Finite Group Databasebeta

← #14682587

Subgroups — #14682587

Order 2816.

1102 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×#10622549C211yesmaximal, characteristic
2#13066874C212yesmaximal
3#13066871C212yesmaximal
4#13066868C212yesmaximal
5#13066850C212yesmaximal
6#13066843C211yesmaximal, characteristic
7#13066842C212yesmaximal
8#13066840C212yesmaximal
9C11×#1434C211yesmaximal, characteristic
10C22×C42×C11C2211yescharacteristic
11C22×C4⋊Dic11C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×Dic11⋊C4C2212yes—
14C22×C4×Dic11C2212yes—
15C2×C11×#95C2212yes—
16C2×C11×#95C2212yes—
17C2×C11×#95C2211yescharacteristic
18C2×C11×#95C2211yescharacteristic
19C2×C11⋊#95C2212yes—
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31#10622549C418yescomplemented
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2312yes—
36C23×C4×C11C2311yescharacteristic
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C23×Dic11C2312yes—
41C2×C42×C11—24no—
42C2×C42×C11C2×C414yes—
43C2×C4⋊Dic11—41no—
44C2×C4⋊Dic11—41no—
45C2×C4⋊Dic11—41no—
46C2×C4⋊Dic11—41no—
47C2×C4⋊Dic11C2×C414yes—
48C2×C4⋊Dic11C2×C414yes—
49C2×Dic11⋊C4—42no—
50C2×Dic11⋊C4—42no—
51C2×Dic11⋊C4—42no—
52C2×C4×Dic11—24no—
53C2×C4×Dic11—24no—
54C2×C4×Dic11—42no—
55C11×#95—24no—
56C11×#95—24no—
57C11×#95—41no—
58C11×#95—41no—
59C11⋊#95—24no—
60C11⋊#95—24no—
61C11⋊#95—24no—
62C11⋊#95—24no—
63C11⋊#95—41no—
64C11⋊#95—42no—
65C11⋊#95—42no—
66C11⋊#95—42no—
67C11⋊#95—42no—
68C11⋊#95—41no—
69C11⋊#95C2×C418yes—
70C11⋊#95C2×C418yes—
71#14476—111nomaximal, Sylow
72C24×C11C2411yescharacteristic
73C22×C4×C11—21no—
74C22×C4×C11—21no—
75C22×C4×C11—22no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—22no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—21no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—21no—
86C22×C4×C11—21no—
87C22×C4×C11—21no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—22no—
91C22×C4×C11—22no—
92C22×C4×C11—22no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—22no—
97C22×C4×C11C22×C412yes—
98C22×C4×C11C22×C412yes—
99C22×C4×C11C22×C412yes—
100C22×C4×C11#4114yes—
101C22×C4×C11#4114yes—
102C22×Dic11—22no—
103C22×Dic11—22no—
104C22×Dic11—22no—
105C22×Dic11—22no—
106C22×Dic11—22no—
107C22×Dic11—22no—
108C22×Dic11—22no—
109C22×Dic11—22no—
110C22×Dic11—22no—
111C22×Dic11—22no—
112C22×Dic11—22no—
113C22×Dic11—22no—
114C22×Dic11—22no—
115C22×Dic11—22no—
116C22×Dic11—22no—
117C22×Dic11—22no—
118C22×Dic11—22no—
119C22×Dic11—22no—
120C22×Dic11—22no—
121C22×Dic11—22no—
122C22×Dic11—22no—
123C22×Dic11—22no—
124C22×Dic11—22no—
125C22×Dic11—22no—
126C22×Dic11—22no—
127C22×Dic11C22×C414yes—
128C22×Dic11C22×C414yes—
129C22×Dic11#4114yes—
130C42×C11—28no—
131C4⋊Dic11—44no—
132C4⋊Dic11—44no—
133Dic11⋊C4—48no—
134C4×Dic11—48no—
135C2×#382—111no—
136#1442—112no—
137#1442—112no—
138#1441—112no—
139#1436—112no—
140#1434—111no—
141#1434—112no—
142#1434—112no—
143#1434D1111yescharacteristic
144C23×C11C23×C411yescharacteristic
145C23×C11C2×#4112yes—
146C23×C11C2×#4112yes—
147C23×C11C2×#4112yes—
148C23×C11H(5,𝔽2)11yescharacteristic
149C23×C11H(5,𝔽2)11yescharacteristic
150C23×C11H(5,𝔽2)11yescharacteristic
151C23×C11H(5,𝔽2)11yescharacteristic
152C23×C112−1+411yescharacteristic
153C23×C112−1+412yes—
154C23×C112−1+411yescharacteristic
