Finite Group Databasebeta

← C2×#13081647 #15634741

Subgroups — C2×#13081647 #15634741

Order 2816.

1906 conjugacy classes of subgroups.

The subgroup lattice has 530 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623101C211yesmaximal, characteristic, complemented
2#13081647C2116yesmaximal, direct product factor
3C2×#10622673C212yesmaximal
4C2×#10622705C211yesmaximal, characteristic, complemented
5C2×#10622667C212yesmaximal
6C2×#10622644C212yesmaximal, complemented
7C2×#10622703C211yesmaximal, characteristic, complemented
8C2×#10622632C211yesmaximal, characteristic
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622643C212yesmaximal, complemented
11C2×C4×#4324C211yesmaximal, characteristic
12C2×C11×#556C211yesmaximal, characteristic
13C11×#556—24no—
14C11×#556C2218yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#126—22no—
17C2×C11×#124C2212yes—
18C2×C11×C22⋊Q8—21no—
19C2×C4×Q8×C11C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117—21no—
23C2×Q8×Dic11—21no—
24C22×#4326C2212yes—
25C22×#4326C2212yes—
26C22×#4326C2212yes—
27C22×#4324C2211yescharacteristic
28C22×#4324C2212yes—
29#10623101—24no—
30#10623101C2218yescomplemented
31C2×#66943—21no—
32C2×#66943—22no—
33C2×#66922C2212yes—
34C2×#66922C2211yescharacteristic
35C2×C4×Dic22C2211yescharacteristic
36C2×C4×Dic22C2212yes—
37C2×#66899C2212yes—
38C2×#66896C2211yescharacteristic
39#10622705C2218yescomplemented
40#10622703C2218yescomplemented
41#10622673C22116yes—
42#10622667C22116yes—
43#10622644C22116yescomplemented
44#10622643C22116yescomplemented
45#10622637C2218yescomplemented
46#10622632C2218yes—
47C4×#4324C2218yes—
48C2×#66874C2212yes—
49C2×#66874C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11D411yescharacteristic
56C22×Q8×C11C2312yes—
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C22×Dic22C2311yescharacteristic
60C22×Dic22C2312yes—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8C2314yes—
63C11×#126—216no—
64C11×#124—24no—
65C11×#124C2318yes—
66C11×C22⋊Q8—28no—
67C4×Q8×C11—24no—
68C4×Q8×C11D414yes—
69C4×Q8×C11C2318yes—
70C4×Q8×C11C2314yes—
71C4×D4×C11—22no—
72C4×D4×C11C2314yes—
73C11×#117—28no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4D412yes—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—22no—
83C2×C42×C11—22no—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2312yes—
86Q8×Dic11—28no—
87C2×#4326—28no—
88C2×#4326—44no—
89C2×#4326—44no—
90C2×#4326C2318yes—
91C2×#4326C2318yes—
92C2×#4326C2318yes—
93C2×#4324—24no—
94C2×#4324—44no—
95C2×#4324C2314yes—
96C2×#4324C2318yes—
97C2×C4⋊Dic11—22no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—21no—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2312yes—
108C22×C11⋊C8C2311yescharacteristic
109#66943—28no—
110#66943—216no—
111#66922—22no—
112#66922—24no—
113#66922C2314yes—
114#66922C2318yes—
115C4×Dic22—22no—
116C4×Dic22—24no—
117C4×Dic22C2314yes—
118C4×Dic22C2318yes—
