Finite Group Databasebeta

← C2×#13069916 #14781649

Subgroups — C2×#13069916 #14781649

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×#66995C211yesmaximal, characteristic
2C22×#66883C211yesmaximal, characteristic, complemented
3C2×#10622579C211yesmaximal, characteristic
4C22×#66900C211yesmaximal, characteristic, complemented
5C2×#10622723C211yesmaximal, characteristic
6#13069916C218yesmaximal, direct product factor
7C2×#10622168C211yesmaximal, characteristic, complemented
8C22×C11×#103C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C22×#4339C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×#4326—21no—
14C2×#66995—24no—
15C2×#66995—22no—
16C2×#66995—24no—
17C2×#66995C2214yes—
18C22×#4325—21no—
19C22×#4318C2211yescharacteristic
20C22×#4318C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C2×C11×#103—22no—
23C2×C11×#103—22no—
24C2×C11×#103C2214yescomplemented
25C2×#66900—24no—
26C2×#66900C2214yescomplemented
27#10622723—22no—
28#10622723C2214yes—
29C2×(C2×D11)⋊C8—22no—
30C2×#66883—24no—
31C2×#66883C2214yescomplemented
32C2×#66874—21no—
33#10622579—22no—
34#10622579C2214yes—
35C2×#66873—21no—
36#10622168C2214yescomplemented
37C22×Q8×C11—22no—
38C22×Q8×C11—21no—
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C22×Q8×C11—22no—
42C22×Q8×C11—21no—
43C22×Q8×C11—21no—
44C22×Q8×C11—22no—
45C22×Q8×C11D414yes—
46C22×Q8×C11C2312yes—
47C23×C4×C11—21no—
48C23×C4×C11—21no—
49C23×C4×C11C2311yescharacteristic
50C22×C22⋊D11—21no—
51C2×#4339—21no—
52C2×#4339—21no—
53C2×#4339—22no—
54C2×#4339—22no—
55C2×#4339—22no—
56C2×#4339—22no—
57C2×#4339D412yes—
58C2×#4339C2312yes—
59C22×D44D411yescharacteristic
60C22×C4×D11—21no—
61C22×Dic22D411yescharacteristic
62C22×C8×C11—22no—
63C22×C8×C11—22no—
64C22×C8×C11D412yes—
65C22×C8×C11D412yes—
66C22×C8×C11C2312yes—
67C2×C11×C4⋊C4—21no—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2312yes—
73C2×#4326—28no—
74C2×#4326—24no—
75#66995—216no—
76#66995—28no—
77#66995—28no—
78C2×#4325—28no—
79C2×#4325—24no—
80C2×#4318—22no—
81C2×#4318—21no—
82C2×#4318—21no—
83C2×#4318—21no—
84C2×#4318—22no—
85C2×#4318—22no—
86C2×#4318—22no—
87C2×#4318—22no—
88C2×#4318D414yes—
89C2×#4318C2312yes—
90C2×#4318C2312yes—
91C2×#4318C2312yes—
92C22×C11⋊C8—21no—
93C22×C11⋊C8—21no—
94C22×C11⋊C8—21no—
95C11×#103—28no—
96#66900—28no—
97(C2×D11)⋊C8—28no—
98#66883—28no—
99#66874—24no—
100#66873—24no—
101C2×#2052—111nomaximal, Sylow
102C24×C11#4111yescharacteristic
103C23×D11—21no—
104C2×Q8×C11—24no—
105C2×Q8×C11—22no—
106C2×Q8×C11—24no—
107C2×Q8×C11—24no—
108C2×Q8×C11—24no—
109C2×Q8×C11—24no—
110C2×Q8×C11—22no—
111C2×Q8×C11—22no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—41no—
115C2×Q8×C11—41no—
116C2×Q8×C11—42no—
117C2×Q8×C11—42no—
118C2×Q8×C11—42no—
119C2×Q8×C11—42no—
120C2×Q8×C11—42no—
121C2×Q8×C11C2×D414yes—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—41no—
126C22×C4×C11—41no—
127C22×C4×C11—42no—
128C22×C4×C11—41no—
129C22×C4×C11—41no—
130C22×C4×C11—82no—
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
141C2×C22⋊D11—22no—
142C2×C22⋊D11—22no—
143C2×C22⋊D11—42no—
144C2×C22⋊D11—42no—
145C22×Dic11—21no—
146#4339—24no—
147#4339—24no—
148#4339—22no—
149#4339—22no—
150#4339—22no—
151#4339—22no—
152#4339—42no—
153#4339—42no—
154#4339—42no—
155#4339—42no—
156C2×D44—22no—
157C2×D44—21no—
158C2×D44—22no—
159C2×D44C2×D412yes—
160C2×C4×D11—22no—
161C2×C4×D11—22no—
162C2×C4×D11—42no—
163C2×C4×D11—42no—
164C2×Dic22—22no—
165C2×Dic22—21no—
166C2×Dic22—22no—
167C2×Dic22C2×D412yes—
168C2×C8×C11—24no—
169C2×C8×C11—24no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11C2×D414yes—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—22no—
