Finite Group Databasebeta

← C2×#13067843 #14729702

Subgroups — C2×#13067843 #14729702

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×#10623094C211yesmaximal, characteristic
2C2×#10622706C211yesmaximal, characteristic, complemented
3C2×#10622696C211yesmaximal, characteristic, complemented
4#13067843C218yesmaximal, direct product factor
5C2×#10622119C211yesmaximal, characteristic, complemented
6C2×D4⋊(C11⋊C8)C211yesmaximal, characteristic, complemented
7C2×#10622121C211yesmaximal, characteristic, complemented
8C2×C11×#474C211yesmaximal, characteristic, complemented
9C2×C11×C4⋊Q8C2211yescharacteristic
10C2×C4×D4×C11C2211yescharacteristic
11C22×#4325—21no—
12C2×#66991—21no—
13C2×#66983—21no—
14C2×#66979—21no—
15#10623094—22no—
16#10623094—22no—
17#10623094—22no—
18#10623094C2214yes—
19C2×#66945—21no—
20C2×#66938—22no—
21C2×C4×D44C2211yescharacteristic
22C2×#66922C2211yescharacteristic
23C11×#474—22no—
24C11×#474C2214yescomplemented
25C2×C11×#107—21no—
26C2×C11×C4⋊C8C2211yescharacteristic
27C2×C11×#102—21no—
28C2×#66899—21no—
29#10622706—22no—
30#10622706C2214yescomplemented
31#10622696—22no—
32#10622696C2214yescomplemented
33C2×#66874—22no—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36D4⋊(C11⋊C8)C2214yescomplemented
37#10622121C2214yescomplemented
38#10622119C2214yescomplemented
39C22×Q8×C11—21no—
40C22×D4×C11D411yescharacteristic
41C23×C4×C11—21no—
42C22×C22⋊D11—22no—
43C22×D44D411yescharacteristic
44C22×C4×D11—21no—
45C22×Dic22D412yes—
46C22×C8×C11—21no—
47C11×C4⋊Q8—21no—
48C11×C4⋊Q8—21no—
49C11×C4⋊Q8—21no—
50C11×C4⋊Q8C2312yes—
51C4×D4×C11—21no—
52C4×D4×C11—21no—
53C4×D4×C11D412yes—
54C4×D4×C11C2312yes—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C22⋊C4—21no—
59C2×C42×C11C2311yescharacteristic
60C2×C22⋊Dic11—22no—
61C2×#4325—24no—
62C2×#4325—44no—
63#66991—24no—
64#66991—24no—
65#66983—24no—
66#66983—24no—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—21no—
69#66979—24no—
70#66979—24no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4×Dic11—22no—
75C22×C11⋊C8—21no—
76C22×C11⋊C8—21no—
77#66945—24no—
78#66945—24no—
79#66938—28no—
80#66938—28no—
81C4×D44—21no—
82C4×D44—21no—
83C4×D44D412yes—
84C4×D44C2312yes—
85#66922—21no—
86#66922—21no—
87#66922D412yes—
88#66922C2312yes—
89C11×#107—24no—
90C11×C4⋊C8—21no—
91C11×C4⋊C8C2312yes—
92C11×#102—24no—
93#66899—24no—
94#66874—28no—
95C4⋊(C11⋊C8)—21no—
96C4⋊(C11⋊C8)C2312yes—
97C4×C11⋊C8—21no—
98C4×C11⋊C8C2312yes—
99C2×#1646—111nomaximal, Sylow
100C24×C11—21no—
101C23×D11—21no—
102C2×Q8×C11—22no—
103C2×Q8×C11—41no—
104C2×Q8×C11—42no—
105C2×Q8×C11—42no—
106C2×D4×C11—21no—
107C2×D4×C11—22no—
108C2×D4×C11—22no—
109C2×D4×C11C2×D412yes—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11—22no—
113C22×C4×C11—42no—
114C22×C4×C11—42no—
115C22×C4×C11—41no—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2×D411yescharacteristic
119C2×C22⋊D11—28no—
120C2×C22⋊D11—84no—
121C22×Dic11—21no—
122C22×Dic11—22no—
123C2×D44—21no—
124C2×D44—22no—
125C2×D44—22no—
126C2×D44C2×D412yes—
127C2×C4×D11—22no—
128C2×C4×D11—22no—
129C2×C4×D11—42no—
130C2×C4×D11—42no—
131C2×Dic22—22no—
132C2×Dic22—44no—
133C2×Dic22C2×D414yes—
134C2×C8×C11—22no—
135C2×C8×C11—42no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—22no—
138C11×C4⋊C4—22no—
139C11×C4⋊C4—41no—
140C11×C4⋊C4—41no—
141C11×C4⋊C4C2×D412yes—
142C11×C22⋊C4—22no—
143C11×C22⋊C4—22no—
144C42×C11C2×D411yescharacteristic
