Finite Group Databasebeta

← #14651642

Subgroups — #14651642

Order 2816.

602 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 115 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#13073513C211yesmaximal, characteristic
2#13068608C211yesmaximal, characteristic, complemented
3#13067042C212yesmaximal, complemented
4#13066475C212yesmaximal, complemented
5C11×#2975C211yesmaximal, characteristic, complemented
6C2×C4×D4×C11C2211yescharacteristic
7C2×#66991—21no—
8C2×C4×D44C2211yescharacteristic
9C11×#436—24no—
10C11×#431C2212yes—
11C11×#407—22no—
12C2×#66897—21no—
13#10622826—22no—
14#10622600—21no—
15#10622573C412yes—
16#10622566C412yes—
17#10622549C2211yescharacteristic
18#10622537C2212yes—
19#10622168—21no—
20#10622097—24no—
21C22×D4×C11D411yescharacteristic
22C23×C4×C11D412yes—
23C22×C22⋊D11—22no—
24C22×D44C2×C411yescharacteristic
25C22×C4×D11—21no—
26C2×C11×M16—24no—
27C4×D4×C11—22no—
28C4×D4×C11—22no—
29C2×C11×C4⋊C4D411yescharacteristic
30C2×C11×C22⋊C4C2×C412yes—
31C2×C42×C11C2311yescharacteristic
32C2×C22⋊Dic11—22no—
33#66991—44no—
34C2×(C2×D11)⋊C4—21no—
35C2×(C2×D11)⋊C4—22no—
36C2×C4⋊Dic11—21no—
37C2×C4⋊Dic11C2×C411yescharacteristic
38C2×#4318—22no—
39C4×D44—22no—
40C4×D44—22no—
41C11×C4⋊C8—22no—
42C11×C22⋊C8—24no—
43C11×C22⋊C8—22no—
44C4×C8×C11D414yescomplemented
45#66897—42no—
46C11⋊#95—22no—
47C11⋊#95—21no—
48C11⋊#95C2×C412yes—
49C4⋊(C11⋊C8)—22no—
50C4⋊(C11⋊C8)—22no—
51#9489—111nomaximal, Sylow
52C24×C11C22⋊C412yes—
53C23×D11—21no—
54C2×D4×C11—22no—
55C2×D4×C11—21no—
56C2×D4×C11—22no—
57C2×D4×C11—21no—
58C22×C4×C11—22no—
59C22×C4×C11—22no—
60C22×C4×C11—82no—
61C22×C4×C11C22⋊C412yes—
62C22×C4×C11C22×C411yescharacteristic
63C22×C4×C11C2×D411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C2×C22⋊D11—44no—
66C2×C22⋊D11—44no—
67C2×C22⋊D11—82no—
68C22×Dic11—22no—
69C22×Dic11—21no—
70C2×D44—22no—
71C2×D44—42no—
72C2×C4×D11—42no—
73C2×C4×D11—42no—
74C2×C4×D11—41no—
75C2×C4×D11—41no—
76C11×M16—84no—
77C2×C8×C11—24no—
78C11×C4⋊C4—22no—
79C11×C22⋊C4—24no—
80C42×C11C2×D412yes—
81C42×C11#4112yes—
82C22⋊Dic11—44no—
83(C2×D11)⋊C4—41no—
84(C2×D11)⋊C4—41no—
85(C2×D11)⋊C4—82no—
86C4⋊Dic11—22no—
87C4⋊Dic11—42no—
88#4318—42no—
89#4318—42no—
90C2×C11⋊C8—42no—
91#2975D1111yescharacteristic, complemented
92#2535—111no—
93#1800—111no—
94#1486—112no—
95#1286—112no—
96C23×C11—22no—
97C23×C11—22no—
98C23×C11—22no—
99C23×C11—42no—
100C23×C11—42no—
101C23×C11C2×C22⋊C411yescharacteristic
102C22×D11—22no—
103C22×D11—41no—
104C22×D11—41no—
105C22×D11—41no—
106C22×D11—41no—
107C22×D11—41no—
108C22×D11—41no—
109D4×C11—42no—
110D4×C11—42no—
111C2×C4×C11—22no—
112C2×C4×C11—41no—
113C2×C4×C11—41no—
114C2×C4×C11—44no—
115C2×C4×C11—42no—
116C2×C4×C11—82no—
117C2×C4×C11C4×D412yes—
118C2×C4×C11#12011yescharacteristic
119C2×C4×C11#12112yes—
120C2×C4×C11#12311yescharacteristic
121C2×C4×C11AGL(1,ℤ/8)12yes—
122C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C11#13711yescharacteristic
124C22⋊D11—88no—
125C2×Dic11—42no—
126C2×Dic11—42no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—42no—
130C2×Dic11—41no—
131D44—24no—
132D44—42no—
133C4×D11—82no—
134C4×D11—82no—
135C8×C11—44no—
136C11⋊C8—82no—
137C2×#121—221no—
138C2×C4×D4—111no—
139C2×C4×D4C2×D1111yescharacteristic
140#436—24no—
141#431C2×D1112yes—
142#423—112no—
143C2×#100—221no—
144#407—22no—
145#397—112no—
146#392—112no—
147#386—222no—
148#382—111no—
149#380—221no—
150#343—221no—
151D4⋊C8—224no—
152C22×C11—21no—
153C22×C11—21no—
154C22×C11—44no—
155C22×C11—42no—
156C22×C11—42no—
157C22×C11—42no—
158C22×C11—82no—
159C22×C11#38611yescharacteristic
160C22×C11#41711yescharacteristic
161C22×C11#41811yescharacteristic
162C2×D11—42no—
163C2×D11—42no—
164C2×D11—42no—
