Finite Group Databasebeta

← #14803283

Subgroups — #14803283

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×#10622454C211yesmaximal, characteristic
2C2×#10622443C211yesmaximal, characteristic, complemented
3#13073831C211yesmaximal, characteristic, complemented
4#13073539C211yesmaximal, characteristic
5#13069992C212yesmaximal, complemented
6#13069935C212yesmaximal
7#13069468C212yesmaximal
8#13069417C211yesmaximal, characteristic, complemented
9#13069293C212yesmaximal, complemented
10C4×#66873C211yesmaximal, characteristic
11C11×#1948C211yesmaximal, characteristic, complemented
12C22×#4314C2212yes—
13C2×#66950—21no—
14C2×C4×D44C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C2×C4×Dic22C2211yescharacteristic
17C2×C11×#106C2212yes—
18C2×C11×C4⋊C8C2211yescharacteristic
19C11×#384C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×#66880C2212yes—
22C2×Dic11⋊C8C2212yes—
23C2×C8×Dic11C2212yes—
24#10622607—22no—
25#10622601C2212yes—
26#10622600—21no—
27#10622598C2212yes—
28#10622587C2212yes—
29#10622587C2212yes—
30C2×#66874C2212yes—
31C2×#66874C2212yes—
32C2×#66873C2211yescharacteristic
33C2×#66873C2211yescharacteristic
34#10622549—21no—
35#10622542—21no—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622454—24no—
38#10622443—24no—
39#10622272—22no—
40C11×#340C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×Dic22D411yescharacteristic
46C22×Dic22C2312yes—
47C22×C8×C11C2312yes—
48C2×C11×C4⋊C4—21no—
49C2×C11×C4⋊C4—21no—
50C2×C11×C4⋊C4C2311yescharacteristic
51C2×C11×C4⋊C4C2312yes—
52C2×C11×C4⋊C4C2311yescharacteristic
53C2×C42×C11—21no—
54C2×C42×C11C2311yescharacteristic
55C2×(C2×D11)⋊C4—21no—
56C2×(C2×D11)⋊C4—22no—
57C2×(C2×D11)⋊C4—22no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11—22no—
61C2×C4⋊Dic11D411yescharacteristic
62C2×C4⋊Dic11C2311yescharacteristic
63C2×Dic11⋊C4D412yes—
64C2×C4×Dic11C2312yes—
65C22×C11⋊C8C2311yescharacteristic
66C22×C11⋊C8C2311yescharacteristic
67C2×#4314—24no—
68C2×#4314—24no—
69C2×#4314—42no—
70#66950—44no—
71C4×D44—22no—
72C4×D44—22no—
73#66922—22no—
74#66922—22no—
75C4×Dic22—22no—
76C4×Dic22—22no—
77C11×#106—42no—
78C11×C4⋊C8D414yes—
79C11×#95—21no—
80C11⋊#95—22no—
81C11⋊#95—22no—
82C11⋊#95—22no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85#66880—24no—
86Dic11⋊C8—24no—
87C8×Dic11—24no—
88#66874—24no—
89#66874—42no—
90#66873—22no—
91#66873—22no—
92C4×C11⋊C8—22no—
93#25293—111nomaximal, Sylow
94C23×D11—21no—
95C22×C4×C11—21no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11C2×D411yescharacteristic
99C22×C4×C11C2×D411yescharacteristic
100C22×C4×C11C2411yescharacteristic
101C22×Dic11—22no—
102C22×Dic11—21no—
103C22×Dic11C2×D412yes—
104C22×Dic11C2×D412yes—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44—21no—
110C2×D44#4112yes—
111C2×C4×D11—42no—
112C2×C4×D11—42no—
113C2×C4×D11—42no—
114C2×Dic22—22no—
115C2×Dic22—22no—
116C2×Dic22—22no—
117C2×Dic22—22no—
118C2×Dic22—22no—
119C2×Dic22—22no—
120C2×Dic22—22no—
121C2×Dic22—22no—
122C2×Dic22SD1614yescomplemented
123C2×C8×C11—22no—
124C2×C8×C11—22no—
125C2×C8×C11C2×D414yes—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—22no—
130C11×C4⋊C4—21no—
131C11×C4⋊C4—21no—
132C11×C4⋊C4—42no—
133C11×C4⋊C4—81no—
134C42×C11—42no—
135C42×C11C2×D412yes—
136C42×C11#4112yes—
