Finite Group Databasebeta

← C2×#13080943 #15630706

Subgroups — C2×#13080943 #15630706

Order 2816.

2426 conjugacy classes of subgroups.

The subgroup lattice has 592 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623086C211yesmaximal, characteristic, complemented
2#13080943C2116yesmaximal, direct product factor
3C2×#10622683C211yesmaximal, characteristic, complemented
4C2×#10622647C212yesmaximal, complemented
5C2×#10622633C211yesmaximal, characteristic, complemented
6C2×#10622652C212yesmaximal, complemented
7C2×#10622685C211yesmaximal, characteristic, complemented
8C2×#10622851C212yesmaximal, complemented
9C2×C4×#4325C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622845C212yesmaximal, complemented
12C2×C11×#550C211yesmaximal, characteristic, complemented
13C22×C11×#41C2212yes—
14C22×#4341—21no—
15C11×#550—24no—
16C11×#550C2218yescomplemented
17C2×C11×#127—21no—
18C2×C11×#127C2211yescharacteristic
19C2×C11×#121—22no—
20C2×C11×#121C2212yes—
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C4×D4×C11—21no—
23C2×C4×D4×C11C2211yescharacteristic
24C22×#4325C2211yescharacteristic
25C22×#4323C2212yes—
26C2×#66983C2212yes—
27C22×C4⋊Dic11C2212yes—
28C22×#4318C2212yes—
29#10623086—24no—
30#10623086C2218yescomplemented
31C2×#66950—21no—
32C2×#66939—22no—
33C2×C4×D44C2211yescharacteristic
34C2×#66922C2211yescharacteristic
35#10622851C22116yescomplemented
36#10622845C22116yescomplemented
37C2×#66899C2212yes—
38C2×#66899C2211yescharacteristic
39C2×#66896C2212yes—
40C2×#66896C2212yes—
41C2×#66896C2212yes—
42C2×C22⋊(C11⋊C8)C2212yes—
43#10622685C2218yescomplemented
44#10622683C2218yescomplemented
45#10622652C22116yescomplemented
46#10622647C22116yescomplemented
47C4×#4325C2218yescomplemented
48#10622633C2218yescomplemented
49#10622625C2218yescomplemented
50C2×#66873C2211yescharacteristic
51C2×#66872C2212yes—
52C2×#66872C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C11×#41—24no—
56C2×C11×#41—28no—
57C2×C11×#41—44no—
58C2×C11×#41C2318yes—
59C22×Q8×C11C2311yescharacteristic
60C22×D4×C11—22no—
61C22×D4×C11—22no—
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11D411yescharacteristic
65C22×D4×C11C2312yes—
66C23×C4×C11—22no—
67C23×C4×C11C2312yes—
68C22×C22⋊D11—22no—
69C23×Dic11—22no—
70C2×#4341—28no—
71C2×#4341—48no—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×Dic22—21no—
75C11×#127—28no—
76C11×#127—22no—
77C11×#127C2314yes—
78C11×#121—24no—
79C11×#121—216no—
80C11×#121C2318yes—
81C4×Q8×C11—22no—
82C4×Q8×C11C2314yes—
83C4×D4×C11—28no—
84C4×D4×C11D414yes—
85C4×D4×C11C2314yes—
86C2×C11×C4⋊C4—21no—
87C2×C11×C4⋊C4D411yescharacteristic
88C2×C11×C4⋊C4C2311yescharacteristic
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4D412yes—
91C2×C42×C11—21no—
92C2×C42×C11C2311yescharacteristic
