Finite Group Databasebeta

← #14719624

Subgroups — #14719624

Order 2816.

1322 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66945C211yesmaximal, characteristic
2#13077245C212yesmaximal, complemented
3#13066949C214yesmaximal, complemented
4#13066946C211yesmaximal, characteristic, complemented
5#13066942C212yesmaximal
6#13066929C214yesmaximal, complemented
7C11×#1463C211yesmaximal, characteristic, complemented
8C23×C4×D11C411yescharacteristic
9C22×C11×C4⋊C4C2211yescharacteristic
10C22×(C2×D11)⋊C4C411yescharacteristic
11C22×(C2×D11)⋊C4C2211yescharacteristic
12C22×C4⋊Dic11C411yescharacteristic
13C22×C4×Dic11C411yescharacteristic
14C22×C4×Dic11C2211yescharacteristic
15C2×#66945—22no—
16C2×#66945—22no—
17C2×#66945—22no—
18C2×#66945—22no—
19C2×#66945C412yes—
20C2×#66945C412yes—
21C2×#66945C2212yes—
22C2×#66945C2212yes—
23C11×#407C2212yes—
24#10622820C2212yes—
25#10622731—22no—
26M16×Dic11—22no—
27#10622332—22no—
28#10622332C2214yescomplemented
29#10622331—22no—
30#10622331C2214yescomplemented
31C11×#324C2214yescomplemented
32#10622166C2214yescomplemented
33#10622106C2218yes—
34C24×D11C2×C411yescharacteristic
35C23×C4×C11C2×C411yescharacteristic
36C23×C4×C11C2×C411yescharacteristic
37C23×C4×C11C2311yescharacteristic
38C23×Dic11C2×C411yescharacteristic
39C23×Dic11C2×C411yescharacteristic
40C23×Dic11C2×C411yescharacteristic
41C22×C4×D11—21no—
42C22×C4×D11—21no—
43C22×C4×D11—21no—
44C22×C4×D11—21no—
45C22×C4×D11—28no—
46C22×C4×D11C2×C412yes—
47C22×C4×D11C2×C412yes—
48C2×C11×M16—22no—
49C2×C11×C4⋊C4—22no—
50C2×C11×C4⋊C4—22no—
51C2×C11×C4⋊C4C2×C412yes—
52C2×C11×C4⋊C4C2312yes—
53C2×(C2×D11)⋊C4—22no—
54C2×(C2×D11)⋊C4—22no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4C2×C412yes—
58C2×(C2×D11)⋊C4C2×C412yes—
59C2×(C2×D11)⋊C4C2×C412yes—
60C2×(C2×D11)⋊C4C2312yes—
61C2×C4⋊Dic11—22no—
62C2×C4⋊Dic11—22no—
63C2×C4⋊Dic11C2×C412yes—
64C2×C4⋊Dic11C2×C412yes—
65C2×C4×Dic11—21no—
66C2×C4×Dic11—21no—
67C2×C4×Dic11—21no—
68C2×C4×Dic11—21no—
69C2×C4×Dic11C2×C412yes—
70C2×C4×Dic11C2×C412yes—
71C2×C4×Dic11C2×C411yescharacteristic
72C2×C4×Dic11C2×C411yescharacteristic
73C2×C4×Dic11D412yes—
74C2×C4×Dic11D412yes—
75C2×C4×Dic11D412yes—
76C2×C4×Dic11D412yes—
77C2×C4×Dic11C2311yescharacteristic
78C2×C4×Dic11C2311yescharacteristic
79C2×#4318—22no—
80#66945—24no—
81#66945—24no—
82#66945—24no—
83#66945—24no—
84#66945—24no—
85#66945—24no—
86#66945—24no—
87#66945—24no—
88C11×C22⋊C8—22no—
89C11×C22⋊C8C2314yes—
90C22⋊(C11⋊C8)—22no—
91C22⋊(C11⋊C8)C2314yes—
92#66879—24no—
93Dic11⋊C8—24no—
94Dic11⋊C8—24no—
95C8×Dic11—24no—
96#17357—111nomaximal, Sylow
97C24×C11C22×C411yescharacteristic
98C23×D11—21no—
99C23×D11—21no—
100C23×D11—24no—
101C23×D11—42no—
102C23×D11—42no—
103C23×D11C22×C412yes—
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—24no—
107C22×C4×C11—21no—
108C22×C4×C11—21no—
109C22×C4×C11—42no—
110C22×C4×C11—42no—
111C22×C4×C11C22×C412yes—
