Finite Group Databasebeta

← #14647920

Subgroups — #14647920

Order 2816.

432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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#13077333C211yesmaximal, characteristic
2#13069340C211yesmaximal, characteristic, complemented
3#13067388C211yesmaximal, characteristic, complemented
4#13067110C211yesmaximal, characteristic
5#13067016C211yesmaximal, characteristic
6#13066460C211yesmaximal, characteristic, complemented
7C11×#1303C211yesmaximal, characteristic, complemented
8C2×#66960—21no—
9#10623008C2211yescharacteristic
10C11×#431C2211yescharacteristic
11C11×#423C2211yescharacteristic
12C4×C11×C4⋊C4C2211yescharacteristic
13#10622742—21no—
14#10622538C2211yescharacteristic
15C2×C4⋊(C11⋊C8)—21no—
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C2×#66867C2211yescharacteristic
18#10622449—22no—
19#10622449—22no—
20#10622162—21no—
21#10622118—22no—
22#10622097—22no—
23#10622089C412yes—
24#10622089C412yes—
25C2×#4339—21no—
26C2×C11×M16—21no—
27C2×C11×C4⋊C4—21no—
28C2×C42×C11—21no—
29C2×C42×C11C2311yescharacteristic
30#66983—21no—
31#66983C2×C412yes—
32C22×C11⋊C8—21no—
33C22×C11⋊C8D411yescharacteristic
34C22×C11⋊C8D411yescharacteristic
35#66960—42no—
36#66960—42no—
37C2×#4313—22no—
38C2×C8×D11—22no—
39#66928—21no—
40#66927Q811yescharacteristic
41C4×D44—21no—
42C4×D44D412yes—
43#66922Q811yescharacteristic
44C11×C4⋊C8—21no—
45C11×C4⋊C8—21no—
46C11×C4⋊C8D412yes—
47C11×C22⋊C8—21no—
48C4×C8×C11—21no—
49C11×#95C2×C411yescharacteristic
50C11×#95C2×C411yescharacteristic
51C22⋊(C11⋊C8)C2×C412yes—
52(C2×D11)⋊C8—24no—
53C4⋊(C11⋊C8)—21no—
54C4⋊(C11⋊C8)—21no—
55C4⋊(C11⋊C8)—21no—
56C4⋊(C11⋊C8)—42no—
57#66867—21no—
58#66867—21no—
59C4×C11⋊C8—21no—
60#8880—111nomaximal, Sylow
61C22×C4×C11—21no—
62C22×C4×C11—21no—
63C22×C4×C11C22×C411yescharacteristic
64C22×C4×C11C2×D411yescharacteristic
65C22×C4×C11#4111yescharacteristic
66C2×C22⋊D11—22no—
67#4339—41no—
68#4339—41no—
69#4339—41no—
70#4339—41no—
71C2×D44—21no—
72C2×D44—21no—
73C2×D44C4⋊C412yes—
74C2×C4×D11—22no—
75C2×Dic22—21no—
76C11×M16—41no—
77C11×M16—41no—
78C2×C8×C11—22no—
79C2×C8×C11—41no—
80C11×C4⋊C4—42no—
81C42×C11—41no—
82C42×C11—41no—
83C42×C11C2×D411yescharacteristic
84C42×C11C2×D411yescharacteristic
85C42×C11C2×Q811yescharacteristic
86C42×C11#4111yescharacteristic
87(C2×D11)⋊C4—22no—
88(C2×D11)⋊C4—22no—
89C4⋊Dic11—21no—
90C4⋊Dic11C4⋊C412yes—
91C2×C11⋊C8—22no—
92C2×C11⋊C8—21no—
93C2×C11⋊C8—21no—
94C2×C11⋊C8—21no—
95C2×C11⋊C8—21no—
96C2×C11⋊C8—21no—
97C2×C11⋊C8—41no—
98C2×C11⋊C8—41no—
99C2×C11⋊C8—41no—
100C2×C11⋊C8SD1612yes—
101#4313—44no—
102C8×D11—44no—
103#2932—111no—
104#1940—111no—
105#1570—111no—
106#1502—111no—
107#1480—111no—
108#1303D1111yescharacteristic, complemented
109#1281—111no—
110C23×C11C4×D411yescharacteristic
111C22×D11—22no—
112C2×C4×C11—22no—
113C2×C4×C11—41no—
114C2×C4×C11—41no—
115C2×C4×C11—41no—
116C2×C4×C11—41no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11C2×C4⋊C411yescharacteristic
121C2×C4×C11C4×D411yescharacteristic
122C2×C4×C11#12011yescharacteristic
123C2×C4×C11C22⋊Q811yescharacteristic
124C2×C4×C11C22⋊Q811yescharacteristic
125C2×C4×C11#12311yescharacteristic
126C2×C4×C11C2×SD1611yescharacteristic
127C2×C4×C11#13511yescharacteristic
128C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
129C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
130C22⋊D11—42no—
131C22⋊D11—42no—
132C2×Dic11—22no—
133D44—42no—
134D44—41no—
135D44—41no—
136D44—81no—
137C4×D11—42no—
138C4×D11—42no—
139Dic22—41no—
140Dic22—41no—
141C8×C11—42no—
142C8×C11—81no—
143C11⋊C8—22no—
144C11⋊C8—42no—
145C11⋊C8—41no—
146C11⋊C8—81no—
147C2×#131—221no—
148#532—111no—
149#435—222no—
150#435—222no—
151#431—111no—
152#431C2×D1111yescharacteristic
153#423C2×D1111yescharacteristic
154C2×C4⋊C8—111no—
155C2×C4⋊C8—221no—
156#408—221no—
157C2×#97—111no—
158C4×C4⋊C4C2×D1111yescharacteristic
159#336—221no—
160#334—222no—
161#327—112no—
162#327—112no—
163D4⋊C8—222no—
164C22×C11—21no—
165C22×C11—21no—