137(C2×D11)⋊C4—44no—
138(C2×D11)⋊C4—42no—
139(C2×D11)⋊C4—82no—
140C4⋊Dic11—22no—
141C4⋊Dic11—21no—
142C4⋊Dic11—21no—
143C4⋊Dic11—44no—
144C4⋊Dic11—42no—
145C4⋊Dic11—42no—
146Dic11⋊C4—24no—
147C4×Dic11—22no—
148C4×Dic11—22no—
149C2×C11⋊C8—21no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8#4112yes—
155#4314—48no—
156C2×#461—111no—
157C2×C8×Q8—111no—
158#2568—111no—
159#2538—111no—
160#2066—112no—
161#2055—112no—
162#1968—112no—
163#1956—111no—
164#1948D1111yescharacteristic, complemented
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—
175C2×C4×C11—21no—
176C2×C4×C11—21no—
177C2×C4×C11—41no—
178C2×C4×C11—42no—
179C2×C4×C11—41no—
180C2×C4×C11—42no—
181C2×C4×C11—41no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11#12112yes—
187C2×C4×C11#12112yes—
188C2×C4×C11C2×SD1612yes—
189C2×C4×C11#13512yes—
190C2×C4×C11C22×D411yescharacteristic
191C2×C4×C11C2×#4111yescharacteristic
192C2×C4×C11C2×#4111yescharacteristic
193C2×C4×C11C2×#4111yescharacteristic
194C2×C4×C11H(5,𝔽2)11yescharacteristic
195C2×C4×C112−1+411yescharacteristic
196C2×Dic11—22no—
197C2×Dic11—22no—
198C2×Dic11—22no—
199C2×Dic11—22no—
200C2×Dic11—22no—
201C2×Dic11—41no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—41no—
206C2×Dic11—41no—
207C2×Dic11C2×SD1614yes—
208D44—22no—
209D44—22no—
210D44—41no—
211D44—41no—
212C4×D11—84no—
213Dic22—28no—
214Dic22—42no—
215Dic22—42no—
216Dic22—42no—
217Dic22—42no—
218C8×C11—24no—
219C11⋊C8—22no—
220C11⋊C8—41no—
221C22×SD16—112no—
222C2×C4⋊Q8—111no—
223C2×C22⋊Q8—221no—
224C2×C4×Q8—111no—
225C2×C4×D4—111no—
226#461—224no—
227C8×Q8—224no—
228C2×#106C2×D1112yes—
229C2×C4⋊C8—112no—
230C2×C4⋊C8C2×D1111yescharacteristic
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—222no—
239#396—222no—
240#391—112no—
241#391—112no—
242#391—221no—
243#390—112no—
244#389—112no—
245#384C2×D1111yescharacteristic
246#382—221no—
247#380—221no—
248C4×C4⋊C4C2×D1111yescharacteristic
249#340—111no—
250#340—111no—
251#340C2×D1112yes—
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—22no—
267C4×C11—81no—
268C4×C11—82no—
269C4×C11—81no—
270C4×C11#46514yes—
271C4×C11#52911yescharacteristic
272C4×C11#54211yescharacteristic
273C4×C11#54611yescharacteristic
274C4×C11#54811yescharacteristic
275Dic11—24no—
276Dic11—42no—
277Dic11—82no—
278Dic11—81no—
279C22×Q8—111no—
280C22×Q8—112no—
281C22×D4—111no—
282C23×C4—221no—
283C2×SD16—224no—
284C2×SD16—224no—
285C2×SD16—442no—
286C22×C8—111no—
287C22×C8—111no—
288C22×C8C22×D1112yes—
289C4⋊Q8—222no—
290C4⋊Q8—222no—
291C22⋊Q8—444no—
292C4×Q8—222no—
293C4×Q8—222no—
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—111no—
301C2×C4⋊C4—222no—
302C2×C4⋊C4—221no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4C22×D1111yescharacteristic
305C2×C4⋊C4C22×D1111yescharacteristic
306C2×C4⋊C4C22×D1112yes—
307C2×C22⋊C4—222no—
308C2×C22⋊C4—221no—
309C2×C22⋊C4—222no—
310C2×C42—21no—
311C2×C42—112no—
312C2×C42C22×D1111yescharacteristic
313#106—42no—
314C4⋊C8—224no—
315C4⋊C8D4414yes—
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—222no—
325#95—222no—
326#95—222no—
327#95—222no—
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—114no—
339C2×Q8—222no—
340C2×Q8—222no—
341C2×Q8—222no—
342C2×Q8—222no—
343C2×Q8—222no—
344C2×Q8—222no—
345C2×Q8—222no—
346C2×Q8—222no—
