Finite Group Databasebeta

← #14667342

Subgroups — #14667342

Order 2816.

324 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 63 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#13081697C211yesmaximal, characteristic, complemented
2#13070880C211yesmaximal, characteristic
3#13070653C211yesmaximal, characteristic, complemented
4#13066658C211yesmaximal, characteristic, complemented
5#13066598C211yesmaximal, characteristic, complemented
6#13066585C211yesmaximal, characteristic, complemented
7C11×#1688C211yesmaximal, characteristic, complemented
8#10623115—21no—
9C11×#493C2211yescharacteristic
10C11×#460—21no—
11C11×#446C2211yescharacteristic
12C2×#66891—21no—
13C2×#66891—21no—
14C2×#66890—21no—
15#10622462—21no—
16#10622458—21no—
17#10622457—21no—
18#10622328—21no—
19#10622323—21no—
20C4×Dic44C2211yescharacteristic
21#10622309C2211yescharacteristic
22C11×#334C2211yescharacteristic
23C11×#331—21no—
24#10622200—21no—
25C4⋊(C11⋊C16)C2211yescharacteristic
26#10622099C2211yescharacteristic
27C2×C11×SD16—41no—
28C2×C11×D8—21no—
29C2×C11×D8—21no—
30C11×#127—21no—
31C4×Q8×C11D411yescharacteristic
32#66999—41no—
33C2×Dic44—21no—
34C2×Dic44D411yescharacteristic
35C2×Dic44D411yescharacteristic
36C2×D88D411yescharacteristic
37C2×#4314—21no—
38C2×#4314—21no—
39#66951—41no—
40#66951—41no—
41#66945—41no—
42#66928—21no—
43#66928—21no—
44C4×D44—21no—
45#66922—21no—
46C4×Dic22—21no—
47C4×Dic22—21no—
48C11×C4⋊C8—21no—
49C11×C4⋊C8—21no—
50C11×C4⋊C8D411yescharacteristic
51C11×#102—41no—
52C11×#97—21no—
53C4×C8×C11C2311yescharacteristic
54#66891—42no—
55#66891—42no—
56#66890—42no—
57#66885—21no—
58#66882D411yescharacteristic
59#66880—21no—
60#66880—21no—
61C2×C11⋊C16—21no—
62C2×C11⋊C16—21no—
63#12337—111nomaximal, Sylow
64C2×Q8×C11D811yescharacteristic
65C2×D4×C11—41no—
66C2×D4×C11—41no—
67C2×D4×C11—41no—
68C2×D44—21no—
69C2×C4×D11—41no—
70C2×Dic22—21no—
71C2×Dic22—21no—
72C11×SD16—82no—
73C11×D8—41no—
74C11×D8—41no—
75C11×D8—41no—
76C11×D8—41no—
77C2×C8×C11—21no—
78C2×C8×C11—41no—
79C2×C8×C11C2×D411yescharacteristic
80C2×C8×C11C2×D411yescharacteristic
81C11×C4⋊C4—21no—
82C11×C4⋊C4D811yescharacteristic
83C42×C11—21no—
84C42×C11C2×D411yescharacteristic
85(C2×D11)⋊C4—41no—
86(C2×D11)⋊C4—41no—
87(C2×D11)⋊C4—41no—
88(C2×D11)⋊C4—41no—
89(C2×D11)⋊C4—41no—
90C4⋊Dic11—21no—
91C4⋊Dic11—41no—
92C4⋊Dic11—41no—
93Dic11⋊C4—41no—
94Dic11⋊C4—41no—
95C4×Dic11—41no—
96C4×Dic11—41no—
97Dic44—21no—
98Dic44—21no—
99Dic44—41no—
100Dic44—81no—
101D88—41no—
102#4314—41no—
103#4314—41no—
104#4314—81no—
105C11⋊C16—22no—
106C11⋊C16—41no—
107#3402—111no—
108#2250—111no—
109#2207—111no—
110#1688D1111yescharacteristic, complemented
111#1360—111no—
112#1338—111no—
113#1334—111no—
114C23×C11—81no—
115C22×D11—41no—
116Q8×C11—41no—
117D4×C11—81no—
118D4×C11—81no—
119D4×C11—81no—
120D4×C11—81no—
121D4×C11—161no—
122C2×C4×C11—21no—
123C2×C4×C11—21no—
124C2×C4×C11#12011yescharacteristic
125C2×C4×C11C2×D811yescharacteristic
126C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
127C2×Dic11—41no—
128C2×Dic11—41no—
129C2×Dic11—41no—
130D44—41no—
131D44—41no—
132C4×D11—82no—
133Dic22—41no—
134Dic22—41no—
135Dic22—41no—
136Dic22—41no—
137C8×C11—21no—
138C8×C11—41no—
139C8×C11—81no—
140C8×C11#13511yescharacteristic
141C8×C11AGL(1,ℤ/8)11yescharacteristic
142#556—221no—
143C2×SD32—221no—
144C2×SD32—221no—
145C2×D16—221no—
146#497—221no—
147#495—111no—
148#493C2×D1111yescharacteristic
149#464—221no—
150#463—221no—
151#462—221no—
152#460—21no—
153#446C2×D1111yescharacteristic
154#440—221no—
