Finite Group Databasebeta

← C2×#13066945 #14719613

Subgroups — C2×#13066945 #14719613

Order 2816.

1718 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×Dic11⋊C4C211yesmaximal, characteristic
2C2×#10622820C211yesmaximal, characteristic
3#13066945C218yesmaximal, direct product factor
4C2×#10622107C214yesmaximal, complemented
5C2×C11×#407C211yesmaximal, characteristic
6C24×C4×C11C2211yescharacteristic
7C24×Dic11C411yescharacteristic
8C24×Dic11C411yescharacteristic
9C22×C11×M16—21no—
10C22×Dic11⋊C4—21no—
11C22×Dic11⋊C4—21no—
12C22×Dic11⋊C4—22no—
13C22×Dic11⋊C4—21no—
14C22×Dic11⋊C4—21no—
15C22×Dic11⋊C4—22no—
16C22×Dic11⋊C4C414yes—
17C22×Dic11⋊C4C412yes—
18C22×Dic11⋊C4C2212yes—
19C22×Dic11⋊C4C2214yes—
20C22×#4318—21no—
21C11×#407—22no—
22C11×#407C2214yes—
23C2×C11×C22⋊C8—21no—
24C2×C11×C22⋊C8C2212yes—
25#10622820—22no—
26#10622820C2214yes—
27C2×C22⋊(C11⋊C8)—21no—
28C2×C22⋊(C11⋊C8)C2212yes—
29#10622107C22116yescomplemented
30C25×C11C2×C411yescharacteristic
31C23×C4×C11—44no—
32C23×C4×C11C2×C412yes—
33C23×C4×C11C2×C411yescharacteristic
34C23×C4×C11D411yescharacteristic
35C23×C4×C11D411yescharacteristic
36C23×C4×C11D412yes—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11D412yes—
40C23×C4×C11C2311yescharacteristic
41C23×C4×C11C2312yes—
42C23×Dic11—22no—
43C23×Dic11—21no—
44C23×Dic11—21no—
45C23×Dic11—28no—
46C23×Dic11—22no—
47C23×Dic11—21no—
48C23×Dic11—21no—
49C23×Dic11—44no—
50C23×Dic11C2×C414yes—
51C23×Dic11C2×C412yes—
52C23×Dic11C2×C414yes—
53C23×Dic11C2×C412yes—
54C2×C11×M16—24no—
55C2×C11×M16—44no—
56C22×C8×C11—22no—
57C2×Dic11⋊C4—24no—
58C2×Dic11⋊C4—24no—
59C2×Dic11⋊C4—22no—
60C2×Dic11⋊C4—22no—
61C2×Dic11⋊C4—24no—
62C2×Dic11⋊C4—24no—
63C2×Dic11⋊C4—24no—
64C2×Dic11⋊C4—22no—
65C2×Dic11⋊C4—24no—
66C2×Dic11⋊C4—22no—
67C2×Dic11⋊C4—24no—
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—24no—
70C2×Dic11⋊C4—22no—
71C2×Dic11⋊C4—24no—
72C2×Dic11⋊C4C2×C414yes—
73C2×Dic11⋊C4C2×C418yes—
74C2×Dic11⋊C4C2314yes—
75C2×#4318—24no—
76C2×#4318—44no—
77C22×C11⋊C8—22no—
78C11×C22⋊C8—24no—
79C11×C22⋊C8—22no—
80C11×C22⋊C8C2314yes—
81C22⋊(C11⋊C8)—24no—
82C22⋊(C11⋊C8)—22no—
83C22⋊(C11⋊C8)C2314yes—
84C2×#1463—111nomaximal, Sylow
85C24×C11—24no—
86C24×C11—24no—
87C24×C11—24no—
88C24×C11C22⋊C412yes—
89C24×C11C22⋊C411yescharacteristic
90C24×C11C22⋊C411yescharacteristic
91C24×C11C22×C412yes—
92C24×C11C22×C411yescharacteristic
93C22×C4×C11—24no—
94C22×C4×C11—24no—
95C22×C4×C11—44no—
96C22×C4×C11—42no—
97C22×C4×C11—42no—
98C22×C4×C11—44no—
99C22×C4×C11—42no—
100C22×C4×C11—44no—
101C22×C4×C11—42no—
102C22×C4×C11—44no—
103C22×C4×C11C22⋊C412yes—
104C22×C4×C11C22⋊C412yes—
105C22×C4×C11C22⋊C411yescharacteristic
106C22×C4×C11C22⋊C411yescharacteristic
107C22×C4×C11C22⋊C412yes—
108C22×C4×C11C22⋊C412yes—
109C22×C4×C11C22⋊C412yes—
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C22×C412yes—
