Finite Group Databasebeta

← C2×#13069650 #14780671

Subgroups — C2×#13069650 #14780671

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×#67004C211yesmaximal, characteristic
2C22×#66997C211yesmaximal, characteristic, complemented
3C22×#66901C211yesmaximal, characteristic
4C2×#10622617C211yesmaximal, characteristic, complemented
5C22×#66900C211yesmaximal, characteristic, complemented
6#13069650C218yesmaximal, direct product factor
7C2×#10622170C211yesmaximal, characteristic, complemented
8C2×C11×#536C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C23×Q8×C11C2211yescharacteristic
11C23×Dic22C2211yescharacteristic
12C11×#536—22no—
13C11×#536—22no—
14C11×#536—22no—
15C11×#536C2214yes—
16C2×C11×C4⋊Q8—21no—
17C2×C11×#124—21no—
18C2×C11×#123—22no—
19C2×C11×C22⋊Q8—22no—
20C2×C11×#117C2211yescharacteristic
21C2×#67004—22no—
22C2×#67004—24no—
23C2×#67004—24no—
24C2×#67004C2214yes—
25C2×#66997—22no—
26C2×#66997—24no—
27C2×#66997—24no—
28C2×#66997C2214yescomplemented
29C22×#4326—21no—
30C22×#4324—21no—
31C22×Dic11⋊C4—22no—
32C22×C4×Dic11C2211yescharacteristic
33C22×#4318C2211yescharacteristic
34C22×#4318C2211yescharacteristic
35C2×#66901—24no—
36C2×#66901C2214yes—
37C2×#66900—24no—
38C2×#66900C2214yescomplemented
39#10622617—22no—
40#10622617C2214yescomplemented
41C2×#66874—22no—
42#10622170C2214yescomplemented
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—22no—
46C2×C11×#41—22no—
47C2×C11×#41—22no—
48C2×C11×#41—22no—
49C2×C11×#41D412yes—
50C2×C11×#41C2312yes—
51C22×Q8×C11—22no—
52C22×Q8×C11—22no—
53C22×Q8×C11—22no—
54C22×Q8×C11—21no—
55C22×Q8×C11—21no—
56C22×Q8×C11—21no—
57C22×Q8×C11—21no—
58C22×Q8×C11—22no—
59C22×Q8×C11D411yescharacteristic
60C22×Q8×C11D412yes—
61C22×Q8×C11C2312yes—
62C22×D4×C11—21no—
63C22×D4×C11D411yescharacteristic
64C23×C4×C11—21no—
65C23×C4×C11D412yes—
66C23×C4×C11C2311yescharacteristic
67C23×Dic11—21no—
68C23×Dic11—21no—
69C22×Dic22—21no—
70C22×Dic22—21no—
71C22×Dic22—22no—
72C22×Dic22—21no—
73C22×Dic22—21no—
74C22×Dic22—22no—
75C22×Dic22—22no—
76C22×Dic22—21no—
77C22×Dic22D414yes—
78C22×Dic22C2312yes—
79C11×C4⋊Q8—24no—
80C11×C4⋊Q8—24no—
81C11×#124—24no—
82C11×#124—24no—
83C11×#123—28no—
84C11×#123—28no—
85C11×C22⋊Q8—28no—
86C11×C22⋊Q8—28no—
87C11×#117—21no—
88C11×#117—21no—
89C11×#117D412yes—
90C11×#117C2312yes—
91C2×C11×C4⋊C4—24no—
92C2×C11×C4⋊C4D412yes—
93C2×C11×C22⋊C4—24no—
94C2×C11×C22⋊C4—21no—
95C2×C42×C11—21no—
96#67004—216no—
97#67004—28no—
98#67004—28no—
99#66997—216no—
100#66997—28no—
101#66997—28no—
102C2×#4326—28no—
103C2×#4326—24no—
104C2×#4324—28no—
105C2×#4324—24no—
106C2×Dic11⋊C4—216no—
107C2×Dic11⋊C4—28no—
108C2×C4×Dic11—22no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11D414yes—