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—24no—
158C2×C4×C11—24no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—24no—
168C2×C4×C11—42no—
169C2×C4×C11—42no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—42no—
173C2×C4×C11—42no—
174C2×C4×C11—42no—
175C2×C4×C11—42no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×C4×C11#11714yes—
184C2×Dic11—24no—
185C2×Dic11—24no—
186C2×Dic11—24no—
187C2×Dic11—24no—
188C2×Dic11—24no—
189C2×Dic11—24no—
190C2×Dic11—24no—
191C2×Dic11—24no—
192C2×Dic11—24no—
193C2×Dic11—42no—
194C2×Dic11—42no—
195C2×Dic11—42no—
196C2×Dic11—42no—
197C2×Dic11—42no—
198C2×Dic11—42no—
199C2×Dic11—42no—
200C2×Dic11—42no—
201C2×Dic11—42no—
202C2×Dic11—42no—
203C2×Dic11—42no—
204C2×Dic11—42no—
205C2×Dic11—42no—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C2×Dic11—42no—
212C22×C4⋊C4—111no—
213C22×C4⋊C4—111no—
214C22×C4⋊C4—112no—
215C22×C42—112no—
216C22×C42C2×D1111yescharacteristic
217#382—118no—
218C2×#95—112no—
219C2×#95—112no—
220C2×#95—112no—
221C2×#95—112no—
222C2×#95—112no—
223C2×#95—112no—
224C2×#95—111no—
225C2×#95—112no—
226C2×#95—112no—
227C2×#95—112no—
228C2×#95—111no—
229C2×#95—112no—
230C2×#95C2×D1112yes—
231C2×#95C2×D1112yes—
232C2×#95C2×D1111yescharacteristic
233C2×#95C2×D1111yescharacteristic
234C22×C11C2×#11711yescharacteristic
235C22×C11C4×#4111yescharacteristic
236C22×C11C4×#4111yescharacteristic
237C22×C11#51811yescharacteristic
238C22×C11#51911yescharacteristic
239C22×C11#52011yescharacteristic
240C22×C11#52011yescharacteristic
241C22×C11#53912yes—
242C22×C11#53912yes—
243C22×C11#53912yes—
244C22×C11#53912yes—
245C22×C11#54112yes—
246C22×C11#54112yes—
247C22×C11#55112yes—
248C22×C11#55212yes—
249C22×C11#55212yes—
250C22×C11#55512yes—
251C22×C11#55512yes—
252C22×C11#55512yes—
253C22×C11H(3,𝔽4)11yescharacteristic
254C22×C11#56211yescharacteristic
255C22×C11#56211yescharacteristic
256C22×C11#56311yescharacteristic
257C4×C11—24no—
258C4×C11—42no—
259C4×C11—42no—
260C4×C11—44no—
261C4×C11—82no—
262Dic11—44no—
263Dic11—44no—
264Dic11—44no—
265Dic11—82no—
266C23×C4—112no—
267C23×C4—112no—
268C23×C4—112no—
269C23×C4—112no—
270C23×C4C22×D1112yes—
271C23×C4C22×D1111yescharacteristic
272C23×C4C22×D1111yescharacteristic
273C23×C4C22×D1112yes—
274C23×C4C22×D1111yescharacteristic
275C2×C4⋊C4—114no—
276C2×C4⋊C4—114no—
277C2×C4⋊C4—442no—
278C2×C4⋊C4—442no—
279C2×C4⋊C4—442no—
280C2×C4⋊C4—441no—
281C2×C4⋊C4—441no—
282C2×C4⋊C4—441no—
283C2×C4⋊C4—441no—
284C2×C42—24no—
285C2×C42—224no—
286C2×C42—224no—
287C2×C42—442no—
288C2×C42C4×D1114yes—
289#95—24no—
290#95—24no—
291#95—41no—
292#95—41no—
293#95—118no—
294#95—118no—
295#95—224no—
296#95—224no—
297#95—224no—
298#95—224no—
299#95—442no—
300#95—441no—
301#95—441no—
302#95—442no—
303#95—442no—
304#95—442no—
305C2×C11#231311yescharacteristic
306C2×C11#233611yescharacteristic
307C2×C11#233611yescharacteristic
308C2×C11#234611yescharacteristic
309C2×C11#234611yescharacteristic
310C2×C11#237211yescharacteristic
311C2×C11#237911yescharacteristic
312C2×C11#274412yes—
313C2×C11#274412yes—
314C2×C11#276912yes—
315C2×C11#278512yes—
316C24C23×D1111yescharacteristic
317C22×C4—21no—
318C22×C4—21no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—21no—
