Finite Group Databasebeta

← C2×#13068983 #14755261

Subgroups — C2×#13068983 #14755261

Order 2816.

1802 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
1C22×#67004C211yesmaximal, characteristic
2C2×#10623358C211yesmaximal, characteristic
3C2×#10622733C211yesmaximal, characteristic, complemented
4C2×#10622542C211yesmaximal, characteristic, complemented
5#13068983C218yesmaximal, direct product factor
6C2×#10622192C211yesmaximal, characteristic, complemented
7C2×#10622161C211yesmaximal, characteristic, complemented
8C22×C11×#104C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13#10623358—22no—
14#10623358—22no—
15#10623358—22no—
16#10623358C2214yes—
17C2×#67004—22no—
18C2×#67004—24no—
19C2×#67004C418yescomplemented
20C2×#67004C2214yes—
21C2×Q8×Dic11—21no—
22C22×#4326—21no—
23C2×D4×Dic11—21no—
24C2×D4×Dic11—22no—
25C22×#4324—21no—
26C2×#66979—21no—
27C2×#66979C2211yescharacteristic
28C22×C4⋊Dic11—21no—
29C22×C4⋊Dic11C2211yescharacteristic
30C22×#4318C2211yescharacteristic
31C2×C11×#104—24no—
32C2×C11×#104C2214yes—
33C2×C11⋊#95—22no—
34#10622733—22no—
35#10622733C2214yescomplemented
36C2×#66880—21no—
37C2×#66880—21no—
38#10622542—22no—
39#10622542C2214yescomplemented
40#10622192C2214yescomplemented
41#10622161C2214yescomplemented
42C2×C11×#41—21no—
43C2×C11×#41—21no—
44C2×C11×#41—22no—
45C2×C11×#41—22no—
46C2×C11×#41C2×C414yes—
47C2×C11×#41D412yes—
48C2×C11×#41D414yes—
49C2×C11×#41C2312yes—
50C22×Q8×C11D411yescharacteristic
51C22×D4×C11—21no—
52C22×D4×C11D411yescharacteristic
53C23×C4×C11—21no—
54C23×C4×C11—21no—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11—21no—
57C23×Dic11—22no—
58C23×Dic11D412yes—
59C22×Dic22—21no—
60C22×Dic22—21no—
61C22×Dic22—21no—
62C22×Dic22—22no—
63C22×Dic22—21no—
64C22×Dic22—22no—
65C22×Dic22—21no—
66C22×Dic22—22no—
67C22×Dic22C2×C414yescomplemented
68C22×Dic22C2312yes—
69C2×C11×M16—21no—
70C2×C11×M16—22no—
71C2×C11×M16—22no—
72C2×C11×M16C2312yes—
73C22×C8×C11—21no—
74C2×C42×C11—22no—
75C2×C42×C11—22no—
76C2×C42×C11—21no—
77C2×C42×C11C2312yes—
78C2×C22⋊Dic11—22no—
79C2×C22⋊Dic11—21no—
80#67004—216no—
81#67004—28no—
82#67004C2×C4116yescomplemented
83Q8×Dic11—24no—
84Q8×Dic11—24no—
85C2×#4326—28no—
86C2×#4326—24no—
87D4×Dic11—28no—
88D4×Dic11—24no—
89D4×Dic11—24no—
90D4×Dic11—28no—
91C2×#4324—28no—
92C2×#4324—24no—
93#66979—24no—
94#66979—21no—
95#66979—21no—
96#66979—24no—
97#66979D412yes—
98#66979C2312yes—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11—24no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—21no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11—24no—
106C2×C4⋊Dic11D412yes—
107C2×C4⋊Dic11D411yescharacteristic
108C2×C4⋊Dic11D411yescharacteristic
109C2×C4⋊Dic11C2312yes—
110C2×C4×Dic11—22no—
111C2×C4×Dic11—21no—
112C2×#4318—21no—
113C2×#4318—22no—
114C2×#4318C2×C414yescomplemented
115C2×#4318C2312yes—
116C22×C11⋊C8—21no—
117C11×#104—28no—
118C11⋊#95—28no—
119#66880—24no—
120#66880—24no—
