Finite Group Databasebeta

← C2×#13069775 #14781137

Subgroups — C2×#13069775 #14781137

Order 2816.

1238 conjugacy classes of subgroups.

The subgroup lattice has 562 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623050C211yesmaximal, characteristic
2C2×#10622838C211yesmaximal, characteristic
3C2×#10622843C211yesmaximal, characteristic
4#13069775C218yesmaximal, direct product factor
5C2×#10622192C211yesmaximal, characteristic
6C2×#10622193C211yesmaximal, characteristic
7C2×#10622170C211yesmaximal, characteristic
8C2×C11×#419C211yesmaximal, characteristic
9C23×Q8×C11C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C2×#66979C2211yescharacteristic
13C22×C4⋊Dic11C2211yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16#10623050—22no—
17#10623050—22no—
18#10623050—22no—
19#10623050C2214yes—
20C2×#66943—21no—
21C2×#66941—21no—
22C2×#66931—22no—
23C2×#66923—21no—
24C2×#66922—21no—
25C11×#419—22no—
26C11×#419C2214yes—
27C2×C11×#103—21no—
28C2×C11×#103—21no—
29#10622843—22no—
30#10622843C2214yes—
31#10622838—22no—
32#10622838C2214yes—
33C2×#66899—21no—
34C2×#66899—21no—
35C2×C11⋊#95—22no—
36#10622193C2214yes—
37#10622192C2214yes—
38#10622170C2214yes—
39C22×Q8×C11—21no—
40C22×Q8×C11—22no—
41C22×Q8×C11—21no—
42C22×Q8×C11—21no—
43C22×Q8×C11—21no—
44C22×Q8×C11—21no—
45C22×Q8×C11—22no—
46C22×Q8×C11—22no—
47C22×Q8×C11Q814yescomplemented
48C22×Q8×C11C2312yes—
49C23×C4×C11—21no—
50C23×C4×C11C2311yescharacteristic
51C23×Dic11—21no—
52C23×Dic11D412yes—
53C22×Dic22—22no—
54C2×C11×M16—21no—
55C2×C11×M16—22no—
56C2×C11×M16—22no—
57C2×C11×M16C2312yes—
58C22×C8×C11—21no—
59C11×#117—21no—
60C11×#117—21no—
61C11×#117D412yes—
62C11×#117C2312yes—
63C2×C11×C4⋊C4D411yescharacteristic
64C2×C11×C4⋊C4D411yescharacteristic
65C2×C11×C22⋊C4—21no—
66C2×C42×C11—21no—
67C2×C22⋊Dic11—21no—
68#66979—21no—
69#66979—21no—
70#66979D412yes—
71#66979C2312yes—
72C2×C4⋊Dic11—22no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11—21no—
77C2×C4⋊Dic11D412yes—
78C2×C4⋊Dic11D411yescharacteristic
79C2×C4⋊Dic11D411yescharacteristic
80C2×C4⋊Dic11C2312yes—
81C2×Dic11⋊C4—22no—
82C2×Dic11⋊C4—22no—
83C2×C4×Dic11—21no—
84C2×C4×Dic11—22no—
85C2×C4×Dic11—22no—
86C2×C4×Dic11—21no—
87C2×C4×Dic11C2312yes—
88C2×#4318—21no—
89C2×#4318—22no—
90C2×#4318—22no—
91C2×#4318C2312yes—
92C22×C11⋊C8—21no—
93#66943—24no—
94#66943—24no—
95#66941—24no—
96#66941—24no—
97#66931—28no—
98#66931—28no—
99#66923—24no—
100#66923—24no—
101#66922—24no—
102#66922—24no—
103C11×#103—24no—
104C11×#103—24no—
105#66899—24no—
106#66899—24no—
107C11⋊#95—28no—
108C2×#2028—111nomaximal, Sylow
109C24×C11C2×D411yescharacteristic
110C2×Q8×C11—24no—
111C2×Q8×C11—22no—
112C2×Q8×C11—24no—
113C2×Q8×C11—24no—
114C2×Q8×C11—24no—
115C2×Q8×C11—24no—
116C2×Q8×C11—22no—
117C2×Q8×C11—22no—
118C2×Q8×C11—22no—
119C2×Q8×C11—22no—
120C2×Q8×C11—41no—
121C2×Q8×C11—41no—
122C2×Q8×C11—42no—
123C2×Q8×C11—42no—
124C2×Q8×C11—42no—
125C2×Q8×C11—42no—
126C2×Q8×C11—42no—
127C2×Q8×C11C2×Q814yescomplemented
128C22×C4×C11—21no—
129C22×C4×C11—21no—
130C22×C4×C11—24no—
131C22×C4×C11—22no—
