Finite Group Databasebeta

← C2×#13077461 #15617884

Subgroups — C2×#13077461 #15617884

Order 2816.

2730 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66962C211yesmaximal, characteristic
2C2×#10623054C211yesmaximal, characteristic
3C2×#10623047C211yesmaximal, characteristic, complemented
4#13077461C2116yesmaximal, direct product factor
5C2×#10622329C212yesmaximal, complemented
6C2×#10622323C212yesmaximal, complemented
7C2×C4×Dic44C212yesmaximal, complemented
8C2×C4×#4314C212yesmaximal, complemented
9C2×#10622734C211yesmaximal, characteristic, complemented
10C2×#10622726C211yesmaximal, characteristic
11C22×#66880C211yesmaximal, characteristic, complemented
12C2×C11×#405C211yesmaximal, characteristic, complemented
13C22×#4339C2211yescharacteristic
14C23×Dic22C2211yescharacteristic
15C22×C11×M16C2211yescharacteristic
16C23×C8×C11C2211yescharacteristic
17C2×C11×#117C2211yescharacteristic
18C2×#66979C2211yescharacteristic
19C22×C4⋊Dic11C2211yescharacteristic
20C2×#66962C4116yescomplemented
21C2×#66962C2218yes—
22C22×Dic44C2212yes—
23C22×#4314C2212yes—
24#10623054—24no—
25#10623054C2218yes—
26#10623047—24no—
27#10623047C2218yescomplemented
28C2×#66945—21no—
29C2×C4⋊C4×D11—21no—
30C2×#66940—21no—
31C2×#66940—21no—
32C2×(C22⋊D11)⋊C4—22no—
33C2×#66930—22no—
34C2×C4×D44C2212yes—
35C2×C4×Dic22C2212yes—
36C2×C4×Dic22C2212yes—
37C2×C4×Dic22C2212yes—
38C11×#405C2218yescomplemented
39C2×C11×#97C2212yes—
40C2×C4×C8×C11C2212yes—
41#10622734C2218yescomplemented
42#10622726C2218yes—
43C2×#66885C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45C2×#66882C2212yes—
46C2×#66881C2212yes—
47C2×#66880C2212yes—
48C2×#66880C2212yes—
49C2×#66880C2211yescharacteristic
50C2×#66880C2211yescharacteristic
51C2×#66880C2218yescomplemented
52#10622329C22116yescomplemented
53#10622323C22116yescomplemented
54C4×Dic44C22116yescomplemented
55C4×#4314C22116yescomplemented
56C23×C4×C11C2311yescharacteristic
57C22×C22⋊D11—21no—
58C23×Dic11—21no—
59C23×Dic11—21no—
60C2×#4339—22no—
61C2×#4339—24no—
62C2×#4339C2×C418yes—
63C2×#4339C2314yes—
64C22×D44C2311yescharacteristic
65C22×C4×D11—21no—
66C22×C4×D11—22no—
67C22×Dic22—21no—
68C22×Dic22—22no—
69C22×Dic22—24no—
70C22×Dic22C2×C418yescomplemented
71C22×Dic22C2312yes—
72C22×Dic22C2311yescharacteristic
73C22×Dic22C2314yes—
74C2×C11×M16C2×C418yescomplemented
75C2×C11×M16C2314yes—
76C22×C8×C11—24no—
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2314yes—
80C22×C8×C11C2312yes—
81C11×#117D414yes—
82C11×#117C2314yes—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C22⋊C4D412yes—
86C2×C42×C11C2312yes—
87C2×C22⋊Dic11—21no—
88C2×(C2×D11)⋊C4—22no—
89#66979—22no—
90#66979C2314yes—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2314yes—
