Finite Group Databasebeta

← C2×#13073198 #14922907

Subgroups — C2×#13073198 #14922907

Order 2816.

2726 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66951C212yesmaximal, complemented
2#13073198C2116yesmaximal, direct product factor
3C2×#10622606C212yesmaximal, complemented
4C2×#10622607C212yesmaximal, complemented
5C2×#10622552C211yesmaximal, characteristic
6C2×#10622601C211yesmaximal, characteristic
7C2×#10622601C211yesmaximal, characteristic
8C2×#10622598C211yesmaximal, characteristic, complemented
9C2×#10622603C212yesmaximal, complemented
10C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
11C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
12C2×C11×#384C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C22×C11×C4⋊C4C2212yes—
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2212yes—
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×C4⋊Dic11C2212yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2211yescharacteristic
29C22×C4×Dic11C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2211yescharacteristic
32C2×#66951—216no—
33C2×#66951C22116yescomplemented
34C11×#384C2218yescomplemented
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39#10622607C22116yescomplemented
40#10622606C22116yescomplemented
41#10622603C22116yescomplemented
42#10622601C2218yes—
43#10622601C2218yes—
44#10622598C2218yescomplemented
45C4⋊C4×Dic11C2218yescomplemented
46#10622552C2218yes—
47C4×Dic11⋊C4C2218yescomplemented
48C24×D11C2312yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C22×D44—24no—
60C22×D44—24no—
61C22×D44—24no—
62C22×D44C2314yes—
63C2×C11×C4⋊C4—28no—
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4—44no—
67C2×C11×C4⋊C4C2318yes—
68C2×C11×C4⋊C4C2314yes—
69C2×C11×C4⋊C4C2314yes—
70C2×C11×C4⋊C4C2318yes—
71C2×C42×C11—24no—
72C2×C42×C11C2314yes—
73C2×(C2×D11)⋊C4—28no—
74C2×(C2×D11)⋊C4—28no—
75C2×(C2×D11)⋊C4—28no—
76C2×(C2×D11)⋊C4—28no—
77C2×(C2×D11)⋊C4—44no—
78C2×(C2×D11)⋊C4—44no—
79C2×(C2×D11)⋊C4C2318yes—
80C2×(C2×D11)⋊C4C2318yes—
81C2×(C2×D11)⋊C4C2318yes—
82C2×(C2×D11)⋊C4C2318yes—
83C2×(C2×D11)⋊C4C2318yes—
84C2×(C2×D11)⋊C4C2318yes—
85C2×C4⋊Dic11—24no—
86C2×C4⋊Dic11—28no—
87C2×C4⋊Dic11C2318yes—
88C2×C4⋊Dic11C2314yes—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4D418yescomplemented
91C2×Dic11⋊C4C2314yes—
92C2×Dic11⋊C4C2314yes—
93C2×C4×Dic11—24no—
94C2×C4×Dic11—24no—
95C2×C4×Dic11—28no—
96C2×C4×Dic11C2318yes—
97C2×C4×Dic11C2314yes—
98C2×C4×Dic11C2314yes—
99#66951—264no—
100C11⋊#95C2314yes—
101C11⋊#95C2314yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C2×#2512—111nomaximal, Sylow
105C24×C11C2411yescharacteristic
106C23×D11—24no—
107C23×D11—24no—
108C23×D11—24no—
109C23×D11—24no—
110C23×D11—24no—
111C23×D11—24no—
112C23×D11—24no—
113C23×D11C2414yes—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11—22no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11—24no—
120C22×C4×C11—24no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11C2×D414yes—
125C22×C4×C11#4114yes—
126C22×C4×C11#4114yes—
127C22×C4×C11#4114yes—
128C22×C4×C11#4114yes—
129C22×C4×C11C2414yes—
130C22×C4×C11C2414yes—
131C22×C4×C11C2412yes—
132C22×C4×C11C2412yes—
133C22×C4×C11C2412yes—
134C22×Dic11—24no—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—22no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11C2×D414yes—
148C22×Dic11C2×D414yes—
149C22×Dic11C2412yes—
150C22×Dic11C2412yes—
151C22×Dic11C2414yes—
152C22×Dic11C2412yes—
153C22×Dic11C2412yes—
154C2×D44—28no—
155C2×D44—28no—
156C2×D44—28no—
157C2×D44—416no—
158C11×C4⋊C4—216no—
159C11×C4⋊C4—28no—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—48no—
162C42×C11—28no—
163(C2×D11)⋊C4—216no—
164(C2×D11)⋊C4—216no—
165(C2×D11)⋊C4—216no—
166(C2×D11)⋊C4—216no—
167(C2×D11)⋊C4—48no—
168(C2×D11)⋊C4—48no—
169C4⋊Dic11—216no—
170C4⋊Dic11—28no—
171Dic11⋊C4—28no—
