Finite Group Databasebeta

← #14656367

Subgroups — #14656367

Order 2816.

626 conjugacy classes of subgroups; only the 139 normal subgroups are shown.

normal subgroups only

This group has 626 conjugacy classes of subgroups — too many to draw. Only its 139 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
1C2×#10622700C212yesmaximal
2#13069410C211yesmaximal, characteristic
3C2×#10622185C212yesmaximal, complemented
4#13066451C211yesmaximal, characteristic, complemented
5C2×C11×#494C211yesmaximal, characteristic, complemented
6C22×C11×Q16—22no—
7C2×C11×C4⋊Q8C2212yes—
8C2×C4×D44C2211yescharacteristic
9C11×#494—24no—
10C2×C4×C8×C11C2211yescharacteristic
11C2×(C2×D11)⋊C8—22no—
12#10622700—24no—
13#10622700—24no—
14C2×#66873—22no—
15C2×#66871—22no—
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2212yes—
18#10622185—24no—
19C22×Q8×C11—22no—
20C22×D44D411yescharacteristic
21C22×C4×D11—21no—
22C2×C11×Q16—28no—
23C2×C11×Q16—44no—
24C2×C11×Q16—44no—
25C22×C8×C11D412yes—
26C11×C4⋊Q8—22no—
27C11×C4⋊Q8—22no—
28C11×C4⋊Q8—22no—
29C11×C4⋊Q8D414yes—
30C2×C11×C4⋊C4—22no—
31C2×C11×C4⋊C4—22no—
32C2×C42×C11C2311yescharacteristic
33C2×(C2×D11)⋊C4—21no—
34C2×C4⋊Dic11D411yescharacteristic
35C22×C11⋊C8—22no—
36C22×C11⋊C8—21no—
37C4×D44—22no—
38C4×D44—22no—
39C4×C8×C11—22no—
40(C2×D11)⋊C8—44no—
41#66873—28no—
42#66871—28no—
43C4⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)D414yes—
46#10274—111nomaximal, Sylow
47C23×D11—21no—
48C2×Q8×C11—24no—
49C2×Q8×C11—42no—
50C2×Q8×C11—44no—
51C2×Q8×C11—44no—
52C22×C4×C11—42no—
53C22×C4×C11C2×D411yescharacteristic
54C22×C4×C11C2×D411yescharacteristic
55C22×C4×C11#4111yescharacteristic
56C22×Dic11—21no—
57C2×D44—22no—
58C2×D44—21no—
59C2×D44—22no—
60C2×D44Q1612yescomplemented
61C2×C4×D11—41no—
62C2×C4×D11—41no—
63C2×C4×D11—42no—
64C2×C4×D11—42no—
65C11×Q16—416no—
66C2×C8×C11—22no—
67C2×C8×C11—22no—
68C2×C8×C11D814yes—
69C11×C4⋊C4—24no—
70C11×C4⋊C4—24no—
71C11×C4⋊C4—42no—
72C11×C4⋊C4—42no—
73C42×C11C2×D412yes—
74C42×C11C2×D412yes—
75(C2×D11)⋊C4—42no—
76C4⋊Dic11—22no—
77C2×C11⋊C8—24no—
78C2×C11⋊C8—41no—
79C2×C11⋊C8—42no—
80C2×C11⋊C8—42no—
81C2×C11⋊C8—42no—
82C2×#494D1111yescharacteristic, complemented
83C2×#474—112no—
84#1954—111no—
85C2×#332—112no—
86#1277—111no—
87C23×C11#12111yescharacteristic
88C22×D11—22no—
89C22×D11—41no—
90C22×D11—42no—
91C22×D11—41no—
92C22×D11—42no—
93Q8×C11—48no—
94Q8×C11—82no—
95Q8×C11—82no—
96C2×C4×C11—22no—
97C2×C4×C11—44no—
98C2×C4×C11—84no—
99C2×C4×C11#12012yes—
100C2×C4×C11#12011yescharacteristic
101C2×C4×C11#12112yes—
102C2×C4×C11#12711yescharacteristic
103C2×C4×C11C2×D812yes—
104C2×C4×C11C2×Q1611yescharacteristic
105C2×C4×C11#13511yescharacteristic
106C2×C4×C11AGL(1,ℤ/8)12yes—
107C2×C4×C11#13712yes—
108C2×Dic11—41no—
109C2×Dic11—42no—
110D44—24no—
111D44—42no—
112C4×D11—82no—
113C4×D11—81no—
114C4×D11—81no—
115C8×C11—24no—
116C11⋊C8—44no—
117C11⋊C8—81no—
118C22×Q16—22no—
119C2×C4⋊Q8C2×D1112yes—
120C2×C4×D4—111no—
121#494—24no—
122#474—224no—
123#474—224no—
124C2×#107—222no—
125C2×C4⋊C8—112no—
126C2×C4⋊C8—111no—
127C2×#102—222no—
128C2×C22⋊C8—222no—
129C2×C4×C8C2×D1111yescharacteristic
130#332—224no—
131C22×C11#39211yescharacteristic
132C22×C11#45912yes—
133C22×C11#46711yescharacteristic
134C22×C11#47011yescharacteristic
135C22×C11#47312yes—
136C2×D11—44no—