155C4×Q16—111no—
156C4⋊C16—111no—
157#357—221no—
158#346—111no—
159#334C2×D1111yescharacteristic
160#331—21no—
161C22×C11—161no—
162C22×C11—161no—
163C22×C11—161no—
164C22×C11#44711yescharacteristic
165C2×D11—81no—
166C2×D11—81no—
167C2×D11—81no—
168C4×C11—21no—
169C4×C11—21no—
170C4×C11—41no—
171C4×C11—41no—
172C4×C11#44911yescharacteristic
173C4×C11#45311yescharacteristic
174Dic11—81no—
175Dic11—81no—
176Dic11—81no—
177C2×Q16—111no—
178C2×Q16—111no—
179C2×Q16—221no—
180C2×SD16—41no—
181C2×SD16—221no—
182C2×SD16—221no—
183C2×D8—21no—
184C2×D8—21no—
185C2×D8—111no—
186C4⋊Q8—221no—
187#127—21no—
188#126—441no—
189#126—441no—
190#124—221no—
191#124—221no—
192C22⋊Q8—441no—
193C4×Q8—221no—
194C4×Q8—221no—
195C4×Q8C22⋊D1111yescharacteristic
196C4×D4—221no—
197#117—441no—
198SD32—442no—
199SD32—442no—
200D16—442no—
201C2×C16—221no—
202C2×C16—221no—
203#107—111no—
204C4⋊C8—21no—
205C4⋊C8—21no—
206C4⋊C8C22⋊D1111yescharacteristic
207#103—221no—
208#103—221no—
209#102—41no—
210#102—221no—
211#97—21no—
212C4×C8C22×D1111yescharacteristic
213C2×C11—321no—
214C2×C11#162111yescharacteristic
215C2×C11#219011yescharacteristic
216C2×C11#219311yescharacteristic
217D11—161no—
218C2×Q8—221no—
219C2×Q8—221no—
220C2×Q8#432311yescharacteristic
221C2×D4—41no—
222C2×D4—41no—
223C2×D4—41no—
224C2×D4—221no—
225C22×C4—441no—
226Q16—221no—
227Q16—221no—
228Q16—441no—
229Q16—881no—
230SD16—82no—
231SD16—441no—
232SD16—441no—
233SD16—881no—
234D8—41no—
235D8—41no—
236D8—41no—
237D8—41no—
238D8—441no—
239C2×C8—21no—
240C2×C8—41no—
241C2×C8D4×D1111yescharacteristic
242C2×C8D4×D1111yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—221no—
245C4⋊C4—441no—
246C4⋊C4—441no—
247C4⋊C4—441no—
248C4⋊C4—441no—
249C4⋊C4#432311yescharacteristic
250C22⋊C4—441no—
251C22⋊C4—441no—
252C22⋊C4—441no—
253C22⋊C4—441no—
254C22⋊C4—441no—
255C42—21no—
256C42—441no—
257C42—441no—
258C42C2×C22⋊D1111yescharacteristic
259C16—222no—
260C16—441no—
261C11#1233711yescharacteristic, complemented, Sylow
262C23—81no—
263C23—441no—
264Q8—41no—
265Q8—441no—
266Q8—441no—
267Q8—441no—
268Q8—441no—
269D4—81no—
270D4—81no—
271D4—81no—
272D4—81no—
273D4—161no—
274D4—441no—
275D4—441no—
276C2×C4—21no—
277C2×C4—21no—
278C2×C4—441no—
279C2×C4—441no—
280C2×C4—441no—
281C2×C4—882no—
282C2×C4C2×#432311yescharacteristic
283C2×C4#6699011yescharacteristic
284C2×C4#6700211yescharacteristic
285C8—21no—
286C8—41no—
287C8—81no—
288C8#6696711yescharacteristic
289C8#6696911yescharacteristic
290C22—161no—
291C22—161no—
292C22—161no—
293C22—881no—
294C22—881no—
295C22—881no—
296C22#1062264911yescharacteristic
297C4—21no—
298C4—21no—
299C4—41no—
300C4—41no—
301C4—881no—
302C4—881no—
303C4—881no—
304C4#1062278511yescharacteristic
305C4#1062281111yescharacteristic
306C2—321no—
307C2—1761no—
308C2#1306767911yescharacteristic
309C2#1307056111yescharacteristic
310C2#1307057811yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1688C2
socleC22×C11#447
prime radical#13070880C2
hypercenter#1688D11
hypocenterC11#12337
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #446 ◁ #1688

Complements

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

NH ≅ G/Ntype
1. #13081697C2semidirect
3. #13070653C2semidirect
4. #13066658C2semidirect
5. #13066598C2semidirect
6. #13066585C2semidirect
7. C11×#1688C2semidirect
110. #1688D11semidirect
261. C11#12337semidirect

Maximal subgroups

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

subgroupindex
#130816972
#130708802
#130706532
#130666582
#130665982
#130665852
C11×#16882
#1233711