121C2×#1882—111nomaximal, Sylow
122C24×C11—21no—
123C24×C11C2×D411yescharacteristic
124C11×#41—24no—
125C11×#41—24no—
126C11×#41—24no—
127C11×#41—24no—
128C11×#41—24no—
129C11×#41—22no—
130C11×#41—22no—
131C11×#41C22⋊C418yes—
132C11×#41C22×C414yes—
133C11×#41C2×D414yes—
134C2×Q8×C11—21no—
135C2×Q8×C11—22no—
136C2×Q8×C11C22⋊C414yes—
137C2×Q8×C11C2×D412yes—
138C2×D4×C11—24no—
139C2×D4×C11—22no—
140C2×D4×C11—24no—
141C2×D4×C11—22no—
142C2×D4×C11—21no—
143C2×D4×C11—22no—
144C2×D4×C11C22⋊C414yes—
145C2×D4×C11C2×D412yes—
146C22×C4×C11—21no—
147C22×C4×C11—24no—
148C22×C4×C11—22no—
149C22×C4×C11—24no—
150C22×C4×C11—22no—
151C22×C4×C11—24no—
152C22×C4×C11—22no—
153C22×C4×C11—42no—
154C22×C4×C11—42no—
155C22×C4×C11C22×C412yes—
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D412yes—
159C22×C4×C11C2×D411yescharacteristic
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D411yescharacteristic
162C22×C4×C11#4112yes—
163C22×C4×C11#4112yes—
164C22×C4×C11C2411yescharacteristic
165C22×Dic11—28no—
166C22×Dic11—24no—
167C22×Dic11—21no—
168C22×Dic11—22no—
169C22×Dic11—21no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—44no—
173C22×Dic11—41no—
174C22×Dic11—41no—
175C22×Dic11—42no—
176C22×Dic11—84no—
177C22×Dic11C2×D414yes—
178C2×Dic22—24no—
179C2×Dic22—24no—
180C2×Dic22—24no—
181C2×Dic22—24no—
182C2×Dic22—24no—
183C2×Dic22—22no—
184C2×Dic22—22no—
185C2×Dic22—22no—
186C2×Dic22—22no—
187C2×Dic22—22no—
188C2×Dic22—41no—
189C2×Dic22—41no—
190C2×Dic22—42no—
191C2×Dic22—42no—
192C2×Dic22—42no—
193C2×Dic22—42no—
194C2×Dic22—42no—
195C2×Dic22C22×C414yescomplemented
196C11×M16—22no—
197C11×M16—22no—
198C11×M16—42no—
199C2×C8×C11—22no—
200C2×C8×C11—42no—
201C42×C11—22no—
202C42×C11—22no—
203C42×C11—42no—
204C22⋊Dic11—28no—
205C22⋊Dic11—22no—
206C22⋊Dic11—22no—
207#4326—216no—
208#4324—216no—
209C4⋊Dic11—28no—
210C4⋊Dic11—22no—
211C4⋊Dic11—21no—
212C4⋊Dic11—22no—
213C4⋊Dic11—21no—
214C4⋊Dic11—22no—
215C4⋊Dic11—22no—
216C4⋊Dic11C2×D412yes—
217C4⋊Dic11C2×D412yes—
218C4×Dic11—28no—
219C4×Dic11—22no—
220C4×Dic11—22no—
221#4318—24no—
222#4318—22no—
223#4318C22×C414yescomplemented
224C2×C11⋊C8—24no—
225C2×C11⋊C8—22no—
226C22×#137—111no—
227C2×#520—111no—
228C22×#104D1111yescharacteristic
229C2×#419—111no—
230C2×#391—111no—
231#1882—118no—
232C2×#343—111no—
233C2×#339—111no—
234C23×C11—22no—
235C23×C11—22no—
236C23×C11—22no—
237C23×C11—24no—
238C23×C11—42no—
239C23×C11—42no—
240C23×C11C4×D412yes—
241C23×C11#12011yescharacteristic
242C23×C11#12011yescharacteristic
243C23×C11#12112yes—
244C23×C11C22×D411yescharacteristic
245Q8×C11—22no—
246Q8×C11—24no—
247Q8×C11C2×C22⋊C414yes—
248D4×C11—24no—
249D4×C11—24no—
250D4×C11—28no—
251D4×C11—22no—
252D4×C11—24no—
253D4×C11C2×C22⋊C414yes—
254C2×C4×C11—22no—
255C2×C4×C11—24no—
256C2×C4×C11—24no—
257C2×C4×C11—24no—
258C2×C4×C11—28no—
259C2×C4×C11—24no—
260C2×C4×C11—48no—
261C2×C4×C11—42no—
262C2×C4×C11—42no—
263C2×C4×C11C2×C22⋊C412yes—
264C2×C4×C11C2×C22⋊C412yes—
