Finite Group Databasebeta

← C2×#13067778 #14729491

Subgroups — C2×#13067778 #14729491

Order 2816.

1174 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×#10623258C211yesmaximal, characteristic
2C2×#10622704C211yesmaximal, characteristic, complemented
3C2×#10622697C211yesmaximal, characteristic
4#13067778C218yesmaximal, direct product factor
5C2×#10622185C211yesmaximal, characteristic, complemented
6C2×#10622094C211yesmaximal, characteristic, complemented
7C2×#10622097C211yesmaximal, characteristic
8C2×C11×#487C211yesmaximal, characteristic, complemented
9C22×Q8×D11—21no—
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×C11×C4⋊Q8C2211yescharacteristic
12C2×#66999—21no—
13#10623258—22no—
14#10623258—22no—
15#10623258—22no—
16#10623258C2214yes—
17C2×#66949—22no—
18C2×#66946—21no—
19C2×#66941—21no—
20C2×C4×D44C2211yescharacteristic
21C2×C4×Dic22C2211yescharacteristic
22C11×#487—22no—
23C11×#487C2214yescomplemented
24C2×C11×#103—22no—
25C2×C4×C8×C11C2211yescharacteristic
26#10622704—22no—
27#10622704C2214yescomplemented
28#10622697—22no—
29#10622697C2214yes—
30C2×#66874—21no—
31C2×#66873—21no—
32C2×#66872—21no—
33C2×#66871—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622185C2214yescomplemented
37#10622097C2214yes—
38#10622094C2214yescomplemented
39C22×Q8×C11—21no—
40C22×Q8×C11—21no—
41C2×Q8×D11—24no—
42C2×Q8×D11—24no—
43C2×Q8×D11—44no—
44C2×Q8×D11—44no—
45C22×D44D411yescharacteristic
46C22×C4×D11—22no—
47C22×C4×D11—21no—
48C22×Dic22—22no—
49C22×Dic22D411yescharacteristic
50C22×C8×C11—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8—21no—
53C11×C4⋊Q8—21no—
54C11×C4⋊Q8—21no—
55C11×C4⋊Q8—21no—
56C11×C4⋊Q8D412yes—
57C11×C4⋊Q8C2312yes—
58C11×C4⋊Q8C2312yes—
59C2×C11×C4⋊C4—21no—
60C2×C11×C4⋊C4—21no—
61C2×C11×C4⋊C4—21no—
62C2×C11×C4⋊C4D412yes—
63C2×C42×C11C2311yescharacteristic
64#66999—24no—
65#66999—24no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—21no—
68C2×C4⋊Dic11D411yescharacteristic
69C2×C4⋊Dic11D411yescharacteristic
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—21no—
72C2×C4×Dic11—21no—
73C22×C11⋊C8—21no—
74C22×C11⋊C8—21no—
75#66949—28no—
76#66949—28no—
77#66946—24no—
78#66946—24no—
79#66941—24no—
80#66941—24no—
81C4×D44—21no—
82C4×D44—21no—
83C4×D44D412yes—
84C4×D44C2312yes—
85C4×Dic22—21no—
86C4×Dic22—21no—
87C4×Dic22D412yes—
88C4×Dic22C2312yes—
89C11×#103—28no—
90C4×C8×C11—21no—
91C4×C8×C11C2312yes—
92#66874—24no—
93#66873—24no—
94#66872—24no—
95#66871—24no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)—21no—
98C4⋊(C11⋊C8)C2312yes—
99C4⋊(C11⋊C8)C2312yes—
100C2×#1637—111nomaximal, Sylow
101C23×D11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—22no—
105C2×Q8×C11—44no—
106C2×Q8×C11—41no—
107C2×Q8×C11—42no—
108C2×Q8×C11—42no—
109C22×C4×C11—22no—
110C22×C4×C11—41no—
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D411yescharacteristic
114C22×Dic11—21no—
115C22×Dic11—21no—
116C22×Dic11—21no—
117Q8×D11—48no—
118Q8×D11—416no—
119Q8×D11—48no—
120C2×D44—21no—
121C2×D44—22no—
122C2×D44Q1614yes—
123C2×D44C2×D412yes—
124C2×C4×D11—28no—
125C2×C4×D11—22no—
126C2×C4×D11—22no—
127C2×C4×D11—48no—
128C2×C4×D11—42no—
129C2×C4×D11—42no—
130C2×Dic22—28no—
131C2×Dic22—21no—
132C2×Dic22—22no—
133C2×Dic22—48no—
134C2×Dic22SD1614yes—
135C2×Dic22C2×D412yes—
136C2×C8×C11—22no—
137C2×C8×C11—42no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—22no—
143C11×C4⋊C4—41no—
144C11×C4⋊C4—41no—
145C11×C4⋊C4C2×D414yes—
146C42×C11C2×D411yescharacteristic
147C42×C11C2×D411yescharacteristic
