Finite Group Databasebeta

← C2×#13067739 #14729413

Subgroups — C2×#13067739 #14729413

Order 2816.

1074 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic
2C2×#10622306C211yesmaximal, characteristic
3C2×#10622463C211yesmaximal, characteristic, complemented
4C2×#10622634C211yesmaximal, characteristic, complemented
5#13067739C218yesmaximal, direct product factor
6C2×#10622123C211yesmaximal, characteristic
7C2×#10622094C211yesmaximal, characteristic, complemented
8C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#67000—21no—
11C22×#4314—22no—
12#10623116—22no—
13#10623116—22no—
14#10623116—22no—
15#10623116C2214yes—
16C2×#66947—22no—
17C2×#66946—21no—
18C2×#66928—21no—
19C2×#66927C2211yescharacteristic
20C2×C4×D44—21no—
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C2×C11×C4⋊C8C2211yescharacteristic
24C2×C4×C8×C11C2211yescharacteristic
25C2×#66899—21no—
26C2×#66882—21no—
27C2×#66880—21no—
28#10622634—22no—
29#10622634C2214yescomplemented
30C2×#66871—21no—
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622463—22no—
33#10622463C2214yescomplemented
34#10622306—22no—
35#10622306C2214yes—
36C11×Q8⋊C8C2214yescomplemented
37#10622123C2214yes—
38#10622094C2214yescomplemented
39C22×Q8×C11D411yescharacteristic
40C22×D44—21no—
41C22×D44—21no—
42C22×D44D412yes—
43C22×C4×D11—22no—
44C22×Dic22—21no—
45C22×Dic22D411yescharacteristic
46C22×C8×C11—21no—
47C22×C8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11—21no—
50C4×Q8×C11D412yes—
51C4×Q8×C11C2312yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C42×C11—21no—
55C2×C42×C11C2311yescharacteristic
56#67000—24no—
57#67000—24no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4—22no—
61C2×C4⋊Dic11—21no—
62C2×C4⋊Dic11—21no—
63C2×C4⋊Dic11D411yescharacteristic
64C2×Dic11⋊C4—21no—
65C2×C4×Dic11—21no—
66C22×C11⋊C8—21no—
67C2×#4314—28no—
68C2×#4314—48no—
69#66947—28no—
70#66947—28no—
71#66946—24no—
72#66946—24no—
73#66928—24no—
74#66928—24no—
75#66927—21no—
76#66927—21no—
77#66927D412yes—
78#66927C2312yes—
79C4×D44—24no—
80C4×D44—24no—
81#66922—21no—
82#66922—21no—
83#66922—21no—
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#66899—24no—
94#66882—24no—
95#66880—24no—
96#66871—24no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C2×#1630—111nomaximal, Sylow
100C23×D11—22no—
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—21no—
112C22×Dic11—41no—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—22no—
118C2×D44—44no—
119C2×D44—42no—
120C2×D44—42no—
121C2×D44—42no—
122C2×D44—42no—
123C2×D44C2×D414yes—
124C2×C4×D11—28no—
125C2×C4×D11—84no—
126C2×Dic22—21no—
127C2×Dic22—22no—
128C2×Dic22—22no—
129C2×Dic22—22no—
130C2×Dic22—44no—
131C2×Dic22—41no—
132C2×Dic22C2×D412yes—
133C2×C8×C11—24no—
134C2×C8×C11—22no—
135C2×C8×C11—22no—
136C2×C8×C11—42no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4C2×D412yes—
141C42×C11—22no—
142C42×C11—22no—
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11C2411yescharacteristic
147(C2×D11)⋊C4—28no—
148(C2×D11)⋊C4—28no—
149(C2×D11)⋊C4—28no—
150C4⋊Dic11—21no—
151C4⋊Dic11—22no—
152C4⋊Dic11—22no—
153C4⋊Dic11—41no—
154C4⋊Dic11—41no—
155C4⋊Dic11C2×D412yes—
156Dic11⋊C4—22no—
157Dic11⋊C4—22no—
158C4×Dic11—22no—
159C4×Dic11—22no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—42no—
