Finite Group Databasebeta

← C2×#13079956 #15626581

Subgroups — C2×#13079956 #15626581

Order 2816.

1930 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×#10623111C211yesmaximal, characteristic
3#13079956C2116yesmaximal, direct product factor
4C2×#10622470C212yesmaximal, complemented
5C2×#10622700C211yesmaximal, characteristic, complemented
6C2×#10622426C212yesmaximal, complemented
7C2×#10622477C212yesmaximal
8C2×#10622411C212yesmaximal, complemented
9C2×#10622644C211yesmaximal, characteristic, complemented
10C2×#10622454C211yesmaximal, characteristic, complemented
11C2×D11×C4⋊C8C211yesmaximal, characteristic, complemented
12C2×C11×#475C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#67000C2211yescharacteristic
16C2×#66999—21no—
17C2×#66999C2211yescharacteristic
18C2×Q8×Dic11—21no—
19C22×#4326C2212yes—
20C22×#4314C2212yes—
21C22×C8×D11C2212yes—
22#10623259—24no—
23#10623259C2218yescomplemented
24#10623111—24no—
25#10623111C2218yes—
26C2×#66951—21no—
27C2×#66950C2212yes—
28C2×#66948C2211yescharacteristic
29C2×#66947—21no—
30C2×#66945—21no—
31C2×#66943—21no—
32C2×#66943C2211yescharacteristic
33C2×#66940C2212yes—
34C2×C4×D44—21no—
35C2×C4×D44C2211yescharacteristic
36C2×#66925—21no—
37C2×C42×D11C2211yescharacteristic
38C2×#66922C2211yescharacteristic
39C11×#475C2218yescomplemented
40C2×C11×#106C2212yes—
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#103C2212yes—
43C2×#66880C2212yes—
44C2×Dic11⋊C8C2212yes—
45#10622700C2218yescomplemented
46#10622644C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66873C2212yes—
49C2×#66871C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622477C22116yes—
52#10622470C22116yescomplemented
53#10622454C2218yescomplemented
54D11×C4⋊C8C2218yescomplemented
55#10622426C22116yescomplemented
56#10622411C22116yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11C2311yescharacteristic
59C22×D44—21no—
60C22×D44C2311yescharacteristic
61C22×C4×D11—21no—
62C22×C4×D11D411yescharacteristic
63C22×C4×D11D411yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×Dic22C2312yes—
66C22×C8×C11C2312yes—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2314yes—
69C4×Q8×C11—22no—
70C4×Q8×C11C2314yes—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4—21no—
73C2×C11×C4⋊C4C2312yes—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C42×C11—21no—
76C2×C42×C11C2311yescharacteristic
77#67000—22no—
78#67000C2314yes—
79#66999—28no—
80#66999—22no—
81#66999C2314yes—
82Q8×Dic11—28no—
83C2×#4326—44no—
84C2×#4326C2318yes—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—21no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—22no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11D411yescharacteristic
101C2×C4×Dic11D411yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2312yes—
104C2×#4314—44no—
105C2×#4314C2318yes—
106C2×C8×D11—44no—
107C2×C8×D11C2318yes—
108#66951—28no—
109#66950—24no—
110#66950C2318yes—
111#66948—22no—
112#66948C2314yes—
113#66947—28no—
114#66945—28no—
115#66943—28no—
116#66943—22no—
117#66943C2314yes—
118#66940—24no—
119#66940C2318yes—
120C4×D44—28no—
121C4×D44—22no—
122C4×D44C2314yes—
123#66925—28no—
124C42×D11D414yes—
