Finite Group Databasebeta

← C2×#13079985 #15626625

Subgroups — C2×#13079985 #15626625

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×#10623088C211yesmaximal, characteristic
3#13079985C2116yesmaximal, direct product factor
4C2×#10622409C212yesmaximal, complemented
5C2×#10622463C211yesmaximal, characteristic, complemented
6C2×#10622621C211yesmaximal, characteristic, complemented
7C2×#10622429C212yesmaximal, complemented
8C2×#10622787C212yesmaximal
9C2×#10622779C212yesmaximal, complemented
10C2×#10622703C211yesmaximal, characteristic, complemented
11C2×#10622450C211yesmaximal, characteristic, complemented
12C2×C11×#461C211yesmaximal, characteristic, complemented
13C22×C11×SD16C2212yes—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66999C2212yes—
17C2×Q8×Dic11C2212yes—
18C22×#4326C2212yes—
19C2×#66991C2211yescharacteristic
20C2×#66989C2211yescharacteristic
21C2×C4×C22⋊D11—21no—
22C2×#66979—21no—
23C22×#4313C2212yes—
24#10623259—24no—
25#10623259C2218yescomplemented
26#10623088—24no—
27#10623088C2218yes—
28C2×#66950—21no—
29C2×#66950C2211yescharacteristic
30C2×#66945—21no—
31C2×#66943—21no—
32C2×#66943C2211yescharacteristic
33C2×#66940—21no—
34C2×#66936—21no—
35C2×#66932—21no—
36C2×C42×D11C2211yescharacteristic
37C2×#66922C2211yescharacteristic
38C2×C4×Dic22C2211yescharacteristic
39C11×#461C2218yescomplemented
40C2×C11×C4⋊C8C2211yescharacteristic
41C2×C11×#103C2212yes—
42C2×#66899C2212yes—
43C2×#66896C2212yes—
44#10622787C22116yes—
45#10622779C22116yescomplemented
46C2×#66882C2212yes—
47C2×#66880C2212yes—
48C2×Dic11⋊C8C2212yes—
49#10622703C2218yescomplemented
50#10622621C2218yescomplemented
51C2×#66872C2212yes—
52C2×C4⋊(C11⋊C8)C2211yescharacteristic
53#10622463C2218yescomplemented
54#10622450C2218yescomplemented
55#10622429C22116yescomplemented
56#10622409C22116yescomplemented
57C22×Q8×C11C2312yes—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C22×C22⋊D11—21no—
61C22×C4×D11D411yescharacteristic
62C22×C4×D11D411yescharacteristic
63C22×C4×D11C2311yescharacteristic
64C22×Dic22—21no—
65C22×Dic22C2311yescharacteristic
66C2×C11×SD16—44no—
67C2×C11×SD16C2318yes—
68C22×C8×C11C2312yes—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8C2314yes—
71C4×D4×C11—22no—
72C4×D4×C11C2314yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4C2311yescharacteristic
76C2×C11×C22⋊C4—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—21no—
79C2×C22⋊Dic11—21no—
80C2×C22⋊Dic11—21no—
81#66999—24no—
82#66999C2318yes—
83Q8×Dic11—24no—
84Q8×Dic11C2318yes—
85C2×#4326—44no—
86C2×#4326C2318yes—
87#66991—22no—
88#66991C2314yes—
89#66989—22no—
90#66989C2314yes—
91C4×C22⋊D11—28no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—22no—
94#66979—28no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11C2311yescharacteristic
100C2×C4⋊Dic11C2312yes—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—22no—
104C2×C4×Dic11—21no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11D411yescharacteristic
107C2×C4×Dic11D411yescharacteristic
108C2×C4×Dic11C2311yescharacteristic
109C22×C11⋊C8C2312yes—
110C2×#4313—44no—
111C2×#4313C2318yes—
112#66950—28no—
113#66950—22no—
114#66950C2314yes—
115#66945—28no—
116#66943—28no—
117#66943—22no—
118#66943C2314yes—
119#66940—28no—
120#66936—28no—
121#66932—28no—
122C42×D11D414yes—
