Finite Group Databasebeta

← C2×#13081297 #15633381

Subgroups — C2×#13081297 #15633381

Order 2816.

1830 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623098C211yesmaximal, characteristic, complemented
2#13081297C2116yesmaximal, direct product factor
3C2×#10622669C212yesmaximal
4C2×#10622694C211yesmaximal, characteristic, complemented
5C2×#10622635C212yesmaximal, complemented
6C2×#10622620C211yesmaximal, characteristic
7C2×#10622667C212yesmaximal
8C2×#10622703C211yesmaximal, characteristic, complemented
9C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
10C2×C4×#4326C212yesmaximal, 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×#66997—21no—
24C22×#4326C2212yes—
25C22×#4324C2211yescharacteristic
26#10623098—24no—
27#10623098C2218yescomplemented
28C2×#66942—22no—
29C2×#66940—21no—
30C2×#66923C2212yes—
31C2×#66922C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C4×Dic22C2212yes—
34C2×#66899C2212yes—
35C2×#66899C2212yes—
36C2×#66899C2212yes—
37C2×#66896C2212yes—
38C2×#66896C2211yescharacteristic
39#10622703C2218yescomplemented
40#10622694C2218yescomplemented
41#10622669C22116yes—
42#10622667C22116yes—
43C4×#4326C22116yescomplemented
44Q8×C11⋊C8C2218yescomplemented
45#10622635C22116yescomplemented
46C4×#4324C2218yes—
47#10622620C2218yes—
48C2×#66874C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66871C2212yes—
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×C4×C11⋊C8C2211yescharacteristic
54C2×C4×C11⋊C8C2212yes—
55C22×Q8×C11D411yescharacteristic
56C22×Q8×C11C2312yes—
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C22×Dic22—21no—
60C22×Dic22C2311yescharacteristic
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—
86#66997—28no—
87C2×#4326—28no—
88C2×#4326C2318yes—
89C2×#4324—24no—
90C2×#4324C2314yes—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11C2312yes—
93C2×C4⋊Dic11C2311yescharacteristic
94C2×Dic11⋊C4—21no—
95C2×Dic11⋊C4—22no—
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×C4×Dic11—22no—
99C2×C4×Dic11—21no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2312yes—
103#66942—216no—
104#66940—28no—
105#66923—24no—
106#66923C2318yes—
107#66922—22no—
108#66922C2314yes—
109C4×Dic22—24no—
110C4×Dic22—22no—
111C4×Dic22C2314yes—
112C4×Dic22C2318yes—
113#66899C2318yes—
114#66899C2318yes—
115#66899C2318yes—
116#66896C2318yes—
117#66896C2314yes—
118#66874C2314yes—
119#66872C2314yes—
120#66871C2318yes—
121C4⋊(C11⋊C8)C2314yes—
122C4⋊(C11⋊C8)C2318yes—
123C4×C11⋊C8C2314yes—
124C4×C11⋊C8C2318yes—
125C2×#3364—111nomaximal, Sylow
126C24×C11—21no—
127C2×Q8×C11—24no—
128C2×Q8×C11—22no—
129C2×Q8×C11—24no—
130C2×Q8×C11—24no—
131C2×Q8×C11C2×D414yes—
132C2×Q8×C11C2414yes—
133C2×D4×C11—21no—
