Finite Group Databasebeta

← C2×#13080910 #15630670

Subgroups — C2×#13080910 #15630670

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×#10623094C211yesmaximal, characteristic
2#13080910C2116yesmaximal, direct product factor
3C2×#10622694C211yesmaximal, characteristic, complemented
4C2×#10622658C212yesmaximal, complemented
5C2×#10622634C211yesmaximal, characteristic, complemented
6C2×#10622662C212yesmaximal, complemented
7C2×#10622696C211yesmaximal, characteristic, complemented
8C2×#10622840C212yesmaximal, complemented
9C2×C4×#4325C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622838C212yesmaximal, complemented
12C2×D4×Q8×C11C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2212yes—
14D4×Q8×C11—24no—
15D4×Q8×C11C2218yescomplemented
16C2×C11×C4⋊Q8—21no—
17C2×C11×C4⋊Q8C2211yescharacteristic
18C2×C11×C22⋊Q8—22no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11—21no—
22C2×C4×D4×C11C2211yescharacteristic
23C22×#4325C2211yescharacteristic
24C22×#4325C2212yes—
25C2×#66991—21no—
26C2×#66983C2212yes—
27C2×#66979C2212yes—
28C22×#4318C2212yes—
29#10623094—24no—
30#10623094C2218yes—
31C2×#66945—21no—
32C2×#66938—22no—
33C2×C4×D44C2211yescharacteristic
34C2×#66922C2211yescharacteristic
35#10622840C22116yescomplemented
36#10622838C22116yescomplemented
37C2×#66899C2212yes—
38C2×#66899C2212yes—
39C2×#66899C2212yes—
40C2×#66899C2211yescharacteristic
41C2×#66899C2212yes—
42C2×C22⋊(C11⋊C8)C2212yes—
43#10622696C2218yescomplemented
44#10622694C2218yescomplemented
45#10622662C22116yescomplemented
46#10622658C22116yescomplemented
47C4×#4325C2218yescomplemented
48#10622634C2218yescomplemented
49#10622625C2218yescomplemented
50C2×#66873C2211yescharacteristic
51C2×#66872C2211yescharacteristic
52C2×#66871C2212yes—
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—22no—
56C22×Q8×C11—24no—
57C22×Q8×C11—28no—
58C22×Q8×C11—44no—
59C22×Q8×C11C2312yes—
60C22×Q8×C11C2318yes—
61C22×Q8×C11C2311yescharacteristic
62C22×D4×C11D411yescharacteristic
63C23×C4×C11—22no—
64C23×C4×C11C2312yes—
65C22×C22⋊D11—22no—
66C22×D44C2311yescharacteristic
67C22×C4×D11—21no—
68C22×Dic22—21no—
69C11×C4⋊Q8—28no—
70C11×C4⋊Q8—22no—
71C11×C4⋊Q8C2314yes—
72C11×C22⋊Q8—24no—
73C11×C22⋊Q8—216no—
74C11×C22⋊Q8C2318yes—
75C4×Q8×C11—22no—
76C4×Q8×C11C2314yes—
77C4×D4×C11—28no—
78C4×D4×C11D414yes—
79C4×D4×C11C2314yes—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—21no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4D411yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4D412yes—
88C2×C42×C11—21no—
89C2×C42×C11C2311yescharacteristic
90C2×C22⋊Dic11—22no—
91C2×#4325—24no—
92C2×#4325—44no—
93C2×#4325C2314yes—
94C2×#4325C2318yes—
95#66991—28no—
96#66983—24no—
97#66983C2318yes—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—22no—
100#66979—24no—
101#66979C2318yes—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11C2312yes—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4×Dic11—22no—
106C2×#4318—44no—
107C2×#4318C2318yes—
108C22×C11⋊C8C2311yescharacteristic
109C22×C11⋊C8C2311yescharacteristic
110C22×C11⋊C8C2312yes—
111#66945—28no—
112#66938—216no—
113C4×D44—22no—
114C4×D44C2314yes—
115#66922—22no—
116#66922C2314yes—
117#66899C2314yes—
