Finite Group Databasebeta

← #14672650

Subgroups — #14672650

Order 2816.

546 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 546 conjugacy classes of subgroups — too many to draw. Only its 105 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×#10622792C212yesmaximal
2C2×#10622203C212yesmaximal, complemented
3#13069504C211yesmaximal, characteristic
4#13066698C211yesmaximal, characteristic, complemented
5C2×C11×#494C211yesmaximal, characteristic, complemented
6C22×C11×Q16—21no—
7C22×C11×Q16C2212yes—
8C2×C11×C4⋊Q8—21no—
9C2×#66957C2211yescharacteristic
10C11×#494—24no—
11C2×C4×C8×C11C2211yescharacteristic
12C2×#66893—22no—
13#10622792—24no—
14#10622792—24no—
15C2×#66892—22no—
16#10622723—21no—
17C2×#66883C2211yescharacteristic
18C2×#66876C2212yes—
19C2×#66869—21no—
20#10622203—24no—
21C22×Q8×C11—22no—
22C2×#4339—21no—
23C2×C11×Q16—24no—
24C2×C11×Q16—22no—
25C2×C11×Q16—22no—
26C2×C11×Q16—22no—
27C2×C11×Q16—22no—
28C2×C11×Q16—22no—
29C2×C11×Q16—42no—
30C2×C11×Q16—42no—
31C2×C11×Q16D414yes—
32C22×C8×C11D411yescharacteristic
33C22×C8×C11C2311yescharacteristic
34C11×C4⋊Q8—24no—
35C11×C4⋊Q8—42no—
36C2×C11×C4⋊C4—42no—
37C2×C42×C11D411yescharacteristic
38C2×#4318—21no—
39C2×Dic44D411yescharacteristic
40#66957—22no—
41#66957—22no—
42C2×D88D411yescharacteristic
43C2×#4314—21no—
44C4×C8×C11—22no—
45#66893—28no—
46#66892—28no—
47(C2×D11)⋊C8—42no—
48#66883—22no—
49#66876—22no—
50#66876D414yes—
51C2×C11⋊C16—22no—
52#66869—42no—
53#13333—111nomaximal, Sylow
54C2×Q8×C11—24no—
55C2×Q8×C11—42no—
56C2×Q8×C11—42no—
57C2×Q8×C11—42no—
58C2×Q8×C11—42no—
59C2×Q8×C11—42no—
60C22×C4×C11—21no—
61C22×C4×C11—42no—
62C22×C4×C11C2×D411yescharacteristic
63C2×C22⋊D11—41no—
64#4339—41no—
65#4339—41no—
66#4339—41no—
67#4339—41no—
68C2×D44—21no—
69C2×C4×D11—41no—
70C2×Dic22—21no—
71C11×Q16—24no—
72C11×Q16—24no—
73C11×Q16—48no—
74C11×Q16—42no—
75C11×Q16—42no—
76C2×C8×C11—21no—
77C2×C8×C11—21no—
78C2×C8×C11D812yes—
79C2×C8×C11C2×D412yes—
80C2×C8×C11C2×D411yescharacteristic
81C2×C8×C11C2×D412yes—
82C2×C8×C11#4111yescharacteristic
83C11×C4⋊C4—48no—
84C42×C11—21no—
85C42×C11D812yes—
86#4318—41no—
87#4318—41no—
88C2×C11⋊C8—41no—
89Dic44—22no—
90D88—22no—
91#4314—42no—
92C11⋊C16—24no—
93C2×#510—112no—
94C2×#494D1111yescharacteristic, complemented
95C2×#362—112no—
96#1974—111no—
97#1376—111no—
98C23×C11AGL(1,ℤ/8)11yescharacteristic
99C22×D11—41no—
100Q8×C11—44no—
101Q8×C11—44no—
102Q8×C11—82no—
103Q8×C11—82no—
104C2×C4×C11—24no—
105C2×C4×C11—22no—
106C2×C4×C11—44no—
107C2×C4×C11—82no—
108C2×C4×C11—82no—
109C2×C4×C11#12011yescharacteristic
110C2×C4×C11#12111yescharacteristic
111C2×C4×C11#12711yescharacteristic
112C2×C4×C11C2×D811yescharacteristic
113C2×C4×C11C2×D811yescharacteristic
114C2×C4×C11AGL(1,ℤ/8)11yescharacteristic
115C22⋊D11—81no—
116C22⋊D11—81no—
117C2×Dic11—41no—
118D44—41no—
119D44—41no—
120C4×D11—81no—
121C4×D11—81no—
122Dic22—41no—
123Dic22—41no—
124C8×C11—22no—
125C8×C11#12012yes—
126C8×C11#12112yes—
127C11⋊C8—81no—
128C2×#135—111no—
129C22×Q16—21no—
130C22×Q16C2×D1112yes—
131C2×C4⋊Q8—21no—
132#510—224no—
133#510—224no—
134C2×Q32—222no—
135C2×SD32—222no—
136C2×M32—112no—
137#494—24no—
138C2×#108—111no—
139C2×#104—221no—
140#408—221no—
141C2×C4×C8C2×D1111yescharacteristic
142#362—224no—
143C22×C11—22no—
144C22×C11#44711yescharacteristic
