Finite Group Databasebeta

← C2×#13073960 #14923975

Subgroups — C2×#13073960 #14923975

Order 2816.

3374 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic11C211yesmaximal, characteristic
2C23×C4⋊Dic11C211yesmaximal, characteristic, complemented
3#13073960C2116yesmaximal, direct product factor
4C2×#10622274C212yesmaximal, complemented
5C2×#10622561C212yesmaximal, complemented
6C2×#10622268C212yesmaximal, complemented
7C2×#10622833C211yesmaximal, characteristic
8C2×#10622563C212yesmaximal, complemented
9C2×#10622563C211yesmaximal, characteristic, complemented
10C2×#10622823C211yesmaximal, characteristic, complemented
11C2×#10622555C211yesmaximal, characteristic, complemented
12C2×C11×#386C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C24×Dic11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2212yes—
24C2×D4×Dic11—28no—
25C2×D4×Dic11C2218yes—
26C22×C4⋊Dic11—28no—
27C22×C4⋊Dic11C2212yes—
28C22×C4⋊Dic11C2212yes—
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2212yes—
31C22×C4⋊Dic11C2218yescomplemented
32C22×Dic11⋊C4C2212yes—
33C22×Dic11⋊C4C2212yes—
34C22×C4×Dic11C2211yescharacteristic
35C11×#386C2218yes—
36C2×C11×#95C2212yes—
37#10622833C2218yes—
38#10622823C2218yescomplemented
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622563C22116yescomplemented
44#10622563C2218yescomplemented
45#10622561C22116yescomplemented
46#10622555C2218yescomplemented
47#10622274C22116yescomplemented
48#10622268C22116yescomplemented
49C25×C11C2311yescharacteristic
50C25×C11C2311yescharacteristic
51C22×D4×C11—24no—
52C22×D4×C11—24no—
53C22×D4×C11Q818yes—
54C22×D4×C11C2314yes—
55C23×C4×C11—24no—
56C23×C4×C11—28no—
57C23×C4×C11C2312yes—
58C23×C4×C11C2314yes—
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2312yes—
61C23×Dic11—24no—
62C23×Dic11—24no—
63C23×Dic11—44no—
64C23×Dic11—44no—
65C23×Dic11—44no—
66C23×Dic11D418yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2312yes—
69C23×Dic11C2312yes—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2314yes—
74C23×Dic11C2314yes—
75C23×Dic11C2314yes—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4—28no—
78C2×C11×C22⋊C4C2314yes—
79C2×C11×C22⋊C4C2318yes—
80C2×C22⋊Dic11—24no—
81C2×C22⋊Dic11—24no—
82C2×C22⋊Dic11—24no—
83C2×C22⋊Dic11—44no—
84C2×C22⋊Dic11C2314yes—
85C2×C22⋊Dic11C2314yes—
86C2×C22⋊Dic11C2314yes—
87C2×C22⋊Dic11C2318yes—
88D4×Dic11—232no—
89C2×C4⋊Dic11—28no—
90C2×C4⋊Dic11—28no—
91C2×C4⋊Dic11—232no—
92C2×C4⋊Dic11—24no—
93C2×C4⋊Dic11—44no—
94C2×C4⋊Dic11C2318yes—
95C2×C4⋊Dic11C2314yes—
96C2×C4⋊Dic11C2318yes—
97C2×C4⋊Dic11C2318yes—
98C2×Dic11⋊C4—28no—
99C2×Dic11⋊C4—44no—
100C2×Dic11⋊C4C2318yes—
101C2×Dic11⋊C4C2318yes—
102C2×C4×Dic11—24no—
103C2×C4×Dic11C2314yes—
104C11×#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C2×#2579—111nomaximal, Sylow
110C24×C11—24no—
111C24×C11—24no—
112C24×C11—22no—
113C24×C11—24no—
114C24×C11—22no—
115C24×C11—24no—
116C24×C11C2×D414yes—
117C24×C11C2×Q814yes—
118C24×C11C2×Q814yes—
119C24×C11#4114yes—
120C24×C11C2412yes—
121C24×C11C2412yes—
122C24×C11C2411yescharacteristic
123C2×D4×C11—232no—
