Finite Group Databasebeta

← C2×#13067649 #14725923

Subgroups — C2×#13067649 #14725923

Order 2816.

1016 conjugacy classes of subgroups.

The subgroup lattice has 538 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623046C211yesmaximal, characteristic
2C2×#10622335C211yesmaximal, characteristic, complemented
3C2×#10622348C211yesmaximal, characteristic
4C2×#10622599C211yesmaximal, characteristic, complemented
5#13067649C218yesmaximal, direct product factor
6C2×#10622105C211yesmaximal, characteristic, complemented
7C2×#10622108C211yesmaximal, characteristic
8C2×C11×#324C211yesmaximal, characteristic, complemented
9C22×C11×C4⋊C4C2211yescharacteristic
10C2×#66983C2211yescharacteristic
11C2×#66982—21no—
12C2×C4×C22⋊D11—21no—
13C22×C4⋊Dic11C2211yescharacteristic
14C2×#66977C2211yescharacteristic
15#10623046—22no—
16#10623046—22no—
17#10623046—22no—
18#10623046C2214yes—
19C2×#66951—21no—
20C2×#66949—21no—
21C2×#66947—21no—
22C2×#66942—21no—
23C2×C11×C22⋊C8C2211yescharacteristic
24C2×C11×C22⋊C8C2211yescharacteristic
25C2×C11⋊#95—21no—
26C2×C11⋊#95—21no—
27C2×C11⋊#95C2211yescharacteristic
28C2×#66885—21no—
29C2×#66882—21no—
30C2×#66881—21no—
31C2×#66880—21no—
32#10622599—22no—
33#10622599C2214yescomplemented
34#10622348—22no—
35#10622348C2214yes—
36#10622335—22no—
37#10622335C2214yescomplemented
38C11×#324C2214yescomplemented
39#10622108C2214yes—
40#10622105C2214yescomplemented
41C23×C4×C11D411yescharacteristic
42C23×C4×C11D411yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—21no—
45C23×Dic11—21no—
46C23×Dic11—21no—
47C22×D44D411yescharacteristic
48C22×C4×D11—21no—
49C22×Dic22D411yescharacteristic
50C22×C8×C11—21no—
51C22×C8×C11—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—21no—
56C2×C11×C4⋊C4D412yes—
57C2×C11×C4⋊C4C2312yes—
58C2×C22⋊Dic11—21no—
59#66983—21no—
60#66983—21no—
61#66983D412yes—
62#66983C2312yes—
63#66982—24no—
64#66982—24no—
65C4×C22⋊D11—24no—
66C4×C22⋊D11—24no—
67C2×(C2×D11)⋊C4—21no—
68C2×(C2×D11)⋊C4—21no—
69C2×(C2×D11)⋊C4—21no—
70C2×(C2×D11)⋊C4—21no—
71C2×C4⋊Dic11—21no—
72C2×C4⋊Dic11—21no—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11—21no—
76C2×C4⋊Dic11D411yescharacteristic
77C2×C4⋊Dic11D411yescharacteristic
78C2×C4⋊Dic11C2312yes—
79#66977—21no—
80#66977—21no—
81#66977D412yes—
82#66977C2312yes—
83C2×Dic11⋊C4—21no—
84C2×Dic11⋊C4—21no—
85C2×Dic11⋊C4—21no—
86C2×Dic11⋊C4—21no—
87C2×C4×Dic11—21no—
88#66951—24no—
89#66951—24no—
90#66949—24no—
91#66949—24no—
92#66947—24no—
93#66947—24no—
94#66942—24no—
95#66942—24no—
96C11×C22⋊C8—21no—
97C11×C22⋊C8—21no—
98C11×C22⋊C8C2312yes—
99C11×C22⋊C8C2312yes—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—21no—
103C11⋊#95C2312yes—
104#66885—24no—
105#66882—24no—
106#66881—24no—
107#66880—24no—
108C2×#1615—111nomaximal, Sylow
109C24×C11C2×D411yescharacteristic
110C23×D11—21no—
111C22×C4×C11—21no—
112C22×C4×C11—21no—
113C22×C4×C11—21no—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—21no—
