Finite Group Databasebeta

← C2×#13070072 #14782697

Subgroups — C2×#13070072 #14782697

Order 2816.

906 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622715C211yesmaximal, characteristic, complemented
2C2×#10622752C211yesmaximal, characteristic
3C2×#10622726C211yesmaximal, characteristic
4C2×#10622745C211yesmaximal, characteristic
5#13070072C218yesmaximal, direct product factor
6C2×#10622194C211yesmaximal, characteristic, complemented
7C2×#10622195C211yesmaximal, characteristic, complemented
8C2×C11×#341C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×#66979C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16#10622752—22no—
17#10622752C2214yes—
18C2×#66889—22no—
19C2×#66888—21no—
20#10622745—22no—
21#10622745C2214yes—
22C2×#66887—21no—
23#10622726—22no—
24#10622726C2214yes—
25C2×#66885—21no—
26C2×#66880—21no—
27#10622715—22no—
28#10622715C2214yescomplemented
29C2×Dic11⋊C8—22no—
30C11×#341C2214yescomplemented
31#10622195C2214yescomplemented
32#10622194C2214yescomplemented
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—21no—
35C2×#4339—21no—
36C2×#4339—21no—
37C2×#4339—21no—
38C2×#4339—21no—
39C2×#4339—21no—
40C2×#4339—21no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—21no—
44C2×#4339—21no—
45C2×#4339D412yes—
46C2×#4339C2312yes—
47C22×D44D411yescharacteristic
48C22×C4×D11—21no—
49C22×Dic22D411yescharacteristic
50C2×C11×M16—21no—
51C2×C11×M16—21no—
52C2×C11×M16—21no—
53C2×C11×M16—21no—
54C2×C11×M16—21no—
55C2×C11×M16—21no—
56C2×C11×M16—21no—
57C2×C11×M16—21no—
58C2×C11×M16—21no—
59C2×C11×M16—21no—
60C2×C11×M16C2312yes—
61C2×C11×M16C2312yes—
62C22×C8×C11—21no—
63C22×C8×C11—21no—
64C22×C8×C11—21no—
65C22×C8×C11—21no—
66C22×C8×C11—21no—
67C22×C8×C11—21no—
68C22×C8×C11—21no—
69C22×C8×C11—21no—
70C22×C8×C11C2312yes—
71C2×C22⋊Dic11—21no—
72C2×C22⋊Dic11—21no—
73#66979—21no—
74#66979—21no—
75#66979—21no—
76#66979—21no—
77#66979—21no—
78#66979D412yes—
79#66979C2312yes—
80#66979C2312yes—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11D412yes—
85C2×#4318—21no—
86C2×#4318—21no—
87C2×#4318—21no—
88C2×#4318—21no—
89C2×#4318—21no—
90C2×#4318C2312yes—
91C22×C11⋊C8—21no—
92#66889—28no—
93#66888—24no—
94#66887—24no—
95#66885—24no—
96#66880—24no—
97Dic11⋊C8—28no—
98C2×#2080—111nomaximal, Sylow
99C24×C11#4111yescharacteristic
100C23×D11—21no—
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11C2×D411yescharacteristic
103C22×C4×C11C2×D411yescharacteristic
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11#4111yescharacteristic
106C22×C4×C11#4111yescharacteristic
107C22×C4×C11#4111yescharacteristic
108C22×C4×C11#4111yescharacteristic
109C22×C4×C11#4111yescharacteristic
110C22×C4×C11#4111yescharacteristic
111C22×C4×C11#4111yescharacteristic
112C22×C4×C11#4111yescharacteristic
113C22×C4×C11#4111yescharacteristic
114C22×C4×C11C2411yescharacteristic
115C2×C22⋊D11—22no—
116C2×C22⋊D11—22no—
117C2×C22⋊D11—41no—
118C2×C22⋊D11—41no—
119C2×C22⋊D11—41no—
120C2×C22⋊D11—41no—
121C22×Dic11—22no—
122C22×Dic11—21no—
123C22×Dic11—41no—
124#4339—22no—
125#4339—22no—
126#4339—22no—
127#4339—22no—
128#4339—22no—
129#4339—22no—
130#4339—22no—
131#4339—22no—
132#4339—41no—
133#4339—41no—
134#4339—41no—
135#4339—41no—
136#4339—41no—
137#4339—41no—
138#4339—41no—
139#4339—41no—
140C2×D44—21no—
141C2×D44—21no—
142C2×D44—21no—
143C2×D44—21no—
144C2×D44—21no—
145C2×D44C2×D412yes—
146C2×C4×D11—22no—
147C2×C4×D11—22no—