162#4314—416no—
163C2×#559—111no—
164C2×#492—111no—
165C2×#477—111no—
166C2×#477—111no—
167#1630—118no—
168C2×#331—111no—
169C2×Q8⋊C8—111no—
170C2×Q8⋊C8D1111yescharacteristic, complemented
171C23×C11#12011yescharacteristic
172C22×D11—24no—
173C22×D11—44no—
174C22×D11—44no—
175C22×D11—44no—
176Q8×C11—22no—
177Q8×C11—22no—
178Q8×C11—42no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—42no—
183C2×C4×C11—42no—
184C2×C4×C11#12011yescharacteristic
185C2×C4×C11#12011yescharacteristic
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11#13512yes—
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—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—82no—
200D44—44no—
201D44—42no—
202D44—42no—
203D44—42no—
204D44—42no—
205D44—44no—
206D44—44no—
207D44—82no—
208C4×D11—88no—
209Dic22—22no—
210Dic22—22no—
211Dic22—42no—
212Dic22—44no—
213Dic22—82no—
214C8×C11—24no—
215C8×C11—42no—
216C11⋊C8—42no—
217C22×SD16—222no—
218#559—114no—
219#559—222no—
220#559—222no—
221#559—222no—
222C2×C4⋊Q8—111no—
223C2×#127—111no—
224C2×#124—221no—
225C2×#124—221no—
226C2×#123—222no—
227C2×C4×Q8—111no—
228C2×C4×Q8C2×D1111yescharacteristic
229C2×C4×D4—221no—
230C2×C4×D4—221no—
231#492—114no—
232#492—222no—
233#477—114no—
234#477—114no—
235#477—222no—
236#477—222no—
237C2×#107—221no—
238C2×#107—221no—
239C2×C4⋊C8—111no—
240C2×C4⋊C8C2×D1111yescharacteristic
241C2×#103—221no—
242C2×#103—221no—
243C2×C4×C8C2×D1111yescharacteristic
244#331—114no—
245Q8⋊C8—114no—
246Q8⋊C8C2×D1114yescomplemented
247C22×C11#45212yes—
248C22×C11#45212yes—
249C22×C11#45312yes—
250C22×C11C2×#12011yescharacteristic
251C2×D11—44no—
252C2×D11—44no—
253C2×D11—44no—
254C2×D11—88no—
255C4×C11—21no—
256C4×C11—21no—
257C4×C11—42no—
258C4×C11—42no—
259C4×C11#45212yes—
260C4×C11#45212yes—
261C4×C11C2×#13511yescharacteristic
262C4×C11C2×#13511yescharacteristic
263C4×C11C2×#13711yescharacteristic
264C4×C11C2×#13711yescharacteristic
265Dic11—42no—
266Dic11—42no—
267Dic11—82no—
268C22×Q8—111no—
269C22×Q8—221no—
270C22×Q8D4411yescharacteristic
271C22×D4—112no—
272C22×D4—221no—
273C22×D4—221no—
274C23×C4—222no—
275C2×SD16—228no—
276C2×SD16—448no—
277C22×C8—21no—
278C22×C8—21no—
279C22×C8—221no—
280C4⋊Q8—112no—
281C4⋊Q8—221no—
282C4⋊Q8—221no—
283C4⋊Q8—221no—
284#127—112no—
285#127—112no—
286#127—221no—
287#127—221no—
288#124—224no—
289#124—224no—
290#124—224no—
291#124—224no—
292#123—228no—
293#123—228no—
294C4×Q8—21no—
295C4×Q8—21no—
296C4×Q8—112no—
297C4×Q8—112no—
298C4×Q8—221no—
299C4×Q8—221no—
300C4×Q8D4412yes—
301C4×Q8C22×D1112yes—
302C4×D4—224no—
303C4×D4—224no—
304C4×D4—224no—
305C4×D4—224no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4—221no—
310C2×C4⋊C4—221no—
311C2×C4⋊C4D4411yescharacteristic
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C22⋊C4—222no—
315C2×C42—21no—
316C2×C42—221no—
317C2×C42C22×D1111yescharacteristic
318#107—224no—
319#107—224no—
320C4⋊C8—21no—
321C4⋊C8—112no—
322C4⋊C8—221no—
323C4⋊C8C22×D1112yes—
324#103—224no—
325#103—224no—
326C4×C8—21no—
327C4×C8C22×D1112yes—
328C2×C11#163014yescomplemented
329C2×C11C2×#45211yescharacteristic
330C2×C11C2×#45211yescharacteristic
331C2×C11C2×#45311yescharacteristic
332D11—84no—
333C24—222no—
334C2×Q8—21no—
335C2×Q8—22no—
336C2×Q8—22no—
