Finite Group Databasebeta

← C2×#13072309 #14922121

Subgroups — C2×#13072309 #14922121

Order 2816.

2854 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×#66922C211yesmaximal, characteristic, complemented
2C22×#66945C211yesmaximal, characteristic
3#13072309C2116yesmaximal, direct product factor
4C2×#10622607C212yesmaximal
5C2×#10622286C212yesmaximal
6C2×#10622259C212yesmaximal, complemented
7C2×#10622586C211yesmaximal, characteristic, complemented
8C2×#10622594C212yesmaximal, complemented
9C2×#10622590C211yesmaximal, characteristic, complemented
10C2×#10622600C211yesmaximal, characteristic
11C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
12C2×C11×#389C211yesmaximal, characteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C23×Dic22C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2212yes—
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×C4⋊Dic11C2211yescharacteristic
24C22×C4⋊Dic11C2212yes—
25C22×C4⋊Dic11C2211yescharacteristic
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2212yes—
29C2×#66945—28no—
30C2×#66945C2218yes—
31C2×#66922—28no—
32C2×#66922C2218yescomplemented
33C11×#389C2218yescomplemented
34C2×C11×#95C2212yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622607C22116yes—
42#10622600C2218yes—
43#10622594C22116yescomplemented
44#10622590C2218yescomplemented
45#10622586C2218yescomplemented
46C4×(C2×D11)⋊C4C2218yes—
47#10622286C22116yes—
48#10622259C22116yescomplemented
49C24×D11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C22×C4×D11—24no—
61C22×C4×D11—24no—
62C22×C4×D11Q818yescomplemented
63C22×C4×D11C2314yes—
64C22×Dic22—28no—
65C22×Dic22—28no—
66C22×Dic22—44no—
67C22×Dic22C2318yes—
68C2×C11×C4⋊C4—24no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4—28no—
71C2×C11×C4⋊C4C2314yes—
72C2×C11×C4⋊C4C2314yes—
73C2×C11×C4⋊C4C2318yes—
74C2×C42×C11—24no—
75C2×C42×C11C2314yes—
76C2×(C2×D11)⋊C4—24no—
77C2×(C2×D11)⋊C4—24no—
78C2×(C2×D11)⋊C4—28no—
79C2×(C2×D11)⋊C4—44no—
80C2×(C2×D11)⋊C4C2318yes—
81C2×(C2×D11)⋊C4C2314yes—
82C2×(C2×D11)⋊C4C2314yes—
83C2×(C2×D11)⋊C4C2318yes—
84C2×C4⋊Dic11—24no—
85C2×C4⋊Dic11—28no—
86C2×C4⋊Dic11D418yes—
87C2×C4⋊Dic11C2314yes—
88C2×C4⋊Dic11C2318yes—
89C2×C4⋊Dic11C2314yes—
90C2×Dic11⋊C4—44no—
91C2×Dic11⋊C4C2318yes—
92C2×C4×Dic11—24no—
93C2×C4×Dic11—28no—
94C2×C4×Dic11C2318yes—
95C2×C4×Dic11C2314yes—
96#66945—232no—
97#66922—232no—
98C11×#95C2318yes—
99C11⋊#95C2314yes—
100C11⋊#95C2318yes—
101C11⋊#95C2318yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2314yes—
105C2×#2439—111nomaximal, Sylow
106C24×C11C2411yescharacteristic
107C23×D11—22no—
108C23×D11—22no—
109C23×D11—22no—
110C23×D11—22no—
111C23×D11—22no—
112C23×D11—22no—
113C23×D11C2×Q814yes—
114C23×D11C2412yes—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11C2×D414yes—
126C22×C4×C11C2×Q814yes—
127C22×C4×C11#4114yes—
128C22×C4×C11#4114yes—
129C22×C4×C11#4114yes—
130C22×C4×C11C2414yes—
131C22×C4×C11C2414yes—
132C22×C4×C11C2412yes—
133C22×C4×C11C2412yes—
