Finite Group Databasebeta

← C2×#13081004 #15632230

Subgroups — C2×#13081004 #15632230

Order 2816.

1942 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623074C211yesmaximal, characteristic
2#13081004C2116yesmaximal, direct product factor
3C2×#10622691C211yesmaximal, characteristic, complemented
4C2×#10622583C212yesmaximal, complemented
5C2×#10622657C212yesmaximal, complemented
6C2×#10622634C211yesmaximal, characteristic, complemented
7C2×#10622704C211yesmaximal, characteristic, complemented
8C2×#10622664C212yesmaximal, complemented
9C2×C4×#4326C211yesmaximal, characteristic, complemented
10C2×D4×C11⋊C8C211yesmaximal, characteristic
11C22×#66871C212yesmaximal, complemented
12C2×C11×#554C211yesmaximal, characteristic
13C11×#554—24no—
14C11×#554C2218yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—21no—
17C2×C11×C22⋊Q8—22no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C4×Q8×C11C2211yescharacteristic
20C2×C4×D4×C11—21no—
21C2×C4×D4×C11C2211yescharacteristic
22C22×C11×C4⋊C4C2212yes—
23C22×#4326C2211yescharacteristic
24C2×D4×Dic11—21no—
25C22×C4⋊Dic11C2212yes—
26C2×#66977C2212yes—
27C23×C11⋊C8C2212yes—
28#10623074—24no—
29#10623074C2218yes—
30C2×#66943—21no—
31C2×#66931—22no—
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C2×#66899C2212yes—
35C2×#66899C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2212yes—
37#10622704C2218yescomplemented
38#10622691C2218yescomplemented
39#10622664C22116yescomplemented
40#10622657C22116yescomplemented
41C4×#4326C2218yescomplemented
42#10622634C2218yescomplemented
43D4×C11⋊C8C2218yes—
44#10622583C22116yescomplemented
45C2×#66874C2212yes—
46C2×#66874C2211yescharacteristic
47C2×#66871C2212yes—
48C2×#66871C2212yes—
49C2×#66871C2212yes—
50C2×#66871C2212yes—
51C2×#66871C2211yescharacteristic
52C2×#66871C22116yescomplemented
53C2×C4⋊(C11⋊C8)C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55C22×Q8×C11—21no—
56C22×Q8×C11C2311yescharacteristic
57C22×D4×C11D411yescharacteristic
58C23×C4×C11—22no—
59C23×C4×C11C2312yes—
60C23×Dic11—22no—
61C22×Dic22—21no—
62C22×Dic22C2311yescharacteristic
63C11×C4⋊Q8—22no—
64C11×C4⋊Q8C2314yes—
65C11×#125—28no—
66C11×C22⋊Q8—24no—
67C11×C22⋊Q8—216no—
68C11×C22⋊Q8C2318yes—
69C4×Q8×C11—22no—
70C4×Q8×C11C2314yes—
71C4×D4×C11—28no—
72C4×D4×C11D414yes—
73C4×D4×C11C2314yes—
74C2×C11×C4⋊C4—22no—
75C2×C11×C4⋊C4—24no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—22no—
79C2×C11×C4⋊C4D411yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2312yes—
82C2×C11×C4⋊C4C2318yes—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4D412yes—
85C2×C42×C11—21no—
86C2×C42×C11C2311yescharacteristic
87C2×C22⋊Dic11—22no—
88C2×#4326—24no—
89C2×#4326C2314yes—
90D4×Dic11—28no—
91C2×C4⋊Dic11—21no—
92C2×C4⋊Dic11—22no—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11C2311yescharacteristic
95C2×C4⋊Dic11C2312yes—
96C2×C4⋊Dic11C2318yes—
97#66977—24no—
98#66977C2318yes—
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—22no—
101C2×C4×Dic11—21no—
102C22×C11⋊C8—28no—
103C22×C11⋊C8C2311yescharacteristic
104C22×C11⋊C8C2312yes—
105C22×C11⋊C8C2318yes—
106C22×C11⋊C8C2311yescharacteristic
