Finite Group Databasebeta

← C2×#13069925 #14781700

Subgroups — C2×#13069925 #14781700

Order 2816.

1918 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×#4323C211yesmaximal, characteristic
2C22×Dic11⋊C8C211yesmaximal, characteristic, complemented
3C22×#66885C211yesmaximal, characteristic, complemented
4C2×#10622834C211yesmaximal, characteristic, complemented
5C2×#10622601C211yesmaximal, characteristic, complemented
6#13069925C218yesmaximal, direct product factor
7C2×#10622167C211yesmaximal, characteristic, complemented
8C22×C11×#102C211yesmaximal, characteristic, complemented
9C23×D4×C11C2211yescharacteristic
10C23×D44C2211yescharacteristic
11C23×C8×C11C2211yescharacteristic
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C22⋊Dic11—21no—
14C22×C22⋊Dic11—21no—
15C22×#4323—24no—
16C22×#4323—24no—
17C22×#4323—24no—
18C22×#4323C2214yes—
19C22×(C2×D11)⋊C4—21no—
20C22×(C2×D11)⋊C4—21no—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4×Dic11C2211yescharacteristic
23C23×C11⋊C8C2211yescharacteristic
24C2×C11×#102—24no—
25C2×C11×#102C2214yescomplemented
26#10622834—22no—
27#10622834C2214yescomplemented
28C2×#66885—24no—
29C2×#66885C2214yescomplemented
30C2×Dic11⋊C8—24no—
31C2×Dic11⋊C8C2214yescomplemented
32#10622601—22no—
33#10622601C2214yescomplemented
34#10622167C2214yescomplemented
35C25×C11—21no—
36C24×D11—21no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11—21no—
40C22×D4×C11—22no—
41C22×D4×C11—22no—
42C22×D4×C11—22no—
43C22×D4×C11D414yes—
44C22×D4×C11C2312yes—
45C23×C4×C11—21no—
46C23×C4×C11C2311yescharacteristic
47C23×Dic11—21no—
48C23×Dic11D411yescharacteristic
49C23×Dic11D411yescharacteristic
50C22×D44—22no—
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—21no—
55C22×D44—22no—
56C22×D44D414yes—
57C22×D44C2312yes—
58C22×C8×C11—22no—
59C22×C8×C11—22no—
60C22×C8×C11—22no—
61C22×C8×C11C2312yes—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4C2312yes—
66C2×C22⋊Dic11—24no—
67C2×C22⋊Dic11—24no—
68C2×C22⋊Dic11—44no—
69C2×C22⋊Dic11—44no—
70C2×#4323—232no—
71C2×#4323—28no—
72C2×#4323—28no—
73C2×#4323—28no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—44no—
77C2×(C2×D11)⋊C4—44no—
78C2×C4⋊Dic11—22no—
79C2×C4⋊Dic11—22no—
80C2×C4⋊Dic11—21no—
81C2×C4⋊Dic11C2312yes—
82C2×C4×Dic11—22no—
83C2×C4×Dic11—22no—
84C2×C4×Dic11D412yes—
85C2×C4×Dic11C2312yes—
86C22×C11⋊C8—22no—
87C22×C11⋊C8—22no—
88C22×C11⋊C8D414yes—
89C22×C11⋊C8C2312yes—
90C11×#102—28no—
91#66885—28no—
92Dic11⋊C8—28no—
93C2×#2054—111nomaximal, Sylow
94C24×C11—24no—
95C24×C11—22no—
96C24×C11—42no—
97C24×C11—42no—
98C24×C11—42no—
99C24×C11—42no—
100C24×C11—42no—
101C24×C11—42no—
102C24×C11C2×D411yescharacteristic
103C23×D11—24no—
104C23×D11—22no—
105C23×D11—42no—
106C23×D11—42no—
107C23×D11—42no—
108C23×D11—42no—
109C23×D11—42no—
110C23×D11—42no—
111C2×D4×C11—28no—
112C2×D4×C11—24no—
113C2×D4×C11—28no—
114C2×D4×C11—22no—
115C2×D4×C11—22no—
116C2×D4×C11—22no—
117C2×D4×C11—22no—
118C2×D4×C11—22no—
119C2×D4×C11—42no—
120C2×D4×C11—42no—
121C2×D4×C11—44no—
122C2×D4×C11—44no—
123C2×D4×C11C2×D414yes—
124C22×C4×C11—22no—
125C22×C4×C11—42no—
126C22×C4×C11—42no—
127C22×C4×C11—42no—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D412yes—
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×D411yescharacteristic
132C22×C4×C11#4112yes—
133C22×C4×C11#4112yes—
134C22×C4×C11#4112yes—
135C22×C4×C11C2411yescharacteristic
