Finite Group Databasebeta

← #14682537

Subgroups — #14682537

Order 2816.

1254 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622843C211yesmaximal, characteristic
2#13066887C211yesmaximal, characteristic
3#13066874C212yesmaximal
4#13066871C212yesmaximal
5#13066851C212yesmaximal
6#13066850C212yesmaximal
7#13066847C212yesmaximal
8Dic11⋊#95C212yesmaximal
9C11×#1446C211yesmaximal, characteristic
10C23×Q8×C11C2211yescharacteristic
11C22×C4⋊Dic11C2211yescharacteristic
12C22×Dic11⋊C4C2212yes—
13C22×Dic11⋊C4C2212yes—
14C22×C4×Dic11C2212yes—
15C22×C4×Dic11C2211yescharacteristic
16C2×C11×#95C2212yes—
17C2×C11×#95C2211yescharacteristic
18C2×C11×#95C2212yes—
19C2×C11×#95C2211yescharacteristic
20#10622843C418yescomplemented
21C2×C11⋊#95C2212yes—
22C2×C11⋊#95C2212yes—
23C2×C11⋊#95C2212yes—
24C2×C11⋊#95C2212yes—
25C2×C11⋊#95C2212yes—
26C2×C11⋊#95C2212yes—
27C2×C11⋊#95C2212yes—
28C2×C11⋊#95C2211yescharacteristic
29C2×C11⋊#95C2211yescharacteristic
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C22×Q8×C11—24no—
33C22×Q8×C11—42no—
34C22×Q8×C11—41no—
35C22×Q8×C11—41no—
36C22×Q8×C11C2×C414yes—
37C23×C4×C11C2312yes—
38C23×C4×C11C2311yescharacteristic
39C23×C4×C11C2311yescharacteristic
40C23×C4×C11C2312yes—
41C23×C4×C11C2311yescharacteristic
42C23×Dic11C2312yes—
43C23×Dic11C2312yes—
44C23×Dic11C2312yes—
45C23×Dic11C2312yes—
46C2×C4⋊Dic11—41no—
47C2×C4⋊Dic11—41no—
48C2×C4⋊Dic11C2×C414yes—
49C2×Dic11⋊C4—24no—
50C2×Dic11⋊C4—42no—
51C2×Dic11⋊C4—42no—
52C2×Dic11⋊C4—42no—
53C2×Dic11⋊C4—42no—
54C2×Dic11⋊C4Q818yescomplemented
55C2×C4×Dic11—42no—
56C2×C4×Dic11—42no—
57C2×C4×Dic11—42no—
58C2×C4×Dic11—42no—
59C2×C4×Dic11C2×C414yes—
60C11×#95—24no—
61C11×#95—41no—
62C11×#95—42no—
63C11×#95—41no—
64C11⋊#95—24no—
65C11⋊#95—24no—
66C11⋊#95—24no—
67C11⋊#95—41no—
68C11⋊#95—42no—
69C11⋊#95—42no—
70C11⋊#95—42no—
71C11⋊#95—42no—
72C11⋊#95—41no—
73C11⋊#95C2×C418yes—
74C11⋊#95C2×C418yes—
75#14471—111nomaximal, Sylow
76C24×C11C2411yescharacteristic
77C2×Q8×C11—28no—
78C2×Q8×C11—44no—
79C2×Q8×C11—44no—
80C2×Q8×C11—48no—
81C2×Q8×C11—48no—
82C22×C4×C11—22no—
83C22×C4×C11—21no—
84C22×C4×C11—21no—
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—21no—
92C22×C4×C11—21no—
93C22×C4×C11—22no—
94C22×C4×C11—22no—
95C22×C4×C11—22no—
96C22×C4×C11—21no—
97C22×C4×C11—21no—
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×C11—22no—
106C22×C4×C11C22×C412yes—
107C22×C4×C11C22×C412yes—
108C22×C4×C11C22×C412yes—
109C22×C4×C11C2×Q814yes—
110C22×C4×C11#4114yes—
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×Dic11C22×C414yes—
135C22×Dic11C22×C414yes—
136C22×Dic11C2×Q814yes—
137C22×Dic11C2×Q814yes—
138C22×Dic11#4114yes—
139C4⋊Dic11—44no—
140Dic11⋊C4—48no—
141Dic11⋊C4—48no—
142C4×Dic11—44no—
143C4×Dic11—48no—
144C2×#391—111no—
145#1446—111no—
146#1446D1111yescharacteristic
147#1442—112no—
148#1442—112no—
149#1436—112no—
150#1436—112no—
151#1436—112no—
152C4⋊#95—112no—
153C23×C11C23×C411yescharacteristic
154C23×C11C22×Q812yes—
155C23×C11C2×#4112yes—
156C23×C11C2×#4112yes—
157C23×C11H(5,𝔽2)12yes—
