Finite Group Databasebeta

← C2×#13066955 #14719632

Subgroups — C2×#13066955 #14719632

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C2×#10622332C212yesmaximal, complemented
3#13066955C218yesmaximal, direct product factor
4C2×#10622163C211yesmaximal, characteristic, complemented
5C2×#10622106C212yesmaximal, complemented
6C2×C11×#323C211yesmaximal, characteristic, complemented
7C23×C22⋊D11C411yescharacteristic
8C24×Dic11C411yescharacteristic
9C23×C4×D11C411yescharacteristic
10C22×C11×C22⋊C4C2211yescharacteristic
11C22×(C2×D11)⋊C4C2211yescharacteristic
12C22×Dic11⋊C4C411yescharacteristic
13C22×C4×Dic11C2211yescharacteristic
14C2×(C22⋊D11)⋊C4—24no—
15C2×(C22⋊D11)⋊C4—22no—
16C2×(C22⋊D11)⋊C4—22no—
17C2×(C22⋊D11)⋊C4C414yes—
18C2×(C22⋊D11)⋊C4C2214yes—
19C2×C11×C22⋊C8C2212yes—
20C2×C22⋊(C11⋊C8)C2212yes—
21C2×#66879—22no—
22C2×Dic11⋊C8—22no—
23#10622332—24no—
24#10622332C2218yescomplemented
25C11×#323C2214yescomplemented
26#10622163C2214yescomplemented
27#10622106C2218yescomplemented
28C25×C11C2×C411yescharacteristic
29C24×D11C2×C411yescharacteristic
30C23×C4×C11C2×C411yescharacteristic
31C23×C4×C11C2311yescharacteristic
32C22×C22⋊D11—24no—
33C22×C22⋊D11—24no—
34C22×C22⋊D11—22no—
35C22×C22⋊D11—22no—
36C22×C22⋊D11C2×C414yes—
37C23×Dic11—22no—
38C23×Dic11—21no—
39C23×Dic11—21no—
40C23×Dic11—44no—
41C23×Dic11C2×C411yescharacteristic
42C23×Dic11C2×C411yescharacteristic
43C23×Dic11C2×C414yes—
44C23×Dic11C2×C411yescharacteristic
45C22×C4×D11—22no—
46C22×C4×D11—21no—
47C22×C4×D11—21no—
48C22×C4×D11—44no—
49C22×C4×D11C2×C414yes—
50C22×C8×C11—22no—
51C2×C11×C22⋊C4—22no—
52C2×C11×C22⋊C4—22no—
53C2×C11×C22⋊C4C2×C412yes—
54C2×C11×C22⋊C4C2312yes—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4C2×C412yes—
58C2×(C2×D11)⋊C4C2312yes—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4C2×C414yes—
62C2×C4×Dic11C2×C412yes—
63C2×C4×Dic11D414yes—
64C2×C4×Dic11D412yes—
65C2×C4×Dic11D412yes—
66C2×C4×Dic11C2312yes—
67C22×C11⋊C8—22no—
68(C22⋊D11)⋊C4—28no—
69(C22⋊D11)⋊C4—28no—
70(C22⋊D11)⋊C4—28no—
71(C22⋊D11)⋊C4—28no—
72C11×C22⋊C8—22no—
73C11×C22⋊C8C2314yes—
74C22⋊(C11⋊C8)—22no—
75C22⋊(C11⋊C8)C2314yes—
76#66879—28no—
77Dic11⋊C8—28no—
78C2×#1466—111nomaximal, Sylow
79C24×C11—21no—
80C24×C11—21no—
81C24×C11—22no—
82C24×C11—42no—
83C24×C11—42no—
84C24×C11M1614yes—
85C24×C11C22×C411yescharacteristic
86C24×C11C22×C412yes—
87C23×D11—21no—
88C23×D11—21no—
89C23×D11—22no—
90C23×D11—42no—
91C23×D11—42no—
92C23×D11M1614yes—
93C23×D11C22×C412yes—
94C22×C4×C11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11C22×C412yes—
99C22×C4×C11C22×C411yescharacteristic
100C22×C4×C11C2×D412yes—
101C22×C4×C11C2×D412yes—
102C22×C4×C11C2411yescharacteristic
103C2×C22⋊D11—216no—
104C2×C22⋊D11—216no—
105C2×C22⋊D11—28no—
106C2×C22⋊D11—28no—
