Finite Group Databasebeta

← #14721515

Subgroups — #14721515

Order 2816.

1018 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
1#13082465C211yesmaximal, characteristic
2#13077639C211yesmaximal, characteristic, complemented
3#13071591C211yesmaximal, characteristic, complemented
4#13067179C211yesmaximal, characteristic, complemented
5#13067169C214yesmaximal, complemented
6#13067116C211yesmaximal, characteristic, complemented
7#13067111C211yesmaximal, characteristic, complemented
8#13067104C214yesmaximal, complemented
9C11×#1517C211yesmaximal, characteristic, complemented
10C11×#532C2211yescharacteristic
11#10623361—21no—
12#10623358—21no—
13#10623263C412yescomplemented
14#10623249C412yescomplemented
15#10623212—22no—
16#10623148—22no—
17#10623137C2214yes—
18#10623096—22no—
19#10623094C412yescomplemented
20#10623086C412yescomplemented
21C2×C4×D44C2211yescharacteristic
22#10623001C2211yescharacteristic
23C11×#431C2211yescharacteristic
24C11×#382C2211yescharacteristic
25#10622601—21no—
26C4⋊C4×Dic11—21no—
27C4×C4⋊Dic11C2211yescharacteristic
28#10622538C2211yescharacteristic
29#10622447—22no—
30D11×C22⋊C8C2214yes—
31C8×D44—22no—
32#10622283—22no—
33#10622279C2212yes—
34#10622277C2212yes—
35C11×#327C2214yes—
36#10622175C2212yes—
37#10622175C2212yes—
38#10622105C2212yes—
39#10622105C2212yes—
40#10622090C2214yes—
41C2×C11×#41—21no—
42C2×#4341C2×C414yes—
43C22×D44D411yescharacteristic
44C22×C4×D11C2312yes—
45C11×C4⋊Q8C2×C411yescharacteristic
46C11×#127C2×C411yescharacteristic
47C11×#124—21no—
48C11×#121—21no—
49C11×#121C2312yes—
50C4×D4×C11—21no—
51C4×D4×C11C2×C412yes—
52C2×C11×C4⋊C4—21no—
53C2×C42×C11C2311yescharacteristic
54#67000—22no—
55Q8×Dic11—22no—
56#66993—22no—
57#66992—24no—
58#66991C2×C414yes—
59#66990—24no—
60D4×Dic11—24no—
61D4×Dic11—22no—
62#66983—22no—
63#66983—22no—
64C2×(C2×D11)⋊C4—22no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4D412yes—
67#66979—21no—
68#66979—22no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11D411yescharacteristic
72#66977—21no—
73#66977C2312yes—
74C2×C4×Dic11—21no—
75C2×C4×Dic11—22no—
76C2×C8×D11—24no—
77#66951—24no—
78#66950C2×C414yes—
79#66945C2×C414yes—
80#66939—24no—
81#66938—24no—
82#66936—24no—
83(C22⋊D11)⋊C4—24no—
84C4×D44C2×C412yes—
85C4×D44C2×C412yes—
86C4×D44D412yes—
87C4×D44D412yes—
88#66923—21no—
89#66922C2×C411yescharacteristic
90#66922C2×C411yescharacteristic
91C4×Dic22—21no—
92C4×Dic22C2×C412yes—
93C11×C4⋊C8—21no—
94C11×C22⋊C8C2312yes—
95C4×C8×C11—21no—
96C11×#95—21no—
97C11×#95C2312yes—
98C11⋊#95—22no—
99C11⋊#95C2311yescharacteristic
100C11⋊#95C2311yescharacteristic
101C22⋊(C11⋊C8)C2312yes—
102(C2×D11)⋊C8—24no—
103C4⋊(C11⋊C8)—21no—
104C4×C11⋊C8—21no—
105#17617—111nomaximal, Sylow
106C23×D11C2×D412yes—
107C11×#41—42no—
108C11×#41—42no—
