Finite Group Databasebeta

← C2×#13080935 #15630697

Subgroups — C2×#13080935 #15630697

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×#10623257C211yesmaximal, characteristic
3#13080935C2116yesmaximal, direct product factor
4C2×#10622694C211yesmaximal, characteristic, complemented
5C2×#10622418C212yesmaximal, complemented
6C2×#10622455C211yesmaximal, characteristic, complemented
7C2×#10622802C212yesmaximal, complemented
8C2×#10622800C212yesmaximal, complemented
9C2×C4×#4325C211yesmaximal, characteristic, complemented
10C2×#10622451C211yesmaximal, characteristic, complemented
11C2×#10622416C212yesmaximal, complemented
12C2×C11×#462C211yesmaximal, characteristic, complemented
13C22×#4343C2212yes—
14C22×C11×Q16C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C2212yes—
18C2×#66999C2212yes—
19C22×#4325C2211yescharacteristic
20C22×#4313C2212yes—
21#10623257—24no—
22#10623257C2218yes—
23#10623110—24no—
24#10623110C2218yescomplemented
25C2×#66949—22no—
26C2×#66948—21no—
27C2×#66947—22no—
28C2×C4⋊C4×D11—21no—
29C2×C4⋊C4×D11C2212yes—
30C2×C4×D44—21no—
31C2×C4×D44C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×#66923—21no—
34C2×#66922C2211yescharacteristic
35C11×#462C2218yescomplemented
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#103C2212yes—
38C2×#66899C2212yes—
39C2×#66899C2211yescharacteristic
40C2×#66899C2212yes—
41#10622802C22116yescomplemented
42#10622800C22116yescomplemented
43C2×#66885C2212yes—
44C2×(C2×D11)⋊C8C2212yes—
45C2×#66881C2212yes—
46#10622694C2218yescomplemented
47C4×#4325C2218yescomplemented
48C2×#66873C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622455C2218yescomplemented
52#10622451C2218yescomplemented
53#10622418C22116yescomplemented
54#10622416C22116yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×Q8×C11C2312yes—
57C2×#4343—24no—
58C2×#4343—28no—
59C2×#4343—44no—
60C2×#4343C2318yes—
61C22×D44—22no—
62C22×D44D411yescharacteristic
63C22×D44C2311yescharacteristic
64C22×C4×D11—21no—
65C22×C4×D11—22no—
66C22×C4×D11—22no—
67C22×C4×D11C2312yes—
68C22×Dic22—21no—
69C2×C11×Q16—44no—
70C2×C11×Q16C2318yes—
71C22×C8×C11C2312yes—
72C11×C4⋊Q8—22no—
73C11×C4⋊Q8C2314yes—
74C4×Q8×C11—22no—
75C4×Q8×C11C2314yes—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82#66999—24no—
83#66999—24no—
84#66999C2318yes—
85#66999C2318yes—
86C2×#4325—24no—
87C2×#4325C2314yes—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4—22no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4D412yes—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11D411yescharacteristic
94C2×C4⋊Dic11C2312yes—
95C2×C4⋊Dic11C2311yescharacteristic
96C2×Dic11⋊C4—22no—
97C2×Dic11⋊C4—22no—
98C2×Dic11⋊C4—22no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×#4313—44no—
102C2×#4313C2318yes—
103#66949—216no—
104#66948—28no—
105#66947—216no—
106C4⋊C4×D11—24no—
107C4⋊C4×D11—28no—
108C4⋊C4×D11C2318yes—
109C4×D44—28no—
110C4×D44—22no—
111C4×D44D414yes—
112C4×D44C2314yes—
113C4×D44C2314yes—
114#66923—28no—
115#66922—22no—
116#66922C2314yes—