132C22×C4×C11—41no—
133C22×C4×C11—41no—
134C22×C4×C11—42no—
135C22×C4×C11C2×D411yescharacteristic
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×Q812yes—
141C22×C4×C11#4112yes—
142C22×C4×C11#4112yes—
143C22×C4×C11#4112yes—
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—24no—
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—42no—
152C22×Dic11—44no—
153C22×Dic11—42no—
154C22×Dic11C2×D414yes—
155C2×Dic22—28no—
156C2×Dic22—84no—
157C11×M16—22no—
158C11×M16—22no—
159C11×M16—42no—
160C2×C8×C11—22no—
161C2×C8×C11—42no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4C2×D412yes—
165C11×C4⋊C4C2×D412yes—
166C11×C22⋊C4—22no—
167C11×C22⋊C4—22no—
168C42×C11—22no—
169C42×C11—22no—
170C22⋊Dic11—22no—
171C22⋊Dic11—22no—
172C4⋊Dic11—28no—
173C4⋊Dic11—21no—
174C4⋊Dic11—22no—
175C4⋊Dic11—21no—
176C4⋊Dic11—22no—
177C4⋊Dic11—22no—
178C4⋊Dic11—22no—
179C4⋊Dic11C2×D412yes—
180C4⋊Dic11C2×D412yes—
181Dic11⋊C4—28no—
182Dic11⋊C4—28no—
183C4×Dic11—22no—
184C4×Dic11—22no—
185C4×Dic11—22no—
186C4×Dic11—22no—
187C4×Dic11—42no—
188#4318—22no—
189#4318—22no—
190#4318—42no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—42no—
193C2×#544—111no—
194C2×#419—111no—
195C2×#419D1111yescharacteristic
196C2×#391—111no—
197#2028—118no—
198C2×#343—111no—
199C2×#339—111no—
200C2×#339—111no—
201C23×C11—22no—
202C23×C11—22no—
203C23×C11#12011yescharacteristic
204C23×C11#12011yescharacteristic
205C23×C11C22⋊Q812yes—
206C23×C11#12412yes—
207C23×C11C22×D411yescharacteristic
208Q8×C11—24no—
209Q8×C11—24no—
210Q8×C11—42no—
211Q8×C11—42no—
212Q8×C11—44no—
213Q8×C11—44no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—42no—
218C2×C4×C11—42no—
219C2×C4×C11—44no—
220C2×C4×C11—44no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11#12011yescharacteristic
224C2×C4×C11#12011yescharacteristic
225C2×C4×C11C22⋊Q812yes—
226C2×C4×C11C22⋊Q812yes—
227C2×C4×C11C22⋊Q812yes—
228C2×C4×C11C22⋊Q812yes—
229C2×C4×C11C22⋊Q812yes—
230C2×C4×C11#12412yes—
231C2×C4×C11#12412yes—
232C2×C4×C11#12412yes—
233C2×C4×C11#12412yes—
234C2×C4×C11#12412yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×Q811yescharacteristic
238C2×C4×C11C2×#4111yescharacteristic
239C2×C4×C11C2×#4111yescharacteristic
240C2×C4×C11C2×#4111yescharacteristic
241C2×Dic11—24no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—42no—
246C2×Dic11—48no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—44no—
250C2×Dic11—42no—
251C2×Dic11—44no—
252C2×Dic11—82no—
253Dic22—88no—
254C8×C11—42no—
255C11⋊C8—42no—
256C23×Q8C2×D1111yescharacteristic
257C22×M16—111no—
258C22×M16C2×D1111yescharacteristic
259#544—114no—
260#544—222no—
261#544—222no—
262#544—222no—
263C2×C4⋊Q8—221no—
264C2×C4⋊Q8—221no—
265C2×#125—221no—
266C2×#125—221no—
267C2×C22⋊Q8—222no—
268C2×#117—111no—
269C2×#117C2×D1111yescharacteristic
270C22×C4⋊C4—111no—
271C22×C42—111no—
272#419—22no—
273#419—114no—
274#419—222no—
275#419C2×D1114yes—
276C2×#103—21no—
277C2×#103—21no—
278C2×#103—221no—
279C2×#103—221no—
280#391—114no—
281#391—222no—
282C2×#95—222no—
283#343—114no—
284#339—114no—
