Finite Group Databasebeta

← C2×#13081208 #15632486

Subgroups — C2×#13081208 #15632486

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×#10623265C211yesmaximal, characteristic, complemented
2C2×#10623082C211yesmaximal, characteristic, complemented
3#13081208C2116yesmaximal, direct product factor
4C2×#10622692C211yesmaximal, characteristic, complemented
5C2×#10622476C212yesmaximal, complemented
6C2×#10622397C212yesmaximal, complemented
7C2×#10622459C211yesmaximal, characteristic, complemented
8C2×#10622395C212yesmaximal, complemented
9C2×C4×#4323C211yesmaximal, characteristic, complemented
10C2×#10622451C211yesmaximal, characteristic, complemented
11C2×#10622474C212yesmaximal, complemented
12C2×C11×#476C211yesmaximal, characteristic, complemented
13C22×#4339—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#67000—22no—
17C2×#66991C2212yes—
18C22×#4323C2211yescharacteristic
19C2×#66977—21no—
20C22×#4313C2212yes—
21#10623265—24no—
22#10623265C2218yescomplemented
23#10623082—24no—
24#10623082C2218yescomplemented
25C2×#66948—21no—
26C2×#66948C2212yes—
27C2×#66945—21no—
28C2×#66945C2212yes—
29C2×C4⋊C4×D11C2212yes—
30C2×#66936—22no—
31C2×C4×D44C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C11×#476C2218yescomplemented
35C2×C11×#106C2212yes—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#102C2212yes—
38C2×#66896C2211yescharacteristic
39C2×#66885C2212yes—
40C2×(C2×D11)⋊C8C2212yes—
41C2×#66882C2212yes—
42#10622692C2218yescomplemented
43C4×#4323C2218yescomplemented
44C2×#66873C2211yescharacteristic
45C2×#66872C2212yes—
46C2×#66872C2212yes—
47C2×#66871C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622476C22116yescomplemented
50#10622474C22116yescomplemented
51#10622459C2218yescomplemented
52#10622451C2218yescomplemented
53#10622397C22116yescomplemented
54#10622395C22116yescomplemented
55C22×Q8×C11—21no—
56C22×D4×C11C2311yescharacteristic
57C23×C4×C11—21no—
58C22×C22⋊D11—22no—
59C2×#4339—28no—
60C2×#4339—48no—
61C22×D44—22no—
62C22×D44D411yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—22no—
65C22×C4×D11—21no—
66C22×C4×D11C2312yes—
67C22×Dic22—21no—
68C22×C8×C11C2312yes—
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8C2314yes—
71C4×D4×C11—22no—
72C4×D4×C11C2314yes—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4C2311yescharacteristic
75C2×C11×C4⋊C4C2312yes—
76C2×C11×C22⋊C4—21no—
77C2×C42×C11C2311yescharacteristic
78C2×C22⋊Dic11—22no—
79#67000—216no—
80#66991—24no—
81#66991C2318yes—
82C2×#4323—24no—
83C2×#4323C2314yes—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—21no—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4D412yes—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11D411yescharacteristic
90C2×C4⋊Dic11C2312yes—
91C2×C4⋊Dic11C2311yescharacteristic
92#66977—28no—
93C2×Dic11⋊C4—22no—
94C2×C4×Dic11—22no—
95C22×C11⋊C8C2311yescharacteristic
96C22×C11⋊C8C2311yescharacteristic
97C2×#4313—28no—
98C2×#4313C2318yes—
99#66948—28no—
100#66948—24no—
101#66948C2318yes—
102#66945—24no—
103#66945—28no—
104#66945C2318yes—
105C4⋊C4×D11—24no—
106C4⋊C4×D11C2318yes—
107#66936—216no—
108C4×D44—22no—
109C4×D44D414yes—
110C4×D44C2314yes—
111C4×D44C2314yes—
112#66922—22no—
113#66922C2314yes—
114C11×#106C2318yes—
115C11×C4⋊C8C2314yes—
