Finite Group Databasebeta

← #14720013

Subgroups — #14720013

Order 2816.

1002 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623094C211yesmaximal, characteristic
2#13077270C212yesmaximal, complemented
3#13066975C212yesmaximal, complemented
4#13066966C214yesmaximal, complemented
5#13066954C211yesmaximal, characteristic, complemented
6#13066949C212yesmaximal, complemented
7#13066929C212yesmaximal, complemented
8C11×#1459C211yesmaximal, characteristic, complemented
9C2×C4×D4×C11C2211yescharacteristic
10C2×#66991C412yes—
11C2×#66983C411yescharacteristic
12C2×#66983C2211yescharacteristic
13C2×#66979C411yescharacteristic
14C2×#66979C2211yescharacteristic
15#10623094—24no—
16#10623094—22no—
17#10623094—22no—
18C2×#66945C2212yes—
19C2×#66938C412yes—
20C2×#66938C2212yes—
21C2×C4×D44C411yescharacteristic
22C2×#66922C411yescharacteristic
23C2×C11×C22⋊C8C2212yes—
24#10622820C2212yes—
25#10622715—22no—
26#10622714—22no—
27#10622333—24no—
28#10622332C2214yes—
29#10622331C2214yes—
30C11×#324C2211yescharacteristic
31C11×#324C2211yescharacteristic
32C11×#323C2212yes—
33#10622166C2212yes—
34#10622163C2212yes—
35#10622106C2214yes—
36#10622106C2214yes—
37C22×D4×C11C2×C411yescharacteristic
38C23×C4×C11C2×C411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×C22⋊D11C2×C412yes—
41C22×C22⋊D11C2×C412yes—
42C22×D44C2×C411yescharacteristic
43C22×C4×D11C2×C412yes—
44C22×Dic22C2×C412yes—
45C22×C8×C11—22no—
46C4×D4×C11—22no—
47C4×D4×C11—22no—
48C2×C11×C4⋊C4C2311yescharacteristic
49C2×C11×C22⋊C4C2×C411yescharacteristic
50C2×C11×C22⋊C4C2311yescharacteristic
51C2×C42×C11C2×C411yescharacteristic
52C2×C22⋊Dic11C2×C412yes—
53C2×C22⋊Dic11C2×C412yes—
54#66991—24no—
55#66991—24no—
56#66983—22no—
57#66983—22no—
58#66983—22no—
59#66983—22no—
60C2×(C2×D11)⋊C4C2×C412yes—
61C2×(C2×D11)⋊C4C2×C412yes—
62C2×(C2×D11)⋊C4C2312yes—
63#66979—22no—
64#66979—21no—
65#66979—21no—
66#66979D414yes—
67#66979D412yes—
68#66979D412yes—
69C2×C4⋊Dic11C2×C412yes—
70C2×C4⋊Dic11C2×C411yescharacteristic
71C2×C4⋊Dic11C2×C411yescharacteristic
72C2×C4⋊Dic11C2×C411yescharacteristic
73C2×C4×Dic11C2×C412yes—
74C2×C4×Dic11C2312yes—
75C2×#4318—22no—
76#66945—24no—
77#66945—24no—
78#66938—24no—
79#66938—24no—
80#66938—24no—
81#66938—24no—
82C4×D44—22no—
83C4×D44—21no—
84C4×D44—21no—
85#66922—22no—
86#66922—22no—
87C11×C22⋊C8—22no—
88C11×C22⋊C8C2312yes—
89C11×C22⋊C8C2312yes—
90C22⋊(C11⋊C8)—22no—
91C22⋊(C11⋊C8)C2314yes—
92#66879—24no—
93Dic11⋊C8—24no—
94Dic11⋊C8—24no—
95C8×Dic11—24no—
96#17418—111nomaximal, Sylow
97C24×C11C22×C411yescharacteristic
98C24×C11C22×C411yescharacteristic
99C23×D11C22×C412yes—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11—41no—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—42no—
106C22×C4×C11—42no—
107C22×C4×C11C22×C411yescharacteristic
108C22×C4×C11C22×C411yescharacteristic
109C22×C4×C11C22×C411yescharacteristic
110C22×C4×C11C22×C411yescharacteristic
111C22×C4×C11C2×D412yes—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2411yescharacteristic
114C2×C22⋊D11—24no—
115C2×C22⋊D11—24no—
116C2×C22⋊D11—82no—
117C2×C22⋊D11—82no—
118C22×Dic11C22×C412yes—
119C22×Dic11C22×C412yes—
120C22×Dic11C22×C412yes—
121C2×D44—21no—
122C2×D44—21no—
123C2×D44—42no—
124C2×C4×D11—22no—
125C2×C4×D11—22no—
126C2×C4×D11—24no—
127C2×C4×D11—42no—
128C2×Dic22—24no—
129C2×Dic22—82no—
130C2×C8×C11—22no—
131C2×C8×C11—22no—
132C2×C8×C11—44no—
133C11×C4⋊C4—22no—
134C11×C22⋊C4—22no—
135C11×C22⋊C4—22no—
136C42×C11—21no—
137C42×C11—21no—
138C22⋊Dic11—22no—
139C22⋊Dic11—22no—
140C22⋊Dic11C22⋊C414yes—
141C22⋊Dic11C22⋊C414yes—
142(C2×D11)⋊C4—22no—
143(C2×D11)⋊C4—22no—
144(C2×D11)⋊C4—24no—
