Finite Group Databasebeta

← C2×#13073034 #14922883

Subgroups — C2×#13073034 #14922883

Order 2816.

2574 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66932C212yesmaximal
2#13073034C2116yesmaximal, direct product factor
3C2×#10622271C212yesmaximal, complemented
4C2×#10622565C212yesmaximal
5C2×#10622598C211yesmaximal, characteristic, complemented
6C2×#10622586C211yesmaximal, characteristic, complemented
7C2×#10622268C212yesmaximal, complemented
8C2×#10622589C211yesmaximal, characteristic, complemented
9C2×#10622825C211yesmaximal, characteristic
10C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊Dic11C211yesmaximal, characteristic
12C2×C11×#380C211yesmaximal, characteristic
13C24×C4×C11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C22⋊C4C2212yes—
17C22×C22⋊Dic11C2212yes—
18C22×C22⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2212yes—
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×C4×Dic11C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C2×#66932—216no—
30C2×#66932C22116yes—
31C11×#380C2218yes—
32C2×C11×#95C2212yes—
33#10622825C2218yes—
34C4×C22⋊Dic11C2218yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622598C2218yescomplemented
42#10622589C2218yescomplemented
43C4⋊C4×Dic11C2218yescomplemented
44#10622586C2218yescomplemented
45#10622565C22116yes—
46#10622271C22116yescomplemented
47#10622268C22116yescomplemented
48C25×C11C2311yescharacteristic
49C23×C4×C11—24no—
50C23×C4×C11—24no—
51C23×C4×C11—24no—
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2314yes—
56C23×C4×C11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4C2314yes—
66C2×C11×C4⋊C4C2314yes—
67C2×C11×C22⋊C4—28no—
68C2×C11×C22⋊C4C2318yes—
69C2×C22⋊Dic11—28no—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11D418yes—
72C2×C22⋊Dic11C2318yes—
73C2×C22⋊Dic11C2314yes—
74C2×C22⋊Dic11C2314yes—
75C2×C4⋊Dic11—24no—
76C2×C4⋊Dic11—24no—
77C2×C4⋊Dic11—28no—
78C2×C4⋊Dic11C2318yes—
79C2×C4⋊Dic11C2314yes—
80C2×C4⋊Dic11C2314yes—
81C2×Dic11⋊C4—28no—
82C2×Dic11⋊C4—28no—
83C2×Dic11⋊C4—28no—
84C2×Dic11⋊C4C2318yes—
85C2×Dic11⋊C4C2318yes—
86C2×Dic11⋊C4C2318yes—
87C2×C4×Dic11—24no—
88C2×C4×Dic11—24no—
89C2×C4×Dic11—28no—
90C2×C4×Dic11C2318yes—
91C2×C4×Dic11C2314yes—
92C2×C4×Dic11C2314yes—
93#66932—264no—
94C11×#95C2318yes—
95C11⋊#95C2314yes—
96C11⋊#95C2318yes—
97C11⋊#95C2318yes—
98C11⋊#95C2314yes—
99C11⋊#95C2318yes—
100C11⋊#95C2318yes—
101C2×#2496—111nomaximal, Sylow
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11—22no—
107C24×C11—22no—
108C24×C11C2×D414yes—
109C24×C11C2412yes—
110C24×C11C2411yescharacteristic
111C22×C4×C11—24no—
112C22×C4×C11—24no—
113C22×C4×C11—24no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—28no—
121C22×C4×C11—28no—
122C22×C4×C11—28no—
123C22×C4×C11—416no—
124C22×C4×C11#4114yes—
125C22×C4×C11#4114yes—
126C22×C4×C11#4114yes—
127C22×C4×C11C2412yes—
128C22×C4×C11C2414yes—
129C22×C4×C11C2414yes—
130C22×C4×C11C2412yes—
