Finite Group Databasebeta

← #14667381

Subgroups — #14667381

Order 2816.

314 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 71 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#13081009C211yesmaximal, characteristic, complemented
2#13070840C211yesmaximal, characteristic, complemented
3#13070657C211yesmaximal, characteristic, complemented
4#13067971C211yesmaximal, characteristic
5#13066673C211yesmaximal, characteristic, complemented
6#13066581C211yesmaximal, characteristic, complemented
7C11×D4⋊C16C211yesmaximal, characteristic, complemented
8#10623074—21no—
9C8×D4×C11C2211yescharacteristic
10#10622729—21no—
11C2×#66882—21no—
12#10622628—21no—
13C2×#66864—21no—
14#10622463—21no—
15#10622335—22no—
16C4×Dic44C2211yescharacteristic
17#10622308C2211yescharacteristic
18#10622295C2211yescharacteristic
19C11×C4⋊C16C2211yescharacteristic
20C4×C11×C16C2211yescharacteristic
21#10622147—21no—
22#10622147—22no—
23#10622123—21no—
24#10622096C2211yescharacteristic
25C22×C8×C11—21no—
26C4×D4×C11D411yescharacteristic
27D4×Dic11—41no—
28C2×#4323—41no—
29C2×C4⋊Dic11—22no—
30#66977—22no—
31C2×Dic44D411yescharacteristic
32C2×D88—21no—
33C2×D88—21no—
34#66943—41no—
35#66931—42no—
36#66927—21no—
37#66922—21no—
38C4×Dic22—21no—
39C2×C11×C16—21no—
40C2×C11×C16—21no—
41C11×C4⋊C8D411yescharacteristic
42C11×C22⋊C8—21no—
43C4×C8×C11C2311yescharacteristic
44#66882—22no—
45#66882—21no—
46#66882D412yes—
47#66882D411yescharacteristic
48#66880—22no—
49#66880—21no—
50#66873—41no—
51C4⋊(C11⋊C8)—21no—
52#66864—42no—
53#12342—111nomaximal, Sylow
54C2×D4×C11D811yescharacteristic
55C22×C4×C11—21no—
56C22×Dic11—42no—
57C2×D44—41no—
58C2×D44—41no—
59C2×D44—41no—
60C2×Dic22—21no—
61C2×Dic22—41no—
62C2×C8×C11—21no—
63C2×C8×C11—41no—
64C2×C8×C11—41no—
65C2×C8×C11C2×D411yescharacteristic
66C2×C8×C11C2×D411yescharacteristic
67C11×C4⋊C4D811yescharacteristic
68C11×C22⋊C4—21no—
69C42×C11C2×D411yescharacteristic
70C22⋊Dic11—42no—
71#4323—82no—
72C4⋊Dic11—21no—
73C4⋊Dic11—22no—
74C4⋊Dic11—42no—
75C4⋊Dic11—41no—
76Dic11⋊C4—42no—
77Dic11⋊C4—41no—
78C4×Dic11—41no—
79C2×C11⋊C8—41no—
80Dic44—21no—
81Dic44—21no—
82D88—42no—
83D88—41no—
84D88—41no—
85C11×C16—41no—
86C11×C16—41no—
87#3338—111no—
88#2240—111no—
89#2207—111no—
90#1667—111no—
91#1365—111no—
92#1332—111no—
93D4⋊C16D1111yescharacteristic, complemented
94C23×C11—21no—
95C22×D11—81no—
96D4×C11—21no—
97D4×C11SD3212yescomplemented
98C2×C4×C11—21no—
99C2×C4×C11—41no—
100C2×C4×C11—41no—
101C2×C4×C11#12011yescharacteristic
102C2×C4×C11C2×D811yescharacteristic
103C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
104C2×Dic11—41no—
105C2×Dic11—41no—
106C2×Dic11—42no—
107C2×Dic11—162no—
108D44—81no—
109D44—81no—
110D44—81no—
111D44—81no—
112D44—161no—
113Dic22—41no—
114Dic22—41no—
115Dic22—161no—
116C8×C11—21no—
117C8×C11—41no—
118C8×C11#13511yescharacteristic
119C8×C11AGL(1,ℤ/8)11yescharacteristic
120C11⋊C8—81no—
121#554—221no—
122C2×SD32—221no—
123#500—111no—
124#493—111no—
125#484—222no—
126#477—221no—
127#467—221no—
128#459—221no—
129C4×Q16—111no—
130C8×D4C2×D1111yescharacteristic
131C2×#107—221no—
132C4⋊C16C2×D1111yescharacteristic
133#357—221no—
134#357—222no—
135C4×C16C2×D1111yescharacteristic
136#335—111no—
137#331—221no—
138C22×C11—22no—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11#44711yescharacteristic
