Finite Group Databasebeta

← #14803909

Subgroups — #14803909

Order 2816.

874 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622704C211yesmaximal, characteristic, complemented
2C2×D4×C11⋊C8C211yesmaximal, characteristic
3#13073538C211yesmaximal, characteristic
4#13070047C212yesmaximal, complemented
5#13069819C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069374C211yesmaximal, characteristic, complemented
8#13069037C212yesmaximal, complemented
9#13068643C212yesmaximal, complemented
10C4×#66874C211yesmaximal, characteristic, complemented
11C11×#2563C211yesmaximal, characteristic
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×D4×C11C2211yescharacteristic
14C2×#66977C2212yes—
15C23×C11⋊C8C2212yes—
16C2×C4×Dic22C2211yescharacteristic
17C11×#393—22no—
18C11×#390—21no—
19C11×#382—21no—
20C11×#380C2212yes—
21C11×#380C2212yes—
22C4×C11×C4⋊C4C2211yescharacteristic
23#10622834—21no—
24#10622825C2212yes—
25C2×C22⋊(C11⋊C8)C2212yes—
26#10622704—24no—
27D4×C11⋊C8—24no—
28#10622586—21no—
29C2×#66874C2212yes—
30C2×#66874C2211yescharacteristic
31C2×#66874C2211yescharacteristic
32C2×#66871C2212yes—
33C2×#66871C2212yes—
34#10622561—22no—
35#10622548C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11—21no—
44C22×D4×C11D411yescharacteristic
45C23×C4×C11C2312yes—
46C22×Dic22C2311yescharacteristic
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—22no—
49C4×D4×C11—22no—
50C4×D4×C11—22no—
51C2×C11×C4⋊C4—21no—
52C2×C11×C4⋊C4D411yescharacteristic
53C2×C11×C4⋊C4C2311yescharacteristic
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C11×C22⋊C4—22no—
57C2×C11×C22⋊C4—22no—
58C2×C11×C22⋊C4D412yes—
59C2×C42×C11—21no—
60C2×C42×C11C2311yescharacteristic
61C2×C22⋊Dic11—22no—
62C2×C22⋊Dic11—22no—
63C2×C4⋊Dic11—21no—
64C2×C4⋊Dic11—21no—
65C2×C4⋊Dic11C2311yescharacteristic
66C2×C4⋊Dic11C2312yes—
67#66977—24no—
68#66977—42no—
69C2×Dic11⋊C4—21no—
70C2×Dic11⋊C4—22no—
71C2×C4×Dic11—21no—
72C22×C11⋊C8—24no—
73C22×C11⋊C8—24no—
74C22×C11⋊C8—42no—
75C22×C11⋊C8C2311yescharacteristic
76C22×C11⋊C8C2312yes—
77C22×C11⋊C8C2311yescharacteristic
78C4×Dic22—22no—
79C4×Dic22—22no—
80C11×#95—21no—
81C11×#95—22no—
82C11×#95—22no—
83C11⋊#95—22no—
84C22⋊(C11⋊C8)—24no—
85#66874—22no—
86#66874—24no—
87#66874—22no—
88#66871—24no—
89#66871—42no—
90C4⋊(C11⋊C8)D414yes—
91C4×C11⋊C8—22no—
92#25340—111nomaximal, Sylow
93C24×C11C2×D412yes—
94C2×Q8×C11—42no—
95C2×Q8×C11—81no—
96C2×Q8×C11—81no—
97C2×D4×C11—22no—
98C2×D4×C11—22no—
99C2×D4×C11Q1614yes—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2×D411yescharacteristic
112C22×C4×C11C2411yescharacteristic
113C22×Dic11—21no—
114C22×Dic11—21no—
115C22×Dic11—22no—
116C2×Dic22—21no—
117C2×Dic22—21no—
118C2×Dic22—21no—
119C2×Dic22—21no—
120C2×Dic22—21no—
121C2×Dic22#4112yes—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—22no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—42no—
130C11×C22⋊C4—24no—
131C11×C22⋊C4—82no—
132C11×C22⋊C4—82no—
133C42×C11—42no—
134C42×C11C2×D412yes—
135C42×C11#4112yes—
136C22⋊Dic11—44no—
137C22⋊Dic11—82no—
138C4⋊Dic11—21no—
139C4⋊Dic11—21no—
140C4⋊Dic11—22no—
141C4⋊Dic11—22no—
142C4⋊Dic11—42no—
143C4⋊Dic11—81no—
144Dic11⋊C4—44no—
145Dic11⋊C4—42no—
146C4×Dic11—42no—
147C2×C11⋊C8—21no—
148C2×C11⋊C8—21no—
149C2×C11⋊C8—22no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—22no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—48no—
155C2×C11⋊C8C2×D414yes—
156C2×C11⋊C8#4112yes—
157C2×#477—111no—
158C2×C8×D4—111no—
159#2563D1111yescharacteristic
