Finite Group Databasebeta

← C2×#13072327 #14922263

Subgroups — C2×#13072327 #14922263

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×#66943C211yesmaximal, characteristic, complemented
2C22×#66945C211yesmaximal, characteristic
3#13072327C2116yesmaximal, direct product factor
4C2×#10622290C212yesmaximal
5C2×#10622607C212yesmaximal
6C2×#10622598C211yesmaximal, characteristic, complemented
7C2×#10622598C212yesmaximal, complemented
8C2×#10622266C212yesmaximal, complemented
9C2×#10622548C211yesmaximal, characteristic, complemented
10C2×#10622600C211yesmaximal, characteristic
11C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
12C2×C11×#389C211yesmaximal, characteristic, complemented
13C23×C4×D11C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C42×C11C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2212yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2212yes—
26C22×C4⋊Dic11C2212yes—
27C22×C4⋊Dic11C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2212yes—
31C2×#66945—28no—
32C2×#66945C2218yes—
33C2×#66943—28no—
34C2×#66943C2218yescomplemented
35C11×#389C2218yescomplemented
36C2×C11×#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622607C22116yes—
42#10622600C2218yes—
43#10622598C22116yescomplemented
44#10622598C2218yescomplemented
45C4×(C2×D11)⋊C4C2218yes—
46#10622548C2218yescomplemented
47#10622290C22116yes—
48#10622266C22116yescomplemented
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×D11Q818yes—
63C22×C4×D11C2314yes—
64C2×C11×C4⋊C4—28no—
65C2×C11×C4⋊C4—24no—
66C2×C11×C4⋊C4D418yes—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2318yes—
69C2×C11×C4⋊C4C2314yes—
70C2×C42×C11—24no—
71C2×C42×C11C2314yes—
72C2×(C2×D11)⋊C4—28no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—24no—
75C2×(C2×D11)⋊C4—44no—
76C2×(C2×D11)⋊C4C2318yes—
77C2×(C2×D11)⋊C4C2314yes—
78C2×(C2×D11)⋊C4C2314yes—
79C2×(C2×D11)⋊C4C2318yes—
80C2×C4⋊Dic11—28no—
81C2×C4⋊Dic11—24no—
82C2×C4⋊Dic11—24no—
83C2×C4⋊Dic11—28no—
84C2×C4⋊Dic11—44no—
85C2×C4⋊Dic11—44no—
86C2×C4⋊Dic11C2318yes—
87C2×C4⋊Dic11C2314yes—
88C2×C4⋊Dic11C2314yes—
89C2×C4⋊Dic11C2318yes—
90C2×C4⋊Dic11C2318yes—
91C2×C4⋊Dic11C2318yes—
92C2×Dic11⋊C4—28no—
93C2×Dic11⋊C4C2318yes—
94C2×C4×Dic11—24no—
95C2×C4×Dic11—28no—
96C2×C4×Dic11C2314yes—
97C2×C4×Dic11C2318yes—
98#66945—232no—
99#66943—232no—
100C11×#95C2318yes—
101C11⋊#95C2314yes—
102C11⋊#95C2318yes—
103C11⋊#95C2318yes—
104C11⋊#95C2314yes—
105C2×#2441—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—24no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11C2×D418yes—
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—22no—
137C22×Dic11—22no—
138C22×Dic11—24no—
139C22×Dic11—24no—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—22no—
144C22×Dic11—22no—