107C2×C22⋊D11—28no—
108C22×Dic11—24no—
109C22×Dic11—24no—
110C22×Dic11—24no—
111C22×Dic11—21no—
112C22×Dic11—21no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—42no—
116C22×Dic11—48no—
117C22×Dic11—48no—
118C22×Dic11—44no—
119C22×Dic11—44no—
120C22×Dic11C22⋊C412yes—
121C22×Dic11C22⋊C412yes—
122C22×Dic11C22⋊C412yes—
123C22×Dic11C22⋊C411yescharacteristic
124C22×Dic11C22⋊C411yescharacteristic
125C22×Dic11C22×C412yes—
126C22×Dic11C22×C412yes—
127C22×Dic11C22×C412yes—
128C2×C4×D11—24no—
129C2×C4×D11—24no—
130C2×C4×D11—48no—
131C2×C4×D11—44no—
132C2×C4×D11—44no—
133C2×C4×D11—48no—
134C2×C8×C11—24no—
135C2×C8×C11—44no—
136C11×C22⋊C4—24no—
137C11×C22⋊C4—24no—
138(C2×D11)⋊C4—24no—
139(C2×D11)⋊C4—24no—
140Dic11⋊C4—28no—
141C4×Dic11C22⋊C414yes—
142C4×Dic11C22⋊C414yes—
143C4×Dic11C2×D414yes—
144C4×Dic11C2×D414yes—
145C2×C11⋊C8—24no—
146C2×C11⋊C8—44no—
147C22×C4×D4—111no—
148C2×#432—112no—
149#1466—118no—
150C2×#323—112no—
151C2×#323—111no—
152C2×#323D1111yescharacteristic, complemented
153C23×C11—22no—
154C23×C11—22no—
155C23×C11—22no—
156C23×C11—22no—
157C23×C11—24no—
158C23×C11—24no—
159C23×C11—42no—
160C23×C11—48no—
161C23×C11—42no—
162C23×C11—42no—
163C23×C11—42no—
164C23×C11—48no—
165C23×C11—42no—
166C23×C11—42no—
167C23×C11C2×C22⋊C411yescharacteristic
168C23×C11C2×C22⋊C411yescharacteristic
169C23×C11C2×M1612yes—
170C23×C11C2×M1614yes—
171C23×C11C2×M1612yes—
172C23×C11C23×C411yescharacteristic
173C22×D11—22no—
174C22×D11—22no—
175C22×D11—24no—
176C22×D11—24no—
177C22×D11—42no—
178C22×D11—42no—
179C22×D11—48no—
180C22×D11—42no—
181C22×D11—42no—
182C22×D11—42no—
183C22×D11—48no—
184C22×D11—42no—
185C22×D11C2×M1614yes—
186C2×C4×C11—24no—
187C2×C4×C11—22no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—42no—
194C2×C4×C11C2×C22⋊C412yes—
195C2×C4×C11C22×D412yes—
196C22⋊D11—232no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—22no—
202C2×Dic11—24no—
203C2×Dic11—24no—
204C2×Dic11—22no—
205C2×Dic11—48no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—48no—
209C2×Dic11—42no—
210C2×Dic11#10014yes—
211C2×Dic11C2×C22⋊C414yes—
212C2×Dic11C2×C22⋊C412yes—
213C2×Dic11C2×C22⋊C412yes—
214C4×D11—48no—
215C4×D11—48no—
216C8×C11—44no—
217C11⋊C8—44no—
218C23×D4—111no—
219C24×C4—111no—
220C24×C4—111no—
221C2×C4×D4—114no—
222C2×C4×D4—114no—
223C2×C4×D4—222no—
224C2×C4×D4—222no—
225C2×C4×D4—224no—
226C22×C4⋊C4—111no—
227C22×C22⋊C4—111no—
228C22×C22⋊C4C2×D1111yescharacteristic
229C22×C42—111no—
230#432—118no—
231#432—224no—
232C2×C4⋊C8—222no—
233C2×C22⋊C8—112no—
234C2×C22⋊C8C2×D1112yes—
235C2×#97—222no—
236#323—114no—
237#323—118no—
238#323C2×D1114yescomplemented
239C22×C11—21no—
240C22×C11—21no—
241C22×C11—21no—
242C22×C11—21no—
243C22×C11—24no—
244C22×C11—24no—
245C22×C11—24no—
246C22×C11—44no—
