Finite Group Databasebeta

← #14719217

Subgroups — #14719217

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066887C212yesmaximal
2#13066885C211yesmaximal, characteristic
3#13066882C212yesmaximal
4#13066880C211yesmaximal, characteristic
5#13066877C212yesmaximal
6#13066870C212yesmaximal
7#13066868C212yesmaximal
8#13066867C212yesmaximal
9C11×#1446C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C22×C4⋊Dic11C2211yescharacteristic
12C22×C4⋊Dic11C2211yescharacteristic
13C22×Dic11⋊C4C2212yes—
14C22×Dic11⋊C4C2212yes—
15C2×C11×#95C2212yes—
16C2×C11×#95C2212yes—
17C2×C11×#95C2211yescharacteristic
18C2×C11×#95C2211yescharacteristic
19C2×C11⋊#95C2211yescharacteristic
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C22×Q8×C11—42no—
32C22×Q8×C11—41no—
33C22×Q8×C11—41no—
34C22×Q8×C11—42no—
35C22×Q8×C11Q814yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2311yescharacteristic
38C23×C4×C11C2312yes—
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C2×C4⋊Dic11—22no—
46C2×C4⋊Dic11—24no—
47C2×C4⋊Dic11—41no—
48C2×C4⋊Dic11—41no—
49C2×C4⋊Dic11—41no—
50C2×Dic11⋊C4—24no—
51C2×Dic11⋊C4—24no—
52C2×Dic11⋊C4—24no—
53C2×Dic11⋊C4—42no—
54C2×Dic11⋊C4—42no—
55C2×Dic11⋊C4—42no—
56C11×#95—42no—
57C11×#95—42no—
58C11×#95—41no—
59C11×#95—41no—
60C11⋊#95—42no—
61C11⋊#95—42no—
62C11⋊#95—42no—
63C11⋊#95—42no—
64C11⋊#95—42no—
65C11⋊#95—42no—
66C11⋊#95—42no—
67C11⋊#95—42no—
68C11⋊#95—42no—
69C11⋊#95—42no—
70C11⋊#95—41no—
71C11⋊#95Q814yescomplemented
72#17295—111nomaximal, Sylow
73C24×C11C2411yescharacteristic
74C2×Q8×C11—44no—
75C2×Q8×C11—48no—
76C2×Q8×C11—48no—
77C2×Q8×C11—44no—
78C2×Q8×C11—44no—
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—22no—
86C22×C4×C11—22no—
87C22×C4×C11—22no—
88C22×C4×C11—22no—
89C22×C4×C11—22no—
90C22×C4×C11—21no—
91C22×C4×C11—21no—
92C22×C4×C11—22no—
93C22×C4×C11—21no—
94C22×C4×C11—21no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—22no—
98C22×C4×C11—22no—
99C22×C4×C11—22no—
100C22×C4×C11—22no—
101C22×C4×C11—22no—
102C22×C4×C11—22no—
103C22×C4×C11—22no—
104C22×C4×C11C2×Q814yes—
105C22×C4×C11C2×Q812yes—
106C22×C4×C11C2×Q812yes—
107C22×C4×C11#4112yes—
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—22no—
133C22×Dic11—22no—
134C22×Dic11C2×Q814yes—
135C22×Dic11#4114yes—
136C4⋊Dic11—44no—
137C4⋊Dic11—44no—
138Dic11⋊C4—48no—
139Dic11⋊C4—48no—
140#1446—112no—
141#1446D1111yescharacteristic
142#1445—112no—
143#1445—111no—
144#1444—111no—
145#1443—112no—
146#1441—112no—
147#1441—112no—
148#1441—112no—
149C23×C11C22×Q811yescharacteristic
150C23×C11C22×Q811yescharacteristic
151C23×C11C2×#4111yescharacteristic
152C23×C11C2×#4112yes—
153C23×C11H(5,𝔽2)12yes—
154C23×C11H(5,𝔽2)11yescharacteristic
155C23×C11H(5,𝔽2)11yescharacteristic
156C23×C11H(5,𝔽2)12yes—
157C23×C11H(5,𝔽2)11yescharacteristic
158C23×C112−1+412yes—
159C23×C112−1+411yescharacteristic
160Q8×C11—416no—
161C2×C4×C11—22no—
162C2×C4×C11—24no—
163C2×C4×C11—24no—
164C2×C4×C11—24no—
165C2×C4×C11—22no—
166C2×C4×C11—24no—
167C2×C4×C11—22no—
168C2×C4×C11—24no—
169C2×C4×C11—24no—
170C2×C4×C11—42no—
171C2×C4×C11—42no—
172C2×C4×C11—41no—
173C2×C4×C11—41no—
174C2×C4×C11—41no—
175C2×C4×C11—41no—
