Finite Group Databasebeta

← #14651730

Subgroups — #14651730

Order 2816.

544 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 103 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#13077645C211yesmaximal, characteristic
2#13072924C211yesmaximal, characteristic
3#13068694C212yesmaximal, complemented
4#13066523C212yesmaximal, complemented
5C11×#1465C211yesmaximal, characteristic
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66988C412yes—
8C22×C4⋊Dic11C2211yescharacteristic
9C11×#407C2212yes—
10#10622825—21no—
11#10622825C2211yescharacteristic
12#10622820C2212yes—
13C2×C22⋊(C11⋊C8)—21no—
14#10622624—24no—
15#10622596—21no—
16#10622566—21no—
17#10622556C412yes—
18#10622541—21no—
19#10622539—21no—
20C11×#324—21no—
21C11×#323—21no—
22#10622192—24no—
23C22×D4×C11C2×C411yescharacteristic
24C23×C4×C11D411yescharacteristic
25C23×C4×C11C2311yescharacteristic
26C23×Dic11C2×C412yes—
27C2×C11×M16—22no—
28C4×D4×C11—22no—
29C4×D4×C11—22no—
30C2×C11×C4⋊C4D411yescharacteristic
31C2×C11×C22⋊C4C2×C411yescharacteristic
32C2×C11×C22⋊C4D411yescharacteristic
33C2×C42×C11D411yescharacteristic
34C2×C22⋊Dic11—22no—
35C2×C22⋊Dic11C2×C412yes—
36#66988—44no—
37C2×C4⋊Dic11—21no—
38C2×C4⋊Dic11—21no—
39C2×C4⋊Dic11—21no—
40C2×C4⋊Dic11—22no—
41C2×C4⋊Dic11—22no—
42C2×Dic11⋊C4—22no—
43C2×#4318D414yes—
44C22×C11⋊C8—22no—
45C11×C22⋊C8—22no—
46C11×C22⋊C8—22no—
47C11⋊#95—22no—
48C11⋊#95—22no—
49C11⋊#95—21no—
50C22⋊(C11⋊C8)—22no—
51C22⋊(C11⋊C8)—22no—
52C22⋊(C11⋊C8)—22no—
53C4⋊(C11⋊C8)—22no—
54#66867—22no—
55#9507—111nomaximal, Sylow
56C24×C11C22⋊C411yescharacteristic
57C24×C11C22×C411yescharacteristic
58C2×D4×C11—22no—
59C2×D4×C11—22no—
60C2×D4×C11—41no—
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11—42no—
64C22×C4×C11—42no—
65C22×C4×C11C22⋊C411yescharacteristic
66C22×C4×C11C22⋊C411yescharacteristic
67C22×C4×C11C22⋊C411yescharacteristic
68C22×C4×C11C2×D412yes—
69C22×C4×C11C2×D411yescharacteristic
70C22×C4×C11C2×D411yescharacteristic
71C22×C4×C11#4112yes—
72C22×Dic11—22no—
73C22×Dic11—22no—
74C22×Dic11—24no—
75C22×Dic11—42no—
76C22×Dic11—42no—
77C11×M16—44no—
78C2×C8×C11—42no—
79C11×C4⋊C4—22no—
80C11×C22⋊C4—22no—
81C11×C22⋊C4—22no—
82C42×C11—21no—
83C42×C11—21no—
84C22⋊Dic11—42no—
85C22⋊Dic11—44no—
86C4⋊Dic11—42no—
87C4⋊Dic11—41no—
88C4⋊Dic11—42no—
89C4⋊Dic11—41no—
90Dic11⋊C4—44no—
91#4318—44no—
92C2×C11⋊C8—24no—
93C2×C11⋊C8—82no—
94#2973—111no—
95#2486—111no—
96#1821—112no—
97#1465D1111yescharacteristic
98#1305—112no—
99C23×C11—21no—
100C23×C11—21no—
101C23×C11—21no—
102C23×C11—21no—
103C23×C11—41no—
104C23×C11—41no—
105C23×C11—41no—
106C23×C11—41no—
107C23×C11#10012yes—
108C23×C11C2×C22⋊C411yescharacteristic
109C23×C11C4×D412yes—
110D4×C11—44no—
111C2×C4×C11—24no—
112C2×C4×C11—22no—
113C2×C4×C11—21no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—21no—
118C2×C4×C11—41no—
119C2×C4×C11—42no—
120C2×C4×C11—42no—
121C2×C4×C11—41no—
122C2×C4×C11—41no—
123C2×C4×C11—81no—
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11#12112yes—
126C2×C4×C11#12311yescharacteristic
127C2×Dic11—42no—
128C2×Dic11—42no—
129C2×Dic11—42no—
130C2×Dic11—42no—
131C2×Dic11—42no—
132C2×Dic11—42no—
133C2×Dic11—84no—
134C8×C11—82no—
135C11⋊C8—44no—
136C2×#123—112no—
137C2×C4×D4C2×D1111yescharacteristic
138C22×C4⋊C4—111no—
139#435—224no—
140#432—221no—
141#407—112no—
142#407C2×D1112yes—
143C2×C22⋊C8—221no—
144#398—221no—
145#397—221no—
146#389—221no—
147#381—112no—
148#380—111no—
149#380—221no—
150#343—224no—
151#324—21no—
152#323—21no—
153C22×C11—21no—
154C22×C11—21no—
155C22×C11—22no—
156C22×C11—22no—
157C22×C11—22no—
158C22×C11—22no—
159C22×C11—42no—
160C22×C11—42no—
161C22×C11—42no—
162C22×C11—41no—
