Finite Group Databasebeta

← C2×#13081210 #15632488

Subgroups — C2×#13081210 #15632488

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×#10623257C211yesmaximal, characteristic, complemented
3#13081210C2116yesmaximal, direct product factor
4C2×#10622476C212yesmaximal, complemented
5C2×#10622479C212yesmaximal, complemented
6C2×#10622697C211yesmaximal, characteristic, complemented
7C2×#10622700C211yesmaximal, characteristic, complemented
8C2×#10622478C212yesmaximal, complemented
9C2×C4×D88C211yesmaximal, characteristic, complemented
10C2×#10622301C211yesmaximal, characteristic, complemented
11C2×#10622474C212yesmaximal, complemented
12C2×C11×#498C211yesmaximal, characteristic, complemented
13C22×#4343—21no—
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×#67000—22no—
17C2×#66999—21no—
18C22×D88C2211yescharacteristic
19C22×#4313C2212yes—
20#10623265—24no—
21#10623265C2218yescomplemented
22#10623257—24no—
23#10623257C2218yescomplemented
24C2×#66948—21no—
25C2×#66948C2212yes—
26C2×#66948C2212yes—
27C2×#66947—22no—
28C2×#66945—21no—
29C2×#66945C2212yes—
30C2×C4⋊C4×D11C2212yes—
31C2×C4×D44C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×C4×D44C2211yescharacteristic
34C11×#498C2218yescomplemented
35C2×C11×#106C2212yes—
36C2×C11×#106C2212yes—
37C2×C4×C8×C11C2211yescharacteristic
38C2×#66885C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×(C2×D11)⋊C8C2212yes—
41C2×#66882C2211yescharacteristic
42#10622700C2218yescomplemented
43#10622697C2218yescomplemented
44C2×#66873C2212yes—
45C2×#66873C2212yes—
46C2×#66872C2212yes—
47C2×#66871C2212yes—
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622479C22116yescomplemented
50#10622478C22116yescomplemented
51#10622476C22116yescomplemented
52#10622474C22116yescomplemented
53C4×D88C2218yescomplemented
54#10622301C2218yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11—21no—
57C2×#4343—28no—
58C2×#4343—48no—
59C22×D44—22no—
60C22×D44—22no—
61C22×D44D411yescharacteristic
62C22×D44C2311yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—22no—
65C22×C4×D11—21no—
66C22×C4×D11—21no—
67C22×C4×D11C2312yes—
68C22×C8×C11C2311yescharacteristic
69C22×C8×C11C2311yescharacteristic
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8C2314yes—
73C11×C4⋊Q8C2314yes—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4C2312yes—
77C2×C11×C4⋊C4C2312yes—
78C2×C42×C11C2311yescharacteristic
79#67000—216no—
80#66999—28no—
81C2×(C2×D11)⋊C4—22no—
82C2×(C2×D11)⋊C4—21no—
83C2×(C2×D11)⋊C4—21no—
84C2×(C2×D11)⋊C4—22no—
85C2×(C2×D11)⋊C4—22no—
86C2×(C2×D11)⋊C4D412yes—
87C2×C4⋊Dic11D411yescharacteristic
88C2×C4⋊Dic11C2311yescharacteristic
89C2×C4⋊Dic11C2311yescharacteristic
90C2×Dic11⋊C4—22no—
91C2×C4×Dic11—22no—
92C22×C11⋊C8C2312yes—
93C2×D88—24no—
94C2×D88C2314yes—
95C2×#4313—28no—
96C2×#4313C2318yes—
97#66948—28no—
98#66948—24no—
99#66948—24no—
100#66948C2318yes—
101#66948C2318yes—
102#66947—216no—
103#66945—24no—
104#66945—28no—
105#66945C2318yes—
106C4⋊C4×D11—24no—
107C4⋊C4×D11C2318yes—
108C4×D44—22no—
109C4×D44—22no—
110C4×D44D414yes—
111C4×D44C2314yes—
112C4×D44C2314yes—
113C4×D44C2314yes—
114C11×#106C2318yes—
115C11×#106C2318yes—
116C4×C8×C11C2314yes—
