Finite Group Databasebeta

← C2×#13078770 #15621902

Subgroups — C2×#13078770 #15621902

Order 2816.

2430 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic, complemented
2C2×C4×#4343C211yesmaximal, characteristic, complemented
3#13078770C2116yesmaximal, direct product factor
4C2×#10622479C212yesmaximal, complemented
5C2×#10622700C211yesmaximal, characteristic, complemented
6C2×#10622640C211yesmaximal, characteristic, complemented
7C2×#10622456C211yesmaximal, characteristic, complemented
8C2×#10622424C212yesmaximal, complemented
9C2×#10622482C212yesmaximal, complemented
10C2×#10622430C212yesmaximal, complemented
11C2×#10622448C211yesmaximal, characteristic, complemented
12C2×C11×#475C211yesmaximal, characteristic, complemented
13C22×#4343—21no—
14C22×#4343C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#67000—21no—
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4325C2212yes—
20C22×D88C2212yes—
21#10623256—24no—
22#10623256C2218yescomplemented
23C4×#4343—24no—
24C4×#4343C2218yescomplemented
25C2×#66948—21no—
26C2×#66948C2212yes—
27C2×#66946—21no—
28C2×#66946—21no—
29C2×#66946C2212yes—
30C2×#66946C2211yescharacteristic
31C2×#66945—21no—
32C2×#66945C2211yescharacteristic
33C2×#66927C2211yescharacteristic
34C2×C4×D44—21no—
35C2×C4×D44C2211yescharacteristic
36C2×C42×D11—21no—
37C2×C42×D11C2211yescharacteristic
38C11×#475C2218yescomplemented
39C2×C11×#106C2212yes—
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×#103C2212yes—
42C2×#66885C2212yes—
43C2×(C2×D11)⋊C8C2212yes—
44C2×#66879C2212yes—
45#10622700C2218yescomplemented
46#10622640C2218yescomplemented
47C2×#66873C2212yes—
48C2×#66873C2212yes—
49C2×#66871C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622482C22116yescomplemented
52#10622479C22116yescomplemented
53#10622456C2218yescomplemented
54#10622448C2218yescomplemented
55#10622430C22116yescomplemented
56#10622424C22116yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11C2311yescharacteristic
59C2×#4343—24no—
60C2×#4343—24no—
61C2×#4343—22no—
62C2×#4343—28no—
63C2×#4343—48no—
64C2×#4343C2314yes—
65C22×D44—21no—
66C22×D44—22no—
67C22×D44—21no—
68C22×D44—21no—
69C22×D44C2312yes—
70C22×D44C2311yescharacteristic
71C22×C4×D11—21no—
72C22×C4×D11—21no—
73C22×C4×D11—21no—
74C22×C4×D11—22no—
75C22×C4×D11D411yescharacteristic
76C22×C4×D11D411yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C22×C8×C11C2312yes—
79C11×C4⋊Q8—22no—
80C11×C4⋊Q8C2314yes—
81C4×Q8×C11—22no—
82C4×Q8×C11C2314yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2312yes—
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89#67000—28no—
90Q8×Dic11—22no—
91Q8×Dic11C2314yes—
92C2×#4325—28no—
93C2×#4325C2318yes—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—22no—
98C2×(C2×D11)⋊C4—22no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4×Dic11—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11D411yescharacteristic
