Finite Group Databasebeta

← C2×#13068863 #14754686

Subgroups — C2×#13068863 #14754686

Order 2816.

1974 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66871C211yesmaximal, characteristic, complemented
2C22×#66896C211yesmaximal, characteristic
3C22×#66896C211yesmaximal, characteristic
4C2×#10622541C211yesmaximal, characteristic, complemented
5#13068863C218yesmaximal, direct product factor
6C2×#10622167C211yesmaximal, characteristic, complemented
7C2×#10622162C211yesmaximal, characteristic, complemented
8C22×C4×D4×C11C211yesmaximal, characteristic
9C23×D4×C11C2211yescharacteristic
10C24×C4×C11—21no—
11C2×C4×D4×C11—24no—
12C2×C4×D4×C11—24no—
13C2×C4×D4×C11—22no—
14C2×C4×D4×C11C2214yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4—21no—
17C22×C42×C11C2211yescharacteristic
18C22×C4⋊Dic11C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C22×Dic11⋊C4—21no—
21C23×C11⋊C8C2211yescharacteristic
22C23×C11⋊C8C2211yescharacteristic
23C2×#66896—24no—
24C2×#66896C418yescomplemented
25C2×#66896C2214yes—
26C2×#66896C2214yes—
27C2×C11⋊#95—21no—
28C2×#66871—24no—
29C2×#66871C2214yescomplemented
30#10622541—22no—
31#10622541C2214yescomplemented
32#10622167C2214yescomplemented
33#10622162C2214yescomplemented
34C25×C11—21no—
35C22×D4×C11—21no—
36C22×D4×C11—22no—
37C22×D4×C11—22no—
38C22×D4×C11—22no—
39C22×D4×C11C2×C414yes—
40C22×D4×C11D414yes—
41C22×D4×C11Q814yes—
42C22×D4×C11C2312yes—
43C23×C4×C11—28no—
44C23×C4×C11—21no—
45C23×C4×C11—24no—
46C23×C4×C11—44no—
47C23×C4×C11—44no—
48C23×C4×C11D411yescharacteristic
49C23×C4×C11D411yescharacteristic
50C23×C4×C11C2311yescharacteristic
51C23×Dic11—21no—
52C23×Dic11—21no—
53C4×D4×C11—216no—
54C4×D4×C11—28no—
55C4×D4×C11—28no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—22no—
58C2×C11×C4⋊C4D414yes—
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4—28no—
61C2×C11×C22⋊C4—24no—
62C2×C42×C11—22no—
63C2×C42×C11—22no—
64C2×C42×C11D412yes—
65C2×C42×C11C2312yes—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11—22no—
68C2×C4⋊Dic11—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11C2×C414yescomplemented
72C2×C4⋊Dic11C2312yes—
73C2×C4⋊Dic11C2312yes—
74C2×Dic11⋊C4—24no—
75C2×Dic11⋊C4—44no—
76C22×C11⋊C8—22no—
77C22×C11⋊C8—22no—
78C22×C11⋊C8—22no—
79C22×C11⋊C8—22no—
80C22×C11⋊C8—22no—
81C22×C11⋊C8C2×C414yescomplemented
82C22×C11⋊C8C2312yes—
83C22×C11⋊C8C2312yes—
84#66896—28no—
85#66896C2×C4116yescomplemented
86C11⋊#95—24no—
87#66871—28no—
88C2×#1862—111nomaximal, Sylow
89C24×C11—24no—
90C24×C11—24no—
91C24×C11—24no—
92C24×C11—22no—
93C24×C11—42no—
94C24×C11—42no—
95C24×C11—42no—
96C24×C11—42no—
97C24×C11C2×D411yescharacteristic
98C2×D4×C11—28no—
99C2×D4×C11—24no—
100C2×D4×C11—24no—
101C2×D4×C11—28no—
102C2×D4×C11—24no—
103C2×D4×C11—28no—
104C2×D4×C11—22no—
105C2×D4×C11—22no—
106C2×D4×C11—22no—
107C2×D4×C11C4⋊C4116yescomplemented
108C2×D4×C11C22×C414yes—
109C2×D4×C11C2×D414yes—
110C2×D4×C11C2×Q814yes—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—216no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—48no—
120C22×C4×C11—432no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11—48no—
124C22×C4×C11D814yes—
125C22×C4×C11C22×C412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2×D411yescharacteristic
