Finite Group Databasebeta

← #14796418

Subgroups — #14796418

Order 2816.

894 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4325C211yesmaximal, characteristic
2#13073570C211yesmaximal, characteristic
3Q8×C4⋊Dic11C211yesmaximal, characteristic, complemented
4#13070095C212yesmaximal, complemented
5#13069985C212yesmaximal
6#13069578C211yesmaximal, characteristic, complemented
7#13069332C211yesmaximal, characteristic, complemented
8#13068969C212yesmaximal
9#13068619C212yesmaximal, complemented
10#13068617C211yesmaximal, characteristic
11C2×C11×#475C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#66999—21no—
15C2×#66999—21no—
16C2×Q8×Dic11C2212yes—
17C22×#4325C2211yescharacteristic
18C2×C4×D44C2211yescharacteristic
19C11×#475—24no—
20C2×C11×#106C2212yes—
21C2×C11×C4⋊C8C2211yescharacteristic
22C2×C11×#103C2212yes—
23C2×#66899C2211yescharacteristic
24C2×#66885C2212yes—
25C2×Dic11⋊C8C2212yes—
26C4×#4325—24no—
27#10622605—22no—
28#10622601C2212yes—
29#10622598—22no—
30#10622598C2212yes—
31#10622589C2212yes—
32C2×#66873C2211yescharacteristic
33C2×#66872C2211yescharacteristic
34#10622548—21no—
35#10622548C2211yescharacteristic
36C4×C4⋊Dic11—21no—
37C4×C4⋊Dic11C2211yescharacteristic
38C2×C4×C11⋊C8C2211yescharacteristic
39#10622189C2212yes—
40#10622188C2212yes—
41#10622167C2212yes—
42#10622167C2212yes—
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D44C2311yescharacteristic
46C22×C4×D11—21no—
47C22×C8×C11C2312yes—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—22no—
50C4×Q8×C11—22no—
51C4×Q8×C11D414yes—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2312yes—
55C2×C11×C4⋊C4C2311yescharacteristic
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58#66999—44no—
59#66999—44no—
60Q8×Dic11—24no—
61Q8×Dic11—42no—
62C2×#4325—22no—
63C2×#4325—22no—
64C2×#4325Q814yescomplemented
65C2×(C2×D11)⋊C4—21no—
66C2×(C2×D11)⋊C4—22no—
67C2×(C2×D11)⋊C4—22no—
68C2×C4⋊Dic11—21no—
69C2×C4⋊Dic11—22no—
70C2×C4⋊Dic11—21no—
71C2×C4⋊Dic11—22no—
72C2×C4⋊Dic11D411yescharacteristic
73C2×C4⋊Dic11D411yescharacteristic
74C2×C4⋊Dic11C2312yes—
75C2×C4⋊Dic11C2311yescharacteristic
76C2×Dic11⋊C4—22no—
77C2×Dic11⋊C4—22no—
78C2×C4×Dic11—22no—
79C2×C4×Dic11C2312yes—
80C22×C11⋊C8C2311yescharacteristic
81C22×C11⋊C8C2311yescharacteristic
82C4×D44—22no—
83C4×D44—22no—
84C11×#106—24no—
85C11×C4⋊C8—22no—
86C11×#103—24no—
87#66899—22no—
88C11⋊#95—22no—
89C11⋊#95D412yes—
90#66885—42no—
91Dic11⋊C8—42no—
92#66873—22no—
93#66872—22no—
94C4×C11⋊C8—22no—
95#24813—111nomaximal, Sylow
96C23×D11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—21no—
100C2×Q8×C11—42no—
101C2×Q8×C11—42no—
102C2×Q8×C11—42no—
103C2×Q8×C11C2×D412yes—
104C2×Q8×C11C2×Q812yes—
105C2×Q8×C11#4112yes—
106C22×C4×C11—21no—
107C22×C4×C11—21no—
108C22×C4×C11—22no—
109C22×C4×C11C2×D411yescharacteristic
110C22×C4×C11C2×D411yescharacteristic
111C22×C4×C11C2411yescharacteristic
112C22×Dic11—22no—
