Finite Group Databasebeta

← C2×#13072612 #14921300

Subgroups — C2×#13072612 #14921300

Order 2816.

3958 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66949C212yesmaximal, complemented
2C22×C4×C22⋊D11C212yesmaximal, complemented
3#13072612C2116yesmaximal, direct product factor
4C2×#10622572C212yesmaximal, complemented
5C2×#10622560C211yesmaximal, characteristic, complemented
6C2×#10622573C211yesmaximal, characteristic
7C2×#10622603C212yesmaximal, complemented
8C2×#10622265C212yesmaximal, complemented
9C2×#10622278C212yesmaximal, complemented
10C2×C11×#385C211yesmaximal, characteristic, complemented
11C24×C4×C11C2211yescharacteristic
12C23×C22⋊D11C2212yes—
13C23×D44C2211yescharacteristic
14C23×C4×D11C2212yes—
15C23×Dic22C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C2×C4×C22⋊D11—216no—
21C2×C4×C22⋊D11C22116yescomplemented
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2212yes—
28C22×C4×Dic11C2212yes—
29C2×#66949—216no—
30C2×#66949C22116yescomplemented
31C11×#385C2218yescomplemented
32C2×C11×#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2211yescharacteristic
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37#10622603C22116yescomplemented
38#10622573C2218yes—
39#10622572C22116yescomplemented
40#10622560C2218yescomplemented
41#10622278C22116yescomplemented
42#10622265C22116yescomplemented
43C25×C11C2311yescharacteristic
44C24×D11C2312yes—
45C23×C4×C11—28no—
46C23×C4×C11—42no—
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2314yes—
51C23×C4×C11C2312yes—
52C22×C22⋊D11—28no—
53C22×C22⋊D11—28no—
54C22×C22⋊D11—28no—
55C22×C22⋊D11C2318yes—
56C23×Dic11C2312yes—
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C22×D44—28no—
60C22×D44—42no—
61C22×D44C2314yes—
62C22×C4×D11—28no—
63C22×C4×D11—28no—
64C22×C4×D11—44no—
65C22×C4×D11C2318yes—
66C22×Dic22—28no—
67C22×Dic22—42no—
68C22×Dic22C2314yes—
69C2×C11×C4⋊C4—28no—
70C2×C11×C4⋊C4C2318yes—
71C2×C11×C22⋊C4—24no—
72C2×C11×C22⋊C4—42no—
73C2×C11×C22⋊C4C2314yes—
74C2×C11×C22⋊C4C2314yes—
75C2×C22⋊Dic11—28no—
76C2×C22⋊Dic11C2318yes—
77C4×C22⋊D11—264no—
78C2×(C2×D11)⋊C4—28no—
79C2×(C2×D11)⋊C4—28no—
80C2×(C2×D11)⋊C4—28no—
81C2×(C2×D11)⋊C4—28no—
82C2×(C2×D11)⋊C4C2318yes—
83C2×(C2×D11)⋊C4C2318yes—
84C2×(C2×D11)⋊C4C2318yes—
85C2×(C2×D11)⋊C4C2318yes—
86C2×Dic11⋊C4—28no—
87C2×Dic11⋊C4D4116yescomplemented
88C2×Dic11⋊C4C2318yes—
89C2×Dic11⋊C4C2318yes—
90C2×C4×Dic11—28no—
91C2×C4×Dic11C2318yes—
92#66949—264no—
93C11×#95C2318yes—
94C11⋊#95C2314yes—
95C11⋊#95C2318yes—
96C11⋊#95C2318yes—
97C11⋊#95C2314yes—
98C2×#2463—111nomaximal, Sylow
99C24×C11—24no—
100C24×C11—24no—
101C24×C11—22no—
102C24×C11—22no—
103C24×C11#4114yes—
104C24×C11C2412yes—
105C24×C11C2411yescharacteristic
106C23×D11—24no—
107C23×D11—24no—
108C23×D11—24no—
109C23×D11—24no—
110C23×D11—24no—
111C23×D11—24no—
112C23×D11#4118yes—
113C23×D11C2414yes—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—22no—
122C22×C4×C11—22no—