119#66899C2318yes—
120#66896C2314yes—
121#66874C2314yes—
122#66874C2318yes—
123#66872C2314yes—
124C4⋊(C11⋊C8)C2314yes—
125C4⋊(C11⋊C8)C2318yes—
126#66867C2318yes—
127C4×C11⋊C8C2314yes—
128C2×#3398—111nomaximal, Sylow
129C24×C11—21no—
130C2×Q8×C11—24no—
131C2×Q8×C11—22no—
132C2×Q8×C11—24no—
133C2×Q8×C11—24no—
134C2×Q8×C11C2×D414yes—
135C2×Q8×C11C2414yes—
136C2×D4×C11—21no—
137C2×D4×C11—22no—
138C2×D4×C11—22no—
139C2×D4×C11C2412yes—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—44no—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D412yes—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—21no—
150C22×Dic11—21no—
151C22×Dic11—22no—
152C2×Dic22—21no—
153C2×Dic22—22no—
154C2×Dic22—22no—
155C2×Dic22—24no—
156C2×Dic22—24no—
157C2×Dic22—22no—
158C2×Dic22C2412yes—
159C2×Dic22C2414yes—
160C11×C4⋊C4—24no—
161C11×C4⋊C4—28no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4C2×D414yes—
165C11×C4⋊C4C2×D418yes—
166C11×C4⋊C4C2412yes—
167C11×C22⋊C4—28no—
168C11×C22⋊C4—24no—
169C11×C22⋊C4—28no—
170C42×C11—28no—
171C42×C11C2×D412yes—
172C42×C11C2×D414yes—
173C42×C11C2412yes—
174C42×C11C2414yes—
175#4326—216no—
176#4326—48no—
177#4326—48no—
178#4324—28no—
179#4324—48no—
180C4⋊Dic11—21no—
181C4⋊Dic11—28no—
182C4⋊Dic11—24no—
183C4⋊Dic11—28no—
184C4⋊Dic11—24no—
185C4⋊Dic11C2412yes—
186Dic11⋊C4—28no—
187Dic11⋊C4—24no—
188C4×Dic11—28no—
189C4×Dic11—24no—
190C2×C11⋊C8—24no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8#4114yes—
193C2×C11⋊C8C2412yes—
194C2×C11⋊C8C2414yes—
195C2×C11⋊C8C2412yes—
196C2×#557—111no—
197C2×#556D1111yescharacteristic
198#3398—1116no—
199C2×#497—112no—
200C2×#494—111no—
201C2×#464—112no—
202C2×#462—111no—
203C2×#462—112no—
204C2×#461—111no—
205C2×#446—111no—
206C2×#441—112no—
207C2×C4×SD16—111no—
208C23×C11—22no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11C22×D411yescharacteristic
213Q8×C11—28no—
214Q8×C11—24no—
215Q8×C11—24no—
216Q8×C11—44no—
217D4×C11—22no—
218D4×C11—22no—
219D4×C11—42no—
220C2×C4×C11—24no—
221C2×C4×C11—24no—
222C2×C4×C11—22no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—44no—
226C2×C4×C11—42no—
227C2×C4×C11—48no—
228C2×C4×C11#13714yes—
229C2×C4×C11C22×D414yes—
230C2×C4×C11C22×D414yes—
231C2×C4×C11C22×D412yes—
232C2×C4×C11C22×D411yescharacteristic
233C2×C4×C11C22×D412yes—
234C2×C4×C11C2×#4112yes—
235C2×C4×C11H(5,𝔽2)12yes—
236C2×C4×C11C2511yescharacteristic
237C2×Dic11—22no—
238C2×Dic11—22no—
239C2×Dic11—24no—
240C2×Dic11—42no—
241C2×Dic11—44no—
242C2×Dic11—42no—
243Dic22—22no—
244Dic22—24no—
245Dic22—24no—
246Dic22—22no—
247Dic22—42no—
248Dic22—44no—
249C11⋊C8—24no—
250C11⋊C8—22no—
251C11⋊C8C2×#4114yes—
252C22×Q16—112no—
253C22×Q16—112no—
254C22×Q16—112no—
255C22×SD16—111no—
256C22×SD16—112no—
257#557—118no—
258#557—224no—
259#556—24no—
260#556C2×D1118yes—
261C2×C4⋊Q8—111no—
262C2×C4⋊Q8—112no—
263C2×C4⋊Q8C2×D1111yescharacteristic
264C2×#126—22no—
265C2×#125—221no—
266C2×#125—222no—
