Finite Group Databasebeta

← C2×#13076628 #14959929

Subgroups — C2×#13076628 #14959929

Order 2816.

2674 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×#66947C211yesmaximal, characteristic
2C22×#66999C211yesmaximal, characteristic, complemented
3#13076628C2116yesmaximal, direct product factor
4C2×#10622593C212yesmaximal, complemented
5C2×#10622596C211yesmaximal, characteristic, complemented
6C2×#10622288C212yesmaximal, complemented
7C2×#10622287C211yesmaximal, characteristic, complemented
8C2×#10622289C212yesmaximal, complemented
9C2×#10622604C212yesmaximal
10C2×#10622844C211yesmaximal, characteristic, complemented
11C2×#10622280C211yesmaximal, characteristic, complemented
12C2×C11×#395C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2212yes—
18C2×#66999—28no—
19C2×#66999C2218yescomplemented
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×C4⋊Dic11C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2212yes—
31C22×Dic11⋊C4C2212yes—
32C2×#66947—28no—
33C2×#66947C2218yes—
34C11×#395C2218yescomplemented
35C2×C11×#95C2211yescharacteristic
36C2×C11×#95C2212yes—
37#10622844C2218yescomplemented
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622604C22116yes—
43#10622596C2218yescomplemented
44#10622593C22116yescomplemented
45#10622289C22116yescomplemented
46#10622288C22116yescomplemented
47#10622287C2218yescomplemented
48#10622280C2218yescomplemented
49C24×D11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C22×Q8×C11—24no—
52C22×Q8×C11—44no—
53C22×Q8×C11C2314yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C23×C4×C11C2311yescharacteristic
59C23×Dic11C2312yes—
60C23×Dic11C2312yes—
61C23×Dic11C2311yescharacteristic
62C23×Dic11C2311yescharacteristic
63C22×D44—24no—
64C22×D44—44no—
65C22×D44C2314yes—
66C22×C4×D11—44no—
67C22×C4×D11D418yes—
68C22×C4×D11C2314yes—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—44no—
71C2×C11×C4⋊C4C2314yes—
72C2×C11×C4⋊C4C2318yes—
73#66999—232no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—28no—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—44no—
79C2×(C2×D11)⋊C4—44no—
80C2×(C2×D11)⋊C4—44no—
81C2×(C2×D11)⋊C4C2314yes—
82C2×(C2×D11)⋊C4C2314yes—
83C2×(C2×D11)⋊C4C2314yes—
84C2×(C2×D11)⋊C4C2318yes—
85C2×(C2×D11)⋊C4C2318yes—
86C2×(C2×D11)⋊C4C2318yes—
87C2×(C2×D11)⋊C4C2318yes—
88C2×C4⋊Dic11—24no—
89C2×C4⋊Dic11C2314yes—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—28no—
92C2×Dic11⋊C4—44no—
93C2×Dic11⋊C4—44no—
94C2×Dic11⋊C4C2314yes—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2318yes—
97C2×Dic11⋊C4C2318yes—
98#66947—232no—
99C11×#95C2314yes—
100C11×#95C2318yes—
101C11⋊#95C2314yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C2×#2814—111nomaximal, Sylow
106C24×C11C2411yescharacteristic
107C23×D11—22no—
108C23×D11—24no—
109C23×D11—24no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11—24no—
114C23×D11—24no—
115C23×D11—22no—
116C23×D11C2×D414yes—
117C23×D11C2412yes—
118C23×D11C2412yes—
