Finite Group Databasebeta

← C2×#13080901 #15630660

Subgroups — C2×#13080901 #15630660

Order 2816.

2082 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623115C211yesmaximal, characteristic
2C2×Q8×D44C211yesmaximal, characteristic
3#13080901C2116yesmaximal, direct product factor
4C2×#10622294C211yesmaximal, characteristic, complemented
5C2×#10622501C212yesmaximal, complemented
6C2×#10622633C211yesmaximal, characteristic, complemented
7C2×#10622429C212yesmaximal, complemented
8C2×#10622644C211yesmaximal, characteristic, complemented
9C2×#10622799C212yesmaximal, complemented
10C2×#10622301C211yesmaximal, characteristic
11C2×#10622415C212yesmaximal, complemented
12C2×C4×C11×Q16C211yesmaximal, characteristic, complemented
13C22×Q8×D11C2212yes—
14C22×C11×Q16C2211yescharacteristic
15C2×C4×Q8×C11C2211yescharacteristic
16C2×C4×Q8×C11C2211yescharacteristic
17C2×#66999C2212yes—
18C22×#4326C2212yes—
19C22×#4313C2212yes—
20#10623115—24no—
21#10623115C2218yes—
22Q8×D44—24no—
23Q8×D44C2218yes—
24C2×#66951—22no—
25C2×#66950—22no—
26C2×#66950C2212yes—
27C2×#66945C2212yes—
28C2×#66928—21no—
29C2×C4×D44—21no—
30C2×C4×D44C2211yescharacteristic
31C2×#66922—21no—
32C2×#66922C2211yescharacteristic
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22—21no—
35C4×C11×Q16C2218yescomplemented
36C2×C11×#107C2211yescharacteristic
37C2×C11×#103C2211yescharacteristic
38C2×C11×#103C2211yescharacteristic
39C2×C4×C8×C11C2211yescharacteristic
40C2×#66899C2212yes—
41#10622799C22116yescomplemented
42C2×(C2×D11)⋊C8C2212yes—
43C2×#66880C2212yes—
44C2×#66880C2212yes—
45#10622644C2218yescomplemented
46#10622633C2218yescomplemented
47C2×#66874C2212yes—
48C2×#66872C2212yes—
49C2×C4⋊(C11⋊C8)C2211yescharacteristic
50#10622501C22116yescomplemented
51#10622429C22116yescomplemented
52#10622415C22116yescomplemented
53#10622301C2218yes—
54#10622294C2218yescomplemented
55C22×Q8×C11C2311yescharacteristic
56C22×Q8×C11C2311yescharacteristic
57C2×Q8×D11—24no—
58C2×Q8×D11—28no—
59C2×Q8×D11—44no—
60C2×Q8×D11C2318yes—
61C22×D44D411yescharacteristic
62C22×C4×D11—22no—
63C22×C4×D11C2312yes—
64C22×Dic22—21no—
65C22×Dic22—22no—
66C22×Dic22C2312yes—
67C2×C11×Q16—24no—
68C2×C11×Q16C2314yes—
69C22×C8×C11C2311yescharacteristic
70C22×C8×C11C2311yescharacteristic
71C4×Q8×C11—22no—
72C4×Q8×C11—22no—
73C4×Q8×C11C2314yes—
74C4×Q8×C11C2314yes—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C42×C11—21no—
80C2×C42×C11—21no—
81C2×C42×C11C2311yescharacteristic
82#66999—24no—
83#66999C2318yes—
84C2×#4326—44no—
85C2×#4326C2318yes—
86C2×(C2×D11)⋊C4—22no—
87C2×(C2×D11)⋊C4—22no—
88C2×(C2×D11)⋊C4—22no—
89C2×(C2×D11)⋊C4D412yes—
90C2×C4⋊Dic11—21no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—21no—
93C2×C4⋊Dic11—22no—
94C2×C4⋊Dic11D411yescharacteristic
95C2×C4⋊Dic11C2312yes—
96C2×Dic11⋊C4—22no—
97C2×C4×Dic11—22no—
98C22×C11⋊C8C2312yes—
99C2×#4313—44no—
100C2×#4313C2318yes—
101#66951—216no—
102#66950—24no—
103#66950—216no—
104#66950C2318yes—
105#66945—24no—
106#66945C2318yes—
107#66928—28no—
108C4×D44—28no—
109C4×D44D414yes—
110C4×D44C2314yes—
111#66922—22no—
112#66922—22no—
113#66922—28no—
114#66922C2314yes—
