Finite Group Databasebeta

← C2×#13080535 #15630214

Subgroups — C2×#13080535 #15630214

Order 2816.

2146 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic, complemented
2C2×#10623086C211yesmaximal, characteristic
3#13080535C2116yesmaximal, direct product factor
4C2×#10622294C211yesmaximal, characteristic, complemented
5C2×#10622480C212yesmaximal, complemented
6C2×#10622620C211yesmaximal, characteristic, complemented
7C2×#10622426C212yesmaximal, complemented
8C2×#10622644C211yesmaximal, characteristic, complemented
9C2×#10622786C212yesmaximal, complemented
10C2×C8×D44C211yesmaximal, characteristic, complemented
11C2×#10622385C212yesmaximal, complemented
12C2×C4×C11×SD16C211yesmaximal, characteristic, complemented
13C22×#4341C2212yes—
14C22×C11×SD16C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66999C2212yes—
18C22×#4326C2212yes—
19C2×#66983—21no—
20C22×C4⋊Dic11—21no—
21C22×C8×D11C2212yes—
22#10623115—24no—
23#10623115C2218yescomplemented
24#10623086—24no—
25#10623086C2218yes—
26C2×#66951—22no—
27C2×#66950C2212yes—
28C2×#66945C2212yes—
29C2×#66939—22no—
30C2×#66928—21no—
31C2×C4×D44C2211yescharacteristic
32C2×#66922C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22—21no—
35C4×C11×SD16C2218yescomplemented
36C2×C11×#106C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#102C2211yescharacteristic
39C2×C4×C8×C11C2211yescharacteristic
40C2×#66896C2212yes—
41#10622786C22116yescomplemented
42C2×(C2×D11)⋊C8C2212yes—
43C2×#66880C2212yes—
44C2×#66880C2212yes—
45#10622644C2218yescomplemented
46#10622620C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66871C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622480C22116yescomplemented
51#10622426C22116yescomplemented
52#10622385C22116yescomplemented
53C8×D44C2218yescomplemented
54#10622294C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C23×Dic11—22no—
60C2×#4341—28no—
61C2×#4341—24no—
62C2×#4341—44no—
63C2×#4341C2318yes—
64C22×D44D411yescharacteristic
65C22×C4×D11C2312yes—
66C22×Dic22—21no—
67C22×Dic22C2312yes—
68C2×C11×SD16—24no—
69C2×C11×SD16C2314yes—
70C22×C8×C11C2311yescharacteristic
71C22×C8×C11C2311yescharacteristic
72C4×Q8×C11—22no—
73C4×Q8×C11C2314yes—
74C4×D4×C11—22no—
75C4×D4×C11C2314yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82#66999—24no—
83#66999C2318yes—
84C2×#4326—44no—
85C2×#4326C2318yes—
86#66983—28no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4D412yes—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—22no—
95C2×C4⋊Dic11—28no—
96C2×C4⋊Dic11D411yescharacteristic
97C2×C4⋊Dic11C2312yes—
98C2×Dic11⋊C4—22no—
99C2×C4×Dic11—22no—
100C22×C11⋊C8C2312yes—
101C2×C8×D11—44no—
102C2×C8×D11C2318yes—
103#66951—216no—
104#66950—24no—
105#66950C2318yes—
106#66945—24no—
107#66945C2318yes—
108#66939—216no—
109#66928—28no—
110C4×D44D414yes—
111C4×D44C2314yes—
112#66922—22no—
113#66922—22no—
114#66922C2314yes—
115#66922C2314yes—
116C4×Dic22—28no—
117C11×#106C2314yes—
118C11×#103C2314yes—
119C11×#102C2314yes—
120C4×C8×C11C2314yes—
121#66896C2318yes—
122(C2×D11)⋊C8C2318yes—
123#66880C2318yes—
124#66880C2318yes—
125#66874C2318yes—
