Finite Group Databasebeta

← C2×#13074450 #14920838

Subgroups — C2×#13074450 #14920838

Order 2816.

2614 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66943C211yesmaximal, characteristic, complemented
2C22×#66979C211yesmaximal, characteristic
3#13074450C2116yesmaximal, direct product factor
4C2×#10622270C212yesmaximal, complemented
5C2×#10622274C212yesmaximal, complemented
6C2×#10622561C212yesmaximal
7C2×#10622561C212yesmaximal
8C2×#10622598C211yesmaximal, characteristic, complemented
9C2×#10622586C211yesmaximal, characteristic, complemented
10C2×#10622589C211yesmaximal, characteristic, complemented
11C2×#10622825C211yesmaximal, 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⋊Dic11C2211yescharacteristic
19C22×C22⋊Dic11C2212yes—
20C2×#66979—28no—
21C2×#66979C2218yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2212yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×Dic11⋊C4C2212yes—
30C22×Dic11⋊C4C2212yes—
31C22×Dic11⋊C4C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C2×#66943—28no—
35C2×#66943C2218yescomplemented
36C11×#380C2218yes—
37C2×C11×#95C2212yes—
38#10622825C2218yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622598C2218yescomplemented
43#10622589C2218yescomplemented
44#10622586C2218yescomplemented
45#10622561C22116yes—
46#10622561C22116yes—
47#10622274C22116yescomplemented
48#10622270C22116yescomplemented
49C25×C11C2311yescharacteristic
50C23×C4×C11—24no—
51C23×C4×C11—24no—
52C23×C4×C11Q818yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2314yes—
57C23×C4×C11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2312yes—
61C23×Dic11C2312yes—
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2311yescharacteristic
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4C2314yes—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C22⋊C4—44no—
69C2×C11×C22⋊C4C2318yes—
70C2×C22⋊Dic11—24no—
71C2×C22⋊Dic11—24no—
72C2×C22⋊Dic11—44no—
73C2×C22⋊Dic11C2314yes—
74C2×C22⋊Dic11C2314yes—
75C2×C22⋊Dic11C2318yes—
76#66979—232no—
77C2×C4⋊Dic11—24no—
78C2×C4⋊Dic11—24no—
79C2×C4⋊Dic11—28no—
80C2×C4⋊Dic11—24no—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11—44no—
83C2×C4⋊Dic11C2318yes—
84C2×C4⋊Dic11C2314yes—
85C2×C4⋊Dic11C2314yes—
86C2×C4⋊Dic11C2314yes—
87C2×C4⋊Dic11C2314yes—
88C2×C4⋊Dic11C2318yes—
89C2×Dic11⋊C4—28no—
90C2×Dic11⋊C4—44no—
91C2×Dic11⋊C4—44no—
92C2×Dic11⋊C4—44no—
93C2×Dic11⋊C4C2318yes—
94C2×Dic11⋊C4C2318yes—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2318yes—
97C2×C4×Dic11—24no—
98C2×C4×Dic11D418yes—
99C2×C4×Dic11C2314yes—
100C2×C4×Dic11C2314yes—
101#66943—232no—
102C11×#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C2×#2629—111nomaximal, Sylow
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11C2×Q814yes—
114C24×C11C2412yes—
115C24×C11C2411yescharacteristic
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—232no—
119C22×C4×C11—28no—
120C22×C4×C11—28no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—24no—
127C22×C4×C11C2×D414yes—
