Finite Group Databasebeta

← #14667111

Subgroups — #14667111

Order 2816.

328 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 55 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#13079458C211yesmaximal, characteristic
2#13070836C211yesmaximal, characteristic, complemented
3#13070831C211yesmaximal, characteristic, complemented
4#13070132C211yesmaximal, characteristic, complemented
5#13066611C211yesmaximal, characteristic, complemented
6#13066608C211yesmaximal, characteristic, complemented
7C11×#1320C211yesmaximal, characteristic, complemented
8#10623322—21no—
9C11×#407C2211yescharacteristic
10#10622820—21no—
11#10622750C2211yescharacteristic
12#10622748C2211yescharacteristic
13#10622747—21no—
14#10622738C2211yescharacteristic
15#10622737—21no—
16#10622350—21no—
17#10622347—21no—
18#10622346—21no—
19#10622336—21no—
20C11×#349C2211yescharacteristic
21C11×#349C2211yescharacteristic
22C11⋊#338C2211yescharacteristic
23#10622155—21no—
24#10622154—21no—
25#10622151—21no—
26#10622151—21no—
27C23×C4×C11D411yescharacteristic
28C2×#4339—21no—
29C2×C11×M16D411yescharacteristic
30C2×C11×M16C2311yescharacteristic
31#67006—41no—
32#66983—21no—
33#66983—21no—
34#66982—41no—
35C4×C22⋊D11—41no—
36C4×C22⋊D11—41no—
37#66979—21no—
38#66977—21no—
39#66977—21no—
40C2×#4318—21no—
41C2×#4318—21no—
42C2×Dic44D411yescharacteristic
43C2×D88D411yescharacteristic
44C2×#4314—21no—
45C11×M32—21no—
46C11×M32—21no—
47C11×C22⋊C8—21no—
48C11×C22⋊C8—21no—
49C22⋊(C11⋊C8)—42no—
50#66886—42no—
51#66885—21no—
52#66885—21no—
53#66883—21no—
54#66883—21no—
55#66882—21no—
56#66881D411yescharacteristic
57#66881D411yescharacteristic
58#66880—21no—
59#66880—21no—
60#12300—111nomaximal, Sylow
61C24×C11SD1611yescharacteristic
62C22×C4×C11—21no—
63C22×C4×C11—21no—
64C22×C4×C11—41no—
65C22×C4×C11—41no—
66C22×C4×C11SD1611yescharacteristic
67C22×C4×C11C2×D411yescharacteristic
68C2×C22⋊D11—41no—
69C2×C22⋊D11—41no—
70C2×C22⋊D11—41no—
71#4339—81no—
72#4339—81no—
73C2×D44—21no—
74C2×C4×D11—41no—
75C2×Dic22—21no—
76C11×M16—41no—
77C11×M16—41no—
78C2×C8×C11—21no—
79C2×C8×C11C2×D411yescharacteristic
80C2×C8×C11C2×D411yescharacteristic
81C22⋊Dic11—41no—
82C22⋊Dic11—41no—
83C22⋊Dic11—41no—
84(C2×D11)⋊C4—41no—
85(C2×D11)⋊C4—41no—
86C4⋊Dic11—21no—
87C4⋊Dic11—21no—
88Dic11⋊C4—41no—
89Dic11⋊C4—41no—
90C4×Dic11—41no—
91#4318—41no—
92#4318—41no—
93#4318—41no—
94#4318—41no—
95C2×C11⋊C8—22no—
96C2×C11⋊C8—41no—
97Dic44—41no—
98D88—41no—
99#4314—81no—
100C11×C16—41no—
101C11×C16—41no—
102#3197—111no—
103#2239—111no—
104#2238—111no—
105#2091—111no—
106#1342—111no—
107#1341—111no—
108#1320D1111yescharacteristic, complemented
109C23×C11—21no—
110C23×C11—41no—
111C23×C11—81no—
112C23×C11C2×SD1611yescharacteristic
113C22×D11—41no—
114C2×C4×C11—21no—
115C2×C4×C11—21no—
116C2×C4×C11—21no—
117C2×C4×C11—41no—
118C2×C4×C11—41no—
119C2×C4×C11—41no—
120C2×C4×C11—81no—
121C2×C4×C11#12011yescharacteristic
122C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
123C22⋊D11—82no—
124C22⋊D11—82no—
125C22⋊D11—82no—
126C2×Dic11—41no—
127C2×Dic11—41no—
128C2×Dic11—41no—
129D44—41no—
130D44—41no—
131C4×D11—82no—
132Dic22—41no—
133Dic22—41no—
134C8×C11—21no—
135C8×C11—21no—
136C8×C11—41no—
137C11⋊C8—42no—
138C11⋊C8—81no—
139#525—221no—
140#485—221no—
141#482—221no—
142#470—111no—
143#469—111no—
144#468—221no—
145#452—221no—
146#449—221no—
147#430—111no—
148#430—221no—
149#407—221no—
150#407C2×D1111yescharacteristic
151#365—221no—
152#365—221no—
153#362—221no—
154#361—221no—