137C2×D11—42no—
138C2×D11—82no—
139C2×D11—81no—
140C2×D11—81no—
141C4×C11—22no—
142C4×C11—84no—
143C4×C11#44712yes—
144C4×C11#45112yes—
145C4×C11#45212yes—
146C4×C11#49311yescharacteristic
147C4×C11#49611yescharacteristic
148Dic11—81no—
149C22×Q8—22no—
150C22×D4—111no—
151C23×C4—221no—
152C2×Q16—28no—
153C2×Q16—44no—
154C2×Q16—44no—
155C22×C8—222no—
156C22×C8—221no—
157C22×C8C22⋊D1112yes—
158C4⋊Q8—22no—
159C4⋊Q8—22no—
160C4⋊Q8—22no—
161C4⋊Q8C22⋊D1114yes—
162C4×D4—222no—
163C4×D4—222no—
164C2×C4⋊C4—22no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4—111no—
167C2×C22⋊C4—221no—
168C2×C42C22×D1111yescharacteristic
169#107—228no—
170C4⋊C8—114no—
171C4⋊C8—222no—
172C4⋊C8—222no—
173#102—228no—
174C22⋊C8—444no—
175C4×C8—22no—
176C2×C11#166912yes—
177C2×C11#168912yes—
178C2×C11#200111yescharacteristic
179C2×C11#201111yescharacteristic
180C2×C11#202011yescharacteristic
181D11—82no—
182C24—221no—
183C2×Q8—24no—
184C2×Q8—42no—
185C2×Q8—44no—
186C2×Q8—44no—
187C2×D4—112no—
188C2×D4—222no—
189C2×D4—221no—
190C2×D4—222no—
191C22×C4—42no—
192C22×C4—221no—
193C22×C4—442no—
194C22×C4—442no—
195C22×C4—441no—
196C22×C4—441no—
197C22×C4D4×D1111yescharacteristic
198C22×C4#434111yescharacteristic
199C22×C4C2×C22⋊D1111yescharacteristic
200Q16—416no—
201C2×C8—22no—
202C2×C8—22no—
203C2×C8—224no—
204C2×C8—442no—
205C2×C8—442no—
206C2×C8—442no—
207C2×C8—441no—
208C2×C8#432314yes—
209C4⋊C4—24no—
210C4⋊C4—24no—
211C4⋊C4—42no—
212C4⋊C4—42no—
213C4⋊C4—222no—
214C22⋊C4—442no—
215C42D4×D1112yes—
216C42C2×C22⋊D1112yes—
217C11#1027411yescharacteristic, complemented, Sylow
218C23—222no—
219C23—441no—
220C23—442no—
221C23—441no—
222C23—442no—
223C23#6699111yescharacteristic
224Q8—48no—
225Q8—82no—
226Q8—82no—
227D4—224no—
228D4—442no—
229C2×C4—22no—
230C2×C4—44no—
231C2×C4—84no—
232C2×C4—441no—
233C2×C4—442no—
234C2×C4—882no—
235C2×C4—881no—
236C2×C4—881no—
237C2×C4Q16×D1111yescharacteristic
238C2×C4#6697112yes—
239C2×C4#6697211yescharacteristic
240C2×C4C2×#432312yes—
241C2×C4#6698512yes—
242C2×C4#6699012yes—
243C2×C4#6699212yes—
244C2×C4#6699311yescharacteristic
245C2×C4#6700611yescharacteristic
246C8—24no—
247C8—444no—
248C8—881no—
249C22—442no—
250C22—444no—
251C22—882no—
252C22—881no—
253C22—881no—
254C22#1062268512yes—
255C22#1062280111yescharacteristic
256C22#1062280211yescharacteristic
257C22#1062280512yes—
258C22#1062283611yescharacteristic
259C4—22no—
260C4—84no—
261C4—881no—
262C4#1062268611yescharacteristic
263C4#1062268711yescharacteristic
264C4#1062279912yes—
265C4#1062280012yes—
266C4#1062283012yes—
267C2—882no—
268C2#1306797812yes—
269C2#1306810212yes—
270C2#1306962311yescharacteristic
271C2#1306968711yescharacteristic
272C2#1306973511yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#494C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenterC2×#494D11
hypocenterC11#10274
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#494

Complements

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

NH ≅ G/Ntype
3. C2×#10622185C2semidirect
4. #13066451C2semidirect
5. C2×C11×#494C2semidirect
60. C2×D44Q16semidirect
82. C2×#494D11semidirect
217. C11#10274semidirect

Maximal subgroups

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

subgroupindex
C2×#106227002
#130694102
C2×#106221852
#130664512
C2×C11×#4942
#1027411