Finite Group Databasebeta

← C2×#13073799 #14923996

Subgroups — C2×#13073799 #14923996

Order 2816.

3374 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66950C211yesmaximal, characteristic, complemented
2C22×#66946C211yesmaximal, characteristic
3#13073799C2116yesmaximal, direct product factor
4C2×#10622605C211yesmaximal, characteristic, complemented
5C2×#10622592C211yesmaximal, characteristic, complemented
6C2×#10622286C211yesmaximal, characteristic, complemented
7C2×#10622268C212yesmaximal, complemented
8C2×#10622278C212yesmaximal
9C2×#10622281C212yesmaximal, complemented
10C2×#10622280C212yesmaximal, complemented
11C2×D11×#95C211yesmaximal, characteristic, complemented
12C2×C11×#400C211yesmaximal, characteristic, complemented
13C23×D44C2211yescharacteristic
14C23×C4×D11C2212yes—
15C23×C4×D11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C23×Dic22C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×C4⋊Dic11C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29C2×#66950—28no—
30C2×#66950C2218yescomplemented
31C2×#66946—28no—
32C2×#66946C2218yes—
33C11×#400C2218yescomplemented
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2212yes—
36C2×C11×#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622605C2218yescomplemented
42#10622592C2218yescomplemented
43#10622286C2218yescomplemented
44#10622281C22116yescomplemented
45#10622280C22116yescomplemented
46#10622278C22116yes—
47D11×#95C2218yescomplemented
48#10622268C22116yescomplemented
49C24×D11C2311yescharacteristic
50C24×D11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2312yes—
60C22×D44—24no—
61C22×D44—24no—
62C22×D44Q818yescomplemented
63C22×D44C2314yes—
64C22×C4×D11—28no—
65C22×C4×D11—24no—
66C22×C4×D11—28no—
67C22×C4×D11—44no—
68C22×C4×D11—44no—
69C22×C4×D11—44no—
70C22×C4×D11D418yes—
71C22×C4×D11C2318yes—
72C22×C4×D11C2314yes—
73C22×C4×D11C2314yes—
74C22×Dic22—24no—
75C22×Dic22—44no—
76C22×Dic22C2314yes—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×(C2×D11)⋊C4—24no—
82C2×(C2×D11)⋊C4—28no—
83C2×(C2×D11)⋊C4—24no—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—44no—
86C2×(C2×D11)⋊C4C2314yes—
87C2×(C2×D11)⋊C4C2314yes—
88C2×(C2×D11)⋊C4C2318yes—
89C2×(C2×D11)⋊C4C2318yes—
90C2×(C2×D11)⋊C4C2318yes—
91C2×C4⋊Dic11—28no—
92C2×C4⋊Dic11C2318yes—
93C2×Dic11⋊C4—28no—
94C2×Dic11⋊C4—44no—
95C2×Dic11⋊C4C2318yes—
96C2×Dic11⋊C4C2318yes—
97C2×C4×Dic11—24no—
98C2×C4×Dic11C2314yes—
99#66950—232no—
100#66946—232no—
101C11×#95C2318yes—
102C11×#95C2314yes—
103C11×#95C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2314yes—
108C2×#2564—111nomaximal, Sylow
109C24×C11C2411yescharacteristic
110C23×D11—24no—
111C23×D11—24no—
112C23×D11—22no—
113C23×D11—24no—
114C23×D11—22no—
115C23×D11—24no—
116C23×D11C2×D414yes—
117C23×D11C2×Q814yes—
118C23×D11C2×Q814yes—
119C23×D11#4114yes—
120C23×D11C2412yes—
121C23×D11C2412yes—
122C22×C4×C11—22no—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—24no—
126C22×C4×C11—22no—
127C22×C4×C11—24no—
128C22×C4×C11—24no—
129C22×C4×C11—24no—
130C22×C4×C11—24no—
131C22×C4×C11—24no—
132C22×C4×C11—24no—
