Finite Group Databasebeta

← C2×#13079828 #15625923

Subgroups — C2×#13079828 #15625923

Order 2816.

1758 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic
2C2×#10623109C211yesmaximal, characteristic
3#13079828C2116yesmaximal, direct product factor
4C2×#10622489C212yesmaximal, complemented
5C2×#10622410C212yesmaximal, complemented
6C2×#10622501C212yesmaximal
7C2×#10622428C212yesmaximal
8C2×#10622704C211yesmaximal, characteristic, complemented
9C2×#10622464C211yesmaximal, characteristic, complemented
10C2×#10622633C211yesmaximal, characteristic, complemented
11C2×#10622448C211yesmaximal, 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
19#10623259—24no—
20#10623259C2218yes—
21#10623109—24no—
22#10623109C2218yes—
23C2×#66950—21no—
24C2×#66950C2211yescharacteristic
25C2×#66949—21no—
26C2×#66945C2212yes—
27C2×#66943C2212yes—
28C2×#66942—21no—
29C2×#66941C2211yescharacteristic
30C2×#66940—21no—
31C2×#66925—21no—
32C2×C42×D11C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22—21no—
35C2×C4×Dic22C2211yescharacteristic
36C11×#477C2218yescomplemented
37C2×C11×#107C2212yes—
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#103C2212yes—
40C2×#66899C2212yes—
41C2×(C2×D11)⋊C8C2212yes—
42C2×#66881C2212yes—
43C2×#66880C2212yes—
44C2×#66879C2212yes—
45#10622704C2218yescomplemented
46#10622633C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66872C2212yes—
49C2×#66871C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622501C22116yes—
52#10622489C22116yescomplemented
53#10622464C2218yescomplemented
54#10622448C2218yes—
55#10622428C22116yes—
56#10622410C22116yescomplemented
57C22×Q8×C11—21no—
58C22×Q8×C11C2311yescharacteristic
59C22×C4×D11D411yescharacteristic
60C22×C4×D11D411yescharacteristic
61C22×C4×D11C2311yescharacteristic
62C22×Dic22—21no—
63C22×Dic22—21no—
64C22×Dic22C2311yescharacteristic
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⋊C4C2311yescharacteristic
73C2×C11×C4⋊C4C2312yes—
74C2×C42×C11—21no—
75C2×C42×C11C2311yescharacteristic
76#66999—28no—
77#66999—22no—
78#66999C2314yes—
79Q8×Dic11—28no—
80#66997—22no—
81#66997C2314yes—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—22no—
85C2×C4⋊Dic11—21no—
86C2×C4⋊Dic11—21no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2312yes—
90C2×Dic11⋊C4—21no—
91C2×Dic11⋊C4—21no—
92C2×Dic11⋊C4—21no—
93C2×Dic11⋊C4—21no—
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—22no—
96C2×C4×Dic11—21no—
97C2×C4×Dic11—22no—
98C2×C4×Dic11D411yescharacteristic
99C2×C4×Dic11D411yescharacteristic
100C2×C4×Dic11C2311yescharacteristic
101C22×C11⋊C8C2312yes—
102#66950—28no—
103#66950—22no—
104#66950C2314yes—
105#66949—28no—
106#66945—24no—
107#66945C2318yes—
108#66943—24no—
109#66943C2318yes—
110#66942—28no—
111#66941—22no—
112#66941C2314yes—
113#66940—28no—
114#66925—28no—
115C42×D11D414yes—
116C42×D11C2314yes—
117#66922—22no—
118#66922C2314yes—
119C4×Dic22—22no—
120C4×Dic22—28no—
121C4×Dic22C2314yes—
122C11×#107C2318yes—
123C11×C4⋊C8C2314yes—
124C11×#103C2318yes—