160#2538—111no—
161#2076—112no—
162#2036—112no—
163#1990—111no—
164#1947—111no—
165#1892—112no—
166#1808—112no—
167C4×#103—111no—
168C23×C11—22no—
169C23×C11—22no—
170C23×C11—22no—
171C23×C11—22no—
172C23×C11—22no—
173C23×C11—22no—
174C23×C11C2×Q1614yes—
175C23×C11C22×D411yescharacteristic
176Q8×C11—84no—
177D4×C11—28no—
178C2×C4×C11—21no—
179C2×C4×C11—21no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—22no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—41no—
190C2×C4×C11—41no—
191C2×C4×C11—41no—
192C2×C4×C11—41no—
193C2×C4×C11—42no—
194C2×C4×C11—41no—
195C2×C4×C11—42no—
196C2×C4×C11#12112yes—
197C2×C4×C11#12112yes—
198C2×C4×C11C2×Q1612yes—
199C2×C4×C11#13512yes—
200C2×C4×C11C22×D411yescharacteristic
201C2×C4×C11C2×#4111yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11H(5,𝔽2)11yescharacteristic
205C2×C4×C112−1+411yescharacteristic
206C2×Dic11—22no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—42no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215Dic22—22no—
216Dic22—22no—
217Dic22—41no—
218Dic22—41no—
219C11⋊C8—22no—
220C11⋊C8—24no—
221C11⋊C8—41no—
222C23×C8—112no—
223C2×C4⋊Q8C2×D1111yescharacteristic
224C2×C22⋊Q8—112no—
225C2×C4×Q8—111no—
226C2×C4×D4C2×D1111yescharacteristic
227#477—224no—
228C8×D4—224no—
229C2×#107—112no—
230C2×#107—112no—
231C2×C4⋊C8—111no—
232C2×#103—112no—
233C2×#103—111no—
234C2×#103—111no—
235C2×C22⋊C8—112no—
236C2×C4×C8—111no—
237#396—222no—
238#393—22no—
239#390—21no—
240#390—221no—
241#389—221no—
242#384—111no—
243#382—21no—
244#380—112no—
245#380C2×D1112yes—
246#380C2×D1112yes—
247C4×C4⋊C4C2×D1111yescharacteristic
248#340—111no—
249#340—112no—
250#340—111no—
251#340—112no—
252#340—112no—
253C22×C11—24no—
254C22×C11—24no—
255C22×C11—24no—
256C22×C11—42no—
257C22×C11—42no—
258C22×C11—42no—
259C22×C11—42no—
260C22×C11C2×#12111yescharacteristic
261C22×C11#54611yescharacteristic
262C22×C11#54711yescharacteristic
263C22×C11C22×Q1611yescharacteristic
264C22×C11C2×#13511yescharacteristic
265C22×C11#57611yescharacteristic
266C22×C11#57711yescharacteristic
267C4×C11—22no—
268C4×C11—42no—
269C4×C11—81no—
270C4×C11—81no—
271C4×C11—82no—
272C4×C11#46714yes—
273C4×C11#52911yescharacteristic
274C4×C11#54211yescharacteristic
275C4×C11#54611yescharacteristic
276C4×C11#54811yescharacteristic
277Dic11—42no—
278Dic11—82no—
279Dic11—81no—
280C22×Q8—21no—
281C22×Q8—111no—
282C22×D4C22⋊D1111yescharacteristic
283C23×C4C22×D1112yes—
284C22×C8—111no—
285C22×C8—112no—
286C22×C8—111no—
287C22×C8—224no—
288C22×C8—224no—
289C22×C8—442no—
290C4⋊Q8—22no—
291C4⋊Q8—22no—
292C22⋊Q8—224no—
293C22⋊Q8—442no—
294C4×Q8—222no—
295C4×Q8—222no—
296C4×D4—22no—
297C4×D4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—112no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4—221no—
305C2×C4⋊C4C22⋊D1111yescharacteristic
306C2×C4⋊C4C22×D1112yes—
307C2×C4⋊C4C22×D1111yescharacteristic
308C2×C4⋊C4C22×D1111yescharacteristic
309C2×C22⋊C4—22no—
310C2×C22⋊C4—22no—
311C2×C22⋊C4—222no—
312C2×C22⋊C4—222no—
313C2×C22⋊C4C22⋊D1112yes—
314C2×C42—21no—
315C2×C42—221no—
316C2×C42C22×D1111yescharacteristic
317#107—224no—
318#107—442no—
319C4⋊C8—114no—
320#103—222no—
321#103—224no—
322#103—222no—
323C22⋊C8—224no—
324C4×C8—222no—
325#95—21no—
326#95—22no—
327#95—22no—
328#95—222no—
329C2×C11—44no—
330C2×C11#242711yescharacteristic
331C2×C11C2×#46711yescharacteristic
332C2×C11#306211yescharacteristic
333C2×C11#329911yescharacteristic
334C2×C11#330511yescharacteristic
