Finite Group Databasebeta

← #14765821

Subgroups — #14765821

Order 2816.

848 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×#10622455C211yesmaximal, characteristic
2#13071183C211yesmaximal, characteristic, complemented
3#13071077C211yesmaximal, characteristic
4#13069564C211yesmaximal, characteristic, complemented
5#13069342C212yesmaximal, complemented
6#13069297C212yesmaximal
7#13069242C212yesmaximal
8#13069193C212yesmaximal, complemented
9#13068613C211yesmaximal, characteristic
10C4⋊C8×Dic11C211yesmaximal, characteristic, complemented
11C11×#1948C211yesmaximal, characteristic, complemented
12C2×#66940—21no—
13C2×C4×D44C2211yescharacteristic
14C2×#66925—21no—
15C2×#66922C2211yescharacteristic
16C2×C11×#106C2212yes—
17C2×C11×C4⋊C8C2211yescharacteristic
18C11×#384C2211yescharacteristic
19C4×C11×C4⋊C4C2211yescharacteristic
20C2×#66885C2212yes—
21C2×#66881C2212yes—
22C2×C8×Dic11C2212yes—
23#10622601C2211yescharacteristic
24#10622601C2211yescharacteristic
25C4⋊C4×Dic11—21no—
26C4⋊C4×Dic11C2212yes—
27#10622587—21no—
28#10622586—21no—
29#10622586C2211yescharacteristic
30#10622586C2212yes—
31#10622586C2211yescharacteristic
32C2×#66873C2212yes—
33C4×(C2×D11)⋊C4—21no—
34C42×Dic11C2211yescharacteristic
35C2×C4⋊(C11⋊C8)C2211yescharacteristic
36#10622455C418yescomplemented
37#10622282—21no—
38#10622282—21no—
39C11×#340C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43#10622167C2212yes—
44C22×D44C2311yescharacteristic
45C22×C4×D11—21no—
46C22×Dic22—21no—
47C22×C8×C11C2312yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C42×C11—21no—
54C2×C42×C11C2311yescharacteristic
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—21no—
57C2×(C2×D11)⋊C4—21no—
58C2×(C2×D11)⋊C4—21no—
59C2×(C2×D11)⋊C4—21no—
60C2×C4⋊Dic11—21no—
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×Dic11⋊C4—21no—
64C2×Dic11⋊C4—21no—
65C2×Dic11⋊C4—22no—
66C2×C4×Dic11—22no—
67C2×C4×Dic11D411yescharacteristic
68C2×C4×Dic11D411yescharacteristic
69C2×C4×Dic11D411yescharacteristic
70C2×C4×Dic11D411yescharacteristic
71C2×C4×Dic11C2311yescharacteristic
72C2×C4×Dic11C2311yescharacteristic
73C22×C11⋊C8C2312yes—
74#66940—44no—
75C4×D44—22no—
76C4×D44C2×C414yes—
77#66925—44no—
78#66922—22no—
79#66922C2×C414yes—
80C11×#106—42no—
81C11×C4⋊C8C2×C414yes—
82C11×#95—21no—
83C11⋊#95—21no—
84C11⋊#95—21no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87#66885C2×C418yes—
88#66881C2×C418yes—
89C8×Dic11—42no—
90#66873—42no—
91C4⋊(C11⋊C8)—22no—
92#22111—111nomaximal, Sylow
93C23×D11—21no—
94C22×C4×C11—22no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2411yescharacteristic
100C22×Dic11—22no—
101C22×Dic11—21no—
102C22×Dic11C2×D411yescharacteristic
103C22×Dic11C2×D411yescharacteristic
104C22×Dic11C2×D411yescharacteristic
105C22×Dic11C2×D411yescharacteristic
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44C22×C412yes—
112C2×C4×D11—24no—
113C2×C4×D11—42no—
114C2×C4×D11—42no—
115C2×Dic22—24no—
116C2×Dic22—42no—
117C2×Dic22—42no—
118C2×C8×C11—22no—
119C2×C8×C11—22no—
120C2×C8×C11C22×C414yes—
121C11×C4⋊C4—22no—
122C11×C4⋊C4—21no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—42no—
128C11×C4⋊C4—42no—
129C42×C11—42no—
130C42×C11C22×C412yes—
131C42×C11#4112yes—
132(C2×D11)⋊C4—24no—
133(C2×D11)⋊C4—42no—
134(C2×D11)⋊C4—42no—
135(C2×D11)⋊C4—42no—
136(C2×D11)⋊C4—42no—
137C4⋊Dic11—24no—
138C4⋊Dic11—22no—
139C4⋊Dic11—21no—
140C4⋊Dic11C22×C412yes—
141C4⋊Dic11C22×C414yes—
142Dic11⋊C4—42no—
143Dic11⋊C4—42no—
144Dic11⋊C4—44no—
145C4×Dic11—22no—
146C4×Dic11—22no—
147C4×Dic11—21no—
148C4×Dic11—21no—
149C4×Dic11—21no—
150C4×Dic11—21no—
151C4×Dic11—41no—
152C4×Dic11—44no—