148C42×C11C2×D411yescharacteristic
149C42×C11C2411yescharacteristic
150(C2×D11)⋊C4—28no—
151(C2×D11)⋊C4—22no—
152(C2×D11)⋊C4—22no—
153C4⋊Dic11—21no—
154C4⋊Dic11—21no—
155C4⋊Dic11C2×D412yes—
156C4⋊Dic11C2×D412yes—
157Dic11⋊C4—28no—
158Dic11⋊C4—22no—
159Dic11⋊C4—22no—
160C4×Dic11—22no—
161C4×Dic11—22no—
162C2×C11⋊C8—22no—
163C2×C11⋊C8—22no—
164C2×C11⋊C8—42no—
165C2×C11⋊C8—42no—
166C2×D4×Q8—111no—
167C2×#487D1111yescharacteristic, complemented
168C2×#477—111no—
169C2×#476—111no—
170#1637—118no—
171C2×#332—111no—
172C2×Q8⋊C8—111no—
173C2×D4⋊C8—111no—
174C23×C11#12011yescharacteristic
175C22×D11—22no—
176C22×D11—24no—
177C22×D11—42no—
178C22×D11—42no—
179Q8×C11—44no—
180Q8×C11—42no—
181Q8×C11—42no—
182Q8×C11—44no—
183Q8×C11—82no—
184C2×C4×C11—22no—
185C2×C4×C11—24no—
186C2×C4×C11—44no—
187C2×C4×C11—42no—
188C2×C4×C11—82no—
189C2×C4×C11#12011yescharacteristic
190C2×C4×C11#12011yescharacteristic
191C2×C4×C11#12011yescharacteristic
192C2×C4×C11C2×SD1612yes—
193C2×C4×C11C2×Q1612yes—
194C2×C4×C11AGL(1,ℤ/8)12yes—
195C2×C4×C11#13712yes—
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C22×D411yescharacteristic
198C2×C4×C11C22×D411yescharacteristic
199C2×Dic11—22no—
200C2×Dic11—24no—
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205D44—22no—
206D44—24no—
207D44C2×Q1614yes—
208C4×D11—416no—
209C4×D11—42no—
210C4×D11—42no—
211C4×D11—44no—
212Dic22—22no—
213Dic22—24no—
214Dic22—416no—
215Dic22C2×SD1614yes—
216C8×C11—42no—
217C11⋊C8—42no—
218C11⋊C8—42no—
219C23×Q8—221no—
220D4×Q8—114no—
221D4×Q8—222no—
222D4×Q8—222no—
223D4×Q8—222no—
224C2×C4⋊Q8—221no—
225C2×C4⋊Q8C2×D1111yescharacteristic
226C2×C4⋊Q8C2×D1111yescharacteristic
227C2×C22⋊Q8—221no—
228C2×C22⋊Q8—222no—
229C2×C4×Q8—111no—
230C2×C4×D4—111no—
231C2×C4×D4—221no—
232#487—22no—
233#487C2×D1114yescomplemented
234#477—114no—
235#477—222no—
236#476—114no—
237#476—222no—
238C2×#107—221no—
239C2×#106—221no—
240C2×C4⋊C8—111no—
241C2×C4⋊C8—111no—
242C2×#103—22no—
243C2×#103—221no—
244C2×#102—221no—
245C2×C4×C8C2×D1111yescharacteristic
246#332—114no—
247Q8⋊C8—114no—
248D4⋊C8—114no—
249C22×C11#45012yes—
250C22×C11#45112yes—
251C22×C11#45412yes—
252C22×C11C2×#12011yescharacteristic
253C2×D11—24no—
254C2×D11—48no—
255C2×D11—42no—
256C2×D11—42no—
257C4×C11—21no—
258C4×C11—21no—
259C4×C11—44no—
260C4×C11—82no—
261C4×C11#45012yes—
262C4×C11#45112yes—
263C4×C11C22×SD1611yescharacteristic
264C4×C11C22×Q1611yescharacteristic
265C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
266C4×C11C2×#13711yescharacteristic
267Dic11—24no—
268Dic11—42no—
269Dic11—42no—
270C22×Q8—21no—
271C22×Q8—21no—
272C22×Q8—111no—
273C22×Q8—222no—
274C22×Q8—224no—
275C22×Q8—224no—
276C22×Q8—444no—
277C22×Q8—444no—
278C22×D4—111no—
279C23×C4—222no—
280C23×C4—221no—
281C22×C8—21no—
282C22×C8—221no—
283C22×C8—221no—
284C4⋊Q8—21no—
285C4⋊Q8—21no—
286C4⋊Q8—21no—
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8—224no—
290C4⋊Q8—224no—
291C4⋊Q8C22⋊D1112yes—
292C4⋊Q8C22×D1112yes—
293C4⋊Q8C22×D1112yes—
294C22⋊Q8—228no—
295C22⋊Q8—224no—
296C22⋊Q8—224no—
297C22⋊Q8—228no—
298C4×Q8—112no—
299C4×Q8—112no—
300C4×Q8—221no—
301C4×Q8—221no—
302C4×D4—112no—
303C4×D4—112no—
304C4×D4—224no—
305C4×D4—224no—
306C4×D4—221no—
307C4×D4—221no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4—21no—
310C2×C4⋊C4—21no—
311C2×C4⋊C4—111no—
312C2×C4⋊C4—111no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4C22⋊D1112yes—
316C2×C22⋊C4—222no—
317C2×C22⋊C4—221no—
318C2×C42—221no—
319C2×C42C22×D1111yescharacteristic
320#107—224no—
321#106—224no—
322C4⋊C8—112no—
