Finite Group Databasebeta

← #14680944

Subgroups — #14680944

Order 2816.

3390 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊Dic11C211yesmaximal, characteristic
2C2×#10622555C212yesmaximal, complemented
3C2×#10622860C211yesmaximal, characteristic
4#13066859C218yesmaximal, complemented
5#13066838C212yesmaximal, complemented
6C2×C11×#379C211yesmaximal, characteristic
7C26×C11C2211yescharacteristic
8C24×Dic11C2211yescharacteristic
9C24×Dic11C2211yescharacteristic
10C22×C11×C22⋊C4C2212yes—
11C22×C11×C22⋊C4C2214yes—
12C22×C22⋊Dic11—28no—
13C22×C22⋊Dic11C418yescomplemented
14C22×C22⋊Dic11C2212yes—
15C22×C22⋊Dic11C2214yes—
16C22×C22⋊Dic11C2214yes—
17C22×Dic11⋊C4C2214yescomplemented
18C11×#379—24no—
19#10622860—24no—
20C2×C11⋊#95C2214yescomplemented
21C2×C11⋊#95C2218yescomplemented
22#10622555—28no—
23C25×C11—24no—
24C25×C11—24no—
25C25×C11—44no—
26C25×C11—44no—
27C25×C11C2×C414yes—
28C25×C11D414yes—
29C25×C11Q814yes—
30C25×C11C2312yes—
31C25×C11C2311yescharacteristic
32C23×C4×C11C2314yes—
33C23×Dic11—24no—
34C23×Dic11—44no—
35C23×Dic11—44no—
36C23×Dic11C2×C414yes—
37C23×Dic11C2×C414yes—
38C23×Dic11D418yes—
39C23×Dic11C2314yes—
40C23×Dic11C2312yes—
41C23×Dic11C2312yes—
42C2×C11×C22⋊C4—24no—
43C2×C11×C22⋊C4—28no—
44C2×C11×C22⋊C4—24no—
45C2×C11×C22⋊C4—24no—
46C2×C11×C22⋊C4—44no—
47C2×C11×C22⋊C4—44no—
48C2×C22⋊Dic11—232no—
49C2×C22⋊Dic11—28no—
50C2×C22⋊Dic11—28no—
51C2×C22⋊Dic11—24no—
52C2×C22⋊Dic11—28no—
53C2×C22⋊Dic11—24no—
54C2×C22⋊Dic11—24no—
55C2×C22⋊Dic11—44no—
56C2×C22⋊Dic11—44no—
57C2×C22⋊Dic11C2×C4116yes—
58C2×Dic11⋊C4—28no—
59C2×Dic11⋊C4—48no—
60C11⋊#95—28no—
61C11⋊#95—48no—
62#14338—111nomaximal, Sylow
63C24×C11—24no—
64C24×C11—24no—
65C24×C11—28no—
66C24×C11—28no—
67C24×C11—216no—
68C24×C11—216no—
69C24×C11—24no—
70C24×C11—24no—
71C24×C11—24no—
72C24×C11—24no—
73C24×C11—24no—
74C24×C11—24no—
75C24×C11—48no—
76C24×C11—48no—
77C24×C11—416no—
78C24×C11—416no—
79C24×C11—416no—
80C24×C11—416no—
81C24×C11—432no—
82C24×C11C4⋊C4116yescomplemented
83C24×C11C22×C414yes—
84C24×C11C22×C412yes—
85C24×C11C2×D414yes—
86C24×C11C2×D414yes—
87C24×C11C2×D412yes—
88C24×C11C2×Q814yes—
89C24×C11C2×Q812yes—
90C24×C11#4114yes—
91C24×C11C2411yescharacteristic
92C22×C4×C11—24no—
93C22×C4×C11—24no—
94C22×C4×C11—24no—
95C22×C4×C11—28no—
96C22×C4×C11—28no—
97C22×Dic11—28no—
98C22×Dic11—24no—
99C22×Dic11—24no—
100C22×Dic11—24no—
101C22×Dic11—24no—
102C22×Dic11—28no—
