Finite Group Databasebeta

← C2×#13067766 #14729477

Subgroups — C2×#13067766 #14729477

Order 2816.

1206 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623082C211yesmaximal, characteristic
2C2×#10622694C211yesmaximal, characteristic, complemented
3C2×#10622697C211yesmaximal, characteristic, complemented
4#13067766C218yesmaximal, direct product factor
5C2×#10622124C211yesmaximal, characteristic, complemented
6C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic, complemented
8C2×C11×#476C211yesmaximal, characteristic, complemented
9C22×#4339—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C4×D4×C11C2211yescharacteristic
12C2×#66991—21no—
13C2×#66977—21no—
14#10623082—22no—
15#10623082—22no—
16#10623082—22no—
17#10623082C2214yes—
18C2×C4⋊C4×D11—21no—
19C2×#66936—22no—
20C2×C4×D44C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C11×#476—22no—
23C11×#476C2214yescomplemented
24C2×C11×#106—21no—
25C2×C11×C4⋊C8C2211yescharacteristic
26C2×C11×#102—21no—
27C2×#66899—22no—
28#10622697—22no—
29#10622697C2214yescomplemented
30#10622694—22no—
31#10622694C2214yescomplemented
32C2×#66873—21no—
33C2×#66872—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36D4⋊(C11⋊C8)C2214yescomplemented
37#10622124C2214yescomplemented
38#10622121C2214yescomplemented
39C22×Q8×C11—21no—
40C22×D4×C11D411yescharacteristic
41C23×C4×C11—21no—
42C22×C22⋊D11—22no—
43C2×#4339—24no—
44C2×#4339—24no—
45C2×#4339—44no—
46C2×#4339—44no—
47C22×D44D411yescharacteristic
48C22×C4×D11—22no—
49C22×C4×D11—21no—
50C22×Dic22—21no—
51C22×C8×C11—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8C2312yes—
56C4×D4×C11—21no—
57C4×D4×C11—21no—
58C4×D4×C11D412yes—
59C4×D4×C11C2312yes—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D411yescharacteristic
63C2×C11×C22⋊C4—21no—
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—22no—
66#66991—24no—
67#66991—24no—
68C2×(C2×D11)⋊C4—21no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11D412yes—
71C2×C4⋊Dic11D411yescharacteristic
72#66977—24no—
73#66977—24no—
74C2×Dic11⋊C4—22no—
75C22×C11⋊C8—21no—
76C22×C11⋊C8—21no—
77C4⋊C4×D11—24no—
78C4⋊C4×D11—24no—
79#66936—28no—
80#66936—28no—
81C4×D44—21no—
82C4×D44—21no—
83C4×D44D412yes—
84C4×D44C2312yes—
85#66922—21no—
86#66922—21no—
87#66922D412yes—
88#66922C2312yes—
89C11×#106—24no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8C2312yes—
92C11×#102—24no—
93#66899—28no—
94#66873—24no—
95#66872—24no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)C2312yes—
98C4×C11⋊C8—21no—
99C4×C11⋊C8C2312yes—
100C2×#1635—111nomaximal, Sylow
101C24×C11—21no—
102C23×D11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—44no—
105C2×Q8×C11—41no—
106C2×D4×C11—21no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11C2×D412yes—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11—41no—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C2×C22⋊D11—28no—
