Finite Group Databasebeta

← #14803902

Subgroups — #14803902

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×#10622447C211yesmaximal, characteristic
2#13073790C211yesmaximal, characteristic
3#13073534C211yesmaximal, characteristic
4#13070045C212yesmaximal, complemented
5#13069818C212yesmaximal, complemented
6#13069578C211yesmaximal, characteristic, complemented
7#13069375C211yesmaximal, characteristic, complemented
8#13069036C212yesmaximal, complemented
9#13068642C212yesmaximal, complemented
10C4×#66899C211yesmaximal, characteristic, complemented
11C2×C11×#477C211yesmaximal, characteristic, complemented
12C2×C11×C4⋊Q8C2211yescharacteristic
13C2×C4×Q8×C11C2211yescharacteristic
14C2×#66999C2212yes—
15C22×C8×D11C2212yes—
16C2×C4×D44C2211yescharacteristic
17C11×#477—24no—
18C2×C11×#107C2212yes—
19C2×C11×C4⋊C8C2211yescharacteristic
20C2×C11×#103C2212yes—
21#10622844—22no—
22C2×#66899C2211yescharacteristic
23C2×#66899C2211yescharacteristic
24C2×(C2×D11)⋊C8C2212yes—
25C2×#66882C2212yes—
26#10622607—22no—
27#10622601—21no—
28#10622600C2212yes—
29#10622600C2212yes—
30#10622600C2212yes—
31#10622590—21no—
32#10622552—21no—
33#10622548C2211yescharacteristic
34C4×C4⋊Dic11C2211yescharacteristic
35#10622541—21no—
36C2×C4×C11⋊C8C2211yescharacteristic
37#10622447—24no—
38#10622189C2212yes—
39#10622167C2212yes—
40#10622167C2212yes—
41#10622167C2211yescharacteristic
42#10622167C2211yescharacteristic
43C22×Q8×C11—21no—
44C22×Q8×C11C2311yescharacteristic
45C22×D44D411yescharacteristic
46C22×C4×D11C2312yes—
47C22×C8×C11C2312yes—
48C11×C4⋊Q8—22no—
49C11×C4⋊Q8—22no—
50C4×Q8×C11—22no—
51C4×Q8×C11—22no—
52C2×C11×C4⋊C4—21no—
53C2×C11×C4⋊C4—21no—
54C2×C11×C4⋊C4C2311yescharacteristic
55C2×C11×C4⋊C4C2312yes—
56C2×C42×C11—21no—
57C2×C42×C11C2311yescharacteristic
58#66999—24no—
59#66999—42no—
60C2×(C2×D11)⋊C4—22no—
61C2×(C2×D11)⋊C4—22no—
62C2×(C2×D11)⋊C4—22no—
63C2×(C2×D11)⋊C4—22no—
64C2×(C2×D11)⋊C4D412yes—
65C2×C4⋊Dic11—21no—
66C2×C4⋊Dic11—21no—
67C2×C4⋊Dic11D411yescharacteristic
68C2×C4⋊Dic11C2311yescharacteristic
69C2×C4⋊Dic11C2311yescharacteristic
70C2×C4⋊Dic11C2312yes—
71C2×Dic11⋊C4—22no—
72C2×C4×Dic11—21no—
73C22×C11⋊C8C2311yescharacteristic
74C22×C11⋊C8C2311yescharacteristic
75C2×C8×D11—24no—
76C2×C8×D11—24no—
77C2×C8×D11—42no—
78C4×D44—22no—
79C4×D44—22no—
80C11×#107—24no—
81C11×C4⋊C8D414yes—
82C11×#103—24no—
83#66899—22no—
84#66899—22no—
85C11⋊#95—21no—
86C11⋊#95—22no—
87C11⋊#95—22no—
88C11⋊#95—22no—
89(C2×D11)⋊C8—24no—
90#66882—42no—
91C4×C11⋊C8—22no—
92#25340—111nomaximal, Sylow
93C23×D11C2×D412yes—
94C2×Q8×C11—21no—
95C2×Q8×C11—21no—
96C2×Q8×C11—21no—
97C2×Q8×C11—21no—
98C2×Q8×C11—21no—
99C2×Q8×C11—42no—
100C2×Q8×C11—81no—
101C2×Q8×C11—81no—
102C2×Q8×C11#4112yes—
103C22×C4×C11—21no—
104C22×C4×C11—21no—
105C22×C4×C11—22no—
