Finite Group Databasebeta

← C2×#13069914 #14781647

Subgroups — C2×#13069914 #14781647

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×#67004C211yesmaximal, characteristic
2C22×#66883C211yesmaximal, characteristic, complemented
3C2×#10622845C211yesmaximal, characteristic
4C22×#66880C211yesmaximal, characteristic, complemented
5C22×#66888C211yesmaximal, characteristic, complemented
6#13069914C218yesmaximal, direct product factor
7C2×#10622192C211yesmaximal, characteristic, complemented
8C2×C11×#408C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C23×Dic22C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C23×C8×C11C2211yescharacteristic
13C2×#67004—22no—
14C2×#67004—24no—
15C2×#67004—24no—
16C2×#67004C2214yes—
17C22×#4326—21no—
18C22×#4324—21no—
19C22×C4⋊Dic11C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C11×#408—22no—
23C11×#408C2214yes—
24C2×C11×C22⋊C8—22no—
25#10622845—22no—
26#10622845C2214yes—
27C2×#66899—21no—
28C2×#66896—21no—
29C2×#66888—24no—
30C2×#66888C2214yescomplemented
31C2×#66883—24no—
32C2×#66883C2214yescomplemented
33C2×#66880—22no—
34C2×#66880—22no—
35C2×#66880C2214yescomplemented
36#10622192C2214yescomplemented
37C2×C11×#41—21no—
38C2×C11×#41—21no—
39C2×C11×#41—22no—
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—22no—
43C2×C11×#41D412yes—
44C2×C11×#41C2312yes—
45C22×Q8×C11D411yescharacteristic
46C22×D4×C11—21no—
47C22×D4×C11D411yescharacteristic
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
50C23×Dic11—21no—
51C23×Dic11—21no—
52C22×Dic22—21no—
53C22×Dic22—21no—
54C22×Dic22—22no—
55C22×Dic22—21no—
56C22×Dic22—21no—
57C22×Dic22—22no—
58C22×Dic22—21no—
59C22×Dic22—22no—
60C22×Dic22D414yes—
61C22×Dic22C2312yes—
62C2×C11×M16—21no—
63C2×C11×M16—22no—
64C2×C11×M16—22no—
65C2×C11×M16C2312yes—
66C22×C8×C11—22no—
67C22×C8×C11—22no—
68C22×C8×C11—21no—
69C22×C8×C11D412yes—
70C22×C8×C11D412yes—
71C22×C8×C11C2312yes—
72#67004—216no—
73#67004—28no—
74#67004—28no—
75C2×#4326—28no—
76C2×#4326—24no—
77C2×#4324—28no—
78C2×#4324—24no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11—21no—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—21no—
84C2×C4⋊Dic11C2312yes—
85C2×#4318—21no—
86C2×#4318—22no—
87C2×#4318—21no—
88C2×#4318—22no—
89C2×#4318—22no—
90C2×#4318D414yes—
91C2×#4318C2312yes—
92C2×#4318C2312yes—
93C22×C11⋊C8—21no—
94C22×C11⋊C8—21no—
95C11×C22⋊C8—28no—
96#66899—24no—
97#66896—24no—
98#66888—28no—
99#66883—28no—
100#66880—28no—
101C2×#2052—111nomaximal, Sylow
102C24×C11—21no—
103C24×C11#4111yescharacteristic
104C11×#41—24no—
105C11×#41—24no—
106C11×#41—22no—
107C11×#41—22no—
108C11×#41—22no—
109C11×#41—22no—
110C11×#41—42no—
111C11×#41—42no—
112C11×#41—42no—
113C11×#41—42no—
114C2×Q8×C11—21no—
115C2×Q8×C11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11C2×D412yes—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11—22no—
121C2×D4×C11—21no—
122C2×D4×C11—22no—
123C2×D4×C11—42no—
124C2×D4×C11—42no—
125C2×D4×C11C2×D412yes—
126C22×C4×C11—21no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—42no—
130C22×C4×C11—42no—
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D412yes—
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2×D411yescharacteristic