265C2×C4×C11C4×D412yes—
266C2×C4×C11C4×D412yes—
267C2×C4×C11C4×D412yes—
268C2×C4×C11#12011yescharacteristic
269C2×C4×C11#12011yescharacteristic
270C2×C4×C11#12112yes—
271C2×C4×C11#12112yes—
272C2×C4×C11#12112yes—
273C2×C4×C11#12312yes—
274C2×C4×C11#12312yes—
275C2×C4×C11C23×C411yescharacteristic
276C2×C4×C11C22×D411yescharacteristic
277C2×C4×C11C22×D411yescharacteristic
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C2×#4111yescharacteristic
280C2×C4×C11C2×#4111yescharacteristic
281C2×Dic11—24no—
282C2×Dic11—22no—
283C2×Dic11—24no—
284C2×Dic11—22no—
285C2×Dic11—42no—
286C2×Dic11—42no—
287C2×Dic11—44no—
288C2×Dic11—44no—
289C2×Dic11—44no—
290C2×Dic11—42no—
291C2×Dic11—42no—
292C2×Dic11—44no—
293C2×Dic11—82no—
294C2×Dic11—88no—
295Dic22—24no—
296Dic22—24no—
297Dic22—42no—
298Dic22—42no—
299Dic22—44no—
300Dic22—44no—
301C8×C11—42no—
302C11⋊C8—24no—
303C22×#41C2×D1111yescharacteristic
304C23×Q8—111no—
305C2×#137—114no—
306C2×#137—118no—
307C2×#137—222no—
308C2×#137—224no—
309C22×Q16—221no—
310C22×SD16—221no—
311C22×M16—111no—
312C22×M16C2×D1111yescharacteristic
313#520—114no—
314#520—222no—
315#520—222no—
316#520—222no—
317C2×C4×Q8—221no—
318C2×C4×D4—222no—
319C2×C4×D4—221no—
320C2×#117—111no—
321C2×#117—221no—
322C22×C4⋊C4—111no—
323C22×C4⋊C4—221no—
324C22×C42C2×D1111yescharacteristic
325C2×#104—24no—
326C2×#104C2×D1114yes—
327#419—114no—
328#419—222no—
329C2×#103—221no—
330C2×#103—221no—
331#391—114no—
332#391—222no—
333C2×#95—222no—
334#343—114no—
335#339—114no—
336C22×C11—24no—
337C22×C11—24no—
338C22×C11—21no—
339C22×C11—21no—
340C22×C11—21no—
341C22×C11—21no—
342C22×C11—24no—
343C22×C11—48no—
344C22×C11—42no—
345C22×C11—42no—
346C22×C11#38612yes—
347C22×C11#38612yes—
348C22×C11#45512yes—
349C22×C11#45612yes—
350C22×C11C2×C4×D411yescharacteristic
351C22×C11C2×#12011yescharacteristic
352C22×C11C2×#12111yescharacteristic
353C4×C11—24no—
354C4×C11—44no—
355C4×C11#38612yes—
356C4×C11#38612yes—
357C4×C11C22×C22⋊C411yescharacteristic
358C4×C11C2×C4×D411yescharacteristic
359C4×C11C2×#12111yescharacteristic
360C4×C11C2×#12311yescharacteristic
361Dic11—44no—
362Dic11—42no—
363Dic11—42no—
364Dic11—44no—
365C2×#41—21no—
366C2×#41—21no—
367C2×#41—22no—
368C2×#41—22no—
369C2×#41C4×D1114yes—
370C2×#41D4412yes—
371C2×#41C22⋊D1114yes—
372C2×#41C22×D1112yes—
373C22×Q8—114no—
374C22×Q8—112no—
375C22×Q8—221no—
376C22×Q8—222no—
377C22×Q8—221no—
378C22×Q8—221no—
379C22×Q8—221no—
380C22×Q8—221no—
381C22×Q8—222no—
382C22×Q8—222no—
383C22×Q8D4411yescharacteristic
384C22×D4—21no—
385C22×D4D4411yescharacteristic
386C23×C4—21no—
387C23×C4—21no—
388C23×C4—112no—
389C23×C4—221no—
390C23×C4—222no—
391C23×C4C22×D1111yescharacteristic
392#137—1116no—
393#137—2216no—
394#137—228no—
395C2×Q16—228no—
396C2×Q16—224no—
397C2×SD16—228no—
398C2×SD16—224no—
399C2×M16—21no—
400C2×M16—22no—
401C2×M16—22no—
402C2×M16—114no—
403C2×M16—112no—
404C2×M16—221no—
405C2×M16—222no—
