Finite Group Databasebeta

← #14667300

Subgroups — #14667300

Order 2816.

328 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 328 conjugacy classes of subgroups — too many to draw. Only its 67 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#13081605C211yesmaximal, characteristic, complemented
2#13070871C211yesmaximal, characteristic, complemented
3#13070648C211yesmaximal, characteristic
4#13066664C211yesmaximal, characteristic, complemented
5Q8⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
6#13066576C211yesmaximal, characteristic, complemented
7C11×#1668C211yesmaximal, characteristic, complemented
8#10623115—21no—
9C11×#493C2211yescharacteristic
10C11×#460—21no—
11C8×Q8×C11C2211yescharacteristic
12C2×#66891—22no—
13C2×#66890—21no—
14#10622458—22no—
15#10622454—21no—
16#10622312C2211yescharacteristic
17C4×Dic44—21no—
18#10622309—21no—
19C4×D88C2211yescharacteristic
20C11×#335C2211yescharacteristic
21C11×#331—21no—
22#10622200—21no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24C4×C11⋊C16C2211yescharacteristic
25C2×C11×SD16—41no—
26C2×C11×D8—21no—
27C2×C11×D8—21no—
28C11×#127—21no—
29C4×Q8×C11D411yescharacteristic
30#66999—41no—
31C2×Dic44—21no—
32C2×Dic44D412yes—
33C2×D88D411yescharacteristic
34C2×#4314—22no—
35#66951—42no—
36#66945—41no—
37#66928—22no—
38C4×D44—21no—
39#66922—21no—
40C4×Dic22—22no—
41C11×C4⋊C8—21no—
42C11×C4⋊C8—21no—
43C11×C4⋊C8D411yescharacteristic
44C11×#102—41no—
45C4×C8×C11—21no—
46C4×C8×C11C2311yescharacteristic
47#66891—44no—
48#66890—42no—
49#66885—21no—
50#66882D411yescharacteristic
51#66880—22no—
52C2×C11⋊C16—21no—
53C2×C11⋊C16—21no—
54#12331—111nomaximal, Sylow
55C2×Q8×C11D811yescharacteristic
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D4×C11—41no—
59C2×D44—21no—
60C2×C4×D11—41no—
61C2×Dic22—22no—
62C11×SD16—82no—
63C11×D8—42no—
64C11×D8—41no—
65C11×D8—41no—
66C2×C8×C11—21no—
67C2×C8×C11—41no—
68C2×C8×C11C2×D411yescharacteristic
69C2×C8×C11C2×D411yescharacteristic
70C11×C4⋊C4—21no—
71C11×C4⋊C4D811yescharacteristic
72C42×C11—21no—
73C42×C11C2×D411yescharacteristic
74(C2×D11)⋊C4—42no—
75(C2×D11)⋊C4—42no—
76(C2×D11)⋊C4—41no—
77C4⋊Dic11—21no—
78C4⋊Dic11—41no—
79C4⋊Dic11—41no—
80Dic11⋊C4—42no—
81C4×Dic11—42no—
82Dic44—42no—
83Dic44—41no—
84Dic44—41no—
85D88—21no—
86D88—21no—
87#4314—82no—
88C11⋊C16—22no—
89C11⋊C16—41no—
90#3393—111no—
91#2248—111no—
92#2206—111no—
93#1668D1111yescharacteristic, complemented
94#1362—111no—
95Q8⋊C16—111no—
96#1331—111no—
97C23×C11—81no—
98C22×D11—41no—
99Q8×C11—21no—
100Q8×C11—21no—
101D4×C11—81no—
102D4×C11—81no—
103D4×C11—81no—
104D4×C11—81no—
105D4×C11—161no—
106C2×C4×C11—21no—
107C2×C4×C11—21no—
108C2×C4×C11#12011yescharacteristic
109C2×C4×C11C2×D811yescharacteristic
110C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
111C2×Dic11—41no—
112C2×Dic11—42no—
113D44—41no—
114D44—41no—
115C4×D11—81no—
116C4×D11—81no—
117Dic22—42no—
118Dic22—42no—
119C8×C11—21no—
120C8×C11—41no—
121C8×C11—81no—
122C8×C11#13511yescharacteristic
123C8×C11AGL(1,ℤ/8)11yescharacteristic
124#556—221no—
125C2×SD32—222no—
126C2×D16—221no—
127#495—221no—
128#494—111no—
129#493C2×D1111yescharacteristic
130#464—222no—
131#461—221no—
132#460—21no—
133C8×Q8C2×D1111yescharacteristic
134C4×Q16—221no—
135C4×D8—111no—
136C4⋊C16—111no—
137#357—221no—
138C4×C16—111no—
