Finite Group Databasebeta

← C2×#13069918 #14781651

Subgroups — C2×#13069918 #14781651

Order 2816.

1362 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66962C211yesmaximal, characteristic
2C22×#66886C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic
4C22×#66874C211yesmaximal, characteristic, complemented
5C22×#66888C211yesmaximal, characteristic, complemented
6C2×#10622742C211yesmaximal, characteristic
7#13069918C218yesmaximal, direct product factor
8C2×C11×#343C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C22×C11×M16C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×#4318C2211yescharacteristic
15C23×C11⋊C8C2211yescharacteristic
16C2×#66962—22no—
17C2×#66962—24no—
18C2×#66962—24no—
19C2×#66962C2214yes—
20C22×Dic44—21no—
21C22×#4314—21no—
22C2×#66888—24no—
23C2×#66888C2214yescomplemented
24#10622742—22no—
25#10622742C2214yes—
26C2×#66886—24no—
27C2×#66886C2214yescomplemented
28C2×(C2×D11)⋊C8—22no—
29C2×#66874—21no—
30C2×#66874—22no—
31C2×#66874—22no—
32C2×#66874C2214yescomplemented
33#10622579—22no—
34#10622579C2214yes—
35C2×#66873—21no—
36C11×#343C2214yescomplemented
37C23×C4×C11—21no—
38C23×C4×C11C2311yescharacteristic
39C22×C22⋊D11—21no—
40C23×Dic11—21no—
41C2×#4339—21no—
42C2×#4339—21no—
43C2×#4339—22no—
44C2×#4339—22no—
45C2×#4339—22no—
46C2×#4339—22no—
47C2×#4339D412yes—
48C2×#4339C2312yes—
49C22×D44D411yescharacteristic
50C22×C4×D11—21no—
51C22×Dic22—21no—
52C22×Dic22—22no—
53C22×Dic22—21no—
54C22×Dic22—21no—
55C22×Dic22—21no—
56C22×Dic22—22no—
57C22×Dic22—21no—
58C22×Dic22—22no—
59C22×Dic22D414yes—
60C22×Dic22D411yescharacteristic
61C22×Dic22C2312yes—
62C2×C11×M16—22no—
63C2×C11×M16—21no—
64C2×C11×M16—21no—
65C2×C11×M16—22no—
66C2×C11×M16—22no—
67C2×C11×M16D414yes—
68C2×C11×M16C2312yes—
69C2×C11×M16C2312yes—
70C22×C8×C11—21no—
71C22×C8×C11—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2312yes—
78C2×#4318—21no—
79C2×#4318—22no—
80C2×#4318—22no—
81C2×#4318C2312yes—
82C22×C11⋊C8—22no—
83C22×C11⋊C8—22no—
84C22×C11⋊C8—21no—
85C22×C11⋊C8D412yes—
86C22×C11⋊C8D412yes—
87C22×C11⋊C8C2312yes—
88#66962—216no—
89#66962—28no—
90#66962—28no—
91C2×Dic44—28no—
92C2×Dic44—24no—
93C2×#4314—28no—
94C2×#4314—24no—
95#66888—28no—
96#66886—28no—
97(C2×D11)⋊C8—28no—
98#66874—24no—
99#66874—28no—
100#66873—24no—
101C2×#2052—111nomaximal, Sylow
102C24×C11#4111yescharacteristic
103C23×D11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—41no—
106C22×C4×C11—41no—
107C22×C4×C11—82no—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11#4112yes—
115C22×C4×C11#4111yescharacteristic
116C22×C4×C11#4112yes—
117C22×C4×C11C2411yescharacteristic
118C2×C22⋊D11—22no—
119C2×C22⋊D11—22no—
120C2×C22⋊D11—42no—
121C2×C22⋊D11—42no—
122C22×Dic11—21no—
123C22×Dic11—24no—
124C22×Dic11—22no—
125C22×Dic11—41no—
126C22×Dic11—41no—
127C22×Dic11—42no—
128#4339—24no—
129#4339—24no—
130#4339—22no—
131#4339—22no—
132#4339—22no—
133#4339—22no—
134#4339—42no—
135#4339—42no—
136#4339—42no—
137#4339—42no—
138C2×D44—22no—
139C2×D44—21no—
140C2×D44—22no—
141C2×D44C2×D412yes—
142C2×C4×D11—22no—
143C2×C4×D11—22no—