120C2×C22⋊D11—48no—
121C22×Dic11—21no—
122C22×Dic11—22no—
123#4339—48no—
124#4339—416no—
125#4339—48no—
126C2×D44—21no—
127C2×D44—22no—
128C2×D44SD1614yes—
129C2×D44C2×D412yes—
130C2×C4×D11—28no—
131C2×C4×D11—22no—
132C2×C4×D11—22no—
133C2×C4×D11—48no—
134C2×C4×D11—42no—
135C2×C4×D11—42no—
136C2×Dic22—22no—
137C2×Dic22—22no—
138C2×Dic22—42no—
139C2×Dic22—42no—
140C2×C8×C11—22no—
141C2×C8×C11—42no—
142C11×C4⋊C4—21no—
143C11×C4⋊C4—22no—
144C11×C4⋊C4—22no—
145C11×C4⋊C4—41no—
146C11×C4⋊C4—41no—
147C11×C4⋊C4C2×D412yes—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—22no—
150C42×C11C2×D411yescharacteristic
151C42×C11C2×D411yescharacteristic
152C42×C11C2×D411yescharacteristic
153C42×C11C2411yescharacteristic
154C22⋊Dic11—28no—
155(C2×D11)⋊C4—22no—
156(C2×D11)⋊C4—22no—
157C4⋊Dic11—22no—
158C4⋊Dic11—22no—
159C4⋊Dic11—21no—
160C4⋊Dic11—22no—
161C4⋊Dic11C2×D412yes—
162C4⋊Dic11C2×D414yes—
163Dic11⋊C4—28no—
164C2×C11⋊C8—22no—
165C2×C11⋊C8—22no—
166C2×C11⋊C8—42no—
167C2×C11⋊C8—42no—
168C2×#547—111no—
169C2×#487—111no—
170C2×#476—111no—
171C2×#476D1111yescharacteristic, complemented
172#1635—118no—
173C2×#332—111no—
174C2×D4⋊C8—111no—
175C2×D4⋊C8—111no—
176C23×C11—22no—
177C23×C11—42no—
178C23×C11—42no—
179C23×C11—42no—
180C23×C11#12011yescharacteristic
181C22×D11—22no—
182C22×D11—24no—
183C22×D11—42no—
184C22×D11—42no—
185Q8×C11—44no—
186Q8×C11—82no—
187D4×C11—22no—
188D4×C11—22no—
189D4×C11—42no—
190C2×C4×C11—22no—
191C2×C4×C11—22no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—44no—
196C2×C4×C11—42no—
197C2×C4×C11—82no—
198C2×C4×C11#12011yescharacteristic
199C2×C4×C11#12011yescharacteristic
200C2×C4×C11#12011yescharacteristic
201C2×C4×C11C2×SD1612yes—
202C2×C4×C11#13512yes—
203C2×C4×C11AGL(1,ℤ/8)12yes—
204C2×C4×C11#13712yes—
205C2×C4×C11C22×D411yescharacteristic
206C2×C4×C11C22×D411yescharacteristic
207C2×C4×C11C22×D411yescharacteristic
208C22⋊D11—416no—
209C2×Dic11—22no—
210C2×Dic11—24no—
211C2×Dic11—44no—
212C2×Dic11—42no—
213D44—22no—
214D44—24no—
215D44C2×SD1614yes—
216C4×D11—416no—
217C4×D11—42no—
218C4×D11—42no—
219C4×D11—44no—
220Dic22—42no—
221Dic22—42no—
222Dic22—44no—
223C8×C11—42no—
224C11⋊C8—42no—
225C11⋊C8—42no—
226C22×#41—221no—
227#547—114no—
228#547—222no—
229#547—222no—
230#547—222no—
231C2×C4⋊Q8—111no—
232C2×C4⋊Q8C2×D1111yescharacteristic
233C2×#123—222no—
234C2×C22⋊Q8—221no—
235C2×#121—221no—
236C2×C4×D4—111no—
237C2×C4×D4C2×D1111yescharacteristic
238C22×C4⋊C4—221no—
239#487—114no—
240#487—222no—
241#476—22no—
242#476—114no—
243#476—222no—
244#476C2×D1114yescomplemented
245C2×#106—21no—
246C2×#106—221no—
247C2×C4⋊C8—111no—
248C2×C4⋊C8C2×D1111yescharacteristic
249C2×#103—222no—
250C2×#102—21no—
251C2×#102—221no—
