Finite Group Databasebeta

← C2×#13067827 #14729442

Subgroups — C2×#13067827 #14729442

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×#10623261C211yesmaximal, characteristic
2C2×#10622700C211yesmaximal, characteristic
3C2×#10622703C211yesmaximal, characteristic, complemented
4#13067827C218yesmaximal, direct product factor
5C2×#10622184C211yesmaximal, characteristic, complemented
6C2×#10622094C211yesmaximal, characteristic, complemented
7C2×#10622097C211yesmaximal, characteristic
8C2×C11×#487C211yesmaximal, characteristic, complemented
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#66999—22no—
12C22×#4326—21no—
13#10623261—22no—
14#10623261—22no—
15#10623261—22no—
16#10623261C2214yes—
17C2×#66950—21no—
18C2×#66946—21no—
19C2×C4⋊C4×D11—21no—
20C2×#66943—21no—
21C2×C4×D44C2211yescharacteristic
22C2×C4×Dic22C2211yescharacteristic
23C11×#487—22no—
24C11×#487C2214yescomplemented
25C2×C11×#103—22no—
26C2×C4×C8×C11C2211yescharacteristic
27C2×#66899—21no—
28#10622703—22no—
29#10622703C2214yescomplemented
30#10622700—22no—
31#10622700C2214yes—
32C2×#66873—21no—
33C2×#66871—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622184C2214yescomplemented
37#10622097C2214yes—
38#10622094C2214yescomplemented
39C22×Q8×C11—21no—
40C22×Q8×C11D412yes—
41C22×D44D411yescharacteristic
42C22×C4×D11—21no—
43C22×C4×D11—22no—
44C22×Dic22D411yescharacteristic
45C22×C8×C11—21no—
46C11×C4⋊Q8—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8D412yes—
52C11×C4⋊Q8C2312yes—
53C11×C4⋊Q8C2312yes—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C42×C11C2311yescharacteristic
59#66999—28no—
60#66999—28no—
61C2×#4326—24no—
62C2×#4326—44no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4—21no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11D411yescharacteristic
67C2×C4⋊Dic11D411yescharacteristic
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—21no—
70C2×C4×Dic11—21no—
71C22×C11⋊C8—21no—
72C22×C11⋊C8—21no—
73#66950—24no—
74#66950—24no—
75#66946—24no—
76#66946—24no—
77C4⋊C4×D11—24no—
78C4⋊C4×D11—24no—
79#66943—24no—
80#66943—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#66899—24no—
93#66873—24no—
94#66871—24no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)—21no—
97C4⋊(C11⋊C8)C2312yes—
98C4⋊(C11⋊C8)C2312yes—
99C2×#1644—111nomaximal, Sylow
100C23×D11—21no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11—44no—
104C2×Q8×C11—41no—
105C2×Q8×C11—42no—
106C2×Q8×C11—42no—
107C2×Q8×C11C2×D414yes—
108C22×C4×C11—22no—
109C22×C4×C11—41no—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2×D411yescharacteristic
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—21no—
116C2×D44—21no—
117C2×D44—22no—
118C2×D44Q1614yescomplemented
119C2×D44C2×D412yes—
120C2×C4×D11—28no—
121C2×C4×D11—22no—
122C2×C4×D11—22no—
123C2×C4×D11—42no—
124C2×C4×D11—42no—
125C2×C4×D11—84no—
126C2×Dic22—21no—
127C2×Dic22—22no—
128C2×Dic22—22no—
129C2×Dic22C2×D412yes—
130C2×C8×C11—22no—
131C2×C8×C11—42no—
132C11×C4⋊C4—22no—
133C11×C4⋊C4—22no—
134C11×C4⋊C4—22no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—41no—
139C11×C4⋊C4—41no—
140C42×C11C2×D411yescharacteristic
141C42×C11C2×D411yescharacteristic
142C42×C11C2×D411yescharacteristic
143C42×C11C2411yescharacteristic
144#4326—48no—
145(C2×D11)⋊C4—28no—
146(C2×D11)⋊C4—22no—
147(C2×D11)⋊C4—22no—
148C4⋊Dic11—28no—
149C4⋊Dic11—21no—
150C4⋊Dic11—21no—
151C4⋊Dic11C2×D412yes—
152C4⋊Dic11C2×D412yes—
153Dic11⋊C4—28no—