172Dic11⋊C4C2×D4116yescomplemented
173C4×Dic11—216no—
174C4×Dic11—28no—
175C4×Dic11—28no—
176C22×#126—112no—
177#2512—1116no—
178C2×#397—112no—
179C2×#396—112no—
180C2×#390—111no—
181C2×#390—111no—
182C2×#390—111no—
183C2×#389—111no—
184C2×#388—112no—
185C2×#384D1111yescharacteristic, complemented
186C2×C4×C4⋊C4—111no—
187C2×C4×C4⋊C4—111no—
188C23×C11C22×D412yes—
189C23×C11C2×#4112yes—
190C23×C11C2×#4112yes—
191C23×C11C2×#4112yes—
192C23×C11C2×#4112yes—
193C23×C11H(5,𝔽2)12yes—
194C23×C112−1+412yes—
195C23×C11C2511yescharacteristic
196C22×D11—24no—
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×D11—48no—
208C22×D11—48no—
209C22×D11—48no—
210C2×C4×C11—28no—
211C2×C4×C11—28no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—22no—
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×C11#126116yescomplemented
225C2×C4×C11C22×D414yes—
226C2×C4×C11C2×#4114yes—
227C2×C4×C11C2×#4114yes—
228C2×C4×C11C2×#4114yes—
229C2×C4×C11C2×#4114yes—
230C2×Dic11—28no—
231C2×Dic11—28no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—22no—
236C2×Dic11—24no—
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—22no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—48no—
246C2×Dic11—44no—
247C2×Dic11—44no—
248C2×Dic11C22×D414yes—
249C2×Dic11C22×D414yes—
250D44—416no—
251C23×D4—111no—
252C2×#126—1116no—
253C2×#126—2216no—
254C22×C4⋊C4—111no—
255C22×C4⋊C4—111no—
256C22×C4⋊C4—112no—
257C22×C4⋊C4—111no—
258C22×C4⋊C4C2×D1112yes—
259C22×C4⋊C4C2×D1111yescharacteristic
260C22×C4⋊C4C2×D1111yescharacteristic
261C22×C4⋊C4C2×D1112yes—
262C22×C22⋊C4—112no—
263C22×C22⋊C4—112no—
264C22×C22⋊C4—112no—
265C22×C22⋊C4—112no—
266C22×C22⋊C4—112no—
267C22×C22⋊C4—112no—
268C22×C42—112no—
269C22×C42—111no—
270C22×C42—111no—
271C22×C42C2×D1111yescharacteristic
272#397—1116no—
273#396—1116no—
274#390—118no—
275#390—118no—
276#390—118no—
277#389—118no—
278#388—1116no—
279#384C2×D1118yescomplemented
280C4×C4⋊C4—118no—
281C4×C4⋊C4—118no—
282C2×#95—112no—
283C2×#95—111no—
284C2×#95—112no—
285C2×#95—111no—
286C22×C11C2×#12614yes—
287C22×C11#53214yes—
288C22×C11#54214yes—
289C22×C11#54714yes—
290C22×C11#55014yes—
291C22×C11#55314yes—
292C22×C11#55614yes—
293C22×C11C23×D411yescharacteristic
294C22×C11C22×#4111yescharacteristic
295C22×C11C22×#4111yescharacteristic
296C22×C11C22×#4111yescharacteristic
297C22×C11C22×#4111yescharacteristic
298C22×C11C2×H(5,𝔽2)11yescharacteristic
299C22×C11C2×2−1+411yescharacteristic
300C2×D11—44no—
301C2×D11—44no—
302C2×D11—44no—
303C2×D11—44no—
304C2×D11—44no—
305C2×D11—44no—
306C2×D11—44no—
307C2×D11—816no—
308C4×C11—24no—
309C4×C11—24no—
310C4×C11—44no—
311C4×C11—44no—
312C4×C11C2×#12618yescomplemented
313Dic11—24no—
314Dic11—24no—
315Dic11—44no—
316Dic11—42no—
317Dic11—42no—
318C25—112no—
319C22×D4—114no—
320C22×D4—224no—
321C22×D4—224no—
322C22×D4—224no—
323C23×C4—111no—
324C23×C4—111no—
325C23×C4—112no—
326C23×C4—111no—
327C23×C4—111no—
328C23×C4C22×D1112yes—
329C23×C4C22×D1112yes—
330C23×C4C22×D1111yescharacteristic
331C23×C4C22×D1111yescharacteristic
332C23×C4C22×D1111yescharacteristic
333#126—2264no—
334C2×C4⋊C4—28no—
335C2×C4⋊C4—24no—
336C2×C4⋊C4—24no—
337C2×C4⋊C4—44no—
338C2×C4⋊C4—118no—
339C2×C4⋊C4—114no—
340C2×C4⋊C4—118no—
341C2×C4⋊C4—114no—
342C2×C4⋊C4—114no—
343C2×C4⋊C4—228no—
344C2×C4⋊C4—224no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4C22×D1118yes—
347C2×C4⋊C4C22×D1114yes—
348C2×C4⋊C4C22×D1114yes—
349C2×C4⋊C4C22×D1118yes—
350C2×C22⋊C4—118no—
351C2×C22⋊C4—118no—
352C2×C22⋊C4—118no—
353C2×C22⋊C4—118no—
354C2×C22⋊C4—118no—
355C2×C22⋊C4—118no—
356C2×C22⋊C4—228no—
357C2×C22⋊C4—228no—
358C2×C22⋊C4—228no—
359C2×C22⋊C4—228no—
360C2×C22⋊C4—444no—
361C2×C22⋊C4—444no—
362C2×C42—24no—
363C2×C42—118no—
364C2×C42—114no—
365C2×C42—114no—
366C2×C42—228no—
367C2×C42—224no—
368C2×C42—224no—
369C2×C42C22×D1114yes—
370#95—114no—
371#95—118no—