153C4×Dic11SD1614yes—
154C2×C11⋊C8—22no—
155C2×C11⋊C8—22no—
156C2×C11⋊C8—22no—
157C2×#476—111no—
158C4×C4⋊Q8—111no—
159#2293—111no—
160#1987—111no—
161#1948D1111yescharacteristic, complemented
162#1941—112no—
163#1934—112no—
164#1926—112no—
165#1919—112no—
166#1802—111no—
167C4×C4⋊C8—111no—
168C23×C11C22×D411yescharacteristic
169C22×D11—22no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C2×C4×C11—21no—
177C2×C4×C11—21no—
178C2×C4×C11—41no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11C4×D412yes—
188C2×C4×C11C4×D412yes—
189C2×C4×C11C2×SD1612yes—
190C2×C4×C11#13512yes—
191C2×C4×C11C23×C411yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11H(5,𝔽2)11yescharacteristic
194C2×C4×C112−1+411yescharacteristic
195C2×C4×C112−1+411yescharacteristic
196C2×C4×C112−1+411yescharacteristic
197C2×Dic11—21no—
198C2×Dic11—21no—
199C2×Dic11—21no—
200C2×Dic11—21no—
201C2×Dic11—21no—
202C2×Dic11—21no—
203C2×Dic11—24no—
204C2×Dic11—22no—
205C2×Dic11—21no—
206C2×Dic11—21no—
207C2×Dic11—21no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11C2×SD1612yes—
213C2×Dic11C2×SD1612yes—
214C2×Dic11AGL(1,ℤ/8)12yes—
215D44—22no—
216D44—22no—
217D44—41no—
218D44—41no—
219C4×D11—48no—
220Dic22—48no—
221C8×C11—24no—
222C11⋊C8—42no—
223C2×C4⋊Q8—111no—
224C2×C4×Q8—221no—
225C2×C4×D4—111no—
226C2×#117—221no—
227#476—118no—
228C2×#106—112no—
229C2×#106C2×D1112yes—
230C2×C4⋊C8—111no—
231C2×C4⋊C8C2×D1111yescharacteristic
232C2×#102—112no—
233C2×#102—112no—
234C2×C4×C8—112no—
235#391—221no—
236#390—111no—
237#390—111no—
238#389—112no—
239#389—111no—
240#389—111no—
241#389—221no—
242#388—221no—
243#388—221no—
244#384C2×D1111yescharacteristic
245C4×C4⋊C4—112no—
246C4×C4⋊C4—221no—
247C4×C4⋊C4C2×D1111yescharacteristic
248C4×C22⋊C4—221no—
249C43—111no—
250#340—112no—
251#340—112no—
252#340—112no—
253#340C2×D1112yes—
254#336—112no—
255C22×C11C2×C4×D411yescharacteristic
256C22×C11#53611yescharacteristic
257C22×C11#53711yescharacteristic
258C22×C11C22×SD1611yescharacteristic
259C22×C11C2×#13511yescharacteristic
260C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
261C22×C11#57511yescharacteristic
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—81no—
266C2×D11—81no—
267C2×D11—81no—
268C2×D11—81no—
269C4×C11—22no—
270C4×C11—81no—
271C4×C11—81no—
272C4×C11—82no—
273C4×C11C4×SD1614yes—
274C4×C11#51911yescharacteristic
275C4×C11#52011yescharacteristic
276C4×C11#54111yescharacteristic
277C4×C11#54211yescharacteristic
278Dic11—22no—
279Dic11—22no—
280Dic11—22no—
281Dic11—42no—
282Dic11—44no—
283Dic11—41no—
284C22×Q8—221no—
285C22×D4—111no—
286C23×C4—221no—
287C22×C8—112no—
288C22×C8C22×D1112yes—
289C4⋊Q8—114no—
290C4⋊Q8—222no—
291C4×Q8—444no—
292C4×D4—114no—
293C4×D4—222no—
294#117—444no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—112no—
299C2×C4⋊C4—221no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4C22×D1111yescharacteristic
304C2×C4⋊C4C22×D1111yescharacteristic
305C2×C4⋊C4C22×D1112yes—
306C2×C22⋊C4—221no—
307C2×C22⋊C4—221no—
308C2×C22⋊C4—221no—
309C2×C22⋊C4—221no—
310C2×C22⋊C4—221no—
311C2×C42—21no—
312C2×C42—111no—
313C2×C42—111no—
314C2×C42—111no—
315C2×C42—111no—
316C2×C42—111no—
317C2×C42—111no—
318C2×C42—222no—
319C2×C42C22×D1111yescharacteristic
320#106—42no—
321#106—118no—
322C4⋊C8—222no—
323C4⋊C8C4×D1114yes—
324#102—118no—
325#102—442no—
326C4×C8—442no—
327#95—21no—
328#95—221no—
329#95—221no—
330#95—222no—
331#95—222no—
332C2×C11#232311yescharacteristic
333C2×C11C2×C4×SD1611yescharacteristic
334C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
335C2×C11#322711yescharacteristic
336C2×C11#323311yescharacteristic
