Finite Group Databasebeta

← C2×#13072301 #14922116

Subgroups — C2×#13072301 #14922116

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×#66941C211yesmaximal, characteristic, complemented
2#13072301C2116yesmaximal, direct product factor
3C2×#10622561C212yesmaximal
4C2×#10622560C212yesmaximal
5C2×#10622542C212yesmaximal, complemented
6C2×#10622598C211yesmaximal, characteristic, complemented
7C2×#10622586C211yesmaximal, characteristic, complemented
8C2×#10622546C212yesmaximal, complemented
9C2×#10622590C211yesmaximal, characteristic, complemented
10C2×#10622825C211yesmaximal, characteristic
11C2×C4×C22⋊Dic11C211yesmaximal, characteristic
12C22×C11×#117C211yesmaximal, characteristic
13C24×C4×C11C2211yescharacteristic
14C23×Dic22C2212yes—
15C2×C11×#117—28no—
16C2×C11×#117C2218yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C42×C11C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2212yes—
24C22×C4⋊Dic11C2211yescharacteristic
25C22×C4⋊Dic11C2211yescharacteristic
26C22×C4⋊Dic11C2212yes—
27C22×Dic11⋊C4C2212yes—
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×#66941—28no—
32C2×#66941C2218yescomplemented
33#10622825C2218yes—
34C4×C22⋊Dic11C2218yes—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622598C2218yescomplemented
43#10622590C2218yescomplemented
44#10622586C2218yescomplemented
45#10622561C22116yes—
46#10622560C22116yes—
47#10622546C22116yescomplemented
48#10622542C22116yescomplemented
49C25×C11C2311yescharacteristic
50C23×C4×C11—24no—
51C23×C4×C11—24no—
52C23×C4×C11Q818yescomplemented
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
64C22×Dic22—28no—
65C22×Dic22—28no—
66C22×Dic22—44no—
67C22×Dic22C2318yes—
68C11×#117—232no—
69C2×C11×C4⋊C4—24no—
70C2×C11×C4⋊C4D418yes—
71C2×C11×C4⋊C4C2314yes—
72C2×C11×C4⋊C4C2314yes—
73C2×C11×C22⋊C4—28no—
74C2×C11×C22⋊C4C2318yes—
75C2×C42×C11—28no—
76C2×C42×C11C2318yes—
77C2×C22⋊Dic11—24no—
78C2×C22⋊Dic11—24no—
79C2×C22⋊Dic11—44no—
80C2×C22⋊Dic11C2314yes—
81C2×C22⋊Dic11C2314yes—
82C2×C22⋊Dic11C2318yes—
83C2×C4⋊Dic11—24no—
84C2×C4⋊Dic11—24no—
85C2×C4⋊Dic11—44no—
86C2×C4⋊Dic11C2314yes—
87C2×C4⋊Dic11C2314yes—
88C2×C4⋊Dic11C2318yes—
89C2×Dic11⋊C4—28no—
90C2×Dic11⋊C4—28no—
91C2×Dic11⋊C4C2318yes—
92C2×Dic11⋊C4C2318yes—
93C2×C4×Dic11—24no—
94C2×C4×Dic11—24no—
95C2×C4×Dic11C2314yes—
96C2×C4×Dic11C2314yes—
97#66941—232no—
98C11⋊#95C2314yes—
99C11⋊#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2318yes—
102C11⋊#95C2314yes—
103C11⋊#95C2318yes—
104C11⋊#95C2318yes—
105C2×#2439—111nomaximal, Sylow
106C24×C11—22no—
107C24×C11—22no—
108C24×C11—22no—
109C24×C11—22no—
110C24×C11—22no—
111C24×C11—22no—
112C24×C11C2×Q814yes—
113C24×C11C2412yes—
114C24×C11C2411yescharacteristic
115C22×C4×C11—22no—
116C22×C4×C11—24no—
117C22×C4×C11—22no—
118C22×C4×C11—24no—
119C22×C4×C11—232no—
120C22×C4×C11—28no—
121C22×C4×C11—28no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—24no—
125C22×C4×C11C2×D418yes—
126C22×C4×C11C2×D414yes—
127C22×C4×C11C2×Q814yes—
128C22×C4×C11C2×Q814yes—
129C22×C4×C11C2×Q8116yescomplemented
130C22×C4×C11#4114yes—
131C22×C4×C11C2414yes—
132C22×C4×C11C2414yes—
133C22×C4×C11C2412yes—
