Finite Group Databasebeta

← C2×#13068876 #14754693

Subgroups — C2×#13068876 #14754693

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×C4×D44C211yesmaximal, characteristic
2C22×#66872C211yesmaximal, characteristic, complemented
3C22×#66873C211yesmaximal, characteristic
4C22×#66873C211yesmaximal, characteristic
5#13068876C218yesmaximal, direct product factor
6C2×#10622167C211yesmaximal, characteristic, complemented
7C2×#10622162C211yesmaximal, characteristic, complemented
8C2×C11×#389C211yesmaximal, characteristic, complemented
9C23×D44C2211yescharacteristic
10C23×C4×D11—21no—
11C22×C11×C4⋊C4—21no—
12C22×C11×C4⋊C4C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C42×C11C2211yescharacteristic
15C22×(C2×D11)⋊C4—21no—
16C22×C4⋊Dic11C2211yescharacteristic
17C23×C11⋊C8C2211yescharacteristic
18C23×C11⋊C8C2211yescharacteristic
19C2×C4×D44—24no—
20C2×C4×D44—22no—
21C2×C4×D44—24no—
22C2×C4×D44C2214yes—
23C11×#389—22no—
24C11×#389C2214yescomplemented
25C2×C11×#95—21no—
26C2×#66873—24no—
27C2×#66873C418yescomplemented
28C2×#66873C2214yes—
29C2×#66873C2214yes—
30C2×#66872—24no—
31C2×#66872C2214yescomplemented
32#10622167C2214yescomplemented
33#10622162C2214yescomplemented
34C24×D11—21no—
35C23×C4×C11—21no—
36C23×C4×C11—21no—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×Dic11—21no—
41C22×D44—22no—
42C22×D44—21no—
43C22×D44—22no—
44C22×D44—22no—
45C22×D44C2×C414yes—
46C22×D44D414yes—
47C22×D44Q814yes—
48C22×D44C2312yes—
49C22×C4×D11—28no—
50C22×C4×D11—24no—
51C22×C4×D11—44no—
52C22×C4×D11—44no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—22no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—22no—
57C2×C11×C4⋊C4—24no—
58C2×C11×C4⋊C4—21no—
59C2×C11×C4⋊C4—44no—
60C2×C11×C4⋊C4C2×C414yescomplemented
61C2×C11×C4⋊C4C2312yes—
62C2×C11×C4⋊C4C2312yes—
63C2×C42×C11—22no—
64C2×C42×C11—22no—
65C2×C42×C11D412yes—
66C2×C42×C11C2312yes—
67C2×(C2×D11)⋊C4—28no—
68C2×(C2×D11)⋊C4—24no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11D414yes—
72C2×C4⋊Dic11C2312yes—
73C22×C11⋊C8—22no—
74C22×C11⋊C8—22no—
75C22×C11⋊C8—22no—
76C22×C11⋊C8—22no—
77C22×C11⋊C8—22no—
78C22×C11⋊C8C2×C414yescomplemented
79C22×C11⋊C8C2312yes—
80C22×C11⋊C8C2312yes—
81C4×D44—216no—
82C4×D44—28no—
83C4×D44—28no—
84C11×#95—24no—
85#66873—28no—
86#66873C2×C4116yescomplemented
87#66872—28no—
88C2×#1864—111nomaximal, Sylow
89C24×C11C2×D411yescharacteristic
90C23×D11—24no—
91C23×D11—24no—
92C23×D11—24no—
93C23×D11—22no—
94C23×D11—42no—
95C23×D11—42no—
96C23×D11—42no—
97C23×D11—42no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—24no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11SD1614yes—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×Q812yes—
119C22×C4×C11#4112yes—
120C22×C4×C11#4112yes—
121C22×C4×C11C2411yescharacteristic
122C22×Dic11—24no—
123C22×Dic11—22no—
124C22×Dic11—42no—
125C22×Dic11—42no—
126C2×D44—28no—
127C2×D44—24no—
128C2×D44—24no—
129C2×D44—28no—
130C2×D44—24no—
131C2×D44—28no—
132C2×D44—22no—
133C2×D44—22no—
134C2×D44—22no—
135C2×D44C4⋊C4116yescomplemented
