Finite Group Databasebeta

← #14667371

Subgroups — #14667371

Order 2816.

306 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 65 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#13081048C211yesmaximal, characteristic, complemented
2#13070839C211yesmaximal, characteristic, complemented
3#13067968C211yesmaximal, characteristic
4#13066670C211yesmaximal, characteristic, complemented
5#13066580C211yesmaximal, characteristic, complemented
6#13066570C211yesmaximal, characteristic, complemented
7C11×#2207C211yesmaximal, characteristic, complemented
8#10623115—21no—
9C2×C11×SD32—21no—
10C11×#493C2211yescharacteristic
11C4×C11×Q16C2211yescharacteristic
12#10622801—21no—
13#10622685—21no—
14#10622633—21no—
15#10622493—21no—
16#10622427—22no—
17C8×D44C2211yescharacteristic
18#10622295C2211yescharacteristic
19C11×C4⋊C16C2211yescharacteristic
20C11×#357—21no—
21#10622200—22no—
22#10622182—21no—
23C4×C11⋊C16C2211yescharacteristic
24#10622096C2211yescharacteristic
25C2×C11×Q16D411yescharacteristic
26C2×C11×D8—21no—
27C2×C11×D8—21no—
28C11×#127—21no—
29C4×Q8×C11—21no—
30#66999—22no—
31C2×#4323—41no—
32C2×C8×D11—21no—
33#66951—42no—
34#66945—22no—
35#66928—41no—
36C4×D44D411yescharacteristic
37#66922—21no—
38C4×Dic22—41no—
39C11×SD32—42no—
40C2×C11×C16—21no—
41C11×#107D411yescharacteristic
42C11×#103—21no—
43C4×C8×C11C2311yescharacteristic
44#66899—22no—
45#66896—41no—
46(C2×D11)⋊C8—21no—
47#66882—21no—
48#66882D412yes—
49C2×C11⋊C16—21no—
50#66872—22no—
51C4⋊(C11⋊C8)—21no—
52C4⋊(C11⋊C8)D411yescharacteristic
53#12341—111nomaximal, Sylow
54C2×Q8×C11—21no—
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11—41no—
58C2×D44D811yescharacteristic
59C2×C4×D11—21no—
60C2×Dic22—41no—
61C11×Q16—21no—
62C11×Q16—21no—
63C11×D8—42no—
64C11×D8—41no—
65C11×D8—41no—
66C2×C8×C11C2×D411yescharacteristic
67C2×C8×C11C2×D411yescharacteristic
68C11×C4⋊C4—21no—
69C11×C4⋊C4—41no—
70C42×C11—41no—
71C42×C11C2×D411yescharacteristic
72#4323—82no—
73(C2×D11)⋊C4—21no—
74(C2×D11)⋊C4—42no—
75(C2×D11)⋊C4—42no—
76C4⋊Dic11—22no—
77C4⋊Dic11—41no—
78C4⋊Dic11D811yescharacteristic
79Dic11⋊C4—42no—
80C4×Dic11—42no—
81C2×C11⋊C8—21no—
82C2×C11⋊C8—41no—
83C8×D11—41no—
84C8×D11—41no—
85C11×C16—41no—
86C11⋊C16—41no—
87#3342—111no—
88#2240—111no—
89#2207D1111yescharacteristic, complemented
90#1667—111no—
91#1364—111no—
92#1332—111no—
93D4⋊C16—111no—
94C23×C11—81no—
95C22×D11—21no—
96Q8×C11—41no—
97Q8×C11—41no—
98D4×C11—81no—
99D4×C11—81no—
100D4×C11—81no—
101D4×C11—81no—
102D4×C11—161no—
103C2×C4×C11—41no—
104C2×C4×C11—41no—
105C2×C4×C11#12011yescharacteristic
106C2×C4×C11C2×D811yescharacteristic
107C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
108C2×Dic11—21no—
109C2×Dic11—42no—
110D44—21no—
111D44—21no—
112C4×D11—41no—
113C4×D11—41no—
114Dic22—81no—
115Dic22—81no—
116C8×C11—21no—
117C8×C11#13511yescharacteristic
118C8×C11AGL(1,ℤ/8)11yescharacteristic
119C11⋊C8—41no—
120C11⋊C8—81no—
121#556—221no—
122C2×SD32—21no—
123#500—111no—
124#493C2×D1111yescharacteristic
125#485—222no—
126#475—221no—
127#467—221no—
128#459—221no—
129C4×Q16C2×D1111yescharacteristic
130C8×D4—111no—
131#427—221no—
132C4⋊C16C2×D1111yescharacteristic
133#357—21no—
134#357—222no—
135C4×C16—111no—
136#335—111no—