267C2×#124C2×D1112yes—
268C2×C22⋊Q8—21no—
269C2×C4×Q8—111no—
270C2×C4×Q8—112no—
271C2×C4×Q8—221no—
272C2×C4×Q8C2×D1112yes—
273C2×C4×Q8C2×D1111yescharacteristic
274C2×C4×D4C2×D1111yescharacteristic
275C2×#117—21no—
276#497—1116no—
277#494—118no—
278#464—1116no—
279#462—118no—
280#462—1116no—
281#461—118no—
282#446—118no—
283#441—1116no—
284C4×SD16—118no—
285C2×#106—111no—
286C2×C4⋊C8—111no—
287C2×C4⋊C8—112no—
288C2×#103—112no—
289C2×#103—111no—
290C2×#103—112no—
291C2×#102—111no—
292C2×#97—112no—
293C2×C4×C8—111no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11—42no—
297C22×C11—84no—
298C22×C11#55012yes—
299C22×C11C2×#13712yes—
300C22×C11#57812yes—
301C22×C11C23×D411yescharacteristic
302C4×C11—24no—
303C4×C11—24no—
304C4×C11—22no—
305C4×C11—44no—
306C4×C11—42no—
307C4×C11#55012yes—
308C4×C11C2×#13714yes—
309C4×C11C22×#4111yescharacteristic
310C4×C11C2×H(5,𝔽2)11yescharacteristic
311Dic11—42no—
312Dic11—44no—
313Dic11—42no—
314C22×Q8—111no—
315C22×Q8—112no—
316C22×Q8C22⋊D1111yescharacteristic
317C22×Q8C22×D1112yes—
318C22×D4C22×D1111yescharacteristic
319C23×C4—21no—
320C2×Q16—118no—
321C2×Q16—118no—
322C2×Q16—118no—
323C2×Q16—228no—
324C2×Q16—444no—
325C2×Q16—444no—
326C2×SD16—114no—
327C2×SD16—118no—
328C2×SD16—224no—
329C2×SD16—444no—
330C22×C8—111no—
331C22×C8—112no—
332C22×C8—111no—
333C4⋊Q8—22no—
334C4⋊Q8—114no—
335C4⋊Q8—118no—
336C4⋊Q8—222no—
337C4⋊Q8—224no—
338C4⋊Q8C22×D1114yes—
339#126—216no—
340#125—228no—
341#125—2216no—
342#124—24no—
343#124C22×D1118yes—
344C22⋊Q8—28no—
345C4×Q8—24no—
346C4×Q8—114no—
347C4×Q8—118no—
348C4×Q8—228no—
349C4×Q8—222no—
350C4×Q8—224no—
351C4×Q8C22⋊D1114yes—
352C4×Q8C22×D1118yes—
353C4×Q8C22×D1114yes—
354C4×D4—22no—
355C4×D4C22×D1114yes—
356#117—28no—
357C2×C4⋊C4—21no—
358C2×C4⋊C4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—111no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4—221no—
363C2×C4⋊C4—222no—
364C2×C4⋊C4—221no—
365C2×C4⋊C4—222no—
366C2×C4⋊C4—221no—
367C2×C4⋊C4C22⋊D1111yescharacteristic
368C2×C4⋊C4C22⋊D1112yes—
369C2×C4⋊C4C22×D1111yescharacteristic
370C2×C22⋊C4—22no—
371C2×C22⋊C4—21no—
372C2×C22⋊C4—22no—
373C2×C42—22no—
374C2×C42—222no—
375C2×C42—221no—
376C2×C42C22×D1111yescharacteristic
377C2×C42C22×D1112yes—
378#106—114no—
379C4⋊C8—114no—
380C4⋊C8—118no—
381#103—118no—
382#103—114no—
383#103—118no—
384#102—114no—
385#97—118no—
386C4×C8—114no—
387C2×C11—82no—
388C2×C11#339814yescomplemented
389C2×C11C2×#55011yescharacteristic
390C2×C11C22×#13711yescharacteristic
391C2×C11C2×#57811yescharacteristic
392C24—21no—
393C2×Q8—24no—
394C2×Q8—22no—
395C2×Q8—24no—
396C2×Q8—24no—
397C2×Q8—112no—
398C2×Q8—114no—
399C2×Q8—221no—
400C2×Q8—222no—
401C2×Q8—222no—
402C2×Q8—224no—
403C2×Q8—224no—
404C2×Q8—222no—
405C2×Q8C2×C22⋊D1114yes—
406C2×Q8C23×D1114yes—
407C2×D4—22no—
408C2×D4—22no—
409C2×D4—21no—
410C2×D4C23×D1112yes—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—24no—
414C22×C4—44no—