136C2×D44C22×C414yes—
137C2×D44C2×D414yes—
138C2×D44C2×Q814yes—
139C2×C4×D11—216no—
140C2×C4×D11—48no—
141C2×C4×D11—432no—
142C2×C4×D11—48no—
143C11×C4⋊C4—24no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—48no—
148C11×C4⋊C4—42no—
149C11×C4⋊C4C22×C414yescomplemented
150C42×C11—24no—
151C42×C11—22no—
152C42×C11—22no—
153(C2×D11)⋊C4—216no—
154C4⋊Dic11—24no—
155C4⋊Dic11—22no—
156C4⋊Dic11C2×D414yes—
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×D4—111no—
166C22×#106—111no—
167C22×#102—111no—
168C22×#102—111no—
169C2×#389D1111yescharacteristic, complemented
170#1864—118no—
171C2×#340—111no—
172C2×#336—111no—
173C23×C11C4×D412yes—
174C23×C11#12012yes—
175C23×C11C22⋊Q812yes—
176C23×C11C2×SD1612yes—
177C23×C11#13512yes—
178C23×C11AGL(1,ℤ/8)12yes—
179C23×C11AGL(1,ℤ/8)12yes—
180C23×C11C22×D411yescharacteristic
181C22×D11—24no—
182C22×D11—24no—
183C22×D11—24no—
184C22×D11—216no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—48no—
190C22×D11—48no—
191C22×D11—48no—
192C22×D11—48no—
193C22×D11—48no—
194C22×D11—48no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—28no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—42no—
203C2×C4×C11—42no—
204C2×C4×C11—48no—
205C2×C4×C11—44no—
206C2×C4×C11—42no—
207C2×C4×C11—42no—
208C2×C4×C11—42no—
209C2×C4×C11—84no—
210C2×C4×C11C2×C4⋊C414yes—
211C2×C4×C11C4×D414yes—
212C2×C4×C11C4×D412yes—
213C2×C4×C11#12012yes—
214C2×C4×C11C22⋊Q814yes—
215C2×C4×C11C22⋊Q812yes—
216C2×C4×C11#12314yes—
217C2×C4×C11C2×SD1614yes—
218C2×C4×C11C23×C411yescharacteristic
219C2×C4×C11C22×D411yescharacteristic
220C2×C4×C11C22×D411yescharacteristic
221C2×C4×C11C22×Q811yescharacteristic
222C2×C4×C11C2×#4111yescharacteristic
223C2×C4×C11C2×#4111yescharacteristic
224C2×Dic11—24no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—48no—
228D44—24no—
229D44—24no—
230D44—24no—
231D44—216no—
232D44C2×C4⋊C418yescomplemented
233C4×D11—432no—
234C11⋊C8—24no—
235C11⋊C8—42no—
236C23×D4—111no—
237C24×C4—221no—
238C23×C8—111no—
239C23×C8—111no—
240C2×C4×D4—114no—
241C2×C4×D4—224no—
242C2×C4×D4—224no—
243C2×C4×D4—222no—
244C22×C4⋊C4—21no—
245C22×C4⋊C4—111no—
246C22×C4⋊C4C2×D1111yescharacteristic
247C22×C4⋊C4C2×D1111yescharacteristic
248C22×C22⋊C4—221no—
249C22×C42C2×D1111yescharacteristic
250C2×#106—114no—
251C2×#106—224no—
252C2×#102—114no—
253C2×#102—118no—
254C2×#102—114no—
255C2×#102—224no—
256#389—22no—
257#389C2×D1114yescomplemented
258C2×#95—21no—
259#340—114no—
260#336—114no—
261C22×C11#38514yes—
262C22×C11C4×SD1614yes—
263C22×C11#44214yes—
264C22×C11#44914yes—
265C22×C11#45014yes—
266C22×C11#47614yes—
267C22×C11#47814yes—
268C22×C11C2×C4×D411yescharacteristic
269C22×C11C2×#12011yescharacteristic
270C22×C11C2×C22⋊Q811yescharacteristic
271C22×C11C22×SD1611yescharacteristic
272C22×C11C2×#13511yescharacteristic
273C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
274C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
275C2×D11—28no—
276C2×D11—44no—
277C2×D11—432no—
278C2×D11—44no—
279C2×D11—44no—