109C2×Q8×C11—21no—
110C2×D4×C11—22no—
111C2×D4×C11—21no—
112C2×D4×C11—21no—
113C2×D4×C11C22×C412yes—
114C22×C4×C11—22no—
115C22×C4×C11—22no—
116C22×C4×C11C2×D411yescharacteristic
117C22×C4×C11C2×D411yescharacteristic
118C22×C4×C11C2411yescharacteristic
119C2×C22⋊D11—24no—
120C2×C22⋊D11—24no—
121C22×Dic11—24no—
122C22×Dic11—21no—
123C22×Dic11—21no—
124C22×Dic11C2×D412yes—
125#4341—84no—
126C2×D44—22no—
127C2×D44—22no—
128C2×D44C22⋊C412yes—
129C2×D44C22⋊C412yes—
130C2×C4×D11—82no—
131C2×C4×D11C22×C414yes—
132C2×C4×D11C2×D414yes—
133C2×Dic22—21no—
134C2×Dic22C22×C412yes—
135C2×C8×C11—22no—
136C11×C4⋊C4—21no—
137C11×C4⋊C4—42no—
138C11×C4⋊C4C22×C412yes—
139C11×C22⋊C4—22no—
140C11×C22⋊C4—22no—
141C42×C11C22×C411yescharacteristic
142C42×C11C22×C411yescharacteristic
143C42×C11C2×D411yescharacteristic
144C42×C11C2×D411yescharacteristic
145C22⋊Dic11—24no—
146C22⋊Dic11—22no—
147(C2×D11)⋊C4—24no—
148(C2×D11)⋊C4—24no—
149(C2×D11)⋊C4—44no—
150(C2×D11)⋊C4—82no—
151(C2×D11)⋊C4C22⋊C414yes—
152(C2×D11)⋊C4C22⋊C414yes—
153C4⋊Dic11—24no—
154C4⋊Dic11—21no—
155C4⋊Dic11—21no—
156C4⋊Dic11—21no—
157C4⋊Dic11—42no—
158C4⋊Dic11C22⋊C412yes—
159C4⋊Dic11C22⋊C412yes—
160C4⋊Dic11C22×C412yes—
161Dic11⋊C4—22no—
162Dic11⋊C4—22no—
163C4×Dic11—24no—
164C4×Dic11—22no—
165C4×Dic11—42no—
166C4×Dic11—82no—
167C2×C11⋊C8—22no—
168C8×D11—84no—
169#3506—111no—
170#2972—111no—
171#2357—111no—
172#1518—111no—
173#1517D1111yescharacteristic, complemented
174#1516—114no—
175#1503—111no—
176#1502—111no—
177#1501—114no—
178C23×C11—22no—
179C23×C11C22×D411yescharacteristic
180C22×D11—22no—
181C22×D11—22no—
182C22×D11—42no—
183C22×D11—42no—
184C22×D11C2×C22⋊C414yes—
185Q8×C11—42no—
186D4×C11—42no—
187D4×C11—42no—
188D4×C11—42no—
189D4×C11—42no—
190D4×C11—81no—
191C2×C4×C11—22no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—44no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11—42no—
198C2×C4×C11C2×C22⋊C411yescharacteristic
199C2×C4×C11C2×C22⋊C411yescharacteristic
200C2×C4×C11C2×C22⋊C411yescharacteristic
201C2×C4×C11C2×C22⋊C411yescharacteristic
202C2×C4×C11#13512yes—
203C2×C4×C11#13512yes—
204C2×C4×C11C23×C411yescharacteristic
205C2×C4×C11C22×D411yescharacteristic
206C22⋊D11—84no—
207C22⋊D11—84no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—41no—
217C2×Dic11—84no—
218C2×Dic11C2×C22⋊C414yes—
219D44—24no—
220D44—24no—
221C4×D11—44no—
222C4×D11—44no—
223Dic22—42no—
224Dic22—81no—
225C8×C11—42no—
226C11⋊C8—42no—
227#559—222no—
228#556—112no—
229#555—112no—
230#553—222no—
231#550—112no—
232#547—112no—
233#538—222no—
234#535—221no—
235#533—111no—
236#532C2×D1111yescharacteristic
237#525—114no—
238#520—221no—
239C2×C4×D4—111no—
240C8×D4—222no—
241C8×D4—222no—
242#431—111no—
243#431C2×D1111yescharacteristic
244C2×C22⋊C8—114no—
245#390—221no—
