Finite Group Databasebeta

← C2×#13069652 #14780673

Subgroups — C2×#13069652 #14780673

Order 2816.

1998 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic
2C2×#10623347C211yesmaximal, characteristic
3C22×#66869C211yesmaximal, characteristic
4C2×#10622838C211yesmaximal, characteristic, complemented
5C22×#66900C211yesmaximal, characteristic, complemented
6#13069652C218yesmaximal, direct product factor
7C2×#10622161C211yesmaximal, characteristic, complemented
8C22×C11×C4⋊Q8C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C23×Q8×C11C2211yescharacteristic
11C22×#4339C2211yescharacteristic
12C2×C11×C4⋊Q8—24no—
13C2×C11×C4⋊Q8—22no—
14C2×C11×C4⋊Q8—24no—
15C2×C11×C4⋊Q8C2214yescomplemented
16C22×C11×C4⋊C4—22no—
17C22×C42×C11C2211yescharacteristic
18#10623347—22no—
19#10623347—22no—
20#10623347—22no—
21#10623347C2214yes—
22C2×#67000—21no—
23C2×#66999—22no—
24C2×#66997—21no—
25C22×#4326—21no—
26C2×#66995—24no—
27C2×#66995—22no—
28C2×#66995—24no—
29C2×#66995C2214yes—
30C22×#4325—21no—
31C2×#66982—22no—
32C2×#66979C2211yescharacteristic
33C22×#4318C2211yescharacteristic
34C22×#4318C2211yescharacteristic
35C2×#66900—24no—
36C2×#66900C2214yescomplemented
37#10622838—22no—
38#10622838C2214yescomplemented
39C2×#66899—22no—
40C2×#66869—24no—
41C2×#66869C2214yes—
42#10622161C2214yescomplemented
43C22×Q8×C11—21no—
44C22×Q8×C11—21no—
45C22×Q8×C11—21no—
46C22×Q8×C11—21no—
47C22×Q8×C11—22no—
48C22×Q8×C11—22no—
49C22×Q8×C11—22no—
50C22×Q8×C11—22no—
51C22×Q8×C11—21no—
52C22×Q8×C11—22no—
53C22×Q8×C11—21no—
54C22×Q8×C11—21no—
55C22×Q8×C11—22no—
56C22×Q8×C11—21no—
57C22×Q8×C11—21no—
58C22×Q8×C11—22no—
59C22×Q8×C11D414yes—
60C22×Q8×C11D412yes—
61C22×Q8×C11C2312yes—
62C22×Q8×C11C2312yes—
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11D412yes—
66C23×C4×C11C2311yescharacteristic
67C22×C22⋊D11—21no—
68C2×#4339—21no—
69C2×#4339—21no—
70C2×#4339—22no—
71C2×#4339—22no—
72C2×#4339—22no—
73C2×#4339—22no—
74C2×#4339D412yes—
75C2×#4339C2312yes—
76C22×D44D411yescharacteristic
77C22×C4×D11—21no—
78C22×Dic22D411yescharacteristic
79C11×C4⋊Q8—216no—
80C11×C4⋊Q8—28no—
81C11×C4⋊Q8—28no—
82C2×C11×C4⋊C4—216no—
83C2×C11×C4⋊C4—28no—
84C2×C42×C11—21no—
85C2×C42×C11—22no—
86C2×C42×C11D414yes—
87C2×C42×C11C2312yes—
88C2×C22⋊Dic11—21no—
89#67000—24no—
90#67000—24no—
91#66999—28no—
92#66999—28no—
93#66997—24no—
94#66997—24no—
95C2×#4326—28no—
96C2×#4326—24no—
97#66995—216no—
98#66995—28no—
99#66995—28no—
100C2×#4325—28no—
101C2×#4325—24no—
102#66982—28no—
103#66982—28no—
104C2×(C2×D11)⋊C4—24no—
105#66979—21no—
106#66979—21no—
107#66979D412yes—
108#66979C2312yes—
109C2×C4⋊Dic11D412yes—
110C2×Dic11⋊C4—24no—
111C2×C4×Dic11—21no—
112C2×#4318—21no—
113C2×#4318—22no—
114C2×#4318—21no—
115C2×#4318—22no—
116C2×#4318—22no—
117C2×#4318D414yes—
118C2×#4318C2312yes—
119C2×#4318C2312yes—
120C22×C11⋊C8—21no—