119C2×Q8×C11—28no—
120C2×Q8×C11—48no—
121C2×Q8×C11—416no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—24no—
134C22×C4×C11C2×D414yes—
135C22×C4×C11C2412yes—
136C22×C4×C11C2414yes—
137C22×C4×C11C2414yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2412yes—
140C22×Dic11—24no—
141C22×Dic11—22no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11C2×D414yes—
150C22×Dic11C2412yes—
151C22×Dic11C2414yes—
152C22×Dic11C2414yes—
153C22×Dic11C2412yes—
154C2×D44—28no—
155C2×D44—48no—
156C2×D44—416no—
157C2×C4×D11—416no—
158C2×C4×D11—48no—
159C2×C4×D11C2×D4116yes—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—48no—
162(C2×D11)⋊C4—28no—
163(C2×D11)⋊C4—28no—
164(C2×D11)⋊C4—216no—
165(C2×D11)⋊C4—28no—
166(C2×D11)⋊C4—48no—
167(C2×D11)⋊C4—48no—
168(C2×D11)⋊C4—48no—
169C4⋊Dic11—28no—
170Dic11⋊C4—28no—
171Dic11⋊C4—216no—
172Dic11⋊C4—48no—
173Dic11⋊C4—48no—
174C22×#123—111no—
175C22×C22⋊Q8—111no—
176#2814—1116no—
177C2×#398—111no—
178C2×#398—112no—
179C2×#397—111no—
180C2×#397—112no—
181C2×#396—112no—
182C2×#395D1111yescharacteristic, complemented
183C2×#394—112no—
184C2×#393—111no—
185C2×#380—111no—
186C23×C11C22×D412yes—
187C23×C11H(5,𝔽2)14yes—
188C23×C11H(5,𝔽2)12yes—
189C23×C112−1+414yes—
190C23×C112−1+412yes—
191C23×C11C2511yescharacteristic
192C22×D11—28no—
193C22×D11—28no—
194C22×D11—28no—
195C22×D11—22no—
196C22×D11—24no—
197C22×D11—24no—
198C22×D11—22no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—24no—
202C22×D11—24no—
203C22×D11—22no—
204C22×D11—48no—
205C22×D11—48no—
206C22×D11—44no—
207C22×D11—44no—
208C22×D11—44no—
209C22×D11—48no—
210C22×D11—48no—
211C22×D11C22×D414yes—
212Q8×C11—416no—
213C2×C4×C11—28no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—24no—
224C2×C4×C11—22no—
225C2×C4×C11—24no—
226C2×C4×C11—44no—
227C2×C4×C11—48no—
228C2×C4×C11—44no—
229C2×C4×C11—48no—
230C2×C4×C11C22×D414yes—
231C2×Dic11—28no—
232C2×Dic11—24no—
233C2×Dic11—24no—
234C2×Dic11—22no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—44no—
242C2×Dic11—48no—
243C2×Dic11—48no—
244C2×Dic11C22×D414yes—
245D44—416no—
246C4×D11—416no—
247C23×Q8C2×D1111yescharacteristic
248C23×D4—111no—
249C24×C4—111no—
250C2×#123—118no—
251C2×#123—228no—
252C2×C22⋊Q8—118no—
253C2×C22⋊Q8—228no—
254C22×C4⋊C4—112no—
255C22×C4⋊C4—111no—
256C22×C4⋊C4—111no—
257C22×C4⋊C4—112no—
258C22×C4⋊C4—112no—
259C22×C4⋊C4C2×D1111yescharacteristic
260C22×C4⋊C4C2×D1112yes—
261C22×C22⋊C4—111no—
262C22×C22⋊C4—112no—
263C22×C22⋊C4—111no—
264C22×C22⋊C4—111no—
265C22×C22⋊C4—112no—
266C22×C22⋊C4—112no—
267C22×C22⋊C4—112no—
268#398—1116no—
269#398—118no—
270#397—118no—
271#397—1116no—
272#396—1116no—
273#395C2×D1118yescomplemented
274#394—1116no—
275#393—118no—
276#380—118no—
277C2×#95—112no—
278C2×#95—111no—
279C2×#95—112no—
280C2×#95—112no—
281C2×#95C2×D1112yes—
282C2×#95C2×D1111yescharacteristic
283C22×C11#53414yes—
284C22×C11#53614yes—
285C22×C11#53714yes—
286C22×C11#56218yes—
287C22×C11#56318yes—
288C22×C11C23×D411yescharacteristic