134C22×C4×C11C2412yes—
135C22×Dic11—22no—
136C22×Dic11—22no—
137C22×Dic11—24no—
138C22×Dic11—22no—
139C22×Dic11—22no—
140C22×Dic11—24no—
141C22×Dic11—24no—
142C22×Dic11—22no—
143C22×Dic11—22no—
144C22×Dic11—24no—
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11—24no—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11#4114yes—
152C22×Dic11#4114yes—
153C22×Dic11C2412yes—
154C22×Dic11C2412yes—
155C22×Dic11C2414yes—
156C22×Dic11C2414yes—
157C22×Dic11C2412yes—
158C22×Dic11C2412yes—
159C2×Dic22—216no—
160C2×Dic22—216no—
161C2×Dic22—48no—
162C2×Dic22—432no—
163C11×C4⋊C4—28no—
164C11×C4⋊C4C2×D4116yes—
165C11×C22⋊C4—216no—
166C42×C11—216no—
167C22⋊Dic11—28no—
168C22⋊Dic11—28no—
169C22⋊Dic11—48no—
170C4⋊Dic11—28no—
171C4⋊Dic11—28no—
172C4⋊Dic11—48no—
173Dic11⋊C4—216no—
174Dic11⋊C4—216no—
175C4×Dic11—28no—
176C4×Dic11—28no—
177C22×C4⋊Q8—111no—
178C22×#117D1111yescharacteristic
179#2439—1116no—
180C2×#396—112no—
181C2×#393—112no—
182C2×#391—112no—
183C2×#389—111no—
184C2×#389—111no—
185C2×#387—112no—
186C2×#382—111no—
187C2×#380—111no—
188C2×C4×C22⋊C4—111no—
189C23×C11—28no—
190C23×C11—28no—
191C23×C11—28no—
192C23×C11—22no—
193C23×C11—22no—
194C23×C11—22no—
195C23×C11—22no—
196C23×C11—22no—
197C23×C11—22no—
198C23×C11—44no—
199C23×C11—44no—
200C23×C11—44no—
201C23×C11—44no—
202C23×C11C22×D412yes—
203C23×C11C22×Q814yes—
204C23×C11C22×Q812yes—
205C23×C11C2×#4112yes—
206C23×C11C2×#4112yes—
207C23×C11C2×#4112yes—
208C23×C11H(5,𝔽2)12yes—
209C23×C112−1+412yes—
210C23×C11C2511yescharacteristic
211C2×C4×C11—28no—
212C2×C4×C11—216no—
213C2×C4×C11—22no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—232no—
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—24no—
221C2×C4×C11—48no—
222C2×C4×C11C22⋊Q8116yes—
223C2×C4×C11C22×D418yes—
224C2×C4×C11C22×D414yes—
225C2×C4×C11C22×Q814yes—
226C2×C4×C11C22×Q814yes—
227C2×C4×C11C2×#4114yes—
228C2×Dic11—28no—
229C2×Dic11—28no—
230C2×Dic11—22no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—22no—
234C2×Dic11—24no—
235C2×Dic11—22no—
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—24no—
239C2×Dic11—22no—
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—22no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—22no—
246C2×Dic11—48no—
247C2×Dic11—44no—
248C2×Dic11—48no—
249C2×Dic11—44no—
250C2×Dic11C2×#4114yes—
251C2×Dic11C2×#4114yes—
252Dic22—432no—
253C23×Q8—112no—
254C24×C4C2×D1111yescharacteristic
255C2×C4⋊Q8—118no—
256C2×C4⋊Q8—228no—
257C2×#117—28no—
258C2×#117C2×D1118yes—
259C22×C4⋊C4—112no—
260C22×C4⋊C4—112no—
261C22×C4⋊C4—111no—
262C22×C4⋊C4—111no—
263C22×C4⋊C4—112no—
264C22×C4⋊C4C2×D1111yescharacteristic
265C22×C4⋊C4C2×D1111yescharacteristic
266C22×C22⋊C4—111no—
267C22×C22⋊C4—111no—
268C22×C22⋊C4—112no—
269C22×C22⋊C4C2×D1112yes—
270C22×C42—111no—
271C22×C42—111no—
272C22×C42C2×D1112yes—
273#396—1116no—
274#393—1116no—
275#391—1116no—
276#389—118no—
277#389—118no—
278#387—1116no—
279#382—118no—
280#380—118no—
281C4×C22⋊C4—118no—
282C2×#95—112no—
283C2×#95—112no—
284C2×#95—112no—
285C2×#95—112no—
286C2×#95—111no—
287C2×#95—111no—
288C2×#95—112no—
