Finite Group Databasebeta

← C2×#13068971 #14755113

Subgroups — C2×#13068971 #14755113

Order 2816.

2038 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
1C23×#4325C211yesmaximal, characteristic
2C22×#66899C211yesmaximal, characteristic, complemented
3C22×#66873C211yesmaximal, characteristic
4C2×#10622552C211yesmaximal, characteristic
5#13068971C218yesmaximal, direct product factor
6C2×#10622167C211yesmaximal, characteristic, complemented
7C2×#10622162C211yesmaximal, characteristic, complemented
8C22×C4×Q8×C11C211yesmaximal, characteristic, complemented
9C23×Q8×C11C2211yescharacteristic
10C23×D44C2211yescharacteristic
11C2×C4×Q8×C11—24no—
12C2×C4×Q8×C11—24no—
13C2×C4×Q8×C11—22no—
14C2×C4×Q8×C11C2214yescomplemented
15C22×C11×C4⋊C4—21no—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11—21no—
18C22×C42×C11C2211yescharacteristic
19C22×#4325—24no—
20C22×#4325—24no—
21C22×#4325C418yescomplemented
22C22×#4325C2214yes—
23C22×(C2×D11)⋊C4—21no—
24C22×(C2×D11)⋊C4—21no—
25C22×C4⋊Dic11C2211yescharacteristic
26C23×C11⋊C8C2211yescharacteristic
27C23×C11⋊C8C2211yescharacteristic
28C2×#66899—24no—
29C2×#66899C2214yescomplemented
30C2×#66873—24no—
31C2×#66873C2214yes—
32#10622552—22no—
33#10622552C2214yes—
34#10622167C2214yescomplemented
35#10622162C2214yescomplemented
36C24×D11—21no—
37C22×Q8×C11—22no—
38C22×Q8×C11—21no—
39C22×Q8×C11—22no—
40C22×Q8×C11—22no—
41C22×Q8×C11C2×C414yes—
42C22×Q8×C11D414yes—
43C22×Q8×C11D414yes—
44C22×Q8×C11C2312yes—
45C23×C4×C11—21no—
46C23×C4×C11—21no—
47C23×C4×C11D411yescharacteristic
48C23×C4×C11D411yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×Dic11—21no—
51C22×D44—22no—
52C22×D44—22no—
53C22×D44—22no—
54C22×D44—22no—
55C22×D44—21no—
56C22×D44—22no—
57C22×D44C2×C414yes—
58C22×D44C2312yes—
59C4×Q8×C11—216no—
60C4×Q8×C11—28no—
61C4×Q8×C11—28no—
62C2×C11×C4⋊C4—28no—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4—21no—
65C2×C11×C4⋊C4—22no—
66C2×C11×C4⋊C4D414yes—
67C2×C11×C4⋊C4C2312yes—
68C2×C42×C11—28no—
69C2×C42×C11—24no—
70C2×C42×C11—22no—
71C2×C42×C11—22no—
72C2×C42×C11D412yes—
73C2×C42×C11C2312yes—
74C2×#4325—232no—
75C2×#4325—28no—
76C2×#4325—28no—
77C2×#4325C2×C4116yescomplemented
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—44no—
81C2×(C2×D11)⋊C4—44no—
82C2×C4⋊Dic11—22no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—21no—
85C2×C4⋊Dic11C2312yes—
86C22×C11⋊C8—22no—
87C22×C11⋊C8—22no—
88C22×C11⋊C8—22no—
89C22×C11⋊C8—22no—
90C22×C11⋊C8—22no—
91C22×C11⋊C8C2×C414yes—
92C22×C11⋊C8C2312yes—
93C22×C11⋊C8C2312yes—
94#66899—28no—
95#66873—28no—
96C2×#1880—111nomaximal, Sylow
97C24×C11C2×D411yescharacteristic
98C23×D11—24no—
99C23×D11—22no—
100C23×D11—42no—
101C23×D11—42no—
102C23×D11—42no—
