Finite Group Databasebeta

← C2×#13067536 #14725839

Subgroups — C2×#13067536 #14725839

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×#10622345C212yesmaximal, complemented
3C2×#10622573C211yesmaximal, characteristic, complemented
4#13067536C218yesmaximal, direct product factor
5C2×#10622108C212yesmaximal, complemented
6C2×C11×#323C211yesmaximal, characteristic, complemented
7C23×C22⋊D11—21no—
8C23×C22⋊D11—21no—
9C23×D44C2211yescharacteristic, complemented
10C22×C11×C22⋊C4C2211yescharacteristic
11C2×#66983—21no—
12C2×#66983C2212yes—
13C22×(C2×D11)⋊C4—21no—
14C22×D88—22no—
15#10623024—22no—
16#10623024—24no—
17#10623024C2214yescomplemented
18C2×#66939—22no—
19C2×#66935—22no—
20C2×C11×C22⋊C8C2212yescomplemented
21C2×C11⋊#95C2211yescharacteristic, complemented
22C2×#66885—22no—
23#10622573—22no—
24#10622573C2214yescomplemented
25#10622345—24no—
26#10622345C2218yescomplemented
27C11×#323C2214yescomplemented
28#10622108C2218yescomplemented
29C25×C11D411yescharacteristic
30C24×D11—21no—
31C24×D11—21no—
32C23×C4×C11D411yescharacteristic
33C23×C4×C11C2311yescharacteristic
34C22×C22⋊D11—22no—
35C22×C22⋊D11—24no—
36C22×C22⋊D11—24no—
37C22×C22⋊D11—22no—
38C22×C22⋊D11—24no—
39C22×C22⋊D11—44no—
40C22×C22⋊D11—44no—
41C22×C22⋊D11—44no—
42C22×C22⋊D11—44no—
43C22×C22⋊D11—44no—
44C23×Dic11—21no—
45C23×Dic11—21no—
46C22×D44—22no—
47C22×D44—21no—
48C22×D44—22no—
49C22×D44—21no—
50C22×D44—44no—
51C22×D44D412yescomplemented
52C22×D44C2312yescomplemented
53C22×C8×C11—22no—
54C2×C11×C22⋊C4—22no—
55C2×C11×C22⋊C4—22no—
56C2×C11×C22⋊C4D412yes—
57C2×C11×C22⋊C4C2312yes—
58#66983—24no—
59#66983—22no—
60#66983—22no—
61#66983—24no—
62#66983D414yescomplemented
63#66983C2314yes—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—24no—
67C2×(C2×D11)⋊C4—44no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11D412yescomplemented
70C2×D88—28no—
71C2×D88—48no—
72#66939—28no—
73#66939—28no—
74#66935—28no—
75#66935—28no—
76C11×C22⋊C8—22no—
77C11×C22⋊C8C2314yescomplemented
78C11⋊#95—21no—
79C11⋊#95C2312yescomplemented
80#66885—28no—
81C2×#1595—111nomaximal, Sylow
82C24×C11—21no—
83C24×C11—21no—
84C24×C11—22no—
85C24×C11—42no—
86C24×C11—42no—
87C24×C11D814yescomplemented
88C24×C11C2×D411yescharacteristic
89C24×C11C2×D412yes—
90C23×D11—24no—
91C23×D11—22no—
92C23×D11—22no—
93C23×D11—24no—
94C23×D11—42no—
95C23×D11—42no—
96C23×D11—42no—
97C23×D11—44no—
98C23×D11—41no—
99C23×D11—41no—
100C23×D11—42no—
101C23×D11—42no—
102C23×D11—82no—
103C23×D11—82no—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—42no—
107C22×C4×C11—42no—
108C22×C4×C11C2×D412yes—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2411yescharacteristic
113C2×C22⋊D11—28no—
114C2×C22⋊D11—24no—
115C2×C22⋊D11—24no—
116C2×C22⋊D11—48no—
117C2×C22⋊D11—48no—
118C2×C22⋊D11—416no—
119C2×C22⋊D11—48no—
120C2×C22⋊D11—48no—
121C2×C22⋊D11—432no—
122C2×C22⋊D11—44no—
123C2×C22⋊D11—48no—
124C2×C22⋊D11—48no—
125C2×C22⋊D11—44no—