118#66899C2318yes—
119#66899C2318yes—
120#66899C2318yes—
121#66899C2318yes—
122C22⋊(C11⋊C8)C2318yes—
123#66873C2314yes—
124#66872C2314yes—
125#66871C2318yes—
126C4⋊(C11⋊C8)C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3329—111nomaximal, Sylow
129C24×C11C2×D412yes—
130C23×D11—21no—
131C2×Q8×C11—21no—
132C2×Q8×C11—28no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11—216no—
136C2×Q8×C11—24no—
137C2×Q8×C11—24no—
138C2×Q8×C11—48no—
139C2×Q8×C11—48no—
140C2×Q8×C11—416no—
141C2×Q8×C11#4114yes—
142C2×Q8×C11C2414yes—
143C2×Q8×C11C2412yes—
144C2×D4×C11—24no—
145C2×D4×C11C2×D414yes—
146C22×C4×C11—21no—
147C22×C4×C11—24no—
148C22×C4×C11—24no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—28no—
152C22×C4×C11—48no—
153C22×C4×C11C2×D412yes—
154C22×C4×C11C2×D414yes—
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2×D411yescharacteristic
157C22×C4×C11C2414yes—
158C22×C4×C11C2411yescharacteristic
159C2×C22⋊D11—28no—
160C2×C22⋊D11—84no—
161C22×Dic11—21no—
162C22×Dic11—22no—
163C2×D44—21no—
164C2×D44—22no—
165C2×D44—22no—
166C2×D44C2412yes—
167C2×C4×D11—24no—
168C2×C4×D11—44no—
169C2×Dic22—24no—
170C2×Dic22—82no—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—24no—
173C11×C4⋊C4—24no—
174C11×C4⋊C4—28no—
175C11×C4⋊C4—21no—
176C11×C4⋊C4C2×D414yes—
177C11×C4⋊C4C2412yes—
178C11×C22⋊C4—28no—
179C11×C22⋊C4C2×D418yes—
180C42×C11—24no—
181C42×C11C2×D412yes—
182C42×C11C2412yes—
183C22⋊Dic11—28no—
184#4325—28no—
185#4325—48no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—28no—
188C4⋊Dic11—22no—
189C4⋊Dic11—24no—
190C4⋊Dic11—21no—
191C4⋊Dic11C2414yes—
192C4⋊Dic11C2412yes—
193C4×Dic11—28no—
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×#555—111no—
202C2×D4×Q8D1111yescharacteristic, complemented
203#3329—1116no—
204C2×#487—111no—
205C2×#485—112no—
206C2×#477—111no—
207C2×#468—112no—
208C2×#461—111no—
209C2×#448—112no—
210C2×C4×SD16—111no—
211C2×#436—111no—
212C2×#419—112no—
213C23×C11—24no—
214C23×C11—24no—
215C23×C11—24no—
216C23×C11C22×D414yes—
217C23×C11C22×D411yescharacteristic
218C22×D11—22no—
219C22×D11—42no—
220C22×D11—42no—
221C22×D11—42no—
222Q8×C11—24no—
223Q8×C11—22no—
224Q8×C11—24no—
225Q8×C11—24no—
226Q8×C11—416no—
227Q8×C11—44no—
228Q8×C11C2×#4114yes—
229D4×C11—28no—
230C2×C4×C11—24no—
231C2×C4×C11—24no—
232C2×C4×C11—22no—
233C2×C4×C11—22no—
234C2×C4×C11—28no—
235C2×C4×C11—24no—
236C2×C4×C11—24no—
237C2×C4×C11—22no—
238C2×C4×C11—24no—
239C2×C4×C11—416no—
240C2×C4×C11—44no—
241C2×C4×C11—42no—
242C2×C4×C11#13714yes—
243C2×C4×C11C22×D414yes—
244C2×C4×C11C22×D412yes—
245C2×C4×C11C22×D411yescharacteristic
246C2×C4×C11C22×D412yes—
247C2×C4×C11C2×#4112yes—
248C2×C4×C11H(5,𝔽2)12yes—
249C2×C4×C11C2511yescharacteristic
250C22⋊D11—88no—
251C2×Dic11—22no—
252C2×Dic11—24no—
253C2×Dic11—42no—
254C2×Dic11—44no—
255D44—22no—
256D44—22no—
257D44—42no—
258C4×D11—48no—
259Dic22—84no—
260C11⋊C8—22no—
261C11⋊C8—22no—
262C11⋊C8—24no—
263C23×Q8C2×D1112yes—
264C22×SD16—111no—
265C22×SD16—112no—
266C22×M16—112no—
267#555—118no—
268#555—224no—
269D4×Q8—24no—
270D4×Q8C2×D1118yescomplemented
271C2×C4⋊Q8—21no—
272C2×C4⋊Q8—111no—
273C2×C4⋊Q8C2×D1111yescharacteristic
274C2×#124—222no—
275C2×C22⋊Q8—22no—
276C2×C22⋊Q8C2×D1112yes—
