Finite Group Databasebeta

← C2×#13073045 #14923004

Subgroups — C2×#13073045 #14923004

Order 2816.

2270 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13073045C2116yesmaximal, direct product factor
2C2×#10622272C212yesmaximal, complemented
3C2×#10622561C212yesmaximal
4C2×#10622598C211yesmaximal, characteristic, complemented
5C2×#10622586C211yesmaximal, characteristic, complemented
6C2×#10622557C212yesmaximal
7C2×#10622265C212yesmaximal, 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⋊Dic11C2211yescharacteristic
18C22×C22⋊Dic11C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C4⋊Dic11C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2212yes—
23C22×Dic11⋊C4C2212yes—
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×C4×Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2212yes—
29C11×#380C2218yes—
30C2×C11×#95C2212yes—
31#10622825C2218yes—
32C4×C22⋊Dic11C2218yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39#10622598C2218yescomplemented
40#10622589C2218yescomplemented
41C4⋊C4×Dic11C2218yescomplemented
42#10622586C2218yescomplemented
43#10622561C22116yes—
44#10622557C22116yes—
45#10622272C22116yescomplemented
46#10622265C22116yescomplemented
47C25×C11C2311yescharacteristic
48C23×C4×C11—24no—
49C23×C4×C11—24no—
50C23×C4×C11—24no—
51C23×C4×C11C2312yes—
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2314yes—
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2312yes—
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2311yescharacteristic
62C2×C11×C4⋊C4—24no—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4C2314yes—
65C2×C11×C4⋊C4C2314yes—
66C2×C11×C22⋊C4—44no—
67C2×C11×C22⋊C4C2318yes—
68C2×C22⋊Dic11—24no—
69C2×C22⋊Dic11—44no—
70C2×C22⋊Dic11Q818yes—
71C2×C22⋊Dic11C2314yes—
72C2×C22⋊Dic11C2318yes—
73C2×C22⋊Dic11C2314yes—
74C2×C4⋊Dic11—24no—
75C2×C4⋊Dic11—24no—
76C2×C4⋊Dic11—44no—
77C2×C4⋊Dic11C2314yes—
78C2×C4⋊Dic11C2314yes—
79C2×C4⋊Dic11C2318yes—
80C2×Dic11⋊C4—28no—
81C2×Dic11⋊C4—44no—
82C2×Dic11⋊C4—44no—
83C2×Dic11⋊C4C2318yes—
84C2×Dic11⋊C4C2318yes—
85C2×Dic11⋊C4C2318yes—
86C2×C4×Dic11—24no—
87C2×C4×Dic11—24no—
88C2×C4×Dic11—44no—
89C2×C4×Dic11C2314yes—
90C2×C4×Dic11C2314yes—
91C2×C4×Dic11C2318yes—
92C11×#95C2318yes—
93C11⋊#95C2314yes—
94C11⋊#95C2318yes—
95C11⋊#95C2318yes—
96C11⋊#95C2314yes—
97C11⋊#95C2318yes—
98C11⋊#95C2318yes—
99C2×#2497—111nomaximal, Sylow
100C24×C11—22no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11—22no—
104C24×C11—22no—
105C24×C11—22no—
106C24×C11C2×Q814yes—
107C24×C11C2412yes—
108C24×C11C2411yescharacteristic
109C22×C4×C11—24no—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—22no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—28no—
119C22×C4×C11—28no—
120C22×C4×C11—28no—
121C22×C4×C11—416no—
122C22×C4×C11#4114yes—
123C22×C4×C11#4114yes—
124C22×C4×C11#4114yes—
125C22×C4×C11C2412yes—
126C22×C4×C11C2414yes—
127C22×C4×C11C2414yes—
128C22×C4×C11C2412yes—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11—22no—