285#339—114no—
286C22×C11—21no—
287C22×C11—21no—
288C22×C11—21no—
289C22×C11—21no—
290C22×C11—24no—
291C22×C11—24no—
292C22×C11#39312yes—
293C22×C11#39312yes—
294C22×C11#45512yes—
295C22×C11#45612yes—
296C22×C11C2×#12011yescharacteristic
297C22×C11C2×C22⋊Q811yescharacteristic
298C22×C11C2×#12411yescharacteristic
299C4×C11—44no—
300C4×C11—42no—
301C4×C11—42no—
302C4×C11#39312yes—
303C4×C11#39312yes—
304C4×C11C2×C22⋊Q811yescharacteristic
305C4×C11C2×C22⋊Q811yescharacteristic
306C4×C11C2×#12411yescharacteristic
307C4×C11C2×#12411yescharacteristic
308Dic11—44no—
309Dic11—42no—
310Dic11—44no—
311Dic11—42no—
312C22×Q8—21no—
313C22×Q8—22no—
314C22×Q8—22no—
315C22×Q8—21no—
316C22×Q8—21no—
317C22×Q8—22no—
318C22×Q8—21no—
319C22×Q8—21no—
320C22×Q8—222no—
321C22×Q8Dic2214yescomplemented
322C22×Q8C22×D1112yes—
323C23×C4—21no—
324C23×C4—112no—
325C23×C4—221no—
326C23×C4C22×D1111yescharacteristic
327C2×M16—21no—
328C2×M16—22no—
329C2×M16—22no—
330C2×M16—112no—
331C2×M16—221no—
332C2×M16—222no—
333C2×M16—222no—
334C2×M16C22×D1112yes—
335C22×C8—21no—
336C22×C8—221no—
337C4⋊Q8—224no—
338C4⋊Q8—224no—
339C4⋊Q8—224no—
340C4⋊Q8—224no—
341#125—224no—
342#125—224no—
343#125—224no—
344#125—224no—
345C22⋊Q8—228no—
346C22⋊Q8—228no—
347#117—21no—
348#117—21no—
349#117—112no—
350#117—112no—
351#117—221no—
352#117—221no—
353#117C22⋊D1112yes—
354#117C22×D1112yes—
355C2×C4⋊C4—111no—
356C2×C4⋊C4—111no—
357C2×C4⋊C4—112no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—221no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—221no—
366C2×C4⋊C4C22⋊D1111yescharacteristic
367C2×C4⋊C4C22⋊D1111yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—221no—
370C2×C42—21no—
371C2×C42—112no—
372C2×C42—221no—
373C2×C42—222no—
374C2×C42—222no—
375C2×C42—221no—
376#103—24no—
377#103—24no—
378#103—224no—
379#103—224no—
380#95—228no—
381C2×C11—21no—
382C2×C11—21no—
383C2×C11—22no—
384C2×C11#202814yescomplemented
385C2×C11C2×#39311yescharacteristic
386C2×C11C2×#45511yescharacteristic
387C2×C11C2×#45611yescharacteristic
388C24D4×D1111yescharacteristic
389C2×Q8—24no—
390C2×Q8—22no—
391C2×Q8—24no—
392C2×Q8—24no—
393C2×Q8—24no—
394C2×Q8—24no—
395C2×Q8—22no—
396C2×Q8—22no—
397C2×Q8—22no—
398C2×Q8—22no—
399C2×Q8—42no—
400C2×Q8—42no—
401C2×Q8—42no—
402C2×Q8—42no—
403C2×Q8—42no—
404C2×Q8—41no—
405C2×Q8—41no—
406C2×Q8—228no—
407C2×Q8—884no—
408C2×Q8C2×Dic2214yescomplemented
409C22×C4—24no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—42no—
414C22×C4—41no—
415C22×C4—41no—
416C22×C4—114no—
417C22×C4—224no—
418C22×C4—221no—
419C22×C4—221no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—442no—
424C22×C4—442no—
425C22×C4—444no—
426C22×C4C2×Dic2212yes—
427C22×C4#433912yes—
428C22×C4D4×D1111yescharacteristic
429C22×C4D4×D1111yescharacteristic
430C22×C4D4×D1111yescharacteristic
431C22×C4#434112yes—
432C22×C4#434112yes—
433C22×C4C2×C22⋊D1111yescharacteristic
434C22×C4C2×C22⋊D1111yescharacteristic
435C22×C4C23×D1111yescharacteristic
436M16—22no—
437M16—22no—
438M16—42no—
439M16—222no—
440M16—222no—
441M16—442no—
442C2×C8—22no—
