Finite Group Databasebeta

← C2×#13067539 #14725849

Subgroups — C2×#13067539 #14725849

Order 2816.

1696 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622659C212yesmaximal, complemented
2C2×#10622573C211yesmaximal, characteristic
3#13067539C218yesmaximal, direct product factor
4C2×#10622176C212yesmaximal, complemented
5C2×#10622163C211yesmaximal, characteristic, complemented
6C2×C11×#543C211yesmaximal, characteristic, complemented
7C23×C22⋊D11—21no—
8C23×D44C2211yescharacteristic
9C11×#543—24no—
10C11×#543—22no—
11C11×#543C2214yescomplemented
12C2×C11×C22⋊Q8—22no—
13C2×C11×C22⋊Q8—21no—
14C2×C11×C22⋊Q8—22no—
15C2×C11×C22⋊Q8C2212yes—
16C22×C11×C22⋊C4—21no—
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×#4325—22no—
19C22×(C2×D11)⋊C4—21no—
20C2×C11⋊#95C2211yescharacteristic
21C2×C22⋊(C11⋊C8)C2212yes—
22#10622659—24no—
23#10622659C2218yescomplemented
24C2×#66873—22no—
25#10622573—22no—
26#10622573C2214yes—
27#10622176C2218yescomplemented
28#10622163C2214yescomplemented
29C25×C11D411yescharacteristic
30C24×D11—21no—
31C22×Q8×C11—21no—
32C22×Q8×C11D412yescomplemented
33C23×C4×C11—21no—
34C23×C4×C11—21no—
35C23×C4×C11D411yescharacteristic
36C23×C4×C11C2311yescharacteristic
37C22×C22⋊D11—24no—
38C22×C22⋊D11—44no—
39C22×C22⋊D11—44no—
40C22×C22⋊D11—44no—
41C23×Dic11—21no—
42C22×D44—22no—
43C22×D44—22no—
44C22×D44—21no—
45C22×D44—44no—
46C22×D44C2312yes—
47C11×C22⋊Q8—28no—
48C11×C22⋊Q8—28no—
49C11×C22⋊Q8—24no—
50C11×C22⋊Q8—28no—
51C11×C22⋊Q8—24no—
52C11×C22⋊Q8—22no—
53C11×C22⋊Q8—22no—
54C11×C22⋊Q8—28no—
55C11×C22⋊Q8D414yescomplemented
56C11×C22⋊Q8C2314yes—
57C2×C11×C4⋊C4—21no—
58C2×C11×C4⋊C4—22no—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4D412yescomplemented
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4—24no—
63C2×C11×C22⋊C4—22no—
64C2×C11×C22⋊C4—24no—
65C2×C11×C22⋊C4—22no—
66C2×C11×C22⋊C4—22no—
67C2×C11×C22⋊C4D412yes—
68C2×C11×C22⋊C4C2312yes—
69C2×#4325—28no—
70C2×#4325—48no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—44no—
73C22×C11⋊C8—22no—
74C11⋊#95—21no—
75C11⋊#95C2312yes—
76C22⋊(C11⋊C8)—22no—
77C22⋊(C11⋊C8)C2314yes—
78#66873—28no—
79C2×#1596—111nomaximal, Sylow
80C24×C11—21no—
81C24×C11—21no—
82C24×C11—22no—
83C24×C11—42no—
84C24×C11—42no—
85C24×C11SD1614yescomplemented
86C24×C11C2×D411yescharacteristic
87C24×C11C2×D412yes—
88C23×D11—24no—
89C23×D11—22no—
90C23×D11—42no—
91C23×D11—42no—
92C23×D11—42no—
93C23×D11—41no—
94C23×D11—41no—
95C23×D11—42no—
96C23×D11—42no—
97C2×Q8×C11—24no—
98C2×Q8×C11—22no—
99C2×Q8×C11—44no—
100C2×Q8×C11—82no—
101C2×Q8×C11C2×D414yescomplemented
102C22×C4×C11—22no—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—24no—
106C22×C4×C11—24no—
107C22×C4×C11—21no—
108C22×C4×C11—42no—
109C22×C4×C11—42no—
110C22×C4×C11—82no—
111C22×C4×C11—82no—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2411yescharacteristic
117C2×C22⋊D11—48no—
118C2×C22⋊D11—48no—
119C2×C22⋊D11—432no—
120C2×C22⋊D11—48no—
121C22×Dic11—24no—
122C22×Dic11—22no—
123C22×Dic11—42no—
124C22×Dic11—42no—
125C2×D44—28no—
126C2×D44—24no—
127C2×D44—44no—
128C2×D44—44no—
129C2×D44—44no—
130C2×D44—48no—
131C2×D44—42no—
132C11×C4⋊C4—24no—
133C11×C4⋊C4—28no—
134C11×C4⋊C4—24no—
135C11×C4⋊C4—22no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4C2×D414yescomplemented
138C11×C22⋊C4—28no—
139C11×C22⋊C4—24no—
140C11×C22⋊C4—24no—
141C11×C22⋊C4—24no—
142C11×C22⋊C4—24no—
143#4325—416no—
144(C2×D11)⋊C4—48no—
145C2×C11⋊C8—24no—
146C2×C11⋊C8—44no—
147C2×#543D1111yescharacteristic, complemented