134C2×D4×C11—22no—
135C2×D4×C11—22no—
136C2×D4×C11C2412yes—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—24no—
140C22×C4×C11—44no—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C22×Dic11—21no—
147C22×Dic11—21no—
148C22×Dic11—22no—
149C2×Dic22—21no—
150C2×Dic22—24no—
151C2×Dic22—22no—
152C2×Dic22—44no—
153C2×Dic22#4114yes—
154C2×Dic22C2412yes—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—24no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4C2×D414yes—
160C11×C4⋊C4C2×D418yes—
161C11×C4⋊C4C2412yes—
162C11×C22⋊C4—28no—
163C11×C22⋊C4—24no—
164C11×C22⋊C4—28no—
165C42×C11—28no—
166C42×C11C2×D412yes—
167C42×C11C2×D414yes—
168C42×C11C2412yes—
169C42×C11C2414yes—
170#4326—216no—
171#4324—28no—
172C4⋊Dic11—22no—
173C4⋊Dic11—21no—
174C4⋊Dic11—24no—
175C4⋊Dic11C2414yes—
176C4⋊Dic11C2412yes—
177Dic11⋊C4—24no—
178Dic11⋊C4—28no—
179Dic11⋊C4—28no—
180Dic11⋊C4—28no—
181C4×Dic11—28no—
182C4×Dic11—24no—
183C2×C11⋊C8—22no—
184C2×C11⋊C8—24no—
185C2×C11⋊C8—22no—
186C2×C11⋊C8C2412yes—
187C2×C11⋊C8C2414yes—
188C2×C11⋊C8C2412yes—
189C2×#557—111no—
190C2×#556D1111yescharacteristic
191#3364—1116no—
192C2×#488—112no—
193C2×#487—111no—
194C2×#479—112no—
195C2×#474—111no—
196C2×#464—112no—
197C2×#462—111no—
198C2×C8×Q8—111no—
199C2×C4×Q16—112no—
200C2×C4×SD16—111no—
201C23×C11—22no—
202C23×C11—42no—
203C23×C11—42no—
204C23×C11—42no—
205C23×C11C22×D411yescharacteristic
206Q8×C11—28no—
207Q8×C11—24no—
208Q8×C11—24no—
209Q8×C11—44no—
210D4×C11—22no—
211D4×C11—22no—
212D4×C11—42no—
213C2×C4×C11—24no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—22no—
217C2×C4×C11—24no—
218C2×C4×C11—44no—
219C2×C4×C11—42no—
220C2×C4×C11—48no—
221C2×C4×C11#13514yes—
222C2×C4×C11C22×D414yes—
223C2×C4×C11C22×D414yes—
224C2×C4×C11C22×D412yes—
225C2×C4×C11C22×D411yescharacteristic
226C2×C4×C11C22×D412yes—
227C2×C4×C11C2×#4112yes—
228C2×C4×C112−1+412yes—
229C2×C4×C11C2511yescharacteristic
230C2×Dic11—24no—
231C2×Dic11—22no—
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—44no—
235C2×Dic11—42no—
236Dic22—24no—
237Dic22—22no—
238Dic22—48no—
239Dic22C2×#4114yes—
240C11⋊C8—22no—
241C11⋊C8—24no—
242C11⋊C8—22no—
243C22×Q16—112no—
244C22×SD16—111no—
245#557—118no—
246#557—224no—
247#556—24no—
248#556C2×D1118yes—
249C2×C4⋊Q8—111no—
250C2×C4⋊Q8—221no—
251C2×C4⋊Q8C2×D1111yescharacteristic
252C2×#126—22no—
253C2×#125—112no—
254C2×#125—222no—
255C2×#124C2×D1112yes—
256C2×C22⋊Q8—21no—
257C2×C4×Q8—111no—
258C2×C4×Q8—112no—
259C2×C4×Q8—221no—
260C2×C4×Q8C2×D1112yes—
261C2×C4×Q8C2×D1111yescharacteristic
262C2×C4×D4C2×D1111yescharacteristic
263C2×#117—21no—
264#488—1116no—
265#487—118no—
266#479—1116no—
267#474—118no—
268#464—1116no—
269#462—118no—
270C8×Q8—118no—