124C2×D4×C11—28no—
125C2×D4×C11—28no—
126C2×D4×C11C2×Q8116yes—
127C22×C4×C11—232no—
128C22×C4×C11—22no—
129C22×C4×C11—28no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—216no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11C2×Q814yes—
138C22×C4×C11#4118yes—
139C22×C4×C11C2414yes—
140C22×C4×C11C2412yes—
141C22×C4×C11C2414yes—
142C22×Dic11—28no—
143C22×Dic11—22no—
144C22×Dic11—28no—
145C22×Dic11—24no—
146C22×Dic11—22no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—24no—
150C22×Dic11—24no—
151C22×Dic11—24no—
152C22×Dic11—24no—
153C22×Dic11—24no—
154C22×Dic11—24no—
155C22×Dic11—24no—
156C22×Dic11—416no—
157C22×Dic11—48no—
158C22×Dic11—48no—
159C22×Dic11—48no—
160C22×Dic11—416no—
161C22×Dic11—416no—
162C22×Dic11C2×D414yes—
163C22×Dic11C2×D414yes—
164C22×Dic11C2×D4116yes—
165C22×Dic11C2414yes—
166C22×Dic11C2412yes—
167C22×Dic11C2414yes—
168C22×Dic11C2412yes—
169C22×Dic11C2412yes—
170C22×Dic11C2412yes—
171C11×C22⋊C4—28no—
172C11×C22⋊C4—216no—
173C22⋊Dic11—28no—
174C22⋊Dic11—28no—
175C22⋊Dic11—28no—
176C22⋊Dic11—48no—
177C4⋊Dic11—216no—
178C4⋊Dic11—216no—
179C4⋊Dic11—28no—
180C4⋊Dic11—48no—
181Dic11⋊C4—216no—
182Dic11⋊C4—48no—
183C4×Dic11—28no—
184C22×C4×D4—111no—
185C23×C4⋊C4—111no—
186#2579—1116no—
187C2×#398—112no—
188C2×#396—112no—
189C2×#387—112no—
190C2×#386—111no—
191C2×#386D1111yescharacteristic
192C2×#385—111no—
193C2×#385—111no—
194C2×#385—112no—
195C2×#380—111no—
196C23×C11—28no—
197C23×C11—28no—
198C23×C11—216no—
199C23×C11—216no—
200C23×C11—24no—
201C23×C11—24no—
202C23×C11—28no—
203C23×C11—216no—
204C23×C11—22no—
205C23×C11—24no—
206C23×C11—22no—
207C23×C11—24no—
208C23×C11—44no—
209C23×C11—44no—
210C23×C11—48no—
211C23×C11C22⋊Q8116yes—
212C23×C11C22×D414yes—
213C23×C11C22×D412yes—
214C23×C11C22×Q814yes—
215C23×C11C22×Q814yes—
216C23×C11C22×Q812yes—
217C23×C11C2×#4114yes—
218C23×C11C2×#4112yes—
219C23×C11C2×#4114yes—
220C23×C11H(5,𝔽2)14yes—
221C23×C11C2511yescharacteristic
222D4×C11—232no—
223C2×C4×C11—232no—
224C2×C4×C11—28no—
225C2×C4×C11—216no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—48no—
234C2×C4×C11C22×Q814yes—
235C2×C4×C11C2×#4118yes—
236C2×Dic11—28no—
237C2×Dic11—28no—
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—22no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—24no—
250C2×Dic11—416no—
251C2×Dic11—416no—
252C2×Dic11—416no—
253C2×Dic11—44no—
254C2×Dic11—48no—
255C2×Dic11—44no—
256C2×Dic11—48no—
257C2×Dic11C22×D414yes—
258C2×Dic11C22×D414yes—
259C23×D4C2×D1111yescharacteristic
260C24×C4—111no—
261C24×C4—111no—
262C24×C4—111no—
263C24×C4C2×D1111yescharacteristic
264C2×C4×D4—118no—
265C2×C4×D4—228no—
266C22×C4⋊C4—118no—
267C22×C4⋊C4—112no—
268C22×C4⋊C4—112no—
269C22×C4⋊C4—111no—
270C22×C4⋊C4—112no—
271C22×C4⋊C4—112no—
272C22×C4⋊C4—112no—
273C22×C4⋊C4—228no—
274C22×C22⋊C4—111no—
275C22×C22⋊C4—111no—
276C22×C22⋊C4—111no—
277C22×C22⋊C4—112no—
278C22×C22⋊C4C2×D1112yes—
279C22×C22⋊C4C2×D1111yescharacteristic
280C22×C42—111no—
281#398—1116no—
282#396—1116no—
283#387—1116no—
284#386—118no—
285#386C2×D1118yes—
286#385—118no—
