Finite Group Databasebeta

← C2×#13080932 #15630694

Subgroups — C2×#13080932 #15630694

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×#10623074C211yesmaximal, characteristic, complemented
2#13080932C2116yesmaximal, direct product factor
3C2×#10622694C211yesmaximal, characteristic, complemented
4C2×#10622656C212yesmaximal, complemented
5C2×#10622621C211yesmaximal, characteristic, complemented
6C2×#10622665C212yesmaximal, complemented
7C2×#10622703C211yesmaximal, characteristic, complemented
8C2×#10622852C212yesmaximal, complemented
9C2×C4×#4324C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622845C212yesmaximal, complemented
12C2×C11×#547C211yesmaximal, characteristic
13C22×C11×#41C2212yes—
14C11×#547—24no—
15C11×#547C2218yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#123—22no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×#121—21no—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C22×C11×C4⋊C4—21no—
23C22×#4326C2212yes—
24C2×D4×Dic11—21no—
25C22×#4324C2211yescharacteristic
26C22×C4⋊Dic11C2212yes—
27C2×#66977C2212yes—
28C22×#4318C2212yes—
29#10623074—24no—
30#10623074C2218yescomplemented
31C2×#66943—21no—
32C2×#66931—22no—
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35#10622852C22116yescomplemented
36#10622845C22116yescomplemented
37C2×#66899C2212yes—
38C2×#66899C2212yes—
39C2×#66899C2212yes—
40C2×#66896C2212yes—
41C2×#66896C2211yescharacteristic
42C2×C22⋊(C11⋊C8)C2212yes—
43#10622703C2218yescomplemented
44#10622694C2218yescomplemented
45#10622665C22116yescomplemented
46#10622656C22116yescomplemented
47C4×#4324C2218yescomplemented
48#10622625C2218yescomplemented
49#10622621C2218yescomplemented
50C2×#66874C2211yescharacteristic
51C2×#66872C2212yes—
52C2×#66872C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C2×C11×#41—24no—
56C2×C11×#41—28no—
57C2×C11×#41—44no—
58C2×C11×#41C2318yes—
59C22×Q8×C11C2312yes—
60C22×D4×C11—22no—
61C22×D4×C11D411yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C23×C4×C11—22no—
65C23×C4×C11C2312yes—
66C23×Dic11—22no—
67C22×Dic22—21no—
68C22×Dic22C2311yescharacteristic
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8C2314yes—
71C11×#123—216no—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8C2318yes—
74C11×#121—28no—
75C4×D4×C11—22no—
76C4×D4×C11D414yes—
77C4×D4×C11C2314yes—
78C4×D4×C11C2314yes—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—22no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—28no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4D412yes—
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—22no—
90C2×#4326—44no—
91C2×#4326C2318yes—
92D4×Dic11—28no—
93C2×#4324—24no—
94C2×#4324C2314yes—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11—24no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2318yes—
101#66977—24no—
102#66977C2318yes—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—22no—
105C2×C4×Dic11—21no—
106C2×#4318—44no—
107C2×#4318C2318yes—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2312yes—
111#66943—28no—
112#66931—216no—
113#66922—22no—
114#66922C2314yes—
115C4×Dic22—22no—
116C4×Dic22C2314yes—
117#66899C2318yes—
118#66899C2318yes—
119#66899C2318yes—
120#66896C2314yes—
121#66896C2318yes—
