Finite Group Databasebeta

← #14803625

Subgroups — #14803625

Order 2816.

838 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622294C211yesmaximal, characteristic, complemented
2C2×#10622454C211yesmaximal, characteristic
3#13073785C211yesmaximal, characteristic
4#13071672C211yesmaximal, characteristic, complemented
5#13070036C212yesmaximal, complemented
6#13069934C212yesmaximal
7#13069563C211yesmaximal, characteristic, complemented
8#13068970C212yesmaximal
9#13068632C212yesmaximal, complemented
10C4×#66885C211yesmaximal, characteristic
11C11×#1939C211yesmaximal, characteristic, complemented
12C22×#4314C2212yes—
13C2×C4×D44C2211yescharacteristic
14C2×#66922C2211yescharacteristic
15C2×#66922C2211yescharacteristic
16C2×C4×Dic22C2212yes—
17C2×C11×C4⋊C8C2211yescharacteristic
18C2×C11×C4⋊C8C2212yes—
19C2×C4×C8×C11C2211yescharacteristic
20C4×C11×C4⋊C4C2211yescharacteristic
21C2×#66885C2211yescharacteristic
22C2×#66885C2211yescharacteristic
23C2×#66880C2212yes—
24C2×#66880C2212yes—
25C2×#66880C2212yes—
26#10622600—21no—
27#10622600—21no—
28C4⋊C4×Dic11—21no—
29#10622586—21no—
30#10622552C2212yes—
31#10622549C2212yes—
32C4×C4⋊Dic11C2211yescharacteristic
33#10622542C2212yes—
34#10622454—24no—
35#10622294—24no—
36#10622286—22no—
37#10622267—22no—
38C11×#336C2212yes—
39#10622189C2211yescharacteristic
40#10622189C2212yes—
41#10622189C2212yes—
42#10622189C2211yescharacteristic
43C22×D44C2311yescharacteristic
44C22×C4×D11—21no—
45C22×Dic22—21no—
46C22×Dic22C2312yes—
47C22×C8×C11C2311yescharacteristic
48C22×C8×C11C2311yescharacteristic
49C22×C8×C11C2312yes—
50C2×C11×C4⋊C4D411yescharacteristic
51C2×C11×C4⋊C4D411yescharacteristic
52C2×C42×C11C2312yes—
53C2×C42×C11C2311yescharacteristic
54C2×(C2×D11)⋊C4—21no—
55C2×(C2×D11)⋊C4—22no—
56C2×(C2×D11)⋊C4—22no—
57C2×C4⋊Dic11—21no—
58C2×C4⋊Dic11—21no—
59C2×C4⋊Dic11—21no—
60C2×C4⋊Dic11C2311yescharacteristic
61C2×C4⋊Dic11C2312yes—
62C2×C4⋊Dic11C2311yescharacteristic
63C2×C4⋊Dic11C2311yescharacteristic
64C2×Dic11⋊C4—22no—
65C2×C4×Dic11—22no—
66C2×C4×Dic11—21no—
67C2×#4314—24no—
68C2×#4314—24no—
69C2×#4314—42no—
70C4×D44—22no—
71C4×D44—22no—
72#66922—22no—
73#66922—22no—
74#66922—22no—
75#66922D414yes—
76C4×Dic22—24no—
77C4×Dic22—42no—
78C11×C4⋊C8—22no—
79C11×C4⋊C8—42no—
80C4×C8×C11—22no—
81C11×#95D412yes—
82C11⋊#95—21no—
83C11⋊#95—22no—
84C11⋊#95—22no—
85C11⋊#95—22no—
86C11⋊#95—22no—
87#66885—22no—
88#66885—22no—
89#66880—24no—
90#66880—24no—
91#66880—24no—
92#25319—111nomaximal, Sylow
93C23×D11—21no—
94C22×C4×C11C2×D412yes—
95C22×C4×C11C2×D412yes—
96C22×C4×C11C2×D411yescharacteristic
97C22×C4×C11C2×D411yescharacteristic
98C22×C4×C11C2411yescharacteristic
99C22×Dic11—22no—
100C22×Dic11—21no—
101C22×Dic11—21no—
102C22×Dic11—21no—
103C22×Dic11—22no—
104C2×D44—21no—
105C2×D44—21no—