289C22×C11C2×H(5,𝔽2)12yes—
290C22×C11C2×H(5,𝔽2)11yescharacteristic
291C22×C11C2×2−1+412yes—
292C22×C11C2×2−1+411yescharacteristic
293C2×D11—24no—
294C2×D11—24no—
295C2×D11—24no—
296C2×D11—44no—
297C2×D11—44no—
298C2×D11—416no—
299C2×D11—42no—
300C2×D11—42no—
301C2×D11—42no—
302C2×D11—44no—
303C2×D11—44no—
304C2×D11—88no—
305C4×C11—24no—
306C4×C11—44no—
307C4×C11—42no—
308C4×C11—42no—
309C4×C11—44no—
310Dic11—24no—
311Dic11—42no—
312Dic11—44no—
313Dic11—44no—
314C25—111no—
315C25—111no—
316C22×Q8—24no—
317C22×Q8—44no—
318C22×Q8C22×D1114yes—
319C22×D4—114no—
320C22×D4—224no—
321C22×D4—444no—
322C23×C4—111no—
323C23×C4—118no—
324C23×C4—114no—
325C23×C4—112no—
326C23×C4—112no—
327C23×C4—111no—
328C23×C4—444no—
329C23×C4C22×D1111yescharacteristic
330C23×C4C22×D1112yes—
331C23×C4C22×D1112yes—
332C23×C4C22×D1111yescharacteristic
333C23×C4C22×D1111yescharacteristic
334#123—2232no—
335C22⋊Q8—2232no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—118no—
339C2×C4⋊C4—114no—
340C2×C4⋊C4—114no—
341C2×C4⋊C4—118no—
342C2×C4⋊C4—118no—
343C2×C4⋊C4—228no—
344C2×C4⋊C4—224no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4—444no—
347C2×C4⋊C4—444no—
348C2×C4⋊C4C22×D1114yes—
349C2×C4⋊C4C22×D1118yes—
350C2×C22⋊C4—118no—
351C2×C22⋊C4—114no—
352C2×C22⋊C4—114no—
353C2×C22⋊C4—114no—
354C2×C22⋊C4—118no—
355C2×C22⋊C4—118no—
356C2×C22⋊C4—118no—
357C2×C22⋊C4—224no—
358C2×C22⋊C4—228no—
359C2×C22⋊C4—224no—
360C2×C22⋊C4—224no—
361C2×C22⋊C4—444no—
362C2×C22⋊C4—444no—
363C2×C22⋊C4—444no—
364#95—114no—
365#95—118no—
366#95—118no—
367#95—118no—
368#95C22×D1114yes—
369#95C22×D1118yes—
370C2×C11#281418yescomplemented
371C2×C11C2×#53411yescharacteristic
372C2×C11C2×#53611yescharacteristic
373C2×C11C2×#53711yescharacteristic
374C2×C11C2×#56212yes—
375C2×C11C2×#56312yes—
376D11—44no—
377D11—82no—
378C24—114no—
379C24—112no—
380C24—112no—
381C24—224no—
382C24—224no—
383C24—222no—
384C24—222no—
385C24—222no—
386C24—224no—
387C24—224no—
388C24—222no—
389C24—222no—
390C24C23×D1111yescharacteristic
391C2×Q8—28no—
392C2×Q8—48no—
393C2×Q8—416no—
394C2×D4—228no—
395C2×D4—448no—
396C2×D4—4416no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—22no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—22no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—22no—
409C22×C4—114no—
410C22×C4—112no—
411C22×C4—1116no—
412C22×C4—112no—
413C22×C4—114no—
414C22×C4—114no—
415C22×C4—224no—
416C22×C4—222no—
417C22×C4—224no—
418C22×C4—224no—
419C22×C4—224no—
420C22×C4—224no—
421C22×C4—224no—
422C22×C4—224no—
423C22×C4—224no—
424C22×C4—4416no—
425C22×C4—448no—
426C22×C4D4×D1114yes—
427C22×C4C23×D1112yes—
428C22×C4C23×D1114yes—
429C22×C4C23×D1114yes—
430C22×C4C23×D1112yes—
431C22×C4C23×D1112yes—
432C4⋊C4—28no—
433C4⋊C4—48no—
434C4⋊C4—2216no—
435C4⋊C4—228no—
436C4⋊C4—228no—
437C4⋊C4—448no—
438C4⋊C4—448no—
439C22⋊C4—228no—
440C22⋊C4—2216no—
441C22⋊C4—228no—
442C22⋊C4—228no—
443C22⋊C4—448no—
444C22⋊C4—448no—
445C22⋊C4—448no—
