Finite Group Databasebeta

← #14770365

Subgroups — #14770365

Order 2816.

1086 conjugacy classes of subgroups.

The subgroup lattice has 490 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic
2C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
3#13069580C212yesmaximal, complemented
4#13069576C211yesmaximal, characteristic, complemented
5#13069573C212yesmaximal, complemented
6#13069564C211yesmaximal, characteristic, complemented
7#13068623C212yesmaximal
8#13068613C211yesmaximal, characteristic
9C4×#66873C211yesmaximal, characteristic
10C4×#66873C212yesmaximal
11C11×#2355C211yesmaximal, characteristic, complemented
12C2×C4×Q8×C11C2211yescharacteristic
13C2×#66999—21no—
14#10623110—24no—
15#10623110C418yescomplemented
16C2×#66949—22no—
17C2×C4⋊C4×D11—21no—
18C2×C4×D44C2211yescharacteristic
19C2×C4×D44C2212yes—
20C2×#66923C2212yes—
21C2×#66922C2211yescharacteristic
22C11×#391—21no—
23C11×#387—22no—
24C11×#384C2211yescharacteristic
25C11×#382C2212yes—
26C4×C11×C4⋊C4—21no—
27C4×C11×C4⋊C4C2212yes—
28C4×C11×C4⋊C4C2211yescharacteristic
29Q8×C11⋊C8—24no—
30C2×#66873C2212yes—
31C2×#66873C2211yescharacteristic
32C2×#66873C2211yescharacteristic
33C2×C4⋊(C11⋊C8)C2212yes—
34C2×C4⋊(C11⋊C8)C2211yescharacteristic
35C2×C4×C11⋊C8C2211yescharacteristic
36C2×C4×C11⋊C8C2212yes—
37#10622167C2211yescharacteristic
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2212yes—
42#10622167C2211yescharacteristic
43#10622167C2212yes—
44C22×Q8×C11D411yescharacteristic
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×C4×D11—22no—
48C22×Dic22—21no—
49C4×Q8×C11C2×C414yes—
50C4×Q8×C11D414yes—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4D411yescharacteristic
54C2×C11×C4⋊C4D412yes—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C4⋊C4C2312yes—
57C2×C11×C4⋊C4C2311yescharacteristic
58C2×C42×C11—21no—
59C2×C42×C11—22no—
60C2×C42×C11C2311yescharacteristic
61C2×C42×C11C2312yes—
62#66999—28no—
63C2×(C2×D11)⋊C4—21no—
64C2×(C2×D11)⋊C4—22no—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11C2312yes—
67C2×C4⋊Dic11C2311yescharacteristic
68C2×Dic11⋊C4—22no—
69C2×Dic11⋊C4—22no—
70C22×C11⋊C8C2311yescharacteristic
71C22×C11⋊C8C2312yes—
72C22×C11⋊C8C2311yescharacteristic
73#66949—216no—
74C4⋊C4×D11—28no—
75C4×D44—24no—
76C4×D44—22no—
77C4×D44C2×C418yes—
78C4×D44C2×C414yes—
79#66923—24no—
80#66923C2×C418yes—
81#66922—22no—
82#66922C2×C414yes—
83C11×#95—22no—
84C11×#95—21no—
85C11×#95—22no—
86C11×#95—22no—
87#66873—24no—
88#66873—22no—
89#66873Q814yescomplemented
90C4⋊(C11⋊C8)—22no—
91C4⋊(C11⋊C8)—24no—
92C4×C11⋊C8—22no—
93C4×C11⋊C8—24no—
94#22519—111nomaximal, Sylow
95C23×D11—21no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11C22⋊C414yes—
99C22×C4×C11—21no—
100C22×C4×C11—21no—
101C22×C4×C11—22no—
102C22×C4×C11C2×D412yes—