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—42no—
143C22×Dic11—42no—
144C22×Dic11—42no—
145C22×Dic11D814yescomplemented
146C22×Dic11C2×D412yes—
147C22×Dic11C2×D412yes—
148C2×D44—28no—
149C2×D44—24no—
150C2×D44—28no—
151C2×D44—22no—
152C2×D44—22no—
153C2×D44—22no—
154C2×D44—22no—
155C2×D44—22no—
156C2×D44—42no—
157C2×D44—42no—
158C2×D44—44no—
159C2×D44—44no—
160C2×D44C2×D414yes—
161C2×C8×C11—22no—
162C2×C8×C11—22no—
163C2×C8×C11—22no—
164C2×C8×C11—44no—
165C11×C4⋊C4—22no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4—42no—
168C22⋊Dic11—48no—
169C22⋊Dic11—48no—
170#4323—232no—
171(C2×D11)⋊C4—48no—
172(C2×D11)⋊C4—48no—
173C4⋊Dic11—22no—
174C4⋊Dic11—22no—
175C4⋊Dic11—42no—
176C4×Dic11—24no—
177C4×Dic11—22no—
178C4×Dic11—22no—
179C2×C11⋊C8—28no—
180C2×C11⋊C8—22no—
181C2×C11⋊C8—22no—
182C2×C11⋊C8C2×D414yes—
183C23×D8—111no—
184C22×C4⋊C8—111no—
185C22×#102—111no—
186C22×#102D1111yescharacteristic, complemented
187C2×#390—111no—
188C2×#390—111no—
189#2054—118no—
190C2×#340—111no—
191C23×C11—24no—
192C23×C11—42no—
193C23×C11—42no—
194C23×C11—42no—
195C23×C11—42no—
196C23×C11—42no—
197C23×C11—42no—
198C23×C11—48no—
199C23×C11—48no—
200C23×C11—48no—
201C23×C11—84no—
202C23×C11—84no—
203C23×C11—84no—
204C23×C11—84no—
205C23×C11#12112yes—
206C23×C11#12112yes—
207C23×C11#12112yes—
208C23×C11C2×D812yes—
209C23×C11#13512yes—
210C23×C11AGL(1,ℤ/8)12yes—
211C23×C11AGL(1,ℤ/8)12yes—
212C23×C11C22×D411yescharacteristic
213C22×D11—24no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11—48no—
221C22×D11—48no—
222C22×D11—48no—
223C22×D11—84no—
224C22×D11—84no—
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—42no—
234C2×C4×C11—42no—
235C2×C4×C11—84no—
236C2×C4×C11#12014yes—
237C2×C4×C11#12112yes—
238C2×C4×C11#12112yes—
239C2×C4×C11#12112yes—
240C2×C4×C11#12314yes—
241C2×C4×C11#12314yes—
242C2×C4×C11#12414yes—
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C2×#4111yescharacteristic
247C2×C4×C11C2×#4111yescharacteristic
248C2×C4×C11C2×#4111yescharacteristic
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—28no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—44no—
256C2×Dic11—42no—
257C2×Dic11—42no—
258C2×Dic11—42no—
259C2×Dic11—84no—
260C2×Dic11C2×D814yescomplemented
261D44—24no—
262D44—24no—
263D44—42no—
264D44—42no—
265D44—48no—
266C8×C11—42no—
267C11⋊C8—24no—
268C23×D4—111no—
269C23×D4C2×D1111yescharacteristic
270C22×D8—114no—
271C22×D8—224no—
272C22×D8—224no—
273C22×D8—224no—
274C23×C8—111no—
275C23×C8C2×D1111yescharacteristic
276C22×C4⋊C4—111no—
277C22×C4⋊C4C2×D1111yescharacteristic
278C22×C22⋊C4—221no—
279C22×C22⋊C4—221no—
280C22×C22⋊C4—221no—
281C22×C22⋊C4—221no—
282C22×C42—111no—
283C2×C4⋊C8—114no—
284C2×C4⋊C8—224no—
285C2×#102—24no—
286C2×#102—114no—
287C2×#102—224no—
288C2×#102C2×D1114yescomplemented
289#390—114no—
290#390—114no—
291#390—222no—
292#390—222no—
293#340—114no—
294C22×C11—44no—
295C22×C11—44no—
296C22×C11—44no—
297C22×C11—816no—
298C22×C11—82no—
299C22×C11—82no—
300C22×C11—82no—
301C22×C11—82no—
302C22×C11#39414yes—
303C22×C11#45914yes—
304C22×C11#45914yes—
305C22×C11#46314yes—
306C22×C11#46314yes—
307C22×C11#46614yes—
308C22×C11#46914yes—
309C22×C11C2×#12111yescharacteristic
310C22×C11C2×#12111yescharacteristic
311C22×C11C2×#12111yescharacteristic
312C22×C11C22×D811yescharacteristic
313C22×C11C2×#13511yescharacteristic
314C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
315C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