116C11×#102C2318yes—
117#66896C2314yes—
118#66885C2318yes—
119(C2×D11)⋊C8C2318yes—
120#66882C2318yes—
121#66873C2314yes—
122#66872C2318yes—
123#66872C2318yes—
124#66871C2314yes—
125C4×C11⋊C8C2314yes—
126C2×#3354—111nomaximal, Sylow
127C24×C11—21no—
128C23×D11—21no—
129C23×D11C2×D412yes—
130C2×Q8×C11—24no—
131C2×Q8×C11—82no—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11—22no—
135C2×D4×C11C2412yes—
136C22×C4×C11—22no—
137C22×C4×C11—21no—
138C22×C4×C11—24no—
139C22×C4×C11—44no—
140C22×C4×C11C2×D411yescharacteristic
141C22×C4×C11C2×D411yescharacteristic
142C22×C4×C11C2411yescharacteristic
143C2×C22⋊D11—28no—
144C2×C22⋊D11—48no—
145C22×Dic11—21no—
146C22×Dic11—22no—
147C22×Dic11C2×D412yes—
148#4339—432no—
149C2×D44—28no—
150C2×D44—24no—
151C2×D44—21no—
152C2×D44—22no—
153C2×D44—22no—
154C2×D44—84no—
155C2×D44C2×D414yes—
156C2×D44C2412yes—
157C2×C4×D11—28no—
158C2×C4×D11—24no—
159C2×C4×D11—24no—
160C2×C4×D11—24no—
161C2×C4×D11—48no—
162C2×C4×D11—44no—
163C2×C4×D11C2×D414yes—
164C2×C4×D11C2414yes—
165C2×Dic22—24no—
166C2×Dic22—44no—
167C2×C8×C11—24no—
168C2×C8×C11C2414yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4—24no—
171C11×C4⋊C4—22no—
172C11×C4⋊C4C2412yes—
173C11×C4⋊C4C2414yes—
174C11×C22⋊C4—24no—
175C42×C11C2×D412yes—
176C42×C11C2412yes—
177C22⋊Dic11—28no—
178#4323—28no—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—24no—
182(C2×D11)⋊C4C2×D418yes—
183C4⋊Dic11—22no—
184C4⋊Dic11—24no—
185C4⋊Dic11—21no—
186C4⋊Dic11C2×D414yes—
187C4⋊Dic11C2412yes—
188C4⋊Dic11C2414yes—
189Dic11⋊C4—28no—
190C4×Dic11—28no—
191C2×C11⋊C8—22no—
192C2×C11⋊C8#4114yescomplemented
193C2×C11⋊C8C2412yes—
194C2×C11⋊C8C2412yes—
195#4313—216no—
196C2×#555—111no—
197C2×#547—111no—
198#3354—1116no—
199C2×#498—111no—
200C2×#481—112no—
201C2×#482—112no—
202C2×#476D1111yescharacteristic, complemented
203C2×#474—111no—
204C2×#469—112no—
205C2×C4×D8—111no—
206C2×#436—111no—
207C2×#428—112no—
208C23×C11—22no—
209C23×C11—42no—
210C23×C11—42no—
211C23×C11—42no—
212C23×C11C22×D411yescharacteristic
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—22no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11C22×D414yes—
221Q8×C11—84no—
222D4×C11—22no—
223D4×C11—22no—
224D4×C11—42no—
225C2×C4×C11—22no—
226C2×C4×C11—24no—
227C2×C4×C11—22no—
228C2×C4×C11—42no—
229C2×C4×C11—44no—
230C2×C4×C11—48no—
231C2×C4×C11AGL(1,ℤ/8)14yes—
232C2×C4×C11C22×D412yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D412yes—
235C2×C4×C11C2×#4112yes—
236C2×C4×C112−1+412yes—
237C2×C4×C11C2511yescharacteristic
238C22⋊D11—416no—
239C2×Dic11—24no—
240C2×Dic11—22no—
241C2×Dic11—24no—
242C2×Dic11—44no—
243C2×Dic11—42no—
244C2×Dic11C22×D414yes—
245D44—28no—
246D44—22no—
247D44—22no—
248D44—42no—
249D44—88no—
250C4×D11—28no—
251C4×D11—24no—
252C4×D11—24no—
253C4×D11—416no—
254C4×D11—48no—
255Dic22—48no—
256C8×C11—24no—
257C11⋊C8—22no—
258C11⋊C8C2×#4114yescomplemented
259C22×#41—221no—
260C22×D8—111no—
261C22×M16—112no—
262#555—118no—
263#555—224no—
264#547—118no—
265#547—224no—
266C2×C4⋊Q8—111no—
267C2×C4⋊Q8C2×D1111yescharacteristic
268C2×#124—222no—
269C2×#123—222no—
270C2×C22⋊Q8—221no—
271C2×#121—112no—
272C2×#121—112no—
273C2×#121—221no—
274C2×C4×D4—111no—
275C2×C4×D4—111no—
276C2×C4×D4C2×D1111yescharacteristic
