Finite Group Databasebeta

← C2×#13066933 #14719571

Subgroups — C2×#13066933 #14719571

Order 2816.

1826 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
1C22×#66946C211yesmaximal, characteristic
2C2×D11×C22⋊C8C212yesmaximal, complemented
3#13066933C218yesmaximal, direct product factor
4C2×#10622166C211yesmaximal, characteristic, complemented
5C2×#10622106C212yesmaximal, complemented
6C2×C11×#324C211yesmaximal, characteristic, complemented
7C23×D44C411yescharacteristic
8C23×C4×D11C411yescharacteristic
9C23×C4×D11C2211yescharacteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×(C2×D11)⋊C4C411yescharacteristic
12C22×(C2×D11)⋊C4C2211yescharacteristic
13C22×C4×Dic11C411yescharacteristic
14C22×C8×D11—22no—
15C2×#66946—22no—
16C2×#66946—22no—
17C2×#66946—24no—
18C2×#66946C414yes—
19C2×#66946C2214yes—
20C2×C11×C22⋊C8C2212yes—
21C2×C22⋊(C11⋊C8)C2212yes—
22C2×(C2×D11)⋊C8—22no—
23D11×C22⋊C8—24no—
24D11×C22⋊C8C2218yescomplemented
25C11×#324C2214yescomplemented
26#10622166C2214yescomplemented
27#10622106C2218yescomplemented
28C24×D11C2×C411yescharacteristic
29C24×D11C2×C411yescharacteristic
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2×C411yescharacteristic
32C23×C4×C11C2311yescharacteristic
33C23×Dic11C2×C411yescharacteristic
34C23×Dic11C2×C411yescharacteristic
35C22×D44—22no—
36C22×D44—22no—
37C22×D44—24no—
38C22×D44C818yescomplemented
39C22×D44C2×C414yes—
40C22×C4×D11—22no—
41C22×C4×D11—21no—
42C22×C4×D11—21no—
43C22×C4×D11—44no—
44C22×C4×D11—44no—
45C22×C4×D11C2×C414yes—
46C22×C4×D11C2×C412yes—
47C22×C4×D11D412yes—
48C22×C4×D11D412yes—
49C22×C4×D11D414yes—
50C22×C4×D11C2312yes—
51C22×C8×C11—22no—
52C2×C11×C4⋊C4—22no—
53C2×C11×C4⋊C4—22no—
54C2×C11×C4⋊C4C2×C412yes—
55C2×C11×C4⋊C4C2312yes—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×(C2×D11)⋊C4—22no—
59C2×(C2×D11)⋊C4—22no—
60C2×(C2×D11)⋊C4C2×C412yes—
61C2×(C2×D11)⋊C4C2×C414yes—
62C2×(C2×D11)⋊C4C2312yes—
63C2×C4×Dic11—22no—
64C2×C4×Dic11—21no—
65C2×C4×Dic11—21no—
66C2×C4×Dic11C2×C414yes—
67C22×C11⋊C8—22no—
68C2×C8×D11—28no—
69C2×C8×D11—48no—
70#66946—28no—
71#66946—28no—
72#66946—28no—
73#66946—28no—
74C11×C22⋊C8—22no—
75C11×C22⋊C8C2314yes—
76C22⋊(C11⋊C8)—22no—
77C22⋊(C11⋊C8)C2314yes—
78(C2×D11)⋊C8—28no—
79C2×#1459—111nomaximal, Sylow
80C24×C11C22×C411yescharacteristic
81C23×D11—21no—
82C23×D11—21no—
83C23×D11—22no—
84C23×D11—42no—
85C23×D11—42no—
86C23×D11—42no—
87C23×D11—42no—
88C23×D11C22⋊C412yes—
89C23×D11C22⋊C412yes—
90C23×D11C2×C814yes—
91C23×D11C2×C814yescomplemented
92C23×D11M1614yes—
93C23×D11C22×C412yes—
94C23×D11C22×C412yes—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—21no—
99C22×C4×C11—21no—
100C22×C4×C11—42no—
101C22×C4×C11—42no—
102C22×C4×C11C2×C814yescomplemented
103C22×C4×C11C22×C412yes—
104C22×C4×C11C22×C412yes—
105C22×C4×C11C22×C411yescharacteristic
106C22×C4×C11C2×D412yes—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—24no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—42no—