103C22×Dic11—28no—
104C22×Dic11—28no—
105C22×Dic11—28no—
106C22×Dic11—48no—
107C22×Dic11—48no—
108C22×Dic11—416no—
109C22×Dic11—416no—
110C22×Dic11C22⋊C4116yescomplemented
111C22×Dic11C22×C414yes—
112C22×Dic11C22×C414yes—
113C22×Dic11C2×D414yes—
114C22×Dic11C2×D414yes—
115C11×C22⋊C4—416no—
116C11×C22⋊C4—48no—
117C22⋊Dic11—232no—
118C22⋊Dic11—416no—
119C22⋊Dic11—48no—
120Dic11⋊C4—416no—
121C23×C22⋊C4—111no—
122C2×#380—112no—
123C2×#379—111no—
124C2×#379D1111yescharacteristic
125#1439—118no—
126C22⋊#95—112no—
127C23×C11—24no—
128C23×C11—24no—
129C23×C11—28no—
130C23×C11—28no—
131C23×C11—28no—
132C23×C11—216no—
133C23×C11—28no—
134C23×C11—24no—
135C23×C11—24no—
136C23×C11—24no—
137C23×C11—24no—
138C23×C11—24no—
139C23×C11—24no—
140C23×C11—28no—
141C23×C11—28no—
142C23×C11—28no—
143C23×C11—28no—
144C23×C11—28no—
145C23×C11—28no—
146C23×C11—232no—
147C23×C11—432no—
148C23×C11—416no—
149C23×C11—416no—
150C23×C11—432no—
151C23×C11—464no—
152C23×C11—464no—
153C23×C11—48no—
154C23×C11—48no—
155C23×C11—48no—
156C23×C11—48no—
157C23×C11C2×C22⋊C414yes—
158C23×C11C2×C4⋊C418yes—
159C23×C11C2×C4⋊C414yes—
160C23×C11#11714yes—
161C23×C11#12118yes—
162C23×C11C22⋊Q818yes—
163C23×C11C23×C411yescharacteristic
164C23×C11C22×D412yes—
165C23×C11C22×D411yescharacteristic
166C23×C11C22×Q811yescharacteristic
167C23×C11C2×#4112yes—
168C23×C11H(5,𝔽2)14yes—
169C23×C11H(5,𝔽2)14yes—
170C2×C4×C11—44no—
171C2×C4×C11—44no—
172C2×C4×C11—48no—
173C2×C4×C11—44no—
174C2×C4×C11—48no—
175C2×Dic11—28no—
176C2×Dic11—28no—
177C2×Dic11—28no—
178C2×Dic11—24no—
179C2×Dic11—28no—
180C2×Dic11—416no—
181C2×Dic11—416no—
182C2×Dic11—48no—
183C2×Dic11—44no—
184C2×Dic11—44no—
185C2×Dic11—48no—
186C2×Dic11—44no—
187C2×Dic11—48no—
188C2×Dic11C2×C22⋊C418yes—
189C26C2×D1111yescharacteristic
190C24×C4—111no—
191C24×C4—111no—
192C22×C4⋊C4—114no—
193C22×C22⋊C4—114no—
194C22×C22⋊C4—118no—
195C22×C22⋊C4—112no—
196C22×C22⋊C4—114no—
197C22×C22⋊C4—228no—
198C22×C22⋊C4C2×D1112yes—
199C22×C22⋊C4C2×D1114yes—
200#380—228no—
201#379—24no—
202#379—224no—
203C2×#95—114no—
204C2×#95—118no—
205C22×C11—24no—
206C22×C11—24no—
207C22×C11—28no—
208C22×C11—28no—
209C22×C11—216no—
210C22×C11—216no—
211C22×C11—28no—
212C22×C11—28no—
213C22×C11—28no—
214C22×C11—464no—
215C22×C11—44no—
216C22×C11—44no—
217C22×C11—44no—
218C22×C11—44no—
219C22×C11—416no—
220C22×C11—416no—
221C22×C11#38018yes—
222C22×C11C22×C22⋊C411yescharacteristic