277C2×#117—112no—
278C2×#117—221no—
279C22×C4⋊C4—112no—
280#498—118no—
281#482—1116no—
282#481—1116no—
283#476C2×D1118yescomplemented
284#474—118no—
285#469—1116no—
286C4×D8—118no—
287#436—118no—
288#428—1116no—
289C2×#107—112no—
290C2×#107—111no—
291C2×#106—112no—
292C2×#106—112no—
293C2×#106C2×D1112yes—
294C2×C4⋊C8C2×D1111yescharacteristic
295C2×#102—111no—
296C2×#102—112no—
297C2×#102—111no—
298C2×#102C2×D1112yes—
299C2×C22⋊C8—112no—
300C2×C4×C8—111no—
301C22×C11—42no—
302C22×C11—42no—
303C22×C11—42no—
304C22×C11—84no—
305C22×C11#54712yes—
306C22×C11C2×AGL(1,ℤ/8)12yes—
307C22×C11#57712yes—
308C22×C11C23×D411yescharacteristic
309C2×D11—24no—
310C2×D11—24no—
311C2×D11—24no—
312C2×D11—48no—
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—42no—
316C2×D11—84no—
317C4×C11—22no—
318C4×C11—42no—
319C4×C11—44no—
320C4×C11#54712yes—
321C4×C11C2×AGL(1,ℤ/8)14yes—
322C4×C11C22×#4111yescharacteristic
323C4×C11C2×2−1+411yescharacteristic
324Dic11—24no—
325Dic11—44no—
326Dic11—42no—
327C2×#41—228no—
328C2×#41—448no—
329C22×Q8—21no—
330C22×Q8—221no—
331C22×D4—111no—
332C22×D4—111no—
333C22×D4—222no—
334C22×D4—222no—
335C22×D4C22×D1111yescharacteristic
336C23×C4—21no—
337C23×C4—112no—
338C23×C4—222no—
339C23×C4—221no—
340C2×D8—114no—
341C2×D8—224no—
342C2×M16—118no—
343C2×M16—228no—
344C22×C8—111no—
345C22×C8—111no—
346C22×C8C22×D1112yes—
347C4⋊Q8—22no—
348C4⋊Q8—114no—
349C4⋊Q8—222no—
350C4⋊Q8C22×D1114yes—
351#124—2216no—
352#123—2216no—
353C22⋊Q8—228no—
354#121—118no—
355#121—118no—
356#121—224no—
357#121—228no—
358#121—224no—
359C4×D4—22no—
360C4×D4—114no—
361C4×D4—114no—
362C4×D4—114no—
363C4×D4—222no—
364C4×D4C22×D1114yes—
365#117—118no—
366#117—228no—
367#117—224no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—111no—
370C2×C4⋊C4—112no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—118no—
373C2×C4⋊C4—224no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4C22×D1111yescharacteristic
377C2×C4⋊C4C22×D1112yes—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—112no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—221no—
384C2×C42—222no—
385C2×C42C22×D1111yescharacteristic
386#107—118no—
387#107—114no—
388#106—118no—
389#106—118no—
390#106C22×D1118yes—
391C4⋊C8C22×D1114yes—
392#102—114no—
393#102—118no—
394#102—114no—
395#102C22×D1118yes—
396C22⋊C8—118no—
397C4×C8—114no—
398C2×C11—82no—
399C2×C11#335414yescomplemented
400C2×C11C2×#54711yescharacteristic
401C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
402C2×C11C2×#57711yescharacteristic
403D11—44no—
404D11—82no—
405C24—21no—
406C24—112no—
407C24—221no—
408#41—4432no—
409C2×Q8—24no—
410C2×Q8—82no—
411C2×Q8—224no—
412C2×Q8—444no—
413C2×D4—21no—
414C2×D4—22no—
415C2×D4—22no—
416C2×D4—114no—
417C2×D4—112no—
418C2×D4—228no—
419C2×D4—228no—
420C2×D4—224no—
421C2×D4—221no—
422C2×D4—222no—
423C2×D4—222no—
424C2×D4—448no—
425C2×D4—884no—
426C2×D4C23×D1112yes—
427C22×C4—22no—
428C22×C4—21no—
429C22×C4—24no—
430C22×C4—44no—
431C22×C4—112no—
432C22×C4—114no—
433C22×C4—114no—
434C22×C4—228no—
435C22×C4—224no—
436C22×C4—224no—
437C22×C4—221no—
438C22×C4—222no—
439C22×C4—224no—
440C22×C4—448no—
441C22×C4—444no—
442C22×C4D4×D1111yescharacteristic
443C22×C4D4×D1111yescharacteristic
