Finite Group Databasebeta

← C2×#13067875 #14729607

Subgroups — C2×#13067875 #14729607

Order 2816.

978 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic
2C2×#10622295C211yesmaximal, characteristic, complemented
3C2×#10622633C211yesmaximal, characteristic, complemented
4C2×#10622454C211yesmaximal, characteristic
5#13067875C218yesmaximal, direct product factor
6C2×#10622120C211yesmaximal, characteristic, complemented
7C2×#10622097C211yesmaximal, characteristic
8C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66999—21no—
11C22×#4314—21no—
12#10623115—22no—
13#10623115—22no—
14#10623115—22no—
15#10623115C2214yes—
16C2×#66951—22no—
17C2×#66945—21no—
18C2×#66928—21no—
19C2×C4×D44C2211yescharacteristic
20C2×#66922C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22—21no—
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C2×#66899—21no—
26C2×#66882—22no—
27C2×#66880—21no—
28#10622633—22no—
29#10622633C2214yescomplemented
30C2×#66872—21no—
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622454—22no—
33#10622454C2214yes—
34#10622295—22no—
35#10622295C2214yescomplemented
36C11×Q8⋊C8C2214yescomplemented
37#10622120C2214yescomplemented
38#10622097C2214yes—
39C22×Q8×C11D411yescharacteristic
40C22×D44D411yescharacteristic
41C22×C4×D11—21no—
42C22×Dic22—21no—
43C22×Dic22—21no—
44C22×C8×C11—21no—
45C22×C8×C11—21no—
46C4×Q8×C11—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11D412yes—
49C4×Q8×C11C2312yes—
50C2×C11×C4⋊C4—21no—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C42×C11—21no—
53C2×C42×C11C2311yescharacteristic
54#66999—24no—
55#66999—24no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11D411yescharacteristic
63C2×C4⋊Dic11D412yes—
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—22no—
66C22×C11⋊C8—21no—
67C2×#4314—24no—
68C2×#4314—44no—
69#66951—28no—
70#66951—28no—
71#66945—24no—
72#66945—24no—
73#66928—24no—
74#66928—24no—
75C4×D44—21no—
76C4×D44—21no—
77C4×D44D412yes—
78C4×D44C2312yes—
79#66922—21no—
80#66922—21no—
81#66922—21no—
82#66922—21no—
83#66922—21no—
84#66922D412yes—
85#66922C2312yes—
86#66922C2312yes—
87C4×Dic22—24no—
88C4×Dic22—24no—
89C11×C4⋊C8—21no—
90C11×C4⋊C8C2312yes—
91C4×C8×C11—21no—
92C4×C8×C11C2312yes—
93#66899—24no—
94#66882—28no—
95#66880—24no—
96#66872—24no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C2×#1650—111nomaximal, Sylow
100C23×D11—21no—
101C2×Q8×C11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11C2×D412yes—
105C22×C4×C11—21no—
106C22×C4×C11—21no—
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×Dic11—21no—
111C22×Dic11—22no—
112C22×Dic11—41no—
113C2×D44—21no—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44C2×D412yes—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—42no—
120C2×C4×D11—42no—
121C2×Dic22—22no—
122C2×Dic22—22no—
123C2×Dic22—22no—
124C2×Dic22—41no—
125C2×Dic22—42no—
126C2×Dic22—42no—
127C2×Dic22—42no—
128C2×Dic22—42no—
129C2×C8×C11—24no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—42no—
133C11×C4⋊C4—21no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4C2×D412yes—
137C42×C11—22no—
138C42×C11—22no—
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11C2411yescharacteristic
143(C2×D11)⋊C4—28no—
144(C2×D11)⋊C4—28no—
145(C2×D11)⋊C4—22no—
146(C2×D11)⋊C4—22no—
147C4⋊Dic11—21no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11—41no—
