Finite Group Databasebeta

← C2×#13067825 #14729439

Subgroups — C2×#13067825 #14729439

Order 2816.

1022 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×#10623074C211yesmaximal, characteristic
2C2×#10622294C211yesmaximal, characteristic, complemented
3C2×#10622464C211yesmaximal, characteristic, complemented
4C2×#10622632C211yesmaximal, characteristic
5#13067825C218yesmaximal, direct product factor
6C2×#10622119C211yesmaximal, characteristic, complemented
7C2×#10622094C211yesmaximal, characteristic, complemented
8C2×C11×D4⋊C8C211yesmaximal, characteristic
9C2×C4×D4×C11C2211yescharacteristic
10C2×D4×Dic11—21no—
11C22×#4324—21no—
12C22×C4⋊Dic11—21no—
13C2×#66977—21no—
14#10623074—22no—
15#10623074—22no—
16#10623074—22no—
17#10623074C2214yes—
18C2×#66943—21no—
19C2×#66931—22no—
20C2×#66922C2211yescharacteristic
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C2×#66881—21no—
26C2×#66880—21no—
27C2×#66880—22no—
28#10622632—22no—
29#10622632C2214yes—
30C2×#66874—21no—
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622464—22no—
33#10622464C2214yescomplemented
34#10622294—22no—
35#10622294C2214yescomplemented
36C11×D4⋊C8C2214yes—
37#10622119C2214yescomplemented
38#10622094C2214yescomplemented
39C22×D4×C11D411yescharacteristic
40C23×C4×C11—21no—
41C23×Dic11—22no—
42C22×Dic22—21no—
43C22×Dic22D411yescharacteristic
44C22×Dic22D412yes—
45C22×C8×C11—21no—
46C22×C8×C11—21no—
47C4×D4×C11—21no—
48C4×D4×C11—21no—
49C4×D4×C11D412yes—
50C4×D4×C11C2312yes—
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C11×C22⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54C2×C22⋊Dic11—22no—
55D4×Dic11—24no—
56D4×Dic11—24no—
57C2×#4324—24no—
58C2×#4324—44no—
59C2×C4⋊Dic11—22no—
60C2×C4⋊Dic11—24no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11—24no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11D411yescharacteristic
67#66977—24no—
68#66977—24no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—21no—
71C2×C4×Dic11—21no—
72C22×C11⋊C8—21no—
73#66943—24no—
74#66943—24no—
75#66931—28no—
76#66931—28no—
77#66922—21no—
78#66922—21no—
79#66922—21no—
80#66922—21no—
81#66922—21no—
82#66922D412yes—
83#66922C2312yes—
84#66922C2312yes—
85C4×Dic22—21no—
86C4×Dic22—21no—
87C4×Dic22D412yes—
88C4×Dic22C2312yes—
89C11×C4⋊C8—21no—
90C11×C4⋊C8C2312yes—
91C4×C8×C11—21no—
92C4×C8×C11C2312yes—
93#66881—24no—
94#66880—24no—
95#66880—28no—
96#66874—24no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C2×#1643—111nomaximal, Sylow
100C24×C11—21no—
101C2×D4×C11—21no—
102C2×D4×C11—22no—
103C2×D4×C11SD1614yes—
104C2×D4×C11C2×D412yes—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×Dic11—28no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—22no—
117C22×Dic11—41no—
118C22×Dic11—84no—
119C2×Dic22—21no—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22—22no—
123C2×Dic22—22no—
124C2×Dic22—44no—
125C2×Dic22—41no—
126C2×Dic22—42no—
127C2×Dic22—42no—
128C2×Dic22C2×D412yes—
129C2×Dic22C2×D414yes—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—42no—
133C2×C8×C11—42no—
134C11×C4⋊C4—21no—
135C11×C4⋊C4C2×D412yes—
136C11×C22⋊C4—22no—
137C11×C22⋊C4—22no—
138C42×C11C2×D411yescharacteristic
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11C2411yescharacteristic
142C22⋊Dic11—28no—
143#4324—48no—
144C4⋊Dic11—28no—
145C4⋊Dic11—21no—
146C4⋊Dic11—22no—
147C4⋊Dic11—22no—
148C4⋊Dic11—22no—
