Finite Group Databasebeta

← C2×#13071882 #14920022

Subgroups — C2×#13071882 #14920022

Order 2816.

3182 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66946C211yesmaximal, characteristic
2C22×#66945C211yesmaximal, characteristic, complemented
3#13071882C2116yesmaximal, direct product factor
4C2×#10622605C211yesmaximal, characteristic, complemented
5C2×#10622596C211yesmaximal, characteristic, complemented
6C2×#10622288C212yesmaximal, complemented
7C2×#10622287C211yesmaximal, characteristic, complemented
8C2×#10622285C212yesmaximal
9C2×#10622262C212yesmaximal, complemented
10C2×#10622279C211yesmaximal, characteristic, complemented
11C2×#10622279C212yesmaximal, complemented
12C2×C11×#400C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2212yes—
28C22×C4×Dic11C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C2×#66946—28no—
31C2×#66946C2218yes—
32C2×#66945—28no—
33C2×#66945C2218yescomplemented
34C11×#400C2218yescomplemented
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2212yes—
37C2×C11×#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41#10622605C2218yescomplemented
42#10622596C2218yescomplemented
43#10622288C22116yescomplemented
44#10622287C2218yescomplemented
45#10622285C22116yes—
46#10622279C22116yescomplemented
47#10622279C2218yescomplemented
48#10622262C22116yescomplemented
49C24×D11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C22×D44—24no—
61C22×D44—24no—
62C22×D44—24no—
63C22×D44C2314yes—
64C22×C4×D11—28no—
65C22×C4×D11—24no—
66C22×C4×D11—28no—
67C22×C4×D11D418yes—
68C22×C4×D11C2314yes—
69C22×C4×D11C2314yes—
70C2×C11×C4⋊C4—24no—
71C2×C11×C4⋊C4—24no—
72C2×C11×C4⋊C4C2314yes—
73C2×C11×C4⋊C4C2314yes—
74C2×(C2×D11)⋊C4—28no—
75C2×(C2×D11)⋊C4—24no—
76C2×(C2×D11)⋊C4—28no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—28no—
79C2×(C2×D11)⋊C4—28no—
80C2×(C2×D11)⋊C4C2318yes—
81C2×(C2×D11)⋊C4C2314yes—
82C2×(C2×D11)⋊C4C2314yes—
83C2×(C2×D11)⋊C4C2318yes—
84C2×(C2×D11)⋊C4C2318yes—
85C2×(C2×D11)⋊C4C2318yes—
86C2×C4⋊Dic11—24no—
87C2×C4⋊Dic11C2314yes—
88C2×Dic11⋊C4—28no—
89C2×Dic11⋊C4—28no—
90C2×Dic11⋊C4C2318yes—
91C2×Dic11⋊C4C2318yes—
92C2×C4×Dic11—28no—
93C2×C4×Dic11—24no—
94C2×C4×Dic11—28no—
95C2×C4×Dic11C2314yes—
96C2×C4×Dic11C2318yes—
97C2×C4×Dic11C2318yes—
98#66946—232no—
99#66945—232no—
100C11×#95C2318yes—
101C11×#95C2314yes—
102C11×#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2314yes—
106C2×#2395—111nomaximal, Sylow
107C24×C11C2411yescharacteristic
108C23×D11—22no—
109C23×D11—24no—
110C23×D11—24no—
111C23×D11—24no—
112C23×D11—24no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—22no—
116C23×D11C2×D414yes—
117C23×D11#4114yes—
118C23×D11C2412yes—
119C23×D11C2412yes—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—22no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11C2×D414yes—
132C22×C4×C11#4114yes—
133C22×C4×C11C2412yes—
