Finite Group Databasebeta

← C2×#13067534 #14725837

Subgroups — C2×#13067534 #14725837

Order 2816.

2040 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622649C212yesmaximal, complemented
2C2×#10622573C211yesmaximal, characteristic, complemented
3#13067534C218yesmaximal, direct product factor
4C2×#10622175C212yesmaximal, complemented
5C2×#10622163C211yesmaximal, characteristic, complemented
6C2×C11×#534C211yesmaximal, characteristic, complemented
7C23×D4×C11—21no—
8C23×C22⋊D11—21no—
9C23×D44C2211yescharacteristic, complemented
10C11×#534—24no—
11C11×#534—22no—
12C11×#534C2214yescomplemented
13C2×C11×#123—22no—
14C2×C11×#121—21no—
15C2×C11×#121C2212yes—
16C2×C11×#120—22no—
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×#4323—22no—
19C22×(C2×D11)⋊C4—21no—
20C2×C11⋊#95C2211yescharacteristic, complemented
21C2×C22⋊(C11⋊C8)C2212yescomplemented
22#10622649—24no—
23#10622649C2218yescomplemented
24C2×#66873—22no—
25#10622573—22no—
26#10622573C2214yescomplemented
27#10622175C2218yescomplemented
28#10622163C2214yescomplemented
29C25×C11—21no—
30C25×C11D411yescharacteristic
31C24×D11—21no—
32C22×D4×C11—22no—
33C22×D4×C11—24no—
34C22×D4×C11—22no—
35C22×D4×C11—24no—
36C22×D4×C11—21no—
37C22×D4×C11—44no—
38C22×D4×C11—44no—
39C22×D4×C11D412yescomplemented
40C23×C4×C11—21no—
41C23×C4×C11D411yescharacteristic
42C23×C4×C11C2311yescharacteristic
43C22×C22⋊D11—24no—
44C22×C22⋊D11—44no—
45C22×C22⋊D11—44no—
46C22×C22⋊D11—44no—
47C23×Dic11—21no—
48C22×D44—22no—
49C22×D44—22no—
50C22×D44—21no—
51C22×D44—44no—
52C22×D44C2312yescomplemented
53C11×#123—28no—
54C11×#123—28no—
55C11×#121—24no—
56C11×#121—24no—
57C11×#121—22no—
58C11×#121—22no—
59C11×#121D414yescomplemented
60C11×#121C2314yes—
61C11×#120—28no—
62C11×#120—28no—
63C2×C11×C4⋊C4—21no—
64C2×C11×C4⋊C4D412yescomplemented
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4—22no—
68C2×C11×C22⋊C4—22no—
69C2×C11×C22⋊C4D412yes—
70C2×C11×C22⋊C4C2312yes—
71C2×#4323—28no—
72C2×#4323—48no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—44no—
75C22×C11⋊C8—22no—
76C11⋊#95—21no—
77C11⋊#95C2312yescomplemented
78C22⋊(C11⋊C8)—22no—
79C22⋊(C11⋊C8)C2314yescomplemented
80#66873—28no—
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—44no—
90C24×C11—82no—
91C24×C11—82no—
92C24×C11D814yescomplemented
93C24×C11C2×D411yescharacteristic
94C24×C11C2×D412yes—
95C23×D11—24no—
96C23×D11—22no—
97C23×D11—42no—
98C23×D11—42no—
99C23×D11—42no—
100C23×D11—41no—
101C23×D11—41no—
102C23×D11—42no—
103C23×D11—42no—
104C2×D4×C11—28no—
105C2×D4×C11—24no—
106C2×D4×C11—24no—
107C2×D4×C11—24no—
108C2×D4×C11—22no—
109C2×D4×C11—44no—
110C2×D4×C11—48no—
111C2×D4×C11—416no—
112C2×D4×C11—48no—
113C2×D4×C11—44no—
114C2×D4×C11—48no—
115C2×D4×C11—44no—
116C2×D4×C11—82no—
117C2×D4×C11C2×D414yescomplemented
118C22×C4×C11—24no—
119C22×C4×C11—21no—
120C22×C4×C11—22no—
121C22×C4×C11—21no—
122C22×C4×C11—42no—
123C22×C4×C11—44no—
124C22×C4×C11—42no—
125C22×C4×C11C2×D412yes—
126C22×C4×C11C2×D412yes—
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D412yes—
129C22×C4×C11C2411yescharacteristic
130C2×C22⋊D11—48no—
131C2×C22⋊D11—48no—
132C2×C22⋊D11—432no—
133C2×C22⋊D11—48no—
134C22×Dic11—24no—
135C22×Dic11—22no—
136C22×Dic11—42no—
137C22×Dic11—42no—
138C2×D44—28no—
139C2×D44—24no—
140C2×D44—44no—
141C2×D44—44no—
142C2×D44—44no—
143C2×D44—48no—
144C2×D44—42no—
145C11×C4⋊C4—24no—
146C11×C4⋊C4—22no—
147C11×C4⋊C4C2×D414yescomplemented
