Finite Group Databasebeta

← #14718923

Subgroups — #14718923

Order 2816.

1426 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13066882C214yesmaximal, complemented
2#13066859C214yesmaximal, complemented
3#13066859C214yesmaximal, complemented
4#13066857C211yesmaximal, characteristic
5#13066857C211yesmaximal, characteristic
6C11×#1438C211yesmaximal, characteristic
7C23×D4×C11C2211yescharacteristic
8C22×C11×C22⋊C4C2212yes—
9C22×C11×C22⋊C4C2212yes—
10C22×C22⋊Dic11C2212yes—
11C22×C22⋊Dic11C2212yes—
12C22×C22⋊Dic11C2212yes—
13C22×C22⋊Dic11C2212yes—
14C22×Dic11⋊C4C2214yes—
15C2×C11×#95C2212yes—
16C2×C11⋊#95C2212yes—
17C2×C11⋊#95C2212yes—
18C2×C11⋊#95C2214yes—
19C2×C11⋊#95C2214yes—
20C2×C11⋊#95C2214yes—
21C25×C11C2311yescharacteristic
22C25×C11C2311yescharacteristic
23C22×D4×C11—42no—
24C22×D4×C11—42no—
25C22×D4×C11—42no—
26C22×D4×C11Q814yes—
27C23×C4×C11C2314yes—
28C23×C4×C11C2311yescharacteristic
29C23×Dic11C2314yes—
30C23×Dic11C2314yes—
31C2×C11×C22⋊C4—42no—
32C2×C11×C22⋊C4—44no—
33C2×C11×C22⋊C4—42no—
34C2×C11×C22⋊C4—44no—
35C2×C22⋊Dic11—28no—
36C2×C22⋊Dic11—28no—
37C2×C22⋊Dic11—42no—
38C2×C22⋊Dic11—42no—
39C2×C22⋊Dic11—42no—
40C2×C22⋊Dic11—44no—
41C2×C22⋊Dic11—42no—
42C2×C22⋊Dic11—44no—
43C2×Dic11⋊C4—28no—
44C2×Dic11⋊C4—44no—
45C2×Dic11⋊C4—44no—
46C11×#95—42no—
47C11⋊#95—42no—
48C11⋊#95—44no—
49C11⋊#95—44no—
50C11⋊#95—44no—
51C11⋊#95—42no—
52#17273—111nomaximal, Sylow
53C24×C11—24no—
54C24×C11—24no—
55C24×C11—24no—
56C24×C11—24no—
57C24×C11—22no—
58C24×C11—22no—
59C24×C11—22no—
60C24×C11—22no—
61C24×C11—22no—
62C24×C11—22no—
63C24×C11C2×Q812yes—
64C24×C11C2×Q812yes—
65C24×C11C2411yescharacteristic
66C2×D4×C11—44no—
67C2×D4×C11—44no—
68C2×D4×C11—44no—
69C2×D4×C11—416no—
70C22×C4×C11—22no—
71C22×C4×C11—22no—
72C22×C4×C11—22no—
73C22×C4×C11—24no—
74C22×C4×C11—24no—
75C22×C4×C11—24no—
76C22×C4×C11—24no—
77C22×C4×C11—24no—
78C22×C4×C11—24no—
79C22×C4×C11—24no—
80C22×C4×C11C2×Q812yes—
81C22×Dic11—24no—
82C22×Dic11—24no—
83C22×Dic11—24no—
84C22×Dic11—24no—
85C22×Dic11—24no—
86C22×Dic11—24no—
87C22×Dic11—24no—
88C22×Dic11—24no—
89C22×Dic11—24no—
90C22×Dic11—24no—
91C22×Dic11—24no—
92C22×Dic11—24no—
93C22×Dic11—24no—
94C22×Dic11#4118yes—
95C11×C22⋊C4—48no—
96C11×C22⋊C4—48no—
97C22⋊Dic11—48no—
98C22⋊Dic11—48no—
99C22⋊Dic11—48no—
100C22⋊Dic11—48no—
101Dic11⋊C4—416no—
102#1445—114no—
103#1439—114no—
104#1439—114no—
105#1438—111no—
106#1438—111no—
107#1438D1111yescharacteristic
108C23×C11—22no—
109C23×C11—22no—
110C23×C11—22no—
111C23×C11—22no—
112C23×C11—22no—
113C23×C11—22no—
114C23×C11—28no—
115C23×C11—28no—
116C23×C11—44no—
117C23×C11—44no—
118C23×C11—44no—
119C23×C11—44no—
120C23×C11—44no—
121C23×C11—44no—
122C23×C11—42no—
123C23×C11—42no—
124C23×C11—42no—
125C23×C11—42no—
