Finite Group Databasebeta

← C2×#13080904 #15630664

Subgroups — C2×#13080904 #15630664

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×D4×Dic22C211yesmaximal, characteristic, complemented
2#13080904C2116yesmaximal, direct product factor
3C2×#10622706C211yesmaximal, characteristic, complemented
4C2×#10622609C212yesmaximal, complemented
5C2×#10622704C211yesmaximal, characteristic, complemented
6C2×#10622655C212yesmaximal, complemented
7C2×#10622632C211yesmaximal, characteristic, complemented
8C2×#10622653C212yesmaximal, complemented
9C2×C4×#4324C211yesmaximal, characteristic, complemented
10C2×#10622625C211yesmaximal, characteristic, complemented
11C2×#10622617C212yesmaximal, complemented
12C2×C11×#555C211yesmaximal, characteristic
13C23×Dic22C2212yes—
14C11×#555—24no—
15C11×#555C2218yes—
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#124—22no—
18C2×C11×#121—21no—
19C2×C11×#121C2212yes—
20C2×C4×D4×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C11×#117—21no—
23C2×C11×#117C2212yes—
24C2×D4×Dic11—21no—
25C22×#4324C2211yescharacteristic
26C22×#4324C2212yes—
27C2×#66977C2212yes—
28C22×#4318C2212yes—
29D4×Dic22—24no—
30D4×Dic22C2218yescomplemented
31C2×#66941—21no—
32C2×#66931—22no—
33C2×#66922C2211yescharacteristic
34C2×C4×Dic22C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622706C2218yescomplemented
38#10622704C2218yescomplemented
39#10622655C22116yescomplemented
40#10622653C22116yescomplemented
41#10622632C2218yescomplemented
42C4×#4324C2218yescomplemented
43#10622625C2218yescomplemented
44#10622617C22116yescomplemented
45#10622609C22116yescomplemented
46C2×#66874C2212yes—
47C2×#66874C2212yes—
48C2×#66874C2212yes—
49C2×#66874C2211yescharacteristic
50C2×#66874C2212yes—
51C2×#66872C2211yescharacteristic
52C2×#66871C2212yes—
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—21no—
56C22×D4×C11—22no—
57C22×D4×C11D411yescharacteristic
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×C4×C11C2312yes—
61C23×Dic11—22no—
62C22×Dic22—28no—
63C22×Dic22—22no—
64C22×Dic22—24no—
65C22×Dic22—44no—
66C22×Dic22C2312yes—
67C22×Dic22C2318yes—
68C22×Dic22C2311yescharacteristic
69C11×C4⋊Q8—22no—
70C11×C4⋊Q8C2314yes—
71C11×#124—216no—
72C11×#121—28no—
73C11×#121—24no—
74C11×#121C2318yes—
75C4×D4×C11—22no—
76C4×D4×C11D414yes—
77C4×D4×C11C2314yes—
78C4×D4×C11C2314yes—
79C11×#117—24no—
80C11×#117—28no—
81C11×#117C2318yes—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4C2312yes—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—21no—
89C2×C11×C22⋊C4D412yes—
90C2×C42×C11—22no—
91C2×C42×C11C2311yescharacteristic
92C2×C22⋊Dic11—22no—
93D4×Dic11—28no—
94C2×#4324—24no—
95C2×#4324—44no—
96C2×#4324C2314yes—
97C2×#4324C2318yes—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11C2311yescharacteristic
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#66941—28no—
