Finite Group Databasebeta

← C2×#13080913 #15630673

Subgroups — C2×#13080913 #15630673

Order 2816.

2146 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623094C211yesmaximal, characteristic
2C2×#10623258C211yesmaximal, characteristic, complemented
3#13080913C2116yesmaximal, direct product factor
4C2×#10622694C211yesmaximal, characteristic, complemented
5C2×#10622427C212yesmaximal, complemented
6C2×#10622463C211yesmaximal, characteristic, complemented
7C2×#10622787C212yesmaximal, complemented
8C2×#10622783C212yesmaximal, complemented
9C2×C4×#4324C211yesmaximal, characteristic, complemented
10C2×#10622451C211yesmaximal, characteristic, complemented
11C2×#10622415C212yesmaximal, complemented
12C2×C11×#461C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2212yes—
14C22×C11×SD16C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66999C2212yes—
18C2×#66991C2212yes—
19C22×#4324C2211yescharacteristic
20C2×#66983—21no—
21C2×#66979—21no—
22C22×#4313C2212yes—
23#10623258—24no—
24#10623258C2218yescomplemented
25#10623094—24no—
26#10623094C2218yes—
27C2×#66949—22no—
28C2×#66946—21no—
29C2×#66945C2212yes—
30C2×#66941—21no—
31C2×#66938—22no—
32C2×C4×D44C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35C11×#461C2218yescomplemented
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#103C2212yes—
38C2×#66899C2212yes—
39C2×#66899C2212yes—
40C2×#66896C2211yescharacteristic
41#10622787C22116yescomplemented
42#10622783C22116yescomplemented
43C2×(C2×D11)⋊C8C2212yes—
44C2×#66882C2212yes—
45C2×#66880C2212yes—
46#10622694C2218yescomplemented
47C4×#4324C2218yescomplemented
48C2×#66874C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622463C2218yescomplemented
52#10622451C2218yescomplemented
53#10622427C22116yescomplemented
54#10622415C22116yescomplemented
55C22×Q8×C11C2312yes—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C2×Q8×D11—24no—
60C2×Q8×D11—28no—
61C2×Q8×D11—44no—
62C2×Q8×D11C2318yes—
63C22×D44D411yescharacteristic
64C22×C4×D11—22no—
65C22×C4×D11C2312yes—
66C22×Dic22—22no—
67C22×Dic22—21no—
68C22×Dic22C2311yescharacteristic
69C2×C11×SD16—44no—
70C2×C11×SD16C2318yes—
71C22×C8×C11C2312yes—
72C11×C4⋊Q8—22no—
73C11×C4⋊Q8C2314yes—
74C4×D4×C11—22no—
75C4×D4×C11C2314yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11—22no—
82#66999—24no—
83#66999C2318yes—
84#66991—24no—
85#66991C2318yes—
86C2×#4324—24no—
87C2×#4324C2314yes—
88#66983—28no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4D412yes—
92#66979—28no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11D411yescharacteristic
95C2×C4⋊Dic11C2311yescharacteristic
96C2×C4⋊Dic11C2312yes—
97C2×Dic11⋊C4—21no—
98C2×Dic11⋊C4—22no—
99C2×C4×Dic11—21no—
100C2×C4×Dic11—22no—
101C22×C11⋊C8C2311yescharacteristic
102C22×C11⋊C8C2311yescharacteristic
103C2×#4313—44no—
104C2×#4313C2318yes—
105#66949—216no—
106#66946—28no—
107#66945—24no—
108#66945C2318yes—
109#66941—28no—
110#66938—216no—
111C4×D44D414yes—
112C4×D44C2314yes—
113#66922—22no—
114#66922C2314yes—
115C4×Dic22—22no—
116C4×Dic22C2314yes—
117C11×C4⋊C8C2314yes—
118C11×#103C2318yes—
119#66899C2318yes—
120#66899C2318yes—
121#66896C2314yes—