252C2×C4×C8—111no—
253#332—114no—
254D4⋊C8—114no—
255D4⋊C8—114no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—84no—
260C22×C11#45012yes—
261C22×C11#45212yes—
262C22×C11#45412yes—
263C22×C11C2×#12011yescharacteristic
264C2×D11—24no—
265C2×D11—48no—
266C2×D11—42no—
267C2×D11—42no—
268C4×C11—21no—
269C4×C11—21no—
270C4×C11—42no—
271C4×C11—82no—
272C4×C11#45012yes—
273C4×C11#45212yes—
274C4×C11C22×SD1611yescharacteristic
275C4×C11C2×#13511yescharacteristic
276C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
277C4×C11C2×#13711yescharacteristic
278Dic11—44no—
279Dic11—42no—
280C2×#41—224no—
281C2×#41—224no—
282C2×#41—444no—
283C2×#41—444no—
284C22×Q8—21no—
285C22×Q8—221no—
286C22×D4—111no—
287C22×D4—222no—
288C22×D4C22⋊D1111yescharacteristic
289C23×C4—21no—
290C23×C4—222no—
291C23×C4—221no—
292C22×C8—21no—
293C22×C8—221no—
294C22×C8—221no—
295C4⋊Q8—21no—
296C4⋊Q8—21no—
297C4⋊Q8—21no—
298C4⋊Q8—112no—
299C4⋊Q8—112no—
300C4⋊Q8—221no—
301C4⋊Q8—221no—
302C4⋊Q8C22×D1112yes—
303#123—228no—
304#123—228no—
305C22⋊Q8—224no—
306C22⋊Q8—224no—
307#121—224no—
308#121—224no—
309C4×D4—21no—
310C4×D4—21no—
311C4×D4—112no—
312C4×D4—112no—
313C4×D4—221no—
314C4×D4—221no—
315C4×D4C22⋊D1112yes—
316C4×D4C22×D1112yes—
317C2×C4⋊C4—21no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—111no—
320C2×C4⋊C4—112no—
321C2×C4⋊C4—224no—
322C2×C4⋊C4—222no—
323C2×C4⋊C4—221no—
324C2×C4⋊C4—224no—
325C2×C4⋊C4C22⋊D1111yescharacteristic
326C2×C22⋊C4—21no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—221no—
329C2×C42C22×D1111yescharacteristic
330#106—24no—
331#106—224no—
332C4⋊C8—21no—
333C4⋊C8—112no—
334C4⋊C8—221no—
335C4⋊C8C22×D1112yes—
336#103—228no—
337#102—24no—
338#102—224no—
339C4×C8—112no—
340C4×C8—221no—
341C2×C11—82no—
342C2×C11#163514yescomplemented
343C2×C11C2×#45011yescharacteristic
344C2×C11C2×#45211yescharacteristic
345C2×C11C2×#45411yescharacteristic
346D11—44no—
347C24—21no—
348C24—221no—
349#41—448no—
350#41—448no—
351#41—4416no—
352C2×Q8—22no—
353C2×Q8—44no—
354C2×Q8—41no—
355C2×Q8—222no—
356C2×Q8—222no—
357C2×Q8—442no—
358C2×Q8—442no—
359C2×D4—21no—
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—114no—
363C2×D4—112no—
364C2×D4—228no—
365C2×D4—222no—
366C2×D4—221no—
367C2×D4—448no—
368C2×D4C2×C22⋊D1112yes—
369C22×C4—21no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—42no—
373C22×C4—42no—
374C22×C4—41no—
375C22×C4—228no—
376C22×C4—221no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—448no—
381C22×C4—442no—
382C22×C4—442no—
383C22×C4D4×D1111yescharacteristic
384C22×C4D4×D1111yescharacteristic
385C22×C4C2×C22⋊D1111yescharacteristic
386C2×C8—22no—
387C2×C8—42no—
388C2×C8—222no—
389C2×C8—222no—
390C2×C8—442no—
391C2×C8—442no—
392C4⋊C4—21no—
393C4⋊C4—22no—
394C4⋊C4—22no—
395C4⋊C4—41no—
396C4⋊C4—41no—