121C22×C11⋊C8—21no—
122#66900—28no—
123#66899—28no—
124#66869—28no—
125C2×#2005—111nomaximal, Sylow
126C24×C11C2×D411yescharacteristic
127C23×D11—21no—
128C2×Q8×C11—22no—
129C2×Q8×C11—22no—
130C2×Q8×C11—24no—
131C2×Q8×C11—24no—
132C2×Q8×C11—24no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11—22no—
136C2×Q8×C11—22no—
137C2×Q8×C11—22no—
138C2×Q8×C11—22no—
139C2×Q8×C11—22no—
140C2×Q8×C11—24no—
141C2×Q8×C11—24no—
142C2×Q8×C11—24no—
143C2×Q8×C11—24no—
144C2×Q8×C11—22no—
145C2×Q8×C11—22no—
146C2×Q8×C11—22no—
147C2×Q8×C11—22no—
148C2×Q8×C11—41no—
149C2×Q8×C11—41no—
150C2×Q8×C11—42no—
151C2×Q8×C11—42no—
152C2×Q8×C11—42no—
153C2×Q8×C11—42no—
154C2×Q8×C11—42no—
155C2×Q8×C11—42no—
156C2×Q8×C11—42no—
157C2×Q8×C11—42no—
158C2×Q8×C11—42no—
159C2×Q8×C11—42no—
160C2×Q8×C11—42no—
161C2×Q8×C11—42no—
162C2×Q8×C11—42no—
163C2×Q8×C11C2×D414yes—
164C22×C4×C11—28no—
165C22×C4×C11—24no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—24no—
170C22×C4×C11—24no—
171C22×C4×C11—24no—
172C22×C4×C11—22no—
173C22×C4×C11—41no—
174C22×C4×C11—41no—
175C22×C4×C11—42no—
176C22×C4×C11C2×D414yes—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2×D412yes—
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D412yes—
185C22×C4×C11#4112yes—
186C22×C4×C11C2411yescharacteristic
187C2×C22⋊D11—22no—
188C2×C22⋊D11—22no—
189C2×C22⋊D11—42no—
190C2×C22⋊D11—42no—
191C22×Dic11—22no—
192C22×Dic11—21no—
193#4339—24no—
194#4339—24no—
195#4339—22no—
196#4339—22no—
197#4339—22no—
198#4339—22no—
199#4339—42no—
200#4339—42no—
201#4339—42no—
202#4339—42no—
203C2×D44—21no—
204C2×D44—22no—
205C2×D44—22no—
206C2×D44C2×D412yes—
207C2×C4×D11—22no—
208C2×C4×D11—22no—
209C2×C4×D11—42no—
210C2×C4×D11—42no—
211C2×Dic22—22no—
212C2×Dic22—21no—
213C2×Dic22—22no—
214C2×Dic22C2×D412yes—
215C11×C4⋊C4—232no—
216C42×C11—24no—
217C42×C11—22no—
218C42×C11C2×D414yes—
219C22⋊Dic11—22no—
220C22⋊Dic11—22no—
221#4326—216no—
222#4325—216no—
223(C2×D11)⋊C4—216no—
224C4⋊Dic11—22no—
225C4⋊Dic11C2×D414yes—
226Dic11⋊C4—216no—
227C4×Dic11—22no—
228C4×Dic11—22no—
229#4318—24no—
230#4318—22no—
231#4318—22no—
232#4318—22no—
233#4318—42no—
234#4318C2×D414yes—
235C2×C11⋊C8—24no—
236C2×C11⋊C8—22no—
237C2×C11⋊C8—22no—
238C2×C11⋊C8—42no—
239C22×#137—111no—
240C2×#536—111no—
241C22×C4⋊Q8D1111yescharacteristic, complemented
242C22×#104—111no—
243C2×#419—111no—
244C22×#101—111no—
245#2005—118no—
246C2×#339—111no—
247C23×C11—24no—
248C23×C11#12011yescharacteristic
249C23×C11#12011yescharacteristic
250C23×C11#12012yes—
251C23×C11#12112yes—
252C23×C11C22×D411yescharacteristic
253C22×D11—22no—
254C22×D11—42no—
255C22×D11—44no—
256Q8×C11—24no—
257Q8×C11—24no—
258Q8×C11—42no—
259Q8×C11—42no—
260Q8×C11—42no—
261Q8×C11—42no—
262Q8×C11—42no—
263Q8×C11—42no—
264Q8×C11—44no—
265Q8×C11—44no—
266Q8×C11—44no—
267Q8×C11—44no—
268C2×C4×C11—28no—
269C2×C4×C11—216no—