126#66871C2318yes—
127C4⋊(C11⋊C8)C2314yes—
128C2×#3302—111nomaximal, Sylow
129C24×C11—21no—
130C23×D11C2×D412yes—
131C2×Q8×C11—21no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11C2412yes—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11#4114yes—
138C2×D4×C11C2412yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11—24no—
143C22×C4×C11—44no—
144C22×C4×C11C2×D411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C2×C22⋊D11—28no—
148C2×C22⋊D11—48no—
149C22×Dic11—28no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—48no—
153C22×Dic11C2×D412yes—
154#4341—216no—
155#4341—48no—
156#4341—416no—
157C2×D44—24no—
158C2×D44C2×D414yes—
159C2×C4×D11—24no—
160C2×C4×D11—24no—
161C2×C4×D11C2×D414yes—
162C2×C4×D11C2414yes—
163C2×Dic22—24no—
164C2×Dic22—22no—
165C2×Dic22—24no—
166C2×Dic22—24no—
167C2×Dic22—44no—
168C2×Dic22C2414yes—
169C11×SD16—28no—
170C2×C8×C11—22no—
171C2×C8×C11—22no—
172C2×C8×C11C2412yes—
173C2×C8×C11C2412yes—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4C2412yes—
178C11×C4⋊C4C2412yes—
179C11×C22⋊C4—24no—
180C42×C11—24no—
181C42×C11C2×D412yes—
182C42×C11C2412yes—
183#4326—48no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4C2×D418yes—
188C4⋊Dic11—28no—
189C4⋊Dic11—22no—
190C4⋊Dic11—24no—
191C4⋊Dic11—24no—
192C4⋊Dic11—24no—
193C4⋊Dic11C2×D414yes—
194C4⋊Dic11C2414yes—
195Dic11⋊C4—28no—
196C4×Dic11—28no—
197C2×C11⋊C8—24no—
198C2×C11⋊C8C2414yes—
199C8×D11—48no—
200C2×#556—111no—
201C2×#547—111no—
202#3302—1116no—
203C2×#487—111no—
204C2×#485—112no—
205C2×#474—111no—
206C2×#467—112no—
207C2×#462—111no—
208C2×#452—112no—
209C2×C4×SD16D1111yescharacteristic, complemented
210C2×C8×D4—111no—
211C2×#416—112no—
212C23×C11—24no—
213C23×C11—22no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11C22×D411yescharacteristic
217C22×D11—24no—
218C22×D11—24no—
219C22×D11—24no—
220C22×D11C22×D414yes—
221Q8×C11—22no—
222Q8×C11—22no—
223Q8×C11—42no—
224D4×C11—24no—
225D4×C11—22no—
226D4×C11C2×#4114yes—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—42no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—48no—
235C2×C4×C11#13514yes—
236C2×C4×C11C22×D412yes—
237C2×C4×C11C22×D411yescharacteristic
238C2×C4×C11C22×D412yes—
239C2×C4×C11C2×#4112yes—
240C2×C4×C11H(5,𝔽2)12yes—
241C2×C4×C11C2511yescharacteristic
242C22⋊D11—416no—
243C2×Dic11—24no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—416no—
247C2×Dic11—44no—
248C2×Dic11—44no—
249C2×Dic11C22×D414yes—
250D44—28no—
251C4×D11—28no—
252C4×D11—24no—
253C4×D11—24no—
254Dic22—24no—
255Dic22—24no—
256Dic22—44no—
257Dic22—48no—
258C8×C11—22no—
259C8×C11—22no—
260C11⋊C8—24no—
261C22×#41—112no—
262C22×Q16—112no—
263C22×SD16C2×D1111yescharacteristic
264C23×C8—112no—
265#556—118no—
266#556—224no—
267#547—118no—
268#547—224no—
269C2×C4⋊Q8—111no—
270C2×C4⋊Q8—111no—
271C2×#126—222no—
272C2×#124—221no—
273C2×#123—222no—
274C2×C22⋊Q8—112no—
275C2×C22⋊Q8—112no—
276C2×#121—221no—
277C2×C4×Q8—221no—
278C2×C4×Q8C2×D1111yescharacteristic
279C2×C4×D4—111no—
280C2×C4×D4C2×D1111yescharacteristic
281C2×#117—112no—
282C22×C4⋊C4—221no—
283#487—118no—