103C22×C4×C11C2×D412yes—
104C22×C4×C11C2×D411yescharacteristic
105C22×C4×C11C2×D411yescharacteristic
106C22×C4×C11C2411yescharacteristic
107C22×Dic11—21no—
108C22×Dic11—22no—
109C2×D44—21no—
110C2×D44—21no—
111C2×D44—21no—
112C2×D44C22×C412yes—
113C2×D44C2×Q812yes—
114C2×D44#4112yes—
115C2×C4×D11—24no—
116C2×C4×D11—28no—
117C2×C4×D11—42no—
118C2×C4×D11—42no—
119C2×C4×D11—82no—
120C2×C4×D11—82no—
121C2×Dic22—24no—
122C2×Dic22—81no—
123C2×Dic22—81no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—81no—
131C11×C4⋊C4C22⋊C414yes—
132C11×C4⋊C4C22⋊C418yes—
133C11×C4⋊C4C2×Q812yes—
134C42×C11—42no—
135C42×C11—82no—
136C42×C11C22×C412yes—
137C42×C11C22×C414yes—
138C42×C11C2×D412yes—
139C42×C11C2×D414yes—
140(C2×D11)⋊C4—24no—
141(C2×D11)⋊C4—28no—
142C4⋊Dic11—24no—
143C4⋊Dic11—22no—
144C4⋊Dic11—21no—
145C4⋊Dic11C22×C414yes—
146C4⋊Dic11C22×C412yes—
147Dic11⋊C4—28no—
148Dic11⋊C4—28no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—22no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8—21no—
156C2×C11⋊C8—22no—
157C2×C11⋊C8C2×Q812yes—
158C2×#554—111no—
159C2×C8×Q8—111no—
160#2355D1111yescharacteristic, complemented
161#1991—112no—
162#1990—111no—
163#1989—112no—
164#1987—111no—
165#1804—112no—
166#1802—111no—
167C4×#102—111no—
168C4×#102—112no—
169C23×C11C22×D411yescharacteristic
170C22×D11—22no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—41no—
174C22×D11—41no—
175C22×D11—41no—
176C22×D11—41no—
177Q8×C11—28no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—41no—
188C2×C4×C11—42no—
189C2×C4×C11—41no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11C2×C22⋊C414yes—
194C2×C4×C11C2×C22⋊C414yes—
195C2×C4×C11C2×C22⋊C412yes—
196C2×C4×C11C2×C22⋊C412yes—
197C2×C4×C11#13512yes—
198C2×C4×C11#13512yes—
199C2×C4×C11C23×C411yescharacteristic
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C22×Q811yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C112−1+411yescharacteristic
204C2×C4×C112−1+411yescharacteristic
205C2×Dic11—22no—
206C2×Dic11—24no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211D44—22no—
212D44—22no—
213D44—22no—
214D44C4×Q814yes—
215C4×D11—48no—
216C4×D11—88no—
217Dic22—84no—
218C11⋊C8—22no—
219C11⋊C8—41no—
220C11⋊C8—42no—
221#554—118no—
222#554—224no—
223C2×C4⋊Q8—111no—
224C2×#125—112no—
225C2×C22⋊Q8—221no—
226C2×C22⋊Q8—222no—
227C2×C4×Q8C2×D1111yescharacteristic
228C2×C4×D4—111no—
229C2×C4×D4—112no—
230C22×C4⋊C4—221no—
231C8×Q8—224no—
232C2×C4⋊C8—111no—
233C2×C4⋊C8—112no—
234C2×#102—111no—
235C2×#102—112no—
236C2×#102—111no—
237C2×C4×C8—111no—
238C2×C4×C8—112no—
239#391—21no—
240#387—22no—
241#384C2×D1111yescharacteristic
242#382C2×D1112yes—
243C4×C4⋊C4—21no—
244C4×C4⋊C4C2×D1111yescharacteristic
245C4×C4⋊C4C2×D1112yes—
246#340—112no—
247#340—112no—
248#340—112no—
249#340—112no—
