Finite Group Databasebeta

← #14721513

Subgroups — #14721513

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#13077640C211yesmaximal, characteristic, complemented
2#13071589C211yesmaximal, characteristic, complemented
3#13067180C211yesmaximal, characteristic, complemented
4#13067176C211yesmaximal, characteristic, complemented
5#13067172C214yesmaximal, complemented
6#13067115C211yesmaximal, characteristic, complemented
7#13067111C211yesmaximal, characteristic, complemented
8#13067107C214yesmaximal, complemented
9C11×#3506C211yesmaximal, characteristic
10C11×#559—22no—
11C11×#556C412yescomplemented
12C11×#555C412yescomplemented
13C11×#553—22no—
14C11×#550C412yescomplemented
15C11×#547C412yescomplemented
16C11×#538—22no—
17C11×#535—21no—
18C11×#533C2211yescharacteristic
19C11×#532C2211yescharacteristic
20C11×#525C2214yes—
21C11×#520—21no—
22C2×C4×D4×C11C2211yescharacteristic
23#10622834—21no—
24#10622824C2212yes—
25C4×C22⋊Dic11C2212yes—
26C2×C22⋊(C11⋊C8)C2214yes—
27D4×C11⋊C8—22no—
28D4×C11⋊C8—22no—
29C4⋊C4×Dic11—21no—
30#10622564—22no—
31#10622549C2211yescharacteristic
32C4×C4⋊Dic11C2211yescharacteristic
33#10622538C2211yescharacteristic
34#10622538C2211yescharacteristic
35#10622176C2212yes—
36#10622176C2214yes—
37#10622176C2212yes—
38#10622175C2212yes—
39#10622175C2214yes—
40#10622175C2212yes—
41C2×C11×#41—21no—
42C2×C11×#41C2×C414yes—
43C22×D4×C11D411yescharacteristic
44C23×C4×C11C2312yes—
45C11×C4⋊Q8C2×C411yescharacteristic
46C11×C4⋊Q8C2×C411yescharacteristic
47C11×C4⋊Q8C2×C411yescharacteristic
48C11×#127—22no—
49C11×#127C2×C411yescharacteristic
50C11×#126—24no—
51C11×#125—21no—
52C11×#124—22no—
53C11×#124—24no—
54C11×#124—21no—
55C11×#123—24no—
56C11×#123—24no—
57C11×C22⋊Q8—21no—
58C11×C22⋊Q8C2×C414yes—
59C11×C22⋊Q8C2312yes—
60C11×#121—22no—
61C11×#121—22no—
62C11×#121—21no—
63C11×#121—24no—
64C11×#121C2×C414yes—
65C11×#121C2312yes—
66C11×#120—24no—
67C4×Q8×C11—22no—
68C4×Q8×C11—21no—
69C4×Q8×C11C2×C412yes—
70C4×D4×C11—24no—
71C4×D4×C11—24no—
72C4×D4×C11—22no—
73C4×D4×C11—21no—
74C4×D4×C11C2×C412yes—
75C4×D4×C11C2×C412yes—
76C4×D4×C11C2×C412yes—
77C4×D4×C11D412yes—
78C4×D4×C11D412yes—
79C11×#117—21no—
80C11×#117—22no—
81C11×#117C2×C414yes—
82C2×C11×C4⋊C4—22no—
83C2×C11×C4⋊C4D411yescharacteristic
84C2×C11×C22⋊C4D412yes—
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88C2×C4⋊Dic11—21no—
89C2×C4⋊Dic11—21no—
90C2×C4×Dic11—21no—
91C2×C4×Dic11—22no—
92C22×C11⋊C8—24no—
93C11⋊#95—21no—
94C11⋊#95—22no—
95C11⋊#95C2311yescharacteristic
96C11⋊#95C2311yescharacteristic
97C11⋊#95C2312yes—
98C22⋊(C11⋊C8)—24no—
99C22⋊(C11⋊C8)C2312yes—
100C22⋊(C11⋊C8)C2312yes—
101C4⋊(C11⋊C8)—21no—
102C4⋊(C11⋊C8)—21no—
103C4×C11⋊C8—21no—
104C4×C11⋊C8—21no—
105#17617—111nomaximal, Sylow
106C24×C11C2×D412yes—
107C11×#41—42no—
108C11×#41—42no—
109C11×#41—84no—
110C2×Q8×C11—21no—
111C2×Q8×C11—21no—
112C2×Q8×C11C22×C412yes—
113C2×D4×C11—22no—
114C2×D4×C11—24no—
