Finite Group Databasebeta

← C2×#13081393 #15633432

Subgroups — C2×#13081393 #15633432

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic
2#13081393C2116yesmaximal, direct product factor
3C2×#10622695C212yesmaximal, complemented
4C2×#10622694C211yesmaximal, characteristic, complemented
5C2×#10622635C212yesmaximal, complemented
6C2×#10622634C211yesmaximal, characteristic, complemented
7C2×#10622696C211yesmaximal, characteristic
8C2×#10622696C212yesmaximal
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622639C212yesmaximal
11C2×C4×#4325C211yesmaximal, characteristic
12C2×C11×#557C211yesmaximal, characteristic, complemented
13C11×#557—24no—
14C11×#557C2218yescomplemented
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×C4⋊Q8C2212yes—
17C2×C11×#125—21no—
18C2×C11×#125—22no—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×Q8×C11C2212yes—
22C2×C4×Q8×C11C2211yescharacteristic
23C2×#66999—21no—
24C22×#4325C2211yescharacteristic
25C22×#4325C2212yes—
26#10623110—24no—
27#10623110C2218yes—
28C2×#66949—22no—
29C2×C4⋊C4×D11—21no—
30C2×C4×D44C2211yescharacteristic
31C2×C4×D44C2212yes—
32C2×#66923C2212yes—
33C2×#66922C2211yescharacteristic
34C2×#66899C2212yes—
35C2×#66899C2212yes—
36C2×#66899C2212yes—
37C2×#66899C2211yescharacteristic
38C2×#66899C2212yes—
39#10622696C2218yes—
40#10622696C22116yes—
41#10622695C22116yescomplemented
42#10622694C2218yescomplemented
43#10622639C22116yes—
44C4×#4325C2218yes—
45#10622637C2218yescomplemented
46#10622635C22116yescomplemented
47#10622634C2218yescomplemented
48C2×#66873C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66871C2212yes—
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11D411yescharacteristic
56C22×Q8×C11C2311yescharacteristic
57C22×Q8×C11C2312yes—
58C22×D44C2311yescharacteristic
59C22×C4×D11—21no—
60C22×C4×D11—22no—
61C22×Dic22—21no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8—24no—
64C11×C4⋊Q8C2314yes—
65C11×C4⋊Q8C2318yes—
66C11×#125—28no—
67C11×#125—216no—
68C4×Q8×C11—28no—
69C4×Q8×C11—22no—
70C4×Q8×C11—24no—
71C4×Q8×C11D414yes—
72C4×Q8×C11C2314yes—
73C4×Q8×C11C2318yes—
74C4×Q8×C11C2314yes—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4D412yes—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C42×C11—22no—
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C42×C11C2312yes—
88#66999—28no—
89C2×#4325—24no—
90C2×#4325—28no—
91C2×#4325C2314yes—
92C2×#4325C2318yes—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—22no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2312yes—
97C2×C4⋊Dic11C2311yescharacteristic
98C2×Dic11⋊C4—22no—
99C2×Dic11⋊C4—22no—
100C22×C11⋊C8C2311yescharacteristic
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2312yes—
103#66949—216no—
104C4⋊C4×D11—28no—
105C4×D44—24no—
106C4×D44—22no—
107C4×D44C2314yes—
108C4×D44C2318yes—
109#66923—24no—
110#66923C2318yes—
111#66922—22no—
112#66922C2314yes—
