Finite Group Databasebeta

← C2×#13081515 #15634250

Subgroups — C2×#13081515 #15634250

Order 2816.

2082 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×Q8×D44C211yesmaximal, characteristic, complemented
2#13081515C2116yesmaximal, direct product factor
3C2×#10622678C212yesmaximal, complemented
4C2×#10622692C211yesmaximal, characteristic, complemented
5C2×#10622679C212yesmaximal, complemented
6C2×#10622621C212yesmaximal, complemented
7C2×#10622697C211yesmaximal, characteristic, complemented
8C2×#10622620C211yesmaximal, characteristic, complemented
9C2×#10622637C211yesmaximal, characteristic, complemented
10C2×#10622627C212yesmaximal
11C2×C4×#4323C211yesmaximal, characteristic
12C2×C11×#554C211yesmaximal, characteristic, complemented
13C22×Q8×D11—21no—
14C11×#554—24no—
15C11×#554C2218yescomplemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×#125C2212yes—
18C2×C11×C22⋊Q8—21no—
19C2×C11×C22⋊Q8—22no—
20C2×C4×Q8×C11C2211yescharacteristic
21C2×C4×D4×C11C2211yescharacteristic
22C2×C4×D4×C11C2212yes—
23C22×C11×C4⋊C4—21no—
24C22×#4323C2211yescharacteristic
25Q8×D44—24no—
26Q8×D44C2218yescomplemented
27C2×#66950—21no—
28C2×#66950—22no—
29C2×C4×D44C2211yescharacteristic
30C2×C4×D44C2212yes—
31C2×#66922C2211yescharacteristic
32C2×#66922C2212yes—
33C2×#66896C2212yes—
34C2×#66896C2211yescharacteristic
35#10622697C2218yescomplemented
36#10622692C2218yescomplemented
37#10622679C22116yescomplemented
38#10622678C22116yescomplemented
39#10622637C2218yescomplemented
40#10622627C22116yes—
41C4×#4323C2218yes—
42#10622621C22116yescomplemented
43#10622620C2218yescomplemented
44C2×#66873C2212yes—
45C2×#66873C2211yescharacteristic
46C2×#66872C2212yes—
47C2×#66872C2212yes—
48C2×#66872C2212yes—
49C2×#66871C2212yes—
50C2×#66871C2211yescharacteristic
51C2×C4⋊(C11⋊C8)C2211yescharacteristic
52C2×C4⋊(C11⋊C8)C2212yes—
53C2×#66867C2212yes—
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—21no—
56C22×Q8×C11D411yescharacteristic
57C22×D4×C11C2311yescharacteristic
58C23×C4×C11—21no—
59C23×C4×C11—22no—
60C2×Q8×D11—28no—
61C2×Q8×D11—48no—
62C22×D44C2311yescharacteristic
63C22×C4×D11—22no—
64C22×C4×D11—21no—
65C22×Dic22—22no—
66C22×Dic22—21no—
67C11×C4⋊Q8—22no—
68C11×C4⋊Q8C2314yes—
69C11×#125—24no—
70C11×#125C2318yes—
71C11×C22⋊Q8—28no—
72C11×C22⋊Q8—216no—
73C4×Q8×C11D414yes—
74C4×Q8×C11C2314yes—
75C4×D4×C11—24no—
76C4×D4×C11—22no—
77C4×D4×C11C2314yes—
78C4×D4×C11C2318yes—
79C2×C11×C4⋊C4—22no—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—22no—