277C2×#121—112no—
278C2×#121—221no—
279C2×C4×Q8C2×D1111yescharacteristic
280C2×C4×D4—21no—
281C2×C4×D4—111no—
282C2×C4×D4C2×D1111yescharacteristic
283C2×#117—112no—
284C2×#117—221no—
285#487—118no—
286#485—1116no—
287#477—118no—
288#468—1116no—
289#461—118no—
290#448—1116no—
291C4×SD16—118no—
292#436—118no—
293C2×#107—112no—
294C2×#106—111no—
295C2×C4⋊C8—111no—
296#419—1116no—
297C2×#103—112no—
298C2×#103—112no—
299C2×#103—112no—
300C2×#103—112no—
301C2×#103—111no—
302C2×#102—111no—
303C2×C22⋊C8—112no—
304C2×C4×C8—111no—
305C22×C11—24no—
306C22×C11—24no—
307C22×C11—24no—
308C22×C11—48no—
309C22×C11#54612yes—
310C22×C11C2×#13712yes—
311C22×C11#57712yes—
312C22×C11C23×D411yescharacteristic
313C2×D11—42no—
314C2×D11—42no—
315C2×D11—42no—
316C2×D11—84no—
317C4×C11—24no—
318C4×C11—24no—
319C4×C11—22no—
320C4×C11—44no—
321C4×C11—42no—
322C4×C11#54612yes—
323C4×C11C2×#13714yes—
324C4×C11C22×#4111yescharacteristic
325C4×C11C2×H(5,𝔽2)11yescharacteristic
326Dic11—42no—
327Dic11—44no—
328C22×Q8—22no—
329C22×Q8—24no—
330C22×Q8—28no—
331C22×Q8—44no—
332C22×Q8—221no—
333C22×Q8C22×D1112yes—
334C22×Q8C22×D1118yes—
335C22×Q8C22×D1111yescharacteristic
336C22×D4—111no—
337C22×D4—222no—
338C22×D4C22⋊D1111yescharacteristic
339C23×C4—22no—
340C23×C4—221no—
341C23×C4C22×D1112yes—
342C2×SD16—114no—
343C2×SD16—118no—
344C2×SD16—224no—
345C2×SD16—444no—
346C2×M16—118no—
347C2×M16—444no—
348C22×C8—111no—
349C22×C8—112no—
350C22×C8—111no—
351C4⋊Q8—28no—
352C4⋊Q8—22no—
353C4⋊Q8—114no—
354C4⋊Q8—222no—
355C4⋊Q8C22×D1114yes—
356#124—2216no—
357C22⋊Q8—24no—
358C22⋊Q8—216no—
359C22⋊Q8C22×D1118yes—
360#121—118no—
361#121—228no—
362#121—224no—
363C4×Q8—22no—
364C4×Q8C22×D1114yes—
365C4×D4—28no—
366C4×D4—114no—
367C4×D4—222no—
368C4×D4C22⋊D1114yes—
369C4×D4C22×D1114yes—
370#117—118no—
371#117—224no—
372#117—228no—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—22no—
377C2×C4⋊C4—111no—
378C2×C4⋊C4—112no—
379C2×C4⋊C4—221no—
380C2×C4⋊C4C22⋊D1111yescharacteristic
381C2×C4⋊C4C22×D1111yescharacteristic
382C2×C22⋊C4—22no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—222no—
385C2×C22⋊C4—221no—
386C2×C22⋊C4C22⋊D1112yes—
387C2×C42—21no—
388C2×C42—222no—
389C2×C42C22×D1111yescharacteristic
390#107—118no—
391#106—114no—
392C4⋊C8—114no—
393#103—114no—
394#103—118no—
395#103—118no—
396#103—118no—
397#103—118no—
398#102—114no—
399C22⋊C8—118no—
400C4×C8—114no—
401C2×C11—44no—
402C2×C11#332914yescomplemented
403C2×C11C2×#54611yescharacteristic
404C2×C11C22×#13711yescharacteristic
405C2×C11C2×#57711yescharacteristic
406D11—82no—
407C24—221no—
408C24C2×C22⋊D1112yes—
409C2×Q8—22no—
410C2×Q8—21no—
411C2×Q8—28no—
412C2×Q8—22no—
413C2×Q8—216no—
414C2×Q8—24no—
415C2×Q8—24no—
416C2×Q8—48no—
417C2×Q8—48no—
418C2×Q8—416no—
419C2×Q8—224no—
420C2×Q8—882no—
421C2×Q8#434114yes—
422C2×Q8C23×D1114yes—
423C2×Q8C23×D1112yes—
424C2×D4—24no—
425C2×D4—112no—
426C2×D4—228no—
427C2×D4—222no—
428C2×D4—222no—
429C2×D4—221no—
430C2×D4—884no—
431C2×D4C2×C22⋊D1114yes—
432C22×C4—21no—
433C22×C4—24no—
434C22×C4—24no—
435C22×C4—28no—
436C22×C4—21no—
437C22×C4—22no—
438C22×C4—48no—
439C22×C4—221no—
440C22×C4—222no—
441C22×C4—224no—
442C22×C4—444no—
443C22×C4C2×C22⋊D1114yes—
444C22×C4C2×C22⋊D1112yes—