117C22×C4×C11—42no—
118C22×C4×C11—42no—
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2×D411yescharacteristic
121C22×C4×C11C2×D411yescharacteristic
122C22×C4×C11C2×D412yes—
123C22×C4×C11C2×D411yescharacteristic
124C22×C4×C11C2×D411yescharacteristic
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2411yescharacteristic
127C2×C22⋊D11—22no—
128C2×C22⋊D11—22no—
129C2×C22⋊D11—42no—
130C2×C22⋊D11—42no—
131C22×Dic11—21no—
132C22×Dic11—21no—
133C22×Dic11—21no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—42no—
137C22×Dic11—44no—
138C22×Dic11—42no—
139C22×Dic11—41no—
140C22×Dic11—41no—
141C22×Dic11—42no—
142C2×D44—21no—
143C2×D44—42no—
144C2×D44C2×D412yes—
145C2×C4×D11—24no—
146C2×C4×D11—82no—
147C2×Dic22—21no—
148C2×Dic22—42no—
149C2×Dic22C2×D412yes—
150C2×C8×C11—22no—
151C2×C8×C11—22no—
152C2×C8×C11—42no—
153C2×C8×C11—42no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—22no—
158C22⋊Dic11—22no—
159C22⋊Dic11—22no—
160(C2×D11)⋊C4—24no—
161(C2×D11)⋊C4—24no—
162(C2×D11)⋊C4—24no—
163(C2×D11)⋊C4—22no—
164(C2×D11)⋊C4—22no—
165C4⋊Dic11—21no—
166C4⋊Dic11—21no—
167C4⋊Dic11—22no—
168C4⋊Dic11—22no—
169C4⋊Dic11—41no—
170C4⋊Dic11—41no—
171C4⋊Dic11C2×D412yes—
172C4⋊Dic11C2×D412yes—
173Dic11⋊C4—24no—
174Dic11⋊C4—24no—
175Dic11⋊C4—24no—
176Dic11⋊C4—22no—
177Dic11⋊C4—22no—
178C4×Dic11—24no—
179C2×#539—111no—
180C2×#484—111no—
181C2×#481—111no—
182C2×#400—111no—
183#1615—118no—
184C2×#328—111no—
185C2×#327—111no—
186C2×#324D1111yescharacteristic, complemented
187C23×C11—22no—
188C23×C11—22no—
189C23×C11#12011yescharacteristic
190C23×C11#12011yescharacteristic
191C23×C11#13512yes—
192C23×C11#13712yes—
193C23×C11C22×D411yescharacteristic
194C22×D11—22no—
195C22×D11—42no—
196C22×D11—42no—
197C22×D11—42no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—22no—
204C2×C4×C11—41no—
205C2×C4×C11—41no—
206C2×C4×C11—41no—
207C2×C4×C11—41no—
208C2×C4×C11—42no—
209C2×C4×C11—42no—
210C2×C4×C11—42no—
211C2×C4×C11—42no—
212C2×C4×C11—81no—
213C2×C4×C11#12011yescharacteristic
214C2×C4×C11#12011yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×C4×C11C22×D411yescharacteristic
217C22⋊D11—42no—
218C22⋊D11—42no—
219C22⋊D11—44no—
220C2×Dic11—22no—
221C2×Dic11—22no—
222C2×Dic11—22no—
223C2×Dic11—42no—
224C2×Dic11—42no—
225C2×Dic11—42no—
226C2×Dic11—42no—
227C2×Dic11—42no—
228C2×Dic11—44no—
229C2×Dic11—42no—
230C2×Dic11—42no—
231C2×Dic11—84no—
232C2×Dic11—82no—
233C2×Dic11—82no—
234D44—42no—
235D44—81no—
236C4×D11—84no—
237Dic22—42no—
238Dic22—81no—
239C8×C11—42no—
240C8×C11—42no—
241#539—114no—
242#539—222no—
243#539—222no—
244#539—222no—
245C2×#126—221no—
246C2×#125—221no—
247C2×#123—221no—
248C2×#123—221no—
249C2×C22⋊Q8—111no—
250C2×C22⋊Q8—221no—
251C2×#121—111no—
252C2×C4×D4—221no—
253C22×C4⋊C4—111no—
254C22×C4⋊C4C2×D1111yescharacteristic
255#484—114no—
256#484—222no—
257#481—114no—
258#481—222no—
259C2×#107—221no—
260C2×#106—221no—
