Finite Group Databasebeta

← C2×#13069705 #14780809

Subgroups — C2×#13069705 #14780809

Order 2816.

2726 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4314C211yesmaximal, characteristic, complemented
2C23×#4324C211yesmaximal, characteristic, complemented
3C22×#66993C211yesmaximal, characteristic
4C22×#66873C211yesmaximal, characteristic, complemented
5C2×#10622587C211yesmaximal, characteristic, complemented
6#13069705C218yesmaximal, direct product factor
7C2×#10622188C211yesmaximal, characteristic, complemented
8C22×C11×#102C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C23×C22⋊D11—22no—
11C23×D44C2211yescharacteristic
12C23×Dic22C2211yescharacteristic
13C23×C8×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C2×#66993—24no—
16C2×#66993—24no—
17C2×#66993—22no—
18C2×#66993C2214yes—
19C22×#4324—24no—
20C22×#4324—24no—
21C22×#4324—24no—
22C22×#4324C2214yescomplemented
23C22×C4×Dic11C2211yescharacteristic
24C23×C11⋊C8C2211yescharacteristic
25C22×#4314—24no—
26C22×#4314—24no—
27C22×#4314—24no—
28C22×#4314C2214yescomplemented
29C2×C11×#102—24no—
30C2×C11×#102C2214yescomplemented
31C2×C11⋊#95—22no—
32#10622587—22no—
33#10622587C2214yescomplemented
34C2×#66873—24no—
35C2×#66873C2214yescomplemented
36#10622188C2214yescomplemented
37C25×C11—21no—
38C24×D11—21no—
39C22×D4×C11—22no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11—21no—
44C22×D4×C11—22no—
45C22×D4×C11D414yes—
46C22×D4×C11C2312yes—
47C23×C4×C11—21no—
48C23×C4×C11C2311yescharacteristic
49C22×C22⋊D11—216no—
50C22×C22⋊D11—28no—
51C22×C22⋊D11—48no—
52C22×C22⋊D11—48no—
53C23×Dic11—21no—
54C23×Dic11D412yes—
55C22×D44—22no—
56C22×D44—22no—
57C22×D44—22no—
58C22×D44—22no—
59C22×D44—22no—
60C22×D44—21no—
61C22×D44D414yes—
62C22×D44C2312yes—
63C22×Dic22—22no—
64C22×Dic22—22no—
65C22×Dic22—22no—
66C22×Dic22—22no—
67C22×Dic22—21no—
68C22×Dic22—22no—
69C22×Dic22D414yescomplemented
70C22×Dic22C2312yes—
71C22×C8×C11—22no—
72C22×C8×C11—22no—
73C22×C8×C11D414yescomplemented
74C22×C8×C11C2312yes—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2312yes—
79#66993—216no—
80#66993—28no—
81#66993—28no—
82C2×#4324—232no—
83C2×#4324—28no—
84C2×#4324—28no—
85C2×#4324—28no—
86C2×C4×Dic11—22no—
87C2×C4×Dic11—22no—
88C2×C4×Dic11D412yes—
89C2×C4×Dic11C2312yes—
90C22×C11⋊C8—22no—
91C22×C11⋊C8—22no—
92C22×C11⋊C8D414yescomplemented
93C22×C11⋊C8C2312yes—
94C2×#4314—232no—
95C2×#4314—28no—
96C2×#4314—28no—
97C2×#4314—28no—
98C11×#102—28no—
99C11⋊#95—28no—
100#66873—28no—
101C2×#2014—111nomaximal, Sylow
102C24×C11—24no—
103C24×C11—22no—
104C24×C11—42no—
105C24×C11—42no—
106C24×C11—44no—
107C24×C11—44no—
108C24×C11C2×D411yescharacteristic
109C23×D11—24no—
110C23×D11—22no—
111C23×D11—42no—
112C23×D11—42no—
113C23×D11—44no—
114C23×D11—44no—
115C2×D4×C11—28no—
116C2×D4×C11—24no—
117C2×D4×C11—28no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—22no—
122C2×D4×C11—22no—
123C2×D4×C11—44no—
124C2×D4×C11—44no—
125C2×D4×C11—42no—
126C2×D4×C11—42no—
127C2×D4×C11C2×D414yes—
128C22×C4×C11—22no—
129C22×C4×C11—42no—
130C22×C4×C11—44no—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D412yes—
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11#4112yes—
138C22×C4×C11C2411yescharacteristic
139C2×C22⋊D11—232no—
140C2×C22⋊D11—416no—
141C2×C22⋊D11—464no—
142C2×C22⋊D11—416no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—22no—
147C22×Dic11—42no—
148C22×Dic11—42no—
149C22×Dic11SD1618yescomplemented
150C22×Dic11C2×D414yes—
151C2×D44—24no—
152C2×D44—28no—
153C2×D44—28no—
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—22no—
157C2×D44—22no—
158C2×D44—22no—
159C2×D44—44no—
160C2×D44—42no—
161C2×D44—44no—
162C2×D44—42no—
163C2×D44C2×D414yes—
164C2×Dic22—28no—
165C2×Dic22—28no—
166C2×Dic22—24no—
167C2×Dic22—22no—
168C2×Dic22—22no—
169C2×Dic22—22no—
170C2×Dic22—22no—
171C2×Dic22—22no—
172C2×Dic22—42no—
173C2×Dic22—44no—
174C2×Dic22—44no—
175C2×Dic22—42no—
176C2×Dic22C2×D414yescomplemented
177C2×C8×C11—28no—
178C2×C8×C11—22no—
179C2×C8×C11—22no—
180C2×C8×C11C2×D414yescomplemented