115C2×D4×C11—24no—
116C2×D4×C11—21no—
117C2×D4×C11—21no—
118C2×D4×C11—22no—
119C2×D4×C11—22no—
120C2×D4×C11C22⋊C412yes—
121C2×D4×C11C22⋊C412yes—
122C2×D4×C11C22×C412yes—
123C22×C4×C11—22no—
124C22×C4×C11—24no—
125C22×C4×C11—82no—
126C22×C4×C11C22×C414yes—
127C22×C4×C11C2×D412yes—
128C22×C4×C11C2×D411yescharacteristic
129C22×C4×C11C2×D414yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2411yescharacteristic
132C22×Dic11—21no—
133C22×Dic11—22no—
134C22×Dic11—21no—
135C11×C4⋊C4—21no—
136C11×C4⋊C4—24no—
137C11×C4⋊C4—21no—
138C11×C4⋊C4—21no—
139C11×C4⋊C4—21no—
140C11×C4⋊C4—22no—
141C11×C4⋊C4—22no—
142C11×C4⋊C4C22⋊C412yes—
143C11×C4⋊C4C22⋊C412yes—
144C11×C4⋊C4C22×C412yes—
145C11×C4⋊C4C22×C412yes—
146C11×C22⋊C4—24no—
147C11×C22⋊C4—24no—
148C11×C22⋊C4—22no—
149C11×C22⋊C4—24no—
150C11×C22⋊C4—22no—
151C11×C22⋊C4—22no—
152C11×C22⋊C4C22⋊C414yes—
153C11×C22⋊C4C22⋊C414yes—
154C42×C11—24no—
155C42×C11—22no—
156C42×C11C22×C411yescharacteristic
157C42×C11C22×C411yescharacteristic
158C42×C11C2×D411yescharacteristic
159C42×C11C2×D411yescharacteristic
160C22⋊Dic11—44no—
161C22⋊Dic11—82no—
162C4⋊Dic11—42no—
163C4⋊Dic11—42no—
164C4×Dic11—42no—
165C4×Dic11—82no—
166C2×C11⋊C8—22no—
167C2×C11⋊C8—22no—
168C2×C11⋊C8—84no—
169#3506D1111yescharacteristic
170#2972—111no—
171#2357—111no—
172#1518—111no—
173#1517—111no—
174#1516—114no—
175#1503—111no—
176#1502—111no—
177#1501—114no—
178C23×C11—22no—
179C23×C11—22no—
180C23×C11—22no—
181C23×C11—42no—
182C23×C11—42no—
183C23×C11C2×C22⋊C414yes—
184C23×C11C22×D411yescharacteristic
185Q8×C11—42no—
186Q8×C11—42no—
187Q8×C11—81no—
188D4×C11—24no—
189D4×C11—24no—
190D4×C11—42no—
191D4×C11—42no—
192D4×C11—42no—
193D4×C11—42no—
194D4×C11—81no—
195D4×C11—84no—
196D4×C11—84no—
197C2×C4×C11—22no—
198C2×C4×C11—22no—
199C2×C4×C11—22no—
200C2×C4×C11—44no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—41no—
204C2×C4×C11—44no—
205C2×C4×C11—44no—
206C2×C4×C11—84no—
207C2×C4×C11C2×C22⋊C414yes—
208C2×C4×C11C2×C22⋊C411yescharacteristic
209C2×C4×C11C2×C22⋊C411yescharacteristic
210C2×C4×C11C2×C22⋊C411yescharacteristic
211C2×C4×C11C2×C22⋊C411yescharacteristic
212C2×C4×C11#13512yes—
213C2×C4×C11#13512yes—
214C2×C4×C11C23×C411yescharacteristic
215C2×C4×C11C22×D411yescharacteristic
216C2×Dic11—22no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—41no—
221C2×Dic11—42no—
222C2×Dic11—41no—
223C2×Dic11—41no—
224C2×Dic11—42no—
225C11⋊C8—42no—
226C11⋊C8—42no—
227#559—22no—
228#556Dic1112yescomplemented
229#555Dic1112yescomplemented
230#553—22no—
231#550Dic1112yescomplemented
232#547Dic1112yescomplemented
233#538—22no—
234#535—21no—
235#533C2×D1111yescharacteristic
236#532C2×D1111yescharacteristic
237#525C2×D1114yes—
238#520—21no—
239C2×C4×D4C2×D1111yescharacteristic
240C8×D4—222no—
241C8×D4—222no—
242#431—111no—
243#431—111no—
244C2×C22⋊C8—114no—
245#390—221no—
246#388—222no—
247#382—111no—
248#381—112no—
249C4×C4⋊C4—111no—