144C2×C4×D11—42no—
145C2×C4×D11—42no—
146C2×Dic22—24no—
147C2×Dic22—22no—
148C2×Dic22—24no—
149C2×Dic22—24no—
150C2×Dic22—24no—
151C2×Dic22—21no—
152C2×Dic22—22no—
153C2×Dic22—24no—
154C2×Dic22—22no—
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—22no—
158C2×Dic22—22no—
159C2×Dic22—41no—
160C2×Dic22—41no—
161C2×Dic22—42no—
162C2×Dic22—42no—
163C2×Dic22—42no—
164C2×Dic22—42no—
165C2×Dic22—42no—
166C2×Dic22C2×D412yes—
167C2×Dic22C2×D414yes—
168C11×M16—24no—
169C11×M16—22no—
170C11×M16—22no—
171C11×M16—22no—
172C11×M16—42no—
173C11×M16C2×D414yes—
174C2×C8×C11—24no—
175C2×C8×C11—22no—
176C2×C8×C11—22no—
177C2×C8×C11—42no—
178C11×C4⋊C4—22no—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—41no—
181C11×C4⋊C4—41no—
182#4318—22no—
183#4318—22no—
184#4318—42no—
185C2×C11⋊C8—24no—
186C2×C11⋊C8—24no—
187C2×C11⋊C8—22no—
188C2×C11⋊C8—22no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—42no—
191C2×C11⋊C8C2×D414yes—
192Dic44—216no—
193#4314—216no—
194C22×#137—111no—
195C22×#108—111no—
196C2×#417—111no—
197C22×#103—111no—
198C22×#101—111no—
199C2×#408—111no—
200#2052—118no—
201C2×#343D1111yescharacteristic, complemented
202C23×C11—22no—
203C23×C11—22no—
204C23×C11#12111yescharacteristic
205C23×C11#12111yescharacteristic
206C23×C11#12312yes—
207C23×C11#12412yes—
208C23×C11C2×#4111yescharacteristic
209C22×D11—22no—
210C22×D11—42no—
211C22×D11—42no—
212C22×D11—42no—
213C2×C4×C11—42no—
214C2×C4×C11—82no—
215C2×C4×C11—82no—
216C2×C4×C11—82no—
217C2×C4×C11#12012yes—
218C2×C4×C11#12012yes—
219C2×C4×C11#12112yes—
220C2×C4×C11#12112yes—
221C2×C4×C11#12111yescharacteristic
222C2×C4×C11#12111yescharacteristic
223C2×C4×C11#12112yes—
224C2×C4×C11#12112yes—
225C2×C4×C11#12312yes—
226C2×C4×C11#12312yes—
227C2×C4×C11#12312yes—
228C2×C4×C11#12412yes—
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×C4×C11C2×#4111yescharacteristic
235C22⋊D11—42no—
236C22⋊D11—42no—
237C22⋊D11—44no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—42no—
241C2×Dic11—42no—
242C2×Dic11—44no—
243C2×Dic11—44no—
244C2×Dic11—42no—
245D44—22no—
246D44—22no—
247D44—42no—
248C4×D11—42no—
249C4×D11—42no—
250C4×D11—44no—
251Dic22—24no—
252Dic22—22no—
253Dic22—24no—
254Dic22—22no—
255Dic22—42no—
256Dic22—42no—
257Dic22—44no—
258Dic22—44no—
259Dic22—42no—
260C8×C11—24no—
261C8×C11—42no—
262C11⋊C8—24no—
263C11⋊C8—42no—
264C22×#41—111no—
265C23×Q8—111no—
266C2×#137—114no—
267C2×#137—224no—
268C2×#137—222no—
269C2×#137—224no—
270C22×Q16—221no—
271C22×SD16—221no—
272C22×M16—111no—
273C22×M16C2×D1111yescharacteristic
274C22×M16C2×D1111yescharacteristic
275C23×C8—111no—
276C22×C4⋊C4C2×D1111yescharacteristic
277C2×#108—114no—
278C2×#108—224no—
279#417—114no—
280#417—222no—
281C2×#103—114no—
282C2×#103—222no—
283C2×#103—222no—
284C2×#103—221no—
285C2×#102—221no—
286C2×#101—114no—
287C2×#101—224no—
288#408—114no—
289#408—222no—
290C2×C22⋊C8—222no—
291#343C2×D1114yescomplemented
292C22×C11—24no—
293C22×C11—24no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11#39412yes—
299C22×C11#39412yes—
300C22×C11#47112yes—
301C22×C11#47312yes—
