Finite Group Databasebeta

← #14667377

Subgroups — #14667377

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#13070839C211yesmaximal, characteristic, complemented
3#13070653C211yesmaximal, characteristic, complemented
4#13066675C211yesmaximal, characteristic, complemented
5#13066579C211yesmaximal, characteristic, complemented
6D4⋊(C11⋊C16)C211yesmaximal, characteristic, complemented
7C11×#1667C211yesmaximal, characteristic
8#10623074—21no—
9C11×#493C2211yescharacteristic
10C11×#459—21no—
11C8×D4×C11C2211yescharacteristic
12C2×#66891—21no—
13#10622729—21no—
14C2×#66882—21no—
15#10622463—21no—
16#10622335—22no—
17C4×Dic44C2211yescharacteristic
18#10622295C2211yescharacteristic
19C11×#335C2211yescharacteristic
20C11×#331—21no—
21#10622200—21no—
22#10622200—22no—
23C4⋊(C11⋊C16)C2211yescharacteristic
24C4×C11⋊C16C2211yescharacteristic
25C2×C11×D8—21no—
26C2×C11×D8—21no—
27C2×C11×D8—41no—
28C22×C8×C11—21no—
29C11×#127—21no—
30C4×D4×C11D411yescharacteristic
31D4×Dic11—41no—
32C2×C4⋊Dic11—22no—
33#66977—22no—
34C2×Dic44D411yescharacteristic
35#66943—41no—
36#66931—42no—
37#66922—21no—
38C4×Dic22—21no—
39C11×C4⋊C8—21no—
40C11×C4⋊C8D411yescharacteristic
41C11×#102—41no—
42C11×C22⋊C8—21no—
43C4×C8×C11C2311yescharacteristic
44#66891—42no—
45#66882—22no—
46#66882—21no—
47#66882D412yes—
48#66882D411yescharacteristic
49#66880—22no—
50#66880—21no—
51C2×C11⋊C16—21no—
52C2×C11⋊C16—21no—
53#12342—111nomaximal, Sylow
54C2×D4×C11—41no—
55C2×D4×C11—41no—
56C2×D4×C11—41no—
57C2×D4×C11D811yescharacteristic
58C22×C4×C11—21no—
59C22×Dic11—42no—
60C2×Dic22—21no—
61C2×Dic22—41no—
62C11×D8—42no—
63C11×D8—41no—
64C11×D8—41no—
65C11×D8—82no—
66C2×C8×C11—21no—
67C2×C8×C11—41no—
68C2×C8×C11—41no—
69C2×C8×C11—41no—
70C2×C8×C11C2×D411yescharacteristic
71C2×C8×C11C2×D411yescharacteristic
72C11×C4⋊C4D811yescharacteristic
73C11×C22⋊C4—21no—
74C42×C11C2×D411yescharacteristic
75C22⋊Dic11—42no—
76C4⋊Dic11—21no—
77C4⋊Dic11—22no—
78C4⋊Dic11—42no—
79C4⋊Dic11—41no—
80Dic11⋊C4—42no—
81Dic11⋊C4—41no—
82C4×Dic11—41no—
83Dic44—21no—
84Dic44—21no—
85C11⋊C16—41no—
86C11⋊C16—41no—
87#3338—111no—
88#2240—111no—
89#2207—111no—
90#1667D1111yescharacteristic
91#1365—111no—
92#1332—111no—
93D4⋊C16—111no—
94C23×C11—21no—
95C23×C11—81no—
96D4×C11—21no—
97D4×C11—81no—
98D4×C11—81no—
99D4×C11—81no—
100D4×C11—81no—
101D4×C11—161no—
102D4×C11SD3212yescomplemented
103C2×C4×C11—21no—
104C2×C4×C11—41no—
105C2×C4×C11—41no—
106C2×C4×C11#12011yescharacteristic
107C2×C4×C11C2×D811yescharacteristic
108C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
109C2×Dic11—41no—
110C2×Dic11—41no—
111C2×Dic11—42no—
112C2×Dic11—162no—
113Dic22—41no—
114Dic22—41no—
115Dic22—161no—
116C8×C11—21no—
117C8×C11—41no—
118C8×C11—81no—
119C8×C11#13511yescharacteristic
120C8×C11AGL(1,ℤ/8)11yescharacteristic
121#554—221no—
122C2×SD32—221no—
123#500—111no—
124#493C2×D1111yescharacteristic
125#484—222no—
126#477—221no—
127#467—221no—
128#459—21no—
129C4×Q16—111no—
130C8×D4C2×D1111yescharacteristic
131C2×#107—221no—
132C4⋊C16—111no—
133#357—221no—
134#357—222no—
135C4×C16—111no—
