Finite Group Databasebeta

← C2×#13067714 #14729504

Subgroups — C2×#13067714 #14729504

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×#10623098C211yesmaximal, characteristic, complemented
2C2×#10622307C211yesmaximal, characteristic
3C2×#10622461C211yesmaximal, characteristic
4C2×#10622640C211yesmaximal, characteristic
5#13067714C218yesmaximal, direct product factor
6C2×#10622124C211yesmaximal, characteristic, complemented
7C2×#10622094C211yesmaximal, characteristic, complemented
8C2×C11×Q8⋊C8C211yesmaximal, characteristic, complemented
9C2×C4×Q8×C11C2211yescharacteristic
10C2×#66997—21no—
11C22×#4325—21no—
12C22×#4314—21no—
13#10623098—22no—
14#10623098—22no—
15#10623098—22no—
16#10623098C2214yescomplemented
17C2×#66942—22no—
18C2×#66940—21no—
19C2×#66927C2211yescharacteristic
20C2×#66923—21no—
21C2×#66922C2211yescharacteristic
22C2×C4×Dic22—21no—
23C2×C4×Dic22C2211yescharacteristic
24C2×C11×C4⋊C8C2211yescharacteristic
25C2×C4×C8×C11C2211yescharacteristic
26C2×#66885—21no—
27C2×#66885—22no—
28#10622640—22no—
29#10622640C2214yes—
30C2×#66873—21no—
31C2×C4⋊(C11⋊C8)C2211yescharacteristic
32#10622461—22no—
33#10622461C2214yes—
34#10622307—22no—
35#10622307C2214yes—
36C11×Q8⋊C8C2214yescomplemented
37#10622124C2214yescomplemented
38#10622094C2214yescomplemented
39C22×Q8×C11D411yescharacteristic
40C22×D44—21no—
41C22×D44—21no—
42C22×D44—21no—
43C22×Dic22—21no—
44C22×Dic22D411yescharacteristic
45C22×C8×C11—21no—
46C22×C8×C11—21no—
47C4×Q8×C11—21no—
48C4×Q8×C11—21no—
49C4×Q8×C11D412yes—
50C4×Q8×C11C2312yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C42×C11—21no—
54C2×C42×C11C2311yescharacteristic
55#66997—24no—
56#66997—24no—
57C2×#4325—24no—
58C2×#4325—44no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11D411yescharacteristic
61C2×C4⋊Dic11D412yes—
62C2×Dic11⋊C4—22no—
63C2×Dic11⋊C4—22no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—21no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11—21no—
68C22×C11⋊C8—21no—
69C2×#4314—24no—
70C2×#4314—44no—
71#66942—28no—
72#66942—28no—
73#66940—24no—
74#66940—24no—
75#66927—21no—
76#66927—21no—
77#66927—21no—
78#66927C2312yes—
79#66923—24no—
80#66923—24no—
81#66922—21no—
82#66922—21no—
83#66922D412yes—
84#66922C2312yes—
85C4×Dic22—24no—
86C4×Dic22—24no—
87C4×Dic22—21no—
88C4×Dic22—21no—
89C4×Dic22D412yes—
90C4×Dic22C2312yes—
91C11×C4⋊C8—21no—
92C11×C4⋊C8C2312yes—
93C4×C8×C11—21no—
94C4×C8×C11C2312yes—
95#66885—28no—
96#66885—24no—
97#66873—24no—
98C4⋊(C11⋊C8)—21no—
99C4⋊(C11⋊C8)C2312yes—
100C2×#1626—111nomaximal, Sylow
101C23×D11—41no—
102C2×Q8×C11—21no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11C2×D412yes—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—22no—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44—22no—
117C2×D44—44no—
118C2×D44—41no—
119C2×D44—41no—
120C2×D44—41no—
121C2×D44—42no—
122C2×D44—42no—
123C2×D44—42no—
124C2×D44—42no—
125C2×Dic22—21no—
126C2×Dic22—22no—
127C2×Dic22—22no—
128C2×Dic22—22no—
129C2×Dic22—42no—
130C2×Dic22—42no—
131C2×Dic22SD1614yescomplemented
132C2×Dic22C2×D412yes—
133C2×C8×C11—22no—
134C2×C8×C11—22no—
135C2×C8×C11—42no—
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#4325—48no—
148C4⋊Dic11—22no—
149C4⋊Dic11—21no—
150C4⋊Dic11—22no—
151C4⋊Dic11—22no—
152C4⋊Dic11C2×D412yes—
153C4⋊Dic11C2×D414yes—
154Dic11⋊C4—28no—
155Dic11⋊C4—28no—
156Dic11⋊C4—28no—
157Dic11⋊C4—22no—
158Dic11⋊C4—22no—
159C4×Dic11—28no—
