Finite Group Databasebeta

← C2×#13077848 #15620126

Subgroups — C2×#13077848 #15620126

Order 2816.

4970 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Q8×D11C211yesmaximal, characteristic, complemented
2C22×#67004C211yesmaximal, characteristic, complemented
3C2×#10623359C211yesmaximal, characteristic
4#13077848C2116yesmaximal, direct product factor
5C2×#10622799C214yesmaximal, complemented
6C2×#10622783C214yesmaximal, complemented
7C2×#10622733C211yesmaximal, characteristic, complemented
8C2×#10622838C211yesmaximal, characteristic, complemented
9C2×#10622739C211yesmaximal, characteristic, complemented
10C22×C11×#137C211yesmaximal, characteristic, complemented
11C22×C11×#41C2211yescharacteristic
12C23×Q8×C11C2211yescharacteristic
13C22×Q8×D11—28no—
14C22×Q8×D11—22no—
15C22×Q8×D11—24no—
16C22×Q8×D11—28no—
17C22×Q8×D11C2214yes—
18C22×Q8×D11C2218yescomplemented
19C23×C4×D11—21no—
20C23×C4×D11C2211yescharacteristic
21C23×Dic22—21no—
22C23×Dic22C2211yescharacteristic
23C2×C11×#137—28no—
24C2×C11×#137C2218yescomplemented
25C22×C11×Q16C2212yescomplemented
26C22×C11×SD16C2212yescomplemented
27C22×C11×M16C2211yescharacteristic
28#10623359—24no—
29#10623359C2218yes—
30C2×#67004—28no—
31C2×#67004C2218yescomplemented
32C2×#66999C2212yes—
33C22×#4326C2212yescomplemented
34C2×#66991C2212yes—
35C2×#66990—21no—
36C2×#66988—21no—
37C22×#4324C2212yescomplemented
38C2×C4×C22⋊D11—22no—
39C2×#66979C2211yescharacteristic
40C22×#4318C2211yescharacteristic
41#10622838C2218yescomplemented
42C2×#66899C2214yescomplemented
43#10622799C22132yescomplemented
44#10622783C22132yescomplemented
45#10622739C2218yescomplemented
46#10622733C2218yescomplemented
47C2×(C2×D11)⋊C8C2214yes—
48C2×#66880C2214yescomplemented
49C24×D11D411yescharacteristic
50C2×C11×#41—22no—
51C2×C11×#41—24no—
52C2×C11×#41—24no—
53C2×C11×#41C2314yes—
54C22×Q8×C11—24no—
55C22×Q8×C11—21no—
56C22×Q8×C11—22no—
57C22×Q8×C11D418yescomplemented
58C22×Q8×C11C2311yescharacteristic
59C22×Q8×C11C2312yes—
60C22×Q8×C11C2314yes—
61C22×D4×C11—21no—
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—21no—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—22no—
67C23×Dic11—21no—
68C23×Dic11D411yescharacteristic
69C2×Q8×D11—232no—
70C2×Q8×D11—264no—
71C2×Q8×D11—216no—
72C2×Q8×D11—232no—
73C2×Q8×D11—28no—
74C2×Q8×D11—216no—
75C2×Q8×D11—216no—
76C2×Q8×D11—232no—
77C2×Q8×D11C23116yes—
78C22×C4×D11—216no—
79C22×C4×D11—24no—
80C22×C4×D11—28no—
81C22×C4×D11—24no—
82C22×C4×D11—24no—
83C22×C4×D11D412yes—
84C22×C4×D11D414yes—
85C22×C4×D11C2312yes—
86C22×C4×D11C2314yes—
87C22×Dic22—216no—
88C22×Dic22—21no—
89C22×Dic22—22no—
90C22×Dic22—24no—
91C22×Dic22—24no—
92C22×Dic22—28no—
93C22×Dic22D418yescomplemented
94C22×Dic22C2312yes—
95C22×Dic22C2314yes—
96C11×#137—232no—
97C2×C11×Q16—28no—
98C2×C11×Q16C2318yescomplemented
99C2×C11×SD16—28no—
100C2×C11×SD16C2318yescomplemented
101C2×C11×M16—24no—
102C2×C11×M16C2314yes—
103C22×C8×C11C2312yes—