145(C2×D11)⋊C4—24no—
146C4⋊Dic11—24no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11C22⋊C412yes—
150C4⋊Dic11C22⋊C412yes—
151C4⋊Dic11C22⋊C412yes—
152C4⋊Dic11C22⋊C411yescharacteristic
153C4⋊Dic11C22⋊C411yescharacteristic
154C4×Dic11—22no—
155C4×Dic11—22no—
156C4×Dic11C2×D414yes—
157C4×Dic11C2×D414yes—
158#4318—44no—
159C2×C11⋊C8—24no—
160C2×#555—111no—
161#2924—112no—
162#1471—112no—
163#1469—114no—
164#1465—111no—
165#1464—112no—
166#1459D1111yescharacteristic, complemented
167#1458—112no—
168C23×C11—21no—
169C23×C11—21no—
170C23×C11—21no—
171C23×C11—21no—
172C23×C11—21no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11—41no—
177C23×C11C2×C22⋊C412yes—
178C23×C11C23×C411yescharacteristic
179C22×D11—22no—
180C22×D11—22no—
181C22×D11—22no—
182C22×D11—42no—
183C22×D11—42no—
184D4×C11—44no—
185C2×C4×C11—21no—
186C2×C4×C11—21no—
187C2×C4×C11—24no—
188C2×C4×C11—22no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—41no—
196C2×C4×C11—41no—
197C2×C4×C11C2×C22⋊C411yescharacteristic
198C2×C4×C11C2×C22⋊C411yescharacteristic
199C2×C4×C11#13112yes—
200C2×C4×C11C22×D412yes—
201C22⋊D11—84no—
202C22⋊D11—84no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—22no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11C2×C22⋊C412yes—
209C2×Dic11C2×C22⋊C412yes—
210C2×Dic11C2×C22⋊C414yes—
211D44—42no—
212D44—42no—
213C4×D11—44no—
214C4×D11—44no—
215Dic22—84no—
216C8×C11—42no—
217C8×C11—42no—
218C11⋊C8—44no—
219#555—222no—
220#555—222no—
221#555—224no—
222C2×C4⋊Q8—111no—
223C2×#124—112no—
224C2×#124—112no—
225C2×#121—112no—
226C2×#121—111no—
227C2×#121—111no—
228C2×C4×D4—111no—
229C2×C4×D4C2×D1111yescharacteristic
230C2×#117—111no—
231C2×#117—111no—
232C2×#117—112no—
233#433—224no—
234#432—114no—
235#431—114no—
236#424—222no—
237#407—112no—
238C2×C22⋊C8C2×D1112yes—
239#405—222no—
240#324—112no—
241#324C2×D1111yescharacteristic
242#324C2×D1111yescharacteristic
243#323—112no—
244#323—114no—
245#323—114no—
246#323C2×D1112yes—
247C22×C11—21no—
248C22×C11—21no—
249C22×C11—22no—
250C22×C11—22no—
251C22×C11—22no—
252C22×C11—41no—
253C22×C11—41no—
254C22×C11—41no—
255C22×C11—81no—
256C22×C11—81no—
257C22×C11—81no—
258C22×C11—81no—
259C22×C11C22×C22⋊C411yescharacteristic
260C22×C11C2×#13111yescharacteristic
261C22×C11#56811yescharacteristic
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—82no—
266C2×D11—82no—
267C4×C11—22no—
268C4×C11—21no—
269C4×C11—22no—
270C4×C11—41no—
271C4×C11—41no—
272C4×C11#41012yes—
273Dic11—22no—
274Dic11—22no—
275Dic11—24no—
276Dic11—42no—
277C22×Q8—112no—
278C22×D4—112no—
279C22×D4—112no—
280C22×D4—111no—
281C22×D4C4×D1111yescharacteristic
282C23×C4—112no—
283C23×C4C4×D1111yescharacteristic
284C23×C4C22×D1111yescharacteristic
285C2×M16—222no—
286C22×C8—22no—
287C4⋊Q8—222no—
288C4⋊Q8—222no—
289#124—224no—
290#124—224no—
291#124—224no—
292#124—224no—
293#121—224no—
294#121—224no—
295#121—222no—
296#121—222no—
297#121—222no—
298#121—222no—
299C4×D4—22no—
300C4×D4—22no—
301C4×D4—222no—
302C4×D4—221no—
303C4×D4—221no—
304#117—112no—
305#117—112no—
306#117—114no—
307#117—224no—
308#117—224no—
309#117—222no—
310#117—221no—
311#117—221no—
312C2×C4⋊C4—111no—
313C2×C4⋊C4—111no—
314C2×C4⋊C4—112no—
315C2×C4⋊C4—111no—
316C2×C4⋊C4C22×D1111yescharacteristic
317C2×C22⋊C4—112no—
318C2×C22⋊C4—112no—
319C2×C22⋊C4—112no—
320C2×C22⋊C4—112no—
321C2×C22⋊C4—112no—
322C2×C22⋊C4C4×D1111yescharacteristic
323C2×C22⋊C4C22×D1111yescharacteristic
324C2×C42—112no—
325C2×C42—112no—
326C2×C42C4×D1111yescharacteristic
327C4⋊C8—224no—
328C4⋊C8—224no—
329C22⋊C8—22no—
330C22⋊C8—114no—
331C22⋊C8—222no—
332C22⋊C8C22×D1112yes—