154C4⋊Dic11—41no—
155C4⋊Dic11C2×D412yes—
156C4⋊Dic11C2×D414yes—
157Dic11⋊C4—28no—
158C4×Dic11—28no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—42no—
161#4314—48no—
162C2×#556—111no—
163C2×#500—111no—
164C2×#475—111no—
165C2×#461—111no—
166#1650—118no—
167C2×#332—111no—
168C2×Q8⋊C8D1111yescharacteristic, complemented
169C2×D4⋊C8—111no—
170C23×C11#12011yescharacteristic
171C22×D11—22no—
172C22×D11—42no—
173C22×D11—42no—
174C22×D11—42no—
175Q8×C11—22no—
176Q8×C11—22no—
177Q8×C11—42no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11#12011yescharacteristic
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12011yescharacteristic
186C2×C4×C11#13512yes—
187C2×C4×C11#13512yes—
188C2×C4×C11AGL(1,ℤ/8)12yes—
189C2×C4×C11#13712yes—
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C22×D411yescharacteristic
193C2×Dic11—22no—
194C2×Dic11—24no—
195C2×Dic11—44no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—82no—
199D44—22no—
200D44—22no—
201D44—42no—
202C4×D11—42no—
203C4×D11—42no—
204C4×D11—44no—
205Dic22—42no—
206Dic22—42no—
207Dic22—44no—
208Dic22—42no—
209Dic22—42no—
210Dic22—82no—
211C8×C11—24no—
212C8×C11—42no—
213C11⋊C8—42no—
214C22×SD16—221no—
215#556—114no—
216#556—222no—
217#556—222no—
218#556—222no—
219C2×C4⋊Q8—111no—
220C2×C4⋊Q8—111no—
221C2×#126—222no—
222C2×#124—221no—
223C2×C22⋊Q8—221no—
224C2×C4×Q8—221no—
225C2×C4×Q8C2×D1111yescharacteristic
226C2×C4×D4—111no—
227C2×#117—221no—
228#500—114no—
229#500—222no—
230#475—114no—
231#475—222no—
232#461—114no—
233#461—222no—
234C2×#107—222no—
235C2×#106—221no—
236C2×C4⋊C8—111no—
237C2×C4⋊C8C2×D1111yescharacteristic
238C2×#103—221no—
239C2×#103—221no—
240C2×C4×C8C2×D1111yescharacteristic
241#332—114no—
242Q8⋊C8C2×D1114yescomplemented
243D4⋊C8—114no—
244C22×C11#44912yes—
245C22×C11#45212yes—
246C22×C11#45612yes—
247C22×C11C2×#12011yescharacteristic
248C2×D11—42no—
249C2×D11—42no—
250C2×D11—42no—
251C2×D11—84no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11#44912yes—
257C4×C11#45212yes—
258C4×C11C2×#13511yescharacteristic
259C4×C11C2×#13511yescharacteristic
260C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
261C4×C11C2×#13711yescharacteristic
262Dic11—44no—
263Dic11—42no—
264Dic11—82no—
265C22×Q8—221no—
266C22×Q8—221no—
267C22×Q8D4411yescharacteristic
268C22×D4—111no—
269C23×C4—221no—
270C2×SD16—224no—
271C2×SD16—444no—
272C22×C8—21no—
273C22×C8—21no—
274C22×C8—221no—
275C4⋊Q8—112no—
276C4⋊Q8—112no—
277C4⋊Q8—112no—
278C4⋊Q8—221no—
279C4⋊Q8—221no—
280C4⋊Q8—221no—
281C4⋊Q8—221no—
282C4⋊Q8—221no—
283#126—228no—
284#126—228no—
285#124—224no—
286#124—224no—
287C22⋊Q8—224no—
288C22⋊Q8—224no—
289C4×Q8—21no—
290C4×Q8—21no—
291C4×Q8—224no—
292C4×Q8—224no—
293C4×Q8D4412yes—
294C4×Q8C22×D1112yes—
295C4×D4—112no—
296C4×D4—112no—
297C4×D4—221no—
298C4×D4—221no—
299#117—224no—
300#117—224no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—112no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4D4411yescharacteristic
309C2×C22⋊C4—222no—
310C2×C22⋊C4—222no—
311C2×C22⋊C4—221no—
312C2×C42—21no—
313C2×C42—222no—
314C2×C42C22×D1111yescharacteristic
315#107—228no—
316#106—224no—
317C4⋊C8—21no—
318C4⋊C8—112no—
319C4⋊C8—221no—
320C4⋊C8C22×D1112yes—
321#103—224no—
322#103—224no—
323C4×C8—21no—
324C4×C8C22×D1112yes—
325C2×C11#165014yescomplemented