158C23×C11H(5,𝔽2)11yescharacteristic
159C23×C11H(5,𝔽2)11yescharacteristic
160C23×C11H(5,𝔽2)12yes—
161C23×C112−1+412yes—
162Q8×C11—416no—
163C2×C4×C11—22no—
164C2×C4×C11—22no—
165C2×C4×C11—24no—
166C2×C4×C11—24no—
167C2×C4×C11—22no—
168C2×C4×C11—22no—
169C2×C4×C11—22no—
170C2×C4×C11—22no—
171C2×C4×C11—22no—
172C2×C4×C11—22no—
173C2×C4×C11—24no—
174C2×C4×C11—24no—
175C2×C4×C11—24no—
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×C4×C11—42no—
190C2×C4×C11—42no—
191C2×C4×C11#11714yes—
192C2×Dic11—24no—
193C2×Dic11—24no—
194C2×Dic11—24no—
195C2×Dic11—24no—
196C2×Dic11—24no—
197C2×Dic11—24no—
198C2×Dic11—24no—
199C2×Dic11—24no—
200C2×Dic11—24no—
201C2×Dic11—24no—
202C2×Dic11—24no—
203C2×Dic11—24no—
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—
218C2×Dic11—42no—
219C2×Dic11C4×Q818yes—
220C23×Q8C2×D1111yescharacteristic
221C22×C4⋊C4—112no—
222C22×C4⋊C4—111no—
223C22×C4⋊C4—112no—
224C22×C42—111no—
225C22×C42—112no—
226#391—118no—
227C2×#95—112no—
228C2×#95—112no—
229C2×#95—112no—
230C2×#95—112no—
231C2×#95—112no—
232C2×#95—112no—
233C2×#95—112no—
234C2×#95—111no—
235C2×#95—112no—
236C2×#95—112no—
237C2×#95—111no—
238C2×#95C2×D1112yes—
239C2×#95C2×D1111yescharacteristic
240C2×#95C2×D1112yes—
241C2×#95C2×D1111yescharacteristic
242C22×C11C2×#11711yescharacteristic
243C22×C11C2×C4×Q812yes—
244C22×C11#51811yescharacteristic
245C22×C11#51811yescharacteristic
246C22×C11#52012yes—
247C22×C11#53812yes—
248C22×C11#53812yes—
249C22×C11#53812yes—
250C22×C11#53912yes—
251C22×C11#54312yes—
252C22×C11#54412yes—
253C22×C11#55412yes—
254C22×C11#55412yes—
255C22×C11#55511yescharacteristic
256C22×C11#55612yes—
257C22×C11#55712yes—
258C22×C11Q8211yescharacteristic
259C22×C11#55912yes—
260C22×C11H(3,𝔽4)11yescharacteristic
261C22×C11#56212yes—
262C22×C11#56311yescharacteristic
263C4×C11—24no—
264C4×C11—42no—
265C4×C11—42no—
266C4×C11—44no—
267C4×C11—82no—
268Dic11—28no—
269Dic11—44no—
270Dic11—44no—
271Dic11—82no—
272C22×Q8—24no—
273C22×Q8—42no—
274C22×Q8—41no—
275C22×Q8—41no—
276C22×Q8C4×D1114yes—
277C23×C4—112no—
278C23×C4—112no—
279C23×C4—112no—
280C23×C4—112no—
281C23×C4C22×D1112yes—
282C23×C4C22×D1111yescharacteristic
283C23×C4C22×D1111yescharacteristic
284C23×C4C22×D1112yes—
285C23×C4C22×D1111yescharacteristic
286C2×C4⋊C4—114no—
287C2×C4⋊C4—118no—
288C2×C4⋊C4—224no—
289C2×C4⋊C4—442no—
290C2×C4⋊C4—442no—
291C2×C4⋊C4—442no—
292C2×C4⋊C4—442no—
293C2×C4⋊C4—441no—
294C2×C4⋊C4—441no—
295C2×C42—114no—
296C2×C42—442no—
297C2×C42—442no—
298C2×C42—442no—
299C2×C42—442no—
300#95—24no—
301#95—41no—
302#95—42no—
303#95—41no—
304#95—118no—
305#95—118no—
306#95—224no—
307#95—224no—
308#95—224no—
309#95—441no—
310#95—442no—
311#95—441no—
312#95—442no—
313#95—442no—
314#95—442no—
315C2×C11#231211yescharacteristic
316C2×C11#232912yes—
317C2×C11#235512yes—
318C2×C11#236911yescharacteristic
319C2×C11#237911yescharacteristic
320C2×C11#280412yes—
321C2×C11#280512yes—
322C2×C11#280612yes—
323C2×C11#280812yes—
324C24C23×D1111yescharacteristic
325C2×Q8—28no—
326C2×Q8—44no—