123C42×D11C2314yes—
124#66922—22no—
125#66922C2314yes—
126C4×Dic22—22no—
127C4×Dic22C2314yes—
128C11×C4⋊C8C2314yes—
129C11×#103C2318yes—
130#66899C2318yes—
131#66896C2318yes—
132#66882C2318yes—
133#66880C2318yes—
134Dic11⋊C8C2318yes—
135#66872C2318yes—
136C4⋊(C11⋊C8)C2314yes—
137C2×#3252—111nomaximal, Sylow
138C24×C11—21no—
139C23×D11C2×D411yescharacteristic
140C2×Q8×C11—22no—
141C2×Q8×C11—24no—
142C2×Q8×C11—24no—
143C2×Q8×C11C2414yes—
144C2×D4×C11—21no—
145C2×D4×C11—22no—
146C2×D4×C11—22no—
147C2×D4×C11C2412yes—
148C22×C4×C11—22no—
149C22×C4×C11—21no—
150C22×C4×C11—24no—
151C22×C4×C11—44no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—24no—
156C2×C22⋊D11—44no—
157C22×Dic11—21no—
158C22×Dic11—22no—
159C22×Dic11—21no—
160C22×Dic11C2×D411yescharacteristic
161C22×Dic11C2×D411yescharacteristic
162C22×Dic11C2×D411yescharacteristic
163C2×C4×D11—24no—
164C2×C4×D11—22no—
165C2×C4×D11—22no—
166C2×C4×D11—42no—
167C2×C4×D11C2×D412yes—
168C2×C4×D11C2×D414yes—
169C2×C4×D11C2×D414yes—
170C2×C4×D11C2412yes—
171C2×Dic22—21no—
172C2×Dic22—24no—
173C2×Dic22—22no—
174C2×Dic22—22no—
175C2×Dic22—44no—
176C2×Dic22C2412yes—
177C11×SD16—48no—
178C2×C8×C11—24no—
179C2×C8×C11C2414yes—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C2412yes—
184C11×C22⋊C4—24no—
185C42×C11C2×D412yes—
186C42×C11C2412yes—
187C22⋊Dic11—24no—
188C22⋊Dic11—24no—
189C22⋊Dic11—24no—
190#4326—48no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—28no—
193C4⋊Dic11—24no—
194C4⋊Dic11—24no—
195C4⋊Dic11—28no—
196C4⋊Dic11—21no—
197C4⋊Dic11—22no—
198C4⋊Dic11—24no—
199C4⋊Dic11C2414yes—
200C4⋊Dic11C2412yes—
201Dic11⋊C4—24no—
202Dic11⋊C4—28no—
203Dic11⋊C4—24no—
204C4×Dic11—28no—
205C4×Dic11—24no—
206C4×Dic11C2×D412yes—
207C4×Dic11C2×D414yes—
208C4×Dic11C2×D414yes—
209C4×Dic11C2412yes—
210C2×C11⋊C8—24no—
211C2×C11⋊C8C2414yes—
212#4313—48no—
213C2×#533—111no—
214C2×#529—111no—
215#3252—1116no—
216C2×#479—112no—
217C2×#477—111no—
218C2×#476—111no—
219C2×#470—112no—
220C2×#468—112no—
221C2×#464—112no—
222C2×#462—111no—
223C2×#461D1111yescharacteristic, complemented
224C2×#423—111no—
225C23×C11—22no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11—42no—
229C23×C11C22×D411yescharacteristic
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—22no—
233C22×D11C22×D412yes—
234Q8×C11—24no—
235Q8×C11—24no—
236Q8×C11—44no—
237D4×C11—22no—
238D4×C11—22no—
239D4×C11—42no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—22no—
243C2×C4×C11—44no—
244C2×C4×C11—42no—
245C2×C4×C11—48no—
246C2×C4×C11#13714yes—
247C2×C4×C11C22×D412yes—
248C2×C4×C11C22×D411yescharacteristic
249C2×C4×C11C22×D412yes—
250C2×C4×C11H(5,𝔽2)12yes—
251C2×C4×C112−1+412yes—
252C2×C4×C11C2511yescharacteristic
253C22⋊D11—48no—
254C2×Dic11—22no—
255C2×Dic11—22no—
256C2×Dic11—22no—
257C2×Dic11—22no—
258C2×Dic11—24no—
259C2×Dic11—22no—
260C2×Dic11—42no—
261C2×Dic11—44no—
262C2×Dic11—42no—
263C2×Dic11C22×D412yes—
264C2×Dic11C22×D412yes—
265C2×Dic11C22×D412yes—
266C4×D11—24no—
267C4×D11—28no—
268C4×D11—22no—
269C4×D11—22no—
270C4×D11—44no—
271Dic22—22no—
272Dic22—22no—
273Dic22—48no—
274Dic22—42no—
275C8×C11—24no—
276C11⋊C8—24no—
277C22×Q16—112no—
278C22×SD16C2×D1112yes—
279C22×M16—112no—
280#533—118no—
281#533—224no—
282C2×C4⋊Q8—111no—
283C2×C4⋊Q8C2×D1111yescharacteristic
284#529—118no—
285#529—224no—