148C2×C4×D11—41no—
149C2×C4×D11—41no—
150C2×C4×D11—41no—
151C2×C4×D11—41no—
152C2×Dic22—21no—
153C2×Dic22—21no—
154C2×Dic22—21no—
155C2×Dic22—21no—
156C2×Dic22—21no—
157C2×Dic22C2×D412yes—
158C11×M16—22no—
159C11×M16—22no—
160C11×M16—22no—
161C11×M16—22no—
162C11×M16—41no—
163C11×M16—41no—
164C11×M16—41no—
165C11×M16—41no—
166C2×C8×C11—22no—
167C2×C8×C11—22no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11—22no—
171C2×C8×C11—41no—
172C2×C8×C11—41no—
173C2×C8×C11—41no—
174C2×C8×C11—41no—
175C2×C8×C11—41no—
176C2×C8×C11—41no—
177C2×C8×C11—41no—
178C2×C8×C11—41no—
179C22⋊Dic11—22no—
180C22⋊Dic11—22no—
181C22⋊Dic11—22no—
182C22⋊Dic11—41no—
183C4⋊Dic11—22no—
184C4⋊Dic11—22no—
185C4⋊Dic11—22no—
186C4⋊Dic11—41no—
187C4×Dic11—22no—
188C4×Dic11—22no—
189C4×Dic11—41no—
190C4×Dic11C2×D414yes—
191#4318—22no—
192#4318—22no—
193#4318—41no—
194#4318—41no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—41no—
198C2×#424—111no—
199C2×#421—111no—
200C2×#416—111no—
201C2×#413—111no—
202#2080—118no—
203C2×#344—111no—
204C2×#341D1111yescharacteristic, complemented
205C2×H(3,ℤ/4)—111no—
206C23×C11—42no—
207C23×C11#12311yescharacteristic
208C23×C11#12311yescharacteristic
209C23×C11#12311yescharacteristic
210C23×C11#12311yescharacteristic
211C23×C11#12611yescharacteristic
212C23×C11#12611yescharacteristic
213C23×C11C2×#4111yescharacteristic
214C22×D11—22no—
215C22×D11—41no—
216C22×D11—41no—
217C22×D11—82no—
218C2×C4×C11#12111yescharacteristic
219C2×C4×C11#12111yescharacteristic
220C2×C4×C11#12111yescharacteristic
221C2×C4×C11#12111yescharacteristic
222C2×C4×C11#12311yescharacteristic
223C2×C4×C11#12311yescharacteristic
224C2×C4×C11#12311yescharacteristic
225C2×C4×C11#12311yescharacteristic
226C2×C4×C11#12311yescharacteristic
227C2×C4×C11#12311yescharacteristic
228C2×C4×C11#12311yescharacteristic
229C2×C4×C11#12311yescharacteristic
230C2×C4×C11#12411yescharacteristic
231C2×C4×C11#12411yescharacteristic
232C2×C4×C11#12411yescharacteristic
233C2×C4×C11#12411yescharacteristic
234C2×C4×C11#12611yescharacteristic
235C2×C4×C11#12611yescharacteristic
236C2×C4×C11#12611yescharacteristic
237C2×C4×C11#12611yescharacteristic
238C2×C4×C11#12611yescharacteristic
239C2×C4×C11#12611yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C2×#4111yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—42no—
247C22⋊D11—42no—
248C22⋊D11—42no—
249C22⋊D11—42no—
250C2×Dic11—24no—
251C2×Dic11—22no—
252C2×Dic11—44no—
253C2×Dic11—41no—
254C2×Dic11—41no—
255C2×Dic11—42no—
256C2×Dic11—82no—
257D44—22no—
258D44—22no—
259D44—41no—
260D44—41no—
261C4×D11—42no—
262C4×D11—42no—
263C4×D11—42no—
264C4×D11—42no—
265Dic22—22no—
266Dic22—22no—
267Dic22—41no—
268Dic22—41no—
269C8×C11—42no—
270C8×C11—42no—
271C8×C11—42no—
272C11⋊C8—42no—
273C22×#41—111no—
274C22×M16—111no—
275C22×M16C2×D1111yescharacteristic
276C22×M16C2×D1111yescharacteristic
277C23×C8C2×D1111yescharacteristic
278C2×#117—111no—
279C2×#117—111no—
280#424—114no—
281#424—222no—
282C2×C4⋊C8—222no—
283#421—114no—
284#421—222no—
285C2×#104—222no—
286#416—114no—
287#416—222no—
288C2×#103—221no—
289C2×#102—221no—
290#413—114no—
291#413—222no—
292C2×#101—221no—
293C2×#100—221no—
294#344—114no—
295#341C2×D1114yescomplemented
296H(3,ℤ/4)—114no—
297C22×C11—22no—
298C22×C11—22no—
299C22×C11—22no—
300C22×C11—41no—
301C22×C11—41no—
302C22×C11—41no—
303C22×C11—41no—
304C22×C11#39711yescharacteristic
305C22×C11#39711yescharacteristic