82C2×C11×C4⋊C4—28no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C4⋊C4D412yes—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—22no—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2312yes—
91C2×#4323Q818yescomplemented
92C2×#4323C2314yes—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—22no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—22no—
97C2×C4⋊Dic11C2312yes—
98C2×C4⋊Dic11C2311yescharacteristic
99C22×C11⋊C8C2311yescharacteristic
100C22×C11⋊C8C2312yes—
101C22×C11⋊C8C2311yescharacteristic
102#66950—28no—
103#66950—216no—
104C4×D44—24no—
105C4×D44—22no—
106C4×D44C2314yes—
107C4×D44C2318yes—
108#66922—24no—
109#66922—22no—
110#66922C2314yes—
111#66922C2318yes—
112#66896C2318yes—
113#66896C2314yes—
114#66873C2314yes—
115#66873C2318yes—
116#66872C2318yes—
117#66872C2318yes—
118#66872C2318yes—
119#66871C2318yes—
120#66871C2314yes—
121C4⋊(C11⋊C8)C2314yes—
122C4⋊(C11⋊C8)C2318yes—
123#66867C2318yes—
124C4×C11⋊C8C2314yes—
125C2×#3384—111nomaximal, Sylow
126C24×C11—21no—
127C23×D11—21no—
128C2×Q8×C11—24no—
129C2×Q8×C11—24no—
130C2×Q8×C11—82no—
131C2×Q8×C11C2×D414yes—
132C2×D4×C11—21no—
133C2×D4×C11—22no—
134C2×D4×C11C2×Q814yescomplemented
135C2×D4×C11C2412yes—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11—28no—
140C22×C4×C11—44no—
141C22×C4×C11—84no—
142C22×C4×C11C2×D411yescharacteristic
143C22×C4×C11C2×D412yes—
144C22×C4×C11C2×D412yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2411yescharacteristic
147C22×Dic11—21no—
148C22×Dic11—22no—
149Q8×D11—432no—
150C2×D44—21no—
151C2×D44—22no—
152C2×D44C2×Q814yes—
153C2×D44C2412yes—
154C2×C4×D11—28no—
155C2×C4×D11—24no—
156C2×C4×D11—48no—
157C2×C4×D11—44no—
158C2×Dic22—28no—
159C2×Dic22—24no—
160C2×Dic22—48no—
161C2×Dic22—44no—
162C11×C4⋊C4—28no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—28no—
165C11×C4⋊C4—21no—
166C11×C4⋊C4—22no—
167C11×C4⋊C4C2×D414yes—
168C11×C4⋊C4C2×D418yes—
169C11×C4⋊C4C2412yes—
170C11×C4⋊C4C2414yes—
171C11×C22⋊C4—24no—
172C11×C22⋊C4—28no—
173C42×C11C2×D414yes—
174C42×C11C2×D412yes—
175C42×C11C2412yes—
176C42×C11C2414yes—
177#4323C2×Q8116yescomplemented
178(C2×D11)⋊C4—24no—
179(C2×D11)⋊C4—28no—
180C4⋊Dic11—21no—
181C4⋊Dic11—22no—
182C4⋊Dic11—24no—
183C4⋊Dic11—28no—
184C4⋊Dic11C2414yes—
185C4⋊Dic11C2412yes—
186C2×C11⋊C8—22no—
187C2×C11⋊C8—24no—
188C2×C11⋊C8C2×Q814yescomplemented
189C2×C11⋊C8C2412yes—
190C2×C11⋊C8C2414yes—
191C2×C11⋊C8C2412yes—
192C2×#554D1111yescharacteristic, complemented
193C2×D4×Q8—111no—
194#3384—1116no—
195C2×#501—112no—
196C2×#498—111no—
197C2×#478—112no—
198C2×#476—111no—
199C2×#476—112no—
200C2×#474—111no—
201C2×#446—111no—
202C2×#442—112no—
203C2×C4×D8—111no—