112C22×C4×C11C22×C412yes—
113C22×C4×C11C22×C411yescharacteristic
114C22×C4×C11C2×D412yes—
115C22×C4×C11C2×D412yes—
116C22×C4×C11C2411yescharacteristic
117C22×Dic11—24no—
118C22×Dic11—21no—
119C22×Dic11—21no—
120C22×Dic11—42no—
121C22×Dic11—42no—
122C22×Dic11C22⋊C411yescharacteristic
123C22×Dic11C22⋊C411yescharacteristic
124C22×Dic11C22⋊C411yescharacteristic
125C22×Dic11C22⋊C411yescharacteristic
126C22×Dic11C22⋊C412yes—
127C22×Dic11C22⋊C412yes—
128C22×Dic11C22×C411yescharacteristic
129C22×Dic11C22×C412yes—
130C22×Dic11C22×C411yescharacteristic
131C22×Dic11C22×C411yescharacteristic
132C22×Dic11C22×C411yescharacteristic
133C2×C4×D11—28no—
134C2×C4×D11—28no—
135C2×C4×D11—28no—
136C2×C4×D11—28no—
137C2×C4×D11—22no—
138C2×C4×D11—22no—
139C2×C4×D11—22no—
140C2×C4×D11—22no—
141C2×C4×D11—24no—
142C2×C4×D11—24no—
143C2×C4×D11—24no—
144C2×C4×D11M1618yescomplemented
145C11×M16—44no—
146C2×C8×C11—24no—
147C11×C4⋊C4—24no—
148C11×C4⋊C4—24no—
149(C2×D11)⋊C4—24no—
150(C2×D11)⋊C4—24no—
151(C2×D11)⋊C4—24no—
152(C2×D11)⋊C4—24no—
153C4⋊Dic11—24no—
154C4⋊Dic11—24no—
155C4×Dic11—22no—
156C4×Dic11—22no—
157C4×Dic11—22no—
158C4×Dic11—22no—
159C4×Dic11C22⋊C412yes—
160C4×Dic11C22⋊C412yes—
161C4×Dic11C22⋊C412yes—
162C4×Dic11C22⋊C412yes—
163C4×Dic11C2×D412yes—
164C4×Dic11C2×D412yes—
165C4×Dic11C2×D412yes—
166C4×Dic11C2×D412yes—
167#4318—44no—
168C2×C11⋊C8—24no—
169C22×#117—111no—
170#2920—112no—
171#1464—114no—
172#1463—111no—
173#1463D1111yescharacteristic, complemented
174#1462—112no—
175#1458—114no—
176C23×C11—22no—
177C23×C11—22no—
178C23×C11—22no—
179C23×C11C2×C22⋊C411yescharacteristic
180C23×C11C2×C22⋊C411yescharacteristic
181C23×C11C23×C411yescharacteristic
182C22×D11—24no—
183C22×D11—24no—
184C22×D11—22no—
185C22×D11—22no—
186C22×D11—416no—
187C22×D11—42no—
188C22×D11—42no—
189C22×D11—42no—
190C22×D11—42no—
191C22×D11—42no—
192C22×D11—42no—
193C22×D11C2×M1614yes—
194C2×C4×C11—24no—
195C2×C4×C11—24no—
196C2×C4×C11—22no—
197C2×C4×C11—22no—
198C2×C4×C11—24no—
199C2×C4×C11—22no—
200C2×C4×C11—41no—
201C2×C4×C11—42no—
202C2×C4×C11—41no—
203C2×C4×C11—42no—
204C2×C4×C11—42no—
205C2×C4×C11—42no—
206C2×C4×C11C2×C22⋊C412yes—
207C2×C4×C11C2×M1614yes—
208C2×C4×C11C22×D412yes—
209C2×Dic11—22no—
210C2×Dic11—24no—
211C2×Dic11—22no—
212C2×Dic11—22no—
213C2×Dic11—22no—
214C2×Dic11—22no—
215C2×Dic11—22no—
216C2×Dic11—42no—
217C2×Dic11—41no—
218C2×Dic11—41no—
219C2×Dic11—42no—
220C2×Dic11—42no—
221C2×Dic11—42no—
222C2×Dic11C2×C22⋊C411yescharacteristic
223C2×Dic11C2×C22⋊C411yescharacteristic
224C2×Dic11C2×C22⋊C412yes—
225C2×Dic11C2×C22⋊C412yes—
226C2×Dic11C2×C22⋊C411yescharacteristic
227C2×Dic11C2×C22⋊C411yescharacteristic
228C2×Dic11C2×M1614yes—
229C4×D11—28no—
230C4×D11—28no—
231C4×D11—28no—
232C4×D11—28no—
233C8×C11—44no—
234C11⋊C8—44no—
235C24×C4—111no—
236C2×#117—112no—
237C2×#117—112no—
238C2×#117—112no—
239C2×#117—112no—
240C2×#117—222no—
241C2×#117—222no—
242C2×#117—222no—