96C2×C4⋊Dic11C2312yes—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C2×C4×Dic11—22no—
101C2×C4×Dic11—22no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—21no—
104#66962C2×C4164yescomplemented
105C2×Dic44C2×C4116yescomplemented
106C2×Dic44C2318yes—
107C2×#4314C2×C4116yescomplemented
108C2×#4314C2318yes—
109#66945—28no—
110C4⋊C4×D11—28no—
111#66940—28no—
112#66940—28no—
113(C22⋊D11)⋊C4—216no—
114#66930—216no—
115C4×D44—24no—
116C4×D44C2318yes—
117C4×Dic22—24no—
118C4×Dic22—24no—
119C4×Dic22—24no—
120C4×Dic22C2318yes—
121C4×Dic22C2318yes—
122C4×Dic22C2318yes—
123C11×#97C2318yes—
124C4×C8×C11C2318yes—
125#66885C2314yes—
126#66885C2314yes—
127#66882C2318yes—
128#66881C2318yes—
129#66880C2314yes—
130#66880C2314yes—
131#66880C2318yes—
132#66880C2318yes—
133C2×#2947—111nomaximal, Sylow
134C24×C11C2×D411yescharacteristic
135C23×D11—21no—
136C22×C4×C11C22×C414yes—
137C22×C4×C11C2×D412yes—
138C22×C4×C11C2×D412yes—
139C22×C4×C11C2×D411yescharacteristic
140C22×C4×C11C2×D412yes—
141C22×C4×C11#4114yes—
142C22×C4×C11C2411yescharacteristic
143C22×C4×C11C2412yes—
144C2×C22⋊D11—28no—
145C2×C22⋊D11—24no—
146C22×Dic11—28no—
147C22×Dic11—24no—
148C22×Dic11—22no—
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—21no—
152C22×Dic11—22no—
153C22×Dic11—24no—
154C22×Dic11—82no—
155#4339—216no—
156#4339—28no—
157#4339C22×C4116yes—
158C2×D44—21no—
159C2×D44—22no—
160C2×D44C22×C414yes—
161C2×D44C2412yes—
162C2×C4×D11—28no—
163C2×C4×D11—24no—
164C2×C4×D11—28no—
165C2×C4×D11—84no—
166C2×Dic22—28no—
167C2×Dic22—216no—
168C2×Dic22—22no—
169C2×Dic22—21no—
170C2×Dic22—24no—
171C2×Dic22—24no—
172C2×Dic22—28no—
173C2×Dic22—22no—
174C2×Dic22C22×C418yes—
175C2×Dic22C22×C414yes—
176C2×Dic22C22×C4116yescomplemented
177C2×Dic22C2414yes—
178C2×Dic22C2412yes—
179C11×M16C22×C4116yescomplemented
180C2×C8×C11—22no—
181C2×C8×C11—22no—
182C2×C8×C11—28no—
183C2×C8×C11C22×C418yes—
184C2×C8×C11C2412yes—
185C2×C8×C11C2412yes—
186C2×C8×C11C2414yes—
187C11×C4⋊C4C2×D414yes—
188C11×C4⋊C4C2×D414yes—
189C11×C22⋊C4C2×D418yes—
190C42×C11C2×D414yes—
191C42×C11C2414yes—
192C22⋊Dic11—24no—
193(C2×D11)⋊C4—28no—
194C4⋊Dic11—21no—
195C4⋊Dic11—21no—
196C4⋊Dic11—22no—
197C4⋊Dic11—24no—
198C4⋊Dic11C2414yes—
199C4⋊Dic11C2412yes—
200C4⋊Dic11C2412yes—
201Dic11⋊C4—28no—
202Dic11⋊C4—28no—
203Dic11⋊C4—28no—
204C4×Dic11—28no—
205C4×Dic11—28no—
206C4×Dic11—28no—
207C4×Dic11—24no—
208Dic44C22×C4132yescomplemented
209#4314C22×C4132yescomplemented
210C22×#137—111no—
211C2×#520—111no—
212C2×#519—111no—
213#2947—1116no—
214C2×#441—112no—
215C2×#440—112no—
216C2×C4×Q16—112no—
217C2×C4×SD16—112no—
218C2×#428—111no—
219C2×#416—111no—
220C22×#103—111no—
221C2×#405D1111yescharacteristic, complemented
222C23×C11—22no—
223C23×C11—22no—
224C23×C11C4×D414yes—