306C22×C11#39711yescharacteristic
307C22×C11#39711yescharacteristic
308C22×C11C2×#12311yescharacteristic
309C22×C11C2×#12311yescharacteristic
310C22×C11C2×#12611yescharacteristic
311C2×D11—42no—
312C2×D11—82no—
313C2×D11—82no—
314C2×D11—82no—
315C4×C11#39711yescharacteristic
316C4×C11#39711yescharacteristic
317C4×C11#39711yescharacteristic
318C4×C11#39711yescharacteristic
319C4×C11C2×#12111yescharacteristic
320C4×C11C2×#12311yescharacteristic
321C4×C11C2×#12411yescharacteristic
322C4×C11C2×#12611yescharacteristic
323Dic11—44no—
324Dic11—42no—
325Dic11—82no—
326C2×#41—112no—
327C2×#41—112no—
328C2×#41—221no—
329C2×#41—221no—
330C2×#41—221no—
331C2×#41—221no—
332C2×#41—221no—
333C2×#41—221no—
334C2×#41—221no—
335C2×#41—221no—
336C2×#41—221no—
337C2×#41—221no—
338C22×Q8—111no—
339C22×D4—111no—
340C22×D4—221no—
341C23×C4—221no—
342C23×C4C22×D1111yescharacteristic
343C2×M16—21no—
344C2×M16—21no—
345C2×M16—21no—
346C2×M16—21no—
347C2×M16—21no—
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—112no—
354C2×M16—221no—
355C2×M16—221no—
356C2×M16—221no—
357C2×M16—221no—
358C2×M16—221no—
359C2×M16C22×D1112yes—
360C2×M16C22×D1112yes—
361C22×C8—21no—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—21no—
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—221no—
370C22×C8C22×D1112yes—
371#117—112no—
372#117—112no—
373#117—112no—
374#117—221no—
375#117—221no—
376#117—221no—
377#117—221no—
378#117—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C22⋊C4—221no—
382C2×C22⋊C4—221no—
383C2×C42—112no—
384C2×C42—221no—
385C4⋊C8—228no—
386#104—228no—
387#103—224no—
388#102—224no—
389#101—224no—
390#100—224no—
391C2×C11—21no—
392C2×C11—21no—
393C2×C11—21no—
394C2×C11—21no—
395C2×C11—21no—
396C2×C11—21no—
397C2×C11#208012yescomplemented
398C2×C11C2×#39711yescharacteristic
399D11—82no—
400C24—221no—
401C24#434311yescharacteristic
402#41—222no—
403#41—222no—
404#41—222no—
405#41—222no—
406#41—222no—
407#41—222no—
408#41—222no—
409#41—222no—
410#41—441no—
411#41—441no—
412#41—441no—
413#41—441no—
414#41—441no—
415#41—441no—
416#41—441no—
417#41—441no—
418C2×Q8—112no—
419C2×Q8—221no—
420C2×Q8—221no—
421C2×Q8—221no—
422C2×Q8—221no—
423C2×Q8—221no—
424C2×D4—112no—
425C2×D4—222no—
426C2×D4—222no—
427C2×D4—221no—
428C2×D4—221no—
429C2×D4—221no—
430C2×D4—221no—
431C2×D4—221no—
432C2×D4—441no—
433C2×D4—441no—
434C2×D4—441no—
435C2×D4—441no—
436C22×C4—222no—
437C22×C4—221no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—441no—
441C22×C4—441no—
442C22×C4—441no—
443C22×C4—441no—
444C22×C4—441no—
445C22×C4#433911yescharacteristic
446C22×C4#433911yescharacteristic
447C22×C4#433911yescharacteristic
448C22×C4#433911yescharacteristic
449C22×C4#433911yescharacteristic
450C22×C4#433911yescharacteristic
451C22×C4D4×D1111yescharacteristic
452C22×C4D4×D1111yescharacteristic
453C22×C4D4×D1111yescharacteristic
454C22×C4D4×D1111yescharacteristic
455C22×C4#434111yescharacteristic
456C22×C4#434111yescharacteristic
457C22×C4#434311yescharacteristic
458C22×C4C23×D1111yescharacteristic
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—41no—
464M16—41no—
465M16—41no—
466M16—41no—
467M16—222no—
468M16—222no—
469M16—441no—
470M16—441no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—222no—
485C2×C8—441no—
486C2×C8—441no—
487C4⋊C4—222no—
488C4⋊C4—222no—
489C4⋊C4—222no—
490C4⋊C4—441no—
491C22⋊C4—222no—
492C22⋊C4—222no—
493C22⋊C4—222no—
