Finite Group Databasebeta

← C2×#13079960 #15626586

Subgroups — C2×#13079960 #15626586

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×#10623109C211yesmaximal, characteristic
3#13079960C2116yesmaximal, direct product factor
4C2×#10622488C212yesmaximal, complemented
5C2×#10622704C211yesmaximal, characteristic, complemented
6C2×#10622500C212yesmaximal
7C2×#10622426C212yesmaximal
8C2×#10622462C211yesmaximal, characteristic, complemented
9C2×#10622644C211yesmaximal, characteristic, complemented
10C2×#10622406C212yesmaximal, complemented
11C2×D11×C4⋊C8C211yesmaximal, characteristic
12C2×C11×#477C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#66999—21no—
16C2×#66999C2211yescharacteristic
17C2×Q8×Dic11—21no—
18C2×#66997C2211yescharacteristic
19C22×#4326C2212yes—
20C22×Dic44C2212yes—
21C22×C8×D11C2212yes—
22#10623259—24no—
23#10623259C2218yes—
24#10623109—24no—
25#10623109C2218yes—
26C2×#66950C2211yescharacteristic
27C2×#66950C2212yes—
28C2×#66949—21no—
29C2×#66945—21no—
30C2×#66943—21no—
31C2×#66942—21no—
32C2×#66941C2211yescharacteristic
33C2×#66940C2212yes—
34C2×#66925—21no—
35C2×C42×D11C2211yescharacteristic
36C2×#66922C2211yescharacteristic
37C2×C4×Dic22—21no—
38C2×C4×Dic22C2211yescharacteristic
39C11×#477C2218yescomplemented
40C2×C11×#107C2212yes—
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#103C2212yes—
43C2×#66880C2212yes—
44C2×Dic11⋊C8C2212yes—
45#10622704C2218yescomplemented
46#10622644C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66874C2212yes—
49C2×#66871C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622500C22116yes—
52#10622488C22116yescomplemented
53#10622462C2218yescomplemented
54D11×C4⋊C8C2218yes—
55#10622426C22116yes—
56#10622406C22116yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11C2311yescharacteristic
59C22×C4×D11D411yescharacteristic
60C22×C4×D11D411yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C22×Dic22—21no—
63C22×Dic22C2311yescharacteristic
64C22×Dic22C2312yes—
65C22×C8×C11C2312yes—
66C11×C4⋊Q8—22no—
67C11×C4⋊Q8C2314yes—
68C4×Q8×C11—22no—
69C4×Q8×C11C2314yes—
70C2×C11×C4⋊C4—21no—
71C2×C11×C4⋊C4—21no—
72C2×C11×C4⋊C4C2312yes—
73C2×C11×C4⋊C4C2311yescharacteristic
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76#66999—28no—
77#66999—22no—
78#66999C2314yes—
79Q8×Dic11—28no—
80#66997—22no—
81#66997C2314yes—
82C2×#4326—44no—
83C2×#4326C2318yes—
84C2×(C2×D11)⋊C4—21no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—22no—
87C2×C4⋊Dic11—21no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4⋊Dic11—22no—
91C2×C4⋊Dic11C2311yescharacteristic
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—21no—
96C2×Dic11⋊C4—21no—
97C2×Dic11⋊C4—22no—
98C2×C4×Dic11—21no—
99C2×C4×Dic11—22no—
100C2×C4×Dic11D411yescharacteristic
101C2×C4×Dic11D411yescharacteristic
102C2×C4×Dic11C2311yescharacteristic
103C22×C11⋊C8C2312yes—
104C2×Dic44—44no—
105C2×Dic44C2318yes—
106C2×C8×D11—44no—
107C2×C8×D11C2318yes—
108#66950—24no—
109#66950—22no—
110#66950C2318yes—
111#66950C2314yes—
112#66949—28no—
113#66945—28no—
114#66943—28no—
115#66942—28no—
116#66941—22no—
117#66941C2314yes—
118#66940—24no—
119#66940C2318yes—
120#66925—28no—
121C42×D11D414yes—
122C42×D11C2314yes—
