Finite Group Databasebeta

← C2×#13080536 #15630215

Subgroups — C2×#13080536 #15630215

Order 2816.

2146 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic, complemented
2C2×#10623257C211yesmaximal, characteristic
3#13080536C2116yesmaximal, direct product factor
4C2×#10622694C211yesmaximal, characteristic, complemented
5C2×#10622427C212yesmaximal, complemented
6C2×#10622459C211yesmaximal, characteristic, complemented
7C2×#10622801C212yesmaximal, complemented
8C2×#10622800C212yesmaximal, complemented
9C2×C4×#4325C211yesmaximal, characteristic, complemented
10C2×#10622447C211yesmaximal, characteristic, complemented
11C2×#10622417C212yesmaximal, 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×C8×D11C2212yes—
21#10623257—24no—
22#10623257C2218yes—
23#10623115—24no—
24#10623115C2218yescomplemented
25C2×#66951—22no—
26C2×#66948—21no—
27C2×#66947—22no—
28C2×#66945C2212yes—
29C2×C4⋊C4×D11—21no—
30C2×#66928—21no—
31C2×C4×D44C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22—21no—
35C11×#462C2218yescomplemented
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#103C2212yes—
38C2×#66899C2212yes—
39C2×#66899C2212yes—
40C2×#66899C2211yescharacteristic
41#10622801C22116yescomplemented
42#10622800C22116yescomplemented
43C2×#66885C2212yes—
44C2×(C2×D11)⋊C8C2212yes—
45C2×#66882C2212yes—
46#10622694C2218yescomplemented
47C4×#4325C2218yescomplemented
48C2×#66873C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622459C2218yescomplemented
52#10622447C2218yescomplemented
53#10622427C22116yescomplemented
54#10622417C22116yescomplemented
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×D11C2312yes—
67C22×Dic22—21no—
68C2×C11×Q16—44no—
69C2×C11×Q16C2318yes—
70C22×C8×C11C2312yes—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8C2314yes—
73C4×Q8×C11—22no—
74C4×Q8×C11C2314yes—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11C2311yescharacteristic
81#66999—24no—
82#66999—24no—
83#66999C2318yes—
84#66999C2318yes—
85C2×#4325—24no—
86C2×#4325C2314yes—
87C2×(C2×D11)⋊C4—22no—
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×C4×Dic11—22no—
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2311yescharacteristic
101C2×C8×D11—44no—
102C2×C8×D11C2318yes—
103#66951—216no—
104#66948—28no—
105#66947—216no—
106#66945—24no—
107#66945C2318yes—
108C4⋊C4×D11—28no—
109#66928—28no—
110C4×D44—22no—
111C4×D44D414yes—
112C4×D44C2314yes—
113C4×D44C2314yes—
114#66922—22no—
115#66922C2314yes—
116C4×Dic22—28no—
117C11×C4⋊C8C2314yes—
118C11×#103C2318yes—
119#66899C2318yes—
120#66899C2314yes—
121#66899C2318yes—
122#66885C2318yes—
123(C2×D11)⋊C8C2318yes—
124#66882C2318yes—
125#66873C2314yes—
126#66872C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3302—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—24no—
161C2×C4×D11—24no—
162C2×C4×D11—24no—
163C2×C4×D11—48no—
