Finite Group Databasebeta

← #14719281

Subgroups — #14719281

Order 2816.

926 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066880C211yesmaximal, characteristic
2#13066877C212yesmaximal
3#13066876C212yesmaximal
4#13066875C212yesmaximal
5#13066873C212yesmaximal
6#13066872C211yesmaximal, characteristic
7#13066871C212yesmaximal
8#13066870C212yesmaximal
9C11×#1442C211yesmaximal, characteristic
10C22×C11×C4⋊C4C2211yescharacteristic
11C22×C4⋊Dic11C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×Dic11⋊C4C2212yes—
14C2×C11×#95C2212yes—
15C2×C11×#95C2211yescharacteristic
16C2×C11×#95C2212yes—
17C2×C11×#95C2211yescharacteristic
18C2×C11⋊#95C2212yes—
19C2×C11⋊#95C2212yes—
20C2×C11⋊#95C2211yescharacteristic
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2211yescharacteristic
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C23×C4×C11C2312yes—
32C23×C4×C11C2312yes—
33C23×C4×C11C2311yescharacteristic
34C23×C4×C11C2311yescharacteristic
35C23×C4×C11C2311yescharacteristic
36C23×Dic11C2312yes—
37C23×Dic11C2312yes—
38C23×Dic11C2312yes—
39C23×Dic11C2312yes—
40C2×C11×C4⋊C4—42no—
41C2×C11×C4⋊C4—41no—
42C2×C4⋊Dic11—41no—
43C2×C4⋊Dic11—41no—
44C2×C4⋊Dic11—42no—
45C2×C4⋊Dic11—42no—
46C2×Dic11⋊C4—24no—
47C2×Dic11⋊C4—42no—
48C2×Dic11⋊C4—42no—
49C11×#95—22no—
50C11×#95—24no—
51C11×#95—42no—
52C11×#95—41no—
53C11⋊#95—24no—
54C11⋊#95—22no—
55C11⋊#95—22no—
56C11⋊#95—24no—
57C11⋊#95—24no—
58C11⋊#95—24no—
59C11⋊#95—42no—
60C11⋊#95—42no—
61C11⋊#95—42no—
62C11⋊#95—42no—
63C11⋊#95—42no—
64C11⋊#95—42no—
65C11⋊#95—42no—
66#17300—111nomaximal, Sylow
67C24×C11C2411yescharacteristic
68C22×C4×C11—22no—
69C22×C4×C11—22no—
70C22×C4×C11—22no—
71C22×C4×C11—21no—
72C22×C4×C11—21no—
73C22×C4×C11—21no—
74C22×C4×C11—22no—
75C22×C4×C11—21no—
76C22×C4×C11—21no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—21no—
80C22×C4×C11—22no—
81C22×C4×C11—22no—
82C22×C4×C11—22no—
83C22×C4×C11—22no—
84C22×C4×C11—22no—
85C22×C4×C11—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
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#4112yes—
95C22×C4×C11#4112yes—
96C22×C4×C11#4112yes—
97C22×Dic11—22no—
98C22×Dic11—22no—
99C22×Dic11—22no—
100C22×Dic11—22no—
101C22×Dic11—22no—
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#4114yes—
125C11×C4⋊C4—44no—
126C4⋊Dic11—44no—
127C4⋊Dic11—44no—
128Dic11⋊C4—48no—
129#1444—111no—
130#1443—112no—
131#1443—112no—
132#1442—112no—
133#1442—111no—
134#1442—112no—
135#1442—112no—
136#1442D1111yescharacteristic
137#1441—112no—
138C23×C11C2×#4111yescharacteristic
139C23×C11C2×#4111yescharacteristic
140C23×C11C2×#4111yescharacteristic
141C23×C11C2×#4112yes—
142C23×C11H(5,𝔽2)12yes—
143C23×C11H(5,𝔽2)11yescharacteristic
144C23×C11H(5,𝔽2)12yes—
145C23×C112−1+411yescharacteristic
146C23×C112−1+412yes—
147C23×C112−1+411yescharacteristic
148C23×C112−1+411yescharacteristic
149C2×C4×C11—24no—
150C2×C4×C11—22no—
151C2×C4×C11—24no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—24no—
155C2×C4×C11—41no—
156C2×C4×C11—41no—
157C2×C4×C11—41no—
158C2×C4×C11—41no—
159C2×C4×C11—42no—
160C2×C4×C11—42no—
161C2×C4×C11—42no—
162C2×C4×C11—41no—
