Finite Group Databasebeta

← C2×#13080934 #15630696

Subgroups — C2×#13080934 #15630696

Order 2816.

2158 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×#10623110C211yesmaximal, characteristic, complemented
2C2×#10623086C211yesmaximal, characteristic
3#13080934C2116yesmaximal, direct product factor
4C2×#10622294C211yesmaximal, characteristic, complemented
5C2×#10622475C212yesmaximal, complemented
6C2×#10622621C211yesmaximal, characteristic, complemented
7C2×#10622429C212yesmaximal, complemented
8C2×#10622644C211yesmaximal, characteristic, complemented
9C2×#10622786C212yesmaximal, complemented
10C2×#10622301C211yesmaximal, characteristic, complemented
11C2×#10622384C212yesmaximal, 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×#4313C2212yes—
22#10623110—24no—
23#10623110C2218yescomplemented
24#10623086—24no—
25#10623086C2218yes—
26C2×#66950C2212yes—
27C2×#66949—22no—
28C2×C4⋊C4×D11C2212yes—
29C2×#66939—22no—
30C2×C4×D44—21no—
31C2×C4×D44C2211yescharacteristic
32C2×#66923—21no—
33C2×#66922C2211yescharacteristic
34C2×#66922C2211yescharacteristic
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#10622621C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66872C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622475C22116yescomplemented
51#10622429C22116yescomplemented
52#10622384C22116yescomplemented
53#10622301C2218yescomplemented
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×D11—22no—
66C22×C4×D11C2312yes—
67C22×Dic22—21no—
68C22×Dic22C2312yes—
69C2×C11×SD16—24no—
70C2×C11×SD16C2314yes—
71C22×C8×C11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C4×Q8×C11—22no—
74C4×Q8×C11C2314yes—
75C4×D4×C11—22no—
76C4×D4×C11C2314yes—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C22⋊C4—21no—
81C2×C42×C11—21no—
82C2×C42×C11C2311yescharacteristic
83#66999—24no—
84#66999C2318yes—
85C2×#4326—44no—
86C2×#4326C2318yes—
87#66983—28no—
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×Dic11⋊C4—22no—
100C22×C11⋊C8C2312yes—
101C2×#4313—44no—
102C2×#4313C2318yes—
103#66950—24no—
104#66950C2318yes—
105#66949—216no—
106C4⋊C4×D11—24no—
107C4⋊C4×D11C2318yes—
108#66939—216no—
109C4×D44—28no—
110C4×D44D414yes—
111C4×D44C2314yes—
112#66923—28no—
113#66922—22no—
114#66922—22no—
115#66922C2314yes—
116#66922C2314yes—
117C11×#106C2314yes—
118C11×#103C2314yes—
119C11×#102C2314yes—
120C4×C8×C11C2314yes—
121#66896C2318yes—
122(C2×D11)⋊C8C2318yes—
123#66880C2318yes—
124#66880C2318yes—
125#66874C2318yes—
126#66872C2318yes—
127C4⋊(C11⋊C8)C2314yes—
128C2×#3331—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—28no—
160C2×C4×D11—24no—
161C2×C4×D11—24no—
162C2×C4×D11—84no—
163C2×C4×D11C2×D414yes—
164C2×C4×D11C2414yes—
165C2×Dic22—22no—
166C2×Dic22—24no—
167C2×Dic22—24no—
168C2×Dic22—24no—
169C2×Dic22—82no—
170C2×Dic22C2414yes—
171C11×SD16—28no—