181C11×C4⋊C4—22no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—42no—
184#4324—232no—
185C4×Dic11—24no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188C2×C11⋊C8—28no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8C2×D414yescomplemented
192#4314—232no—
193C23×SD16—111no—
194C23×SD16—111no—
195C22×#127—111no—
196C22×#102—111no—
197C22×#102D1111yescharacteristic, complemented
198C2×#391—111no—
199#2014—118no—
200C2×#336—111no—
201C23×C11—24no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—44no—
205C23×C11—44no—
206C23×C11—48no—
207C23×C11—416no—
208C23×C11—88no—
209C23×C11—84no—
210C23×C11—84no—
211C23×C11#12012yes—
212C23×C11#12112yes—
213C23×C11#12712yes—
214C23×C11C2×SD1614yes—
215C23×C11AGL(1,ℤ/8)14yes—
216C23×C11C22×D411yescharacteristic
217C22×D11—24no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—44no—
221C22×D11—44no—
222C22×D11—48no—
223C22×D11—416no—
224C22×D11—88no—
225C22×D11—84no—
226C22×D11—84no—
227D4×C11—24no—
228D4×C11—24no—
229D4×C11—42no—
230D4×C11—42no—
231D4×C11—48no—
232C2×C4×C11—42no—
233C2×C4×C11—44no—
234C2×C4×C11—84no—
235C2×C4×C11#12014yes—
236C2×C4×C11#12012yes—
237C2×C4×C11#12014yes—
238C2×C4×C11#12114yes—
239C2×C4×C11#12112yes—
240C2×C4×C11#12114yes—
241C2×C4×C11#12712yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C22⋊D11—464no—
249C2×Dic11—24no—
250C2×Dic11—24no—
251C2×Dic11—216no—
252C2×Dic11—24no—
253C2×Dic11—42no—
254C2×Dic11—42no—
255C2×Dic11—48no—
256C2×Dic11C2×SD1618yescomplemented
257D44—24no—
258D44—24no—
259D44—42no—
260D44—42no—
261D44—48no—
262Dic22—24no—
263Dic22—24no—
264Dic22—42no—
265Dic22—42no—
266Dic22—48no—
267C8×C11—24no—
268C11⋊C8—24no—
269C23×Q8—111no—
270C23×D4—111no—
271C23×D4—222no—
272C23×D4C2×D1111yescharacteristic
273C22×SD16—114no—
274C22×SD16—114no—
275C22×SD16—224no—
276C22×SD16—224no—
277C22×SD16—224no—
278C22×SD16—224no—
279C22×SD16—224no—
280C22×SD16—224no—
281C23×C8—111no—
282C23×C8C2×D1111yescharacteristic
283C2×#127—114no—
284C2×#127—222no—
285C2×#127—224no—
286C2×#127—224no—
287C22×C4⋊C4C2×D1111yescharacteristic
288C22×C42—111no—
289C2×#102—24no—
290C2×#102—114no—
291C2×#102—224no—
292C2×#102C2×D1114yescomplemented
293#391—114no—
294#391—222no—
295C2×#95—222no—
296#336—114no—
297C22×C11—44no—
298C22×C11—48no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11—84no—
302C22×C11—816no—
303C22×C11#39214yes—
304C22×C11#45018yes—
305C22×C11#46018yes—
306C22×C11#49214yes—
307C22×C11#49614yes—
308C22×C11C2×#12011yescharacteristic
309C22×C11C2×#12111yescharacteristic
310C22×C11C2×#12711yescharacteristic
311C22×C11C22×SD1612yes—
312C22×C11C2×AGL(1,ℤ/8)12yes—
313C2×D11—44no—
314C2×D11—48no—
315C2×D11—82no—
316C2×D11—82no—
317C2×D11—84no—
318C2×D11—816no—
319C4×C11—82no—
320C4×C11#39214yes—
321C4×C11C2×#12011yescharacteristic
322C4×C11C2×#12011yescharacteristic
323C4×C11C2×#12111yescharacteristic
324C4×C11C2×#12111yescharacteristic
325Dic11—28no—
326Dic11—44no—
327C25—21no—
328C25—221no—
329C22×Q8—114no—
330C22×Q8—112no—
331C22×Q8—222no—
332C22×Q8—221no—
333C22×Q8—222no—
334C22×Q8—222no—
335C22×Q8—222no—
336C22×Q8—222no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—22no—
340C22×D4—21no—
341C22×D4—22no—
342C22×D4—22no—
343C22×D4—114no—
344C22×D4—112no—
345C22×D4—228no—
346C22×D4—2216no—
347C22×D4—222no—
348C22×D4—222no—
349C22×D4—222no—
350C22×D4—222no—
351C22×D4—221no—
352C22×D4—222no—
353C22×D4—448no—
354C22×D4—448no—
355C22×D4D4414yes—
356C22×D4C22×D1112yes—
357C23×C4—21no—
358C23×C4—112no—
359C23×C4—221no—
360C23×C4C22×D1111yescharacteristic
361C2×SD16—228no—
362C2×SD16—228no—
363C2×SD16—2232no—
364C2×SD16—228no—
365C2×SD16—228no—
366C2×SD16—2232no—
367C2×SD16—228no—
368C2×SD16—228no—
369C22×C8—22no—
370C22×C8—22no—
371C22×C8—114no—
372C22×C8—112no—
373C22×C8—222no—
374C22×C8—222no—
375C22×C8C22⋊D1114yescomplemented
376C22×C8C22×D1112yes—
377#127—228no—
378#127—2216no—
379#127—228no—
380C2×C4⋊C4—22no—
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4C22×D1112yes—
384C2×C42—112no—
385C2×C42—112no—
386C2×C42—222no—
387C2×C42—222no—
388#102—28no—
389#102—228no—