250C4×C4⋊C4—221no—
251C4×C22⋊C4—112no—
252#328—112no—
253#328—114no—
254#328—112no—
255#327—112no—
256#327—114no—
257#327—112no—
258C22×C11—21no—
259C22×C11—21no—
260C22×C11—24no—
261C22×C11—24no—
262C22×C11—24no—
263C22×C11—42no—
264C22×C11—42no—
265C22×C11—42no—
266C22×C11—82no—
267C22×C11—82no—
268C22×C11C22×C22⋊C411yescharacteristic
269C22×C11C2×#13511yescharacteristic
270C22×C11C2×#13511yescharacteristic
271C4×C11—21no—
272C4×C11—21no—
273C4×C11—24no—
274C4×C11—21no—
275C4×C11—21no—
276C4×C11—42no—
277C4×C11—42no—
278C4×C11—42no—
279C4×C11#41612yes—
280C4×C11#41612yes—
281Dic11—42no—
282Dic11—81no—
283Dic11—82no—
284C2×#41—21no—
285C2×#41C2×Dic1114yes—
286C22×D4C22⋊D1111yescharacteristic
287C23×C4C22×D1112yes—
288C22×C8—224no—
289C4⋊Q8C2×Dic1111yescharacteristic
290C4⋊Q8C2×Dic1111yescharacteristic
291C4⋊Q8C2×Dic1111yescharacteristic
292#127—22no—
293#127C2×Dic1111yescharacteristic
294#126—24no—
295#125—21no—
296#124—22no—
297#124—24no—
298#124—21no—
299#123—24no—
300#123—24no—
301C22⋊Q8—21no—
302C22⋊Q8C2×Dic1114yes—
303C22⋊Q8C22×D1112yes—
304#121—22no—
305#121—22no—
306#121—21no—
307#121—24no—
308#121C2×Dic1114yes—
309#121C22×D1112yes—
310#120—24no—
311C4×Q8—22no—
312C4×Q8—21no—
313C4×Q8C2×Dic1112yes—
314C4×D4—24no—
315C4×D4—24no—
316C4×D4—22no—
317C4×D4—21no—
318C4×D4C2×Dic1112yes—
319C4×D4C2×Dic1112yes—
320C4×D4C2×Dic1112yes—
321C4×D4C22⋊D1112yes—
322C4×D4C22⋊D1112yes—
323#117—21no—
324#117—22no—
325#117C2×Dic1114yes—
326C2×C4⋊C4—22no—
327C2×C4⋊C4—221no—
328C2×C4⋊C4—221no—
329C2×C4⋊C4C22⋊D1111yescharacteristic
330C2×C22⋊C4—222no—
331C2×C22⋊C4—222no—
332C2×C22⋊C4C22⋊D1112yes—
333C2×C42—221no—
334C2×C42—222no—
335C2×C42C22×D1111yescharacteristic
336C4⋊C8—221no—
337C4⋊C8—221no—
338C22⋊C8—112no—
339C22⋊C8—112no—
340C22⋊C8—224no—
341C4×C8—221no—
342C4×C8—221no—
343#95—111no—
344#95—112no—
345#95—111no—
346#95—222no—
347#95—221no—
348C2×C11—21no—
349C2×C11—21no—
350C2×C11—44no—
351C2×C11—82no—
352C2×C11#288311yescharacteristic
353C2×C11C2×#41611yescharacteristic
354C2×C11#290111yescharacteristic
355C24C2×C22⋊D1112yes—
356#41—42no—
357#41—42no—
358#41—84no—
359C2×Q8—21no—
360C2×Q8—21no—
361C2×Q8C22×Dic1112yes—
362C2×D4—22no—
363C2×D4—24no—
364C2×D4—24no—
365C2×D4—22no—
366C2×D4—22no—
367C2×D4—21no—
368C2×D4—21no—
369C2×D4C22⋊Dic1112yes—
370C2×D4C22⋊Dic1112yes—
371C2×D4C22×Dic1112yes—
372C22×C4—22no—
373C22×C4—24no—
374C22×C4—82no—
375C22×C4—221no—
376C22×C4—222no—
377C22×C4—221no—
378C22×C4C22×Dic1114yes—
379C22×C4C2×C22⋊D1112yes—
380C22×C4C2×C22⋊D1111yescharacteristic
381C22×C4C2×C22⋊D1114yes—
382C22×C4C2×C22⋊D1111yescharacteristic
383C22×C4C23×D1111yescharacteristic
384C2×C8—222no—
385C2×C8—222no—
386C2×C8—884no—
387C4⋊C4—21no—
388C4⋊C4—24no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—22no—
393C4⋊C4—22no—
394C4⋊C4—442no—
395C4⋊C4—442no—
396C4⋊C4C22⋊Dic1112yes—
397C4⋊C4C22⋊Dic1112yes—
398C4⋊C4C22×Dic1112yes—
399C4⋊C4C22×Dic1112yes—
