Finite Group Databasebeta

← C2×#13067841 #14729700

Subgroups — C2×#13067841 #14729700

Order 2816.

1042 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623265C211yesmaximal, characteristic
2C2×#10622700C211yesmaximal, characteristic, complemented
3C2×#10622696C211yesmaximal, characteristic, complemented
4#13067841C218yesmaximal, direct product factor
5C2×#10622184C211yesmaximal, characteristic, complemented
6C2×#10622097C211yesmaximal, characteristic, complemented
7C2×#10622097C211yesmaximal, characteristic, complemented
8C2×C11×#487C211yesmaximal, characteristic, complemented
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C11×C4⋊Q8C2211yescharacteristic
11C2×#67000—22no—
12C22×#4325—21no—
13#10623265—22no—
14#10623265—22no—
15#10623265—22no—
16#10623265C2214yes—
17C2×#66948—21no—
18C2×#66948—21no—
19C2×#66945—21no—
20C2×#66945—21no—
21C2×C4×D44C2211yescharacteristic
22C2×C4×D44C2211yescharacteristic
23C11×#487—22no—
24C11×#487C2214yescomplemented
25C2×C11×#103—22no—
26C2×C4×C8×C11C2211yescharacteristic
27C2×#66899—21no—
28#10622700—22no—
29#10622700C2214yescomplemented
30#10622696—22no—
31#10622696C2214yescomplemented
32C2×#66873—21no—
33C2×#66871—21no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622184C2214yescomplemented
37#10622097C2214yescomplemented
38#10622097C2214yescomplemented
39C22×Q8×C11—21no—
40C22×Q8×C11D412yes—
41C22×D44—22no—
42C22×D44D411yescharacteristic
43C22×D44D411yescharacteristic
44C22×C4×D11—21no—
45C22×C4×D11—21no—
46C22×C8×C11—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8—21no—
51C11×C4⋊Q8—21no—
52C11×C4⋊Q8D412yes—
53C11×C4⋊Q8C2312yes—
54C11×C4⋊Q8C2312yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60#67000—28no—
61#67000—28no—
62C2×#4325—24no—
63C2×#4325—44no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—21no—
67C2×(C2×D11)⋊C4—21no—
68C2×C4⋊Dic11D411yescharacteristic
69C2×C4⋊Dic11D411yescharacteristic
70C2×C4×Dic11—22no—
71C22×C11⋊C8—21no—
72C22×C11⋊C8—21no—
73#66948—24no—
74#66948—24no—
75#66948—24no—
76#66948—24no—
77#66945—24no—
78#66945—24no—
79#66945—24no—
80#66945—24no—
81C4×D44—21no—
82C4×D44—21no—
83C4×D44—21no—
84C4×D44—21no—
85C4×D44D412yes—
86C4×D44D412yes—
87C4×D44C2312yes—
88C4×D44C2312yes—
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×#1646—111nomaximal, Sylow
100C23×D11—21no—
101C23×D11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—22no—
104C2×Q8×C11—44no—
105C2×Q8×C11—41no—
106C2×Q8×C11—42no—
107C2×Q8×C11—42no—
108C2×Q8×C11C2×D414yes—
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—
116C2×D44—28no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—22no—
120C2×D44—22no—
121C2×D44—22no—
122C2×D44—22no—
123C2×D44—84no—
124C2×D44C2×D412yes—
125C2×D44C2×D412yes—
126C2×C4×D11—22no—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—22no—
130C2×C4×D11—42no—
131C2×C4×D11—42no—
132C2×C4×D11—42no—
133C2×C4×D11—42no—
134C2×C8×C11—22no—
135C2×C8×C11—42no—
136C11×C4⋊C4—22no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—22no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4—41no—
143C11×C4⋊C4—41no—
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11C2×D411yescharacteristic
147C42×C11C2411yescharacteristic
148#4325—48no—
149(C2×D11)⋊C4—28no—
150(C2×D11)⋊C4—28no—
151(C2×D11)⋊C4—22no—
152(C2×D11)⋊C4—22no—
153(C2×D11)⋊C4—22no—
154(C2×D11)⋊C4—22no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11C2×D412yes—
158C4⋊Dic11C2×D412yes—
159C4×Dic11—28no—
160C2×C11⋊C8—22no—
161C2×C11⋊C8—22no—
162C2×C11⋊C8—42no—
163C2×C11⋊C8—42no—