223C22×C11C22×C4⋊C411yescharacteristic
224C22×C11C2×#11711yescharacteristic
225C22×C11#51812yes—
226C22×C11#51812yes—
227C22×C11C2×#12112yes—
228C22×C11C2×C22⋊Q812yes—
229C22×C11#53414yes—
230C22×C11#53414yes—
231C22×C11#53514yes—
232C22×C11#53818yes—
233C22×C11#54314yes—
234C4×C11—84no—
235Dic11—28no—
236Dic11—44no—
237Dic11—84no—
238C25—24no—
239C25—24no—
240C25—44no—
241C25—44no—
242C25Dic2214yes—
243C25C4×D1114yes—
244C25C22⋊D1114yes—
245C25C22×D1112yes—
246C25C22×D1111yescharacteristic
247C23×C4—112no—
248C23×C4—114no—
249C23×C4—118no—
250C23×C4—112no—
251C23×C4—114no—
252C23×C4—114no—
253C23×C4—224no—
254C23×C4—444no—
255C23×C4—444no—
256C23×C4C22×D1114yes—
257C2×C4⋊C4—228no—
258C2×C4⋊C4—448no—
259C2×C22⋊C4—24no—
260C2×C22⋊C4—24no—
261C2×C22⋊C4—28no—
262C2×C22⋊C4—24no—
263C2×C22⋊C4—44no—
264C2×C22⋊C4—44no—
265C2×C22⋊C4—1116no—
266C2×C22⋊C4—228no—
267C2×C22⋊C4—228no—
268C2×C22⋊C4—2232no—
269C2×C22⋊C4—224no—
270C2×C22⋊C4—224no—
271C2×C22⋊C4—228no—
272C2×C22⋊C4—224no—
273C2×C22⋊C4—444no—
274C2×C22⋊C4—444no—
275#95—228no—
276#95—448no—
277C2×C11—28no—
278C2×C11—48no—
279C2×C11C2×#38011yescharacteristic
280C2×C11#230811yescharacteristic
281C2×C11#230911yescharacteristic
282C2×C11#231212yes—
283C2×C11#231512yes—
284C2×C11#261714yes—
285C2×C11#262614yes—
286C24—24no—
287C24—24no—
288C24—28no—
289C24—216no—
290C24—28no—
291C24—216no—
292C24—24no—
293C24—24no—
294C24—24no—
295C24—24no—
296C24—24no—
297C24—24no—
298C24—416no—
299C24—48no—
300C24—48no—
301C24—416no—
302C24—416no—
303C24—416no—
304C24—432no—
305C24Dic11⋊C4116yescomplemented
306C24C2×Dic2214yes—
307C24C2×Dic2212yes—
308C24C2×C4×D1114yes—
309C24C2×C4×D1112yes—
310C24D4×D1114yes—
311C24#434114yes—
312C24C2×C22⋊D1114yes—
313C24C2×C22⋊D1112yes—
314C24C23×D1111yescharacteristic
315C22×C4—24no—
316C22×C4—24no—
317C22×C4—28no—
318C22×C4—28no—
319C22×C4—24no—
320C22×C4—114no—
321C22×C4—114no—
322C22×C4—114no—
323C22×C4—1116no—
324C22×C4—114no—
325C22×C4—228no—
326C22×C4—228no—
327C22×C4—224no—
328C22×C4—228no—
329C22×C4—224no—
330C22×C4—224no—
331C22×C4—228no—
332C22×C4—228no—
333C22×C4—224no—
334C22×C4—448no—
335C22×C4—4416no—
336C22×C4—448no—
337C22×C4—4416no—
338C4⋊C4—4416no—
339C22⋊C4—416no—
340C22⋊C4—48no—
341C22⋊C4—2232no—
342C22⋊C4—4416no—
343C22⋊C4—448no—
344C11#1433811yescharacteristic, complemented, Sylow
345C23—28no—
346C23—24no—
347C23—24no—
348C23—28no—
349C23—28no—