443C2×C8—42no—
444C2×C8—222no—
445C2×C8—442no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—112no—
449C4⋊C4—112no—
450C4⋊C4—228no—
451C4⋊C4—228no—
452C4⋊C4—228no—
453C4⋊C4—222no—
454C4⋊C4—222no—
455C4⋊C4—221no—
456C4⋊C4—221no—
457C4⋊C4—222no—
458C4⋊C4—222no—
459C4⋊C4C2×C22⋊D1112yes—
460C4⋊C4C2×C22⋊D1112yes—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—222no—
464C22⋊C4—222no—
465C42—22no—
466C42—22no—
467C42—222no—
468C42—222no—
469C42—222no—
470C42—222no—
471C42—442no—
472C11C2×#202811yescharacteristic, complemented, Sylow
473C23—22no—
474C23—22no—
475C23#6693112yes—
476C23#6693812yes—
477C23#6699011yescharacteristic
478C23#6699011yescharacteristic
479C23C2×D4×D1111yescharacteristic
480Q8—24no—
481Q8—24no—
482Q8—42no—
483Q8—44no—
484Q8—44no—
485Q8—42no—
486Q8—888no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—42no—
491C2×C4—42no—
492C2×C4—44no—
493C2×C4—44no—
494C2×C4—42no—
495C2×C4—42no—
496C2×C4—224no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—224no—
500C2×C4—442no—
501C2×C4—448no—
502C2×C4—442no—
503C2×C4—444no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—444no—
507C2×C4—882no—
508C2×C4#6693112yes—
509C2×C4#6693112yes—
510C2×C4#6693112yes—
511C2×C4#6693812yes—
512C2×C4#6693812yes—
513C2×C4#6693812yes—
514C2×C4#6697712yes—
515C2×C4#6697712yes—
516C2×C4#6698912yes—
517C2×C4#6698912yes—
518C2×C4#6699011yescharacteristic
519C2×C4#6699011yescharacteristic
520C2×C4C22×Dic2211yescharacteristic
521C2×C4C2×#433911yescharacteristic
522C2×C4C2×D4×D1111yescharacteristic
523C2×C4C2×#434111yescharacteristic
524C2×C4C2×#434111yescharacteristic
525C2×C4C22×C22⋊D1111yescharacteristic
526C8—42no—
527C8—442no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—24no—
533C22—24no—
534C22#1062256012yes—
535C22#1062256012yes—
536C22#1062281512yes—
537C22#1062281812yes—
538C22C2×#6693111yescharacteristic
539C22C2×#6693811yescharacteristic
540C22C2×#6699011yescharacteristic
541C4—42no—
542C4—42no—
543C4—44no—
544C4—444no—
545C4—444no—
546C4—442no—
547C4—442no—
548C4#1062256012yes—
549C4#1062256012yes—
550C4C2×#6693111yescharacteristic
551C4C2×#6693811yescharacteristic
552C4C2×#6697711yescharacteristic
553C4C2×#6698911yescharacteristic
554C2—21no—
555C2—21no—
556C2—22no—
557C2#1306977514yesdirect product factor
558C2C2×#1062256011yescharacteristic
559C2C2×#1062281511yescharacteristic
560C2C2×#1062281811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#419C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenterC2×#419D11
hypocenterC11C2×#2028
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#419

Complements

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

NH ≅ G/Ntype
4. #13069775C2direct (N × H)
47. C22×Q8×C11Q8semidirect
127. C2×Q8×C11C2×Q8semidirect
321. C22×Q8Dic22semidirect
384. C2×C11#2028semidirect
408. C2×Q8C2×Dic22semidirect
472. C11C2×#2028semidirect
557. C2#13069775direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230502
C2×#106228382
C2×#106228432
#130697752
C2×#106221922
C2×#106221932
C2×#106221702
C2×C11×#4192
C2×#202811