Finite Group Databasebeta

← C2×#13067897 #14729554

Subgroups — C2×#13067897 #14729554

Order 2816.

1238 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623257C211yesmaximal, characteristic
2C2×#10622700C211yesmaximal, characteristic, complemented
3C2×#10622696C211yesmaximal, characteristic, complemented
4#13067897C218yesmaximal, direct product factor
5C2×#10622185C211yesmaximal, characteristic, complemented
6C2×#10622097C211yesmaximal, characteristic, complemented
7C2×#10622097C211yesmaximal, characteristic, complemented
8C2×C11×#498C211yesmaximal, characteristic, complemented
9C22×#4343—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66999—21no—
13C22×#4325—21no—
14#10623257—22no—
15#10623257—22no—
16#10623257—22no—
17#10623257C2214yes—
18C2×#66948—21no—
19C2×#66947—22no—
20C2×C4⋊C4×D11—21no—
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#498—22no—
24C11×#498C2214yescomplemented
25C2×C11×#106—22no—
26C2×C4×C8×C11C2211yescharacteristic
27C2×#66899—21no—
28#10622700—22no—
29#10622700C2214yescomplemented
30#10622696—22no—
31#10622696C2214yescomplemented
32C2×#66873—21no—
33C2×#66871—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622185C2214yescomplemented
37#10622097C2214yescomplemented
38#10622097C2214yescomplemented
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C2×#4343—24no—
42C2×#4343—24no—
43C2×#4343—44no—
44C2×#4343—44no—
45C22×D44—22no—
46C22×D44D411yescharacteristic
47C22×D44D411yescharacteristic
48C22×C4×D11—22no—
49C22×C4×D11—21no—
50C22×C4×D11—21no—
51C22×C8×C11—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8—21no—
57C11×C4⋊Q8D412yes—
58C11×C4⋊Q8C2312yes—
59C11×C4⋊Q8C2312yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4D412yes—
64C2×C42×C11C2311yescharacteristic
65#66999—24no—
66#66999—24no—
67C2×#4325—24no—
68C2×#4325—44no—
69C2×(C2×D11)⋊C4—22no—
70C2×(C2×D11)⋊C4—21no—
71C2×(C2×D11)⋊C4—21no—
72C2×C4⋊Dic11D411yescharacteristic
73C2×C4⋊Dic11D411yescharacteristic
74C2×Dic11⋊C4—22no—
75C22×C11⋊C8—21no—
76C22×C11⋊C8—21no—
77#66948—24no—
78#66948—24no—
79#66947—28no—
80#66947—28no—
81C4⋊C4×D11—24no—
82C4⋊C4×D11—24no—
83C4×D44—21no—
84C4×D44—21no—
85C4×D44—21no—
86C4×D44—21no—
87C4×D44D412yes—
88C4×D44D412yes—
89C4×D44C2312yes—
90C4×D44C2312yes—
91C11×#106—28no—
92C4×C8×C11—21no—
93C4×C8×C11C2312yes—
94#66899—24no—
95#66873—24no—
96#66871—24no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)C2312yes—
100C4⋊(C11⋊C8)C2312yes—
101C2×#1654—111nomaximal, Sylow
102C23×D11—21no—
103C23×D11—21no—
104C2×Q8×C11—22no—
105C2×Q8×C11—22no—
106C2×Q8×C11—22no—
107C2×Q8×C11—41no—
108C2×Q8×C11—42no—
109C2×Q8×C11—42no—
110C2×Q8×C11—42no—
111C2×Q8×C11—42no—
112C22×C4×C11—22no—
113C22×C4×C11—41no—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D411yescharacteristic
116C22×C4×C11C2×D411yescharacteristic
