Finite Group Databasebeta

← C2×#13073522 #14925041

Subgroups — C2×#13073522 #14925041

Order 2816.

3526 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×#66949C212yesmaximal, complemented
2C22×#66940C211yesmaximal, characteristic, complemented
3C22×#66946C211yesmaximal, characteristic
4#13073522C2116yesmaximal, direct product factor
5C2×#10622593C211yesmaximal, characteristic, complemented
6C2×#10622285C211yesmaximal, characteristic
7C2×#10622604C211yesmaximal, characteristic
8C2×#10622603C212yesmaximal, complemented
9C2×#10622282C212yesmaximal, complemented
10C2×#10622263C211yesmaximal, characteristic, complemented
11C2×#10622280C212yesmaximal, complemented
12C2×C11×#398C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11C2212yes—
15C23×Dic22C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×Dic11⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×#66949—216no—
32C2×#66949C22116yescomplemented
33C2×#66946—28no—
34C2×#66946C2218yes—
35C2×#66940—28no—
36C2×#66940C2218yescomplemented
37C11×#398C2218yescomplemented
38C2×C11×#95C2212yes—
39C2×C11×#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2211yescharacteristic
43#10622604C2218yes—
44#10622603C22116yescomplemented
45#10622593C2218yescomplemented
46#10622285C2218yes—
47#10622282C22116yescomplemented
48#10622280C22116yescomplemented
49#10622263C2218yescomplemented
50C24×D11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C22×D44—28no—
62C22×D44—24no—
63C22×D44C2314yes—
64C22×C4×D11—28no—
65C22×C4×D11—28no—
66C22×C4×D11—28no—
67C22×C4×D11C2318yes—
68C22×Dic22—24no—
69C22×Dic22—24no—
70C22×Dic22D418yescomplemented
71C22×Dic22C2314yes—
72C2×C11×C4⋊C4—24no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4—28no—
75C2×C11×C4⋊C4C2314yes—
76C2×C11×C4⋊C4C2314yes—
77C2×C11×C4⋊C4C2318yes—
78C2×(C2×D11)⋊C4—28no—
79C2×(C2×D11)⋊C4—28no—
80C2×(C2×D11)⋊C4—28no—
81C2×(C2×D11)⋊C4—28no—
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4C2318yes—
84C2×(C2×D11)⋊C4C2318yes—
85C2×(C2×D11)⋊C4C2318yes—
86C2×(C2×D11)⋊C4C2318yes—
87C2×(C2×D11)⋊C4C2318yes—
88C2×Dic11⋊C4—24no—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—28no—
91C2×Dic11⋊C4—28no—
92C2×Dic11⋊C4C2314yes—
93C2×Dic11⋊C4C2314yes—
94C2×Dic11⋊C4C2318yes—
95C2×Dic11⋊C4C2318yes—
96C2×C4×Dic11—24no—
97C2×C4×Dic11—24no—
98C2×C4×Dic11D418yes—
99C2×C4×Dic11C2314yes—
100C2×C4×Dic11C2314yes—
101C2×C4×Dic11C2314yes—
102#66949—264no—
103#66946—232no—
104#66940—232no—
105C11×#95C2314yes—
106C11×#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2314yes—
109C11⋊#95C2318yes—
110C2×#2536—111nomaximal, Sylow
111C24×C11C2411yescharacteristic
112C23×D11—24no—
113C23×D11—24no—
114C23×D11—24no—
115C23×D11—24no—
116C23×D11—24no—
117C23×D11—24no—
118C23×D11#4118yes—
119C23×D11C2414yes—
120C22×C4×C11—22no—
121C22×C4×C11—22no—
122C22×C4×C11—24no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
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×C11C2×D414yes—