131C22×Dic11—24no—
132C22×Dic11—24no—
133C22×Dic11—22no—
134C22×Dic11—22no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11C2×D414yes—
147C22×Dic11C2×D414yes—
148C22×Dic11#4114yes—
149C22×Dic11C2412yes—
150C22×Dic11C2414yes—
151C22×Dic11C2414yes—
152C22×Dic11C2412yes—
153C22×Dic11C2412yes—
154C22×Dic11C2412yes—
155C11×C4⋊C4—28no—
156C11×C4⋊C4—28no—
157C11×C22⋊C4—216no—
158C22⋊Dic11—28no—
159C22⋊Dic11—216no—
160C22⋊Dic11C2×D4116yes—
161C4⋊Dic11—216no—
162C4⋊Dic11—28no—
163C4⋊Dic11—28no—
164Dic11⋊C4—216no—
165Dic11⋊C4—216no—
166Dic11⋊C4—216no—
167C4×Dic11—216no—
168C4×Dic11—28no—
169C4×Dic11—28no—
170C22×#126—112no—
171#2496—1116no—
172C2×#400—112no—
173C2×#397—112no—
174C2×#389—111no—
175C2×#389—111no—
176C2×#387—112no—
177C2×#384—111no—
178C2×#380—111no—
179C2×#380D1111yescharacteristic
180C2×C4×C4⋊C4—111no—
181C2×C4×C22⋊C4—111no—
182C23×C11—28no—
183C23×C11—28no—
184C23×C11—28no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11—44no—
192C23×C11—44no—
193C23×C11—44no—
194C23×C11—44no—
195C23×C11C22×D414yes—
196C23×C11C22×D412yes—
197C23×C11C2×#4112yes—
198C23×C11C2×#4112yes—
199C23×C11C2×#4112yes—
200C23×C11C2×#4112yes—
201C23×C112−1+412yes—
202C23×C112−1+412yes—
203C23×C11C2511yescharacteristic
204C2×C4×C11—24no—
205C2×C4×C11—24no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—22no—
210C2×C4×C11—22no—
211C2×C4×C11—22no—
212C2×C4×C11—24no—
213C2×C4×C11—44no—
214C2×C4×C11—48no—
215C2×C4×C11—48no—
216C2×C4×C11—416no—
217C2×C4×C11#126116yescomplemented
218C2×C4×C11C2×#4114yes—
219C2×C4×C11C2×#4114yes—
220C2×C4×C11C2×#4114yes—
221C2×Dic11—28no—
222C2×Dic11—28no—
223C2×Dic11—28no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—22no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—24no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—22no—
239C2×Dic11—48no—
240C2×Dic11—48no—
241C2×Dic11—44no—
242C2×Dic11C22×D414yes—
243C2×Dic11C22×D414yes—
244C2×Dic11C2×#4114yes—
245C24×C4C2×D1111yescharacteristic
246C2×#126—1116no—
247C2×#126—2216no—
248C22×C4⋊C4—112no—
249C22×C4⋊C4—112no—
250C22×C4⋊C4—112no—
251C22×C4⋊C4—112no—
252C22×C4⋊C4—111no—
253C22×C4⋊C4—111no—
254C22×C4⋊C4C2×D1111yescharacteristic
255C22×C4⋊C4C2×D1111yescharacteristic
256C22×C22⋊C4—111no—
257C22×C22⋊C4—111no—
258C22×C22⋊C4—112no—
259C22×C22⋊C4C2×D1112yes—
260C22×C42—112no—
261C22×C42—111no—
262C22×C42—111no—
263#400—1116no—
264#397—1116no—
265#389—118no—
266#389—118no—
267#387—1116no—
268#384—118no—
269#380—118no—
270#380C2×D1118yes—
271C4×C4⋊C4—118no—
272C4×C22⋊C4—118no—
273C2×#95—112no—
274C2×#95—112no—
275C2×#95—112no—
276C2×#95—111no—
277C2×#95—112no—
278C2×#95—111no—
279C2×#95C2×D1112yes—
280C22×C11—24no—
281C22×C11—24no—
282C22×C11—24no—
283C22×C11—42no—
284C22×C11—42no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—416no—
288C22×C11C2×#12614yes—
289C22×C11#53214yes—
290C22×C11#54114yes—
291C22×C11#54714yes—
292C22×C11#54714yes—
293C22×C11#55214yes—