123#66922—22no—
124#66922C2314yes—
125C4×Dic22—22no—
126C4×Dic22—28no—
127C4×Dic22C2314yes—
128C11×#107C2318yes—
129C11×C4⋊C8C2314yes—
130C11×#103C2318yes—
131#66880C2318yes—
132Dic11⋊C8C2318yes—
133#66874C2318yes—
134#66874C2318yes—
135#66871C2318yes—
136C4⋊(C11⋊C8)C2314yes—
137C2×#3249—111nomaximal, Sylow
138C23×D11C2×D411yescharacteristic
139C2×Q8×C11—21no—
140C2×Q8×C11—24no—
141C2×Q8×C11—22no—
142C2×Q8×C11—22no—
143C2×Q8×C11—44no—
144C2×Q8×C11C2412yes—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2411yescharacteristic
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—22no—
154C22×Dic11C2×D411yescharacteristic
155C22×Dic11C2×D411yescharacteristic
156C22×Dic11C2×D411yescharacteristic
157C2×C4×D11—22no—
158C2×C4×D11—22no—
159C2×C4×D11—42no—
160C2×C4×D11Q1618yescomplemented
161C2×C4×D11C2×D412yes—
162C2×C4×D11C2×D414yes—
163C2×C4×D11C2×D414yes—
164C2×C4×D11C2412yes—
165C2×Dic22—24no—
166C2×Dic22—21no—
167C2×Dic22—22no—
168C2×Dic22—22no—
169C2×Dic22—24no—
170C2×Dic22—22no—
171C2×Dic22—24no—
172C2×Dic22—44no—
173C2×Dic22C2412yes—
174C2×Dic22C2414yes—
175C2×C8×C11—24no—
176C2×C8×C11C2414yes—
177C11×C4⋊C4—22no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4—24no—
180C11×C4⋊C4—24no—
181C11×C4⋊C4C2414yes—
182C11×C4⋊C4C2412yes—
183C42×C11—24no—
184C42×C11C2×D412yes—
185C42×C11C2412yes—
186#4326—48no—
187(C2×D11)⋊C4—24no—
188(C2×D11)⋊C4—24no—
189(C2×D11)⋊C4—28no—
190C4⋊Dic11—24no—
191C4⋊Dic11—28no—
192C4⋊Dic11—21no—
193C4⋊Dic11—24no—
194C4⋊Dic11—24no—
195C4⋊Dic11C2412yes—
196Dic11⋊C4—24no—
197Dic11⋊C4—24no—
198Dic11⋊C4—24no—
199Dic11⋊C4—24no—
200Dic11⋊C4—28no—
201Dic11⋊C4—24no—
202C4×Dic11—28no—
203C4×Dic11—24no—
204C4×Dic11C2×D414yes—
205C4×Dic11C2×D412yes—
206C4×Dic11C2×D414yes—
207C4×Dic11C2412yes—
208C2×C11⋊C8—24no—
209C2×C11⋊C8C2414yes—
210Dic44—48no—
211C8×D11—48no—
212C2×#533—111no—
213C2×#533—111no—
214#3249—1116no—
215C2×#477—112no—
216C2×#477—111no—
217C2×#477D1111yescharacteristic, complemented
218C2×#467—112no—
219C2×#467—112no—
220C2×#462—111no—
221C2×#462—112no—
222C2×#462—111no—
223C22×C4⋊C8—111no—
224C23×C11C22×D411yescharacteristic
225C22×D11—22no—
226C22×D11—22no—
227C22×D11C2×Q1614yes—
228C22×D11C22×D412yes—
229Q8×C11—22no—
230Q8×C11—22no—
231Q8×C11—48no—
232Q8×C11—42no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—22no—
237C2×C4×C11—42no—
238C2×C4×C11—42no—
239C2×C4×C11—44no—
240C2×C4×C11C2×Q1614yes—
241C2×C4×C11C22×D412yes—
242C2×C4×C11C22×D411yescharacteristic
243C2×C4×C11C22×D412yes—
244C2×C4×C11H(5,𝔽2)12yes—
245C2×C4×C112−1+412yes—
246C2×C4×C11C2511yescharacteristic
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—24no—
252C2×Dic11—42no—
253C2×Dic11—44no—
254C2×Dic11—42no—
255C2×Dic11C2×Q1614yes—
256C2×Dic11C22×D412yes—
257C2×Dic11C22×D412yes—
258C2×Dic11C22×D412yes—
259C4×D11—24no—
260C4×D11—22no—
261C4×D11—22no—
262C4×D11—44no—
263C4×D11C2×Q16116yescomplemented
264Dic22—22no—
265Dic22—24no—
266Dic22—22no—
267Dic22—24no—
268Dic22—48no—
269Dic22—42no—
270Dic22—44no—
271C8×C11—24no—
272C11⋊C8—24no—
273C22×Q16—112no—
274C22×Q16—112no—
275C23×C8—112no—
276#533—118no—
277#533—118no—
278#533—224no—
279#533—224no—
280C2×C4⋊Q8—111no—
281C2×C4⋊Q8—111no—