326C2×C11C2×#44911yescharacteristic
327C2×C11C2×#45211yescharacteristic
328C2×C11C2×#45611yescharacteristic
329D11—82no—
330C24—221no—
331C2×Q8—21no—
332C2×Q8—22no—
333C2×Q8—22no—
334C2×Q8—222no—
335C2×Q8—222no—
336C2×Q8—222no—
337C2×Q8—441no—
338C2×Q8—442no—
339C2×Q8—442no—
340C2×Q8—442no—
341C2×Q8—442no—
342C2×Q8C2×D4412yes—
343C2×D4—112no—
344C2×D4—221no—
345C2×D4—222no—
346C2×D4—222no—
347C22×C4—21no—
348C22×C4—21no—
349C22×C4—221no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—442no—
354C22×C4—442no—
355C22×C4—441no—
356C22×C4C2×D4411yescharacteristic
357C22×C4D4×D1111yescharacteristic
358C22×C4D4×D1111yescharacteristic
359SD16—448no—
360C2×C8—24no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—42no—
364C2×C8—222no—
365C2×C8—442no—
366C4⋊C4—22no—
367C4⋊C4—21no—
368C4⋊C4—22no—
369C4⋊C4—112no—
370C4⋊C4—114no—
371C4⋊C4—228no—
372C4⋊C4—221no—
373C4⋊C4—222no—
374C4⋊C4—222no—
375C4⋊C4—222no—
376C4⋊C4—222no—
377C4⋊C4—222no—
378C4⋊C4—441no—
379C4⋊C4—441no—
380C4⋊C4C2×D4412yes—
381C22⋊C4—228no—
382C22⋊C4—228no—
383C22⋊C4—222no—
384C22⋊C4—222no—
385C42—22no—
386C42—22no—
387C42—228no—
388C42C2×D4411yescharacteristic
389C42D4×D1111yescharacteristic
390C42D4×D1111yescharacteristic
391C42C23×D1111yescharacteristic
392C11C2×#165011yescharacteristic, complemented, Sylow
393C23—222no—
394C23—442no—
395C23—442no—
396C23—442no—
397C23#6693511yescharacteristic
398Q8—22no—
399Q8—22no—
400Q8—42no—
401Q8—442no—
402Q8—442no—
403Q8—444no—
404Q8—442no—
405Q8—442no—
406Q8—882no—
407D4—222no—
408D4—222no—
409D4—442no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—222no—
416C2×C4—224no—
417C2×C4—442no—
418C2×C4—444no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—444no—
422C2×C4—442no—
423C2×C4—882no—
424C2×C4#6693511yescharacteristic
425C2×C4#6693511yescharacteristic
426C2×C4#6693511yescharacteristic
427C2×C4#6695712yes—
428C2×C4#6696212yes—
429C2×C4#6696712yes—
430C2×C4#6697212yes—
431C2×C4C22×D4411yescharacteristic
432C2×C4C2×D4×D1111yescharacteristic
433C2×C4C2×D4×D1111yescharacteristic
434C8—24no—
435C8—42no—
436C8—442no—
437C22—442no—
438C22—442no—
439C22—442no—
440C22—884no—
441C22#1062234612yes—
442C22#1062242412yes—
443C22#1062243912yes—
444C22C2×#6693511yescharacteristic
445C4—21no—
446C4—21no—
447C4—42no—
448C4—42no—
449C4—444no—
450C4—442no—
451C4—882no—
452C4#1062234612yes—
453C4#1062242412yes—
454C4C2×#6695711yescharacteristic
455C4C2×#6696211yescharacteristic
456C4C2×#6696711yescharacteristic
457C4C2×#6697211yescharacteristic
458C2—882no—
459C2#1306787514yesdirect product factor
460C2C2×#1062242411yescharacteristic
461C2C2×#1062234611yescharacteristic
462C2C2×#1062243911yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenterC2×Q8⋊C8D11
hypocenterC11C2×#1650
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#10622295C2semidirect
3. C2×#10622633C2semidirect
5. #13067875C2direct (N × H)
6. C2×#10622120C2semidirect
8. C2×C11×Q8⋊C8C2semidirect
29. #10622633C22semidirect
35. #10622295C22semidirect
36. C11×Q8⋊C8C22semidirect
37. #10622120C22semidirect
168. C2×Q8⋊C8D11semidirect
242. Q8⋊C8C2×D11semidirect
325. C2×C11#1650semidirect
392. C11C2×#1650semidirect
459. C2#13067875direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231152
C2×#106222952
C2×#106226332
C2×#106224542
#130678752
C2×#106221202
C2×#106220972
C2×C11×Q8⋊C82
C2×#165011