133C22×Dic11—24no—
134C22×Dic11—24no—
135C22×Dic11—24no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—22no—
143C22×Dic11—24no—
144C22×Dic11C2×Q814yes—
145C22×Dic11C2×Q814yes—
146C22×Dic11#4114yes—
147C22×Dic11C2412yes—
148C22×Dic11C2414yes—
149C22×Dic11C2414yes—
150C22×Dic11C2412yes—
151C22×Dic11C2412yes—
152C22×Dic11C2412yes—
153C11×C4⋊C4—28no—
154C11×C4⋊C4—28no—
155C11×C22⋊C4—48no—
156C22⋊Dic11—28no—
157C22⋊Dic11—48no—
158C22⋊Dic11C2×Q8116yes—
159C4⋊Dic11—28no—
160C4⋊Dic11—28no—
161C4⋊Dic11—48no—
162Dic11⋊C4—216no—
163Dic11⋊C4—48no—
164Dic11⋊C4—48no—
165C4×Dic11—28no—
166C4×Dic11—28no—
167C4×Dic11—48no—
168#2497—1116no—
169C2×#400—112no—
170C2×#396—112no—
171C2×#389—111no—
172C2×#389—111no—
173C2×#388—112no—
174C2×#387—112no—
175C2×#384—111no—
176C2×#380—111no—
177C2×#380D1111yescharacteristic
178C2×C4×C4⋊C4—111no—
179C2×C4×C22⋊C4—111no—
180C23×C11—28no—
181C23×C11—28no—
182C23×C11—28no—
183C23×C11—22no—
184C23×C11—22no—
185C23×C11—22no—
186C23×C11—22no—
187C23×C11—22no—
188C23×C11—22no—
189C23×C11—44no—
190C23×C11—44no—
191C23×C11—44no—
192C23×C11—44no—
193C23×C11C22×Q814yes—
194C23×C11C22×Q812yes—
195C23×C11C2×#4112yes—
196C23×C11C2×#4112yes—
197C23×C11C2×#4112yes—
198C23×C11C2×#4112yes—
199C23×C11H(5,𝔽2)12yes—
200C23×C11H(5,𝔽2)12yes—
201C23×C11C2511yescharacteristic
202C2×C4×C11—24no—
203C2×C4×C11—24no—
204C2×C4×C11—24no—
205C2×C4×C11—22no—
206C2×C4×C11—22no—
207C2×C4×C11—22no—
208C2×C4×C11—24no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—44no—
212C2×C4×C11—48no—
213C2×C4×C11—48no—
214C2×C4×C11—416no—
215C2×C4×C11#126116yes—
216C2×C4×C11C2×#4114yes—
217C2×C4×C11C2×#4114yes—
218C2×C4×C11C2×#4114yes—
219C2×Dic11—28no—
220C2×Dic11—28no—
221C2×Dic11—28no—
222C2×Dic11—22no—
223C2×Dic11—22no—
224C2×Dic11—22no—
225C2×Dic11—22no—
226C2×Dic11—22no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—48no—
238C2×Dic11—44no—
239C2×Dic11—48no—
240C2×Dic11C22×Q814yes—
241C2×Dic11C22×Q814yes—
242C2×Dic11C2×#4114yes—
243C24×C4C2×D1111yescharacteristic
244C22×C4⋊C4—112no—
245C22×C4⋊C4—111no—
246C22×C4⋊C4—111no—
247C22×C4⋊C4—112no—
248C22×C4⋊C4—112no—
249C22×C4⋊C4—112no—
250C22×C4⋊C4C2×D1111yescharacteristic
251C22×C4⋊C4C2×D1111yescharacteristic
252C22×C22⋊C4—111no—
253C22×C22⋊C4—111no—
254C22×C22⋊C4—112no—
255C22×C22⋊C4C2×D1112yes—
256C22×C42—111no—
257C22×C42—111no—
258C22×C42—112no—
259#400—1116no—
260#396—1116no—
261#389—118no—
262#389—118no—
263#388—1116no—
264#387—1116no—
265#384—118no—
266#380—118no—
267#380C2×D1118yes—
268C4×C4⋊C4—118no—
269C4×C22⋊C4—118no—
270C2×#95—112no—
271C2×#95—111no—
272C2×#95—112no—
273C2×#95—112no—
274C2×#95—111no—
275C2×#95—112no—
276C2×#95C2×D1112yes—
277C22×C11—24no—
278C22×C11—24no—
279C22×C11—24no—
280C22×C11—42no—
281C22×C11—42no—
282C22×C11—42no—
283C22×C11—42no—
284C22×C11—416no—
285C22×C11C2×#12614yes—
286C22×C11#53314yes—
287C22×C11#54014yes—
288C22×C11#55314yes—
289C22×C11#55414yes—