282C2×C4⋊Q8—111no—
283C2×C4⋊Q8C2×D1111yescharacteristic
284C2×#125—221no—
285C2×#125—221no—
286C2×C22⋊Q8—111no—
287C2×C22⋊Q8—112no—
288C2×C22⋊Q8—111no—
289C2×C22⋊Q8—221no—
290C2×C22⋊Q8—221no—
291C2×C4×Q8—112no—
292C2×C4×Q8—111no—
293C2×C4×Q8—221no—
294C2×C4×Q8—221no—
295C2×C4×Q8C2×D1111yescharacteristic
296C2×#117—221no—
297C2×#117—221no—
298C22×C42—111no—
299#477—118no—
300#477—1116no—
301#477C2×D1118yescomplemented
302#467—1116no—
303#467—1116no—
304#462—118no—
305#462—118no—
306#462—1116no—
307C2×#107—112no—
308C2×#107C2×D1112yes—
309C2×C4⋊C8—112no—
310C2×C4⋊C8—111no—
311C2×C4⋊C8—118no—
312C2×C4⋊C8C2×D1111yescharacteristic
313C2×#103—112no—
314C2×#103—112no—
315C2×#103—112no—
316C2×#103C2×D1112yes—
317C22×C11#53712yes—
318C22×C11C22×Q1612yes—
319C22×C11#57512yes—
320C22×C11C23×D411yescharacteristic
321C2×D11—22no—
322C2×D11—28no—
323C2×D11—22no—
324C2×D11C22×Q1614yes—
325C4×C11—22no—
326C4×C11—42no—
327C4×C11—44no—
328C4×C11—42no—
329C4×C11#53712yes—
330C4×C11C22×Q1614yes—
331C4×C11C2×H(5,𝔽2)11yescharacteristic
332C4×C11C2×2−1+411yescharacteristic
333Dic11—22no—
334Dic11—22no—
335Dic11—42no—
336Dic11—44no—
337Dic11—42no—
338Dic11C22×Q1614yes—
339C22×Q8—21no—
340C22×Q8—112no—
341C22×Q8—111no—
342C22×Q8—221no—
343C22×Q8C22×D1111yescharacteristic
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—111no—
347C2×Q16—118no—
348C2×Q16—118no—
349C2×Q16—444no—
350C2×Q16—444no—
351C22×C8—112no—
352C22×C8—118no—
353C22×C8—444no—
354C22×C8C22×D1112yes—
355C4⋊Q8—22no—
356C4⋊Q8—114no—
357C4⋊Q8—114no—
358C4⋊Q8—114no—
359C4⋊Q8—222no—
360C4⋊Q8—222no—
361C4⋊Q8—222no—
362C4⋊Q8C22×D1114yes—
363#125—228no—
364#125—228no—
365C22⋊Q8—114no—
366C22⋊Q8—114no—
367C22⋊Q8—118no—
368C22⋊Q8—222no—
369C22⋊Q8—224no—
370C22⋊Q8—228no—
371C22⋊Q8—222no—
372C22⋊Q8—228no—
373C4×Q8—22no—
374C4×Q8—118no—
375C4×Q8—114no—
376C4×Q8—228no—
377C4×Q8—224no—
378C4×Q8—228no—
379C4×Q8—222no—
380C4×Q8C22×D1114yes—
381#117—228no—
382#117—228no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—221no—
387C2×C4⋊C4—221no—
388C2×C4⋊C4—222no—
389C2×C4⋊C4—221no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4C22×D1112yes—
397C2×C4⋊C4C22×D1111yescharacteristic
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—222no—
401C2×C42—21no—
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—111no—
405C2×C42—114no—
406C2×C42—114no—
407C2×C42—222no—
408C2×C42—221no—
409C2×C42C22×D1111yescharacteristic
410#107—118no—
411#107C22×D1118yes—
412C4⋊C8—118no—
413C4⋊C8—114no—
414C4⋊C8C22×D1114yes—
415#103—118no—
416#103—118no—
417#103—118no—
418#103C22×D1118yes—
419C2×C11#324914yescomplemented
420C2×C11C2×#53711yescharacteristic
421C2×C11C23×Q1611yescharacteristic
422C2×C11C2×#57511yescharacteristic
423D11—24no—
424C24—111no—
425C2×Q8—21no—
426C2×Q8—24no—
427C2×Q8—22no—
428C2×Q8—22no—
429C2×Q8—44no—
430C2×Q8—114no—
431C2×Q8—112no—
432C2×Q8—224no—
433C2×Q8—222no—
434C2×Q8—221no—
435C2×Q8—224no—
436C2×Q8—222no—
437C2×Q8—222no—
438C2×Q8—224no—
439C2×Q8—444no—
440C2×Q8C23×D1112yes—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—22no—
444C22×C4—111no—
445C22×C4—118no—
446C22×C4—114no—
447C22×C4—111no—
448C22×C4—111no—
449C22×C4—112no—
450C22×C4—112no—
451C22×C4—114no—
