Finite Group Databasebeta

← #14810430

Subgroups — #14810430

Order 2816.

1320 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66922C211yesmaximal, characteristic, complemented
2C2×#10622327C212yesmaximal, complemented
3#13076917C211yesmaximal, characteristic
4#13069758C212yesmaximal, complemented
5#13069753C212yesmaximal, complemented
6#13069589C212yesmaximal, complemented
7#13068931C212yesmaximal
8#13068921C212yesmaximal, complemented
9C11×#1749C211yesmaximal, characteristic, complemented
10C23×Dic22—21no—
11C22×C42×C11C2211yescharacteristic
12C2×#66983C2211yescharacteristic
13C22×C4⋊Dic11—21no—
14C22×C4⋊Dic11C2212yes—
15C2×#66977C2211yescharacteristic
16C2×#66928C2211yescharacteristic
17C2×#66922—21no—
18C2×#66922—21no—
19C2×#66922—28no—
20C2×#66922C2212yes—
21C2×#66922C2212yes—
22C2×C11×C22⋊C8C2212yes—
23C2×C11×#97C2212yes—
24#10622826—21no—
25#10622826—21no—
26C2×#66885C2214yes—
27C2×#66880C2214yes—
28#10622553—21no—
29#10622553—21no—
30#10622552C2211yescharacteristic
31#10622549C2211yescharacteristic
32#10622542C2211yescharacteristic
33#10622327—28no—
34C11×#336C2212yes—
35#10622189C2214yes—
36#10622189C2214yes—
37C23×C4×C11D411yescharacteristic
38C23×C4×C11D411yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C22×C22⋊D11—21no—
41C23×Dic11—22no—
42C22×D44C2311yescharacteristic
43C22×Dic22—28no—
44C22×Dic22—22no—
45C22×Dic22—22no—
46C22×Dic22—44no—
47C22×Dic22—44no—
48C22×Dic22C2311yescharacteristic
49C22×C8×C11C2314yes—
50C2×C42×C11—24no—
51C2×C42×C11D411yescharacteristic
52C2×C42×C11D411yescharacteristic
53C2×C42×C11C2311yescharacteristic
54C2×C42×C11C2311yescharacteristic
55C2×C22⋊Dic11—21no—
56#66983—24no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—21no—
60C2×(C2×D11)⋊C4—21no—
61C2×(C2×D11)⋊C4—21no—
62C2×C4⋊Dic11—28no—
63C2×C4⋊Dic11—22no—
64C2×C4⋊Dic11—22no—
65C2×C4⋊Dic11—22no—
66C2×C4⋊Dic11—28no—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2314yes—
70#66977—24no—
71C2×Dic11⋊C4—21no—
72#66928—24no—
73#66922—28no—
74#66922—28no—
75#66922—24no—
76#66922—28no—
77#66922D418yescomplemented
78C11×C22⋊C8—24no—
79C11×#97—24no—
80C11⋊#95—21no—
81C11⋊#95—21no—
82C11⋊#95—21no—
83C11⋊#95—21no—
84#66885—28no—
85#66880—28no—
86#25908—111nomaximal, Sylow
87C24×C11C2×D411yescharacteristic
88C23×D11—21no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2×D411yescharacteristic
101C22×C4×C11C2×D411yescharacteristic
102C22×C4×C11#4114yes—
103C22×C4×C11C2411yescharacteristic
104C2×C22⋊D11—42no—
105C2×C22⋊D11—42no—
106C2×C22⋊D11—42no—
107C22×Dic11—28no—
108C22×Dic11—24no—
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—21no—
112C22×Dic11—44no—
113C22×Dic11—44no—
114C2×D44—22no—
115C2×D44—22no—
116C2×D44—22no—
117C2×Dic22—28no—
118C2×Dic22—28no—
119C2×Dic22—22no—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22—432no—
123C2×Dic22—44no—
124C2×Dic22—44no—
125C2×Dic22—44no—
126C2×Dic22—44no—
127C2×C8×C11—24no—
128C2×C8×C11—24no—
129C2×C8×C11—24no—
130C42×C11—22no—
131C42×C11—22no—
132C42×C11—22no—
133C42×C11C2×D414yes—
134C22⋊Dic11—42no—
135(C2×D11)⋊C4—42no—
136(C2×D11)⋊C4—42no—
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—42no—
139(C2×D11)⋊C4—42no—
140C4⋊Dic11—28no—
141C4⋊Dic11—28no—
142C4⋊Dic11—28no—
143C4⋊Dic11—24no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11C2×D418yes—
147Dic11⋊C4—42no—
148C22×C4⋊Q8—111no—
149C2×#489—112no—
150#2850—111no—
151#2024—112no—
152#2023—112no—
153#1993—112no—
154#1874—112no—