113#66899C2318yes—
114#66899C2318yes—
115#66899C2318yes—
116#66899C2314yes—
117#66899C2318yes—
118#66873C2314yes—
119#66872C2314yes—
120#66871C2318yes—
121C4⋊(C11⋊C8)C2314yes—
122C4⋊(C11⋊C8)C2318yes—
123#66867C2318yes—
124C4×C11⋊C8C2314yes—
125C2×#3372—111nomaximal, Sylow
126C23×D11—21no—
127C2×Q8×C11—24no—
128C2×Q8×C11—21no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—24no—
132C2×Q8×C11—22no—
133C2×Q8×C11—24no—
134C2×Q8×C11C2×D414yes—
135C2×Q8×C11C2412yes—
136C2×Q8×C11C2414yes—
137C22×C4×C11—21no—
138C22×C4×C11—22no—
139C22×C4×C11—21no—
140C22×C4×C11C2×D412yes—
141C22×C4×C11C2×D412yes—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—21no—
146C22×Dic11—22no—
147C2×D44—21no—
148C2×D44—22no—
149C2×D44#4114yes—
150C2×D44C2412yes—
151C2×C4×D11—24no—
152C2×C4×D11—28no—
153C2×C4×D11—44no—
154C2×C4×D11—84no—
155C2×Dic22—24no—
156C2×Dic22—82no—
157C11×C4⋊C4—28no—
158C11×C4⋊C4—24no—
159C11×C4⋊C4—28no—
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—
167C42×C11—28no—
168C42×C11—24no—
169C42×C11C2×D412yes—
170C42×C11C2×D414yes—
171C42×C11C2412yes—
172C42×C11C2414yes—
173#4325—28no—
174#4325—216no—
175(C2×D11)⋊C4—24no—
176(C2×D11)⋊C4—28no—
177C4⋊Dic11—22no—
178C4⋊Dic11—24no—
179C4⋊Dic11—21no—
180C4⋊Dic11C2414yes—
181C4⋊Dic11C2412yes—
182Dic11⋊C4—28no—
183Dic11⋊C4—28no—
184C2×C11⋊C8—22no—
185C2×C11⋊C8—24no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8C2412yes—
188C2×C11⋊C8C2412yes—
189C2×C11⋊C8C2414yes—
190C2×#557D1111yescharacteristic, complemented
191C2×#554—111no—
192#3372—1116no—
193C2×#491—112no—
194C2×#487—111no—
195C2×#479—112no—
196C2×#477—111no—
197C2×#461—111no—
198C2×#461—112no—
199C2×#446—111no—
200C2×#440—112no—
201C2×C4×SD16—111no—
202C23×C11C22×D411yescharacteristic
203C22×D11—24no—
204C22×D11—22no—
205C22×D11—42no—
206C22×D11—42no—
207Q8×C11—28no—
208Q8×C11—22no—
209Q8×C11—24no—
210Q8×C11—22no—
211Q8×C11—24no—
212Q8×C11—42no—
213Q8×C11—44no—
214C2×C4×C11—24no—
215C2×C4×C11—22no—
216C2×C4×C11—24no—
217C2×C4×C11—22no—
218C2×C4×C11—24no—
219C2×C4×C11—22no—
220C2×C4×C11—44no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11#13714yes—
224C2×C4×C11C22×D414yes—
225C2×C4×C11C22×D414yes—
226C2×C4×C11C22×D412yes—
227C2×C4×C11C22×D411yescharacteristic
228C2×C4×C11C22×D412yes—
229C2×C4×C11C2×#4112yes—
230C2×C4×C112−1+412yes—
231C2×C4×C11C2511yescharacteristic
232C2×Dic11—22no—
233C2×Dic11—24no—
234C2×Dic11—42no—
235C2×Dic11—44no—
236D44—24no—
237D44—22no—
238D44C2×#4114yes—
239C4×D11—48no—
240C4×D11—88no—
241Dic22—84no—
242C11⋊C8—22no—
243C11⋊C8—24no—
244C11⋊C8—22no—
245C22×SD16—111no—
246C22×SD16—112no—
247#557—24no—
248#557C2×D1118yescomplemented
249#554—118no—
250#554—224no—
251C2×C4⋊Q8—111no—
252C2×C4⋊Q8C2×D1111yescharacteristic
253C2×C4⋊Q8C2×D1112yes—
254C2×#125—21no—
255C2×#125—22no—
256C2×#125—112no—
257C2×C22⋊Q8—221no—
258C2×C22⋊Q8—222no—
259C2×C4×Q8—21no—
260C2×C4×Q8C2×D1111yescharacteristic