287#385—1116no—
288#385—118no—
289#380—118no—
290C2×#95—112no—
291C2×#95—112no—
292C2×#95—112no—
293C2×#95—112no—
294C2×#95C2×D1112yes—
295C22×C11—232no—
296C22×C11—24no—
297C22×C11—24no—
298C22×C11—28no—
299C22×C11—28no—
300C22×C11—24no—
301C22×C11—28no—
302C22×C11—416no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—44no—
306C22×C11C2×C22⋊Q818yes—
307C22×C11C2×C22⋊Q814yes—
308C22×C11#52514yes—
309C22×C11#53414yes—
310C22×C11#55318yes—
311C22×C11#55418yes—
312C22×C11C23×D411yescharacteristic
313C22×C11C23×Q811yescharacteristic
314C22×C11C22×#4111yescharacteristic
315C22×C11C22×#4112yes—
316C22×C11C2×H(5,𝔽2)12yes—
317C4×C11—24no—
318C4×C11—28no—
319C4×C11—44no—
320Dic11—24no—
321Dic11—24no—
322Dic11—42no—
323Dic11—44no—
324Dic11—42no—
325Dic11—44no—
326C25C22×D1111yescharacteristic
327C25C22×D1111yescharacteristic
328C22×D4—24no—
329C22×D4—24no—
330C22×D4Dic2218yes—
331C22×D4C22×D1114yes—
332C23×C4—24no—
333C23×C4—28no—
334C23×C4—111no—
335C23×C4—111no—
336C23×C4—118no—
337C23×C4—114no—
338C23×C4—112no—
339C23×C4—111no—
340C23×C4—111no—
341C23×C4—112no—
342C23×C4—114no—
343C23×C4—114no—
344C23×C4—224no—
345C23×C4—224no—
346C23×C4—444no—
347C23×C4—444no—
348C23×C4—444no—
349C23×C4C22×D1114yes—
350C23×C4C22×D1112yes—
351C23×C4C22×D1111yescharacteristic
352C23×C4C22×D1112yes—
353C4×D4—2232no—
354C2×C4⋊C4—118no—
355C2×C4⋊C4—118no—
356C2×C4⋊C4—114no—
357C2×C4⋊C4—118no—
358C2×C4⋊C4—118no—
359C2×C4⋊C4—118no—
360C2×C4⋊C4—228no—
361C2×C4⋊C4—228no—
362C2×C4⋊C4—2232no—
363C2×C4⋊C4—224no—
364C2×C4⋊C4—228no—
365C2×C4⋊C4—444no—
366C2×C4⋊C4—444no—
367C2×C22⋊C4—24no—
368C2×C22⋊C4—28no—
369C2×C22⋊C4—114no—
370C2×C22⋊C4—114no—
371C2×C22⋊C4—114no—
372C2×C22⋊C4—118no—
373C2×C22⋊C4—224no—
374C2×C22⋊C4—224no—
375C2×C22⋊C4—224no—
376C2×C22⋊C4—444no—
377C2×C22⋊C4C22×D1114yes—
378C2×C22⋊C4C22×D1118yes—
379C2×C42—114no—
380C2×C42—224no—
381#95—118no—
382#95—118no—
383#95—118no—
384#95—118no—
385#95C22×D1118yes—
386C2×C11—28no—
387C2×C11—44no—
388C2×C11#257918yescomplemented
389C2×C11C22×C22⋊Q811yescharacteristic
390C2×C11C2×#52511yescharacteristic
391C2×C11C2×#53411yescharacteristic
392C2×C11C2×#55312yes—
393C2×C11C2×#55412yes—
394C24—24no—
395C24—24no—
396C24—22no—
397C24—24no—
398C24—22no—
399C24—24no—
400C24C2×Dic2214yes—
401C24C2×Dic2214yes—
402C24D4×D1114yes—
403C24#434114yes—
404C24C23×D1112yes—
405C24C23×D1112yes—
406C24C23×D1111yescharacteristic
407C2×D4—232no—
408C2×D4—28no—
409C2×D4—28no—
410C2×D4C2×Dic22116yes—
411C22×C4—232no—
412C22×C4—22no—
413C22×C4—28no—
414C22×C4—24no—
415C22×C4—24no—
416C22×C4—22no—
417C22×C4—216no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—114no—
422C22×C4—114no—
423C22×C4—112no—
424C22×C4—112no—
425C22×C4—1116no—
426C22×C4—114no—
427C22×C4—112no—
428C22×C4—112no—
429C22×C4—114no—
430C22×C4—228no—
431C22×C4—224no—
432C22×C4—224no—
433C22×C4—222no—
434C22×C4—222no—
435C22×C4—228no—
436C22×C4—224no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—224no—
443C22×C4—224no—
444C22×C4—4416no—
445C22×C4—448no—
446C22×C4—448no—
447C22×C4—448no—
448C22×C4—4416no—