280C2×D11—44no—
281C2×D11—44no—
282C2×D11—44no—
283C4×C11—24no—
284C4×C11—44no—
285C4×C11—42no—
286C4×C11—82no—
287C4×C11#38514yes—
288C4×C11C22×C4⋊C411yescharacteristic
289C4×C11C2×C4×D411yescharacteristic
290C4×C11C2×C22⋊Q811yescharacteristic
291C4×C11C2×#12311yescharacteristic
292Dic11—44no—
293C25—221no—
294C22×D4—114no—
295C22×D4—114no—
296C22×D4—114no—
297C22×D4—112no—
298C22×D4—222no—
299C22×D4—222no—
300C22×D4—222no—
301C22×D4—221no—
302C23×C4—21no—
303C23×C4—21no—
304C23×C4—228no—
305C23×C4—221no—
306C23×C4—224no—
307C23×C4—444no—
308C23×C4—444no—
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—228no—
321C4×D4—228no—
322C4×D4—2216no—
323C2×C4⋊C4—22no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—22no—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—24no—
328C2×C4⋊C4—21no—
329C2×C4⋊C4—44no—
330C2×C4⋊C4—114no—
331C2×C4⋊C4—112no—
332C2×C4⋊C4—222no—
333C2×C4⋊C4—221no—
334C2×C4⋊C4C4×D1114yescomplemented
335C2×C4⋊C4C22×D1112yes—
336C2×C4⋊C4C22×D1112yes—
337C2×C22⋊C4—228no—
338C2×C22⋊C4—224no—
339C2×C42—22no—
340C2×C42—22no—
341C2×C42C22⋊D1112yes—
342C2×C42C22×D1112yes—
343#106—228no—
344#102—1116no—
345#102—228no—
346#95—24no—
347C2×C11#186418yescomplemented
348C2×C11C2×#38511yescharacteristic
349C2×C11C2×C4×SD1611yescharacteristic
350C2×C11C2×#44211yescharacteristic
351C2×C11C2×#45011yescharacteristic
352C2×C11C2×#44911yescharacteristic
353C2×C11C2×#47611yescharacteristic
354C2×C11C2×#47811yescharacteristic
355D11—48no—
356C24—224no—
357C24—224no—
358C24—224no—
359C24—222no—
360C24—442no—
361C24—442no—
362C24—442no—
363C24—442no—
364C24C2×C22⋊D1111yescharacteristic
365C2×D4—1116no—
366C2×D4—114no—
367C2×D4—114no—
368C2×D4—114no—
369C2×D4—228no—
370C2×D4—228no—
371C2×D4—228no—
372C2×D4—224no—
373C2×D4—224no—
374C2×D4—224no—
375C2×D4—222no—
376C2×D4—222no—
377C2×D4—222no—
378C22×C4—22no—
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—22no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—22no—
385C22×C4—22no—
386C22×C4—42no—
387C22×C4—42no—
388C22×C4—42no—
389C22×C4—42no—
390C22×C4—42no—
391C22×C4—2216no—
392C22×C4—224no—
393C22×C4—222no—
394C22×C4—448no—
395C22×C4—4432no—
396C22×C4—442no—
397C22×C4—442no—
398C22×C4—448no—
399C22×C4#432514yes—
400C22×C4C2×C4×D1112yes—
401C22×C4#433912yes—
402C22×C4D4×D1112yes—
403C22×C4D4×D1112yes—
404C22×C4Q8×D1112yes—
405C22×C4#434312yes—
406C22×C4C2×C22⋊D1112yes—
407C22×C4C2×C22⋊D1112yes—
408C22×C4C2×C22⋊D1111yescharacteristic
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—22no—
421C4⋊C4—22no—
422C4⋊C4—48no—
423C4⋊C4—42no—
424C4⋊C4—114no—
425C4⋊C4—224no—
426C4⋊C4—222no—
427C4⋊C4C2×C4×D1114yescomplemented
428C22⋊C4—2216no—
429C42—24no—
430C42—22no—
431C42—22no—
432C11C2×#186411yescharacteristic, complemented, Sylow
433C23—224no—
434C23—224no—
435C23—224no—
436C23—2216no—
437C23—442no—
438C23—442no—
439C23—442no—
440C23—442no—
441C23—448no—
442C23—448no—
443C23—448no—
444C23—448no—
445C23—448no—
446C23—448no—
447C23C4×C22⋊D1112yes—
448C23#6698512yes—
449C23#6699012yes—