104C2×C4×Dic11D411yescharacteristic
105C2×C4×Dic11C2311yescharacteristic
106C22×C11⋊C8C2312yes—
107C2×D88—28no—
108C2×D88C2318yes—
109#66948—24no—
110#66948—28no—
111#66948C2318yes—
112#66946—28no—
113#66946—24no—
114#66946—28no—
115#66946—22no—
116#66946C2314yes—
117#66946C2318yes—
118#66945—22no—
119#66945—28no—
120#66945C2314yes—
121#66927—22no—
122#66927C2314yes—
123C4×D44—28no—
124C4×D44—22no—
125C4×D44C2314yes—
126C42×D11—28no—
127C42×D11D414yes—
128C42×D11C2314yes—
129C11×#106C2318yes—
130C11×C4⋊C8C2314yes—
131C11×#103C2318yes—
132#66885C2318yes—
133(C2×D11)⋊C8C2318yes—
134#66879C2318yes—
135#66873C2318yes—
136#66873C2318yes—
137#66871C2318yes—
138C4⋊(C11⋊C8)C2314yes—
139C2×#3115—111nomaximal, Sylow
140C23×D11—21no—
141C23×D11—22no—
142C23×D11C2×D411yescharacteristic
143C2×Q8×C11—21no—
144C2×Q8×C11—24no—
145C2×Q8×C11—22no—
146C2×Q8×C11—44no—
147C2×Q8×C11#4114yescomplemented
148C2×Q8×C11C2412yes—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C22×Dic11—21no—
156C22×Dic11C2×D411yescharacteristic
157C22×Dic11C2×D411yescharacteristic
158C22×Dic11C2×D411yescharacteristic
159#4343—216no—
160#4343—28no—
161#4343—28no—
162#4343—432no—
163C2×D44—28no—
164C2×D44—24no—
165C2×D44—28no—
166C2×D44—21no—
167C2×D44—22no—
168C2×D44—24no—
169C2×D44—24no—
170C2×D44—22no—
171C2×D44—24no—
172C2×D44—24no—
173C2×D44—44no—
174C2×D44—48no—
175C2×D44—44no—
176C2×D44#4114yescomplemented
177C2×D44C2414yes—
178C2×D44C2412yes—
179C2×C4×D11—28no—
180C2×C4×D11—24no—
181C2×C4×D11—24no—
182C2×C4×D11—28no—
183C2×C4×D11—24no—
184C2×C4×D11—24no—
185C2×C4×D11—22no—
186C2×C4×D11—22no—
187C2×C4×D11—42no—
188C2×C4×D11—44no—
189C2×C4×D11—48no—
190C2×C4×D11—44no—
191C2×C4×D11C2×D412yes—
192C2×C4×D11C2×D414yes—
193C2×C4×D11C2×D414yes—
194C2×C4×D11C2412yes—
195C2×C8×C11—24no—
196C2×C8×C11C2414yes—
197C11×C4⋊C4—24no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—24no—
200C11×C4⋊C4—22no—
201C11×C4⋊C4C2414yes—
202C11×C4⋊C4C2412yes—
203C42×C11—24no—
204C42×C11C2×D412yes—
205C42×C11C2412yes—
206#4325—216no—
207(C2×D11)⋊C4—24no—
208(C2×D11)⋊C4—28no—
209(C2×D11)⋊C4—28no—
210(C2×D11)⋊C4—24no—
211(C2×D11)⋊C4—24no—
212C4⋊Dic11—24no—
213C4⋊Dic11—21no—
214C4⋊Dic11C2412yes—
215C4×Dic11—24no—
216C4×Dic11—24no—
217C4×Dic11C2×D414yes—
218C4×Dic11C2×D412yes—
219C4×Dic11C2×D414yes—
220C4×Dic11C2412yes—
221C2×C11⋊C8—24no—
222C2×C11⋊C8C2414yes—
223D88—216no—
224C2×#532—111no—
225C2×C4×#41—111no—
226#3115—1116no—
227C2×#482—112no—
228C2×#475D1111yescharacteristic, complemented
229C2×#474—111no—
230C2×#460—111no—
231C2×#459—111no—
232C2×#449—112no—
233C2×#442—112no—
234C2×#440—112no—
235C2×#432—111no—
236C23×C11C22×D411yescharacteristic
237C22×D11—22no—
238C22×D11—24no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—24no—
243C22×D11—42no—