133C22×C4×C11C2×D414yes—
134C22×C4×C11C2×Q814yes—
135C22×C4×C11C2414yes—
136C22×C4×C11C2412yes—
137C22×C4×C11C2414yes—
138C22×C4×C11C2412yes—
139C22×C4×C11C2412yes—
140C22×Dic11—22no—
141C22×Dic11—24no—
142C22×Dic11—24no—
143C22×Dic11—24no—
144C22×Dic11—24no—
145C22×Dic11—24no—
146C22×Dic11—24no—
147C22×Dic11—24no—
148C22×Dic11C2×D414yes—
149C22×Dic11#4118yes—
150C22×Dic11C2412yes—
151C22×Dic11C2414yes—
152C22×Dic11C2412yes—
153C22×Dic11C2414yes—
154C2×D44—232no—
155C2×D44—28no—
156C2×D44—28no—
157C2×D44C2×Q8116yescomplemented
158C2×C4×D11—28no—
159C2×C4×D11—216no—
160C2×C4×D11—216no—
161C2×C4×D11—416no—
162C2×C4×D11—48no—
163C2×C4×D11—48no—
164C2×C4×D11—48no—
165C2×C4×D11—432no—
166C2×C4×D11—416no—
167C2×C4×D11C2×D4116yes—
168C2×Dic22—28no—
169C2×Dic22—48no—
170C2×Dic22—416no—
171C11×C4⋊C4—28no—
172C11×C4⋊C4—28no—
173(C2×D11)⋊C4—216no—
174(C2×D11)⋊C4—28no—
175(C2×D11)⋊C4—216no—
176(C2×D11)⋊C4—28no—
177(C2×D11)⋊C4—48no—
178C4⋊Dic11—216no—
179Dic11⋊C4—216no—
180Dic11⋊C4—48no—
181C4×Dic11—28no—
182C22×C22⋊Q8—111no—
183C22×C4×D4—111no—
184#2564—1116no—
185C2×#400D1111yescharacteristic, complemented
186C2×#399—111no—
187C2×#395—111no—
188C2×#393—111no—
189C2×#387—112no—
190C2×#386—112no—
191C2×#385—112no—
192C2×#380—112no—
193C22×#95—111no—
194C23×C11C22×D412yes—
195C23×C11C22×Q812yes—
196C23×C11C2×#4112yes—
197C23×C11C2×#4114yes—
198C23×C11H(5,𝔽2)14yes—
199C23×C11C2511yescharacteristic
200C22×D11—28no—
201C22×D11—28no—
202C22×D11—216no—
203C22×D11—216no—
204C22×D11—24no—
205C22×D11—24no—
206C22×D11—28no—
207C22×D11—216no—
208C22×D11—22no—
209C22×D11—24no—
210C22×D11—22no—
211C22×D11—24no—
212C22×D11—44no—
213C22×D11—44no—
214C22×D11—48no—
215C22×D11C22⋊Q8116yes—
216C22×D11C22×D414yes—
217C22×D11C22×Q814yes—
218C22×D11C22×Q814yes—
219C22×D11C2×#4114yes—
220C2×C4×C11—28no—
221C2×C4×C11—28no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—24no—
229C2×C4×C11—24no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—48no—
234C2×C4×C11—44no—
235C2×C4×C11—48no—
236C2×C4×C11C22×D414yes—
237C2×C4×C11C22×Q814yes—
238C2×Dic11—28no—
239C2×Dic11—216no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—24no—
248C2×Dic11—44no—
249C2×Dic11—48no—
250C2×Dic11C22×D414yes—
251C2×Dic11C2×#4118yes—
252D44—232no—
253C4×D11—416no—
254C4×D11—432no—
255C4×D11—416no—
256Dic22—416no—
257C23×Q8—111no—
258C23×D4—111no—
259C24×C4—111no—
260C24×C4—112no—
261C24×C4—111no—
262C2×C22⋊Q8—118no—
263C2×C22⋊Q8—228no—
264C2×C4×D4—118no—
265C2×C4×D4—228no—
266C22×C4⋊C4—112no—
267C22×C4⋊C4—112no—
268C22×C4⋊C4—112no—
269C22×C4⋊C4C2×D1111yescharacteristic
270C22×C4⋊C4C2×D1111yescharacteristic
271C22×C22⋊C4—111no—
272C22×C22⋊C4—112no—
273C22×C22⋊C4—111no—
274C22×C22⋊C4—112no—
275C22×C22⋊C4—112no—
276C22×C42—111no—
277#400C2×D1118yescomplemented
278#399—118no—
279#395—118no—
280#393—118no—
281#387—1116no—
282#386—1116no—
283#385—1116no—
284#380—1116no—
285C2×#95—112no—
286C2×#95—111no—
287C2×#95—112no—
288C2×#95—112no—
289C2×#95—118no—
290C2×#95C2×D1111yescharacteristic
291C2×#95C2×D1112yes—
292C2×#95C2×D1112yes—
293C22×C11C2×C22⋊Q814yes—
294C22×C11#53214yes—
