Finite Group Databasebeta

← C2×#13072498 #14921274

Subgroups — C2×#13072498 #14921274

Order 2816.

3894 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C212yesmaximal, complemented
2C22×C4×C22⋊D11C212yesmaximal, complemented
3#13072498C2116yesmaximal, direct product factor
4C2×#10622562C211yesmaximal, characteristic, complemented
5C2×#10622572C212yesmaximal, complemented
6C2×#10622573C211yesmaximal, characteristic
7C2×#10622585C212yesmaximal, complemented
8C2×#10622282C212yesmaximal, complemented
9C2×#10622281C212yesmaximal, complemented
10C2×C11×#385C211yesmaximal, characteristic, complemented
11C24×C4×C11C2211yescharacteristic
12C23×C22⋊D11C2212yes—
13C23×D44C2211yescharacteristic
14C23×C4×D11C2212yes—
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C2×C4×C22⋊D11—216no—
20C2×C4×C22⋊D11C22116yescomplemented
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2212yes—
30C2×#66947—216no—
31C2×#66947C22116yescomplemented
32C11×#385C2218yescomplemented
33C2×C11×#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37#10622585C22116yescomplemented
38#10622573C2218yes—
39#10622572C22116yescomplemented
40#10622562C2218yescomplemented
41#10622282C22116yescomplemented
42#10622281C22116yescomplemented
43C25×C11C2311yescharacteristic
44C24×D11C2312yes—
45C23×C4×C11—28no—
46C23×C4×C11—42no—
47C23×C4×C11C2311yescharacteristic
48C23×C4×C11C2312yes—
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2314yes—
51C23×C4×C11C2312yes—
52C22×C22⋊D11—28no—
53C22×C22⋊D11—28no—
54C22×C22⋊D11—28no—
55C22×C22⋊D11C2318yes—
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C22×D44—28no—
60C22×D44—42no—
61C22×D44C2314yes—
62C22×C4×D11—28no—
63C22×C4×D11—28no—
64C22×C4×D11—44no—
65C22×C4×D11C2318yes—
66C2×C11×C4⋊C4—28no—
67C2×C11×C4⋊C4C2318yes—
68C2×C11×C22⋊C4—24no—
69C2×C11×C22⋊C4—42no—
70C2×C11×C22⋊C4C2314yes—
71C2×C11×C22⋊C4C2314yes—
72C2×C22⋊Dic11—28no—
73C2×C22⋊Dic11C2318yes—
74C4×C22⋊D11—264no—
75C2×(C2×D11)⋊C4—28no—
76C2×(C2×D11)⋊C4—28no—
77C2×(C2×D11)⋊C4—28no—
78C2×(C2×D11)⋊C4D4116yescomplemented
79C2×(C2×D11)⋊C4C2318yes—
80C2×(C2×D11)⋊C4C2318yes—
81C2×(C2×D11)⋊C4C2318yes—
82C2×(C2×D11)⋊C4C2318yes—
83C2×C4⋊Dic11—42no—
84C2×C4⋊Dic11C2314yes—
85C2×Dic11⋊C4—28no—
86C2×Dic11⋊C4—28no—
87C2×Dic11⋊C4—28no—
88C2×Dic11⋊C4C2318yes—
89C2×Dic11⋊C4C2318yes—
90C2×Dic11⋊C4C2318yes—
91C2×C4×Dic11—28no—
92C2×C4×Dic11C2318yes—
93#66947—264no—
94C11×#95C2318yes—
95C11⋊#95C2318yes—
96C11⋊#95C2314yes—
97C11⋊#95C2314yes—
98C2×#2455—111nomaximal, Sylow
99C24×C11—24no—
100C24×C11—24no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11#4114yes—
104C24×C11C2412yes—
105C24×C11C2411yescharacteristic
106C23×D11—24no—
107C23×D11—24no—
108C23×D11—24no—
109C23×D11—24no—
110C23×D11—24no—
111C23×D11—24no—
112C23×D11C2×D418yes—
113C23×D11C2414yes—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—216no—