284#485—1116no—
285#474—118no—
286#467—1116no—
287#462—118no—
288#452—1116no—
289C4×SD16C2×D1118yescomplemented
290C8×D4—118no—
291C2×#107—112no—
292C2×#106C2×D1111yescharacteristic
293C2×C4⋊C8—111no—
294#416—1116no—
295C2×#103—112no—
296C2×#103—112no—
297C2×#103—112no—
298C2×#103C2×D1111yescharacteristic
299C2×#102—112no—
300C2×#102C2×D1111yescharacteristic
301C2×C22⋊C8—112no—
302C2×C4×C8C2×D1111yescharacteristic
303C22×C11—24no—
304C22×C11—48no—
305C22×C11—42no—
306C22×C11—42no—
307C22×C11#54612yes—
308C22×C11C2×#13512yes—
309C22×C11#57812yes—
310C22×C11C23×D411yescharacteristic
311C2×D11—24no—
312C2×D11—24no—
313C2×D11—24no—
314C2×D11—48no—
315C4×C11—22no—
316C4×C11—42no—
317C4×C11—42no—
318C4×C11—42no—
319C4×C11#54612yes—
320C4×C11C2×#13514yes—
321C4×C11C22×#4111yescharacteristic
322C4×C11C2×H(5,𝔽2)11yescharacteristic
323Dic11—24no—
324Dic11—44no—
325Dic11—44no—
326C2×#41—118no—
327C2×#41—224no—
328C2×#41—228no—
329C2×#41—444no—
330C22×Q8—112no—
331C22×Q8—221no—
332C22×Q8C22×D1111yescharacteristic
333C22×D4—111no—
334C22×D4—222no—
335C22×D4C22×D1111yescharacteristic
336C23×C4—21no—
337C23×C4—112no—
338C23×C4—222no—
339C2×Q16—118no—
340C2×Q16—444no—
341C2×SD16—24no—
342C2×SD16C22×D1114yes—
343C22×C8—112no—
344C22×C8—118no—
345C22×C8—444no—
346C22×C8C22×D1111yescharacteristic
347C22×C8C22×D1111yescharacteristic
348C4⋊Q8—114no—
349C4⋊Q8—114no—
350C4⋊Q8—222no—
351C4⋊Q8—222no—
352#126—2216no—
353#124—228no—
354#123—2216no—
355C22⋊Q8—118no—
356C22⋊Q8—118no—
357C22⋊Q8—224no—
358C22⋊Q8—224no—
359#121—228no—
360C4×Q8—22no—
361C4×Q8—228no—
362C4×Q8C22×D1114yes—
363C4×D4—22no—
364C4×D4—114no—
365C4×D4—114no—
366C4×D4C22×D1114yes—
367#117—118no—
368#117—224no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—112no—
372C2×C4⋊C4—228no—
373C2×C4⋊C4—222no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C22⋊C4—21no—
381C2×C22⋊C4—112no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—222no—
385C2×C42—21no—
386C2×C42—222no—
387C2×C42C22×D1111yescharacteristic
388#107—118no—
389#106C22×D1114yes—
390C4⋊C8—114no—
391#103—118no—
392#103—118no—
393#103—118no—
394#103C22×D1114yes—
395#102—118no—
396#102C22×D1114yes—
397C22⋊C8—118no—
398C4×C8C22×D1114yes—
399C2×C11—44no—
400C2×C11#330214yescomplemented
401C2×C11C2×#54611yescharacteristic
402C2×C11C22×#13511yescharacteristic
403C2×C11C2×#57811yescharacteristic
404D11—44no—
405C24—21no—
406C24—112no—
407#41—2216no—
408#41—448no—
409#41—4416no—
410C2×Q8—21no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—114no—
414C2×Q8—224no—
415C2×Q8—222no—
416C2×Q8—224no—
417C2×Q8—224no—
418C2×Q8—444no—
419C2×Q8C23×D1112yes—
420C2×D4—21no—
421C2×D4—22no—
422C2×D4—114no—
423C2×D4—228no—
424C2×D4—224no—
425C2×D4—448no—
426C2×D4#433914yes—
427C2×D4C23×D1112yes—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—24no—
432C22×C4—44no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—114no—
436C22×C4—228no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—222no—
440C22×C4—222no—
441C22×C4—448no—
442C22×C4D4×D1111yescharacteristic
443C22×C4D4×D1111yescharacteristic
444C22×C4C23×D1111yescharacteristic