154Dic11⋊C4—22no—
155Dic11⋊C4—22no—
156C4×Dic11—22no—
157C4×Dic11—22no—
158C2×C11⋊C8—22no—
159C2×C11⋊C8—22no—
160C2×C11⋊C8—42no—
161C2×C11⋊C8—42no—
162C2×#554—111no—
163C2×#487D1111yescharacteristic, complemented
164C2×#474—111no—
165C2×#462—111no—
166#1644—118no—
167C2×#333—111no—
168C2×Q8⋊C8—111no—
169C2×D4⋊C8—111no—
170C23×C11#12011yescharacteristic
171C22×D11—22no—
172C22×D11—24no—
173C22×D11—42no—
174C22×D11—42no—
175Q8×C11—44no—
176Q8×C11—42no—
177Q8×C11—42no—
178Q8×C11—82no—
179Q8×C11—82no—
180C2×C4×C11—22no—
181C2×C4×C11—24no—
182C2×C4×C11—44no—
183C2×C4×C11—42no—
184C2×C4×C11—82no—
185C2×C4×C11#12011yescharacteristic
186C2×C4×C11#12011yescharacteristic
187C2×C4×C11#12011yescharacteristic
188C2×C4×C11C2×Q1612yes—
189C2×C4×C11#13512yes—
190C2×C4×C11AGL(1,ℤ/8)12yes—
191C2×C4×C11#13712yes—
192C2×C4×C11C22×D411yescharacteristic
193C2×C4×C11C22×D411yescharacteristic
194C2×C4×C11C22×D411yescharacteristic
195C2×Dic11—22no—
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201D44—22no—
202D44—24no—
203D44C2×Q1614yescomplemented
204C4×D11—42no—
205C4×D11—42no—
206C4×D11—44no—
207C4×D11—88no—
208Dic22—22no—
209Dic22—22no—
210Dic22—42no—
211C8×C11—42no—
212C11⋊C8—42no—
213C11⋊C8—42no—
214C22×Q16—221no—
215#554—114no—
216#554—222no—
217#554—222no—
218#554—222no—
219C2×C4⋊Q8C2×D1111yescharacteristic
220C2×C4⋊Q8C2×D1111yescharacteristic
221C2×#125—221no—
222C2×C22⋊Q8—221no—
223C2×C22⋊Q8—222no—
224C2×C4×Q8—111no—
225C2×C4×D4—111no—
226C2×C4×D4—221no—
227C22×C4⋊C4—221no—
228#487—22no—
229#487C2×D1114yescomplemented
230#474—114no—
231#474—222no—
232#462—114no—
233#462—222no—
234C2×#107—221no—
235C2×C4⋊C8—111no—
236C2×C4⋊C8—111no—
237C2×#103—22no—
238C2×#103—221no—
239C2×#102—221no—
240C2×C4×C8C2×D1111yescharacteristic
241#333—114no—
242Q8⋊C8—114no—
243D4⋊C8—114no—
244C22×C11#44912yes—
245C22×C11#45112yes—
246C22×C11#45512yes—
247C22×C11C2×#12011yescharacteristic
248C2×D11—24no—
249C2×D11—48no—
250C2×D11—42no—
251C2×D11—42no—
252C4×C11—21no—
253C4×C11—21no—
254C4×C11—44no—
255C4×C11—82no—
256C4×C11#44912yes—
257C4×C11#45112yes—
258C4×C11C22×Q1611yescharacteristic
259C4×C11C2×#13511yescharacteristic
260C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
261C4×C11C2×#13711yescharacteristic
262Dic11—42no—
263Dic11—42no—
264Dic11—42no—
265C22×Q8—21no—
266C22×Q8—111no—
267C22×Q8C22⋊D1112yes—
268C22×D4—111no—
269C23×C4—222no—
270C23×C4—221no—
271C2×Q16—224no—
272C2×Q16—444no—
273C22×C8—21no—
274C22×C8—221no—
275C22×C8—221no—
276C4⋊Q8—21no—
277C4⋊Q8—21no—
278C4⋊Q8—21no—
279C4⋊Q8—21no—
280C4⋊Q8—21no—
281C4⋊Q8C22⋊D1112yes—
282C4⋊Q8C22×D1112yes—
283C4⋊Q8C22×D1112yes—
284#125—224no—
285#125—224no—
286C22⋊Q8—224no—
287C22⋊Q8—224no—
288C22⋊Q8—228no—
289C22⋊Q8—228no—
290C4×Q8—112no—
291C4×Q8—112no—
292C4×Q8—221no—
293C4×Q8—221no—
294C4×D4—112no—
295C4×D4—112no—
296C4×D4—224no—
297C4×D4—224no—
298C4×D4—221no—
299C4×D4—221no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—21no—
303C2×C4⋊C4—21no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—224no—
307C2×C4⋊C4—224no—
308C2×C4⋊C4—222no—
309C2×C4⋊C4—222no—
310C2×C4⋊C4—221no—
311C2×C22⋊C4—222no—
312C2×C22⋊C4—221no—
313C2×C42—221no—
314C2×C42C22×D1111yescharacteristic
315#107—224no—
316C4⋊C8—112no—
317C4⋊C8—112no—
318C4⋊C8—221no—
319C4⋊C8—221no—
320#103—28no—
321#103—224no—
322#102—224no—
323C4×C8—21no—
324C4×C8C22×D1112yes—
325C2×C11#164414yescomplemented
326C2×C11C2×#45111yescharacteristic