337C2×Q8—112no—
338C2×Q8—221no—
339C2×Q8—222no—
340C2×Q8—222no—
341C2×Q8—222no—
342C2×Q8—444no—
343C2×Q8—441no—
344C2×Q8C2×D4412yes—
345C2×D4—114no—
346C2×D4—222no—
347C2×D4—222no—
348C2×D4—222no—
349C2×D4—222no—
350C2×D4—222no—
351C2×D4—444no—
352C2×D4—442no—
353C2×D4—442no—
354C2×D4—442no—
355C2×D4—442no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—228no—
359C22×C4—221no—
360C22×C4—221no—
361C22×C4—441no—
362C22×C4—884no—
363C22×C4C2×D4411yescharacteristic
364C22×C4D4×D1111yescharacteristic
365C22×C4D4×D1111yescharacteristic
366SD16—4416no—
367C2×C8—24no—
368C2×C8—22no—
369C2×C8—22no—
370C2×C8—42no—
371C2×C8—222no—
372C2×C8—442no—
373C4⋊C4—22no—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—112no—
377C4⋊C4—221no—
378C4⋊C4—222no—
379C4⋊C4—222no—
380C4⋊C4—222no—
381C4⋊C4—222no—
382C4⋊C4—441no—
383C4⋊C4—441no—
384C4⋊C4C2×D4412yes—
385C22⋊C4—228no—
386C22⋊C4—228no—
387C22⋊C4—228no—
388C42—22no—
389C42—22no—
390C42—222no—
391C42—222no—
392C42C2×D4411yescharacteristic
393C42D4×D1111yescharacteristic
394C42D4×D1111yescharacteristic
395C42C23×D1111yescharacteristic
396C11C2×#163011yescharacteristic, complemented, Sylow
397C23—224no—
398C23—444no—
399C23—444no—
400C23—444no—
401C23#6693511yescharacteristic
402Q8—22no—
403Q8—22no—
404Q8—42no—
405Q8—222no—
406Q8—222no—
407Q8—444no—
408Q8—442no—
409Q8—882no—
410D4—444no—
411D4—442no—
412D4—442no—
413D4—442no—
414D4—442no—
415D4—444no—
416D4—444no—
417D4—882no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—222no—
424C2×C4—222no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—442no—
428C2×C4—888no—
429C2×C4—882no—
430C2×C4#6693511yescharacteristic
431C2×C4#6693511yescharacteristic
432C2×C4#6693511yescharacteristic
433C2×C4#6695712yes—
434C2×C4#6696212yes—
435C2×C4#6696912yes—
436C2×C4#6697112yes—
437C2×C4C22×D4411yescharacteristic
438C2×C4C2×D4×D1111yescharacteristic
439C2×C4C2×D4×D1111yescharacteristic
440C8—24no—
441C8—42no—
442C8—442no—
443C22—444no—
444C22—444no—
445C22—444no—
446C22—888no—
447C22#1062234612yes—
448C22#1062242312yes—
449C22#1062243512yes—
450C22C2×#6693511yescharacteristic
451C4—21no—
452C4—21no—
453C4—42no—
454C4—42no—
455C4—442no—
456C4—442no—
457C4—882no—
458C4#1062234612yes—
459C4#1062242312yes—
460C4C2×#6695711yescharacteristic
461C4C2×#6696211yescharacteristic
462C4C2×#6696911yescharacteristic
463C4C2×#6697111yescharacteristic
464C2—884no—
465C2#1306773914yesdirect product factor
466C2C2×#1062234611yescharacteristic
467C2C2×#1062242311yescharacteristic
468C2C2×#1062243511yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11#120
prime radicalC2×#66927C22
hypercenterC2×Q8⋊C8D11
hypocenterC11C2×#1630
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
3. C2×#10622463C2semidirect
4. C2×#10622634C2semidirect
5. #13067739C2direct (N × H)
7. C2×#10622094C2semidirect
8. C2×C11×Q8⋊C8C2semidirect
29. #10622634C22semidirect
33. #10622463C22semidirect
36. C11×Q8⋊C8C22semidirect
38. #10622094C22semidirect
170. C2×Q8⋊C8D11semidirect
246. Q8⋊C8C2×D11semidirect
328. C2×C11#1630semidirect
396. C11C2×#1630semidirect
465. C2#13067739direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
C2×#106223062
C2×#106224632
C2×#106226342
#130677392
C2×#106221232
C2×#106220942
C2×C11×Q8⋊C82
C2×#163011