271C4×Q16—1116no—
272C4×SD16—118no—
273C2×#107—112no—
274C2×#106—111no—
275C2×C4⋊C8—112no—
276C2×C4⋊C8—111no—
277C2×#103—112no—
278C2×#103—112no—
279C2×#103—112no—
280C2×#103—111no—
281C2×#102—111no—
282C2×#102—112no—
283C2×C4×C8—111no—
284C2×C4×C8—112no—
285C22×C11—42no—
286C22×C11—42no—
287C22×C11—42no—
288C22×C11—84no—
289C22×C11#54812yes—
290C22×C11C2×#13512yes—
291C22×C11#57812yes—
292C22×C11C23×D411yescharacteristic
293C4×C11—24no—
294C4×C11—24no—
295C4×C11—22no—
296C4×C11—44no—
297C4×C11—42no—
298C4×C11#54812yes—
299C4×C11C2×#13514yes—
300C4×C11C22×#4111yescharacteristic
301C4×C11C2×2−1+411yescharacteristic
302Dic11—24no—
303Dic11—44no—
304Dic11—42no—
305C22×Q8—111no—
306C22×Q8—221no—
307C22×Q8C22⋊D1111yescharacteristic
308C22×Q8C22×D1112yes—
309C22×D4C22×D1111yescharacteristic
310C23×C4—21no—
311C2×Q16—118no—
312C2×Q16—228no—
313C2×SD16—114no—
314C2×SD16—224no—
315C22×C8—111no—
316C22×C8—112no—
317C22×C8—111no—
318C4⋊Q8—22no—
319C4⋊Q8—114no—
320C4⋊Q8—228no—
321C4⋊Q8—222no—
322C4⋊Q8C22×D1114yes—
323#126—216no—
324#125—118no—
325#125—2216no—
326#125—224no—
327#124—24no—
328#124C22×D1118yes—
329C22⋊Q8—28no—
330C4×Q8—24no—
331C4×Q8—114no—
332C4×Q8—118no—
333C4×Q8—228no—
334C4×Q8—224no—
335C4×Q8—222no—
336C4×Q8C22⋊D1114yes—
337C4×Q8C22×D1118yes—
338C4×Q8C22×D1114yes—
339C4×D4—22no—
340C4×D4C22×D1114yes—
341#117—28no—
342C2×C4⋊C4—21no—
343C2×C4⋊C4—22no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—111no—
346C2×C4⋊C4—112no—
347C2×C4⋊C4—221no—
348C2×C4⋊C4—222no—
349C2×C4⋊C4—222no—
350C2×C4⋊C4—222no—
351C2×C4⋊C4—221no—
352C2×C4⋊C4C22⋊D1111yescharacteristic
353C2×C4⋊C4C22⋊D1112yes—
354C2×C4⋊C4C22×D1111yescharacteristic
355C2×C22⋊C4—22no—
356C2×C22⋊C4—21no—
357C2×C22⋊C4—22no—
358C2×C42—22no—
359C2×C42—222no—
360C2×C42—221no—
361C2×C42C22×D1111yescharacteristic
362C2×C42C22×D1112yes—
363#107—118no—
364#106—114no—
365C4⋊C8—114no—
366C4⋊C8—118no—
367#103—118no—
368#103—118no—
369#103—118no—
370#103—114no—
371#102—114no—
372#102—118no—
373C4×C8—114no—
374C4×C8—118no—
375C2×C11—82no—
376C2×C11#336414yescomplemented
377C2×C11C2×#54811yescharacteristic
378C2×C11C22×#13511yescharacteristic
379C2×C11C2×#57811yescharacteristic
380C24—21no—
381C2×Q8—24no—
382C2×Q8—22no—
383C2×Q8—24no—
384C2×Q8—24no—
385C2×Q8—114no—
386C2×Q8—112no—
387C2×Q8—222no—
388C2×Q8—221no—
389C2×Q8—224no—
390C2×Q8—444no—
391C2×Q8C2×C22⋊D1114yes—
392C2×Q8C23×D1114yes—
393C2×D4—22no—
394C2×D4—22no—
395C2×D4—21no—
396C2×D4C23×D1112yes—
397C22×C4—21no—
398C22×C4—22no—
399C22×C4—24no—
400C22×C4—44no—
401C22×C4—221no—
402C22×C4—221no—
403C22×C4—222no—
404C22×C4C2×C22⋊D1112yes—
405C22×C4C2×C22⋊D1111yescharacteristic
406C22×C4C2×C22⋊D1112yes—
407C22×C4C2×C22⋊D1111yescharacteristic
