Finite Group Databasebeta

← #14656301

Subgroups — #14656301

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×#10622696C212yesmaximal
2#13069410C211yesmaximal, characteristic
3C2×#10622185C212yesmaximal, complemented
4#13066451C211yesmaximal, characteristic, complemented
5C2×C11×#500C211yesmaximal, characteristic, complemented
6C2×C11×C4⋊Q8C2212yes—
7C22×#4325—22no—
8C2×C4×D44C2211yescharacteristic
9C11×#500—24no—
10C2×C11×#107—22no—
11C2×C4×C8×C11C2211yescharacteristic
12C2×#66899—22no—
13C2×(C2×D11)⋊C8—22no—
14#10622696—24no—
15#10622696—24no—
16C2×C4⋊(C11⋊C8)C2211yescharacteristic
17C2×C4⋊(C11⋊C8)C2212yes—
18#10622185—24no—
19C22×Q8×C11—22no—
20C22×D44D411yescharacteristic
21C22×C4×D11—21no—
22C22×C8×C11D412yes—
23C11×C4⋊Q8—22no—
24C11×C4⋊Q8—22no—
25C11×C4⋊Q8—22no—
26C11×C4⋊Q8D414yes—
27C2×C11×C4⋊C4—22no—
28C2×C11×C4⋊C4—22no—
29C2×C42×C11C2311yescharacteristic
30C2×#4325—28no—
31C2×#4325—44no—
32C2×#4325—44no—
33C2×(C2×D11)⋊C4—21no—
34C2×C4⋊Dic11D411yescharacteristic
35C22×C11⋊C8—22no—
36C22×C11⋊C8—21no—
37C4×D44—22no—
38C4×D44—22no—
39C11×#107—28no—
40C4×C8×C11—22no—
41#66899—28no—
42(C2×D11)⋊C8—44no—
43C4⋊(C11⋊C8)—22no—
44C4⋊(C11⋊C8)—22no—
45C4⋊(C11⋊C8)D414yes—
46#10264—111nomaximal, Sylow
47C23×D11—21no—
48C2×Q8×C11—24no—
49C2×Q8×C11—42no—
50C2×Q8×C11—42no—
51C2×Q8×C11—42no—
52C2×Q8×C11—42no—
53C2×Q8×C11—42no—
54C22×C4×C11—42no—
55C22×C4×C11C2×D411yescharacteristic
56C22×C4×C11C2×D411yescharacteristic
57C22×C4×C11#4111yescharacteristic
58C22×Dic11—21no—
59C2×D44—22no—
60C2×D44—21no—
61C2×D44—22no—
62C2×D44D812yes—
63C2×C4×D11—41no—
64C2×C4×D11—41no—
65C2×C4×D11—42no—
66C2×C4×D11—42no—
67C2×C8×C11—22no—
68C2×C8×C11—22no—
69C2×C8×C11SD1614yescomplemented
70C11×C4⋊C4—24no—
71C11×C4⋊C4—24no—
72C11×C4⋊C4—42no—
73C11×C4⋊C4—42no—
74C42×C11C2×D412yes—
75C42×C11C2×D412yes—
76#4325—416no—
77(C2×D11)⋊C4—42no—
78C4⋊Dic11—22no—
79C2×C11⋊C8—24no—
80C2×C11⋊C8—41no—
81C2×C11⋊C8—42no—
82C2×C11⋊C8—42no—
83C2×C11⋊C8—42no—
84C2×#500D1111yescharacteristic, complemented
85C2×#461—112no—
86#1954—111no—
87C2×#332—112no—
88#1277—111no—
89C23×C11#12111yescharacteristic
90C22×D11—22no—
91C22×D11—41no—
92C22×D11—42no—
93C22×D11—41no—
94C22×D11—42no—
95Q8×C11—44no—
96Q8×C11—44no—
97Q8×C11—82no—
98Q8×C11—82no—
99C2×C4×C11—22no—
100C2×C4×C11—44no—
101C2×C4×C11—82no—
102C2×C4×C11—82no—
103C2×C4×C11#12012yes—
104C2×C4×C11#12011yescharacteristic
105C2×C4×C11#12112yes—
106C2×C4×C11#12711yescharacteristic
107C2×C4×C11C2×D811yescharacteristic
108C2×C4×C11C2×SD1612yes—
109C2×C4×C11#13511yescharacteristic
110C2×C4×C11AGL(1,ℤ/8)12yes—
111C2×C4×C11#13712yes—
112C2×Dic11—41no—
113C2×Dic11—42no—
114D44—24no—
115D44—42no—
116C4×D11—82no—
117C4×D11—81no—
118C4×D11—81no—
119C8×C11—24no—
120C11⋊C8—44no—
121C11⋊C8—81no—
122C22×SD16—222no—
123C2×C4⋊Q8C2×D1112yes—
124C2×C4×D4—111no—
125#500—24no—
126#461—224no—
127#461—224no—
128C2×#107—22no—
129C2×C4⋊C8—112no—
130C2×C4⋊C8—111no—
131C2×#103—222no—
132C2×C22⋊C8—222no—
133C2×C4×C8C2×D1111yescharacteristic
134#332—224no—
135C22×C11#39211yescharacteristic
136C22×C11#46112yes—
137C22×C11#46611yescharacteristic
138C22×C11#46911yescharacteristic
139C22×C11#47312yes—
140C2×D11—44no—
141C2×D11—42no—
142C2×D11—82no—
143C2×D11—81no—
144C2×D11—81no—
145C4×C11—22no—
146C4×C11—84no—
147C4×C11#44712yes—
148C4×C11#44812yes—
149C4×C11#44912yes—