106C2×D44—21no—
107C2×D44—21no—
108C2×D44—21no—
109C2×D44#4112yes—
110C2×C4×D11—42no—
111C2×C4×D11—42no—
112C2×C4×D11—42no—
113C2×Dic22—22no—
114C2×Dic22—22no—
115C2×Dic22—22no—
116C2×Dic22—22no—
117C2×Dic22—22no—
118C2×Dic22—42no—
119C2×Dic22—81no—
120C2×Dic22—81no—
121C2×Dic22C2×D414yes—
122C2×C8×C11—21no—
123C2×C8×C11—21no—
124C2×C8×C11—22no—
125C2×C8×C11—21no—
126C2×C8×C11—21no—
127C2×C8×C11—22no—
128C2×C8×C11—21no—
129C2×C8×C11—22no—
130C2×C8×C11—21no—
131C11×C4⋊C4—22no—
132C11×C4⋊C4—22no—
133C42×C11—22no—
134C42×C11—22no—
135C42×C11C2×D412yes—
136C42×C11#4112yes—
137(C2×D11)⋊C4—42no—
138(C2×D11)⋊C4—82no—
139(C2×D11)⋊C4—82no—
140C4⋊Dic11—24no—
141C4⋊Dic11—24no—
142C4⋊Dic11—22no—
143C4⋊Dic11—21no—
144C4⋊Dic11—21no—
145C4⋊Dic11—22no—
146C4⋊Dic11—21no—
147C4⋊Dic11—21no—
148C4⋊Dic11—21no—
149C4⋊Dic11—42no—
150C4⋊Dic11#4112yes—
151Dic11⋊C4—44no—
152C4×Dic11—44no—
153C4×Dic11—42no—
154#4314—48no—
155C2×#487—111no—
156C2×#461—111no—
157#2563—111no—
158#2365—111no—
159#2074—112no—
160#2055—112no—
161#1987—111no—
162#1939D1111yescharacteristic, complemented
163#1880—112no—
164#1805—112no—
165C4×#102—111no—
166C23×C11C22×D411yescharacteristic
167C22×D11—22no—
168C22×D11—41no—
169C22×D11—41no—
170C22×D11—41no—
171C22×D11—41no—
172C22×D11—41no—
173C22×D11—41no—
174C2×C4×C11—21no—
175C2×C4×C11—21no—
176C2×C4×C11—22no—
177C2×C4×C11—22no—
178C2×C4×C11—22no—
179C2×C4×C11—22no—
180C2×C4×C11—22no—
181C2×C4×C11—22no—
182C2×C4×C11#12112yes—
183C2×C4×C11#12112yes—
184C2×C4×C11#13512yes—
185C2×C4×C11#13712yes—
186C2×C4×C11C22×D411yescharacteristic
187C2×C4×C11C2×#4111yescharacteristic
188C2×C4×C11C2×#4111yescharacteristic
189C2×C4×C11C2×#4111yescharacteristic
190C2×C4×C11H(5,𝔽2)11yescharacteristic
191C2×C4×C112−1+411yescharacteristic
192C2×Dic11—24no—
193C2×Dic11—22no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—41no—
197C2×Dic11—41no—
198C2×Dic11—42no—
199C2×Dic11—41no—
200C2×Dic11—41no—
201C2×Dic11—41no—
202C2×Dic11—41no—
203C2×Dic11—41no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—41no—
207D44—22no—
208D44—22no—
209D44—41no—
210D44—41no—
211C4×D11—84no—
212Dic22—24no—
213Dic22—24no—
214Dic22—42no—
215Dic22—42no—
216Dic22—84no—
217C8×C11—42no—
218C8×C11—41no—
219C8×C11—41no—
220C22×SD16—112no—
221C2×C4⋊Q8—111no—
222C2×C4⋊Q8—111no—
223C2×C4×Q8—112no—
224C2×C4×D4—111no—
225#487—224no—
226#461—224no—
227C2×C4⋊C8C2×D1111yescharacteristic
228C2×C4⋊C8C2×D1112yes—
229C2×#103—112no—
230C2×#103—112no—
231C2×#103—112no—
232C2×#102—111no—
233C2×#102—111no—
234C2×C4×C8C2×D1111yescharacteristic
235#393—222no—
236#391—112no—
237#390—112no—
238#389—221no—
239#387—222no—
240#382—112no—
241#380—221no—
242#380—221no—
243C4×C4⋊C4—111no—
244C4×C4⋊C4—221no—
245C4×C4⋊C4C2×D1111yescharacteristic
246#340—112no—
247#340—111no—