172C2×C8×C11—22no—
173C2×C8×C11—22no—
174C2×C8×C11C2412yes—
175C2×C8×C11C2412yes—
176C11×C4⋊C4—21no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4—21no—
179C11×C4⋊C4C2412yes—
180C11×C4⋊C4C2412yes—
181C11×C22⋊C4—24no—
182C42×C11—24no—
183C42×C11C2×D412yes—
184C42×C11C2412yes—
185#4326—48no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4C2×D418yes—
189C4⋊Dic11—28no—
190C4⋊Dic11—22no—
191C4⋊Dic11—24no—
192C4⋊Dic11—24no—
193C4⋊Dic11—24no—
194C4⋊Dic11C2×D414yes—
195C4⋊Dic11C2414yes—
196Dic11⋊C4—28no—
197Dic11⋊C4—28no—
198C2×C11⋊C8—24no—
199C2×C11⋊C8C2414yes—
200#4313—48no—
201C2×#554—111no—
202C2×#547—111no—
203#3331—1116no—
204C2×#487—111no—
205C2×#483—112no—
206C2×#476—111no—
207C2×#470—112no—
208C2×#462—111no—
209C2×#452—112no—
210C2×C4×SD16D1111yescharacteristic, complemented
211C2×#436—111no—
212C2×#417—112no—
213C23×C11—24no—
214C23×C11—22no—
215C23×C11—42no—
216C23×C11—42no—
217C23×C11C22×D411yescharacteristic
218C22×D11—24no—
219C22×D11—24no—
220C22×D11—24no—
221C22×D11C22×D414yes—
222Q8×C11—22no—
223Q8×C11—22no—
224Q8×C11—42no—
225D4×C11—24no—
226D4×C11—22no—
227D4×C11C2×#4114yes—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—22no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11—48no—
236C2×C4×C11#13714yes—
237C2×C4×C11C22×D412yes—
238C2×C4×C11C22×D411yescharacteristic
239C2×C4×C11C22×D412yes—
240C2×C4×C11C2×#4112yes—
241C2×C4×C11H(5,𝔽2)12yes—
242C2×C4×C11C2511yescharacteristic
243C22⋊D11—416no—
244C2×Dic11—24no—
245C2×Dic11—24no—
246C2×Dic11—24no—
247C2×Dic11—416no—
248C2×Dic11—44no—
249C2×Dic11—44no—
250C2×Dic11C22×D414yes—
251D44—28no—
252C4×D11—28no—
253C4×D11—24no—
254C4×D11—24no—
255C4×D11—88no—
256Dic22—24no—
257Dic22—24no—
258Dic22—44no—
259Dic22—84no—
260C8×C11—22no—
261C8×C11—22no—
262C11⋊C8—24no—
263C22×#41—112no—
264C22×Q16—112no—
265C22×SD16C2×D1111yescharacteristic
266C22×M16—112no—
267#554—118no—
268#554—224no—
269#547—118no—
270#547—224no—
271C2×C4⋊Q8—111no—
272C2×C4⋊Q8—111no—
273C2×#125—221no—
274C2×#123—222no—
275C2×C22⋊Q8—112no—
276C2×C22⋊Q8—112no—
277C2×C22⋊Q8—222no—
278C2×#121—221no—
279C2×C4×Q8C2×D1111yescharacteristic
280C2×C4×D4—111no—
281C2×C4×D4—221no—
282C2×C4×D4C2×D1111yescharacteristic
283C22×C4⋊C4—112no—
284C22×C4⋊C4—221no—
285#487—118no—
286#483—1116no—
287#476—118no—
288#470—1116no—
289#462—118no—
290#452—1116no—
291C4×SD16C2×D1118yescomplemented
292#436—118no—
293C2×#106—112no—
294C2×#106C2×D1111yescharacteristic
295C2×C4⋊C8—111no—
296#417—1116no—
297C2×#103—112no—
298C2×#103—112no—
299C2×#103—112no—
300C2×#103C2×D1111yescharacteristic
301C2×#102—112no—
302C2×#102C2×D1111yescharacteristic
303C2×C22⋊C8—112no—
304C2×C4×C8C2×D1111yescharacteristic
305C22×C11—24no—
306C22×C11—48no—
307C22×C11—42no—
308C22×C11—42no—
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—42no—
319C4×C11—42no—