128C22×C4×C11C2×Q814yes—
129C22×C4×C11C2×Q8116yes—
130C22×C4×C11C2×Q814yes—
131C22×C4×C11#4114yes—
132C22×C4×C11C2414yes—
133C22×C4×C11C2414yes—
134C22×C4×C11C2412yes—
135C22×C4×C11C2412yes—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—22no—
142C22×Dic11—22no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11—24no—
147C22×Dic11—22no—
148C22×Dic11—22no—
149C22×Dic11—22no—
150C22×Dic11—24no—
151C22×Dic11—22no—
152C22×Dic11C2×D414yes—
153C22×Dic11C2×D414yes—
154C22×Dic11C2412yes—
155C22×Dic11C2412yes—
156C22×Dic11C2414yes—
157C22×Dic11C2414yes—
158C22×Dic11C2412yes—
159C22×Dic11C2412yes—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—28no—
162C11×C22⋊C4—48no—
163C22⋊Dic11—28no—
164C22⋊Dic11—28no—
165C22⋊Dic11—48no—
166C4⋊Dic11—216no—
167C4⋊Dic11—28no—
168C4⋊Dic11—28no—
169C4⋊Dic11—28no—
170C4⋊Dic11—28no—
171C4⋊Dic11—48no—
172Dic11⋊C4—216no—
173Dic11⋊C4—48no—
174Dic11⋊C4—48no—
175Dic11⋊C4—48no—
176C4×Dic11—28no—
177C4×Dic11C2×D4116yes—
178C22×#125—111no—
179C22×#117—111no—
180#2629—1116no—
181C2×#398—112no—
182C2×#398—112no—
183C2×#396—112no—
184C2×#396—112no—
185C2×#389—111no—
186C2×#389—111no—
187C2×#384—111no—
188C2×#380—111no—
189C2×#380D1111yescharacteristic
190C23×C11—28no—
191C23×C11—28no—
192C23×C11—28no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—22no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11—44no—
203C23×C11C22×D412yes—
204C23×C11C22×Q814yes—
205C23×C11C22×Q812yes—
206C23×C11C2×#4112yes—
207C23×C11H(5,𝔽2)12yes—
208C23×C11H(5,𝔽2)12yes—
209C23×C112−1+412yes—
210C23×C112−1+412yes—
211C23×C11C2511yescharacteristic
212C2×C4×C11—28no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—232no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—48no—
223C2×C4×C11—48no—
224C2×C4×C11C22⋊Q8116yes—
225C2×C4×C11C22×D414yes—
226C2×C4×C11C22×Q814yes—
227C2×C4×C11C22×Q814yes—
228C2×C4×C11C2×#4114yes—
229C2×Dic11—28no—
230C2×Dic11—28no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—22no—
243C2×Dic11—24no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—22no—
247C2×Dic11—44no—
248C2×Dic11—44no—
249C2×Dic11—48no—
250C2×Dic11—48no—
251C2×Dic11C22×D414yes—
252C2×Dic11C22×D414yes—
253C24×C4C2×D1111yescharacteristic
254C2×#125—118no—
255C2×#125—228no—
256C2×#117—118no—
257C2×#117—228no—
258C22×C4⋊C4—112no—
259C22×C4⋊C4—112no—
260C22×C4⋊C4—111no—
261C22×C4⋊C4—111no—
262C22×C4⋊C4—111no—
263C22×C4⋊C4—111no—
264C22×C4⋊C4—112no—
265C22×C4⋊C4—112no—
266C22×C4⋊C4—112no—
267C22×C4⋊C4—112no—
268C22×C4⋊C4C2×D1111yescharacteristic
269C22×C4⋊C4C2×D1111yescharacteristic
270C22×C22⋊C4—111no—
271C22×C22⋊C4—111no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4C2×D1112yes—
274C22×C42—111no—
275C22×C42—111no—
276#398—1116no—
277#398—1116no—
278#396—1116no—
279#396—1116no—
280#389—118no—
281#389—118no—
282#384—118no—
283#380—118no—
284#380C2×D1118yes—
285C2×#95—112no—
286C2×#95—112no—
287C2×#95—112no—
288C2×#95C2×D1112yes—
289C22×C11—24no—
290C22×C11—24no—
291C22×C11—24no—