93C2×#4325—24no—
94C2×#4325C2314yes—
95C2×#4323—44no—
96C2×#4323C2318yes—
97#66983—24no—
98#66983C2318yes—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—22no—
101C2×C4⋊Dic11—21no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11—24no—
104C2×C4⋊Dic11C2312yes—
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2318yes—
107C2×#4318—44no—
108C2×#4318C2318yes—
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2311yescharacteristic
111C22×C11⋊C8C2312yes—
112#66950—28no—
113#66939—216no—
114C4×D44—22no—
115C4×D44C2314yes—
116#66922—22no—
117#66922C2314yes—
118#66899C2314yes—
119#66899C2318yes—
120#66896C2318yes—
121#66896C2318yes—
122#66896C2318yes—
123C22⋊(C11⋊C8)C2318yes—
124#66873C2314yes—
125#66872C2318yes—
126#66872C2314yes—
127C4⋊(C11⋊C8)C2314yes—
128C4×C11⋊C8C2314yes—
129C2×#3332—111nomaximal, Sylow
130C24×C11—22no—
131C24×C11C2×D412yes—
132C23×D11—21no—
133C11×#41—216no—
134C11×#41—48no—
135C11×#41—416no—
136C2×Q8×C11—21no—
137C2×Q8×C11—22no—
138C2×Q8×C11#4114yescomplemented
139C2×Q8×C11C2412yes—
140C2×D4×C11—28no—
141C2×D4×C11—28no—
142C2×D4×C11—24no—
143C2×D4×C11—24no—
144C2×D4×C11—22no—
145C2×D4×C11—24no—
146C2×D4×C11—24no—
147C2×D4×C11—24no—
148C2×D4×C11—48no—
149C2×D4×C11—44no—
150C2×D4×C11—82no—
151C2×D4×C11—84no—
152C2×D4×C11C2×D414yes—
153C2×D4×C11C2414yes—
154C22×C4×C11—21no—
155C22×C4×C11—24no—
156C22×C4×C11—24no—
157C22×C4×C11—21no—
158C22×C4×C11—28no—
159C22×C4×C11—48no—
160C22×C4×C11C2×D411yescharacteristic
161C22×C4×C11C2×D412yes—
162C22×C4×C11C2×D414yes—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2414yes—
165C22×C4×C11C2411yescharacteristic
166C2×C22⋊D11—28no—
167C2×C22⋊D11—48no—
168C22×Dic11—28no—
169C22×Dic11—22no—
170C22×Dic11—21no—
171C22×Dic11—48no—
172#4341—432no—
173C2×D44—21no—
174C2×D44—22no—
175C2×D44—22no—
176C2×D44C2412yes—
177C2×C4×D11—24no—
178C2×C4×D11—44no—
179C2×Dic22—24no—
180C2×Dic22—44no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—21no—
183C11×C4⋊C4C2×D414yes—
184C11×C4⋊C4C2412yes—
185C11×C22⋊C4—28no—
186C11×C22⋊C4C2×D418yes—
187C42×C11—24no—
188C42×C11C2×D412yes—
189C42×C11C2412yes—
190#4325—28no—
191#4323—48no—
192(C2×D11)⋊C4—24no—
193(C2×D11)⋊C4—28no—
194C4⋊Dic11—22no—
195C4⋊Dic11—24no—
196C4⋊Dic11—21no—
197C4⋊Dic11—28no—
198C4⋊Dic11C2414yes—
199C4⋊Dic11C2412yes—
200#4318—48no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—22no—
203C2×C11⋊C8—24no—
204C2×C11⋊C8C2412yes—
205C2×C11⋊C8C2412yes—
206C2×C11⋊C8C2414yes—
207C2×#550D1111yescharacteristic, complemented
208C2×#547—111no—
209#3332—1116no—
210C2×#486—111no—
211C2×#481—112no—
212C2×#475—111no—
213C2×#469—112no—
214C2×#459—111no—
215C2×#449—112no—
216C2×C4×SD16—111no—
217C2×#436—111no—
218C2×#417—112no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—44no—
224C23×C11—44no—