261C2×C4×Q8C2×D1112yes—
262C2×C4×Q8C2×D1111yescharacteristic
263C2×C4×D4—111no—
264C2×C4×D4—112no—
265C22×C4⋊C4—221no—
266#491—1116no—
267#487—118no—
268#479—1116no—
269#477—118no—
270#461—1116no—
271#461—118no—
272#446—118no—
273#440—1116no—
274C4×SD16—118no—
275C2×#107—112no—
276C2×#106—111no—
277C2×C4⋊C8—111no—
278C2×C4⋊C8—112no—
279C2×#103—112no—
280C2×#103—112no—
281C2×#103—112no—
282C2×#103—112no—
283C2×#103—111no—
284C2×#102—111no—
285C2×#97—112no—
286C2×C4×C8—111no—
287C22×C11#54812yes—
288C22×C11C2×#13712yes—
289C22×C11#57712yes—
290C22×C11C23×D411yescharacteristic
291C2×D11—24no—
292C2×D11—48no—
293C2×D11—42no—
294C2×D11—42no—
295C4×C11—24no—
296C4×C11—22no—
297C4×C11—24no—
298C4×C11—44no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11#54812yes—
302C4×C11C2×#13714yes—
303C4×C11C22×#4111yescharacteristic
304C4×C11C2×2−1+411yescharacteristic
305Dic11—42no—
306Dic11—44no—
307C22×Q8—221no—
308C22×Q8C22⋊D1111yescharacteristic
309C22×Q8C22×D1111yescharacteristic
310C22×Q8C22×D1112yes—
311C22×D4—111no—
312C23×C4—221no—
313C23×C4—222no—
314C2×SD16—114no—
315C2×SD16—118no—
316C2×SD16—224no—
317C2×SD16—228no—
318C22×C8—111no—
319C22×C8—112no—
320C22×C8—111no—
321C4⋊Q8—24no—
322C4⋊Q8—22no—
323C4⋊Q8—114no—
324C4⋊Q8—222no—
325C4⋊Q8C22×D1114yes—
326C4⋊Q8C22×D1118yes—
327#125—28no—
328#125—216no—
329#125—118no—
330#125—224no—
331C22⋊Q8—228no—
332C22⋊Q8—2216no—
333C4×Q8—28no—
334C4×Q8—24no—
335C4×Q8—22no—
336C4×Q8C22⋊D1114yes—
337C4×Q8C22×D1114yes—
338C4×Q8C22×D1118yes—
339C4×Q8C22×D1114yes—
340C4×D4—114no—
341C4×D4—118no—
342C4×D4—224no—
343C4×D4—222no—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—22no—
348C2×C4⋊C4—21no—
349C2×C4⋊C4—22no—
350C2×C4⋊C4—111no—
351C2×C4⋊C4—112no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—221no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—228no—
356C2×C4⋊C4C22⋊D1111yescharacteristic
357C2×C4⋊C4C22⋊D1112yes—
358C2×C4⋊C4C22×D1111yescharacteristic
359C2×C22⋊C4—221no—
360C2×C22⋊C4—222no—
361C2×C42—22no—
362C2×C42—21no—
363C2×C42C22×D1112yes—
364C2×C42C22×D1111yescharacteristic
365#107—118no—
366#106—114no—
367C4⋊C8—114no—
368C4⋊C8—118no—
369#103—114no—
370#103—118no—
371#103—118no—
372#103—118no—
373#103—118no—
374#102—114no—
375#97—118no—
376C4×C8—114no—
377C2×C11#337214yescomplemented
378C2×C11C2×#54811yescharacteristic
379C2×C11C22×#13711yescharacteristic
380C2×C11C2×#57711yescharacteristic
381D11—44no—
382C24—221no—
383C2×Q8—24no—
384C2×Q8—22no—
385C2×Q8—21no—
386C2×Q8—22no—
387C2×Q8—24no—
388C2×Q8—22no—
389C2×Q8—24no—
390C2×Q8—224no—
391C2×Q8—882no—
392C2×Q8C2×C22⋊D1114yes—
393C2×Q8C23×D1112yes—
394C2×Q8C23×D1114yes—
395C2×D4—114no—
396C2×D4—112no—
397C2×D4—222no—
398C2×D4—221no—
399C22×C4—21no—
400C22×C4—22no—
401C22×C4—21no—
402C22×C4—221no—
403C22×C4—222no—
404C22×C4—224no—
405C22×C4—228no—
406C22×C4—444no—
407C22×C4—884no—
408C22×C4C2×C22⋊D1112yes—