113C22×Dic11—21no—
114C22×Dic11C2×D412yes—
115C22×Dic11C2×D412yes—
116C2×D44—21no—
117C2×D44—21no—
118C2×D44—21no—
119C2×D44—21no—
120C2×D44—21no—
121C2×D44C2×Q812yes—
122C2×C4×D11—42no—
123C2×C4×D11—42no—
124C2×C4×D11—42no—
125C2×C8×C11—22no—
126C2×C8×C11—22no—
127C2×C8×C11—22no—
128C11×C4⋊C4—24no—
129C11×C4⋊C4—21no—
130C11×C4⋊C4—22no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4C2×D412yes—
134C42×C11—24no—
135C42×C11C2×D412yes—
136C42×C11#4112yes—
137#4325—28no—
138(C2×D11)⋊C4—44no—
139(C2×D11)⋊C4—44no—
140(C2×D11)⋊C4—42no—
141C4⋊Dic11—22no—
142C4⋊Dic11—21no—
143C4⋊Dic11—21no—
144C4⋊Dic11—22no—
145C4⋊Dic11—22no—
146C4⋊Dic11—44no—
147C4⋊Dic11—42no—
148C4⋊Dic11—81no—
149C4⋊Dic11—82no—
150C4⋊Dic11SD1614yescomplemented
151Dic11⋊C4—44no—
152Dic11⋊C4—44no—
153C4×Dic11—22no—
154C4×Dic11—22no—
155C4×Dic11—44no—
156C2×C11⋊C8—21no—
157C2×C11⋊C8—21no—
158C2×C11⋊C8—21no—
159C2×C11⋊C8—21no—
160C2×C11⋊C8—21no—
161C2×C11⋊C8C2×Q812yes—
162C2×#475D1111yescharacteristic, complemented
163C2×C4×SD16—111no—
164#2542—111no—
165Q8×C4⋊C4—111no—
166#2084—112no—
167#2065—112no—
168#1990—111no—
169#1939—111no—
170#1880—112no—
171#1803—112no—
172#1802—111no—
173C23×C11C22×D411yescharacteristic
174C22×D11—22no—
175C22×D11—41no—
176C22×D11—41no—
177C22×D11—41no—
178C22×D11—41no—
179C22×D11—41no—
180C22×D11—41no—
181Q8×C11—22no—
182Q8×C11—22no—
183Q8×C11—22no—
184Q8×C11—84no—
185Q8×C11C22⋊Q814yescomplemented
186C2×C4×C11—22no—
187C2×C4×C11—22no—
188C2×C4×C11—22no—
189C2×C4×C11—21no—
190C2×C4×C11—21no—
191C2×C4×C11—22no—
192C2×C4×C11—41no—
193C2×C4×C11—41no—
194C2×C4×C11—42no—
195C2×C4×C11—42no—
196C2×C4×C11—42no—
197C2×C4×C11#12112yes—
198C2×C4×C11#12112yes—
199C2×C4×C11C2×SD1612yes—
200C2×C4×C11AGL(1,ℤ/8)12yes—
201C2×C4×C11C22×D411yescharacteristic
202C2×C4×C11C22×Q811yescharacteristic
203C2×C4×C11C2×#4111yescharacteristic
204C2×C4×C11C2×#4111yescharacteristic
205C2×C4×C11H(5,𝔽2)11yescharacteristic
206C2×C4×C112−1+411yescharacteristic
207C2×Dic11—22no—
208C2×Dic11—22no—
209C2×Dic11—22no—
210C2×Dic11—22no—
211C2×Dic11—22no—
212C2×Dic11—41no—
213C2×Dic11—42no—
214C2×Dic11—41no—
215C2×Dic11—41no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C2×Dic11C2×SD1614yes—
219D44—22no—
220D44—22no—
221D44—41no—
222D44—41no—
223C4×D11—84no—
224C8×C11—42no—
225C11⋊C8—22no—
226C11⋊C8—41no—
227C22×SD16—111no—
228C2×C4⋊Q8C2×D1111yescharacteristic
229C2×C22⋊Q8—221no—
230C2×C22⋊Q8—221no—
231C2×C4×Q8—112no—
232C2×C4×Q8C2×D1111yescharacteristic
233C2×C4×D4—111no—
234#475—24no—
235C4×SD16—224no—
236C2×#106—111no—
237C2×#106C2×D1112yes—
238C2×C4⋊C8—112no—
239C2×C4⋊C8C2×D1111yescharacteristic
240C2×#103—111no—
241C2×#103C2×D1112yes—
242C2×#102—111no—
243C2×#102—112no—
244C2×C4×C8—111no—
245#399—222no—
246#390—112no—
247#389—112no—
248#389—222no—
249#384—112no—
250#384—111no—
251#384—221no—
252C4×C4⋊C4—111no—
253C4×C4⋊C4—221no—
254#340—112no—
255#340—112no—