106C22×C4×C11C2×D411yescharacteristic
107C22×C4×C11C2×D411yescharacteristic
108C22×C4×C11C2411yescharacteristic
109C22×Dic11—21no—
110C22×Dic11—21no—
111C22×Dic11—22no—
112C22×Dic11C2×D412yes—
113C2×D44—22no—
114C2×D44—22no—
115C2×D44Q1614yes—
116C2×C4×D11—22no—
117C2×C4×D11—22no—
118C2×C4×D11—22no—
119C2×C4×D11—22no—
120C2×C4×D11—22no—
121C2×C4×D11—22no—
122C2×C8×C11—22no—
123C2×C8×C11—22no—
124C2×C8×C11C2×D414yes—
125C11×C4⋊C4—22no—
126C11×C4⋊C4—21no—
127C11×C4⋊C4—21no—
128C11×C4⋊C4—22no—
129C11×C4⋊C4—42no—
130C11×C4⋊C4—42no—
131C42×C11—42no—
132C42×C11C2×D412yes—
133C42×C11#4112yes—
134(C2×D11)⋊C4—24no—
135(C2×D11)⋊C4—44no—
136(C2×D11)⋊C4—82no—
137(C2×D11)⋊C4—82no—
138(C2×D11)⋊C4—82no—
139C4⋊Dic11—22no—
140C4⋊Dic11—21no—
141C4⋊Dic11—21no—
142C4⋊Dic11—22no—
143C4⋊Dic11—21no—
144C4⋊Dic11—22no—
145C4⋊Dic11—21no—
146C4⋊Dic11—42no—
147C4⋊Dic11—81no—
148Dic11⋊C4—44no—
149C4×Dic11—42no—
150C2×C11⋊C8—21no—
151C2×C11⋊C8—21no—
152C2×C11⋊C8—21no—
153C2×C11⋊C8—21no—
154C2×C11⋊C8—21no—
155C2×C11⋊C8#4112yes—
156C8×D11—48no—
157C2×#477D1111yescharacteristic, complemented
158C2×C8×D4—111no—
159#2563—111no—
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×C11C22×D411yescharacteristic
169C22×D11—22no—
170C22×D11—22no—
171C22×D11—22no—
172C22×D11—22no—
173C22×D11—22no—
174C22×D11—22no—
175C22×D11C2×Q1614yes—
176Q8×C11—22no—
177Q8×C11—22no—
178Q8×C11—41no—
179Q8×C11—41no—
180Q8×C11—84no—
181C2×C4×C11—21no—
182C2×C4×C11—21no—
183C2×C4×C11—22no—
184C2×C4×C11—41no—
185C2×C4×C11—41no—
186C2×C4×C11—41no—
187C2×C4×C11—42no—
188C2×C4×C11—41no—
189C2×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11—41no—
192C2×C4×C11#12112yes—
193C2×C4×C11#12112yes—
194C2×C4×C11C2×Q1612yes—
195C2×C4×C11#13512yes—
196C2×C4×C11C22×D411yescharacteristic
197C2×C4×C11C2×#4111yescharacteristic
198C2×C4×C11C2×#4111yescharacteristic
199C2×C4×C11C2×#4111yescharacteristic
200C2×C4×C11H(5,𝔽2)11yescharacteristic
201C2×C4×C112−1+411yescharacteristic
202C2×Dic11—22no—
203C2×Dic11—22no—
204C2×Dic11—22no—
205C2×Dic11—42no—
206C2×Dic11—41no—
207C2×Dic11—41no—
208C2×Dic11—41no—
209C2×Dic11—41no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C2×Dic11—41no—
213C2×Dic11—41no—
214D44—28no—
215C4×D11—42no—
216C4×D11—42no—
217C4×D11—42no—
218C4×D11—42no—
219C8×C11—24no—
220C11⋊C8—22no—
221C11⋊C8—41no—
222C23×C8—112no—
223C2×C4⋊Q8C2×D1111yescharacteristic
224C2×C22⋊Q8—112no—
225C2×C4×Q8C2×D1111yescharacteristic
226C2×C4×D4—111no—
227#477—24no—
228C8×D4—224no—
229C2×#107—112no—
230C2×#107C2×D1112yes—
231C2×C4⋊C8C2×D1111yescharacteristic
232C2×#103—111no—
233C2×#103—111no—
234C2×#103C2×D1112yes—
235C2×C22⋊C8—112no—
236C2×C4×C8—111no—
237#396—222no—
238#393—222no—
239#390—221no—
240#390—221no—
241#389—221no—
242#384—111no—
243#382—221no—
244#380—112no—