204C23×C11—24no—
205C23×C11—22no—
206C23×C11—42no—
207C23×C11—42no—
208C23×C11C22×D411yescharacteristic
209C22×D11—24no—
210C22×D11—22no—
211C22×D11—42no—
212C22×D11—42no—
213Q8×C11—28no—
214Q8×C11—84no—
215D4×C11—24no—
216D4×C11—22no—
217D4×C11C22×Q814yescomplemented
218C2×C4×C11—24no—
219C2×C4×C11—24no—
220C2×C4×C11—22no—
221C2×C4×C11—22no—
222C2×C4×C11—24no—
223C2×C4×C11—42no—
224C2×C4×C11—44no—
225C2×C4×C11—48no—
226C2×C4×C11—88no—
227C2×C4×C11AGL(1,ℤ/8)14yes—
228C2×C4×C11C22×D412yes—
229C2×C4×C11C22×D414yes—
230C2×C4×C11C22×D414yes—
231C2×C4×C11C22×D411yescharacteristic
232C2×C4×C11C22×D412yes—
233C2×C4×C11C22×Q812yes—
234C2×C4×C112−1+412yes—
235C2×C4×C11C2511yescharacteristic
236C2×Dic11—22no—
237C2×Dic11—24no—
238C2×Dic11—42no—
239C2×Dic11—44no—
240D44—24no—
241D44—22no—
242D44C22×Q814yes—
243C4×D11—416no—
244C4×D11—48no—
245Dic22—416no—
246Dic22—48no—
247C11⋊C8—22no—
248C11⋊C8—24no—
249C11⋊C8C22×Q814yescomplemented
250C23×Q8—221no—
251C22×D8—111no—
252#554—24no—
253#554C2×D1118yescomplemented
254D4×Q8—118no—
255D4×Q8—224no—
256C2×C4⋊Q8—111no—
257C2×C4⋊Q8—112no—
258C2×C4⋊Q8C2×D1111yescharacteristic
259C2×#125C2×D1112yes—
260C2×C22⋊Q8—21no—
261C2×C22⋊Q8—22no—
262C2×C22⋊Q8—221no—
263C2×C22⋊Q8—222no—
264C2×C4×Q8C2×D1111yescharacteristic
265C2×C4×D4—112no—
266C2×C4×D4—111no—
267C2×C4×D4C2×D1111yescharacteristic
268C2×C4×D4C2×D1112yes—
269C22×C4⋊C4—21no—
270#501—1116no—
271#498—118no—
272#478—1116no—
273#476—118no—
274#476—1116no—
275#474—118no—
276#446—118no—
277#442—1116no—
278C4×D8—118no—
279C2×#107—112no—
280C2×#107—111no—
281C2×#106—112no—
282C2×#106—112no—
283C2×#106—112no—
284C2×C4⋊C8—112no—
285C2×C4⋊C8—111no—
286C2×#102—111no—
287C2×#102—112no—
288C2×#102—111no—
289C2×#102—112no—
290C2×#97—112no—
291C2×C4×C8—111no—
292C22×C11—24no—
293C22×C11—48no—
294C22×C11—42no—
295C22×C11—42no—
296C22×C11D4×Q812yes—
297C22×C11C2×AGL(1,ℤ/8)12yes—
298C22×C11#57712yes—
299C22×C11C23×D411yescharacteristic
300C2×D11—24no—
301C2×D11—48no—
302C2×D11—42no—
303C2×D11—42no—
304C4×C11—24no—
305C4×C11—24no—
306C4×C11—22no—
307C4×C11—42no—
308C4×C11—44no—
309C4×C11D4×Q812yes—
310C4×C11C2×AGL(1,ℤ/8)14yes—
311C4×C11C23×Q811yescharacteristic
312C4×C11C2×2−1+411yescharacteristic
313Dic11—42no—
314Dic11—44no—
315C22×Q8—21no—
316C22×Q8—228no—
317C22×Q8—222no—
318C22×Q8—221no—
319C22×Q8—448no—
320C22×Q8C22⋊D1111yescharacteristic
321C22×D4—111no—
322C22×D4C22×D1111yescharacteristic
323C23×C4—21no—
324C23×C4—22no—
325C23×C4—222no—
326C23×C4—221no—
327C2×D8—118no—
328C2×D8—114no—
329C22×C8—111no—
330C22×C8—111no—
331C22×C8—112no—