113C22×Dic11C22⋊C412yes—
114C22×Dic11C22⋊C411yescharacteristic
115C22×Dic11C22⋊C411yescharacteristic
116C22×Dic11C22×C412yes—
117C22×Dic11C22×C412yes—
118C2×D44—216no—
119C2×D44—216no—
120C2×D44—28no—
121C2×D44—28no—
122C2×D44C2×C8116yescomplemented
123C2×C4×D11—28no—
124C2×C4×D11—24no—
125C2×C4×D11—24no—
126C2×C4×D11—44no—
127C2×C4×D11—44no—
128C2×C4×D11—48no—
129C2×C4×D11—44no—
130C2×C4×D11—48no—
131C2×C4×D11—44no—
132C2×C4×D11—44no—
133C2×C4×D11—48no—
134C2×C4×D11C22⋊C414yes—
135C2×C4×D11C22⋊C414yes—
136C2×C4×D11C2×D414yes—
137C2×C4×D11C2×D414yes—
138C2×C8×C11—24no—
139C2×C8×C11—44no—
140C11×C4⋊C4—24no—
141C11×C4⋊C4—24no—
142(C2×D11)⋊C4—28no—
143(C2×D11)⋊C4—24no—
144(C2×D11)⋊C4—24no—
145C4×Dic11—24no—
146C4×Dic11—24no—
147C2×C11⋊C8—24no—
148C2×C11⋊C8—44no—
149C8×D11—416no—
150C22×C4×D4—111no—
151C22×C22⋊C8—112no—
152#1459—118no—
153C2×#324—111no—
154C2×#324D1111yescharacteristic, complemented
155C2×#323—112no—
156C23×C11—22no—
157C23×C11—22no—
158C23×C11C2×C22⋊C411yescharacteristic
159C23×C11C2×C22⋊C411yescharacteristic
160C23×C11C22×C812yes—
161C23×C11C2×M1612yes—
162C23×C11C23×C411yescharacteristic
163C22×D11—24no—
164C22×D11—24no—
165C22×D11—22no—
166C22×D11—22no—
167C22×D11—24no—
168C22×D11—24no—
169C22×D11—42no—
170C22×D11—42no—
171C22×D11—42no—
172C22×D11—48no—
173C22×D11—48no—
174C22×D11—42no—
175C22×D11—42no—
176C22×D11—42no—
177C22×D11—48no—
178C22×D11—42no—
179C22×D11—42no—
180C22×D11—42no—
181C22×D11—48no—
182C22×D11—42no—
183C22×D11C22⋊C818yes—
184C22×D11C22⋊C818yes—
185C22×D11C2×C22⋊C414yes—
186C22×D11C22×C814yes—
187C22×D11C22×C814yescomplemented
188C22×D11C2×M1614yes—
189C2×C4×C11—22no—
190C2×C4×C11—22no—
191C2×C4×C11—24no—
192C2×C4×C11—24no—
193C2×C4×C11—24no—
194C2×C4×C11—22no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11—42no—
199C2×C4×C11—42no—
200C2×C4×C11—42no—
201C2×C4×C11C2×C22⋊C412yes—
202C2×C4×C11C22×C814yescomplemented
203C2×C4×C11C22×D412yes—
204C2×Dic11—22no—
205C2×Dic11—24no—
206C2×Dic11—24no—
207C2×Dic11—22no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11#9914yes—
212C2×Dic11C2×C22⋊C412yes—
213C2×Dic11C2×C22⋊C412yes—
214D44—232no—
215C4×D11—28no—
216C4×D11—28no—
217C4×D11—44no—
218C4×D11—44no—
219C4×D11—48no—
220C4×D11—48no—
221C8×C11—44no—
222C11⋊C8—44no—
223C23×D4—111no—
224C24×C4—111no—
225C24×C4—111no—
226C23×C8—222no—
227C2×C4×D4—114no—
228C2×C4×D4—114no—
229C2×C4×D4—222no—
230C2×C4×D4—224no—
231C2×C4×D4—222no—
232C22×C4⋊C4C2×D1111yescharacteristic
233C22×C22⋊C4—111no—
234C22×C22⋊C4—111no—
235C22×C42—111no—
236C2×C22⋊C8—112no—
237C2×C22⋊C8—118no—
238C2×C22⋊C8—224no—
239C2×C22⋊C8—222no—
240C2×C22⋊C8C2×D1112yes—
241#324—114no—
242#324C2×D1114yescomplemented
243#323—118no—
244C22×C11—21no—
245C22×C11—21no—
246C22×C11—21no—
247C22×C11—21no—
248C22×C11—24no—
249C22×C11—24no—
250C22×C11C2×C22⋊C812yes—
251C22×C11C2×C22⋊C812yes—
252C22×C11C2×#9912yes—