139#335C2×D1111yescharacteristic
140#331—21no—
141C22×C11—161no—
142C22×C11—161no—
143C22×C11—161no—
144C22×C11#44711yescharacteristic
145C2×D11—81no—
146C2×D11—81no—
147C2×D11—81no—
148C4×C11—21no—
149C4×C11—41no—
150C4×C11—41no—
151C4×C11#44911yescharacteristic
152C4×C11#45311yescharacteristic
153C4×C11#50811yescharacteristic
154C4×C11#50911yescharacteristic
155Dic11—82no—
156Dic11—81no—
157C2×Q16—112no—
158C2×Q16—221no—
159C2×SD16—41no—
160C2×SD16—222no—
161C2×D8—21no—
162C2×D8—21no—
163C2×D8—111no—
164C4⋊Q8—221no—
165#127—21no—
166#126—442no—
167#124—222no—
168C22⋊Q8—441no—
169C4×Q8—222no—
170C4×Q8C22⋊D1111yescharacteristic
171C4×D4—221no—
172#117—441no—
173SD32—444no—
174D16—442no—
175C2×C16—221no—
176C2×C16—221no—
177#107—111no—
178C4⋊C8—21no—
179C4⋊C8—21no—
180C4⋊C8C22⋊D1111yescharacteristic
181#103—222no—
182#102—41no—
183#102—221no—
184C4×C8—21no—
185C4×C8C22×D1111yescharacteristic
186C2×C11—321no—
187C2×C11#162111yescharacteristic
188C2×C11#218611yescharacteristic
189C2×C11#219311yescharacteristic
190D11—161no—
191C2×Q8—222no—
192C2×Q8#432311yescharacteristic
193C2×D4—41no—
194C2×D4—41no—
195C2×D4—41no—
196C2×D4—221no—
197C22×C4—441no—
198Q16—442no—
199Q16—441no—
200Q16—441no—
201SD16—82no—
202SD16—882no—
203D8—42no—
204D8—41no—
205D8—41no—
206D8—221no—
207D8—221no—
208C2×C8—21no—
209C2×C8—41no—
210C2×C8D4×D1111yescharacteristic
211C2×C8D4×D1111yescharacteristic
212C4⋊C4—21no—
213C4⋊C4—221no—
214C4⋊C4—442no—
215C4⋊C4—441no—
216C4⋊C4—441no—
217C4⋊C4#432311yescharacteristic
218C22⋊C4—442no—
219C22⋊C4—442no—
220C22⋊C4—441no—
221C42—21no—
222C42—442no—
223C42C2×C22⋊D1111yescharacteristic
224C16—222no—
225C16—441no—
226C11#1233111yescharacteristic, complemented, Sylow
227C23—81no—
228C23—441no—
229Q8—21no—
230Q8—21no—
231Q8—442no—
232Q8—442no—
233D4—81no—
234D4—81no—
235D4—81no—
236D4—81no—
237D4—161no—
238D4—441no—
239D4—441no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—441no—
243C2×C4—442no—
244C2×C4—881no—
245C2×C4—881no—
246C2×C4C2×#432311yescharacteristic
247C2×C4#6699011yescharacteristic
248C2×C4#6700211yescharacteristic
249C8—21no—
250C8—41no—
251C8—81no—
252C8#6696711yescharacteristic
253C8#6696911yescharacteristic
254C22—161no—
255C22—161no—
256C22—161no—
257C22—881no—
258C22—881no—
259C22—881no—
260C22#1062264911yescharacteristic
261C4—21no—
262C4—41no—
263C4—41no—
264C4—882no—
265C4—881no—
266C4#1062276011yescharacteristic
267C4#1062278511yescharacteristic
268C4#1062280711yescharacteristic
269C4#1062281111yescharacteristic
270C2—321no—
271C2—1761no—
272C2#1306767911yescharacteristic
273C2#1307053711yescharacteristic
274C2#1307057811yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#1668C2
socleC22×C11#447
prime radical#13070648C2
hypercenter#1668D11
hypocenterC11#12331
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×Q8 ◁ #1668

Complements

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

NH ≅ G/Ntype
1. #13081605C2semidirect
2. #13070871C2semidirect
4. #13066664C2semidirect
5. Q8⋊(C11⋊C16)C2semidirect
6. #13066576C2semidirect
7. C11×#1668C2semidirect
93. #1668D11semidirect
226. C11#12331semidirect

Maximal subgroups

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

subgroupindex
#130816052
#130708712
#130706482
#130666642
Q8⋊(C11⋊C16)2
#130665762
C11×#16682
#1233111