445C22×C4C2×C22⋊D1111yescharacteristic
446C22×C4C2×C22⋊D1111yescharacteristic
447C22×C4C23×D1114yes—
448C22×C4C23×D1111yescharacteristic
449SD16—228no—
450SD16—448no—
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—24no—
460C4⋊C4—24no—
461C4⋊C4—28no—
462C4⋊C4—21no—
463C4⋊C4—112no—
464C4⋊C4—114no—
465C4⋊C4—221no—
466C4⋊C4—222no—
467C4⋊C4—224no—
468C4⋊C4C2×C22⋊D1114yes—
469C4⋊C4C23×D1112yes—
470C22⋊C4—28no—
471C22⋊C4—228no—
472C22⋊C4—228no—
473C22⋊C4—224no—
474C22⋊C4C2×C22⋊D1118yes—
475C42—24no—
476C42—228no—
477C42C2×C22⋊D1112yes—
478C42C23×D1112yes—
479C11C2×#332911yescharacteristic, complemented, Sylow
480C23—24no—
481C23—24no—
482C23—24no—
483C23—222no—
484C23—442no—
485C23—442no—
486C23—442no—
487C23C22×C22⋊D1114yes—
488C23C22×C22⋊D1111yescharacteristic
489Q8—24no—
490Q8—22no—
491Q8—24no—
492Q8—24no—
493Q8—416no—
494Q8—44no—
495Q8—884no—
496Q8C2×#434114yes—
497D4—28no—
498D4—222no—
499D4—222no—
500D4—442no—
501D4—888no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—22no—
505C2×C4—22no—
506C2×C4—28no—
507C2×C4—24no—
508C2×C4—24no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—416no—
512C2×C4—44no—
513C2×C4—42no—
514C2×C4—222no—
515C2×C4—224no—
516C2×C4—442no—
517C2×C4—444no—
518C2×C4—448no—
519C2×C4#6699514yes—
520C2×C4C2×#434112yes—
521C2×C4#6703712yes—
522C2×C4C22×C22⋊D1114yes—
523C2×C4C22×C22⋊D1112yes—
524C2×C4C22×C22⋊D1111yescharacteristic
525C2×C4C22×C22⋊D1112yes—
526C2×C4C24×D1111yescharacteristic
527C8—222no—
528C8—222no—
529C8—224no—
530C22—24no—
531C22—24no—
532C22—24no—
533C22—48no—
534C22—442no—
535C22—442no—
536C22—442no—
537C22—884no—
538C22#1062333712yes—
539C22C2×#6699512yes—
540C22#1062336812yes—
541C22C23×C22⋊D1111yescharacteristic
542C4—24no—
543C4—24no—
544C4—22no—
545C4—44no—
546C4—42no—
547C4—442no—
548C4—444no—
549C4#1062333712yes—
550C4C2×#6699514yes—
551C4C22×#434111yescharacteristic
552C4C2×#6703711yescharacteristic
553C2—44no—
554C2—882no—
555C2#1308091014yesdirect product factor
556C2C2×#1062333711yescharacteristic
557C2C22×#6699511yescharacteristic
558C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×D4×Q8×C11C2
socleC23×C11C22×D4
prime radicalC2×#10623094C2
hypercenterC2×D4×Q8D11
hypocenterC11C2×#3329
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
2. #13080910C2direct (N × H)
3. C2×#10622694C2semidirect
4. C2×#10622658C2semidirect
5. C2×#10622634C2semidirect
6. C2×#10622662C2semidirect
7. C2×#10622696C2semidirect
8. C2×#10622840C2semidirect
9. C2×C4×#4325C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622838C2semidirect
12. C2×D4×Q8×C11C2semidirect
15. D4×Q8×C11C22semidirect
35. #10622840C22semidirect
36. #10622838C22semidirect
43. #10622696C22semidirect
44. #10622694C22semidirect
45. #10622662C22semidirect
46. #10622658C22semidirect
47. C4×#4325C22semidirect
48. #10622634C22semidirect
49. #10622625C22semidirect
202. C2×D4×Q8D11semidirect
270. D4×Q8C2×D11semidirect
402. C2×C11#3329semidirect
479. C11C2×#3329semidirect
555. C2#13080910direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230942
#130809102
C2×#106226942
C2×#106226582
C2×#106226342
C2×#106226622
C2×#106226962
C2×#106228402
C2×C4×#43252
C2×#106226252
C2×#106228382
C2×D4×Q8×C112
C2×#332911