452C22×C4—222no—
453C22×C4—222no—
454C22×C4—221no—
455C22×C4—222no—
456C22×C4—221no—
457C22×C4—442no—
458C22×C4D4×D1111yescharacteristic
459C22×C4D4×D1111yescharacteristic
460C22×C4C23×D1111yescharacteristic
461Q16—448no—
462Q16—448no—
463C2×C8—24no—
464C2×C8—114no—
465C2×C8—224no—
466C2×C8—448no—
467C2×C8C23×D1114yes—
468C4⋊C4—24no—
469C4⋊C4—24no—
470C4⋊C4—21no—
471C4⋊C4—22no—
472C4⋊C4—112no—
473C4⋊C4—224no—
474C4⋊C4—224no—
475C4⋊C4—228no—
476C4⋊C4—224no—
477C4⋊C4—224no—
478C4⋊C4—228no—
479C4⋊C4—224no—
480C4⋊C4—221no—
481C4⋊C4—224no—
482C4⋊C4—224no—
483C4⋊C4—224no—
484C4⋊C4C23×D1112yes—
485C4⋊C4C23×D1114yes—
486C22⋊C4—224no—
487C22⋊C4—224no—
488C22⋊C4—228no—
489C42—24no—
490C42—114no—
491C42—114no—
492C42—112no—
493C42—112no—
494C42—228no—
495C42—224no—
496C42D4×D1112yes—
497C42C23×D1112yes—
498C11C2×#324911yescharacteristic, complemented, Sylow
499C23—114no—
500C23—112no—
501C23—222no—
502C23—222no—
503C23C2×D4×D1111yescharacteristic
504Q8—22no—
505Q8—22no—
506Q8—48no—
507Q8—42no—
508Q8—224no—
509Q8—222no—
510Q8—222no—
511Q8—224no—
512Q8—448no—
513Q8—444no—
514Q8—442no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—44no—
520C2×C4—42no—
521C2×C4—42no—
522C2×C4—114no—
523C2×C4—112no—
524C2×C4—1116no—
525C2×C4—112no—
526C2×C4—112no—
527C2×C4—222no—
528C2×C4—222no—
529C2×C4—224no—
530C2×C4—222no—
531C2×C4—222no—
532C2×C4—222no—
533C2×C4—224no—
534C2×C4—222no—
535C2×C4—444no—
536C2×C4—442no—
537C2×C4—444no—
538C2×C4—442no—
539C2×C4Q16×D1114yes—
540C2×C4C2×D4×D1112yes—
541C2×C4C2×D4×D1112yes—
542C2×C4C2×D4×D1111yescharacteristic
543C2×C4#6704012yes—
544C2×C4#6704212yes—
545C2×C4C24×D1111yescharacteristic
546C8—24no—
547C8—224no—
548C22—114no—
549C22—222no—
550C22—228no—
551C22—222no—
552C22#1062316012yes—
553C22C2×Q16×D1112yes—
554C22#1062330412yes—
555C22C22×D4×D1111yescharacteristic
556C4—22no—
557C4—42no—
558C4—44no—
559C4—42no—
560C4—114no—
561C4—222no—
562C4—222no—
563C4—444no—
564C4—442no—
565C4—442no—
566C4#1062316012yes—
567C4C2×Q16×D1114yes—
568C4C2×#6704011yescharacteristic
569C4C2×#6704211yescharacteristic
570C2—224no—
571C2#1307996014yesdirect product factor
572C2C2×#1062316011yescharacteristic
573C2C22×Q16×D1111yescharacteristic
574C2C2×#1062330411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#477C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
hypercenterC2×#477D11
hypocenterC11C2×#3249
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. #13079960C2direct (N × H)
4. C2×#10622488C2semidirect
5. C2×#10622704C2semidirect
8. C2×#10622462C2semidirect
9. C2×#10622644C2semidirect
10. C2×#10622406C2semidirect
12. C2×C11×#477C2semidirect
39. C11×#477C22semidirect
45. #10622704C22semidirect
46. #10622644C22semidirect
52. #10622488C22semidirect
53. #10622462C22semidirect
56. #10622406C22semidirect
160. C2×C4×D11Q16semidirect
217. C2×#477D11semidirect
263. C4×D11C2×Q16semidirect
301. #477C2×D11semidirect
419. C2×C11#3249semidirect
498. C11C2×#3249semidirect
571. C2#13079960direct (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×#106231092
#130799602
C2×#106224882
C2×#106227042
C2×#106225002
C2×#106224262
C2×#106224622
C2×#106226442
C2×#106224062
C2×D11×C4⋊C82
C2×C11×#4772
C2×#324911