Finite Group Databasebeta

← #14719138

Subgroups — #14719138

Order 2816.

1034 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066887C211yesmaximal, characteristic
2#13066887C211yesmaximal, characteristic
3#13066885C212yesmaximal
4#13066882C212yesmaximal
5#13066877C212yesmaximal
6#13066877C212yesmaximal
7#13066870C212yesmaximal
8#13066868C212yesmaximal
9C11×#1446C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C22×C4⋊Dic11C2212yes—
12C22×Dic11⋊C4C2212yes—
13C2×C11×#95C2211yescharacteristic
14C2×C11×#95C2212yes—
15C2×C11×#95C2211yescharacteristic
16C2×C11×#95C2212yes—
17C2×C11⋊#95C2212yes—
18C2×C11⋊#95C2212yes—
19C2×C11⋊#95C2212yes—
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2211yescharacteristic
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C22×Q8×C11—41no—
32C22×Q8×C11—41no—
33C22×Q8×C11—42no—
34C22×Q8×C11—42no—
35C22×Q8×C11Q814yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2312yes—
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C2×C4⋊Dic11—24no—
46C2×C4⋊Dic11—24no—
47C2×C4⋊Dic11—42no—
48C2×Dic11⋊C4—24no—
49C2×Dic11⋊C4—24no—
50C2×Dic11⋊C4—42no—
51C11×#95—41no—
52C11×#95—42no—
53C11×#95—42no—
54C11×#95—41no—
55C11⋊#95—24no—
56C11⋊#95—24no—
57C11⋊#95—41no—
58C11⋊#95—42no—
59C11⋊#95—42no—
60C11⋊#95—42no—
61C11⋊#95—42no—
62C11⋊#95—41no—
63C11⋊#95—41no—
64C11⋊#95—41no—
65C11⋊#95—42no—
66C11⋊#95—42no—
67C11⋊#95—42no—
68C11⋊#95—42no—
69#17289—111nomaximal, Sylow
70C24×C11C2411yescharacteristic
71C2×Q8×C11—44no—
72C2×Q8×C11—44no—
73C2×Q8×C11—44no—
74C2×Q8×C11—48no—
75C2×Q8×C11—48no—
76C22×C4×C11—22no—
77C22×C4×C11—22no—
78C22×C4×C11—22no—
79C22×C4×C11—21no—
80C22×C4×C11—21no—
81C22×C4×C11—21no—
82C22×C4×C11—21no—
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—21no—
90C22×C4×C11—21no—
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×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11C2×Q812yes—
102C22×C4×C11C2×Q812yes—
103C22×C4×C11C2×Q812yes—
104C22×C4×C11#4114yes—
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×Dic11—22no—
128C22×Dic11—22no—
129C22×Dic11—22no—
130C22×Dic11—22no—
131C22×Dic11—22no—
132C22×Dic11#4114yes—
133C4⋊Dic11—48no—
134Dic11⋊C4—48no—
135#1446—111no—
136#1446—111no—
137#1446D1111yescharacteristic
138#1445—112no—
139#1445—112no—
140#1443—112no—
141#1443—112no—
142#1441—112no—
143#1441—112no—
144C23×C11C22×Q811yescharacteristic
145C23×C11C2×#4112yes—
146C23×C11C2×#4112yes—
147C23×C11H(5,𝔽2)11yescharacteristic
148C23×C11H(5,𝔽2)11yescharacteristic
149C23×C11H(5,𝔽2)12yes—
150C23×C11H(5,𝔽2)12yes—
151C23×C112−1+412yes—
152C23×C112−1+412yes—
153Q8×C11—416no—
154C2×C4×C11—24no—
155C2×C4×C11—22no—
156C2×C4×C11—22no—
157C2×C4×C11—22no—
158C2×C4×C11—22no—
159C2×C4×C11—22no—
160C2×C4×C11—22no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—24no—
165C2×C4×C11—24no—
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×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—42no—
181C2×C4×C11—42no—
182C2×C4×C11—42no—
183C2×Dic11—24no—
184C2×Dic11—24no—
185C2×Dic11—24no—
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—
206C2×Dic11—42no—
207C2×Dic11—42no—
208C2×Dic11—42no—
209C2×Dic11—42no—
210C2×Dic11—42no—
211C23×Q8C2×D1111yescharacteristic
212C22×C4⋊C4—112no—
213C22×C4⋊C4—112no—
214C2×#95—112no—
215C2×#95—112no—
216C2×#95—111no—
217C2×#95—112no—
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—111no—
227C2×#95—111no—
228C2×#95C2×D1111yescharacteristic
229C2×#95C2×D1112yes—
230C2×#95C2×D1111yescharacteristic
231C2×#95C2×D1112yes—
232C22×C11#53912yes—
233C22×C11#53912yes—
234C22×C11#54212yes—
235C22×C11#54212yes—
236C22×C11#54212yes—
237C22×C11#54212yes—
238C22×C11#54311yescharacteristic
239C22×C11#54311yescharacteristic
240C22×C11#54311yescharacteristic
241C22×C11#55112yes—
242C22×C11#55112yes—
243C22×C11#55511yescharacteristic
244C22×C11#55511yescharacteristic
245C22×C11#55712yes—
246C22×C11#55712yes—
247C22×C11#56012yes—
248C22×C11#56012yes—
249C22×C11#56311yescharacteristic
250C22×C11#56312yes—