333C22⋊C8C22×D1112yes—
334#97—224no—
335C4×C8—224no—
336C2×C11—21no—
337C2×C11—21no—
338C2×C11—42no—
339C2×C11—81no—
340C2×C11#288011yescharacteristic
341C2×C11C2×#41011yescharacteristic
342C2×C11#288811yescharacteristic
343D11—82no—
344C24—112no—
345C24C2×C4×D1111yescharacteristic
346C24C2×C4×D1111yescharacteristic
347C2×Q8—224no—
348C2×Q8—882no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—41no—
352C2×D4—224no—
353C2×D4—224no—
354C2×D4—221no—
355C2×D4—221no—
356C2×D4—442no—
357C2×D4—882no—
358C2×D4—882no—
359C22×C4—21no—
360C22×C4—21no—
361C22×C4—42no—
362C22×C4—42no—
363C22×C4—112no—
364C22×C4—112no—
365C22×C4—112no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—224no—
369C22×C4—442no—
370C22×C4C2×C4×D1111yescharacteristic
371C22×C4C2×C4×D1111yescharacteristic
372C22×C4C2×C4×D1111yescharacteristic
373C22×C4C2×C4×D1111yescharacteristic
374C22×C4D4×D1112yes—
375C22×C4D4×D1112yes—
376C22×C4C23×D1111yescharacteristic
377M16—444no—
378C2×C8—22no—
379C2×C8—22no—
380C2×C8—44no—
381C2×C8—224no—
382C4⋊C4—22no—
383C4⋊C4—112no—
384C4⋊C4—111no—
385C4⋊C4—111no—
386C4⋊C4—112no—
387C4⋊C4—112no—
388C4⋊C4—224no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—114no—
394C22⋊C4—114no—
395C22⋊C4—224no—
396C22⋊C4—222no—
397C22⋊C4—222no—
398C22⋊C4—222no—
399C22⋊C4—222no—
400C22⋊C4—224no—
401C42—21no—
402C42—21no—
403C42—114no—
404C42—114no—
405C42—222no—
406C42—222no—
407C11#1741811yescharacteristic, complemented, Sylow
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—41no—
414C23—41no—
415C23—41no—
416C23—41no—
417C23—222no—
418C23—222no—
419C23—222no—
420C23—442no—
421C23—442no—
422C23C22⋊C4×D1112yes—
423C23C22×C4×D1111yescharacteristic
424Q8—884no—
425D4—44no—
426D4—442no—
427D4—442no—
428D4—884no—
429D4—884no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—42no—
437C2×C4—41no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—41no—
441C2×C4—41no—
442C2×C4—112no—
443C2×C4—112no—
444C2×C4—114no—
445C2×C4—222no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—444no—
449C2×C4—444no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4C22⋊C4×D1111yescharacteristic
453C2×C4C22⋊C4×D1111yescharacteristic
454C2×C4#6695412yes—
455C2×C4C2×D4×D1112yes—
456C8—42no—
457C8—42no—
458C8—444no—
459C22—21no—
460C22—21no—
461C22—22no—
462C22—22no—
463C22—22no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—81no—
468C22—81no—
469C22—81no—
470C22—81no—
471C22—442no—
472C22—442no—
473C22—442no—
474C22—882no—
475C22—882no—
476C22C2×C22⋊C4×D1111yescharacteristic
477C22C2×#6695411yescharacteristic
478C22#1062327611yescharacteristic
479C4—22no—
480C4—22no—
481C4—21no—
482C4—41no—
483C4—41no—
484C4—222no—
485C4—222no—
486C4—224no—
487C4—442no—
488C4#1062235312yes—
489C2—21no—
490C2—21no—
491C2—42no—
492C2—81no—
493C2—882no—
494C2#1307706211yescharacteristic
495C2C2×#1062235311yescharacteristic
496C2#1307709311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1459C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623094C2
cosocleC22×C4×C11C24
hypercenter#1459D11
hypocenterC11#17418
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1459

Complements

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

NH ≅ G/Ntype
2. #13077270C2semidirect
3. #13066975C2semidirect
4. #13066966C2semidirect
5. #13066954C2semidirect
6. #13066949C2semidirect
7. #13066929C2semidirect
8. C11×#1459C2semidirect
166. #1459D11semidirect
407. C11#17418semidirect

Maximal subgroups

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

subgroupindex
C2×#106230942
#130772702
#130669752
#130669662
#130669542
#130669492
#130669292
C11×#14592
#1741811