Finite Group Databasebeta

← C2×#13067533 #14725836

Subgroups — C2×#13067533 #14725836

Order 2816.

2040 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 2040 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623024C211yesmaximal, characteristic, complemented
2C2×#10622830C212yesmaximal, complemented
3#13067533C218yesmaximal, direct product factor
4C2×#10622089C212yesmaximal, complemented
5C2×#10622163C211yesmaximal, characteristic, complemented
6C2×C11×#392C211yesmaximal, characteristic, complemented
7C23×D4×C11—21no—
8C23×D4×C11C2211yescharacteristic, complemented
9C23×C22⋊D11—21no—
10C22×C11×C22⋊C4—21no—
11C22×C11×C22⋊C4C2211yescharacteristic
12C22×#4323—22no—
13C2×#66983—21no—
14C2×#66983C2212yes—
15#10623024—22no—
16#10623024—24no—
17#10623024C2214yescomplemented
18C2×#66939—22no—
19C2×#66935—22no—
20C11×#392—22no—
21C11×#392C2214yescomplemented
22C2×C11×#95C2211yescharacteristic, complemented
23#10622830—24no—
24#10622830C2218yescomplemented
25C2×#66896—22no—
26C2×C22⋊(C11⋊C8)C2212yescomplemented
27#10622163C2214yescomplemented
28#10622089C2218yescomplemented
29C25×C11—21no—
30C25×C11D411yescharacteristic
31C24×D11—21no—
32C22×D4×C11—24no—
33C22×D4×C11—22no—
34C22×D4×C11—22no—
35C22×D4×C11—21no—
36C22×D4×C11—44no—
37C22×D4×C11—44no—
38C22×D4×C11—44no—
39C22×D4×C11—44no—
40C22×D4×C11C2312yescomplemented
41C23×C4×C11—21no—
42C23×C4×C11D411yescharacteristic
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—22no—
45C22×C22⋊D11—24no—
46C22×C22⋊D11—24no—
47C22×C22⋊D11—22no—
48C22×C22⋊D11—44no—
49C22×C22⋊D11—44no—
50C23×Dic11—21no—
51C22×D44—21no—
52C22×D44D412yescomplemented
53C2×C11×C22⋊C4—22no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—24no—
56C2×C11×C22⋊C4—44no—
57C2×C11×C22⋊C4D412yes—
58C2×C11×C22⋊C4C2312yes—
59C2×#4323—28no—
60C2×#4323—48no—
61#66983—24no—
62#66983—22no—
63#66983—22no—
64#66983—24no—
65#66983D414yescomplemented
66#66983C2314yes—
67C2×(C2×D11)⋊C4—22no—
68C2×(C2×D11)⋊C4—22no—
69C2×C4⋊Dic11—21no—
70C2×C4⋊Dic11D412yescomplemented
71C22×C11⋊C8—22no—
72#66939—28no—
73#66939—28no—
74#66935—28no—
75#66935—28no—
76C11×#95—21no—
77C11×#95C2312yescomplemented
78#66896—28no—
79C22⋊(C11⋊C8)—22no—
80C22⋊(C11⋊C8)C2314yescomplemented
81C2×#1595—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11—21no—
84C24×C11—22no—
85C24×C11—24no—
86C24×C11—22no—
87C24×C11—42no—
88C24×C11—42no—
89C24×C11—42no—
90C24×C11—42no—
91C24×C11—42no—
92C24×C11—41no—
93C24×C11—41no—
94C24×C11—42no—
95C24×C11—42no—
96C24×C11D814yescomplemented
97C24×C11C2×D411yescharacteristic
98C24×C11C2×D412yes—
99C23×D11—22no—
100C23×D11—24no—
101C23×D11—44no—
102C23×D11—82no—
103C23×D11—82no—
104C2×D4×C11—28no—
105C2×D4×C11—24no—
106C2×D4×C11—44no—
107C2×D4×C11—48no—
108C2×D4×C11—44no—
109C2×D4×C11—48no—
110C2×D4×C11—44no—
111C2×D4×C11—48no—
112C2×D4×C11—432no—
113C2×D4×C11—48no—
114C2×D4×C11—42no—
115C22×C4×C11—24no—
116C22×C4×C11—21no—
117C22×C4×C11—22no—
118C22×C4×C11—21no—
119C22×C4×C11—42no—
120C22×C4×C11—42no—
121C22×C4×C11—42no—
122C22×C4×C11—42no—
123C22×C4×C11C2×D412yes—