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—22no—
106#67004—232no—
107#66999—24no—
108#66999C2318yes—
109C2×#4326—28no—
110C2×#4326C2318yescomplemented
111#66991—24no—
112#66991C2318yes—
113#66990—28no—
114#66988—28no—
115C2×#4324—28no—
116C2×#4324C2318yescomplemented
117C4×C22⋊D11—216no—
118C2×(C2×D11)⋊C4—22no—
119#66979—22no—
120#66979C2314yes—
121C2×C4⋊Dic11C2312yes—
122C2×Dic11⋊C4—22no—
123C2×C4×Dic11—21no—
124C2×#4318—24no—
125C2×#4318C2314yes—
126C22×C11⋊C8C2312yes—
127#66899C23116yescomplemented
128(C2×D11)⋊C8C23116yes—
129#66880C23116yescomplemented
130C2×#3004—111nomaximal, Sylow
131C24×C11—21no—
132C24×C11C2×D411yescharacteristic
133C23×D11—24no—
134C23×D11—28no—
135C23×D11C2×D414yes—
136C23×D11C2×D412yes—
137C11×#41—28no—
138C11×#41—28no—
139C11×#41—48no—
140C2×Q8×C11—28no—
141C2×Q8×C11—216no—
142C2×Q8×C11—24no—
143C2×Q8×C11—28no—
144C2×Q8×C11—24no—
145C2×Q8×C11—22no—
146C2×Q8×C11—21no—
147C2×Q8×C11—22no—
148C2×Q8×C11—22no—
149C2×Q8×C11C2×D418yes—
150C2×Q8×C11C2×D4116yescomplemented
151C2×Q8×C11C2412yes—
152C2×Q8×C11C2414yes—
153C2×D4×C11—24no—
154C2×D4×C11—22no—
155C2×D4×C11—22no—
156C2×D4×C11—21no—
157C2×D4×C11—44no—
158C2×D4×C11C2412yes—
159C22×C4×C11—28no—
160C22×C4×C11—22no—
161C22×C4×C11—24no—
162C22×C4×C11—21no—
163C22×C4×C11—24no—
164C22×C4×C11—44no—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D412yes—
167C22×C4×C11C2×D414yes—
168C22×C4×C11C2×D414yes—
169C22×C4×C11C2411yescharacteristic
170C22×C4×C11C2412yes—
171C2×C22⋊D11—28no—
172C2×C22⋊D11—48no—
173C22×Dic11—24no—
174C22×Dic11—28no—
175C22×Dic11—24no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11C2×D412yes—
179C22×Dic11C2×D414yes—
180Q8×D11—264no—
181Q8×D11—2128no—
182Q8×D11—232no—
183Q8×D11—232no—
184C2×C4×D11—232no—
185C2×C4×D11—264no—
186C2×C4×D11—216no—
187C2×C4×D11—28no—
188C2×C4×D11—216no—
189C2×C4×D11—24no—
190C2×C4×D11—28no—
191C2×C4×D11—24no—
192C2×C4×D11—28no—
193C2×C4×D11C2×D418yes—
194C2×C4×D11C2×D414yes—
195C2×C4×D11C2414yes—
196C2×Dic22—232no—
197C2×Dic22—264no—
198C2×Dic22—216no—
199C2×Dic22—28no—
200C2×Dic22—216no—
201C2×Dic22—24no—
202C2×Dic22—22no—
203C2×Dic22—24no—
204C2×Dic22—28no—
205C2×Dic22C2×D418yes—
206C2×Dic22C2×D4116yescomplemented
207C2×Dic22C2414yes—
208C11×Q16—216no—
209C11×SD16—216no—
210C11×M16—28no—
211C2×C8×C11—24no—
212C2×C8×C11C2414yes—
213C22⋊Dic11—28no—
214C22⋊Dic11—24no—
215#4326—216no—
216#4324—216no—
217(C2×D11)⋊C4—28no—
218C4⋊Dic11—22no—
219C4⋊Dic11C2414yes—
220Dic11⋊C4—28no—
221C4×Dic11—24no—
222#4318—28no—
223C2×C11⋊C8—24no—
224C2×C11⋊C8C2414yes—
225C24×Q8—111no—
226C22×#137—111no—
227C22×#137D1111yescharacteristic, complemented
228C2×#525—111no—
229#3004—1116no—
230C2×#451—114no—
231C2×#448—114no—
232C2×#419—111no—
233C2×#419—111no—
234C2×#407—111no—
235C23×C11—24no—
236C23×C11—22no—
237C23×C11—42no—
238C23×C11—44no—
239C23×C11#12014yes—
240C23×C11C22×D412yes—
241C23×C11C22×D411yescharacteristic
242C22×D11—232no—
243C22×D11—28no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—216no—