290C22×C11#55414yes—
291C22×C11#55514yes—
292C22×C11C23×Q811yescharacteristic
293C22×C11C22×#4111yescharacteristic
294C22×C11C22×#4111yescharacteristic
295C22×C11C22×#4111yescharacteristic
296C22×C11C22×#4111yescharacteristic
297C22×C11C2×H(5,𝔽2)11yescharacteristic
298C22×C11C2×H(5,𝔽2)11yescharacteristic
299C4×C11—42no—
300C4×C11—44no—
301C4×C11—44no—
302C4×C11C2×#12618yes—
303Dic11—24no—
304Dic11—24no—
305Dic11—24no—
306Dic11—44no—
307Dic11—42no—
308Dic11—44no—
309C25C22×D1111yescharacteristic
310C23×C4—24no—
311C23×C4—24no—
312C23×C4—24no—
313C23×C4—111no—
314C23×C4—111no—
315C23×C4—111no—
316C23×C4—112no—
317C23×C4—112no—
318C23×C4—111no—
319C23×C4C22×D1114yes—
320C23×C4C22×D1112yes—
321C23×C4C22×D1112yes—
322C23×C4C22×D1111yescharacteristic
323C23×C4C22×D1111yescharacteristic
324C2×C4⋊C4—24no—
325C2×C4⋊C4—24no—
326C2×C4⋊C4—114no—
327C2×C4⋊C4—114no—
328C2×C4⋊C4—118no—
329C2×C4⋊C4—118no—
330C2×C4⋊C4—118no—
331C2×C4⋊C4—118no—
332C2×C4⋊C4—228no—
333C2×C4⋊C4—224no—
334C2×C4⋊C4—224no—
335C2×C4⋊C4—444no—
336C2×C4⋊C4—444no—
337C2×C4⋊C4—444no—
338C2×C4⋊C4C22×D1114yes—
339C2×C4⋊C4C22×D1114yes—
340C2×C22⋊C4—44no—
341C2×C22⋊C4—118no—
342C2×C22⋊C4—114no—
343C2×C22⋊C4—114no—
344C2×C22⋊C4—118no—
345C2×C22⋊C4—224no—
346C2×C22⋊C4—444no—
347C2×C22⋊C4C22×D1118yes—
348C2×C42—114no—
349C2×C42—114no—
350C2×C42—118no—
351C2×C42—224no—
352C2×C42—224no—
353C2×C42—444no—
354#95—114no—
355#95—114no—
356#95—118no—
357#95—118no—
358#95—118no—
359#95—118no—
360#95C22×D1118yes—
361C2×C11—44no—
362C2×C11#249718yescomplemented
363C2×C11C22×#12611yescharacteristic
364C2×C11C2×#53311yescharacteristic
365C2×C11C2×#54011yescharacteristic
366C2×C11C2×#55311yescharacteristic
367C2×C11C2×#55411yescharacteristic
368C2×C11C2×#55411yescharacteristic
369C2×C11C2×#55511yescharacteristic
370C24—22no—
371C24—22no—
372C24—22no—
373C24—22no—
374C24—22no—
375C24—22no—
376C24Q8×D1114yes—
377C24C23×D1112yes—
378C24C23×D1111yescharacteristic
379C22×C4—22no—
380C22×C4—24no—
381C22×C4—24no—
382C22×C4—22no—
383C22×C4—22no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—24no—
388C22×C4—28no—
389C22×C4—28no—
390C22×C4—28no—
391C22×C4—416no—
392C22×C4—114no—
393C22×C4—114no—
394C22×C4—114no—
395C22×C4—112no—
396C22×C4—112no—
397C22×C4—112no—
398C22×C4—112no—
399C22×C4—114no—
400C22×C4—114no—
401C22×C4—222no—
402C22×C4—222no—
403C22×C4—222no—
404C22×C4—222no—
405C22×C4—222no—
406C22×C4—222no—
407C22×C4—222no—
408C22×C4—224no—
409C22×C4—224no—
410C22×C4—224no—
411C22×C4—222no—
412C22×C4—224no—
413C22×C4—224no—
414C22×C4—224no—
415C22×C4—222no—
416C22×C4#433914yes—
417C22×C4#434114yes—
418C22×C4#434114yes—
419C22×C4C23×D1112yes—
420C22×C4C23×D1114yes—
421C22×C4C23×D1114yes—
422C22×C4C23×D1112yes—
423C4⋊C4—28no—
424C4⋊C4—28no—
425C4⋊C4—2216no—
426C4⋊C4—228no—
427C4⋊C4—228no—
428C4⋊C4—448no—
429C4⋊C4—448no—
430C4⋊C4—448no—
431C22⋊C4—48no—
432C22⋊C4—1116no—
433C22⋊C4—228no—
434C22⋊C4—448no—
435C42—228no—
436C42—228no—