125#66899C2318yes—
126(C2×D11)⋊C8C2318yes—
127#66881C2318yes—
128#66880C2318yes—
129#66879C2318yes—
130#66874C2318yes—
131#66872C2318yes—
132#66871C2318yes—
133C4⋊(C11⋊C8)C2314yes—
134C2×#3237—111nomaximal, Sylow
135C23×D11C2×D411yescharacteristic
136C2×Q8×C11—21no—
137C2×Q8×C11—24no—
138C2×Q8×C11—22no—
139C2×Q8×C11—22no—
140C2×Q8×C11—44no—
141C2×Q8×C11C2412yes—
142C22×C4×C11—22no—
143C22×C4×C11—21no—
144C22×C4×C11—21no—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—22no—
151C22×Dic11C2×D411yescharacteristic
152C22×Dic11C2×D411yescharacteristic
153C22×Dic11C2×D411yescharacteristic
154C2×C4×D11—24no—
155C2×C4×D11—22no—
156C2×C4×D11—22no—
157C2×C4×D11—42no—
158C2×C4×D11C2×D412yes—
159C2×C4×D11C2×D414yes—
160C2×C4×D11C2×D414yes—
161C2×C4×D11C2412yes—
162C2×Dic22—24no—
163C2×Dic22—21no—
164C2×Dic22—24no—
165C2×Dic22—22no—
166C2×Dic22—22no—
167C2×Dic22—44no—
168C2×Dic22—44no—
169C2×Dic22C2412yes—
170C2×C8×C11—24no—
171C2×C8×C11C2414yes—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—22no—
176C11×C4⋊C4C2414yes—
177C11×C4⋊C4C2412yes—
178C42×C11—24no—
179C42×C11C2×D412yes—
180C42×C11C2412yes—
181(C2×D11)⋊C4—24no—
182(C2×D11)⋊C4—24no—
183(C2×D11)⋊C4—28no—
184C4⋊Dic11—24no—
185C4⋊Dic11—28no—
186C4⋊Dic11—21no—
187C4⋊Dic11—22no—
188C4⋊Dic11—24no—
189C4⋊Dic11C2412yes—
190C4⋊Dic11C2414yes—
191Dic11⋊C4—24no—
192Dic11⋊C4—24no—
193Dic11⋊C4—24no—
194Dic11⋊C4—24no—
195Dic11⋊C4—28no—
196Dic11⋊C4—24no—
197C4×Dic11—28no—
198C4×Dic11—24no—
199C4×Dic11C2×D414yes—
200C4×Dic11C2×D412yes—
201C4×Dic11C2×D414yes—
202C4×Dic11C2412yes—
203C2×C11⋊C8—24no—
204C2×C11⋊C8C2414yes—
205C2×#533—111no—
206C2×#533—111no—
207#3237—1116no—
208C2×#501—112no—
209C2×#491—112no—
210C2×#485—112no—
211C2×#485—112no—
212C2×#477—111no—
213C2×#477D1111yescharacteristic, complemented
214C2×#475—111no—
215C2×#475—111no—
216C2×#432—111no—
217C23×C11C22×D411yescharacteristic
218C22×D11—22no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11C22×D412yes—
222Q8×C11—22no—
223Q8×C11—22no—
224Q8×C11—48no—
225Q8×C11—42no—
226C2×C4×C11—22no—
227C2×C4×C11—24no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—42no—
231C2×C4×C11—42no—
232C2×C4×C11—44no—
233C2×C4×C11#13714yes—
234C2×C4×C11C22×D412yes—
235C2×C4×C11C22×D411yescharacteristic
236C2×C4×C11C22×D412yes—
237C2×C4×C112−1+412yes—
238C2×C4×C112−1+412yes—
239C2×C4×C11C2511yescharacteristic
240C2×Dic11—22no—
241C2×Dic11—22no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—22no—
245C2×Dic11—24no—
246C2×Dic11—42no—
247C2×Dic11—44no—
248C2×Dic11—42no—
249C2×Dic11C22×D412yes—
250C2×Dic11C22×D412yes—
251C2×Dic11C22×D412yes—
252C4×D11—24no—
253C4×D11—28no—
254C4×D11—22no—
255C4×D11—22no—
256C4×D11—44no—
257Dic22—22no—
258Dic22—22no—
259Dic22—48no—
260Dic22—42no—
261Dic22—48no—
262C8×C11—24no—
263C11⋊C8—24no—
264#533—118no—
265#533—118no—
266#533—224no—
267#533—224no—
268C2×C4⋊Q8—111no—
269C2×C4⋊Q8—111no—
270C2×C4⋊Q8—111no—
271C2×C4⋊Q8C2×D1111yescharacteristic
272C2×#125—112no—
273C2×#125—221no—
274C2×C22⋊Q8—111no—