245#380—112no—
246#380—112no—
247C4×C4⋊C4—111no—
248#340—112no—
249#340—111no—
250#340—112no—
251#340—111no—
252#340—112no—
253C22×C11C2×#12111yescharacteristic
254C22×C11#54611yescharacteristic
255C22×C11#54711yescharacteristic
256C22×C11C22×Q1611yescharacteristic
257C22×C11C2×#13511yescharacteristic
258C22×C11#57611yescharacteristic
259C22×C11#57711yescharacteristic
260C2×D11—24no—
261C2×D11—24no—
262C2×D11—24no—
263C2×D11—42no—
264C2×D11—42no—
265C2×D11—42no—
266C2×D11—42no—
267C4×C11—22no—
268C4×C11—42no—
269C4×C11—81no—
270C4×C11—82no—
271C4×C11#46714yes—
272C4×C11#52911yescharacteristic
273C4×C11#54211yescharacteristic
274C4×C11#54611yescharacteristic
275C4×C11#54811yescharacteristic
276Dic11—42no—
277Dic11—81no—
278Dic11—82no—
279Dic11—81no—
280C22×Q8—21no—
281C22×Q8C22×D1111yescharacteristic
282C22×D4—111no—
283C23×C4—112no—
284C22×C8—111no—
285C22×C8—111no—
286C22×C8—224no—
287C22×C8—224no—
288C22×C8—442no—
289C22×C8C22×D1112yes—
290C4⋊Q8—22no—
291C4⋊Q8—22no—
292C22⋊Q8—224no—
293C22⋊Q8—442no—
294C4×Q8—22no—
295C4×Q8—22no—
296C4×D4—222no—
297C4×D4—222no—
298C2×C4⋊C4—21no—
299C2×C4⋊C4—21no—
300C2×C4⋊C4—111no—
301C2×C4⋊C4—112no—
302C2×C4⋊C4—111no—
303C2×C4⋊C4—111no—
304C2×C4⋊C4—222no—
305C2×C4⋊C4—221no—
306C2×C4⋊C4—221no—
307C2×C4⋊C4C22×D1111yescharacteristic
308C2×C4⋊C4C22×D1112yes—
309C2×C22⋊C4—112no—
310C2×C22⋊C4—222no—
311C2×C22⋊C4—222no—
312C2×C22⋊C4—222no—
313C2×C22⋊C4—222no—
314C2×C42—21no—
315C2×C42—221no—
316C2×C42C22×D1111yescharacteristic
317#107—24no—
318#107—442no—
319C4⋊C8C22⋊D1114yes—
320#103—24no—
321#103—222no—
322#103—222no—
323C22⋊C8—224no—
324C4×C8—222no—
325#95—222no—
326#95—222no—
327#95—222no—
328#95—221no—
329C2×C11#242711yescharacteristic
330C2×C11C2×#46711yescharacteristic
331C2×C11#306211yescharacteristic
332C2×C11#329911yescharacteristic
333C2×C11#330511yescharacteristic
334C2×C11#333811yescharacteristic
335C2×C11#334011yescharacteristic
336D11—44no—
337C24—112no—
338C2×Q8—21no—
339C2×Q8—21no—
340C2×Q8—21no—
341C2×Q8—21no—
342C2×Q8—21no—
343C2×Q8—42no—
344C2×Q8—81no—
345C2×Q8—81no—
346C2×Q8#434312yes—
347C2×D4—114no—
348C2×D4—222no—
349C2×D4—222no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—112no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—221no—
361C22×C4—221no—
362C22×C4—222no—
363C22×C4D4×D1111yescharacteristic
364C22×C4D4×D1111yescharacteristic
365C22×C4C23×D1111yescharacteristic
366C2×C8—22no—
367C2×C8—22no—
368C2×C8—112no—
369C2×C8—221no—
370C2×C8—221no—
371C2×C8—221no—
372C2×C8—221no—
373C2×C8—221no—
374C2×C8—448no—
375C2×C8C2×C22⋊D1114yes—
376C4⋊C4—21no—
377C4⋊C4—22no—
378C4⋊C4—22no—
379C4⋊C4—21no—
380C4⋊C4—42no—
381C4⋊C4—42no—
382C4⋊C4—222no—
383C4⋊C4—221no—
384C4⋊C4—222no—
385C4⋊C4—221no—
386C4⋊C4—221no—
387C4⋊C4—221no—
388C4⋊C4—222no—