134C22×C4×C11C2414yes—
135C22×C4×C11C2414yes—
136C22×C4×C11C2412yes—
137C22×C4×C11C2412yes—
138C22×Dic11—24no—
139C22×Dic11—22no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11C2×D414yes—
146C22×Dic11#4118yes—
147C22×Dic11#4118yes—
148C22×Dic11C2412yes—
149C22×Dic11C2414yes—
150C22×Dic11C2414yes—
151C22×Dic11C2412yes—
152C2×D44—232no—
153C2×D44—28no—
154C2×D44—28no—
155C2×D44—28no—
156C2×C4×D11—232no—
157C2×C4×D11—216no—
158C2×C4×D11—28no—
159C2×C4×D11—216no—
160C2×C4×D11—416no—
161C2×C4×D11C2×D4116yes—
162C11×C4⋊C4—28no—
163C11×C4⋊C4—28no—
164(C2×D11)⋊C4—216no—
165(C2×D11)⋊C4—216no—
166(C2×D11)⋊C4—216no—
167(C2×D11)⋊C4—28no—
168(C2×D11)⋊C4—216no—
169(C2×D11)⋊C4—28no—
170C4⋊Dic11—28no—
171Dic11⋊C4—216no—
172Dic11⋊C4—216no—
173C4×Dic11—216no—
174C4×Dic11—28no—
175C4×Dic11—216no—
176C22×C4×D4—111no—
177C22×#117—111no—
178#2395—1116no—
179C2×#400D1111yescharacteristic, complemented
180C2×#399—111no—
181C2×#398—111no—
182C2×#397—111no—
183C2×#397—112no—
184C2×#394—112no—
185C2×C4×C4⋊C4—112no—
186C2×C4×C22⋊C4—111no—
187C2×C4×C22⋊C4—112no—
188C23×C11C22×D412yes—
189C23×C11C2×#4112yes—
190C23×C11C2×#4114yes—
191C23×C11C2×#4112yes—
192C23×C11C2×#4114yes—
193C23×C11C2511yescharacteristic
194C22×D11—28no—
195C22×D11—28no—
196C22×D11—28no—
197C22×D11—216no—
198C22×D11—28no—
199C22×D11—22no—
200C22×D11—24no—
201C22×D11—24no—
202C22×D11—24no—
203C22×D11—24no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—22no—
207C22×D11—44no—
208C22×D11—48no—
209C22×D11—48no—
210C22×D11—48no—
211C22×D11—44no—
212C22×D11C22×D414yes—
213C22×D11C2×#4114yes—
214C2×C4×C11—28no—
215C2×C4×C11—28no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—24no—
227C2×C4×C11—44no—
228C2×C4×C11—48no—
229C2×C4×C11—48no—
230C2×C4×C11C22×D414yes—
231C2×C4×C11C2×#4114yes—
232C2×Dic11—216no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—48no—
241C2×Dic11—44no—
242C2×Dic11#123116yes—
243C2×Dic11C22×D414yes—
244C2×Dic11C2×#4118yes—
245C2×Dic11C2×#4118yes—
246D44—232no—
247C4×D11—232no—
248C4×D11—416no—
249C23×D4—111no—
250C24×C4—111no—
251C24×C4—111no—
252C2×C4×D4—118no—
253C2×C4×D4—228no—
254C2×#117—118no—
255C2×#117—228no—
256C22×C4⋊C4—112no—
257C22×C4⋊C4—112no—
258C22×C4⋊C4—111no—
259C22×C4⋊C4C2×D1111yescharacteristic
260C22×C4⋊C4C2×D1111yescharacteristic
261C22×C22⋊C4—112no—
262C22×C22⋊C4—112no—
263C22×C22⋊C4—112no—
264C22×C22⋊C4—112no—
265C22×C22⋊C4—111no—
266C22×C22⋊C4—111no—
267C22×C42—112no—
268C22×C42—111no—
269C22×C42—112no—
270#400C2×D1118yescomplemented
271#399—118no—
272#398—118no—
273#397—118no—
274#397—1116no—
275#394—1116no—
276C4×C4⋊C4—1116no—
277C4×C22⋊C4—1116no—
278C4×C22⋊C4—118no—
279C2×#95—112no—
280C2×#95—112no—
281C2×#95—111no—
282C2×#95C2×D1112yes—
283C2×#95C2×D1112yes—
284C2×#95C2×D1111yescharacteristic
285C22×C11C2×#12314yes—
286C22×C11#52514yes—
287C22×C11#52918yes—
288C22×C11#52918yes—