244C22×D11—42no—
245C22×D11—44no—
246C22×D11—44no—
247C22×D11—44no—
248C22×D11C22×D412yes—
249Q8×C11—24no—
250Q8×C11—22no—
251Q8×C11—48no—
252Q8×C11C2×#4114yescomplemented
253C2×C4×C11—24no—
254C2×C4×C11—22no—
255C2×C4×C11—22no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—44no—
259C2×C4×C11—42no—
260C2×C4×C11AGL(1,ℤ/8)14yes—
261C2×C4×C11C22×D412yes—
262C2×C4×C11C22×D411yescharacteristic
263C2×C4×C11C22×D412yes—
264C2×C4×C11C2×#4112yes—
265C2×C4×C11C2×#4112yes—
266C2×C4×C11C2511yescharacteristic
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—42no—
272C2×Dic11C22×D412yes—
273C2×Dic11C22×D412yes—
274C2×Dic11C22×D412yes—
275D44—216no—
276D44—24no—
277D44—22no—
278D44—24no—
279D44—24no—
280D44—48no—
281D44—416no—
282D44—44no—
283D44—48no—
284D44C2×#4114yescomplemented
285C4×D11—216no—
286C4×D11—24no—
287C4×D11—28no—
288C4×D11—22no—
289C4×D11—22no—
290C4×D11—44no—
291C4×D11—48no—
292C4×D11—416no—
293C4×D11—48no—
294C8×C11—24no—
295C11⋊C8—24no—
296C22×#41—111no—
297C22×#41—221no—
298C22×SD16—112no—
299C22×D8—112no—
300#532—118no—
301#532—224no—
302C2×C4⋊Q8C2×D1111yescharacteristic
303C2×#127—111no—
304C2×#124—221no—
305C2×#121—112no—
306C2×#121—221no—
307C4×#41—118no—
308C4×#41—224no—
309C2×C4×Q8—111no—
310C2×C4×Q8C2×D1111yescharacteristic
311C2×C4×D4—111no—
312C2×C4×D4—112no—
313C2×C4×D4—111no—
314C2×C4×D4—221no—
315C2×C4×D4—221no—
316C2×C4×D4—221no—
317C2×#117—111no—
318C2×#117—221no—
319C22×C42—111no—
320C22×C42—221no—
321#482—1116no—
322#475C2×D1118yescomplemented
323#474—118no—
324#460—118no—
325#459—118no—
326#449—1116no—
327#442—1116no—
328#440—1116no—
329#432—118no—
330C2×#107—112no—
331C2×#106C2×D1112yes—
332C2×C4⋊C8—111no—
333C2×C4⋊C8C2×D1111yescharacteristic
334C2×#103C2×D1112yes—
335C2×#102—112no—
336C2×#102—112no—
337C2×#102—112no—
338C2×C22⋊C8—112no—
339C2×#97—112no—
340C22×C11#52512yes—
341C22×C11C2×AGL(1,ℤ/8)12yes—
342C22×C11#57512yes—
343C22×C11C23×D411yescharacteristic
344C2×D11—24no—
345C2×D11—22no—
346C2×D11—22no—
347C2×D11—22no—
348C2×D11—44no—
349C2×D11—48no—
350C2×D11—42no—
351C2×D11—42no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—88no—
356C4×C11—24no—
357C4×C11—22no—
358C4×C11—44no—
359C4×C11—42no—
360C4×C11#52512yes—
361C4×C11C2×AGL(1,ℤ/8)14yes—
362C4×C11C22×#4111yescharacteristic
363C4×C11C22×#4111yescharacteristic
364Dic11—22no—
365Dic11—22no—
366Dic11—22no—
367Dic11—42no—
368C2×#41—114no—
369C2×#41—222no—
370C2×#41—228no—
371C2×#41—224no—
372C2×#41—224no—
373C2×#41—448no—
374C22×Q8—21no—
375C22×Q8C22×D1111yescharacteristic
376C22×D4—111no—
377C22×D4—112no—
378C22×D4—221no—
379C22×D4—222no—
380C22×D4—221no—
381C22×D4—221no—
382C23×C4—111no—
383C23×C4—111no—
384C23×C4—111no—
385C23×C4—221no—
386C23×C4—222no—
387C23×C4—221no—
388C23×C4—221no—
389C2×SD16—118no—
390C2×SD16—228no—
391C2×D8—118no—
392C2×D8—228no—
393C22×C8—112no—