335C2×C11#333811yescharacteristic
336C2×C11#334011yescharacteristic
337C24C2×C22⋊D1112yes—
338C2×Q8—42no—
339C2×Q8—81no—
340C2×Q8—81no—
341C2×Q8—112no—
342C2×Q8—221no—
343C2×Q8—221no—
344C2×Q8—221no—
345C2×Q8—221no—
346C2×Q8—221no—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4#432614yes—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—21no—
357C22×C4—21no—
358C22×C4—22no—
359C22×C4—221no—
360C22×C4—221no—
361C22×C4—222no—
362C22×C4C2×C22⋊D1112yes—
363C22×C4C2×C22⋊D1111yescharacteristic
364C22×C4C2×C22⋊D1111yescharacteristic
365C22×C4C23×D1111yescharacteristic
366C2×C8—114no—
367C2×C8—112no—
368C2×C8—221no—
369C2×C8—222no—
370C2×C8—222no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8—448no—
376C4⋊C4—22no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—21no—
383C4⋊C4—42no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—444no—
389C4⋊C4—442no—
390C4⋊C4—442no—
391C4⋊C4—881no—
392C22⋊C4—24no—
393C22⋊C4—82no—
394C22⋊C4—82no—
395C22⋊C4—444no—
396C22⋊C4—882no—
397C42—42no—
398C42—442no—
399C42D4×D1112yes—
400C42#434112yes—
401C11#2534011yescharacteristic, complemented, Sylow
402C23—22no—
403C23—22no—
404C23—22no—
405C23—22no—
406C23—22no—
407C23—22no—
408C23C2×#432614yes—
409C23C22×C22⋊D1111yescharacteristic
410Q8—84no—
411Q8—222no—
412Q8—222no—
413Q8—441no—
414Q8—441no—
415D4—28no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—41no—
429C2×C4—41no—
430C2×C4—41no—
431C2×C4—42no—
432C2×C4—41no—
433C2×C4—42no—
434C2×C4—222no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—441no—
441C2×C4—442no—
442C2×C4—441no—
443C2×C4#6699212yes—
444C2×C4#6699212yes—
445C2×C4C2×#432612yes—
446C2×C4#6700312yes—
447C2×C4C2×D4×D1111yescharacteristic
448C2×C4C2×#434111yescharacteristic
449C2×C4#41×D1111yescharacteristic
450C2×C4#41×D1111yescharacteristic
451C2×C4#6704211yescharacteristic
452C2×C4#6704311yescharacteristic
453C8—222no—
454C8—224no—
455C8—441no—
456C22—24no—
457C22—24no—
458C22—24no—
459C22—42no—
460C22—42no—
461C22—42no—
462C22—42no—
463C22C2×#6699211yescharacteristic
464C22C22×#432611yescharacteristic
465C22C2×#6700311yescharacteristic
466C22#1062335511yescharacteristic
467C22#1062336011yescharacteristic
468C22#1062336611yescharacteristic
469C22#1062336711yescharacteristic
470C4—22no—
471C4—42no—
472C4—82no—
473C4—81no—
474C4—81no—
475C4—442no—
476C4—881no—
477C4—882no—
478C4#1062266414yes—
479C4#1062320711yescharacteristic
480C4#1062320811yescharacteristic
481C4#1062321111yescharacteristic
482C4#1062321311yescharacteristic
483C2—44no—
484C2#1307219611yescharacteristic
485C2C2×#1062266411yescharacteristic
486C2#1307829211yescharacteristic
487C2#1308048611yescharacteristic
488C2#1308056011yescharacteristic
489C2#1308100411yescharacteristic
490C2#1308102911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2563C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2563D11
hypocenterC11#25340
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2563

Complements

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

NH ≅ G/Ntype
1. C2×#10622704C2semidirect
4. #13070047C2semidirect
5. #13069819C2semidirect
6. #13069578C2semidirect
7. #13069374C2semidirect
8. #13069037C2semidirect
9. #13068643C2semidirect
10. C4×#66874C2semidirect
401. C11#25340semidirect

Maximal subgroups

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

subgroupindex
C2×#106227042
C2×D4×C11⋊C82
#130735382
#130700472
#130698192
#130695782
#130693742
#130690372
#130686432
C4×#668742
C11×#25632
#2534011