148C11×C22⋊C4—28no—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—24no—
151C11×C22⋊C4—24no—
152C11×C22⋊C4—24no—
153#4323—416no—
154(C2×D11)⋊C4—48no—
155C2×C11⋊C8—24no—
156C2×C11⋊C8—44no—
157C2×#534D1111yescharacteristic, complemented
158C2×#447—112no—
159C2×#392—111no—
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—48no—
174C23×C11—42no—
175C23×C11—42no—
176C23×C11—44no—
177C23×C11—44no—
178C23×C11—44no—
179C23×C11—84no—
180C23×C11—81no—
181C23×C11—81no—
182C23×C11—84no—
183C23×C11—84no—
184C23×C11—816no—
185C23×C11#12011yescharacteristic
186C23×C11#12011yescharacteristic
187C23×C11C2×D812yes—
188C23×C11C2×D814yescomplemented
189C23×C11AGL(1,ℤ/8)12yes—
190C23×C11C22×D411yescharacteristic
191C22×D11—24no—
192C22×D11—42no—
193C22×D11—42no—
194C22×D11—44no—
195C22×D11—48no—
196C22×D11—42no—
197C22×D11—48no—
198C22×D11—42no—
199C22×D11—42no—
200C22×D11—42no—
201C22×D11—44no—
202C22×D11—84no—
203C22×D11—84no—
204C22×D11—82no—
205C22×D11—82no—
206C22×D11—82no—
207C22×D11—82no—
208D4×C11—44no—
209D4×C11—416no—
210D4×C11—44no—
211D4×C11—44no—
212D4×C11—48no—
213D4×C11—82no—
214D4×C11—84no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—41no—
219C2×C4×C11—42no—
220C2×C4×C11—41no—
221C2×C4×C11—48no—
222C2×C4×C11—44no—
223C2×C4×C11—42no—
224C2×C4×C11—42no—
225C2×C4×C11—81no—
226C2×C4×C11#12012yes—
227C2×C4×C11C22×D412yes—
228C22⋊D11—432no—
229C2×Dic11—24no—
230C2×Dic11—48no—
231C2×Dic11—42no—
232C2×Dic11—42no—
233D44—28no—
234D44—48no—
235D44—44no—
236C11⋊C8—44no—
237C23×D4—21no—
238C23×D4—111no—
239C23×D4—221no—
240C22×D8—222no—
241#534—24no—
242#534—22no—
243#534C2×D1114yescomplemented
244C2×#123—22no—
245C2×#121—21no—
246C2×#121C2×D1112yes—
247C2×#120—22no—
248C22×C22⋊C4—221no—
249C22×C22⋊C4C2×D1111yescharacteristic
250#447—118no—
251#447—224no—
252C2×#102—222no—
253C2×C22⋊C8—112no—
254#392—114no—
255#392—222no—
256C2×#95—111no—
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—48no—
268C22×C11—42no—
269C22×C11—42no—
270C22×C11—44no—
271C22×C11—44no—
272C22×C11—44no—
273C22×C11—82no—
274C22×C11—84no—
275C22×C11—816no—
276C22×C11—88no—
277C22×C11#44712yes—
278C22×C11#44712yes—
279C22×C11#45312yes—
280C22×C11B(4,𝔽2)12yes—
281C22×C11C2×#12011yescharacteristic
282C22×C11C22×D811yescharacteristic
283C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
284C2×D11—44no—
285C2×D11—44no—
286C2×D11—44no—
287C2×D11—82no—
288C2×D11—82no—
289C2×D11—88no—
290C2×D11—88no—
291C2×D11—82no—
292C2×D11—82no—
293C4×C11—22no—
294C4×C11—22no—
295C4×C11—44no—
296C4×C11—42no—
297Dic11—44no—
298C25—21no—
299C25—221no—
300C25C22⋊D1111yescharacteristic
301C22×D4—22no—
302C22×D4—24no—
303C22×D4—22no—
304C22×D4—24no—
305C22×D4—21no—
306C22×D4—44no—
307C22×D4—44no—
308C22×D4—112no—
309C22×D4—224no—
310C22×D4—222no—
311C22×D4—222no—
312C22×D4—221no—
313C22×D4—444no—
314C22×D4—444no—
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—28no—
326#123—28no—
327#121—24no—
328#121—24no—
329#121—22no—
330#121—22no—
331#121C22⋊D1114yescomplemented
332#121C22×D1114yes—
333#120—28no—
334#120—28no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4C22⋊D1112yescomplemented
337C2×C22⋊C4—22no—
338C2×C22⋊C4—22no—
339C2×C22⋊C4—22no—
340C2×C22⋊C4—22no—
341C2×C22⋊C4—224no—
342C2×C22⋊C4—444no—
343C2×C22⋊C4C22⋊D1112yes—
344C2×C22⋊C4C22×D1112yes—
345#102—228no—
346C22⋊C8—114no—
347C22⋊C8—222no—
348#95—112no—
349#95—221no—
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—22no—
362C24—21no—
363C24—24no—
364C24—22no—
365C24—42no—