117#66885C2314yes—
118#66885C2314yes—
119(C2×D11)⋊C8C2318yes—
120#66882C2314yes—
121#66873C2318yes—
122#66873C2318yes—
123#66872C2318yes—
124#66871C2318yes—
125C4⋊(C11⋊C8)C2314yes—
126C2×#3354—111nomaximal, Sylow
127C23×D11—21no—
128C23×D11—21no—
129C23×D11C2×D412yes—
130C2×Q8×C11—24no—
131C2×Q8×C11—24no—
132C2×Q8×C11—44no—
133C2×Q8×C11—82no—
134C22×C4×C11—22no—
135C22×C4×C11—22no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11C2×D412yes—
142#4343—432no—
143C2×D44—28no—
144C2×D44—28no—
145C2×D44—24no—
146C2×D44—21no—
147C2×D44—21no—
148C2×D44—22no—
149C2×D44—22no—
150C2×D44—22no—
151C2×D44—22no—
152C2×D44—48no—
153C2×D44—84no—
154C2×D44C2×D414yes—
155C2×D44C2412yes—
156C2×D44C2412yes—
157C2×C4×D11—28no—
158C2×C4×D11—24no—
159C2×C4×D11—24no—
160C2×C4×D11—24no—
161C2×C4×D11—24no—
162C2×C4×D11—48no—
163C2×C4×D11—44no—
164C2×C4×D11—44no—
165C2×C4×D11C2×D414yes—
166C2×C4×D11C2414yes—
167C2×C8×C11—22no—
168C2×C8×C11#4114yescomplemented
169C2×C8×C11C2412yes—
170C2×C8×C11C2412yes—
171C11×C4⋊C4—22no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4C2414yes—
176C11×C4⋊C4C2414yes—
177C42×C11C2×D412yes—
178C42×C11C2412yes—
179(C2×D11)⋊C4—28no—
180(C2×D11)⋊C4—28no—
181(C2×D11)⋊C4—28no—
182(C2×D11)⋊C4—24no—
183(C2×D11)⋊C4—24no—
184(C2×D11)⋊C4C2×D418yes—
185C4⋊Dic11—21no—
186C4⋊Dic11—21no—
187C4⋊Dic11C2×D414yes—
188C4⋊Dic11C2412yes—
189C4⋊Dic11C2412yes—
190Dic11⋊C4—28no—
191C4×Dic11—28no—
192C2×C11⋊C8—24no—
193C2×C11⋊C8C2414yes—
194D88—28no—
195#4313—216no—
196C2×#555—111no—
197C2×#547—111no—
198#3354—1116no—
199C2×#498D1111yescharacteristic, complemented
200C2×#481—112no—
201C2×#482—112no—
202C2×#476—111no—
203C2×#474—111no—
204C2×#469—112no—
205C2×C4×D8—111no—
206C2×#436—111no—
207C2×#428—112no—
208C23×C11C22×D411yescharacteristic
209C22×D11—24no—
210C22×D11—24no—
211C22×D11—24no—
212C22×D11—22no—
213C22×D11—22no—
214C22×D11—42no—
215C22×D11—42no—
216C22×D11—42no—
217C22×D11—42no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11C22×D414yes—
221Q8×C11—48no—
222Q8×C11—84no—
223C2×C4×C11—22no—
224C2×C4×C11—24no—
225C2×C4×C11—24no—
226C2×C4×C11—44no—
227C2×C4×C11—44no—
228C2×C4×C11AGL(1,ℤ/8)14yes—
229C2×C4×C11C22×D412yes—
230C2×C4×C11C22×D411yescharacteristic
231C2×C4×C11C22×D412yes—
232C2×C4×C11C2×#4112yes—
233C2×C4×C112−1+412yes—
234C2×C4×C11C2511yescharacteristic
235C2×Dic11—24no—
236C2×Dic11—22no—
237C2×Dic11—22no—
238C2×Dic11—42no—
239C2×Dic11—42no—
240C2×Dic11C22×D414yes—
241D44—28no—
242D44—22no—
243D44—22no—
244D44—22no—
245D44—22no—
246D44—416no—
247D44—42no—
248D44—42no—
249D44—88no—
250C4×D11—28no—
251C4×D11—24no—
252C4×D11—24no—
253C4×D11—416no—
254C4×D11—48no—
255C4×D11—48no—
256C8×C11—22no—
257C8×C11C2×#4114yescomplemented
258C11⋊C8—24no—
259C22×#41—221no—
260C22×D8—111no—
261C22×M16—112no—
262#555—118no—
263#555—224no—
264#547—118no—
265#547—224no—
266C2×C4⋊Q8C2×D1111yescharacteristic
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×D4—111no—
277C2×#117—112no—
278C2×#117—221no—
279C22×C4⋊C4—112no—
280#498C2×D1118yescomplemented
281#482—1116no—
282#481—1116no—
283#476—118no—
284#474—118no—
285#469—1116no—
286C4×D8—118no—
287#436—118no—
288#428—1116no—
289C2×#107—111no—
290C2×#107—112no—