111C2×C4×Dic11C2312yes—
112C2×#4318—22no—
113C2×#4318—21no—
114C2×#4318—21no—
115C2×#4318—22no—
116C2×#4318—22no—
117C2×#4318D414yes—
118C2×#4318C2312yes—
119C2×#4318C2312yes—
120C22×C11⋊C8—21no—
121C22×C11⋊C8—21no—
122#66901—28no—
123#66900—28no—
124#66874—28no—
125C2×#2005—111nomaximal, Sylow
126C24×C11—21no—
127C24×C11C2×D411yescharacteristic
128C11×#41—24no—
129C11×#41—24no—
130C11×#41—22no—
131C11×#41—22no—
132C11×#41—22no—
133C11×#41—22no—
134C11×#41—42no—
135C11×#41—42no—
136C11×#41—42no—
137C11×#41—42no—
138C2×Q8×C11—24no—
139C2×Q8×C11—22no—
140C2×Q8×C11—22no—
141C2×Q8×C11—21no—
142C2×Q8×C11—24no—
143C2×Q8×C11—22no—
144C2×Q8×C11—22no—
145C2×Q8×C11—22no—
146C2×Q8×C11—22no—
147C2×Q8×C11—22no—
148C2×Q8×C11—22no—
149C2×Q8×C11—22no—
150C2×Q8×C11—22no—
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×C11C2×D412yes—
160C2×D4×C11—22no—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
163C2×D4×C11—21no—
164C2×D4×C11—22no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11C2×D412yes—
168C22×C4×C11—24no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—21no—
172C22×C4×C11—22no—
173C22×C4×C11—24no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—42no—
177C22×C4×C11—42no—
178C22×C4×C11C2×D414yes—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D411yescharacteristic
183C22×C4×C11C2×D412yes—
184C22×C4×C11C2×D412yes—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11#4112yes—
188C22×C4×C11C2411yescharacteristic
189C22×Dic11—28no—
190C22×Dic11—24no—
191C22×Dic11—24no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—41no—
195C22×Dic11—41no—
196C22×Dic11—42no—
197C2×Dic22—24no—
198C2×Dic22—24no—
199C2×Dic22—24no—
200C2×Dic22—24no—
201C2×Dic22—24no—
202C2×Dic22—22no—
203C2×Dic22—22no—
204C2×Dic22—22no—
205C2×Dic22—22no—
206C2×Dic22—22no—
207C2×Dic22—41no—
208C2×Dic22—41no—
209C2×Dic22—42no—
210C2×Dic22—42no—
211C2×Dic22—42no—
212C2×Dic22—42no—
213C2×Dic22—42no—
214C2×Dic22C2×D414yes—
215C11×C4⋊C4—216no—
216C11×C4⋊C4—22no—
217C11×C4⋊C4C2×D414yes—
218C11×C22⋊C4—216no—
219C11×C22⋊C4—22no—
220C11×C22⋊C4—22no—
221C42×C11—22no—
222C42×C11—22no—
223#4326—216no—
224#4324—216no—
225Dic11⋊C4—232no—
226C4×Dic11—24no—
227C4×Dic11—22no—
228C4×Dic11C2×D414yes—
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×#536D1111yescharacteristic
241C22×C4⋊Q8—111no—
242C22×#104—111no—
243C2×#419—111no—
244C22×#101—111no—
245#2005—118no—
246C2×#339—111no—
247C23×C11—24no—
248C23×C11—22no—
249C23×C11—42no—
250C23×C11—44no—
251C23×C11#12012yes—
252C23×C11#12011yescharacteristic
253C23×C11#12011yescharacteristic
254C23×C11#12112yes—
255C23×C11C22×D411yescharacteristic
256Q8×C11—22no—
257Q8×C11—22no—
258Q8×C11—42no—
259Q8×C11—42no—