136#335C2×D1111yescharacteristic
137#331—21no—
138C22×C11—22no—
139C22×C11—41no—
140C22×C11—41no—
141C22×C11—161no—
142C22×C11—161no—
143C22×C11—161no—
144C22×C11#44711yescharacteristic
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—21no—
156C2×D8—21no—
157C2×D8—41no—
158C22×C8—21no—
159C4⋊Q8—221no—
160#127—21no—
161#125—441no—
162C22⋊Q8—222no—
163C22⋊Q8—442no—
164C4×Q8—221no—
165C4×D4—441no—
166C4×D4C22⋊D1111yescharacteristic
167C2×C4⋊C4—222no—
168SD32—442no—
169C2×C16—221no—
170C2×C16—221no—
171#107—111no—
172#107—112no—
173#107—222no—
174#107—221no—
175C4⋊C8—21no—
176C4⋊C8C22⋊D1111yescharacteristic
177#103—222no—
178#103—221no—
179#102—41no—
180C22⋊C8—21no—
181C4×C8C22×D1111yescharacteristic
182C2×C11—42no—
183C2×C11—321no—
184C2×C11#162511yescharacteristic
185C2×C11#218511yescharacteristic
186C2×C11#219211yescharacteristic
187C2×Q8—221no—
188C2×Q8—441no—
189C2×D4—41no—
190C2×D4—41no—
191C2×D4—41no—
192C2×D4#432311yescharacteristic
193C22×C4—21no—
194C22×C4—442no—
195Q16—221no—
196Q16—221no—
197D8—42no—
198D8—41no—
199D8—41no—
200D8—82no—
201C2×C8—21no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
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⋊C4#432311yescharacteristic
214C22⋊C4—21no—
215C22⋊C4—442no—
216C42—441no—
217C42C2×C22⋊D1111yescharacteristic
218C16—441no—
219C16—441no—
220C11#1234211yescharacteristic, complemented, Sylow
221C23—21no—
222C23—81no—
223Q8—441no—
224Q8—441no—
225Q8—1761no—
226D4—21no—
227D4—81no—
228D4—81no—
229D4—81no—
230D4—81no—
231D4—161no—
232D4#6689112yescomplemented
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—41no—
236C2×C4—441no—
237C2×C4—441no—
238C2×C4—442no—
239C2×C4—1762no—
240C2×C4C2×#432311yescharacteristic
241C2×C4#6699011yescharacteristic
242C2×C4#6700211yescharacteristic
243C8—21no—
244C8—41no—
245C8—81no—
246C8#6696411yescharacteristic
247C8#6696511yescharacteristic
248C22—22no—
249C22—41no—
250C22—41no—
251C22—161no—
252C22—161no—
253C22—161no—
254C22#1062264911yescharacteristic
255C4—21no—
256C4—41no—
257C4—881no—
258C4—881no—
259C4—882no—
260C4C2×#6689111yescharacteristic
261C4#1062277111yescharacteristic
262C4#1062280811yescharacteristic
263C4#1062281411yescharacteristic
264C2—42no—
265C2—321no—
266C2#1306770311yescharacteristic
267C2#1307053211yescharacteristic
268C2#1307057111yescharacteristic
subgroupG/H
centerC22#10622649
commutator, cosocleC4×C8×C11C23
FrattiniC4×C8C22×D11
Fitting, prime radicalC11×#1667C2
socleC22×C11#447
hypercenter#1667D11
hypocenterC11#12342
LCSG ▷ C4×C8×C11 ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ C8×D4 ◁ #1667

Complements

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

NH ≅ G/Ntype
1. #13081009C2semidirect
2. #13070839C2semidirect
3. #13070653C2semidirect
4. #13066675C2semidirect
5. #13066579C2semidirect
6. D4⋊(C11⋊C16)C2semidirect
102. D4×C11SD32semidirect
220. C11#12342semidirect
232. D4#66891semidirect

Maximal subgroups

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

subgroupindex
#130810092
#130708392
#130706532
#130666752
#130665792
D4⋊(C11⋊C16)2
C11×#16672
#1234211