112C22×C4×C11C2×D411yescharacteristic
113C22×C4×C11C2×D412yes—
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D412yes—
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—216no—
122C22×Dic11—28no—
123C22×Dic11—28no—
124C22×Dic11—216no—
125C22×Dic11—22no—
126C22×Dic11—24no—
127C22×Dic11—24no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—24no—
131C22×Dic11—24no—
132C22×Dic11—22no—
133C22×Dic11—24no—
134C22×Dic11—48no—
135C22×Dic11—44no—
136C22×Dic11—48no—
137C22×Dic11—44no—
138C22×Dic11—44no—
139C22×Dic11M1618yescomplemented
140C22×Dic11C22×C414yes—
141C22×Dic11C22×C414yes—
142C11×M16—48no—
143C2×C8×C11—24no—
144C2×C8×C11—44no—
145Dic11⋊C4—24no—
146Dic11⋊C4—28no—
147Dic11⋊C4—24no—
148Dic11⋊C4—28no—
149Dic11⋊C4—24no—
150Dic11⋊C4—24no—
151#4318—48no—
152C2×C11⋊C8—24no—
153C2×C11⋊C8—44no—
154C23×C4⋊C4—111no—
155C2×#407—111no—
156C2×#407D1111yescharacteristic
157#1463—118no—
158C2×#324—114no—
159C23×C11—232no—
160C23×C11—24no—
161C23×C11—24no—
162C23×C11—22no—
163C23×C11—22no—
164C23×C11—24no—
165C23×C11—22no—
166C23×C11—24no—
167C23×C11—22no—
168C23×C11—24no—
169C23×C11—22no—
170C23×C11—24no—
171C23×C11—22no—
172C23×C11#9914yes—
173C23×C11#10114yes—
174C23×C11C2×C22⋊C411yescharacteristic
175C23×C11C2×C22⋊C412yes—
176C23×C11C2×C22⋊C412yes—
177C23×C11C2×C22⋊C411yescharacteristic
178C23×C11C2×M1614yes—
179C23×C11C23×C411yescharacteristic
180C2×C4×C11—22no—
181C2×C4×C11—24no—
182C2×C4×C11—22no—
183C2×C4×C11—24no—
184C2×C4×C11—24no—
185C2×C4×C11—24no—
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—42no—
197C2×C4×C11—41no—
198C2×C4×C11C2×C22⋊C411yescharacteristic
199C2×C4×C11C2×C22⋊C412yes—
200C2×C4×C11C2×C22⋊C411yescharacteristic
201C2×C4×C11C2×C22⋊C412yes—
202C2×C4×C11C22×D411yescharacteristic
203C2×C4×C11C22×D411yescharacteristic
204C2×Dic11—216no—
205C2×Dic11—216no—
206C2×Dic11—24no—
207C2×Dic11—24no—
208C2×Dic11—28no—
209C2×Dic11—28no—
210C2×Dic11—24no—
211C2×Dic11—44no—
212C2×Dic11—48no—
213C2×Dic11—48no—
214C2×Dic11—44no—
215C2×Dic11—44no—
216C2×Dic11C2×M1618yescomplemented
217C8×C11—44no—
218C11⋊C8—44no—
219C24×C4—111no—
220C24×C4—111no—
221C24×C4C2×D1111yescharacteristic
222C22×M16—21no—
223C22×M16—221no—
224C22×C4⋊C4—112no—
225C22×C4⋊C4—114no—
226C22×C4⋊C4—112no—
227C22×C4⋊C4—114no—
228C22×C4⋊C4—221no—
229C22×C4⋊C4—221no—
230C22×C4⋊C4—222no—
231C22×C4⋊C4—221no—
232C22×C4⋊C4—221no—
233C22×C4⋊C4—222no—
234#407—22no—
235#407—114no—
236#407—222no—
237#407C2×D1114yes—
238C2×C22⋊C8—21no—
239C2×C22⋊C8—112no—
240C2×C22⋊C8—221no—
241C2×C22⋊C8C2×D1112yes—
242#324—1116no—
243C22×C11—216no—
244C22×C11—216no—
245C22×C11—22no—
246C22×C11—22no—
247C22×C11—21no—
248C22×C11—22no—
249C22×C11—21no—
250C22×C11—21no—
251C22×C11—22no—
252C22×C11—21no—
253C22×C11—28no—
254C22×C11—28no—
255C22×C11—28no—
256C22×C11#40712yes—