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—21no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—22no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—114no—
342C22×C4—114no—
343C22×C4—114no—
344C22×C4—222no—
345C22×C4—222no—
346C22×C4—222no—
347C22×C4—222no—
348C22×C4—222no—
349C22×C4—222no—
350C22×C4—222no—
351C22×C4—222no—
352C22×C4—222no—
353C22×C4—222no—
354C22×C4—222no—
355C22×C4—222no—
356C22×C4—222no—
357C22×C4—222no—
358C22×C4—222no—
359C22×C4—222no—
360C22×C4—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4—222no—
369C22×C4C2×C4×D1112yes—
370C22×C4C2×C4×D1112yes—
371C22×C4C2×C4×D1112yes—
372C22×C4#433914yes—
373C22×C4#434114yes—
374C4⋊C4—444no—
375C4⋊C4—444no—
376C4⋊C4—448no—
377C42—28no—
378C42—448no—
379C11#1447611yescharacteristic, complemented, Sylow
380C23C22×C4×D1111yescharacteristic
381C23C2×#433912yes—
382C23C2×#434112yes—
383C23#6703711yescharacteristic
384C23#6704011yescharacteristic
385C23#41×D1112yes—
386C23#6704211yescharacteristic
387C23#6704211yescharacteristic
388C23#6704211yescharacteristic
389C23#6704311yescharacteristic
390C23#6704312yes—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—24no—
394C2×C4—24no—
395C2×C4—22no—
396C2×C4—22no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—24no—
402C2×C4—24no—
403C2×C4—24no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—42no—
415C2×C4—42no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—224no—
420C2×C4—224no—
421C2×C4—224no—
422C2×C4—224no—
423C2×C4—224no—
424C2×C4—224no—
425C2×C4—224no—
426C2×C4—224no—
427C2×C4—224no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—442no—
442C2×C4—442no—
443C2×C4—442no—
444C2×C4—442no—
445C2×C4—442no—
446C2×C4—442no—
447C2×C4#6693014yes—
448C22C4×#433911yescharacteristic
449C22C2×#6693011yescharacteristic
450C22#1062303511yescharacteristic
451C22#1062304711yescharacteristic
452C22#1062305211yescharacteristic
453C22#1062305311yescharacteristic
454C22#1062305411yescharacteristic
455C22#1062305812yes—
456C22#1062306312yes—
457C22#1062307212yes—
458C22#1062309412yes—
459C22#1062309512yes—
460C22#1062311412yes—
461C22#1062314712yes—
462C22#1062317012yes—
463C22#1062319612yes—
464C22#1062319612yes—
465C22#1062321411yescharacteristic
466C22#1062321511yescharacteristic
467C22#1062323011yescharacteristic
468C22#1062323111yescharacteristic
469C22#1062323212yes—
470C22#1062323812yes—
471C4—24no—
472C4—44no—
473C4—42no—
474C4—42no—
475C4—82no—
476C4—444no—
477C4—444no—
478C4—444no—
479C4—882no—
480C2#1307121711yescharacteristic
481C2#1307141711yescharacteristic
482C2#1307142011yescharacteristic
483C2#1307149911yescharacteristic
484C2#1307150311yescharacteristic
485C2#1307172611yescharacteristic
486C2#1307178711yescharacteristic
487C2#1307576412yes—
488C2#1307577312yes—
489C2#1307610812yes—
490C2#1307632112yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1434C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1434D11
hypocenterC11#14476
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1434

Complements

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

NH ≅ G/Ntype
31. #10622549C4semidirect
379. C11#14476semidirect

Maximal subgroups

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

subgroupindex
C2×#106225492
#130668742
#130668712
#130668682
#130668502
#130668432
#130668422
#130668402
C11×#14342
#1447611