125C42×D11C2314yes—
126#66922—22no—
127#66922C2314yes—
128C11×#106C2318yes—
129C11×C4⋊C8C2314yes—
130C11×#103C2318yes—
131#66880C2318yes—
132Dic11⋊C8C2318yes—
133#66874C2318yes—
134#66873C2318yes—
135#66871C2318yes—
136C4⋊(C11⋊C8)C2314yes—
137C2×#3248—111nomaximal, Sylow
138C23×D11—21no—
139C23×D11C2×D411yescharacteristic
140C2×Q8×C11—24no—
141C2×Q8×C11—21no—
142C2×Q8×C11—22no—
143C2×Q8×C11—22no—
144C2×Q8×C11—44no—
145C2×Q8×C11C2412yes—
146C22×C4×C11—22no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2411yescharacteristic
152C22×Dic11—22no—
153C22×Dic11—21no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×D44—24no—
158C2×D44—21no—
159C2×D44—22no—
160C2×D44—22no—
161C2×D44—44no—
162C2×D44C2412yes—
163C2×C4×D11—24no—
164C2×C4×D11—24no—
165C2×C4×D11—24no—
166C2×C4×D11—22no—
167C2×C4×D11—22no—
168C2×C4×D11—44no—
169C2×C4×D11C2×D412yes—
170C2×C4×D11C2×D414yes—
171C2×C4×D11C2×D414yes—
172C2×C4×D11C2412yes—
173C2×Dic22—22no—
174C2×Dic22—24no—
175C2×Dic22—24no—
176C2×Dic22C2414yes—
177C2×C8×C11—24no—
178C2×C8×C11C2414yes—
179C11×C4⋊C4—22no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4—21no—
182C11×C4⋊C4—24no—
183C11×C4⋊C4C2414yes—
184C11×C4⋊C4C2412yes—
185C42×C11—24no—
186C42×C11C2×D412yes—
187C42×C11C2412yes—
188#4326—48no—
189(C2×D11)⋊C4—24no—
190(C2×D11)⋊C4—24no—
191(C2×D11)⋊C4—24no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—28no—
194(C2×D11)⋊C4—24no—
195C4⋊Dic11—24no—
196C4⋊Dic11—28no—
197C4⋊Dic11—24no—
198C4⋊Dic11—24no—
199C4⋊Dic11—21no—
200C4⋊Dic11C2412yes—
201Dic11⋊C4—24no—
202Dic11⋊C4—24no—
203Dic11⋊C4—28no—
204C4×Dic11—28no—
205C4×Dic11C2×D412yes—
206C4×Dic11C2×D414yes—
207C4×Dic11C2×D414yes—
208C4×Dic11C2412yes—
209C2×C11⋊C8—24no—
210C2×C11⋊C8C2414yes—
211#4314—48no—
212C8×D11—48no—
213C2×#533—111no—
214C2×#529—111no—
215#3248—1116no—
216C2×#479—112no—
217C2×#475D1111yescharacteristic, complemented
218C2×#474—111no—
219C2×#467—112no—
220C2×#465—112no—
221C2×#464—112no—
222C2×#462—111no—
223C2×#461—111no—
224C22×C4⋊C8—111no—
225C23×C11C22×D411yescharacteristic
226C22×D11—22no—
227C22×D11—22no—
228C22×D11—22no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232C22×D11#13714yes—
233C22×D11C22×D412yes—
234Q8×C11—22no—
235Q8×C11—22no—
236Q8×C11—42no—
237Q8×C11—48no—
238C2×C4×C11—22no—
239C2×C4×C11—24no—
240C2×C4×C11—22no—
241C2×C4×C11—22no—
242C2×C4×C11—42no—
243C2×C4×C11—44no—
244C2×C4×C11—42no—
245C2×C4×C11#13514yes—
246C2×C4×C11C22×D412yes—
247C2×C4×C11C22×D411yescharacteristic
248C2×C4×C11C22×D412yes—
249C2×C4×C11H(5,𝔽2)12yes—
250C2×C4×C112−1+412yes—
251C2×C4×C11C2511yescharacteristic
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—22no—
255C2×Dic11—24no—
256C2×Dic11—22no—
257C2×Dic11—44no—
258C2×Dic11—42no—
259C2×Dic11C22×D412yes—
260C2×Dic11C22×D412yes—
261C2×Dic11C22×D412yes—
262D44—22no—
263D44—22no—
264D44—48no—
265D44—42no—
266C4×D11—28no—
267C4×D11—24no—
268C4×D11—28no—
269C4×D11—22no—
270C4×D11—22no—
271C4×D11—48no—
272Dic22—24no—
273Dic22—24no—
274Dic22—44no—
275C8×C11—24no—
276C11⋊C8—24no—
277C22×Q16—112no—
278C22×SD16—112no—
279C23×C8—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—111no—
292C2×C22⋊Q8—112no—
293C2×C22⋊Q8—221no—
294C2×#121—111no—