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#53314yes—
299C22×C11#54414yes—
300C22×C11#54614yes—
301C22×C11#54814yes—
302C22×C11#55514yes—
303C22×C11#55614yes—
304C22×C11C23×D411yescharacteristic
305C22×C11C23×Q811yescharacteristic
306C22×C11C22×#4111yescharacteristic
307C22×C11C22×#4111yescharacteristic
308C22×C11C22×#4111yescharacteristic
309C22×C11C2×H(5,𝔽2)11yescharacteristic
310C22×C11C2×2−1+411yescharacteristic
311C4×C11—24no—
312C4×C11—28no—
313C4×C11—44no—
314C4×C11C2×C22⋊Q818yes—
315Dic11—24no—
316Dic11—24no—
317Dic11—44no—
318Dic11—42no—
319Dic11—44no—
320Dic11—42no—
321C25C22×D1111yescharacteristic
322C22×Q8—118no—
323C22×Q8—228no—
324C22×Q8—228no—
325C22×Q8—444no—
326C23×C4—24no—
327C23×C4—24no—
328C23×C4—111no—
329C23×C4—111no—
330C23×C4—112no—
331C23×C4—112no—
332C23×C4—111no—
333C23×C4—111no—
334C23×C4Dic2218yescomplemented
335C23×C4C22×D1112yes—
336C23×C4C22×D1111yescharacteristic
337C23×C4C22×D1114yes—
338C23×C4C22×D1112yes—
339C23×C4C22×D1111yescharacteristic
340C4⋊Q8—2232no—
341#117—232no—
342C2×C4⋊C4—24no—
343C2×C4⋊C4—114no—
344C2×C4⋊C4—118no—
345C2×C4⋊C4—114no—
346C2×C4⋊C4—118no—
347C2×C4⋊C4—118no—
348C2×C4⋊C4—228no—
349C2×C4⋊C4—224no—
350C2×C4⋊C4—228no—
351C2×C4⋊C4—224no—
352C2×C4⋊C4—444no—
353C2×C4⋊C4C22⋊D1118yes—
354C2×C4⋊C4C22×D1114yes—
355C2×C4⋊C4C22×D1114yes—
356C2×C22⋊C4—28no—
357C2×C22⋊C4—114no—
358C2×C22⋊C4—114no—
359C2×C22⋊C4—118no—
360C2×C22⋊C4—224no—
361C2×C22⋊C4—224no—
362C2×C22⋊C4—444no—
363C2×C22⋊C4C22×D1118yes—
364C2×C42—28no—
365C2×C42—114no—
366C2×C42—114no—
367C2×C42—224no—
368C2×C42—224no—
369C2×C42C22×D1118yes—
370#95—114no—
371#95—114no—
372#95—118no—
373#95—118no—
374#95—118no—
375#95—118no—
376#95—118no—
377C2×C11—44no—
378C2×C11#243918yescomplemented
379C2×C11C22×C22⋊Q811yescharacteristic
380C2×C11C2×#53311yescharacteristic
381C2×C11C2×#54411yescharacteristic
382C2×C11C2×#54611yescharacteristic
383C2×C11C2×#54811yescharacteristic
384C2×C11C2×#55511yescharacteristic
385C2×C11C2×#55611yescharacteristic
386C24—22no—
387C24—22no—
388C24—22no—
389C24—22no—
390C24—22no—
391C24—22no—
392C24C2×Dic2214yes—
393C24C23×D1112yes—
394C24C23×D1111yescharacteristic
395C2×Q8—2216no—
396C2×Q8—2216no—
397C2×Q8—448no—
398C2×Q8—4432no—
399C22×C4—22no—
400C22×C4—24no—
401C22×C4—24no—
402C22×C4—22no—
403C22×C4—232no—
404C22×C4—28no—
405C22×C4—28no—
406C22×C4—24no—
407C22×C4—24no—
408C22×C4—24no—
409C22×C4—114no—
410C22×C4—114no—
411C22×C4—112no—
412C22×C4—112no—
413C22×C4—112no—
414C22×C4—112no—
415C22×C4—114no—
416C22×C4—114no—
417C22×C4—222no—
418C22×C4—222no—
419C22×C4—222no—
420C22×C4—222no—
421C22×C4—222no—
422C22×C4—222no—
423C22×C4—224no—
424C22×C4—222no—
425C22×C4—222no—
426C22×C4—224no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—224no—
430C22×C4—222no—
431C22×C4—222no—
432C22×C4—224no—
433C22×C4C2×Dic2214yes—
434C22×C4C2×Dic2214yes—
435C22×C4C2×Dic22116yescomplemented
436C22×C4#433914yes—
437C22×C4C2×C22⋊D1118yes—
438C22×C4C2×C22⋊D1114yes—
439C22×C4C23×D1114yes—
440C22×C4C23×D1112yes—
441C22×C4C23×D1114yes—
442C22×C4C23×D1112yes—
443C4⋊C4—28no—
444C4⋊C4—2216no—
445C4⋊C4—228no—
446C4⋊C4—2216no—
447C4⋊C4—228no—
448C4⋊C4—448no—