246#388—222no—
247#382C2×D1111yescharacteristic
248#381—112no—
249C4×C4⋊C4—111no—
250C4×C4⋊C4—221no—
251C4×C22⋊C4—112no—
252#328—112no—
253#328—112no—
254#328—114no—
255#327—112no—
256#327—112no—
257#327C2×D1114yes—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—42no—
261C22×C11—42no—
262C22×C11—42no—
263C22×C11C22×C22⋊C411yescharacteristic
264C22×C11C2×#13511yescharacteristic
265C22×C11C2×#13511yescharacteristic
266C2×D11—24no—
267C2×D11—24no—
268C2×D11—24no—
269C2×D11—82no—
270C2×D11—82no—
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—21no—
274C4×C11—21no—
275C4×C11—42no—
276C4×C11—82no—
277C4×C11#41612yes—
278C4×C11#41612yes—
279Dic11—24no—
280Dic11—42no—
281Dic11—42no—
282Dic11—42no—
283Dic11—81no—
284C2×#41—21no—
285C2×#41—114no—
286C22×D4—111no—
287C23×C4—112no—
288C22×C8—224no—
289C4⋊Q8—111no—
290C4⋊Q8—111no—
291C4⋊Q8C4×D1111yescharacteristic
292#127—222no—
293#127C4×D1111yescharacteristic
294#126—224no—
295#125—221no—
296#124—21no—
297#124—224no—
298#124—222no—
299#123—224no—
300#123—224no—
301C22⋊Q8—112no—
302C22⋊Q8—114no—
303C22⋊Q8—221no—
304#121—21no—
305#121—114no—
306#121—224no—
307#121—222no—
308#121—222no—
309#121C22×D1112yes—
310#120—224no—
311C4×Q8—112no—
312C4×Q8—222no—
313C4×Q8—221no—
314C4×D4—21no—
315C4×D4—112no—
316C4×D4—112no—
317C4×D4—112no—
318C4×D4—112no—
319C4×D4—224no—
320C4×D4—222no—
321C4×D4—224no—
322C4×D4C4×D1112yes—
323#117—114no—
324#117—222no—
325#117—221no—
326C2×C4⋊C4—21no—
327C2×C4⋊C4—111no—
328C2×C4⋊C4—222no—
329C2×C4⋊C4—221no—
330C2×C22⋊C4—112no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4—222no—
333C2×C42—221no—
334C2×C42—222no—
335C2×C42C22×D1111yescharacteristic
336C4⋊C8—21no—
337C4⋊C8—221no—
338C22⋊C8—112no—
339C22⋊C8—224no—
340C22⋊C8C22×D1112yes—
341C4×C8—21no—
342C4×C8—221no—
343#95—21no—
344#95—111no—
345#95—111no—
346#95—222no—
347#95C22×D1112yes—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11—82no—
351C2×C11#288311yescharacteristic
352C2×C11C2×#41611yescharacteristic
353C2×C11#290111yescharacteristic
354D11—44no—
355C24—112no—
356#41—42no—
357#41—42no—
358#41—884no—
359C2×Q8—21no—
360C2×Q8—112no—
361C2×Q8—221no—
362C2×D4—22no—
363C2×D4—21no—
364C2×D4—21no—
365C2×D4—112no—
366C2×D4—112no—
367C2×D4—224no—
368C2×D4—224no—
369C2×D4—222no—
370C2×D4—222no—
371C2×D4C2×C4×D1112yes—
372C22×C4—22no—
373C22×C4—22no—
374C22×C4—112no—
375C22×C4—114no—
376C22×C4—114no—
377C22×C4—224no—
378C22×C4—221no—
379C22×C4—221no—
380C22×C4—882no—
381C22×C4D4×D1111yescharacteristic
382C22×C4D4×D1111yescharacteristic
383C22×C4C23×D1111yescharacteristic
384C2×C8—22no—
385C2×C8—222no—
386C2×C8—884no—
387C4⋊C4—21no—
388C4⋊C4—42no—
389C4⋊C4—112no—
390C4⋊C4—112no—
391C4⋊C4—112no—
392C4⋊C4—224no—
393C4⋊C4—221no—
394C4⋊C4—221no—
395C4⋊C4—222no—
396C4⋊C4—221no—