115#66922C2314yes—
116C4×Dic22—28no—
117C11×#107C2314yes—
118C11×#103C2314yes—
119C11×#103C2314yes—
120C4×C8×C11C2314yes—
121#66899C2318yes—
122(C2×D11)⋊C8C2318yes—
123#66880C2318yes—
124#66880C2318yes—
125#66874C2318yes—
126#66872C2318yes—
127C4⋊(C11⋊C8)C2314yes—
128C2×#3328—111nomaximal, Sylow
129C23×D11C2×D412yes—
130C2×Q8×C11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—22no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11#4114yes—
136C2×Q8×C11C2412yes—
137C2×Q8×C11C2412yes—
138C22×C4×C11—21no—
139C22×C4×C11—21no—
140C22×C4×C11—21no—
141C22×C4×C11—21no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2411yescharacteristic
145C22×Dic11—22no—
146C22×Dic11—22no—
147C22×Dic11C2×D412yes—
148Q8×D11—216no—
149Q8×D11—48no—
150Q8×D11—416no—
151C2×D44—24no—
152C2×D44C2×D414yes—
153C2×C4×D11—28no—
154C2×C4×D11—24no—
155C2×C4×D11—24no—
156C2×C4×D11—48no—
157C2×C4×D11C2×D414yes—
158C2×C4×D11C2414yes—
159C2×Dic22—28no—
160C2×Dic22—24no—
161C2×Dic22—22no—
162C2×Dic22—24no—
163C2×Dic22—24no—
164C2×Dic22—48no—
165C2×Dic22—44no—
166C2×Dic22C2414yes—
167C11×Q16—28no—
168C2×C8×C11—22no—
169C2×C8×C11—22no—
170C2×C8×C11C2412yes—
171C2×C8×C11C2412yes—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4—24no—
176C11×C4⋊C4C2412yes—
177C11×C4⋊C4C2412yes—
178C42×C11—24no—
179C42×C11—24no—
180C42×C11C2×D412yes—
181C42×C11C2412yes—
182#4326—48no—
183(C2×D11)⋊C4—28no—
184(C2×D11)⋊C4—28no—
185(C2×D11)⋊C4—28no—
186(C2×D11)⋊C4C2×D418yes—
187C4⋊Dic11—28no—
188C4⋊Dic11—24no—
189C4⋊Dic11—22no—
190C4⋊Dic11—24no—
191C4⋊Dic11—24no—
192C4⋊Dic11C2×D414yes—
193C4⋊Dic11C2414yes—
194Dic11⋊C4—28no—
195C4×Dic11—28no—
196C2×C11⋊C8—24no—
197C2×C11⋊C8C2414yes—
198#4313—48no—
199C2×#556—111no—
200C2×D4×Q8—111no—
201#3328—1116no—
202C2×#487—111no—
203C2×#485—112no—
204C2×#475—111no—
205C2×#470—112no—
206C2×#462—111no—
207C2×#451—112no—
208C2×C4×Q16D1111yescharacteristic, complemented
209C2×#436—111no—
210C2×#419—112no—
211C23×C11C22×D411yescharacteristic
212C22×D11—24no—
213C22×D11—24no—
214C22×D11—24no—
215C22×D11C22×D414yes—
216Q8×C11—24no—
217Q8×C11—22no—
218Q8×C11—22no—
219Q8×C11—22no—
220Q8×C11—42no—
221Q8×C11C2×#4114yes—
222C2×C4×C11—24no—
223C2×C4×C11—22no—
224C2×C4×C11—22no—
225C2×C4×C11—22no—
226C2×C4×C11—22no—
227C2×C4×C11—22no—
228C2×C4×C11—42no—
229C2×C4×C11—42no—
230C2×C4×C11—42no—
231C2×C4×C11#13714yes—
232C2×C4×C11C22×D412yes—
233C2×C4×C11C22×D411yescharacteristic
234C2×C4×C11C22×D412yes—
235C2×C4×C11C2×#4112yes—
236C2×C4×C11H(5,𝔽2)12yes—
237C2×C4×C11C2511yescharacteristic
238C2×Dic11—24no—
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—44no—
242C2×Dic11—44no—
243C2×Dic11C22×D414yes—
244D44—28no—
245C4×D11—28no—
246C4×D11—24no—
247C4×D11—24no—
248C4×D11—416no—
249Dic22—24no—
250Dic22—24no—
251Dic22—416no—
252Dic22—44no—
253Dic22—48no—
254C8×C11—22no—
255C8×C11—22no—
256C11⋊C8—24no—
257C23×Q8—112no—
258C22×Q16—112no—
259C22×Q16C2×D1111yescharacteristic
260C22×M16—112no—
261#556—118no—
262#556—224no—
263D4×Q8—118no—
264D4×Q8—224no—
265C2×C4⋊Q8—111no—
266C2×C4⋊Q8—111no—
267C2×C4⋊Q8—221no—
268C2×#126—222no—
269C2×#124—221no—
270C2×C22⋊Q8—112no—
271C2×C22⋊Q8—112no—