397C4⋊C4—114no—
398C4⋊C4—112no—
399C4⋊C4—228no—
400C4⋊C4—221no—
401C4⋊C4—222no—
402C4⋊C4—222no—
403C4⋊C4—222no—
404C4⋊C4C2×C22⋊D1112yes—
405C22⋊C4—22no—
406C22⋊C4—22no—
407C22⋊C4—228no—
408C22⋊C4—222no—
409C22⋊C4—222no—
410C42D4×D1111yescharacteristic
411C42D4×D1111yescharacteristic
412C42C2×C22⋊D1111yescharacteristic
413C42C23×D1111yescharacteristic
414C11C2×#163511yescharacteristic, complemented, Sylow
415C23—22no—
416C23—42no—
417C23—42no—
418C23—42no—
419C23—224no—
420C23—222no—
421C23—442no—
422C23—442no—
423C23#6699011yescharacteristic
424Q8—44no—
425Q8—82no—
426Q8—442no—
427Q8—442no—
428Q8—444no—
429D4—22no—
430D4—22no—
431D4—42no—
432D4—114no—
433D4—222no—
434D4—224no—
435D4—4416no—
436C2×C4—22no—
437C2×C4—22no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—42no—
441C2×C4—44no—
442C2×C4—42no—
443C2×C4—82no—
444C2×C4—222no—
445C2×C4—224no—
446C2×C4—4416no—
447C2×C4—444no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—444no—
452C2×C4SD16×D1112yes—
453C2×C4#6696712yes—
454C2×C4#6699011yescharacteristic
455C2×C4#6699011yescharacteristic
456C2×C4#6699011yescharacteristic
457C2×C4#6699512yes—
458C2×C4#6700312yes—
459C2×C4C2×D4×D1111yescharacteristic
460C2×C4C2×D4×D1111yescharacteristic
461C2×C4C22×C22⋊D1111yescharacteristic
462C8—42no—
463C8—442no—
464C8—442no—
465C22—42no—
466C22—42no—
467C22—42no—
468C22—84no—
469C22—224no—
470C22—442no—
471C22—442no—
472C22—448no—
473C22#1062266012yes—
474C22#1062278212yes—
475C22#1062281412yes—
476C22C2×#6699011yescharacteristic
477C4—21no—
478C4—21no—
479C4—42no—
480C4—82no—
481C4—444no—
482C4—442no—
483C4#1062266012yes—
484C4#1062278212yes—
485C4C2×SD16×D1111yescharacteristic
486C4C2×#6696711yescharacteristic
487C4C2×#6699511yescharacteristic
488C4C2×#6700311yescharacteristic
489C2—82no—
490C2—444no—
491C2#1306776614yesdirect product factor
492C2C2×#1062278211yescharacteristic
493C2C2×#1062266011yescharacteristic
494C2C2×#1062281411yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#476C2
socleC23×C11#120
prime radicalC2×#10623082C2
hypercenterC2×#476D11
hypocenterC11C2×#1635
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
2. C2×#10622694C2semidirect
3. C2×#10622697C2semidirect
4. #13067766C2direct (N × H)
5. C2×#10622124C2semidirect
6. C2×D4⋊(C11⋊C8)C2semidirect
7. C2×#10622121C2semidirect
8. C2×C11×#476C2semidirect
23. C11×#476C22semidirect
29. #10622697C22semidirect
31. #10622694C22semidirect
36. D4⋊(C11⋊C8)C22semidirect
37. #10622124C22semidirect
38. #10622121C22semidirect
171. C2×#476D11semidirect
244. #476C2×D11semidirect
342. C2×C11#1635semidirect
414. C11C2×#1635semidirect
491. C2#13067766direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230822
C2×#106226942
C2×#106226972
#130677662
C2×#106221242
C2×D4⋊(C11⋊C8)2
C2×#106221212
C2×C11×#4762
C2×#163511