103C23×D11—42no—
104C23×D11—42no—
105C23×D11—42no—
106C2×Q8×C11—24no—
107C2×Q8×C11—28no—
108C2×Q8×C11—24no—
109C2×Q8×C11—24no—
110C2×Q8×C11—28no—
111C2×Q8×C11—28no—
112C2×Q8×C11—22no—
113C2×Q8×C11—22no—
114C2×Q8×C11—22no—
115C2×Q8×C11C22⋊C4116yescomplemented
116C2×Q8×C11C22×C414yes—
117C2×Q8×C11C2×D414yes—
118C2×Q8×C11C2×D414yes—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—24no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—42no—
131C22×C4×C11—42no—
132C22×C4×C11SD1614yescomplemented
133C22×C4×C11C22×C412yes—
134C22×C4×C11C2×D412yes—
135C22×C4×C11C2×D412yes—
136C22×C4×C11C2×D412yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D411yescharacteristic
139C22×C4×C11C2×D412yes—
140C22×C4×C11#4112yes—
141C22×C4×C11#4112yes—
142C22×C4×C11C2411yescharacteristic
143C22×Dic11—22no—
144C22×Dic11—42no—
145C22×Dic11—42no—
146C22×Dic11—42no—
147C2×D44—28no—
148C2×D44—24no—
149C2×D44—28no—
150C2×D44—22no—
151C2×D44—22no—
152C2×D44—22no—
153C2×D44—22no—
154C2×D44—22no—
155C2×D44—42no—
156C2×D44—44no—
157C2×D44—42no—
158C2×D44—44no—
159C2×D44C22×C414yes—
160C11×C4⋊C4—216no—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—22no—
163C11×C4⋊C4C2×D414yes—
164C42×C11—216no—
165C42×C11—24no—
166C42×C11—22no—
167C42×C11—22no—
168#4325—232no—
169(C2×D11)⋊C4—48no—
170(C2×D11)⋊C4—48no—
171C4⋊Dic11—22no—
172C4⋊Dic11—22no—
173C4⋊Dic11—42no—
174C2×C11⋊C8—28no—
175C2×C11⋊C8—22no—
176C2×C11⋊C8—22no—
177C2×C11⋊C8—22no—
178C2×C11⋊C8—22no—
179C2×C11⋊C8—22no—
180C2×C11⋊C8—44no—
181C2×C11⋊C8C22×C414yes—
182C23×SD16—111no—
183C22×C4×Q8D1111yescharacteristic, complemented
184C22×#103—111no—
185C22×#102—111no—
186C2×#390—111no—
187#1880—118no—
188C2×#340—111no—
189C2×#336—111no—
190C23×C11C4×D412yes—
191C23×C11#12012yes—
192C23×C11#12112yes—
193C23×C11C2×SD1612yes—
194C23×C11#13512yes—
195C23×C11AGL(1,ℤ/8)12yes—
196C23×C11#13712yes—
197C23×C11C22×D411yescharacteristic
198C22×D11—24no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—42no—
202C22×D11—42no—
203C22×D11—42no—
204C22×D11—42no—
205C22×D11—48no—
206C22×D11—48no—
207C22×D11—48no—
208C22×D11—84no—
209C22×D11—84no—
210C22×D11—84no—
211C22×D11—84no—
212Q8×C11—24no—
213Q8×C11—24no—
214Q8×C11—24no—
215Q8×C11—216no—
216Q8×C11C2×C22⋊C418yescomplemented
217C2×C4×C11—24no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—22no—
222C2×C4×C11—216no—
223C2×C4×C11—28no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—44no—
231C2×C4×C11—48no—
232C2×C4×C11C2×C22⋊C414yes—
233C2×C4×C11C4×D414yes—
234C2×C4×C11C4×D412yes—
235C2×C4×C11#12012yes—
236C2×C4×C11#12114yes—
237C2×C4×C11#12112yes—
238C2×C4×C11#12314yes—
239C2×C4×C11C2×SD1614yescomplemented
240C2×C4×C11C23×C411yescharacteristic