175C11×C4⋊C4—41no—
176C11×C4⋊C4—41no—
177#4326—216no—
178#4325—216no—
179#4318—24no—
180#4318—22no—
181#4318—22no—
182#4318—22no—
183#4318—22no—
184#4318—22no—
185#4318—42no—
186#4318—42no—
187#4318C2×D414yes—
188C2×C11⋊C8—24no—
189C2×C11⋊C8—22no—
190C2×C11⋊C8—22no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—42no—
193C2×C11⋊C8—42no—
194C22×#137—111no—
195C22×#108—111no—
196C2×#417—111no—
197C22×#103D1111yescharacteristic, complemented
198C22×#101—111no—
199C2×#408—111no—
200#2052—118no—
201C2×#343—111no—
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—
213Q8×C11—24no—
214Q8×C11—24no—
215Q8×C11—42no—
216Q8×C11—42no—
217Q8×C11—44no—
218Q8×C11—44no—
219C2×C4×C11—24no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—44no—
223C2×C4×C11—44no—
224C2×C4×C11—42no—
225C2×C4×C11—82no—
226C2×C4×C11—82no—
227C2×C4×C11—82no—
228C2×C4×C11#12012yes—
229C2×C4×C11#12012yes—
230C2×C4×C11#12112yes—
231C2×C4×C11#12112yes—
232C2×C4×C11#12111yescharacteristic
233C2×C4×C11#12111yescharacteristic
234C2×C4×C11#12112yes—
235C2×C4×C11#12112yes—
236C2×C4×C11#12312yes—
237C2×C4×C11#12312yes—
238C2×C4×C11#12312yes—
239C2×C4×C11#12412yes—
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C22⋊D11—42no—
247C22⋊D11—42no—
248C22⋊D11—44no—
249C2×Dic11—22no—
250C2×Dic11—42no—
251D44—22no—
252D44—22no—
253D44—42no—
254C4×D11—42no—
255C4×D11—42no—
256C4×D11—44no—
257Dic22—22no—
258Dic22—22no—
259Dic22—42no—
260C8×C11—24no—
261C11⋊C8—24no—
262C11⋊C8—42no—
263C11⋊C8—42no—
264C22×#41—111no—
265C23×Q8C2×D1111yescharacteristic
266C2×#137—114no—
267C2×#137—224no—
268C2×#137—222no—
269C2×#137—224no—
270C22×Q16—221no—
271C22×SD16—221no—
272C22×M16—111no—
273C22×M16—111no—
274C22×M16—111no—
275C23×C8C2×D1111yescharacteristic
276C22×C4⋊C4C2×D1111yescharacteristic
277C2×#108—114no—
278C2×#108—224no—
279#417—114no—
280#417—222no—
281C2×#103—22no—
282C2×#103—22no—
283C2×#103—221no—
284C2×#103C2×D1114yescomplemented
285C2×#102—221no—
286C2×#101—114no—
287C2×#101—224no—
288#408—114no—
289#408—222no—
290C2×C22⋊C8—222no—
291#343—114no—
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—44no—
310C4×C11—82no—
311C4×C11#39412yes—
312C4×C11#39412yes—
313C4×C11C2×#12011yescharacteristic
314C4×C11C2×#12111yescharacteristic
315C4×C11C2×#12111yescharacteristic
316C4×C11C2×#12311yescharacteristic
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—22no—
327C22×Q8—21no—
328C22×Q8—22no—
329C22×Q8—21no—
330C22×Q8—22no—
331C22×Q8—21no—
332C22×Q8—21no—
333C22×Q8—21no—
334C22×Q8—111no—
335C22×Q8D4414yes—
336C22×Q8C22×D1112yes—
337C22×D4—111no—
338C22×D4—221no—
339C23×C4—21no—
340C23×C4—21no—
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—114no—
351C2×M16—112no—
352C2×M16—112no—
353C2×M16—112no—
354C2×M16—222no—
355C2×M16—221no—
356C2×M16—221no—
357C2×M16—221no—
358C2×M16—222no—
359C2×M16—222no—
360C2×M16—222no—
361C2×M16—222no—
362C22×C8—22no—
363C22×C8—22no—
364C22×C8—221no—
365C22×C8—221no—
366C22×C8—221no—
367C22×C8C22⋊D1112yes—
368C22×C8C22⋊D1112yes—
369C22×C8C22×D1112yes—
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—28no—
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#434111yescharacteristic
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—24no—
403C2×Q8—22no—
404C2×Q8—24no—
405C2×Q8—24no—
406C2×Q8—24no—
407C2×Q8—24no—
408C2×Q8—22no—
409C2×Q8—22no—
410C2×Q8—22no—
411C2×Q8—22no—
412C2×Q8—42no—
413C2×Q8—42no—
414C2×Q8—42no—
415C2×Q8—41no—
416C2×Q8—41no—
417C2×Q8—42no—
418C2×Q8—42no—
419C2×Q8—112no—
420C2×Q8—221no—
421C2×Q8—222no—
422C2×Q8—222no—
423C2×Q8C2×D4414yes—
424C2×D4—112no—
425C2×D4—222no—