150C4×C11#49211yescharacteristic
151C4×C11#49711yescharacteristic
152Dic11—81no—
153C22×Q8—22no—
154C22×D4—111no—
155C23×C4—221no—
156C2×SD16—228no—
157C2×SD16—444no—
158C2×SD16—444no—
159C22×C8—222no—
160C22×C8—221no—
161C22×C8C22⋊D1112yes—
162C4⋊Q8—22no—
163C4⋊Q8—22no—
164C4⋊Q8—22no—
165C4⋊Q8C22⋊D1114yes—
166C4×D4—222no—
167C4×D4—222no—
168C2×C4⋊C4—22no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—111no—
171C2×C22⋊C4—221no—
172C2×C42C22×D1111yescharacteristic
173#107—28no—
174C4⋊C8—114no—
175C4⋊C8—222no—
176C4⋊C8—222no—
177#103—228no—
178C22⋊C8—444no—
179C4×C8—22no—
180C2×C11#167312yes—
181C2×C11#169312yes—
182C2×C11#199911yescharacteristic
183C2×C11#201311yescharacteristic
184C2×C11#202011yescharacteristic
185D11—82no—
186C24—221no—
187C2×Q8—24no—
188C2×Q8—42no—
189C2×Q8—42no—
190C2×Q8—42no—
191C2×Q8—42no—
192C2×Q8—42no—
193C2×D4—112no—
194C2×D4—222no—
195C2×D4—221no—
196C2×D4—222no—
197C22×C4—42no—
198C22×C4—221no—
199C22×C4—441no—
200C22×C4—442no—
201C22×C4—442no—
202C22×C4—441no—
203C22×C4D4×D1111yescharacteristic
204C22×C4#434111yescharacteristic
205C22×C4C2×C22⋊D1111yescharacteristic
206SD16—4416no—
207C2×C8—22no—
208C2×C8—22no—
209C2×C8—224no—
210C2×C8—442no—
211C2×C8—442no—
212C2×C8—441no—
213C2×C8—442no—
214C2×C8#432514yescomplemented
215C4⋊C4—24no—
216C4⋊C4—24no—
217C4⋊C4—42no—
218C4⋊C4—42no—
219C4⋊C4—222no—
220C22⋊C4—442no—
221C42D4×D1112yes—
222C42C2×C22⋊D1112yes—
223C11#1026411yescharacteristic, complemented, Sylow
224C23—222no—
225C23—441no—
226C23—442no—
227C23—441no—
228C23—442no—
229C23#6699111yescharacteristic
230Q8—44no—
231Q8—44no—
232Q8—82no—
233Q8—82no—
234D4—224no—
235D4—442no—
236C2×C4—22no—
237C2×C4—44no—
238C2×C4—82no—
239C2×C4—82no—
240C2×C4—441no—
241C2×C4—442no—
242C2×C4—882no—
243C2×C4—881no—
244C2×C4—881no—
245C2×C4D8×D1111yescharacteristic
246C2×C4#6696412yes—
247C2×C4#6696511yescharacteristic
248C2×C4#6699012yes—
249C2×C4#6699212yes—
250C2×C4#6699311yescharacteristic
251C2×C4C2×#432512yes—
252C2×C4#6699512yes—
253C2×C4#6700611yescharacteristic
254C8—24no—
255C8—444no—
256C8—881no—
257C22—442no—
258C22—444no—
259C22—882no—
260C22—881no—
261C22—881no—
262C22#1062269612yes—
263C22#1062277011yescharacteristic
264C22#1062277211yescharacteristic
265C22#1062280512yes—
266C22#1062283611yescharacteristic
267C4—22no—
268C4—84no—
269C4—881no—
270C4#1062269811yescharacteristic
271C4#1062269911yescharacteristic
272C4#1062276912yes—
273C4#1062277112yes—
274C4#1062284012yes—
275C2—882no—
276C2#1306800212yes—
277C2#1306812612yes—
278C2#1306961111yescharacteristic
279C2#1306969911yescharacteristic
280C2#1306973511yescharacteristic
subgroupG/H
centerC23#66991
commutator, cosocleC2×C42×C11C23
FrattiniC2×C42C22×D11
FittingC2×C11×#500C2
socleC23×C11#121
prime radicalC22×D44D4
hypercenterC2×#500D11
hypocenterC11#10264
LCSG ▷ C2×C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#500

Complements

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

NH ≅ G/Ntype
3. C2×#10622185C2semidirect
4. #13066451C2semidirect
5. C2×C11×#500C2semidirect
69. C2×C8×C11SD16semidirect
84. C2×#500D11semidirect
214. C2×C8#4325semidirect
223. C11#10264semidirect

Maximal subgroups

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

subgroupindex
C2×#106226962
#130694102
C2×#106221852
#130664512
C2×C11×#5002
#1026411