123C22×C4×C11—216no—
124C22×C4×C11—44no—
125C22×C4×C11—416no—
126C22×C4×C11C2×D418yes—
127C22×C4×C11C2412yes—
128C22×C4×C11C2414yes—
129C22×C4×C11C2412yes—
130C22×C4×C11C2414yes—
131C2×C22⋊D11—264no—
132C2×C22⋊D11—216no—
133C2×C22⋊D11—216no—
134C2×C22⋊D11—216no—
135C22×Dic11—24no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11C2×D418yes—
143C22×Dic11C2×D418yes—
144C22×Dic11C2414yes—
145C22×Dic11C2414yes—
146C22×Dic11C2414yes—
147C2×D44—216no—
148C2×D44—44no—
149C2×D44—416no—
150C2×C4×D11—216no—
151C2×C4×D11—216no—
152C2×C4×D11—48no—
153C2×C4×D11—432no—
154C2×Dic22—216no—
155C2×Dic22—44no—
156C2×Dic22—416no—
157C11×C4⋊C4—216no—
158C11×C22⋊C4—28no—
159C11×C22⋊C4—44no—
160C22⋊Dic11—216no—
161(C2×D11)⋊C4—216no—
162(C2×D11)⋊C4—216no—
163(C2×D11)⋊C4—216no—
164(C2×D11)⋊C4—216no—
165Dic11⋊C4—216no—
166Dic11⋊C4C2×D4132yescomplemented
167C4×Dic11—216no—
168C22×C22⋊Q8—112no—
169C22×C4×D4—112no—
170#2463—1116no—
171C2×#394—112no—
172C2×#393—111no—
173C2×#392—111no—
174C2×#388—112no—
175C2×#387—112no—
176C2×#386—112no—
177C2×#385D1111yescharacteristic, complemented
178C23×C11—216no—
179C23×C11—28no—
180C23×C11—24no—
181C23×C11—24no—
182C23×C11—22no—
183C23×C11—22no—
184C23×C11—44no—
185C23×C11—48no—
186C23×C11—44no—
187C23×C11C22×D414yes—
188C23×C11C2×#4114yes—
189C23×C11C2×#4112yes—
190C23×C11C2×#4114yes—
191C23×C11H(5,𝔽2)12yes—
192C23×C112−1+412yes—
193C23×C11C2511yescharacteristic
194C22×D11—216no—
195C22×D11—216no—
196C22×D11—216no—
197C22×D11—24no—
198C22×D11—24no—
199C22×D11—24no—
200C22×D11—24no—
201C22×D11—24no—
202C22×D11—24no—
203C22×D11—48no—
204C22×D11—48no—
205C22×D11—48no—
206C22×D11—48no—
207C22×D11C2×#4118yes—
208C2×C4×C11—216no—
209C2×C4×C11—24no—
210C2×C4×C11—24no—
211C2×C4×C11—24no—
212C2×C4×C11—24no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—22no—
218C2×C4×C11—416no—
219C2×C4×C11—48no—
220C2×C4×C11—44no—
221C2×C4×C11—44no—
222C2×C4×C11C22×D418yes—
223C22⋊D11—264no—
224C2×Dic11—216no—
225C2×Dic11—216no—
226C2×Dic11—24no—
227C2×Dic11—24no—
228C2×Dic11—24no—
229C2×Dic11—24no—
230C2×Dic11—24no—
231C2×Dic11—24no—
232C2×Dic11—24no—
233C2×Dic11—48no—
234C2×Dic11C22×D418yes—
235C2×Dic11C22×D418yes—
236D44—416no—
237C4×D11—432no—
238Dic22—416no—
239C23×Q8—111no—
240C23×D4—112no—
241C23×D4—111no—
242C24×C4—112no—
243C24×C4C2×D1111yescharacteristic
244C2×C22⋊Q8—1116no—
245C2×C22⋊Q8—2216no—
246C2×C4×D4—1116no—
247C2×C4×D4—2216no—
248C22×C4⋊C4—112no—
249C22×C4⋊C4—112no—
250C22×C4⋊C4C2×D1112yes—
251C22×C22⋊C4—112no—
252C22×C22⋊C4—112no—
253C22×C22⋊C4—112no—
254C22×C22⋊C4—112no—
255C22×C22⋊C4—112no—
256C22×C22⋊C4C2×D1111yescharacteristic
257C22×C22⋊C4C2×D1111yescharacteristic
258C22×C42—112no—
259#394—1116no—
260#393—118no—
261#392—118no—
262#388—1116no—
263#387—1116no—
264#386—1116no—
265#385C2×D1118yescomplemented
266C2×#95—111no—
267C2×#95—112no—
268C2×#95—111no—
269C2×#95—112no—
270C2×#95C2×D1112yes—
271C22×C11—28no—
272C22×C11—24no—
273C22×C11—42no—