372#95—114no—
373#95—118no—
374C2×C11#251218yescomplemented
375C2×C11C22×#12611yescharacteristic
376C2×C11C2×#53211yescharacteristic
377C2×C11C2×#54211yescharacteristic
378C2×C11C2×#54711yescharacteristic
379C2×C11C2×#55011yescharacteristic
380C2×C11C2×#55311yescharacteristic
381C2×C11C2×#55611yescharacteristic
382D11—84no—
383C24—114no—
384C24—224no—
385C24—224no—
386C24—224no—
387C24—224no—
388C24—224no—
389C24—224no—
390C24—224no—
391C24C23×D1111yescharacteristic
392C2×D4—228no—
393C2×D4—228no—
394C2×D4—228no—
395C2×D4—4416no—
396C22×C4—22no—
397C22×C4—22no—
398C22×C4—22no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—24no—
403C22×C4—24no—
404C22×C4—24no—
405C22×C4—24no—
406C22×C4—114no—
407C22×C4—114no—
408C22×C4—112no—
409C22×C4—112no—
410C22×C4—112no—
411C22×C4—112no—
412C22×C4—114no—
413C22×C4—222no—
414C22×C4—222no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—222no—
418C22×C4—224no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—224no—
423C22×C4—224no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4#433914yes—
427C22×C4D4×D1114yes—
428C22×C4#434114yes—
429C22×C4#434314yes—
430C22×C4#434314yes—
431C22×C4C23×D1114yes—
432C22×C4C23×D1114yes—
433C22×C4C23×D1112yes—
434C22×C4C23×D1112yes—
435C22×C4C23×D1112yes—
436C4⋊C4—216no—
437C4⋊C4—28no—
438C4⋊C4—28no—
439C4⋊C4—48no—
440C4⋊C4—1116no—
441C4⋊C4—2216no—
442C4⋊C4—228no—
443C4⋊C4—228no—
444C22⋊C4—2216no—
445C22⋊C4—2216no—
446C22⋊C4—2216no—
447C22⋊C4—2216no—
448C22⋊C4—448no—
449C22⋊C4—448no—
450C42—28no—
451C42—2216no—
452C42—228no—
453C42—228no—
454C11C2×#251211yescharacteristic, complemented, Sylow
455C23—224no—
456C23—224no—
457C23—224no—
458C23—224no—
459C23—224no—
460C23—224no—
461C23—224no—
462C23—448no—
463C23—448no—
464C23—448no—
465C23—448no—
466C23—448no—
467C23—448no—
468C23—448no—
469C23C2×#433912yes—
470C23C2×D4×D1112yes—
471C23C2×#434112yes—
472C23#6703712yes—
473C23C2×#434312yes—
474C23C2×#434312yes—
475C23#6704012yes—
476C23C24×D1111yescharacteristic
477D4—4416no—
478C2×C4—28no—
479C2×C4—28no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—22no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—48no—
491C2×C4—48no—
492C2×C4—114no—
493C2×C4—114no—
494C2×C4—228no—
495C2×C4—228no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—222no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—224no—
502C2×C4—222no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—224no—
506C2×C4—222no—
507C2×C4—224no—
508C2×C4—222no—
509C2×C4—448no—
510C2×C4—444no—
511C2×C4—444no—
512C2×C4#66951116yescomplemented
513C2×C4C2×#433914yes—
514C2×C4C2×D4×D1114yes—
515C2×C4C2×#434114yes—
516C2×C4C2×#434314yes—
517C2×C4C2×#434314yes—
518C22—444no—
519C22—444no—
520C22—444no—
521C22—444no—
522C22—444no—
523C22—444no—
524C22—444no—
525C22—8816no—
526C22#1062303814yes—
527C22C2×#6695114yes—
528C22#1062304514yes—
529C22#1062324914yes—
530C22#1062325614yes—
531C22#1062326314yes—
532C22#1062326414yes—
533C22C22×#433911yescharacteristic
534C22C22×D4×D1111yescharacteristic
535C22C22×#434111yescharacteristic
536C22C2×#6703711yescharacteristic
537C22C22×#434311yescharacteristic
538C22C22×#434311yescharacteristic
539C22C2×#6704011yescharacteristic
540C4—24no—
541C4—24no—
542C4—44no—
543C4—44no—
544C4—224no—
545C4—224no—
546C4—442no—
547C4—444no—
548C4—442no—
549C4C2×#6695118yescomplemented
550C2—884no—
551C2#1307319818yesdirect product factor
552C2C22×#6695111yescharacteristic
553C2C2×#1062325611yescharacteristic
554C2C2×#1062326411yescharacteristic
555C2C2×#1062303811yescharacteristic
556C2C2×#1062324911yescharacteristic
557C2C2×#1062304511yescharacteristic
558C2C2×#1062326311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#384C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#384D11
hypocenterC11C2×#2512
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#384