450C23C2×#432512yes—
451C23#6699912yes—
452C23#6700212yes—
453C23#6700312yes—
454C23C22×C22⋊D1111yescharacteristic
455D4—118no—
456D4—224no—
457D4—224no—
458D4—224no—
459D4—2216no—
460C2×C4—22no—
461C2×C4—22no—
462C2×C4—28no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—42no—
468C2×C4—42no—
469C2×C4—48no—
470C2×C4—44no—
471C2×C4—42no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—84no—
475C2×C4—224no—
476C2×C4—4432no—
477C2×C4—442no—
478C2×C4—442no—
479C2×C4—448no—
480C2×C4C4⋊C4×D1114yes—
481C2×C4#6694614yes—
482C2×C4#6694714yes—
483C2×C4#6694914yes—
484C2×C4C4×C22⋊D1112yes—
485C2×C4#6699012yes—
486C2×C4C2×#432514yes—
487C2×C4#6699912yes—
488C2×C4C22×C4×D1111yescharacteristic
489C2×C4C2×#433911yescharacteristic
490C2×C4C2×D4×D1111yescharacteristic
491C2×C4C2×D4×D1111yescharacteristic
492C2×C4C2×Q8×D1111yescharacteristic
493C2×C4C2×#434311yescharacteristic
494C8—224no—
495C8—442no—
496C22—228no—
497C22—444no—
498C22—444no—
499C22—4432no—
500C22—444no—
501C22—444no—
502C22—444no—
503C22—444no—
504C22#1062260214yes—
505C22#1062262714yes—
506C22C4×#432514yes—
507C22#1062265014yes—
508C22#1062265914yes—
509C22#1062267914yes—
510C22#1062269714yes—
511C22C2×C4×C22⋊D1111yescharacteristic
512C22C2×#6698511yescharacteristic
513C22C2×#6699011yescharacteristic
514C22C22×#432511yescharacteristic
515C22C2×#6699911yescharacteristic
516C22C2×#6700211yescharacteristic
517C22C2×#6700311yescharacteristic
518C4—24no—
519C4—42no—
520C4—44no—
521C4—82no—
522C4—444no—
523C4#1062260214yes—
524C4C2×C4⋊C4×D1111yescharacteristic
525C4C2×#6694611yescharacteristic
526C4C2×#6694711yescharacteristic
527C4C2×#6694911yescharacteristic
528C2—448no—
529C2#1306887618yesdirect product factor
530C2C2×#1062260211yescharacteristic
531C2C2×C4×#432511yescharacteristic
532C2C2×#1062262711yescharacteristic
533C2C2×#1062265911yescharacteristic
534C2C2×#1062265011yescharacteristic
535C2C2×#1062269711yescharacteristic
536C2C2×#1062267911yescharacteristic
subgroupG/H
centerC24C2×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#389C2
socleC24×C11C2×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenterC2×#389D11
hypocenterC11C2×#1864
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C22×#66872C2semidirect
5. #13068876C2direct (N × H)
6. C2×#10622167C2semidirect
7. C2×#10622162C2semidirect
8. C2×C11×#389C2semidirect
24. C11×#389C22semidirect
27. C2×#66873C4semidirect
31. C2×#66872C22semidirect
32. #10622167C22semidirect
33. #10622162C22semidirect
60. C2×C11×C4⋊C4C2×C4semidirect
78. C22×C11⋊C8C2×C4semidirect
86. #66873C2×C4semidirect
135. C2×D44C4⋊C4semidirect
149. C11×C4⋊C4C22×C4semidirect
164. C2×C11⋊C8C22×C4semidirect
169. C2×#389D11semidirect
232. D44C2×C4⋊C4semidirect
257. #389C2×D11semidirect
334. C2×C4⋊C4C4×D11semidirect
347. C2×C11#1864semidirect
427. C4⋊C4C2×C4×D11semidirect
432. C11C2×#1864semidirect
529. C2#13068876direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D442
C22×#668722
C22×#668732
#130688762
C2×#106221672
C2×#106221622
C2×C11×#3892
C2×#186411