400C22⋊C4—24no—
401C22⋊C4—24no—
402C22⋊C4—22no—
403C22⋊C4—24no—
404C22⋊C4—22no—
405C22⋊C4—22no—
406C22⋊C4—444no—
407C22⋊C4—882no—
408C22⋊C4C22⋊Dic1114yes—
409C22⋊C4C22⋊Dic1114yes—
410C42—24no—
411C42—22no—
412C42—442no—
413C42—882no—
414C42C22×Dic1111yescharacteristic
415C42C22×Dic1111yescharacteristic
416C42C2×C22⋊D1111yescharacteristic
417C42C2×C22⋊D1111yescharacteristic
418C11#1761711yescharacteristic, complemented, Sylow
419C23—22no—
420C23—22no—
421C23—22no—
422C23—42no—
423C23—42no—
424C23C2×C22⋊Dic1114yes—
425C23C22×C22⋊D1111yescharacteristic
426Q8—42no—
427Q8—42no—
428Q8—81no—
429D4—24no—
430D4—24no—
431D4—42no—
432D4—42no—
433D4—42no—
434D4—42no—
435D4—81no—
436D4—84no—
437D4—84no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—22no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—44no—
444C2×C4—41no—
445C2×C4—44no—
446C2×C4—44no—
447C2×C4—84no—
448C2×C4—222no—
449C2×C4—441no—
450C2×C4—441no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—441no—
454C2×C4—441no—
455C2×C4—441no—
456C2×C4—442no—
457C2×C4#6700312yes—
458C2×C4#6700312yes—
459C2×C4C2×C22⋊Dic1114yes—
460C2×C4C2×C22⋊Dic1111yescharacteristic
461C2×C4C2×C22⋊Dic1111yescharacteristic
462C2×C4C2×C22⋊Dic1111yescharacteristic
463C2×C4C2×C22⋊Dic1111yescharacteristic
464C2×C4C23×Dic1111yescharacteristic
465C2×C4C22×C22⋊D1111yescharacteristic
466C8—442no—
467C8—442no—
468C22—21no—
469C22—21no—
470C22—24no—
471C22—24no—
472C22—24no—
473C22—42no—
474C22—42no—
475C22—42no—
476C22—82no—
477C22—82no—
478C22C2×#6700311yescharacteristic
479C22C2×#6700311yescharacteristic
480C22C22×C22⋊Dic1111yescharacteristic
481C4—21no—
482C4—21no—
483C4—24no—
484C4—21no—
485C4—21no—
486C4—42no—
487C4—42no—
488C4—42no—
489C4—442no—
490C4—881no—
491C4—882no—
492C4#1062284612yes—
493C4#1062284612yes—
494C2—21no—
495C2—21no—
496C2—44no—
497C2—82no—
498C2#1307707711yescharacteristic
499C2C2×#1062284611yescharacteristic
500C2#1307716311yescharacteristic
subgroupG/H
centerC22C22×C22⋊Dic11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC11×#3506C2
socleC22×C11C22×C22⋊C4
cosocleC22×C4×C11C24
hypercenter#3506D11
hypocenterC11#17617
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ #3506

Complements

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

NH ≅ G/Ntype
1. #13077640C2semidirect
2. #13071589C2semidirect
3. #13067180C2semidirect
4. #13067176C2semidirect
5. #13067172C2semidirect
6. #13067115C2semidirect
7. #13067111C2semidirect
8. #13067107C2semidirect
11. C11×#556C4semidirect
12. C11×#555C4semidirect
14. C11×#550C4semidirect
15. C11×#547C4semidirect
228. #556Dic11semidirect
229. #555Dic11semidirect
231. #550Dic11semidirect
232. #547Dic11semidirect
418. C11#17617semidirect

Maximal subgroups

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

subgroupindex
#130776402
#130715892
#130671802
#130671762
#130671722
#130671152
#130671112
#130671072
C11×#35062
#1761711