270C2×C4×C11—24no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—24no—
275C2×C4×C11—42no—
276C2×C4×C11—42no—
277C2×C4×C11—44no—
278C2×C4×C11—44no—
279C2×C4×C11—44no—
280C2×C4×C11—44no—
281C2×C4×C11#12012yes—
282C2×C4×C11#12012yes—
283C2×C4×C11#12011yescharacteristic
284C2×C4×C11#12011yescharacteristic
285C2×C4×C11#12012yes—
286C2×C4×C11#12112yes—
287C2×C4×C11#12112yes—
288C2×C4×C11#12112yes—
289C2×C4×C11#12112yes—
290C2×C4×C11#12112yes—
291C2×C4×C11#12712yes—
292C2×C4×C11#12712yes—
293C2×C4×C11C22×D411yescharacteristic
294C2×C4×C11C22×D411yescharacteristic
295C2×C4×C11C22×D411yescharacteristic
296C2×C4×C11C22×D411yescharacteristic
297C2×C4×C11C22×D411yescharacteristic
298C2×C4×C11C2×#4111yescharacteristic
299C22⋊D11—42no—
300C22⋊D11—42no—
301C22⋊D11—44no—
302C2×Dic11—24no—
303C2×Dic11—22no—
304C2×Dic11—42no—
305C2×Dic11—44no—
306D44—22no—
307D44—22no—
308D44—42no—
309C4×D11—42no—
310C4×D11—42no—
311C4×D11—44no—
312Dic22—22no—
313Dic22—22no—
314Dic22—42no—
315C11⋊C8—24no—
316C11⋊C8—42no—
317C22×#41—111no—
318C23×Q8C2×D1111yescharacteristic
319C23×Q8C2×D1111yescharacteristic
320C2×#137—114no—
321C2×#137—224no—
322C2×#137—222no—
323C2×#137—224no—
324C22×Q16—221no—
325C22×SD16—221no—
326C22×M16—111no—
327C22×M16—111no—
328#536—114no—
329#536—222no—
330#536—222no—
331#536—222no—
332C2×C4⋊Q8—24no—
333C2×C4⋊Q8—22no—
334C2×C4⋊Q8—24no—
335C2×C4⋊Q8—221no—
336C2×C4⋊Q8C2×D1114yescomplemented
337C2×#124—221no—
338C2×#123—222no—
339C2×C22⋊Q8—222no—
340C2×#117—111no—
341C22×C4⋊C4—22no—
342C22×C42C2×D1111yescharacteristic
343C2×#104—114no—
344C2×#104—224no—
345#419—114no—
346#419—222no—
347C2×#103—222no—
348C2×#101—114no—
349C2×#101—224no—
350#339—114no—
351C22×C11—22no—
352C22×C11—22no—
353C22×C11—24no—
354C22×C11—24no—
355C22×C11#39212yes—
356C22×C11#39212yes—
357C22×C11#45614yes—
358C22×C11C2×#12011yescharacteristic
359C22×C11C2×#12011yescharacteristic
360C22×C11C2×#12111yescharacteristic
361C2×D11—42no—
362C2×D11—44no—
363C2×D11—84no—
364C4×C11—28no—
365C4×C11—44no—
366C4×C11—44no—
367C4×C11#39212yes—
368C4×C11#39212yes—
369C4×C11C2×#12011yescharacteristic
370C4×C11C2×#12111yescharacteristic
371C4×C11C2×#12111yescharacteristic
372C4×C11C2×#12711yescharacteristic
373Dic11—42no—
374Dic11—44no—
375C2×#41—112no—
376C2×#41—112no—
377C2×#41—221no—
378C2×#41—221no—
379C2×#41—222no—
380C2×#41—222no—
381C2×#41—222no—
382C2×#41—222no—
383C22×Q8—21no—
384C22×Q8—21no—
385C22×Q8—21no—
386C22×Q8—21no—
387C22×Q8—22no—
388C22×Q8—22no—
389C22×Q8—22no—
390C22×Q8—22no—
391C22×Q8—22no—
392C22×Q8—21no—
393C22×Q8—21no—
394C22×Q8—21no—
395C22×Q8—22no—
396C22×Q8—21no—
397C22×Q8—21no—
398C22×Q8—22no—
399C22×Q8—111no—
400C22×Q8C22⋊D1114yes—
401C22×Q8C22⋊D1112yes—
402C22×Q8C22×D1112yes—
403C22×Q8C22×D1112yes—
404C22×D4—111no—
405C22×D4—221no—
406C23×C4—21no—
407C23×C4—21no—
408C23×C4—221no—
409C23×C4C22⋊D1112yes—