394C22×C8C22×D1112yes—
395C4⋊Q8—22no—
396C4⋊Q8C22×D1114yes—
397#127—114no—
398#127—222no—
399#124—228no—
400#121—118no—
401#121—224no—
402#121—228no—
403C4×Q8—22no—
404C4×Q8—114no—
405C4×Q8—222no—
406C4×Q8C22×D1114yes—
407C4×D4—114no—
408C4×D4—118no—
409C4×D4—114no—
410C4×D4—228no—
411C4×D4—222no—
412C4×D4—224no—
413C4×D4—228no—
414C4×D4—228no—
415C4×D4—222no—
416#117—114no—
417#117—228no—
418#117—222no—
419C2×C4⋊C4—21no—
420C2×C4⋊C4—21no—
421C2×C4⋊C4—111no—
422C2×C4⋊C4—221no—
423C2×C4⋊C4C22×D1111yescharacteristic
424C2×C4⋊C4C22×D1112yes—
425C2×C22⋊C4—221no—
426C2×C22⋊C4—222no—
427C2×C22⋊C4—222no—
428C2×C22⋊C4—221no—
429C2×C22⋊C4—221no—
430C2×C42—21no—
431C2×C42—111no—
432C2×C42—111no—
433C2×C42—111no—
434C2×C42—114no—
435C2×C42—114no—
436C2×C42—228no—
437C2×C42—221no—
438C2×C42—221no—
439C2×C42C22×D1111yescharacteristic
440#107—118no—
441#106C22×D1118yes—
442C4⋊C8—114no—
443C4⋊C8C22×D1114yes—
444#103C22×D1118yes—
445#102—118no—
446#102—118no—
447#102—118no—
448C22⋊C8—118no—
449#97—118no—
450C2×C11#311514yescomplemented
451C2×C11C2×#52511yescharacteristic
452C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
453C2×C11C2×#57511yescharacteristic
454D11—42no—
455D11—44no—
456D11—84no—
457C24—111no—
458C24—221no—
459C24—222no—
460#41—228no—
461#41—2216no—
462#41—228no—
463#41—4432no—
464C2×Q8—21no—
465C2×Q8—24no—
466C2×Q8—22no—
467C2×Q8—44no—
468C2×Q8#434314yescomplemented
469C2×Q8C23×D1112yes—
470C2×D4—114no—
471C2×D4—112no—
472C2×D4—114no—
473C2×D4—224no—
474C2×D4—228no—
475C2×D4—228no—
476C2×D4—221no—
477C2×D4—224no—
478C2×D4—222no—
479C2×D4—224no—
480C2×D4—222no—
481C2×D4—224no—
482C2×D4—224no—
483C2×D4—444no—
484C2×D4—448no—
485C2×D4—444no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—22no—
489C22×C4—111no—
490C22×C4—111no—
491C22×C4—111no—
492C22×C4—112no—
493C22×C4—114no—
494C22×C4—112no—
495C22×C4—114no—
496C22×C4—224no—
497C22×C4—224no—
498C22×C4—228no—
499C22×C4—228no—
500C22×C4—224no—
501C22×C4—222no—
502C22×C4—222no—
503C22×C4—221no—
504C22×C4—224no—
505C22×C4—442no—
506C22×C4—448no—
507C22×C4—444no—
508C22×C4—444no—
509C22×C4D4×D1111yescharacteristic
510C22×C4D4×D1111yescharacteristic
511C22×C4C23×D1111yescharacteristic
512SD16—2216no—
513D8—2216no—
514C2×C8—24no—
515C2×C8—114no—
516C2×C8—224no—
517C2×C8C23×D1114yes—
518C4⋊C4—24no—
519C4⋊C4—24no—
520C4⋊C4—21no—
521C4⋊C4—22no—
522C4⋊C4—112no—
523C4⋊C4—224no—
524C4⋊C4—221no—
525C4⋊C4C23×D1112yes—
526C4⋊C4C23×D1114yes—
527C22⋊C4—224no—
528C22⋊C4—228no—
529C22⋊C4—228no—
530C22⋊C4—224no—
531C22⋊C4—224no—
532C42—24no—
533C42—114no—
534C42—114no—
535C42—112no—
536C42—112no—
537C42—224no—
538C42—224no—
539C42D4×D1112yes—
540C42C23×D1112yes—
541C11C2×#311511yescharacteristic, complemented, Sylow
542C23—112no—
543C23—222no—
544C23—222no—
545C23—224no—
546C23—222no—
547C23—222no—
548C23—224no—