390#95—228no—
391C2×C11—84no—
392C2×C11#201418yescomplemented
393C2×C11C2×#39211yescharacteristic
394C2×C11C2×#45012yes—
395C2×C11C2×#46012yes—
396C2×C11C2×#49211yescharacteristic
397C2×C11C2×#49611yescharacteristic
398D11—84no—
399C24—24no—
400C24—22no—
401C24—42no—
402C24—44no—
403C24—44no—
404C24—42no—
405C24—224no—
406C24—222no—
407C24—442no—
408C24—444no—
409C24—444no—
410C24—442no—
411C24D4×D1111yescharacteristic
412C2×Q8—114no—
413C2×Q8—224no—
414C2×Q8—222no—
415C2×Q8—228no—
416C2×Q8—228no—
417C2×Q8—222no—
418C2×Q8—222no—
419C2×Q8—222no—
420C2×Q8—222no—
421C2×Q8—442no—
422C2×Q8—444no—
423C2×Q8—444no—
424C2×Q8—442no—
425C2×D4—28no—
426C2×D4—24no—
427C2×D4—28no—
428C2×D4—22no—
429C2×D4—22no—
430C2×D4—22no—
431C2×D4—22no—
432C2×D4—22no—
433C2×D4—44no—
434C2×D4—42no—
435C2×D4—44no—
436C2×D4—42no—
437C2×D4—114no—
438C2×D4—2232no—
439C2×D4—224no—
440C2×D4—228no—
441C2×D4—228no—
442C2×D4—222no—
443C2×D4—222no—
444C2×D4—222no—
445C2×D4—222no—
446C2×D4—222no—
447C2×D4—4416no—
448C2×D4—4416no—
449C2×D4—4464no—
450C2×D4—444no—
451C2×D4—442no—
452C2×D4—444no—
453C2×D4—442no—
454C2×D4C2×D4414yes—
455C22×C4—22no—
456C22×C4—44no—
457C22×C4—42no—
458C22×C4—118no—
459C22×C4—114no—
460C22×C4—224no—
461C22×C4—224no—
462C22×C4—224no—
463C22×C4—222no—
464C22×C4—442no—
465C22×C4—442no—
466C22×C4C2×D4412yes—
467C22×C4#433912yes—
468C22×C4D4×D1111yescharacteristic
469C22×C4D4×D1112yes—
470C22×C4D4×D1112yes—
471C22×C4D4×D1112yes—
472C22×C4C2×C22⋊D1112yes—
473C22×C4C23×D1111yescharacteristic
474SD16—2232no—
475SD16—2232no—
476C2×C8—28no—
477C2×C8—22no—
478C2×C8—22no—
479C2×C8—114no—
480C2×C8—228no—
481C2×C8—222no—
482C2×C8—222no—
483C2×C8C2×C22⋊D1114yescomplemented
484C4⋊C4—22no—
485C4⋊C4—22no—
486C4⋊C4—42no—
487C42—224no—
488C42—222no—
489C42—222no—
490C11C2×#201411yescharacteristic, complemented, Sylow
491C23—24no—
492C23—42no—
493C23—44no—
494C23—44no—
495C23—42no—
496C23—48no—
497C23—416no—
498C23—84no—
499C23—84no—
500C23—88no—
501C23—224no—
502C23—442no—
503C23—444no—
504C23—444no—
505C23—442no—
506C23—448no—
507C23—4416no—
508C23—884no—
509C23—884no—
510C23—888no—
511C23#6693512yes—
512C23#6693712yes—
513C23#6696414yes—
514C23SD16×D1114yes—
515C23#6699312yes—
516C23C2×D4×D1111yescharacteristic
517Q8—224no—
518Q8—224no—
519Q8—442no—
520Q8—442no—
521Q8—448no—
522D4—24no—
523D4—24no—
524D4—42no—
525D4—42no—
526D4—48no—
527D4—224no—
528D4—224no—
529D4—4464no—
530D4—442no—
531D4—442no—
532D4—448no—
533C2×C4—44no—
534C2×C4—42no—
535C2×C4—84no—
536C2×C4—118no—
537C2×C4—224no—
538C2×C4—224no—
539C2×C4—2216no—
540C2×C4—224no—
541C2×C4—442no—
542C2×C4—442no—
543C2×C4—448no—
544C2×C4#6693514yes—
545C2×C4#6693512yes—
546C2×C4#6693714yes—
547C2×C4#6693712yes—
548C2×C4#6698314yes—
549C2×C4#6699014yes—
550C2×C4#6699312yes—
551C2×C4C22×D4411yescharacteristic
552C2×C4C2×#433911yescharacteristic
553C2×C4C2×D4×D1111yescharacteristic
554C2×C4C2×D4×D1111yescharacteristic
555C2×C4C2×D4×D1111yescharacteristic
556C2×C4C22×C22⋊D1111yescharacteristic
557C8—24no—
558C8—224no—
559C22—48no—
560C22—44no—
561C22—82no—
562C22—84no—
563C22—816no—
564C22—82no—
565C22—448no—
566C22—444no—
567C22—882no—
568C22—884no—
569C22—8816no—
570C22—882no—
571C22#1062237518yes—
572C22#1062238918yes—
573C22#1062257314yes—
574C22#1062276714yes—
575C22#1062278814yes—
576C22C2×#6693511yescharacteristic
577C22C2×#6693711yescharacteristic
578C22C2×#6696412yes—
579C22C2×SD16×D1112yes—
580C22C2×#6699311yescharacteristic
581C4—82no—
582C4—228no—
583C4—444no—
584C4#1062257314yes—
585C4C2×#6693511yescharacteristic
586C4C2×#6693711yescharacteristic
587C4C2×#6698311yescharacteristic
588C4C2×#6699011yescharacteristic
589C2—84no—
590C2—884no—
591C2#1306970518yesdirect product factor
592C2C2×#1062257311yescharacteristic
593C2C2×#1062238912yes—
594C2C2×#1062237512yes—
595C2C2×#1062278811yescharacteristic
596C2C2×#1062276711yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC24×C11C2×D4
prime radicalC22×#66993C2
hypercenterC22×#102D11
hypocenterC11C2×#2014
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×#102