260Q8×C11—42no—
261Q8×C11—42no—
262Q8×C11—44no—
263Q8×C11—44no—
264Q8×C11—42no—
265D4×C11—22no—
266D4×C11—22no—
267D4×C11—42no—
268D4×C11—42no—
269D4×C11—44no—
270D4×C11—42no—
271C2×C4×C11—24no—
272C2×C4×C11—24no—
273C2×C4×C11—24no—
274C2×C4×C11—22no—
275C2×C4×C11—24no—
276C2×C4×C11—44no—
277C2×C4×C11—44no—
278C2×C4×C11—42no—
279C2×C4×C11—44no—
280C2×C4×C11—42no—
281C2×C4×C11—42no—
282C2×C4×C11—44no—
283C2×C4×C11#12012yes—
284C2×C4×C11#12012yes—
285C2×C4×C11#12012yes—
286C2×C4×C11#12011yescharacteristic
287C2×C4×C11#12011yescharacteristic
288C2×C4×C11#12112yes—
289C2×C4×C11#12112yes—
290C2×C4×C11#12112yes—
291C2×C4×C11#12112yes—
292C2×C4×C11#12112yes—
293C2×C4×C11#12712yes—
294C2×C4×C11#12712yes—
295C2×C4×C11C22×D411yescharacteristic
296C2×C4×C11C22×D411yescharacteristic
297C2×C4×C11C22×D411yescharacteristic
298C2×C4×C11C22×D411yescharacteristic
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11C2×#4111yescharacteristic
301C2×Dic11—28no—
302C2×Dic11—216no—
303C2×Dic11—24no—
304C2×Dic11—24no—
305C2×Dic11—42no—
306C2×Dic11—42no—
307C2×Dic11—44no—
308C2×Dic11—44no—
309Dic22—24no—
310Dic22—24no—
311Dic22—42no—
312Dic22—42no—
313Dic22—44no—
314Dic22—44no—
315C11⋊C8—24no—
316C11⋊C8—42no—
317C22×#41C2×D1111yescharacteristic
318C23×Q8—111no—
319C23×Q8C2×D1111yescharacteristic
320C2×#137—114no—
321C2×#137—224no—
322C2×#137—224no—
323C2×#137—222no—
324C22×Q16—221no—
325C22×SD16—221no—
326C22×M16—111no—
327C22×M16—111no—
328#536—22no—
329#536—22no—
330#536—22no—
331#536C2×D1114yes—
332C2×C4⋊Q8—21no—
333C2×C4⋊Q8—114no—
334C2×C4⋊Q8—224no—
335C2×C4⋊Q8—224no—
336C2×C4⋊Q8—222no—
337C2×#124—21no—
338C2×#123—22no—
339C2×C22⋊Q8—22no—
340C2×#117C2×D1111yescharacteristic
341C22×C4⋊C4—222no—
342C22×C42—111no—
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—42no—
356C22×C11—44no—
357C22×C11—84no—
358C22×C11#39212yes—
359C22×C11#39212yes—
360C22×C11#45614yes—
361C22×C11C2×#12011yescharacteristic
362C22×C11C2×#12011yescharacteristic
363C22×C11C2×#12111yescharacteristic
364C4×C11—44no—
365C4×C11—42no—
366C4×C11—44no—
367C4×C11#39212yes—
368C4×C11#39212yes—
369C4×C11C2×#12011yescharacteristic
370C4×C11C2×#12111yescharacteristic
371C4×C11C2×#12111yescharacteristic
372C4×C11C2×#12711yescharacteristic
373Dic11—28no—
374Dic11—44no—
375C2×#41—21no—
376C2×#41—21no—
377C2×#41—22no—
378C2×#41—22no—
379C2×#41—22no—
380C2×#41—22no—
381C2×#41C22⋊D1112yes—
382C2×#41C22×D1112yes—
383C22×Q8—22no—
384C22×Q8—22no—
385C22×Q8—22no—
386C22×Q8—22no—
387C22×Q8—21no—
388C22×Q8—21no—
389C22×Q8—21no—
390C22×Q8—21no—
391C22×Q8—114no—
392C22×Q8—112no—
393C22×Q8—222no—
394C22×Q8—221no—
395C22×Q8—222no—
396C22×Q8—222no—
397C22×Q8—221no—
398C22×Q8—221no—
399C22×Q8—221no—
400C22×Q8—221no—