446C11C2×#281411yescharacteristic, complemented, Sylow
447C23—114no—
448C23—228no—
449C23—228no—
450C23—228no—
451C23—224no—
452C23—224no—
453C23—222no—
454C23—222no—
455C23—222no—
456C23—224no—
457C23—224no—
458C23—222no—
459C23—222no—
460C23—448no—
461C23—448no—
462C23—444no—
463C23—448no—
464C23—444no—
465C23—444no—
466C23—448no—
467C23C2×D4×D1112yes—
468C23#6703714yes—
469C23#6704014yes—
470C23#6704012yes—
471C23#6704212yes—
472C23C24×D1111yescharacteristic
473Q8—416no—
474D4—4416no—
475C2×C4—28no—
476C2×C4—24no—
477C2×C4—22no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—24no—
481C2×C4—24no—
482C2×C4—24no—
483C2×C4—24no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—44no—
489C2×C4—48no—
490C2×C4—44no—
491C2×C4—48no—
492C2×C4—114no—
493C2×C4—228no—
494C2×C4—224no—
495C2×C4—222no—
496C2×C4—224no—
497C2×C4—224no—
498C2×C4—224no—
499C2×C4—224no—
500C2×C4—224no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—4416no—
504C2×C4—444no—
505C2×C4—448no—
506C2×C4—448no—
507C2×C4C2×D4×D1114yes—
508C22—224no—
509C22—224no—
510C22—224no—
511C22—444no—
512C22—444no—
513C22—4416no—
514C22—442no—
515C22—442no—
516C22—442no—
517C22—444no—
518C22—444no—
519C22—888no—
520C22#1062312014yes—
521C22#1062316014yes—
522C22#1062317818yes—
523C22#1062325514yes—
524C22#1062326618yes—
525C22C22×D4×D1111yescharacteristic
526C22C2×#6703712yes—
527C22C2×#6704012yes—
528C22C2×#6704011yescharacteristic
529C22C2×#6704211yescharacteristic
530C4—24no—
531C4—42no—
532C4—44no—
533C4—42no—
534C4—44no—
535C4—224no—
536C4—442no—
537C4—444no—
538C4—444no—
539C2—444no—
540C2—882no—
541C2#1307662818yesdirect product factor
542C2C2×#1062312011yescharacteristic
543C2C2×#1062325511yescharacteristic
544C2C2×#1062316011yescharacteristic
545C2C2×#1062317812yes—
546C2C2×#1062326612yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#395C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#395D11
hypocenterC11C2×#2814
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#395

Complements

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

NH ≅ G/Ntype
2. C22×#66999C2semidirect
3. #13076628C2direct (N × H)
4. C2×#10622593C2semidirect
5. C2×#10622596C2semidirect
6. C2×#10622288C2semidirect
7. C2×#10622287C2semidirect
8. C2×#10622289C2semidirect
10. C2×#10622844C2semidirect
11. C2×#10622280C2semidirect
12. C2×C11×#395C2semidirect
19. C2×#66999C22semidirect
34. C11×#395C22semidirect
37. #10622844C22semidirect
43. #10622596C22semidirect
44. #10622593C22semidirect
45. #10622289C22semidirect
46. #10622288C22semidirect
47. #10622287C22semidirect
48. #10622280C22semidirect
182. C2×#395D11semidirect
273. #395C2×D11semidirect
370. C2×C11#2814semidirect
446. C11C2×#2814semidirect
541. C2#13076628direct (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×#669992
#130766282
C2×#106225932
C2×#106225962
C2×#106222882
C2×#106222872
C2×#106222892
C2×#106226042
C2×#106228442
C2×#106222802
C2×C11×#3952
C2×#281411