295C22×C11#53414yes—
296C22×C11#55118yes—
297C22×C11#55418yes—
298C22×C11C23×D411yescharacteristic
299C22×C11C23×Q811yescharacteristic
300C22×C11C22×#4111yescharacteristic
301C22×C11C22×#4112yes—
302C22×C11C2×H(5,𝔽2)12yes—
303C2×D11—232no—
304C2×D11—24no—
305C2×D11—24no—
306C2×D11—28no—
307C2×D11—28no—
308C2×D11—24no—
309C2×D11—28no—
310C2×D11—416no—
311C2×D11—42no—
312C2×D11—42no—
313C2×D11—44no—
314C2×D11C2×C22⋊Q818yes—
315C4×C11—24no—
316C4×C11—24no—
317C4×C11—44no—
318C4×C11—42no—
319C4×C11—44no—
320Dic11—24no—
321Dic11—28no—
322Dic11—42no—
323Dic11—44no—
324C25—111no—
325C25—111no—
326C22×Q8—114no—
327C22×Q8—224no—
328C22×Q8—444no—
329C22×D4—118no—
330C22×D4—114no—
331C22×D4—224no—
332C22×D4—224no—
333C23×C4—112no—
334C23×C4—111no—
335C23×C4—118no—
336C23×C4—114no—
337C23×C4—112no—
338C23×C4—111no—
339C23×C4—118no—
340C23×C4—114no—
341C23×C4—224no—
342C23×C4—228no—
343C23×C4—228no—
344C23×C4—444no—
345C23×C4—444no—
346C23×C4—444no—
347C23×C4C22×D1112yes—
348C23×C4C22×D1111yescharacteristic
349C23×C4C22×D1112yes—
350C23×C4C22×D1111yescharacteristic
351C23×C4C22×D1111yescharacteristic
352C22⋊Q8—2232no—
353C4×D4—2232no—
354C2×C4⋊C4—24no—
355C2×C4⋊C4—24no—
356C2×C4⋊C4—118no—
357C2×C4⋊C4—118no—
358C2×C4⋊C4—118no—
359C2×C4⋊C4—228no—
360C2×C4⋊C4—228no—
361C2×C4⋊C4—444no—
362C2×C4⋊C4C22×D1114yes—
363C2×C4⋊C4C22×D1114yes—
364C2×C22⋊C4—114no—
365C2×C22⋊C4—114no—
366C2×C22⋊C4—118no—
367C2×C22⋊C4—118no—
368C2×C22⋊C4—118no—
369C2×C22⋊C4—228no—
370C2×C22⋊C4—224no—
371C2×C22⋊C4—228no—
372C2×C22⋊C4—224no—
373C2×C22⋊C4—444no—
374C2×C42—114no—
375C2×C42—224no—
376#95—118no—
377#95—114no—
378#95—118no—
379#95—118no—
380#95C22×D1114yes—
381#95C22×D1118yes—
382#95C22×D1118yes—
383C2×C11#256418yescomplemented
384C2×C11C22×C22⋊Q811yescharacteristic
385C2×C11C2×#53211yescharacteristic
386C2×C11C2×#53411yescharacteristic
387C2×C11C2×#55112yes—
388C2×C11C2×#55412yes—
389D11—28no—
390D11—44no—
391C24—114no—
392C24—114no—
393C24—114no—
394C24—112no—
395C24—114no—
396C24—112no—
397C24—224no—
398C24—224no—
399C24—222no—
400C24—224no—
401C24—222no—
402C24—224no—
403C24C23×D1111yescharacteristic
404C2×Q8—228no—
405C2×Q8—448no—
406C2×Q8—4416no—
407C2×D4—1116no—
408C2×D4—228no—
409C2×D4—2232no—
410C2×D4—228no—
411C22×C4—22no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—24no—
415C22×C4—22no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—24no—
419C22×C4—24no—
420C22×C4—24no—
421C22×C4—24no—
422C22×C4—114no—
423C22×C4—118no—
424C22×C4—114no—
425C22×C4—112no—
426C22×C4—1116no—
427C22×C4—112no—
428C22×C4—114no—
429C22×C4—228no—
430C22×C4—2216no—
431C22×C4—2216no—
432C22×C4—224no—
433C22×C4—224no—
434C22×C4—224no—
435C22×C4—222no—
436C22×C4—224no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—4416no—
441C22×C4—448no—
442C22×C4—448no—
443C22×C4—448no—
444C22×C4—4432no—
445C22×C4—4416no—
446C22×C4D4×D1114yes—
447C22×C4Q8×D1114yes—
448C22×C4C23×D1114yes—
449C22×C4C23×D1114yes—
450C22×C4C23×D1112yes—
451C22×C4C23×D1112yes—
452C22×C4C23×D1112yes—
453C4⋊C4—28no—
454C4⋊C4—28no—
455C4⋊C4—2216no—
456C4⋊C4—2216no—
457C4⋊C4—448no—