142C2×D11—161no—
143C2×D11—161no—
144C2×D11—161no—
145C4×C11—21no—
146C4×C11—41no—
147C4×C11#44911yescharacteristic
148C4×C11#45411yescharacteristic
149C4×C11C2×SD3211yescharacteristic
150C4×C11#51011yescharacteristic
151Dic11—81no—
152Dic11—82no—
153Dic11—81no—
154C2×Q16—111no—
155C2×D8—221no—
156C2×D8—221no—
157C2×D8—441no—
158C22×C8—21no—
159C4⋊Q8—221no—
160#127—221no—
161#125—441no—
162C22⋊Q8—222no—
163C22⋊Q8—442no—
164C4×Q8—221no—
165C4×D4—441no—
166C4×D4D4411yescharacteristic
167C2×C4⋊C4—222no—
168SD32—442no—
169C2×C16—21no—
170C2×C16—21no—
171#107—111no—
172#107—112no—
173#107—222no—
174#107—221no—
175C4⋊C8—221no—
176C4⋊C8D4411yescharacteristic
177#103—222no—
178#103—221no—
179#102—441no—
180C22⋊C8—21no—
181C4×C8C22×D1111yescharacteristic
182C2×C11—42no—
183C2×C11#162511yescharacteristic
184C2×C11#218511yescharacteristic
185C2×C11#219211yescharacteristic
186D11—321no—
187C2×Q8—221no—
188C2×Q8—441no—
189C2×D4—441no—
190C2×D4—441no—
191C2×D4—441no—
192C2×D4D8811yescharacteristic
193C22×C4—21no—
194C22×C4—442no—
195Q16—221no—
196Q16—221no—
197D8—442no—
198D8—441no—
199D8—441no—
200D8—882no—
201C2×C8—21no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—441no—
205C2×C8D4×D1111yescharacteristic
206C2×C8D4×D1111yescharacteristic
207C4⋊C4—221no—
208C4⋊C4—222no—
209C4⋊C4—442no—
210C4⋊C4—442no—
211C4⋊C4—441no—
212C4⋊C4—441no—
213C4⋊C4D8811yescharacteristic
214C22⋊C4—21no—
215C22⋊C4—442no—
216C42—441no—
217C42C2×D4411yescharacteristic
218C16—41no—
219C16—41no—
220C11#1234211yescharacteristic, complemented, Sylow
221C23—21no—
222C23—881no—
223Q8—441no—
224Q8—441no—
225Q8—1761no—
226D4—21no—
227D4—881no—
228D4—881no—
229D4—881no—
230D4—881no—
231D4—1761no—
232D4#6686412yescomplemented
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—441no—
237C2×C4—441no—
238C2×C4—442no—
239C2×C4—1762no—
240C2×C4#6693511yescharacteristic
241C2×C4C2×D8811yescharacteristic
242C2×C4#6696111yescharacteristic
243C8—21no—
244C8—41no—
245C8—881no—
246C8#6696411yescharacteristic
247C8#6696911yescharacteristic
248C22—22no—
249C22—41no—
250C22—41no—
251C22—1761no—
252C22—1761no—
253C22—1761no—
254C22#1062234511yescharacteristic
255C4—21no—
256C4—41no—
257C4—881no—
258C4—881no—
259C4—882no—
260C4#1062239411yescharacteristic
261C4#1062244011yescharacteristic
262C4C2×#6686411yescharacteristic
263C4#1062252211yescharacteristic
264C2—42no—
265C2—3521no—
266C2#1306770711yescharacteristic
267C2#1307053511yescharacteristic
268C2#1307057511yescharacteristic
subgroupG/H
centerC22#10622345
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
FittingC11×D4⋊C16C2
socleC22×C11#447
prime radical#13067971C2
hypercenterD4⋊C16D11
hypocenterC11#12342
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ D4⋊C16

Complements

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

NH ≅ G/Ntype
1. #13081009C2semidirect
2. #13070840C2semidirect
3. #13070657C2semidirect
5. #13066673C2semidirect
6. #13066581C2semidirect
7. C11×D4⋊C16C2semidirect
93. D4⋊C16D11semidirect
97. D4×C11SD32semidirect
220. C11#12342semidirect
232. D4#66864semidirect

Maximal subgroups

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

subgroupindex
#130810092
#130708402
#130706572
#130679712
#130666732
#130665812
C11×D4⋊C162
#1234211