Finite Group Databasebeta

← #14803288

Subgroups — #14803288

Order 2816.

850 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×#10622696C211yesmaximal, characteristic
2C2×Q8×C11⋊C8C211yesmaximal, characteristic, complemented
3#13073534C211yesmaximal, characteristic
4#13069997C212yesmaximal, complemented
5#13069931C212yesmaximal
6#13069473C212yesmaximal
7#13069419C211yesmaximal, characteristic, complemented
8#13069379C211yesmaximal, characteristic, complemented
9#13069295C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic
11C11×#2568C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#66999—21no—
15C22×#4325C2212yes—
16C2×C4×D44C2211yescharacteristic
17C11×#400—22no—
18C11×#391—21no—
19C11×#391C2212yes—
20C11×#391C2212yes—
21C11×#382—21no—
22C4×C11×C4⋊C4C2211yescharacteristic
23C2×#66899C2212yes—
24C2×#66899C2212yes—
25C2×#66899C2212yes—
26#10622696—24no—
27Q8×C11⋊C8—24no—
28#10622607—22no—
29#10622600—21no—
30C2×#66873C2211yescharacteristic
31C2×#66873C2211yescharacteristic
32C2×#66872C2212yes—
33#10622552C2212yes—
34#10622548C2211yescharacteristic
35#10622541C2212yes—
36C2×C4⋊(C11⋊C8)C2212yes—
37C2×C4⋊(C11⋊C8)C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39C2×C4×C11⋊C8C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11D411yescharacteristic
44C22×Q8×C11C2312yes—
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C11×C4⋊Q8—22no—
48C11×C4⋊Q8—22no—
49C4×Q8×C11—22no—
50C4×Q8×C11—22no—
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⋊C4C2311yescharacteristic
57C2×C42×C11—21no—
58C2×C42×C11C2312yes—
59C2×C42×C11C2311yescharacteristic
60#66999—44no—
61C2×#4325—24no—
62C2×#4325—24no—
63C2×#4325—42no—
64C2×(C2×D11)⋊C4—21no—
65C2×(C2×D11)⋊C4—22no—
66C2×(C2×D11)⋊C4—22no—
67C2×C4⋊Dic11—21no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2312yes—
71C2×Dic11⋊C4—22no—
72C22×C11⋊C8C2311yescharacteristic
73C22×C11⋊C8C2312yes—
74C22×C11⋊C8C2311yescharacteristic
75C4×D44—22no—
76C4×D44—22no—
77C11×#95—21no—
78C11×#95—22no—
79C11×#95—22no—
80C11×#95—22no—
81C11×#95—22no—
82#66899—24no—
83#66899—24no—
84#66899—42no—
85C11⋊#95—22no—
86#66873—22no—
87#66873—22no—
88#66872—42no—
89C4⋊(C11⋊C8)—24no—
90C4⋊(C11⋊C8)D414yes—
91C4×C11⋊C8—22no—
92C4×C11⋊C8—24no—
93#25293—111nomaximal, Sylow
94C23×D11—21no—
95C2×Q8×C11—22no—
96C2×Q8×C11—22no—
97C2×Q8×C11—22no—
98C2×Q8×C11—22no—
99C2×Q8×C11—22no—
100C2×Q8×C11—22no—
101C2×Q8×C11—22no—
102C2×Q8×C11—22no—
103C2×Q8×C11SD1614yescomplemented
104C22×C4×C11—21no—
105C22×C4×C11—21no—
106C22×C4×C11—22no—
107C22×C4×C11C2×D412yes—
108C22×C4×C11C2×D411yescharacteristic
109C22×C4×C11C2×D412yes—
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2411yescharacteristic
112C22×Dic11—21no—
113C22×Dic11—22no—
114C2×D44—21no—
115C2×D44—21no—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44#4112yes—
120C2×C4×D11—42no—
121C2×C4×D11—42no—
122C2×C4×D11—42no—
123C11×C4⋊C4—24no—
124C11×C4⋊C4—22no—
125C11×C4⋊C4—21no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—21no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—42no—
131C42×C11—22no—
132C42×C11—22no—
133C42×C11—42no—
134C42×C11C2×D412yes—
135C42×C11#4112yes—
136#4325—48no—
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—44no—
139(C2×D11)⋊C4—82no—
140C4⋊Dic11—21no—
141C4⋊Dic11—22no—
142C4⋊Dic11—21no—
143C4⋊Dic11—22no—
144C4⋊Dic11—42no—
145C4⋊Dic11—81no—
146Dic11⋊C4—44no—
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⋊C8C2×D414yes—
155C2×C11⋊C8#4112yes—
156C2×#461—111no—
157C2×C8×Q8—111no—
158#2568D1111yescharacteristic, complemented
159#2538—111no—
160#2066—112no—
161#2055—112no—
162#1968—112no—
163#1956—111no—