261C2×#103—221no—
262C2×#102—221no—
263C2×C22⋊C8C2×D1111yescharacteristic
264C2×C22⋊C8C2×D1111yescharacteristic
265#400—114no—
266#400—222no—
267C2×#95—111no—
268C2×#95—221no—
269C2×#95—221no—
270#328—114no—
271#327—114no—
272#324C2×D1114yescomplemented
273C22×C11—24no—
274C22×C11—24no—
275C22×C11—21no—
276C22×C11—21no—
277C22×C11—21no—
278C22×C11—21no—
279C22×C11#45212yes—
280C22×C11#45212yes—
281C22×C11#45412yes—
282C22×C11#45812yes—
283C22×C11C2×#12011yescharacteristic
284C22×C11C2×#13511yescharacteristic
285C22×C11C2×#13711yescharacteristic
286C2×D11—42no—
287C2×D11—42no—
288C2×D11—42no—
289C2×D11—84no—
290C4×C11—21no—
291C4×C11—21no—
292C4×C11—21no—
293C4×C11—21no—
294C4×C11—42no—
295C4×C11—42no—
296Dic11—42no—
297Dic11—42no—
298Dic11—42no—
299Dic11—82no—
300Dic11—82no—
301C22×Q8—111no—
302C22×D4—111no—
303C22×D4—221no—
304C23×C4—221no—
305C23×C4—221no—
306C23×C4—221no—
307C23×C4D4411yescharacteristic
308C23×C4D4411yescharacteristic
309C23×C4C22×D1111yescharacteristic
310C22×C8—21no—
311C22×C8—21no—
312#126—224no—
313#126—224no—
314#125—224no—
315#125—224no—
316#123—224no—
317#123—224no—
318#123—224no—
319#123—224no—
320C22⋊Q8—112no—
321C22⋊Q8—112no—
322C22⋊Q8—224no—
323C22⋊Q8—224no—
324C22⋊Q8—221no—
325C22⋊Q8—221no—
326#121—112no—
327#121—112no—
328#121—221no—
329#121—221no—
330C4×D4—224no—
331C4×D4—224no—
332C2×C4⋊C4—21no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—111no—
337C2×C4⋊C4—111no—
338C2×C4⋊C4—112no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4—221no—
341C2×C4⋊C4—221no—
342C2×C4⋊C4—221no—
343C2×C4⋊C4—221no—
344C2×C4⋊C4—221no—
345C2×C4⋊C4—221no—
346C2×C4⋊C4—221no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4D4412yes—
349C2×C4⋊C4C22×D1112yes—
350C2×C22⋊C4—221no—
351C2×C22⋊C4—221no—
352C2×C22⋊C4—221no—
353C2×C22⋊C4—221no—
354C2×C22⋊C4—221no—
355C2×C42—221no—
356#107—224no—
357#106—224no—
358#103—224no—
359#102—224no—
360C22⋊C8—21no—
361C22⋊C8—21no—
362C22⋊C8C22×D1112yes—
363C22⋊C8C22×D1112yes—
364#95—112no—
365#95—221no—
366#95—224no—
367#95—224no—
368C2×C11—21no—
369C2×C11—21no—
370C2×C11—22no—
371C2×C11#161514yescomplemented
372C2×C11C2×#45211yescharacteristic
373C2×C11C2×#45411yescharacteristic
374C2×C11C2×#45811yescharacteristic
375D11—82no—
376C24—221no—
377C24C2×D4411yescharacteristic
378C2×Q8—112no—
379C2×Q8—221no—
380C2×Q8—442no—
381C2×D4—112no—
382C2×D4—222no—
383C2×D4—222no—
384C2×D4—221no—
385C2×D4—442no—
386C2×D4—442no—
387C2×D4—442no—
388C22×C4—21no—
389C22×C4—21no—
390C22×C4—21no—
391C22×C4—22no—
392C22×C4—22no—
393C22×C4—21no—
394C22×C4—42no—
395C22×C4—42no—
396C22×C4—224no—
397C22×C4—221no—
398C22×C4—221no—
399C22×C4—221no—
400C22×C4—222no—
401C22×C4—222no—
402C22×C4—442no—
403C22×C4—442no—
404C22×C4—444no—
405C22×C4—441no—
406C22×C4—441no—
407C22×C4—442no—
408C22×C4—882no—
409C22×C4C2×D4412yes—
410C22×C4C2×D4412yes—
411C22×C4C2×D4411yescharacteristic
412C22×C4D4×D1111yescharacteristic
