Finite Group Databasebeta

← C2×#13081007 #15632233

Subgroups — C2×#13081007 #15632233

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×#10623261C211yesmaximal, characteristic
2C2×#10623110C211yesmaximal, characteristic
3#13081007C2116yesmaximal, direct product factor
4C2×#10622691C211yesmaximal, characteristic, complemented
5C2×#10622497C212yesmaximal, complemented
6C2×#10622422C212yesmaximal, complemented
7C2×#10622463C211yesmaximal, characteristic, complemented
8C2×#10622426C212yesmaximal, complemented
9C2×C4×#4326C211yesmaximal, characteristic, complemented
10C2×#10622447C211yesmaximal, characteristic
11C2×D11×#107C212yesmaximal, complemented
12C2×C11×#477C211yesmaximal, characteristic, complemented
13C2×C11×C4⋊Q8C2211yescharacteristic
14C2×C4×Q8×C11C2211yescharacteristic
15C2×#66999—22no—
16C2×#66999C2212yes—
17C22×#4326C2211yescharacteristic
18C22×C8×D11C2212yes—
19#10623261—24no—
20#10623261C2218yes—
21#10623110—24no—
22#10623110C2218yes—
23C2×#66950C2212yes—
24C2×#66949—22no—
25C2×#66946—21no—
26C2×C4⋊C4×D11C2212yes—
27C2×C4⋊C4×D11C2212yes—
28C2×#66943—21no—
29C2×C4×D44—21no—
30C2×C4×D44C2211yescharacteristic
31C2×#66923—21no—
32C2×#66922C2211yescharacteristic
33C2×C4×Dic22C2211yescharacteristic
34C11×#477C2218yescomplemented
35C2×C11×#107C2212yes—
36C2×C11×C4⋊C8C2211yescharacteristic
37C2×C11×#103C2212yes—
38C2×#66899C2211yescharacteristic
39C2×(C2×D11)⋊C8C2212yes—
40C2×#66882C2212yes—
41C2×#66880C2212yes—
42#10622691C2218yescomplemented
43C4×#4326C2218yescomplemented
44C2×#66874C2211yescharacteristic
45C2×#66871C2212yes—
46C2×#66871C2212yes—
47C2×#66871C2211yescharacteristic
48C2×C4×C11⋊C8C2211yescharacteristic
49#10622497C22116yescomplemented
50D11×#107C22116yescomplemented
51#10622463C2218yescomplemented
52#10622447C2218yes—
53#10622426C22116yescomplemented
54#10622422C22116yescomplemented
55C22×Q8×C11—21no—
56C22×Q8×C11C2311yescharacteristic
57C22×D44D411yescharacteristic
58C22×C4×D11—22no—
59C22×C4×D11—22no—
60C22×C4×D11C2312yes—
61C22×Dic22—21no—
62C22×Dic22C2311yescharacteristic
63C22×C8×C11C2312yes—
64C11×C4⋊Q8—22no—
65C11×C4⋊Q8C2314yes—
66C4×Q8×C11—22no—
67C4×Q8×C11C2314yes—
68C2×C11×C4⋊C4—21no—
69C2×C11×C4⋊C4—21no—
70C2×C11×C4⋊C4C2311yescharacteristic
71C2×C11×C4⋊C4C2312yes—
72C2×C42×C11—21no—
73C2×C42×C11C2311yescharacteristic
74#66999—24no—
75#66999—216no—
76#66999C2318yes—
77C2×#4326—24no—
78C2×#4326C2314yes—
79C2×(C2×D11)⋊C4—22no—
80C2×(C2×D11)⋊C4—22no—
81C2×(C2×D11)⋊C4D412yes—
82C2×C4⋊Dic11—21no—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11D411yescharacteristic
85C2×C4⋊Dic11C2311yescharacteristic
86C2×C4⋊Dic11C2312yes—
87C2×Dic11⋊C4—21no—
88C2×Dic11⋊C4—22no—
89C2×Dic11⋊C4—22no—
90C2×Dic11⋊C4—22no—
91C2×C4×Dic11—21no—
92C22×C11⋊C8C2311yescharacteristic
93C22×C11⋊C8C2311yescharacteristic
94C2×C8×D11—28no—
95C2×C8×D11C2318yes—
96#66950—24no—
97#66950C2318yes—
98#66949—216no—
99#66946—28no—
100C4⋊C4×D11—24no—
101C4⋊C4×D11—24no—
102C4⋊C4×D11C2318yes—
103C4⋊C4×D11C2318yes—
104#66943—28no—