250#340—111no—
251#340—112no—
252#340—111no—
253C22×C11C22×C22⋊C411yescharacteristic
254C22×C11#54811yescharacteristic
255C22×C11D4×Q811yescharacteristic
256C22×C11C2×#13511yescharacteristic
257C22×C11C2×#13511yescharacteristic
258C22×C11#57611yescharacteristic
259C22×C11#57711yescharacteristic
260C2×D11—24no—
261C2×D11—42no—
262C2×D11—42no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—42no—
266C2×D11—42no—
267C4×C11—24no—
268C4×C11—22no—
269C4×C11—24no—
270C4×C11—42no—
271C4×C11—81no—
272C4×C11—82no—
273C4×C11#41614yes—
274C4×C11C2×C4×Q811yescharacteristic
275C4×C11#51911yescharacteristic
276C4×C11#54811yescharacteristic
277C4×C11D4×Q811yescharacteristic
278Dic11—42no—
279Dic11—44no—
280C22×Q8—221no—
281C22×Q8C22⋊D1111yescharacteristic
282C22×D4—111no—
283C23×C4—221no—
284C23×C4—222no—
285C22×C8—111no—
286C22×C8—112no—
287C22×C8—111no—
288C4⋊Q8—114no—
289C4⋊Q8—222no—
290#125—118no—
291#125—224no—
292C22⋊Q8—228no—
293C22⋊Q8—2216no—
294C4×Q8C4×D1114yes—
295C4×Q8D4414yes—
296C4×D4—118no—
297C4×D4—114no—
298C4×D4—224no—
299C4×D4—222no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—112no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—222no—
307C2×C4⋊C4—228no—
308C2×C4⋊C4C22⋊D1111yescharacteristic
309C2×C4⋊C4C22⋊D1112yes—
310C2×C4⋊C4C22×D1111yescharacteristic
311C2×C4⋊C4C22×D1112yes—
312C2×C4⋊C4C22×D1111yescharacteristic
313C2×C22⋊C4—221no—
314C2×C22⋊C4—222no—
315C2×C42—21no—
316C2×C42—22no—
317C2×C42C22×D1112yes—
318C2×C42C22×D1111yescharacteristic
319C4⋊C8—224no—
320C4⋊C8—222no—
321#102—114no—
322#102—224no—
323#102—222no—
324C4×C8—224no—
325C4×C8—222no—
326#95—22no—
327#95—21no—
328#95—22no—
329#95—22no—
330C2×C11Q8×C22⋊C411yescharacteristic
331C2×C11C2×#41611yescharacteristic
332C2×C11#289711yescharacteristic
333C2×C11#336011yescharacteristic
334C2×C11#336111yescharacteristic
335C2×C11#338011yescharacteristic
336C2×C11#338111yescharacteristic
337D11—44no—
338C24—221no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—224no—
342C2×Q8—881no—
343C2×Q8—881no—
344C2×Q8(C2×D11)⋊C414yes—
345C2×D4—112no—
346C2×D4—112no—
347C2×D4—112no—
348C2×D4—221no—
349C2×D4—221no—
350C2×D4—221no—
351C22×C4—21no—
352C22×C4—21no—
353C22×C4—22no—
354C22×C4—221no—
355C22×C4—222no—
356C22×C4—224no—
357C22×C4—228no—
358C22×C4—442no—
359C22×C4—442no—
360C22×C4—882no—
361C22×C4—882no—
362C22×C4C2×C22⋊D1112yes—
363C22×C4C2×C22⋊D1112yes—
364C22×C4C2×C22⋊D1111yescharacteristic
365C22×C4C2×C22⋊D1111yescharacteristic
366C22×C4C23×D1111yescharacteristic
367C2×C8—112no—
368C2×C8—221no—
369C2×C8—221no—
370C2×C8—222no—
371C2×C8—221no—
372C2×C8—222no—
373C2×C8—221no—
374C2×C8—222no—
375C2×C8—221no—
376C4⋊C4—21no—
377C4⋊C4—21no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—42no—
382C4⋊C4—81no—
383C4⋊C4—112no—