366C24—42no—
367C24—44no—
368C24—82no—
369C24—82no—
370C24—224no—
371C24—222no—
372C24—442no—
373C24—442no—
374C24—442no—
375C24—442no—
376C24—442no—
377C24—441no—
378C24—441no—
379C24#432314yescomplemented
380C24C2×C22⋊D1111yescharacteristic
381C24C2×C22⋊D1112yes—
382C2×D4—28no—
383C2×D4—24no—
384C2×D4—24no—
385C2×D4—24no—
386C2×D4—22no—
387C2×D4—44no—
388C2×D4—48no—
389C2×D4—416no—
390C2×D4—48no—
391C2×D4—44no—
392C2×D4—48no—
393C2×D4—44no—
394C2×D4—82no—
395C2×D4—228no—
396C2×D4—224no—
397C2×D4—444no—
398C2×D4—444no—
399C2×D4—448no—
400C2×D4—444no—
401C2×D4—448no—
402C2×D4—448no—
403C2×D4—4432no—
404C2×D4—448no—
405C2×D4—442no—
406C2×D4C2×C22⋊D1114yescomplemented
407C22×C4—24no—
408C22×C4—21no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—42no—
412C22×C4—44no—
413C22×C4—42no—
414C22×C4—224no—
415C22×C4—222no—
416C22×C4—442no—
417C22×C4—442no—
418C22×C4C2×C22⋊D1112yes—
419C22×C4C2×C22⋊D1112yes—
420C22×C4C2×C22⋊D1111yescharacteristic
421C22×C4C2×C22⋊D1112yes—
422C22×C4C23×D1111yescharacteristic
423D8—4416no—
424C2×C8—224no—
425C2×C8—444no—
426C4⋊C4—24no—
427C4⋊C4—22no—
428C4⋊C4C2×C22⋊D1114yescomplemented
429C22⋊C4—28no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—24no—
433C22⋊C4—24no—
434C22⋊C4—448no—
435C11C2×#159511yescharacteristic, complemented, Sylow
436C23—22no—
437C23—22no—
438C23—24no—
439C23—22no—
440C23—22no—
441C23—24no—
442C23—24no—
443C23—48no—
444C23—42no—
445C23—42no—
446C23—48no—
447C23—42no—
448C23—42no—
449C23—44no—
450C23—44no—
451C23—44no—
452C23—84no—
453C23—81no—
454C23—81no—
455C23—84no—
456C23—84no—
457C23—816no—
458C23—224no—
459C23—442no—
460C23—448no—
461C23—442no—
462C23—442no—
463C23—444no—
464C23—448no—
465C23—442no—
466C23—442no—
467C23—444no—
468C23—442no—
469C23—884no—
470C23—884no—
471C23—882no—
472C23—882no—
473C23—882no—
474C23—882no—
475C23C2×#432312yes—
476C23C2×#432314yescomplemented
477C23#6698512yes—
478C23#6700611yescharacteristic
479C23#6700611yescharacteristic
480C23C22×C22⋊D1111yescharacteristic
481D4—44no—
482D4—416no—
483D4—44no—
484D4—44no—
485D4—48no—
486D4—82no—
487D4—84no—
488D4—228no—
489D4—444no—
490D4—448no—
491D4—4432no—
492C2×C4—24no—
493C2×C4—22no—
494C2×C4—24no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—48no—
499C2×C4—44no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—81no—
503C2×C4—224no—
504C2×C4—448no—
505C2×C4—442no—
506C2×C4—442no—
507C2×C4#6700612yes—
508C2×C4C22×C22⋊D1112yes—
509C8—444no—
510C22—24no—
511C22—24no—
512C22—21no—
513C22—21no—
514C22—21no—
515C22—21no—
516C22—24no—
517C22—44no—
518C22—48no—
519C22—42no—
520C22—42no—
521C22—44no—
522C22—44no—
523C22—44no—
524C22—82no—
525C22—84no—
526C22—816no—
527C22—88no—
528C22—444no—
529C22—444no—
530C22—444no—
531C22—882no—
532C22—882no—
533C22—888no—
534C22—888no—
535C22—882no—
536C22—882no—
537C22#1062283012yes—
538C22#1062283012yes—
539C22#1062285412yes—
540C22#1062285712yes—
541C22C22×#432311yescharacteristic
542C22C2×#6698511yescharacteristic
543C22C2×#6700611yescharacteristic
544C4—22no—
545C4—22no—
546C4—44no—
547C4—42no—
548C4—444no—
549C2—21no—
550C2—21no—
551C2—22no—
552C2—44no—
553C2—84no—
554C2—884no—
555C2#1306753414yesdirect product factor
556C2C2×#1062283011yescharacteristic
557C2C2×#1062285411yescharacteristic
558C2C2×#1062285711yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#534C2
socleC23×C11#120
hypercenterC2×#534D11
hypocenterC11C2×#1595
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#534