243C2×#117—222no—
244C22×C4⋊C4—111no—
245C22×C4⋊C4C2×D1111yescharacteristic
246C22×C22⋊C4—111no—
247C22×C22⋊C4—111no—
248C22×C42—111no—
249C22×C42—111no—
250#432—114no—
251#432—222no—
252#431—114no—
253#431—222no—
254#423—222no—
255#407—112no—
256#407C2×D1112yes—
257C4×M16—222no—
258#324—114no—
259#324C2×D1114yescomplemented
260#323—118no—
261C22×C11—28no—
262C22×C11—21no—
263C22×C11—21no—
264C22×C11—21no—
265C22×C11—21no—
266C22×C11—21no—
267C22×C11—21no—
268C22×C11#41012yes—
269C22×C11#41312yes—
270C22×C11C22×C22⋊C411yescharacteristic
271C22×C11C22×M1612yes—
272C2×D11—24no—
273C2×D11—44no—
274C2×D11—48no—
275C2×D11—48no—
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—44no—
279C4×C11—24no—
280C4×C11—22no—
281C4×C11—22no—
282C4×C11—42no—
283Dic11—21no—
284Dic11—21no—
285Dic11—22no—
286Dic11—22no—
287Dic11—42no—
288Dic11#40712yes—
289Dic11#40712yes—
290C25—111no—
291C23×C4—111no—
292C23×C4—111no—
293C23×C4—112no—
294C23×C4—111no—
295C23×C4—112no—
296C23×C4—221no—
297C23×C4—221no—
298C23×C4—221no—
299C23×C4—221no—
300C23×C4—228no—
301C23×C4C4×D1111yescharacteristic
302C23×C4C4×D1111yescharacteristic
303C23×C4C22×D1111yescharacteristic
304C2×M16—22no—
305C2×M16—222no—
306#117—224no—
307#117—224no—
308#117—224no—
309#117—224no—
310#117—224no—
311#117—224no—
312#117—224no—
313#117—224no—
314C2×C4⋊C4—22no—
315C2×C4⋊C4—22no—
316C2×C4⋊C4—112no—
317C2×C4⋊C4—112no—
318C2×C4⋊C4—222no—
319C2×C4⋊C4—222no—
320C2×C4⋊C4C4×D1112yes—
321C2×C4⋊C4C22×D1112yes—
322C2×C22⋊C4—112no—
323C2×C22⋊C4—112no—
324C2×C22⋊C4—112no—
325C2×C22⋊C4—112no—
326C2×C22⋊C4—222no—
327C2×C22⋊C4—222no—
328C2×C22⋊C4—222no—
329C2×C22⋊C4—222no—
330C2×C42—111no—
331C2×C42—111no—
332C2×C42—112no—
333C2×C42—112no—
334C2×C42—112no—
335C2×C42—112no—
336C2×C42—111no—
337C2×C42—111no—
338C2×C42—112no—
339C2×C42—112no—
340C2×C42—221no—
341C2×C42—221no—
342C2×C42—221no—
343C2×C42—221no—
344C4⋊C8—224no—
345C4⋊C8—224no—
346C22⋊C8—22no—
347C22⋊C8—114no—
348C22⋊C8—222no—
349C22⋊C8C22×D1114yes—
350#97—224no—
351C4×C8—224no—
352C2×C11—22no—
353C2×C11—22no—
354C2×C11—22no—
355C2×C11C2×#40711yescharacteristic
356C2×C11C2×#41011yescharacteristic
357C2×C11C2×#41311yescharacteristic
358D11—44no—
359C24—112no—
360C24—224no—
361C24—221no—
362C24—221no—
363C24—442no—
364C24—442no—
365C24C2×C4×D1111yescharacteristic
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—24no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—42no—
372C22×C4—42no—
373C22×C4—111no—
374C22×C4—111no—
375C22×C4—111no—
376C22×C4—111no—
377C22×C4—111no—
378C22×C4—112no—
379C22×C4—111no—
380C22×C4—112no—
381C22×C4—111no—
382C22×C4—111no—
383C22×C4—118no—
384C22×C4—112no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—222no—
388C22×C4—222no—
389C22×C4—224no—
390C22×C4—224no—
391C22×C4—228no—
392C22×C4—228no—
393C22×C4—228no—
394C22×C4—228no—
395C22×C4—224no—
396C22×C4—224no—
397C22×C4—221no—
398C22×C4—221no—