117C11×C4⋊C8C2314yes—
118C11×#103C2318yes—
119#66899C2318yes—
120#66899C2314yes—
121#66899C2318yes—
122#66885C2318yes—
123(C2×D11)⋊C8C2318yes—
124#66881C2318yes—
125#66873C2314yes—
126#66872C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3331—111nomaximal, Sylow
129C23×D11—21no—
130C23×D11C2×D412yes—
131C2×Q8×C11—21no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—24no—
135C2×Q8×C11—22no—
136C2×Q8×C11—24no—
137C2×Q8×C11C2414yes—
138C2×Q8×C11C2412yes—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—22no—
146C22×Dic11—21no—
147C22×Dic11C2×D412yes—
148#4343—216no—
149#4343—48no—
150#4343—416no—
151C2×D44—28no—
152C2×D44—24no—
153C2×D44—21no—
154C2×D44—22no—
155C2×D44—48no—
156C2×D44C2×D414yes—
157C2×D44#4114yes—
158C2×D44C2412yes—
159C2×C4×D11—28no—
160C2×C4×D11—28no—
161C2×C4×D11—24no—
162C2×C4×D11—24no—
163C2×C4×D11—24no—
164C2×C4×D11—48no—
165C2×C4×D11—44no—
166C2×C4×D11—84no—
167C2×C4×D11C2×D414yes—
168C2×C4×D11C2414yes—
169C2×Dic22—24no—
170C2×Dic22—82no—
171C11×Q16—48no—
172C2×C8×C11—24no—
173C2×C8×C11C2414yes—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4—24no—
177C11×C4⋊C4—24no—
178C11×C4⋊C4C2412yes—
179C42×C11—24no—
180C42×C11C2×D412yes—
181C42×C11C2412yes—
182#4325—28no—
183(C2×D11)⋊C4—28no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—24no—
186(C2×D11)⋊C4C2×D418yes—
187C4⋊Dic11—22no—
188C4⋊Dic11—24no—
189C4⋊Dic11—21no—
190C4⋊Dic11C2×D414yes—
191C4⋊Dic11C2412yes—
192C4⋊Dic11C2414yes—
193Dic11⋊C4—28no—
194Dic11⋊C4—28no—
195Dic11⋊C4—28no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—22no—
198C2×C11⋊C8C2412yes—
199C2×C11⋊C8C2412yes—
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×#462D1111yescharacteristic, complemented
209C2×#452—112no—
210C2×C4×SD16—111no—
211C2×#436—111no—
212C2×#417—112no—
213C23×C11C22×D411yescharacteristic
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—24no—
218C22×D11—22no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11C22×D414yes—
222Q8×C11—22no—
223Q8×C11—24no—
224Q8×C11—22no—
225Q8×C11—24no—
226Q8×C11—44no—
227Q8×C11—42no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—22no—
231C2×C4×C11—24no—
232C2×C4×C11—44no—
233C2×C4×C11—42no—
234C2×C4×C11—42no—
235C2×C4×C11#13714yes—
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
242C2×Dic11—24no—
243C2×Dic11—24no—
244C2×Dic11—22no—
245C2×Dic11—42no—
246C2×Dic11—44no—
247C2×Dic11C22×D414yes—
248D44—24no—
249D44—28no—
250D44—22no—
251D44—416no—
252D44C2×#4114yes—
253C4×D11—28no—
254C4×D11—24no—
255C4×D11—24no—
256C4×D11—416no—
257C4×D11—48no—
258C4×D11—88no—
259Dic22—84no—
260C8×C11—24no—
261C11⋊C8—22no—
262C11⋊C8—22no—
263C22×#41—112no—
264C22×Q16C2×D1112yes—
265C22×SD16—111no—
266C22×M16—112no—
267#554—118no—
268#554—224no—
269#547—118no—
270#547—224no—
271C2×C4⋊Q8—111no—
272C2×C4⋊Q8C2×D1111yescharacteristic
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—111no—
282C2×C4×D4—221no—
283C22×C4⋊C4—112no—
284C22×C4⋊C4—221no—
285#487—118no—
286#483—1116no—
287#476—118no—
288#470—1116no—
289#462C2×D1118yescomplemented