413C22×C4D4×D1111yescharacteristic
414C22×C4D4×D1111yescharacteristic
415C22×C4D4×D1111yescharacteristic
416C22×C4C23×D1111yescharacteristic
417C2×C8—22no—
418C2×C8—22no—
419C2×C8—42no—
420C2×C8—42no—
421C4⋊C4—22no—
422C4⋊C4—22no—
423C4⋊C4—22no—
424C4⋊C4—22no—
425C4⋊C4—112no—
426C4⋊C4—112no—
427C4⋊C4—224no—
428C4⋊C4—224no—
429C4⋊C4—224no—
430C4⋊C4—221no—
431C4⋊C4—221no—
432C4⋊C4—222no—
433C4⋊C4—222no—
434C4⋊C4—222no—
435C4⋊C4—222no—
436C4⋊C4—441no—
437C4⋊C4—441no—
438C22⋊C4—224no—
439C22⋊C4—224no—
440C22⋊C4—224no—
441C22⋊C4—222no—
442C22⋊C4—222no—
443C22⋊C4—222no—
444C22⋊C4—222no—
445C42—224no—
446C11C2×#161511yescharacteristic, complemented, Sylow
447C23—22no—
448C23—22no—
449C23—222no—
450C23—442no—
451C23—442no—
452C23—442no—
453C23#6693511yescharacteristic
454C23#6693511yescharacteristic
455C23#6695712yes—
456C23#6696212yes—
457C23C22×D4411yescharacteristic
458Q8—442no—
459Q8—881no—
460D4—442no—
461D4—442no—
462D4—442no—
463D4—444no—
464D4—881no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—22no—
468C2×C4—22no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—42no—
476C2×C4—42no—
477C2×C4—42no—
478C2×C4—42no—
479C2×C4—81no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4—442no—
487C2×C4—442no—
488C2×C4—444no—
489C2×C4—442no—
490C2×C4—442no—
491C2×C4—884no—
492C2×C4—884no—
493C2×C4—882no—
494C2×C4—882no—
495C2×C4#6693511yescharacteristic
496C2×C4#6693511yescharacteristic
497C2×C4C2×D4×D1111yescharacteristic
498C2×C4C2×D4×D1111yescharacteristic
499C8—42no—
500C8—42no—
501C22—24no—
502C22—24no—
503C22—21no—
504C22—21no—
505C22—21no—
506C22—21no—
507C22—442no—
508C22—442no—
509C22—442no—
510C22—884no—
511C22#1062234612yes—
512C22#1062234612yes—
513C22#1062235512yes—
514C22#1062236612yes—
515C22C2×#6693511yescharacteristic
516C22C2×#6695711yescharacteristic
517C22C2×#6696211yescharacteristic
518C4—21no—
519C4—21no—
520C4—21no—
521C4—21no—
522C4—42no—
523C4—42no—
524C4—442no—
525C4—442no—
526C4—442no—
527C4—882no—
528C4—882no—
529C2—21no—
530C2—21no—
531C2—22no—
532C2—882no—
533C2#1306764914yesdirect product factor
534C2C2×#1062234611yescharacteristic
535C2C2×#1062236611yescharacteristic
536C2C2×#1062235511yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#324C2
socleC23×C11#120
prime radicalC2×#66983C22
hypercenterC2×#324D11
hypocenterC11C2×#1615
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. C2×#10622335C2semidirect
4. C2×#10622599C2semidirect
5. #13067649C2direct (N × H)
6. C2×#10622105C2semidirect
8. C2×C11×#324C2semidirect
33. #10622599C22semidirect
37. #10622335C22semidirect
38. C11×#324C22semidirect
40. #10622105C22semidirect
186. C2×#324D11semidirect
272. #324C2×D11semidirect
371. C2×C11#1615semidirect
446. C11C2×#1615semidirect
533. C2#13067649direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230462
C2×#106223352
C2×#106223482
C2×#106225992
#130676492
C2×#106221052
C2×#106221082
C2×C11×#3242
C2×#161511