137#331—221no—
138C22×C11—161no—
139C22×C11—161no—
140C22×C11—161no—
141C22×C11#44711yescharacteristic
142C2×D11—41no—
143C2×D11—41no—
144C2×D11—41no—
145C4×C11—21no—
146C4×C11—81no—
147C4×C11—81no—
148C4×C11#44911yescharacteristic
149C4×C11#45411yescharacteristic
150C4×C11#50811yescharacteristic
151C4×C11#50911yescharacteristic
152Dic11—41no—
153Dic11—82no—
154C2×Q16C22⋊D1111yescharacteristic
155C2×D8—21no—
156C2×D8—21no—
157C2×D8—441no—
158C22×C8—221no—
159C4⋊Q8—221no—
160#127—21no—
161#126—442no—
162#124—441no—
163C22⋊Q8—222no—
164C4×Q8—21no—
165C4×Q8—441no—
166C4×D4—111no—
167#117—222no—
168SD32—42no—
169C2×C16—21no—
170C2×C16—221no—
171#107—112no—
172#107—221no—
173#107C22⋊D1111yescharacteristic
174#106—222no—
175C4⋊C8—111no—
176C4⋊C8—221no—
177#103—21no—
178#103—222no—
179#102—441no—
180C22⋊C8—221no—
181C4×C8C22×D1111yescharacteristic
182C2×C11—321no—
183C2×C11#162511yescharacteristic
184C2×C11#218611yescharacteristic
185C2×C11#219311yescharacteristic
186D11—81no—
187C2×Q8—21no—
188C2×Q8—441no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4—111no—
193C22×C4—221no—
194Q16—21no—
195Q16—21no—
196D8—42no—
197D8—41no—
198D8—41no—
199D8—882no—
200C2×C8—221no—
201C2×C8—441no—
202C2×C8—441no—
203C2×C8—441no—
204C2×C8D4×D1111yescharacteristic
205C2×C8C2×C22⋊D1111yescharacteristic
206C4⋊C4—21no—
207C4⋊C4—41no—
208C4⋊C4—111no—
209C4⋊C4—222no—
210C4⋊C4—442no—
211C4⋊C4—441no—
212C22⋊C4—221no—
213C22⋊C4—442no—
214C22⋊C4—442no—
215C42—41no—
216C42—442no—
217C42D4×D1111yescharacteristic
218C16—41no—
219C16—441no—
220C11#1234111yescharacteristic, complemented, Sylow
221C23—81no—
222C23—221no—
223Q8—41no—
224Q8—41no—
225Q8—881no—
226Q8—881no—
227D4—81no—
228D4—81no—
229D4—81no—
230D4—81no—
231D4—161no—
232D4—221no—
233D4—221no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—221no—
237C2×C4—441no—
238C2×C4—441no—
239C2×C4—442no—
240C2×C4D8×D1111yescharacteristic
241C2×C4#6696411yescharacteristic
242C2×C4#6699011yescharacteristic
243C8—21no—
244C8—441no—
245C8—881no—
246C8#6698511yescharacteristic
247C8#6700311yescharacteristic
248C22—161no—
249C22—161no—
250C22—161no—
251C22—441no—
252C22—441no—
253C22—441no—
254C22#1062276911yescharacteristic
255C4—21no—
256C4—81no—
257C4—81no—
258C4—441no—
259C4—882no—
260C4#1062252711yescharacteristic
261C4#1062252911yescharacteristic
262C4#1062265011yescharacteristic
263C4#1062281411yescharacteristic
264C2—321no—
265C2—881no—
266C2#1306770411yescharacteristic
267C2#1307053811yescharacteristic
268C2#1307057711yescharacteristic
subgroupG/H
centerC22#10622769
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×#2207C2
socleC22×C11#447
prime radical#13067968C2
hypercenter#2207D11
hypocenterC11#12341
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2207

Complements

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

NH ≅ G/Ntype
1. #13081048C2semidirect
2. #13070839C2semidirect
4. #13066670C2semidirect
5. #13066580C2semidirect
6. #13066570C2semidirect
7. C11×#2207C2semidirect
89. #2207D11semidirect
220. C11#12341semidirect

Maximal subgroups

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

subgroupindex
#130810482
#130708392
#130679682
#130666702
#130665802
#130665702
C11×#22072
#1234111