327C2×Q8—44no—
328C2×Q8—48no—
329C2×Q8—48no—
330C22×C4—22no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—22no—
334C22×C4—22no—
335C22×C4—22no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—22no—
340C22×C4—21no—
341C22×C4—21no—
342C22×C4—22no—
343C22×C4—21no—
344C22×C4—22no—
345C22×C4—22no—
346C22×C4—22no—
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—114no—
357C22×C4—114no—
358C22×C4—114no—
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×C4×D1112yes—
383C22×C4C2×C4×D1112yes—
384C22×C4C2×C4×D1112yes—
385C22×C4#434114yes—
386C22×C4Q8×D1114yes—
387C4⋊C4—448no—
388C4⋊C4—444no—
389C4⋊C4—448no—
390C42—444no—
391C42—448no—
392C11#1447111yescharacteristic, complemented, Sylow
393C23C22×C4×D1111yescharacteristic
394C23C2×#434112yes—
395C23#6703711yescharacteristic
396C23#6703712yes—
397C23#6703711yescharacteristic
398C23C2×Q8×D1112yes—
399C23#6704012yes—
400C23#41×D1112yes—
401C23#6704212yes—
402Q8—416no—
403C2×C4—22no—
404C2×C4—22no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—22no—
408C2×C4—22no—
409C2×C4—22no—
410C2×C4—22no—
411C2×C4—22no—
412C2×C4—22no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
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—42no—
427C2×C4—42no—
428C2×C4—42no—
429C2×C4—42no—
430C2×C4—42no—
431C2×C4—118no—
432C2×C4—224no—
433C2×C4—224no—
434C2×C4—224no—
435C2×C4—224no—
436C2×C4—224no—
437C2×C4—224no—
438C2×C4—224no—
439C2×C4—224no—
440C2×C4—224no—
441C2×C4—224no—
442C2×C4—224no—
443C2×C4—224no—
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#6693014yes—
460C22C2×#6693011yescharacteristic
461C22#1062301711yescharacteristic
462C22#1062301711yescharacteristic
463C22C4×Q8×D1112yes—
464C22#1062310512yes—
465C22#1062312412yes—
466C22#1062312412yes—
467C22#1062316512yes—
468C22#1062316612yes—
469C22#1062316712yes—
470C22#1062316912yes—
471C22#1062317212yes—
472C22#1062317812yes—
473C22#1062320111yescharacteristic
474C22#1062320912yes—
475C22#1062321212yes—
476C22#1062321411yescharacteristic
477C22#1062325212yes—
478C22#1062325311yescharacteristic
479C22#1062326012yes—
480C22#1062326611yescharacteristic
481C4—24no—
482C4—44no—
483C4—42no—
484C4—42no—
485C4—82no—
486C4—228no—
487C4—444no—
488C4—444no—
489C4—882no—
490C2#1307121211yescharacteristic
491C2#1307134812yes—
492C2#1307157212yes—
493C2#1307170411yescharacteristic
494C2#1307178811yescharacteristic
495C2#1307655712yes—
496C2#1307656312yes—
497C2#1307657912yes—
498C2#1307659012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1446C2
socle, prime radical, cosocleC24×C11C24
hypercenter#1446D11
hypocenterC11#14471
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1446

Complements

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

NH ≅ G/Ntype
20. #10622843C4semidirect
54. C2×Dic11⋊C4Q8semidirect
392. C11#14471semidirect

Maximal subgroups

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

subgroupindex
C2×#106228432
#130668872
#130668742
#130668712
#130668512
#130668502
#130668472
Dic11⋊#952
C11×#14462
#1447111