155#1872—112no—
156#1749D1111yescharacteristic, complemented
157C23×C11—21no—
158C23×C11—21no—
159C23×C11—21no—
160C23×C11—21no—
161C23×C11#12412yes—
162C23×C11AGL(1,ℤ/8)12yes—
163C23×C11#13712yes—
164C23×C11C22×D411yescharacteristic
165C22×D11—41no—
166C22×D11—41no—
167C22×D11—41no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—41no—
171C22×D11—41no—
172C2×C4×C11—28no—
173C2×C4×C11—28no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—21no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—28no—
185C2×C4×C11#12012yes—
186C2×C4×C11#12012yes—
187C2×C4×C11#12412yes—
188C2×C4×C11AGL(1,ℤ/8)12yes—
189C2×C4×C11#13712yes—
190C2×C4×C11C22×D412yes—
191C2×C4×C11C2×#4112yes—
192C2×C4×C112−1+412yes—
193C22⋊D11—84no—
194C2×Dic11—28no—
195C2×Dic11—416no—
196C2×Dic11—44no—
197C2×Dic11—44no—
198C2×Dic11—41no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—41no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207D44—44no—
208Dic22—416no—
209Dic22—416no—
210Dic22—44no—
211C8×C11—44no—
212C23×Q8—221no—
213C2×C4⋊Q8—112no—
214C2×C4⋊Q8—112no—
215C2×C4⋊Q8—228no—
216C2×C4⋊Q8—221no—
217C2×C4⋊Q8—221no—
218C2×#124—111no—
219C2×C22⋊Q8—111no—
220C2×#121—111no—
221C22×C4⋊C4—112no—
222C22×C4⋊C4—221no—
223C22×C42C2×D1111yescharacteristic
224#489—228no—
225C2×#103—114no—
226C2×#102—114no—
227C2×C22⋊C8C2×D1112yes—
228C2×#97C2×D1112yes—
229#391—111no—
230#390—111no—
231#388—221no—
232#388—221no—
233#386—221no—
234#386—221no—
235#382—111no—
236#340—114no—
237#340—114no—
238#336C2×D1112yes—
239C22×C11—22no—
240C22×C11—22no—
241C22×C11—22no—
242C22×C11—22no—
243C22×C11—22no—
244C22×C11—22no—
245C22×C11#48914yescomplemented
246C22×C11C2×#12011yescharacteristic
247C22×C11C2×#12411yescharacteristic
248C22×C11#53611yescharacteristic
249C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
250C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
251C22×C11C2×#13711yescharacteristic
252C22×C11C2×#13711yescharacteristic
253C2×D11—81no—
254C2×D11—81no—
255C2×D11—81no—
256C2×D11—81no—
257C2×D11—81no—
258C2×D11—81no—
259C2×D11—81no—
260C4×C11—22no—
261C4×C11—22no—
262C4×C11—22no—
263C4×C11—22no—
264C4×C11—22no—
265C4×C11#54814yes—
266Dic11—48no—
267Dic11—81no—
268Dic11—81no—
269Dic11—81no—
270C22×Q8—111no—
271C22×Q8—228no—
272C22×Q8—222no—
273C22×Q8—222no—
274C22×Q8—444no—
275C22×Q8—444no—
276C22×D4—111no—
277C22×D4—221no—
278C23×C4—222no—
279C23×C4D4411yescharacteristic
280C23×C4D4411yescharacteristic
281C23×C4C22×D1111yescharacteristic
282C22×C8C22×D1114yes—
283C4⋊Q8—118no—
284C4⋊Q8—228no—
285C4⋊Q8—228no—
286C4⋊Q8—228no—
287C4⋊Q8—224no—
288#124—224no—
289C22⋊Q8—224no—
290#121—224no—
291C2×C4⋊C4—114no—
292C2×C4⋊C4—111no—
293C2×C4⋊C4—111no—
294C2×C4⋊C4—228no—
295C2×C4⋊C4—228no—
296C2×C4⋊C4—222no—
297C2×C4⋊C4—222no—
298C2×C4⋊C4—222no—
299C2×C4⋊C4—221no—
300C2×C22⋊C4—221no—
301C2×C22⋊C4—221no—
302C2×C22⋊C4—221no—
303C2×C22⋊C4—221no—
304C2×C22⋊C4—221no—
305C2×C22⋊C4—221no—
306C2×C42—24no—
307C2×C42D4411yescharacteristic
308C2×C42D4411yescharacteristic
309C2×C42C22×D1111yescharacteristic
310C2×C42C22×D1111yescharacteristic
311#103—228no—
312#102—228no—
313C22⋊C8—24no—
314#97—24no—
315#95—221no—
316#95—221no—
317#95—221no—
318#95—221no—
319C2×C11—24no—
320C2×C11#243611yescharacteristic
321C2×C11#300311yescharacteristic
322C2×C11#300411yescharacteristic
323C2×C11C2×#48911yescharacteristic
324C2×C11#314111yescharacteristic
325C2×C11#323811yescharacteristic
326C2×C11#323911yescharacteristic