164C2×#555—111no—
165C2×#487D1111yescharacteristic, complemented
166C2×#474—111no—
167C2×#461—111no—
168#1646—118no—
169C2×#333—111no—
170C2×D4⋊C8—111no—
171C2×D4⋊C8—111no—
172C23×C11#12011yescharacteristic
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—42no—
176C22×D11—42no—
177C22×D11—42no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—42no—
181Q8×C11—44no—
182Q8×C11—42no—
183Q8×C11—42no—
184Q8×C11—82no—
185Q8×C11—82no—
186C2×C4×C11—22no—
187C2×C4×C11—24no—
188C2×C4×C11—44no—
189C2×C4×C11—42no—
190C2×C4×C11—82no—
191C2×C4×C11#12011yescharacteristic
192C2×C4×C11#12011yescharacteristic
193C2×C4×C11#12011yescharacteristic
194C2×C4×C11#13512yes—
195C2×C4×C11#13512yes—
196C2×C4×C11AGL(1,ℤ/8)12yes—
197C2×C4×C11#13712yes—
198C2×C4×C11C22×D411yescharacteristic
199C2×C4×C11C22×D411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×Dic11—22no—
202C2×Dic11—22no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205D44—22no—
206D44—22no—
207D44—22no—
208D44—22no—
209D44—42no—
210D44—42no—
211D44—88no—
212C4×D11—42no—
213C4×D11—42no—
214C4×D11—42no—
215C4×D11—42no—
216C4×D11—44no—
217C4×D11—44no—
218C8×C11—42no—
219C11⋊C8—42no—
220C11⋊C8—42no—
221C22×SD16—221no—
222#555—114no—
223#555—222no—
224#555—222no—
225#555—222no—
226C2×C4⋊Q8C2×D1111yescharacteristic
227C2×C4⋊Q8C2×D1111yescharacteristic
228C2×#124—222no—
229C2×#121—221no—
230C2×#121—221no—
231C2×C4×D4—111no—
232C2×C4×D4—111no—
233C2×#117—221no—
234C2×#117—221no—
235#487—22no—
236#487C2×D1114yescomplemented
237#474—114no—
238#474—222no—
239#461—114no—
240#461—222no—
241C2×#107—221no—
242C2×C4⋊C8—111no—
243C2×C4⋊C8—111no—
244C2×#103—22no—
245C2×#103—221no—
246C2×#102—221no—
247C2×C4×C8C2×D1111yescharacteristic
248#333—114no—
249D4⋊C8—114no—
250D4⋊C8—114no—
251C22×C11#44912yes—
252C22×C11#45212yes—
253C22×C11#45512yes—
254C22×C11C2×#12011yescharacteristic
255C2×D11—42no—
256C2×D11—42no—
257C2×D11—42no—
258C2×D11—42no—
259C2×D11—42no—
260C2×D11—42no—
261C2×D11—84no—
262C2×D11—84no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—44no—
266C4×C11—82no—
267C4×C11#44912yes—
268C4×C11#45212yes—
269C4×C11C2×#13511yescharacteristic
270C4×C11C2×#13511yescharacteristic
271C4×C11C2×AGL(1,ℤ/8)11yescharacteristic
272C4×C11C2×#13711yescharacteristic
273Dic11—42no—
274Dic11—42no—
275C22×Q8—21no—
276C22×Q8C22⋊D1112yes—
277C22×D4—111no—
278C22×D4—111no—
279C22×D4—222no—
280C23×C4—221no—
281C23×C4—221no—
282C2×SD16—224no—
283C2×SD16—444no—
284C22×C8—21no—
285C22×C8—221no—
286C22×C8—221no—
287C4⋊Q8—21no—
288C4⋊Q8—21no—
289C4⋊Q8—21no—
290C4⋊Q8—21no—
291C4⋊Q8—21no—
292C4⋊Q8C22⋊D1112yes—
293C4⋊Q8C22×D1112yes—
294C4⋊Q8C22×D1112yes—
295#124—228no—
296#124—228no—
297#121—224no—
298#121—224no—
299#121—224no—
300#121—224no—
301C4×D4—112no—
302C4×D4—112no—
303C4×D4—112no—
304C4×D4—112no—
305C4×D4—221no—
306C4×D4—221no—
307C4×D4—221no—
308C4×D4—221no—
309#117—224no—
310#117—224no—
311#117—224no—
312#117—224no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—21no—
316C2×C4⋊C4—21no—
317C2×C4⋊C4—111no—
318C2×C4⋊C4—111no—
319C2×C22⋊C4—222no—
320C2×C22⋊C4—222no—
321C2×C22⋊C4—221no—
322C2×C22⋊C4—221no—
323C2×C42—222no—
324C2×C42C22×D1111yescharacteristic
325#107—224no—
326C4⋊C8—112no—
327C4⋊C8—112no—
328C4⋊C8—221no—
329C4⋊C8—221no—
330#103—28no—
331#103—224no—
332#102—224no—
333C4×C8—21no—
334C4×C8C22×D1112yes—
335C2×C11#164614yescomplemented
336C2×C11C2×#44911yescharacteristic
337C2×C11C2×#45211yescharacteristic
338C2×C11C2×#45511yescharacteristic
339D11—82no—
340D11—82no—