316C2×D11—44no—
317C2×D11—44no—
318C2×D11—44no—
319C2×D11—816no—
320C2×D11—82no—
321C2×D11—82no—
322C2×D11—82no—
323C2×D11—82no—
324C4×C11—82no—
325C4×C11#39414yes—
326C4×C11C2×#12011yescharacteristic
327C4×C11C2×#12311yescharacteristic
328C4×C11C2×#12311yescharacteristic
329C4×C11C2×#12411yescharacteristic
330Dic11—24no—
331Dic11—42no—
332Dic11—82no—
333C25—21no—
334C25—221no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4—22no—
339C22×D4—21no—
340C22×D4—22no—
341C22×D4—114no—
342C22×D4—112no—
343C22×D4—222no—
344C22×D4—222no—
345C22×D4—222no—
346C22×D4—221no—
347C22×D4—222no—
348C22×D4—222no—
349C22×D4C22⋊D1114yes—
350C22×D4C22×D1112yes—
351C23×C4—21no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—221no—
355C23×C4C22×D1111yescharacteristic
356C2×D8—228no—
357C2×D8—228no—
358C2×D8—2232no—
359C2×D8—228no—
360C22×C8—22no—
361C22×C8—22no—
362C22×C8—22no—
363C22×C8—114no—
364C22×C8—112no—
365C22×C8—222no—
366C22×C8—222no—
367C22×C8C22×D1112yes—
368C2×C4⋊C4—22no—
369C2×C4⋊C4—22no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—112no—
372C2×C4⋊C4—222no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4C22×D1112yes—
376C2×C22⋊C4—224no—
377C2×C22⋊C4—224no—
378C2×C22⋊C4—224no—
379C2×C22⋊C4—224no—
380C2×C22⋊C4—444no—
381C2×C22⋊C4—444no—
382C2×C22⋊C4—444no—
383C2×C22⋊C4—444no—
384C2×C42—112no—
385C2×C42—112no—
386C2×C42—222no—
387C2×C42—222no—
388C4⋊C8—228no—
389#102—28no—
390#102—228no—
391C2×C11—84no—
392C2×C11#205418yescomplemented
393C2×C11C2×#39411yescharacteristic
394C2×C11C2×#45911yescharacteristic
395C2×C11C2×#45911yescharacteristic
396C2×C11C2×#46311yescharacteristic
397C2×C11C2×#46311yescharacteristic
398C2×C11C2×#46611yescharacteristic
399C2×C11C2×#46911yescharacteristic
400D11—84no—
401C24—24no—
402C24—22no—
403C24—42no—
404C24—42no—
405C24—42no—
406C24—42no—
407C24—42no—
408C24—42no—
409C24—224no—
410C24—222no—
411C24—442no—
412C24—442no—
413C24—442no—
414C24—442no—
415C24—442no—
416C24—442no—
417C24D4×D1111yescharacteristic
418C2×D4—28no—
419C2×D4—28no—
420C2×D4—24no—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—22no—
424C2×D4—22no—
425C2×D4—22no—
426C2×D4—44no—
427C2×D4—42no—
428C2×D4—42no—
429C2×D4—44no—
430C2×D4—114no—
431C2×D4—228no—
432C2×D4—224no—
433C2×D4—228no—
434C2×D4—222no—
435C2×D4—222no—
436C2×D4—222no—
437C2×D4—222no—
438C2×D4—222no—
439C2×D4—442no—
440C2×D4—444no—
441C2×D4—444no—
442C2×D4—442no—
443C2×D4C2×C22⋊D1114yes—
444C22×C4—22no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4—42no—
448C22×C4—114no—
449C22×C4—112no—
450C22×C4—112no—
451C22×C4—222no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—222no—
455C22×C4—222no—
456C22×C4—222no—
457C22×C4—442no—
458C22×C4—442no—
459C22×C4—442no—
460C22×C4#433912yes—
461C22×C4#433912yes—
462C22×C4D4×D1112yes—
463C22×C4D4×D1111yescharacteristic
464C22×C4D4×D1112yes—
465C22×C4#434112yes—
466C22×C4C2×C22⋊D1112yes—
467C22×C4C23×D1111yescharacteristic
468D8—2232no—
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—22no—
472C2×C8—44no—
473C2×C8—114no—
474C2×C8—228no—
475C2×C8—222no—
476C2×C8—222no—
477C4⋊C4—22no—
478C4⋊C4—22no—
479C4⋊C4—42no—
480C4⋊C4—222no—
481C4⋊C4—222no—
482C4⋊C4—442no—
483C22⋊C4—448no—
484C22⋊C4—448no—
485C22⋊C4—448no—
486C22⋊C4—448no—
487C42—224no—
488C42—222no—
489C42—222no—
490C11C2×#205411yescharacteristic, complemented, Sylow
491C23—24no—