397C4⋊C4—222no—
398C4⋊C4—442no—
399C4⋊C4C2×C4×D1112yes—
400C22⋊C4—22no—
401C22⋊C4—22no—
402C22⋊C4—114no—
403C22⋊C4—114no—
404C22⋊C4—224no—
405C22⋊C4—224no—
406C22⋊C4—224no—
407C22⋊C4—222no—
408C22⋊C4—444no—
409C22⋊C4—882no—
410C42—224no—
411C42—222no—
412C42—442no—
413C42—882no—
414C42C2×C4×D1111yescharacteristic
415C42C2×C4×D1111yescharacteristic
416C42D4×D1111yescharacteristic
417C42D4×D1111yescharacteristic
418C11#1761711yescharacteristic, complemented, Sylow
419C23—22no—
420C23—114no—
421C23—222no—
422C23—222no—
423C23—442no—
424C23—442no—
425C23C2×D4×D1111yescharacteristic
426Q8—42no—
427Q8—442no—
428Q8—881no—
429D4—42no—
430D4—42no—
431D4—42no—
432D4—42no—
433D4—81no—
434D4—224no—
435D4—224no—
436D4—884no—
437D4—884no—
438C2×C4—22no—
439C2×C4—41no—
440C2×C4—41no—
441C2×C4—44no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—114no—
446C2×C4—222no—
447C2×C4—222no—
448C2×C4—222no—
449C2×C4—444no—
450C2×C4—444no—
451C2×C4—442no—
452C2×C4—441no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—441no—
457C2×C4—884no—
458C2×C4C22⋊C4×D1111yescharacteristic
459C2×C4C22⋊C4×D1111yescharacteristic
460C2×C4C22⋊C4×D1111yescharacteristic
461C2×C4C22⋊C4×D1111yescharacteristic
462C2×C4#6696512yes—
463C2×C4#6696912yes—
464C2×C4C22×C4×D1111yescharacteristic
465C2×C4C2×D4×D1111yescharacteristic
466C8—42no—
467C8—442no—
468C22—21no—
469C22—21no—
470C22—42no—
471C22—42no—
472C22—42no—
473C22—224no—
474C22—224no—
475C22—224no—
476C22—882no—
477C22—882no—
478C22C2×C22⋊C4×D1111yescharacteristic
479C22C2×#6696511yescharacteristic
480C22C2×#6696911yescharacteristic
481C4—21no—
482C4—21no—
483C4—21no—
484C4—21no—
485C4—42no—
486C4—82no—
487C4—224no—
488C4—442no—
489C4—442no—
490C4—442no—
491C4—881no—
492C4#1062238512yes—
493C4#1062238512yes—
494C2—21no—
495C2—21no—
496C2—82no—
497C2—444no—
498C2#1307707511yescharacteristic
499C2C2×#1062238511yescharacteristic
500C2#1307716211yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1517C2
socleC22×C11C22×C22⋊C4
prime radical#13082465C2
cosocleC22×C4×C11C24
hypercenter#1517D11
hypocenterC11#17617
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1517

Complements

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

NH ≅ G/Ntype
2. #13077639C2semidirect
3. #13071591C2semidirect
4. #13067179C2semidirect
5. #13067169C2semidirect
6. #13067116C2semidirect
7. #13067111C2semidirect
8. #13067104C2semidirect
9. C11×#1517C2semidirect
13. #10623263C4semidirect
14. #10623249C4semidirect
19. #10623094C4semidirect
20. #10623086C4semidirect
173. #1517D11semidirect
418. C11#17617semidirect

Maximal subgroups

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

subgroupindex
#130824652
#130776392
#130715912
#130671792
#130671692
#130671162
#130671112
#130671042
C11×#15172
#1761711