124C22×C4×C11—44no—
125C22×C4×C11—416no—
126C22×C4×C11C2×D418yes—
127C22×C4×C11C2412yes—
128C22×C4×C11C2414yes—
129C22×C4×C11C2412yes—
130C22×C4×C11C2414yes—
131C2×C22⋊D11—264no—
132C2×C22⋊D11—216no—
133C2×C22⋊D11—216no—
134C2×C22⋊D11—216no—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11C2×D418yes—
143C22×Dic11#4118yes—
144C22×Dic11C2414yes—
145C22×Dic11C2414yes—
146C22×Dic11C2414yes—
147C2×D44—216no—
148C2×D44—44no—
149C2×D44—416no—
150C2×C4×D11—216no—
151C2×C4×D11—216no—
152C2×C4×D11—48no—
153C2×C4×D11—432no—
154C11×C4⋊C4—216no—
155C11×C22⋊C4—28no—
156C11×C22⋊C4—44no—
157C22⋊Dic11—216no—
158(C2×D11)⋊C4—216no—
159(C2×D11)⋊C4—216no—
160(C2×D11)⋊C4—216no—
161(C2×D11)⋊C4C2×D4132yescomplemented
162C4⋊Dic11—44no—
163Dic11⋊C4—216no—
164Dic11⋊C4—216no—
165Dic11⋊C4—216no—
166C4×Dic11—216no—
167C22×#123—112no—
168C22×C4×D4—112no—
169#2455—1116no—
170C2×#399—111no—
171C2×#394—112no—
172C2×#392—111no—
173C2×#389—112no—
174C2×#388—112no—
175C2×#385—112no—
176C2×#385D1111yescharacteristic, complemented
177C23×C11—216no—
178C23×C11—28no—
179C23×C11—24no—
180C23×C11—24no—
181C23×C11—22no—
182C23×C11—22no—
183C23×C11—44no—
184C23×C11—48no—
185C23×C11—44no—
186C23×C11C22×D414yes—
187C23×C11C2×#4114yes—
188C23×C11C2×#4112yes—
189C23×C11C2×#4114yes—
190C23×C11H(5,𝔽2)12yes—
191C23×C112−1+412yes—
192C23×C11C2511yescharacteristic
193C22×D11—216no—
194C22×D11—216no—
195C22×D11—216no—
196C22×D11—24no—
197C22×D11—24no—
198C22×D11—24no—
199C22×D11—24no—
200C22×D11—24no—
201C22×D11—24no—
202C22×D11—48no—
203C22×D11—48no—
204C22×D11—48no—
205C22×D11—48no—
206C22×D11C22×D418yes—
207C2×C4×C11—216no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—416no—
218C2×C4×C11—48no—
219C2×C4×C11—44no—
220C2×C4×C11—44no—
221C2×C4×C11C22×D418yes—
222C22⋊D11—264no—
223C2×Dic11—216no—
224C2×Dic11—216no—
225C2×Dic11—24no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—48no—
233C2×Dic11C22×D418yes—
234C2×Dic11C2×#4118yes—
235D44—416no—
236C4×D11—432no—
237C23×D4—112no—
238C23×D4—111no—
239C24×C4—112no—
240C24×C4C2×D1111yescharacteristic
241C2×#123—1116no—
242C2×#123—2216no—
243C2×C4×D4—1116no—
244C2×C4×D4—2216no—
245C22×C4⋊C4—112no—
246C22×C4⋊C4—112no—
247C22×C4⋊C4—112no—
248C22×C4⋊C4—111no—
249C22×C4⋊C4C2×D1112yes—
250C22×C22⋊C4—112no—
251C22×C22⋊C4—112no—
252C22×C22⋊C4—112no—
253C22×C22⋊C4—112no—
254C22×C22⋊C4—112no—
255C22×C22⋊C4C2×D1111yescharacteristic
256C22×C22⋊C4C2×D1111yescharacteristic
257C22×C42—112no—
258#399—118no—
259#394—1116no—
260#392—118no—
261#389—1116no—
262#388—1116no—
263#385—1116no—
264#385C2×D1118yescomplemented
265C2×#95—111no—
266C2×#95—112no—
267C2×#95—111no—
268C2×#95C2×D1112yes—
269C22×C11—28no—
270C22×C11—24no—
271C22×C11—42no—
272C22×C11—44no—
273C22×C11—416no—
274C22×C11—42no—
275C22×C11#52518yes—
276C22×C11#53914yes—
277C22×C11D4214yes—