274C22×C11—44no—
275C22×C11—42no—
276C22×C11—416no—
277C22×C11#52518yes—
278C22×C11#53914yes—
279C22×C11D4214yes—
280C22×C11#54818yes—
281C22×C11#55114yes—
282C22×C11C23×D412yes—
283C22×C11C22×#4111yescharacteristic
284C22×C11C22×#4112yes—
285C22×C11C2×H(5,𝔽2)11yescharacteristic
286C22×C11C2×2−1+411yescharacteristic
287C2×D11—28no—
288C2×D11—28no—
289C2×D11—28no—
290C2×D11—44no—
291C2×D11—44no—
292C2×D11—44no—
293C2×D11—44no—
294C2×D11—432no—
295C4×C11—28no—
296C4×C11—44no—
297C4×C11—42no—
298C4×C11—42no—
299Dic11—28no—
300Dic11—28no—
301Dic11—44no—
302C25—112no—
303C25C22×D1111yescharacteristic
304C22×Q8—114no—
305C22×Q8—228no—
306C22×Q8—442no—
307C22×D4—118no—
308C22×D4—114no—
309C22×D4—228no—
310C22×D4—228no—
311C22×D4—228no—
312C22×D4—228no—
313C22×D4—442no—
314C23×C4—28no—
315C23×C4—42no—
316C23×C4—112no—
317C23×C4—112no—
318C23×C4—112no—
319C23×C4—118no—
320C23×C4—228no—
321C23×C4—228no—
322C23×C4—444no—
323C23×C4C22×D1112yes—
324C23×C4C22×D1111yescharacteristic
325C23×C4C22×D1111yescharacteristic
326C23×C4C22×D1114yes—
327C23×C4C22×D1112yes—
328C22⋊Q8—2264no—
329C4×D4—2264no—
330C2×C4⋊C4—28no—
331C2×C4⋊C4—1116no—
332C2×C4⋊C4—118no—
333C2×C4⋊C4—118no—
334C2×C4⋊C4—228no—
335C2×C4⋊C4C22×D1118yes—
336C2×C22⋊C4—24no—
337C2×C22⋊C4—42no—
338C2×C22⋊C4—118no—
339C2×C22⋊C4—118no—
340C2×C22⋊C4—118no—
341C2×C22⋊C4—118no—
342C2×C22⋊C4—118no—
343C2×C22⋊C4—228no—
344C2×C22⋊C4—228no—
345C2×C22⋊C4—228no—
346C2×C22⋊C4—228no—
347C2×C22⋊C4—228no—
348C2×C22⋊C4C22×D1114yes—
349C2×C22⋊C4C22×D1114yes—
350C2×C42—118no—
351C2×C42—228no—
352#95—118no—
353#95—114no—
354#95—118no—
355#95—114no—
356#95C22×D1118yes—
357C2×C11—44no—
358C2×C11#246318yescomplemented
359C2×C11C2×#52512yes—
360C2×C11C2×#53911yescharacteristic
361C2×C11C2×D4211yescharacteristic
362C2×C11C2×#54812yes—
363C2×C11C2×#55111yescharacteristic
364D11—48no—
365C24—24no—
366C24—22no—
367C24—22no—
368C24—24no—
369C24—118no—
370C24—114no—
371C24—224no—
372C24—224no—
373C24—224no—
374C24—224no—
375C24—224no—
376C24—224no—
377C24#433914yes—
378C24C23×D1112yes—
379C24C23×D1111yescharacteristic
380C2×Q8—2216no—
381C2×Q8—444no—
382C2×Q8—4416no—
383C2×D4—2216no—
384C2×D4—2216no—
385C2×D4—2216no—
386C2×D4—2264no—
387C2×D4—2216no—
388C2×D4—444no—
389C2×D4—4416no—
390C22×C4—24no—
391C22×C4—24no—
392C22×C4—24no—
393C22×C4—24no—
394C22×C4—24no—
395C22×C4—22no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—24no—
399C22×C4—216no—
400C22×C4—44no—
401C22×C4—416no—
402C22×C4—118no—
403C22×C4—118no—
404C22×C4—114no—
405C22×C4—114no—
406C22×C4—114no—
407C22×C4—2216no—
408C22×C4—224no—
409C22×C4—224no—
410C22×C4—224no—
411C22×C4—224no—
412C22×C4—224no—
413C22×C4—224no—
414C22×C4—224no—
415C22×C4—2216no—
416C22×C4—448no—
417C22×C4—4432no—
418C22×C4D4×D1118yes—
419C22×C4C23×D1112yes—
420C22×C4C23×D1114yes—
421C22×C4C23×D1112yes—
422C22×C4C23×D1114yes—
423C4⋊C4—216no—
424C4⋊C4—1132no—
425C4⋊C4—2216no—
426C22⋊C4—28no—
427C22⋊C4—44no—