126C22×Dic11—24no—
127C22×Dic11—24no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—42no—
131C22×Dic11—44no—
132C22×Dic11—42no—
133C2×D44—24no—
134C2×D44—28no—
135C2×D44—22no—
136C2×D44—24no—
137C2×D44—44no—
138C2×D44—44no—
139C2×D44—44no—
140C2×D44—44no—
141C2×D44—48no—
142C2×D44—42no—
143C2×D44—82no—
144C2×D44C2×D414yescomplemented
145C2×C8×C11—24no—
146C2×C8×C11—44no—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—24no—
149(C2×D11)⋊C4—28no—
150(C2×D11)⋊C4—24no—
151(C2×D11)⋊C4—24no—
152(C2×D11)⋊C4—48no—
153C4⋊Dic11—24no—
154C4⋊Dic11—22no—
155C4⋊Dic11C2×D414yescomplemented
156D88—416no—
157C2×#534—111no—
158C2×#447—112no—
159C2×#392—111no—
160#1595—118no—
161C2×#327—112no—
162C2×#323D1111yescharacteristic, complemented
163C23×C11—22no—
164C23×C11—22no—
165C23×C11—22no—
166C23×C11—24no—
167C23×C11—22no—
168C23×C11—24no—
169C23×C11—48no—
170C23×C11—42no—
171C23×C11—42no—
172C23×C11—42no—
173C23×C11—42no—
174C23×C11—84no—
175C23×C11—81no—
176C23×C11—81no—
177C23×C11#12011yescharacteristic
178C23×C11#12011yescharacteristic
179C23×C11C2×D812yes—
180C23×C11C2×D814yescomplemented
181C23×C11AGL(1,ℤ/8)12yes—
182C23×C11C22×D411yescharacteristic
183C22×D11—24no—
184C22×D11—24no—
185C22×D11—42no—
186C22×D11—42no—
187C22×D11—44no—
188C22×D11—48no—
189C22×D11—42no—
190C22×D11—48no—
191C22×D11—48no—
192C22×D11—42no—
193C22×D11—42no—
194C22×D11—42no—
195C22×D11—44no—
196C22×D11—44no—
197C22×D11—44no—
198C22×D11—44no—
199C22×D11—84no—
200C22×D11—84no—
201C22×D11—84no—
202C22×D11—84no—
203C22×D11—82no—
204C22×D11—816no—
205C22×D11—82no—
206C22×D11—82no—
207C22×D11—82no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—41no—
211C2×C4×C11—42no—
212C2×C4×C11—41no—
213C2×C4×C11—42no—
214C2×C4×C11—42no—
215C2×C4×C11—81no—
216C2×C4×C11#12012yes—
217C2×C4×C11C22×D412yes—
218C22⋊D11—416no—
219C22⋊D11—432no—
220C22⋊D11—44no—
221C22⋊D11—44no—
222C22⋊D11—48no—
223C2×Dic11—24no—
224C2×Dic11—24no—
225C2×Dic11—48no—
226C2×Dic11—42no—
227C2×Dic11—48no—
228C2×Dic11—42no—
229C2×Dic11—44no—
230D44—28no—
231D44—44no—
232D44—48no—
233D44—44no—
234D44—82no—
235D44—84no—
236C8×C11—44no—
237C23×D4—111no—
238C23×D4—221no—
239C23×D4—221no—
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—221no—
249C22×C22⋊C4C2×D1111yescharacteristic
250#447—118no—
251#447—224no—
252C2×#102—222no—
253C2×C22⋊C8C2×D1112yescomplemented
254#392—114no—
255#392—222no—
256C2×#95—111no—
257#327—118no—
258#323C2×D1114yescomplemented
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—48no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—82no—
271C22×C11—84no—
272C22×C11#44712yes—
273C22×C11#44712yes—
274C22×C11#45312yes—
275C22×C11B(4,𝔽2)12yes—
276C22×C11C2×#12011yescharacteristic
277C22×C11C22×D811yescharacteristic
278C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
279C2×D11—44no—
280C2×D11—44no—
281C2×D11—44no—
282C2×D11—44no—
283C2×D11—44no—
284C2×D11—44no—
285C2×D11—82no—
286C2×D11—82no—
287C2×D11—88no—