145C22×C11#45911yescharacteristic
146C22×C11#49611yescharacteristic
147C2×D11—82no—
148C2×D11—81no—
149C4×C11—24no—
150C4×C11—84no—
151C4×C11#39211yescharacteristic
152C4×C11#44711yescharacteristic
153C4×C11#45911yescharacteristic
154C4×C11#49311yescharacteristic
155Dic11—81no—
156C2×#41—221no—
157C22×Q8—22no—
158#135—222no—
159#135—222no—
160C2×Q16—24no—
161C2×Q16—22no—
162C2×Q16—22no—
163C2×Q16—22no—
164C2×Q16—22no—
165C2×Q16—22no—
166C2×Q16—42no—
167C2×Q16—42no—
168C2×Q16—111no—
169C2×Q16C22⋊D1114yes—
170C2×SD16—221no—
171C2×D8—111no—
172C2×M16—221no—
173C22×C8C22⋊D1111yescharacteristic
174C22×C8C22×D1111yescharacteristic
175C4⋊Q8—24no—
176C4⋊Q8—42no—
177C2×C4⋊C4—42no—
178C2×C42C22⋊D1111yescharacteristic
179Q32—228no—
180SD32—228no—
181M32—114no—
182M32—222no—
183C2×C16—222no—
184#108—222no—
185#104—442no—
186C22⋊C8—442no—
187C4×C8—22no—
188C2×C11—21no—
189C2×C11—21no—
190C2×C11#201111yescharacteristic
191C2×C11#221412yes—
192D11—161no—
193#41—441no—
194#41—441no—
195#41—441no—
196#41—441no—
197C2×Q8—24no—
198C2×Q8—42no—
199C2×Q8—42no—
200C2×Q8—42no—
201C2×Q8—42no—
202C2×Q8—42no—
203C2×Q8—221no—
204C2×D4—221no—
205C2×D4—441no—
206C22×C4—21no—
207C22×C4—42no—
208C22×C4—441no—
209C22×C4C2×C22⋊D1111yescharacteristic
210Q16—24no—
211Q16—24no—
212Q16—48no—
213Q16—42no—
214Q16—42no—
215Q16—222no—
216SD16—442no—
217D8—222no—
218M16—441no—
219M16—441no—
220C2×C8—21no—
221C2×C8—21no—
222C2×C8—441no—
223C2×C8#432312yes—
224C2×C8D4×D1111yescharacteristic
225C2×C8D4×D1112yes—
226C2×C8#434111yescharacteristic
227C2×C8C2×C22⋊D1112yes—
228C4⋊C4—48no—
229C42—21no—
230C42#432312yes—
231C16—224no—
232C11#1333311yescharacteristic, complemented, Sylow
233C23—441no—
234C23#6698511yescharacteristic
235Q8—44no—
236Q8—44no—
237Q8—82no—
238Q8—82no—
239Q8—441no—
240Q8—441no—
241D4—441no—
242D4—441no—
243D4—881no—
244D4—881no—
245C2×C4—24no—
246C2×C4—22no—
247C2×C4—44no—
248C2×C4—82no—
249C2×C4—82no—
250C2×C4—441no—
251C2×C4—881no—
252C2×C4—881no—
253C2×C4C2×#432311yescharacteristic
254C2×C4C2×#432311yescharacteristic
255C2×C4#6698511yescharacteristic
256C2×C4#6699111yescharacteristic
257C2×C4#6699311yescharacteristic
258C2×C4#6700611yescharacteristic
259C8—22no—
260C8—881no—
261C8#6699012yes—
262C8#6699212yes—
263C22—22no—
264C22—882no—
265C22—881no—
266C22#1062268511yescharacteristic
267C22#1062268711yescharacteristic
268C22#1062283011yescharacteristic
269C4—24no—
270C4—84no—
271C4—881no—
272C4#1062268511yescharacteristic
273C4#1062268611yescharacteristic
274C4#1062283011yescharacteristic
275C4#1062283611yescharacteristic
276C2—21no—
277C2—21no—
278C2—1761no—
279C2#1306968711yescharacteristic
280C2#1307069412yes—
subgroupG/H
centerC22#10622685
commutator, cosocleC22×C8×C11C23
FrattiniC22×C8C22×D11
FittingC2×C11×#494C2
socleC22×C11#459
prime radicalC2×#66957C22
hypercenterC2×#494D11
hypocenterC11#13333
LCSG ▷ C22×C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×C8 ◁ C2×#494

Complements

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

NH ≅ G/Ntype
2. C2×#10622203C2semidirect
4. #13066698C2semidirect
5. C2×C11×#494C2semidirect
94. C2×#494D11semidirect
232. C11#13333semidirect

Maximal subgroups

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

subgroupindex
C2×#106227922
C2×#106222032
#130695042
#130666982
C2×C11×#4942
#1333311