Finite Group Databasebeta

← C2×#13067709 #14729499

Subgroups — C2×#13067709 #14729499

Order 2816.

1030 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623252C211yesmaximal, characteristic, complemented
2C2×#10622688C211yesmaximal, characteristic
3C2×#10622688C211yesmaximal, characteristic
4#13067709C218yesmaximal, direct product factor
5C2×#10622185C211yesmaximal, characteristic, complemented
6C2×#10622094C211yesmaximal, characteristic, complemented
7C2×#10622094C211yesmaximal, characteristic, complemented
8C2×C11×#486C211yesmaximal, characteristic
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×#127C2211yescharacteristic
11C2×Q8×Dic11—21no—
12C2×#66997—21no—
13C22×#4324—21no—
14C22×#4324—21no—
15#10623252—22no—
16#10623252—22no—
17#10623252—22no—
18#10623252C2214yescomplemented
19C2×#66943—21no—
20C2×#66942—22no—
21C2×#66940—21no—
22C2×C4×Dic22C2211yescharacteristic
23C2×C4×Dic22C2211yescharacteristic
24C11×#486—22no—
25C11×#486C2214yes—
26C2×C11×#102—22no—
27C2×C4×C8×C11C2211yescharacteristic
28C2×#66896—21no—
29C2×#66896—21no—
30#10622688—22no—
31#10622688—22no—
32#10622688C2214yes—
33#10622688C2214yes—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622185C2214yescomplemented
37#10622094C2214yescomplemented
38#10622094C2214yescomplemented
39C22×Q8×C11—21no—
40C22×D4×C11—21no—
41C22×D4×C11—21no—
42C22×D4×C11—21no—
43C22×Dic22D411yescharacteristic
44C22×Dic22D411yescharacteristic
45C22×C8×C11—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8D412yes—
49C11×C4⋊Q8C2312yes—
50C11×#127—21no—
51C11×#127—21no—
52C11×#127—21no—
53C11×#127C2312yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4D412yes—
56C2×C42×C11C2311yescharacteristic
57Q8×Dic11—24no—
58Q8×Dic11—24no—
59#66997—24no—
60#66997—24no—
61C2×#4324—24no—
62C2×#4324—24no—
63C2×#4324—44no—
64C2×#4324—44no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11D411yescharacteristic
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C2×Dic11⋊C4—21no—
71C2×Dic11⋊C4—21no—
72C2×C4×Dic11—22no—
73C2×C4×Dic11—21no—
74C2×C4×Dic11—21no—
75C22×C11⋊C8—21no—
76C22×C11⋊C8—21no—
77#66943—24no—
78#66943—24no—
79#66942—28no—
80#66942—28no—
81#66940—24no—
82#66940—24no—
83C4×Dic22—21no—
84C4×Dic22—21no—
85C4×Dic22—21no—
86C4×Dic22—21no—
87C4×Dic22D412yes—
88C4×Dic22D412yes—
89C4×Dic22C2312yes—
90C4×Dic22C2312yes—
91C11×#102—28no—
92C4×C8×C11—21no—
93C4×C8×C11C2312yes—
94#66896—24no—
95#66896—24no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2312yes—
100C2×#1626—111nomaximal, Sylow
101C24×C11—41no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—42no—
105C2×Q8×C11—42no—
106C2×D4×C11—22no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11—44no—
110C2×D4×C11—41no—
111C2×D4×C11—41no—
112C2×D4×C11—41no—
113C2×D4×C11—42no—
114C2×D4×C11—42no—
115C2×D4×C11—42no—
116C2×D4×C11—42no—
117C22×C4×C11—22no—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2×D411yescharacteristic
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11—21no—
125C2×Dic22—21no—
126C2×Dic22—21no—
127C2×Dic22—22no—
128C2×Dic22—22no—
129C2×Dic22—22no—
130C2×Dic22SD1614yescomplemented
131C2×Dic22C2×D412yes—
132C2×Dic22C2×D412yes—
133C2×C8×C11—22no—
134C2×C8×C11—42no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4C2×D414yes—
139C42×C11C2×D411yescharacteristic
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11C2411yescharacteristic
143#4324—48no—
144#4324—48no—
145C4⋊Dic11—28no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11C2×D412yes—