164#1948—111no—
165#1933—112no—
166C4×#102—111no—
167C23×C11C22×D411yescharacteristic
168C22×D11—22no—
169C22×D11—41no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C22×D11—41no—
175Q8×C11—28no—
176Q8×C11—42no—
177Q8×C11—42no—
178Q8×C11—42no—
179Q8×C11—42no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11—21no—
183C2×C4×C11—21no—
184C2×C4×C11—22no—
185C2×C4×C11—22no—
186C2×C4×C11—22no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—41no—
191C2×C4×C11—42no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—41no—
195C2×C4×C11—41no—
196C2×C4×C11#12112yes—
197C2×C4×C11#12112yes—
198C2×C4×C11C2×SD1614yes—
199C2×C4×C11C2×SD1612yes—
200C2×C4×C11#13512yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C2×#4111yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11H(5,𝔽2)11yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C2×Dic11—41no—
208C2×Dic11—42no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11—41no—
212C2×Dic11—42no—
213D44—22no—
214D44—22no—
215D44—41no—
216D44—41no—
217C4×D11—84no—
218C11⋊C8—24no—
219C11⋊C8—22no—
220C11⋊C8—41no—
221C22×SD16—112no—
222C2×C4⋊Q8C2×D1111yescharacteristic
223C2×C22⋊Q8—221no—
224C2×C4×Q8C2×D1111yescharacteristic
225C2×C4×D4—111no—
226#461—224no—
227C8×Q8—224no—
228C2×#106—112no—
229C2×C4⋊C8—111no—
230C2×C4⋊C8—112no—
231C2×#103—112no—
232C2×#103—112no—
233C2×#103—112no—
234C2×#102—111no—
235C2×#102—111no—
236C2×C4×C8—112no—
237C2×C4×C8—111no—
238#400—22no—
239#396—222no—
240#391—21no—
241#391C2×D1112yes—
242#391C2×D1112yes—
243#390—112no—
244#389—112no—
245#384—111no—
246#382—21no—
247#380—221no—
248C4×C4⋊C4C2×D1111yescharacteristic
249#340—112no—
250#340—111no—
251#340—111no—
252C22×C11C2×#12111yescharacteristic
253C22×C11#54811yescharacteristic
254C22×C11#55011yescharacteristic
255C22×C11C22×SD1611yescharacteristic
256C22×C11C2×#13511yescharacteristic
257C22×C11#57711yescharacteristic
258C22×C11#57811yescharacteristic
259C2×D11—42no—
260C2×D11—42no—
261C2×D11—42no—
262C2×D11—81no—
263C2×D11—81no—
264C2×D11—81no—
265C2×D11—81no—
266C4×C11—24no—
267C4×C11—22no—
268C4×C11—42no—
269C4×C11—81no—
270C4×C11—81no—
271C4×C11—82no—
272C4×C11#46514yes—
273C4×C11#52911yescharacteristic
274C4×C11#54211yescharacteristic
275C4×C11#54611yescharacteristic
276C4×C11#54811yescharacteristic
277Dic11—82no—
278Dic11—81no—
279C22×Q8C22⋊D1111yescharacteristic
280C22×Q8C22×D1112yes—
281C22×D4—111no—
282C23×C4—221no—
283C2×SD16—224no—
284C2×SD16—224no—
285C2×SD16—442no—
286C22×C8—112no—
287C22×C8—111no—
288C22×C8—111no—
289C4⋊Q8—22no—
290C4⋊Q8—22no—
291C22⋊Q8—444no—
292C4×Q8—22no—
293C4×Q8—22no—
294C4×D4—222no—
295C4×D4—222no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4—111no—
299C2×C4⋊C4—112no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—222no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4C22⋊D1111yescharacteristic
304C2×C4⋊C4C22⋊D1112yes—
305C2×C4⋊C4C22×D1111yescharacteristic
306C2×C4⋊C4C22×D1111yescharacteristic
307C2×C22⋊C4—221no—
308C2×C22⋊C4—222no—
309C2×C22⋊C4—222no—
310C2×C42—21no—
311C2×C42C22×D1112yes—
312C2×C42C22×D1111yescharacteristic
313#106—442no—
314C4⋊C8—114no—
315C4⋊C8—224no—
316#103—224no—
317#103—224no—
318#103—442no—
319#102—222no—
320#102—222no—
321C4×C8—224no—
322C4×C8—222no—
323#95—21no—
324#95—22no—
325#95—22no—
326#95—22no—
327#95—22no—
328#95—222no—
329C2×C11#242611yescharacteristic
330C2×C11C2×#46511yescharacteristic
331C2×C11#306311yescharacteristic
332C2×C11#335911yescharacteristic
333C2×C11#336011yescharacteristic
334C2×C11#339211yescharacteristic
335C2×C11#339311yescharacteristic
336D11—82no—
337C24—221no—
338C2×Q8—22no—
339C2×Q8—22no—