247C22×C11—44no—
248C22×C11—48no—
249C22×C11—42no—
250C22×C11—42no—
251C22×C11—48no—
252C22×C11#40712yes—
253C22×C11#40712yes—
254C22×C11#41012yes—
255C22×C11C2×#10012yes—
256C22×C11C22×C22⋊C411yescharacteristic
257C22×C11C22×M1611yescharacteristic
258C22×C11C22×M1611yescharacteristic
259C2×D11—24no—
260C2×D11—44no—
261C2×D11—48no—
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—48no—
265C2×D11—44no—
266C4×C11—22no—
267C4×C11—22no—
268C4×C11—42no—
269Dic11—24no—
270Dic11—22no—
271Dic11—42no—
272Dic11C2×#10014yes—
273C25—111no—
274C25C4×D1111yescharacteristic
275C22×D4—114no—
276C22×D4—222no—
277C22×D4—222no—
278C22×D4—224no—
279C22×D4—224no—
280C23×C4—111no—
281C23×C4—111no—
282C23×C4—111no—
283C23×C4—114no—
284C23×C4—114no—
285C23×C4—222no—
286C23×C4—221no—
287C23×C4—221no—
288C23×C4—221no—
289C23×C4—222no—
290C23×C4—221no—
291C23×C4—444no—
292C23×C4—444no—
293C23×C4C4×D1111yescharacteristic
294C23×C4C22×D1111yescharacteristic
295C22×C8—22no—
296C22×C8—222no—
297C4×D4—228no—
298C4×D4—228no—
299C4×D4—228no—
300C4×D4—228no—
301C2×C4⋊C4—114no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—222no—
304C2×C22⋊C4—22no—
305C2×C22⋊C4—22no—
306C2×C22⋊C4—112no—
307C2×C22⋊C4—112no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4—222no—
310C2×C22⋊C4C4×D1112yes—
311C2×C22⋊C4C22×D1112yes—
312C2×C42—112no—
313C2×C42—112no—
314C2×C42—112no—
315C2×C42—114no—
316C2×C42—112no—
317C4⋊C8—228no—
318C22⋊C8—22no—
319C22⋊C8—114no—
320C22⋊C8—222no—
321C22⋊C8C22×D1114yes—
322#97—228no—
323C2×C11—21no—
324C2×C11—21no—
325C2×C11—22no—
326C2×C11—44no—
327C2×C11#146614yescomplemented
328C2×C11C2×#40711yescharacteristic
329C2×C11C2×#41011yescharacteristic
330C2×C11C22×#10011yescharacteristic
331D11—44no—
332C24—21no—
333C24—21no—
334C24—22no—
335C24—42no—
336C24—42no—
337C24—114no—
338C24—112no—
339C24—221no—
340C24—221no—
341C24—222no—
342C24—442no—
343C24—442no—
344C24#431314yes—
345C24C2×C4×D1111yescharacteristic
346C24C2×C4×D1112yes—
347C2×D4—228no—
348C2×D4—228no—
349C2×D4—2216no—
350C2×D4—2216no—
351C2×D4—228no—
352C22×C4—21no—
353C22×C4—21no—
354C22×C4—42no—
355C22×C4—42no—
356C22×C4—111no—
357C22×C4—112no—
358C22×C4—112no—
359C22×C4—112no—
360C22×C4—111no—
361C22×C4—112no—
362C22×C4—112no—
363C22×C4—112no—
364C22×C4—224no—
365C22×C4—224no—
366C22×C4—224no—
367C22×C4—224no—
368C22×C4—224no—
369C22×C4—222no—
370C22×C4—222no—
371C22×C4—221no—
372C22×C4—221no—
373C22×C4—444no—
374C22×C4—448no—
375C22×C4—444no—
376C22×C4—448no—
377C22×C4—444no—
378C22×C4—448no—
379C22×C4—444no—
380C22×C4—448no—
381C22×C4—442no—
382C22×C4C2×C4×D1112yes—
383C22×C4C2×C4×D1111yescharacteristic
384C22×C4D4×D1112yes—
385C22×C4D4×D1112yes—
386C22×C4C23×D1111yescharacteristic
387C2×C8—24no—
388C2×C8—44no—
389C2×C8—224no—