292C22×C11—416no—
293C22×C11—42no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11C2×C22⋊Q814yes—
298C22×C11#53714yes—
299C22×C11#53714yes—
300C22×C11#54014yes—
301C22×C11#54114yes—
302C22×C11#54414yes—
303C22×C11#54414yes—
304C22×C11C23×D411yescharacteristic
305C22×C11C23×Q811yescharacteristic
306C22×C11C22×#4111yescharacteristic
307C22×C11C2×H(5,𝔽2)11yescharacteristic
308C22×C11C2×H(5,𝔽2)11yescharacteristic
309C22×C11C2×2−1+411yescharacteristic
310C22×C11C2×2−1+411yescharacteristic
311C4×C11—24no—
312C4×C11—44no—
313C4×C11—44no—
314C4×C11C2×C22⋊Q818yes—
315Dic11—24no—
316Dic11—24no—
317Dic11—42no—
318Dic11—42no—
319Dic11—44no—
320Dic11—44no—
321C25C22×D1111yescharacteristic
322C23×C4—24no—
323C23×C4—24no—
324C23×C4—111no—
325C23×C4—111no—
326C23×C4—112no—
327C23×C4—112no—
328C23×C4—111no—
329C23×C4—111no—
330C23×C4Dic2218yes—
331C23×C4C22×D1112yes—
332C23×C4C22×D1112yes—
333C23×C4C22×D1114yes—
334C23×C4C22×D1111yescharacteristic
335C23×C4C22×D1111yescharacteristic
336#125—2232no—
337#117—2232no—
338C2×C4⋊C4—24no—
339C2×C4⋊C4—24no—
340C2×C4⋊C4—114no—
341C2×C4⋊C4—114no—
342C2×C4⋊C4—114no—
343C2×C4⋊C4—118no—
344C2×C4⋊C4—118no—
345C2×C4⋊C4—114no—
346C2×C4⋊C4—118no—
347C2×C4⋊C4—118no—
348C2×C4⋊C4—118no—
349C2×C4⋊C4—118no—
350C2×C4⋊C4—224no—
351C2×C4⋊C4—224no—
352C2×C4⋊C4—228no—
353C2×C4⋊C4—228no—
354C2×C4⋊C4—224no—
355C2×C4⋊C4—224no—
356C2×C4⋊C4—444no—
357C2×C4⋊C4—444no—
358C2×C4⋊C4—444no—
359C2×C4⋊C4—444no—
360C2×C4⋊C4C22×D1114yes—
361C2×C4⋊C4C22×D1114yes—
362C2×C22⋊C4—44no—
363C2×C22⋊C4—114no—
364C2×C22⋊C4—114no—
365C2×C22⋊C4—118no—
366C2×C22⋊C4—224no—
367C2×C22⋊C4—224no—
368C2×C22⋊C4—444no—
369C2×C22⋊C4C22×D1118yes—
370C2×C42—118no—
371C2×C42—114no—
372C2×C42—114no—
373C2×C42—224no—
374#95—118no—
375#95—118no—
376#95—118no—
377#95C22×D1118yes—
378C2×C11—44no—
379C2×C11#262918yescomplemented
380C2×C11C22×C22⋊Q811yescharacteristic
381C2×C11C2×#53711yescharacteristic
382C2×C11C2×#53711yescharacteristic
383C2×C11C2×#54011yescharacteristic
384C2×C11C2×#54111yescharacteristic
385C2×C11C2×#54411yescharacteristic
386C2×C11C2×#54411yescharacteristic
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24—22no—
393C24C2×Dic2214yes—
394C24C23×D1112yes—
395C24C23×D1111yescharacteristic
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—232no—
399C22×C4—28no—
400C22×C4—28no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—114no—
408C22×C4—114no—
409C22×C4—112no—
410C22×C4—112no—
411C22×C4—112no—
412C22×C4—112no—
413C22×C4—114no—
414C22×C4—114no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—224no—
422C22×C4—224no—
423C22×C4—222no—
424C22×C4—224no—
425C22×C4—224no—
426C22×C4—222no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4C2×Dic2214yes—
432C22×C4C2×Dic22116yes—
433C22×C4C2×Dic2214yes—
434C22×C4D4×D1114yes—
435C22×C4#434114yes—
436C22×C4C23×D1114yes—
437C22×C4C23×D1114yes—
438C22×C4C23×D1112yes—
439C22×C4C23×D1112yes—
440C4⋊C4—28no—
441C4⋊C4—28no—
442C4⋊C4—228no—
443C4⋊C4—228no—