122C22⋊(C11⋊C8)C2318yes—
123#66874C2314yes—
124#66872C2318yes—
125#66872C2314yes—
126C4⋊(C11⋊C8)C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3331—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11C2×D412yes—
131C11×#41—216no—
132C11×#41—48no—
133C11×#41—416no—
134C2×Q8×C11—22no—
135C2×Q8×C11—24no—
136C2×Q8×C11—24no—
137C2×Q8×C11C2414yes—
138C2×D4×C11—28no—
139C2×D4×C11—24no—
140C2×D4×C11—21no—
141C2×D4×C11—22no—
142C2×D4×C11—48no—
143C2×D4×C11C2×D414yes—
144C2×D4×C11#4114yes—
145C2×D4×C11C2412yes—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11—21no—
149C22×C4×C11—22no—
150C22×C4×C11—24no—
151C22×C4×C11—28no—
152C22×C4×C11—48no—
153C22×C4×C11—44no—
154C22×C4×C11C2×D412yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2414yes—
159C22×C4×C11C2411yescharacteristic
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—22no—
163C22×Dic11—28no—
164C22×Dic11—84no—
165C2×Dic22—21no—
166C2×Dic22—24no—
167C2×Dic22—22no—
168C2×Dic22—22no—
169C2×Dic22—82no—
170C2×Dic22C2412yes—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—28no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—21no—
175C11×C4⋊C4C2×D414yes—
176C11×C4⋊C4C2412yes—
177C11×C22⋊C4—28no—
178C11×C22⋊C4—24no—
179C11×C22⋊C4C2×D418yes—
180C42×C11C2×D412yes—
181C42×C11C2412yes—
182C22⋊Dic11—28no—
183#4326—48no—
184#4324—28no—
185C4⋊Dic11—21no—
186C4⋊Dic11—22no—
187C4⋊Dic11—24no—
188C4⋊Dic11—28no—
189C4⋊Dic11C2412yes—
190C4⋊Dic11C2414yes—
191Dic11⋊C4—24no—
192Dic11⋊C4—28no—
193C4×Dic11—24no—
194#4318—48no—
195C2×C11⋊C8—22no—
196C2×C11⋊C8—22no—
197C2×C11⋊C8—24no—
198C2×C11⋊C8C2412yes—
199C2×C11⋊C8C2412yes—
200C2×C11⋊C8C2414yes—
201C2×#554—111no—
202C2×#547D1111yescharacteristic
203#3331—1116no—
204C2×#487—111no—
205C2×#483—112no—
206C2×#476—111no—
207C2×#470—112no—
208C2×#462—111no—
209C2×#452—112no—
210C2×C4×SD16—111no—
211C2×#436—111no—
212C2×#417—112no—
213C23×C11—24no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11—24no—
217C23×C11—22no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11C22×D414yes—
221C23×C11C22×D411yescharacteristic
222Q8×C11—24no—
223Q8×C11—24no—
224Q8×C11—44no—
225D4×C11—24no—
226D4×C11—28no—
227D4×C11—22no—
228D4×C11—416no—
229D4×C11C2×#4114yes—
230C2×C4×C11—24no—
231C2×C4×C11—22no—
232C2×C4×C11—28no—
233C2×C4×C11—24no—
234C2×C4×C11—24no—
235C2×C4×C11—22no—
236C2×C4×C11—24no—
237C2×C4×C11—416no—
238C2×C4×C11—44no—
239C2×C4×C11—42no—
240C2×C4×C11—48no—
241C2×C4×C11#13714yes—
242C2×C4×C11C22×D414yes—
243C2×C4×C11C22×D412yes—
244C2×C4×C11C22×D411yescharacteristic
245C2×C4×C11C22×D412yes—
246C2×C4×C11C2×#4112yes—
247C2×C4×C11H(5,𝔽2)12yes—
248C2×C4×C11C2511yescharacteristic
249C2×Dic11—22no—
250C2×Dic11—22no—
251C2×Dic11—24no—
252C2×Dic11—42no—
253C2×Dic11—44no—
254C2×Dic11—42no—
255C2×Dic11—88no—
256Dic22—22no—
257Dic22—22no—
258Dic22—42no—
259Dic22—84no—
260C11⋊C8—22no—
261C11⋊C8—22no—
262C11⋊C8—24no—
263C22×#41C2×D1112yes—
264C22×Q16—112no—
265C22×SD16—111no—
266C22×M16—112no—
267#554—118no—
268#554—224no—
269#547—24no—
270#547C2×D1118yes—
271C2×C4⋊Q8—111no—
272C2×C4⋊Q8C2×D1111yescharacteristic
273C2×#125—221no—
274C2×#123—22no—
275C2×C22⋊Q8—112no—
276C2×C22⋊Q8—222no—
277C2×C22⋊Q8C2×D1112yes—
278C2×#121—21no—
279C2×C4×Q8—111no—