145C42×C11C2×D411yescharacteristic
146C42×C11C2×D411yescharacteristic
147C42×C11C2411yescharacteristic
148C22⋊Dic11—28no—
149#4325—48no—
150(C2×D11)⋊C4—28no—
151(C2×D11)⋊C4—22no—
152(C2×D11)⋊C4—22no—
153C4⋊Dic11—22no—
154C4⋊Dic11—22no—
155C4⋊Dic11—21no—
156C4⋊Dic11—22no—
157C4⋊Dic11—22no—
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×#487—111no—
166C2×#474D1111yescharacteristic, complemented
167C2×#461—111no—
168#1646—118no—
169C2×#333—111no—
170C2×D4⋊C8—111no—
171C2×D4⋊C8—111no—
172C23×C11—22no—
173C23×C11—42no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11#12011yescharacteristic
177C22×D11—22no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—42no—
181Q8×C11—42no—
182Q8×C11—42no—
183Q8×C11—82no—
184D4×C11—22no—
185D4×C11—22no—
186D4×C11—42no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—44no—
193C2×C4×C11—42no—
194C2×C4×C11—82no—
195C2×C4×C11#12011yescharacteristic
196C2×C4×C11#12011yescharacteristic
197C2×C4×C11#12011yescharacteristic
198C2×C4×C11#13512yes—
199C2×C4×C11#13512yes—
200C2×C4×C11AGL(1,ℤ/8)12yes—
201C2×C4×C11#13712yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C22⋊D11—88no—
206C2×Dic11—22no—
207C2×Dic11—24no—
208C2×Dic11—42no—
209C2×Dic11—44no—
210D44—22no—
211D44—22no—
212D44—42no—
213C4×D11—42no—
214C4×D11—42no—
215C4×D11—44no—
216Dic22—44no—
217Dic22—82no—
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⋊Q8—111no—
227C2×C4⋊Q8C2×D1111yescharacteristic
228C2×#124—222no—
229C2×#121—221no—
230C2×#121—221no—
231C2×C4×D4—111no—
232C2×C4×D4C2×D1111yescharacteristic
233C2×#117—221no—
234C2×#117—221no—
235#487—114no—
236#487—222no—
237#474—22no—
238#474C2×D1114yescomplemented
239#461—114no—
240#461—222no—
241C2×#107—21no—
242C2×C4⋊C8—111no—
243C2×C4⋊C8C2×D1111yescharacteristic
244C2×#103—222no—
245C2×#103—221no—
246C2×#102—21no—
247C2×C4×C8—111no—
248#333—114no—
249D4⋊C8—114no—
250D4⋊C8—114no—
251C22×C11—42no—
252C22×C11—42no—
253C22×C11—42no—
254C22×C11—84no—
255C22×C11#44912yes—
256C22×C11#45212yes—
257C22×C11#45512yes—
258C22×C11C2×#12011yescharacteristic
259C2×D11—42no—
260C2×D11—42no—
261C2×D11—42no—
262C2×D11—84no—
263C4×C11—21no—
264C4×C11—21no—
265C4×C11—42no—
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—44no—
275C22×Q8—21no—
276C22×Q8—112no—
277C22×D4—111no—
278C22×D4—222no—
279C22×D4C22⋊D1111yescharacteristic
280C23×C4—21no—
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—112no—
291C4⋊Q8—112no—
292C4⋊Q8—221no—
293C4⋊Q8—221no—
294C4⋊Q8C22×D1112yes—
295#124—228no—
296#124—228no—
297#121—224no—
298#121—224no—
299#121—224no—
300#121—224no—
301C4×D4—21no—
302C4×D4—21no—
303C4×D4—112no—
304C4×D4—112no—
305C4×D4—221no—
306C4×D4—221no—
307C4×D4C22⋊D1112yes—
308C4×D4C22×D1112yes—
309#117—224no—
310#117—224no—
311#117—224no—
312#117—224no—
313C2×C4⋊C4—21no—
314C2×C4⋊C4—21no—
315C2×C4⋊C4—111no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4—221no—
318C2×C4⋊C4C22⋊D1111yescharacteristic
319C2×C22⋊C4—21no—
320C2×C22⋊C4—222no—
321C2×C22⋊C4—222no—
322C2×C22⋊C4—221no—
323C2×C42—222no—
324C2×C42C22×D1111yescharacteristic
325#107—24no—
326C4⋊C8—21no—
327C4⋊C8—112no—
328C4⋊C8—221no—
329C4⋊C8C22×D1112yes—
330#103—228no—
331#103—224no—
332#102—24no—
333C4×C8—112no—
334C4×C8—221no—
335C2×C11—82no—
336C2×C11#164614yescomplemented
337C2×C11C2×#44911yescharacteristic
338C2×C11C2×#45211yescharacteristic
339C2×C11C2×#45511yescharacteristic
340D11—82no—