437C42—448no—
438C11C2×#249711yescharacteristic, complemented, Sylow
439C23—28no—
440C23—28no—
441C23—28no—
442C23—22no—
443C23—22no—
444C23—22no—
445C23—22no—
446C23—22no—
447C23—22no—
448C23—44no—
449C23—44no—
450C23—44no—
451C23—44no—
452C23C2×#433912yes—
453C23C2×#434112yes—
454C23C2×#434112yes—
455C23#6703712yes—
456C23C2×Q8×D1114yes—
457C23C2×Q8×D1112yes—
458C23#41×D1112yes—
459C23#6704212yes—
460C23C24×D1111yescharacteristic
461C2×C4—22no—
462C2×C4—24no—
463C2×C4—24no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—24no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—24no—
470C2×C4—44no—
471C2×C4—48no—
472C2×C4—48no—
473C2×C4—416no—
474C2×C4—114no—
475C2×C4—114no—
476C2×C4—114no—
477C2×C4—228no—
478C2×C4—228no—
479C2×C4—228no—
480C2×C4—222no—
481C2×C4—222no—
482C2×C4—222no—
483C2×C4—222no—
484C2×C4—222no—
485C2×C4—222no—
486C2×C4—222no—
487C2×C4—224no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—222no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—224no—
494C2×C4—222no—
495C2×C4—444no—
496C2×C4—448no—
497C2×C4—448no—
498C2×C4#66932116yes—
499C2×C4C2×#433914yes—
500C2×C4C2×#434114yes—
501C2×C4C2×#434114yes—
502C22—24no—
503C22—24no—
504C22—24no—
505C22—42no—
506C22—42no—
507C22—42no—
508C22—42no—
509C22—416no—
510C22C2×#6693214yes—
511C22#1062304214yes—
512C22#1062306314yes—
513C22#1062314514yes—
514C22#1062315014yes—
515C22#1062315314yes—
516C22#1062316614yes—
517C22C22×#433911yescharacteristic
518C22C22×#434111yescharacteristic
519C22C22×#434111yescharacteristic
520C22C2×#6703711yescharacteristic
521C22C22×Q8×D1111yescharacteristic
522C22C2×#41×D1111yescharacteristic
523C22C2×#6704211yescharacteristic
524C4—42no—
525C4—44no—
526C4—44no—
527C4—224no—
528C4—224no—
529C4—224no—
530C4—442no—
531C4—444no—
532C4—444no—
533C4C2×#6693218yes—
534C2—44no—
535C2#1307304518yesdirect product factor
536C2C22×#6693211yescharacteristic
537C2C2×#1062315311yescharacteristic
538C2C2×#1062315011yescharacteristic
539C2C2×#1062314511yescharacteristic
540C2C2×#1062304211yescharacteristic
541C2C2×#1062316611yescharacteristic
542C2C2×#1062306311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11C2×#2497
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. #13073045C2direct (N × H)
2. C2×#10622272C2semidirect
4. C2×#10622598C2semidirect
5. C2×#10622586C2semidirect
7. C2×#10622265C2semidirect
8. C2×#10622589C2semidirect
10. C2×C4⋊C4×Dic11C2semidirect
39. #10622598C22semidirect
40. #10622589C22semidirect
41. C4⋊C4×Dic11C22semidirect
42. #10622586C22semidirect
45. #10622272C22semidirect
46. #10622265C22semidirect
362. C2×C11#2497semidirect
438. C11C2×#2497semidirect
535. C2#13073045direct (N × H)

Maximal subgroups

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

subgroupindex
#130730452
C2×#106222722
C2×#106225612
C2×#106225982
C2×#106225862
C2×#106225572
C2×#106222652
C2×#106225892
C2×#106228252
C2×C4⋊C4×Dic112
C2×C4×C22⋊Dic112
C2×C11×#3802
C2×#249711