428C22⋊C4—2216no—
429C22⋊C4—2216no—
430C22⋊C4—2216no—
431C22⋊C4—2216no—
432C22⋊C4—2216no—
433C42—2216no—
434C11C2×#246311yescharacteristic, complemented, Sylow
435C23—28no—
436C23—216no—
437C23—24no—
438C23—22no—
439C23—22no—
440C23—24no—
441C23—44no—
442C23—48no—
443C23—44no—
444C23—118no—
445C23—2216no—
446C23—2216no—
447C23—224no—
448C23—224no—
449C23—224no—
450C23—2216no—
451C23—224no—
452C23—224no—
453C23—224no—
454C23—448no—
455C23—448no—
456C23—448no—
457C23—448no—
458C23C2×#433914yes—
459C23C2×#433912yes—
460C23C2×D4×D1114yes—
461C23#6703712yes—
462C23#6704012yes—
463C23#41×D1114yes—
464C23C24×D1111yescharacteristic
465Q8—4416no—
466D4—2264no—
467D4—4416no—
468C2×C4—216no—
469C2×C4—24no—
470C2×C4—24no—
471C2×C4—24no—
472C2×C4—24no—
473C2×C4—24no—
474C2×C4—22no—
475C2×C4—22no—
476C2×C4—24no—
477C2×C4—24no—
478C2×C4—416no—
479C2×C4—48no—
480C2×C4—44no—
481C2×C4—44no—
482C2×C4—118no—
483C2×C4—118no—
484C2×C4—2216no—
485C2×C4—2216no—
486C2×C4—224no—
487C2×C4—224no—
488C2×C4—224no—
489C2×C4—224no—
490C2×C4—224no—
491C2×C4—224no—
492C2×C4—224no—
493C2×C4—4432no—
494C2×C4—448no—
495C2×C4C2×D4×D1118yes—
496C22—28no—
497C22—24no—
498C22—42no—
499C22—42no—
500C22—44no—
501C22—416no—
502C22—228no—
503C22—228no—
504C22—228no—
505C22—444no—
506C22—444no—
507C22—444no—
508C22—444no—
509C22—4432no—
510C22#1062304614yes—
511C22#1062307818yes—
512C22#1062312114yes—
513C22#1062316418yes—
514C22#1062319014yes—
515C22C22×#433911yescharacteristic
516C22C22×D4×D1112yes—
517C22C2×#6703711yescharacteristic
518C22C2×#6704011yescharacteristic
519C22C2×#41×D1112yes—
520C4—28no—
521C4—44no—
522C4—42no—
523C4—42no—
524C4—228no—
525C4—228no—
526C4—444no—
527C2—44no—
528C2—448no—
529C2#1307261218yesdirect product factor
530C2C2×#1062307812yes—
531C2C2×#1062304611yescharacteristic
532C2C2×#1062312111yescharacteristic
533C2C2×#1062316412yes—
534C2C2×#1062319011yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#385C2
socleC24×C11C24
prime radicalC2×#10622573C2
hypercenterC2×#385D11
hypocenterC11C2×#2463
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
1. C22×#66949C2semidirect
2. C22×C4×C22⋊D11C2semidirect
3. #13072612C2direct (N × H)
4. C2×#10622572C2semidirect
5. C2×#10622560C2semidirect
7. C2×#10622603C2semidirect
8. C2×#10622265C2semidirect
9. C2×#10622278C2semidirect
10. C2×C11×#385C2semidirect
21. C2×C4×C22⋊D11C22semidirect
30. C2×#66949C22semidirect
31. C11×#385C22semidirect
37. #10622603C22semidirect
39. #10622572C22semidirect
40. #10622560C22semidirect
41. #10622278C22semidirect
42. #10622265C22semidirect
87. C2×Dic11⋊C4D4semidirect
166. Dic11⋊C4C2×D4semidirect
177. C2×#385D11semidirect
265. #385C2×D11semidirect
358. C2×C11#2463semidirect
434. C11C2×#2463semidirect
529. C2#13072612direct (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×C4×C22⋊D112
#130726122
C2×#106225722
C2×#106225602
C2×#106225732
C2×#106226032
C2×#106222652
C2×#106222782
C2×C11×#3852
C2×#246311