290#452—1116no—
291C4×SD16—118no—
292#436—118no—
293C2×#106—112no—
294C2×#106—111no—
295C2×C4⋊C8C2×D1111yescharacteristic
296#417—1116no—
297C2×#103—112no—
298C2×#103—112no—
299C2×#103—111no—
300C2×#103C2×D1112yes—
301C2×#102—112no—
302C2×#102—111no—
303C2×C22⋊C8—112no—
304C2×C4×C8—111no—
305C22×C11#54612yes—
306C22×C11C2×#13712yes—
307C22×C11#57712yes—
308C22×C11C23×D411yescharacteristic
309C2×D11—24no—
310C2×D11—24no—
311C2×D11—24no—
312C2×D11—24no—
313C2×D11—48no—
314C2×D11—48no—
315C2×D11—42no—
316C2×D11—42no—
317C4×C11—22no—
318C4×C11—42no—
319C4×C11—44no—
320C4×C11—42no—
321C4×C11#54612yes—
322C4×C11C2×#13714yes—
323C4×C11C22×#4111yescharacteristic
324C4×C11C2×H(5,𝔽2)11yescharacteristic
325Dic11—24no—
326Dic11—42no—
327Dic11—44no—
328C2×#41—118no—
329C2×#41—224no—
330C2×#41—228no—
331C2×#41—444no—
332C22×Q8—221no—
333C22×Q8C22×D1111yescharacteristic
334C22×Q8C22×D1112yes—
335C22×D4—111no—
336C22×D4—111no—
337C22×D4—222no—
338C23×C4—112no—
339C23×C4—222no—
340C23×C4—222no—
341C23×C4—221no—
342C2×Q16—44no—
343C2×Q16C22×D1118yes—
344C2×SD16—114no—
345C2×SD16—224no—
346C2×M16—118no—
347C2×M16—444no—
348C22×C8—111no—
349C22×C8—111no—
350C22×C8C22×D1112yes—
351C4⋊Q8—22no—
352C4⋊Q8—114no—
353C4⋊Q8—222no—
354C4⋊Q8C22×D1114yes—
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—114no—
366C4×D4—114no—
367C4×D4—114no—
368C4×D4—228no—
369C4×D4—222no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—112no—
375C2×C4⋊C4—111no—
376C2×C4⋊C4—118no—
377C2×C4⋊C4—228no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—222no—
380C2×C4⋊C4—222no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4—221no—
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C22⋊C4—112no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4—221no—
388C2×C42—21no—
389C2×C42C22×D1111yescharacteristic
390#106—118no—
391#106—114no—
392C4⋊C8C22×D1114yes—
393#103—118no—
394#103—114no—
395#103—118no—
396#103C22×D1118yes—
397#102—118no—
398#102—114no—
399C22⋊C8—118no—
400C4×C8—114no—
401C2×C11#333114yescomplemented
402C2×C11C2×#54611yescharacteristic
403C2×C11C22×#13711yescharacteristic
404C2×C11C2×#57711yescharacteristic
405D11—44no—
406D11—44no—
407C24—112no—
408C24—221no—
409#41—2216no—
410#41—448no—
411#41—4416no—
412C2×Q8—21no—
413C2×Q8—22no—
414C2×Q8—22no—
415C2×Q8—24no—
416C2×Q8—22no—
417C2×Q8—24no—
418C2×Q8—224no—
419C2×Q8—882no—
420C2×Q8C23×D1114yes—
421C2×Q8C23×D1112yes—
422C2×D4—114no—
423C2×D4—114no—
424C2×D4—112no—
425C2×D4—228no—
426C2×D4—224no—
427C2×D4—221no—
428C2×D4—222no—
429C2×D4—448no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—22no—
433C22×C4—112no—
434C22×C4—114no—
435C22×C4—114no—
436C22×C4—228no—
437C22×C4—228no—
438C22×C4—224no—
439C22×C4—224no—
440C22×C4—221no—
441C22×C4—222no—
442C22×C4—224no—
443C22×C4—448no—
444C22×C4—444no—
445C22×C4—884no—
446C22×C4D4×D1111yescharacteristic
447C22×C4D4×D1111yescharacteristic
448C22×C4C23×D1111yescharacteristic
449Q16—48no—
450SD16—228no—
451M16—448no—
452C2×C8—24no—
453C2×C8—112no—
454C2×C8—112no—