251C22×C11#56312yes—
252C22×C11#56311yescharacteristic
253C4×C11—42no—
254C4×C11—42no—
255C4×C11—42no—
256C4×C11—44no—
257C4×C11—82no—
258Dic11—44no—
259Dic11—82no—
260Dic11—82no—
261Dic11—82no—
262C22×Q8—42no—
263C22×Q8—42no—
264C22×Q8—41no—
265C22×Q8—41no—
266C22×Q8Dic2214yes—
267C23×C4—112no—
268C23×C4—112no—
269C23×C4—112no—
270C23×C4—112no—
271C23×C4C22×D1112yes—
272C23×C4C22×D1111yescharacteristic
273C23×C4C22×D1111yescharacteristic
274C23×C4C22×D1111yescharacteristic
275C23×C4C22×D1112yes—
276C2×C4⋊C4—224no—
277C2×C4⋊C4—224no—
278C2×C4⋊C4—224no—
279C2×C4⋊C4—224no—
280C2×C4⋊C4—442no—
281C2×C4⋊C4—442no—
282#95—41no—
283#95—42no—
284#95—42no—
285#95—41no—
286#95—224no—
287#95—224no—
288#95—442no—
289#95—441no—
290#95—442no—
291#95—442no—
292#95—441no—
293#95—441no—
294#95—441no—
295#95—442no—
296#95—442no—
297#95—442no—
298#95—442no—
299#95—442no—
300C2×C11#273712yes—
301C2×C11#273712yes—
302C2×C11#279912yes—
303C2×C11#279912yes—
304C2×C11#280911yescharacteristic
305C2×C11#280911yescharacteristic
306C2×C11#283812yes—
307C2×C11#283812yes—
308C2×C11#284211yescharacteristic
309C24C23×D1111yescharacteristic
310C2×Q8—44no—
311C2×Q8—44no—
312C2×Q8—44no—
313C2×Q8—48no—
314C2×Q8—48no—
315C22×C4—22no—
316C22×C4—22no—
317C22×C4—22no—
318C22×C4—22no—
319C22×C4—22no—
320C22×C4—21no—
321C22×C4—21no—
322C22×C4—22no—
323C22×C4—22no—
324C22×C4—22no—
325C22×C4—22no—
326C22×C4—21no—
327C22×C4—21no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—22no—
331C22×C4—22no—
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—114no—
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—222no—
361C22×C4—222no—
362C22×C4—222no—
363C22×C4—222no—
364C22×C4—222no—
365C22×C4—222no—
366C22×C4—222no—
367C22×C4—222no—
368C22×C4C2×Dic2212yes—
369C22×C4C2×Dic2212yes—
370C22×C4C2×Dic2212yes—
371C22×C4#434314yes—
372C4⋊C4—448no—
373C4⋊C4—448no—
374C11#1728911yescharacteristic, complemented, Sylow
375C23C22×Dic2211yescharacteristic
376C23#6703712yes—
377C23#6703712yes—
378C23#6703711yescharacteristic
379C23#6703711yescharacteristic
380C23C2×#434312yes—
381C23#6704012yes—
382C23#41×D1112yes—
383C23#6704312yes—
384Q8—416no—
385C2×C4—22no—
386C2×C4—22no—
387C2×C4—22no—
388C2×C4—22no—
389C2×C4—22no—
390C2×C4—22no—
391C2×C4—22no—
392C2×C4—22no—
393C2×C4—22no—
394C2×C4—24no—
395C2×C4—24no—
396C2×C4—24no—
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—42no—
409C2×C4—42no—
410C2×C4—42no—
411C2×C4—42no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—224no—
415C2×C4—224no—
416C2×C4—224no—
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—
436C2×C4—442no—
437C2×C4—442no—
438C2×C4—442no—
439C2×C4—442no—
440C2×C4—442no—
441C2×C4—442no—
442C22#1062301411yescharacteristic
443C22#1062301411yescharacteristic
444C22#1062301411yescharacteristic
445C22#1062310012yes—
446C22#1062310112yes—
447C22#1062312612yes—
448C22#1062312612yes—
449C22#1062316812yes—
450C22#1062316812yes—
451C22#1062316912yes—
452C22#1062317612yes—
453C22#1062317712yes—
454C22#1062317712yes—
455C22#1062320012yes—
456C22#1062320012yes—
457C22#1062320111yescharacteristic
458C22#1062320311yescharacteristic
459C22#1062326412yes—
460C22#1062326412yes—
461C22#1062326511yescharacteristic
462C22#1062326611yescharacteristic
463C4—42no—
464C4—42no—
465C4—42no—
466C4—44no—
467C4—82no—
468C4—444no—
469C4—882no—
470C4—882no—
471C4—882no—
472C2#1307567712yes—
473C2#1307567812yes—
474C2#1307650212yes—
475C2#1307650212yes—
476C2#1307660211yescharacteristic
477C2#1307660411yescharacteristic
478C2#1307685012yes—
479C2#1307685112yes—
480C2#1307688011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, prime radical, cosocleC24×C11C24
FittingC11×#1446C2
hypercenter#1446D11
hypocenterC11#17289
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
374. C11#17289semidirect

Maximal subgroups

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

subgroupindex
#130668872
#130668852
#130668822
#130668772
#130668702
#130668682
C11×#14462
#1728911