406C2×M16C22×D1112yes—
407C22×C8—21no—
408C22×C8—221no—
409C4×Q8—224no—
410C4×Q8—224no—
411C4×D4—228no—
412C4×D4—228no—
413C4×D4—224no—
414C4×D4—224no—
415#117—112no—
416#117—112no—
417#117—224no—
418#117—224no—
419#117—221no—
420#117—221no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—111no—
423C2×C4⋊C4—112no—
424C2×C4⋊C4—112no—
425C2×C4⋊C4—224no—
426C2×C4⋊C4—222no—
427C2×C4⋊C4—224no—
428C2×C4⋊C4—221no—
429C2×C4⋊C4—221no—
430C2×C4⋊C4—221no—
431C2×C4⋊C4—221no—
432C2×C22⋊C4—222no—
433C2×C22⋊C4—221no—
434C2×C42—22no—
435C2×C42—22no—
436C2×C42—21no—
437C2×C42—222no—
438C2×C42—221no—
439C2×C42C22×D1112yes—
440#104—28no—
441#103—224no—
442#103—224no—
443#95—228no—
444C2×C11—21no—
445C2×C11—21no—
446C2×C11—22no—
447C2×C11—44no—
448C2×C11#188214yescomplemented
449C2×C11C2×#38611yescharacteristic
450C2×C11C2×#45511yescharacteristic
451C2×C11C2×#45611yescharacteristic
452C24—21no—
453C24D4×D1111yescharacteristic
454#41—24no—
455#41—24no—
456#41—24no—
457#41—24no—
458#41—24no—
459#41—22no—
460#41—22no—
461#41(C2×D11)⋊C418yes—
462#41C2×C4×D1114yes—
463#41C2×C22⋊D1114yes—
464C2×Q8—21no—
465C2×Q8—22no—
466C2×Q8—114no—
467C2×Q8—224no—
468C2×Q8—222no—
469C2×Q8—224no—
470C2×Q8—224no—
471C2×Q8—224no—
472C2×Q8—224no—
473C2×Q8—222no—
474C2×Q8—222no—
475C2×Q8—222no—
476C2×Q8—222no—
477C2×Q8—441no—
478C2×Q8—441no—
479C2×Q8—442no—
480C2×Q8—442no—
481C2×Q8—442no—
482C2×Q8—442no—
483C2×Q8—442no—
484C2×Q8(C2×D11)⋊C414yes—
485C2×Q8C2×D4412yes—
486C2×D4—24no—
487C2×D4—22no—
488C2×D4—24no—
489C2×D4—22no—
490C2×D4—21no—
491C2×D4—22no—
492C2×D4(C2×D11)⋊C414yes—
493C2×D4C2×D4412yes—
494C22×C4—21no—
495C22×C4—24no—
496C22×C4—22no—
497C22×C4—24no—
498C22×C4—22no—
499C22×C4—24no—
500C22×C4—22no—
501C22×C4—42no—
502C22×C4—42no—
503C22×C4—114no—
504C22×C4—224no—
505C22×C4—221no—
506C22×C4—221no—
507C22×C4—222no—
508C22×C4—222no—
509C22×C4—228no—
510C22×C4—222no—
511C22×C4—441no—
512C22×C4—441no—
513C22×C4—442no—
514C22×C4—444no—
515C22×C4—884no—
516C22×C4C2×C4×D1112yes—
517C22×C4C2×D4411yescharacteristic
518C22×C4C2×D4411yescharacteristic
519C22×C4D4×D1111yescharacteristic
520C22×C4D4×D1111yescharacteristic
521C22×C4D4×D1111yescharacteristic
522C22×C4#434112yes—
523C22×C4#434112yes—
524C22×C4C2×C22⋊D1112yes—
525C22×C4C23×D1111yescharacteristic
526Q16—2216no—
527SD16—2216no—
528M16—22no—
529M16—22no—
530M16—42no—
531M16—114no—
532M16—224no—
533M16—222no—
534C2×C8—22no—
535C2×C8—42no—
536C2×C8—224no—
537C2×C8—222no—
538C4⋊C4—112no—
539C4⋊C4—112no—
540C4⋊C4—228no—
541C4⋊C4—221no—
542C4⋊C4—222no—
543C4⋊C4—222no—
544C4⋊C4—221no—
545C4⋊C4—222no—
546C4⋊C4—222no—
547C22⋊C4—228no—
548C22⋊C4—222no—
549C22⋊C4—222no—
550C42—22no—
551C42—22no—
552C42—42no—
553C42—228no—
554C42—222no—
555C42—222no—
556C11C2×#188211yescharacteristic, complemented, Sylow
557C23—22no—
558C23—22no—
559C23—22no—
560C23—24no—
561C23—42no—
562C23—42no—
563C23(C22⋊D11)⋊C412yes—
564C23#6693511yescharacteristic
565C23#6693511yescharacteristic