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D411yescharacteristic
244C2×C4×C11C2×#4111yescharacteristic
245C2×C4×C11C2×#4111yescharacteristic
246C2×Dic11—42no—
247C2×Dic11—42no—
248C2×Dic11—42no—
249C2×Dic11—84no—
250D44—24no—
251D44—24no—
252D44—42no—
253D44—42no—
254D44—48no—
255C11⋊C8—24no—
256C11⋊C8—42no—
257C23×Q8C2×D1111yescharacteristic
258C23×D4—111no—
259C22×SD16—114no—
260C22×SD16—118no—
261C22×SD16—224no—
262C22×SD16—224no—
263C23×C8—111no—
264C23×C8—111no—
265C2×C4×Q8—24no—
266C2×C4×Q8—24no—
267C2×C4×Q8—22no—
268C2×C4×Q8C2×D1114yescomplemented
269C22×C4⋊C4—21no—
270C22×C4⋊C4—111no—
271C22×C4⋊C4C2×D1111yescharacteristic
272C22×C22⋊C4—221no—
273C22×C22⋊C4—221no—
274C22×C42—21no—
275C22×C42C2×D1111yescharacteristic
276C2×#103—114no—
277C2×#103—224no—
278C2×#102—114no—
279C2×#102—224no—
280#390—114no—
281#390—222no—
282#340—114no—
283#336—114no—
284C22×C11#38614yes—
285C22×C11C4×SD1614yes—
286C22×C11#44014yes—
287C22×C11#44814yes—
288C22×C11#44914yes—
289C22×C11#46014yes—
290C22×C11#46414yes—
291C22×C11C2×C4×D411yescharacteristic
292C22×C11C2×#12011yescharacteristic
293C22×C11C2×#12111yescharacteristic
294C22×C11C22×SD1611yescharacteristic
295C22×C11C2×#13511yescharacteristic
296C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
297C22×C11C2×#13711yescharacteristic
298C2×D11—44no—
299C2×D11—44no—
300C2×D11—44no—
301C2×D11—816no—
302C2×D11—82no—
303C2×D11—82no—
304C2×D11—82no—
305C2×D11—82no—
306C4×C11—24no—
307C4×C11—28no—
308C4×C11—42no—
309C4×C11—44no—
310C4×C11#38614yes—
311C4×C11C22×C22⋊C411yescharacteristic
312C4×C11C2×C4×D411yescharacteristic
313C4×C11C2×#12111yescharacteristic
314C4×C11C2×#12311yescharacteristic
315Dic11—82no—
316C25—221no—
317C22×Q8—22no—
318C22×Q8—22no—
319C22×Q8—22no—
320C22×Q8—21no—
321C22×Q8C4×D1114yes—
322C22×Q8D4414yes—
323C22×Q8C22⋊D1114yes—
324C22×Q8C22×D1112yes—
325C22×D4—114no—
326C22×D4—112no—
327C22×D4—222no—
328C22×D4—222no—
329C22×D4—222no—
330C22×D4—222no—
331C22×D4—222no—
332C22×D4—221no—
333C23×C4—21no—
334C23×C4—21no—
335C23×C4—221no—
336C23×C4C22⋊D1111yescharacteristic
337C23×C4C22⋊D1111yescharacteristic
338C23×C4C22×D1111yescharacteristic
339C2×SD16—1116no—
340C2×SD16—2232no—
341C2×SD16—228no—
342C2×SD16—228no—
343C22×C8—114no—
344C22×C8—112no—
345C22×C8—112no—
346C22×C8—222no—
347C22×C8—222no—
348C22×C8—222no—
349C22×C8—222no—
350C22×C8—222no—
351C4×Q8—216no—
352C4×Q8—28no—
353C4×Q8—28no—
354C2×C4⋊C4—28no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—21no—
357C2×C4⋊C4—22no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—222no—
360C2×C4⋊C4—222no—
361C2×C4⋊C4—221no—
362C2×C4⋊C4C22⋊D1114yes—
363C2×C4⋊C4C22×D1112yes—
364C2×C22⋊C4—224no—
365C2×C22⋊C4—224no—
366C2×C22⋊C4—444no—
367C2×C22⋊C4—444no—