302C22×C11C2×#12111yescharacteristic
303C22×C11C2×#12311yescharacteristic
304C22×C11C2×#12411yescharacteristic
305C2×D11—42no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—84no—
309C4×C11—82no—
310C4×C11#39412yes—
311C4×C11#39412yes—
312C4×C11C2×#12011yescharacteristic
313C4×C11C2×#12111yescharacteristic
314C4×C11C2×#12111yescharacteristic
315C4×C11C2×#12311yescharacteristic
316Dic11—44no—
317Dic11—42no—
318C2×#41—112no—
319C2×#41—112no—
320C2×#41—221no—
321C2×#41—221no—
322C2×#41—222no—
323C2×#41—222no—
324C2×#41—222no—
325C2×#41—222no—
326C22×Q8—111no—
327C22×Q8—114no—
328C22×Q8—112no—
329C22×Q8—221no—
330C22×Q8—222no—
331C22×Q8—222no—
332C22×Q8—222no—
333C22×Q8—221no—
334C22×Q8—221no—
335C22×Q8—221no—
336C22×Q8—221no—
337C22×D4—111no—
338C22×D4—221no—
339C23×C4—21no—
340C23×C4—221no—
341C23×C4—221no—
342C23×C4C22×D1111yescharacteristic
343#137—228no—
344#137—2216no—
345#137—228no—
346C2×Q16—224no—
347C2×Q16—228no—
348C2×SD16—224no—
349C2×SD16—228no—
350C2×M16—22no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—22no—
354C2×M16—22no—
355C2×M16—112no—
356C2×M16—221no—
357C2×M16—222no—
358C2×M16—222no—
359C2×M16D4414yes—
360C2×M16C22×D1112yes—
361C2×M16C22×D1112yes—
362C22×C8—21no—
363C22×C8—21no—
364C22×C8—112no—
365C22×C8—112no—
366C22×C8—112no—
367C22×C8—222no—
368C22×C8—222no—
369C22×C8—221no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4C22×D1112yes—
376#108—228no—
377#103—228no—
378#103—224no—
379#102—224no—
380#101—228no—
381C22⋊C8—228no—
382C2×C11—21no—
383C2×C11—21no—
384C2×C11—22no—
385C2×C11#205214yescomplemented
386C2×C11C2×#39411yescharacteristic
387C2×C11C2×#47111yescharacteristic
388C2×C11C2×#47311yescharacteristic
389D11—82no—
390C24—221no—
391C24#433911yescharacteristic
392#41—224no—
393#41—224no—
394#41—222no—
395#41—222no—
396#41—222no—
397#41—222no—
398#41—442no—
399#41—442no—
400#41—442no—
401#41—442no—
402C2×Q8—114no—
403C2×Q8—112no—
404C2×Q8—221no—
405C2×Q8—224no—
406C2×Q8—222no—
407C2×Q8—224no—
408C2×Q8—222no—
409C2×Q8—224no—
410C2×Q8—224no—
411C2×Q8—224no—
412C2×Q8—222no—
413C2×Q8—222no—
414C2×Q8—222no—
415C2×Q8—222no—
416C2×Q8—222no—
417C2×Q8—442no—
418C2×Q8—441no—
419C2×Q8—441no—
420C2×Q8—442no—
421C2×Q8—442no—
422C2×Q8—442no—
423C2×Q8—442no—
424C2×D4—112no—
425C2×D4—222no—
426C2×D4—222no—
427C2×D4—222no—
428C2×D4—221no—
429C2×D4—222no—
430C2×D4—442no—
431C2×D4—442no—
432C22×C4—22no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—82no—
436C22×C4—221no—
437C22×C4—224no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—442no—
442C22×C4—441no—
443C22×C4—441no—
444C22×C4—442no—
445C22×C4—442no—
446C22×C4C2×D4412yes—
447C22×C4#433911yescharacteristic
448C22×C4#433912yes—
449C22×C4D4×D1112yes—
450C22×C4D4×D1111yescharacteristic
451C22×C4D4×D1111yescharacteristic
452C22×C4D4×D1111yescharacteristic
453C22×C4D4×D1111yescharacteristic
454C22×C4#434312yes—
455C22×C4C23×D1111yescharacteristic
456Q16—2216no—
457SD16—2216no—
458M16—24no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—42no—
463M16—222no—
464M16—222no—
465M16—442no—
466M16C2×D4414yes—
467C2×C8—24no—