401C22×Q8C22⋊D1111yescharacteristic
402C22×Q8C22⋊D1112yes—
403C22×Q8C22×D1112yes—
404C22×D4—21no—
405C22×D4C22⋊D1111yescharacteristic
406C23×C4—21no—
407C23×C4—221no—
408C23×C4—221no—
409C23×C4C22⋊D1112yes—
410C23×C4C22×D1111yescharacteristic
411#137—228no—
412#137—228no—
413#137—2216no—
414C2×Q16—228no—
415C2×Q16—224no—
416C2×SD16—228no—
417C2×SD16—224no—
418C2×M16—114no—
419C2×M16—112no—
420C2×M16—112no—
421C2×M16—222no—
422C2×M16—221no—
423C2×M16—221no—
424C2×M16—222no—
425C2×M16—222no—
426C22×C8—221no—
427C22×C8—221no—
428C4⋊Q8—24no—
429C4⋊Q8—24no—
430C4⋊Q8—228no—
431C4⋊Q8—228no—
432C4⋊Q8—2216no—
433#124—24no—
434#124—24no—
435#123—28no—
436#123—28no—
437C22⋊Q8—28no—
438C22⋊Q8—28no—
439#117—21no—
440#117—21no—
441#117C22⋊D1112yes—
442#117C22×D1112yes—
443C2×C4⋊C4—24no—
444C2×C4⋊C4—2216no—
445C2×C4⋊C4—228no—
446C2×C4⋊C4C22⋊D1112yes—
447C2×C22⋊C4—24no—
448C2×C22⋊C4—21no—
449C2×C42—21no—
450C2×C42—114no—
451C2×C42—112no—
452C2×C42—222no—
453C2×C42—221no—
454#104—228no—
455#103—228no—
456#101—228no—
457C2×C11—21no—
458C2×C11—21no—
459C2×C11—22no—
460C2×C11—82no—
461C2×C11#200514yescomplemented
462C2×C11C2×#39211yescharacteristic
463C2×C11C2×#45612yes—
464C24—21no—
465C24C2×C22⋊D1111yescharacteristic
466#41—24no—
467#41—24no—
468#41—22no—
469#41—22no—
470#41—22no—
471#41—22no—
472#41—42no—
473#41—42no—
474#41—42no—
475#41—42no—
476C2×Q8—24no—
477C2×Q8—24no—
478C2×Q8—22no—
479C2×Q8—22no—
480C2×Q8—21no—
481C2×Q8—22no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—22no—
485C2×Q8—22no—
486C2×Q8—22no—
487C2×Q8—22no—
488C2×Q8—22no—
489C2×Q8—42no—
490C2×Q8—42no—
491C2×Q8—42no—
492C2×Q8—42no—
493C2×Q8—42no—
494C2×Q8—42no—
495C2×Q8—42no—
496C2×Q8—42no—
497C2×Q8—114no—
498C2×Q8—224no—
499C2×Q8—222no—
500C2×Q8—224no—
501C2×Q8—224no—
502C2×Q8—224no—
503C2×Q8—224no—
504C2×Q8—222no—
505C2×Q8—222no—
506C2×Q8—222no—
507C2×Q8—222no—
508C2×Q8—442no—
509C2×Q8—442no—
510C2×Q8—442no—
511C2×Q8—442no—
512C2×Q8—442no—
513C2×Q8—441no—
514C2×Q8—441no—
515C2×Q8C2×C22⋊D1112yes—
516C2×D4—22no—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4—22no—
520C2×D4—21no—
521C2×D4—42no—
522C2×D4—42no—
523C2×D4C2×C22⋊D1112yes—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—21no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—228no—
535C22×C4—224no—
536C22×C4—222no—
537C22×C4—224no—
538C22×C4—222no—
539C22×C4—442no—
540C22×C4—441no—
541C22×C4—441no—
542C22×C4D4×D1112yes—
543C22×C4D4×D1112yes—
544C22×C4D4×D1112yes—
545C22×C4#434112yes—
546C22×C4C2×C22⋊D1114yes—
547C22×C4C2×C22⋊D1111yescharacteristic
548C22×C4C2×C22⋊D1111yescharacteristic
549C22×C4C2×C22⋊D1111yescharacteristic
550C22×C4C2×C22⋊D1111yescharacteristic
551C22×C4C2×C22⋊D1111yescharacteristic