256#340—112no—
257#336—112no—
258C22×C11C2×#12111yescharacteristic
259C22×C11#54611yescharacteristic
260C22×C11D4×Q811yescharacteristic
261C22×C11C22×SD1611yescharacteristic
262C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
263C22×C11#57711yescharacteristic
264C22×C11#57811yescharacteristic
265C2×D11—42no—
266C2×D11—42no—
267C2×D11—42no—
268C2×D11—81no—
269C2×D11—81no—
270C2×D11—81no—
271C2×D11—81no—
272C4×C11—24no—
273C4×C11—22no—
274C4×C11—42no—
275C4×C11—82no—
276C4×C11#46014yes—
277C4×C11C2×C22⋊Q811yescharacteristic
278C4×C11#53711yescharacteristic
279C4×C11#55211yescharacteristic
280C4×C11#55411yescharacteristic
281Dic11—24no—
282Dic11—42no—
283Dic11—82no—
284Dic11—81no—
285C22×Q8—21no—
286C22×Q8C22×D1111yescharacteristic
287C22×D4—111no—
288C23×C4—221no—
289C2×SD16—114no—
290C2×SD16—222no—
291C2×SD16—222no—
292C22×C8—111no—
293C22×C8—111no—
294C22×C8C22×D1112yes—
295C4⋊Q8—22no—
296C4⋊Q8—22no—
297C22⋊Q8—444no—
298C22⋊Q8—444no—
299C4×Q8—22no—
300C4×Q8—224no—
301C4×Q8—442no—
302C4×Q8C22⋊D1114yes—
303C4×D4—222no—
304C4×D4—222no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—111no—
308C2×C4⋊C4—111no—
309C2×C4⋊C4—111no—
310C2×C4⋊C4—112no—
311C2×C4⋊C4—222no—
312C2×C4⋊C4—222no—
313C2×C4⋊C4—222no—
314C2×C4⋊C4—221no—
315C2×C4⋊C4—222no—
316C2×C4⋊C4—221no—
317C2×C4⋊C4C22×D1112yes—
318C2×C4⋊C4C22×D1111yescharacteristic
319C2×C22⋊C4—222no—
320C2×C22⋊C4—222no—
321C2×C22⋊C4—221no—
322C2×C42—21no—
323C2×C42—112no—
324C2×C42—222no—
325C2×C42C22×D1111yescharacteristic
326#106—24no—
327#106—222no—
328C4⋊C8—22no—
329C4⋊C8—442no—
330#103—24no—
331#103—222no—
332#102—222no—
333#102—442no—
334C4×C8—222no—
335#95—112no—
336#95—222no—
337C2×C11#241711yescharacteristic
338C2×C11C2×#46011yescharacteristic
339C2×C11#304611yescharacteristic
340C2×C11#329811yescharacteristic
341C2×C11#333211yescharacteristic
342C2×C11Q8×SD1611yescharacteristic
343C2×C11#338611yescharacteristic
344D11—82no—
345C24—221no—
346C2×Q8—21no—
347C2×Q8—21no—
348C2×Q8—21no—
349C2×Q8—42no—
350C2×Q8—42no—
351C2×Q8—42no—
352C2×Q8Q8×D1112yes—
353C2×Q8#434312yes—
354C2×Q8C2×C22⋊D1112yes—
355C2×D4—112no—
356C2×D4—221no—
357C2×D4—221no—
358C2×D4—221no—
359C2×D4—221no—
360C2×D4—221no—
361C22×C4—21no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—112no—
365C22×C4—112no—
366C22×C4—222no—
367C22×C4—221no—
368C22×C4—442no—
369C22×C4—442no—
370C22×C4—442no—
371C22×C4D4×D1111yescharacteristic
372C22×C4D4×D1111yescharacteristic
373C22×C4C23×D1111yescharacteristic
374SD16—228no—
375C2×C8—22no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—112no—
379C2×C8—221no—
380C2×C8—221no—
381C2×C8—221no—
382C2×C8—221no—
383C2×C8—221no—
384C4⋊C4—24no—
385C4⋊C4—21no—
386C4⋊C4—22no—
387C4⋊C4—22no—
388C4⋊C4—42no—
389C4⋊C4—114no—
390C4⋊C4—222no—
391C4⋊C4—221no—
392C4⋊C4—222no—
393C4⋊C4—222no—
394C4⋊C4—221no—
395C4⋊C4—444no—
396C4⋊C4—444no—
397C4⋊C4—444no—
398C4⋊C4—442no—