286C2×#126—221no—
287C2×#125—111no—
288C2×#125—221no—
289C2×#124—111no—
290C2×#123—221no—
291C2×C22⋊Q8—112no—
292C2×C22⋊Q8—111no—
293C2×C22⋊Q8—221no—
294C2×#121—111no—
295C2×C4×Q8—112no—
296C2×C4×Q8—111no—
297C2×C4×Q8—221no—
298C2×C4×D4—221no—
299C2×C4×D4C2×D1111yescharacteristic
300C2×#117—221no—
301C2×#117—221no—
302C22×C42—111no—
303#479—1116no—
304#477—118no—
305#476—118no—
306#470—1116no—
307#468—1116no—
308#464—1116no—
309#462—118no—
310#461C2×D1118yescomplemented
311C2×#107—112no—
312C2×#106—112no—
313#423—118no—
314C2×C4⋊C8—112no—
315C2×C4⋊C8—111no—
316C2×C4⋊C8C2×D1111yescharacteristic
317C2×#103—112no—
318C2×#103—112no—
319C2×#103C2×D1112yes—
320C2×#102—112no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—84no—
325C22×C11#53712yes—
326C22×C11C2×#13712yes—
327C22×C11#57512yes—
328C22×C11C23×D411yescharacteristic
329C2×D11—22no—
330C2×D11—22no—
331C2×D11—22no—
332C2×D11—44no—
333C4×C11—22no—
334C4×C11—44no—
335C4×C11—42no—
336C4×C11#53712yes—
337C4×C11C2×#13714yes—
338C4×C11C2×H(5,𝔽2)11yescharacteristic
339C4×C11C2×2−1+411yescharacteristic
340Dic11—22no—
341Dic11—22no—
342Dic11—22no—
343Dic11—42no—
344Dic11—44no—
345Dic11—42no—
346C22×Q8—111no—
347C22×Q8—221no—
348C22×Q8C22×D1112yes—
349C22×D4—221no—
350C22×D4C22×D1111yescharacteristic
351C23×C4—21no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—111no—
355C2×Q16—118no—
356C2×Q16—444no—
357C2×SD16—44no—
358C2×SD16C22×D1118yes—
359C2×M16—118no—
360C2×M16—444no—
361C22×C8—112no—
362C22×C8C22×D1112yes—
363C4⋊Q8—22no—
364C4⋊Q8—114no—
365C4⋊Q8—222no—
366C4⋊Q8C22×D1114yes—
367#126—228no—
368#125—114no—
369#125—222no—
370#125—228no—
371#124—114no—
372#124—222no—
373#123—228no—
374C22⋊Q8—118no—
375C22⋊Q8—114no—
376C22⋊Q8—222no—
377C22⋊Q8—228no—
378C22⋊Q8—224no—
379#121—114no—
380#121—222no—
381C4×Q8—118no—
382C4×Q8—114no—
383C4×Q8—228no—
384C4×Q8—224no—
385C4×Q8—222no—
386C4×D4—22no—
387C4×D4—228no—
388C4×D4C22×D1114yes—
389#117—228no—
390#117—228no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—112no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4—222no—
399C2×C4⋊C4—222no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4—221no—
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C22⋊C4—21no—
404C2×C22⋊C4—222no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—221no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C42—111no—
410C2×C42—111no—
411C2×C42—111no—
412C2×C42—114no—
413C2×C42—114no—
414C2×C42—222no—
415C2×C42—221no—
416C2×C42C22×D1111yescharacteristic
417#107—118no—
418#106—118no—
419C4⋊C8—118no—
420C4⋊C8—114no—
421C4⋊C8C22×D1114yes—
422#103—118no—
423#103—118no—
424#103C22×D1118yes—
425#102—118no—
426C2×C11—82no—
427C2×C11#325214yescomplemented
428C2×C11C2×#53711yescharacteristic
429C2×C11C22×#13711yescharacteristic
430C2×C11C2×#57511yescharacteristic
431D11—42no—
432C24—21no—
433C24—111no—
434C2×Q8—22no—
435C2×Q8—24no—
436C2×Q8—24no—
437C2×Q8—112no—
438C2×Q8—221no—
439C2×Q8—224no—
440C2×Q8—222no—
441C2×Q8—222no—
442C2×Q8—444no—
443C2×Q8C23×D1114yes—
444C2×D4—21no—
445C2×D4—22no—
446C2×D4—22no—
447C2×D4—224no—
448C2×D4—444no—
449C2×D4C23×D1112yes—
450C22×C4—22no—
451C22×C4—21no—
452C22×C4—24no—
453C22×C4—44no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—111no—
457C22×C4—114no—
458C22×C4—112no—
459C22×C4—112no—