280C2×C4×D4—221no—
281C2×C4×D4C2×D1111yescharacteristic
282C2×C4×D4C2×D1111yescharacteristic
283C22×C4⋊C4—21no—
284C22×C4⋊C4—112no—
285#487—118no—
286#483—1116no—
287#476—118no—
288#470—1116no—
289#462—118no—
290#452—1116no—
291C4×SD16—118no—
292#436—118no—
293C2×#106—111no—
294C2×#106—112no—
295C2×C4⋊C8—111no—
296#417—1116no—
297C2×#103—112no—
298C2×#103—112no—
299C2×#103—112no—
300C2×#103—111no—
301C2×#102—111no—
302C2×#102—112no—
303C2×C22⋊C8—112no—
304C2×C4×C8—111no—
305C22×C11—24no—
306C22×C11—24no—
307C22×C11—24no—
308C22×C11—24no—
309C22×C11—48no—
310C22×C11—48no—
311C22×C11—42no—
312C22×C11—42no—
313C22×C11#54612yes—
314C22×C11C2×#13712yes—
315C22×C11#57712yes—
316C22×C11C23×D411yescharacteristic
317C4×C11—24no—
318C4×C11—22no—
319C4×C11—44no—
320C4×C11—42no—
321C4×C11#54612yes—
322C4×C11C2×#13714yes—
323C4×C11C22×#4111yescharacteristic
324C4×C11C2×H(5,𝔽2)11yescharacteristic
325Dic11—42no—
326Dic11—44no—
327Dic11—42no—
328C2×#41—24no—
329C2×#41—28no—
330C2×#41—44no—
331C2×#41C22×D1118yes—
332C22×Q8—111no—
333C22×Q8—221no—
334C22×Q8C22×D1112yes—
335C22×D4—22no—
336C22×D4C22⋊D1111yescharacteristic
337C22×D4C22×D1111yescharacteristic
338C23×C4—21no—
339C23×C4—22no—
340C23×C4—222no—
341C23×C4C22×D1112yes—
342C2×Q16—118no—
343C2×Q16—444no—
344C2×SD16—114no—
345C2×SD16—224no—
346C2×M16—118no—
347C2×M16—444no—
348C22×C8—111no—
349C22×C8—112no—
350C22×C8—111no—
351C4⋊Q8—22no—
352C4⋊Q8—114no—
353C4⋊Q8—222no—
354C4⋊Q8C22×D1114yes—
355#125—228no—
356#123—216no—
357C22⋊Q8—24no—
358C22⋊Q8—118no—
359C22⋊Q8—224no—
360C22⋊Q8—2216no—
361C22⋊Q8C22×D1118yes—
362#121—28no—
363C4×Q8—114no—
364C4×Q8—222no—
365C4×D4—22no—
366C4×D4—228no—
367C4×D4C22⋊D1114yes—
368C4×D4C22×D1114yes—
369C4×D4C22×D1114yes—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—22no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4—28no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—112no—
376C2×C4⋊C4—118no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—224no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4—221no—
381C2×C4⋊C4—222no—
382C2×C4⋊C4C22⋊D1111yescharacteristic
383C2×C4⋊C4C22×D1111yescharacteristic
384C2×C22⋊C4—22no—
385C2×C22⋊C4—21no—
386C2×C22⋊C4—222no—
387C2×C22⋊C4C22⋊D1112yes—
388C2×C42—221no—
389C2×C42C22×D1111yescharacteristic
390#106—114no—
391#106—118no—
392C4⋊C8—114no—
393#103—118no—
394#103—118no—
395#103—118no—
396#103—114no—
397#102—114no—
398#102—118no—
399C22⋊C8—118no—
400C4×C8—114no—
401C2×C11—44no—
402C2×C11—44no—
403C2×C11#333114yescomplemented
404C2×C11C2×#54611yescharacteristic
405C2×C11C22×#13711yescharacteristic
406C2×C11C2×#57711yescharacteristic
407C24—21no—
408C24C2×C22⋊D1112yes—
409#41—216no—
410#41—48no—
411#41—416no—
412C2×Q8—22no—
413C2×Q8—24no—
414C2×Q8—24no—
415C2×Q8—112no—
416C2×Q8—221no—
417C2×Q8—224no—
418C2×Q8—222no—
419C2×Q8—222no—
420C2×Q8—882no—
421C2×Q8C23×D1114yes—
422C2×D4—28no—
423C2×D4—24no—
424C2×D4—22no—
425C2×D4—21no—
426C2×D4—48no—
427C2×D4#434114yes—
428C2×D4C2×C22⋊D1114yes—
429C2×D4C23×D1112yes—
430C22×C4—24no—
431C22×C4—24no—
432C22×C4—21no—
433C22×C4—22no—
434C22×C4—24no—
435C22×C4—28no—
436C22×C4—48no—
437C22×C4—44no—
438C22×C4—221no—
439C22×C4—221no—
440C22×C4—222no—
441C22×C4—228no—
442C22×C4—884no—