124C22×C4×C11C2×D412yes—
125C22×C4×C11C2×D411yescharacteristic
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2411yescharacteristic
128C2×C22⋊D11—28no—
129C2×C22⋊D11—24no—
130C2×C22⋊D11—24no—
131C2×C22⋊D11—48no—
132C2×C22⋊D11—416no—
133C2×C22⋊D11—48no—
134C2×C22⋊D11—44no—
135C2×C22⋊D11—48no—
136C2×C22⋊D11—44no—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—44no—
140C2×D44—24no—
141C2×D44—22no—
142C2×D44—44no—
143C2×D44—82no—
144C2×D44C2×D414yescomplemented
145C11×C22⋊C4—24no—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—48no—
148#4323—416no—
149(C2×D11)⋊C4—28no—
150(C2×D11)⋊C4—24no—
151(C2×D11)⋊C4—24no—
152C4⋊Dic11—24no—
153C4⋊Dic11—22no—
154C4⋊Dic11C2×D414yescomplemented
155C2×C11⋊C8—24no—
156C2×C11⋊C8—44no—
157C2×#534—111no—
158C2×#447—112no—
159C2×#392D1111yescharacteristic, complemented
160#1595—118no—
161C2×#327—112no—
162C2×#323—111no—
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—24no—
167C23×C11—22no—
168C23×C11—24no—
169C23×C11—24no—
170C23×C11—48no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—48no—
175C23×C11—42no—
176C23×C11—42no—
177C23×C11—44no—
178C23×C11—48no—
179C23×C11—42no—
180C23×C11—42no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11—42no—
184C23×C11—44no—
185C23×C11—84no—
186C23×C11—81no—
187C23×C11—81no—
188C23×C11—84no—
189C23×C11—84no—
190C23×C11—82no—
191C23×C11—82no—
192C23×C11—82no—
193C23×C11—82no—
194C23×C11#12011yescharacteristic
195C23×C11#12011yescharacteristic
196C23×C11C2×D812yes—
197C23×C11C2×D814yescomplemented
198C23×C11AGL(1,ℤ/8)12yes—
199C23×C11C22×D411yescharacteristic
200C22×D11—24no—
201C22×D11—48no—
202C22×D11—44no—
203C22×D11—44no—
204C22×D11—44no—
205C22×D11—84no—
206C22×D11—84no—
207C22×D11—816no—
208D4×C11—28no—
209D4×C11—48no—
210D4×C11—44no—
211D4×C11—432no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—42no—
216C2×C4×C11—41no—
217C2×C4×C11—41no—
218C2×C4×C11—48no—
219C2×C4×C11—42no—
220C2×C4×C11—42no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—81no—
224C2×C4×C11#12012yes—
225C2×C4×C11C22×D412yes—
226C22⋊D11—416no—
227C22⋊D11—44no—
228C22⋊D11—44no—
229C22⋊D11—48no—
230C2×Dic11—24no—
231C2×Dic11—48no—
232C2×Dic11—44no—
233D44—44no—
234D44—82no—
235D44—84no—
236C11⋊C8—44no—
237C23×D4—21no—
238C23×D4—221no—
239C23×D4C2×D1111yescharacteristic, complemented
240C22×D8—222no—
241#534—114no—
242#534—224no—
243#534—222no—
244C2×#123—222no—
245C2×#121—112no—
246C2×#121—221no—
247C2×#120—222no—
248C22×C22⋊C4—21no—
249C22×C22⋊C4C2×D1111yescharacteristic
250#447—118no—
251#447—224no—
252C2×#102—222no—
253C2×C22⋊C8—112no—
254#392—22no—
255#392C2×D1114yescomplemented
256C2×#95C2×D1111yescharacteristic, complemented
257#327—118no—
258#323—114no—
259C22×C11—24no—
260C22×C11—24no—
261C22×C11—21no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—24no—
266C22×C11—44no—
267C22×C11—44no—
268C22×C11—44no—
269C22×C11—48no—
270C22×C11—42no—
271C22×C11—42no—
272C22×C11—44no—
273C22×C11—82no—
274C22×C11—84no—
275C22×C11—82no—
276C22×C11—82no—
277C22×C11—88no—
278C22×C11—88no—
279C22×C11—82no—
280C22×C11—82no—