253C22×C11#41312yes—
254C22×C11C22×C22⋊C411yescharacteristic
255C22×C11C23×C811yescharacteristic
256C22×C11C22×M1611yescharacteristic
257C2×D11—24no—
258C2×D11—24no—
259C2×D11—216no—
260C2×D11—24no—
261C2×D11—48no—
262C2×D11—44no—
263C2×D11—44no—
264C2×D11—44no—
265C2×D11—48no—
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—48no—
269C2×D11—44no—
270C2×D11C2×C22⋊C818yes—
271C4×C11—24no—
272C4×C11—22no—
273C4×C11—22no—
274C4×C11—42no—
275Dic11—22no—
276Dic11—42no—
277Dic11C2×#9914yes—
278C25—111no—
279C25—111no—
280C22×D4—118no—
281C22×D4—114no—
282C22×D4—222no—
283C22×D4—222no—
284C22×D4—224no—
285C23×C4—111no—
286C23×C4—112no—
287C23×C4—112no—
288C23×C4—114no—
289C23×C4—112no—
290C23×C4—112no—
291C23×C4—111no—
292C23×C4—114no—
293C23×C4—222no—
294C23×C4—221no—
295C23×C4—221no—
296C23×C4—444no—
297C23×C4—444no—
298C23×C4C4×D1111yescharacteristic
299C23×C4C4×D1111yescharacteristic
300C23×C4C22×D1111yescharacteristic
301C22×C8—22no—
302C22×C8—228no—
303C22×C8—222no—
304C22×C8—448no—
305C4×D4—228no—
306C4×D4—228no—
307C4×D4—228no—
308C4×D4—228no—
309C2×C4⋊C4—22no—
310C2×C4⋊C4—22no—
311C2×C4⋊C4C4×D1112yes—
312C2×C4⋊C4C22×D1112yes—
313C2×C22⋊C4—114no—
314C2×C22⋊C4—112no—
315C2×C22⋊C4—112no—
316C2×C22⋊C4—222no—
317C2×C22⋊C4—222no—
318C2×C22⋊C4—222no—
319C2×C22⋊C4—222no—
320C2×C42—114no—
321C2×C42—222no—
322C2×C42—221no—
323C2×C42—221no—
324C22⋊C8—22no—
325C22⋊C8—114no—
326C22⋊C8—228no—
327C22⋊C8—222no—
328C22⋊C8C22×D1114yes—
329C2×C11—21no—
330C2×C11—21no—
331C2×C11—22no—
332C2×C11#145914yescomplemented
333C2×C11C22×C22⋊C811yescharacteristic
334C2×C11C22×#9911yescharacteristic
335C2×C11C2×#41311yescharacteristic
336D11—28no—
337D11—44no—
338C24—112no—
339C24—112no—
340C24—114no—
341C24—114no—
342C24—112no—
343C24—114no—
344C24—112no—
345C24—221no—
346C24—221no—
347C24—222no—
348C24—442no—
349C24—442no—
350C24—442no—
351C24—442no—
352C24C2×C4×D1111yescharacteristic
353C2×D4—1116no—
354C2×D4—228no—
355C2×D4—228no—
356C2×D4—2216no—
357C2×D4—2216no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—42no—
364C22×C4—42no—
365C22×C4—111no—
366C22×C4—112no—
367C22×C4—111no—
368C22×C4—112no—
369C22×C4—114no—
370C22×C4—114no—
371C22×C4—114no—
372C22×C4—114no—
373C22×C4—112no—
374C22×C4—228no—
375C22×C4—224no—
376C22×C4—224no—
377C22×C4—224no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—444no—
381C22×C4—444no—
382C22×C4—444no—
383C22×C4—448no—
384C22×C4—444no—
385C22×C4—448no—
386C22×C4—444no—
387C22×C4—448no—
388C22×C4—442no—
389C22×C4C8×D1114yescomplemented
390C22×C4C2×C4×D1112yes—
391C22×C4C2×C4×D1112yes—
392C22×C4C2×C4×D1111yescharacteristic
393C22×C4D4×D1112yes—
394C22×C4D4×D1112yes—
395C22×C4C23×D1111yescharacteristic
396C2×C8—24no—
397C2×C8—44no—
398C2×C8—224no—
399C2×C8—4416no—
400C2×C8—444no—
401C4⋊C4—24no—
402C4⋊C4—24no—
403C22⋊C4—228no—
404C22⋊C4—224no—
405C22⋊C4—224no—
406C42—224no—
407C42—224no—
408C11C2×#145911yescharacteristic, complemented, Sylow