443C22×C4C2×C22⋊D1114yes—
444C22×C4C2×C22⋊D1111yescharacteristic
445C22×C4C2×C22⋊D1112yes—
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C23×D1114yes—
448C22×C4C23×D1111yescharacteristic
449Q16—448no—
450SD16—228no—
451M16—448no—
452C2×C8—112no—
453C2×C8—112no—
454C2×C8—114no—
455C2×C8—222no—
456C2×C8—222no—
457C2×C8—224no—
458C4⋊C4—24no—
459C4⋊C4—28no—
460C4⋊C4—24no—
461C4⋊C4—21no—
462C4⋊C4—112no—
463C4⋊C4—114no—
464C4⋊C4—221no—
465C4⋊C4—228no—
466C4⋊C4—222no—
467C4⋊C4—224no—
468C4⋊C4—224no—
469C4⋊C4—228no—
470C4⋊C4C2×C22⋊D1114yes—
471C4⋊C4C23×D1112yes—
472C22⋊C4—28no—
473C22⋊C4—24no—
474C22⋊C4—228no—
475C22⋊C4C2×C22⋊D1118yes—
476C42—224no—
477C42C2×C22⋊D1112yes—
478C42C23×D1112yes—
479C11C2×#333111yescharacteristic, complemented, Sylow
480C23—24no—
481C23—24no—
482C23—24no—
483C23—24no—
484C23—22no—
485C23—42no—
486C23—42no—
487C23C22×C22⋊D1114yes—
488C23C22×C22⋊D1111yescharacteristic
489Q8—24no—
490Q8—24no—
491Q8—44no—
492Q8—222no—
493Q8—222no—
494Q8—442no—
495Q8—884no—
496D4—24no—
497D4—28no—
498D4—22no—
499D4—416no—
500D4C2×#434114yes—
501C2×C4—24no—
502C2×C4—22no—
503C2×C4—28no—
504C2×C4—24no—
505C2×C4—24no—
506C2×C4—22no—
507C2×C4—24no—
508C2×C4—416no—
509C2×C4—44no—
510C2×C4—42no—
511C2×C4—48no—
512C2×C4—222no—
513C2×C4—222no—
514C2×C4—224no—
515C2×C4—442no—
516C2×C4—442no—
517C2×C4—444no—
518C2×C4—888no—
519C2×C4#6700414yes—
520C2×C4C2×#434112yes—
521C2×C4#6703712yes—
522C2×C4C22×C22⋊D1112yes—
523C2×C4C22×C22⋊D1114yes—
524C2×C4C22×C22⋊D1111yescharacteristic
525C2×C4C22×C22⋊D1112yes—
526C2×C4C24×D1111yescharacteristic
527C8—222no—
528C8—222no—
529C8—224no—
530C22—24no—
531C22—24no—
532C22—24no—
533C22—24no—
534C22—48no—
535C22—48no—
536C22—42no—
537C22—42no—
538C22#1062333712yes—
539C22C2×#6700412yes—
540C22#1062336812yes—
541C22C23×C22⋊D1111yescharacteristic
542C4—24no—
543C4—22no—
544C4—44no—
545C4—42no—
546C4—442no—
547C4—442no—
548C4—444no—
549C4#1062333712yes—
550C4C2×#6700414yes—
551C4C22×#434111yescharacteristic
552C4C2×#6703711yescharacteristic
553C2—44no—
554C2—44no—
555C2#1308093214yesdirect product factor
556C2C2×#1062333711yescharacteristic
557C2C22×#6700411yescharacteristic
558C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#547C2
socleC23×C11C22×D4
hypercenterC2×#547D11
hypocenterC11C2×#3331
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#10623074C2semidirect
2. #13080932C2direct (N × H)
3. C2×#10622694C2semidirect
4. C2×#10622656C2semidirect
5. C2×#10622621C2semidirect
6. C2×#10622665C2semidirect
7. C2×#10622703C2semidirect
8. C2×#10622852C2semidirect
9. C2×C4×#4324C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622845C2semidirect
30. #10623074C22semidirect
35. #10622852C22semidirect
36. #10622845C22semidirect
43. #10622703C22semidirect
44. #10622694C22semidirect
45. #10622665C22semidirect
46. #10622656C22semidirect
47. C4×#4324C22semidirect
48. #10622625C22semidirect
49. #10622621C22semidirect
403. C2×C11#3331semidirect
479. C11C2×#3331semidirect
555. C2#13080932direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230742
#130809322
C2×#106226942
C2×#106226562
C2×#106226212
C2×#106226652
C2×#106227032
C2×#106228522
C2×C4×#43242
C2×#106226252
C2×#106228452
C2×C11×#5472
C2×#333111