122(C2×D11)⋊C8C2318yes—
123#66882C2318yes—
124#66880C2318yes—
125#66874C2314yes—
126#66872C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3329—111nomaximal, Sylow
129C24×C11—21no—
130C23×D11C2×D412yes—
131C2×Q8×C11—22no—
132C2×Q8×C11—24no—
133C2×Q8×C11—24no—
134C2×Q8×C11C2414yes—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11C2412yes—
139C22×C4×C11—21no—
140C22×C4×C11—22no—
141C22×C4×C11—24no—
142C22×C4×C11—44no—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2411yescharacteristic
146C2×C22⋊D11—28no—
147C2×C22⋊D11—84no—
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—22no—
151C22×Dic11C2×D412yes—
152Q8×D11—216no—
153Q8×D11—48no—
154Q8×D11—416no—
155C2×D44—24no—
156C2×D44C2×D414yes—
157C2×C4×D11—28no—
158C2×C4×D11—24no—
159C2×C4×D11—24no—
160C2×C4×D11—48no—
161C2×C4×D11C2×D414yes—
162C2×C4×D11C2414yes—
163C2×Dic22—28no—
164C2×Dic22—21no—
165C2×Dic22—24no—
166C2×Dic22—22no—
167C2×Dic22—48no—
168C2×Dic22—82no—
169C2×Dic22#4114yes—
170C2×Dic22C2412yes—
171C11×SD16—48no—
172C2×C8×C11—24no—
173C2×C8×C11C2414yes—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4C2412yes—
178C11×C22⋊C4—24no—
179C42×C11C2×D412yes—
180C42×C11C2412yes—
181C22⋊Dic11—28no—
182#4324—28no—
183(C2×D11)⋊C4—28no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4C2×D418yes—
186C4⋊Dic11—21no—
187C4⋊Dic11—22no—
188C4⋊Dic11—24no—
189C4⋊Dic11C2×D414yes—
190C4⋊Dic11C2412yes—
191C4⋊Dic11C2414yes—
192Dic11⋊C4—28no—
193Dic11⋊C4—24no—
194C4×Dic11—28no—
195C4×Dic11—24no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8C2412yes—
199C2×C11⋊C8C2412yes—
200#4313—48no—
201C2×#555—111no—
202C2×D4×Q8—111no—
203#3329—1116no—
204C2×#487—111no—
205C2×#485—112no—
206C2×#477—111no—
207C2×#468—112no—
208C2×#461D1111yescharacteristic, complemented
209C2×#448—112no—
210C2×C4×SD16—111no—
211C2×#436—111no—
212C2×#419—112no—
213C23×C11—22no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11C22×D411yescharacteristic
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11C22×D414yes—
222Q8×C11—24no—
223Q8×C11—24no—
224Q8×C11—44no—
225D4×C11—22no—
226D4×C11—22no—
227D4×C11—42no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—44no—
232C2×C4×C11—42no—
233C2×C4×C11—48no—
234C2×C4×C11#13714yes—
235C2×C4×C11C22×D412yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D412yes—
238C2×C4×C11C2×#4112yes—
239C2×C4×C11H(5,𝔽2)12yes—
240C2×C4×C11C2511yescharacteristic
241C22⋊D11—88no—
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—22no—
245C2×Dic11—22no—
246C2×Dic11—24no—
247C2×Dic11—44no—
248C2×Dic11—42no—
249C2×Dic11C22×D414yes—
250D44—28no—
251C4×D11—28no—
252C4×D11—24no—
253C4×D11—24no—
254C4×D11—416no—
255Dic22—24no—
256Dic22—22no—
257Dic22—416no—
258Dic22—84no—
259Dic22C2×#4114yes—
260C8×C11—24no—
261C11⋊C8—22no—
262C11⋊C8—22no—
263C23×Q8—112no—
264C22×SD16—111no—
265C22×SD16C2×D1112yes—
266C22×M16—112no—
267#555—118no—
268#555—224no—
269D4×Q8—118no—
270D4×Q8—224no—
271C2×C4⋊Q8—111no—
272C2×C4⋊Q8—221no—
273C2×C4⋊Q8C2×D1111yescharacteristic
274C2×#124—222no—
275C2×C22⋊Q8—112no—
276C2×C22⋊Q8—222no—
277C2×#121—112no—
278C2×#121—221no—
279C2×C4×Q8—111no—
280C2×C4×D4—111no—