275C2×C22⋊Q8—111no—
276C2×C22⋊Q8—221no—
277C2×C22⋊Q8—221no—
278C2×C22⋊Q8—221no—
279C2×C4×Q8—111no—
280C2×C4×Q8—221no—
281C2×C4×Q8—221no—
282C2×C4×Q8—221no—
283C2×C4×Q8C2×D1111yescharacteristic
284C2×#117—112no—
285C2×#117—221no—
286C22×C42—111no—
287#501—1116no—
288#491—1116no—
289#485—1116no—
290#485—1116no—
291#477—118no—
292#477C2×D1118yescomplemented
293#475—118no—
294#475—118no—
295#432—118no—
296C2×#107—112no—
297C2×#107C2×D1112yes—
298C2×#106—112no—
299C2×#106—112no—
300C2×C4⋊C8—111no—
301C2×C4⋊C8C2×D1111yescharacteristic
302C2×#103—112no—
303C2×#103—112no—
304C2×#103—112no—
305C2×#103C2×D1112yes—
306C2×C22⋊C8—112no—
307C2×#97—112no—
308C22×C11#53612yes—
309C22×C11C2×#13712yes—
310C22×C11#57512yes—
311C22×C11C23×D411yescharacteristic
312C2×D11—22no—
313C2×D11—22no—
314C2×D11—22no—
315C2×D11—44no—
316C4×C11—22no—
317C4×C11—42no—
318C4×C11—44no—
319C4×C11—42no—
320C4×C11#53612yes—
321C4×C11C2×#13714yes—
322C4×C11C2×2−1+411yescharacteristic
323C4×C11C2×2−1+411yescharacteristic
324Dic11—22no—
325Dic11—22no—
326Dic11—22no—
327Dic11—42no—
328Dic11—44no—
329Dic11—42no—
330C22×Q8—21no—
331C22×Q8—111no—
332C22×Q8—221no—
333C22×Q8—221no—
334C22×Q8C22×D1111yescharacteristic
335C23×C4—111no—
336C23×C4—111no—
337C23×C4—111no—
338C22×C8—112no—
339C22×C8C22×D1112yes—
340C4⋊Q8—22no—
341C4⋊Q8—114no—
342C4⋊Q8—114no—
343C4⋊Q8—114no—
344C4⋊Q8—222no—
345C4⋊Q8—222no—
346C4⋊Q8—222no—
347C4⋊Q8C22×D1114yes—
348#125—118no—
349#125—224no—
350#125—228no—
351C22⋊Q8—114no—
352C22⋊Q8—114no—
353C22⋊Q8—222no—
354C22⋊Q8—228no—
355C22⋊Q8—228no—
356C22⋊Q8—222no—
357C22⋊Q8—228no—
358C4×Q8—22no—
359C4×Q8—114no—
360C4×Q8—228no—
361C4×Q8—228no—
362C4×Q8—228no—
363C4×Q8—222no—
364C4×Q8C22×D1114yes—
365#117—118no—
366#117—228no—
367#117—224no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—221no—
373C2×C4⋊C4—221no—
374C2×C4⋊C4—221no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4C22×D1112yes—
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C22⋊C4—222no—
384C2×C22⋊C4—221no—
385C2×C22⋊C4—221no—
386C2×C42—21no—
387C2×C42—111no—
388C2×C42—111no—
389C2×C42—111no—
390C2×C42—114no—
391C2×C42—114no—
392C2×C42—222no—
393C2×C42—221no—
394C2×C42C22×D1111yescharacteristic
395#107—118no—
396#107C22×D1118yes—
397#106—118no—
398#106—118no—
399C4⋊C8—114no—
400C4⋊C8C22×D1114yes—
401#103—118no—
402#103—118no—
403#103—118no—
404#103C22×D1118yes—
405C22⋊C8—118no—
406#97—118no—
407C2×C11#323714yescomplemented
408C2×C11C2×#53611yescharacteristic
409C2×C11C22×#13711yescharacteristic
410C2×C11C2×#57511yescharacteristic
411D11—42no—
412C24—111no—
413C2×Q8—21no—
414C2×Q8—24no—
415C2×Q8—22no—
416C2×Q8—22no—
417C2×Q8—44no—
418C2×Q8—112no—
419C2×Q8—224no—
420C2×Q8—224no—
421C2×Q8—221no—
422C2×Q8—222no—
423C2×Q8—222no—
424C2×Q8—444no—
425C2×Q8—444no—
426C2×Q8C23×D1112yes—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—22no—
430C22×C4—111no—
431C22×C4—111no—
432C22×C4—111no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—112no—
436C22×C4—114no—
437C22×C4—224no—
