Finite Group Databasebeta

← C2×#13069776 #14781138

Subgroups — C2×#13069776 #14781138

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×#10622733C211yesmaximal, characteristic
3C2×#10622617C211yesmaximal, characteristic
4C2×#10622542C211yesmaximal, characteristic
5#13069776C218yesmaximal, direct product factor
6C2×#10622192C211yesmaximal, characteristic
7C2×#10622161C211yesmaximal, characteristic
8C2×C11×#339C211yesmaximal, characteristic
9C23×Dic22C2211yescharacteristic
10C22×C11×M16C2211yescharacteristic
11C2×C11×#117C2211yescharacteristic
12C22×C42×C11C2211yescharacteristic
13C2×#66979C2211yescharacteristic
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—
25C2×C11⋊#95—22no—
26#10622733—22no—
27#10622733C2214yes—
28C2×#66880—21no—
29C2×#66880—21no—
30#10622617—22no—
31#10622617C2214yes—
32C2×#66874—21no—
33C2×#66874—21no—
34#10622542—22no—
35#10622542C2214yes—
36C11×#339C2214yes—
37#10622192C2214yes—
38#10622161C2214yes—
39C23×C4×C11—21no—
40C23×C4×C11C2311yescharacteristic
41C23×Dic11—21no—
42C23×Dic11D412yes—
43C22×Dic22—21no—
44C22×Dic22—21no—
45C22×Dic22—21no—
46C22×Dic22—21no—
47C22×Dic22—22no—
48C22×Dic22—22no—
49C22×Dic22—21no—
50C22×Dic22—22no—
51C22×Dic22—22no—
52C22×Dic22Q814yescomplemented
53C22×Dic22C2312yes—
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×C42×C11—22no—
68C2×C42×C11—22no—
69C2×C42×C11—21no—
70C2×C42×C11C2312yes—
71C2×C22⋊Dic11—21no—
72#66979—21no—
73#66979—21no—
74#66979D412yes—
75#66979C2312yes—
76C2×C4⋊Dic11—22no—
77C2×C4⋊Dic11—21no—
78C2×C4⋊Dic11—21no—
79C2×C4⋊Dic11—21no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11D412yes—
82C2×C4⋊Dic11D411yescharacteristic
83C2×C4⋊Dic11D411yescharacteristic
84C2×C4⋊Dic11C2312yes—
85C2×Dic11⋊C4—22no—
86C2×Dic11⋊C4—22no—
87C2×C4×Dic11—21no—
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⋊#95—28no—
104#66880—24no—
105#66880—24no—
106#66874—24no—
107#66874—24no—
108C2×#2028—111nomaximal, Sylow
109C24×C11C2×D411yescharacteristic
110C22×C4×C11—24no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—22no—
114C22×C4×C11—42no—
115C22×C4×C11—42no—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×Q812yes—
122C22×C4×C11#4112yes—
123C22×C4×C11#4112yes—
124C22×C4×C11#4112yes—
125C22×C4×C11C2411yescharacteristic
126C22×Dic11—21no—
127C22×Dic11—21no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—24no—
131C22×Dic11—22no—
132C22×Dic11—44no—
133C22×Dic11—41no—
134C22×Dic11—41no—
135C22×Dic11—42no—
136C22×Dic11C2×D414yes—
137C2×Dic22—28no—
138C2×Dic22—24no—
139C2×Dic22—24no—
140C2×Dic22—24no—
141C2×Dic22—24no—
142C2×Dic22—24no—
143C2×Dic22—22no—
144C2×Dic22—22no—
145C2×Dic22—22no—
146C2×Dic22—22no—
147C2×Dic22—22no—
148C2×Dic22—41no—
149C2×Dic22—41no—
150C2×Dic22—42no—
151C2×Dic22—42no—
152C2×Dic22—42no—
153C2×Dic22—42no—
154C2×Dic22—42no—
155C2×Dic22—84no—
156C2×Dic22C2×Q814yescomplemented
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—
170C42×C11—22no—
171C42×C11—22no—
172C42×C11—42no—
173C22⋊Dic11—22no—
174C22⋊Dic11—22no—
175C4⋊Dic11—28no—
176C4⋊Dic11—21no—
177C4⋊Dic11—22no—
