Finite Group Databasebeta

← #14803908

Subgroups — #14803908

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×#10622634C211yesmaximal, characteristic, complemented
2C2×D4×C11⋊C8C211yesmaximal, characteristic
3#13073789C211yesmaximal, characteristic
4#13070047C212yesmaximal, complemented
5#13069816C212yesmaximal, complemented
6#13069576C211yesmaximal, characteristic, complemented
7#13069372C211yesmaximal, characteristic, complemented
8#13069040C212yesmaximal, complemented
9#13068643C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C11×#2538C211yesmaximal, characteristic
12C2×C11×C22⋊Q8C2212yes—
13C2×C4×Q8×C11C2211yescharacteristic
14C2×C4×D4×C11C2211yescharacteristic
15C23×C11⋊C8C2212yes—
16C2×#66922C2211yescharacteristic
17C11×#396—22no—
18C11×#390—21no—
19C11×#389—21no—
20C11×#384C2211yescharacteristic
21C11×#380C2212yes—
22C2×#66899C2212yes—
23C2×#66899C2211yescharacteristic
24C2×#66899C2211yescharacteristic
25#10622834—21no—
26#10622825C2212yes—
27#10622825C2212yes—
28C2×C22⋊(C11⋊C8)C2212yes—
29#10622634—24no—
30D4×C11⋊C8—24no—
31#10622590—21no—
32C2×#66871C2212yes—
33C2×#66871C2212yes—
34#10622560—22no—
35C4×C4⋊Dic11C2211yescharacteristic
36C2×C4⋊(C11⋊C8)C2211yescharacteristic
37C2×C4×C11⋊C8C2211yescharacteristic
38#10622167C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11C2311yescharacteristic
44C22×D4×C11D411yescharacteristic
45C23×C4×C11C2312yes—
46C22×Dic22—21no—
47C11×C22⋊Q8—24no—
48C11×C22⋊Q8—42no—
49C4×Q8×C11—22no—
50C4×Q8×C11—22no—
51C4×D4×C11—22no—
52C4×D4×C11—22no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4—21no—
55C2×C11×C4⋊C4—22no—
56C2×C11×C4⋊C4—21no—
57C2×C11×C4⋊C4D411yescharacteristic
58C2×C11×C4⋊C4C2311yescharacteristic
59C2×C11×C4⋊C4C2312yes—
60C2×C11×C22⋊C4—22no—
61C2×C11×C22⋊C4—22no—
62C2×C11×C22⋊C4D412yes—
63C2×C42×C11—21no—
64C2×C42×C11C2311yescharacteristic
65C2×C22⋊Dic11—22no—
66C2×C22⋊Dic11—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11C2312yes—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2311yescharacteristic
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
78#66922—22no—
79#66922—22no—
80C11×#95—22no—
81#66899—22no—
82#66899—24no—
83#66899—22no—
84C11⋊#95—21no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87C22⋊(C11⋊C8)—24no—
88#66871—24no—
89#66871—42no—
90C4⋊(C11⋊C8)D414yes—
91C4×C11⋊C8—22no—
92#25340—111nomaximal, Sylow
93C24×C11C2×D412yes—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11#4112yes—
100C2×D4×C11—22no—
101C2×D4×C11—22no—
102C2×D4×C11Q1614yes—
103C22×C4×C11—21no—
104C22×C4×C11—22no—
105C22×C4×C11—22no—
106C22×C4×C11—22no—
107C22×C4×C11—22no—
108C22×C4×C11—22no—
109C22×C4×C11—22no—
110C22×C4×C11—21no—
111C22×C4×C11—22no—
112C22×C4×C11C2×D412yes—
113C22×C4×C11C2×D411yescharacteristic
114C22×C4×C11C2×D411yescharacteristic
115C22×C4×C11C2411yescharacteristic
116C22×Dic11—21no—
117C22×Dic11—21no—
118C22×Dic11—22no—
119C2×Dic22—42no—
120C2×Dic22—81no—
121C2×Dic22—81no—
122C11×C4⋊C4—22no—
123C11×C4⋊C4—21no—
124C11×C4⋊C4—21no—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—22no—
127C11×C4⋊C4—44no—
128C11×C4⋊C4—42no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—81no—
131C11×C22⋊C4—24no—
132C11×C22⋊C4—44no—
133C11×C22⋊C4—82no—
134C42×C11—42no—
135C42×C11C2×D412yes—
136C42×C11#4112yes—
137C22⋊Dic11—82no—
138C22⋊Dic11—82no—
139C4⋊Dic11—22no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—22no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—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#2563—111no—
160#2538D1111yescharacteristic
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—22no—
177Q8×C11—22no—
178Q8×C11—41no—
179Q8×C11—41no—
180D4×C11—28no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—41no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—42no—
192C2×C4×C11—42no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—41no—
197C2×C4×C11—42no—
198C2×C4×C11—41no—
199C2×C4×C11#12112yes—
200C2×C4×C11#12112yes—
201C2×C4×C11C2×Q1612yes—
202C2×C4×C11#13512yes—
203C2×C4×C11C22×D411yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11C2×#4111yescharacteristic
206C2×C4×C11C2×#4111yescharacteristic
207C2×C4×C11H(5,𝔽2)11yescharacteristic
208C2×C4×C112−1+411yescharacteristic
209C2×Dic11—42no—
210C2×Dic11—41no—
211C2×Dic11—41no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214C2×Dic11—41no—
215C2×Dic11—42no—
216C2×Dic11—41no—