105C4×D44—28no—
106C4×D44D414yes—
107C4×D44C2314yes—
108#66923—28no—
109#66922—22no—
110#66922C2314yes—
111C4×Dic22—22no—
112C4×Dic22C2314yes—
113C11×#107C2318yes—
114C11×C4⋊C8C2314yes—
115C11×#103C2318yes—
116#66899C2314yes—
117(C2×D11)⋊C8C2318yes—
118#66882C2318yes—
119#66880C2318yes—
120#66874C2314yes—
121#66871C2314yes—
122#66871C2318yes—
123#66871C2318yes—
124C4×C11⋊C8C2314yes—
125C2×#3338—111nomaximal, Sylow
126C23×D11C2×D412yes—
127C2×Q8×C11—21no—
128C2×Q8×C11—24no—
129C2×Q8×C11—22no—
130C2×Q8×C11—22no—
131C2×Q8×C11—82no—
132C2×Q8×C11C2412yes—
133C22×C4×C11—21no—
134C22×C4×C11—21no—
135C22×C4×C11—22no—
136C22×C4×C11C2×D411yescharacteristic
137C22×C4×C11C2×D411yescharacteristic
138C22×C4×C11C2411yescharacteristic
139C22×Dic11—21no—
140C22×Dic11—21no—
141C22×Dic11—22no—
142C22×Dic11C2×D412yes—
143C2×D44Q1618yescomplemented
144C2×D44C2×D414yes—
145C2×C4×D11—28no—
146C2×C4×D11—28no—
147C2×C4×D11—24no—
148C2×C4×D11—24no—
149C2×C4×D11—84no—
150C2×C4×D11—84no—
151C2×C4×D11C2×D414yes—
152C2×C4×D11C2414yes—
153C2×Dic22—21no—
154C2×Dic22—24no—
155C2×Dic22—22no—
156C2×Dic22—22no—
157C2×Dic22—82no—
158C2×Dic22C2412yes—
159C2×C8×C11—24no—
160C2×C8×C11C2414yes—
161C11×C4⋊C4—24no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—22no—
164C11×C4⋊C4—24no—
165C11×C4⋊C4C2414yes—
166C11×C4⋊C4C2412yes—
167C42×C11—24no—
168C42×C11C2×D412yes—
169C42×C11C2412yes—
170#4326—28no—
171(C2×D11)⋊C4—28no—
172(C2×D11)⋊C4—28no—
173(C2×D11)⋊C4C2×D418yes—
174C4⋊Dic11—28no—
175C4⋊Dic11—21no—
176C4⋊Dic11—22no—
177C4⋊Dic11—24no—
178C4⋊Dic11C2×D414yes—
179C4⋊Dic11C2414yes—
180C4⋊Dic11C2412yes—
181Dic11⋊C4—28no—
182Dic11⋊C4—28no—
183Dic11⋊C4—28no—
184Dic11⋊C4—24no—
185C4×Dic11—24no—
186C2×C11⋊C8—22no—
187C2×C11⋊C8#4114yes—
188C2×C11⋊C8C2412yes—
189C2×C11⋊C8C2412yes—
190C8×D11—216no—
191C2×#554—111no—
192C2×#554—111no—
193#3338—1116no—
194C2×#500—111no—
195C2×#484—112no—
196C2×#484—112no—
197C2×#477—111no—
198C2×#477D1111yescharacteristic, complemented
199C2×#467—112no—
200C2×C4×Q16—111no—
201C2×C8×D4—111no—
202C22×#107—112no—
203C23×C11C22×D411yescharacteristic
204C22×D11—24no—
205C22×D11—24no—
206C22×D11C2×Q1618yes—
207C22×D11C22×D414yes—
208Q8×C11—22no—
209Q8×C11—22no—
210Q8×C11—42no—
211Q8×C11—84no—
212C2×C4×C11—22no—
213C2×C4×C11—22no—
214C2×C4×C11—22no—
215C2×C4×C11—24no—
216C2×C4×C11—42no—
217C2×C4×C11—42no—
218C2×C4×C11—44no—
219C2×C4×C11C2×Q1614yes—
220C2×C4×C11C22×D412yes—
221C2×C4×C11C22×D411yescharacteristic
222C2×C4×C11C22×D412yes—
223C2×C4×C11C2×#4112yes—
224C2×C4×C112−1+412yes—
225C2×C4×C11C2511yescharacteristic
226C2×Dic11—24no—
227C2×Dic11—22no—
228C2×Dic11—22no—
229C2×Dic11—24no—
230C2×Dic11—42no—
231C2×Dic11—44no—
232C2×Dic11—42no—
233C2×Dic11C22×D414yes—
234D44C2×Q16116yescomplemented
235C4×D11—28no—
236C4×D11—24no—
237C4×D11—24no—
238C4×D11—88no—
239C4×D11—88no—
240Dic22—22no—
241Dic22—22no—
242Dic22—42no—
243Dic22—84no—
244C8×C11—24no—
245C11⋊C8—22no—
246C11⋊C8C2×#4114yes—
247C22×Q16—111no—
248C23×C8—112no—
249#554—118no—
250#554—118no—
251#554—224no—