145C22×Dic11—22no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11—22no—
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×Q8116yes—
159C11×C4⋊C4—216no—
160C11×C4⋊C4—28no—
161C11×C4⋊C4C2×D4116yes—
162C42×C11—28no—
163(C2×D11)⋊C4—216no—
164(C2×D11)⋊C4—28no—
165(C2×D11)⋊C4—28no—
166(C2×D11)⋊C4—48no—
167C4⋊Dic11—216no—
168C4⋊Dic11—28no—
169C4⋊Dic11—28no—
170C4⋊Dic11—216no—
171C4⋊Dic11—48no—
172C4⋊Dic11—48no—
173Dic11⋊C4—216no—
174C4×Dic11—28no—
175C4×Dic11—216no—
176C22×#125—111no—
177C22×#117—111no—
178#2441—1116no—
179C2×#399—112no—
180C2×#396—112no—
181C2×#389—112no—
182C2×#389—111no—
183C2×#389D1111yescharacteristic, complemented
184C2×#387—112no—
185C2×#384—111no—
186C2×#380—111no—
187C2×C4×C22⋊C4—111no—
188C23×C11C22×D412yes—
189C23×C11C22×Q812yes—
190C23×C11C2×#4112yes—
191C23×C11C2×#4112yes—
192C23×C11C2×#4112yes—
193C23×C11H(5,𝔽2)12yes—
194C23×C112−1+412yes—
195C23×C11C2511yescharacteristic
196C22×D11—28no—
197C22×D11—28no—
198C22×D11—28no—
199C22×D11—22no—
200C22×D11—22no—
201C22×D11—22no—
202C22×D11—22no—
203C22×D11—22no—
204C22×D11—22no—
205C22×D11—44no—
206C22×D11—44no—
207C22×D11—44no—
208C22×D11—44no—
209C22×D11C22×Q814yes—
210C2×C4×C11—216no—
211C2×C4×C11—28no—
212C2×C4×C11—28no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—22no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—48no—
223C2×C4×C11C22⋊Q8116yes—
224C2×C4×C11C22×D418yes—
225C2×C4×C11C22×D414yes—
226C2×C4×C11C22×Q814yes—
227C2×C4×C11C2×#4114yes—
228C2×C4×C11C2×#4114yes—
229C2×C4×C11C2×#4114yes—
230C2×Dic11—28no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—24no—
236C2×Dic11—24no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—22no—
245C2×Dic11—44no—
246C2×Dic11—44no—
247C2×Dic11—48no—
248C2×Dic11—48no—
249C2×Dic11C22×Q814yes—
250C4×D11—232no—
251C24×C4—111no—
252C2×#125—118no—
253C2×#125—228no—
254C2×#117—118no—
255C2×#117—228no—
256C22×C4⋊C4—112no—
257C22×C4⋊C4—112no—
258C22×C4⋊C4—112no—
259C22×C4⋊C4—111no—
260C22×C4⋊C4—111no—
261C22×C4⋊C4—112no—
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#399—1116no—
274#396—1116no—
275#389—1116no—
276#389—118no—
277#389C2×D1118yescomplemented
278#387—1116no—
279#384—118no—
280#380—118no—
281C4×C22⋊C4—118no—
282C2×#95—112no—
283C2×#95—111no—
284C2×#95—111no—
285C2×#95—112no—
286C2×#95C2×D1112yes—
287C22×C11C2×C22⋊Q814yes—
288C22×C11#53314yes—
289C22×C11#54414yes—
290C22×C11#54714yes—
291C22×C11#55014yes—
292C22×C11#55214yes—
293C22×C11#55314yes—
294C22×C11C23×D411yescharacteristic
295C22×C11C23×Q811yescharacteristic
296C22×C11C22×#4111yescharacteristic
297C22×C11C22×#4111yescharacteristic
298C22×C11C22×#4111yescharacteristic
299C22×C11C2×H(5,𝔽2)11yescharacteristic
300C22×C11C2×2−1+411yescharacteristic
301C2×D11—24no—
302C2×D11—24no—