566C23#6699212yes—
567C23C2×D4×D1111yescharacteristic
568Q8—22no—
569Q8—24no—
570Q8—224no—
571Q8—224no—
572Q8—442no—
573Q8—442no—
574Q8—444no—
575Q8—444no—
576Q8C2×(C2×D11)⋊C414yes—
577D4—24no—
578D4—24no—
579D4—28no—
580D4—22no—
581D4—24no—
582D4C2×(C2×D11)⋊C414yes—
583C2×C4—22no—
584C2×C4—24no—
585C2×C4—24no—
586C2×C4—24no—
587C2×C4—28no—
588C2×C4—24no—
589C2×C4—48no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—224no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—224no—
596C2×C4—442no—
597C2×C4—442no—
598C2×C4—444no—
599C2×C4—444no—
600C2×C4—444no—
601C2×C4—442no—
602C2×C4—442no—
603C2×C4—444no—
604C2×C4—882no—
605C2×C4—888no—
606C2×C4(C22⋊D11)⋊C412yes—
607C2×C4(C22⋊D11)⋊C412yes—
608C2×C4(C22⋊D11)⋊C412yes—
609C2×C4#6693511yescharacteristic
610C2×C4#6693511yescharacteristic
611C2×C4#6693912yes—
612C2×C4#6693912yes—
613C2×C4C2×(C2×D11)⋊C412yes—
614C2×C4C2×(C2×D11)⋊C412yes—
615C2×C4#6699212yes—
616C2×C4#6699212yes—
617C2×C4#6699212yes—
618C2×C4C22×C4×D1111yescharacteristic
619C2×C4C22×D4411yescharacteristic
620C2×C4C2×D4×D1111yescharacteristic
621C2×C4C2×#434111yescharacteristic
622C2×C4C2×#434111yescharacteristic
623C2×C4C22×C22⋊D1111yescharacteristic
624C8—42no—
625C8—224no—
626C22—24no—
627C22—24no—
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—24no—
633C22—48no—
634C22—42no—
635C22—42no—
636C22#1062243812yes—
637C22#1062243912yes—
638C22#1062257112yes—
639C22#1062257112yes—
640C22C2×(C22⋊D11)⋊C411yescharacteristic
641C22C2×#6693511yescharacteristic
642C22C2×#6699211yescharacteristic
643C4—24no—
644C4—44no—
645C4—444no—
646C4—444no—
647C4—442no—
648C4—442no—
649C4#1062257112yes—
650C4#1062257112yes—
651C4C2×(C22⋊D11)⋊C411yescharacteristic
652C4C2×#6693911yescharacteristic
653C4C22×(C2×D11)⋊C411yescharacteristic
654C4C2×#6699211yescharacteristic
655C2—21no—
656C2—21no—
657C2—22no—
658C2—44no—
659C2#1306898314yesdirect product factor
660C2C2×#1062257111yescharacteristic
661C2C2×#1062243811yescharacteristic
662C2C2×#1062243911yescharacteristic
subgroupG/H
centerC23#66935
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C11×#104C2
socleC23×C11#120
prime radicalC22×C11×#41C22
cosocleC22×C4×C11C24
hypercenterC22×#104D11
hypocenterC11C2×#1882
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
3. C2×#10622733C2semidirect
4. C2×#10622542C2semidirect
5. #13068983C2direct (N × H)
6. C2×#10622192C2semidirect
7. C2×#10622161C2semidirect
19. C2×#67004C4semidirect
35. #10622733C22semidirect
39. #10622542C22semidirect
40. #10622192C22semidirect
41. #10622161C22semidirect
67. C22×Dic22C2×C4semidirect
82. #67004C2×C4semidirect
114. C2×#4318C2×C4semidirect
195. C2×Dic22C22×C4semidirect
223. #4318C22×C4semidirect
448. C2×C11#1882semidirect
556. C11C2×#1882semidirect
659. C2#13068983direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670042
C2×#106233582
C2×#106227332
C2×#106225422
#130689832
C2×#106221922
C2×#106221612
C22×C11×#1042
C2×#188211