291C2×#106—112no—
292C2×#106C2×D1112yes—
293C2×#106C2×D1112yes—
294C2×C4⋊C8—111no—
295C2×#102—111no—
296C2×#102—111no—
297C2×#102—112no—
298C2×#102—112no—
299C2×C22⋊C8—112no—
300C2×C4×C8C2×D1111yescharacteristic
301C22×C11#54712yes—
302C22×C11C2×AGL(1,ℤ/8)12yes—
303C22×C11#57712yes—
304C22×C11C23×D411yescharacteristic
305C2×D11—24no—
306C2×D11—24no—
307C2×D11—24no—
308C2×D11—48no—
309C2×D11—42no—
310C2×D11—42no—
311C2×D11—42no—
312C2×D11—42no—
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—84no—
316C2×D11—84no—
317C4×C11—22no—
318C4×C11—44no—
319C4×C11—44no—
320C4×C11#54712yes—
321C4×C11C2×AGL(1,ℤ/8)14yes—
322C4×C11C22×#4111yescharacteristic
323C4×C11C2×2−1+411yescharacteristic
324Dic11—24no—
325Dic11—42no—
326Dic11—42no—
327C2×#41—228no—
328C2×#41—448no—
329C22×Q8—21no—
330C22×Q8—21no—
331C22×D4—111no—
332C22×D4—111no—
333C22×D4—111no—
334C22×D4—222no—
335C22×D4—222no—
336C23×C4—112no—
337C23×C4—222no—
338C23×C4—221no—
339C23×C4—221no—
340C2×D8—114no—
341C2×D8—224no—
342C2×M16—118no—
343C2×M16—228no—
344C22×C8—112no—
345C22×C8C22×D1111yescharacteristic
346C22×C8C22×D1111yescharacteristic
347C4⋊Q8—22no—
348C4⋊Q8—22no—
349C4⋊Q8C22×D1114yes—
350C4⋊Q8C22×D1114yes—
351#124—2216no—
352#123—2216no—
353C22⋊Q8—228no—
354#121—118no—
355#121—118no—
356#121—224no—
357#121—224no—
358#121—228no—
359C4×D4—114no—
360C4×D4—114no—
361C4×D4—114no—
362C4×D4—114no—
363C4×D4—222no—
364C4×D4—222no—
365#117—118no—
366#117—228no—
367#117—224no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—111no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—118no—
374C2×C4⋊C4—224no—
375C2×C4⋊C4—222no—
376C2×C4⋊C4C22×D1112yes—
377C2×C4⋊C4C22×D1112yes—
378C2×C22⋊C4—112no—
379C2×C22⋊C4—222no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—221no—
383C2×C22⋊C4—221no—
384C2×C42—222no—
385C2×C42C22×D1111yescharacteristic
386#107—114no—
387#107—118no—
388#106—118no—
389#106C22×D1118yes—
390#106C22×D1118yes—
391C4⋊C8—114no—
392#102—114no—
393#102—114no—
394#102—118no—
395#102—118no—
396C22⋊C8—118no—
397C4×C8C22×D1114yes—
398C2×C11#335414yescomplemented
399C2×C11C2×#54711yescharacteristic
400C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
401C2×C11C2×#57711yescharacteristic
402D11—44no—
403D11—82no—
404D11—82no—
405C24—112no—
406C24—221no—
407C24—221no—
408#41—4432no—
409C2×Q8—24no—
410C2×Q8—24no—
411C2×Q8—44no—
412C2×Q8—82no—
413C2×D4—114no—
414C2×D4—112no—
415C2×D4—112no—
416C2×D4—228no—
417C2×D4—228no—
418C2×D4—224no—
419C2×D4—221no—
420C2×D4—221no—
421C2×D4—222no—
422C2×D4—222no—
423C2×D4—222no—
424C2×D4—222no—
425C2×D4—448no—
426C2×D4—884no—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—112no—
430C22×C4—114no—
431C22×C4—114no—
432C22×C4—228no—
433C22×C4—224no—
434C22×C4—224no—
435C22×C4—221no—
436C22×C4—221no—
437C22×C4—224no—
438C22×C4—224no—
439C22×C4—448no—
440C22×C4—444no—
441C22×C4—444no—
442C22×C4D4×D1111yescharacteristic
443C22×C4D4×D1111yescharacteristic
444C22×C4C23×D1111yescharacteristic
445D8—228no—
446M16—2216no—
447C2×C8—22no—
448C2×C8—114no—
449C2×C8—224no—
450C2×C8#434314yescomplemented
451C2×C8C23×D1112yes—
452C2×C8C23×D1112yes—
453C4⋊C4—24no—
454C4⋊C4—24no—
455C4⋊C4—22no—
456C4⋊C4—22no—