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11#4112yes—
138C22×C4×C11#4111yescharacteristic
139C22×C4×C11#4112yes—
140C22×C4×C11C2411yescharacteristic
141C22×Dic11—24no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—41no—
145C22×Dic11—41no—
146C22×Dic11—41no—
147C22×Dic11—41no—
148C22×Dic11—42no—
149C22×Dic11—82no—
150C2×Dic22—24no—
151C2×Dic22—24no—
152C2×Dic22—24no—
153C2×Dic22—24no—
154C2×Dic22—24no—
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—22no—
158C2×Dic22—22no—
159C2×Dic22—22no—
160C2×Dic22—41no—
161C2×Dic22—41no—
162C2×Dic22—42no—
163C2×Dic22—42no—
164C2×Dic22—42no—
165C2×Dic22—42no—
166C2×Dic22—42no—
167C2×Dic22C2×D414yes—
168C11×M16—22no—
169C11×M16—22no—
170C11×M16—42no—
171C2×C8×C11—24no—
172C2×C8×C11—24no—
173C2×C8×C11—22no—
174C2×C8×C11—22no—
175C2×C8×C11—22no—
176C2×C8×C11—42no—
177C2×C8×C11C2×D414yes—
178#4326—216no—
179#4324—216no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11—41no—
183C4⋊Dic11—41no—
184#4318—24no—
185#4318—22no—
186#4318—22no—
187#4318—22no—
188#4318—42no—
189#4318C2×D414yes—
190C2×C11⋊C8—24no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—22no—
193C2×C11⋊C8—42no—
194C22×#137—111no—
195C22×#108—111no—
196C2×#417—111no—
197C22×#103—111no—
198C22×#101—111no—
199C2×#408D1111yescharacteristic
200#2052—118no—
201C2×#343—111no—
202C23×C11—22no—
203C23×C11—22no—
204C23×C11—22no—
205C23×C11—42no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11#12111yescharacteristic
209C23×C11#12111yescharacteristic
210C23×C11#12312yes—
211C23×C11#12412yes—
212C23×C11C2×#4111yescharacteristic
213Q8×C11—22no—
214Q8×C11—22no—
215Q8×C11—42no—
216D4×C11—22no—
217D4×C11—22no—
218D4×C11—42no—
219D4×C11—42no—
220D4×C11—44no—
221D4×C11—42no—
222C2×C4×C11—22no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—42no—
226C2×C4×C11—44no—
227C2×C4×C11#12012yes—
228C2×C4×C11#12012yes—
229C2×C4×C11#12111yescharacteristic
230C2×C4×C11#12111yescharacteristic
231C2×C4×C11#12112yes—
232C2×C4×C11#12112yes—
233C2×C4×C11#12112yes—
234C2×C4×C11#12112yes—
235C2×C4×C11#12312yes—
236C2×C4×C11#12312yes—
237C2×C4×C11#12312yes—
238C2×C4×C11#12412yes—
239C2×C4×C11C22×D411yescharacteristic
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C2×#4111yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×Dic11—24no—
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—44no—
249C2×Dic11—44no—
250C2×Dic11—42no—
251C2×Dic11—82no—
252C2×Dic11—82no—
253C2×Dic11—82no—
254Dic22—24no—
255Dic22—24no—
256Dic22—42no—
257Dic22—42no—
258Dic22—44no—
259Dic22—44no—
260C8×C11—24no—
261C8×C11—42no—
262C11⋊C8—24no—
263C11⋊C8—42no—
264C22×#41C2×D1111yescharacteristic
265C23×Q8—111no—
266C2×#137—114no—
267C2×#137—224no—
268C2×#137—224no—
269C2×#137—222no—
270C22×Q16—221no—
271C22×SD16—221no—
272C22×M16—111no—
273C22×M16—111no—
274C22×M16C2×D1111yescharacteristic
275C23×C8C2×D1111yescharacteristic
276C22×C4⋊C4—111no—
277C2×#108—114no—
278C2×#108—224no—
279#417—114no—
280#417—222no—
281C2×#103—114no—
282C2×#103—221no—
283C2×#103—222no—
284C2×#103—222no—
285C2×#102—221no—
286C2×#101—114no—
287C2×#101—224no—
288#408—22no—
289#408C2×D1114yes—