252#554—224no—
253C2×C4⋊Q8—111no—
254C2×C4⋊Q8C2×D1111yescharacteristic
255C2×#125—221no—
256C2×#125—221no—
257C2×C22⋊Q8—112no—
258C2×C22⋊Q8—112no—
259C2×C22⋊Q8—222no—
260C2×C22⋊Q8—222no—
261C2×C4×Q8—111no—
262C2×C4×Q8C2×D1111yescharacteristic
263C2×C4×D4—111no—
264C2×C4×D4—221no—
265C2×C4×D4—221no—
266C22×C4⋊C4—112no—
267C22×C4⋊C4—112no—
268#500—118no—
269#484—1116no—
270#484—1116no—
271#477—118no—
272#477C2×D1118yescomplemented
273#467—1116no—
274C4×Q16—118no—
275C8×D4—118no—
276C2×#107—112no—
277C2×#107—112no—
278C2×#107—112no—
279C2×#107—111no—
280C2×#107—1116no—
281C2×#107C2×D1112yes—
282C2×C4⋊C8C2×D1111yescharacteristic
283C2×#103—111no—
284C2×#103—112no—
285C2×#103—111no—
286C2×#103C2×D1112yes—
287C2×C22⋊C8—112no—
288C2×C4×C8—111no—
289C22×C11#54712yes—
290C22×C11C22×Q1612yes—
291C22×C11#57612yes—
292C22×C11C23×D411yescharacteristic
293C2×D11—216no—
294C2×D11—24no—
295C2×D11—24no—
296C2×D11C22×Q1618yes—
297C4×C11—22no—
298C4×C11—42no—
299C4×C11—44no—
300C4×C11—42no—
301C4×C11#54712yes—
302C4×C11C22×Q1614yes—
303C4×C11C22×#4111yescharacteristic
304C4×C11C2×2−1+411yescharacteristic
305Dic11—24no—
306Dic11—42no—
307Dic11—44no—
308Dic11—42no—
309C22×Q8—21no—
310C22×Q8—111no—
311C22×Q8—221no—
312C22×Q8C22×D1111yescharacteristic
313C22×D4—111no—
314C23×C4—112no—
315C23×C4—222no—
316C23×C4—222no—
317C2×Q16—114no—
318C2×Q16—224no—
319C22×C8—111no—
320C22×C8—111no—
321C22×C8—118no—
322C22×C8—228no—
323C22×C8C22×D1112yes—
324C4⋊Q8—22no—
325C4⋊Q8—114no—
326C4⋊Q8—222no—
327C4⋊Q8C22×D1114yes—
328#125—228no—
329#125—228no—
330C22⋊Q8—118no—
331C22⋊Q8—118no—
332C22⋊Q8—2216no—
333C22⋊Q8—2216no—
334C22⋊Q8—224no—
335C22⋊Q8—224no—
336C4×Q8—22no—
337C4×Q8—114no—
338C4×Q8—222no—
339C4×Q8C22×D1114yes—
340C4×D4—114no—
341C4×D4—114no—
342C4×D4—228no—
343C4×D4—228no—
344C2×C4⋊C4—21no—
345C2×C4⋊C4—21no—
346C2×C4⋊C4—111no—
347C2×C4⋊C4—111no—
348C2×C4⋊C4—112no—
349C2×C4⋊C4—118no—
350C2×C4⋊C4—118no—
351C2×C4⋊C4—224no—
352C2×C4⋊C4—224no—
353C2×C4⋊C4—222no—
354C2×C4⋊C4—222no—
355C2×C4⋊C4—222no—
356C2×C4⋊C4—222no—
357C2×C4⋊C4—221no—
358C2×C4⋊C4—221no—
359C2×C4⋊C4C22×D1111yescharacteristic
360C2×C4⋊C4C22×D1112yes—
361C2×C22⋊C4—112no—
362C2×C22⋊C4—222no—
363C2×C22⋊C4—222no—
364C2×C42—21no—
365C2×C42—221no—
366C2×C42C22×D1111yescharacteristic
367#107—118no—
368#107—114no—
369#107—118no—
370#107—118no—
371#107C22×D1118yes—
372C4⋊C8C22×D1114yes—
373#103—114no—
374#103—118no—
375#103—114no—
376#103C22×D1118yes—
377C22⋊C8—118no—
378C4×C8—114no—
379C2×C11#333814yescomplemented
380C2×C11C2×#54711yescharacteristic
381C2×C11C23×Q1611yescharacteristic
382C2×C11C2×#57611yescharacteristic
383D11—28no—
384C24—112no—
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—118no—
398C2×D4—114no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—22no—
402C22×C4—112no—
403C22×C4—114no—
404C22×C4—114no—
405C22×C4—228no—
406C22×C4—228no—
407C22×C4—224no—
408C22×C4—224no—
409C22×C4—221no—
410C22×C4—221no—
411C22×C4—222no—
412C22×C4—884no—
413C22×C4—884no—