178C4⋊Dic11—21no—
179C4⋊Dic11—22no—
180C4⋊Dic11—22no—
181C4⋊Dic11—22no—
182C4⋊Dic11C2×D412yes—
183C4⋊Dic11C2×D412yes—
184Dic11⋊C4—28no—
185Dic11⋊C4—28no—
186C4×Dic11—22no—
187C4×Dic11—22no—
188#4318—22no—
189#4318—22no—
190#4318—42no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8—42no—
193C2×#544—111no—
194C2×#419—111no—
195C2×#419—111no—
196C2×#391—111no—
197#2028—118no—
198C2×#343—111no—
199C2×#339—111no—
200C2×#339D1111yescharacteristic
201C23×C11—22no—
202C23×C11—22no—
203C23×C11#12011yescharacteristic
204C23×C11#12011yescharacteristic
205C23×C11C22⋊Q812yes—
206C23×C11#12412yes—
207C23×C11C22×D411yescharacteristic
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—42no—
212C2×C4×C11—48no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—42no—
216C2×C4×C11#12011yescharacteristic
217C2×C4×C11#12011yescharacteristic
218C2×C4×C11C22⋊Q812yes—
219C2×C4×C11C22⋊Q812yes—
220C2×C4×C11C22⋊Q812yes—
221C2×C4×C11C22⋊Q812yes—
222C2×C4×C11C22⋊Q812yes—
223C2×C4×C11#12412yes—
224C2×C4×C11#12412yes—
225C2×C4×C11#12412yes—
226C2×C4×C11#12412yes—
227C2×C4×C11#12412yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D411yescharacteristic
230C2×C4×C11C22×Q811yescharacteristic
231C2×C4×C11C2×#4111yescharacteristic
232C2×C4×C11C2×#4111yescharacteristic
233C2×C4×C11C2×#4111yescharacteristic
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11—44no—
241C2×Dic11—44no—
242C2×Dic11—42no—
243C2×Dic11—44no—
244C2×Dic11—42no—
245C2×Dic11—44no—
246C2×Dic11—82no—
247Dic22—24no—
248Dic22—24no—
249Dic22—42no—
250Dic22—42no—
251Dic22—44no—
252Dic22—44no—
253Dic22—88no—
254C8×C11—42no—
255C11⋊C8—42no—
256C23×Q8—111no—
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×C42C2×D1111yescharacteristic
272#419—114no—
273#419—114no—
274#419—222no—
275#419—222no—
276C2×#103—221no—
277C2×#103—221no—
278C2×#103—221no—
279C2×#103—221no—
280#391—114no—
281#391—222no—
282C2×#95—222no—
283#343—114no—
284#339—114no—
285#339C2×D1114yes—
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—114no—
313C22×Q8—112no—
314C22×Q8—222no—
315C22×Q8—222no—
316C22×Q8—221no—
317C22×Q8—221no—
318C22×Q8—221no—
319C22×Q8—222no—
320C22×Q8—221no—
321C22×Q8—221no—
322C22×Q8—222no—
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#117D4412yes—
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⋊C4D4411yescharacteristic
367C2×C4⋊C4D4411yescharacteristic
368C2×C22⋊C4—21no—
369C2×C22⋊C4—221no—
370C2×C42—21no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—21no—
374C2×C42—221no—
375C2×C42C22×D1112yes—
376#103—224no—
377#103—224no—
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—114no—
390C2×Q8—228no—
391C2×Q8—224no—
392C2×Q8—222no—
393C2×Q8—224no—
394C2×Q8—224no—
395C2×Q8—224no—
396C2×Q8—224no—
397C2×Q8—222no—
398C2×Q8—222no—
399C2×Q8—222no—
400C2×Q8—222no—
401C2×Q8—442no—
402C2×Q8—442no—
403C2×Q8—441no—
404C2×Q8—441no—
405C2×Q8—442no—
406C2×Q8—442no—
407C2×Q8—442no—
408C2×Q8—884no—
409C22×C4—24no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—114no—
416C22×C4—221no—
417C22×C4—221no—
418C22×C4—222no—