107#66943—28no—
108#66931—216no—
109#66922—22no—
110#66922C2314yes—
111C4×Dic22—22no—
112C4×Dic22C2314yes—
113#66899C2318yes—
114#66899C2314yes—
115C22⋊(C11⋊C8)C2318yes—
116#66874C2314yes—
117#66874C2318yes—
118#66871C2314yes—
119#66871C2318yes—
120#66871C2318yes—
121#66871C2318yes—
122#66871C2318yes—
123C4⋊(C11⋊C8)C2314yes—
124C4×C11⋊C8C2314yes—
125C2×#3338—111nomaximal, Sylow
126C24×C11C2×D412yes—
127C2×Q8×C11—21no—
128C2×Q8×C11—24no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—82no—
132C2×Q8×C11C2412yes—
133C2×D4×C11Q1618yescomplemented
134C2×D4×C11C2×D414yes—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—21no—
138C22×C4×C11—21no—
139C22×C4×C11—22no—
140C22×C4×C11—28no—
141C22×C4×C11—84no—
142C22×C4×C11C2×D412yes—
143C22×C4×C11C2×D411yescharacteristic
144C22×C4×C11C2×D414yes—
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2414yes—
147C22×C4×C11C2411yescharacteristic
148C22×Dic11—21no—
149C22×Dic11—21no—
150C22×Dic11—22no—
151C22×Dic11—28no—
152C22×Dic11—84no—
153C2×Dic22—21no—
154C2×Dic22—24no—
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—82no—
158C2×Dic22C2412yes—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—28no—
161C11×C4⋊C4—22no—
162C11×C4⋊C4—24no—
163C11×C4⋊C4—24no—
164C11×C4⋊C4—28no—
165C11×C4⋊C4C2×D414yes—
166C11×C4⋊C4C2412yes—
167C11×C4⋊C4C2414yes—
168C11×C22⋊C4—28no—
169C11×C22⋊C4C2×D418yes—
170C42×C11—24no—
171C42×C11C2×D412yes—
172C42×C11C2412yes—
173C22⋊Dic11—28no—
174#4326—28no—
175C4⋊Dic11—21no—
176C4⋊Dic11—22no—
177C4⋊Dic11—24no—
178C4⋊Dic11—28no—
179C4⋊Dic11C2412yes—
180C4⋊Dic11C2414yes—
181Dic11⋊C4—24no—
182Dic11⋊C4—28no—
183C4×Dic11—24no—
184C2×C11⋊C8—216no—
185C2×C11⋊C8—24no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8#4114yes—
188C2×C11⋊C8C2412yes—
189C2×C11⋊C8C2414yes—
190C2×C11⋊C8C2412yes—
191C2×#554—111no—
192C2×#554D1111yescharacteristic
193#3338—1116no—
194C2×#500—111no—
195C2×#484—112no—
196C2×#484—112no—
197C2×#477—111no—
198C2×#477—111no—
199C2×#467—112no—
200C2×C4×Q16—111no—
201C2×C8×D4—111no—
202C22×#107—112no—
203C23×C11—24no—
204C23×C11—24no—
205C23×C11C2×Q1618yes—
206C23×C11C22×D414yes—
207C23×C11C22×D411yescharacteristic
208Q8×C11—22no—
209Q8×C11—22no—
210Q8×C11—42no—
211Q8×C11—84no—
212D4×C11C2×Q16116yescomplemented
213C2×C4×C11—24no—
214C2×C4×C11—22no—
215C2×C4×C11—28no—
216C2×C4×C11—24no—
217C2×C4×C11—24no—
218C2×C4×C11—22no—
219C2×C4×C11—22no—
220C2×C4×C11—24no—
221C2×C4×C11—42no—
222C2×C4×C11—42no—
223C2×C4×C11—44no—
224C2×C4×C11—88no—
225C2×C4×C11C2×Q1614yes—
226C2×C4×C11C22×D414yes—
227C2×C4×C11C22×D412yes—
228C2×C4×C11C22×D411yescharacteristic
229C2×C4×C11C22×D412yes—
230C2×C4×C11C2×#4112yes—
231C2×C4×C112−1+412yes—
232C2×C4×C11C2511yescharacteristic
233C2×Dic11—22no—
234C2×Dic11—22no—
235C2×Dic11—24no—
236C2×Dic11—42no—
237C2×Dic11—44no—
238C2×Dic11—42no—
239C2×Dic11—88no—
240Dic22—22no—
241Dic22—22no—
242Dic22—42no—
243Dic22—84no—
244C11⋊C8—24no—
245C11⋊C8—22no—
246C11⋊C8C2×#4114yes—
247C22×Q16—111no—
248C23×C8—112no—
249#554—24no—
250#554—118no—
251#554—224no—
252#554C2×D1118yes—
253C2×C4⋊Q8—111no—
254C2×C4⋊Q8C2×D1111yescharacteristic