414C22×C4D4×D1111yescharacteristic
415C22×C4D4×D1111yescharacteristic
416C22×C4C23×D1111yescharacteristic
417Q16—228no—
418C2×C8—24no—
419C2×C8—114no—
420C2×C8—112no—
421C2×C8—112no—
422C2×C8—2216no—
423C2×C8—222no—
424C2×C8C23×D1114yes—
425C4⋊C4—24no—
426C4⋊C4—24no—
427C4⋊C4—21no—
428C4⋊C4—22no—
429C4⋊C4—114no—
430C4⋊C4—112no—
431C4⋊C4—114no—
432C4⋊C4—228no—
433C4⋊C4—228no—
434C4⋊C4—228no—
435C4⋊C4—228no—
436C4⋊C4—221no—
437C4⋊C4—222no—
438C4⋊C4—224no—
439C4⋊C4—224no—
440C4⋊C4C23×D1112yes—
441C4⋊C4C23×D1114yes—
442C22⋊C4—118no—
443C22⋊C4—228no—
444C22⋊C4—228no—
445C42—24no—
446C42—224no—
447C42D4×D1112yes—
448C42C23×D1112yes—
449C11C2×#333811yescharacteristic, complemented, Sylow
450C23—118no—
451C23—114no—
452C23—224no—
453C23—224no—
454C23C2×D4×D1111yescharacteristic
455Q8—22no—
456Q8—22no—
457Q8—42no—
458Q8—84no—
459Q8—222no—
460Q8—222no—
461Q8—442no—
462Q8—884no—
463D4—1116no—
464C2×C4—22no—
465C2×C4—22no—
466C2×C4—22no—
467C2×C4—24no—
468C2×C4—42no—
469C2×C4—44no—
470C2×C4—42no—
471C2×C4—114no—
472C2×C4—224no—
473C2×C4—228no—
474C2×C4—224no—
475C2×C4—224no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—224no—
479C2×C4—442no—
480C2×C4—444no—
481C2×C4—442no—
482C2×C4—888no—
483C2×C4—888no—
484C2×C4Q16×D1114yes—
485C2×C4C2×D4×D1112yes—
486C2×C4C2×D4×D1112yes—
487C2×C4C2×D4×D1111yescharacteristic
488C2×C4#6704012yes—
489C2×C4#41×D1112yes—
490C2×C4C24×D1111yescharacteristic
491C8—24no—
492C8—114no—
493C8—222no—
494C22—118no—
495C22—2216no—
496C22—224no—
497C22—224no—
498C22#1062316212yes—
499C22C2×Q16×D1112yes—
500C22#1062330512yes—
501C22C22×D4×D1111yescharacteristic
502C4—22no—
503C4—42no—
504C4—42no—
505C4—44no—
506C4—224no—
507C4—442no—
508C4—442no—
509C4—444no—
510C4#1062316212yes—
511C4C2×Q16×D1114yes—
512C4C2×#6704011yescharacteristic
513C4C2×#41×D1111yescharacteristic
514C2—228no—
515C2#1308100714yesdirect product factor
516C2C2×#1062316211yescharacteristic
517C2C22×Q16×D1111yescharacteristic
518C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#477C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×#477D11
hypocenterC11C2×#3338
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
3. #13081007C2direct (N × H)
4. C2×#10622691C2semidirect
5. C2×#10622497C2semidirect
6. C2×#10622422C2semidirect
7. C2×#10622463C2semidirect
8. C2×#10622426C2semidirect
9. C2×C4×#4326C2semidirect
11. C2×D11×#107C2semidirect
12. C2×C11×#477C2semidirect
34. C11×#477C22semidirect
42. #10622691C22semidirect
43. C4×#4326C22semidirect
49. #10622497C22semidirect
50. D11×#107C22semidirect
51. #10622463C22semidirect
53. #10622426C22semidirect
54. #10622422C22semidirect
143. C2×D44Q16semidirect
198. C2×#477D11semidirect
234. D44C2×Q16semidirect
272. #477C2×D11semidirect
379. C2×C11#3338semidirect
449. C11C2×#3338semidirect
515. C2#13081007direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232612
C2×#106231102
#130810072
C2×#106226912
C2×#106224972
C2×#106224222
C2×#106224632
C2×#106224262
C2×C4×#43262
C2×#106224472
C2×D11×#1072
C2×C11×#4772
C2×#333811