419C22×C4—224no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—441no—
423C22×C4—441no—
424C22×C4—442no—
425C22×C4—444no—
426C22×C4C2×D4411yescharacteristic
427C22×C4C2×D4411yescharacteristic
428C22×C4#433912yes—
429C22×C4#433912yes—
430C22×C4D4×D1111yescharacteristic
431C22×C4D4×D1111yescharacteristic
432C22×C4D4×D1111yescharacteristic
433C22×C4#434112yes—
434C22×C4Q8×D1112yes—
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×D4412yes—
460C4⋊C4C2×D4412yes—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—222no—
464C22⋊C4—222no—
465C42—22no—
466C42—22no—
467C42—22no—
468C42—22no—
469C42—42no—
470C42—222no—
471C42—222no—
472C11C2×#202811yescharacteristic, complemented, Sylow
473C23—22no—
474C23—22no—
475C23#6693511yescharacteristic
476C23#6693511yescharacteristic
477C23#6693812yes—
478C23#6694912yes—
479C23C2×D4×D1111yescharacteristic
480Q8—224no—
481Q8—224no—
482Q8—442no—
483Q8—442no—
484Q8—444no—
485Q8—444no—
486Q8—888no—
487C2×C4—24no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—42no—
491C2×C4—48no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—42no—
495C2×C4—222no—
496C2×C4—222no—
497C2×C4—224no—
498C2×C4—224no—
499C2×C4—442no—
500C2×C4—442no—
501C2×C4—444no—
502C2×C4—444no—
503C2×C4—444no—
504C2×C4—442no—
505C2×C4—442no—
506C2×C4—444no—
507C2×C4—882no—
508C2×C4#6692812yes—
509C2×C4#6692812yes—
510C2×C4#6693511yescharacteristic
511C2×C4#6693511yescharacteristic
512C2×C4#6693812yes—
513C2×C4#6693812yes—
514C2×C4#6693812yes—
515C2×C4#6694912yes—
516C2×C4#6694912yes—
517C2×C4#6694912yes—
518C2×C4#6695012yes—
519C2×C4#6695012yes—
520C2×C4C22×D4411yescharacteristic
521C2×C4C2×#433911yescharacteristic
522C2×C4C2×#433911yescharacteristic
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4C2×#434111yescharacteristic
525C2×C4C2×Q8×D1111yescharacteristic
526C8—42no—
527C8—442no—
528C22—21no—
529C22—21no—
530C22—21no—
531C22—21no—
532C22—24no—
533C22—24no—
534C22#1062228612yes—
535C22#1062228612yes—
536C22#1062243812yes—
537C22#1062243912yes—
538C22C2×#6693511yescharacteristic
539C22C2×#6693811yescharacteristic
540C22C2×#6694911yescharacteristic
541C4—44no—
542C4—42no—
543C4—42no—
544C4—444no—
545C4—442no—
546C4—442no—
547C4—444no—
548C4#1062228612yes—
549C4#1062228612yes—
550C4C2×#6692811yescharacteristic
551C4C2×#6693811yescharacteristic
552C4C2×#6694911yescharacteristic
553C4C2×#6695011yescharacteristic
554C2—21no—
555C2—21no—
556C2—22no—
557C2#1306977614yesdirect product factor
558C2C2×#1062228611yescharacteristic
559C2C2×#1062243811yescharacteristic
560C2C2×#1062243911yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#339C2
socleC23×C11#120
prime radicalC24×C11C2×D4
hypercenterC2×#339D11
hypocenterC11C2×#2028
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
5. #13069776C2direct (N × H)
52. C22×Dic22Q8semidirect
156. C2×Dic22C2×Q8semidirect
384. C2×C11#2028semidirect
472. C11C2×#2028semidirect
557. C2#13069776direct (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×#106227332
C2×#106226172
C2×#106225422
#130697762
C2×#106221922
C2×#106221612
C2×C11×#3392
C2×#202811