327C2×C11C2×#44911yescharacteristic
328C2×C11C2×#45511yescharacteristic
329D11—44no—
330C24—221no—
331C2×Q8—22no—
332C2×Q8—22no—
333C2×Q8—44no—
334C2×Q8—41no—
335C2×Q8—42no—
336C2×Q8—42no—
337C2×Q8—112no—
338C2×Q8—221no—
339C2×Q8—222no—
340C2×Q8—222no—
341C2×Q8C2×C22⋊D1114yes—
342C2×D4—114no—
343C2×D4—112no—
344C2×D4—222no—
345C2×D4—221no—
346C22×C4—22no—
347C22×C4—41no—
348C22×C4—228no—
349C22×C4—221no—
350C22×C4—221no—
351C22×C4—221no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—442no—
355C22×C4—442no—
356C22×C4—884no—
357C22×C4D4×D1111yescharacteristic
358C22×C4D4×D1111yescharacteristic
359C22×C4C2×C22⋊D1111yescharacteristic
360Q16—448no—
361C2×C8—22no—
362C2×C8—42no—
363C2×C8—222no—
364C2×C8—222no—
365C2×C8—442no—
366C2×C8—442no—
367C4⋊C4—22no—
368C4⋊C4—22no—
369C4⋊C4—22no—
370C4⋊C4—22no—
371C4⋊C4—22no—
372C4⋊C4—22no—
373C4⋊C4—41no—
374C4⋊C4—41no—
375C4⋊C4—112no—
376C4⋊C4—112no—
377C4⋊C4—228no—
378C4⋊C4—228no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—222no—
382C4⋊C4—222no—
383C22⋊C4—228no—
384C22⋊C4—222no—
385C22⋊C4—222no—
386C42—222no—
387C42—222no—
388C42D4×D1111yescharacteristic
389C42D4×D1111yescharacteristic
390C42C2×C22⋊D1111yescharacteristic
391C42C23×D1111yescharacteristic
392C11C2×#164411yescharacteristic, complemented, Sylow
393C23—224no—
394C23—222no—
395C23—442no—
396C23—442no—
397C23#6699011yescharacteristic
398Q8—44no—
399Q8—42no—
400Q8—42no—
401Q8—82no—
402Q8—82no—
403Q8—222no—
404Q8—222no—
405Q8—442no—
406D4—114no—
407D4—222no—
408D4—224no—
409C2×C4—22no—
410C2×C4—24no—
411C2×C4—44no—
412C2×C4—42no—
413C2×C4—82no—
414C2×C4—222no—
415C2×C4—222no—
416C2×C4—222no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—444no—
423C2×C4—888no—
424C2×C4#6696712yes—
425C2×C4#6696912yes—
426C2×C4Q16×D1112yes—
427C2×C4#6697112yes—
428C2×C4#6699011yescharacteristic
429C2×C4#6699011yescharacteristic
430C2×C4#6699011yescharacteristic
431C2×C4C2×D4×D1111yescharacteristic
432C2×C4C2×D4×D1111yescharacteristic
433C2×C4C22×C22⋊D1111yescharacteristic
434C8—42no—
435C8—442no—
436C8—442no—
437C22—224no—
438C22—448no—
439C22—442no—
440C22—442no—
441C22#1062267412yes—
442C22#1062278512yes—
443C22#1062279912yes—
444C22C2×#6699011yescharacteristic
445C4—21no—
446C4—21no—
447C4—44no—
448C4—82no—
449C4—442no—
450C4—442no—
451C4—442no—
452C4#1062278512yes—
453C4#1062279912yes—
454C4C2×#6696711yescharacteristic
455C4C2×#6696911yescharacteristic
456C4C2×Q16×D1111yescharacteristic
457C4C2×#6697111yescharacteristic
458C2—444no—
459C2#1306782714yesdirect product factor
460C2C2×#1062279911yescharacteristic
461C2C2×#1062278511yescharacteristic
462C2C2×#1062267411yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#487C2
socleC23×C11#120
prime radicalC22×D44D4
hypercenterC2×#487D11
hypocenterC11C2×#1644
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
3. C2×#10622703C2semidirect
4. #13067827C2direct (N × H)
5. C2×#10622184C2semidirect
6. C2×#10622094C2semidirect
8. C2×C11×#487C2semidirect
24. C11×#487C22semidirect
29. #10622703C22semidirect
36. #10622184C22semidirect
38. #10622094C22semidirect
118. C2×D44Q16semidirect
163. C2×#487D11semidirect
203. D44C2×Q16semidirect
229. #487C2×D11semidirect
325. C2×C11#1644semidirect
392. C11C2×#1644semidirect
459. C2#13067827direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232612
C2×#106227002
C2×#106227032
#130678272
C2×#106221842
C2×#106220942
C2×#106220972
C2×C11×#4872
C2×#164411