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—216no—
566C4⋊C4—22no—
567C4⋊C4—2232no—
568C4⋊C4C2×C22⋊D1114yes—
569C22⋊C4—216no—
570C22⋊C4—22no—
571C22⋊C4—22no—
572C42—22no—
573C42—22no—
574C42—114no—
575C42—224no—
576C42—222no—
577C11C2×#200511yescharacteristic, complemented, Sylow
578C23—24no—
579C23—22no—
580C23—42no—
581C23—44no—
582C23#6699012yes—
583C23#6699212yes—
584C23#6700611yescharacteristic
585C23#6700611yescharacteristic
586C23C22×C22⋊D1111yescharacteristic
587Q8—22no—
588Q8—22no—
589Q8—42no—
590Q8—42no—
591Q8—42no—
592Q8—42no—
593Q8—44no—
594Q8—44no—
595Q8—42no—
596Q8—224no—
597Q8—224no—
598Q8—442no—
599Q8—442no—
600Q8—444no—
601Q8—444no—
602D4—22no—
603D4—22no—
604D4—42no—
605D4—42no—
606D4—44no—
607D4—42no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—24no—
611C2×C4—24no—
612C2×C4—22no—
613C2×C4—44no—
614C2×C4—44no—
615C2×C4—42no—
616C2×C4—44no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—44no—
620C2×C4—2216no—
621C2×C4—228no—
622C2×C4—224no—
623C2×C4—224no—
624C2×C4—442no—
625C2×C4—444no—
626C2×C4—444no—
627C2×C4—442no—
628C2×C4#6699012yes—
629C2×C4#6699012yes—
630C2×C4#6699012yes—
631C2×C4#6699112yes—
632C2×C4#6699112yes—
633C2×C4#6699212yes—
634C2×C4#6699212yes—
635C2×C4#6699212yes—
636C2×C4#6699312yes—
637C2×C4#6699312yes—
638C2×C4#6700611yescharacteristic
639C2×C4#6700611yescharacteristic
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—42no—
653C22—44no—
654C22—84no—
655C22#1062283612yes—
656C22#1062283612yes—
657C22#1062285914yes—
658C22C2×#6699011yescharacteristic
659C22C2×#6699211yescharacteristic
660C22C2×#6700611yescharacteristic
661C4—44no—
662C4—42no—
663C4—44no—
664C4—228no—
665C4—444no—
666C4#1062283612yes—
667C4#1062283612yes—
668C4C2×#6699011yescharacteristic
669C4C2×#6699111yescharacteristic
670C4C2×#6699211yescharacteristic
671C4C2×#6699311yescharacteristic
672C2—21no—
673C2—21no—
674C2—22no—
675C2—82no—
676C2#1306965014yesdirect product factor
677C2C2×#1062283611yescharacteristic
678C2C2×#1062285912yes—
subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#536C2
socleC23×C11#120
prime radicalC22×C11×#41C22
hypercenterC2×#536D11
hypocenterC11C2×#2005
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
2. C22×#66997C2semidirect
4. C2×#10622617C2semidirect
5. C22×#66900C2semidirect
6. #13069650C2direct (N × H)
7. C2×#10622170C2semidirect
28. C2×#66997C22semidirect
38. C2×#66900C22semidirect
40. #10622617C22semidirect
42. #10622170C22semidirect
461. C2×C11#2005semidirect
577. C11C2×#2005semidirect
676. C2#13069650direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670042
C22×#669972
C22×#669012
C2×#106226172
C22×#669002
#130696502
C2×#106221702
C2×C11×#5362
C2×#200511