368C2×C42—28no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—24no—
372C2×C42C22⋊D1112yes—
373C2×C42C22×D1112yes—
374#103—228no—
375#102—228no—
376C2×C11#188018yescomplemented
377C2×C11C2×#38611yescharacteristic
378C2×C11C2×C4×SD1611yescharacteristic
379C2×C11C2×#44011yescharacteristic
380C2×C11C2×#44811yescharacteristic
381C2×C11C2×#44911yescharacteristic
382C2×C11C2×#46011yescharacteristic
383C2×C11C2×#46411yescharacteristic
384D11—84no—
385C24—224no—
386C24—222no—
387C24—442no—
388C24—442no—
389C24—442no—
390C24—442no—
391C24—442no—
392C24—442no—
393C24C2×C22⋊D1111yescharacteristic
394C2×Q8—24no—
395C2×Q8—28no—
396C2×Q8—28no—
397C2×Q8—24no—
398C2×Q8—28no—
399C2×Q8—24no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8(C2×D11)⋊C4116yescomplemented
404C2×Q8C2×C4×D1114yes—
405C2×Q8C2×D4414yes—
406C2×Q8C2×C22⋊D1114yes—
407C2×D4—114no—
408C2×D4—228no—
409C2×D4—228no—
410C2×D4—224no—
411C2×D4—222no—
412C2×D4—222no—
413C2×D4—222no—
414C2×D4—222no—
415C2×D4—222no—
416C2×D4—444no—
417C2×D4—444no—
418C2×D4—442no—
419C2×D4—442no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—24no—
425C22×C4—22no—
426C22×C4—22no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—24no—
430C22×C4—22no—
431C22×C4—42no—
432C22×C4—42no—
433C22×C4—222no—
434C22×C4—442no—
435C22×C4—442no—
436C22×C4—442no—
437C22×C4#432514yescomplemented
438C22×C4C2×C4×D1112yes—
439C22×C4C2×D4412yes—
440C22×C4#433912yes—
441C22×C4#433912yes—
442C22×C4C2×C22⋊D1112yes—
443C22×C4C2×C22⋊D1112yes—
444C22×C4C2×C22⋊D1112yes—
445C22×C4C2×C22⋊D1111yescharacteristic
446C22×C4C2×C22⋊D1112yes—
447C22×C4C23×D1111yescharacteristic
448SD16—2232no—
449C2×C8—114no—
450C2×C8—228no—
451C2×C8—222no—
452C2×C8—222no—
453C2×C8—222no—
454C2×C8—222no—
455C2×C8—222no—
456C2×C8—444no—
457C4⋊C4—216no—
458C4⋊C4—24no—
459C4⋊C4—22no—
460C4⋊C4—222no—
461C4⋊C4—222no—
462C4⋊C4—442no—
463C4⋊C4C2×C22⋊D1114yes—
464C22⋊C4—448no—
465C22⋊C4—448no—
466C42—216no—
467C42—24no—
468C42—22no—
469C42—22no—
470C11C2×#188011yescharacteristic, complemented, Sylow
471C23—224no—
472C23—442no—
473C23—448no—
474C23—442no—
475C23—442no—
476C23—442no—
477C23—442no—
478C23—442no—
479C23—448no—
480C23—448no—
481C23—884no—
482C23—884no—
483C23—884no—
484C23—884no—
485C23C4×C22⋊D1112yes—
486C23#6698312yes—
487C23C2×#432512yes—
488C23#6699512yes—
489C23#6700212yes—
490C23#6700312yes—
491C23#6700612yes—
492C23C22×C22⋊D1111yescharacteristic
493Q8—24no—
494Q8—24no—
495Q8—24no—
496Q8—216no—
497Q8C2×(C2×D11)⋊C418yescomplemented
498D4—224no—
499D4—224no—
500D4—442no—
501D4—442no—
502D4—448no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—216no—
506C2×C4—22no—
507C2×C4—28no—
508C2×C4—22no—
509C2×C4—24no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—44no—