288C2×D11—816no—
289C2×D11—88no—
290C2×D11—88no—
291C2×D11—82no—
292C2×D11—82no—
293C4×C11—22no—
294C4×C11—22no—
295C4×C11—42no—
296Dic11—44no—
297Dic11—44no—
298C25—221no—
299C25—221no—
300C25D4411yescharacteristic
301C22×D4—112no—
302C22×D4—112no—
303C22×D4—221no—
304C22×D4—222no—
305C22×D4—224no—
306C22×D4—222no—
307C22×D4—224no—
308C22×D4—224no—
309C22×D4—221no—
310C22×D4—222no—
311C22×D4—222no—
312C22×D4—444no—
313C22×D4—444no—
314C22×D4—444no—
315C22×D4—444no—
316C22×D4—444no—
317C22×D4—444no—
318C23×C4—221no—
319C23×C4—221no—
320C23×C4D4411yescharacteristic
321C23×C4C22×D1111yescharacteristic
322C2×D8—228no—
323C2×D8—448no—
324C22×C8—22no—
325#123—228no—
326#123—228no—
327#121—114no—
328#121—114no—
329#121—224no—
330#121—222no—
331#121—224no—
332#121—222no—
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—222no—
340C2×C22⋊C4—222no—
341C2×C22⋊C4—224no—
342C2×C22⋊C4—444no—
343C2×C22⋊C4D4412yes—
344C2×C22⋊C4C22×D1112yes—
345#102—228no—
346C22⋊C8—22no—
347C22⋊C8C22×D1114yescomplemented
348#95—112no—
349#95—221no—
350C2×C11—21no—
351C2×C11—21no—
352C2×C11—22no—
353C2×C11—44no—
354C2×C11#159514yescomplemented
355C2×C11C2×#44711yescharacteristic
356C2×C11C2×#45311yescharacteristic
357C2×C11C2×B(4,𝔽2)11yescharacteristic
358D11—84no—
359D11—84no—
360C24—21no—
361C24—21no—
362C24—22no—
363C24—42no—
364C24—42no—
365C24—224no—
366C24—224no—
367C24—222no—
368C24—222no—
369C24—442no—
370C24—442no—
371C24—442no—
372C24—444no—
373C24—441no—
374C24—441no—
375C24—442no—
376C24—442no—
377C24—882no—
378C24—882no—
379C24D8814yescomplemented
380C24C2×D4411yescharacteristic
381C24C2×D4412yes—
382C2×D4—114no—
383C2×D4—228no—
384C2×D4—224no—
385C2×D4—228no—
386C2×D4—224no—
387C2×D4—224no—
388C2×D4—222no—
389C2×D4—224no—
390C2×D4—444no—
391C2×D4—444no—
392C2×D4—444no—
393C2×D4—448no—
394C2×D4—444no—
395C2×D4—448no—
396C2×D4—448no—
397C2×D4—4416no—
398C2×D4—448no—
399C2×D4—448no—
400C2×D4—4432no—
401C2×D4—444no—
402C2×D4—448no—
403C2×D4—448no—
404C2×D4—444no—
405C2×D4—442no—
406C2×D4—882no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—42no—
410C22×C4—42no—
411C22×C4—224no—
412C22×C4—224no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—442no—
416C22×C4—444no—
417C22×C4—442no—
418C22×C4C2×D4412yes—
419C22×C4C2×D4411yescharacteristic
420C22×C4D4×D1112yes—
421C22×C4D4×D1112yes—
422C22×C4C23×D1111yescharacteristic
423D8—4416no—
424C2×C8—24no—
425C2×C8—44no—
426C4⋊C4—114no—
427C4⋊C4—224no—
428C4⋊C4—222no—
429C22⋊C4—24no—
430C22⋊C4—24no—
431C22⋊C4—228no—
432C22⋊C4—224no—
433C22⋊C4—224no—
434C22⋊C4—448no—
435C11C2×#159511yescharacteristic, complemented, Sylow
436C23—22no—
437C23—22no—
438C23—22no—
439C23—24no—
440C23—22no—
441C23—24no—
442C23—48no—
443C23—42no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—84no—
448C23—81no—
449C23—81no—
450C23—224no—
451C23—224no—
452C23—442no—
453C23—448no—
454C23—442no—
455C23—442no—
456C23—444no—
457C23—448no—
458C23—448no—