294C22×C11#55614yes—
295C22×C11C23×D411yescharacteristic
296C22×C11C22×#4111yescharacteristic
297C22×C11C22×#4111yescharacteristic
298C22×C11C22×#4111yescharacteristic
299C22×C11C22×#4111yescharacteristic
300C22×C11C2×2−1+411yescharacteristic
301C22×C11C2×2−1+411yescharacteristic
302C4×C11—42no—
303C4×C11—44no—
304C4×C11—44no—
305C4×C11C2×#12618yescomplemented
306Dic11—24no—
307Dic11—24no—
308Dic11—24no—
309Dic11—44no—
310Dic11—44no—
311Dic11—42no—
312C25C22×D1111yescharacteristic
313C23×C4—24no—
314C23×C4—24no—
315C23×C4—24no—
316C23×C4—111no—
317C23×C4—111no—
318C23×C4—111no—
319C23×C4—112no—
320C23×C4—112no—
321C23×C4—111no—
322C23×C4C22×D1114yes—
323C23×C4C22×D1112yes—
324C23×C4C22×D1112yes—
325C23×C4C22×D1111yescharacteristic
326C23×C4C22×D1111yescharacteristic
327#126—2264no—
328C2×C4⋊C4—24no—
329C2×C4⋊C4—24no—
330C2×C4⋊C4—118no—
331C2×C4⋊C4—118no—
332C2×C4⋊C4—118no—
333C2×C4⋊C4—114no—
334C2×C4⋊C4—114no—
335C2×C4⋊C4—118no—
336C2×C4⋊C4—228no—
337C2×C4⋊C4—228no—
338C2×C4⋊C4—228no—
339C2×C4⋊C4—228no—
340C2×C4⋊C4—224no—
341C2×C4⋊C4—224no—
342C2×C4⋊C4C22×D1114yes—
343C2×C4⋊C4C22×D1114yes—
344C2×C22⋊C4—28no—
345C2×C22⋊C4—118no—
346C2×C22⋊C4—114no—
347C2×C22⋊C4—118no—
348C2×C22⋊C4—114no—
349C2×C22⋊C4—224no—
350C2×C22⋊C4—228no—
351C2×C22⋊C4C22×D1118yes—
352C2×C42—118no—
353C2×C42—114no—
354C2×C42—114no—
355C2×C42—228no—
356C2×C42—224no—
357C2×C42—224no—
358#95—114no—
359#95—114no—
360#95—118no—
361#95—118no—
362#95—118no—
363#95—118no—
364#95C22×D1118yes—
365C2×C11—44no—
366C2×C11#249618yescomplemented
367C2×C11C22×#12611yescharacteristic
368C2×C11C2×#53211yescharacteristic
369C2×C11C2×#54111yescharacteristic
370C2×C11C2×#54711yescharacteristic
371C2×C11C2×#54711yescharacteristic
372C2×C11C2×#55211yescharacteristic
373C2×C11C2×#55611yescharacteristic
374C24—22no—
375C24—22no—
376C24—22no—
377C24—22no—
378C24—22no—
379C24—22no—
380C24D4×D1114yes—
381C24C23×D1112yes—
382C24C23×D1111yescharacteristic
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—22no—
389C22×C4—22no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—28no—
393C22×C4—28no—
394C22×C4—28no—
395C22×C4—416no—
396C22×C4—114no—
397C22×C4—114no—
398C22×C4—114no—
399C22×C4—112no—
400C22×C4—112no—
401C22×C4—112no—
402C22×C4—112no—
403C22×C4—114no—
404C22×C4—114no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—222no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—222no—
412C22×C4—224no—
413C22×C4—224no—
414C22×C4—224no—
415C22×C4—224no—
416C22×C4—224no—
417C22×C4—222no—
418C22×C4—224no—
419C22×C4—222no—
420C22×C4#433914yes—
421C22×C4#434114yes—
422C22×C4#434114yes—
423C22×C4C23×D1112yes—
424C22×C4C23×D1114yes—
425C22×C4C23×D1114yes—
426C22×C4C23×D1112yes—
427C4⋊C4—28no—
428C4⋊C4—28no—
429C4⋊C4—2216no—
430C4⋊C4—2216no—
431C4⋊C4—2216no—
432C4⋊C4—2216no—
433C4⋊C4—228no—
434C4⋊C4—228no—
435C22⋊C4—216no—
436C22⋊C4—1116no—
437C22⋊C4—228no—
438C22⋊C4—2216no—
439C42—2216no—