163C22×C11—41no—
164C22×C11—81no—
165C22×C11#38611yescharacteristic
166C22×C11C2×#10011yescharacteristic
167C22×C11#41311yescharacteristic
168C4×C11—21no—
169C4×C11—22no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11—41no—
173C4×C11#45812yes—
174Dic11—82no—
175Dic11—82no—
176C22×D4C4×D1111yescharacteristic
177C23×C4—112no—
178C23×C4D4411yescharacteristic
179C23×C4C22×D1111yescharacteristic
180C2×M16—22no—
181C2×M16—114no—
182C22×C8—222no—
183#123—444no—
184C4×D4—22no—
185C4×D4—22no—
186C2×C4⋊C4—222no—
187C2×C4⋊C4—221no—
188C2×C4⋊C4—221no—
189C2×C4⋊C4—222no—
190C2×C4⋊C4—222no—
191C2×C4⋊C4—221no—
192C2×C4⋊C4C22⋊D1111yescharacteristic
193C2×C22⋊C4—112no—
194C2×C22⋊C4—222no—
195C2×C22⋊C4C4×D1111yescharacteristic
196C2×C22⋊C4C22⋊D1111yescharacteristic
197C2×C42D4411yescharacteristic
198C4⋊C8—222no—
199C22⋊C8—22no—
200C22⋊C8—22no—
201C22⋊C8—222no—
202C22⋊C8—222no—
203C22⋊C8—222no—
204#97—222no—
205#95—222no—
206#95—222no—
207#95—221no—
208C2×C11—21no—
209C2×C11—21no—
210C2×C11—42no—
211C2×C11—42no—
212C2×C11#189011yescharacteristic
213C2×C11#190011yescharacteristic
214C2×C11#191511yescharacteristic
215C24(C2×D11)⋊C411yescharacteristic
216C24C2×C4×D1111yescharacteristic
217C2×D4—22no—
218C2×D4—22no—
219C2×D4—41no—
220C22×C4—21no—
221C22×C4—21no—
222C22×C4—42no—
223C22×C4—42no—
224C22×C4—222no—
225C22×C4—222no—
226C22×C4—224no—
227C22×C4—442no—
228C22×C4—442no—
229C22×C4(C2×D11)⋊C411yescharacteristic
230C22×C4(C2×D11)⋊C411yescharacteristic
231C22×C4(C2×D11)⋊C411yescharacteristic
232C22×C4C2×D4411yescharacteristic
233C22×C4D4×D1112yes—
234C22×C4#434112yes—
235C22×C4C2×C22⋊D1111yescharacteristic
236M16—44no—
237M16—444no—
238C2×C8—42no—
239C2×C8—224no—
240C2×C8—882no—
241C4⋊C4—22no—
242C4⋊C4—444no—
243C4⋊C4—442no—
244C4⋊C4—441no—
245C4⋊C4—441no—
246C4⋊C4—442no—
247C22⋊C4—22no—
248C22⋊C4—22no—
249C22⋊C4—444no—
250C22⋊C4—442no—
251C42—21no—
252C42—21no—
253C11#950711yescharacteristic, complemented, Sylow
254C23—21no—
255C23—21no—
256C23—21no—
257C23—21no—
258C23—41no—
259C23—41no—
260C23—41no—
261C23—41no—
262C23#6688712yes—
263C23(C22⋊D11)⋊C412yes—
264C23C2×(C2×D11)⋊C411yescharacteristic
265D4—44no—
266C2×C4—22no—
267C2×C4—24no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—21no—
272C2×C4—21no—
273C2×C4—42no—
274C2×C4—41no—
275C2×C4—42no—
276C2×C4—41no—
277C2×C4—41no—
278C2×C4—81no—
279C2×C4—442no—
280C2×C4—442no—
281C2×C4—442no—
282C2×C4—442no—
283C2×C4—442no—
284C2×C4—442no—
285C2×C4—884no—
286C2×C4#6693511yescharacteristic
287C2×C4#6693911yescharacteristic
288C2×C4#6699212yes—
289C8—82no—
290C8—444no—
291C22—21no—
292C22—21no—
293C22—22no—
294C22—22no—
295C22—22no—
296C22—22no—
297C22—42no—
298C22—42no—
299C22—42no—
300C22—41no—
301C22—41no—
302C22—81no—
303C22#1062257111yescharacteristic
304C22C2×#6688711yescharacteristic
305C22#1062274511yescharacteristic
306C4—22no—
307C4—21no—
308C4—41no—
309C4—41no—
310C4—41no—
311C4—882no—
312C4—882no—
313C4#1062235512yes—
314C2—21no—
315C2—21no—
316C2—42no—
317C2—42no—
318C2#1306902711yescharacteristic
319C2#1306907711yescharacteristic
320C2#1306916611yescharacteristic
subgroupG/H
centerC22#10622571
commutatorC24×C11C22×C4
FrattiniC23×C4C22×D11
FittingC11×#1465C2
socleC22×C11#386
prime radicalC22×D4×C11C2×C4
cosocleC23×C4×C11C23
hypercenter#1465D11
hypocenterC11#9507
LCSG ▷ C24×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1465

Complements

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

NH ≅ G/Ntype
3. #13068694C2semidirect
4. #13066523C2semidirect
253. C11#9507semidirect

Maximal subgroups

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

subgroupindex
#130776452
#130729242
#130686942
#130665232
C11×#14652
#950711