133C22×C4×C11C2414yes—
134C22×C4×C11C2414yes—
135C22×C4×C11C2412yes—
136C22×C4×C11C2412yes—
137C22×C4×C11C2412yes—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—24no—
141C22×Dic11—22no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11C2×D414yes—
147C22×Dic11C2×D414yes—
148C22×Dic11C2×D414yes—
149C22×Dic11C2×D414yes—
150C22×Dic11#4114yes—
151C22×Dic11C2414yes—
152C22×Dic11C2412yes—
153C22×Dic11C2412yes—
154C22×Dic11C2412yes—
155C22×Dic11C2412yes—
156C2×D44—232no—
157C2×D44—216no—
158C2×D44—28no—
159C2×C4×D11—216no—
160C2×C4×D11—216no—
161C2×C4×D11—216no—
162C2×C4×D11—432no—
163C2×Dic22—232no—
164C2×Dic22—28no—
165C2×Dic22—28no—
166C2×Dic22C2×D4116yescomplemented
167C11×C4⋊C4—28no—
168C11×C4⋊C4—28no—
169C11×C4⋊C4—216no—
170(C2×D11)⋊C4—216no—
171(C2×D11)⋊C4—216no—
172(C2×D11)⋊C4—216no—
173(C2×D11)⋊C4—216no—
174(C2×D11)⋊C4—216no—
175Dic11⋊C4—28no—
176Dic11⋊C4—216no—
177Dic11⋊C4—216no—
178Dic11⋊C4—28no—
179C4×Dic11—28no—
180C4×Dic11—28no—
181C4×Dic11C2×D4116yes—
182C22×C22⋊Q8—112no—
183C22×C4×Q8—111no—
184C22×C4×D4—111no—
185#2536—1116no—
186C2×#398—111no—
187C2×#398D1111yescharacteristic, complemented
188C2×#394—111no—
189C2×#394—111no—
190C2×#388—112no—
191C2×#388—112no—
192C2×#382—111no—
193C2×#380—112no—
194C23×C11C22×D412yes—
195C23×C11C22×D412yes—
196C23×C11C2×#4112yes—
197C23×C11C2×#4114yes—
198C23×C112−1+414yes—
199C23×C11C2511yescharacteristic
200C22×D11—216no—
201C22×D11—216no—
202C22×D11—216no—
203C22×D11—24no—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—24no—
207C22×D11—24no—
208C22×D11—24no—
209C22×D11—48no—
210C22×D11—48no—
211C22×D11—48no—
212C22×D11—48no—
213C22×D11C2×#4118yes—
214C2×C4×C11—28no—
215C2×C4×C11—28no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
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—48no—
228C2×C4×C11—44no—
229C2×C4×C11—48no—
230C2×C4×C11C22×D414yes—
231C2×C4×C11C22×D414yes—
232C2×Dic11—28no—
233C2×Dic11—28no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—22no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—44no—
243C2×Dic11—48no—
244C2×Dic11#121116yes—
245C2×Dic11C22×D414yes—
246C2×Dic11C22×D414yes—
247C2×Dic11C22×D414yes—
248C2×Dic11C22×D414yes—
249C2×Dic11C2×#4114yes—
250D44—232no—
251C4×D11—432no—
252Dic22—232no—
253C23×Q8—111no—
254C23×D4—111no—
255C24×C4—112no—
256C2×C22⋊Q8—1116no—
257C2×C22⋊Q8—2216no—
258C2×C4×Q8—118no—
259C2×C4×Q8—228no—
260C2×C4×D4—118no—
261C2×C4×D4—228no—
262C22×C4⋊C4—111no—
263C22×C4⋊C4—112no—
264C22×C4⋊C4—111no—
265C22×C4⋊C4—112no—
266C22×C4⋊C4C2×D1111yescharacteristic
267C22×C4⋊C4C2×D1111yescharacteristic
268C22×C4⋊C4C2×D1112yes—
269C22×C22⋊C4—112no—
270C22×C22⋊C4—112no—
271C22×C22⋊C4—112no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—112no—
274C22×C42—111no—
275C22×C42—111no—
276C22×C42—111no—
277#398—118no—
278#398C2×D1118yescomplemented
279#394—118no—
280#394—118no—
281#388—1116no—
282#388—1116no—
283#382—118no—