440C42—228no—
441C42—228no—
442C11C2×#249611yescharacteristic, complemented, Sylow
443C23—28no—
444C23—28no—
445C23—28no—
446C23—22no—
447C23—22no—
448C23—22no—
449C23—22no—
450C23—22no—
451C23—22no—
452C23—44no—
453C23—44no—
454C23—44no—
455C23—44no—
456C23C2×#433912yes—
457C23C2×D4×D1114yes—
458C23C2×D4×D1112yes—
459C23C2×#434112yes—
460C23C2×#434112yes—
461C23#6704012yes—
462C23#41×D1112yes—
463C23#6704312yes—
464C23C24×D1111yescharacteristic
465C2×C4—22no—
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—44no—
475C2×C4—48no—
476C2×C4—48no—
477C2×C4—416no—
478C2×C4—114no—
479C2×C4—114no—
480C2×C4—114no—
481C2×C4—228no—
482C2×C4—228no—
483C2×C4—228no—
484C2×C4—222no—
485C2×C4—222no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—222no—
489C2×C4—222no—
490C2×C4—222no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—224no—
495C2×C4—224no—
496C2×C4—222no—
497C2×C4—224no—
498C2×C4—222no—
499C2×C4—448no—
500C2×C4—444no—
501C2×C4—448no—
502C2×C4#66932116yescomplemented
503C2×C4C2×#433914yes—
504C2×C4C2×#434114yes—
505C2×C4C2×#434114yes—
506C22—24no—
507C22—24no—
508C22—24no—
509C22—42no—
510C22—42no—
511C22—42no—
512C22—42no—
513C22—416no—
514C22C2×#6693214yes—
515C22#1062303814yes—
516C22#1062306414yes—
517C22#1062312714yes—
518C22#1062314214yes—
519C22#1062315614yes—
520C22#1062317014yes—
521C22C22×#433911yescharacteristic
522C22C22×D4×D1111yescharacteristic
523C22C22×#434111yescharacteristic
524C22C22×#434111yescharacteristic
525C22C2×#6704011yescharacteristic
526C22C2×#41×D1111yescharacteristic
527C22C2×#6704311yescharacteristic
528C4—42no—
529C4—44no—
530C4—44no—
531C4—224no—
532C4—224no—
533C4—224no—
534C4—444no—
535C4—442no—
536C4—444no—
537C4C2×#6693218yescomplemented
538C2—44no—
539C2#1307303418yesdirect product factor
540C2C22×#6693211yescharacteristic
541C2C2×#1062312711yescharacteristic
542C2C2×#1062315611yescharacteristic
543C2C2×#1062314211yescharacteristic
544C2C2×#1062303811yescharacteristic
545C2C2×#1062317011yescharacteristic
546C2C2×#1062306411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11C2×#2496
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. #13073034C2direct (N × H)
3. C2×#10622271C2semidirect
5. C2×#10622598C2semidirect
6. C2×#10622586C2semidirect
7. C2×#10622268C2semidirect
8. C2×#10622589C2semidirect
10. C2×C4⋊C4×Dic11C2semidirect
41. #10622598C22semidirect
42. #10622589C22semidirect
43. C4⋊C4×Dic11C22semidirect
44. #10622586C22semidirect
46. #10622271C22semidirect
47. #10622268C22semidirect
217. C2×C4×C11#126semidirect
305. C4×C11C2×#126semidirect
366. C2×C11#2496semidirect
442. C11C2×#2496semidirect
502. C2×C4#66932semidirect
537. C4C2×#66932semidirect
539. C2#13073034direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669322
#130730342
C2×#106222712
C2×#106225652
C2×#106225982
C2×#106225862
C2×#106222682
C2×#106225892
C2×#106228252
C2×C4⋊C4×Dic112
C2×C4×C22⋊Dic112
C2×C11×#3802
C2×#249611