303C2×D11—24no—
304C2×D11—42no—
305C2×D11—416no—
306C2×D11—42no—
307C2×D11—42no—
308C2×D11—42no—
309C4×C11—28no—
310C4×C11—24no—
311C4×C11—24no—
312C4×C11—44no—
313C4×C11C2×C22⋊Q818yes—
314Dic11—24no—
315Dic11—42no—
316Dic11—42no—
317Dic11—44no—
318Dic11—44no—
319C25—111no—
320C23×C4—111no—
321C23×C4—118no—
322C23×C4—114no—
323C23×C4—112no—
324C23×C4—112no—
325C23×C4—111no—
326C23×C4—111no—
327C23×C4—224no—
328C23×C4—224no—
329C23×C4C22×D1112yes—
330C23×C4C22×D1112yes—
331C23×C4C22×D1111yescharacteristic
332C23×C4C22×D1111yescharacteristic
333C23×C4C22×D1111yescharacteristic
334#125—2232no—
335#117—2232no—
336C2×C4⋊C4—28no—
337C2×C4⋊C4—24no—
338C2×C4⋊C4—114no—
339C2×C4⋊C4—114no—
340C2×C4⋊C4—118no—
341C2×C4⋊C4—118no—
342C2×C4⋊C4—118no—
343C2×C4⋊C4—118no—
344C2×C4⋊C4—118no—
345C2×C4⋊C4—224no—
346C2×C4⋊C4—228no—
347C2×C4⋊C4—228no—
348C2×C4⋊C4—224no—
349C2×C4⋊C4—228no—
350C2×C4⋊C4—444no—
351C2×C4⋊C4—444no—
352C2×C4⋊C4D4418yes—
353C2×C4⋊C4C22×D1114yes—
354C2×C4⋊C4C22×D1118yes—
355C2×C4⋊C4C22×D1114yes—
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#95C22×D1118yes—
375C2×C11#244118yescomplemented
376C2×C11C22×C22⋊Q811yescharacteristic
377C2×C11C2×#53311yescharacteristic
378C2×C11C2×#54411yescharacteristic
379C2×C11C2×#54711yescharacteristic
380C2×C11C2×#55011yescharacteristic
381C2×C11C2×#55211yescharacteristic
382C2×C11C2×#55311yescharacteristic
383D11—44no—
384C24—114no—
385C24—112no—
386C24—222no—
387C24—222no—
388C24—222no—
389C24—222no—
390C24—222no—
391C24—222no—
392C24C23×D1111yescharacteristic
393C22×C4—22no—
394C22×C4—22no—
395C22×C4—24no—
396C22×C4—22no—
397C22×C4—24no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—114no—
403C22×C4—112no—
404C22×C4—1116no—
405C22×C4—112no—
406C22×C4—114no—
407C22×C4—112no—
408C22×C4—114no—
409C22×C4—222no—
410C22×C4—222no—
411C22×C4—2232no—
412C22×C4—228no—
413C22×C4—228no—
414C22×C4—224no—
415C22×C4—222no—
416C22×C4—222no—
417C22×C4—224no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—224no—
421C22×C4—224no—
422C22×C4—224no—
423C22×C4—224no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4C2×D4418yes—
427C22×C4C2×D4414yes—
428C22×C4#434114yes—
429C22×C4#434114yes—
430C22×C4Q8×D1114yes—
431C22×C4#434314yes—
432C22×C4C23×D1114yes—
433C22×C4C23×D1114yes—
434C22×C4C23×D1112yes—
435C22×C4C23×D1112yes—
436C22×C4C23×D1112yes—
437C4⋊C4—216no—
438C4⋊C4—28no—
439C4⋊C4—228no—
440C4⋊C4—2216no—
441C4⋊C4—2216no—
442C4⋊C4—228no—
443C4⋊C4—2216no—
444C4⋊C4—448no—
445C4⋊C4—448no—
446C4⋊C4C2×D44116yes—
447C22⋊C4—2216no—
448C22⋊C4—228no—
449C22⋊C4—228no—
450C22⋊C4—448no—
451C42—28no—
452C42—2216no—
453C42—228no—
454C11C2×#244111yescharacteristic, complemented, Sylow
455C23—114no—
456C23—228no—
457C23—228no—
458C23—222no—
459C23—222no—
460C23—222no—