289C22×C11#53214yes—
290C22×C11C23×D411yescharacteristic
291C22×C11C22×#4111yescharacteristic
292C22×C11C22×#4112yes—
293C22×C11C22×#4111yescharacteristic
294C22×C11C22×#4112yes—
295C2×D11—24no—
296C2×D11—24no—
297C2×D11—24no—
298C2×D11—28no—
299C2×D11—24no—
300C2×D11—416no—
301C2×D11—416no—
302C2×D11—42no—
303C2×D11—44no—
304C2×D11—44no—
305C2×D11—44no—
306C2×D11—42no—
307C4×C11—24no—
308C4×C11—24no—
309C4×C11—42no—
310C4×C11—44no—
311C4×C11—44no—
312Dic11—28no—
313Dic11—44no—
314Dic11—42no—
315Dic11C2×#12318yes—
316C25—111no—
317C25—111no—
318C22×D4—114no—
319C22×D4—224no—
320C22×D4—224no—
321C22×D4—224no—
322C23×C4—111no—
323C23×C4—112no—
324C23×C4—118no—
325C23×C4—114no—
326C23×C4—111no—
327C23×C4—112no—
328C23×C4—114no—
329C23×C4—228no—
330C23×C4—224no—
331C23×C4—228no—
332C23×C4C22×D1112yes—
333C23×C4C22×D1112yes—
334C23×C4C22×D1111yescharacteristic
335C23×C4C22×D1111yescharacteristic
336C23×C4C22×D1111yescharacteristic
337C4×D4—2232no—
338#117—2232no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—24no—
341C2×C4⋊C4—114no—
342C2×C4⋊C4—118no—
343C2×C4⋊C4—118no—
344C2×C4⋊C4—228no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4—228no—
347C2×C4⋊C4C22×D1114yes—
348C2×C4⋊C4C22×D1114yes—
349C2×C22⋊C4—118no—
350C2×C22⋊C4—114no—
351C2×C22⋊C4—114no—
352C2×C22⋊C4—118no—
353C2×C22⋊C4—118no—
354C2×C22⋊C4—118no—
355C2×C22⋊C4—228no—
356C2×C22⋊C4—228no—
357C2×C22⋊C4—228no—
358C2×C22⋊C4—224no—
359C2×C22⋊C4—228no—
360C2×C22⋊C4—224no—
361C2×C42—118no—
362C2×C42—114no—
363C2×C42—118no—
364C2×C42—228no—
365C2×C42—224no—
366C2×C42—228no—
367#95—118no—
368#95—114no—
369#95—118no—
370#95C22×D1118yes—
371#95C22×D1114yes—
372#95C22×D1118yes—
373C2×C11#239518yescomplemented
374C2×C11C22×#12311yescharacteristic
375C2×C11C2×#52511yescharacteristic
376C2×C11C2×#52912yes—
377C2×C11C2×#52912yes—
378C2×C11C2×#53211yescharacteristic
379D11—44no—
380D11—44no—
381C24—114no—
382C24—114no—
383C24—112no—
384C24—112no—
385C24—222no—
386C24—222no—
387C24—222no—
388C24—224no—
389C24—224no—
390C24—224no—
391C24—224no—
392C24—222no—
393C24C23×D1111yescharacteristic
394C2×D4—228no—
395C2×D4—228no—
396C2×D4—2232no—
397C2×D4—228no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—114no—
410C22×C4—118no—
411C22×C4—112no—
412C22×C4—118no—
413C22×C4—114no—
414C22×C4—1116no—
415C22×C4—112no—
416C22×C4—114no—
417C22×C4—2232no—
418C22×C4—2216no—
419C22×C4—228no—
420C22×C4—2216no—
421C22×C4—224no—
422C22×C4—224no—
423C22×C4—222no—
424C22×C4—224no—
425C22×C4—224no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—4416no—
429C22×C4D4×D1114yes—
430C22×C4#434314yes—
431C22×C4C23×D1112yes—
432C22×C4C23×D1114yes—
433C22×C4C23×D1114yes—
434C22×C4C23×D1112yes—
435C22×C4C23×D1112yes—
436C4⋊C4—28no—
437C4⋊C4—28no—
438C4⋊C4—2216no—
439C4⋊C4—228no—
440C4⋊C4—2216no—
441C22⋊C4—2216no—
442C22⋊C4—2216no—
443C22⋊C4—2216no—
444C22⋊C4—228no—