278C22×C11#54718yes—
279C22×C11#55914yes—
280C22×C11C23×D412yes—
281C22×C11C22×#4111yescharacteristic
282C22×C11C22×#4112yes—
283C22×C11C2×H(5,𝔽2)11yescharacteristic
284C22×C11C2×2−1+411yescharacteristic
285C2×D11—28no—
286C2×D11—28no—
287C2×D11—28no—
288C2×D11—44no—
289C2×D11—44no—
290C2×D11—44no—
291C2×D11—432no—
292C2×D11—44no—
293C4×C11—28no—
294C4×C11—44no—
295C4×C11—42no—
296C4×C11—42no—
297Dic11—28no—
298Dic11—28no—
299Dic11—44no—
300C25—112no—
301C25C22×D1111yescharacteristic
302C22×D4—118no—
303C22×D4—114no—
304C22×D4—228no—
305C22×D4—228no—
306C22×D4—228no—
307C22×D4—228no—
308C22×D4—442no—
309C23×C4—28no—
310C23×C4—42no—
311C23×C4—112no—
312C23×C4—112no—
313C23×C4—112no—
314C23×C4—118no—
315C23×C4—228no—
316C23×C4—228no—
317C23×C4—444no—
318C23×C4C22×D1112yes—
319C23×C4C22×D1111yescharacteristic
320C23×C4C22×D1111yescharacteristic
321C23×C4C22×D1114yes—
322C23×C4C22×D1112yes—
323#123—2264no—
324C4×D4—2264no—
325C2×C4⋊C4—28no—
326C2×C4⋊C4—118no—
327C2×C4⋊C4—118no—
328C2×C4⋊C4—118no—
329C2×C4⋊C4—114no—
330C2×C4⋊C4—228no—
331C2×C4⋊C4—228no—
332C2×C4⋊C4—228no—
333C2×C4⋊C4—442no—
334C2×C4⋊C4C22×D1118yes—
335C2×C22⋊C4—24no—
336C2×C22⋊C4—42no—
337C2×C22⋊C4—1116no—
338C2×C22⋊C4—118no—
339C2×C22⋊C4—118no—
340C2×C22⋊C4—118no—
341C2×C22⋊C4—118no—
342C2×C22⋊C4—118no—
343C2×C22⋊C4—228no—
344C2×C22⋊C4—228no—
345C2×C22⋊C4—228no—
346C2×C22⋊C4—228no—
347C2×C22⋊C4C22×D1114yes—
348C2×C22⋊C4C22×D1114yes—
349C2×C42—118no—
350C2×C42—228no—
351#95—118no—
352#95—114no—
353#95—114no—
354#95C22×D1118yes—
355C2×C11—44no—
356C2×C11#245518yescomplemented
357C2×C11C2×#52512yes—
358C2×C11C2×#53911yescharacteristic
359C2×C11C2×D4211yescharacteristic
360C2×C11C2×#54712yes—
361C2×C11C2×#55911yescharacteristic
362D11—48no—
363C24—24no—
364C24—22no—
365C24—22no—
366C24—24no—
367C24—118no—
368C24—114no—
369C24—224no—
370C24—224no—
371C24—224no—
372C24—224no—
373C24—224no—
374C24—224no—
375C24#433914yes—
376C24C23×D1112yes—
377C24C23×D1111yescharacteristic
378C2×D4—2216no—
379C2×D4—2216no—
380C2×D4—2216no—
381C2×D4—2264no—
382C2×D4—2216no—
383C2×D4—444no—
384C2×D4—4416no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—24no—
389C22×C4—24no—
390C22×C4—22no—
391C22×C4—22no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—216no—
395C22×C4—44no—
396C22×C4—416no—
397C22×C4—118no—
398C22×C4—118no—
399C22×C4—114no—
400C22×C4—114no—
401C22×C4—114no—
402C22×C4—2216no—
403C22×C4—224no—
404C22×C4—224no—
405C22×C4—224no—
406C22×C4—224no—
407C22×C4—224no—
408C22×C4—224no—
409C22×C4—224no—
410C22×C4—2216no—
411C22×C4—448no—
412C22×C4—4432no—
413C22×C4D4×D1118yes—
414C22×C4C23×D1112yes—
415C22×C4C23×D1114yes—
416C22×C4C23×D1112yes—
417C22×C4C23×D1114yes—
418C4⋊C4—216no—
419C4⋊C4—2216no—
420C4⋊C4—2216no—
421C4⋊C4—2216no—
422C4⋊C4—444no—
423C22⋊C4—28no—
424C22⋊C4—44no—
425C22⋊C4—1132no—