272C2×C22⋊Q8—222no—
273C2×C4×Q8—221no—
274C2×C4×Q8C2×D1111yescharacteristic
275C2×C4×Q8C2×D1111yescharacteristic
276C2×C4×D4—111no—
277C2×C4×D4—221no—
278C2×#117—112no—
279#487—118no—
280#485—1116no—
281#475—118no—
282#470—1116no—
283#462—118no—
284#451—1116no—
285C4×Q16C2×D1118yescomplemented
286#436—118no—
287C2×#107C2×D1111yescharacteristic
288C2×#106—112no—
289C2×C4⋊C8—111no—
290#419—1116no—
291C2×#103—112no—
292C2×#103—112no—
293C2×#103—112no—
294C2×#103—112no—
295C2×#103C2×D1111yescharacteristic
296C2×#103C2×D1111yescharacteristic
297C2×C22⋊C8—112no—
298C2×C4×C8C2×D1111yescharacteristic
299C22×C11#54612yes—
300C22×C11C2×#13712yes—
301C22×C11#57812yes—
302C22×C11C23×D411yescharacteristic
303C2×D11—24no—
304C2×D11—24no—
305C2×D11—24no—
306C2×D11—48no—
307C4×C11—24no—
308C4×C11—22no—
309C4×C11—42no—
310C4×C11—42no—
311C4×C11—42no—
312C4×C11#54612yes—
313C4×C11C2×#13714yes—
314C4×C11C22×#4111yescharacteristic
315C4×C11C2×H(5,𝔽2)11yescharacteristic
316Dic11—24no—
317Dic11—44no—
318Dic11—44no—
319C22×Q8—118no—
320C22×Q8—112no—
321C22×Q8—222no—
322C22×Q8—224no—
323C22×Q8—221no—
324C22×Q8—228no—
325C22×Q8—444no—
326C22×Q8C22×D1111yescharacteristic
327C22×Q8C22×D1111yescharacteristic
328C22×D4—111no—
329C23×C4—112no—
330C23×C4—222no—
331C2×Q16—24no—
332C2×Q16—118no—
333C2×Q16—444no—
334C2×Q16C22×D1114yes—
335C2×M16—118no—
336C2×M16—444no—
337C22×C8—112no—
338C22×C8C22×D1111yescharacteristic
339C22×C8C22×D1111yescharacteristic
340C4⋊Q8—114no—
341C4⋊Q8—114no—
342C4⋊Q8—228no—
343C4⋊Q8—222no—
344C4⋊Q8—222no—
345#126—2216no—
346#124—228no—
347C22⋊Q8—118no—
348C22⋊Q8—118no—
349C22⋊Q8—2216no—
350C22⋊Q8—224no—
351C22⋊Q8—224no—
352C4×Q8—22no—
353C4×Q8—22no—
354C4×Q8—228no—
355C4×Q8C22×D1114yes—
356C4×Q8C22×D1114yes—
357C4×D4—114no—
358C4×D4—114no—
359C4×D4—228no—
360#117—118no—
361#117—224no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—111no—
365C2×C4⋊C4—112no—
366C2×C4⋊C4—222no—
367C2×C4⋊C4—222no—
368C2×C4⋊C4—221no—
369C2×C4⋊C4—221no—
370C2×C4⋊C4—221no—
371C2×C4⋊C4C22×D1111yescharacteristic
372C2×C4⋊C4C22×D1111yescharacteristic
373C2×C22⋊C4—112no—
374C2×C22⋊C4—222no—
375C2×C22⋊C4—222no—
376C2×C22⋊C4—222no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42—222no—
380C2×C42C22×D1111yescharacteristic
381#107C22×D1114yes—
382#106—118no—
383C4⋊C8—114no—
384#103—118no—
385#103—118no—
386#103—118no—
387#103—118no—
388#103C22×D1114yes—
389#103C22×D1114yes—
390C22⋊C8—118no—
391C4×C8C22×D1114yes—
392C2×C11#332814yescomplemented
393C2×C11C2×#54611yescharacteristic
394C2×C11C22×#13711yescharacteristic
395C2×C11C2×#57811yescharacteristic
396D11—44no—
397C24—112no—
398C2×Q8—21no—
399C2×Q8—21no—
400C2×Q8—22no—
401C2×Q8—22no—
402C2×Q8—22no—
403C2×Q8—114no—
404C2×Q8—228no—
405C2×Q8—224no—
406C2×Q8—222no—
407C2×Q8—2216no—
408C2×Q8—224no—
409C2×Q8—224no—
410C2×Q8—448no—
411C2×Q8—448no—
412C2×Q8—4416no—
413C2×Q8—444no—
414C2×Q8#433914yes—
415C2×Q8C23×D1112yes—
416C2×Q8C23×D1112yes—
417C2×D4—114no—
418C2×D4—224no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—112no—
424C22×C4—114no—
425C22×C4—114no—
426C22×C4—228no—
427C22×C4—224no—
428C22×C4—224no—
429C22×C4—222no—