459C23—442no—
460C23—442no—
461C23—442no—
462C23—444no—
463C23—444no—
464C23—444no—
465C23—444no—
466C23—884no—
467C23—884no—
468C23—882no—
469C23—884no—
470C23—884no—
471C23—8816no—
472C23—882no—
473C23—882no—
474C23—882no—
475C23#6693511yescharacteristic
476C23#6693511yescharacteristic
477C23C2×D8812yes—
478C23C2×D8814yescomplemented
479C23#6696112yes—
480C23C22×D4411yescharacteristic
481D4—228no—
482D4—444no—
483D4—444no—
484D4—448no—
485D4—4416no—
486D4—4432no—
487D4—444no—
488D4—444no—
489D4—448no—
490D4—882no—
491D4—884no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—41no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—42no—
498C2×C4—42no—
499C2×C4—81no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—448no—
503C2×C4—442no—
504C2×C4—448no—
505C2×C4—442no—
506C2×C4—444no—
507C2×C4#6693512yes—
508C2×C4C2×D4×D1112yes—
509C8—44no—
510C22—24no—
511C22—24no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—24no—
517C22—44no—
518C22—48no—
519C22—42no—
520C22—42no—
521C22—82no—
522C22—84no—
523C22—444no—
524C22—444no—
525C22—444no—
526C22—444no—
527C22—444no—
528C22—444no—
529C22—882no—
530C22—882no—
531C22—888no—
532C22—8816no—
533C22—888no—
534C22—888no—
535C22—882no—
536C22—882no—
537C22#1062234512yes—
538C22#1062234512yes—
539C22#1062235412yes—
540C22#1062236012yes—
541C22C2×#6693511yescharacteristic
542C22C22×D8811yescharacteristic
543C22C2×#6696111yescharacteristic
544C4—22no—
545C4—22no—
546C4—42no—
547C4—444no—
548C4—444no—
549C2—21no—
550C2—21no—
551C2—22no—
552C2—44no—
553C2—884no—
554C2—884no—
555C2#1306753614yesdirect product factor
556C2C2×#1062234511yescharacteristic
557C2C2×#1062236011yescharacteristic
558C2C2×#1062235411yescharacteristic
subgroupG/H
centerC23#66935
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#323C2
socleC23×C11#120
hypercenterC2×#323D11
hypocenterC11C2×#1595
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
1. C2×#10623024C2semidirect
2. C2×#10622345C2semidirect
3. C2×#10622573C2semidirect
4. #13067536C2direct (N × H)
5. C2×#10622108C2semidirect
6. C2×C11×#323C2semidirect
9. C23×D44C22semidirect
17. #10623024C22semidirect
20. C2×C11×C22⋊C8C22semidirect
21. C2×C11⋊#95C22semidirect
24. #10622573C22semidirect
26. #10622345C22semidirect
27. C11×#323C22semidirect
28. #10622108C22semidirect
51. C22×D44D4semidirect
52. C22×D44C23semidirect
62. #66983D4semidirect
69. C2×C4⋊Dic11D4semidirect
77. C11×C22⋊C8C23semidirect
79. C11⋊#95C23semidirect
87. C24×C11D8semidirect
144. C2×D44C2×D4semidirect
155. C4⋊Dic11C2×D4semidirect
162. C2×#323D11semidirect
180. C23×C11C2×D8semidirect
253. C2×C22⋊C8C2×D11semidirect
258. #323C2×D11semidirect
347. C22⋊C8C22×D11semidirect
354. C2×C11#1595semidirect
379. C24D88semidirect
435. C11C2×#1595semidirect
478. C23C2×D88semidirect
555. C2#13067536direct (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×#106223452
C2×#106225732
#130675362
C2×#106221082
C2×C11×#3232
C2×#159511