248#340—112no—
249#340—111no—
250#336C2×D1112yes—
251C22×C11C2×#12111yescharacteristic
252C22×C11#54611yescharacteristic
253C22×C11#54811yescharacteristic
254C22×C11C2×#13511yescharacteristic
255C22×C11C2×#13711yescharacteristic
256C22×C11#57711yescharacteristic
257C22×C11#57711yescharacteristic
258C2×D11—42no—
259C2×D11—42no—
260C2×D11—42no—
261C2×D11—81no—
262C2×D11—81no—
263C2×D11—81no—
264C2×D11—81no—
265C4×C11—22no—
266C4×C11—42no—
267C4×C11—42no—
268C4×C11#46414yes—
269C4×C11#52911yescharacteristic
270C4×C11#54211yescharacteristic
271C4×C11#54611yescharacteristic
272C4×C11#54711yescharacteristic
273Dic11—44no—
274Dic11—42no—
275Dic11—81no—
276Dic11—81no—
277Dic11—82no—
278C22×Q8—112no—
279C22×Q8—221no—
280C22×D4—111no—
281C23×C4—221no—
282C2×SD16—224no—
283C2×SD16—224no—
284C2×SD16—442no—
285C22×C8C22×D1112yes—
286C22×C8C22×D1111yescharacteristic
287C22×C8C22×D1111yescharacteristic
288C4⋊Q8—114no—
289C4⋊Q8—222no—
290C4⋊Q8—222no—
291C4⋊Q8—222no—
292C4×Q8—224no—
293C4×Q8—442no—
294C4×D4—222no—
295C4×D4—222no—
296C2×C4⋊C4—111no—
297C2×C4⋊C4—111no—
298C2×C4⋊C4—112no—
299C2×C4⋊C4—111no—
300C2×C4⋊C4—221no—
301C2×C4⋊C4—221no—
302C2×C4⋊C4—222no—
303C2×C4⋊C4—221no—
304C2×C4⋊C4D4411yescharacteristic
305C2×C4⋊C4D4411yescharacteristic
306C2×C22⋊C4—221no—
307C2×C22⋊C4—222no—
308C2×C22⋊C4—222no—
309C2×C42—222no—
310C2×C42—221no—
311C2×C42C22×D1112yes—
312C2×C42C22×D1111yescharacteristic
313C4⋊C8—22no—
314C4⋊C8—42no—
315#103—224no—
316#103—224no—
317#103—224no—
318#102—222no—
319#102—222no—
320C4×C8—22no—
321#95—221no—
322#95—222no—
323#95—222no—
324#95—222no—
325#95—222no—
326#95D4412yes—
327C2×C11#242711yescharacteristic
328C2×C11C2×#46411yescharacteristic
329C2×C11#304311yescharacteristic
330C2×C11#330311yescharacteristic
331C2×C11#332911yescharacteristic
332C2×C11#336011yescharacteristic
333C2×C11#337211yescharacteristic
334D11—82no—
335C24—221no—
336C2×Q8—114no—
337C2×Q8—222no—
338C2×Q8—222no—
339C2×Q8—222no—
340C2×Q8—222no—
341C2×Q8—222no—
342C2×Q8—442no—
343C2×Q8—881no—
344C2×Q8—881no—
345C2×D4—112no—
346C2×D4—221no—
347C2×D4—221no—
348C2×D4—221no—
349C2×D4—221no—
350C2×D4—221no—
351C22×C4—222no—
352C22×C4—221no—
353C22×C4—221no—
354C22×C4—221no—
355C22×C4—222no—
356C22×C4—442no—
357C22×C4—442no—
358C22×C4—442no—
359C22×C4C2×D4412yes—
360C22×C4C2×D4412yes—
361C22×C4C2×D4411yescharacteristic
362C22×C4C2×D4411yescharacteristic
363C22×C4C23×D1111yescharacteristic
364SD16—448no—
365C2×C8—21no—
366C2×C8—21no—
367C2×C8—22no—
368C2×C8—21no—
369C2×C8—22no—
370C2×C8—21no—
371C2×C8—21no—
372C2×C8—21no—
373C2×C8—22no—
374C4⋊C4—22no—
375C4⋊C4—22no—
376C4⋊C4—112no—
377C4⋊C4—224no—
378C4⋊C4—224no—
379C4⋊C4—221no—
380C4⋊C4—221no—
381C4⋊C4—222no—
382C4⋊C4—221no—
383C4⋊C4—222no—
384C4⋊C4—221no—
385C4⋊C4—221no—
386C4⋊C4—444no—