340C2×Q8—22no—
341C2×Q8—22no—
342C2×Q8—22no—
343C2×Q8—22no—
344C2×Q8—22no—
345C2×Q8—22no—
346C2×Q8#432514yescomplemented
347C2×D4—112no—
348C2×D4—221no—
349C2×D4—221no—
350C2×D4—221no—
351C2×D4—221no—
352C2×D4—221no—
353C22×C4—21no—
354C22×C4—21no—
355C22×C4—22no—
356C22×C4—221no—
357C22×C4—222no—
358C22×C4—442no—
359C22×C4—442no—
360C22×C4—442no—
361C22×C4C2×C22⋊D1112yes—
362C22×C4C2×C22⋊D1111yescharacteristic
363C22×C4C2×C22⋊D1112yes—
364C22×C4C2×C22⋊D1111yescharacteristic
365C22×C4C23×D1111yescharacteristic
366SD16—448no—
367C2×C8—114no—
368C2×C8—112no—
369C2×C8—221no—
370C2×C8—222no—
371C2×C8—222no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8—221no—
376C4⋊C4—24no—
377C4⋊C4—22no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—21no—
382C4⋊C4—42no—
383C4⋊C4—42no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—222no—
387C4⋊C4—222no—
388C4⋊C4—444no—
389C4⋊C4—442no—
390C4⋊C4—881no—
391C22⋊C4—442no—
392C22⋊C4—444no—
393C22⋊C4—882no—
394C42—22no—
395C42—22no—
396C42—42no—
397C42D4×D1112yes—
398C42#434112yes—
399C11#2529311yescharacteristic, complemented, Sylow
400C23—222no—
401C23—441no—
402C23—441no—
403C23—441no—
404C23—441no—
405C23—441no—
406C23—441no—
407C23C22×C22⋊D1111yescharacteristic
408Q8—28no—
409Q8—42no—
410Q8—42no—
411Q8—42no—
412Q8—42no—
413D4—222no—
414D4—222no—
415D4—441no—
416D4—441no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—22no—
424C2×C4—42no—
425C2×C4—41no—
426C2×C4—41no—
427C2×C4—41no—
428C2×C4—42no—
429C2×C4—41no—
430C2×C4—42no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—441no—
434C2×C4—442no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—884no—
440C2×C4#6699212yes—
441C2×C4#6699212yes—
442C2×C4C2×#432514yes—
443C2×C4C2×#432512yes—
444C2×C4#6700312yes—
445C2×C4C2×D4×D1111yescharacteristic
446C2×C4C2×#434111yescharacteristic
447C2×C4#41×D1111yescharacteristic
448C2×C4#41×D1111yescharacteristic
449C2×C4#6704211yescharacteristic
450C2×C4#6704311yescharacteristic
451C8—224no—
452C8—222no—
453C8—441no—
454C22—442no—
455C22—442no—
456C22—442no—
457C22—881no—
458C22—881no—
459C22—881no—
460C22—881no—
461C22C2×#6699211yescharacteristic
462C22C22×#432511yescharacteristic
463C22C2×#6700311yescharacteristic
464C22#1062336211yescharacteristic
465C22#1062336511yescharacteristic
466C22#1062336811yescharacteristic
467C22#1062336911yescharacteristic
468C4—22no—
469C4—24no—
470C4—42no—
471C4—81no—
472C4—82no—
473C4—81no—
474C4—881no—
475C4—882no—
476C4#1062266114yes—
477C4#1062320711yescharacteristic
478C4#1062320811yescharacteristic
479C4#1062321111yescharacteristic
480C4#1062321311yescharacteristic
481C2—882no—
482C2#1307218511yescharacteristic
483C2C2×#1062266111yescharacteristic
484C2#1307830311yescharacteristic
485C2#1308125411yescharacteristic
486C2#1308126111yescharacteristic
487C2#1308159311yescharacteristic
488C2#1308160011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2568C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#2568D11
hypocenterC11#25293
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2568

Complements

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

NH ≅ G/Ntype
2. C2×Q8×C11⋊C8C2semidirect
4. #13069997C2semidirect
7. #13069419C2semidirect
8. #13069379C2semidirect
9. #13069295C2semidirect
11. C11×#2568C2semidirect
103. C2×Q8×C11SD16semidirect
158. #2568D11semidirect
346. C2×Q8#4325semidirect
399. C11#25293semidirect

Maximal subgroups

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

subgroupindex
C2×#106226962
C2×Q8×C11⋊C82
#130735342
#130699972
#130699312
#130694732
#130694192
#130693792
#130692952
C4×#668732
C11×#25682
#2529311