430C22×C4—222no—
431C22×C4—448no—
432C22×C4D4×D1111yescharacteristic
433C22×C4D4×D1111yescharacteristic
434C22×C4C23×D1111yescharacteristic
435Q16—28no—
436Q16—448no—
437M16—448no—
438C2×C8—22no—
439C2×C8—22no—
440C2×C8—114no—
441C2×C8—224no—
442C2×C8C23×D1112yes—
443C2×C8C23×D1112yes—
444C4⋊C4—24no—
445C4⋊C4—24no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—114no—
449C4⋊C4—114no—
450C4⋊C4—228no—
451C4⋊C4—228no—
452C4⋊C4—222no—
453C4⋊C4—224no—
454C4⋊C4—224no—
455C4⋊C4—224no—
456C4⋊C4C23×D1112yes—
457C4⋊C4C23×D1112yes—
458C22⋊C4—118no—
459C22⋊C4—228no—
460C22⋊C4—228no—
461C22⋊C4—228no—
462C42—24no—
463C42—24no—
464C42—228no—
465C42D4×D1112yes—
466C42C23×D1112yes—
467C11C2×#332811yescharacteristic, complemented, Sylow
468C23—114no—
469C23—224no—
470C23—224no—
471C23—224no—
472C23C2×D4×D1111yescharacteristic
473Q8—24no—
474Q8—22no—
475Q8—22no—
476Q8—22no—
477Q8—42no—
478Q8—224no—
479Q8—224no—
480Q8—4416no—
481Q8—448no—
482Q8—444no—
483Q8C2×#433914yes—
484D4—228no—
485C2×C4—22no—
486C2×C4—24no—
487C2×C4—22no—
488C2×C4—22no—
489C2×C4—22no—
490C2×C4—22no—
491C2×C4—42no—
492C2×C4—42no—
493C2×C4—42no—
494C2×C4—114no—
495C2×C4—224no—
496C2×C4—228no—
497C2×C4—224no—
498C2×C4—224no—
499C2×C4—224no—
500C2×C4—224no—
501C2×C4—4416no—
502C2×C4—444no—
503C2×C4—444no—
504C2×C4#6697114yes—
505C2×C4C2×#433912yes—
506C2×C4C2×D4×D1112yes—
507C2×C4C2×D4×D1112yes—
508C2×C4C2×D4×D1111yescharacteristic
509C2×C4#6704212yes—
510C2×C4C24×D1111yescharacteristic
511C8—22no—
512C8—22no—
513C8—224no—
514C22—224no—
515C22—224no—
516C22—224no—
517C22—448no—
518C22#1062308112yes—
519C22C2×#6697112yes—
520C22#1062330212yes—
521C22C22×D4×D1111yescharacteristic
522C4—24no—
523C4—22no—
524C4—42no—
525C4—42no—
526C4—42no—
527C4—224no—
528C4—444no—
529C4—444no—
530C4#1062308112yes—
531C4C2×#6697114yes—
532C4C22×#433911yescharacteristic
533C4C2×#6704211yescharacteristic
534C2—444no—
535C2#1308090114yesdirect product factor
536C2C2×#1062308111yescharacteristic
537C2C22×#6697111yescharacteristic
538C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C4×C11×Q16C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×C4×Q16D11
hypocenterC11C2×#3328
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×Q16

Complements

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

NH ≅ G/Ntype
3. #13080901C2direct (N × H)
4. C2×#10622294C2semidirect
5. C2×#10622501C2semidirect
6. C2×#10622633C2semidirect
7. C2×#10622429C2semidirect
8. C2×#10622644C2semidirect
9. C2×#10622799C2semidirect
11. C2×#10622415C2semidirect
12. C2×C4×C11×Q16C2semidirect
35. C4×C11×Q16C22semidirect
41. #10622799C22semidirect
45. #10622644C22semidirect
46. #10622633C22semidirect
50. #10622501C22semidirect
51. #10622429C22semidirect
52. #10622415C22semidirect
54. #10622294C22semidirect
208. C2×C4×Q16D11semidirect
285. C4×Q16C2×D11semidirect
392. C2×C11#3328semidirect
467. C11C2×#3328semidirect
535. C2#13080901direct (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×Q8×D442
#130809012
C2×#106222942
C2×#106225012
C2×#106226332
C2×#106224292
C2×#106226442
C2×#106227992
C2×#106223012
C2×#106224152
C2×C4×C11×Q162
C2×#332811