445C22⋊C4—2216no—
446C22⋊C4—228no—
447C42—2216no—
448C42—228no—
449C42—2216no—
450C11C2×#239511yescharacteristic, complemented, Sylow
451C23—114no—
452C23—114no—
453C23—2216no—
454C23—228no—
455C23—228no—
456C23—228no—
457C23—222no—
458C23—222no—
459C23—222no—
460C23—224no—
461C23—224no—
462C23—224no—
463C23—224no—
464C23—222no—
465C23—228no—
466C23—448no—
467C23—444no—
468C23—444no—
469C23—448no—
470C23—448no—
471C23C2×D4×D1112yes—
472C23C2×#434312yes—
473C23#41×D1112yes—
474C23#41×D1114yes—
475C23#41×D1114yes—
476C23C24×D1111yescharacteristic
477D4—2232no—
478C2×C4—28no—
479C2×C4—28no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—22no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—48no—
492C2×C4—44no—
493C2×C4—48no—
494C2×C4—1116no—
495C2×C4—114no—
496C2×C4—118no—
497C2×C4—118no—
498C2×C4—2232no—
499C2×C4—224no—
500C2×C4—224no—
501C2×C4—2216no—
502C2×C4—222no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—4416no—
508C2×C4—448no—
509C2×C4—444no—
510C2×C4C2×D4×D1114yes—
511C2×C4C2×#434314yes—
512C22—224no—
513C22—224no—
514C22—228no—
515C22—224no—
516C22—224no—
517C22—4416no—
518C22—4416no—
519C22—444no—
520C22—444no—
521C22—444no—
522C22—442no—
523C22—442no—
524C22#1062315814yes—
525C22D11×#12314yes—
526C22#1062319914yes—
527C22#1062322218yes—
528C22#1062323718yes—
529C22C22×D4×D1111yescharacteristic
530C22C22×#434311yescharacteristic
531C22C2×#41×D1111yescharacteristic
532C22C2×#41×D1112yes—
533C22C2×#41×D1112yes—
534C4—24no—
535C4—24no—
536C4—44no—
537C4—44no—
538C4—42no—
539C4—118no—
540C4—228no—
541C4—444no—
542C4—442no—
543C2—444no—
544C2—444no—
545C2#1307188218yesdirect product factor
546C2C2×D11×#12311yescharacteristic
547C2C2×#1062315811yescharacteristic
548C2C2×#1062323712yes—
549C2C2×#1062322212yes—
550C2C2×#1062319911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#400C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#400D11
hypocenterC11C2×#2395
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
2. C22×#66945C2semidirect
3. #13071882C2direct (N × H)
4. C2×#10622605C2semidirect
5. C2×#10622596C2semidirect
6. C2×#10622288C2semidirect
7. C2×#10622287C2semidirect
9. C2×#10622262C2semidirect
10. C2×#10622279C2semidirect
11. C2×#10622279C2semidirect
12. C2×C11×#400C2semidirect
33. C2×#66945C22semidirect
34. C11×#400C22semidirect
41. #10622605C22semidirect
42. #10622596C22semidirect
43. #10622288C22semidirect
44. #10622287C22semidirect
46. #10622279C22semidirect
47. #10622279C22semidirect
48. #10622262C22semidirect
179. C2×#400D11semidirect
270. #400C2×D11semidirect
373. C2×C11#2395semidirect
450. C11C2×#2395semidirect
545. C2#13071882direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669462
C22×#669452
#130718822
C2×#106226052
C2×#106225962
C2×#106222882
C2×#106222872
C2×#106222852
C2×#106222622
C2×#106222792
C2×C11×#4002
C2×#239511