225C23×C11C22×D412yes—
226C23×C11C22×D411yescharacteristic
227C22×D11—24no—
228C22×D11—22no—
229C22×D11—42no—
230C22×D11—42no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11C4×D414yes—
234C2×C4×C11C4×D418yes—
235C2×C4×C11C23×C412yes—
236C2×C4×C11C23×C414yes—
237C2×C4×C11C22×D414yes—
238C2×C4×C11C22×D414yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D411yescharacteristic
241C2×C4×C11C2×#4112yes—
242C2×C4×C11C2×#4114yes—
243C2×C4×C11C2511yescharacteristic
244C22⋊D11—216no—
245C2×Dic11—28no—
246C2×Dic11—216no—
247C2×Dic11—24no—
248C2×Dic11—24no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—44no—
254C2×Dic11—42no—
255C2×Dic11—42no—
256C2×Dic11—84no—
257D44—24no—
258D44—22no—
259D44C23×C414yes—
260C4×D11—216no—
261C4×D11—88no—
262Dic22—28no—
263Dic22—216no—
264Dic22—24no—
265Dic22—24no—
266Dic22—22no—
267Dic22C23×C418yes—
268Dic22C23×C414yes—
269C8×C11—22no—
270C8×C11—22no—
271C8×C11C23×C418yes—
272C22×#41—111no—
273C23×Q8—111no—
274C2×#137—118no—
275C2×#137—1116no—
276C22×Q16—112no—
277C22×SD16—112no—
278C22×M16C2×D1111yescharacteristic
279C23×C8C2×D1111yescharacteristic
280#520—118no—
281#520—224no—
282#519—118no—
283#519—224no—
284C2×C4×Q8—112no—
285C2×C4×Q8—112no—
286C2×C4×Q8—112no—
287C2×C4×Q8—221no—
288C2×C4×Q8—221no—
289C2×C4×D4—112no—
290C2×C4×D4—222no—
291C2×#117—111no—
292C2×#117—221no—
293C2×#117—222no—
294C2×#117C2×D1111yescharacteristic
295C22×C4⋊C4—111no—
296C22×C4⋊C4—221no—
297#441—1116no—
298#440—1116no—
299C4×Q16—1116no—
300C4×SD16—1116no—
301#428—118no—
302C2×#107—112no—
303C2×#106—112no—
304#416—118no—
305C2×#103—112no—
306C2×#103—112no—
307C2×#103—118no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#102—111no—
311C2×#102—111no—
312#405C2×D1118yescomplemented
313C2×#97C2×D1112yes—
314C2×C4×C8C2×D1112yes—
315C22×C11—28no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11C2×C4×D414yes—
319C22×C11C2×C4×D412yes—
320C22×C11#57712yes—
321C22×C11#57812yes—
322C22×C11C23×D411yescharacteristic
323C2×D11—24no—
324C2×D11—48no—
325C2×D11—42no—
326C2×D11—42no—
327C4×C11—24no—
328C4×C11—24no—
329C4×C11C2×C4×D412yes—
330C4×C11C2×C4×D414yes—
331C4×C11C24×C411yescharacteristic
332C4×C11C22×#4111yescharacteristic
333Dic11—28no—
334Dic11—24no—
335Dic11—44no—
336Dic11—42no—
337Dic11—42no—
338C2×#41—118no—
339C2×#41—114no—
340C2×#41—222no—
341C2×#41—224no—
342C22×Q8—118no—
343C22×Q8—112no—
344C22×Q8—111no—
345C22×Q8—114no—
346C22×Q8—221no—
347C22×Q8—222no—
348C22×Q8—224no—
349C22×D4—111no—
350C22×D4—221no—
351C23×C4—221no—
352C23×C4—221no—
353C23×C4—221no—
354C23×C4—222no—
355C23×C4C22×D1111yescharacteristic
356#137—1164no—
357C2×Q16—1116no—
358C2×Q16—118no—
359C2×SD16—1116no—
360C2×SD16—118no—
361C2×M16C4×D1118yescomplemented
362C2×M16C22×D1114yes—