460C22×C4—114no—
461C22×C4—224no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—221no—
465C22×C4—221no—
466C22×C4—222no—
467C22×C4—442no—
468C22×C4D4×D1111yescharacteristic
469C22×C4D4×D1111yescharacteristic
470C22×C4C23×D1111yescharacteristic
471Q16—448no—
472SD16—48no—
473M16—448no—
474C2×C8—24no—
475C2×C8—114no—
476C2×C8—224no—
477C2×C8C23×D1114yes—
478C4⋊C4—24no—
479C4⋊C4—24no—
480C4⋊C4—21no—
481C4⋊C4—114no—
482C4⋊C4—112no—
483C4⋊C4—224no—
484C4⋊C4—224no—
485C4⋊C4—224no—
486C4⋊C4—228no—
487C4⋊C4—228no—
488C4⋊C4—221no—
489C4⋊C4—222no—
490C4⋊C4—224no—
491C4⋊C4—224no—
492C4⋊C4C23×D1112yes—
493C22⋊C4—24no—
494C22⋊C4—228no—
495C22⋊C4—224no—
496C22⋊C4—224no—
497C22⋊C4—224no—
498C22⋊C4—224no—
499C42—114no—
500C42—112no—
501C42—114no—
502C42—112no—
503C42—228no—
504C42—224no—
505C42D4×D1112yes—
506C42C23×D1112yes—
507C11C2×#325211yescharacteristic, complemented, Sylow
508C23—22no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—112no—
513C23—222no—
514C23—222no—
515C23—222no—
516C23C2×D4×D1111yescharacteristic
517Q8—24no—
518Q8—24no—
519Q8—44no—
520Q8—222no—
521Q8—222no—
522Q8—448no—
523Q8—442no—
524D4—22no—
525D4—22no—
526D4—42no—
527D4—448no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—48no—
534C2×C4—112no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—222no—
538C2×C4—222no—
539C2×C4—222no—
540C2×C4—228no—
541C2×C4—224no—
542C2×C4—222no—
543C2×C4—222no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—224no—
547C2×C4—444no—
548C2×C4—442no—
549C2×C4—444no—
550C2×C4—442no—
551C2×C4#6696814yes—
552C2×C4C2×D4×D1112yes—
553C2×C4C2×D4×D1112yes—
554C2×C4C2×D4×D1111yescharacteristic
555C2×C4#6703712yes—
556C2×C4#6704312yes—
557C2×C4C24×D1111yescharacteristic
558C8—24no—
559C8—224no—
560C22—42no—
561C22—42no—
562C22—42no—
563C22—84no—
564C22—222no—
565C22—222no—
566C22—222no—
567C22—444no—
568C22#1062313912yes—
569C22C2×#6696812yes—
570C22#1062330812yes—
571C22C22×D4×D1111yescharacteristic
572C4—22no—
573C4—44no—
574C4—42no—
575C4—222no—
576C4—222no—
577C4—222no—
578C4—442no—
579C4—442no—
580C4—444no—
581C4#1062313912yes—
582C4C2×#6696814yes—
583C4C2×#6703711yescharacteristic
584C4C2×#6704311yescharacteristic
585C2—82no—
586C2—442no—
587C2#1307998514yesdirect product factor
588C2C2×#1062313911yescharacteristic
589C2C22×#6696811yescharacteristic
590C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenterC2×#461D11
hypocenterC11C2×#3252
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13079985C2direct (N × H)
4. C2×#10622409C2semidirect
5. C2×#10622463C2semidirect
6. C2×#10622621C2semidirect
7. C2×#10622429C2semidirect
9. C2×#10622779C2semidirect
10. C2×#10622703C2semidirect
11. C2×#10622450C2semidirect
12. C2×C11×#461C2semidirect
25. #10623259C22semidirect
39. C11×#461C22semidirect
45. #10622779C22semidirect
49. #10622703C22semidirect
50. #10622621C22semidirect
53. #10622463C22semidirect
54. #10622450C22semidirect
55. #10622429C22semidirect
56. #10622409C22semidirect
223. C2×#461D11semidirect
310. #461C2×D11semidirect
427. C2×C11#3252semidirect
507. C11C2×#3252semidirect
587. C2#13079985direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106230882
#130799852
C2×#106224092
C2×#106224632
C2×#106226212
C2×#106224292
C2×#106227872
C2×#106227792
C2×#106227032
C2×#106224502
C2×C11×#4612
C2×#325211