155#349C2×D1111yescharacteristic
156#349C2×D1111yescharacteristic
157#338—111no—
158C22×C11—21no—
159C22×C11—41no—
160C22×C11—41no—
161C22×C11—41no—
162C22×C11—42no—
163C22×C11—41no—
164C22×C11—81no—
165C22×C11#45011yescharacteristic
166C2×D11—81no—
167C2×D11—81no—
168C2×D11—81no—
169C4×C11—21no—
170C4×C11—41no—
171C4×C11#45311yescharacteristic
172C4×C11#45811yescharacteristic
173Dic11—81no—
174Dic11—81no—
175Dic11—81no—
176C2×#41—221no—
177C23×C4D4411yescharacteristic
178C2×Q16—111no—
179C2×SD16—221no—
180C2×D8—111no—
181C2×M16—221no—
182C2×M16—221no—
183C2×M16D4411yescharacteristic
184C2×M16C22×D1111yescharacteristic
185#123—441no—
186C22⋊Q8—221no—
187C22⋊Q8—221no—
188#121—221no—
189#121—221no—
190#120—441no—
191C4×D4—441no—
192C4×D4—441no—
193#117—221no—
194M32—21no—
195M32—21no—
196#108—221no—
197#108—221no—
198#108—442no—
199#107—221no—
200#106—111no—
201#106—111no—
202#103—221no—
203#103—221no—
204#102—221no—
205#102—221no—
206C22⋊C8—21no—
207C22⋊C8—21no—
208C22⋊C8—442no—
209C2×C11—21no—
210C2×C11—41no—
211C2×C11—81no—
212C2×C11#161311yescharacteristic
213D11—161no—
214C24#431411yescharacteristic
215#41—881no—
216#41—881no—
217C2×Q8—221no—
218C2×D4—221no—
219C2×D4—441no—
220C2×D4—441no—
221C2×D4—441no—
222C22×C4—21no—
223C22×C4—21no—
224C22×C4—41no—
225C22×C4—41no—
226C22×C4—441no—
227C22×C4#431411yescharacteristic
228C22×C4C2×D4411yescharacteristic
229Q16—441no—
230SD16—881no—
231D8—441no—
232M16—41no—
233M16—41no—
234M16—441no—
235M16—441no—
236M16—441no—
237M16—441no—
238C2×C8—21no—
239C2×C8—222no—
240C2×C8—441no—
241C2×C8D4×D1111yescharacteristic
242C2×C8D4×D1111yescharacteristic
243C4⋊C4—221no—
244C4⋊C4—221no—
245C4⋊C4—441no—
246C4⋊C4—441no—
247C22⋊C4—441no—
248C22⋊C4—441no—
249C22⋊C4—441no—
250C22⋊C4—441no—
251C22⋊C4—441no—
252C42—441no—
253C16—41no—
254C16—41no—
255C11#1230011yescharacteristic, complemented, Sylow
256C23—21no—
257C23—41no—
258C23—81no—
259C23—441no—
260C23C2×#431411yescharacteristic
261Q8—441no—
262Q8—441no—
263D4—441no—
264D4—441no—
265D4—882no—
266D4—882no—
267D4—882no—
268C2×C4—21no—
269C2×C4—21no—
270C2×C4—21no—
271C2×C4—41no—
272C2×C4—41no—
273C2×C4—41no—
274C2×C4—81no—
275C2×C4—441no—
276C2×C4—441no—
277C2×C4—441no—
278C2×C4—882no—
279C2×C4#6693511yescharacteristic
280C2×C4#6696111yescharacteristic
281C8—21no—
282C8—21no—
283C8—41no—
284C8—442no—
285C8—881no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—41no—
290C22—42no—
291C22—41no—
292C22—81no—
293C22—881no—
294C22—881no—
295C22—881no—
296C22#1062234411yescharacteristic
297C4—21no—
298C4—41no—
299C4—881no—
300C4—881no—
301C4—881no—
302C4#1062235511yescharacteristic
303C4#1062236011yescharacteristic
304C2—21no—
305C2—41no—
306C2—81no—
307C2—1761no—
308C2#1306763811yescharacteristic
subgroupG/H
centerC2#13067638
commutator, cosocleC2×C11×M16C23
FrattiniC2×M16C22×D11
FittingC11×#1320C2
socleC2×C11#1613
prime radical#13079458C2
hypercenter#1320D11
hypocenterC11#12300
LCSG ▷ C2×C11×M16 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1320

Complements

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

NH ≅ G/Ntype
2. #13070836C2semidirect
3. #13070831C2semidirect
4. #13070132C2semidirect
5. #13066611C2semidirect
6. #13066608C2semidirect
7. C11×#1320C2semidirect
108. #1320D11semidirect
255. C11#12300semidirect

Maximal subgroups

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

subgroupindex
#130794582
#130708362
#130708312
#130701322
#130666112
#130666082
C11×#13202
#1230011