148C2×#450—112no—
149C2×#392—111no—
150#1596—118no—
151C2×#328—112no—
152C2×#323—111no—
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—24no—
157C23×C11—22no—
158C23×C11—24no—
159C23×C11—48no—
160C23×C11—42no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—84no—
165C23×C11—81no—
166C23×C11—81no—
167C23×C11#12011yescharacteristic
168C23×C11#12011yescharacteristic
169C23×C11C2×SD1612yes—
170C23×C11C2×SD1614yescomplemented
171C23×C11#13712yes—
172C23×C11C22×D411yescharacteristic
173C22×D11—24no—
174C22×D11—42no—
175C22×D11—42no—
176C22×D11—44no—
177C22×D11—48no—
178C22×D11—42no—
179C22×D11—48no—
180C22×D11—42no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—44no—
184C22×D11—84no—
185C22×D11—84no—
186C22×D11—82no—
187C22×D11—82no—
188C22×D11—82no—
189C22×D11—82no—
190Q8×C11—44no—
191Q8×C11—82no—
192Q8×C11—84no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—22no—
196C2×C4×C11—24no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—41no—
200C2×C4×C11—42no—
201C2×C4×C11—44no—
202C2×C4×C11—44no—
203C2×C4×C11—42no—
204C2×C4×C11—81no—
205C2×C4×C11—84no—
206C2×C4×C11—84no—
207C2×C4×C11#12012yes—
208C2×C4×C11C22×D412yes—
209C22⋊D11—432no—
210C2×Dic11—24no—
211C2×Dic11—48no—
212C2×Dic11—42no—
213C2×Dic11—42no—
214D44—28no—
215D44—48no—
216D44—44no—
217C11⋊C8—44no—
218C23×D4—111no—
219C23×D4—221no—
220C22×SD16—222no—
221#543—24no—
222#543—22no—
223#543C2×D1114yescomplemented
224C2×C22⋊Q8—22no—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—22no—
227C2×C22⋊Q8C2×D1112yes—
228C22×C22⋊C4—21no—
229C22×C22⋊C4—221no—
230C22×C22⋊C4C2×D1111yescharacteristic
231#450—118no—
232#450—224no—
233C2×#102—222no—
234C2×C22⋊C8—112no—
235#392—114no—
236#392—222no—
237C2×#95—111no—
238#328—118no—
239#323—114no—
240C22×C11—24no—
241C22×C11—24no—
242C22×C11—21no—
243C22×C11—21no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—24no—
247C22×C11—44no—
248C22×C11—48no—
249C22×C11—42no—
250C22×C11—42no—
251C22×C11—82no—
252C22×C11—84no—
253C22×C11#44812yes—
254C22×C11#44812yes—
255C22×C11#45312yes—
256C22×C11B(4,𝔽2)12yes—
257C22×C11C2×#12011yescharacteristic
258C22×C11C22×SD1611yescharacteristic
259C22×C11C2×#13711yescharacteristic
260C2×D11—44no—
261C2×D11—44no—
262C2×D11—44no—
263C2×D11—82no—
264C2×D11—82no—
265C2×D11—88no—
266C2×D11—88no—
267C2×D11—82no—
268C2×D11—82no—
269C4×C11—22no—
270C4×C11—22no—
271C4×C11—42no—
272C4×C11—44no—
273C4×C11—44no—
274Dic11—44no—
275C25—221no—
276C25C22⋊D1111yescharacteristic
277C22×Q8—21no—
278C22×Q8C22⋊D1112yescomplemented
279C22×D4—112no—
280C22×D4—224no—
281C22×D4—222no—
282C22×D4—222no—
283C22×D4—221no—
284C22×D4—444no—
285C22×D4—444no—
286C22×D4—444no—
287C22×D4—444no—
288C23×C4—21no—
289C23×C4—21no—
290C23×C4—221no—
291C23×C4C22⋊D1111yescharacteristic
292C23×C4C22×D1111yescharacteristic
293C2×SD16—228no—
294C2×SD16—448no—
295C22×C8—222no—
296C22⋊Q8—28no—
297C22⋊Q8—28no—
298C22⋊Q8—24no—
299C22⋊Q8—28no—
300C22⋊Q8—24no—
301C22⋊Q8—22no—
302C22⋊Q8—22no—
303C22⋊Q8—28no—
304C22⋊Q8C22⋊D1114yescomplemented
305C22⋊Q8C22×D1114yes—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—22no—
308C2×C4⋊C4—22no—
309C2×C4⋊C4C22⋊D1112yescomplemented
310C2×C22⋊C4—22no—
311C2×C22⋊C4—24no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—22no—
315C2×C22⋊C4—22no—
316C2×C22⋊C4—224no—
317C2×C22⋊C4—444no—
318C2×C22⋊C4C22⋊D1112yes—
319C2×C22⋊C4C22×D1112yes—
320#102—228no—
321C22⋊C8—114no—
322C22⋊C8—222no—
323#95—112no—
324#95—221no—
325C2×C11—21no—
326C2×C11—21no—
327C2×C11—22no—