455C2×C8—222no—
456C2×C8—222no—
457C2×C8C23×D1114yes—
458C4⋊C4—24no—
459C4⋊C4—24no—
460C4⋊C4—24no—
461C4⋊C4—21no—
462C4⋊C4—114no—
463C4⋊C4—114no—
464C4⋊C4—112no—
465C4⋊C4—228no—
466C4⋊C4—228no—
467C4⋊C4—228no—
468C4⋊C4—222no—
469C4⋊C4—221no—
470C4⋊C4—224no—
471C4⋊C4C23×D1112yes—
472C22⋊C4—118no—
473C22⋊C4—228no—
474C22⋊C4—228no—
475C22⋊C4—224no—
476C42—24no—
477C42D4×D1112yes—
478C42C23×D1112yes—
479C11C2×#333111yescharacteristic, complemented, Sylow
480C23—114no—
481C23—224no—
482C23—224no—
483C23—224no—
484C23—224no—
485C23—222no—
486C23—442no—
487C23—442no—
488C23C2×D4×D1111yescharacteristic
489Q8—22no—
490Q8—24no—
491Q8—22no—
492Q8—24no—
493Q8—42no—
494Q8—44no—
495Q8—884no—
496D4—114no—
497D4—228no—
498D4—224no—
499D4—222no—
500D4—4416no—
501C2×C4—22no—
502C2×C4—22no—
503C2×C4—22no—
504C2×C4—24no—
505C2×C4—42no—
506C2×C4—44no—
507C2×C4—42no—
508C2×C4—114no—
509C2×C4—224no—
510C2×C4—228no—
511C2×C4—224no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—4416no—
516C2×C4—442no—
517C2×C4—444no—
518C2×C4—448no—
519C2×C4—888no—
520C2×C4#6697114yes—
521C2×C4C2×D4×D1112yes—
522C2×C4C2×D4×D1112yes—
523C2×C4C2×D4×D1111yescharacteristic
524C2×C4#6703712yes—
525C2×C4#41×D1112yes—
526C2×C4C24×D1111yescharacteristic
527C8—24no—
528C8—222no—
529C8—222no—
530C22—224no—
531C22—224no—
532C22—224no—
533C22—224no—
534C22—448no—
535C22—448no—
536C22—442no—
537C22—442no—
538C22#1062314312yes—
539C22C2×#6697112yes—
540C22#1062330912yes—
541C22C22×D4×D1111yescharacteristic
542C4—22no—
543C4—44no—
544C4—42no—
545C4—42no—
546C4—224no—
547C4—442no—
548C4—444no—
549C4#1062314312yes—
550C4C2×#6697114yes—
551C4C2×#6703711yescharacteristic
552C4C2×#41×D1111yescharacteristic
553C2—444no—
554C2—444no—
555C2#1308093514yesdirect product factor
556C2C2×#1062314311yescharacteristic
557C2C22×#6697111yescharacteristic
558C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
prime radicalC2×#10623257C2
hypercenterC2×#462D11
hypocenterC11C2×#3331
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#462

Complements

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

NH ≅ G/Ntype
1. C2×#10623110C2semidirect
3. #13080935C2direct (N × H)
4. C2×#10622694C2semidirect
5. C2×#10622418C2semidirect
6. C2×#10622455C2semidirect
7. C2×#10622802C2semidirect
8. C2×#10622800C2semidirect
9. C2×C4×#4325C2semidirect
10. C2×#10622451C2semidirect
11. C2×#10622416C2semidirect
12. C2×C11×#462C2semidirect
24. #10623110C22semidirect
35. C11×#462C22semidirect
41. #10622802C22semidirect
42. #10622800C22semidirect
46. #10622694C22semidirect
47. C4×#4325C22semidirect
51. #10622455C22semidirect
52. #10622451C22semidirect
53. #10622418C22semidirect
54. #10622416C22semidirect
208. C2×#462D11semidirect
289. #462C2×D11semidirect
401. C2×C11#3331semidirect
479. C11C2×#3331semidirect
555. C2#13080935direct (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×#106232572
#130809352
C2×#106226942
C2×#106224182
C2×#106224552
C2×#106228022
C2×#106228002
C2×C4×#43252
C2×#106224512
C2×#106224162
C2×C11×#4622
C2×#333111