281C22×C11#44712yes—
282C22×C11#44712yes—
283C22×C11#45312yes—
284C22×C11B(4,𝔽2)12yes—
285C22×C11C2×#12011yescharacteristic
286C22×C11C22×D811yescharacteristic
287C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
288C2×D11—44no—
289C2×D11—44no—
290C2×D11—44no—
291C2×D11—816no—
292C2×D11—88no—
293C4×C11—22no—
294C4×C11—22no—
295C4×C11—44no—
296C4×C11—42no—
297Dic11—44no—
298C25—21no—
299C25—221no—
300C25C22⋊D1111yescharacteristic
301C22×D4—24no—
302C22×D4—22no—
303C22×D4—22no—
304C22×D4—21no—
305C22×D4—44no—
306C22×D4—44no—
307C22×D4—44no—
308C22×D4—44no—
309C22×D4—112no—
310C22×D4—221no—
311C22×D4—222no—
312C22×D4—224no—
313C22×D4—222no—
314C22×D4—224no—
315C22×D4—444no—
316C22×D4—444no—
317C22×D4C22×D1112yescomplemented
318C23×C4—21no—
319C23×C4—221no—
320C23×C4C22⋊D1111yescharacteristic
321C23×C4C22×D1111yescharacteristic
322C2×D8—228no—
323C2×D8—448no—
324C22×C8—222no—
325#123—228no—
326#123—228no—
327#121—114no—
328#121—114no—
329#121—224no—
330#121—222no—
331#121—222no—
332#121—224no—
333#120—228no—
334#120—228no—
335C2×C4⋊C4—112no—
336C2×C4⋊C4—221no—
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—24no—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—222no—
342C2×C22⋊C4—222no—
343C2×C22⋊C4C22⋊D1112yes—
344C2×C22⋊C4C22×D1112yes—
345#102—228no—
346C22⋊C8—114no—
347C22⋊C8—222no—
348#95—21no—
349#95C22×D1112yescomplemented
350C2×C11—21no—
351C2×C11—21no—
352C2×C11—22no—
353C2×C11—44no—
354C2×C11—84no—
355C2×C11#159514yescomplemented
356C2×C11C2×#44711yescharacteristic
357C2×C11C2×#45311yescharacteristic
358C2×C11C2×B(4,𝔽2)11yescharacteristic
359D11—84no—
360C24—21no—
361C24—21no—
362C24—22no—
363C24—24no—
364C24—22no—
365C24—42no—
366C24—42no—
367C24—42no—
368C24—42no—
369C24—42no—
370C24—42no—
371C24—41no—
372C24—41no—
373C24—42no—
374C24—224no—
375C24—222no—
376C24—444no—
377C24—882no—
378C24—882no—
379C24#432314yescomplemented
380C24C2×C22⋊D1111yescharacteristic
381C24C2×C22⋊D1112yes—
382C2×D4—28no—
383C2×D4—24no—
384C2×D4—44no—
385C2×D4—48no—
386C2×D4—44no—
387C2×D4—48no—
388C2×D4—44no—
389C2×D4—48no—
390C2×D4—432no—
391C2×D4—48no—
392C2×D4—42no—
393C2×D4—114no—
394C2×D4—224no—
395C2×D4—228no—
396C2×D4—224no—
397C2×D4—224no—
398C2×D4—222no—
399C2×D4—444no—
400C2×D4—448no—
401C2×D4—4416no—
402C2×D4—448no—
403C2×D4—444no—
404C2×D4—448no—
405C2×D4—444no—
406C2×D4—882no—
407C22×C4—24no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—42no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—224no—
416C22×C4—222no—
417C22×C4—444no—
418C22×C4D4×D1112yes—
419C22×C4D4×D1112yes—
420C22×C4C2×C22⋊D1112yes—
421C22×C4C2×C22⋊D1111yescharacteristic
422C22×C4C23×D1111yescharacteristic
423D8—4416no—
424C2×C8—224no—
425C2×C8—444no—
426C4⋊C4—114no—
427C4⋊C4—224no—
428C4⋊C4—222no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—48no—
432C22⋊C4—228no—
433C22⋊C4—224no—
434C22⋊C4—224no—
435C11C2×#159511yescharacteristic, complemented, Sylow
436C23—22no—
437C23—22no—
438C23—22no—
439C23—24no—
440C23—22no—
441C23—24no—
442C23—24no—
443C23—48no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—48no—
