Finite Group Databasebeta

← #14664295

Subgroups — #14664295

Order 2816.

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

normal subgroups only

This group has 488 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#13074096C211yesmaximal, characteristic
2C2×#10622168C211yesmaximal, characteristic, complemented
3#13066644C212yesmaximal, complemented
4#13066620C212yesmaximal, complemented
5C11×#1463C211yesmaximal, characteristic, complemented
6C22×C11×C4⋊C4C2211yescharacteristic
7C2×#66983C411yescharacteristic
8C22×#4318—21no—
9C11×#407—21no—
10#10622826—21no—
11#10622826—21no—
12C4×C22⋊Dic11C411yescharacteristic
13#10622604C411yescharacteristic
14#10622604C2211yescharacteristic
15#10622603—21no—
16#10622603—21no—
17#10622599C411yescharacteristic
18#10622599C2211yescharacteristic
19C11×#324—21no—
20C11×#324C2212yes—
21#10622168—21no—
22#10622168C2212yes—
23C23×C4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11D411yescharacteristic
26C22×C22⋊D11—21no—
27C22×D44C2×C411yescharacteristic
28C2×C11×M16—41no—
29C2×C11×C4⋊C4—41no—
30C2×C11×C4⋊C4—41no—
31C2×C11×C4⋊C4C2×C411yescharacteristic
32C2×C11×C4⋊C4D411yescharacteristic
33C2×C11×C4⋊C4D411yescharacteristic
34C2×C11×C4⋊C4C2311yescharacteristic
35C2×C22⋊Dic11—21no—
36#66983—41no—
37#66983—41no—
38C2×(C2×D11)⋊C4—21no—
39C2×(C2×D11)⋊C4—21no—
40C2×(C2×D11)⋊C4—21no—
41C2×(C2×D11)⋊C4—21no—
42C2×(C2×D11)⋊C4—21no—
43C2×C4⋊Dic11C2×C411yescharacteristic
44C2×C4×Dic11—21no—
45C2×#4318—24no—
46C2×#4318—22no—
47C2×#4318—41no—
48C2×#4318—42no—
49C22×C11⋊C8—41no—
50C11×C22⋊C8—22no—
51C11×C22⋊C8—41no—
52C11⋊#95—21no—
53C11⋊#95—21no—
54C11⋊#95—21no—
55C11⋊#95—21no—
56C11⋊#95C2×C411yescharacteristic
57C11⋊#95C2×C411yescharacteristic
58#11766—111nomaximal, Sylow
59C24×C11C22⋊C411yescharacteristic
60C23×D11—21no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—22no—
64C22×C4×C11—21no—
65C22×C4×C11—21no—
66C22×C4×C11—21no—
67C22×C4×C11—21no—
68C22×C4×C11—21no—
69C22×C4×C11—21no—
70C22×C4×C11—81no—
71C22×C4×C11—81no—
72C22×C4×C11C22⋊C411yescharacteristic
73C22×C4×C11C22⋊C411yescharacteristic
74C22×C4×C11C22⋊C411yescharacteristic
75C22×C4×C11C22×C411yescharacteristic
76C22×C4×C11C2×D411yescharacteristic
77C22×C4×C11C2×D411yescharacteristic
78C2×C22⋊D11—42no—
79C2×C22⋊D11—42no—
80C2×C22⋊D11—41no—
81C2×C22⋊D11—41no—
82C22×Dic11—21no—
83C22×Dic11—21no—
84C22×Dic11—21no—
85C2×D44—41no—
86C2×D44—81no—
87C11×M16—82no—
88C2×C8×C11—42no—
89C11×C4⋊C4—41no—
90C11×C4⋊C4—41no—
91C11×C4⋊C4—41no—
92C11×C4⋊C4—41no—
93C22⋊Dic11—42no—
94(C2×D11)⋊C4—42no—
95(C2×D11)⋊C4—42no—
96(C2×D11)⋊C4—41no—
97(C2×D11)⋊C4—41no—
98(C2×D11)⋊C4—81no—
99(C2×D11)⋊C4—81no—
100C4⋊Dic11—41no—
101C4×Dic11—81no—
102#4318—24no—
103#4318—44no—
104#4318—42no—
105C2×C11⋊C8—44no—
106C2×C11⋊C8—42no—
107#2591—111no—
108C2×#343—111no—
109#1463D1111yescharacteristic, complemented
110#1353—112no—
111#1345—112no—
112C23×C11—22no—