164C2×C4×D11—44no—
165C2×C4×D11C2×D414yes—
166C2×C4×D11C2414yes—
167C2×Dic22—24no—
168C2×Dic22—44no—
169C11×Q16—48no—
170C2×C8×C11—24no—
171C2×C8×C11C2414yes—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—21no—
174C11×C4⋊C4—24no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4C2412yes—
177C42×C11—24no—
178C42×C11C2×D412yes—
179C42×C11C2412yes—
180#4325—28no—
181(C2×D11)⋊C4—28no—
182(C2×D11)⋊C4—28no—
183(C2×D11)⋊C4—28no—
184(C2×D11)⋊C4—24no—
185(C2×D11)⋊C4C2×D418yes—
186C4⋊Dic11—22no—
187C4⋊Dic11—24no—
188C4⋊Dic11—21no—
189C4⋊Dic11C2×D414yes—
190C4⋊Dic11C2412yes—
191C4⋊Dic11C2414yes—
192Dic11⋊C4—28no—
193Dic11⋊C4—28no—
194C4×Dic11—28no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8C2412yes—
198C2×C11⋊C8C2412yes—
199C8×D11—48no—
200C2×#556—111no—
201C2×#547—111no—
202#3302—1116no—
203C2×#487—111no—
204C2×#485—112no—
205C2×#474—111no—
206C2×#467—112no—
207C2×#462D1111yescharacteristic, complemented
208C2×#452—112no—
209C2×C4×SD16—111no—
210C2×C8×D4—111no—
211C2×#416—112no—
212C23×C11C22×D411yescharacteristic
213C22×D11—24no—
214C22×D11—24no—
215C22×D11—24no—
216C22×D11—24no—
217C22×D11—22no—
218C22×D11—42no—
219C22×D11—42no—
220C22×D11C22×D414yes—
221Q8×C11—22no—
222Q8×C11—24no—
223Q8×C11—22no—
224Q8×C11—24no—
225Q8×C11—44no—
226Q8×C11—42no—
227C2×C4×C11—22no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—24no—
231C2×C4×C11—44no—
232C2×C4×C11—42no—
233C2×C4×C11—42no—
234C2×C4×C11#13514yes—
235C2×C4×C11C22×D412yes—
236C2×C4×C11C22×D411yescharacteristic
237C2×C4×C11C22×D412yes—
238C2×C4×C11C2×#4112yes—
239C2×C4×C11H(5,𝔽2)12yes—
240C2×C4×C11C2511yescharacteristic
241C2×Dic11—24no—
242C2×Dic11—24no—
243C2×Dic11—22no—
244C2×Dic11—44no—
245C2×Dic11—42no—
246C2×Dic11C22×D414yes—
247D44—24no—
248D44—28no—
249D44—22no—
250D44—416no—
251D44C2×#4114yes—
252C4×D11—28no—
253C4×D11—24no—
254C4×D11—24no—
255C4×D11—416no—
256C4×D11—48no—
257Dic22—48no—
258C8×C11—24no—
259C11⋊C8—22no—
260C11⋊C8—22no—
261C22×#41—112no—
262C22×Q16C2×D1112yes—
263C22×SD16—111no—
264C23×C8—112no—
265#556—118no—
266#556—224no—
267#547—118no—
268#547—224no—
269C2×C4⋊Q8—111no—
270C2×C4⋊Q8C2×D1111yescharacteristic
271C2×#126—222no—
272C2×#124—221no—
273C2×#123—222no—
274C2×C22⋊Q8—112no—
275C2×C22⋊Q8—112no—
276C2×#121—221no—
277C2×C4×Q8—221no—
278C2×C4×Q8C2×D1111yescharacteristic
279C2×C4×D4—111no—
280C2×C4×D4—111no—
281C2×#117—112no—
282C22×C4⋊C4—221no—
283#487—118no—
284#485—1116no—
285#474—118no—
286#467—1116no—
287#462C2×D1118yescomplemented
288#452—1116no—
289C4×SD16—118no—
290C8×D4—118no—
291C2×#107—112no—
292C2×#106—111no—
293C2×C4⋊C8C2×D1111yescharacteristic
294#416—1116no—
295C2×#103—112no—
296C2×#103—112no—
297C2×#103—111no—
298C2×#103C2×D1112yes—
299C2×#102—112no—
300C2×#102—111no—
301C2×C22⋊C8—112no—
302C2×C4×C8—111no—
303C22×C11#54612yes—
304C22×C11C2×#13512yes—