117C22×Dic11—21no—
118C22×Dic11—21no—
119#4343—48no—
120#4343—416no—
121#4343—48no—
122C2×D44—28no—
123C2×D44—21no—
124C2×D44—21no—
125C2×D44—22no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44—48no—
129C2×D44SD1614yescomplemented
130C2×D44C2×D412yes—
131C2×D44C2×D412yes—
132C2×C4×D11—28no—
133C2×C4×D11—22no—
134C2×C4×D11—22no—
135C2×C4×D11—22no—
136C2×C4×D11—22no—
137C2×C4×D11—48no—
138C2×C4×D11—42no—
139C2×C4×D11—42no—
140C2×C4×D11—42no—
141C2×C4×D11—42no—
142C2×C8×C11—24no—
143C2×C8×C11—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—22no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4—22no—
148C11×C4⋊C4—22no—
149C11×C4⋊C4—41no—
150C11×C4⋊C4—41no—
151C11×C4⋊C4C2×D414yes—
152C42×C11C2×D411yescharacteristic
153C42×C11C2×D411yescharacteristic
154C42×C11C2×D411yescharacteristic
155C42×C11C2411yescharacteristic
156#4325—48no—
157(C2×D11)⋊C4—28no—
158(C2×D11)⋊C4—22no—
159(C2×D11)⋊C4—22no—
160(C2×D11)⋊C4—22no—
161(C2×D11)⋊C4—22no—
162C4⋊Dic11—21no—
163C4⋊Dic11—21no—
164C4⋊Dic11C2×D412yes—
165C4⋊Dic11C2×D412yes—
166Dic11⋊C4—28no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—22no—
169C2×C11⋊C8—42no—
170C2×C11⋊C8—42no—
171C2×#547—111no—
172C2×#498D1111yescharacteristic, complemented
173C2×#474—111no—
174C2×#461—111no—
175#1654—118no—
176C2×#332—111no—
177C2×D4⋊C8—111no—
178C2×D4⋊C8—111no—
179C23×C11#12011yescharacteristic
180C22×D11—22no—
181C22×D11—24no—
182C22×D11—22no—
183C22×D11—42no—
184C22×D11—42no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—42no—
188Q8×C11—42no—
189Q8×C11—42no—
190Q8×C11—44no—
191Q8×C11—42no—
192Q8×C11—42no—
193Q8×C11—82no—
194C2×C4×C11—22no—
195C2×C4×C11—24no—
196C2×C4×C11—44no—
197C2×C4×C11—42no—
198C2×C4×C11—82no—
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11#12011yescharacteristic
202C2×C4×C11C2×SD1612yes—
203C2×C4×C11#13512yes—
204C2×C4×C11AGL(1,ℤ/8)12yes—
205C2×C4×C11AGL(1,ℤ/8)12yes—
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C2×C4×C11C22×D411yescharacteristic
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213D44—22no—
214D44—22no—
215D44—22no—
216D44—24no—
217D44—416no—
218D44—42no—
219D44C2×SD1614yescomplemented
220C4×D11—416no—
221C4×D11—42no—
222C4×D11—42no—
223C4×D11—42no—
224C4×D11—42no—
225C4×D11—44no—
226C4×D11—44no—
227C8×C11—24no—
228C11⋊C8—42no—
229C11⋊C8—42no—
230C22×#41—221no—
231C22×SD16—221no—
232#547—114no—
233#547—222no—
234#547—222no—
235#547—222no—
236C2×C4⋊Q8C2×D1111yescharacteristic
237C2×C4⋊Q8C2×D1111yescharacteristic
238C2×#123—222no—
239C2×C22⋊Q8—221no—
240C2×#121—221no—
241C2×C4×D4—111no—
242C2×C4×D4—111no—
243C22×C4⋊C4—221no—
244#498—22no—
245#498C2×D1114yescomplemented
246#474—114no—
247#474—222no—
248#461—114no—
249#461—222no—
250C2×#107—221no—
251C2×#106—22no—
252C2×C4⋊C8—111no—
253C2×C4⋊C8—111no—
254C2×#103—221no—