350C23—28no—
351C23—216no—
352C23—24no—
353C23—28no—
354C23—28no—
355C23—28no—
356C23—24no—
357C23—24no—
358C23—24no—
359C23—24no—
360C23—24no—
361C23—232no—
362C23—28no—
363C23—28no—
364C23—28no—
365C23—432no—
366C23—416no—
367C23—416no—
368C23—432no—
369C23—464no—
370C23—464no—
371C23—48no—
372C23—48no—
373C23—48no—
374C23—48no—
375C23#6693014yes—
376C23#6693118yes—
377C23C22⋊C4×D1114yes—
378C23C2×Dic11⋊C418yes—
379C23C2×Dic11⋊C414yes—
380C23#6699218yes—
381C23C22×Dic2211yescharacteristic
382C23C22×C4×D1111yescharacteristic
383C23C2×D4×D1112yes—
384C23C2×#434112yes—
385C23#6703714yes—
386C23#6703714yes—
387C23C22×C22⋊D1111yescharacteristic
388C2×C4—44no—
389C2×C4—48no—
390C2×C4—44no—
391C2×C4—44no—
392C2×C4—48no—
393C2×C4—118no—
394C2×C4—228no—
395C2×C4—228no—
396C2×C4—228no—
397C2×C4—224no—
398C2×C4—228no—
399C2×C4—4416no—
400C2×C4—4416no—
401C2×C4—448no—
402C2×C4—444no—
403C2×C4—448no—
404C2×C4—444no—
405C2×C4—444no—
406C2×C4—448no—
407C22—24no—
408C22—24no—
409C22—28no—
410C22—28no—
411C22—216no—
412C22—216no—
413C22—28no—
414C22—28no—
415C22—28no—
416C22—464no—
417C22—44no—
418C22—44no—
419C22—44no—
420C22—44no—
421C22—416no—
422C22—416no—
423C22#1062255518yes—
424C22C2×#6693011yescharacteristic
425C22C2×#6693112yes—
426C22#1062301414yes—
427C22C2×C22⋊C4×D1111yescharacteristic
428C22#1062301712yes—
429C22#1062301712yes—
430C22#1062312014yes—
431C22#1062312314yes—
432C22#1062312418yes—
433C22C22×Dic11⋊C411yescharacteristic
434C22C2×#6699212yes—
435C22#1062333514yes—
436C4—84no—
437C4—228no—
438C4—444no—
439C4—884no—
440C2—28no—
441C2—48no—
442C2C2×#1062255511yescharacteristic
443C2#1307119211yescharacteristic
444C2#1307119711yescharacteristic
445C2#1307121212yes—
446C2#1307122812yes—
447C2#1307435414yes—
448C2#1307442514yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#379C2
socle, cosocleC24×C11C24
prime radicalC26×C11C22
hypercenterC2×#379D11
hypocenterC11#14338
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
2. C2×#10622555C2semidirect
4. #13066859C2semidirect
5. #13066838C2semidirect
13. C22×C22⋊Dic11C4semidirect
17. C22×Dic11⋊C4C22semidirect
20. C2×C11⋊#95C22semidirect
21. C2×C11⋊#95C22semidirect
82. C24×C11C4⋊C4semidirect
110. C22×Dic11C22⋊C4semidirect
305. C24Dic11⋊C4semidirect
344. C11#14338semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊Dic112
C2×#106225552
C2×#106228602
#130668592
#130668382
C2×C11×#3792
#1433811