Finite Group Databasebeta

← #14663385

Subgroups — #14663385

Order 2816.

748 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 748 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071972C211yesmaximal, characteristic
2#13066954C211yesmaximal, characteristic, complemented
3#13066543C214yesmaximal, complemented
4C11×#1460C211yesmaximal, characteristic, complemented
5C23×D44C411yescharacteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66990C412yes—
8C2×#66983—21no—
9C11×#431—21no—
10#10622825C411yescharacteristic
11#10622820—21no—
12#10622604—21no—
13#10622573—21no—
14#10622568C2212yes—
15#10622552—21no—
16C11×#323—21no—
17C11×#323C2212yes—
18#10622166—21no—
19#10622163C2212yes—
20C24×D11C2×C412yes—
21C22×D4×C11C2×C411yescharacteristic
22C23×C4×C11C2×C411yescharacteristic
23C23×C4×C11D411yescharacteristic
24C22×C22⋊D11—22no—
25C22×D44—21no—
26C22×D44—21no—
27C22×D44—44no—
28C22×D44—41no—
29C22×D44—41no—
30C4×D4×C11—41no—
31C4×D4×C11—41no—
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C22⋊C4D411yescharacteristic
34C2×C11×C22⋊C4C2311yescharacteristic
35C2×C42×C11D411yescharacteristic
36C2×C22⋊Dic11C2×C412yes—
37#66990—44no—
38#66983—44no—
39C2×(C2×D11)⋊C4—22no—
40C2×(C2×D11)⋊C4—22no—
41C2×(C2×D11)⋊C4—22no—
42C2×C4⋊Dic11—21no—
43C2×#4318—41no—
44C11×C4⋊C8—41no—
45C11×C22⋊C8—22no—
46C4×C8×C11—41no—
47C11⋊#95—21no—
48C22⋊(C11⋊C8)—22no—
49C22⋊(C11⋊C8)—41no—
50#11561—111nomaximal, Sylow
51C24×C11C22⋊C411yescharacteristic
52C24×C11C22×C411yescharacteristic
53C23×D11—22no—
54C23×D11—24no—
55C23×D11—44no—
56C23×D11—42no—
57C23×D11—42no—
58C23×D11—82no—
59C2×D4×C11—22no—
60C2×D4×C11—22no—
61C2×D4×C11—41no—
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—42no—
67C22×C4×C11—42no—
68C22×C4×C11C22⋊C411yescharacteristic
69C22×C4×C11C22⋊C411yescharacteristic
70C22×C4×C11C22⋊C411yescharacteristic
71C22×C4×C11C2×D411yescharacteristic
72C22×C4×C11C2×D411yescharacteristic
73C2×C22⋊D11—44no—
74C2×C22⋊D11—44no—
75C2×C22⋊D11—82no—
76C22×Dic11—22no—
77C2×D44—24no—
78C2×D44—42no—
79C2×D44—42no—
80C2×D44—44no—
81C2×D44—44no—
82C2×D44—48no—
83C2×D44—44no—
84C2×D44—41no—
85C2×D44—41no—
86C2×C8×C11—42no—
87C11×C4⋊C4—41no—
88C11×C22⋊C4—41no—
89C11×C22⋊C4—41no—
90C42×C11—21no—
91C42×C11—21no—
92C22⋊Dic11—42no—
93(C2×D11)⋊C4—44no—
94(C2×D11)⋊C4—44no—
95(C2×D11)⋊C4—82no—
96C4⋊Dic11—42no—
97#4318—82no—
98C2×C11⋊C8—42no—
99#2408—111no—
100#1465—111no—
101#1460D1111yescharacteristic, complemented
102#1316—114no—
103C23×C11—21no—
104C23×C11—21no—
105C23×C11—21no—
106C23×C11—21no—
107C23×C11—21no—
108C23×C11—41no—
109C23×C11—41no—
110C23×C11—41no—
111C23×C11—41no—
112C23×C11C2×C22⋊C411yescharacteristic
113C23×C11#13112yes—
114C22×D11—24no—