247C22×D11#13718yescomplemented
248C22×D11C22×D414yes—
249Q8×C11—28no—
250Q8×C11—216no—
251Q8×C11—24no—
252Q8×C11—22no—
253Q8×C11—22no—
254Q8×C11—42no—
255Q8×C11C22×D418yes—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—48no—
259D4×C11—42no—
260C2×C4×C11—28no—
261C2×C4×C11—216no—
262C2×C4×C11—24no—
263C2×C4×C11—22no—
264C2×C4×C11—42no—
265C2×C4×C11—48no—
266C2×C4×C11#12014yes—
267C2×C4×C11#12018yes—
268C2×C4×C11C22×D412yes—
269C2×C4×C11C22×D411yescharacteristic
270C2×C4×C11C22×D412yes—
271C2×C4×C11C22×D414yes—
272C2×C4×C11C22×D412yes—
273C2×C4×C11C22×D414yes—
274C2×C4×C11C2511yescharacteristic
275C22⋊D11—416no—
276C2×Dic11—28no—
277C2×Dic11—24no—
278C2×Dic11—28no—
279C2×Dic11—216no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—44no—
283C2×Dic11C22×D414yes—
284C4×D11—264no—
285C4×D11—216no—
286C4×D11—28no—
287C4×D11—24no—
288C4×D11—24no—
289Dic22—264no—
290Dic22—28no—
291Dic22—216no—
292Dic22—24no—
293Dic22C22×D418yes—
294C8×C11—24no—
295C11⋊C8—24no—
296C22×#41C2×D1111yescharacteristic
297C23×Q8—114no—
298C23×Q8—118no—
299C23×Q8—111no—
300C23×Q8—221no—
301C23×Q8—222no—
302C23×Q8—224no—
303C23×Q8—228no—
304C23×Q8—228no—
305C23×Q8C2×D1111yescharacteristic
306C24×C4—111no—
307C24×C4—221no—
308C2×#137—28no—
309C2×#137—118no—
310C2×#137—228no—
311C2×#137C2×D1118yescomplemented
312C22×Q16—112no—
313C22×Q16C2×D1112yescomplemented
314C22×SD16—112no—
315C22×SD16C2×D1112yescomplemented
316C22×M16—111no—
317C22×M16C2×D1111yescharacteristic
318#525—118no—
319#525—224no—
320C2×#123—221no—
321C2×C22⋊Q8—112no—
322C2×#121—112no—
323C2×#120—221no—
324C2×C4×D4—222no—
325C2×#117—111no—
326#451—1132no—
327#448—1132no—
328#419—118no—
329#419—118no—
330C2×#103—114no—
331C2×#103—114no—
332#407—118no—
333C2×C22⋊C8—114no—
334C22×C11—28no—
335C22×C11—24no—
336C22×C11—42no—
337C22×C11—44no—
338C22×C11—84no—
339C22×C11C2×#12014yes—
340C22×C11C2×#12012yes—
341C22×C11C2×#13714yes—
342C22×C11C23×D411yescharacteristic
343C2×D11—232no—
344C2×D11—24no—
345C2×D11—216no—
346C2×D11—24no—
347C2×D11C2×#13718yescomplemented
348C4×C11—28no—
349C4×C11—42no—
350C4×C11C2×#12014yes—
351C4×C11C2×#12012yes—
352C4×C11C23×D411yescharacteristic
353C4×C11C23×D411yescharacteristic
354Dic11—24no—
355Dic11—28no—
356Dic11—44no—
357C25—111no—
358C2×#41—22no—
359C2×#41—24no—
360C2×#41—24no—
361C2×#41C22×D1114yes—
362C22×Q8—24no—
363C22×Q8—22no—
364C22×Q8—21no—
365C22×Q8—1116no—
366C22×Q8—118no—
367C22×Q8—112no—
368C22×Q8—114no—
369C22×Q8—228no—
370C22×Q8—224no—
371C22×Q8—2216no—
372C22×Q8—2216no—
373C22×Q8—228no—
374C22×Q8—2216no—
375C22×Q8—2232no—
376C22×Q8—2232no—
377C22×Q8—2264no—
378C22×Q8—2216no—
379C22×Q8—2232no—
380C22×Q8—222no—
381C22×Q8—221no—
382C22×Q8—224no—
383C22×Q8C22⋊D1118yescomplemented
384C22×Q8C22×D1111yescharacteristic
385C22×Q8C22×D1112yes—
386C22×Q8C22×D1114yes—
387C22×D4—21no—
388C22×D4—222no—
389C22×D4C22×D1111yescharacteristic
390C23×C4—21no—
391C23×C4—21no—
392C23×C4—111no—
393C23×C4—112no—