341C24—21no—
342C24—221no—
343C2×Q8—22no—
344C2×Q8—41no—
345C2×Q8—42no—
346C2×Q8—42no—
347C2×Q8—114no—
348C2×Q8—222no—
349C2×Q8—444no—
350C2×D4—21no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—112no—
354C2×D4—228no—
355C2×D4—222no—
356C2×D4—222no—
357C2×D4—221no—
358C2×D4—884no—
359C2×D4C2×C22⋊D1112yes—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—41no—
366C22×C4—221no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4—222no—
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—21no—
383C4⋊C4—22no—
384C4⋊C4—22no—
385C4⋊C4—41no—
386C4⋊C4—41no—
387C4⋊C4—112no—
388C4⋊C4—221no—
389C4⋊C4—222no—
390C4⋊C4—222no—
391C4⋊C4—222no—
392C4⋊C4—222no—
393C4⋊C4C2×C22⋊D1112yes—
394C22⋊C4—22no—
395C22⋊C4—22no—
396C22⋊C4—228no—
397C22⋊C4—228no—
398C22⋊C4—222no—
399C22⋊C4—222no—
400C42—228no—
401C42D4×D1111yescharacteristic
402C42D4×D1111yescharacteristic
403C42C2×C22⋊D1111yescharacteristic
404C42C23×D1111yescharacteristic
405C11C2×#164611yescharacteristic, complemented, Sylow
406C23—22no—
407C23—42no—
408C23—42no—
409C23—42no—
410C23—222no—
411C23—442no—
412C23—442no—
413C23—442no—
414C23#6699011yescharacteristic
415Q8—42no—
416Q8—42no—
417Q8—82no—
418Q8—444no—
419Q8—882no—
420D4—22no—
421D4—22no—
422D4—42no—
423D4—222no—
424D4—222no—
425D4—442no—
426D4—888no—
427C2×C4—22no—
428C2×C4—22no—
429C2×C4—42no—
430C2×C4—44no—
431C2×C4—42no—
432C2×C4—42no—
433C2×C4—42no—
434C2×C4—82no—
435C2×C4—222no—
436C2×C4—224no—
437C2×C4—444no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—444no—
442C2×C4#6696412yes—
443C2×C4#6696512yes—
444C2×C4#6699011yescharacteristic
445C2×C4#6699011yescharacteristic
446C2×C4#6699011yescharacteristic
447C2×C4#6699512yes—
448C2×C4#6700312yes—
449C2×C4C2×D4×D1111yescharacteristic
450C2×C4C2×D4×D1111yescharacteristic
451C2×C4C22×C22⋊D1111yescharacteristic
452C8—42no—
453C8—442no—
454C8—442no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—84no—
459C22—442no—
460C22—442no—
461C22—442no—
462C22—884no—
463C22#1062266012yes—
464C22#1062277112yes—
465C22#1062281512yes—
466C22C2×#6699011yescharacteristic
467C4—21no—
468C4—21no—
469C4—42no—
470C4—82no—
471C4—442no—
472C4—444no—
473C4#1062266012yes—
474C4#1062277112yes—
475C4C2×#6696411yescharacteristic
476C4C2×#6696511yescharacteristic
477C4C2×#6699511yescharacteristic
478C4C2×#6700311yescharacteristic
479C2—82no—
480C2—882no—
481C2#1306784314yesdirect product factor
482C2C2×#1062277111yescharacteristic
483C2C2×#1062266011yescharacteristic
484C2C2×#1062281511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC42×C11C24
FrattiniC42C23×D11
FittingC2×C11×#474C2
socleC23×C11#120
prime radicalC2×#10623094C2
hypercenterC2×#474D11
hypocenterC11C2×#1646
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
2. C2×#10622706C2semidirect
3. C2×#10622696C2semidirect
4. #13067843C2direct (N × H)
5. C2×#10622119C2semidirect
6. C2×D4⋊(C11⋊C8)C2semidirect
7. C2×#10622121C2semidirect
8. C2×C11×#474C2semidirect
24. C11×#474C22semidirect
30. #10622706C22semidirect
32. #10622696C22semidirect
36. D4⋊(C11⋊C8)C22semidirect
37. #10622121C22semidirect
38. #10622119C22semidirect
166. C2×#474D11semidirect
238. #474C2×D11semidirect
336. C2×C11#1646semidirect
405. C11C2×#1646semidirect
481. C2#13067843direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230942
C2×#106227062
C2×#106226962
#130678432
C2×#106221192
C2×D4⋊(C11⋊C8)2
C2×#106221212
C2×C11×#4742
C2×#164611