217C2×Dic11—42no—
218Dic22—84no—
219C11⋊C8—22no—
220C11⋊C8—24no—
221C11⋊C8—41no—
222C23×C8—112no—
223C2×C4⋊Q8—111no—
224C2×C22⋊Q8C2×D1112yes—
225C2×C4×Q8C2×D1111yescharacteristic
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—22no—
238#393—222no—
239#390—21no—
240#390—221no—
241#389—21no—
242#384C2×D1111yescharacteristic
243#382—221no—
244#380—112no—
245#380—112no—
246#380C2×D1112yes—
247C4×C4⋊C4—111no—
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—42no—
270C4×C11—82no—
271C4×C11—81no—
272C4×C11#46714yes—
273C4×C11#52911yescharacteristic
274C4×C11#54211yescharacteristic
275C4×C11#54611yescharacteristic
276C4×C11#54811yescharacteristic
277Dic11—81no—
278Dic11—81no—
279Dic11—82no—
280C22×Q8—221no—
281C22×Q8C22×D1111yescharacteristic
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—222no—
291C4⋊Q8—222no—
292C22⋊Q8—24no—
293C22⋊Q8—42no—
294C4×Q8—22no—
295C4×Q8—22no—
296C4×D4—22no—
297C4×D4—22no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—22no—
300C2×C4⋊C4—21no—
301C2×C4⋊C4—21no—
302C2×C4⋊C4—112no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—111no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4C22⋊D1111yescharacteristic
307C2×C4⋊C4C22×D1111yescharacteristic
308C2×C4⋊C4C22×D1112yes—
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—22no—
326#95—221no—
327#95—222no—
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—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—442no—
344C2×Q8—881no—
345C2×Q8—881no—
346C2×Q8#434112yes—
347C2×D4—22no—
348C2×D4—22no—
349C2×D4#432614yes—
350C22×C4—21no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—22no—
355C22×C4—22no—
356C22×C4—22no—
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—221no—
371C2×C8—222no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8—448no—
376C4⋊C4—22no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—22no—
380C4⋊C4—22no—
381C4⋊C4—44no—
382C4⋊C4—42no—
383C4⋊C4—42no—
384C4⋊C4—81no—
385C4⋊C4—222no—
386C4⋊C4—221no—
387C4⋊C4—222no—
388C4⋊C4—221no—
389C4⋊C4—221no—
390C4⋊C4—221no—
391C4⋊C4—442no—
392C22⋊C4—24no—
393C22⋊C4—44no—
394C22⋊C4—82no—
395C22⋊C4—882no—
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—22no—
411Q8—22no—
412Q8—41no—
413Q8—41no—
414Q8—884no—
415D4—28no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—41no—
423C2×C4—41no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—41no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—42no—
433C2×C4—41no—
434C2×C4—442no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—441no—
438C2×C4—441no—
439C2×C4—441no—
440C2×C4—442no—
441C2×C4—441no—
442C2×C4—442no—
443C2×C4#6699212yes—
444C2×C4#6699212yes—
445C2×C4C2×#432612yes—
446C2×C4#6700312yes—
447C2×C4C2×D4×D1111yescharacteristic
448C2×C4C2×#434111yescharacteristic
449C2×C4C2×#434111yescharacteristic
450C2×C4#6703711yescharacteristic
451C2×C4#41×D1111yescharacteristic
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
464C22#1062333711yescharacteristic
465C22C22×#432611yescharacteristic
466C22C2×#6700311yescharacteristic
467C22#1062335511yescharacteristic
468C22#1062336611yescharacteristic
469C22#1062336811yescharacteristic
470C4—22no—
471C4—42no—
472C4—42no—
473C4—81no—
474C4—82no—
475C4—882no—
476C4—881no—
477C4—881no—
478C4#1062266414yes—
479C4#1062312911yescharacteristic
480C4#1062313111yescharacteristic
481C4#1062313411yescharacteristic
482C4#1062314311yescharacteristic
483C2—44no—
484C2#1307219511yescharacteristic
485C2C2×#1062266411yescharacteristic
486C2#1307829811yescharacteristic
487C2#1308049211yescharacteristic
488C2#1308056611yescharacteristic
489C2#1308100411yescharacteristic
490C2#1308102311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2538C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2538D11
hypocenterC11#25340
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2538

Complements

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

NH ≅ G/Ntype
1. C2×#10622634C2semidirect
4. #13070047C2semidirect
5. #13069816C2semidirect
6. #13069576C2semidirect
7. #13069372C2semidirect
8. #13069040C2semidirect
9. #13068643C2semidirect
10. C4×#66899C2semidirect
401. C11#25340semidirect

Maximal subgroups

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

subgroupindex
C2×#106226342
C2×D4×C11⋊C82
#130737892
#130700472
#130698162
#130695762
#130693722
#130690402
#130686432
C4×#668992
C11×#25382
#2534011