165C2×D11—81no—
166C2×D11—81no—
167C2×D11—81no—
168C2×D11—81no—
169C4×C11—22no—
170C4×C11—21no—
171C4×C11—21no—
172C4×C11—42no—
173C4×C11#46812yes—
174C4×C11#46912yes—
175Dic11—82no—
176Dic11—81no—
177C22×D4—111no—
178C22×D4—222no—
179C22×D4D4411yescharacteristic
180C23×C4—221no—
181C23×C4C22⋊D1112yes—
182C2×M16—24no—
183C2×M16—222no—
184#121—444no—
185C4×D4—22no—
186C4×D4—22no—
187C4×D4—222no—
188C4×D4—222no—
189C2×C4⋊C4—111no—
190C2×C4⋊C4—221no—
191C2×C4⋊C4D4411yescharacteristic
192C2×C22⋊C4—222no—
193C2×C22⋊C4—221no—
194C2×C22⋊C4—222no—
195C2×C22⋊C4C4×D1112yes—
196C2×C42C22×D1111yescharacteristic
197C4⋊C8—22no—
198C4⋊C8—222no—
199C4⋊C8—222no—
200#100—442no—
201C22⋊C8—24no—
202C22⋊C8—22no—
203C4×C8C22⋊D1114yescomplemented
204#95—112no—
205#95—222no—
206#95—221no—
207C2×C11—21no—
208C2×C11—21no—
209C2×C11—82no—
210C2×C11#189111yescharacteristic
211C2×C11#189511yescharacteristic
212C2×C11#191111yescharacteristic
213D11—82no—
214C24—221no—
215C24(C2×D11)⋊C412yes—
216C2×D4—21no—
217C2×D4—22no—
218C2×D4—21no—
219C2×D4—22no—
220C2×D4—222no—
221C2×D4—442no—
222C2×D4—444no—
223C2×D4—444no—
224C2×D4—882no—
225C22×C4—22no—
226C22×C4—22no—
227C22×C4—82no—
228C22×C4—222no—
229C22×C4—221no—
230C22×C4—442no—
231C22×C4—441no—
232C22×C4—441no—
233C22×C4—442no—
234C22×C4(C2×D11)⋊C412yes—
235C22×C4C2×C4×D1111yescharacteristic
236C22×C4C2×D4411yescharacteristic
237C22×C4C2×C22⋊D1111yescharacteristic
238M16—84no—
239M16—442no—
240M16—442no—
241C2×C8—24no—
242C2×C8—442no—
243C4⋊C4—22no—
244C4⋊C4—222no—
245C4⋊C4—442no—
246C22⋊C4—24no—
247C22⋊C4—444no—
248C22⋊C4—441no—
249C22⋊C4—441no—
250C22⋊C4—882no—
251C42#433912yes—
252C42C2×C22⋊D1112yes—
253C11#948911yescharacteristic, complemented, Sylow
254C23—22no—
255C23—22no—
256C23—22no—
257C23—42no—
258C23—42no—
259C23—222no—
260C23—441no—
261C23—441no—
262C23—441no—
263C23—441no—
264C23—441no—
265C23—441no—
266C23C2×(C2×D11)⋊C411yescharacteristic
267D4—42no—
268D4—42no—
269D4—224no—
270D4—442no—
271D4—888no—
272C2×C4—22no—
273C2×C4—41no—
274C2×C4—41no—
275C2×C4—44no—
276C2×C4—42no—
277C2×C4—82no—
278C2×C4—442no—
279C2×C4—442no—
280C2×C4—441no—
281C2×C4—442no—
282C2×C4—441no—
283C2×C4—441no—
284C2×C4—882no—
285C2×C4—882no—
286C2×C4#6696112yes—
287C2×C4#6696111yescharacteristic
288C2×C4#6696211yescharacteristic
289C2×C4C4×C22⋊D1112yes—
290C2×C4#6698211yescharacteristic
291C2×C4#6698312yes—
292C2×C4#6700611yescharacteristic
293C8—44no—
294C8—882no—
295C22—21no—
296C22—21no—
297C22—44no—
298C22—42no—
299C22—42no—
300C22—42no—
301C22—82no—
302C22—442no—
303C22—442no—
304C22—442no—
305C22—881no—
306C22—881no—
307C22—881no—
308C22—881no—
309C22#1062274411yescharacteristic
310C22#1062274611yescharacteristic
311C22#1062282611yescharacteristic
312C4—21no—
313C4—21no—
314C4—22no—
315C4—42no—
316C4—882no—
317C4—881no—
318C4#1062274712yes—
319C4#1062274812yes—
320C2—21no—
321C2—21no—
322C2—82no—
323C2—882no—
324C2#1306903411yescharacteristic
325C2#1306905411yescharacteristic
326C2#1306914811yescharacteristic
subgroupG/H
centerC22#10622826
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#2975C2
socleC22×C11#386
prime radical#13073513C2
cosocleC2×C42×C11C23
hypercenter#2975D11
hypocenterC11#9489
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2975

Complements

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

NH ≅ G/Ntype
2. #13068608C2semidirect
3. #13067042C2semidirect
4. #13066475C2semidirect
5. C11×#2975C2semidirect
44. C4×C8×C11D4semidirect
91. #2975D11semidirect
203. C4×C8C22⋊D11semidirect
253. C11#9489semidirect

Maximal subgroups

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

subgroupindex
#130735132
#130686082
#130670422
#130664752
C11×#29752
#948911