149C4⋊Dic11—22no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11—41no—
153C4⋊Dic11—41no—
154C4⋊Dic11C2×D412yes—
155Dic11⋊C4—28no—
156Dic11⋊C4—22no—
157Dic11⋊C4—22no—
158C4×Dic11—22no—
159C4×Dic11—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—42no—
162C2×#554—111no—
163C2×#487—111no—
164C2×#475—111no—
165C2×#461—111no—
166#1643—118no—
167C2×#333—111no—
168C2×Q8⋊C8—111no—
169C2×D4⋊C8D1111yescharacteristic
170C23×C11—22no—
171C23×C11—24no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11#12011yescharacteristic
175D4×C11—22no—
176D4×C11—24no—
177D4×C11C2×SD1614yes—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11—44no—
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12011yescharacteristic
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11C2×SD1612yes—
188C2×C4×C11#13512yes—
189C2×C4×C11#13712yes—
190C2×C4×C11#13712yes—
191C2×C4×C11C22×D411yescharacteristic
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×Dic11—22no—
195C2×Dic11—22no—
196C2×Dic11—24no—
197C2×Dic11—42no—
198C2×Dic11—44no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—88no—
202C2×Dic11—82no—
203Dic22—22no—
204Dic22—22no—
205Dic22—42no—
206Dic22—44no—
207Dic22—42no—
208Dic22—42no—
209Dic22—82no—
210Dic22—82no—
211C8×C11—42no—
212C8×C11—42no—
213C11⋊C8—42no—
214C22×SD16—221no—
215#554—114no—
216#554—222no—
217#554—222no—
218#554—222no—
219C2×C4⋊Q8—111no—
220C2×C4⋊Q8—111no—
221C2×#125—221no—
222C2×C22⋊Q8—222no—
223C2×C22⋊Q8—221no—
224C2×C4×Q8—111no—
225C2×C4×D4—221no—
226C2×C4×D4C2×D1111yescharacteristic
227C22×C4⋊C4—221no—
228#487—114no—
229#487—222no—
230#475—114no—
231#475—222no—
232#461—114no—
233#461—222no—
234C2×#106—221no—
235C2×C4⋊C8—111no—
236C2×C4⋊C8C2×D1111yescharacteristic
237C2×#103—221no—
238C2×#103—222no—
239C2×#103—221no—
240C2×C4×C8C2×D1111yescharacteristic
241#333—114no—
242Q8⋊C8—114no—
243D4⋊C8C2×D1114yes—
244C22×C11—24no—
245C22×C11—48no—
246C22×C11—42no—
247C22×C11—42no—
248C22×C11#44812yes—
249C22×C11#45212yes—
250C22×C11#45512yes—
251C22×C11C2×#12011yescharacteristic
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—42no—
255C4×C11#44812yes—
256C4×C11#45212yes—
257C4×C11C22×SD1611yescharacteristic
258C4×C11C2×#13511yescharacteristic
259C4×C11C2×#13711yescharacteristic
260C4×C11C2×#13711yescharacteristic
261Dic11—42no—
262Dic11—44no—
263Dic11—42no—
264Dic11—82no—
265C22×Q8—111no—
266C22×Q8—112no—
267C22×Q8—221no—
268C22×D4D4411yescharacteristic
269C23×C4—21no—
270C23×C4—222no—
271C2×SD16—224no—
272C2×SD16—444no—
273C22×C8—21no—
274C22×C8—21no—
275C22×C8—221no—
276C4⋊Q8—112no—
277C4⋊Q8—112no—
278C4⋊Q8—112no—
279C4⋊Q8—221no—
280C4⋊Q8—221no—
281C4⋊Q8—221no—
282C4⋊Q8—221no—
283C4⋊Q8—221no—
284#125—224no—
285#125—224no—
286C22⋊Q8—228no—
287C22⋊Q8—228no—
288C22⋊Q8—224no—
289C22⋊Q8—224no—
290C4×Q8—112no—
291C4×Q8—112no—
292C4×Q8—221no—
293C4×Q8—221no—
294C4×D4—21no—
295C4×D4—21no—
296C4×D4—224no—
297C4×D4—224no—
298C4×D4D4412yes—
299C4×D4C22×D1112yes—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—224no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—224no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4D4411yescharacteristic
311C2×C22⋊C4—21no—
312C2×C22⋊C4—222no—
313C2×C42—221no—
314C2×C42C22×D1111yescharacteristic
315#106—224no—
316C4⋊C8—21no—
317C4⋊C8—112no—
318C4⋊C8—221no—
319C4⋊C8C22×D1112yes—
320#103—224no—
321#103—228no—
322#103—224no—