461C23—222no—
462C23—222no—
463C23—222no—
464C23—228no—
465C23—444no—
466C23—444no—
467C23—444no—
468C23—444no—
469C23C22×D4412yes—
470C23C2×#434112yes—
471C23C2×#434112yes—
472C23C2×Q8×D1112yes—
473C23C2×#434312yes—
474C23#6704212yes—
475C23#6704312yes—
476C23C24×D1111yescharacteristic
477C2×C4—216no—
478C2×C4—28no—
479C2×C4—28no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—22no—
484C2×C4—22no—
485C2×C4—24no—
486C2×C4—24no—
487C2×C4—24no—
488C2×C4—24no—
489C2×C4—48no—
490C2×C4—114no—
491C2×C4—228no—
492C2×C4—222no—
493C2×C4—222no—
494C2×C4—2232no—
495C2×C4—224no—
496C2×C4—222no—
497C2×C4—222no—
498C2×C4—224no—
499C2×C4—222no—
500C2×C4—222no—
501C2×C4—224no—
502C2×C4—224no—
503C2×C4—224no—
504C2×C4—224no—
505C2×C4—222no—
506C2×C4—222no—
507C2×C4—444no—
508C2×C4—448no—
509C2×C4—444no—
510C2×C4—448no—
511C2×C4#66950116yes—
512C2×C4C22×D4418yes—
513C2×C4C22×D4414yes—
514C2×C4C2×#434114yes—
515C2×C4C2×#434114yes—
516C2×C4C2×Q8×D1114yes—
517C2×C4C2×#434314yes—
518C22—224no—
519C22—224no—
520C22—224no—
521C22—442no—
522C22—442no—
523C22—4416no—
524C22—442no—
525C22—442no—
526C22C2×#6695014yes—
527C22#1062308614yes—
528C22#1062310814yes—
529C22#1062314914yes—
530C22#1062317314yes—
531C22#1062322014yes—
532C22#1062325914yes—
533C22C23×D4411yescharacteristic
534C22C22×#434111yescharacteristic
535C22C22×#434111yescharacteristic
536C22C22×Q8×D1111yescharacteristic
537C22C22×#434311yescharacteristic
538C22C2×#6704211yescharacteristic
539C22C2×#6704311yescharacteristic
540C4—24no—
541C4—24no—
542C4—28no—
543C4—44no—
544C4—224no—
545C4—442no—
546C4—444no—
547C4—442no—
548C4—444no—
549C4C2×#6695018yes—
550C2—444no—
551C2#1307232718yesdirect product factor
552C2C22×#6695011yescharacteristic
553C2C2×#1062325911yescharacteristic
554C2C2×#1062322011yescharacteristic
555C2C2×#1062308611yescharacteristic
556C2C2×#1062310811yescharacteristic
557C2C2×#1062317311yescharacteristic
558C2C2×#1062314911yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#389D11
hypocenterC11C2×#2441
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
1. C22×#66943C2semidirect
3. #13072327C2direct (N × H)
6. C2×#10622598C2semidirect
7. C2×#10622598C2semidirect
8. C2×#10622266C2semidirect
9. C2×#10622548C2semidirect
12. C2×C11×#389C2semidirect
34. C2×#66943C22semidirect
35. C11×#389C22semidirect
43. #10622598C22semidirect
44. #10622598C22semidirect
46. #10622548C22semidirect
48. #10622266C22semidirect
183. C2×#389D11semidirect
277. #389C2×D11semidirect
375. C2×C11#2441semidirect
454. C11C2×#2441semidirect
551. C2#13072327direct (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×#669452
#130723272
C2×#106222902
C2×#106226072
C2×#106225982
C2×#106222662
C2×#106225482
C2×#106226002
C2×C4×(C2×D11)⋊C42
C2×C11×#3892
C2×#244111