341C24—221no—
342C24—221no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—44no—
346C2×Q8—41no—
347C2×Q8—42no—
348C2×Q8—42no—
349C2×Q8C2×C22⋊D1114yes—
350C2×D4—112no—
351C2×D4—112no—
352C2×D4—228no—
353C2×D4—222no—
354C2×D4—222no—
355C2×D4—222no—
356C2×D4—222no—
357C2×D4—221no—
358C2×D4—221no—
359C2×D4—884no—
360C22×C4—22no—
361C22×C4—41no—
362C22×C4—221no—
363C22×C4—221no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—442no—
369C22×C4—442no—
370C22×C4—442no—
371C22×C4—442no—
372C22×C4D4×D1111yescharacteristic
373C22×C4D4×D1111yescharacteristic
374C22×C4C2×C22⋊D1111yescharacteristic
375SD16—448no—
376C2×C8—22no—
377C2×C8—42no—
378C2×C8—222no—
379C2×C8—222no—
380C2×C8—442no—
381C2×C8—442no—
382C4⋊C4—22no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—22no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—41no—
389C4⋊C4—41no—
390C4⋊C4—112no—
391C4⋊C4—112no—
392C4⋊C4—221no—
393C4⋊C4—221no—
394C22⋊C4—228no—
395C22⋊C4—228no—
396C22⋊C4—222no—
397C22⋊C4—222no—
398C22⋊C4—222no—
399C22⋊C4—222no—
400C42—228no—
401C42D4×D1111yescharacteristic
402C42D4×D1111yescharacteristic
403C42C2×C22⋊D1111yescharacteristic
404C42C23×D1111yescharacteristic
405C11C2×#164611yescharacteristic, complemented, Sylow
406C23—222no—
407C23—222no—
408C23—442no—
409C23—442no—
410C23—442no—
411C23—442no—
412C23—442no—
413C23—442no—
414C23#6699011yescharacteristic
415Q8—44no—
416Q8—42no—
417Q8—42no—
418Q8—82no—
419Q8—82no—
420D4—222no—
421D4—222no—
422D4—222no—
423D4—222no—
424D4—442no—
425D4—442no—
426D4—888no—
427C2×C4—22no—
428C2×C4—24no—
429C2×C4—44no—
430C2×C4—42no—
431C2×C4—82no—
432C2×C4—222no—
433C2×C4—222no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—444no—
441C2×C4—444no—
442C2×C4#6696712yes—
443C2×C4#6696912yes—
444C2×C4#6697112yes—
445C2×C4#6697212yes—
446C2×C4#6699011yescharacteristic
447C2×C4#6699011yescharacteristic
448C2×C4#6699011yescharacteristic
449C2×C4C2×D4×D1111yescharacteristic
450C2×C4C2×D4×D1111yescharacteristic
451C2×C4C22×C22⋊D1111yescharacteristic
452C8—42no—
453C8—442no—
454C8—442no—
455C22—442no—
456C22—442no—
457C22—442no—
458C22—442no—
459C22—442no—
460C22—442no—
461C22—884no—
462C22—884no—
463C22#1062267412yes—
464C22#1062278512yes—
465C22#1062280012yes—
466C22C2×#6699011yescharacteristic
467C4—21no—
468C4—21no—
469C4—44no—
470C4—82no—
471C4—442no—
472C4—442no—
473C4#1062278512yes—
474C4#1062280012yes—
475C4C2×#6696711yescharacteristic
476C4C2×#6696911yescharacteristic
477C4C2×#6697111yescharacteristic
478C4C2×#6697211yescharacteristic
479C2—882no—
480C2—882no—
481C2#1306784114yesdirect product factor
482C2C2×#1062278511yescharacteristic
483C2C2×#1062280011yescharacteristic
484C2C2×#1062267411yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#487C2
socleC23×C11#120
prime radicalC2×#10623265C2
hypercenterC2×#487D11
hypocenterC11C2×#1646
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×#10622700C2semidirect
3. C2×#10622696C2semidirect
4. #13067841C2direct (N × H)
5. C2×#10622184C2semidirect
6. C2×#10622097C2semidirect
7. C2×#10622097C2semidirect
8. C2×C11×#487C2semidirect
24. C11×#487C22semidirect
29. #10622700C22semidirect
31. #10622696C22semidirect
36. #10622184C22semidirect
37. #10622097C22semidirect
38. #10622097C22semidirect
165. C2×#487D11semidirect
236. #487C2×D11semidirect
335. C2×C11#1646semidirect
405. C11C2×#1646semidirect
481. C2#13067841direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232652
C2×#106227002
C2×#106226962
#130678412
C2×#106221842
C2×#106220972
C2×C11×#4872
C2×#164611