149C4⋊Dic11C2×D412yes—
150Dic11⋊C4—28no—
151Dic11⋊C4—28no—
152Dic11⋊C4—22no—
153Dic11⋊C4—22no—
154Dic11⋊C4—22no—
155Dic11⋊C4—22no—
156C4×Dic11—28no—
157C4×Dic11—22no—
158C4×Dic11—22no—
159C4×Dic11—22no—
160C4×Dic11—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—42no—
164C2×C11⋊C8—42no—
165C2×#557—111no—
166C2×#486D1111yescharacteristic
167C2×#460—111no—
168C2×#460—111no—
169#1626—118no—
170C2×#332—111no—
171C2×Q8⋊C8—111no—
172C2×Q8⋊C8—111no—
173C23×C11—42no—
174C23×C11—82no—
175C23×C11—82no—
176C23×C11—82no—
177C23×C11#12011yescharacteristic
178Q8×C11—42no—
179Q8×C11—42no—
180Q8×C11—44no—
181D4×C11—44no—
182D4×C11—42no—
183D4×C11—42no—
184D4×C11—42no—
185D4×C11—42no—
186D4×C11—82no—
187D4×C11—82no—
188D4×C11—82no—
189C2×C4×C11—22no—
190C2×C4×C11—24no—
191C2×C4×C11—44no—
192C2×C4×C11#12011yescharacteristic
193C2×C4×C11#12011yescharacteristic
194C2×C4×C11#12011yescharacteristic
195C2×C4×C11C2×SD1612yes—
196C2×C4×C11#13512yes—
197C2×C4×C11AGL(1,ℤ/8)12yes—
198C2×C4×C11#13712yes—
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×D411yescharacteristic
202C2×Dic11—22no—
203C2×Dic11—24no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—22no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210Dic22—22no—
211Dic22—24no—
212Dic22—22no—
213Dic22—22no—
214Dic22—42no—
215Dic22C2×SD1614yescomplemented
216C8×C11—42no—
217C11⋊C8—42no—
218C11⋊C8—42no—
219C22×SD16—221no—
220C22×SD16—221no—
221#557—114no—
222#557—222no—
223#557—222no—
224#557—222no—
225C2×C4⋊Q8—221no—
226C2×C4⋊Q8C2×D1111yescharacteristic
227C2×#127C2×D1111yescharacteristic
228C2×#125—221no—
229C2×#125—222no—
230C2×C4×Q8—111no—
231C2×C4×Q8—111no—
232C2×C4×Q8—221no—
233C2×C4×Q8—221no—
234#486—22no—
235#486C2×D1114yes—
236#460—114no—
237#460—114no—
238#460—222no—
239#460—222no—
240C2×C4⋊C8—111no—
241C2×C4⋊C8—111no—
242C2×#102—22no—
243C2×#102—221no—
244C2×#102—221no—
245C2×C4×C8C2×D1111yescharacteristic
246#332—114no—
247Q8⋊C8—114no—
248Q8⋊C8—114no—
249C22×C11—82no—
250C22×C11—82no—
251C22×C11—82no—
252C22×C11—164no—
253C22×C11#44812yes—
254C22×C11#44912yes—
255C22×C11#45412yes—
256C22×C11C2×#12011yescharacteristic
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—44no—
260C4×C11#44812yes—
261C4×C11#44912yes—
262C4×C11C22×SD1611yescharacteristic
263C4×C11C2×#13511yescharacteristic
264C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
265C4×C11C2×#13711yescharacteristic
266Dic11—24no—
267Dic11—42no—
268Dic11—42no—
269Dic11—42no—
270C22×Q8—21no—
271C22×Q8—111no—
272C22×Q8—111no—
273C22×D4—21no—
274C22×D4—21no—
275C22×D4—21no—
276C2×SD16—224no—
277C2×SD16—224no—
278C2×SD16—444no—
279C2×SD16—444no—
280C22×C8—21no—
281C22×C8—221no—
282C22×C8—221no—
283C4⋊Q8—21no—
284C4⋊Q8—21no—
285C4⋊Q8—224no—
286C4⋊Q8—224no—
287C4⋊Q8C22⋊D1112yes—
288C4⋊Q8C22×D1112yes—
289#127—21no—
290#127—21no—
291#127—21no—
292#127C22×D1112yes—
293#125—224no—
294#125—228no—
295#125—224no—
296#125—228no—
297C4×Q8—112no—
298C4×Q8—112no—
299C4×Q8—112no—
300C4×Q8—112no—
301C4×Q8—224no—
302C4×Q8—224no—
303C4×Q8—224no—
304C4×Q8—224no—
305C4×Q8—221no—
306C4×Q8—221no—
307C4×Q8—221no—
308C4×Q8—221no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—111no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4C22⋊D1112yes—
318C2×C42—222no—
319C2×C42—221no—
320C2×C42—221no—
321C2×C42C22×D1111yescharacteristic
322C4⋊C8—112no—
323C4⋊C8—112no—
324C4⋊C8—221no—
325C4⋊C8—221no—
326#102—28no—
327#102—224no—
328#102—224no—
329C4×C8—21no—
330C4×C8C22×D1112yes—