130C22×C4×C11C2×D412yes—
131C22×C4×C11C2×Q812yes—
132C22×C4×C11#4112yes—
133C22×C4×C11#4112yes—
134C22×C4×C11C2411yescharacteristic
135C22×Dic11—24no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—42no—
139C22×Dic11—42no—
140C22×Dic11—42no—
141C22×Dic11—42no—
142C22×Dic11—42no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4C2×D414yes—
146C11×C22⋊C4—216no—
147C42×C11—24no—
148C42×C11—22no—
149C42×C11—22no—
150C4⋊Dic11—24no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—42no—
155C4⋊Dic11C22×C414yescomplemented
156Dic11⋊C4—48no—
157C2×C11⋊C8—28no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—44no—
164C2×C11⋊C8C22×C414yescomplemented
165C22×C4×D4D1111yescharacteristic
166C22×#107—111no—
167C22×#102—111no—
168C22×#102—111no—
169C2×#389—111no—
170#1862—118no—
171C2×#340—111no—
172C2×#336—111no—
173C23×C11—24no—
174C23×C11—24no—
175C23×C11—24no—
176C23×C11—216no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—48no—
182C23×C11—48no—
183C23×C11—48no—
184C23×C11—48no—
185C23×C11—48no—
186C23×C11—48no—
187C23×C11C4×D412yes—
188C23×C11#12012yes—
189C23×C11C22⋊Q812yes—
190C23×C11C2×D812yes—
191C23×C11#13512yes—
192C23×C11AGL(1,ℤ/8)12yes—
193C23×C11#13712yes—
194C23×C11C22×D411yescharacteristic
195D4×C11—24no—
196D4×C11—24no—
197D4×C11—24no—
198D4×C11—216no—
199D4×C11C2×C4⋊C418yescomplemented
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—28no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—432no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—48no—
211C2×C4×C11—44no—
212C2×C4×C11C2×C4⋊C414yes—
213C2×C4×C11C4×D414yes—
214C2×C4×C11C4×D412yes—
215C2×C4×C11#12012yes—
216C2×C4×C11C22⋊Q814yes—
217C2×C4×C11C22⋊Q812yes—
218C2×C4×C11#12314yes—
219C2×C4×C11C2×D814yes—
220C2×C4×C11C23×C411yescharacteristic
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D411yescharacteristic
223C2×C4×C11C22×Q811yescharacteristic
224C2×C4×C11C2×#4111yescharacteristic
225C2×C4×C11C2×#4111yescharacteristic
226C2×Dic11—24no—
227C2×Dic11—42no—
228C2×Dic11—42no—
229C2×Dic11—48no—
230C2×Dic11—42no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233C2×Dic11—84no—
234C11⋊C8—24no—
235C11⋊C8—42no—
236C23×D4C2×D1111yescharacteristic
237C24×C4—21no—
238C23×C8—111no—
239C23×C8—111no—
240C2×C4×D4—24no—
241C2×C4×D4—24no—
242C2×C4×D4—22no—
243C2×C4×D4C2×D1114yes—
244C22×C4⋊C4—111no—
245C22×C4⋊C4—111no—
246C22×C4⋊C4—221no—
247C22×C4⋊C4C2×D1111yescharacteristic
248C22×C22⋊C4—21no—
249C22×C42C2×D1111yescharacteristic
250C2×#107—114no—
251C2×#107—224no—
252C2×#102—114no—
253C2×#102—118no—
254C2×#102—114no—
255C2×#102—224no—
256#389—114no—
257#389—222no—
258C2×#95—221no—
259#340—114no—
260#336—114no—
261C22×C11—28no—
262C22×C11—44no—
263C22×C11—432no—
264C22×C11—44no—
265C22×C11—44no—
266C22×C11—44no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11#38514yes—
270C22×C11C4×D814yes—
271C22×C11#44014yes—
272C22×C11#44714yes—
273C22×C11#45214yes—
274C22×C11#47414yes—
275C22×C11#47814yes—
276C22×C11C2×C4×D411yescharacteristic
277C22×C11C2×#12011yescharacteristic
278C22×C11C2×C22⋊Q811yescharacteristic
279C22×C11C22×D811yescharacteristic
280C22×C11C2×#13511yescharacteristic