549C23—442no—
550C23—442no—
551C23—444no—
552C23—444no—
553C23—444no—
554C23C2×D4×D1111yescharacteristic
555Q8—24no—
556Q8—22no—
557Q8—48no—
558Q8C2×#434314yescomplemented
559D4—114no—
560D4—2216no—
561D4—224no—
562D4—222no—
563D4—224no—
564D4—224no—
565D4—448no—
566D4—4416no—
567D4—448no—
568D4—444no—
569C2×C4—22no—
570C2×C4—24no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—44no—
575C2×C4—42no—
576C2×C4—112no—
577C2×C4—112no—
578C2×C4—112no—
579C2×C4—2216no—
580C2×C4—222no—
581C2×C4—222no—
582C2×C4—222no—
583C2×C4—228no—
584C2×C4—224no—
585C2×C4—222no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—444no—
589C2×C4—4416no—
590C2×C4—448no—
591C2×C4—442no—
592C2×C4—448no—
593C2×C4#6696714yes—
594C2×C4C2×D4×D1112yes—
595C2×C4C2×D4×D1112yes—
596C2×C4C2×D4×D1111yescharacteristic
597C2×C4C2×#434312yes—
598C2×C4#41×D1112yes—
599C2×C4C24×D1111yescharacteristic
600C8—24no—
601C8—224no—
602C22—224no—
603C22—222no—
604C22—222no—
605C22—222no—
606C22—442no—
607C22—442no—
608C22—444no—
609C22—448no—
610C22—444no—
611C22—444no—
612C22—444no—
613C22—888no—
614C22#1062315812yes—
615C22C2×#6696712yes—
616C22#1062330812yes—
617C22C22×D4×D1111yescharacteristic
618C4—24no—
619C4—22no—
620C4—44no—
621C4—42no—
622C4—222no—
623C4—222no—
624C4—222no—
625C4—442no—
626C4#1062315812yes—
627C4C2×#6696714yes—
628C4C22×#434311yescharacteristic
629C4C2×#41×D1111yescharacteristic
630C2—442no—
631C2—444no—
632C2—884no—
633C2#1307877014yesdirect product factor
634C2C2×#1062315811yescharacteristic
635C2C22×#6696711yescharacteristic
636C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
hypercenterC2×#475D11
hypocenterC11C2×#3115
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#10623256C2semidirect
2. C2×C4×#4343C2semidirect
3. #13078770C2direct (N × H)
4. C2×#10622479C2semidirect
5. C2×#10622700C2semidirect
6. C2×#10622640C2semidirect
7. C2×#10622456C2semidirect
8. C2×#10622424C2semidirect
9. C2×#10622482C2semidirect
10. C2×#10622430C2semidirect
11. C2×#10622448C2semidirect
12. C2×C11×#475C2semidirect
22. #10623256C22semidirect
24. C4×#4343C22semidirect
38. C11×#475C22semidirect
45. #10622700C22semidirect
46. #10622640C22semidirect
51. #10622482C22semidirect
52. #10622479C22semidirect
53. #10622456C22semidirect
54. #10622448C22semidirect
55. #10622430C22semidirect
56. #10622424C22semidirect
147. C2×Q8×C11#41semidirect
176. C2×D44#41semidirect
228. C2×#475D11semidirect
252. Q8×C11C2×#41semidirect
284. D44C2×#41semidirect
322. #475C2×D11semidirect
450. C2×C11#3115semidirect
468. C2×Q8#4343semidirect
541. C11C2×#3115semidirect
558. Q8C2×#4343semidirect
633. C2#13078770direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×C4×#43432
#130787702
C2×#106224792
C2×#106227002
C2×#106226402
C2×#106224562
C2×#106224242
C2×#106224822
C2×#106224302
C2×#106224482
C2×C11×#4752
C2×#311511