126C23×C11—42no—
127C23×C11—42no—
128C23×C11—42no—
129C23×C11—42no—
130C23×C11—44no—
131C23×C11—44no—
132C23×C11—42no—
133C23×C11—42no—
134C23×C11—42no—
135C23×C11—42no—
136C23×C11C22×Q811yescharacteristic
137C23×C11C2×#4114yes—
138C23×C11H(5,𝔽2)12yes—
139C23×C11H(5,𝔽2)14yes—
140C23×C11H(5,𝔽2)12yes—
141C23×C11H(5,𝔽2)12yes—
142D4×C11—416no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—44no—
147C2×C4×C11—44no—
148C2×C4×C11—44no—
149C2×C4×C11—44no—
150C2×C4×C11—44no—
151C2×C4×C11—44no—
152C2×C4×C11—44no—
153C2×C4×C11—44no—
154C2×Dic11—28no—
155C2×Dic11—28no—
156C2×Dic11—28no—
157C2×Dic11—44no—
158C2×Dic11—44no—
159C2×Dic11—44no—
160C2×Dic11—44no—
161C2×Dic11—44no—
162C2×Dic11—44no—
163C2×Dic11—44no—
164C2×Dic11—44no—
165C2×Dic11—44no—
166C2×Dic11—44no—
167C2×Dic11—44no—
168C23×D4C2×D1111yescharacteristic
169C22×C4⋊C4—114no—
170C22×C22⋊C4—112no—
171C22×C22⋊C4—112no—
172C22×C22⋊C4—112no—
173C22×C22⋊C4—112no—
174C22×C22⋊C4C2×D1112yes—
175C22×C22⋊C4C2×D1112yes—
176C2×#95—112no—
177C2×#95—112no—
178C2×#95—114no—
179C2×#95—114no—
180C2×#95—114no—
181C2×#95C2×D1112yes—
182C22×C11—42no—
183C22×C11—42no—
184C22×C11—44no—
185C22×C11—44no—
186C22×C11—44no—
187C22×C11—44no—
188C22×C11—44no—
189C22×C11—44no—
190C22×C11—84no—
191C22×C11—84no—
192C22×C11—84no—
193C22×C11—84no—
194C22×C11#53814yes—
195C22×C11#54014yes—
196C22×C11#54014yes—
197C22×C11#54311yescharacteristic
198C22×C11#54311yescharacteristic
199C22×C11#54311yescharacteristic
200C22×C11#55112yes—
201C22×C11#55112yes—
202C22×C11#55414yes—
203C22×C11#55912yes—
204C22×C11#56012yes—
205C22×C11#56012yes—
206C22×C11#56014yes—
207C22×C11H(3,𝔽4)12yes—
208C4×C11—42no—
209C4×C11—84no—
210Dic11—48no—
211Dic11—84no—
212C25C22×D1111yescharacteristic
213C25C22×D1111yescharacteristic
214C22×D4—42no—
215C22×D4—42no—
216C22×D4—42no—
217C22×D4Dic2214yes—
218C23×C4—114no—
219C23×C4—114no—
220C23×C4C22×D1114yes—
221C23×C4C22×D1111yescharacteristic
222C2×C4⋊C4—228no—
223C2×C4⋊C4—444no—
224C2×C4⋊C4—444no—
225C2×C22⋊C4—42no—
226C2×C22⋊C4—44no—
227C2×C22⋊C4—44no—
228C2×C22⋊C4—42no—
229C2×C22⋊C4—228no—
230C2×C22⋊C4—228no—
231C2×C22⋊C4—442no—
232C2×C22⋊C4—442no—
233C2×C22⋊C4—442no—
234C2×C22⋊C4—444no—
235C2×C22⋊C4—444no—
236C2×C22⋊C4—442no—
237#95—42no—
238#95—442no—
239#95—442no—
240#95—444no—
241#95—444no—
242#95—444no—
243C2×C11—82no—
244C2×C11—82no—
245C2×C11#274812yes—
246C2×C11#274812yes—
247C2×C11#275214yes—
248C2×C11#280412yes—
249C2×C11#282814yes—
250C2×C11#284211yescharacteristic
251C24—24no—
252C24—24no—
253C24—22no—
254C24—22no—
255C24—22no—
256C24—22no—
257C24—22no—
258C24—22no—
259C24—24no—
260C24—24no—
261C24C2×Dic2212yes—
262C24C2×Dic2212yes—
263C24C23×D1111yescharacteristic
264C2×D4—44no—
265C2×D4—44no—
266C2×D4—44no—