225C23×C11—44no—
226C23×C11C22×D414yes—
227C23×C11C22×D411yescharacteristic
228C22×D11—22no—
229C22×D11—42no—
230C22×D11—42no—
231C22×D11—42no—
232Q8×C11—24no—
233Q8×C11—22no—
234Q8×C11C2×#4114yescomplemented
235D4×C11—28no—
236D4×C11—24no—
237D4×C11—24no—
238D4×C11—416no—
239D4×C11—44no—
240D4×C11—48no—
241D4×C11—84no—
242D4×C11—88no—
243C2×C4×C11—24no—
244C2×C4×C11—24no—
245C2×C4×C11—22no—
246C2×C4×C11—22no—
247C2×C4×C11—28no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—416no—
252C2×C4×C11—42no—
253C2×C4×C11AGL(1,ℤ/8)14yes—
254C2×C4×C11C22×D412yes—
255C2×C4×C11C22×D414yes—
256C2×C4×C11C22×D411yescharacteristic
257C2×C4×C11C22×D412yes—
258C2×C4×C11C2×#4112yes—
259C2×C4×C11H(5,𝔽2)12yes—
260C2×C4×C11C2511yescharacteristic
261C22⋊D11—416no—
262C2×Dic11—24no—
263C2×Dic11—22no—
264C2×Dic11—416no—
265C2×Dic11—44no—
266C2×Dic11—42no—
267D44—22no—
268D44—22no—
269D44—42no—
270C4×D11—48no—
271Dic22—48no—
272C11⋊C8—22no—
273C11⋊C8—22no—
274C11⋊C8—24no—
275C22×#41—221no—
276C22×#41C2×D1112yes—
277C22×SD16—111no—
278C22×D8—112no—
279C22×M16—112no—
280#550—24no—
281#550C2×D1118yescomplemented
282#547—118no—
283#547—224no—
284C2×C4⋊Q8—111no—
285C2×#127—21no—
286C2×#127C2×D1111yescharacteristic
287C2×#123—222no—
288C2×C22⋊Q8—221no—
289C2×#121—22no—
290C2×#121—112no—
291C2×#121C2×D1112yes—
292C2×C4×Q8C2×D1111yescharacteristic
293C2×C4×D4—21no—
294C2×C4×D4—111no—
295C2×C4×D4C2×D1111yescharacteristic
296C22×C4⋊C4—112no—
297#486—118no—
298#481—1116no—
299#475—118no—
300#469—1116no—
301#459—118no—
302#449—1116no—
303C4×SD16—118no—
304#436—118no—
305C2×#106—112no—
306C2×#106—111no—
307C2×C4⋊C8—111no—
308#417—1116no—
309C2×#103—112no—
310C2×#103—111no—
311C2×#102—112no—
312C2×#102—112no—
313C2×#102—112no—
314C2×#102—111no—
315C2×C22⋊C8—112no—
316C2×C4×C8—111no—
317C22×C11—24no—
318C22×C11—24no—
319C22×C11—24no—
320C22×C11—48no—
321C22×C11—44no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—88no—
325C22×C11#54612yes—
326C22×C11C2×AGL(1,ℤ/8)12yes—
327C22×C11#57712yes—
328C22×C11C23×D411yescharacteristic
329C2×D11—42no—
330C2×D11—42no—
331C2×D11—42no—
332C2×D11—84no—
333C4×C11—24no—
334C4×C11—24no—
335C4×C11—22no—
336C4×C11—42no—
337C4×C11#54612yes—
338C4×C11C2×AGL(1,ℤ/8)14yes—
339C4×C11C22×#4111yescharacteristic
340C4×C11C2×H(5,𝔽2)11yescharacteristic
341Dic11—44no—
342Dic11—42no—
343C2×#41—24no—
344C2×#41—28no—
345C2×#41—44no—
346C2×#41—228no—
347C2×#41—448no—
348C2×#41C22×D1118yes—
349C22×Q8—221no—
350C22×Q8C22×D1111yescharacteristic
351C22×D4—22no—
352C22×D4—22no—
353C22×D4—21no—
354C22×D4—21no—
355C22×D4—111no—
356C22×D4—222no—
357C22×D4C22⋊D1111yescharacteristic
358C22×D4C22×D1112yes—
359C23×C4—22no—
360C23×C4—222no—
361C23×C4—221no—
362C23×C4C22×D1112yes—
363C2×SD16—114no—
364C2×SD16—224no—
365C2×D8—118no—