399C22×C4—442no—
400C22×C4—442no—
401C22×C4C2×C4×D1112yes—
402C22×C4C2×C4×D1112yes—
403C22×C4C2×C4×D1111yescharacteristic
404C22×C4D4×D1112yes—
405C22×C4D4×D1112yes—
406C22×C4C23×D1111yescharacteristic
407M16—44no—
408M16—444no—
409C2×C8—24no—
410C2×C8—224no—
411C4⋊C4—24no—
412C4⋊C4—24no—
413C4⋊C4—224no—
414C4⋊C4—224no—
415C22⋊C4—224no—
416C22⋊C4—224no—
417C22⋊C4—224no—
418C22⋊C4—224no—
419C42—112no—
420C42—112no—
421C42—112no—
422C42—112no—
423C42—112no—
424C42—112no—
425C42—112no—
426C42—112no—
427C42—222no—
428C42—222no—
429C42—222no—
430C42—222no—
431C11#1735711yescharacteristic, complemented, Sylow
432C23—22no—
433C23—22no—
434C23—22no—
435C23—114no—
436C23—224no—
437C23—224no—
438C23—222no—
439C23—222no—
440C23—442no—
441C23—442no—
442C23—4416no—
443C23—442no—
444C23—442no—
445C23—442no—
446C23—442no—
447C23C22⋊C4×D1111yescharacteristic
448C23C22⋊C4×D1111yescharacteristic
449C23C22×C4×D1111yescharacteristic
450C2×C4—24no—
451C2×C4—24no—
452C2×C4—22no—
453C2×C4—22no—
454C2×C4—24no—
455C2×C4—22no—
456C2×C4—41no—
457C2×C4—42no—
458C2×C4—41no—
459C2×C4—42no—
460C2×C4—42no—
461C2×C4—42no—
462C2×C4—111no—
463C2×C4—111no—
464C2×C4—114no—
465C2×C4—111no—
466C2×C4—111no—
467C2×C4—112no—
468C2×C4—112no—
469C2×C4—228no—
470C2×C4—228no—
471C2×C4—228no—
472C2×C4—228no—
473C2×C4—222no—
474C2×C4—222no—
475C2×C4—222no—
476C2×C4—222no—
477C2×C4—222no—
478C2×C4—224no—
479C2×C4—222no—
480C2×C4—442no—
481C2×C4—441no—
482C2×C4—441no—
483C2×C4—442no—
484C2×C4—442no—
485C2×C4—442no—
486C2×C4C22⋊C4×D1112yes—
487C2×C4M16×D1114yes—
488C2×C4C2×D4×D1112yes—
489C8—44no—
490C8—444no—
491C22—28no—
492C22—21no—
493C22—21no—
494C22—21no—
495C22—21no—
496C22—21no—
497C22—21no—
498C22—224no—
499C22—444no—
500C22—444no—
501C22—448no—
502C22—448no—
503C22—442no—
504C22—442no—
505C22#1062235312yes—
506C22#1062236412yes—
507C22C2×C22⋊C4×D1111yescharacteristic
508C22C2×M16×D1112yes—
509C4—24no—
510C4—22no—
511C4—22no—
512C4—42no—
513C4—112no—
514C4—112no—
515C4—221no—
516C4—221no—
517C4—222no—
518C4—222no—
519C4—442no—
520C2—22no—
521C2—22no—
522C2—22no—
523C2—444no—
524C2D11×#40711yescharacteristic
525C2C2×#1062235311yescharacteristic
526C2C2×#1062236411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1463C2
socleC22×C11C22×C22⋊C4
prime radicalC24×D11C2×C4
cosocleC22×C4×C11C24
hypercenter#1463D11
hypocenterC11#17357
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. #13077245C2semidirect
3. #13066949C2semidirect
4. #13066946C2semidirect
6. #13066929C2semidirect
7. C11×#1463C2semidirect
28. #10622332C22semidirect
30. #10622331C22semidirect
31. C11×#324C22semidirect
32. #10622166C22semidirect
144. C2×C4×D11M16semidirect
173. #1463D11semidirect
259. #324C2×D11semidirect
431. C11#17357semidirect

Maximal subgroups

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

subgroupindex
C22×#669452
#130772452
#130669492
#130669462
#130669422
#130669292
C11×#14632
#1735711