394C23×C4—114no—
395C23×C4—112no—
396C23×C4—114no—
397C23×C4—228no—
398C23×C4—224no—
399C23×C4—2216no—
400C23×C4—221no—
401C23×C4—224no—
402C23×C4—224no—
403C23×C4C22×D1111yescharacteristic
404#137—232no—
405#137—2232no—
406C2×Q16—28no—
407C2×Q16—118no—
408C2×Q16—228no—
409C2×Q16C22×D1118yescomplemented
410C2×SD16—28no—
411C2×SD16—118no—
412C2×SD16—228no—
413C2×SD16C22×D1118yescomplemented
414C2×M16—24no—
415C2×M16—114no—
416C2×M16—224no—
417C2×M16C22×D1114yes—
418C22×C8—112no—
419C22×C8C22×D1112yes—
420#123—228no—
421C22⋊Q8—118no—
422C22⋊Q8—224no—
423#121—118no—
424#121—224no—
425#120—228no—
426C4×D4—2216no—
427#117—114no—
428#117—222no—
429C2×C4⋊C4—112no—
430C2×C4⋊C4—222no—
431C2×C22⋊C4—222no—
432C2×C22⋊C4—222no—
433C2×C22⋊C4—221no—
434C2×C42—221no—
435#103—1116no—
436#103—1116no—
437C22⋊C8—1116no—
438C2×C11—24no—
439C2×C11—82no—
440C2×C11#300414yescomplemented
441C2×C11C22×#12011yescharacteristic
442C2×C11C22×#13712yes—
443D11—28no—
444C24—21no—
445C24—112no—
446C24—114no—
447C24—228no—
448C24—224no—
449C24D4×D1111yescharacteristic
450#41—28no—
451#41—28no—
452#41—48no—
453C2×Q8—28no—
454C2×Q8—216no—
455C2×Q8—24no—
456C2×Q8—28no—
457C2×Q8—24no—
458C2×Q8—22no—
459C2×Q8—21no—
460C2×Q8—22no—
461C2×Q8—22no—
462C2×Q8—118no—
463C2×Q8—1116no—
464C2×Q8—114no—
465C2×Q8—2216no—
466C2×Q8—2232no—
467C2×Q8—2264no—
468C2×Q8—2232no—
469C2×Q8—2264no—
470C2×Q8—22128no—
471C2×Q8—2232no—
472C2×Q8—228no—
473C2×Q8—2216no—
474C2×Q8—224no—
475C2×Q8—222no—
476C2×Q8—224no—
477C2×Q8—228no—
478C2×Q8C2×C22⋊D1118yes—
479C2×Q8C2×C22⋊D11116yescomplemented
480C2×Q8C23×D1112yes—
481C2×Q8C23×D1114yes—
482C2×D4—24no—
483C2×D4—22no—
484C2×D4—21no—
485C2×D4—22no—
486C2×D4—44no—
487C2×D4—228no—
488C2×D4—448no—
489C2×D4C23×D1112yes—
490C22×C4—28no—
491C22×C4—24no—
492C22×C4—22no—
493C22×C4—21no—
494C22×C4—24no—
495C22×C4—44no—
496C22×C4—114no—
497C22×C4—112no—
498C22×C4—118no—
499C22×C4—114no—
500C22×C4—114no—
501C22×C4—2216no—
502C22×C4—2232no—
503C22×C4—2264no—
504C22×C4—224no—
505C22×C4—228no—
506C22×C4—224no—
507C22×C4—222no—
508C22×C4—228no—
509C22×C4—2216no—
510C22×C4—224no—
511C22×C4—228no—
512C22×C4—224no—
513C22×C4—228no—
514C22×C4—222no—
515C22×C4D4×D1112yes—
516C22×C4D4×D1111yescharacteristic
517C22×C4D4×D1114yes—
518C22×C4C2×C22⋊D1114yes—
519C22×C4C23×D1112yes—
520C22×C4C23×D1111yescharacteristic
521Q16—216no—
522Q16—2216no—
523SD16—216no—
524SD16—2216no—
525M16—28no—
526M16—228no—
527C2×C8—24no—
528C2×C8—114no—
529C2×C8—224no—
530C2×C8C23×D1114yes—
531C4⋊C4—114no—
532C4⋊C4—228no—
533C4⋊C4—222no—
534C22⋊C4—228no—
535C22⋊C4—228no—
536C22⋊C4—224no—
537C42—224no—
538C11C2×#300411yescharacteristic, complemented, Sylow
539C23—24no—
540C23—22no—
541C23—44no—
542C23—42no—
543C23—118no—
544C23—114no—
545C23—2216no—
546C23—2232no—
547C23—224no—
548C23—228no—
549C23—224no—
550C23#6699014yes—
551C23C2×D4×D1112yes—
552C23C2×D4×D1111yescharacteristic
553Q8—28no—
554Q8—216no—
555Q8—24no—
556Q8—22no—
557Q8—22no—