449C4⋊C4C2×C22⋊D11116yes—
450C22⋊C4—216no—
451C22⋊C4—228no—
452C22⋊C4—228no—
453C22⋊C4—448no—
454C42—216no—
455C42—228no—
456C42—228no—
457C11C2×#243911yescharacteristic, complemented, Sylow
458C23—28no—
459C23—28no—
460C23—28no—
461C23—22no—
462C23—22no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—44no—
468C23—44no—
469C23—44no—
470C23—44no—
471C23C22×Dic2214yes—
472C23C22×Dic2212yes—
473C23C2×#433912yes—
474C23#41×D1112yes—
475C23#41×D1112yes—
476C23#6704212yes—
477C23#6704312yes—
478C23C22×C22⋊D1112yes—
479C23C24×D1111yescharacteristic
480Q8—4432no—
481C2×C4—28no—
482C2×C4—216no—
483C2×C4—22no—
484C2×C4—24no—
485C2×C4—24no—
486C2×C4—22no—
487C2×C4—232no—
488C2×C4—24no—
489C2×C4—24no—
490C2×C4—24no—
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—222no—
502C2×C4—224no—
503C2×C4—222no—
504C2×C4—222no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—224no—
512C2×C4—444no—
513C2×C4—448no—
514C2×C4—444no—
515C2×C4—448no—
516C2×C4#66977116yes—
517C2×C4C22×Dic2214yes—
518C2×C4C22×Dic2214yes—
519C2×C4C2×#433914yes—
520C2×C4C22×C22⋊D1118yes—
521C2×C4C22×C22⋊D1114yes—
522C22—24no—
523C22—24no—
524C22—24no—
525C22—42no—
526C22—42no—
527C22—416no—
528C22—42no—
529C22—42no—
530C22#1062304814yes—
531C22#1062305014yes—
532C22#1062306314yes—
533C22#1062306414yes—
534C22C2×#6697714yes—
535C22#1062336014yes—
536C22#1062336214yes—
537C22C23×Dic2211yescharacteristic
538C22C22×#433911yescharacteristic
539C22C2×#41×D1111yescharacteristic
540C22C2×#41×D1111yescharacteristic
541C22C2×#6704211yescharacteristic
542C22C2×#6704311yescharacteristic
543C22C23×C22⋊D1111yescharacteristic
544C4—28no—
545C4—24no—
546C4—44no—
547C4—224no—
548C4—224no—
549C4—442no—
550C4—444no—
551C4—442no—
552C4—444no—
553C4C2×#6697718yes—
554C2—44no—
555C2#1307230118yesdirect product factor
556C2C22×#6697711yescharacteristic
557C2C2×#1062304811yescharacteristic
558C2C2×#1062305011yescharacteristic
559C2C2×#1062336011yescharacteristic
560C2C2×#1062336211yescharacteristic
561C2C2×#1062306311yescharacteristic
562C2C2×#1062306411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#117C2
socleC24×C11C24
prime radicalC25×C11C23
hypercenterC22×#117D11
hypocenterC11C2×#2439
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#117

Complements

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

NH ≅ G/Ntype
1. C22×#66941C2semidirect
2. #13072301C2direct (N × H)
5. C2×#10622542C2semidirect
6. C2×#10622598C2semidirect
7. C2×#10622586C2semidirect
8. C2×#10622546C2semidirect
9. C2×#10622590C2semidirect
32. C2×#66941C22semidirect
42. #10622598C22semidirect
43. #10622590C22semidirect
44. #10622586C22semidirect
47. #10622546C22semidirect
48. #10622542C22semidirect
52. C23×C4×C11Q8semidirect
129. C22×C4×C11C2×Q8semidirect
334. C23×C4Dic22semidirect
378. C2×C11#2439semidirect
435. C22×C4C2×Dic22semidirect
457. C11C2×#2439semidirect
555. C2#13072301direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669412
#130723012
C2×#106225612
C2×#106225602
C2×#106225422
C2×#106225982
C2×#106225862
C2×#106225462
C2×#106225902
C2×#106228252
C2×C4×C22⋊Dic112
C22×C11×#1172
C2×#243911