281C2×C4×D4—221no—
282C2×C4×D4C2×D1111yescharacteristic
283C2×#117—112no—
284C2×#117—221no—
285#487—118no—
286#485—1116no—
287#477—118no—
288#468—1116no—
289#461C2×D1118yescomplemented
290#448—1116no—
291C4×SD16—118no—
292#436—118no—
293C2×#107—112no—
294C2×#106—111no—
295C2×C4⋊C8C2×D1111yescharacteristic
296#419—1116no—
297C2×#103—112no—
298C2×#103—112no—
299C2×#103—112no—
300C2×#103—111no—
301C2×#103C2×D1112yes—
302C2×#102—111no—
303C2×C22⋊C8—112no—
304C2×C4×C8—111no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11—42no—
308C22×C11—84no—
309C22×C11#54612yes—
310C22×C11C2×#13712yes—
311C22×C11#57712yes—
312C22×C11C23×D411yescharacteristic
313C2×D11—24no—
314C2×D11—24no—
315C2×D11—24no—
316C2×D11—48no—
317C4×C11—22no—
318C4×C11—44no—
319C4×C11—42no—
320C4×C11#54612yes—
321C4×C11C2×#13714yes—
322C4×C11C22×#4111yescharacteristic
323C4×C11C2×H(5,𝔽2)11yescharacteristic
324Dic11—24no—
325Dic11—24no—
326Dic11—44no—
327Dic11—42no—
328C22×Q8—118no—
329C22×Q8—111no—
330C22×Q8—222no—
331C22×Q8—224no—
332C22×Q8—221no—
333C22×Q8—228no—
334C22×Q8—444no—
335C22×Q8C22×D1112yes—
336C22×D4—111no—
337C22×D4—222no—
338C22×D4C22×D1111yescharacteristic
339C23×C4—21no—
340C23×C4—112no—
341C23×C4—222no—
342C2×SD16—44no—
343C2×SD16—114no—
344C2×SD16—224no—
345C2×SD16C22×D1118yes—
346C2×M16—118no—
347C2×M16—444no—
348C22×C8—111no—
349C22×C8—111no—
350C22×C8C22×D1112yes—
351C4⋊Q8—22no—
352C4⋊Q8—114no—
353C4⋊Q8—228no—
354C4⋊Q8—222no—
355C4⋊Q8C22×D1114yes—
356#124—2216no—
357C22⋊Q8—118no—
358C22⋊Q8—2216no—
359C22⋊Q8—224no—
360#121—118no—
361#121—228no—
362#121—224no—
363C4×Q8—114no—
364C4×Q8—222no—
365C4×D4—22no—
366C4×D4—114no—
367C4×D4—114no—
368C4×D4—228no—
369C4×D4C22×D1114yes—
370#117—118no—
371#117—224no—
372#117—228no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—112no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C22⋊C4—21no—
383C2×C22⋊C4—112no—
384C2×C22⋊C4—222no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4—222no—
387C2×C42—222no—
388C2×C42—221no—
389C2×C42C22×D1111yescharacteristic
390#107—118no—
391#106—114no—
392C4⋊C8C22×D1114yes—
393#103—118no—
394#103—118no—
395#103—118no—
396#103—114no—
397#103C22×D1118yes—
398#102—114no—
399C22⋊C8—118no—
400C4×C8—114no—
401C2×C11—82no—
402C2×C11#332914yescomplemented
403C2×C11C2×#54611yescharacteristic
404C2×C11C22×#13711yescharacteristic
405C2×C11C2×#57711yescharacteristic
406D11—44no—
407C24—21no—
408C24—112no—
409C2×Q8—22no—
410C2×Q8—24no—
411C2×Q8—24no—
412C2×Q8—114no—
413C2×Q8—112no—
414C2×Q8—228no—
415C2×Q8—221no—
416C2×Q8—224no—
417C2×Q8—222no—
418C2×Q8—2216no—
419C2×Q8—448no—
420C2×Q8—448no—
421C2×Q8—4416no—
422C2×Q8—882no—
423C2×Q8C23×D1114yes—
424C2×D4—21no—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—114no—
428C2×D4—228no—
429C2×D4—224no—
430C2×D4—884no—
431C2×D4C23×D1112yes—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—44no—
436C22×C4—112no—
437C22×C4—114no—
438C22×C4—114no—
439C22×C4—228no—
440C22×C4—221no—
441C22×C4—224no—
442C22×C4—224no—
443C22×C4—221no—
444C22×C4—222no—
445C22×C4—448no—
446C22×C4D4×D1111yescharacteristic
447C22×C4D4×D1111yescharacteristic