517C2×C4—48no—
518C2×C4—442no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4—884no—
522C2×C4C2×(C2×D11)⋊C414yes—
523C2×C4C4×C22⋊D1114yes—
524C2×C4C4×C22⋊D1112yes—
525C2×C4#6698214yes—
526C2×C4#6698314yes—
527C2×C4#6698312yes—
528C2×C4C2×#432514yescomplemented
529C2×C4#6700612yes—
530C2×C4C22×C4×D1111yescharacteristic
531C2×C4C22×D4411yescharacteristic
532C2×C4C2×#433911yescharacteristic
533C2×C4C2×#433911yescharacteristic
534C2×C4C22×C22⋊D1111yescharacteristic
535C2×C4C22×C22⋊D1111yescharacteristic
536C8—224no—
537C8—442no—
538C22—444no—
539C22—444no—
540C22—444no—
541C22—882no—
542C22—882no—
543C22—882no—
544C22—882no—
545C22—8816no—
546C22C4×#432514yes—
547C22#1062263914yes—
548C22#1062264014yes—
549C22#1062264114yes—
550C22#1062282614yes—
551C22#1062284014yes—
552C22#1062285114yes—
553C22C2×C4×C22⋊D1111yescharacteristic
554C22C2×#6698311yescharacteristic
555C22C22×#432511yescharacteristic
556C22C2×#6699511yescharacteristic
557C22C2×#6700211yescharacteristic
558C22C2×#6700311yescharacteristic
559C22C2×#6700611yescharacteristic
560C4—24no—
561C4—28no—
562C4—42no—
563C4—44no—
564C4—882no—
565C4#1062282614yes—
566C4C22×(C2×D11)⋊C411yescharacteristic
567C4C2×C4×C22⋊D1111yescharacteristic
568C4C2×#6698211yescharacteristic
569C4C2×#6698311yescharacteristic
570C2—884no—
571C2#1306897118yesdirect product factor
572C2C2×#1062282611yescharacteristic
573C2C2×C4×#432511yescharacteristic
574C2C2×#1062263911yescharacteristic
575C2C2×#1062284011yescharacteristic
576C2C2×#1062285111yescharacteristic
577C2C2×#1062264011yescharacteristic
578C2C2×#1062264111yescharacteristic
subgroupG/H
centerC24C2×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C4×Q8×C11C2
socleC24×C11C2×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenterC22×C4×Q8D11
hypocenterC11C2×#1880
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. C22×#66899C2semidirect
5. #13068971C2direct (N × H)
6. C2×#10622167C2semidirect
7. C2×#10622162C2semidirect
8. C22×C4×Q8×C11C2semidirect
14. C2×C4×Q8×C11C22semidirect
21. C22×#4325C4semidirect
29. C2×#66899C22semidirect
34. #10622167C22semidirect
35. #10622162C22semidirect
77. C2×#4325C2×C4semidirect
115. C2×Q8×C11C22⋊C4semidirect
132. C22×C4×C11SD16semidirect
183. C22×C4×Q8D11semidirect
216. Q8×C11C2×C22⋊C4semidirect
239. C2×C4×C11C2×SD16semidirect
268. C2×C4×Q8C2×D11semidirect
376. C2×C11#1880semidirect
403. C2×Q8(C2×D11)⋊C4semidirect
437. C22×C4#4325semidirect
470. C11C2×#1880semidirect
497. Q8C2×(C2×D11)⋊C4semidirect
528. C2×C4C2×#4325semidirect
571. C2#13068971direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#43252
C22×#668992
C22×#668732
C2×#106225522
#130689712
C2×#106221672
C2×#106221622
C22×C4×Q8×C112
C2×#188011