328C2×C11—44no—
329C2×C11#159614yescomplemented
330C2×C11C2×#44811yescharacteristic
331C2×C11C2×#45311yescharacteristic
332C2×C11C2×B(4,𝔽2)11yescharacteristic
333D11—84no—
334C24—21no—
335C24—22no—
336C24—21no—
337C24—42no—
338C24—42no—
339C24—224no—
340C24—222no—
341C24—442no—
342C24—442no—
343C24—442no—
344C24—442no—
345C24—442no—
346C24—441no—
347C24—441no—
348C24#432514yescomplemented
349C24C2×C22⋊D1111yescharacteristic
350C24C2×C22⋊D1112yes—
351C2×Q8—24no—
352C2×Q8—22no—
353C2×Q8—44no—
354C2×Q8—82no—
355C2×Q8C2×C22⋊D1114yescomplemented
356C2×D4—228no—
357C2×D4—224no—
358C2×D4—444no—
359C2×D4—444no—
360C2×D4—448no—
361C2×D4—444no—
362C2×D4—448no—
363C2×D4—448no—
364C2×D4—4432no—
365C2×D4—448no—
366C2×D4—442no—
367C22×C4—22no—
368C22×C4—21no—
369C22×C4—22no—
370C22×C4—24no—
371C22×C4—24no—
372C22×C4—21no—
373C22×C4—42no—
374C22×C4—42no—
375C22×C4—82no—
376C22×C4—82no—
377C22×C4—224no—
378C22×C4—222no—
379C22×C4—442no—
380C22×C4—442no—
381C22×C4C2×C22⋊D1112yes—
382C22×C4C2×C22⋊D1112yes—
383C22×C4C2×C22⋊D1111yescharacteristic
384C22×C4C2×C22⋊D1112yes—
385C22×C4C23×D1111yescharacteristic
386SD16—4416no—
387C2×C8—224no—
388C2×C8—444no—
389C4⋊C4—24no—
390C4⋊C4—28no—
391C4⋊C4—24no—
392C4⋊C4—22no—
393C4⋊C4—24no—
394C4⋊C4C2×C22⋊D1114yescomplemented
395C22⋊C4—28no—
396C22⋊C4—24no—
397C22⋊C4—24no—
398C22⋊C4—24no—
399C22⋊C4—24no—
400C22⋊C4—448no—
401C11C2×#159611yescharacteristic, complemented, Sylow
402C23—22no—
403C23—22no—
404C23—24no—
405C23—22no—
406C23—22no—
407C23—24no—
408C23—48no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—42no—
413C23—84no—
414C23—81no—
415C23—81no—
416C23—224no—
417C23—442no—
418C23—448no—
419C23—442no—
420C23—442no—
421C23—444no—
422C23—448no—
423C23—442no—
424C23—442no—
425C23—444no—
426C23—442no—
427C23—884no—
428C23—884no—
429C23—882no—
430C23—882no—
431C23—882no—
432C23—882no—
433C23C2×#432512yes—
434C23C2×#432514yescomplemented
435C23#6699512yes—
436C23#6700611yescharacteristic
437C23#6700611yescharacteristic
438C23C22×C22⋊D1111yescharacteristic
439Q8—44no—
440Q8—82no—
441Q8—84no—
442D4—228no—
443D4—444no—
444D4—448no—
445D4—4432no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—22no—
449C2×C4—24no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—41no—
453C2×C4—42no—
454C2×C4—44no—
455C2×C4—44no—
456C2×C4—42no—
457C2×C4—81no—
458C2×C4—84no—
459C2×C4—84no—
460C2×C4—224no—
461C2×C4—448no—
462C2×C4—442no—
463C2×C4—442no—
464C2×C4#6700612yes—
465C2×C4C22×C22⋊D1112yes—
466C8—444no—
467C22—24no—
468C22—24no—
469C22—21no—
470C22—21no—
471C22—21no—
472C22—21no—
473C22—24no—
474C22—44no—
475C22—48no—
476C22—42no—
477C22—42no—
478C22—82no—
479C22—84no—
480C22—444no—
481C22—444no—
482C22—444no—
483C22—882no—
484C22—882no—
485C22—888no—
486C22—888no—
487C22—882no—
488C22—882no—
489C22#1062284012yes—
490C22#1062284012yes—
491C22#1062285412yes—
492C22#1062285712yes—
493C22C22×#432511yescharacteristic
494C22C2×#6699511yescharacteristic
495C22C2×#6700611yescharacteristic
496C4—22no—
497C4—22no—
498C4—42no—
499C4—44no—
500C4—44no—
501C4—444no—
502C2—21no—
503C2—21no—
504C2—22no—
505C2—44no—
506C2—884no—
507C2#1306753914yesdirect product factor
508C2C2×#1062284011yescharacteristic
509C2C2×#1062285411yescharacteristic
510C2C2×#1062285711yescharacteristic
subgroupG/H
centerC23#67006
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#543C2
socleC23×C11#120
prime radicalC2×#10622573C2
hypercenterC2×#543D11
hypocenterC11C2×#1596
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#543