448C22×C4C23×D1111yescharacteristic
449SD16—48no—
450SD16—228no—
451M16—448no—
452C2×C8—24no—
453C2×C8—112no—
454C2×C8—112no—
455C2×C8—222no—
456C2×C8—222no—
457C2×C8C23×D1114yes—
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—21no—
461C4⋊C4—114no—
462C4⋊C4—112no—
463C4⋊C4—114no—
464C4⋊C4—228no—
465C4⋊C4—222no—
466C4⋊C4—221no—
467C4⋊C4—224no—
468C4⋊C4—224no—
469C4⋊C4C23×D1112yes—
470C22⋊C4—24no—
471C22⋊C4—118no—
472C22⋊C4—228no—
473C22⋊C4—228no—
474C22⋊C4—228no—
475C42—228no—
476C42—224no—
477C42D4×D1112yes—
478C42C23×D1112yes—
479C11C2×#332911yescharacteristic, complemented, Sylow
480C23—22no—
481C23—42no—
482C23—42no—
483C23—42no—
484C23—114no—
485C23—224no—
486C23—224no—
487C23—224no—
488C23C2×D4×D1111yescharacteristic
489Q8—24no—
490Q8—24no—
491Q8—44no—
492Q8—114no—
493Q8—224no—
494Q8—222no—
495Q8—4416no—
496Q8—884no—
497D4—22no—
498D4—22no—
499D4—42no—
500D4—228no—
501D4—888no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—42no—
506C2×C4—44no—
507C2×C4—48no—
508C2×C4—114no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—222no—
512C2×C4—228no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—222no—
516C2×C4—224no—
517C2×C4—4416no—
518C2×C4—444no—
519C2×C4—442no—
520C2×C4#6696814yes—
521C2×C4C2×D4×D1112yes—
522C2×C4C2×D4×D1112yes—
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4#6703712yes—
525C2×C4#41×D1112yes—
526C2×C4C24×D1111yescharacteristic
527C8—24no—
528C8—222no—
529C8—222no—
530C22—42no—
531C22—42no—
532C22—42no—
533C22—84no—
534C22—224no—
535C22—224no—
536C22—224no—
537C22—448no—
538C22#1062314312yes—
539C22C2×#6696812yes—
540C22#1062330912yes—
541C22C22×D4×D1111yescharacteristic
542C4—22no—
543C4—44no—
544C4—42no—
545C4—224no—
546C4—224no—
547C4—444no—
548C4—442no—
549C4#1062314312yes—
550C4C2×#6696814yes—
551C4C2×#6703711yescharacteristic
552C4C2×#41×D1111yescharacteristic
553C2—82no—
554C2—444no—
555C2#1308091314yesdirect product factor
556C2C2×#1062314311yescharacteristic
557C2C22×#6696811yescharacteristic
558C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#461C2
socleC23×C11C22×D4
prime radicalC2×#10623094C2
hypercenterC2×#461D11
hypocenterC11C2×#3329
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
2. C2×#10623258C2semidirect
3. #13080913C2direct (N × H)
4. C2×#10622694C2semidirect
5. C2×#10622427C2semidirect
6. C2×#10622463C2semidirect
7. C2×#10622787C2semidirect
8. C2×#10622783C2semidirect
9. C2×C4×#4324C2semidirect
10. C2×#10622451C2semidirect
11. C2×#10622415C2semidirect
12. C2×C11×#461C2semidirect
24. #10623258C22semidirect
35. C11×#461C22semidirect
41. #10622787C22semidirect
42. #10622783C22semidirect
46. #10622694C22semidirect
47. C4×#4324C22semidirect
51. #10622463C22semidirect
52. #10622451C22semidirect
53. #10622427C22semidirect
54. #10622415C22semidirect
208. C2×#461D11semidirect
289. #461C2×D11semidirect
402. C2×C11#3329semidirect
479. C11C2×#3329semidirect
555. C2#13080913direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230942
C2×#106232582
#130809132
C2×#106226942
C2×#106224272
C2×#106224632
C2×#106227872
C2×#106227832
C2×C4×#43242
C2×#106224512
C2×#106224152
C2×C11×#4612
C2×#332911