323C4×C8—21no—
324C4×C8C22×D1112yes—
325C2×C11—44no—
326C2×C11#164314yescomplemented
327C2×C11C2×#44811yescharacteristic
328C2×C11C2×#45211yescharacteristic
329C2×C11C2×#45511yescharacteristic
330C24—21no—
331C2×Q8—112no—
332C2×Q8—114no—
333C2×Q8—221no—
334C2×Q8—222no—
335C2×Q8—222no—
336C2×Q8—222no—
337C2×Q8—222no—
338C2×Q8—444no—
339C2×Q8—441no—
340C2×Q8—442no—
341C2×Q8—442no—
342C2×D4—21no—
343C2×D4—22no—
344C2×D4#431414yes—
345C2×D4C2×D4412yes—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—42no—
350C22×C4—42no—
351C22×C4—221no—
352C22×C4—221no—
353C22×C4—222no—
354C22×C4—228no—
355C22×C4—441no—
356C22×C4—884no—
357C22×C4C2×D4411yescharacteristic
358C22×C4D4×D1111yescharacteristic
359C22×C4D4×D1111yescharacteristic
360SD16—448no—
361C2×C8—22no—
362C2×C8—22no—
363C2×C8—42no—
364C2×C8—42no—
365C2×C8—222no—
366C2×C8—442no—
367C4⋊C4—21no—
368C4⋊C4—112no—
369C4⋊C4—228no—
370C4⋊C4—228no—
371C4⋊C4—221no—
372C4⋊C4—222no—
373C4⋊C4—222no—
374C4⋊C4—222no—
375C4⋊C4—222no—
376C4⋊C4—222no—
377C4⋊C4—222no—
378C4⋊C4—222no—
379C4⋊C4—222no—
380C4⋊C4—441no—
381C4⋊C4—441no—
382C4⋊C4C2×D4412yes—
383C22⋊C4—22no—
384C22⋊C4—22no—
385C22⋊C4—228no—
386C42—222no—
387C42—222no—
388C42C2×D4411yescharacteristic
389C42D4×D1111yescharacteristic
390C42D4×D1111yescharacteristic
391C42C23×D1111yescharacteristic
392C11C2×#164311yescharacteristic, complemented, Sylow
393C23—22no—
394C23—24no—
395C23—42no—
396C23—42no—
397C23#6693511yescharacteristic
398Q8—222no—
399Q8—222no—
400Q8—444no—
401Q8—442no—
402Q8—442no—
403Q8—442no—
404Q8—882no—
405Q8—882no—
406D4—22no—
407D4—24no—
408D4C2×#431414yes—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—224no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—444no—
421C2×C4—442no—
422C2×C4—888no—
423C2×C4—882no—
424C2×C4#6693511yescharacteristic
425C2×C4#6693511yescharacteristic
426C2×C4#6693511yescharacteristic
427C2×C4C2×#431412yes—
428C2×C4#6696212yes—
429C2×C4#6696512yes—
430C2×C4#6696812yes—
431C2×C4C22×D4411yescharacteristic
432C2×C4C2×D4×D1111yescharacteristic
433C2×C4C2×D4×D1111yescharacteristic
434C8—42no—
435C8—42no—
436C8—442no—
437C22—24no—
438C22—48no—
439C22—42no—
440C22—42no—
441C22#1062235112yes—
442C22#1062239612yes—
443C22#1062243812yes—
444C22C2×#6693511yescharacteristic
445C4—21no—
446C4—21no—
447C4—42no—
448C4—442no—
449C4—442no—
450C4—444no—
451C4—882no—
452C4#1062235112yes—
453C4#1062239612yes—
454C4C22×#431411yescharacteristic
455C4C2×#6696211yescharacteristic
456C4C2×#6696511yescharacteristic
457C4C2×#6696811yescharacteristic
458C2—44no—
459C2#1306782514yesdirect product factor
460C2C2×#1062235111yescharacteristic
461C2C2×#1062239611yescharacteristic
462C2C2×#1062243811yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×D4⋊C8C2
socleC23×C11#120
prime radicalC22×D4×C11D4
hypercenterC2×D4⋊C8D11
hypocenterC11C2×#1643
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#10622294C2semidirect
3. C2×#10622464C2semidirect
5. #13067825C2direct (N × H)
6. C2×#10622119C2semidirect
7. C2×#10622094C2semidirect
33. #10622464C22semidirect
35. #10622294C22semidirect
37. #10622119C22semidirect
38. #10622094C22semidirect
326. C2×C11#1643semidirect
392. C11C2×#1643semidirect
459. C2#13067825direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230742
C2×#106222942
C2×#106224642
C2×#106226322
#130678252
C2×#106221192
C2×#106220942
C2×C11×D4⋊C82
C2×#164311