115C22×D11—42no—
116C22×D11—42no—
117C22×D11—42no—
118C22×D11—44no—
119C22×D11—42no—
120C22×D11—42no—
121C22×D11—42no—
122C22×D11—44no—
123C22×D11—88no—
124C22×D11—88no—
125C22×D11—84no—
126C22×D11—84no—
127D4×C11—44no—
128C2×C4×C11—21no—
129C2×C4×C11—21no—
130C2×C4×C11—22no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—42no—
135C2×C4×C11—42no—
136C2×C4×C11—42no—
137C2×C4×C11—41no—
138C2×C4×C11—41no—
139C2×C4×C11—41no—
140C2×C4×C11—81no—
141C2×C4×C11#9911yescharacteristic
142C2×C4×C11#9911yescharacteristic
143C2×C4×C11#10012yes—
144C22⋊D11—88no—
145C2×Dic11—42no—
146C2×Dic11—42no—
147C2×Dic11—42no—
148D44—44no—
149D44—48no—
150D44—44no—
151C8×C11—82no—
152C11⋊C8—82no—
153C23×D4—111no—
154C2×#121—221no—
155C2×#120—112no—
156C2×C4×D4C2×D1111yescharacteristic
157#431—21no—
158#407—221no—
159#394—221no—
160#392—221no—
161#390—221no—
162#380—111no—
163#379—112no—
164#324—221no—
165#323—21no—
166#323—112no—
167#323C2×D1112yes—
168C22×C11—21no—
169C22×C11—21no—
170C22×C11—22no—
171C22×C11—42no—
172C22×C11—42no—
173C22×C11—42no—
174C22×C11—41no—
175C22×C11—41no—
176C22×C11—41no—
177C22×C11—41no—
178C22×C11—41no—
179C22×C11—81no—
180C22×C11#40811yescharacteristic
181C22×C11C2×#9911yescharacteristic
182C22×C11C2×#10011yescharacteristic
183C2×D11—44no—
184C2×D11—44no—
185C2×D11—44no—
186C2×D11—82no—
187C2×D11—82no—
188C2×D11—88no—
189C2×D11—82no—
190C2×D11—82no—
191C2×D11—88no—
192C4×C11—21no—
193C4×C11—22no—
194C4×C11—41no—
195C4×C11—41no—
196C4×C11—41no—
197C4×C11AΣL(1,𝔽16)12yes—
198Dic11—82no—
199C25—112no—
200C22×D4—222no—
201C22×D4—221no—
202C22×D4—221no—
203C22×D4—441no—
204C22×D4—441no—
205C22×D4—444no—
206C22×D4C4×D1111yescharacteristic
207C23×C4C4×D1111yescharacteristic
208C23×C4D4411yescharacteristic
209C2×M16—441no—
210#121—444no—
211#120—444no—
212C4×D4—41no—
213C4×D4—41no—
214C2×C4⋊C4—221no—
215C2×C4⋊C4D4411yescharacteristic
216C2×C22⋊C4—112no—
217C2×C22⋊C4—222no—
218C2×C22⋊C4—222no—
219C2×C22⋊C4—222no—
220C2×C22⋊C4C22⋊D1111yescharacteristic
221C2×C22⋊C4C22×D1111yescharacteristic
222C2×C42C22⋊D1111yescharacteristic
223C4⋊C8—41no—
224C22⋊C8—22no—
225C22⋊C8—222no—
226C22⋊C8—441no—
227C4×C8—41no—
228#95—221no—
229C2×C11—21no—
230C2×C11—21no—
231C2×C11—42no—
232C2×C11—81no—
233C2×C11#147111yescharacteristic
234C2×C11C2×AΣL(1,𝔽16)11yescharacteristic
235C2×C11#212211yescharacteristic
236D11—84no—
237C24—222no—
238C24—224no—
239C24—442no—
240C24—442no—
241C24—444no—
242C24—882no—
243C24(C2×D11)⋊C411yescharacteristic
244C24C2×C4×D1111yescharacteristic
245C2×D4—22no—
246C2×D4—22no—
247C2×D4—41no—
248C2×D4—224no—
249C2×D4—442no—
250C2×D4—442no—
251C2×D4—444no—
252C2×D4—448no—
253C2×D4—444no—
254C2×D4—444no—