281C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
282C22×C11C2×#13711yescharacteristic
283C4×C11—24no—
284C4×C11—44no—
285C4×C11—42no—
286C4×C11#38514yes—
287C4×C11C22×C4⋊C411yescharacteristic
288C4×C11C2×C4×D411yescharacteristic
289C4×C11C2×C22⋊Q811yescharacteristic
290C4×C11C2×#12311yescharacteristic
291Dic11—44no—
292Dic11—82no—
293C25—21no—
294C22×D4—22no—
295C22×D4—22no—
296C22×D4—21no—
297C22×D4—22no—
298C22×D4Dic2214yes—
299C22×D4C4×D1114yes—
300C22×D4C22⋊D1114yes—
301C22×D4C22×D1112yes—
302C23×C4—28no—
303C23×C4—21no—
304C23×C4—24no—
305C23×C4—44no—
306C23×C4—44no—
307C23×C4—221no—
308C23×C4—221no—
309C23×C4C22⋊D1111yescharacteristic
310C23×C4C22⋊D1111yescharacteristic
311C23×C4C22×D1111yescharacteristic
312C22×C8—114no—
313C22×C8—112no—
314C22×C8—112no—
315C22×C8—222no—
316C22×C8—222no—
317C22×C8—222no—
318C22×C8—222no—
319C22×C8—222no—
320C4×D4—216no—
321C4×D4—28no—
322C4×D4—28no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—22no—
325C2×C4⋊C4—114no—
326C2×C4⋊C4—112no—
327C2×C4⋊C4—112no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—221no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4—222no—
332C2×C4⋊C4—221no—
333C2×C4⋊C4—224no—
334C2×C4⋊C4—444no—
335C2×C4⋊C4C22⋊D1114yes—
336C2×C4⋊C4C22×D1112yes—
337C2×C22⋊C4—28no—
338C2×C22⋊C4—24no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42C22⋊D1112yes—
342C2×C42C22×D1112yes—
343#107—228no—
344#102—1116no—
345#102—228no—
346#95—224no—
347C2×C11—48no—
348C2×C11#186218yescomplemented
349C2×C11C2×#38511yescharacteristic
350C2×C11C2×C4×D811yescharacteristic
351C2×C11C2×#44011yescharacteristic
352C2×C11C2×#44711yescharacteristic
353C2×C11C2×#45211yescharacteristic
354C2×C11C2×#47411yescharacteristic
355C2×C11C2×#47811yescharacteristic
356C24—24no—
357C24—24no—
358C24—24no—
359C24—22no—
360C24—42no—
361C24—42no—
362C24—42no—
363C24—42no—
364C24C2×C22⋊D1111yescharacteristic
365C2×D4—28no—
366C2×D4—24no—
367C2×D4—28no—
368C2×D4—24no—
369C2×D4—28no—
370C2×D4—24no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4Dic11⋊C4116yescomplemented
375C2×D4C2×Dic2214yes—
376C2×D4C2×C4×D1114yes—
377C2×D4C2×C22⋊D1114yes—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—216no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—22no—
386C22×C4—48no—
387C22×C4—432no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—48no—
391C22×C4—224no—
392C22×C4—222no—
393C22×C4—222no—
394C22×C4—442no—
395C22×C4—442no—
396C22×C4—442no—
397C22×C4—442no—
398C22×C4—442no—
399C22×C4#432314yes—
400C22×C4C2×Dic2212yes—
401C22×C4C2×C4×D1112yes—
402C22×C4#433912yes—
403C22×C4#433912yes—
404C22×C4C2×C22⋊D1112yes—
405C22×C4C2×C22⋊D1112yes—
406C22×C4C2×C22⋊D1112yes—
407C22×C4C2×C22⋊D1111yescharacteristic
408C22×C4C2×C22⋊D1112yes—
409C22×C4C23×D1111yescharacteristic
410C2×C8—114no—
411C2×C8—228no—
412C2×C8—222no—
413C2×C8—222no—
414C2×C8—222no—
415C2×C8—222no—
416C2×C8—222no—
417C2×C8—444no—
418C4⋊C4—24no—
419C4⋊C4—22no—
420C4⋊C4—114no—
421C4⋊C4—224no—
422C4⋊C4—222no—
423C4⋊C4—222no—
424C4⋊C4—222no—
425C4⋊C4—448no—
426C4⋊C4—442no—
427C4⋊C4C2×C22⋊D1114yes—
428C22⋊C4—216no—
429C42—24no—
430C42—22no—
431C42—22no—
432C11C2×#186211yescharacteristic, complemented, Sylow
433C23—24no—
434C23—24no—
435C23—216no—