458C22⋊C4—2216no—
459C22⋊C4—228no—
460C22⋊C4—2216no—
461C22⋊C4—228no—
462C22⋊C4—448no—
463C42—228no—
464C11C2×#256411yescharacteristic, complemented, Sylow
465C23—1116no—
466C23—114no—
467C23—114no—
468C23—114no—
469C23—114no—
470C23—2216no—
471C23—228no—
472C23—224no—
473C23—224no—
474C23—228no—
475C23—2216no—
476C23—228no—
477C23—222no—
478C23—224no—
479C23—222no—
480C23—224no—
481C23—2216no—
482C23—448no—
483C23—444no—
484C23—444no—
485C23C2×D4×D1112yes—
486C23C2×Q8×D1112yes—
487C23#41×D1112yes—
488C23#41×D1114yes—
489C23#6704214yes—
490C23C24×D1111yescharacteristic
491Q8—4416no—
492D4—2232no—
493C2×C4—28no—
494C2×C4—28no—
495C2×C4—22no—
496C2×C4—22no—
497C2×C4—24no—
498C2×C4—24no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—48no—
507C2×C4—44no—
508C2×C4—48no—
509C2×C4—114no—
510C2×C4—118no—
511C2×C4—2216no—
512C2×C4—228no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—222no—
517C2×C4—224no—
518C2×C4—224no—
519C2×C4—224no—
520C2×C4—224no—
521C2×C4—4416no—
522C2×C4—4432no—
523C2×C4—4416no—
524C2×C4—448no—
525C2×C4—444no—
526C2×C4C2×D4×D1114yes—
527C2×C4C2×Q8×D1114yes—
528C22—118no—
529C22—228no—
530C22—228no—
531C22—224no—
532C22—224no—
533C22—2232no—
534C22—228no—
535C22—224no—
536C22—444no—
537C22—442no—
538C22—442no—
539C22—4416no—
540C22D11×C22⋊Q814yes—
541C22#1062318414yes—
542C22#1062319914yes—
543C22#1062322118yes—
544C22#1062323618yes—
545C22C22×D4×D1111yescharacteristic
546C22C22×Q8×D1111yescharacteristic
547C22C2×#41×D1111yescharacteristic
548C22C2×#41×D1112yes—
549C22C2×#6704212yes—
550C4—24no—
551C4—24no—
552C4—44no—
553C4—44no—
554C4—42no—
555C4—228no—
556C4—224no—
557C4—442no—
558C4—444no—
559C2—228no—
560C2—444no—
561C2#1307379918yesdirect product factor
562C2C2×D11×C22⋊Q811yescharacteristic
563C2C2×#1062319911yescharacteristic
564C2C2×#1062318411yescharacteristic
565C2C2×#1062323612yes—
566C2C2×#1062322112yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#400C2
socleC24×C11C24
prime radicalC23×D44C22
hypercenterC2×#400D11
hypocenterC11C2×#2564
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#400

Complements

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

NH ≅ G/Ntype
1. C22×#66950C2semidirect
3. #13073799C2direct (N × H)
4. C2×#10622605C2semidirect
5. C2×#10622592C2semidirect
6. C2×#10622286C2semidirect
7. C2×#10622268C2semidirect
9. C2×#10622281C2semidirect
10. C2×#10622280C2semidirect
11. C2×D11×#95C2semidirect
12. C2×C11×#400C2semidirect
30. C2×#66950C22semidirect
33. C11×#400C22semidirect
41. #10622605C22semidirect
42. #10622592C22semidirect
43. #10622286C22semidirect
44. #10622281C22semidirect
45. #10622280C22semidirect
47. D11×#95C22semidirect
48. #10622268C22semidirect
62. C22×D44Q8semidirect
157. C2×D44C2×Q8semidirect
185. C2×#400D11semidirect
277. #400C2×D11semidirect
383. C2×C11#2564semidirect
464. C11C2×#2564semidirect
561. C2#13073799direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669502
C22×#669462
#130737992
C2×#106226052
C2×#106225922
C2×#106222862
C2×#106222682
C2×#106222782
C2×#106222812
C2×#106222802
C2×D11×#952
C2×C11×#4002
C2×#256411