255C2×#102—221no—
256C2×C4×C8C2×D1111yescharacteristic
257#332—114no—
258D4⋊C8—114no—
259D4⋊C8—114no—
260C22×C11#44912yes—
261C22×C11#45012yes—
262C22×C11#45612yes—
263C22×C11C2×#12011yescharacteristic
264C2×D11—24no—
265C2×D11—48no—
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—42no—
269C2×D11—42no—
270C2×D11—42no—
271C2×D11—84no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—44no—
275C4×C11—82no—
276C4×C11#44912yes—
277C4×C11#45012yes—
278C4×C11C22×SD1611yescharacteristic
279C4×C11C2×#13511yescharacteristic
280C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
281C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
282Dic11—42no—
283Dic11—42no—
284C2×#41—224no—
285C2×#41—224no—
286C2×#41—444no—
287C2×#41—444no—
288C22×Q8—21no—
289C22×Q8—21no—
290C22×D4—111no—
291C22×D4—111no—
292C22×D4—222no—
293C23×C4—222no—
294C23×C4—221no—
295C23×C4—221no—
296C2×SD16—224no—
297C2×SD16—444no—
298C22×C8—21no—
299C22×C8—221no—
300C22×C8—221no—
301C4⋊Q8—21no—
302C4⋊Q8—21no—
303C4⋊Q8—21no—
304C4⋊Q8—21no—
305C4⋊Q8—21no—
306C4⋊Q8C22⋊D1112yes—
307C4⋊Q8C22×D1112yes—
308C4⋊Q8C22×D1112yes—
309#123—228no—
310#123—228no—
311C22⋊Q8—224no—
312C22⋊Q8—224no—
313#121—224no—
314#121—224no—
315C4×D4—112no—
316C4×D4—112no—
317C4×D4—112no—
318C4×D4—112no—
319C4×D4—221no—
320C4×D4—221no—
321C4×D4—221no—
322C4×D4—221no—
323C2×C4⋊C4—21no—
324C2×C4⋊C4—21no—
325C2×C4⋊C4—21no—
326C2×C4⋊C4—111no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—224no—
329C2×C4⋊C4—224no—
330C2×C4⋊C4—222no—
331C2×C4⋊C4C22⋊D1112yes—
332C2×C22⋊C4—222no—
333C2×C22⋊C4—221no—
334C2×C22⋊C4—221no—
335C2×C42C22×D1111yescharacteristic
336#107—224no—
337#106—28no—
338C4⋊C8—112no—
339C4⋊C8—112no—
340C4⋊C8—221no—
341C4⋊C8—221no—
342#103—224no—
343#102—224no—
344C4×C8—21no—
345C4×C8C22×D1112yes—
346C2×C11#165414yescomplemented
347C2×C11C2×#45011yescharacteristic
348C2×C11C2×#44911yescharacteristic
349C2×C11C2×#45611yescharacteristic
350D11—44no—
351D11—82no—
352C24—221no—
353C24—221no—
354#41—448no—
355#41—448no—
356#41—4416no—
357C2×Q8—22no—
358C2×Q8—22no—
359C2×Q8—22no—
360C2×Q8—42no—
361C2×Q8—42no—
362C2×Q8—41no—
363C2×Q8—42no—
364C2×Q8—42no—
365C2×D4—114no—
366C2×D4—112no—
367C2×D4—112no—
368C2×D4—228no—
369C2×D4—222no—
370C2×D4—222no—
371C2×D4—222no—
372C2×D4—221no—
373C2×D4—221no—
374C2×D4—448no—
375C22×C4—22no—
376C22×C4—41no—
377C22×C4—228no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4—222no—
383C22×C4—222no—
384C22×C4—448no—
385C22×C4—442no—
386C22×C4—442no—
387C22×C4—442no—
388C22×C4—442no—
389C22×C4D4×D1111yescharacteristic
390C22×C4D4×D1111yescharacteristic
391C22×C4C2×C22⋊D1111yescharacteristic
392SD16—448no—
393C2×C8—24no—
394C2×C8—22no—
395C2×C8—222no—
396C2×C8—222no—
397C2×C8—442no—
398C2×C8—442no—
399C4⋊C4—22no—
400C4⋊C4—22no—
401C4⋊C4—22no—
402C4⋊C4—22no—
403C4⋊C4—22no—