331C2×C11—162no—
332C2×C11#162614yescomplemented
333C2×C11C2×#44811yescharacteristic
334C2×C11C2×#44911yescharacteristic
335C2×C11C2×#45411yescharacteristic
336C24—41no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—42no—
340C2×Q8—42no—
341C2×Q8—114no—
342C2×Q8—112no—
343C2×Q8—112no—
344C2×Q8—222no—
345C2×Q8—221no—
346C2×Q8—221no—
347C2×Q8—222no—
348C2×Q8—222no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—44no—
353C2×D4—42no—
354C2×D4—42no—
355C2×D4—42no—
356C2×D4—42no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—41no—
360C22×C4—22no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—221no—
365C22×C4D4×D1111yescharacteristic
366C22×C4D4×D1111yescharacteristic
367C22×C4C2×C22⋊D1111yescharacteristic
368SD16—448no—
369SD16—448no—
370C2×C8—22no—
371C2×C8—42no—
372C2×C8—222no—
373C2×C8—222no—
374C2×C8—442no—
375C2×C8—442no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—112no—
380C4⋊C4—112no—
381C4⋊C4—228no—
382C4⋊C4—228no—
383C4⋊C4—228no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4—222no—
390C4⋊C4C2×C22⋊D1114yes—
391C42—228no—
392C42—222no—
393C42—222no—
394C42—222no—
395C42—222no—
396C42D4×D1111yescharacteristic
397C42D4×D1111yescharacteristic
398C42C2×C22⋊D1111yescharacteristic
399C42C23×D1111yescharacteristic
400C11C2×#162611yescharacteristic, complemented, Sylow
401C23—42no—
402C23—82no—
403C23—82no—
404C23—82no—
405C23#6699011yescharacteristic
406Q8—44no—
407Q8—42no—
408Q8—42no—
409Q8—114no—
410Q8—222no—
411Q8—224no—
412Q8—222no—
413Q8—222no—
414Q8—442no—
415D4—44no—
416D4—42no—
417D4—42no—
418D4—42no—
419D4—42no—
420D4—82no—
421D4—82no—
422D4—82no—
423C2×C4—22no—
424C2×C4—24no—
425C2×C4—44no—
426C2×C4—224no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4#6696412yes—
435C2×C4#6696512yes—
436C2×C4SD16×D1112yes—
437C2×C4#6696812yes—
438C2×C4#6699011yescharacteristic
439C2×C4#6699011yescharacteristic
440C2×C4#6699011yescharacteristic
441C2×C4C2×D4×D1111yescharacteristic
442C2×C4C2×D4×D1111yescharacteristic
443C2×C4C22×C22⋊D1111yescharacteristic
444C8—42no—
445C8—442no—
446C8—442no—
447C22—82no—
448C22—82no—
449C22—82no—
450C22—164no—
451C22#1062267512yes—
452C22#1062277112yes—
453C22#1062278312yes—
454C22C2×#6699011yescharacteristic
455C4—21no—
456C4—21no—
457C4—44no—
458C4—224no—
459C4—442no—
460C4—442no—
461C4—442no—
462C4#1062277112yes—
463C4#1062278312yes—
464C4C2×#6696411yescharacteristic
465C4C2×#6696511yescharacteristic
466C4C2×SD16×D1111yescharacteristic
467C4C2×#6696811yescharacteristic
468C2—162no—
469C2#1306770914yesdirect product factor
470C2C2×#1062278311yescharacteristic
471C2C2×#1062277111yescharacteristic
472C2C2×#1062267511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#486C2
socleC23×C11#120
prime radicalC2×C11×#127C22
hypercenterC2×#486D11
hypocenterC11C2×#1626
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#486

Complements

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

NH ≅ G/Ntype
1. C2×#10623252C2semidirect
4. #13067709C2direct (N × H)
5. C2×#10622185C2semidirect
6. C2×#10622094C2semidirect
7. C2×#10622094C2semidirect
18. #10623252C22semidirect
36. #10622185C22semidirect
37. #10622094C22semidirect
38. #10622094C22semidirect
130. C2×Dic22SD16semidirect
215. Dic22C2×SD16semidirect
332. C2×C11#1626semidirect
400. C11C2×#1626semidirect
469. C2#13067709direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232522
C2×#106226882
#130677092
C2×#106221852
C2×#106220942
C2×C11×#4862
C2×#162611