384C4⋊C4—114no—
385C4⋊C4—228no—
386C4⋊C4—224no—
387C4⋊C4—228no—
388C4⋊C4—221no—
389C4⋊C4—222no—
390C4⋊C4(C2×D11)⋊C414yes—
391C4⋊C4(C2×D11)⋊C418yes—
392C4⋊C4Q8×D1112yes—
393C22⋊C4—224no—
394C22⋊C4—228no—
395C42—42no—
396C42—82no—
397C42C2×C4×D1114yes—
398C42C2×C4×D1112yes—
399C42C2×D4414yes—
400C42C2×D4412yes—
401C11#2251911yescharacteristic, complemented, Sylow
402C23—222no—
403C23—222no—
404C23—222no—
405C23—441no—
406C23—441no—
407C23—441no—
408C23—441no—
409C23C22×C22⋊D1111yescharacteristic
410Q8—28no—
411Q8—884no—
412D4—114no—
413D4—222no—
414D4—222no—
415D4—222no—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—41no—
431C2×C4—222no—
432C2×C4—224no—
433C2×C4—441no—
434C2×C4—441no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—448no—
438C2×C4—888no—
439C2×C4C2×(C2×D11)⋊C414yes—
440C2×C4C2×(C2×D11)⋊C412yes—
441C2×C4C2×(C2×D11)⋊C414yes—
442C2×C4C2×(C2×D11)⋊C412yes—
443C2×C4#6700312yes—
444C2×C4#6700312yes—
445C2×C4C22×C4×D1111yescharacteristic
446C2×C4C22×D4411yescharacteristic
447C2×C4C2×Q8×D1111yescharacteristic
448C2×C4#6704011yescharacteristic
449C2×C4#41×D1111yescharacteristic
450C2×C4#6704311yescharacteristic
451C8—222no—
452C8—442no—
453C8—441no—
454C22—224no—
455C22—442no—
456C22—442no—
457C22—442no—
458C22—442no—
459C22—442no—
460C22—442no—
461C22C22×(C2×D11)⋊C411yescharacteristic
462C22Q8×C22⋊D1111yescharacteristic
463C22C2×#6700311yescharacteristic
464C22C2×#6700311yescharacteristic
465C22#1062336211yescharacteristic
466C22#1062336611yescharacteristic
467C22#1062336811yescharacteristic
468C4—24no—
469C4—24no—
470C4—22no—
471C4—42no—
472C4—81no—
473C4—82no—
474C4—442no—
475C4—444no—
476C4#1062261514yes—
477C4C4×Q8×D1111yescharacteristic
478C4#1062310311yescharacteristic
479C4Q8×D4411yescharacteristic
480C4#1062310711yescharacteristic
481C2—444no—
482C2Q8×(C2×D11)⋊C411yescharacteristic
483C2C2×#1062261511yescharacteristic
484C2#1307713911yescharacteristic
485C2#1308126111yescharacteristic
486C2#1308127211yescharacteristic
487C2#1308147911yescharacteristic
488C2#1308148711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2355C2
socleC23×C11C22×D4
prime radicalC22×D44C23
cosocleC22×C4×C11C24
hypercenter#2355D11
hypocenterC11#22519
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2355

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C11⋊C8C2semidirect
3. #13069580C2semidirect
4. #13069576C2semidirect
5. #13069573C2semidirect
6. #13069564C2semidirect
11. C11×#2355C2semidirect
15. #10623110C4semidirect
89. #66873Q8semidirect
160. #2355D11semidirect
401. C11#22519semidirect

Maximal subgroups

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

subgroupindex
C2×#106231102
C2×Q8×C11⋊C82
#130695802
#130695762
#130695732
#130695642
#130686232
#130686132
C4×#668732
C11×#23552
#2251911