255C2×D4—444no—
256C2×D4—444no—
257C2×D4—441no—
258C2×D4—441no—
259C2×D4—882no—
260C22×C4—21no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—21no—
264C22×C4—42no—
265C22×C4—42no—
266C22×C4—222no—
267C22×C4(C2×D11)⋊C411yescharacteristic
268C22×C4(C2×D11)⋊C411yescharacteristic
269C22×C4(C2×D11)⋊C411yescharacteristic
270C22×C4C2×D4411yescharacteristic
271C22×C4C2×C22⋊D1111yescharacteristic
272M16—882no—
273C2×C8—42no—
274C2×C8—442no—
275C4⋊C4—41no—
276C4⋊C4—442no—
277C22⋊C4—41no—
278C22⋊C4—41no—
279C22⋊C4—444no—
280C22⋊C4—444no—
281C22⋊C4—442no—
282C22⋊C4—882no—
283C42—21no—
284C42—21no—
285C11#1156111yescharacteristic, complemented, Sylow
286C23—21no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23—41no—
292C23—41no—
293C23—41no—
294C23—41no—
295C23—224no—
296C23—442no—
297C23—442no—
298C23—442no—
299C23—444no—
300C23—444no—
301C23—442no—
302C23—442no—
303C23—442no—
304C23—884no—
305C23—888no—
306C23—888no—
307C23—884no—
308C23#6695412yes—
309C23C2×(C2×D11)⋊C411yescharacteristic
310D4—44no—
311D4—444no—
312D4—448no—
313D4—444no—
314D4—888no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—22no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—42no—
323C2×C4—42no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4—41no—
327C2×C4—81no—
328C2×C4—442no—
329C2×C4—442no—
330C2×C4—442no—
331C2×C4#6687011yescharacteristic
332C2×C4#6687011yescharacteristic
333C2×C4#6688712yes—
334C8—82no—
335C8—882no—
336C22—21no—
337C22—21no—
338C22—22no—
339C22—42no—
340C22—42no—
341C22—42no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—81no—
348C22—444no—
349C22—444no—
350C22—444no—
351C22—882no—
352C22—882no—
353C22—888no—
354C22—888no—
355C22—882no—
356C22—882no—
357C22C2×#6687011yescharacteristic
358C22#1062272311yescharacteristic
359C22C2×#6688711yescharacteristic
360C4—21no—
361C4—22no—
362C4—41no—
363C4—41no—
364C4—41no—
365C4—882no—
366C4#1062211312yes—
367C2—21no—
368C2—21no—
369C2—42no—
370C2—81no—
371C2—884no—
372C2#1306697511yescharacteristic
373C2C2×#1062211311yescharacteristic
374C2#1307026511yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC24×C11C22×C4
FrattiniC2×C22⋊C4C22×D11
FittingC11×#1460C2
socleC22×C11C2×#99
prime radical#13071972C2
cosocleC2×C11×C22⋊C4C23
hypercenter#1460D11
hypocenterC11#11561
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×D4 ◁ #1460

Complements

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

NH ≅ G/Ntype
2. #13066954C2semidirect
3. #13066543C2semidirect
4. C11×#1460C2semidirect
101. #1460D11semidirect
285. C11#11561semidirect

Maximal subgroups

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

subgroupindex
#130719722
#130669542
#130665432
C11×#14602
#1156111