255C2×#125—21no—
256C2×#125—221no—
257C2×C22⋊Q8—22no—
258C2×C22⋊Q8—112no—
259C2×C22⋊Q8—222no—
260C2×C22⋊Q8C2×D1112yes—
261C2×C4×Q8—111no—
262C2×C4×Q8C2×D1111yescharacteristic
263C2×C4×D4—21no—
264C2×C4×D4—221no—
265C2×C4×D4C2×D1111yescharacteristic
266C22×C4⋊C4—112no—
267C22×C4⋊C4C2×D1112yes—
268#500—118no—
269#484—1116no—
270#484—1116no—
271#477—118no—
272#477—118no—
273#467—1116no—
274C4×Q16—118no—
275C8×D4—118no—
276C2×#107—112no—
277C2×#107—112no—
278C2×#107—1116no—
279C2×#107—112no—
280C2×#107—112no—
281C2×#107—111no—
282C2×C4⋊C8—111no—
283C2×#103—112no—
284C2×#103—111no—
285C2×#103—112no—
286C2×#103—111no—
287C2×C22⋊C8—112no—
288C2×C4×C8—111no—
289C22×C11—216no—
290C22×C11—24no—
291C22×C11—24no—
292C22×C11#54712yes—
293C22×C11C22×Q1618yes—
294C22×C11C22×Q1612yes—
295C22×C11#57612yes—
296C22×C11C23×D411yescharacteristic
297C4×C11—24no—
298C4×C11—22no—
299C4×C11—42no—
300C4×C11—42no—
301C4×C11—44no—
302C4×C11#54712yes—
303C4×C11C22×Q1614yes—
304C4×C11C22×#4111yescharacteristic
305C4×C11C2×2−1+411yescharacteristic
306Dic11—42no—
307Dic11—44no—
308Dic11—42no—
309C22×Q8—21no—
310C22×Q8—111no—
311C22×Q8—221no—
312C22×Q8C22×D1111yescharacteristic
313C22×D4C22⋊D1111yescharacteristic
314C23×C4—22no—
315C23×C4—222no—
316C23×C4C22×D1112yes—
317C2×Q16—114no—
318C2×Q16—224no—
319C22×C8—111no—
320C22×C8—112no—
321C22×C8—118no—
322C22×C8—111no—
323C22×C8—228no—
324C4⋊Q8—22no—
325C4⋊Q8—114no—
326C4⋊Q8—222no—
327C4⋊Q8C22×D1114yes—
328#125—28no—
329#125—228no—
330C22⋊Q8—24no—
331C22⋊Q8—216no—
332C22⋊Q8—118no—
333C22⋊Q8—224no—
334C22⋊Q8—2216no—
335C22⋊Q8C22×D1118yes—
336C4×Q8—22no—
337C4×Q8—114no—
338C4×Q8—222no—
339C4×Q8C22×D1114yes—
340C4×D4—28no—
341C4×D4—228no—
342C4×D4C22⋊D1114yes—
343C4×D4C22×D1114yes—
344C2×C4⋊C4—22no—
345C2×C4⋊C4—24no—
346C2×C4⋊C4—21no—
347C2×C4⋊C4—21no—
348C2×C4⋊C4—22no—
349C2×C4⋊C4—111no—
350C2×C4⋊C4—112no—
351C2×C4⋊C4—118no—
352C2×C4⋊C4—222no—
353C2×C4⋊C4—224no—
354C2×C4⋊C4—221no—
355C2×C4⋊C4—221no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4C22⋊D1111yescharacteristic
358C2×C4⋊C4C22×D1111yescharacteristic
359C2×C4⋊C4C22×D1112yes—
360C2×C4⋊C4C22×D1118yes—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4C22⋊D1112yes—
364C2×C42—21no—
365C2×C42—221no—
366C2×C42C22×D1111yescharacteristic
367#107—114no—
368#107—118no—
369#107—118no—
370#107—118no—
371#107—118no—
372C4⋊C8—114no—
373#103—114no—
374#103—118no—
375#103—114no—
376#103—118no—
377C22⋊C8—118no—
378C4×C8—114no—
379C2×C11—28no—
380C2×C11#333814yescomplemented
381C2×C11C2×#54711yescharacteristic
382C2×C11C23×Q1611yescharacteristic
383C2×C11C2×#57611yescharacteristic
384C24C2×C22⋊D1112yes—
385C2×Q8—21no—
386C2×Q8—24no—
387C2×Q8—22no—
388C2×Q8—22no—
389C2×Q8—82no—
390C2×Q8—112no—
391C2×Q8—221no—
392C2×Q8—224no—
393C2×Q8—222no—
394C2×Q8—222no—
395C2×Q8—882no—
396C2×Q8C23×D1112yes—
397C2×D4#432618yescomplemented
398C2×D4C2×C22⋊D1114yes—
399C22×C4—24no—
400C22×C4—24no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—22no—
404C22×C4—28no—
405C22×C4—84no—
406C22×C4—221no—
407C22×C4—221no—
408C22×C4—222no—
409C22×C4—228no—
410C22×C4—884no—
411C22×C4C2×C22⋊D1114yes—