112#66931—216no—
113#66922—22no—
114#66922C2314yes—
115C4×Dic22—22no—
116C4×Dic22C2314yes—
117#66896C2314yes—
118C22⋊(C11⋊C8)C2318yes—
119#66874C2318yes—
120#66874C2318yes—
121#66874C2314yes—
122#66874C2318yes—
123#66874C2318yes—
124#66872C2314yes—
125#66871C2318yes—
126C4⋊(C11⋊C8)C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3329—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11C2×D412yes—
131C2×Q8×C11—24no—
132C2×Q8×C11—82no—
133C2×D4×C11—28no—
134C2×D4×C11—24no—
135C2×D4×C11—21no—
136C2×D4×C11—22no—
137C2×D4×C11—22no—
138C2×D4×C11—84no—
139C2×D4×C11C2×D414yes—
140C2×D4×C11C2412yes—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—21no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—44no—
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D414yes—
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2414yes—
152C22×C4×C11C2411yescharacteristic
153C22×Dic11—21no—
154C22×Dic11—28no—
155C22×Dic11—21no—
156C22×Dic11—22no—
157C22×Dic11—48no—
158C2×Dic22—216no—
159C2×Dic22—21no—
160C2×Dic22—22no—
161C2×Dic22—28no—
162C2×Dic22—24no—
163C2×Dic22—22no—
164C2×Dic22—24no—
165C2×Dic22—48no—
166C2×Dic22—416no—
167C2×Dic22—48no—
168C2×Dic22#4114yes—
169C2×Dic22C2414yes—
170C2×Dic22C2412yes—
171C11×C4⋊C4—24no—
172C11×C4⋊C4—21no—
173C11×C4⋊C4—22no—
174C11×C4⋊C4C2×D414yes—
175C11×C4⋊C4C2414yes—
176C11×C4⋊C4C2412yes—
177C11×C22⋊C4—28no—
178C11×C22⋊C4—28no—
179C11×C22⋊C4—24no—
180C11×C22⋊C4C2×D418yes—
181C42×C11—28no—
182C42×C11C2×D412yes—
183C42×C11C2412yes—
184C22⋊Dic11—28no—
185#4324—28no—
186#4324—48no—
187C4⋊Dic11—21no—
188C4⋊Dic11—24no—
189C4⋊Dic11—24no—
190C4⋊Dic11C2412yes—
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×#555D1111yescharacteristic
202C2×D4×Q8—111no—
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×C11—22no—
217C23×C11—42no—
218C23×C11—42no—
219C23×C11—42no—
220C23×C11C22×D414yes—
221C23×C11C22×D411yescharacteristic
222Q8×C11—84no—
223D4×C11—28no—
224D4×C11—22no—
225D4×C11—22no—
226D4×C11—42no—
227D4×C11—88no—
228C2×C4×C11—24no—
229C2×C4×C11—22no—
230C2×C4×C11—28no—
231C2×C4×C11—24no—
232C2×C4×C11—24no—
233C2×C4×C11—22no—
234C2×C4×C11—24no—
235C2×C4×C11—42no—
236C2×C4×C11—44no—
237C2×C4×C11—48no—
238C2×C4×C11#13714yes—
239C2×C4×C11C22×D412yes—
240C2×C4×C11C22×D414yes—
241C2×C4×C11C22×D411yescharacteristic
242C2×C4×C11C22×D412yes—
243C2×C4×C11C2×#4112yes—
244C2×C4×C11H(5,𝔽2)12yes—
245C2×C4×C11C2511yescharacteristic
246C2×Dic11—24no—
247C2×Dic11—22no—
248C2×Dic11—22no—
249C2×Dic11—24no—
250C2×Dic11—416no—
251C2×Dic11—44no—
252C2×Dic11—42no—
253Dic22—24no—
254Dic22—22no—
255Dic22—24no—
256Dic22—24no—
257Dic22—416no—
258Dic22—44no—
259Dic22C2×#4114yes—
260C11⋊C8—22no—
261C11⋊C8—22no—
262C11⋊C8—24no—
263C23×Q8—112no—
264C22×SD16—111no—
265C22×SD16—112no—
266C22×M16—112no—
267#555—24no—
268#555C2×D1118yes—
269D4×Q8—118no—