366C2×D8—444no—
367C2×M16—118no—
368C2×M16—444no—
369C22×C8—111no—
370C22×C8—112no—
371C22×C8—111no—
372C4⋊Q8—114no—
373C4⋊Q8—222no—
374#127—28no—
375#127—22no—
376#127C22×D1114yes—
377#123—2216no—
378C22⋊Q8—228no—
379#121—24no—
380#121—216no—
381#121—118no—
382#121—224no—
383#121C22×D1118yes—
384C4×Q8—22no—
385C4×Q8C22×D1114yes—
386C4×D4—28no—
387C4×D4—114no—
388C4×D4—222no—
389C4×D4C22⋊D1114yes—
390C4×D4C22×D1114yes—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—111no—
393C2×C4⋊C4—112no—
394C2×C4⋊C4—118no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4—224no—
397C2×C4⋊C4—221no—
398C2×C4⋊C4C22⋊D1111yescharacteristic
399C2×C4⋊C4C22×D1111yescharacteristic
400C2×C22⋊C4—22no—
401C2×C22⋊C4—221no—
402C2×C22⋊C4—222no—
403C2×C22⋊C4C22⋊D1112yes—
404C2×C42—21no—
405C2×C42C22×D1111yescharacteristic
406#106—114no—
407#106—118no—
408C4⋊C8—114no—
409#103—114no—
410#103—118no—
411#102—118no—
412#102—118no—
413#102—118no—
414#102—114no—
415C22⋊C8—118no—
416C4×C8—114no—
417C2×C11—44no—
418C2×C11—84no—
419C2×C11#333214yescomplemented
420C2×C11C2×#54611yescharacteristic
421C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
422C2×C11C2×#57711yescharacteristic
423D11—82no—
424C24—22no—
425C24—221no—
426C24C2×C22⋊D1112yes—
427#41—216no—
428#41—48no—
429#41—416no—
430#41—4432no—
431C2×Q8—22no—
432C2×Q8—21no—
433C2×Q8—224no—
434C2×Q8—444no—
435C2×Q8#434114yescomplemented
436C2×Q8C23×D1112yes—
437C2×D4—28no—
438C2×D4—28no—
439C2×D4—24no—
440C2×D4—24no—
441C2×D4—24no—
442C2×D4—24no—
443C2×D4—22no—
444C2×D4—24no—
445C2×D4—48no—
446C2×D4—44no—
447C2×D4—82no—
448C2×D4—84no—
449C2×D4—112no—
450C2×D4—228no—
451C2×D4—222no—
452C2×D4—222no—
453C2×D4—221no—
454C2×D4—448no—
455C2×D4C2×C22⋊D1114yes—
456C2×D4C23×D1114yes—
457C22×C4—21no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—21no—
461C22×C4—28no—
462C22×C4—48no—
463C22×C4—228no—
464C22×C4—221no—
465C22×C4—222no—
466C22×C4—224no—
467C22×C4—448no—
468C22×C4—444no—
469C22×C4C2×C22⋊D1114yes—
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C2×C22⋊D1112yes—
472C22×C4C2×C22⋊D1111yescharacteristic
473C22×C4C23×D1114yes—
474C22×C4C23×D1111yescharacteristic
475SD16—228no—
476D8—448no—
477M16—448no—
478C2×C8—112no—
479C2×C8—112no—
480C2×C8—114no—
481C2×C8—222no—
482C2×C8—222no—
483C2×C8—224no—
484C4⋊C4—24no—
485C4⋊C4—21no—
486C4⋊C4—112no—
487C4⋊C4—114no—
488C4⋊C4—221no—
489C4⋊C4—222no—
490C4⋊C4—228no—
491C4⋊C4—224no—
492C4⋊C4C2×C22⋊D1114yes—
493C4⋊C4C23×D1112yes—
494C22⋊C4—28no—
495C22⋊C4—224no—
496C22⋊C4—228no—
497C22⋊C4C2×C22⋊D1118yes—
498C42—24no—
499C42C2×C22⋊D1112yes—
500C42C23×D1112yes—
501C11C2×#333211yescharacteristic, complemented, Sylow
502C23—24no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—44no—
507C23—44no—
508C23—44no—
509C23—222no—
510C23—442no—