389C4⋊C4—444no—
390C4⋊C4—442no—
391C4⋊C4—881no—
392C22⋊C4—224no—
393C22⋊C4—444no—
394C22⋊C4—882no—
395C22⋊C4—882no—
396C22⋊C4—882no—
397C42—42no—
398C42—442no—
399C42#434112yes—
400C42C2×C22⋊D1112yes—
401C11#2534011yescharacteristic, complemented, Sylow
402C23—114no—
403C23—222no—
404C23—222no—
405C23—222no—
406C23—222no—
407C23—222no—
408C23—222no—
409C23C2×D4×D1111yescharacteristic
410Q8—22no—
411Q8—22no—
412Q8—41no—
413Q8—41no—
414Q8—84no—
415D4—228no—
416C2×C4—21no—
417C2×C4—21no—
418C2×C4—22no—
419C2×C4—41no—
420C2×C4—41no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—41no—
425C2×C4—41no—
426C2×C4—42no—
427C2×C4—222no—
428C2×C4—222no—
429C2×C4—222no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—442no—
437C2×C4—441no—
438C2×C4—442no—
439C2×C4—441no—
440C2×C4—442no—
441C2×C4—441no—
442C2×C4—441no—
443C2×C4Q16×D1112yes—
444C2×C4#6697212yes—
445C2×C4#6699112yes—
446C2×C4#6699112yes—
447C2×C4C2×#434111yescharacteristic
448C2×C4C2×#434311yescharacteristic
449C2×C4#6704011yescharacteristic
450C2×C4#41×D1111yescharacteristic
451C2×C4#6704211yescharacteristic
452C2×C4C22×C22⋊D1111yescharacteristic
453C8—24no—
454C8—222no—
455C8—441no—
456C22—224no—
457C22—224no—
458C22—224no—
459C22—442no—
460C22—442no—
461C22—442no—
462C22—442no—
463C22#1062316111yescharacteristic
464C22#1062316211yescharacteristic
465C22C2×Q16×D1111yescharacteristic
466C22C2×#6697211yescharacteristic
467C22#1062330511yescharacteristic
468C22#1062330611yescharacteristic
469C22C2×#6699111yescharacteristic
470C4—22no—
471C4—42no—
472C4—82no—
473C4—81no—
474C4—442no—
475C4—881no—
476C4—881no—
477C4—882no—
478C4#1062280114yes—
479C4#1062315511yescharacteristic
480C4#1062317411yescharacteristic
481C4#1062334811yescharacteristic
482C4#1062336011yescharacteristic
483C2—444no—
484C2#1307218911yescharacteristic
485C2C2×#1062280111yescharacteristic
486C2#1307829011yescharacteristic
487C2#1308048911yescharacteristic
488C2#1308056311yescharacteristic
489C2#1308100711yescharacteristic
490C2#1308103211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#477C2
socleC23×C11C22×D4
prime radicalC22×D44D4
hypercenterC2×#477D11
hypocenterC11#25340
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#477

Complements

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

NH ≅ G/Ntype
4. #13070045C2semidirect
5. #13069818C2semidirect
6. #13069578C2semidirect
7. #13069375C2semidirect
8. #13069036C2semidirect
9. #13068642C2semidirect
10. C4×#66899C2semidirect
11. C2×C11×#477C2semidirect
157. C2×#477D11semidirect
401. C11#25340semidirect

Maximal subgroups

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

subgroupindex
C2×#106224472
#130737902
#130735342
#130700452
#130698182
#130695782
#130693752
#130690362
#130686422
C4×#668992
C2×C11×#4772
#2534011