290C2×C22⋊C8—22no—
291#343—114no—
292C22×C11—24no—
293C22×C11—24no—
294C22×C11—21no—
295C22×C11—21no—
296C22×C11—21no—
297C22×C11—21no—
298C22×C11—42no—
299C22×C11—42no—
300C22×C11—42no—
301C22×C11—84no—
302C22×C11#39412yes—
303C22×C11#39412yes—
304C22×C11#47112yes—
305C22×C11#47312yes—
306C22×C11C2×#12111yescharacteristic
307C22×C11C2×#12311yescharacteristic
308C22×C11C2×#12411yescharacteristic
309C4×C11—42no—
310C4×C11#39412yes—
311C4×C11#39412yes—
312C4×C11C2×#12011yescharacteristic
313C4×C11C2×#12111yescharacteristic
314C4×C11C2×#12111yescharacteristic
315C4×C11C2×#12311yescharacteristic
316Dic11—44no—
317Dic11—82no—
318C2×#41—21no—
319C2×#41—21no—
320C2×#41—22no—
321C2×#41—22no—
322C2×#41—22no—
323C2×#41—22no—
324C2×#41D4412yes—
325C2×#41C22×D1112yes—
326C22×Q8—114no—
327C22×Q8—112no—
328C22×Q8—221no—
329C22×Q8—222no—
330C22×Q8—221no—
331C22×Q8—221no—
332C22×Q8—222no—
333C22×Q8—222no—
334C22×Q8—221no—
335C22×Q8—221no—
336C22×Q8D4411yescharacteristic
337C22×D4—21no—
338C22×D4D4411yescharacteristic
339C23×C4—21no—
340C23×C4—221no—
341C23×C4—221no—
342C23×C4C22×D1111yescharacteristic
343#137—228no—
344#137—228no—
345#137—2216no—
346C2×Q16—228no—
347C2×Q16—224no—
348C2×SD16—228no—
349C2×SD16—224no—
350C2×M16—21no—
351C2×M16—22no—
352C2×M16—22no—
353C2×M16—114no—
354C2×M16—112no—
355C2×M16—112no—
356C2×M16—221no—
357C2×M16—222no—
358C2×M16—221no—
359C2×M16—222no—
360C2×M16—222no—
361C2×M16C22×D1112yes—
362C22×C8—22no—
363C22×C8—22no—
364C22×C8—21no—
365C22×C8—221no—
366C22×C8—221no—
367C22×C8C22⋊D1112yes—
368C22×C8C22⋊D1112yes—
369C22×C8C22×D1112yes—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—221no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376#108—228no—
377#103—224no—
378#103—228no—
379#102—224no—
380#101—228no—
381C22⋊C8—28no—
382C2×C11—21no—
383C2×C11—21no—
384C2×C11—22no—
385C2×C11—82no—
386C2×C11#205214yescomplemented
387C2×C11C2×#39411yescharacteristic
388C2×C11C2×#47111yescharacteristic
389C2×C11C2×#47311yescharacteristic
390C24—21no—
391C24#433911yescharacteristic
392#41—24no—
393#41—24no—
394#41—22no—
395#41—22no—
396#41—22no—
397#41—22no—
398#41—42no—
399#41—42no—
400#41—42no—
401#41—42no—
402C2×Q8—21no—
403C2×Q8—22no—
404C2×Q8—22no—
405C2×Q8—114no—
406C2×Q8—224no—
407C2×Q8—222no—
408C2×Q8—224no—
409C2×Q8—224no—
410C2×Q8—224no—
411C2×Q8—224no—
412C2×Q8—222no—
413C2×Q8—222no—
414C2×Q8—222no—
415C2×Q8—222no—
416C2×Q8—442no—
417C2×Q8—442no—
418C2×Q8—442no—
419C2×Q8—441no—
420C2×Q8—441no—
421C2×Q8—442no—
422C2×Q8—442no—
423C2×Q8C2×D4412yes—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—42no—
430C2×D4—42no—
431C2×D4C2×D4412yes—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—42no—
436C22×C4—42no—
437C22×C4—224no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—442no—
441C22×C4—441no—
442C22×C4—441no—
443C22×C4—441no—
444C22×C4—441no—
445C22×C4—882no—
446C22×C4C2×D4411yescharacteristic
447C22×C4C2×D4411yescharacteristic
448C22×C4#433911yescharacteristic
449C22×C4D4×D1112yes—
450C22×C4D4×D1112yes—
451C22×C4#434112yes—
452C22×C4#434112yes—
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C23×D1111yescharacteristic
456Q16—2216no—