Complements

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

NH ≅ G/Ntype
1. C23×#4314C2semidirect
2. C23×#4324C2semidirect
4. C22×#66873C2semidirect
5. C2×#10622587C2semidirect
6. #13069705C2direct (N × H)
7. C2×#10622188C2semidirect
8. C22×C11×#102C2semidirect
22. C22×#4324C22semidirect
28. C22×#4314C22semidirect
30. C2×C11×#102C22semidirect
33. #10622587C22semidirect
35. C2×#66873C22semidirect
36. #10622188C22semidirect
69. C22×Dic22D4semidirect
73. C22×C8×C11D4semidirect
92. C22×C11⋊C8D4semidirect
149. C22×Dic11SD16semidirect
176. C2×Dic22C2×D4semidirect
180. C2×C8×C11C2×D4semidirect
191. C2×C11⋊C8C2×D4semidirect
197. C22×#102D11semidirect
256. C2×Dic11C2×SD16semidirect
292. C2×#102C2×D11semidirect
375. C22×C8C22⋊D11semidirect
392. C2×C11#2014semidirect
483. C2×C8C2×C22⋊D11semidirect
490. C11C2×#2014semidirect
591. C2#13069705direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43142
C23×#43242
C22×#669932
C22×#668732
C2×#106225872
#130697052
C2×#106221882
C22×C11×#1022
C2×#201411