Complements

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

NH ≅ G/Ntype
1. C22×#66951C2semidirect
2. #13073198C2direct (N × H)
3. C2×#10622606C2semidirect
4. C2×#10622607C2semidirect
8. C2×#10622598C2semidirect
9. C2×#10622603C2semidirect
10. C2×C4⋊C4×Dic11C2semidirect
11. C2×C4×Dic11⋊C4C2semidirect
12. C2×C11×#384C2semidirect
33. C2×#66951C22semidirect
34. C11×#384C22semidirect
39. #10622607C22semidirect
40. #10622606C22semidirect
41. #10622603C22semidirect
44. #10622598C22semidirect
45. C4⋊C4×Dic11C22semidirect
47. C4×Dic11⋊C4C22semidirect
90. C2×Dic11⋊C4D4semidirect
172. Dic11⋊C4C2×D4semidirect
185. C2×#384D11semidirect
224. C2×C4×C11#126semidirect
279. #384C2×D11semidirect
312. C4×C11C2×#126semidirect
374. C2×C11#2512semidirect
454. C11C2×#2512semidirect
512. C2×C4#66951semidirect
549. C4C2×#66951semidirect
551. C2#13073198direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669512
#130731982
C2×#106226062
C2×#106226072
C2×#106225522
C2×#106226012
C2×#106225982
C2×#106226032
C2×C4⋊C4×Dic112
C2×C4×Dic11⋊C42
C2×C11×#3842
C2×#251211