410C23×C4C22×D1111yescharacteristic
411#137—228no—
412#137—2216no—
413#137—228no—
414C2×Q16—224no—
415C2×Q16—228no—
416C2×SD16—224no—
417C2×SD16—228no—
418C2×M16—114no—
419C2×M16—112no—
420C2×M16—112no—
421C2×M16—221no—
422C2×M16—222no—
423C2×M16—221no—
424C2×M16—222no—
425C2×M16—222no—
426C22×C8—221no—
427C22×C8—221no—
428C4⋊Q8—216no—
429C4⋊Q8—28no—
430C4⋊Q8—28no—
431C4⋊Q8—224no—
432C4⋊Q8—224no—
433#124—224no—
434#124—224no—
435#123—228no—
436#123—228no—
437C22⋊Q8—228no—
438C22⋊Q8—228no—
439#117—112no—
440#117—112no—
441#117—221no—
442#117—221no—
443C2×C4⋊C4—216no—
444C2×C4⋊C4—28no—
445C2×C4⋊C4—112no—
446C2×C4⋊C4—224no—
447C2×C22⋊C4—224no—
448C2×C22⋊C4—221no—
449C2×C42—21no—
450C2×C42—22no—
451C2×C42—221no—
452C2×C42C22⋊D1114yes—
453C2×C42C22×D1112yes—
454#104—228no—
455#103—228no—
456#101—228no—
457C2×C11—21no—
458C2×C11—21no—
459C2×C11—22no—
460C2×C11#200514yescomplemented
461C2×C11C2×#39211yescharacteristic
462C2×C11C2×#45612yes—
463D11—82no—
464C24—221no—
465C24C2×C22⋊D1111yescharacteristic
466#41—224no—
467#41—224no—
468#41—222no—
469#41—222no—
470#41—222no—
471#41—222no—
472#41—442no—
473#41—442no—
474#41—442no—
475#41—442no—
476C2×Q8—22no—
477C2×Q8—22no—
478C2×Q8—24no—
479C2×Q8—24no—
480C2×Q8—24no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—24no—
489C2×Q8—24no—
490C2×Q8—24no—
491C2×Q8—24no—
492C2×Q8—22no—
493C2×Q8—22no—
494C2×Q8—22no—
495C2×Q8—22no—
496C2×Q8—41no—
497C2×Q8—41no—
498C2×Q8—42no—
499C2×Q8—42no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8—42no—
503C2×Q8—42no—
504C2×Q8—42no—
505C2×Q8—42no—
506C2×Q8—42no—
507C2×Q8—42no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—42no—
511C2×Q8—112no—
512C2×Q8—221no—
513C2×Q8—222no—
514C2×Q8—222no—
515C2×Q8C2×C22⋊D1114yes—
516C2×D4—112no—
517C2×D4—222no—
518C2×D4—222no—
519C2×D4—222no—
520C2×D4—221no—
521C2×D4—222no—
522C2×D4—442no—
523C2×D4—442no—
524C22×C4—28no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—24no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—22no—
533C22×C4—41no—
534C22×C4—41no—
535C22×C4—42no—
536C22×C4—222no—
537C22×C4—221no—
538C22×C4—222no—
539C22×C4—222no—
540C22×C4—442no—
541C22×C4—442no—
542C22×C4D4×D1111yescharacteristic
543C22×C4D4×D1111yescharacteristic
544C22×C4D4×D1112yes—
545C22×C4D4×D1111yescharacteristic
546C22×C4D4×D1111yescharacteristic
547C22×C4#434112yes—
548C22×C4C2×C22⋊D1114yes—
549C22×C4C2×C22⋊D1111yescharacteristic
550C22×C4C2×C22⋊D1112yes—
551C22×C4C2×C22⋊D1112yes—
552C22×C4C23×D1111yescharacteristic
553Q16—2216no—
554SD16—2216no—
555M16—114no—
556M16—224no—
557M16—222no—
558M16—222no—
559M16—222no—
560M16—442no—
561C2×C8—224no—
562C2×C8—222no—
563C2×C8—222no—
564C2×C8—442no—
565C4⋊C4—232no—
566C4⋊C4—114no—
567C4⋊C4—2216no—
568C4⋊C4—222no—
569C22⋊C4—2216no—
570C22⋊C4—222no—
571C22⋊C4—222no—
572C42—24no—
573C42—22no—
574C42—222no—