444C22×C4C23×D1111yescharacteristic
445D8—228no—
446M16—2216no—
447C2×C8—24no—
448C2×C8—114no—
449C2×C8—112no—
450C2×C8—112no—
451C2×C8—222no—
452C2×C8C23×D1114yes—
453C4⋊C4—24no—
454C4⋊C4—21no—
455C4⋊C4—22no—
456C4⋊C4—114no—
457C4⋊C4—114no—
458C4⋊C4—112no—
459C4⋊C4—228no—
460C4⋊C4—222no—
461C4⋊C4—221no—
462C4⋊C4—224no—
463C4⋊C4C23×D1112yes—
464C4⋊C4C23×D1114yes—
465C22⋊C4—24no—
466C22⋊C4—118no—
467C22⋊C4—228no—
468C22⋊C4—228no—
469C22⋊C4—228no—
470C22⋊C4—224no—
471C42—228no—
472C42D4×D1112yes—
473C42C23×D1112yes—
474C11C2×#335411yescharacteristic, complemented, Sylow
475C23—22no—
476C23—42no—
477C23—42no—
478C23—42no—
479C23—114no—
480C23—224no—
481C23—224no—
482C23—224no—
483C23—222no—
484C23—442no—
485C23—442no—
486C23—442no—
487C23C2×D4×D1111yescharacteristic
488Q8—84no—
489Q8—448no—
490D4—22no—
491D4—22no—
492D4—42no—
493D4—228no—
494D4—222no—
495D4—222no—
496D4—4416no—
497D4—442no—
498D4—888no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—22no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—48no—
505C2×C4—114no—
506C2×C4—224no—
507C2×C4—228no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—222no—
511C2×C4—224no—
512C2×C4—4416no—
513C2×C4—444no—
514C2×C4—442no—
515C2×C4—448no—
516C2×C4#6696714yes—
517C2×C4C2×D4×D1112yes—
518C2×C4C2×D4×D1112yes—
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4#6704012yes—
521C2×C4#41×D1112yes—
522C2×C4C24×D1111yescharacteristic
523C8—24no—
524C8—114no—
525C8—222no—
526C22—42no—
527C22—42no—
528C22—42no—
529C22—84no—
530C22—224no—
531C22—224no—
532C22—224no—
533C22—448no—
534C22—442no—
535C22—442no—
536C22—442no—
537C22—884no—
538C22#1062316212yes—
539C22C2×#6696712yes—
540C22#1062330612yes—
541C22C22×D4×D1111yescharacteristic
542C4—22no—
543C4—42no—
544C4—44no—
545C4—224no—
546C4—444no—
547C4—442no—
548C4#1062316212yes—
549C4C2×#6696714yes—
550C4C2×#6704011yescharacteristic
551C4C2×#41×D1111yescharacteristic
552C2—82no—
553C2—444no—
554C2—882no—
555C2#1308120814yesdirect product factor
556C2C2×#1062316211yescharacteristic
557C2C22×#6696711yescharacteristic
558C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
hypercenterC2×#476D11
hypocenterC11C2×#3354
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10623265C2semidirect
2. C2×#10623082C2semidirect
3. #13081208C2direct (N × H)
4. C2×#10622692C2semidirect
5. C2×#10622476C2semidirect
6. C2×#10622397C2semidirect
7. C2×#10622459C2semidirect
8. C2×#10622395C2semidirect
9. C2×C4×#4323C2semidirect
10. C2×#10622451C2semidirect
11. C2×#10622474C2semidirect
12. C2×C11×#476C2semidirect
22. #10623265C22semidirect
24. #10623082C22semidirect
34. C11×#476C22semidirect
42. #10622692C22semidirect
43. C4×#4323C22semidirect
49. #10622476C22semidirect
50. #10622474C22semidirect
51. #10622459C22semidirect
52. #10622451C22semidirect
53. #10622397C22semidirect
54. #10622395C22semidirect
192. C2×C11⋊C8#41semidirect
202. C2×#476D11semidirect
258. C11⋊C8C2×#41semidirect
283. #476C2×D11semidirect
399. C2×C11#3354semidirect
474. C11C2×#3354semidirect
555. C2#13081208direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232652
C2×#106230822
#130812082
C2×#106226922
C2×#106224762
C2×#106223972
C2×#106224592
C2×#106223952
C2×C4×#43232
C2×#106224512
C2×#106224742
C2×C11×#4762
C2×#335411