305C22×C11#57812yes—
306C22×C11C23×D411yescharacteristic
307C2×D11—24no—
308C2×D11—24no—
309C2×D11—24no—
310C2×D11—24no—
311C2×D11—48no—
312C2×D11—48no—
313C2×D11—42no—
314C2×D11—42no—
315C4×C11—22no—
316C4×C11—42no—
317C4×C11—44no—
318C4×C11—42no—
319C4×C11#54612yes—
320C4×C11C2×#13514yes—
321C4×C11C22×#4111yescharacteristic
322C4×C11C2×H(5,𝔽2)11yescharacteristic
323Dic11—24no—
324Dic11—44no—
325Dic11—42no—
326C2×#41—118no—
327C2×#41—224no—
328C2×#41—228no—
329C2×#41—444no—
330C22×Q8—221no—
331C22×Q8C22×D1111yescharacteristic
332C22×Q8C22×D1112yes—
333C22×D4—111no—
334C22×D4—111no—
335C22×D4—222no—
336C23×C4—112no—
337C23×C4—222no—
338C23×C4—221no—
339C2×Q16—44no—
340C2×Q16C22×D1118yes—
341C2×SD16—114no—
342C2×SD16—224no—
343C22×C8—111no—
344C22×C8—111no—
345C22×C8—118no—
346C22×C8—444no—
347C22×C8C22×D1112yes—
348C4⋊Q8—22no—
349C4⋊Q8—114no—
350C4⋊Q8—222no—
351C4⋊Q8C22×D1114yes—
352#126—2216no—
353#124—228no—
354#123—2216no—
355C22⋊Q8—118no—
356C22⋊Q8—118no—
357C22⋊Q8—224no—
358C22⋊Q8—224no—
359#121—228no—
360C4×Q8—22no—
361C4×Q8—228no—
362C4×Q8C22×D1114yes—
363C4×D4—114no—
364C4×D4—114no—
365C4×D4—114no—
366C4×D4—222no—
367#117—118no—
368#117—224no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—111no—
373C2×C4⋊C4—112no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—228no—
376C2×C4⋊C4—222no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4C22×D1111yescharacteristic
380C2×C22⋊C4—112no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—221no—
385C2×C42—21no—
386C2×C42—222no—
387C2×C42C22×D1111yescharacteristic
388#107—118no—
389#106—114no—
390C4⋊C8C22×D1114yes—
391#103—118no—
392#103—114no—
393#103—118no—
394#103C22×D1118yes—
395#102—118no—
396#102—114no—
397C22⋊C8—118no—
398C4×C8—114no—
399C2×C11#330214yescomplemented
400C2×C11C2×#54611yescharacteristic
401C2×C11C22×#13511yescharacteristic
402C2×C11C2×#57811yescharacteristic
403D11—44no—
404D11—44no—
405C24—112no—
406C24—221no—
407#41—2216no—
408#41—448no—
409#41—4416no—
410C2×Q8—21no—
411C2×Q8—22no—
412C2×Q8—22no—
413C2×Q8—24no—
414C2×Q8—22no—
415C2×Q8—24no—
416C2×Q8—224no—
417C2×Q8—444no—
418C2×Q8C23×D1114yes—
419C2×Q8C23×D1112yes—
420C2×D4—114no—
421C2×D4—114no—
422C2×D4—112no—
423C2×D4—228no—
424C2×D4—224no—
425C2×D4—221no—
426C2×D4—222no—
427C2×D4—448no—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—112no—
432C22×C4—114no—
433C22×C4—114no—
434C22×C4—228no—
435C22×C4—224no—
436C22×C4—224no—
437C22×C4—222no—
438C22×C4—221no—
439C22×C4—224no—
440C22×C4—448no—
441C22×C4—444no—
442C22×C4D4×D1111yescharacteristic
443C22×C4D4×D1111yescharacteristic
444C22×C4C23×D1111yescharacteristic
445Q16—48no—
446SD16—228no—
447C2×C8—24no—
448C2×C8—112no—
449C2×C8—112no—
450C2×C8—222no—
451C2×C8—222no—
452C2×C8—448no—
453C2×C8C23×D1114yes—
454C4⋊C4—24no—
455C4⋊C4—24no—
456C4⋊C4—24no—
457C4⋊C4—21no—