415C22×C4—221no—
416C22×C4—221no—
417C22×C4—222no—
418C22×C4C2×C22⋊D1112yes—
419C22×C4C2×C22⋊D1112yes—
420C22×C4C2×C22⋊D1111yescharacteristic
421C22×C4C2×C22⋊D1111yescharacteristic
422C22×C4C23×D1111yescharacteristic
423Q16—2216no—
424Q16—448no—
425Q16—448no—
426SD16—228no—
427SD16—448no—
428C2×C8—114no—
429C2×C8—112no—
430C2×C8—112no—
431C2×C8—114no—
432C2×C8—224no—
433C2×C8—222no—
434C4⋊C4—24no—
435C4⋊C4—28no—
436C4⋊C4—24no—
437C4⋊C4—21no—
438C4⋊C4—112no—
439C4⋊C4—221no—
440C4⋊C4—228no—
441C4⋊C4—224no—
442C4⋊C4—228no—
443C4⋊C4—224no—
444C4⋊C4—228no—
445C4⋊C4—224no—
446C4⋊C4C2×C22⋊D1114yes—
447C4⋊C4C2×C22⋊D1118yes—
448C4⋊C4C23×D1112yes—
449C22⋊C4—28no—
450C22⋊C4—24no—
451C22⋊C4—28no—
452C42—28no—
453C42—228no—
454C42—224no—
455C42C2×C22⋊D1112yes—
456C42C2×C22⋊D1114yes—
457C42C23×D1112yes—
458C42C23×D1114yes—
459C11C2×#339811yescharacteristic, complemented, Sylow
460C23—22no—
461C23—42no—
462C23—42no—
463C23—42no—
464C23C22×C22⋊D1111yescharacteristic
465Q8—28no—
466Q8—24no—
467Q8—24no—
468Q8—44no—
469Q8—222no—
470Q8—224no—
471Q8—224no—
472Q8—222no—
473Q8—442no—
474Q8—444no—
475D4—22no—
476D4—22no—
477D4—42no—
478C2×C4—24no—
479C2×C4—24no—
480C2×C4—22no—
481C2×C4—22no—
482C2×C4—24no—
483C2×C4—42no—
484C2×C4—44no—
485C2×C4—48no—
486C2×C4—222no—
487C2×C4—222no—
488C2×C4—224no—
489C2×C4—442no—
490C2×C4—444no—
491C2×C4—442no—
492C2×C4#6700414yes—
493C2×C4#41×D1112yes—
494C2×C4#6704212yes—
495C2×C4C22×C22⋊D1114yes—
496C2×C4C22×C22⋊D1114yes—
497C2×C4C22×C22⋊D1112yes—
498C2×C4C22×C22⋊D1112yes—
499C2×C4C22×C22⋊D1111yescharacteristic
500C2×C4C24×D1111yescharacteristic
501C8—114no—
502C8—224no—
503C8—222no—
504C22—42no—
505C22—42no—
506C22—42no—
507C22—84no—
508C22C2×#6700412yes—
509C22#1062336512yes—
510C22#1062336912yes—
511C22C23×C22⋊D1111yescharacteristic
512C4—24no—
513C4—24no—
514C4—22no—
515C4—42no—
516C4—44no—
517C4—442no—
518C4—444no—
519C4—442no—
520C4C2×#6700414yes—
521C4#1062336512yes—
522C4C2×#41×D1111yescharacteristic
523C4C2×#6704211yescharacteristic
524C2—82no—
525C2#1308164714yesdirect product factor
526C2C2×#1062336511yescharacteristic
527C2C22×#6700411yescharacteristic
528C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#556D11
hypocenterC11C2×#3398
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#10623101C2semidirect
2. #13081647C2direct (N × H)
4. C2×#10622705C2semidirect
6. C2×#10622644C2semidirect
7. C2×#10622703C2semidirect
9. C2×#10622637C2semidirect
10. C2×#10622643C2semidirect
30. #10623101C22semidirect
39. #10622705C22semidirect
40. #10622703C22semidirect
43. #10622644C22semidirect
44. #10622643C22semidirect
45. #10622637C22semidirect
388. C2×C11#3398semidirect
459. C11C2×#3398semidirect
525. C2#13081647direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231012
#130816472
C2×#106226732
C2×#106227052
C2×#106226672
C2×#106226442
C2×#106227032
C2×#106226322
C2×#106226372
C2×#106226432
C2×C4×#43242
C2×C11×#5562
C2×#339811