320C4×C11—42no—
321C4×C11#54612yes—
322C4×C11C2×#13714yes—
323C4×C11C22×#4111yescharacteristic
324C4×C11C2×H(5,𝔽2)11yescharacteristic
325Dic11—24no—
326Dic11—44no—
327Dic11—44no—
328C2×#41—118no—
329C2×#41—224no—
330C2×#41—228no—
331C2×#41—444no—
332C22×Q8—112no—
333C22×Q8—221no—
334C22×Q8C22×D1111yescharacteristic
335C22×D4—111no—
336C22×D4—222no—
337C22×D4C22×D1111yescharacteristic
338C23×C4—21no—
339C23×C4—112no—
340C23×C4—222no—
341C23×C4—222no—
342C2×Q16—118no—
343C2×Q16—444no—
344C2×SD16—24no—
345C2×SD16C22×D1114yes—
346C2×M16—118no—
347C2×M16—444no—
348C22×C8—112no—
349C22×C8C22×D1111yescharacteristic
350C22×C8C22×D1111yescharacteristic
351C4⋊Q8—114no—
352C4⋊Q8—114no—
353C4⋊Q8—222no—
354C4⋊Q8—222no—
355#125—228no—
356#123—2216no—
357C22⋊Q8—118no—
358C22⋊Q8—118no—
359C22⋊Q8—2216no—
360C22⋊Q8—224no—
361C22⋊Q8—224no—
362#121—228no—
363C4×Q8—22no—
364C4×Q8C22×D1114yes—
365C4×D4—22no—
366C4×D4—114no—
367C4×D4—114no—
368C4×D4—228no—
369C4×D4C22×D1114yes—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—112no—
373C2×C4⋊C4—118no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—228no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—222no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—221no—
382C2×C4⋊C4C22×D1111yescharacteristic
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C22⋊C4—21no—
385C2×C22⋊C4—112no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4—222no—
388C2×C42—21no—
389C2×C42C22×D1111yescharacteristic
390#106—118no—
391#106C22×D1114yes—
392C4⋊C8—114no—
393#103—118no—
394#103—118no—
395#103—118no—
396#103C22×D1114yes—
397#102—118no—
398#102C22×D1114yes—
399C22⋊C8—118no—
400C4×C8C22×D1114yes—
401C2×C11—44no—
402C2×C11#333114yescomplemented
403C2×C11C2×#54611yescharacteristic
404C2×C11C22×#13711yescharacteristic
405C2×C11C2×#57711yescharacteristic
406D11—44no—
407C24—21no—
408C24—112no—
409#41—2216no—
410#41—448no—
411#41—4416no—
412C2×Q8—21no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—114no—
416C2×Q8—222no—
417C2×Q8—224no—
418C2×Q8—224no—
419C2×Q8—224no—
420C2×Q8—882no—
421C2×Q8C23×D1112yes—
422C2×D4—21no—
423C2×D4—22no—
424C2×D4—114no—
425C2×D4—228no—
426C2×D4—224no—
427C2×D4—448no—
428C2×D4#433914yes—
429C2×D4C23×D1112yes—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—24no—
434C22×C4—44no—
435C22×C4—112no—
436C22×C4—114no—
437C22×C4—114no—
438C22×C4—228no—
439C22×C4—228no—
440C22×C4—224no—
441C22×C4—224no—
442C22×C4—222no—
443C22×C4—222no—
444C22×C4—448no—
445C22×C4—884no—
446C22×C4D4×D1111yescharacteristic
447C22×C4D4×D1111yescharacteristic
448C22×C4C23×D1111yescharacteristic
449Q16—448no—
450SD16—28no—
451M16—448no—
452C2×C8—22no—
453C2×C8—22no—
454C2×C8—114no—
455C2×C8—224no—
456C2×C8C23×D1112yes—
457C2×C8C23×D1112yes—
458C4⋊C4—24no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—114no—