387C4⋊C4—442no—
388C22⋊C4—442no—
389C22⋊C4—882no—
390C22⋊C4—882no—
391C42—22no—
392C42—22no—
393C42—444no—
394C42—442no—
395C42D4×D1112yes—
396C42#434312yes—
397C11#2531911yescharacteristic, complemented, Sylow
398C23—222no—
399C23—441no—
400C23—441no—
401C23—441no—
402C23—441no—
403C23—441no—
404C23—441no—
405C23C22×D4411yescharacteristic
406Q8—224no—
407Q8—224no—
408Q8—442no—
409Q8—442no—
410Q8—884no—
411D4—222no—
412D4—222no—
413D4—441no—
414D4—441no—
415C2×C4—21no—
416C2×C4—21no—
417C2×C4—22no—
418C2×C4—22no—
419C2×C4—22no—
420C2×C4—22no—
421C2×C4—22no—
422C2×C4—22no—
423C2×C4—224no—
424C2×C4—222no—
425C2×C4—441no—
426C2×C4—441no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—441no—
430C2×C4—441no—
431C2×C4—441no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—441no—
435C2×C4—441no—
436C2×C4—442no—
437C2×C4—441no—
438C2×C4—884no—
439C2×C4#6694812yes—
440C2×C4#6694812yes—
441C2×C4#6695712yes—
442C2×C4#6696212yes—
443C2×C4C2×D4×D1111yescharacteristic
444C2×C4#6703711yescharacteristic
445C2×C4C2×#434311yescharacteristic
446C2×C4#6704011yescharacteristic
447C2×C4#41×D1111yescharacteristic
448C2×C4#41×D1111yescharacteristic
449C8—42no—
450C8—41no—
451C8—41no—
452C22—442no—
453C22—442no—
454C22—442no—
455C22—881no—
456C22—881no—
457C22—881no—
458C22—881no—
459C22C2×#6694811yescharacteristic
460C22#1062308511yescharacteristic
461C22#1062310711yescharacteristic
462C22C2×#6695711yescharacteristic
463C22C2×#6696211yescharacteristic
464C22#1062328211yescharacteristic
465C22#1062328211yescharacteristic
466C4—22no—
467C4—42no—
468C4—42no—
469C4—444no—
470C4—442no—
471C4—881no—
472C4—882no—
473C4—881no—
474C4#1062245814yes—
475C4#1062314311yescharacteristic
476C4#1062316211yescharacteristic
477C4#1062322211yescharacteristic
478C4#1062326411yescharacteristic
479C2—882no—
480C2#1307219111yescharacteristic
481C2C2×#1062245811yescharacteristic
482C2#1307813811yescharacteristic
483C2#1308054511yescharacteristic
484C2#1308091111yescharacteristic
485C2#1308126711yescharacteristic
486C2#1308139911yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1939C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenter#1939D11
hypocenterC11#25319
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C4⋊C4 ◁ #1939

Complements

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

NH ≅ G/Ntype
1. C2×#10622294C2semidirect
4. #13071672C2semidirect
5. #13070036C2semidirect
7. #13069563C2semidirect
9. #13068632C2semidirect
11. C11×#1939C2semidirect
162. #1939D11semidirect
397. C11#25319semidirect

Maximal subgroups

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

subgroupindex
C2×#106222942
C2×#106224542
#130737852
#130716722
#130700362
#130699342
#130695632
#130689702
#130686322
C4×#668852
C11×#19392
#2531911