163C2×C4×C11—41no—
164C2×C4×C11—42no—
165C2×C4×C11—42no—
166C2×C4×C11—42no—
167C2×C4×C11—42no—
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×Dic11—24no—
179C2×Dic11—24no—
180C2×Dic11—24no—
181C2×Dic11—42no—
182C2×Dic11—42no—
183C2×Dic11—42no—
184C2×Dic11—42no—
185C2×Dic11—42no—
186C2×Dic11—42no—
187C2×Dic11—42no—
188C2×Dic11—42no—
189C2×Dic11—42no—
190C2×Dic11—42no—
191C2×Dic11—42no—
192C2×Dic11—42no—
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—
206C22×C4⋊C4—112no—
207C22×C4⋊C4—111no—
208C22×C4⋊C4—111no—
209C22×C4⋊C4C2×D1111yescharacteristic
210C2×#95—112no—
211C2×#95—112no—
212C2×#95—111no—
213C2×#95—112no—
214C2×#95—112no—
215C2×#95—111no—
216C2×#95—112no—
217C2×#95—112no—
218C2×#95—112no—
219C2×#95—112no—
220C2×#95—112no—
221C2×#95—112no—
222C2×#95—112no—
223C2×#95C2×D1112yes—
224C2×#95C2×D1111yescharacteristic
225C2×#95C2×D1112yes—
226C2×#95C2×D1111yescharacteristic
227C22×C11#53812yes—
228C22×C11#53911yescharacteristic
229C22×C11#53912yes—
230C22×C11#53911yescharacteristic
231C22×C11#53911yescharacteristic
232C22×C11#53912yes—
233C22×C11#53912yes—
234C22×C11#54112yes—
235C22×C11#54212yes—
236C22×C11#55212yes—
237C22×C11#55312yes—
238C22×C11#55512yes—
239C22×C11#55511yescharacteristic
240C22×C11#55611yescharacteristic
241C22×C11#55611yescharacteristic
242C22×C11#55611yescharacteristic
243C22×C11#56011yescharacteristic
244C22×C11H(3,𝔽4)11yescharacteristic
245C22×C11#56212yes—
246C22×C11#56312yes—
247C22×C11#56312yes—
248C22×C11#56311yescharacteristic
249C22×C11#56411yescharacteristic
250C4×C11—42no—
251C4×C11—42no—
252C4×C11—42no—
253C4×C11—82no—
254C4×C11—82no—
255Dic11—44no—
256Dic11—82no—
257Dic11—82no—
258Dic11—82no—
259C23×C4—112no—
260C23×C4—112no—
261C23×C4—112no—
262C23×C4—112no—
263C23×C4C22×D1112yes—
264C23×C4C22×D1112yes—
265C23×C4C22×D1111yescharacteristic
266C23×C4C22×D1111yescharacteristic
267C23×C4C22×D1111yescharacteristic
268C2×C4⋊C4—41no—
269C2×C4⋊C4—42no—
270C2×C4⋊C4—224no—
271C2×C4⋊C4—442no—
272C2×C4⋊C4—442no—
273C2×C4⋊C4—441no—
274C2×C4⋊C4—441no—
275C2×C4⋊C4—442no—
276C2×C4⋊C4—442no—
277#95—22no—
278#95—24no—
279#95—41no—
280#95—42no—
281#95—224no—
282#95—224no—
283#95—224no—
284#95—224no—
285#95—222no—
286#95—222no—
287#95—442no—
288#95—442no—
289#95—442no—
290#95—442no—
291#95—442no—
292#95—442no—
293#95—442no—
294C2×C11#276911yescharacteristic
295C2×C11#277512yes—
296C2×C11#278312yes—
297C2×C11#278511yescharacteristic
298C2×C11#278712yes—
299C2×C11#279511yescharacteristic
300C2×C11#281011yescharacteristic
301C2×C11#282411yescharacteristic
302C2×C11#283411yescharacteristic
303C2×C11#283511yescharacteristic
304C2×C11#283912yes—
305C24C23×D1111yescharacteristic
306C22×C4—21no—
307C22×C4—21no—
308C22×C4—22no—
309C22×C4—21no—
310C22×C4—22no—
311C22×C4—21no—
312C22×C4—22no—
313C22×C4—22no—
314C22×C4—22no—
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—22no—
321C22×C4—22no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—22no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—22no—
332C22×C4—114no—
333C22×C4—222no—
334C22×C4—222no—
335C22×C4—222no—
336C22×C4—222no—
337C22×C4—222no—
338C22×C4—222no—