449C22×C4—4416no—
450C22×C4C2×Dic2214yes—
451C22×C4#434118yes—
452C22×C4C23×D1114yes—
453C22×C4C23×D1112yes—
454C22×C4C23×D1114yes—
455C4⋊C4—2216no—
456C4⋊C4—2216no—
457C4⋊C4—228no—
458C4⋊C4—2216no—
459C4⋊C4—448no—
460C4⋊C4—448no—
461C22⋊C4—28no—
462C22⋊C4—216no—
463C22⋊C4—228no—
464C22⋊C4—228no—
465C22⋊C4—228no—
466C22⋊C4—448no—
467C42—228no—
468C11C2×#257911yescharacteristic, complemented, Sylow
469C23—216no—
470C23—28no—
471C23—216no—
472C23—28no—
473C23—24no—
474C23—24no—
475C23—28no—
476C23—216no—
477C23—22no—
478C23—24no—
479C23—22no—
480C23—24no—
481C23—44no—
482C23—48no—
483C23—44no—
484C23#66931116yes—
485C23C22×Dic2214yes—
486C23C22×Dic2214yes—
487C23C22×Dic2212yes—
488C23C2×D4×D1114yes—
489C23C2×D4×D1112yes—
490C23C2×#434114yes—
491C23C2×#434112yes—
492C23C2×#434114yes—
493C23#6704214yes—
494C23C24×D1111yescharacteristic
495D4—232no—
496C2×C4—232no—
497C2×C4—28no—
498C2×C4—216no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—48no—
507C2×C4—114no—
508C2×C4—114no—
509C2×C4—228no—
510C2×C4—228no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—224no—
516C2×C4—224no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—224no—
522C2×C4—224no—
523C2×C4—4416no—
524C2×C4—4416no—
525C2×C4—4416no—
526C2×C4—444no—
527C2×C4—448no—
528C2×C4—444no—
529C2×C4—448no—
530C2×C4C22×Dic2214yes—
531C2×C4C2×#434118yes—
532C22—28no—
533C22—28no—
534C22—232no—
535C22—24no—
536C22—24no—
537C22—28no—
538C22—24no—
539C22—44no—
540C22—416no—
541C22—42no—
542C22—42no—
543C22C2×#6693118yes—
544C22C2×#6693114yes—
545C22#1062307418yes—
546C22#1062311714yes—
547C22#1062314918yes—
548C22#1062318414yes—
549C22C23×Dic2211yescharacteristic
550C22C22×D4×D1111yescharacteristic
551C22C22×#434111yescharacteristic
552C22C22×#434112yes—
553C22C2×#6704212yes—
554C4—24no—
555C4—28no—
556C4—44no—
557C4—224no—
558C4—224no—
559C4—444no—
560C4—442no—
561C4—444no—
562C4—442no—
563C2—28no—
564C2—44no—
565C2#1307396018yesdirect product factor
566C2C22×#6693111yescharacteristic
567C2C2×#1062311711yescharacteristic
568C2C2×#1062318411yescharacteristic
569C2C2×#1062314912yes—
570C2C2×#1062307412yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#386C2
socleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11C2×#2579
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
2. C23×C4⋊Dic11C2semidirect
3. #13073960C2direct (N × H)
4. C2×#10622274C2semidirect
5. C2×#10622561C2semidirect
6. C2×#10622268C2semidirect
8. C2×#10622563C2semidirect
9. C2×#10622563C2semidirect
10. C2×#10622823C2semidirect
11. C2×#10622555C2semidirect
31. C22×C4⋊Dic11C22semidirect
38. #10622823C22semidirect
43. #10622563C22semidirect
44. #10622563C22semidirect
45. #10622561C22semidirect
46. #10622555C22semidirect
47. #10622274C22semidirect
48. #10622268C22semidirect
388. C2×C11#2579semidirect
468. C11C2×#2579semidirect
565. C2#13073960direct (N × H)

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C23×C4⋊Dic112
#130739602
C2×#106222742
C2×#106225612
C2×#106222682
C2×#106228332
C2×#106225632
C2×#106228232
C2×#106225552
C2×C11×#3862
C2×#257911