284#380—1116no—
285C2×#95—111no—
286C2×#95—112no—
287C2×#95—112no—
288C2×#95C2×D1111yescharacteristic
289C2×#95C2×D1112yes—
290C22×C11C2×#12114yes—
291C22×C11#52514yes—
292C22×C11#53614yes—
293C22×C11#54818yes—
294C22×C11#55218yes—
295C22×C11C23×D411yescharacteristic
296C22×C11C23×D411yescharacteristic
297C22×C11C22×#4111yescharacteristic
298C22×C11C22×#4112yes—
299C22×C11C2×2−1+412yes—
300C2×D11—28no—
301C2×D11—28no—
302C2×D11—28no—
303C2×D11—44no—
304C2×D11—44no—
305C2×D11—44no—
306C2×D11—44no—
307C2×D11—432no—
308C4×C11—24no—
309C4×C11—24no—
310C4×C11—44no—
311C4×C11—42no—
312C4×C11—44no—
313Dic11—24no—
314Dic11—24no—
315Dic11—42no—
316Dic11—44no—
317Dic11C2×#12118yes—
318C25—112no—
319C22×Q8—118no—
320C22×Q8—114no—
321C22×Q8—224no—
322C22×Q8—224no—
323C22×D4—114no—
324C22×D4—228no—
325C22×D4—224no—
326C23×C4—111no—
327C23×C4—111no—
328C23×C4—111no—
329C23×C4—112no—
330C23×C4—111no—
331C23×C4—118no—
332C23×C4—228no—
333C23×C4—228no—
334C23×C4—228no—
335C23×C4C22×D1112yes—
336C23×C4C22×D1111yescharacteristic
337C23×C4C22×D1112yes—
338C23×C4C22×D1111yescharacteristic
339C23×C4C22×D1111yescharacteristic
340C22⋊Q8—2264no—
341C4×Q8—2232no—
342C4×D4—2232no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—24no—
345C2×C4⋊C4—28no—
346C2×C4⋊C4—114no—
347C2×C4⋊C4—114no—
348C2×C4⋊C4—118no—
349C2×C4⋊C4—118no—
350C2×C4⋊C4—224no—
351C2×C4⋊C4—228no—
352C2×C4⋊C4—228no—
353C2×C4⋊C4—224no—
354C2×C4⋊C4C22×D1114yes—
355C2×C4⋊C4C22×D1114yes—
356C2×C4⋊C4C22×D1118yes—
357C2×C22⋊C4—118no—
358C2×C22⋊C4—118no—
359C2×C22⋊C4—118no—
360C2×C22⋊C4—118no—
361C2×C22⋊C4—118no—
362C2×C22⋊C4—228no—
363C2×C22⋊C4—228no—
364C2×C22⋊C4—228no—
365C2×C22⋊C4—228no—
366C2×C22⋊C4—228no—
367C2×C42—118no—
368C2×C42—114no—
369C2×C42—114no—
370C2×C42—114no—
371C2×C42—224no—
372C2×C42—224no—
373#95—118no—
374#95—118no—
375#95—114no—
376#95C22×D1118yes—
377#95C22×D1114yes—
378C2×C11#253618yescomplemented
379C2×C11C22×#12111yescharacteristic
380C2×C11C2×#52511yescharacteristic
381C2×C11C2×#53611yescharacteristic
382C2×C11C2×#54812yes—
383C2×C11C2×#55212yes—
384D11—48no—
385C24—118no—
386C24—114no—
387C24—224no—
388C24—224no—
389C24—224no—
390C24—224no—
391C24—224no—
392C24—224no—
393C24C23×D1111yescharacteristic
394C2×Q8—1116no—
395C2×Q8—228no—
396C2×Q8—2232no—
397C2×Q8—228no—
398C2×D4—2216no—
399C2×D4—2232no—
400C2×D4—228no—
401C22×C4—22no—
402C22×C4—24no—
403C22×C4—22no—
404C22×C4—22no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—24no—
410C22×C4—24no—
411C22×C4—24no—
412C22×C4—114no—
413C22×C4—114no—
414C22×C4—114no—
415C22×C4—112no—
416C22×C4—114no—
417C22×C4—114no—
418C22×C4—112no—
419C22×C4—112no—
420C22×C4—114no—
421C22×C4—112no—
422C22×C4—2216no—
423C22×C4—2216no—
424C22×C4—2216no—
425C22×C4—222no—
426C22×C4—224no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—224no—
430C22×C4—224no—
431C22×C4—224no—
432C22×C4—224no—
433C22×C4—4432no—
434C22×C4D4×D1114yes—
435C22×C4D4×D1114yes—