134C22×C4×C11C2412yes—
135C22×Dic11—22no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—22no—
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×Dic11C2×D418yes—
149C22×Dic11C2×Q814yes—
150C22×Dic11C2412yes—
151C22×Dic11C2412yes—
152C22×Dic11C2414yes—
153C22×Dic11C2414yes—
154C22×Dic11C2412yes—
155C2×C4×D11—232no—
156C2×C4×D11—28no—
157C2×C4×D11—28no—
158C2×C4×D11C2×Q8116yescomplemented
159C2×Dic22—216no—
160C2×Dic22—216no—
161C2×Dic22—48no—
162C2×Dic22—432no—
163C11×C4⋊C4—28no—
164C11×C4⋊C4—28no—
165C11×C4⋊C4—216no—
166C42×C11—28no—
167(C2×D11)⋊C4—216no—
168(C2×D11)⋊C4—28no—
169(C2×D11)⋊C4—28no—
170(C2×D11)⋊C4—48no—
171C4⋊Dic11—216no—
172C4⋊Dic11—28no—
173C4⋊Dic11C2×D4116yes—
174Dic11⋊C4—48no—
175C4×Dic11—216no—
176C4×Dic11—28no—
177C22×C4⋊Q8—111no—
178C22×#117—111no—
179#2439—1116no—
180C2×#396—112no—
181C2×#393—112no—
182C2×#391—112no—
183C2×#389—111no—
184C2×#389D1111yescharacteristic, complemented
185C2×#387—112no—
186C2×#382—111no—
187C2×#380—111no—
188C2×C4×C22⋊C4—111no—
189C23×C11C22×D412yes—
190C23×C11C22×Q812yes—
191C23×C11C2×#4112yes—
192C23×C11C2×#4112yes—
193C23×C11C2×#4112yes—
194C23×C11H(5,𝔽2)12yes—
195C23×C112−1+412yes—
196C23×C11C2511yescharacteristic
197C22×D11—28no—
198C22×D11—28no—
199C22×D11—28no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—22no—
206C22×D11—44no—
207C22×D11—44no—
208C22×D11—44no—
209C22×D11—44no—
210C22×D11C22×Q814yes—
211C2×C4×C11—28no—
212C2×C4×C11—28no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—24no—
223C2×C4×C11—48no—
224C2×C4×C11—48no—
225C2×C4×C11C22⋊Q8116yes—
226C2×C4×C11C22×D414yes—
227C2×C4×C11C22×Q814yes—
228C2×C4×C11C2×#4114yes—
229C2×C4×C11C2×#4114yes—
230C2×C4×C11C2×#4114yes—
231C2×Dic11—28no—
232C2×Dic11—216no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—22no—
246C2×Dic11—48no—
247C2×Dic11—44no—
248C2×Dic11—44no—
249C2×Dic11C22×D418yes—
250C2×Dic11C22×Q814yes—
251C4×D11—232no—
252Dic22—432no—
253C23×Q8—112no—
254C24×C4—111no—
255C2×C4⋊Q8—118no—
256C2×C4⋊Q8—228no—
257C2×#117—118no—
258C2×#117—228no—
259C22×C4⋊C4—111no—
260C22×C4⋊C4—112no—
261C22×C4⋊C4—111no—
262C22×C4⋊C4—112no—
263C22×C4⋊C4C2×D1112yes—
264C22×C4⋊C4C2×D1111yescharacteristic
265C22×C4⋊C4C2×D1111yescharacteristic
266C22×C22⋊C4—111no—
267C22×C22⋊C4—112no—
268C22×C22⋊C4—111no—
269C22×C22⋊C4—112no—
270C22×C42—112no—
271C22×C42—111no—
272C22×C42C2×D1111yescharacteristic
273#396—1116no—
274#393—1116no—
275#391—1116no—
276#389—118no—
277#389C2×D1118yescomplemented
278#387—1116no—
279#382—118no—
280#380—118no—
281C4×C22⋊C4—118no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95—111no—
286C2×#95—111no—
287C2×#95—112no—
288C2×#95C2×D1112yes—
289C22×C11C2×C22⋊Q814yes—
290C22×C11#53314yes—
291C22×C11#54414yes—
292C22×C11#54614yes—
293C22×C11#54814yes—
294C22×C11#55514yes—
295C22×C11#55614yes—
296C22×C11C23×D411yescharacteristic
297C22×C11C23×Q811yescharacteristic
298C22×C11C22×#4111yescharacteristic
299C22×C11C22×#4111yescharacteristic
300C22×C11C22×#4111yescharacteristic