339C22×C4—222no—
340C22×C4—222no—
341C22×C4—222no—
342C22×C4—222no—
343C22×C4—222no—
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#433912yes—
361C22×C4#434112yes—
362C22×C4#434312yes—
363C4⋊C4—44no—
364C4⋊C4—448no—
365C4⋊C4—444no—
366C4⋊C4—444no—
367C11#1730011yescharacteristic, complemented, Sylow
368C23C2×#433911yescharacteristic
369C23C2×#434111yescharacteristic
370C23#6703711yescharacteristic
371C23#6703712yes—
372C23C2×#434311yescharacteristic
373C23#6704011yescharacteristic
374C23#41×D1112yes—
375C23#6704212yes—
376C23#6704311yescharacteristic
377C23#6704312yes—
378C23#6704311yescharacteristic
379C2×C4—22no—
380C2×C4—24no—
381C2×C4—22no—
382C2×C4—24no—
383C2×C4—22no—
384C2×C4—24no—
385C2×C4—42no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—42no—
389C2×C4—41no—
390C2×C4—41no—
391C2×C4—41no—
392C2×C4—41no—
393C2×C4—42no—
394C2×C4—42no—
395C2×C4—42no—
396C2×C4—42no—
397C2×C4—42no—
398C2×C4—42no—
399C2×C4—42no—
400C2×C4—42no—
401C2×C4—42no—
402C2×C4—42no—
403C2×C4—42no—
404C2×C4—42no—
405C2×C4—42no—
406C2×C4—42no—
407C2×C4—42no—
408C2×C4—224no—
409C2×C4—224no—
410C2×C4—224no—
411C2×C4—442no—
412C2×C4—442no—
413C2×C4—442no—
414C2×C4—442no—
415C2×C4—442no—
416C2×C4—442no—
417C2×C4—442no—
418C2×C4—442no—
419C2×C4—442no—
420C2×C4—442no—
421C2×C4—442no—
422C2×C4—442no—
423C2×C4—442no—
424C2×C4—442no—
425C2×C4—442no—
426C2×C4—442no—
427C2×C4—442no—
428C2×C4—442no—
429C2×C4—442no—
430C2×C4—442no—
431C2×C4—442no—
432C2×C4—442no—
433C2×C4—442no—
434C2×C4—442no—
435C2×C4—442no—
436C22#1062304611yescharacteristic
437C22#1062306312yes—
438C22#1062307311yescharacteristic
439C22#1062309512yes—
440C22#1062311511yescharacteristic
441C22#1062312611yescharacteristic
442C22#1062313311yescharacteristic
443C22#1062314512yes—
444C22#1062317512yes—
445C22#1062317611yescharacteristic
446C22#1062317712yes—
447C22#1062318211yescharacteristic
448C22#1062319312yes—
449C22#1062319612yes—
450C22#1062320111yescharacteristic
451C22#1062321411yescharacteristic
452C22#1062321512yes—
453C22C11⋊#56411yescharacteristic
454C22#1062322312yes—
455C22#1062322512yes—
456C22#1062323212yes—
457C22#1062324312yes—
458C22#1062326311yescharacteristic
459C4—42no—
460C4—42no—
461C4—42no—
462C4—82no—
463C4—82no—
464C4—444no—
465C4—882no—
466C4—882no—
467C4—882no—
468C2#1307611111yescharacteristic
469C2#1307618612yes—
470C2#1307630712yes—
471C2#1307632211yescharacteristic
472C2#1307635312yes—
473C2#1307644911yescharacteristic
474C2#1307660711yescharacteristic
475C2#1307670011yescharacteristic
476C2#1307679911yescharacteristic
477C2#1307680611yescharacteristic
478C2#1307685712yes—
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, prime radical, cosocleC24×C11C24
FittingC11×#1442C2
hypercenter#1442D11
hypocenterC11#17300
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1442

Complements

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

NH ≅ G/Ntype
367. C11#17300semidirect

Maximal subgroups

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

subgroupindex
#130668802
#130668772
#130668762
#130668752
#130668732
#130668722
#130668712
#130668702
C11×#14422
#1730011