438C22×C4—222no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—221no—
442C22×C4—221no—
443C22×C4—442no—
444C22×C4D4×D1111yescharacteristic
445C22×C4D4×D1111yescharacteristic
446C22×C4C23×D1111yescharacteristic
447C2×C8—24no—
448C2×C8—114no—
449C2×C8—224no—
450C2×C8C23×D1114yes—
451C4⋊C4—24no—
452C4⋊C4—24no—
453C4⋊C4—22no—
454C4⋊C4—21no—
455C4⋊C4—114no—
456C4⋊C4—112no—
457C4⋊C4—224no—
458C4⋊C4—224no—
459C4⋊C4—224no—
460C4⋊C4—224no—
461C4⋊C4—228no—
462C4⋊C4—228no—
463C4⋊C4—224no—
464C4⋊C4—222no—
465C4⋊C4—221no—
466C4⋊C4—224no—
467C4⋊C4—224no—
468C4⋊C4C23×D1114yes—
469C4⋊C4C23×D1112yes—
470C22⋊C4—228no—
471C22⋊C4—224no—
472C22⋊C4—224no—
473C42—24no—
474C42—114no—
475C42—114no—
476C42—112no—
477C42—112no—
478C42—228no—
479C42—224no—
480C42D4×D1112yes—
481C42C23×D1112yes—
482C11C2×#323711yescharacteristic, complemented, Sylow
483C23—112no—
484C23—222no—
485C23—222no—
486C23—222no—
487C23C2×D4×D1111yescharacteristic
488Q8—22no—
489Q8—22no—
490Q8—48no—
491Q8—42no—
492Q8—222no—
493Q8—222no—
494Q8—448no—
495Q8—448no—
496Q8—442no—
497C2×C4—22no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—44no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—112no—
505C2×C4—112no—
506C2×C4—112no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—222no—
510C2×C4—228no—
511C2×C4—224no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—222no—
516C2×C4—222no—
517C2×C4—444no—
518C2×C4—444no—
519C2×C4—442no—
520C2×C4—442no—
521C2×C4#6697114yes—
522C2×C4C2×D4×D1112yes—
523C2×C4C2×D4×D1112yes—
524C2×C4C2×D4×D1111yescharacteristic
525C2×C4#6704012yes—
526C2×C4#6704312yes—
527C2×C4C24×D1111yescharacteristic
528C8—24no—
529C8—224no—
530C22—222no—
531C22—222no—
532C22—222no—
533C22—444no—
534C22#1062315912yes—
535C22C2×#6697112yes—
536C22#1062330412yes—
537C22C22×D4×D1111yescharacteristic
538C4—22no—
539C4—42no—
540C4—44no—
541C4—42no—
542C4—222no—
543C4—222no—
544C4—222no—
545C4—442no—
546C4—444no—
547C4—442no—
548C4#1062315912yes—
549C4C2×#6697114yes—
550C4C2×#6704011yescharacteristic
551C4C2×#6704311yescharacteristic
552C2—442no—
553C2#1307982814yesdirect product factor
554C2C2×#1062315911yescharacteristic
555C2C22×#6697111yescharacteristic
556C2C2×#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×#3237
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. #13079828C2direct (N × H)
4. C2×#10622489C2semidirect
5. C2×#10622410C2semidirect
8. C2×#10622704C2semidirect
9. C2×#10622464C2semidirect
10. C2×#10622633C2semidirect
12. C2×C11×#477C2semidirect
36. C11×#477C22semidirect
45. #10622704C22semidirect
46. #10622633C22semidirect
52. #10622489C22semidirect
53. #10622464C22semidirect
56. #10622410C22semidirect
213. C2×#477D11semidirect
292. #477C2×D11semidirect
407. C2×C11#3237semidirect
482. C11C2×#3237semidirect
553. C2#13079828direct (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
#130798282
C2×#106224892
C2×#106224102
C2×#106225012
C2×#106224282
C2×#106227042
C2×#106224642
C2×#106226332
C2×#106224482
C2×C11×#4772
C2×#323711