436C22×C4C23×D1114yes—
437C22×C4C23×D1114yes—
438C22×C4C23×D1112yes—
439C22×C4C23×D1112yes—
440C22×C4C23×D1112yes—
441C4⋊C4—28no—
442C4⋊C4—28no—
443C4⋊C4—216no—
444C4⋊C4—228no—
445C4⋊C4—2216no—
446C4⋊C4—2216no—
447C4⋊C4—228no—
448C22⋊C4—2216no—
449C22⋊C4—2216no—
450C22⋊C4—2216no—
451C22⋊C4—2216no—
452C22⋊C4—2216no—
453C42—1116no—
454C42—228no—
455C42—228no—
456C11C2×#253611yescharacteristic, complemented, Sylow
457C23—118no—
458C23—2216no—
459C23—2216no—
460C23—224no—
461C23—224no—
462C23—224no—
463C23—224no—
464C23—224no—
465C23—224no—
466C23—2216no—
467C23—448no—
468C23—448no—
469C23—448no—
470C23—448no—
471C23C2×D4×D1112yes—
472C23C2×D4×D1112yes—
473C23#6704014yes—
474C23#41×D1112yes—
475C23#41×D1114yes—
476C23C24×D1111yescharacteristic
477Q8—2232no—
478D4—2232no—
479C2×C4—28no—
480C2×C4—28no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—48no—
493C2×C4—48no—
494C2×C4—44no—
495C2×C4—1116no—
496C2×C4—114no—
497C2×C4—114no—
498C2×C4—114no—
499C2×C4—114no—
500C2×C4—114no—
501C2×C4—228no—
502C2×C4—228no—
503C2×C4—222no—
504C2×C4—224no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—4432no—
512C2×C4—448no—
513C2×C4—444no—
514C2×C4C2×D4×D1114yes—
515C2×C4C2×D4×D1114yes—
516C22—228no—
517C22—228no—
518C22—228no—
519C22—444no—
520C22—444no—
521C22—4432no—
522C22—444no—
523C22—444no—
524C22D11×#12114yes—
525C22#1062316418yes—
526C22#1062318714yes—
527C22#1062322418yes—
528C22#1062325514yes—
529C22C22×D4×D1111yescharacteristic
530C22C22×D4×D1111yescharacteristic
531C22C2×#6704012yes—
532C22C2×#41×D1111yescharacteristic
533C22C2×#41×D1112yes—
534C4—24no—
535C4—24no—
536C4—44no—
537C4—44no—
538C4—42no—
539C4—118no—
540C4—224no—
541C4—224no—
542C4—444no—
543C4—442no—
544C2—448no—
545C2#1307352218yesdirect product factor
546C2C2×D11×#12111yescharacteristic
547C2C2×#1062318711yescharacteristic
548C2C2×#1062325511yescharacteristic
549C2C2×#1062316412yes—
550C2C2×#1062322412yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#398D11
hypocenterC11C2×#2536
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#66949C2semidirect
2. C22×#66940C2semidirect
4. #13073522C2direct (N × H)
5. C2×#10622593C2semidirect
8. C2×#10622603C2semidirect
9. C2×#10622282C2semidirect
10. C2×#10622263C2semidirect
11. C2×#10622280C2semidirect
12. C2×C11×#398C2semidirect
32. C2×#66949C22semidirect
36. C2×#66940C22semidirect
37. C11×#398C22semidirect
44. #10622603C22semidirect
45. #10622593C22semidirect
47. #10622282C22semidirect
48. #10622280C22semidirect
49. #10622263C22semidirect
70. C22×Dic22D4semidirect
166. C2×Dic22C2×D4semidirect
187. C2×#398D11semidirect
278. #398C2×D11semidirect
378. C2×C11#2536semidirect
456. C11C2×#2536semidirect
545. C2#13073522direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669492
C22×#669402
C22×#669462
#130735222
C2×#106225932
C2×#106222852
C2×#106226042
C2×#106226032
C2×#106222822
C2×#106222632
C2×#106222802
C2×C11×#3982
C2×#253611