Finite Group Databasebeta

← #14719329

Subgroups — #14719329

Order 2816.

1122 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066887C211yesmaximal, characteristic
2#13066887C211yesmaximal, characteristic
3#13066882C212yesmaximal
4#13066880C212yesmaximal
5#13066870C212yesmaximal
6#13066868C212yesmaximal
7#13066867C212yesmaximal
8#13066867C212yesmaximal
9C11×#1446C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C22×C4⋊Dic11C2212yes—
12C22×Dic11⋊C4C2212yes—
13C22×Dic11⋊C4C2212yes—
14C22×Dic11⋊C4C2212yes—
15C2×C11×#95C2211yescharacteristic
16C2×C11×#95C2212yes—
17C2×C11×#95C2211yescharacteristic
18C2×C11×#95C2212yes—
19C2×C11⋊#95C2212yes—
20C2×C11⋊#95C2212yes—
21C2×C11⋊#95C2211yescharacteristic
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2211yescharacteristic
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2211yescharacteristic
31C22×Q8×C11—42no—
32C22×Q8×C11—42no—
33C22×Q8×C11—41no—
34C22×Q8×C11—41no—
35C22×Q8×C11Q814yes—
36C23×C4×C11C2312yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2311yescharacteristic
41C23×Dic11C2312yes—
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C2×C4⋊Dic11—24no—
46C2×C4⋊Dic11—42no—
47C2×C4⋊Dic11—42no—
48C2×Dic11⋊C4—24no—
49C2×Dic11⋊C4—42no—
50C2×Dic11⋊C4—42no—
51C2×Dic11⋊C4—42no—
52C2×Dic11⋊C4—42no—
53C2×Dic11⋊C4—42no—
54C2×Dic11⋊C4—42no—
55C2×Dic11⋊C4—42no—
56C2×Dic11⋊C4Q818yescomplemented
57C11×#95—42no—
58C11×#95—41no—
59C11×#95—42no—
60C11×#95—41no—
61C11⋊#95—24no—
62C11⋊#95—42no—
63C11⋊#95—42no—
64C11⋊#95—42no—
65C11⋊#95—42no—
66C11⋊#95—42no—
67C11⋊#95—41no—
68C11⋊#95—41no—
69C11⋊#95—41no—
70C11⋊#95—42no—
71C11⋊#95—42no—
72C11⋊#95—41no—
73#17306—111nomaximal, Sylow
74C24×C11C2411yescharacteristic
75C2×Q8×C11—44no—
76C2×Q8×C11—44no—
77C2×Q8×C11—44no—
78C2×Q8×C11—48no—
79C2×Q8×C11—48no—
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—21no—
88C22×C4×C11—21no—
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—21no—
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×C11—22no—
105C22×C4×C11C2×Q812yes—
106C22×C4×C11C2×Q812yes—
107C22×C4×C11C2×Q812yes—
108C22×C4×C11C2×Q814yes—
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×Dic11C2×Q814yes—
136C22×Dic11#4114yes—
137C4⋊Dic11—48no—
138Dic11⋊C4—48no—
139Dic11⋊C4—48no—
140Dic11⋊C4—48no—
141#1446—111no—
142#1446—111no—
143#1446D1111yescharacteristic
144#1445—112no—
145#1444—112no—
146#1441—112no—
147#1441—112no—
148#1441—112no—
149#1441—112no—
150C23×C11C22×Q811yescharacteristic
151C23×C11C22×Q812yes—
152C23×C11C2×#4112yes—
153C23×C11H(5,𝔽2)12yes—
154C23×C11H(5,𝔽2)12yes—
155C23×C11H(5,𝔽2)11yescharacteristic
156C23×C11H(5,𝔽2)11yescharacteristic
157C23×C11H(5,𝔽2)12yes—
158C23×C112−1+412yes—
159Q8×C11—416no—
160C2×C4×C11—24no—
161C2×C4×C11—22no—
162C2×C4×C11—22no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—22no—
166C2×C4×C11—22no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—24no—
171C2×C4×C11—24no—
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—42no—
184C2×C4×C11—42no—
185C2×C4×C11—42no—
186C2×C4×C11—42no—
187C2×C4×C11—42no—
188C2×C4×C11—42no—
189C2×Dic11—24no—
190C2×Dic11—24no—
191C2×Dic11—24no—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—24no—
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—
217C23×Q8C2×D1111yescharacteristic
218C22×C4⋊C4—112no—
219C22×C4⋊C4—112no—
220C22×C4⋊C4—112no—
221C22×C4⋊C4—112no—
222C2×#95—112no—
223C2×#95—112no—
224C2×#95—112no—
225C2×#95—112no—
226C2×#95—112no—
227C2×#95—112no—
228C2×#95—111no—
229C2×#95—112no—
230C2×#95—111no—
231C2×#95—111no—
232C2×#95—112no—
233C2×#95—111no—
234C2×#95C2×D1111yescharacteristic
235C2×#95C2×D1112yes—
236C2×#95C2×D1111yescharacteristic
237C2×#95C2×D1112yes—
238C22×C11#53812yes—
239C22×C11#53812yes—
240C22×C11#53912yes—
241C22×C11#54311yescharacteristic
242C22×C11#54311yescharacteristic
243C22×C11#54311yescharacteristic
244C22×C11#54312yes—
245C22×C11#54412yes—
246C22×C11#54412yes—
247C22×C11#55412yes—
248C22×C11#55412yes—
249C22×C11#55511yescharacteristic
250C22×C11#55712yes—
251C22×C11Q8211yescharacteristic
252C22×C11Q8212yes—
253C22×C11#56012yes—