575C42—222no—
576C42C2×C22⋊D1114yes—
577C11C2×#200511yescharacteristic, complemented, Sylow
578C23—24no—
579C23—222no—
580C23—442no—
581C23—444no—
582C23#6699011yescharacteristic
583C23#6699011yescharacteristic
584C23#6699212yes—
585C23#6700612yes—
586C23C22×C22⋊D1111yescharacteristic
587Q8—24no—
588Q8—24no—
589Q8—42no—
590Q8—42no—
591Q8—42no—
592Q8—42no—
593Q8—42no—
594Q8—42no—
595Q8—44no—
596Q8—44no—
597Q8—44no—
598Q8—44no—
599Q8—222no—
600Q8—222no—
601Q8—442no—
602D4—222no—
603D4—222no—
604D4—442no—
605D4—444no—
606D4—442no—
607D4—442no—
608C2×C4—216no—
609C2×C4—28no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—24no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—42no—
616C2×C4—42no—
617C2×C4—44no—
618C2×C4—44no—
619C2×C4—44no—
620C2×C4—44no—
621C2×C4—224no—
622C2×C4—222no—
623C2×C4—442no—
624C2×C4—444no—
625C2×C4—442no—
626C2×C4—442no—
627C2×C4—444no—
628C2×C4#6699012yes—
629C2×C4#6699012yes—
630C2×C4#6699011yescharacteristic
631C2×C4#6699011yescharacteristic
632C2×C4#6699112yes—
633C2×C4#6699112yes—
634C2×C4#6699212yes—
635C2×C4#6699212yes—
636C2×C4#6699212yes—
637C2×C4#6699312yes—
638C2×C4#6699312yes—
639C2×C4#6700612yes—
640C2×C4C2×D4×D1111yescharacteristic
641C2×C4C2×D4×D1111yescharacteristic
642C2×C4C2×D4×D1111yescharacteristic
643C2×C4C2×#434111yescharacteristic
644C2×C4C22×C22⋊D1111yescharacteristic
645C2×C4C22×C22⋊D1111yescharacteristic
646C8—224no—
647C8—442no—
648C22—24no—
649C22—24no—
650C22—22no—
651C22—22no—
652C22—442no—
653C22—444no—
654C22—884no—
655C22#1062270814yes—
656C22#1062283612yes—
657C22#1062283612yes—
658C22C2×#6699011yescharacteristic
659C22C2×#6699211yescharacteristic
660C22C2×#6700611yescharacteristic
661C4—28no—
662C4—44no—
663C4—44no—
664C4—442no—
665C4—444no—
666C4#1062283612yes—
667C4#1062283612yes—
668C4C2×#6699011yescharacteristic
669C4C2×#6699111yescharacteristic
670C4C2×#6699211yescharacteristic
671C4C2×#6699311yescharacteristic
672C2—21no—
673C2—21no—
674C2—22no—
675C2—882no—
676C2#1306965214yesdirect product factor
677C2C2×#1062283611yescharacteristic
678C2C2×#1062270812yes—
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×C4⋊Q8C2
socleC23×C11#120
prime radicalC22×#4339C22
hypercenterC22×C4⋊Q8D11
hypocenterC11C2×#2005
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. C2×#10622838C2semidirect
5. C22×#66900C2semidirect
6. #13069652C2direct (N × H)
7. C2×#10622161C2semidirect
8. C22×C11×C4⋊Q8C2semidirect
15. C2×C11×C4⋊Q8C22semidirect
36. C2×#66900C22semidirect
38. #10622838C22semidirect
42. #10622161C22semidirect
241. C22×C4⋊Q8D11semidirect
336. C2×C4⋊Q8C2×D11semidirect
460. C2×C11#2005semidirect
577. C11C2×#2005semidirect
676. C2#13069652direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669952
C2×#106233472
C22×#668692
C2×#106228382
C22×#669002
#130696522
C2×#106221612
C22×C11×C4⋊Q82
C2×#200511