448C23—42no—
449C23—42no—
450C23—44no—
451C23—48no—
452C23—42no—
453C23—42no—
454C23—42no—
455C23—42no—
456C23—42no—
457C23—44no—
458C23—84no—
459C23—81no—
460C23—81no—
461C23—84no—
462C23—84no—
463C23—82no—
464C23—82no—
465C23—82no—
466C23—82no—
467C23—224no—
468C23—448no—
469C23—444no—
470C23—444no—
471C23—444no—
472C23—884no—
473C23—884no—
474C23—8816no—
475C23C2×#432312yes—
476C23C2×#432314yescomplemented
477C23#6699011yescharacteristic
478C23#6699011yescharacteristic
479C23#6700212yes—
480C23C22×C22⋊D1111yescharacteristic
481D4—28no—
482D4—44no—
483D4—48no—
484D4—432no—
485D4—444no—
486D4—4416no—
487D4—444no—
488D4—444no—
489D4—448no—
490D4—882no—
491D4—884no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—48no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—81no—
504C2×C4—224no—
505C2×C4—448no—
506C2×C4—444no—
507C2×C4#6699012yes—
508C2×C4C2×D4×D1112yes—
509C8—444no—
510C22—24no—
511C22—24no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—24no—
517C22—44no—
518C22—44no—
519C22—44no—
520C22—48no—
521C22—42no—
522C22—42no—
523C22—44no—
524C22—82no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22—88no—
529C22—88no—
530C22—82no—
531C22—82no—
532C22—444no—
533C22—444no—
534C22—444no—
535C22—8816no—
536C22—888no—
537C22#1062264512yes—
538C22#1062264912yes—
539C22#1062264912yes—
540C22#1062269012yes—
541C22C22×#432311yescharacteristic
542C22C2×#6699011yescharacteristic
543C22C2×#6700211yescharacteristic
544C4—22no—
545C4—22no—
546C4—44no—
547C4—42no—
548C4—444no—
549C2—21no—
550C2—21no—
551C2—22no—
552C2—44no—
553C2—84no—
554C2—884no—
555C2#1306753314yesdirect product factor
556C2C2×#1062264911yescharacteristic
557C2C2×#1062269011yescharacteristic
558C2C2×#1062264511yescharacteristic
subgroupG/H
centerC23#66990
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#392C2
socleC23×C11#120
hypercenterC2×#392D11
hypocenterC11C2×#1595
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×#10623024C2semidirect
2. C2×#10622830C2semidirect
3. #13067533C2direct (N × H)
4. C2×#10622089C2semidirect
5. C2×#10622163C2semidirect
6. C2×C11×#392C2semidirect
8. C23×D4×C11C22semidirect
17. #10623024C22semidirect
21. C11×#392C22semidirect
22. C2×C11×#95C22semidirect
24. #10622830C22semidirect
26. C2×C22⋊(C11⋊C8)C22semidirect
27. #10622163C22semidirect
28. #10622089C22semidirect
40. C22×D4×C11C23semidirect
52. C22×D44D4semidirect
65. #66983D4semidirect
70. C2×C4⋊Dic11D4semidirect
77. C11×#95C23semidirect
80. C22⋊(C11⋊C8)C23semidirect
96. C24×C11D8semidirect
144. C2×D44C2×D4semidirect
154. C4⋊Dic11C2×D4semidirect
159. C2×#392D11semidirect
197. C23×C11C2×D8semidirect
239. C23×D4C2×D11semidirect
255. #392C2×D11semidirect
256. C2×#95C2×D11semidirect
317. C22×D4C22×D11semidirect
349. #95C22×D11semidirect
355. C2×C11#1595semidirect
379. C24#4323semidirect
435. C11C2×#1595semidirect
476. C23C2×#4323semidirect
555. C2#13067533direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230242
C2×#106228302
#130675332
C2×#106220892
C2×#106221632
C2×C11×#3922
C2×#159511