558Q8—42no—
559Q8—118no—
560Q8—2264no—
561Q8—2216no—
562Q8—228no—
563Q8—224no—
564Q8C22×C22⋊D1118yes—
565D4—22no—
566D4—22no—
567D4—48no—
568D4—42no—
569D4—4416no—
570C2×C4—28no—
571C2×C4—216no—
572C2×C4—24no—
573C2×C4—22no—
574C2×C4—42no—
575C2×C4—48no—
576C2×C4—114no—
577C2×C4—2264no—
578C2×C4—228no—
579C2×C4—224no—
580C2×C4—2216no—
581C2×C4—228no—
582C2×C4—224no—
583C2×C4—2216no—
584C2×C4—228no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—444no—
589C2×C4#6699014yes—
590C2×C4#6699018yes—
591C2×C4C2×D4×D1112yes—
592C2×C4C2×D4×D1111yescharacteristic
593C2×C4C2×D4×D1112yes—
594C2×C4C2×D4×D1114yes—
595C2×C4C22×C22⋊D1112yes—
596C2×C4C22×C22⋊D1114yes—
597C2×C4C24×D1111yescharacteristic
598C8—24no—
599C8—224no—
600C22—28no—
601C22—24no—
602C22—44no—
603C22—42no—
604C22—84no—
605C22—118no—
606C22—2232no—
607C22—2216no—
608C22—224no—
609C22—224no—
610C22D11×#13714yes—
611C22C2×#6699014yes—
612C22C2×#6699012yes—
613C22C22×D4×D1111yescharacteristic
614C4—28no—
615C4—42no—
616C4—224no—
617C4—228no—
618C4—444no—
619C4C2×#6699014yes—
620C4C2×#6699012yes—
621C4C22×D4×D1111yescharacteristic
622C4C23×C22⋊D1111yescharacteristic
623C2—24no—
624C2—82no—
625C2—228no—
626C2#1307784814yesdirect product factor
627C2C22×#6699011yescharacteristic
628C2C2×D11×#13712yes—
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#137C2
socleC23×C11C22×D4
prime radicalC2×#10623359C2
hypercenterC22×#137D11
hypocenterC11C2×#3004
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C23×Q8×D11C2semidirect
2. C22×#67004C2semidirect
4. #13077848C2direct (N × H)
5. C2×#10622799C2semidirect
6. C2×#10622783C2semidirect
7. C2×#10622733C2semidirect
8. C2×#10622838C2semidirect
9. C2×#10622739C2semidirect
10. C22×C11×#137C2semidirect
18. C22×Q8×D11C22semidirect
24. C2×C11×#137C22semidirect
25. C22×C11×Q16C22semidirect
26. C22×C11×SD16C22semidirect
31. C2×#67004C22semidirect
33. C22×#4326C22semidirect
37. C22×#4324C22semidirect
41. #10622838C22semidirect
42. C2×#66899C22semidirect
43. #10622799C22semidirect
44. #10622783C22semidirect
45. #10622739C22semidirect
46. #10622733C22semidirect
48. C2×#66880C22semidirect
57. C22×Q8×C11D4semidirect
93. C22×Dic22D4semidirect
98. C2×C11×Q16C23semidirect
100. C2×C11×SD16C23semidirect
110. C2×#4326C23semidirect
116. C2×#4324C23semidirect
127. #66899C23semidirect
129. #66880C23semidirect
150. C2×Q8×C11C2×D4semidirect
206. C2×Dic22C2×D4semidirect
227. C22×#137D11semidirect
247. C22×D11#137semidirect
311. C2×#137C2×D11semidirect
313. C22×Q16C2×D11semidirect
315. C22×SD16C2×D11semidirect
347. C2×D11C2×#137semidirect
383. C22×Q8C22⋊D11semidirect
409. C2×Q16C22×D11semidirect
413. C2×SD16C22×D11semidirect
440. C2×C11#3004semidirect
479. C2×Q8C2×C22⋊D11semidirect
538. C11C2×#3004semidirect
626. C2#13077848direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Q8×D112
C22×#670042
C2×#106233592
#130778482
C2×#106227992
C2×#106227832
C2×#106227332
C2×#106228382
C2×#106227392
C22×C11×#1372
C2×#300411