492C23—48no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—48no—
498C23—42no—
499C23—42no—
500C23—48no—
501C23—84no—
502C23—84no—
503C23—84no—
504C23—84no—
505C23—224no—
506C23—442no—
507C23—442no—
508C23—442no—
509C23—442no—
510C23—442no—
511C23—442no—
512C23—448no—
513C23—448no—
514C23—448no—
515C23—884no—
516C23—884no—
517C23—884no—
518C23—884no—
519C23#6693712yes—
520C23#6693712yes—
521C23D8×D1112yes—
522C23#6696412yes—
523C23#6696712yes—
524C23#6696912yes—
525C23#6699212yes—
526C23C2×D4×D1111yescharacteristic
527D4—24no—
528D4—24no—
529D4—42no—
530D4—42no—
531D4—48no—
532D4—224no—
533D4—224no—
534D4—442no—
535D4—442no—
536D4—448no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—42no—
540C2×C4—84no—
541C2×C4—114no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—228no—
545C2×C4—222no—
546C2×C4—222no—
547C2×C4—222no—
548C2×C4—444no—
549C2×C4—442no—
550C2×C4—442no—
551C2×C4—442no—
552C2×C4—884no—
553C2×C4#6693614yes—
554C2×C4#6693712yes—
555C2×C4#6693712yes—
556C2×C4#6693814yes—
557C2×C4#6698214yes—
558C2×C4#6699014yes—
559C2×C4#6699212yes—
560C2×C4C2×#433911yescharacteristic
561C2×C4C2×#433911yescharacteristic
562C2×C4C2×D4×D1111yescharacteristic
563C2×C4C2×D4×D1111yescharacteristic
564C2×C4C2×#434111yescharacteristic
565C2×C4C22×C22⋊D1111yescharacteristic
566C8—42no—
567C8—224no—
568C22—44no—
569C22—44no—
570C22—44no—
571C22—82no—
572C22—82no—
573C22—816no—
574C22—82no—
575C22—82no—
576C22—444no—
577C22—444no—
578C22—444no—
579C22—882no—
580C22—882no—
581C22—8816no—
582C22—882no—
583C22—882no—
584C22#1062238814yes—
585C22#1062239514yes—
586C22#1062239914yes—
587C22#1062240014yes—
588C22#1062257214yes—
589C22#1062276314yes—
590C22#1062277814yes—
591C22C2×#6693711yescharacteristic
592C22C2×#6693711yescharacteristic
593C22C2×D8×D1111yescharacteristic
594C22C2×#6696411yescharacteristic
595C22C2×#6696711yescharacteristic
596C22C2×#6696911yescharacteristic
597C22C2×#6699211yescharacteristic
598C4—82no—
599C4—224no—
600C4—442no—
601C4—882no—
602C4#1062257214yes—
603C4C2×#6693611yescharacteristic
604C4C2×#6693811yescharacteristic
605C4C2×#6698211yescharacteristic
606C4C2×#6699011yescharacteristic
607C2—84no—
608C2—884no—
609C2#1306992518yesdirect product factor
610C2C2×#1062257211yescharacteristic
611C2C2×#1062276311yescharacteristic
612C2C2×#1062239911yescharacteristic
613C2C2×#1062240011yescharacteristic
614C2C2×#1062277811yescharacteristic
615C2C2×#1062238811yescharacteristic
616C2C2×#1062239511yescharacteristic
subgroupG/H
centerC24D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC22×C11×#102C2
socleC24×C11C2×D4
prime radicalC23×#4323C2
hypercenterC22×#102D11
hypocenterC11C2×#2054
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
2. C22×Dic11⋊C8C2semidirect
3. C22×#66885C2semidirect
4. C2×#10622834C2semidirect
5. C2×#10622601C2semidirect
6. #13069925C2direct (N × H)
7. C2×#10622167C2semidirect
8. C22×C11×#102C2semidirect
25. C2×C11×#102C22semidirect
27. #10622834C22semidirect
29. C2×#66885C22semidirect
31. C2×Dic11⋊C8C22semidirect
33. #10622601C22semidirect
34. #10622167C22semidirect
145. C22×Dic11D8semidirect
186. C22×#102D11semidirect
260. C2×Dic11C2×D8semidirect
288. C2×#102C2×D11semidirect
392. C2×C11#2054semidirect
490. C11C2×#2054semidirect
609. C2#13069925direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43232
C22×Dic11⋊C82
C22×#668852
C2×#106228342
C2×#106226012
#130699252
C2×#106221672
C22×C11×#1022
C2×#205411