2×#254211yescharacteristic, complemented, Sylow
486C23—28no—
487C23—216no—
488C23—24no—
489C23—22no—
490C23—22no—
491C23—24no—
492C23—44no—
493C23—44no—
494C23—48no—
495C23—114no—
496C23—228no—
497C23—2216no—
498C23—224no—
499C23—222no—
500C23—222no—
501C23—224no—
502C23—444no—
503C23—444no—
504C23—448no—
505C23C2×D4×D1112yes—
506C23C2×D4×D1114yes—
507C23C2×Q8×D1114yes—
508C23C2×Q8×D1112yes—
509C23#41×D1112yes—
510C23#6704314yes—
511C23C24×D1111yescharacteristic
512Q8—4432no—
513D4—2232no—
514C2×C4—28no—
515C2×C4—216no—
516C2×C4—24no—
517C2×C4—24no—
518C2×C4—24no—
519C2×C4—22no—
520C2×C4—24no—
521C2×C4—24no—
522C2×C4—24no—
523C2×C4—24no—
524C2×C4—44no—
525C2×C4—48no—
526C2×C4—1116no—
527C2×C4—1116no—
528C2×C4—114no—
529C2×C4—114no—
530C2×C4—118no—
531C2×C4—114no—
532C2×C4—114no—
533C2×C4—118no—
534C2×C4—2216no—
535C2×C4—224no—
536C2×C4—224no—
537C2×C4—222no—
538C2×C4—224no—
539C2×C4—224no—
540C2×C4—224no—
541C2×C4—224no—
542C2×C4—4416no—
543C2×C4—4416no—
544C2×C4—444no—
545C2×C4—448no—
546C2×C4C2×D4×D1114yes—
547C2×C4C2×D4×D1118yes—
548C22—28no—
549C22—24no—
550C22—42no—
551C22—42no—
552C22—416no—
553C22—44no—
554C22—228no—
555C22—224no—
556C22—442no—
557C22—442no—
558C22—4416no—
559C22—444no—
560C22D11×C22⋊Q814yes—
561C22#1062316318yes—
562C22#1062317914yes—
563C22#1062318618yes—
564C22D11×#12714yes—
565C22C22×D4×D1111yescharacteristic
566C22C22×D4×D1112yes—
567C22C22×Q8×D1111yescharacteristic
568C22C2×#41×D1111yescharacteristic
569C22C2×#6704312yes—
570C4—24no—
571C4—28no—
572C4—42no—
573C4—44no—
574C4—118no—
575C4—118no—
576C4—228no—
577C4—442no—
578C4—444no—
579C2—44no—
580C2—444no—
581C2#1307356418yesdirect product factor
582C2C2×D11×C22⋊Q811yescharacteristic
583C2C2×D11×#12711yescharacteristic
584C2C2×#1062317911yescharacteristic
585C2C2×#1062318612yes—
586C2C2×#1062316312yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#399C2
socleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#399D11
hypocenterC11C2×#2542
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
2. C22×#66949C2semidirect
3. C22×#66931C2semidirect
5. #13073564C2direct (N × H)
6. C2×#10622290C2semidirect
7. C2×#10622562C2semidirect
8. C2×#10622605C2semidirect
10. C2×#10622589C2semidirect
11. C2×#10622262C2semidirect
12. C2×C11×#399C2semidirect
35. C2×#66949C22semidirect
37. C2×#66941C22semidirect
41. C2×#66931C22semidirect
42. C11×#399C22semidirect
45. #10622605C22semidirect
46. #10622589C22semidirect
48. #10622562C22semidirect
49. #10622290C22semidirect
50. #10622262C22semidirect
59. C22×C22⋊D11Q8semidirect
100. C2×Dic11⋊C4D4semidirect
147. C2×C22⋊D11C2×Q8semidirect
190. Dic11⋊C4C2×D4semidirect
201. C2×#399D11semidirect
257. C2×Dic11C22⋊Q8semidirect
299. #399C2×D11semidirect
334. Dic11C2×C22⋊Q8semidirect
402. C2×C11#2542semidirect
485. C11C2×#2542semidirect
581. C2#13073564direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669412
C22×#669492
C22×#669312
C22×(C22⋊D11)⋊C42
#130735642
C2×#106222902
C2×#106225622
C2×#106226052
C2×#106225702
C2×#106225892
C2×#106222622
C2×C11×#3992
C2×#254211