404C4⋊C4—41no—
405C4⋊C4—41no—
406C4⋊C4—112no—
407C4⋊C4—112no—
408C4⋊C4—228no—
409C4⋊C4—221no—
410C4⋊C4—221no—
411C4⋊C4C2×C22⋊D1114yes—
412C22⋊C4—228no—
413C22⋊C4—222no—
414C22⋊C4—222no—
415C22⋊C4—222no—
416C22⋊C4—222no—
417C42D4×D1111yescharacteristic
418C42D4×D1111yescharacteristic
419C42C2×C22⋊D1111yescharacteristic
420C42C23×D1111yescharacteristic
421C11C2×#165411yescharacteristic, complemented, Sylow
422C23—224no—
423C23—222no—
424C23—222no—
425C23—442no—
426C23—442no—
427C23—442no—
428C23—442no—
429C23—442no—
430C23#6699011yescharacteristic
431Q8—42no—
432Q8—42no—
433Q8—44no—
434Q8—42no—
435Q8—42no—
436Q8—82no—
437D4—114no—
438D4—222no—
439D4—222no—
440D4—222no—
441D4—224no—
442D4—4416no—
443D4—442no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—44no—
447C2×C4—42no—
448C2×C4—82no—
449C2×C4—222no—
450C2×C4—222no—
451C2×C4—4416no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—444no—
459C2×C4—444no—
460C2×C4SD16×D1112yes—
461C2×C4#6696712yes—
462C2×C4#6696712yes—
463C2×C4#6696912yes—
464C2×C4#6699011yescharacteristic
465C2×C4#6699011yescharacteristic
466C2×C4#6699011yescharacteristic
467C2×C4C2×D4×D1111yescharacteristic
468C2×C4C2×D4×D1111yescharacteristic
469C2×C4C22×C22⋊D1111yescharacteristic
470C8—24no—
471C8—442no—
472C8—442no—
473C22—224no—
474C22—442no—
475C22—448no—
476C22—442no—
477C22—442no—
478C22—442no—
479C22—442no—
480C22—884no—
481C22#1062270812yes—
482C22#1062278212yes—
483C22#1062278512yes—
484C22C2×#6699011yescharacteristic
485C4—21no—
486C4—21no—
487C4—44no—
488C4—82no—
489C4—442no—
490C4—442no—
491C4#1062278212yes—
492C4#1062278512yes—
493C4C2×SD16×D1111yescharacteristic
494C4C2×#6696711yescharacteristic
495C4C2×#6696711yescharacteristic
496C4C2×#6696911yescharacteristic
497C2—444no—
498C2—882no—
499C2#1306789714yesdirect product factor
500C2C2×#1062278211yescharacteristic
501C2C2×#1062278511yescharacteristic
502C2C2×#1062270811yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#498C2
socleC23×C11#120
prime radicalC2×#10623257C2
hypercenterC2×#498D11
hypocenterC11C2×#1654
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
2. C2×#10622700C2semidirect
3. C2×#10622696C2semidirect
4. #13067897C2direct (N × H)
5. C2×#10622185C2semidirect
6. C2×#10622097C2semidirect
7. C2×#10622097C2semidirect
8. C2×C11×#498C2semidirect
24. C11×#498C22semidirect
29. #10622700C22semidirect
31. #10622696C22semidirect
36. #10622185C22semidirect
37. #10622097C22semidirect
38. #10622097C22semidirect
129. C2×D44SD16semidirect
172. C2×#498D11semidirect
219. D44C2×SD16semidirect
245. #498C2×D11semidirect
346. C2×C11#1654semidirect
421. C11C2×#1654semidirect
499. C2#13067897direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232572
C2×#106227002
C2×#106226962
#130678972
C2×#106221852
C2×#106220972
C2×C11×#4982
C2×#165411