462C4⋊C4—114no—
463C4⋊C4—228no—
464C4⋊C4—228no—
465C4⋊C4—228no—
466C4⋊C4—222no—
467C4⋊C4—224no—
468C4⋊C4—224no—
469C4⋊C4—224no—
470C4⋊C4C23×D1112yes—
471C4⋊C4C23×D1112yes—
472C22⋊C4—24no—
473C22⋊C4—118no—
474C22⋊C4—228no—
475C22⋊C4—228no—
476C42—24no—
477C42D4×D1112yes—
478C42C23×D1112yes—
479C11C2×#333111yescharacteristic, complemented, Sylow
480C23—24no—
481C23—22no—
482C23—42no—
483C23—42no—
484C23—114no—
485C23—224no—
486C23—224no—
487C23—224no—
488C23C2×D4×D1111yescharacteristic
489Q8—22no—
490Q8—22no—
491Q8—42no—
492Q8—224no—
493Q8—224no—
494Q8—444no—
495Q8—884no—
496D4—24no—
497D4—22no—
498D4—228no—
499D4—4416no—
500D4C2×#433914yes—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—22no—
505C2×C4—42no—
506C2×C4—42no—
507C2×C4—42no—
508C2×C4—48no—
509C2×C4—114no—
510C2×C4—224no—
511C2×C4—228no—
512C2×C4—224no—
513C2×C4—224no—
514C2×C4—224no—
515C2×C4—224no—
516C2×C4—4416no—
517C2×C4—444no—
518C2×C4—444no—
519C2×C4—888no—
520C2×C4#6696814yes—
521C2×C4C2×#433912yes—
522C2×C4C2×D4×D1112yes—
523C2×C4C2×D4×D1112yes—
524C2×C4C2×D4×D1111yescharacteristic
525C2×C4#6704212yes—
526C2×C4C24×D1111yescharacteristic
527C8—22no—
528C8—22no—
529C8—224no—
530C22—24no—
531C22—48no—
532C22—42no—
533C22—42no—
534C22—224no—
535C22—224no—
536C22—224no—
537C22—448no—
538C22#1062308112yes—
539C22C2×#6696812yes—
540C22#1062330112yes—
541C22C22×D4×D1111yescharacteristic
542C4—22no—
543C4—42no—
544C4—42no—
545C4—42no—
546C4—224no—
547C4—444no—
548C4—444no—
549C4#1062308112yes—
550C4C2×#6696814yes—
551C4C22×#433911yescharacteristic
552C4C2×#6704211yescharacteristic
553C2—44no—
554C2—444no—
555C2#1308093414yesdirect product factor
556C2C2×#1062308111yescharacteristic
557C2C22×#6696811yescharacteristic
558C2C2×#1062330111yescharacteristic
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×#3331
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×#10623110C2semidirect
3. #13080934C2direct (N × H)
4. C2×#10622294C2semidirect
5. C2×#10622475C2semidirect
6. C2×#10622621C2semidirect
7. C2×#10622429C2semidirect
8. C2×#10622644C2semidirect
9. C2×#10622786C2semidirect
10. C2×#10622301C2semidirect
11. C2×#10622384C2semidirect
12. C2×C4×C11×SD16C2semidirect
23. #10623110C22semidirect
35. C4×C11×SD16C22semidirect
41. #10622786C22semidirect
45. #10622644C22semidirect
46. #10622621C22semidirect
50. #10622475C22semidirect
51. #10622429C22semidirect
52. #10622384C22semidirect
53. #10622301C22semidirect
54. #10622294C22semidirect
210. C2×C4×SD16D11semidirect
291. C4×SD16C2×D11semidirect
402. C2×C11#3331semidirect
479. C11C2×#3331semidirect
555. C2#13080934direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231102
C2×#106230862
#130809342
C2×#106222942
C2×#106224752
C2×#106226212
C2×#106224292
C2×#106226442
C2×#106227862
C2×#106223012
C2×#106223842
C2×C4×C11×SD162
C2×#333111