Finite Group Databasebeta

← #14770369

Subgroups — #14770369

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×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
2#13071573C211yesmaximal, characteristic, complemented
3#13069582C212yesmaximal, complemented
4#13069578C211yesmaximal, characteristic, complemented
5#13069574C212yesmaximal, complemented
6#13069565C211yesmaximal, characteristic, complemented
7#13068626C212yesmaximal
8#13068616C211yesmaximal, characteristic
9C4×#66896C211yesmaximal, characteristic
10C4×#66896C212yesmaximal
11C2×C11×#554C211yesmaximal, characteristic
12C11×#554—24no—
13C11×#554C418yescomplemented
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×#125C2212yes—
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—22no—
18C2×C4×Q8×C11C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2212yes—
21C22×C11×C4⋊C4—21no—
22#10622843—21no—
23C2×#66896C2212yes—
24C2×#66896C2211yescharacteristic
25C2×#66896C2211yescharacteristic
26Q8×C11⋊C8—24no—
27#10622594—22no—
28C4⋊C4×Dic11—21no—
29#10622549C2212yes—
30#10622548C2211yescharacteristic
31C4×C4⋊Dic11C2212yes—
32C4×C4⋊Dic11C2211yescharacteristic
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×C11—21no—
45C22×Q8×C11D411yescharacteristic
46C22×D4×C11C2311yescharacteristic
47C23×C4×C11—21no—
48C23×C4×C11—22no—
49C11×C4⋊Q8—22no—
50C11×C4⋊Q8C2×C414yes—
51C11×#125—24no—
52C11×#125C2×C418yes—
53C11×C22⋊Q8—28no—
54C11×C22⋊Q8—216no—
55C4×Q8×C11C2×C414yes—
56C4×Q8×C11D414yes—
57C4×D4×C11—24no—
58C4×D4×C11—22no—
59C4×D4×C11C2×C418yes—
60C4×D4×C11C2×C414yes—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—21no—
63C2×C11×C4⋊C4—22no—
64C2×C11×C4⋊C4—28no—
65C2×C11×C4⋊C4D411yescharacteristic
66C2×C11×C4⋊C4D412yes—
67C2×C11×C4⋊C4C2311yescharacteristic
68C2×C11×C4⋊C4C2312yes—
69C2×C11×C22⋊C4—21no—
70C2×C11×C22⋊C4—22no—
71C2×C42×C11C2311yescharacteristic
72C2×C42×C11C2312yes—
73C2×C4⋊Dic11—21no—
74C2×C4⋊Dic11—21no—
75C2×C4⋊Dic11C2312yes—
76C2×C4⋊Dic11C2311yescharacteristic
77C2×C4⋊Dic11C2311yescharacteristic
78C2×C4×Dic11—21no—
79C2×C4×Dic11—22no—
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2312yes—
82C22×C11⋊C8C2311yescharacteristic
83#66896—24no—
84#66896—22no—
85#66896Q814yescomplemented
86C11⋊#95—22no—
87C11⋊#95—21no—
88C11⋊#95—22no—
89C11⋊#95—22no—
90C4⋊(C11⋊C8)—24no—
91C4⋊(C11⋊C8)—22no—
92C4×C11⋊C8—24no—
93C4×C11⋊C8—22no—
94#22519—111nomaximal, Sylow
95C24×C11—21no—
96C2×Q8×C11—24no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—81no—
100C2×Q8×C11—81no—
101C2×Q8×C11C22⋊C414yes—
102C2×D4×C11—21no—
103C2×D4×C11—21no—
104C2×D4×C11—21no—
105C2×D4×C11C22×C412yes—
106C2×D4×C11C2×Q812yes—
107C2×D4×C11#4112yes—
108C22×C4×C11—21no—
109C22×C4×C11—22no—
110C22×C4×C11—24no—
111C22×C4×C11—28no—
112C22×C4×C11—42no—
113C22×C4×C11—42no—
114C22×C4×C11—82no—
115C22×C4×C11—82no—
116C22×C4×C11C2×D412yes—
117C22×C4×C11C2×D412yes—
118C22×C4×C11C2×D411yescharacteristic
119C22×C4×C11C2×D411yescharacteristic
120C22×C4×C11C2411yescharacteristic
121C22×Dic11—21no—
122C22×Dic11—21no—
123C22×Dic11—22no—
124C11×C4⋊C4—28no—
125C11×C4⋊C4—24no—
126C11×C4⋊C4—28no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4C22⋊C414yes—
130C11×C4⋊C4C22⋊C418yes—
131C11×C4⋊C4C22×C412yes—
132C11×C4⋊C4C22×C414yes—
133C11×C22⋊C4—24no—
134C11×C22⋊C4—28no—
135C42×C11C22×C414yes—
136C42×C11C22×C412yes—
137C42×C11C2×D414yes—
138C42×C11C2×D412yes—
139C4⋊Dic11—22no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—22no—
143C4⋊Dic11—21no—
144C4⋊Dic11—42no—
145C4⋊Dic11—81no—
146C4⋊Dic11C2×Q812yes—