390C2×C8—444no—
391C4⋊C4—228no—
392C22⋊C4—24no—
393C22⋊C4—24no—
394C22⋊C4—224no—
395C22⋊C4—224no—
396C42—114no—
397C42—114no—
398C42—114no—
399C42—114no—
400C11C2×#146611yescharacteristic, complemented, Sylow
401C23—22no—
402C23—22no—
403C23—22no—
404C23—22no—
405C23—24no—
406C23—24no—
407C23—42no—
408C23—48no—
409C23—42no—
410C23—42no—
411C23—42no—
412C23—48no—
413C23—42no—
414C23—42no—
415C23—114no—
416C23—222no—
417C23—222no—
418C23—224no—
419C23—224no—
420C23—442no—
421C23—442no—
422C23—448no—
423C23—442no—
424C23—442no—
425C23—448no—
426C23—442no—
427C23—442no—
428C23C22⋊C4×D1111yescharacteristic
429C23C22⋊C4×D1111yescharacteristic
430C23C2×#431312yes—
431C23C2×#431314yes—
432C23M16×D1112yes—
433C23C22×C4×D1111yescharacteristic
434D4—2232no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—41no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—112no—
444C2×C4—114no—
445C2×C4—114no—
446C2×C4—112no—
447C2×C4—224no—
448C2×C4—224no—
449C2×C4—222no—
450C2×C4—222no—
451C2×C4—224no—
452C2×C4—224no—
453C2×C4—222no—
454C2×C4—222no—
455C2×C4—448no—
456C2×C4—448no—
457C2×C4—448no—
458C2×C4—448no—
459C2×C4—442no—
460C2×C4—442no—
461C2×C4—442no—
462C2×C4C22⋊C4×D1112yes—
463C2×C4C2×D4×D1112yes—
464C8—44no—
465C8—444no—
466C22—21no—
467C22—21no—
468C22—21no—
469C22—21no—
470C22—24no—
471C22—24no—
472C22—24no—
473C22—44no—
474C22—44no—
475C22—48no—
476C22—42no—
477C22—42no—
478C22—48no—
479C22—224no—
480C22—444no—
481C22—444no—
482C22—448no—
483C22—442no—
484C22—442no—
485C22—448no—
486C22#1062233912yes—
487C22#1062233912yes—
488C22#1062235312yes—
489C22D11×#10012yes—
490C22C2×C22⋊C4×D1111yescharacteristic
491C22C22×#431311yescharacteristic
492C22C2×M16×D1111yescharacteristic
493C4—22no—
494C4—22no—
495C4—42no—
496C4—114no—
497C4—224no—
498C4—222no—
499C4—442no—
500C2—21no—
501C2—21no—
502C2—22no—
503C2—44no—
504C2—444no—
505C2#1306695514yesdirect product factor
506C2C2×#1062233911yescharacteristic
507C2C2×#1062235311yescharacteristic
508C2C2×D11×#10011yescharacteristic
subgroupG/H
centerC23C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#323C2
socleC23×C11C2×C22⋊C4
prime radicalC23×C22⋊D11C4
cosocleC22×C4×C11C24
hypercenterC2×#323D11
hypocenterC11C2×#1466
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×#10622332C2semidirect
3. #13066955C2direct (N × H)
4. C2×#10622163C2semidirect
5. C2×#10622106C2semidirect
6. C2×C11×#323C2semidirect
24. #10622332C22semidirect
25. C11×#323C22semidirect
26. #10622163C22semidirect
27. #10622106C22semidirect
152. C2×#323D11semidirect
238. #323C2×D11semidirect
327. C2×C11#1466semidirect
400. C11C2×#1466semidirect
505. C2#13066955direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
C2×#106223322
#130669552
C2×#106221632
C2×#106221062
C2×C11×#3232
C2×#146611