301C22×C11C2×H(5,𝔽2)11yescharacteristic
302C22×C11C2×2−1+411yescharacteristic
303C2×D11—24no—
304C2×D11—24no—
305C2×D11—24no—
306C2×D11—416no—
307C2×D11—42no—
308C2×D11—42no—
309C2×D11—42no—
310C2×D11—42no—
311C4×C11—24no—
312C4×C11—24no—
313C4×C11—44no—
314C4×C11—44no—
315C4×C11C2×C22⋊Q818yes—
316Dic11—24no—
317Dic11—28no—
318Dic11—44no—
319Dic11—42no—
320Dic11—42no—
321C25—111no—
322C22×Q8—118no—
323C22×Q8—228no—
324C22×Q8—228no—
325C22×Q8—444no—
326C23×C4—112no—
327C23×C4—111no—
328C23×C4—118no—
329C23×C4—114no—
330C23×C4—112no—
331C23×C4—111no—
332C23×C4—111no—
333C23×C4—224no—
334C23×C4—224no—
335C23×C4C22×D1112yes—
336C23×C4C22×D1112yes—
337C23×C4C22×D1111yescharacteristic
338C23×C4C22×D1111yescharacteristic
339C23×C4C22×D1111yescharacteristic
340C4⋊Q8—2232no—
341#117—2232no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—24no—
344C2×C4⋊C4—28no—
345C2×C4⋊C4—118no—
346C2×C4⋊C4—114no—
347C2×C4⋊C4—114no—
348C2×C4⋊C4—118no—
349C2×C4⋊C4—118no—
350C2×C4⋊C4—228no—
351C2×C4⋊C4—224no—
352C2×C4⋊C4—444no—
353C2×C4⋊C4C22×D1114yes—
354C2×C4⋊C4C22×D1114yes—
355C2×C4⋊C4C22×D1118yes—
356C2×C22⋊C4—118no—
357C2×C22⋊C4—114no—
358C2×C22⋊C4—114no—
359C2×C22⋊C4—118no—
360C2×C22⋊C4—228no—
361C2×C22⋊C4—224no—
362C2×C22⋊C4—224no—
363C2×C22⋊C4—444no—
364C2×C42—24no—
365C2×C42—118no—
366C2×C42—114no—
367C2×C42—228no—
368C2×C42—224no—
369C2×C42C22×D1114yes—
370#95—114no—
371#95—114no—
372#95—118no—
373#95—118no—
374#95—118no—
375#95—118no—
376#95C22×D1118yes—
377C2×C11#243918yescomplemented
378C2×C11C22×C22⋊Q811yescharacteristic
379C2×C11C2×#53311yescharacteristic
380C2×C11C2×#54411yescharacteristic
381C2×C11C2×#54611yescharacteristic
382C2×C11C2×#54811yescharacteristic
383C2×C11C2×#55511yescharacteristic
384C2×C11C2×#55611yescharacteristic
385D11—44no—
386C24—114no—
387C24—112no—
388C24—222no—
389C24—222no—
390C24—222no—
391C24—222no—
392C24—222no—
393C24—222no—
394C24C23×D1111yescharacteristic
395C2×Q8—2216no—
396C2×Q8—2216no—
397C2×Q8—448no—
398C2×Q8—4432no—
399C22×C4—22no—
400C22×C4—22no—
401C22×C4—22no—
402C22×C4—22no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—118no—
410C22×C4—114no—
411C22×C4—112no—
412C22×C4—114no—
413C22×C4—1116no—
414C22×C4—112no—
415C22×C4—112no—
416C22×C4—114no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—224no—
420C22×C4—224no—
421C22×C4—2232no—
422C22×C4—228no—
423C22×C4—228no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—224no—
427C22×C4—222no—
428C22×C4—222no—
429C22×C4—224no—
430C22×C4—224no—
431C22×C4—222no—
432C22×C4—222no—
433C22×C4#433914yes—
434C22×C4D4×D1114yes—
435C22×C4#434114yes—
436C22×C4Q8×D1114yes—
437C22×C4#434314yes—
438C22×C4C23×D1114yes—
439C22×C4C23×D1114yes—
440C22×C4C23×D1112yes—
441C22×C4C23×D1112yes—
442C22×C4C23×D1112yes—
443C4⋊C4—28no—
444C4⋊C4—28no—
445C4⋊C4—216no—
446C4⋊C4—1116no—
447C4⋊C4—2216no—
448C4⋊C4—228no—
449C4⋊C4—448no—
450C22⋊C4—2216no—
451C22⋊C4—228no—
452C22⋊C4—228no—
453C22⋊C4—448no—
454C42—28no—