Complements

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

NH ≅ G/Ntype
1. C2×#10622649C2semidirect
2. C2×#10622573C2semidirect
3. #13067534C2direct (N × H)
4. C2×#10622175C2semidirect
5. C2×#10622163C2semidirect
6. C2×C11×#534C2semidirect
9. C23×D44C22semidirect
12. C11×#534C22semidirect
20. C2×C11⋊#95C22semidirect
21. C2×C22⋊(C11⋊C8)C22semidirect
23. #10622649C22semidirect
26. #10622573C22semidirect
27. #10622175C22semidirect
28. #10622163C22semidirect
39. C22×D4×C11D4semidirect
52. C22×D44C23semidirect
59. C11×#121D4semidirect
64. C2×C11×C4⋊C4D4semidirect
77. C11⋊#95C23semidirect
79. C22⋊(C11⋊C8)C23semidirect
92. C24×C11D8semidirect
117. C2×D4×C11C2×D4semidirect
147. C11×C4⋊C4C2×D4semidirect
157. C2×#534D11semidirect
188. C23×C11C2×D8semidirect
243. #534C2×D11semidirect
317. C22×D4C22⋊D11semidirect
331. #121C22⋊D11semidirect
336. C2×C4⋊C4C22⋊D11semidirect
355. C2×C11#1595semidirect
379. C24#4323semidirect
406. C2×D4C2×C22⋊D11semidirect
428. C4⋊C4C2×C22⋊D11semidirect
435. C11C2×#1595semidirect
476. C23C2×#4323semidirect
555. C2#13067534direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226492
C2×#106225732
#130675342
C2×#106221752
C2×#106221632
C2×C11×#5342
C2×#159511