270D4×Q8—224no—
271C2×C4⋊Q8—111no—
272C2×C4⋊Q8—221no—
273C2×C4⋊Q8C2×D1111yescharacteristic
274C2×#124—22no—
275C2×C22⋊Q8—112no—
276C2×C22⋊Q8—222no—
277C2×#121—21no—
278C2×#121C2×D1112yes—
279C2×C4×Q8—111no—
280C2×C4×D4—221no—
281C2×C4×D4C2×D1111yescharacteristic
282C2×C4×D4C2×D1111yescharacteristic
283C2×#117—21no—
284C2×#117C2×D1112yes—
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—42no—
310C22×C11—42no—
311C22×C11—42no—
312C22×C11—84no—
313C22×C11#54612yes—
314C22×C11C2×#13712yes—
315C22×C11#57712yes—
316C22×C11C23×D411yescharacteristic
317C4×C11—24no—
318C4×C11—22no—
319C4×C11—42no—
320C4×C11—44no—
321C4×C11#54612yes—
322C4×C11C2×#13714yes—
323C4×C11C22×#4111yescharacteristic
324C4×C11C2×H(5,𝔽2)11yescharacteristic
325Dic11—24no—
326Dic11—44no—
327Dic11—42no—
328C22×Q8—21no—
329C22×Q8—111no—
330C22×Q8—112no—
331C22×Q8—118no—
332C22×Q8—228no—
333C22×Q8—222no—
334C22×Q8—224no—
335C22×Q8—444no—
336C22×D4—22no—
337C22×D4C22⋊D1111yescharacteristic
338C22×D4C22×D1111yescharacteristic
339C23×C4—21no—
340C23×C4—222no—
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—22no—
352C4⋊Q8—114no—
353C4⋊Q8—228no—
354C4⋊Q8—222no—
355C4⋊Q8C22×D1114yes—
356#124—216no—
357C22⋊Q8—118no—
358C22⋊Q8—224no—
359C22⋊Q8—2216no—
360#121—28no—
361#121—24no—
362#121C22×D1118yes—
363C4×Q8—114no—
364C4×Q8—222no—
365C4×D4—22no—
366C4×D4—228no—
367C4×D4C22⋊D1114yes—
368C4×D4C22×D1114yes—
369C4×D4C22×D1114yes—
370#117—24no—
371#117—28no—
372#117C22×D1118yes—
373C2×C4⋊C4—21no—
374C2×C4⋊C4—111no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—222no—
378C2×C4⋊C4—221no—
379C2×C4⋊C4C22⋊D1111yescharacteristic
380C2×C4⋊C4C22×D1111yescharacteristic
381C2×C4⋊C4C22×D1112yes—
382C2×C22⋊C4—22no—
383C2×C22⋊C4—22no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—222no—
386C2×C22⋊C4C22⋊D1112yes—
387C2×C42—22no—
388C2×C42—221no—
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—82no—
403C2×C11#332914yescomplemented
404C2×C11C2×#54611yescharacteristic
405C2×C11C22×#13711yescharacteristic
406C2×C11C2×#57711yescharacteristic
407C24—21no—
408C24C2×C22⋊D1112yes—
409C2×Q8—24no—
410C2×Q8—82no—
411C2×Q8—114no—
412C2×Q8—112no—
413C2×Q8—114no—
414C2×Q8—2216no—
415C2×Q8—222no—
416C2×Q8—221no—
417C2×Q8—228no—
418C2×Q8—222no—
419C2×Q8—224no—
420C2×Q8—224no—
421C2×Q8—448no—
422C2×Q8—448no—
423C2×Q8—4416no—
424C2×D4—28no—
425C2×D4—24no—
426C2×D4—22no—
427C2×D4—22no—
428C2×D4—21no—
429C2×D4—84no—
430C2×D4C2×C22⋊D1114yes—
431C2×D4C23×D1112yes—
432C22×C4—24no—
433C22×C4—24no—
434C22×C4—21no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—44no—
438C22×C4—221no—
439C22×C4—228no—
440C22×C4—221no—
441C22×C4—222no—
442C22×C4—448no—
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—21no—
460C4⋊C4—22no—
461C4⋊C4—112no—
462C4⋊C4—221no—
463C4⋊C4—224no—
464C4⋊C4—224no—
465C4⋊C4—228no—
466C4⋊C4—224no—