147C4×Dic11—42no—
148C4×Dic11—82no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—22no—
151C2×C11⋊C8—21no—
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×#554D1111yescharacteristic
159C2×C8×Q8—111no—
160#2355—111no—
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×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—41no—
173C23×C11—41no—
174C23×C11—41no—
175C23×C11—41no—
176C23×C11C22×D411yescharacteristic
177Q8×C11—28no—
178Q8×C11—84no—
179D4×C11—22no—
180D4×C11—22no—
181D4×C11—22no—
182D4×C11C4×Q814yes—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—21no—
187C2×C4×C11—22no—
188C2×C4×C11—21no—
189C2×C4×C11—22no—
190C2×C4×C11—24no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—42no—
195C2×C4×C11—48no—
196C2×C4×C11—88no—
197C2×C4×C11C2×C22⋊C414yes—
198C2×C4×C11C2×C22⋊C412yes—
199C2×C4×C11C2×C22⋊C414yes—
200C2×C4×C11C2×C22⋊C412yes—
201C2×C4×C11#13512yes—
202C2×C4×C11#13512yes—
203C2×C4×C11C23×C411yescharacteristic
204C2×C4×C11C22×D411yescharacteristic
205C2×C4×C11C22×Q811yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C112−1+411yescharacteristic
208C2×C4×C112−1+411yescharacteristic
209C2×Dic11—22no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—41no—
218C11⋊C8—22no—
219C11⋊C8—42no—
220C11⋊C8—41no—
221#554—24no—
222#554Dic1118yescomplemented
223C2×C4⋊Q8C2×D1111yescharacteristic
224C2×#125C2×D1112yes—
225C2×C22⋊Q8—21no—
226C2×C22⋊Q8—22no—
227C2×C4×Q8C2×D1111yescharacteristic
228C2×C4×D4C2×D1111yescharacteristic
229C2×C4×D4C2×D1112yes—
230C22×C4⋊C4—21no—
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—221no—
240#387—222no—
241#384—111no—
242#382—112no—
243C4×C4⋊C4—111no—
244C4×C4⋊C4—112no—
245C4×C4⋊C4—221no—
246#340—112no—
247#340—112no—
248#340—112no—
249#340—112no—
250#340—111no—
251#340—112no—
252#340—111no—
253C22×C11—24no—
254C22×C11—42no—
255C22×C11—42no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11C22×C22⋊C411yescharacteristic
261C22×C11#54811yescharacteristic
262C22×C11D4×Q811yescharacteristic
263C22×C11C2×#13511yescharacteristic
264C22×C11C2×#13511yescharacteristic
265C22×C11#57611yescharacteristic
266C22×C11#57711yescharacteristic
267C4×C11—24no—
268C4×C11—24no—
269C4×C11—22no—
270C4×C11—42no—
271C4×C11—44no—
272C4×C11#41614yes—
273C4×C11C2×C4×Q811yescharacteristic
274C4×C11#51911yescharacteristic
275C4×C11#54811yescharacteristic
276C4×C11D4×Q811yescharacteristic
277Dic11—42no—
278Dic11—81no—
279Dic11—82no—
280C22×Q8—21no—
281C22×Q8C22⋊D1111yescharacteristic
282C22×D4C22×D1111yescharacteristic
283C23×C4—21no—
284C23×C4—22no—
285C22×C8—111no—
286C22×C8—112no—
287C22×C8—111no—
288C4⋊Q8—22no—
289C4⋊Q8C2×Dic1114yes—
290#125—24no—
291#125C2×Dic1118yes—
292C22⋊Q8—28no—
293C22⋊Q8—216no—
294C4×Q8C2×Dic1114yes—
295C4×Q8C22⋊D1114yes—
296C4×D4—24no—
297C4×D4—22no—
298C4×D4C2×Dic1118yes—
299C4×D4C2×Dic1114yes—
300C2×C4⋊C4—22no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—22no—
303C2×C4⋊C4—28no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—111no—
306C2×C4⋊C4—112no—
307C2×C4⋊C4—221no—
308C2×C4⋊C4—221no—
309C2×C4⋊C4C22⋊D1111yescharacteristic
310C2×C4⋊C4C22⋊D1112yes—
311C2×C4⋊C4C22×D1111yescharacteristic
312C2×C4⋊C4C22×D1112yes—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—22no—
315C2×C42—221no—
316C2×C42—222no—
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—221no—
327#95—222no—
328#95—222no—
329#95—222no—
330C2×C11—44no—
331C2×C11Q8×C22⋊C411yescharacteristic
332C2×C11C2×#41611yescharacteristic
333C2×C11#289711yescharacteristic
334C2×C11#336011yescharacteristic