160C4×Dic11—22no—
161C4×Dic11—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—42no—
164#4314—48no—
165C2×#557—111no—
166C2×#486—111no—
167C2×#460—111no—
168C2×#460—111no—
169#1626—118no—
170C2×#332—111no—
171C2×Q8⋊C8—111no—
172C2×Q8⋊C8D1111yescharacteristic, complemented
173C23×C11#12011yescharacteristic
174C22×D11—42no—
175C22×D11—82no—
176C22×D11—82no—
177C22×D11—82no—
178Q8×C11—22no—
179Q8×C11—22no—
180Q8×C11—42no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—22no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11#12011yescharacteristic
188C2×C4×C11#12011yescharacteristic
189C2×C4×C11C2×SD1612yes—
190C2×C4×C11#13512yes—
191C2×C4×C11AGL(1,ℤ/8)12yes—
192C2×C4×C11#13712yes—
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×C4×C11C22×D411yescharacteristic
196C2×Dic11—22no—
197C2×Dic11—24no—
198C2×Dic11—22no—
199C2×Dic11—24no—
200C2×Dic11—44no—
201C2×Dic11—42no—
202D44—44no—
203D44—42no—
204D44—42no—
205D44—42no—
206D44—42no—
207D44—82no—
208D44—82no—
209D44—82no—
210Dic22—22no—
211Dic22—24no—
212Dic22—42no—
213Dic22—42no—
214Dic22—44no—
215Dic22C2×SD1614yescomplemented
216C8×C11—42no—
217C8×C11—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—111no—
226C2×C4⋊Q8—221no—
227C2×#127—111no—
228C2×#125—221no—
229C2×#125—222no—
230C2×C4×Q8—111no—
231C2×C4×Q8—221no—
232C2×C4×Q8—221no—
233C2×C4×Q8C2×D1111yescharacteristic
234#486—114no—
235#486—222no—
236#460—114no—
237#460—114no—
238#460—222no—
239#460—222no—
240C2×C4⋊C8—111no—
241C2×C4⋊C8C2×D1111yescharacteristic
242C2×#102—222no—
243C2×#102—221no—
244C2×#102—221no—
245C2×C4×C8C2×D1111yescharacteristic
246#332—114no—
247Q8⋊C8—114no—
248Q8⋊C8C2×D1114yescomplemented
249C22×C11#44812yes—
250C22×C11#44912yes—
251C22×C11#45412yes—
252C22×C11C2×#12011yescharacteristic
253C2×D11—82no—
254C2×D11—82no—
255C2×D11—82no—
256C2×D11—164no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—42no—
260C4×C11—42no—
261C4×C11#44812yes—
262C4×C11#44912yes—
263C4×C11C22×SD1611yescharacteristic
264C4×C11C2×#13511yescharacteristic
265C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
266C4×C11C2×#13711yescharacteristic
267Dic11—24no—
268Dic11—44no—
269Dic11—42no—
270C22×Q8—111no—
271C22×Q8—221no—
272C22×Q8D4411yescharacteristic
273C22×D4—221no—
274C22×D4—221no—
275C22×D4—221no—
276C2×SD16—224no—
277C2×SD16—224no—
278C2×SD16—444no—
279C2×SD16—444no—
280C22×C8—21no—
281C22×C8—21no—
282C22×C8—221no—
283C4⋊Q8—112no—
284C4⋊Q8—112no—
285C4⋊Q8—224no—
286C4⋊Q8—224no—
287C4⋊Q8—221no—
288C4⋊Q8—221no—
289#127—112no—
290#127—221no—
291#127—221no—
292#127—221no—
293#125—224no—
294#125—224no—
295#125—228no—
296#125—228no—
297C4×Q8—21no—
298C4×Q8—21no—
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×Q8D4412yes—
308C4×Q8C22×D1112yes—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—111no—
311C2×C4⋊C4—112no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—222no—
315C2×C4⋊C4—221no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4D4411yescharacteristic
318C2×C42—21no—
319C2×C42—222no—
320C2×C42—221no—
321C2×C42C22×D1111yescharacteristic
322C4⋊C8—21no—
323C4⋊C8—112no—
324C4⋊C8—221no—
325C4⋊C8C22×D1112yes—
326#102—224no—
327#102—228no—
328#102—224no—
329C4×C8—21no—
330C4×C8C22×D1112yes—
331C2×C11#162614yescomplemented
332C2×C11C2×#44811yescharacteristic
333C2×C11C2×#44911yescharacteristic
334C2×C11C2×#45411yescharacteristic
335D11—162no—
336C24—441no—
337C2×Q8—21no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—114no—