166C22×C11#38511yescharacteristic
167C22×C11C4×SD1611yescharacteristic
168C22×C11#44211yescharacteristic
169C2×D11—42no—
170C2×D11—42no—
171C2×D11—42no—
172C4×C11—21no—
173C4×C11—21no—
174C4×C11—21no—
175C4×C11—21no—
176C4×C11—42no—
177C4×C11—81no—
178C4×C11#44911yescharacteristic
179C4×C11#45011yescharacteristic
180C4×C11#47611yescharacteristic
181C4×C11#47811yescharacteristic
182Dic11—42no—
183C2×#41—221no—
184#131—442no—
185#131—442no—
186C2×M16—21no—
187C2×M16—222no—
188C22×C8—111no—
189C22×C8—111no—
190C22×C8—222no—
191C22×C8—221no—
192C4⋊Q8—111no—
193#127—111no—
194#124—221no—
195#121—112no—
196#121—221no—
197C4×D4—112no—
198C4×D4—221no—
199C2×C4⋊C4—21no—
200C2×C42—21no—
201C2×C42C22×D1111yescharacteristic
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—221no—
205C4⋊C8—221no—
206C4⋊C8—221no—
207C4⋊C8—442no—
208C4⋊C8D4412yes—
209C22⋊C8—21no—
210C22⋊C8—112no—
211C22⋊C8—224no—
212#97—221no—
213#97—221no—
214C4×C8—21no—
215C4×C8—221no—
216#95C4×D1111yescharacteristic
217#95C4×D1111yescharacteristic
218C2×C11—21no—
219C2×C11—21no—
220C2×C11#186111yescharacteristic
221C2×C11#186411yescharacteristic
222C2×C11#186811yescharacteristic
223D11—82no—
224#41—441no—
225#41—441no—
226#41—441no—
227#41—441no—
228C2×Q8—221no—
229C2×D4—112no—
230C2×D4—222no—
231C2×D4—221no—
232C2×D4—221no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—222no—
236C22×C4C2×C4×D1111yescharacteristic
237C22×C4D4×D1111yescharacteristic
238C22×C4#434111yescharacteristic
239M16—41no—
240M16—41no—
241M16—444no—
242C2×C8—22no—
243C2×C8—41no—
244C2×C8—112no—
245C2×C8—221no—
246C2×C8—221no—
247C2×C8—222no—
248C2×C8—221no—
249C2×C8—221no—
250C2×C8—221no—
251C2×C8—444no—
252C2×C8—441no—
253C2×C8—441no—
254C2×C8—441no—
255C4⋊C4—42no—
256C4⋊C4—112no—
257C4⋊C4—221no—
258C22⋊C4—222no—
259C22⋊C4—222no—
260C42—41no—
261C42—41no—
262C42C2×D4411yescharacteristic
263C42#433911yescharacteristic
264C42D4×D1111yescharacteristic
265C42Q8×D1111yescharacteristic
266C11#888011yescharacteristic, complemented, Sylow
267C23—222no—
268C23(C22⋊D11)⋊C411yescharacteristic
269Q8—441no—
270Q8—441no—
271D4—442no—
272D4—442no—
273D4—442no—
274D4—441no—
275D4—441no—
276D4—881no—
277C2×C4—22no—
278C2×C4—41no—
279C2×C4—41no—
280C2×C4—41no—
281C2×C4—41no—
282C2×C4—41no—
283C2×C4—41no—
284C2×C4—41no—
285C2×C4—222no—
286C2×C4—442no—
287C2×C4—442no—
288C2×C4C4×D4411yescharacteristic
289C2×C4#6693511yescharacteristic
290C2×C4#6693611yescharacteristic
291C2×C4C4⋊C4×D1111yescharacteristic
292C2×C4#6694911yescharacteristic
293C2×C4#6695011yescharacteristic
294C2×C4#6696411yescharacteristic
295C2×C4SD16×D1111yescharacteristic
296C2×C4#6696711yescharacteristic
297C2×C4#6697211yescharacteristic
298C8—42no—
299C8—81no—
300C8—222no—
301C8—442no—
302C8—441no—
303C8—881no—
304C22—21no—
305C22—21no—
306C22—442no—
307C22—442no—
308C22—442no—
309C22#1062228111yescharacteristic
310C22#1062239811yescharacteristic
311C22#1062240111yescharacteristic
312C4—21no—
313C4—21no—
314C4—21no—
315C4—21no—
316C4—42no—
317C4—81no—
318C4—442no—
319C4#1062238911yescharacteristic
320C4#1062242411yescharacteristic
321C4#1062248311yescharacteristic
322C4#1062250411yescharacteristic
323C2—21no—
324C2—21no—
325C2—882no—
326C2#1306885711yescharacteristic
327C2#1306887811yescharacteristic
328C2#1306890311yescharacteristic
subgroupG/H
centerC2×C4#66935
commutatorC22×C4×C11C22×C4
FrattiniC2×C42C22×D11
FittingC11×#1303C2
socleC22×C11#385
prime radical#10623008C22
cosocleC2×C42×C11C23
hypercenter#1303D11
hypocenterC11#8880
LCSG ▷ C22×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1303

Complements

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

NH ≅ G/Ntype
2. #13069340C2semidirect
3. #13067388C2semidirect
6. #13066460C2semidirect
7. C11×#1303C2semidirect
108. #1303D11semidirect
266. C11#8880semidirect

Maximal subgroups

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

subgroupindex
#130773332
#130693402
#130673882
#130671102
#130670162
#130664602
C11×#13032
#888011