363C22×C8—24no—
364C22×C8C22×D1111yescharacteristic
365C22×C8C22×D1111yescharacteristic
366C22×C8C22×D1114yes—
367C22×C8C22×D1112yes—
368C4×Q8—118no—
369C4×Q8—118no—
370C4×Q8—118no—
371C4×Q8—228no—
372C4×Q8—228no—
373C4×Q8—224no—
374C4×Q8—224no—
375C4×Q8—224no—
376C4×D4—118no—
377C4×D4—2216no—
378C4×D4—224no—
379#117—114no—
380#117—222no—
381#117—228no—
382#117—2216no—
383#117D4414yes—
384#117C22×D1114yes—
385C2×C4⋊C4—112no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—111no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—222no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4—228no—
395C2×C4⋊C4D4411yescharacteristic
396C2×C4⋊C4D4411yescharacteristic
397C2×C22⋊C4—221no—
398C2×C22⋊C4—222no—
399C2×C22⋊C4D4412yes—
400C2×C42—221no—
401C2×C42—222no—
402C2×C42—222no—
403C2×C42—222no—
404C2×C42C22×D1112yes—
405#107—118no—
406#106—118no—
407#103—118no—
408#103—118no—
409#103—114no—
410#103—114no—
411#102—114no—
412#102—114no—
413#97C22×D1118yes—
414C4×C8C22×D1118yes—
415C2×C11—24no—
416C2×C11#294714yescomplemented
417C2×C11C22×C4×D411yescharacteristic
418C2×C11C2×#57711yescharacteristic
419C2×C11C2×#57811yescharacteristic
420D11—44no—
421C24—221no—
422C24C2×D4411yescharacteristic
423#41—1116no—
424#41—2216no—
425#41—228no—
426C2×Q8—118no—
427C2×Q8—114no—
428C2×Q8—1116no—
429C2×Q8—114no—
430C2×Q8—112no—
431C2×Q8—228no—
432C2×Q8—2216no—
433C2×Q8—224no—
434C2×Q8—222no—
435C2×Q8—221no—
436C2×Q8—224no—
437C2×Q8—228no—
438C2×Q8—222no—
439C2×D4—114no—
440C2×D4—112no—
441C2×D4—228no—
442C2×D4—224no—
443C2×D4—221no—
444C2×D4—222no—
445C22×C4—228no—
446C22×C4—224no—
447C22×C4—221no—
448C22×C4—222no—
449C22×C4—228no—
450C22×C4—224no—
451C22×C4—221no—
452C22×C4—221no—
453C22×C4—222no—
454C22×C4—224no—
455C22×C4—228no—
456C22×C4—884no—
457C22×C4—882no—
458C22×C4C2×C4×D1114yes—
459C22×C4C2×D4412yes—
460C22×C4C2×D4412yes—
461C22×C4C2×D4412yes—
462C22×C4C2×D4411yescharacteristic
463C22×C4#433914yes—
464C22×C4C23×D1112yes—
465C22×C4C23×D1111yescharacteristic
466Q16—1132no—
467SD16—1132no—
468M16C2×C4×D11116yescomplemented
469C2×C8—22no—
470C2×C8—22no—
471C2×C8—28no—
472C2×C8C2×C4×D1118yes—
473C2×C8C23×D1112yes—
474C2×C8C23×D1112yes—
475C2×C8C23×D1114yes—
476C4⋊C4—112no—
477C4⋊C4—112no—
478C4⋊C4—114no—
479C4⋊C4—224no—
480C4⋊C4—222no—
481C4⋊C4—221no—
482C4⋊C4—221no—
483C4⋊C4—228no—
484C4⋊C4—228no—
485C4⋊C4—228no—
486C4⋊C4C2×D4414yes—
487C4⋊C4C2×D4414yes—
488C22⋊C4—224no—
489C22⋊C4—228no—
490C22⋊C4C2×D4418yes—
491C42—224no—
492C42—228no—
493C42—228no—
494C42—228no—
495C42C2×D4414yes—
496C42C23×D1114yes—
497C11C2×#294711yescharacteristic, complemented, Sylow
498C23—22no—
499C23—22no—
500C23—224no—
501C23—222no—
502C23—442no—
503C23—442no—
504C23C4×D4414yes—
505C23C22×D4412yes—