332C4⋊Q8—22no—
333C4⋊Q8—114no—
334C4⋊Q8—118no—
335C4⋊Q8—224no—
336C4⋊Q8—222no—
337C4⋊Q8C22×D1114yes—
338#125—24no—
339#125C22×D1118yes—
340C22⋊Q8—28no—
341C22⋊Q8—216no—
342C22⋊Q8—228no—
343C22⋊Q8—2216no—
344C4×Q8C22⋊D1114yes—
345C4×Q8C22×D1114yes—
346C4×D4—24no—
347C4×D4—22no—
348C4×D4—114no—
349C4×D4—118no—
350C4×D4—224no—
351C4×D4—222no—
352C4×D4C22×D1114yes—
353C4×D4C22×D1118yes—
354C2×C4⋊C4—22no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4—22no—
357C2×C4⋊C4—28no—
358C2×C4⋊C4—112no—
359C2×C4⋊C4—111no—
360C2×C4⋊C4—221no—
361C2×C4⋊C4—222no—
362C2×C4⋊C4C22⋊D1111yescharacteristic
363C2×C4⋊C4C22⋊D1112yes—
364C2×C4⋊C4C22×D1111yescharacteristic
365C2×C4⋊C4C22×D1112yes—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—22no—
368C2×C22⋊C4—221no—
369C2×C22⋊C4—222no—
370C2×C42C22×D1112yes—
371C2×C42C22×D1111yescharacteristic
372#107—114no—
373#107—118no—
374#106—118no—
375#106—118no—
376#106—118no—
377C4⋊C8—114no—
378C4⋊C8—118no—
379#102—114no—
380#102—118no—
381#102—114no—
382#102—118no—
383#97—118no—
384C4×C8—114no—
385C2×C11—44no—
386C2×C11#338414yescomplemented
387C2×C11C2×D4×Q811yescharacteristic
388C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
389C2×C11C2×#57711yescharacteristic
390D11—44no—
391C24—21no—
392C24—221no—
393C2×Q8—24no—
394C2×Q8—24no—
395C2×Q8—82no—
396C2×Q8—228no—
397C2×Q8—224no—
398C2×Q8—448no—
399C2×Q8—4432no—
400C2×Q8—444no—
401C2×Q8C2×C22⋊D1114yes—
402C2×D4—22no—
403C2×D4—21no—
404C2×D4—114no—
405C2×D4—112no—
406C2×D4—222no—
407C2×D4—221no—
408C2×D4Q8×D1114yescomplemented
409C2×D4C23×D1112yes—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—24no—
413C22×C4—28no—
414C22×C4—44no—
415C22×C4—84no—
416C22×C4—222no—
417C22×C4—221no—
418C22×C4—228no—
419C22×C4—224no—
420C22×C4—448no—
421C22×C4—444no—
422C22×C4C2×C22⋊D1111yescharacteristic
423C22×C4C2×C22⋊D1112yes—
424C22×C4C2×C22⋊D1112yes—
425C22×C4C2×C22⋊D1111yescharacteristic
426C22×C4C23×D1111yescharacteristic
427D8—1116no—
428C2×C8—114no—
429C2×C8—112no—
430C2×C8—112no—
431C2×C8—114no—
432C2×C8—222no—
433C2×C8—224no—
434C4⋊C4—28no—
435C4⋊C4—24no—
436C4⋊C4—28no—
437C4⋊C4—21no—
438C4⋊C4—22no—
439C4⋊C4—112no—
440C4⋊C4—114no—
441C4⋊C4—222no—
442C4⋊C4—221no—
443C4⋊C4—224no—
444C4⋊C4—228no—
445C4⋊C4C2×C22⋊D1114yes—
446C4⋊C4C2×C22⋊D1118yes—
447C4⋊C4C23×D1114yes—
448C4⋊C4C23×D1112yes—
449C22⋊C4—24no—
450C22⋊C4—28no—
451C22⋊C4—224no—
452C22⋊C4—228no—
453C42C2×C22⋊D1114yes—
454C42C2×C22⋊D1112yes—
455C42C23×D1112yes—
456C42C23×D1114yes—
457C11C2×#338411yescharacteristic, complemented, Sylow
458C23—24no—
459C23—22no—