267C2×D4—416no—
268C22×C4—22no—
269C22×C4—22no—
270C22×C4—22no—
271C22×C4—24no—
272C22×C4—24no—
273C22×C4—24no—
274C22×C4—24no—
275C22×C4—24no—
276C22×C4—24no—
277C22×C4—24no—
278C22×C4—118no—
279C22×C4—224no—
280C22×C4—224no—
281C22×C4—224no—
282C22×C4—224no—
283C22×C4—224no—
284C22×C4—224no—
285C22×C4—224no—
286C22×C4—224no—
287C22×C4—224no—
288C22×C4—224no—
289C22×C4—224no—
290C22×C4—224no—
291C22×C4—224no—
292C22×C4C2×Dic2212yes—
293C4⋊C4—4416no—
294C22⋊C4—48no—
295C22⋊C4—48no—
296C22⋊C4—448no—
297C22⋊C4—448no—
298C22⋊C4—448no—
299C22⋊C4—448no—
300C11#1727311yescharacteristic, complemented, Sylow
301C23—22no—
302C23—22no—
303C23—22no—
304C23—22no—
305C23—22no—
306C23—22no—
307C23—28no—
308C23—28no—
309C23—42no—
310C23—42no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—44no—
315C23—44no—
316C23—42no—
317C23—44no—
318C23—44no—
319C23—44no—
320C23—44no—
321C23—44no—
322C23—44no—
323C23—42no—
324C23—42no—
325C23—42no—
326C23—42no—
327C23—42no—
328C23—42no—
329C23C22×Dic2211yescharacteristic
330C23#6703712yes—
331C23#6703714yes—
332C23#6703712yes—
333C23#6703712yes—
334C23#41×D1114yes—
335D4—416no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—44no—
340C2×C4—44no—
341C2×C4—44no—
342C2×C4—44no—
343C2×C4—44no—
344C2×C4—44no—
345C2×C4—44no—
346C2×C4—44no—
347C2×C4—228no—
348C2×C4—228no—
349C2×C4—228no—
350C2×C4—444no—
351C2×C4—444no—
352C2×C4—444no—
353C2×C4—444no—
354C2×C4—444no—
355C2×C4—444no—
356C2×C4—444no—
357C2×C4—444no—
358C2×C4—444no—
359C2×C4—444no—
360C2×C4—444no—
361C22—44no—
362C22—44no—
363C22—44no—
364C22—44no—
365C22—44no—
366C22—44no—
367C22—42no—
368C22—42no—
369C22—84no—
370C22—84no—
371C22—84no—
372C22—84no—
373C22#1062301411yescharacteristic
374C22#1062301411yescharacteristic
375C22#1062301411yescharacteristic
376C22#1062307014yes—
377C22#1062312512yes—
378C22#1062312612yes—
379C22#1062312614yes—
380C22#1062314414yes—
381C22#1062314614yes—
382C22#1062314614yes—
383C22#1062319012yes—
384C22#1062319512yes—
385C22#1062321012yes—
386C22#1062325112yes—
387C4—42no—
388C4—84no—
389C4—448no—
390C4—884no—
391C2—82no—
392C2—82no—
393C2#1307582712yes—
394C2#1307582912yes—
395C2#1307588214yes—
396C2#1307655912yes—
397C2#1307673414yes—
398C2#1307688011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC11×#1438C2
prime radicalC23×D4×C11C22
hypercenter#1438D11
hypocenterC11#17273
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1438

Complements

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

NH ≅ G/Ntype
1. #13066882C2semidirect
2. #13066859C2semidirect
3. #13066859C2semidirect
300. C11#17273semidirect

Maximal subgroups

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

subgroupindex
#130668822
#130668592
#130668572
C11×#14382
#1727311