113C23×C11—21no—
114C23×C11—21no—
115C23×C11—41no—
116C23×C11#9911yescharacteristic
117C23×C11#9911yescharacteristic
118C23×C11C2×C22⋊C411yescharacteristic
119C22×D11—41no—
120C22×D11—41no—
121C22×D11—41no—
122C22×D11—41no—
123C22×D11—41no—
124C22×D11—41no—
125C22×D11—41no—
126C2×C4×C11—22no—
127C2×C4×C11—22no—
128C2×C4×C11—22no—
129C2×C4×C11—22no—
130C2×C4×C11—21no—
131C2×C4×C11—21no—
132C2×C4×C11—21no—
133C2×C4×C11—21no—
134C2×C4×C11—21no—
135C2×C4×C11—21no—
136C2×C4×C11—21no—
137C2×C4×C11—21no—
138C2×C4×C11—42no—
139C2×C4×C11—41no—
140C2×C4×C11—41no—
141C2×C4×C11—41no—
142C2×C4×C11—41no—
143C2×C4×C11—81no—
144C2×C4×C11—81no—
145C2×C4×C11—81no—
146C2×C4×C11#10412yes—
147C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
148C2×C4×C11#13711yescharacteristic
149C22⋊D11—82no—
150C22⋊D11—82no—
151C2×Dic11—41no—
152C2×Dic11—41no—
153C2×Dic11—41no—
154C2×Dic11—41no—
155C2×Dic11—41no—
156C2×Dic11—41no—
157C2×Dic11—41no—
158C2×Dic11—41no—
159C2×Dic11—41no—
160D44—82no—
161C8×C11—82no—
162C11⋊C8—44no—
163C22×M16—221no—
164C2×#121—111no—
165C22×C4⋊C4C2×D1111yescharacteristic
166#407—21no—
167#400—111no—
168#400—111no—
169#394—111no—
170#394—111no—
171#388—221no—
172#388—221no—
173#386—221no—
174#386—221no—
175C4×C22⋊C4—111no—
176#343—112no—
177#343—221no—
178#324—21no—
179#324C2×D1112yes—
180C22×C11—21no—
181C22×C11—21no—
182C22×C11—21no—
183C22×C11—21no—
184C22×C11—21no—
185C22×C11—21no—
186C22×C11—21no—
187C22×C11—42no—
188C22×C11—42no—
189C22×C11#35512yes—
190C22×C11C2×#9911yescharacteristic
191C22×C11#41711yescharacteristic
192C22×C11C2×#10411yescharacteristic
193C2×D11—81no—
194C2×D11—81no—
195C2×D11—81no—
196C2×D11—81no—
197C2×D11—81no—
198C2×D11—81no—
199C2×D11—81no—
200C4×C11—22no—
201C4×C11—21no—
202C4×C11—21no—
203C4×C11—41no—
204C4×C11—41no—
205C4×C11—41no—
206C4×C11—41no—
207Dic11—81no—
208Dic11—81no—
209Dic11—81no—
210C22×D4—111no—
211C22×D4—221no—
212C23×C4C4×D1111yescharacteristic
213C23×C4D4411yescharacteristic
214C23×C4C22⋊D1111yescharacteristic
215C2×M16—41no—
216C2×M16—224no—
217C2×M16—222no—
218C2×M16—441no—
219C2×M16—442no—
220C22×C8—441no—
221#121—441no—
222#121—441no—
223C2×C4⋊C4—41no—
224C2×C4⋊C4—41no—
225C2×C4⋊C4—111no—
226C2×C4⋊C4C4×D1111yescharacteristic
227C2×C4⋊C4D4411yescharacteristic
228C2×C4⋊C4C22⋊D1111yescharacteristic
229C2×C4⋊C4C22×D1111yescharacteristic
230C2×C22⋊C4—221no—
231C2×C22⋊C4—221no—
232C2×C22⋊C4—221no—
233C2×C22⋊C4—221no—
234C2×C22⋊C4—221no—
235C2×C22⋊C4—221no—
236C2×C42—221no—
237C22⋊C8—22no—
238C22⋊C8—41no—
239#95—111no—
240#95—111no—
241#95—221no—
242#95—221no—
243#95—221no—
244#95—221no—
245C2×C11—21no—
246C2×C11—21no—
247C2×C11—22no—
248C2×C11—41no—
249C2×C11#150411yescharacteristic
250C2×C11#212111yescharacteristic
251C2×C11C2×#35511yescharacteristic
252D11—161no—
253C24—221no—
254C24(C2×D11)⋊C411yescharacteristic
255C2×D4—441no—
256C2×D4—442no—
257C2×D4—442no—
258C2×D4—441no—