455C42—2216no—
456C42—228no—
457C11C2×#243911yescharacteristic, complemented, Sylow
458C23—114no—
459C23—228no—
460C23—228no—
461C23—222no—
462C23—222no—
463C23—222no—
464C23—222no—
465C23—222no—
466C23—222no—
467C23—228no—
468C23—444no—
469C23—444no—
470C23—444no—
471C23—444no—
472C23C2×#433912yes—
473C23C2×D4×D1112yes—
474C23C2×#434112yes—
475C23C2×Q8×D1112yes—
476C23C2×#434312yes—
477C23#6704212yes—
478C23#6704312yes—
479C23C24×D1111yescharacteristic
480Q8—4432no—
481C2×C4—28no—
482C2×C4—28no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—22no—
486C2×C4—22no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
491C2×C4—24no—
492C2×C4—24no—
493C2×C4—48no—
494C2×C4—48no—
495C2×C4—118no—
496C2×C4—114no—
497C2×C4—228no—
498C2×C4—2216no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—2232no—
504C2×C4—222no—
505C2×C4—222no—
506C2×C4—224no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—222no—
512C2×C4—222no—
513C2×C4—444no—
514C2×C4—444no—
515C2×C4—448no—
516C2×C4#66949116yes—
517C2×C4C2×#433914yes—
518C2×C4C2×D4×D1114yes—
519C2×C4C2×#434114yes—
520C2×C4C2×Q8×D1114yes—
521C2×C4C2×#434314yes—
522C22—224no—
523C22—224no—
524C22—224no—
525C22—442no—
526C22—442no—
527C22—4416no—
528C22—442no—
529C22—442no—
530C22C2×#6694914yes—
531C22#1062309414yes—
532C22#1062311514yes—
533C22#1062312914yes—
534C22#1062316114yes—
535C22#1062322014yes—
536C22#1062325914yes—
537C22C22×#433911yescharacteristic
538C22C22×D4×D1111yescharacteristic
539C22C22×#434111yescharacteristic
540C22C22×Q8×D1111yescharacteristic
541C22C22×#434311yescharacteristic
542C22C2×#6704211yescharacteristic
543C22C2×#6704311yescharacteristic
544C4—24no—
545C4—24no—
546C4—44no—
547C4—44no—
548C4—228no—
549C4—224no—
550C4—442no—
551C4—442no—
552C4—444no—
553C4C2×#6694918yes—
554C2—444no—
555C2#1307230918yesdirect product factor
556C2C22×#6694911yescharacteristic
557C2C2×#1062325911yescharacteristic
558C2C2×#1062322011yescharacteristic
559C2C2×#1062316111yescharacteristic
560C2C2×#1062312911yescharacteristic
561C2C2×#1062309411yescharacteristic
562C2C2×#1062311511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#389D11
hypocenterC11C2×#2439
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#66922C2semidirect
3. #13072309C2direct (N × H)
6. C2×#10622259C2semidirect
7. C2×#10622586C2semidirect
8. C2×#10622594C2semidirect
9. C2×#10622590C2semidirect
12. C2×C11×#389C2semidirect
32. C2×#66922C22semidirect
33. C11×#389C22semidirect
43. #10622594C22semidirect
44. #10622590C22semidirect
45. #10622586C22semidirect
48. #10622259C22semidirect
62. C22×C4×D11Q8semidirect
158. C2×C4×D11C2×Q8semidirect
184. C2×#389D11semidirect
277. #389C2×D11semidirect
377. C2×C11#2439semidirect
457. C11C2×#2439semidirect
555. C2#13072309direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669222
C22×#669452
#130723092
C2×#106226072
C2×#106222862
C2×#106222592
C2×#106225862
C2×#106225942
C2×#106225902
C2×#106226002
C2×C4×(C2×D11)⋊C42
C2×C11×#3892
C2×#243911