323C4⋊C8—112no—
324C4⋊C8—221no—
325C4⋊C8—221no—
326#103—28no—
327#103—224no—
328#102—224no—
329C4×C8—21no—
330C4×C8C22×D1112yes—
331C2×C11#163714yescomplemented
332C2×C11C2×#45011yescharacteristic
333C2×C11C2×#45111yescharacteristic
334C2×C11C2×#45411yescharacteristic
335D11—44no—
336C24—221no—
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—44no—
341C2×Q8—42no—
342C2×Q8—42no—
343C2×Q8—41no—
344C2×Q8—114no—
345C2×Q8—112no—
346C2×Q8—228no—
347C2×Q8—222no—
348C2×Q8—221no—
349C2×Q8—448no—
350C2×Q8—448no—
351C2×Q8—448no—
352C2×Q8—4416no—
353C2×D4—114no—
354C2×D4—112no—
355C2×D4—222no—
356C2×D4—221no—
357C22×C4—22no—
358C22×C4—41no—
359C22×C4—228no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—221no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—448no—
366C22×C4—442no—
367C22×C4—442no—
368C22×C4D4×D1111yescharacteristic
369C22×C4D4×D1111yescharacteristic
370C22×C4C2×C22⋊D1111yescharacteristic
371C2×C8—22no—
372C2×C8—42no—
373C2×C8—222no—
374C2×C8—222no—
375C2×C8—442no—
376C2×C8—442no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—22no—
382C4⋊C4—41no—
383C4⋊C4—41no—
384C4⋊C4—112no—
385C4⋊C4—112no—
386C4⋊C4—228no—
387C4⋊C4—221no—
388C4⋊C4—221no—
389C4⋊C4—222no—
390C4⋊C4—222no—
391C4⋊C4C2×C22⋊D1114yes—
392C22⋊C4—228no—
393C22⋊C4—222no—
394C22⋊C4—222no—
395C42—222no—
396C42—222no—
397C42D4×D1111yescharacteristic
398C42D4×D1111yescharacteristic
399C42C2×C22⋊D1111yescharacteristic
400C42C23×D1111yescharacteristic
401C11C2×#163711yescharacteristic, complemented, Sylow
402C23—224no—
403C23—222no—
404C23—442no—
405C23—442no—
406C23#6699011yescharacteristic
407Q8—44no—
408Q8—42no—
409Q8—42no—
410Q8—44no—
411Q8—82no—
412Q8—114no—
413Q8—222no—
414Q8—224no—
415Q8—4416no—
416D4—114no—
417D4—222no—
418D4—224no—
419C2×C4—22no—
420C2×C4—24no—
421C2×C4—44no—
422C2×C4—42no—
423C2×C4—82no—
424C2×C4—224no—
425C2×C4—222no—
426C2×C4—222no—
427C2×C4—222no—
428C2×C4—4416no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—444no—
434C2×C4SD16×D1112yes—
435C2×C4#6696712yes—
436C2×C4Q16×D1112yes—
437C2×C4#6697112yes—
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—224no—
448C22—448no—
449C22—442no—
450C22—442no—
451C22#1062267512yes—
452C22#1062278212yes—
453C22#1062279912yes—
454C22C2×#6699011yescharacteristic
455C4—21no—
456C4—21no—
457C4—44no—
458C4—82no—
459C4—224no—
460C4—442no—
461C4—442no—
462C4#1062278212yes—
463C4#1062279912yes—
464C4C2×SD16×D1111yescharacteristic
465C4C2×#6696711yescharacteristic
466C4C2×Q16×D1111yescharacteristic
467C4C2×#6697111yescharacteristic
468C2—444no—
469C2#1306777814yesdirect product factor
470C2C2×#1062278211yescharacteristic
471C2C2×#1062279911yescharacteristic
472C2C2×#1062267511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#487C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenterC2×#487D11
hypocenterC11C2×#1637
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#487

Complements

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

NH ≅ G/Ntype
2. C2×#10622704C2semidirect
4. #13067778C2direct (N × H)
5. C2×#10622185C2semidirect
6. C2×#10622094C2semidirect
8. C2×C11×#487C2semidirect
23. C11×#487C22semidirect
27. #10622704C22semidirect
36. #10622185C22semidirect
38. #10622094C22semidirect
167. C2×#487D11semidirect
233. #487C2×D11semidirect
331. C2×C11#1637semidirect
401. C11C2×#1637semidirect
469. C2#13067778direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232582
C2×#106227042
C2×#106226972
#130677782
C2×#106221852
C2×#106220942
C2×#106220972
C2×C11×#4872
C2×#163711