176C2×C4×C11—42no—
177C2×C4×C11—42no—
178C2×C4×C11—42no—
179C2×C4×C11—42no—
180C2×C4×C11—41no—
181C2×C4×C11—42no—
182C2×C4×C11—41no—
183C2×C4×C11—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×C4×C11—42no—
190C2×Dic11—24no—
191C2×Dic11—24no—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
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—
212C2×Dic11—42no—
213C2×Dic11—42no—
214C2×Dic11—42no—
215C2×Dic11—42no—
216C2×Dic11—42no—
217C2×Dic11—42no—
218C23×Q8C2×D1111yescharacteristic
219C22×C4⋊C4—112no—
220C22×C4⋊C4—111no—
221C22×C4⋊C4—112no—
222C22×C4⋊C4—111no—
223C2×#95—111no—
224C2×#95—112no—
225C2×#95—111no—
226C2×#95—112no—
227C2×#95—112no—
228C2×#95—112no—
229C2×#95—112no—
230C2×#95—112no—
231C2×#95—112no—
232C2×#95—112no—
233C2×#95—112no—
234C2×#95—112no—
235C2×#95C2×D1112yes—
236C2×#95C2×D1112yes—
237C2×#95C2×D1111yescharacteristic
238C2×#95C2×D1111yescharacteristic
239C22×C11#53811yescharacteristic
240C22×C11#53812yes—
241C22×C11#54212yes—
242C22×C11#54212yes—
243C22×C11#54212yes—
244C22×C11#54311yescharacteristic
245C22×C11#54312yes—
246C22×C11#54412yes—
247C22×C11#54411yescharacteristic
248C22×C11#55112yes—
249C22×C11#55111yescharacteristic
250C22×C11#55411yescharacteristic
251C22×C11#55412yes—
252C22×C11#55712yes—
253C22×C11#55711yescharacteristic
254C22×C11Q8211yescharacteristic
255C22×C11#56012yes—
256C22×C11#56011yescharacteristic
257C22×C11#56011yescharacteristic
258C22×C11#56212yes—
259C22×C11#56211yescharacteristic
260C22×C11#56311yescharacteristic
261C22×C11#56312yes—
262C4×C11—42no—
263C4×C11—44no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—82no—
267Dic11—44no—
268Dic11—44no—
269Dic11—82no—
270Dic11—82no—
271C22×Q8—42no—
272C22×Q8—41no—
273C22×Q8—42no—
274C22×Q8—41no—
275C22×Q8Dic2214yes—
276C23×C4—112no—
277C23×C4—112no—
278C23×C4—112no—
279C23×C4—112no—
280C23×C4C22×D1112yes—
281C23×C4C22×D1112yes—
282C23×C4C22×D1111yescharacteristic
283C23×C4C22×D1111yescharacteristic
284C23×C4C22×D1111yescharacteristic
285C2×C4⋊C4—224no—
286C2×C4⋊C4—224no—
287C2×C4⋊C4—224no—
288C2×C4⋊C4—224no—
289C2×C4⋊C4—222no—
290C2×C4⋊C4—442no—
291C2×C4⋊C4—442no—
292C2×C4⋊C4—442no—
293C2×C4⋊C4—441no—
294C2×C4⋊C4—441no—
295C2×C4⋊C4—441no—
296#95—42no—
297#95—41no—
298#95—42no—
299#95—41no—
300#95—114no—
301#95—442no—
302#95—442no—
303#95—442no—
304#95—442no—
305#95—442no—
306#95—442no—
307#95—442no—
308#95—441no—
309#95—442no—
310#95—442no—
311#95—442no—
312C2×C11#274211yescharacteristic
313C2×C11#274212yes—
314C2×C11#276011yescharacteristic
315C2×C11#279911yescharacteristic
316C2×C11#279912yes—
317C2×C11#280612yes—
318C2×C11#280611yescharacteristic
319C2×C11#283012yes—
320C2×C11#283011yescharacteristic
321C2×C11#284211yescharacteristic
322C2×C11#284311yescharacteristic
323C24C23×D1111yescharacteristic
324C2×Q8—44no—
325C2×Q8—48no—
326C2×Q8—44no—
327C2×Q8—48no—
328C2×Q8—44no—
329C22×C4—22no—
330C22×C4—21no—
331C22×C4—22no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—21no—
335C22×C4—22no—
336C22×C4—21no—
337C22×C4—22no—
338C22×C4—22no—
339C22×C4—22no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—22no—
351C22×C4—22no—