457C4⋊C4—114no—
458C4⋊C4—112no—
459C4⋊C4—112no—
460C4⋊C4—228no—
461C4⋊C4—221no—
462C4⋊C4—221no—
463C4⋊C4C23×D1114yes—
464C4⋊C4C23×D1114yes—
465C22⋊C4—118no—
466C22⋊C4—228no—
467C22⋊C4—228no—
468C22⋊C4—228no—
469C22⋊C4—224no—
470C22⋊C4—224no—
471C42—228no—
472C42D4×D1112yes—
473C42C23×D1112yes—
474C11C2×#335411yescharacteristic, complemented, Sylow
475C23—114no—
476C23—224no—
477C23—224no—
478C23—224no—
479C23—222no—
480C23—222no—
481C23—442no—
482C23—442no—
483C23—442no—
484C23—442no—
485C23—442no—
486C23—442no—
487C23C2×D4×D1111yescharacteristic
488Q8—48no—
489Q8—84no—
490D4—228no—
491D4—222no—
492D4—222no—
493D4—222no—
494D4—222no—
495D4—4416no—
496D4—442no—
497D4—442no—
498D4—888no—
499C2×C4—22no—
500C2×C4—24no—
501C2×C4—24no—
502C2×C4—44no—
503C2×C4—44no—
504C2×C4—114no—
505C2×C4—224no—
506C2×C4—228no—
507C2×C4—224no—
508C2×C4—224no—
509C2×C4—222no—
510C2×C4—222no—
511C2×C4—4416no—
512C2×C4—442no—
513C2×C4—442no—
514C2×C4—448no—
515C2×C4—448no—
516C2×C4#6696714yes—
517C2×C4C2×D4×D1112yes—
518C2×C4C2×D4×D1111yescharacteristic
519C2×C4C2×D4×D1112yes—
520C2×C4C2×#434312yes—
521C2×C4#6704012yes—
522C2×C4C24×D1111yescharacteristic
523C8—22no—
524C8—224no—
525C8C2×#434314yescomplemented
526C22—224no—
527C22—224no—
528C22—224no—
529C22—448no—
530C22—442no—
531C22—442no—
532C22—442no—
533C22—442no—
534C22—442no—
535C22—442no—
536C22—884no—
537C22—884no—
538C22#1062325712yes—
539C22C2×#6696712yes—
540C22#1062329312yes—
541C22C22×D4×D1111yescharacteristic
542C4—22no—
543C4—44no—
544C4—44no—
545C4—224no—
546C4—442no—
547C4—442no—
548C4#1062325712yes—
549C4C2×#6696714yes—
550C4C22×#434311yescharacteristic
551C4C2×#6704011yescharacteristic
552C2—444no—
553C2—882no—
554C2—882no—
555C2#1308121014yesdirect product factor
556C2C2×#1062325711yescharacteristic
557C2C22×#6696711yescharacteristic
558C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#498C2
socleC23×C11C22×D4
hypercenterC2×#498D11
hypocenterC11C2×#3354
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#498

Complements

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

NH ≅ G/Ntype
1. C2×#10623265C2semidirect
2. C2×#10623257C2semidirect
3. #13081210C2direct (N × H)
4. C2×#10622476C2semidirect
5. C2×#10622479C2semidirect
6. C2×#10622697C2semidirect
7. C2×#10622700C2semidirect
8. C2×#10622478C2semidirect
9. C2×C4×D88C2semidirect
10. C2×#10622301C2semidirect
11. C2×#10622474C2semidirect
12. C2×C11×#498C2semidirect
21. #10623265C22semidirect
23. #10623257C22semidirect
34. C11×#498C22semidirect
42. #10622700C22semidirect
43. #10622697C22semidirect
49. #10622479C22semidirect
50. #10622478C22semidirect
51. #10622476C22semidirect
52. #10622474C22semidirect
53. C4×D88C22semidirect
54. #10622301C22semidirect
168. C2×C8×C11#41semidirect
199. C2×#498D11semidirect
257. C8×C11C2×#41semidirect
280. #498C2×D11semidirect
398. C2×C11#3354semidirect
450. C2×C8#4343semidirect
474. C11C2×#3354semidirect
525. C8C2×#4343semidirect
555. C2#13081210direct (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×#106232572
#130812102
C2×#106224762
C2×#106224792
C2×#106226972
C2×#106227002
C2×#106224782
C2×C4×D882
C2×#106223012
C2×#106224742
C2×C11×#4982
C2×#335411