Complements

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

NH ≅ G/Ntype
1. C2×#10622659C2semidirect
3. #13067539C2direct (N × H)
4. C2×#10622176C2semidirect
5. C2×#10622163C2semidirect
6. C2×C11×#543C2semidirect
11. C11×#543C22semidirect
23. #10622659C22semidirect
27. #10622176C22semidirect
28. #10622163C22semidirect
32. C22×Q8×C11D4semidirect
55. C11×C22⋊Q8D4semidirect
60. C2×C11×C4⋊C4D4semidirect
85. C24×C11SD16semidirect
101. C2×Q8×C11C2×D4semidirect
137. C11×C4⋊C4C2×D4semidirect
147. C2×#543D11semidirect
170. C23×C11C2×SD16semidirect
223. #543C2×D11semidirect
278. C22×Q8C22⋊D11semidirect
304. C22⋊Q8C22⋊D11semidirect
309. C2×C4⋊C4C22⋊D11semidirect
329. C2×C11#1596semidirect
348. C24#4325semidirect
355. C2×Q8C2×C22⋊D11semidirect
394. C4⋊C4C2×C22⋊D11semidirect
401. C11C2×#1596semidirect
434. C23C2×#4325semidirect
507. C2#13067539direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106226592
C2×#106225732
#130675392
C2×#106221762
C2×#106221632
C2×C11×#5432
C2×#159611