295C2×C4×Q8—112no—
296C2×C4×Q8—221no—
297C2×C4×Q8C2×D1111yescharacteristic
298C2×C4×D4—111no—
299C2×C4×D4—221no—
300C2×#117—221no—
301C2×#117—221no—
302C22×C42—111no—
303#479—1116no—
304#475C2×D1118yescomplemented
305#474—118no—
306#467—1116no—
307#465—1116no—
308#464—1116no—
309#462—118no—
310#461—118no—
311C2×#107—112no—
312C2×#106C2×D1112yes—
313C2×C4⋊C8—112no—
314C2×C4⋊C8—111no—
315C2×C4⋊C8—118no—
316C2×C4⋊C8C2×D1111yescharacteristic
317C2×#103—112no—
318C2×#103—112no—
319C2×#103C2×D1112yes—
320C2×#102—112no—
321C22×C11#53712yes—
322C22×C11C2×#13512yes—
323C22×C11C2×#13712yes—
324C22×C11C23×D411yescharacteristic
325C2×D11—22no—
326C2×D11—28no—
327C2×D11—22no—
328C2×D11—42no—
329C2×D11—42no—
330C2×D11—42no—
331C2×D11—84no—
332C2×D11C2×#13714yes—
333C4×C11—22no—
334C4×C11—42no—
335C4×C11—44no—
336C4×C11—42no—
337C4×C11#53712yes—
338C4×C11C2×#13514yes—
339C4×C11C2×H(5,𝔽2)11yescharacteristic
340C4×C11C2×2−1+411yescharacteristic
341Dic11—22no—
342Dic11—22no—
343Dic11—22no—
344Dic11—44no—
345Dic11—42no—
346C22×Q8—21no—
347C22×Q8—112no—
348C22×Q8C22×D1111yescharacteristic
349C22×D4—111no—
350C22×D4—221no—
351C23×C4—111no—
352C23×C4—111no—
353C23×C4—111no—
354C23×C4—221no—
355C2×Q16—118no—
356C2×Q16—444no—
357C2×SD16—118no—
358C2×SD16—444no—
359C22×C8—112no—
360C22×C8—118no—
361C22×C8—444no—
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—114no—
375C22⋊Q8—118no—
376C22⋊Q8—224no—
377C22⋊Q8—222no—
378C22⋊Q8—228no—
379#121—114no—
380#121—222no—
381C4×Q8—22no—
382C4×Q8—118no—
383C4×Q8—224no—
384C4×Q8—228no—
385C4×Q8C22×D1114yes—
386C4×D4—114no—
387C4×D4—228no—
388C4×D4—222no—
389#117—228no—
390#117—228no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—111no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—221no—
397C2×C4⋊C4—222no—
398C2×C4⋊C4—222no—
399C2×C4⋊C4—221no—
400C2×C4⋊C4—221no—
401C2×C4⋊C4C22×D1112yes—
402C2×C4⋊C4C22×D1111yescharacteristic
403C2×C22⋊C4—221no—
404C2×C22⋊C4—221no—
405C2×C22⋊C4—221no—
406C2×C22⋊C4—222no—
407C2×C22⋊C4—221no—
408C2×C22⋊C4—221no—
409C2×C42—21no—
410C2×C42—111no—
411C2×C42—111no—
412C2×C42—111no—
413C2×C42—114no—
414C2×C42—114no—
415C2×C42—222no—
416C2×C42C22×D1111yescharacteristic
417#107—118no—
418#106C22×D1118yes—
419C4⋊C8—118no—
420C4⋊C8—114no—
421C4⋊C8C22×D1114yes—
422#103—118no—
423#103—118no—
424#103C22×D1118yes—
425#102—118no—
426C2×C11#324814yescomplemented
427C2×C11C2×#53711yescharacteristic
428C2×C11C22×#13511yescharacteristic
429C2×C11C22×#13711yescharacteristic
430D11—24no—
431D11—82no—
432C24—111no—
433C24—221no—
434C2×Q8—21no—
435C2×Q8—24no—
436C2×Q8—22no—
437C2×Q8—22no—
438C2×Q8—44no—
439C2×Q8—114no—
440C2×Q8—222no—
441C2×Q8—224no—
442C2×Q8—224no—
443C2×Q8C23×D1112yes—
444C2×D4—112no—
445C2×D4—224no—
446C2×D4—221no—
447C2×D4—222no—
448C2×D4—222no—
449C2×D4—444no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—22no—
453C22×C4—111no—
454C22×C4—111no—
455C22×C4—111no—
456C22×C4—114no—
457C22×C4—114no—
458C22×C4—112no—
459C22×C4—112no—
460C22×C4—224no—
461C22×C4—224no—
462C22×C4—222no—
463C22×C4—222no—
464C22×C4—222no—
465C22×C4—221no—
466C22×C4—224no—
467C22×C4—444no—
468C22×C4D4×D1111yescharacteristic
469C22×C4D4×D1111yescharacteristic