335C2×C11#336111yescharacteristic
336C2×C11#338011yescharacteristic
337C2×C11#338111yescharacteristic
338C24—21no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—24no—
342C2×Q8—81no—
343C2×Q8—81no—
344C2×Q8C22⋊Dic1114yes—
345C2×D4—21no—
346C2×D4—21no—
347C2×D4—21no—
348C2×D4Q8×D1112yes—
349C2×D4#434312yes—
350C2×D4C22×Dic1112yes—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—24no—
354C22×C4—28no—
355C22×C4—42no—
356C22×C4—42no—
357C22×C4—82no—
358C22×C4—82no—
359C22×C4—221no—
360C22×C4—221no—
361C22×C4—222no—
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—28no—
377C4⋊C4—24no—
378C4⋊C4—28no—
379C4⋊C4—21no—
380C4⋊C4—22no—
381C4⋊C4—112no—
382C4⋊C4—221no—
383C4⋊C4—221no—
384C4⋊C4—222no—
385C4⋊C4—221no—
386C4⋊C4—222no—
387C4⋊C4—442no—
388C4⋊C4—881no—
389C4⋊C4C22⋊Dic1114yes—
390C4⋊C4C22⋊Dic1118yes—
391C4⋊C4C22×Dic1112yes—
392C4⋊C4C22×Dic1114yes—
393C22⋊C4—24no—
394C22⋊C4—28no—
395C42—442no—
396C42—882no—
397C42C22×Dic1114yes—
398C42C22×Dic1112yes—
399C42C2×C22⋊D1114yes—
400C42C2×C22⋊D1112yes—
401C11#2251911yescharacteristic, complemented, Sylow
402C23—22no—
403C23—22no—
404C23—22no—
405C23—41no—
406C23—41no—
407C23—41no—
408C23—41no—
409C23C22×C22⋊D1111yescharacteristic
410Q8—28no—
411Q8—84no—
412D4—22no—
413D4—22no—
414D4—22no—
415D4Q8×Dic1114yes—
416C2×C4—22no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—21no—
422C2×C4—22no—
423C2×C4—24no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—48no—
429C2×C4—88no—
430C2×C4—222no—
431C2×C4—441no—
432C2×C4—441no—
433C2×C4—441no—
434C2×C4—442no—
435C2×C4—441no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—441no—
439C2×C4#6700312yes—
440C2×C4#6700312yes—
441C2×C4C2×C22⋊Dic1114yes—
442C2×C4C2×C22⋊Dic1112yes—
443C2×C4C2×C22⋊Dic1114yes—
444C2×C4C2×C22⋊Dic1112yes—
445C2×C4C2×Q8×D1111yescharacteristic
446C2×C4C2×#434311yescharacteristic
447C2×C4#6704011yescharacteristic
448C2×C4#6704011yescharacteristic
449C2×C4C23×Dic1111yescharacteristic
450C2×C4C22×C22⋊D1111yescharacteristic
451C8—222no—
452C8—442no—
453C8—441no—
454C22—24no—
455C22—42no—
456C22—42no—
457C22—42no—
458C22—42no—
459C22—42no—
460C22—42no—
461C22Q8×C22⋊D1111yescharacteristic
462C22#1062334811yescharacteristic
463C22C2×#6700311yescharacteristic
464C22C2×#6700311yescharacteristic
465C22#1062336611yescharacteristic
466C22#1062336711yescharacteristic
467C22C22×C22⋊Dic1111yescharacteristic
468C4—24no—
469C4—24no—
470C4—22no—
471C4—42no—
472C4—44no—
473C4—442no—
474C4—881no—
475C4—882no—
476C4#1062284614yes—
477C4C2×Q8×Dic1111yescharacteristic
478C4#1062334311yescharacteristic
479C4Q8×C22⋊D1111yescharacteristic
480C4#1062334811yescharacteristic
481C2—44no—
482C2Q8×C22⋊Dic1111yescharacteristic
483C2C2×#1062284611yescharacteristic
484C2#1307714211yescharacteristic
485C2#1308126511yescharacteristic
486C2#1308127611yescharacteristic
487C2#1308147911yescharacteristic
488C2#1308149111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#554C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
cosocleC22×C4×C11C24
hypercenterC2×#554D11
hypocenterC11#22519
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×Q8×C11⋊C8C2semidirect
2. #13071573C2semidirect
3. #13069582C2semidirect
4. #13069578C2semidirect
5. #13069574C2semidirect
6. #13069565C2semidirect
13. C11×#554C4semidirect
85. #66896Q8semidirect
222. #554Dic11semidirect
401. C11#22519semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C11⋊C82
#130715732
#130695822
#130695782
#130695742
#130695652
#130686262
#130686162
C4×#668962
C2×C11×#5542
#2251911