511C23—442no—
512C23—442no—
513C23C22×C22⋊D1114yes—
514C23C22×C22⋊D1111yescharacteristic
515Q8—24no—
516Q8—22no—
517Q8—448no—
518Q8C2×#434114yescomplemented
519D4—28no—
520D4—24no—
521D4—24no—
522D4—416no—
523D4—44no—
524D4—48no—
525D4—84no—
526D4—88no—
527D4—222no—
528D4—222no—
529D4—4416no—
530D4—442no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—28no—
536C2×C4—24no—
537C2×C4—24no—
538C2×C4—22no—
539C2×C4—416no—
540C2×C4—42no—
541C2×C4—222no—
542C2×C4—224no—
543C2×C4—4416no—
544C2×C4—442no—
545C2×C4—444no—
546C2×C4—448no—
547C2×C4#6700214yes—
548C2×C4C2×#434112yes—
549C2×C4#6703712yes—
550C2×C4C22×C22⋊D1112yes—
551C2×C4C22×C22⋊D1114yes—
552C2×C4C22×C22⋊D1111yescharacteristic
553C2×C4C22×C22⋊D1112yes—
554C2×C4C24×D1111yescharacteristic
555C8—222no—
556C8—222no—
557C8—224no—
558C22—24no—
559C22—24no—
560C22—24no—
561C22—48no—
562C22—44no—
563C22—44no—
564C22—44no—
565C22—88no—
566C22—442no—
567C22—442no—
568C22—442no—
569C22—884no—
570C22#1062333712yes—
571C22C2×#6700212yes—
572C22#1062336712yes—
573C22C23×C22⋊D1111yescharacteristic
574C4—24no—
575C4—24no—
576C4—22no—
577C4—42no—
578C4—442no—
579C4—444no—
580C4#1062333712yes—
581C4C2×#6700214yes—
582C4C22×#434111yescharacteristic
583C4C2×#6703711yescharacteristic
584C2—44no—
585C2—84no—
586C2—882no—
587C2#1308094314yesdirect product factor
588C2C2×#1062333711yescharacteristic
589C2C22×#6700211yescharacteristic
590C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#550C2
socleC23×C11C22×D4
hypercenterC2×#550D11
hypocenterC11C2×#3332
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#550

Complements

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

NH ≅ G/Ntype
1. C2×#10623086C2semidirect
2. #13080943C2direct (N × H)
3. C2×#10622683C2semidirect
4. C2×#10622647C2semidirect
5. C2×#10622633C2semidirect
6. C2×#10622652C2semidirect
7. C2×#10622685C2semidirect
8. C2×#10622851C2semidirect
9. C2×C4×#4325C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622845C2semidirect
12. C2×C11×#550C2semidirect
16. C11×#550C22semidirect
30. #10623086C22semidirect
35. #10622851C22semidirect
36. #10622845C22semidirect
43. #10622685C22semidirect
44. #10622683C22semidirect
45. #10622652C22semidirect
46. #10622647C22semidirect
47. C4×#4325C22semidirect
48. #10622633C22semidirect
49. #10622625C22semidirect
138. C2×Q8×C11#41semidirect
207. C2×#550D11semidirect
234. Q8×C11C2×#41semidirect
281. #550C2×D11semidirect
419. C2×C11#3332semidirect
435. C2×Q8#4341semidirect
501. C11C2×#3332semidirect
518. Q8C2×#4341semidirect
587. C2#13080943direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230862
#130809432
C2×#106226832
C2×#106226472
C2×#106226332
C2×#106226522
C2×#106226852
C2×#106228512
C2×C4×#43252
C2×#106226252
C2×#106228452
C2×C11×#5502
C2×#333211