426C2×D4—222no—
427C2×D4—222no—
428C2×D4—222no—
429C2×D4—221no—
430C2×D4—442no—
431C2×D4—442no—
432C22×C4—24no—
433C22×C4—22no—
434C22×C4—22no—
435C22×C4—42no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—82no—
441C22×C4—221no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—442no—
445C22×C4—442no—
446C22×C4C2×D4412yes—
447C22×C4#433912yes—
448C22×C4D4×D1111yescharacteristic
449C22×C4D4×D1111yescharacteristic
450C22×C4D4×D1112yes—
451C22×C4#434112yes—
452C22×C4#434111yescharacteristic
453C22×C4C2×C22⋊D1111yescharacteristic
454C22×C4C2×C22⋊D1111yescharacteristic
455C22×C4C23×D1111yescharacteristic
456Q16—2216no—
457SD16—2216no—
458M16—114no—
459M16—224no—
460M16—222no—
461M16—222no—
462M16—222no—
463M16—222no—
464M16—222no—
465M16—442no—
466M16—442no—
467C2×C8—24no—
468C2×C8—24no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—224no—
472C2×C8—222no—
473C2×C8—222no—
474C2×C8—222no—
475C2×C8—442no—
476C2×C8—442no—
477C2×C8C2×C22⋊D1114yes—
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#6693812yes—
490C23#6693912yes—
491C23#6699111yescharacteristic
492C23#6699111yescharacteristic
493C23C2×#434111yescharacteristic
494Q8—24no—
495Q8—24no—
496Q8—42no—
497Q8—42no—
498Q8—44no—
499Q8—44no—
500Q8—222no—
501Q8—222no—
502Q8—442no—
503D4—222no—
504D4—222no—
505D4—442no—
506D4—442no—
507D4—444no—
508D4—442no—
509C2×C4—24no—
510C2×C4—42no—
511C2×C4—42no—
512C2×C4—44no—
513C2×C4—44no—
514C2×C4—42no—
515C2×C4—82no—
516C2×C4—82no—
517C2×C4—82no—
518C2×C4—222no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—442no—
522C2×C4—444no—
523C2×C4#6693512yes—
524C2×C4#6693512yes—
525C2×C4#6693612yes—
526C2×C4#6693612yes—
527C2×C4#6693812yes—
528C2×C4#6693912yes—
529C2×C4#6698312yes—
530C2×C4#6698312yes—
531C2×C4#6699111yescharacteristic
532C2×C4#6699111yescharacteristic
533C2×C4#6699212yes—
534C2×C4#6699212yes—
535C2×C4C22×D4411yescharacteristic
536C2×C4C2×#433911yescharacteristic
537C2×C4C2×D4×D1111yescharacteristic
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4C2×#434111yescharacteristic
540C2×C4C22×C22⋊D1111yescharacteristic
541C8—24no—
542C8—224no—
543C8—442no—
544C8—442no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—24no—
550C22—24no—
551C22—442no—
552C22—442no—
553C22—442no—
554C22—884no—
555C22#1062257412yes—
556C22#1062257412yes—
557C22#1062279012yes—
558C22#1062280512yes—
559C22C2×#6693811yescharacteristic
560C22C2×#6693911yescharacteristic
561C22C2×#6699111yescharacteristic
562C4—44no—
563C4—82no—
564C4—442no—
565C4#1062257412yes—
566C4#1062257412yes—
567C4C2×#6693511yescharacteristic
568C4C2×#6693611yescharacteristic
569C4C2×#6698311yescharacteristic
570C4C2×#6699211yescharacteristic
571C2—21no—
572C2—21no—
573C2—22no—
574C2—882no—
575C2#1306991614yesdirect product factor
576C2C2×#1062257411yescharacteristic
577C2C2×#1062279011yescharacteristic
578C2C2×#1062280511yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#103C2
socleC23×C11#121
prime radicalC22×#4339C22
hypercenterC22×#103D11
hypocenterC11C2×#2052
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
2. C22×#66883C2semidirect
4. C22×#66900C2semidirect
6. #13069916C2direct (N × H)
7. C2×#10622168C2semidirect
8. C22×C11×#103C2semidirect
24. C2×C11×#103C22semidirect
26. C2×#66900C22semidirect
31. C2×#66883C22semidirect
36. #10622168C22semidirect
197. C22×#103D11semidirect
284. C2×#103C2×D11semidirect
385. C2×C11#2052semidirect
482. C11C2×#2052semidirect
575. C2#13069916direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669952
C22×#668832
C2×#106225792
C22×#669002
C2×#106227232
#130699162
C2×#106221682
C22×C11×#1032
C2×#205211