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—112no—
357C22×C4—112no—
358C22×C4—222no—
359C22×C4—221no—
360C22×C4—442no—
361C22×C4—442no—
362C22×C4—442no—
363C22×C4D4×D1111yescharacteristic
364C22×C4D4×D1111yescharacteristic
365C22×C4C23×D1111yescharacteristic
366SD16—448no—
367C2×C8—22no—
368C2×C8—22no—
369C2×C8—112no—
370C2×C8—221no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—221no—
375C2×C8C2×D4414yes—
376C4⋊C4—22no—
377C4⋊C4—21no—
378C4⋊C4—21no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—22no—
382C4⋊C4—42no—
383C4⋊C4—81no—
384C4⋊C4—224no—
385C4⋊C4—222no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—444no—
389C4⋊C4—442no—
390C4⋊C4—442no—
391C22⋊C4—444no—
392C22⋊C4—442no—
393C22⋊C4—882no—
394C42—42no—
395C42—222no—
396C42—222no—
397C42C2×D4412yes—
398C42#434312yes—
399C11#2529311yescharacteristic, complemented, Sylow
400C23—222no—
401C23—441no—
402C23—441no—
403C23—441no—
404C23—441no—
405C23—441no—
406C23—441no—
407C23C2×D4×D1111yescharacteristic
408Q8—228no—
409Q8—442no—
410Q8—442no—
411Q8—442no—
412Q8—442no—
413D4—222no—
414D4—222no—
415D4—441no—
416D4—441no—
417C2×C4—21no—
418C2×C4—21no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—41no—
428C2×C4—114no—
429C2×C4—222no—
430C2×C4—222no—
431C2×C4—222no—
432C2×C4—222no—
433C2×C4—222no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—441no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—884no—
441C2×C4#6694812yes—
442C2×C4#6694812yes—
443C2×C4SD16×D1112yes—
444C2×C4#6696912yes—
445C2×C4C22×D4411yescharacteristic
446C2×C4#6703711yescharacteristic
447C2×C4C2×#434311yescharacteristic
448C2×C4#6704011yescharacteristic
449C2×C4#41×D1111yescharacteristic
450C2×C4#41×D1111yescharacteristic
451C8—24no—
452C8—222no—
453C8—441no—
454C22—442no—
455C22—442no—
456C22—442no—
457C22—881no—
458C22—881no—
459C22—881no—
460C22—881no—
461C22C2×#6694811yescharacteristic
462C22#1062313011yescharacteristic
463C22#1062316411yescharacteristic
464C22C2×SD16×D1111yescharacteristic
465C22C2×#6696911yescharacteristic
466C22#1062330611yescharacteristic
467C22#1062331011yescharacteristic
468C4—22no—
469C4—81no—
470C4—81no—
471C4—82no—
472C4—224no—
473C4—442no—
474C4—882no—
475C4—881no—
476C4#1062247714yes—
477C4#1062308511yescharacteristic
478C4#1062310711yescharacteristic
479C4#1062322211yescharacteristic
480C4#1062326411yescharacteristic
481C2—882no—
482C2#1307218011yescharacteristic
483C2C2×#1062247711yescharacteristic
484C2#1307830811yescharacteristic
485C2#1308125711yescharacteristic
486C2#1308126411yescharacteristic
487C2#1308159611yescharacteristic
488C2#1308160311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1948C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1948D11
hypocenterC11#25293
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
2. C2×#10622443C2semidirect
3. #13073831C2semidirect
5. #13069992C2semidirect
8. #13069417C2semidirect
9. #13069293C2semidirect
11. C11×#1948C2semidirect
122. C2×Dic22SD16semidirect
164. #1948D11semidirect
399. C11#25293semidirect

Maximal subgroups

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

subgroupindex
C2×#106224542
C2×#106224432
#130738312
#130735392
#130699922
#130699352
#130694682
#130694172
#130692932
C4×#668732
C11×#19482
#2529311