409C22×C4C2×C22⋊D1111yescharacteristic
410C22×C4C2×C22⋊D1112yes—
411C22×C4C2×C22⋊D1111yescharacteristic
412C22×C4C23×D1111yescharacteristic
413SD16—228no—
414SD16—2216no—
415C2×C8—112no—
416C2×C8—112no—
417C2×C8—114no—
418C2×C8—222no—
419C2×C8—224no—
420C2×C8—222no—
421C4⋊C4—28no—
422C4⋊C4—24no—
423C4⋊C4—24no—
424C4⋊C4—28no—
425C4⋊C4—24no—
426C4⋊C4—28no—
427C4⋊C4—21no—
428C4⋊C4—112no—
429C4⋊C4—114no—
430C4⋊C4—221no—
431C4⋊C4—222no—
432C4⋊C4—228no—
433C4⋊C4—224no—
434C4⋊C4—228no—
435C4⋊C4C2×C22⋊D1114yes—
436C4⋊C4C2×C22⋊D1118yes—
437C4⋊C4C23×D1112yes—
438C22⋊C4—224no—
439C22⋊C4—228no—
440C42—28no—
441C42—24no—
442C42C2×C22⋊D1114yes—
443C42C2×C22⋊D1112yes—
444C42C23×D1112yes—
445C42C23×D1114yes—
446C11C2×#337211yescharacteristic, complemented, Sylow
447C23—224no—
448C23—222no—
449C23—442no—
450C23—442no—
451C23C22×C22⋊D1111yescharacteristic
452Q8—28no—
453Q8—22no—
454Q8—24no—
455Q8—22no—
456Q8—24no—
457Q8—44no—
458Q8—42no—
459Q8—884no—
460D4—114no—
461D4—224no—
462D4—222no—
463C2×C4—24no—
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—22no—
469C2×C4—44no—
470C2×C4—42no—
471C2×C4—42no—
472C2×C4—222no—
473C2×C4—224no—
474C2×C4—442no—
475C2×C4—444no—
476C2×C4—448no—
477C2×C4—888no—
478C2×C4#6699514yes—
479C2×C4#41×D1112yes—
480C2×C4#6704312yes—
481C2×C4C22×C22⋊D1114yes—
482C2×C4C22×C22⋊D1112yes—
483C2×C4C22×C22⋊D1114yes—
484C2×C4C22×C22⋊D1112yes—
485C2×C4C22×C22⋊D1111yescharacteristic
486C2×C4C24×D1111yescharacteristic
487C8—222no—
488C8—224no—
489C8—222no—
490C22—224no—
491C22—448no—
492C22—442no—
493C22—442no—
494C22C2×#6699512yes—
495C22#1062336212yes—
496C22#1062336812yes—
497C22C23×C22⋊D1111yescharacteristic
498C4—24no—
499C4—24no—
500C4—22no—
501C4—44no—
502C4—42no—
503C4—42no—
504C4—442no—
505C4—444no—
506C4C2×#6699514yes—
507C4#1062336212yes—
508C4C2×#41×D1111yescharacteristic
509C4C2×#6704311yescharacteristic
510C2—444no—
511C2#1308139314yesdirect product factor
512C2C2×#1062336211yescharacteristic
513C2C22×#6699511yescharacteristic
514C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#557C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#557D11
hypocenterC11C2×#3372
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #13081393C2direct (N × H)
3. C2×#10622695C2semidirect
4. C2×#10622694C2semidirect
5. C2×#10622635C2semidirect
6. C2×#10622634C2semidirect
9. C2×#10622637C2semidirect
12. C2×C11×#557C2semidirect
14. C11×#557C22semidirect
41. #10622695C22semidirect
42. #10622694C22semidirect
45. #10622637C22semidirect
46. #10622635C22semidirect
47. #10622634C22semidirect
190. C2×#557D11semidirect
248. #557C2×D11semidirect
377. C2×C11#3372semidirect
446. C11C2×#3372semidirect
511. C2#13081393direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231102
#130813932
C2×#106226952
C2×#106226942
C2×#106226352
C2×#106226342
C2×#106226962
C2×#106226372
C2×#106226392
C2×C4×#43252
C2×C11×#5572
C2×#337211