460C23—42no—
461C23—42no—
462C23—224no—
463C23—222no—
464C23—442no—
465C23—442no—
466C23C22×C22⋊D1111yescharacteristic
467Q8—28no—
468Q8—84no—
469Q8—4416no—
470Q8—448no—
471D4—24no—
472D4—22no—
473D4—114no—
474D4—224no—
475D4—222no—
476D4C2×Q8×D1114yescomplemented
477C2×C4—24no—
478C2×C4—24no—
479C2×C4—22no—
480C2×C4—22no—
481C2×C4—24no—
482C2×C4—42no—
483C2×C4—44no—
484C2×C4—48no—
485C2×C4—88no—
486C2×C4—224no—
487C2×C4—222no—
488C2×C4—4416no—
489C2×C4—444no—
490C2×C4—442no—
491C2×C4—448no—
492C2×C4#6700214yes—
493C2×C4C2×Q8×D1112yes—
494C2×C4#6704012yes—
495C2×C4C22×C22⋊D1112yes—
496C2×C4C22×C22⋊D1114yes—
497C2×C4C22×C22⋊D1114yes—
498C2×C4C22×C22⋊D1111yescharacteristic
499C2×C4C22×C22⋊D1112yes—
500C2×C4C24×D1111yescharacteristic
501C8—114no—
502C8—222no—
503C8—224no—
504C22—24no—
505C22—48no—
506C22—42no—
507C22—42no—
508C22—224no—
509C22—448no—
510C22—442no—
511C22—442no—
512C22Q8×C22⋊D1112yes—
513C22C2×#6700212yes—
514C22#1062336712yes—
515C22C23×C22⋊D1111yescharacteristic
516C4—24no—
517C4—24no—
518C4—22no—
519C4—42no—
520C4—44no—
521C4—444no—
522C4—442no—
523C4Q8×C22⋊D1112yes—
524C4C2×#6700214yes—
525C4C22×Q8×D1111yescharacteristic
526C4C2×#6704011yescharacteristic
527C2—44no—
528C2—444no—
529C2#1308151514yesdirect product factor
530C2C2×Q8×C22⋊D1111yescharacteristic
531C2C22×#6700211yescharacteristic
532C2C2×#1062336711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#554D11
hypocenterC11C2×#3384
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D44C2semidirect
2. #13081515C2direct (N × H)
3. C2×#10622678C2semidirect
4. C2×#10622692C2semidirect
5. C2×#10622679C2semidirect
6. C2×#10622621C2semidirect
7. C2×#10622697C2semidirect
8. C2×#10622620C2semidirect
9. C2×#10622637C2semidirect
12. C2×C11×#554C2semidirect
15. C11×#554C22semidirect
26. Q8×D44C22semidirect
35. #10622697C22semidirect
36. #10622692C22semidirect
37. #10622679C22semidirect
38. #10622678C22semidirect
39. #10622637C22semidirect
42. #10622621C22semidirect
43. #10622620C22semidirect
91. C2×#4323Q8semidirect
134. C2×D4×C11C2×Q8semidirect
177. #4323C2×Q8semidirect
188. C2×C11⋊C8C2×Q8semidirect
192. C2×#554D11semidirect
217. D4×C11C22×Q8semidirect
249. C11⋊C8C22×Q8semidirect
253. #554C2×D11semidirect
386. C2×C11#3384semidirect
408. C2×D4Q8×D11semidirect
457. C11C2×#3384semidirect
476. D4C2×Q8×D11semidirect
529. C2#13081515direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×D442
#130815152
C2×#106226782
C2×#106226922
C2×#106226792
C2×#106226212
C2×#106226972
C2×#106226202
C2×#106226372
C2×#106226272
C2×C4×#43232
C2×C11×#5542
C2×#338411