254C22×C11#56012yes—
255C22×C11H(3,𝔽4)11yescharacteristic
256C22×C11#56212yes—
257C22×C11#56212yes—
258C22×C11#56311yescharacteristic
259C4×C11—42no—
260C4×C11—42no—
261C4×C11—42no—
262C4×C11—44no—
263C4×C11—82no—
264Dic11—44no—
265Dic11—44no—
266Dic11—44no—
267Dic11—82no—
268C22×Q8—41no—
269C22×Q8—42no—
270C22×Q8—42no—
271C22×Q8—41no—
272C22×Q8Dic2214yes—
273C23×C4—112no—
274C23×C4—112no—
275C23×C4—112no—
276C23×C4—112no—
277C23×C4C22×D1112yes—
278C23×C4C22×D1111yescharacteristic
279C23×C4C22×D1111yescharacteristic
280C23×C4C22×D1111yescharacteristic
281C23×C4C22×D1112yes—
282C2×C4⋊C4—118no—
283C2×C4⋊C4—224no—
284C2×C4⋊C4—224no—
285C2×C4⋊C4—442no—
286C2×C4⋊C4—442no—
287C2×C4⋊C4—442no—
288C2×C4⋊C4—442no—
289C2×C4⋊C4—442no—
290C2×C4⋊C4—442no—
291C2×C4⋊C4—442no—
292C2×C4⋊C4—442no—
293C2×C4⋊C4—442no—
294#95—42no—
295#95—41no—
296#95—42no—
297#95—41no—
298#95—224no—
299#95—442no—
300#95—442no—
301#95—442no—
302#95—442no—
303#95—441no—
304#95—441no—
305#95—441no—
306#95—442no—
307#95—441no—
308#95—442no—
309#95—442no—
310C2×C11#278412yes—
311C2×C11#279212yes—
312C2×C11#280612yes—
313C2×C11#280612yes—
314C2×C11#280911yescharacteristic
315C2×C11#281111yescharacteristic
316C2×C11#282412yes—
317C2×C11#284112yes—
318C2×C11#284211yescharacteristic
319C24C23×D1111yescharacteristic
320C2×Q8—44no—
321C2×Q8—44no—
322C2×Q8—44no—
323C2×Q8—48no—
324C2×Q8—48no—
325C22×C4—22no—
326C22×C4—22no—
327C22×C4—22no—
328C22×C4—21no—
329C22×C4—22no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—22no—
341C22×C4—22no—
342C22×C4—22no—
343C22×C4—22no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—114no—
351C22×C4—114no—
352C22×C4—114no—
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×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×C4C2×Dic2212yes—
379C22×C4C2×Dic2212yes—
380C22×C4C2×Dic2212yes—
381C22×C4Q8×D1114yes—
382C4⋊C4—448no—
383C4⋊C4—448no—
384C4⋊C4—448no—
385C4⋊C4—448no—
386C11#1730611yescharacteristic, complemented, Sylow
387C23C22×Dic2211yescharacteristic
388C23#6703711yescharacteristic
389C23#6703712yes—
390C23#6703712yes—
391C23#6703711yescharacteristic
392C23C2×Q8×D1112yes—
393C23#6704012yes—
394C23#41×D1112yes—
395C23#6704212yes—
396Q8—416no—
397C2×C4—22no—
398C2×C4—22no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—22no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
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—42no—
420C2×C4—42no—
421C2×C4—42no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—224no—
427C2×C4—224no—
428C2×C4—224no—
429C2×C4—224no—
430C2×C4—224no—
431C2×C4—224no—
432C2×C4—224no—
433C2×C4—224no—
434C2×C4—224no—
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—442no—
448C2×C4—442no—
449C2×C4—442no—
450C2×C4—442no—
451C2×C4—442no—
452C2×C4—442no—
453C2×C4—442no—
454C22#1062301411yescharacteristic
455C22#1062301411yescharacteristic
456C22#1062301411yescharacteristic
457C22Q8×Dic2212yes—
458C22#1062310012yes—
459C22#1062312612yes—
460C22#1062312612yes—
461C22#1062316512yes—
462C22#1062316712yes—
463C22#1062316712yes—
464C22#1062316912yes—
465C22#1062317812yes—
466C22#1062317812yes—
467C22#1062320111yescharacteristic
468C22#1062320912yes—
469C22#1062320912yes—
470C22#1062321411yescharacteristic
471C22#1062325311yescharacteristic
472C22#1062326012yes—
473C22#1062326012yes—
474C22#1062326611yescharacteristic
475C4—44no—
476C4—42no—
477C4—42no—
478C4—42no—
479C4—82no—
480C4—444no—
481C4—444no—
482C4—444no—
483C4—882no—
484C2#1307631112yes—
485C2#1307640912yes—
486C2#1307657612yes—
487C2#1307657612yes—
488C2#1307660211yescharacteristic
489C2#1307660911yescharacteristic
490C2#1307669512yes—
491C2#1307687012yes—
492C2#1307688011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, prime radical, cosocleC24×C11C24
FittingC11×#1446C2
hypercenter#1446D11
hypocenterC11#17306
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
56. C2×Dic11⋊C4Q8semidirect
386. C11#17306semidirect

Maximal subgroups

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

subgroupindex
#130668872
#130668822
#130668802
#130668702
#130668682
#130668672
C11×#14462
#1730611