436C23—24no—
437C23—42no—
438C23—42no—
439C23—48no—
440C23—42no—
441C23—42no—
442C23—48no—
443C23—48no—
444C23—48no—
445C23—48no—
446C23—48no—
447C23#6697712yes—
448C23C4×C22⋊D1112yes—
449C23C2×#432312yes—
450C23#6698512yes—
451C23#6700312yes—
452C23#6700412yes—
453C23#6700612yes—
454C23C22×C22⋊D1111yescharacteristic
455D4—24no—
456D4—24no—
457D4—24no—
458D4—216no—
459D4C2×Dic11⋊C418yescomplemented
460C2×C4—22no—
461C2×C4—28no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—432no—
468C2×C4—42no—
469C2×C4—42no—
470C2×C4—48no—
471C2×C4—44no—
472C2×C4—224no—
473C2×C4—442no—
474C2×C4—442no—
475C2×C4—448no—
476C2×C4—442no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—884no—
480C2×C4C2×Dic11⋊C414yes—
481C2×C4#6697714yes—
482C2×C4#6697712yes—
483C2×C4C4×C22⋊D1114yes—
484C2×C4C4×C22⋊D1112yes—
485C2×C4#6698214yes—
486C2×C4C2×#432314yes—
487C2×C4#6700612yes—
488C2×C4C22×Dic2211yescharacteristic
489C2×C4C22×C4×D1111yescharacteristic
490C2×C4C2×#433911yescharacteristic
491C2×C4C2×#433911yescharacteristic
492C2×C4C22×C22⋊D1111yescharacteristic
493C2×C4C22×C22⋊D1111yescharacteristic
494C8—224no—
495C8—442no—
496C22—28no—
497C22—44no—
498C22—432no—
499C22—44no—
500C22—44no—
501C22—44no—
502C22—44no—
503C22—44no—
504C22#1062262014yes—
505C22#1062262214yes—
506C22C4×#432314yes—
507C22#1062263114yes—
508C22#1062282314yes—
509C22#1062283014yes—
510C22#1062285214yes—
511C22C2×#6697711yescharacteristic
512C22C2×C4×C22⋊D1111yescharacteristic
513C22C22×#432311yescharacteristic
514C22C2×#6698511yescharacteristic
515C22C2×#6700311yescharacteristic
516C22C2×#6700411yescharacteristic
517C22C2×#6700611yescharacteristic
518C4—24no—
519C4—44no—
520C4—42no—
521C4—444no—
522C4—882no—
523C4#1062282314yes—
524C4C22×Dic11⋊C411yescharacteristic
525C4C2×#6697711yescharacteristic
526C4C2×C4×C22⋊D1111yescharacteristic
527C4C2×#6698211yescharacteristic
528C2—48no—
529C2#1306886318yesdirect product factor
530C2C2×#1062282311yescharacteristic
531C2C2×C4×#432311yescharacteristic
532C2C2×#1062263111yescharacteristic
533C2C2×#1062283011yescharacteristic
534C2C2×#1062285211yescharacteristic
535C2C2×#1062262011yescharacteristic
536C2C2×#1062262211yescharacteristic
subgroupG/H
centerC24C2×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC22×C4×D4×C11C2
socleC24×C11C2×D4
prime radicalC23×D4×C11C22
cosocleC22×C4×C11C24
hypercenterC22×C4×D4D11
hypocenterC11C2×#1862
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66871C2semidirect
4. C2×#10622541C2semidirect
5. #13068863C2direct (N × H)
6. C2×#10622167C2semidirect
7. C2×#10622162C2semidirect
24. C2×#66896C4semidirect
29. C2×#66871C22semidirect
31. #10622541C22semidirect
32. #10622167C22semidirect
33. #10622162C22semidirect
71. C2×C4⋊Dic11C2×C4semidirect
81. C22×C11⋊C8C2×C4semidirect
85. #66896C2×C4semidirect
107. C2×D4×C11C4⋊C4semidirect
155. C4⋊Dic11C22×C4semidirect
164. C2×C11⋊C8C22×C4semidirect
199. D4×C11C2×C4⋊C4semidirect
348. C2×C11#1862semidirect
374. C2×D4Dic11⋊C4semidirect
432. C11C2×#1862semidirect
459. D4C2×Dic11⋊C4semidirect
529. C2#13068863direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#668712
C22×#668962
C2×#106225412
#130688632
C2×#106221672
C2×#106221622
C22×C4×D4×C112
C2×#186211