409C23—22no—
410C23—22no—
411C23—114no—
412C23—118no—
413C23—114no—
414C23—114no—
415C23—118no—
416C23—114no—
417C23—224no—
418C23—224no—
419C23—222no—
420C23—222no—
421C23—224no—
422C23—224no—
423C23—442no—
424C23—442no—
425C23—442no—
426C23—442no—
427C23—448no—
428C23—448no—
429C23—442no—
430C23—442no—
431C23—448no—
432C23—442no—
433C23—442no—
434C23—448no—
435C23—442no—
436C23—442no—
437C23C22⋊C4×D1111yescharacteristic
438C23C22⋊C4×D1111yescharacteristic
439C23C2×C8×D1112yes—
440C23M16×D1112yes—
441C23C22×C4×D1111yescharacteristic
442D4—2232no—
443C2×C4—22no—
444C2×C4—22no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—22no—
449C2×C4—41no—
450C2×C4—42no—
451C2×C4—41no—
452C2×C4—42no—
453C2×C4—42no—
454C2×C4—42no—
455C2×C4—112no—
456C2×C4—114no—
457C2×C4—112no—
458C2×C4—228no—
459C2×C4—228no—
460C2×C4—224no—
461C2×C4—224no—
462C2×C4—222no—
463C2×C4—222no—
464C2×C4—444no—
465C2×C4—444no—
466C2×C4—448no—
467C2×C4—448no—
468C2×C4—442no—
469C2×C4—442no—
470C2×C4—442no—
471C2×C4C22⋊C4×D1112yes—
472C2×C4C2×C8×D1114yescomplemented
473C2×C4C2×D4×D1112yes—
474C8—44no—
475C8—444no—
476C22—21no—
477C22—21no—
478C22—21no—
479C22—21no—
480C22—24no—
481C22—24no—
482C22—118no—
483C22—224no—
484C22—224no—
485C22—2216no—
486C22—224no—
487C22—444no—
488C22—444no—
489C22—448no—
490C22—444no—
491C22—444no—
492C22—448no—
493C22—442no—
494C22—442no—
495C22—448no—
496C22D11×C22⋊C812yes—
497C22D11×C22⋊C812yes—
498C22D11×#9912yes—
499C22#1062236412yes—
500C22C2×C22⋊C4×D1111yescharacteristic
501C22C22×C8×D1111yescharacteristic
502C22C2×M16×D1111yescharacteristic
503C4—24no—
504C4—22no—
505C4—22no—
506C4—42no—
507C4—114no—
508C4—222no—
509C4—442no—
510C2—21no—
511C2—21no—
512C2—22no—
513C2—228no—
514C2—444no—
515C2#1306693314yesdirect product factor
516C2C2×D11×C22⋊C811yescharacteristic
517C2C2×D11×#9911yescharacteristic
518C2C2×#1062236411yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC22×C11C23×C8
FrattiniC22×C4C23×D11
FittingC2×C11×#324C2
socleC23×C11C2×C22⋊C4
prime radicalC23×D44C4
cosocleC22×C4×C11C24
hypercenterC2×#324D11
hypocenterC11C2×#1459
LCSG ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. C2×D11×C22⋊C8C2semidirect
3. #13066933C2direct (N × H)
4. C2×#10622166C2semidirect
5. C2×#10622106C2semidirect
6. C2×C11×#324C2semidirect
24. D11×C22⋊C8C22semidirect
25. C11×#324C22semidirect
26. #10622166C22semidirect
27. #10622106C22semidirect
38. C22×D44C8semidirect
91. C23×D11C2×C8semidirect
102. C22×C4×C11C2×C8semidirect
122. C2×D44C2×C8semidirect
154. C2×#324D11semidirect
187. C22×D11C22×C8semidirect
202. C2×C4×C11C22×C8semidirect
242. #324C2×D11semidirect
332. C2×C11#1459semidirect
389. C22×C4C8×D11semidirect
408. C11C2×#1459semidirect
472. C2×C4C2×C8×D11semidirect
515. C2#13066933direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669462
C2×D11×C22⋊C82
#130669332
C2×#106221662
C2×#106221062
C2×C11×#3242
C2×#145911