352C22×C4—22no—
353C22×C4—22no—
354C22×C4—114no—
355C22×C4—114no—
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×C4—222no—
370C22×C4—222no—
371C22×C4—222no—
372C22×C4—222no—
373C22×C4—222no—
374C22×C4—222no—
375C22×C4—222no—
376C22×C4—222no—
377C22×C4—222no—
378C22×C4—222no—
379C22×C4—222no—
380C22×C4—222no—
381C22×C4—222no—
382C22×C4C2×Dic2212yes—
383C22×C4C2×Dic2214yes—
384C22×C4Q8×D1112yes—
385C22×C4#434312yes—
386C4⋊C4—448no—
387C4⋊C4—444no—
388C4⋊C4—444no—
389C4⋊C4—448no—
390C11#1729511yescharacteristic, complemented, Sylow
391C23C22×Dic2211yescharacteristic
392C23#6703712yes—
393C23#6703711yescharacteristic
394C23#6703712yes—
395C23#6703711yescharacteristic
396C23C2×Q8×D1111yescharacteristic
397C23C2×#434311yescharacteristic
398C23#6704012yes—
399C23#41×D1112yes—
400C23#6704211yescharacteristic
401C23#6704311yescharacteristic
402Q8—416no—
403C2×C4—22no—
404C2×C4—24no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—22no—
409C2×C4—24no—
410C2×C4—24no—
411C2×C4—22no—
412C2×C4—41no—
413C2×C4—41no—
414C2×C4—42no—
415C2×C4—41no—
416C2×C4—42no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—42no—
420C2×C4—41no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—41no—
424C2×C4—41no—
425C2×C4—42no—
426C2×C4—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—42no—
432C2×C4—224no—
433C2×C4—224no—
434C2×C4—224no—
435C2×C4—224no—
436C2×C4—224no—
437C2×C4—224no—
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—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—442no—
454C2×C4—442no—
455C2×C4—442no—
456C2×C4—442no—
457C2×C4—442no—
458C2×C4—442no—
459C2×C4—442no—
460C22#1062301411yescharacteristic
461C22#1062301412yes—
462C22Q8×Dic2211yescharacteristic
463C22#1062310012yes—
464C22#1062310111yescharacteristic
465C22#1062312611yescharacteristic
466C22#1062312612yes—
467C22#1062312611yescharacteristic
468C22#1062315411yescharacteristic
469C22#1062316712yes—
470C22#1062316812yes—
471C22#1062317112yes—
472C22#1062317511yescharacteristic
473C22#1062317712yes—
474C22#1062317812yes—
475C22#1062320012yes—
476C22#1062320912yes—
477C22#1062321011yescharacteristic
478C22#1062321511yescharacteristic
479C22#1062326012yes—
480C22#1062326111yescharacteristic
481C22#1062326412yes—
482C22#1062326611yescharacteristic
483C4—42no—
484C4—42no—
485C4—42no—
486C4—44no—
487C4—82no—
488C4—444no—
489C4—444no—
490C4—882no—
491C4—882no—
492C2#1307573911yescharacteristic
493C2#1307574712yes—
494C2#1307599111yescharacteristic
495C2#1307650011yescharacteristic
496C2#1307650212yes—
497C2#1307657612yes—
498C2#1307658011yescharacteristic
499C2#1307676012yes—
500C2#1307676411yescharacteristic
501C2#1307688011yescharacteristic
502C2#1307688211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, prime radical, cosocleC24×C11C24
FittingC11×#1446C2
hypercenter#1446D11
hypocenterC11#17295
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
71. C11⋊#95Q8semidirect
390. C11#17295semidirect

Maximal subgroups

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

subgroupindex
#130668872
#130668852
#130668822
#130668802
#130668772
#130668702
#130668682
#130668672
C11×#14462
#1729511