408C22×C4C23×D1111yescharacteristic
409Q16—2216no—
410SD16—228no—
411C2×C8—112no—
412C2×C8—114no—
413C2×C8—112no—
414C2×C8—222no—
415C2×C8—224no—
416C2×C8—222no—
417C4⋊C4—24no—
418C4⋊C4—28no—
419C4⋊C4—24no—
420C4⋊C4—21no—
421C4⋊C4—112no—
422C4⋊C4—114no—
423C4⋊C4—221no—
424C4⋊C4—222no—
425C4⋊C4—224no—
426C4⋊C4—228no—
427C4⋊C4—228no—
428C4⋊C4—228no—
429C4⋊C4—224no—
430C4⋊C4C2×C22⋊D1114yes—
431C4⋊C4C2×C22⋊D1118yes—
432C4⋊C4C23×D1112yes—
433C22⋊C4—28no—
434C22⋊C4—24no—
435C22⋊C4—28no—
436C42—28no—
437C42—228no—
438C42—224no—
439C42C2×C22⋊D1112yes—
440C42C2×C22⋊D1114yes—
441C42C23×D1112yes—
442C42C23×D1114yes—
443C11C2×#336411yescharacteristic, complemented, Sylow
444C23—22no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23C22×C22⋊D1111yescharacteristic
449Q8—28no—
450Q8—24no—
451Q8—24no—
452Q8—44no—
453Q8—114no—
454Q8—224no—
455Q8—222no—
456Q8—448no—
457D4—22no—
458D4—22no—
459D4—42no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—22no—
463C2×C4—22no—
464C2×C4—24no—
465C2×C4—42no—
466C2×C4—44no—
467C2×C4—48no—
468C2×C4—224no—
469C2×C4—222no—
470C2×C4—222no—
471C2×C4—224no—
472C2×C4—444no—
473C2×C4—442no—
474C2×C4#6700314yes—
475C2×C4#41×D1112yes—
476C2×C4#6704312yes—
477C2×C4C22×C22⋊D1114yes—
478C2×C4C22×C22⋊D1112yes—
479C2×C4C22×C22⋊D1114yes—
480C2×C4C22×C22⋊D1112yes—
481C2×C4C22×C22⋊D1111yescharacteristic
482C2×C4C24×D1111yescharacteristic
483C8—222no—
484C8—224no—
485C8—222no—
486C22—42no—
487C22—42no—
488C22—42no—
489C22—84no—
490C22C2×#6700312yes—
491C22#1062336212yes—
492C22#1062336912yes—
493C22C23×C22⋊D1111yescharacteristic
494C4—24no—
495C4—24no—
496C4—22no—
497C4—42no—
498C4—44no—
499C4—224no—
500C4—444no—
501C4—442no—
502C4C2×#6700314yes—
503C4#1062336212yes—
504C4C2×#41×D1111yescharacteristic
505C4C2×#6704311yescharacteristic
506C2—82no—
507C2#1308129714yesdirect product factor
508C2C2×#1062336211yescharacteristic
509C2C22×#6700311yescharacteristic
510C2C2×#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×#3364
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×#10623098C2semidirect
2. #13081297C2direct (N × H)
4. C2×#10622694C2semidirect
5. C2×#10622635C2semidirect
8. C2×#10622703C2semidirect
9. C2×Q8×C11⋊C8C2semidirect
10. C2×C4×#4326C2semidirect
27. #10623098C22semidirect
39. #10622703C22semidirect
40. #10622694C22semidirect
43. C4×#4326C22semidirect
44. Q8×C11⋊C8C22semidirect
45. #10622635C22semidirect
376. C2×C11#3364semidirect
443. C11C2×#3364semidirect
507. C2#13081297direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230982
#130812972
C2×#106226692
C2×#106226942
C2×#106226352
C2×#106226202
C2×#106226672
C2×#106227032
C2×Q8×C11⋊C82
C2×C4×#43262
C2×C4×#43242
C2×C11×#5562
C2×#336411