445Q16—448no—
446SD16—28no—
447C2×C8—22no—
448C2×C8—22no—
449C2×C8—114no—
450C2×C8—224no—
451C2×C8—448no—
452C2×C8C23×D1112yes—
453C2×C8C23×D1112yes—
454C4⋊C4—24no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—114no—
458C4⋊C4—114no—
459C4⋊C4—228no—
460C4⋊C4—228no—
461C4⋊C4—222no—
462C4⋊C4—224no—
463C4⋊C4—224no—
464C4⋊C4—224no—
465C4⋊C4C23×D1112yes—
466C4⋊C4C23×D1112yes—
467C22⋊C4—24no—
468C22⋊C4—118no—
469C22⋊C4—228no—
470C22⋊C4—228no—
471C22⋊C4—228no—
472C42—24no—
473C42—228no—
474C42D4×D1112yes—
475C42C23×D1112yes—
476C11C2×#330211yescharacteristic, complemented, Sylow
477C23—24no—
478C23—22no—
479C23—42no—
480C23—42no—
481C23—114no—
482C23—224no—
483C23—224no—
484C23—224no—
485C23C2×D4×D1111yescharacteristic
486Q8—22no—
487Q8—22no—
488Q8—42no—
489Q8—224no—
490Q8—224no—
491Q8—448no—
492Q8—444no—
493D4—24no—
494D4—22no—
495D4—228no—
496D4—4416no—
497D4C2×#433914yes—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—22no—
502C2×C4—42no—
503C2×C4—42no—
504C2×C4—42no—
505C2×C4—48no—
506C2×C4—114no—
507C2×C4—224no—
508C2×C4—228no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—4416no—
514C2×C4—444no—
515C2×C4—444no—
516C2×C4#6696914yes—
517C2×C4C2×#433912yes—
518C2×C4C2×D4×D1112yes—
519C2×C4C2×D4×D1112yes—
520C2×C4C2×D4×D1111yescharacteristic
521C2×C4#6704212yes—
522C2×C4C24×D1111yescharacteristic
523C8—22no—
524C8—22no—
525C8—224no—
526C22—24no—
527C22—42no—
528C22—48no—
529C22—42no—
530C22—224no—
531C22—224no—
532C22—224no—
533C22—448no—
534C22#1062308112yes—
535C22C2×#6696912yes—
536C22#1062330212yes—
537C22C22×D4×D1111yescharacteristic
538C4—22no—
539C4—42no—
540C4—42no—
541C4—42no—
542C4—224no—
543C4—444no—
544C4—444no—
545C4#1062308112yes—
546C4C2×#6696914yes—
547C4C22×#433911yescharacteristic
548C4C2×#6704211yescharacteristic
549C2—44no—
550C2—444no—
551C2#1308053514yesdirect product factor
552C2C2×#1062308111yescharacteristic
553C2C22×#6696911yescharacteristic
554C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×SD16C2
socleC23×C11C22×D4
prime radicalC2×#10623086C2
hypercenterC2×C4×SD16D11
hypocenterC11C2×#3302
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#10623115C2semidirect
3. #13080535C2direct (N × H)
4. C2×#10622294C2semidirect
5. C2×#10622480C2semidirect
6. C2×#10622620C2semidirect
7. C2×#10622426C2semidirect
8. C2×#10622644C2semidirect
9. C2×#10622786C2semidirect
10. C2×C8×D44C2semidirect
11. C2×#10622385C2semidirect
12. C2×C4×C11×SD16C2semidirect
23. #10623115C22semidirect
35. C4×C11×SD16C22semidirect
41. #10622786C22semidirect
45. #10622644C22semidirect
46. #10622620C22semidirect
50. #10622480C22semidirect
51. #10622426C22semidirect
52. #10622385C22semidirect
53. C8×D44C22semidirect
54. #10622294C22semidirect
209. C2×C4×SD16D11semidirect
289. C4×SD16C2×D11semidirect
400. C2×C11#3302semidirect
476. C11C2×#3302semidirect
551. C2#13080535direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231152
C2×#106230862
#130805352
C2×#106222942
C2×#106224802
C2×#106226202
C2×#106224262
C2×#106226442
C2×#106227862
C2×C8×D442
C2×#106223852
C2×C4×C11×SD162
C2×#330211