468C2×C8—22no—
469C2×C8—22no—
470C2×C8—42no—
471C2×C8—114no—
472C2×C8—224no—
473C2×C8—224no—
474C2×C8—222no—
475C2×C8—222no—
476C2×C8—222no—
477C2×C8—442no—
478C4⋊C4—22no—
479C4⋊C4—22no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C11C2×#205211yescharacteristic, complemented, Sylow
483C23—22no—
484C23—22no—
485C23—222no—
486C23—442no—
487C23—442no—
488C23—442no—
489C23#6692812yes—
490C23#6693711yescharacteristic
491C23#6693711yescharacteristic
492C23#6694712yes—
493C23C2×#433911yescharacteristic
494Q8—224no—
495Q8—222no—
496Q8—224no—
497Q8—222no—
498Q8—442no—
499Q8—442no—
500Q8—444no—
501Q8—444no—
502Q8—442no—
503D4—222no—
504D4—222no—
505D4—442no—
506D4—442no—
507D4—444no—
508D4—442no—
509C2×C4—42no—
510C2×C4—82no—
511C2×C4—82no—
512C2×C4—82no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—442no—
518C2×C4—444no—
519C2×C4—444no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—444no—
523C2×C4#6692812yes—
524C2×C4#6693512yes—
525C2×C4#6693512yes—
526C2×C4#6693712yes—
527C2×C4#6693712yes—
528C2×C4#6693711yescharacteristic
529C2×C4#6693711yescharacteristic
530C2×C4#6694712yes—
531C2×C4#6694712yes—
532C2×C4#6694712yes—
533C2×C4#6694812yes—
534C2×C4#6694812yes—
535C2×C4C22×D4411yescharacteristic
536C2×C4C2×#433911yescharacteristic
537C2×C4C2×D4×D1111yescharacteristic
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4C2×D4×D1111yescharacteristic
540C2×C4C2×#434311yescharacteristic
541C8—24no—
542C8—42no—
543C8—224no—
544C8—442no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—24no—
550C22—24no—
551C22—442no—
552C22—442no—
553C22—442no—
554C22—884no—
555C22#1062228512yes—
556C22#1062228512yes—
557C22#1062236112yes—
558C22#1062236812yes—
559C22C2×#6692811yescharacteristic
560C22C2×#6693711yescharacteristic
561C22C2×#6694711yescharacteristic
562C4—82no—
563C4—442no—
564C4—444no—
565C4#1062228512yes—
566C4#1062228512yes—
567C4C2×#6693511yescharacteristic
568C4C2×#6693711yescharacteristic
569C4C2×#6694711yescharacteristic
570C4C2×#6694811yescharacteristic
571C2—21no—
572C2—21no—
573C2—22no—
574C2—882no—
575C2#1306991814yesdirect product factor
576C2C2×#1062228511yescharacteristic
577C2C2×#1062236111yescharacteristic
578C2C2×#1062236811yescharacteristic
subgroupG/H
centerC23#66937
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#343C2
socleC23×C11#121
prime radicalC22×#4339C22
hypercenterC2×#343D11
hypocenterC11C2×#2052
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#343

Complements

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

NH ≅ G/Ntype
2. C22×#66886C2semidirect
4. C22×#66874C2semidirect
5. C22×#66888C2semidirect
7. #13069918C2direct (N × H)
8. C2×C11×#343C2semidirect
23. C2×#66888C22semidirect
27. C2×#66886C22semidirect
32. C2×#66874C22semidirect
36. C11×#343C22semidirect
201. C2×#343D11semidirect
291. #343C2×D11semidirect
385. C2×C11#2052semidirect
482. C11C2×#2052semidirect
575. C2#13069918direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669622
C22×#668862
C2×#106225792
C22×#668742
C22×#668882
C2×#106227422
#130699182
C2×C11×#3432
C2×#205211