426C22⋊C4—2216no—
427C22⋊C4—2216no—
428C22⋊C4—2216no—
429C22⋊C4—2216no—
430C42—2216no—
431C11C2×#245511yescharacteristic, complemented, Sylow
432C23—28no—
433C23—216no—
434C23—24no—
435C23—22no—
436C23—22no—
437C23—24no—
438C23—44no—
439C23—48no—
440C23—44no—
441C23—118no—
442C23—2216no—
443C23—2216no—
444C23—2216no—
445C23—224no—
446C23—224no—
447C23—224no—
448C23—224no—
449C23—224no—
450C23—224no—
451C23—448no—
452C23—448no—
453C23—448no—
454C23—448no—
455C23C2×#433914yes—
456C23C2×#433912yes—
457C23C2×D4×D1114yes—
458C23#6703712yes—
459C23#6704012yes—
460C23#41×D1114yes—
461C23C24×D1111yescharacteristic
462D4—2264no—
463D4—4416no—
464C2×C4—216no—
465C2×C4—24no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—22no—
471C2×C4—22no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—416no—
475C2×C4—48no—
476C2×C4—44no—
477C2×C4—44no—
478C2×C4—118no—
479C2×C4—118no—
480C2×C4—2216no—
481C2×C4—2216no—
482C2×C4—224no—
483C2×C4—224no—
484C2×C4—224no—
485C2×C4—224no—
486C2×C4—224no—
487C2×C4—224no—
488C2×C4—224no—
489C2×C4—4432no—
490C2×C4—448no—
491C2×C4C2×D4×D1118yes—
492C22—28no—
493C22—24no—
494C22—42no—
495C22—416no—
496C22—42no—
497C22—44no—
498C22—228no—
499C22—228no—
500C22—228no—
501C22—444no—
502C22—444no—
503C22—444no—
504C22—4432no—
505C22—444no—
506C22#1062304614yes—
507C22#1062307818yes—
508C22#1062312114yes—
509C22#1062316218yes—
510C22#1062319514yes—
511C22C22×#433911yescharacteristic
512C22C22×D4×D1112yes—
513C22C2×#6703711yescharacteristic
514C22C2×#6704011yescharacteristic
515C22C2×#41×D1112yes—
516C4—28no—
517C4—44no—
518C4—42no—
519C4—42no—
520C4—228no—
521C4—228no—
522C4—444no—
523C2—44no—
524C2—448no—
525C2#1307249818yesdirect product factor
526C2C2×#1062307812yes—
527C2C2×#1062304611yescharacteristic
528C2C2×#1062312111yescharacteristic
529C2C2×#1062316212yes—
530C2C2×#1062319511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×#385D11
hypocenterC11C2×#2455
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#66947C2semidirect
2. C22×C4×C22⋊D11C2semidirect
3. #13072498C2direct (N × H)
4. C2×#10622562C2semidirect
5. C2×#10622572C2semidirect
7. C2×#10622585C2semidirect
8. C2×#10622282C2semidirect
9. C2×#10622281C2semidirect
10. C2×C11×#385C2semidirect
20. C2×C4×C22⋊D11C22semidirect
31. C2×#66947C22semidirect
32. C11×#385C22semidirect
37. #10622585C22semidirect
39. #10622572C22semidirect
40. #10622562C22semidirect
41. #10622282C22semidirect
42. #10622281C22semidirect
78. C2×(C2×D11)⋊C4D4semidirect
161. (C2×D11)⋊C4C2×D4semidirect
176. C2×#385D11semidirect
264. #385C2×D11semidirect
356. C2×C11#2455semidirect
431. C11C2×#2455semidirect
525. C2#13072498direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669472
C22×C4×C22⋊D112
#130724982
C2×#106225622
C2×#106225722
C2×#106225732
C2×#106225852
C2×#106222822
C2×#106222812
C2×C11×#3852
C2×#245511