470C22×C4C23×D1111yescharacteristic
471Q16—448no—
472SD16—448no—
473C2×C8—24no—
474C2×C8—114no—
475C2×C8—224no—
476C2×C8—448no—
477C2×C8C23×D1114yes—
478C4⋊C4—24no—
479C4⋊C4—24no—
480C4⋊C4—21no—
481C4⋊C4—22no—
482C4⋊C4—112no—
483C4⋊C4—224no—
484C4⋊C4—224no—
485C4⋊C4—224no—
486C4⋊C4—228no—
487C4⋊C4—228no—
488C4⋊C4—221no—
489C4⋊C4—224no—
490C4⋊C4—224no—
491C4⋊C4C23×D1114yes—
492C4⋊C4C23×D1112yes—
493C22⋊C4—224no—
494C22⋊C4—224no—
495C22⋊C4—224no—
496C22⋊C4—228no—
497C22⋊C4—224no—
498C22⋊C4—224no—
499C42—24no—
500C42—114no—
501C42—112no—
502C42—114no—
503C42—112no—
504C42—228no—
505C42D4×D1112yes—
506C42C23×D1112yes—
507C11C2×#324811yescharacteristic, complemented, Sylow
508C23—114no—
509C23—112no—
510C23—222no—
511C23—222no—
512C23—222no—
513C23—442no—
514C23—442no—
515C23—442no—
516C23C2×D4×D1111yescharacteristic
517Q8—22no—
518Q8—22no—
519Q8—48no—
520Q8—42no—
521Q8—224no—
522Q8—224no—
523Q8—444no—
524D4—222no—
525D4—222no—
526D4—448no—
527D4—442no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—24no—
532C2×C4—44no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—112no—
536C2×C4—112no—
537C2×C4—112no—
538C2×C4—228no—
539C2×C4—222no—
540C2×C4—222no—
541C2×C4—222no—
542C2×C4—228no—
543C2×C4—224no—
544C2×C4—222no—
545C2×C4—222no—
546C2×C4—224no—
547C2×C4—222no—
548C2×C4—442no—
549C2×C4—444no—
550C2×C4—448no—
551C2×C4#6696914yes—
552C2×C4C2×D4×D1112yes—
553C2×C4C2×D4×D1112yes—
554C2×C4C2×D4×D1111yescharacteristic
555C2×C4#6704012yes—
556C2×C4#6704212yes—
557C2×C4C24×D1111yescharacteristic
558C8—24no—
559C8—224no—
560C22—114no—
561C22—222no—
562C22—228no—
563C22—222no—
564C22—442no—
565C22—442no—
566C22—442no—
567C22—884no—
568C22#1062316012yes—
569C22C2×#6696912yes—
570C22D11×#13712yes—
571C22C22×D4×D1111yescharacteristic
572C4—22no—
573C4—42no—
574C4—44no—
575C4—42no—
576C4—222no—
577C4—222no—
578C4—222no—
579C4—444no—
580C4—442no—
581C4#1062316012yes—
582C4C2×#6696914yes—
583C4C2×#6704011yescharacteristic
584C4C2×#6704211yescharacteristic
585C2—224no—
586C2—882no—
587C2#1307995614yesdirect product factor
588C2C2×#1062316011yescharacteristic
589C2C22×#6696911yescharacteristic
590C2C2×D11×#13711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC2×#66948C22
hypercenterC2×#475D11
hypocenterC11C2×#3248
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13079956C2direct (N × H)
4. C2×#10622470C2semidirect
5. C2×#10622700C2semidirect
6. C2×#10622426C2semidirect
8. C2×#10622411C2semidirect
9. C2×#10622644C2semidirect
10. C2×#10622454C2semidirect
11. C2×D11×C4⋊C8C2semidirect
12. C2×C11×#475C2semidirect
23. #10623259C22semidirect
39. C11×#475C22semidirect
45. #10622700C22semidirect
46. #10622644C22semidirect
52. #10622470C22semidirect
53. #10622454C22semidirect
54. D11×C4⋊C8C22semidirect
55. #10622426C22semidirect
56. #10622411C22semidirect
217. C2×#475D11semidirect
304. #475C2×D11semidirect
426. C2×C11#3248semidirect
507. C11C2×#3248semidirect
587. C2#13079956direct (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×#106231112
#130799562
C2×#106224702
C2×#106227002
C2×#106224262
C2×#106224772
C2×#106224112
C2×#106226442
C2×#106224542
C2×D11×C4⋊C82
C2×C11×#4752
C2×#324811