506C23C22×D4411yescharacteristic
507Q8—118no—
508Q8—114no—
509Q8—2216no—
510Q8—228no—
511Q8—224no—
512Q8—224no—
513Q8—222no—
514D4—114no—
515D4—2216no—
516D4—224no—
517D4—222no—
518C2×C4—24no—
519C2×C4—24no—
520C2×C4—224no—
521C2×C4—2216no—
522C2×C4—228no—
523C2×C4—222no—
524C2×C4—224no—
525C2×C4—2216no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—224no—
529C2×C4—444no—
530C2×C4—442no—
531C2×C4—442no—
532C2×C4—888no—
533C2×C4—884no—
534C2×C4C4×D4414yes—
535C2×C4C4×D4418yes—
536C2×C4C22×C4×D1112yes—
537C2×C4C22×C4×D1114yes—
538C2×C4C22×D4414yes—
539C2×C4C22×D4414yes—
540C2×C4C22×D4412yes—
541C2×C4C22×D4411yescharacteristic
542C2×C4C2×#433912yes—
543C2×C4C2×#433914yes—
544C2×C4C24×D1111yescharacteristic
545C8—22no—
546C8—22no—
547C8C22×C4×D1118yes—
548C22—28no—
549C22—22no—
550C22—22no—
551C22—224no—
552C22—448no—
553C22—442no—
554C22—442no—
555C22C2×C4×D4414yes—
556C22C2×C4×D4412yes—
557C22#1062328212yes—
558C22#1062328412yes—
559C22C23×D4411yescharacteristic
560C4—24no—
561C4—24no—
562C4—224no—
563C4—228no—
564C4—444no—
565C4—442no—
566C4—442no—
567C4C2×C4×D4414yes—
568C4C2×C4×D4412yes—
569C4C23×C4×D1111yescharacteristic
570C4C22×#433911yescharacteristic
571C2—24no—
572C2—444no—
573C2#1307746114yesdirect product factor
574C2C22×C4×D4411yescharacteristic
575C2C2×#1062328211yescharacteristic
576C2C2×#1062328411yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC2×C11×#405C2
socleC23×C11C22×D4
prime radicalC22×#4339C22
cosocleC2×C4×C11C25
hypercenterC2×#405D11
hypocenterC11C2×#2947
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
3. C2×#10623047C2semidirect
4. #13077461C2direct (N × H)
5. C2×#10622329C2semidirect
6. C2×#10622323C2semidirect
7. C2×C4×Dic44C2semidirect
8. C2×C4×#4314C2semidirect
9. C2×#10622734C2semidirect
11. C22×#66880C2semidirect
12. C2×C11×#405C2semidirect
20. C2×#66962C4semidirect
27. #10623047C22semidirect
38. C11×#405C22semidirect
41. #10622734C22semidirect
51. C2×#66880C22semidirect
52. #10622329C22semidirect
53. #10622323C22semidirect
54. C4×Dic44C22semidirect
55. C4×#4314C22semidirect
70. C22×Dic22C2×C4semidirect
74. C2×C11×M16C2×C4semidirect
104. #66962C2×C4semidirect
105. C2×Dic44C2×C4semidirect
107. C2×#4314C2×C4semidirect
176. C2×Dic22C22×C4semidirect
179. C11×M16C22×C4semidirect
208. Dic44C22×C4semidirect
209. #4314C22×C4semidirect
221. C2×#405D11semidirect
312. #405C2×D11semidirect
361. C2×M16C4×D11semidirect
416. C2×C11#2947semidirect
468. M16C2×C4×D11semidirect
497. C11C2×#2947semidirect
573. C2#13077461direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669622
C2×#106230542
C2×#106230472
#130774612
C2×#106223292
C2×#106223232
C2×C4×Dic442
C2×C4×#43142
C2×#106227342
C2×#106227262
C22×#668802
C2×C11×#4052
C2×#294711