494C22⋊C4—441no—
495C42—114no—
496C42—222no—
497C42—222no—
498C42—441no—
499C11C2×#208011yescharacteristic, complemented, Sylow
500C23—42no—
501C23—222no—
502C23—441no—
503C23—441no—
504C23—882no—
505C23#6694711yescharacteristic
506C23#6694711yescharacteristic
507C23#6694711yescharacteristic
508C23#6694711yescharacteristic
509C23#6695111yescharacteristic
510C23#6695111yescharacteristic
511C23C2×#434311yescharacteristic
512Q8—222no—
513Q8—222no—
514Q8—441no—
515Q8—441no—
516D4—222no—
517D4—222no—
518D4—442no—
519D4—442no—
520D4—442no—
521D4—442no—
522D4—441no—
523D4—441no—
524C2×C4—224no—
525C2×C4—222no—
526C2×C4—444no—
527C2×C4—441no—
528C2×C4—441no—
529C2×C4—442no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—882no—
535C2×C4#6692911yescharacteristic
536C2×C4#6692911yescharacteristic
537C2×C4#6692911yescharacteristic
538C2×C4#6692911yescharacteristic
539C2×C4#6693611yescharacteristic
540C2×C4#6693611yescharacteristic
541C2×C4#6693611yescharacteristic
542C2×C4#6693611yescharacteristic
543C2×C4#6693711yescharacteristic
544C2×C4#6693711yescharacteristic
545C2×C4#6693711yescharacteristic
546C2×C4#6693711yescharacteristic
547C2×C4#6693811yescharacteristic
548C2×C4#6693811yescharacteristic
549C2×C4#6693811yescharacteristic
550C2×C4#6693811yescharacteristic
551C2×C4#6694711yescharacteristic
552C2×C4#6694711yescharacteristic
553C2×C4#6694711yescharacteristic
554C2×C4#6694711yescharacteristic
555C2×C4#6695111yescharacteristic
556C2×C4#6695111yescharacteristic
557C2×C4C2×#433911yescharacteristic
558C2×C4C2×#433911yescharacteristic
559C2×C4C2×#433911yescharacteristic
560C2×C4C2×D4×D1111yescharacteristic
561C2×C4C2×D4×D1111yescharacteristic
562C2×C4C2×#434111yescharacteristic
563C8—42no—
564C8—42no—
565C8—42no—
566C8—442no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—442no—
575C22—882no—
576C22—882no—
577C22—882no—
578C22#1062228811yescharacteristic
579C22#1062228811yescharacteristic
580C22#1062228811yescharacteristic
581C22#1062228811yescharacteristic
582C22C2×#6694711yescharacteristic
583C22C2×#6694711yescharacteristic
584C22C2×#6695111yescharacteristic
585C4—444no—
586C4—442no—
587C4—882no—
588C4#1062228811yescharacteristic
589C4#1062228811yescharacteristic
590C4#1062228811yescharacteristic
591C4#1062228811yescharacteristic
592C4C2×#6692911yescharacteristic
593C4C2×#6693611yescharacteristic
594C4C2×#6693711yescharacteristic
595C4C2×#6693811yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—882no—
603C2#1307007212yesdirect product factor
604C2C2×#1062228811yescharacteristic
subgroupG/H
centerC2×C4#66938
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#341C2
socleC22×C11#397
prime radicalC22×#4339C22
hypercenterC2×#341D11
hypocenterC11C2×#2080
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#341

Complements

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

NH ≅ G/Ntype
1. C2×#10622715C2semidirect
5. #13070072C2direct (N × H)
6. C2×#10622194C2semidirect
7. C2×#10622195C2semidirect
8. C2×C11×#341C2semidirect
28. #10622715C22semidirect
30. C11×#341C22semidirect
31. #10622195C22semidirect
32. #10622194C22semidirect
204. C2×#341D11semidirect
295. #341C2×D11semidirect
397. C2×C11#2080semidirect
499. C11C2×#2080semidirect
603. C2#13070072direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227152
C2×#106227522
C2×#106227262
C2×#106227452
#130700722
C2×#106221942
C2×#106221952
C2×C11×#3412
C2×#208011