412C22×C4C2×C22⋊D1111yescharacteristic
413C22×C4C2×C22⋊D1112yes—
414C22×C4C2×C22⋊D1111yescharacteristic
415C22×C4C23×D1114yes—
416C22×C4C23×D1111yescharacteristic
417Q16—228no—
418C2×C8—114no—
419C2×C8—112no—
420C2×C8—112no—
421C2×C8—114no—
422C2×C8—2216no—
423C2×C8—224no—
424C2×C8—222no—
425C4⋊C4—21no—
426C4⋊C4—28no—
427C4⋊C4—22no—
428C4⋊C4—24no—
429C4⋊C4—24no—
430C4⋊C4—28no—
431C4⋊C4—112no—
432C4⋊C4—114no—
433C4⋊C4—221no—
434C4⋊C4—228no—
435C4⋊C4—222no—
436C4⋊C4—224no—
437C4⋊C4—224no—
438C4⋊C4—228no—
439C4⋊C4C2×C22⋊D1114yes—
440C4⋊C4C23×D1112yes—
441C4⋊C4C23×D1114yes—
442C22⋊C4—28no—
443C22⋊C4—228no—
444C22⋊C4C2×C22⋊D1118yes—
445C42—24no—
446C42—224no—
447C42C2×C22⋊D1112yes—
448C42C23×D1112yes—
449C11C2×#333811yescharacteristic, complemented, Sylow
450C23—24no—
451C23—24no—
452C23C2×#432618yes—
453C23C22×C22⋊D1114yes—
454C23C22×C22⋊D1111yescharacteristic
455Q8—22no—
456Q8—22no—
457Q8—42no—
458Q8—84no—
459Q8—222no—
460Q8—222no—
461Q8—442no—
462Q8—884no—
463D4C2×#4326116yescomplemented
464C2×C4—24no—
465C2×C4—22no—
466C2×C4—28no—
467C2×C4—24no—
468C2×C4—24no—
469C2×C4—22no—
470C2×C4—22no—
471C2×C4—24no—
472C2×C4—42no—
473C2×C4—42no—
474C2×C4—44no—
475C2×C4—88no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—224no—
479C2×C4—442no—
480C2×C4—442no—
481C2×C4—444no—
482C2×C4—888no—
483C2×C4C2×#432614yes—
484C2×C4#41×D1112yes—
485C2×C4#6704312yes—
486C2×C4C22×C22⋊D1112yes—
487C2×C4C22×C22⋊D1114yes—
488C2×C4C22×C22⋊D1112yes—
489C2×C4C22×C22⋊D1111yescharacteristic
490C2×C4C24×D1111yescharacteristic
491C8—114no—
492C8—224no—
493C8—222no—
494C22—216no—
495C22—24no—
496C22—24no—
497C22C22×#432618yes—
498C22C22×#432612yes—
499C22#1062335512yes—
500C22#1062336612yes—
501C22C23×C22⋊D1111yescharacteristic
502C4—24no—
503C4—22no—
504C4—42no—
505C4—42no—
506C4—44no—
507C4—442no—
508C4—442no—
509C4—444no—
510C4C22×#432614yes—
511C4#1062335512yes—
512C4C2×#41×D1111yescharacteristic
513C4C2×#6704311yescharacteristic
514C2—28no—
515C2#1308100414yesdirect product factor
516C2C2×#1062335511yescharacteristic
517C2C23×#432611yescharacteristic
518C2C2×#1062336611yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenterC2×#554D11
hypocenterC11C2×#3338
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #13081004C2direct (N × H)
3. C2×#10622691C2semidirect
4. C2×#10622583C2semidirect
5. C2×#10622657C2semidirect
6. C2×#10622634C2semidirect
7. C2×#10622704C2semidirect
8. C2×#10622664C2semidirect
9. C2×C4×#4326C2semidirect
11. C22×#66871C2semidirect
37. #10622704C22semidirect
38. #10622691C22semidirect
39. #10622664C22semidirect
40. #10622657C22semidirect
41. C4×#4326C22semidirect
42. #10622634C22semidirect
44. #10622583C22semidirect
52. C2×#66871C22semidirect
133. C2×D4×C11Q16semidirect
212. D4×C11C2×Q16semidirect
380. C2×C11#3338semidirect
397. C2×D4#4326semidirect
449. C11C2×#3338semidirect
463. D4C2×#4326semidirect
515. C2#13081004direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230742
#130810042
C2×#106226912
C2×#106225832
C2×#106226572
C2×#106226342
C2×#106227042
C2×#106226642
C2×C4×#43262
C2×D4×C11⋊C82
C22×#668712
C2×C11×#5542
C2×#333811