259C2×D4—441no—
260C2×D4—881no—
261C22×C4—21no—
262C22×C4—21no—
263C22×C4—22no—
264C22×C4—21no—
265C22×C4—21no—
266C22×C4—21no—
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—21no—
270C22×C4—81no—
271C22×C4—81no—
272C22×C4—221no—
273C22×C4—221no—
274C22×C4—221no—
275C22×C4(C2×D11)⋊C411yescharacteristic
276C22×C4(C2×D11)⋊C411yescharacteristic
277C22×C4(C2×D11)⋊C411yescharacteristic
278C22×C4C2×C4×D1111yescharacteristic
279C22×C4C2×D4411yescharacteristic
280C22×C4C2×C22⋊D1111yescharacteristic
281M16—82no—
282M16—224no—
283M16—444no—
284M16—442no—
285C2×C8—42no—
286C2×C8—444no—
287C2×C8—442no—
288C4⋊C4—41no—
289C4⋊C4—41no—
290C4⋊C4—41no—
291C4⋊C4—41no—
292C4⋊C4—441no—
293C22⋊C4—442no—
294C22⋊C4—442no—
295C22⋊C4—442no—
296C22⋊C4—441no—
297C22⋊C4—441no—
298C22⋊C4—881no—
299C22⋊C4—881no—
300C42—881no—
301C11#1176611yescharacteristic, complemented, Sylow
302C23—21no—
303C23—21no—
304C23—22no—
305C23—41no—
306C23—441no—
307C23—441no—
308C23—441no—
309C23—441no—
310C23—441no—
311C23—441no—
312C23—441no—
313C23#6687011yescharacteristic
314C23#6687011yescharacteristic
315C23C2×(C2×D11)⋊C411yescharacteristic
316D4—882no—
317D4—882no—
318D4—882no—
319C2×C4—22no—
320C2×C4—22no—
321C2×C4—22no—
322C2×C4—22no—
323C2×C4—21no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—42no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—441no—
340C2×C4—441no—
341C2×C4—441no—
342C2×C4—441no—
343C2×C4—441no—
344C2×C4—441no—
345C2×C4—441no—
346C2×C4—441no—
347C2×C4—441no—
348C2×C4#6688912yes—
349C2×C4#6696111yescharacteristic
350C2×C4#6696211yescharacteristic
351C8—82no—
352C8—444no—
353C22—21no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—21no—
359C22—21no—
360C22—42no—
361C22—42no—
362C22—881no—
363C22—881no—
364C22—881no—
365C22—881no—
366C22—881no—
367C22—881no—
368C22—881no—
369C22#1062211512yes—
370C22C2×#6687011yescharacteristic
371C22#1062274611yescharacteristic
372C22C2×#6688911yescharacteristic
373C4—21no—
374C4—22no—
375C4—21no—
376C4—41no—
377C4—41no—
378C4—41no—
379C4—41no—
380C4—881no—
381C4—881no—
382C4—881no—
383C2—21no—
384C2—21no—
385C2—22no—
386C2—41no—
387C2—1761no—
388C2#1306712111yescharacteristic
389C2#1307026011yescharacteristic
390C2C2×#1062211511yescharacteristic
subgroupG/H
centerC22C2×#66870
commutatorC22×C4×C11C22×C4
FrattiniC2×C4⋊C4C22×D11
FittingC11×#1463C2
socleC22×C11C2×#99
prime radicalC2×#66983C4
cosocleC2×C11×C4⋊C4C23
hypercenter#1463D11
hypocenterC11#11766
LCSG ▷ C22×C4×C11 ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C24 ◁ C22×C4⋊C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
2. C2×#10622168C2semidirect
3. #13066644C2semidirect
4. #13066620C2semidirect
5. C11×#1463C2semidirect
109. #1463D11semidirect
301. C11#11766semidirect

Maximal subgroups

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

subgroupindex
#130740962
C2×#106221682
#130666442
#130666202
C11×#14632
#1176611