458C4⋊C4—114no—
459C4⋊C4—114no—
460C4⋊C4—112no—
461C4⋊C4—228no—
462C4⋊C4—228no—
463C4⋊C4—222no—
464C4⋊C4—221no—
465C4⋊C4—224no—
466C4⋊C4C23×D1112yes—
467C22⋊C4—118no—
468C22⋊C4—228no—
469C22⋊C4—228no—
470C22⋊C4—228no—
471C22⋊C4—224no—
472C42—24no—
473C42—228no—
474C42D4×D1112yes—
475C42C23×D1112yes—
476C11C2×#330211yescharacteristic, complemented, Sylow
477C23—114no—
478C23—224no—
479C23—224no—
480C23—224no—
481C23—224no—
482C23—222no—
483C23—442no—
484C23—442no—
485C23C2×D4×D1111yescharacteristic
486Q8—22no—
487Q8—24no—
488Q8—22no—
489Q8—24no—
490Q8—42no—
491Q8—44no—
492Q8—448no—
493D4—114no—
494D4—228no—
495D4—224no—
496D4—222no—
497D4—4416no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—42no—
503C2×C4—44no—
504C2×C4—42no—
505C2×C4—114no—
506C2×C4—224no—
507C2×C4—228no—
508C2×C4—224no—
509C2×C4—224no—
510C2×C4—224no—
511C2×C4—222no—
512C2×C4—4416no—
513C2×C4—442no—
514C2×C4—444no—
515C2×C4—448no—
516C2×C4#6697214yes—
517C2×C4C2×D4×D1112yes—
518C2×C4C2×D4×D1112yes—
519C2×C4C2×D4×D1111yescharacteristic
520C2×C4#6703712yes—
521C2×C4#41×D1112yes—
522C2×C4C24×D1111yescharacteristic
523C8—24no—
524C8—222no—
525C8—222no—
526C22—224no—
527C22—224no—
528C22—224no—
529C22—224no—
530C22—442no—
531C22—448no—
532C22—448no—
533C22—442no—
534C22#1062314312yes—
535C22C2×#6697212yes—
536C22#1062331012yes—
537C22C22×D4×D1111yescharacteristic
538C4—22no—
539C4—44no—
540C4—42no—
541C4—42no—
542C4—224no—
543C4—442no—
544C4—444no—
545C4#1062314312yes—
546C4C2×#6697214yes—
547C4C2×#6703711yescharacteristic
548C4C2×#41×D1111yescharacteristic
549C2—444no—
550C2—444no—
551C2#1308053614yesdirect product factor
552C2C2×#1062314311yescharacteristic
553C2C22×#6697211yescharacteristic
554C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#462C2
socleC23×C11C22×D4
prime radicalC2×#10623257C2
hypercenterC2×#462D11
hypocenterC11C2×#3302
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×#10623115C2semidirect
3. #13080536C2direct (N × H)
4. C2×#10622694C2semidirect
5. C2×#10622427C2semidirect
6. C2×#10622459C2semidirect
7. C2×#10622801C2semidirect
8. C2×#10622800C2semidirect
9. C2×C4×#4325C2semidirect
10. C2×#10622447C2semidirect
11. C2×#10622417C2semidirect
12. C2×C11×#462C2semidirect
24. #10623115C22semidirect
35. C11×#462C22semidirect
41. #10622801C22semidirect
42. #10622800C22semidirect
46. #10622694C22semidirect
47. C4×#4325C22semidirect
51. #10622459C22semidirect
52. #10622447C22semidirect
53. #10622427C22semidirect
54. #10622417C22semidirect
207. C2×#462D11semidirect
287. #462C2×D11semidirect
399. C2×C11#3302semidirect
476. C11C2×#3302semidirect
551. C2#13080536direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231152
C2×#106232572
#130805362
C2×#106226942
C2×#106224272
C2×#106224592
C2×#106228012
C2×#106228002
C2×C4×#43252
C2×#106224472
C2×#106224172
C2×C11×#4622
C2×#330211