467C4⋊C4C2×C22⋊D1114yes—
468C4⋊C4C23×D1112yes—
469C4⋊C4C23×D1114yes—
470C22⋊C4—28no—
471C22⋊C4—28no—
472C22⋊C4—24no—
473C22⋊C4—228no—
474C22⋊C4C2×C22⋊D1118yes—
475C42—28no—
476C42—224no—
477C42C2×C22⋊D1112yes—
478C42C23×D1112yes—
479C11C2×#332911yescharacteristic, complemented, Sylow
480C23—24no—
481C23—24no—
482C23—24no—
483C23—22no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23C22×C22⋊D1114yes—
488C23C22×C22⋊D1111yescharacteristic
489Q8—84no—
490Q8—114no—
491Q8—224no—
492Q8—222no—
493Q8—224no—
494Q8—224no—
495Q8—4416no—
496Q8—444no—
497D4—28no—
498D4—22no—
499D4—22no—
500D4—42no—
501D4—88no—
502C2×C4—24no—
503C2×C4—22no—
504C2×C4—28no—
505C2×C4—24no—
506C2×C4—24no—
507C2×C4—22no—
508C2×C4—24no—
509C2×C4—42no—
510C2×C4—44no—
511C2×C4—48no—
512C2×C4—224no—
513C2×C4—222no—
514C2×C4—222no—
515C2×C4—224no—
516C2×C4—4416no—
517C2×C4—444no—
518C2×C4—442no—
519C2×C4#6700414yes—
520C2×C4#41×D1112yes—
521C2×C4#6704212yes—
522C2×C4C22×C22⋊D1114yes—
523C2×C4C22×C22⋊D1112yes—
524C2×C4C22×C22⋊D1112yes—
525C2×C4C22×C22⋊D1111yescharacteristic
526C2×C4C24×D1111yescharacteristic
527C8—222no—
528C8—222no—
529C8—224no—
530C22—24no—
531C22—24no—
532C22—24no—
533C22—48no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—84no—
538C22C2×#6700412yes—
539C22#1062336012yes—
540C22#1062336712yes—
541C22C23×C22⋊D1111yescharacteristic
542C4—24no—
543C4—22no—
544C4—42no—
545C4—44no—
546C4—224no—
547C4—444no—
548C4—442no—
549C4C2×#6700414yes—
550C4#1062336012yes—
551C4C2×#41×D1111yescharacteristic
552C4C2×#6704211yescharacteristic
553C2—44no—
554C2—82no—
555C2#1308090414yesdirect product factor
556C2C2×#1062336011yescharacteristic
557C2C22×#6700411yescharacteristic
558C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#555C2
socleC23×C11C22×D4
hypercenterC2×#555D11
hypocenterC11C2×#3329
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#555

Complements

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

NH ≅ G/Ntype
1. C2×D4×Dic22C2semidirect
2. #13080904C2direct (N × H)
3. C2×#10622706C2semidirect
4. C2×#10622609C2semidirect
5. C2×#10622704C2semidirect
6. C2×#10622655C2semidirect
7. C2×#10622632C2semidirect
8. C2×#10622653C2semidirect
9. C2×C4×#4324C2semidirect
10. C2×#10622625C2semidirect
11. C2×#10622617C2semidirect
30. D4×Dic22C22semidirect
37. #10622706C22semidirect
38. #10622704C22semidirect
39. #10622655C22semidirect
40. #10622653C22semidirect
41. #10622632C22semidirect
42. C4×#4324C22semidirect
43. #10622625C22semidirect
44. #10622617C22semidirect
45. #10622609C22semidirect
403. C2×C11#3329semidirect
479. C11C2×#3329semidirect
555. C2#13080904direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Dic222
#130809042
C2×#106227062
C2×#106226092
C2×#106227042
C2×#106226552
C2×#106226322
C2×#106226532
C2×C4×#43242
C2×#106226252
C2×#106226172
C2×C11×#5552
C2×#332911