327D11—161no—
328C24—221no—
329C24C2×D4411yescharacteristic
330C2×Q8—228no—
331C2×Q8—228no—
332C2×Q8—222no—
333C2×Q8—222no—
334C2×Q8—222no—
335C2×Q8—4432no—
336C2×Q8—444no—
337C2×Q8—444no—
338C2×Q8—444no—
339C2×Q8—444no—
340C2×D4—222no—
341C2×D4—222no—
342C2×D4—222no—
343C2×D4—442no—
344C2×D4—442no—
345C2×D4—442no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—228no—
355C22×C4—224no—
356C22×C4—221no—
357C22×C4—221no—
358C22×C4—221no—
359C22×C4—444no—
360C22×C4—444no—
361C22×C4C2×D4411yescharacteristic
362C22×C4C2×D4411yescharacteristic
363C22×C4C2×D4411yescharacteristic
364C22×C4C2×D4411yescharacteristic
365C22×C4C2×D4411yescharacteristic
366C22×C4#433914yes—
367C22×C4C23×D1111yescharacteristic
368C2×C8—24no—
369C2×C8—24no—
370C2×C8—24no—
371C4⋊C4—118no—
372C4⋊C4—228no—
373C4⋊C4—228no—
374C4⋊C4—228no—
375C4⋊C4—224no—
376C4⋊C4—222no—
377C4⋊C4—222no—
378C4⋊C4—442no—
379C22⋊C4—442no—
380C22⋊C4—442no—
381C22⋊C4—442no—
382C22⋊C4—442no—
383C22⋊C4—442no—
384C22⋊C4—442no—
385C42—22no—
386C42—22no—
387C42—22no—
388C42D4×D1114yes—
389C11#2590811yescharacteristic, complemented, Sylow
390C23—21no—
391C23—21no—
392C23—21no—
393C23—21no—
394C23—441no—
395C23—441no—
396C23—441no—
397C23—441no—
398C23—441no—
399C23—441no—
400C23—441no—
401C23#6692812yes—
402C23#6696112yes—
403C23#6696212yes—
404C23C22×D4411yescharacteristic
405Q8—4416no—
406Q8—4416no—
407Q8—444no—
408D4—444no—
409D4—884no—
410C2×C4—28no—
411C2×C4—28no—
412C2×C4—21no—
413C2×C4—21no—
414C2×C4—21no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—28no—
423C2×C4—228no—
424C2×C4—4416no—
425C2×C4—444no—
426C2×C4—444no—
427C2×C4—441no—
428C2×C4—441no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4#6692812yes—
437C2×C4#6693512yes—
438C2×C4#6693512yes—
439C2×C4#6696112yes—
440C2×C4#6696212yes—
441C2×C4C2×#433912yes—
442C2×C4C2×D4×D1112yes—
443C2×C4#6704312yes—
444C8—44no—
445C22—22no—
446C22—22no—
447C22—22no—
448C22—22no—
449C22—22no—
450C22—22no—
451C22—881no—
452C22—881no—
453C22—881no—
454C22—881no—
455C22—881no—
456C22—881no—
457C22—881no—
458C22#1062232714yescomplemented
459C22C2×#6692811yescharacteristic
460C22C2×#6693511yescharacteristic
461C22#1062305711yescharacteristic
462C22C2×#6696111yescharacteristic
463C22C2×#6696111yescharacteristic
464C22C2×#6696211yescharacteristic
465C22C2×#6696211yescharacteristic
466C4—22no—
467C4—22no—
468C4—22no—
469C4—22no—
470C4—22no—
471C4—448no—
472C4—881no—
473C4—881no—
474C4—881no—
475C4#1062308314yes—
476C2—24no—
477C2—1761no—
478C2#1307227411yescharacteristic
479C2#1307784611yescharacteristic
480C2#1307785311yescharacteristic
481C2C2×#1062232711yescharacteristic
482C2#1307901011yescharacteristic
483C2#1307983911yescharacteristic
484C2#1307984811yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1749C2
socleC23×C11C22×D4
prime radicalC2×#66983C22
hypercenter#1749D11
hypocenterC11#25908
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
1. C22×#66922C2semidirect
2. C2×#10622327C2semidirect
4. #13069758C2semidirect
5. #13069753C2semidirect
6. #13069589C2semidirect
8. #13068921C2semidirect
9. C11×#1749C2semidirect
77. #66922D4semidirect
156. #1749D11semidirect
245. C22×C11#489semidirect
389. C11#25908semidirect
458. C22#10622327semidirect

Maximal subgroups

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

subgroupindex
C22×#669222
C2×#106223272
#130769172
#130697582
#130697532
#130695892
#130689312
#130689212
C11×#17492
#2590811