341C2×Q8—112no—
342C2×Q8—221no—
343C2×Q8—222no—
344C2×Q8—222no—
345C2×Q8—222no—
346C2×Q8—442no—
347C2×Q8—442no—
348C2×Q8C2×D4412yes—
349C2×D4—222no—
350C2×D4—222no—
351C2×D4—222no—
352C2×D4—444no—
353C2×D4—441no—
354C2×D4—441no—
355C2×D4—441no—
356C2×D4—442no—
357C2×D4—442no—
358C2×D4—442no—
359C2×D4—442no—
360C22×C4—21no—
361C22×C4—21no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—222no—
365C22×C4C2×D4411yescharacteristic
366C22×C4D4×D1111yescharacteristic
367C22×C4D4×D1111yescharacteristic
368SD16—448no—
369SD16—448no—
370C2×C8—22no—
371C2×C8—22no—
372C2×C8—42no—
373C2×C8—42no—
374C2×C8—222no—
375C2×C8—442no—
376C4⋊C4—22no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—112no—
380C4⋊C4—114no—
381C4⋊C4—228no—
382C4⋊C4—228no—
383C4⋊C4—228no—
384C4⋊C4—221no—
385C4⋊C4—222no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—222no—
389C4⋊C4—222no—
390C4⋊C4C2×D4412yes—
391C42—22no—
392C42—22no—
393C42—228no—
394C42—222no—
395C42—222no—
396C42C2×D4411yescharacteristic
397C42D4×D1111yescharacteristic
398C42D4×D1111yescharacteristic
399C42C23×D1111yescharacteristic
400C11C2×#162611yescharacteristic, complemented, Sylow
401C23—442no—
402C23—882no—
403C23—882no—
404C23—882no—
405C23#6693511yescharacteristic
406Q8—22no—
407Q8—22no—
408Q8—42no—
409Q8—114no—
410Q8—222no—
411Q8—224no—
412Q8—442no—
413Q8—442no—
414Q8—444no—
415D4—444no—
416D4—442no—
417D4—442no—
418D4—442no—
419D4—442no—
420D4—882no—
421D4—882no—
422D4—882no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—22no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—222no—
429C2×C4—224no—
430C2×C4—222no—
431C2×C4—224no—
432C2×C4—444no—
433C2×C4—442no—
434C2×C4#6693511yescharacteristic
435C2×C4#6693511yescharacteristic
436C2×C4#6693511yescharacteristic
437C2×C4#6695712yes—
438C2×C4#6696112yes—
439C2×C4SD16×D1112yes—
440C2×C4#6697112yes—
441C2×C4C22×D4411yescharacteristic
442C2×C4C2×D4×D1111yescharacteristic
443C2×C4C2×D4×D1111yescharacteristic
444C8—42no—
445C8—42no—
446C8—442no—
447C22—882no—
448C22—882no—
449C22—882no—
450C22—1764no—
451C22#1062234712yes—
452C22#1062241912yes—
453C22#1062244012yes—
454C22C2×#6693511yescharacteristic
455C4—21no—
456C4—21no—
457C4—42no—
458C4—42no—
459C4—224no—
460C4—444no—
461C4—442no—
462C4#1062234712yes—
463C4#1062241912yes—
464C4C2×#6695711yescharacteristic
465C4C2×#6696111yescharacteristic
466C4C2×SD16×D1111yescharacteristic
467C4C2×#6697111yescharacteristic
468C2—1762no—
469C2#1306771414yesdirect product factor
470C2C2×#1062241911yescharacteristic
471C2C2×#1062234711yescharacteristic
472C2C2×#1062244011yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×Q8⋊C8C2
socleC23×C11#120
prime radicalC2×#66927C22
hypercenterC2×Q8⋊C8D11
hypocenterC11C2×#1626
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
1. C2×#10623098C2semidirect
5. #13067714C2direct (N × H)
6. C2×#10622124C2semidirect
7. C2×#10622094C2semidirect
8. C2×C11×Q8⋊C8C2semidirect
16. #10623098C22semidirect
36. C11×Q8⋊C8C22semidirect
37. #10622124C22semidirect
38. #10622094C22semidirect
131. C2×Dic22SD16semidirect
172. C2×Q8⋊C8D11semidirect
215. Dic22C2×SD16semidirect
248. Q8⋊C8C2×D11semidirect
331. C2×C11#1626semidirect
400. C11C2×#1626semidirect
469. C2#13067714direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230982
C2×#106223072
C2×#106224612
C2×#106226402
#130677142
C2×#106221242
C2×#106220942
C2×C11×Q8⋊C82
C2×#162611