457SD16—2216no—
458M16—22no—
459M16—22no—
460M16—42no—
461M16—114no—
462M16—224no—
463M16—222no—
464M16—222no—
465M16—222no—
466M16—442no—
467C2×C8—24no—
468C2×C8—24no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—42no—
473C2×C8—224no—
474C2×C8—222no—
475C2×C8—222no—
476C2×C8—442no—
477C2×C8C2×C22⋊D1114yes—
478C4⋊C4—222no—
479C4⋊C4—222no—
480C4⋊C4—441no—
481C4⋊C4—441no—
482C11C2×#205211yescharacteristic, complemented, Sylow
483C23—22no—
484C23—22no—
485C23—22no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23#6693612yes—
490C23#6693812yes—
491C23#6698311yescharacteristic
492C23#6698311yescharacteristic
493C23C2×#433911yescharacteristic
494Q8—22no—
495Q8—22no—
496Q8—42no—
497Q8—224no—
498Q8—224no—
499Q8—442no—
500Q8—442no—
501Q8—444no—
502Q8—444no—
503D4—22no—
504D4—22no—
505D4—42no—
506D4—42no—
507D4—44no—
508D4—42no—
509C2×C4—22no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—44no—
514C2×C4—224no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—444no—
518C2×C4—444no—
519C2×C4—442no—
520C2×C4—882no—
521C2×C4—882no—
522C2×C4—882no—
523C2×C4#6693512yes—
524C2×C4#6693512yes—
525C2×C4#6693612yes—
526C2×C4#6693812yes—
527C2×C4#6693912yes—
528C2×C4#6693912yes—
529C2×C4#6698311yescharacteristic
530C2×C4#6698311yescharacteristic
531C2×C4#6699112yes—
532C2×C4#6699112yes—
533C2×C4#6699212yes—
534C2×C4#6699212yes—
535C2×C4C22×D4411yescharacteristic
536C2×C4C2×D4×D1111yescharacteristic
537C2×C4C2×D4×D1111yescharacteristic
538C2×C4C2×#434111yescharacteristic
539C2×C4C2×#434111yescharacteristic
540C2×C4C22×C22⋊D1111yescharacteristic
541C8—24no—
542C8—42no—
543C8—224no—
544C8—442no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—24no—
550C22—24no—
551C22—42no—
552C22—42no—
553C22—42no—
554C22—84no—
555C22#1062257412yes—
556C22#1062257412yes—
557C22#1062275412yes—
558C22#1062275612yes—
559C22C2×#6693611yescharacteristic
560C22C2×#6693811yescharacteristic
561C22C2×#6698311yescharacteristic
562C4—42no—
563C4—444no—
564C4—882no—
565C4#1062257412yes—
566C4#1062257412yes—
567C4C2×#6693511yescharacteristic
568C4C2×#6693911yescharacteristic
569C4C2×#6699111yescharacteristic
570C4C2×#6699211yescharacteristic
571C2—21no—
572C2—21no—
573C2—22no—
574C2—82no—
575C2#1306991414yesdirect product factor
576C2C2×#1062257411yescharacteristic
577C2C2×#1062275411yescharacteristic
578C2C2×#1062275611yescharacteristic
subgroupG/H
centerC23#66983
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#408C2
socleC23×C11#121
prime radicalC22×C11×#41C22
hypercenterC2×#408D11
hypocenterC11C2×#2052
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#408

Complements

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

NH ≅ G/Ntype
2. C22×#66883C2semidirect
4. C22×#66880C2semidirect
5. C22×#66888C2semidirect
6. #13069914C2direct (N × H)
7. C2×#10622192C2semidirect
30. C2×#66888C22semidirect
32. C2×#66883C22semidirect
35. C2×#66880C22semidirect
36. #10622192C22semidirect
386. C2×C11#2052semidirect
482. C11C2×#2052semidirect
575. C2#13069914direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#670042
C22×#668832
C2×#106228452
C22×#668802
C22×#668882
#130699142
C2×#106221922
C2×C11×#4082
C2×#205211