399C4⋊C4—881no—
400C4⋊C4—882no—
401C4⋊C4C2×C22⋊D1112yes—
402C22⋊C4—444no—
403C22⋊C4—444no—
404C22⋊C4—442no—
405C42—24no—
406C42—222no—
407C42—222no—
408C42—444no—
409C42#434112yes—
410C42C2×C22⋊D1112yes—
411C11#2481311yescharacteristic, complemented, Sylow
412C23—222no—
413C23—441no—
414C23—441no—
415C23—441no—
416C23—441no—
417C23—441no—
418C23—441no—
419C23C2×D4×D1111yescharacteristic
420Q8—22no—
421Q8—22no—
422Q8—22no—
423Q8—84no—
424Q8#6699914yescomplemented
425D4—222no—
426D4—222no—
427D4—441no—
428D4—441no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—22no—
432C2×C4—22no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—41no—
436C2×C4—41no—
437C2×C4—42no—
438C2×C4—42no—
439C2×C4—42no—
440C2×C4—114no—
441C2×C4—222no—
442C2×C4—222no—
443C2×C4—222no—
444C2×C4—222no—
445C2×C4—222no—
446C2×C4—441no—
447C2×C4—441no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—441no—
451C2×C4—442no—
452C2×C4—884no—
453C2×C4SD16×D1112yes—
454C2×C4#6696712yes—
455C2×C4#6699212yes—
456C2×C4#6699212yes—
457C2×C4C2×#434111yescharacteristic
458C2×C4C2×Q8×D1111yescharacteristic
459C2×C4C2×#434311yescharacteristic
460C2×C4#6704211yescharacteristic
461C2×C4#6704311yescharacteristic
462C2×C4C22×C22⋊D1111yescharacteristic
463C8—42no—
464C8—222no—
465C8—441no—
466C22—442no—
467C22—442no—
468C22—442no—
469C22—881no—
470C22—881no—
471C22—881no—
472C22—881no—
473C22#1062316111yescharacteristic
474C22#1062316311yescharacteristic
475C22C2×SD16×D1111yescharacteristic
476C22C2×#6696711yescharacteristic
477C22#1062330911yescharacteristic
478C22#1062331011yescharacteristic
479C22C2×#6699211yescharacteristic
480C4—22no—
481C4—24no—
482C4—42no—
483C4—82no—
484C4—224no—
485C4—442no—
486C4—881no—
487C4—882no—
488C4#1062277614yes—
489C4#1062316611yescharacteristic
490C4#1062317311yescharacteristic
491C4C2×#6699911yescharacteristic
492C4#1062336411yescharacteristic
493C2—882no—
494C2#1307206811yescharacteristic
495C2C2×#1062277611yescharacteristic
496C2#1307817011yescharacteristic
497C2#1308047811yescharacteristic
498C2#1308094011yescharacteristic
499C2#1308147511yescharacteristic
500C2#1308153611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#475C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#475D11
hypocenterC11#24813
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#475

Complements

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

NH ≅ G/Ntype
3. Q8×C4⋊Dic11C2semidirect
4. #13070095C2semidirect
6. #13069578C2semidirect
7. #13069332C2semidirect
9. #13068619C2semidirect
11. C2×C11×#475C2semidirect
64. C2×#4325Q8semidirect
150. C4⋊Dic11SD16semidirect
162. C2×#475D11semidirect
185. Q8×C11C22⋊Q8semidirect
411. C11#24813semidirect
424. Q8#66999semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43252
#130735702
Q8×C4⋊Dic112
#130700952
#130699852
#130695782
#130693322
#130689692
#130686192
#130686172
C2×C11×#4752
#2481311