257C22×C11#40712yes—
258C22×C11C2×#9914yes—
259C22×C11C2×#9912yes—
260C22×C11C2×#10114yes—
261C22×C11C2×#10112yes—
262C22×C11C22×C22⋊C411yescharacteristic
263C22×C11C22×M1612yes—
264C4×C11—21no—
265C4×C11—22no—
266C4×C11—21no—
267C4×C11—22no—
268C4×C11—21no—
269C4×C11—21no—
270Dic11—28no—
271Dic11—44no—
272C25C4×D1111yescharacteristic
273C23×C4—44no—
274C23×C4—112no—
275C23×C4—114no—
276C23×C4—114no—
277C23×C4—112no—
278C23×C4—228no—
279C23×C4—222no—
280C23×C4—221no—
281C23×C4—221no—
282C23×C4—222no—
283C23×C4—221no—
284C23×C4—221no—
285C23×C4—444no—
286C23×C4C4×D1112yes—
287C23×C4C4×D1111yescharacteristic
288C23×C4D4411yescharacteristic
289C23×C4D4411yescharacteristic
290C23×C4D4412yes—
291C23×C4C22⋊D1111yescharacteristic
292C23×C4C22⋊D1111yescharacteristic
293C23×C4C22⋊D1112yes—
294C23×C4C22×D1111yescharacteristic
295C23×C4C22×D1112yes—
296C2×M16—24no—
297C2×M16—44no—
298C2×M16—224no—
299C2×M16—444no—
300C22×C8—22no—
301C22×C8—222no—
302C2×C4⋊C4—114no—
303C2×C4⋊C4—118no—
304C2×C4⋊C4—114no—
305C2×C4⋊C4—224no—
306C2×C4⋊C4—224no—
307C2×C4⋊C4—224no—
308C2×C4⋊C4—224no—
309C2×C4⋊C4—224no—
310C2×C4⋊C4—222no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—224no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—224no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—224no—
317C2×C4⋊C4—222no—
318C2×C4⋊C4—224no—
319C2×C4⋊C4—222no—
320C22⋊C8—24no—
321C22⋊C8—22no—
322C22⋊C8—114no—
323C22⋊C8—222no—
324C22⋊C8—224no—
325C22⋊C8C22×D1114yes—
326C2×C11—22no—
327C2×C11—22no—
328C2×C11—24no—
329C2×C11—24no—
330C2×C11#146314yescomplemented
331C2×C11C2×#40711yescharacteristic
332C2×C11C22×#9911yescharacteristic
333C2×C11C22×#10111yescharacteristic
334C24—24no—
335C24—24no—
336C24—24no—
337C24(C2×D11)⋊C412yes—
338C24(C2×D11)⋊C411yescharacteristic
339C24(C2×D11)⋊C411yescharacteristic
340C24C2×C4×D1112yes—
341C24C2×C4×D1111yescharacteristic
342C22×C4—24no—
343C22×C4—24no—
344C22×C4—42no—
345C22×C4—44no—
346C22×C4—44no—
347C22×C4—42no—
348C22×C4—42no—
349C22×C4—44no—
350C22×C4—42no—
351C22×C4—44no—
352C22×C4—118no—
353C22×C4—114no—
354C22×C4—114no—
355C22×C4—2216no—
356C22×C4—2216no—
357C22×C4—228no—
358C22×C4—228no—
359C22×C4—224no—
360C22×C4—224no—
361C22×C4—224no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—224no—
366C22×C4—224no—
367C22×C4—222no—
368C22×C4—448no—
369C22×C4—444no—
370C22×C4—444no—
371C22×C4—448no—
372C22×C4—444no—
373C22×C4(C2×D11)⋊C412yes—
374C22×C4(C2×D11)⋊C412yes—
375C22×C4(C2×D11)⋊C411yescharacteristic
376C22×C4(C2×D11)⋊C411yescharacteristic
377C22×C4(C2×D11)⋊C412yes—
378C22×C4(C2×D11)⋊C412yes—
379C22×C4(C2×D11)⋊C412yes—
380C22×C4C2×C4×D1111yescharacteristic
381C22×C4C2×C4×D1112yes—
382C22×C4C2×D4412yes—
383C22×C4C2×D4411yescharacteristic
384C22×C4C2×D4411yescharacteristic
385C22×C4C2×D4412yes—
386C22×C4C2×C22⋊D1112yes—