337C2×C11#324611yescharacteristic
338C2×C11#324711yescharacteristic
339D11—82no—
340C24—221no—
341C2×Q8—224no—
342C2×Q8—442no—
343C2×Q8—442no—
344C2×D4—112no—
345C2×D4—221no—
346C2×D4—221no—
347C2×D4—221no—
348C2×D4—221no—
349C2×D4—221no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—111no—
354C22×C4—111no—
355C22×C4—111no—
356C22×C4—111no—
357C22×C4—222no—
358C22×C4—221no—
359C22×C4—224no—
360C22×C4—442no—
361C22×C4—442no—
362C22×C4D4×D1111yescharacteristic
363C22×C4D4×D1111yescharacteristic
364C22×C4C23×D1111yescharacteristic
365C2×C8—22no—
366C2×C8—22no—
367C2×C8—222no—
368C2×C8—222no—
369C2×C8—222no—
370C2×C8C2×C4×D1114yes—
371C4⋊C4—22no—
372C4⋊C4—21no—
373C4⋊C4—21no—
374C4⋊C4—21no—
375C4⋊C4—22no—
376C4⋊C4—21no—
377C4⋊C4—42no—
378C4⋊C4—42no—
379C4⋊C4—114no—
380C4⋊C4—112no—
381C4⋊C4—224no—
382C4⋊C4—221no—
383C4⋊C4—222no—
384C4⋊C4—442no—
385C4⋊C4—442no—
386C4⋊C4—444no—
387C22⋊C4—224no—
388C22⋊C4—442no—
389C22⋊C4—442no—
390C22⋊C4—442no—
391C22⋊C4—442no—
392C42—42no—
393C42—114no—
394C42—222no—
395C42—222no—
396C42—221no—
397C42—221no—
398C42—221no—
399C42—221no—
400C42—441no—
401C42—444no—
402C42C2×C4×D1112yes—
403C42#434312yes—
404C11#2211111yescharacteristic, complemented, Sylow
405C23—222no—
406C23—441no—
407C23—441no—
408C23—441no—
409C23—441no—
410C23—441no—
411C23—441no—
412C23C2×D4×D1111yescharacteristic
413Q8—448no—
414D4—222no—
415D4—222no—
416D4—441no—
417D4—441no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—112no—
430C2×C4—112no—
431C2×C4—112no—
432C2×C4—221no—
433C2×C4—221no—
434C2×C4—221no—
435C2×C4—221no—
436C2×C4—221no—
437C2×C4—221no—
438C2×C4—222no—
439C2×C4—224no—
440C2×C4—221no—
441C2×C4—221no—
442C2×C4—221no—
443C2×C4—441no—
444C2×C4—441no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4—448no—
448C2×C4#6694612yes—
449C2×C4#6694612yes—
450C2×C4SD16×D1112yes—
451C2×C4#6696912yes—
452C2×C4C22×C4×D1111yescharacteristic
453C2×C4#6703711yescharacteristic
454C2×C4C2×#434311yescharacteristic
455C2×C4#6704011yescharacteristic
456C2×C4#6704311yescharacteristic
457C2×C4#6704311yescharacteristic
458C8—24no—
459C8—442no—
460C22—442no—
461C22—442no—
462C22—442no—
463C22—881no—
464C22—881no—
465C22—881no—
466C22—881no—
467C22C2×#6694611yescharacteristic
468C22#1062313911yescharacteristic
469C22#1062315911yescharacteristic
470C22C2×SD16×D1111yescharacteristic
471C22C2×#6696911yescharacteristic
472C22D11×AGL(1,ℤ/8)11yescharacteristic
473C22#1062330811yescharacteristic
474C4—22no—
475C4—81no—
476C4—82no—
477C4—81no—
478C4—222no—
479C4—222no—
480C4—222no—
481C4—442no—
482C4—444no—
483C4—441no—
484C4#1062246514yes—
485C4#1062307711yescharacteristic
486C4#1062310311yescharacteristic
487C4#1062322811yescharacteristic
488C4#1062326411yescharacteristic
489C2—882no—
490C2#1307129611yescharacteristic
491C2C2×#1062246511yescharacteristic
492C2#1307742311yescharacteristic
493C2#1307974311yescharacteristic
494C2#1307979911yescharacteristic
495C2#1307992911yescharacteristic
496C2#1307994011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1948C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#1948D11
hypocenterC11#22111
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
2. #13071183C2semidirect
4. #13069564C2semidirect
5. #13069342C2semidirect
8. #13069193C2semidirect
10. C4⋊C8×Dic11C2semidirect
11. C11×#1948C2semidirect
36. #10622455C4semidirect
161. #1948D11semidirect
404. C11#22111semidirect

Maximal subgroups

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

subgroupindex
C2×#106224552
#130711832
#130710772
#130695642
#130693422
#130692972
#130692422
#130691932
#130686132
C4⋊C8×Dic112
C11×#19482
#2211111