444C4⋊C4—2216no—
445C4⋊C4—2216no—
446C4⋊C4—228no—
447C4⋊C4—228no—
448C4⋊C4—448no—
449C4⋊C4—448no—
450C4⋊C4—448no—
451C4⋊C4—448no—
452C22⋊C4—48no—
453C22⋊C4—228no—
454C22⋊C4—228no—
455C22⋊C4—448no—
456C42—1116no—
457C42—228no—
458C11C2×#262911yescharacteristic, complemented, Sylow
459C23—28no—
460C23—28no—
461C23—28no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23—44no—
472C23C22×Dic2214yes—
473C23C22×Dic2212yes—
474C23C2×D4×D1112yes—
475C23C2×#434112yes—
476C23#6703712yes—
477C23#6704012yes—
478C23#6704212yes—
479C23#6704312yes—
480C23C24×D1111yescharacteristic
481C2×C4—28no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—232no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—48no—
492C2×C4—48no—
493C2×C4—114no—
494C2×C4—114no—
495C2×C4—228no—
496C2×C4—228no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—222no—
502C2×C4—222no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—222no—
506C2×C4—224no—
507C2×C4—222no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—444no—
514C2×C4—448no—
515C2×C4—444no—
516C2×C4—448no—
517C2×C4#66931116yes—
518C2×C4C22×Dic2214yes—
519C2×C4C22×Dic2214yes—
520C2×C4C2×D4×D1114yes—
521C2×C4C2×#434114yes—
522C22—24no—
523C22—24no—
524C22—24no—
525C22—416no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—42no—
530C22C2×#6693114yes—
531C22#1062303114yes—
532C22#1062305014yes—
533C22#1062313914yes—
534C22#1062315014yes—
535C22#1062315614yes—
536C22#1062316014yes—
537C22C23×Dic2211yescharacteristic
538C22C22×D4×D1111yescharacteristic
539C22C22×#434111yescharacteristic
540C22C2×#6703711yescharacteristic
541C22C2×#6704011yescharacteristic
542C22C2×#6704211yescharacteristic
543C22C2×#6704311yescharacteristic
544C4—24no—
545C4—44no—
546C4—44no—
547C4—224no—
548C4—224no—
549C4—442no—
550C4—442no—
551C4—444no—
552C4—444no—
553C4C2×#6693118yes—
554C2—44no—
555C2#1307445018yesdirect product factor
556C2C22×#6693111yescharacteristic
557C2C2×#1062313911yescharacteristic
558C2C2×#1062316011yescharacteristic
559C2C2×#1062315011yescharacteristic
560C2C2×#1062315611yescharacteristic
561C2C2×#1062305011yescharacteristic
562C2C2×#1062303111yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#380C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC2×#380D11
hypocenterC11C2×#2629
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
1. C22×#66943C2semidirect
3. #13074450C2direct (N × H)
4. C2×#10622270C2semidirect
5. C2×#10622274C2semidirect
8. C2×#10622598C2semidirect
9. C2×#10622586C2semidirect
10. C2×#10622589C2semidirect
35. C2×#66943C22semidirect
42. #10622598C22semidirect
43. #10622589C22semidirect
44. #10622586C22semidirect
47. #10622274C22semidirect
48. #10622270C22semidirect
379. C2×C11#2629semidirect
458. C11C2×#2629semidirect
555. C2#13074450direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669432
C22×#669792
#130744502
C2×#106222702
C2×#106222742
C2×#106225612
C2×#106225982
C2×#106225862
C2×#106225892
C2×#106228252
C2×C11×#3802
C2×#262911