387C22×C4C2×C22⋊D1111yescharacteristic
388C22×C4C2×C22⋊D1111yescharacteristic
389C22×C4C2×C22⋊D1112yes—
390C22×C4C23×D1111yescharacteristic
391M16—48no—
392M16—448no—
393C2×C8—24no—
394C2×C8—44no—
395C2×C8—224no—
396C2×C8—444no—
397C4⋊C4—224no—
398C4⋊C4—224no—
399C4⋊C4—228no—
400C4⋊C4—228no—
401C4⋊C4—224no—
402C4⋊C4—224no—
403C11C2×#146311yescharacteristic, complemented, Sylow
404C23—232no—
405C23—24no—
406C23—22no—
407C23—22no—
408C23—24no—
409C23—22no—
410C23—24no—
411C23—22no—
412C23—24no—
413C23—24no—
414C23—22no—
415C23—24no—
416C23—22no—
417C23#6687014yes—
418C23#6688814yes—
419C23M16×D1114yes—
420C23C2×(C2×D11)⋊C411yescharacteristic
421C23C2×(C2×D11)⋊C412yes—
422C23C2×(C2×D11)⋊C412yes—
423C23C2×(C2×D11)⋊C411yescharacteristic
424C23C22×C4×D1111yescharacteristic
425C2×C4—22no—
426C2×C4—22no—
427C2×C4—24no—
428C2×C4—24no—
429C2×C4—24no—
430C2×C4—24no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—42no—
434C2×C4—42no—
435C2×C4—42no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—41no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—118no—
444C2×C4—2216no—
445C2×C4—2216no—
446C2×C4—228no—
447C2×C4—228no—
448C2×C4—224no—
449C2×C4—224no—
450C2×C4—224no—
451C2×C4—444no—
452C2×C4—448no—
453C2×C4—448no—
454C2×C4—444no—
455C2×C4—444no—
456C2×C4C2×(C2×D11)⋊C411yescharacteristic
457C2×C4C2×(C2×D11)⋊C411yescharacteristic
458C2×C4C2×(C2×D11)⋊C412yes—
459C2×C4C2×(C2×D11)⋊C412yes—
460C2×C4C22×D4411yescharacteristic
461C2×C4C22×C22⋊D1111yescharacteristic
462C8—44no—
463C8—444no—
464C22—216no—
465C22—216no—
466C22—22no—
467C22—22no—
468C22—21no—
469C22—22no—
470C22—21no—
471C22—21no—
472C22—22no—
473C22—21no—
474C22—28no—
475C22—28no—
476C22—28no—
477C22C2×#6687014yes—
478C22C2×#6687012yes—
479C22#1062273912yes—
480C22#1062273912yes—
481C22C2×#6688814yes—
482C22C2×#6688812yes—
483C22C2×M16×D1112yes—
484C22C22×(C2×D11)⋊C411yescharacteristic
485C4—21no—
486C4—21no—
487C4—21no—
488C4—21no—
489C4—22no—
490C4—22no—
491C4—228no—
492C4—444no—
493C2—22no—
494C2—24no—
495C2—22no—
496C2—24no—
497C2#1306694514yesdirect product factor
498C2C2×#1062273911yescharacteristic
499C2C22×#6687011yescharacteristic
500C2C22×#6688811yescharacteristic
subgroupG/H
centerC23C2×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#407C2
socleC23×C11C2×C22⋊C4
prime radicalC25×C11C2×C4
cosocleC22×C4×C11C24
hypercenterC2×#407D11
hypocenterC11C2×#1463
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
3. #13066945C2direct (N × H)
4. C2×#10622107C2semidirect
29. #10622107C22semidirect
139. C22×Dic11M16semidirect
216. C2×Dic11C2×M16semidirect
330. C2×C11#1463semidirect
403. C11C2×#1463semidirect
497. C2#13066945direct (N × H)

Maximal subgroups

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

subgroupindex
C23×Dic11⋊C42
C2×#106228202
#130669452
C2×#106221072
C2×C11×#4072
C2×#146311