Finite Group Databasebeta

← #13069635

Subgroups — #13069635

Order 1408.

382 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 75 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×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
2#10623356C211yesmaximal, characteristic, complemented
3C2×#66989C211yesmaximal, characteristic, complemented
4C2×#66901C211yesmaximal, characteristic, complemented
5#10622828C211yesmaximal, characteristic, complemented
6C2×#66888C211yesmaximal, characteristic, complemented
7#10622193C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C22×D4×C11C2211yescharacteristic
10C22×Dic22C2211yescharacteristic
11C11×AGL(1,ℤ/8)—22no—
12C11×AGL(1,ℤ/8)—22no—
13C2×C11×SD16—21no—
14C2×C11×D8—21no—
15C2×C11×M16C2211yescharacteristic
16C2×C22⋊Dic11—22no—
17#66997—21no—
18#66989—22no—
19#66989—21no—
20#66989—22no—
21#66988—22no—
22#66979C2211yescharacteristic
23#66977—22no—
24C2×C4×Dic11C2211yescharacteristic
25C2×#4318C2211yescharacteristic
26#66901—22no—
27#66896—22no—
28#66888—22no—
29C24×C11—21no—
30C11×#41—21no—
31C11×#41—21no—
32C11×#41—21no—
33C11×#41—21no—
34C2×Q8×C11D411yescharacteristic
35C2×D4×C11—21no—
36C2×D4×C11—21no—
37C2×D4×C11—21no—
38C2×D4×C11—21no—
39C2×D4×C11—21no—
40C2×D4×C11—21no—
41C2×D4×C11D411yescharacteristic
42C2×D4×C11D412yes—
43C22×C4×C11—21no—
44C22×C4×C11C2311yescharacteristic
45C22×Dic11—21no—
46C22×Dic11D412yes—
47C2×Dic22—21no—
48C2×Dic22—21no—
49C2×Dic22—21no—
50C2×Dic22—21no—
51C2×Dic22—21no—
52C2×Dic22—21no—
53C11×SD16—24no—
54C11×D8—24no—
55C11×M16—21no—
56C11×M16D412yes—
57C2×C8×C11—21no—
58C22⋊Dic11—24no—
59C22⋊Dic11—28no—
60C22⋊Dic11—21no—
61C4⋊Dic11D412yes—
62Dic11⋊C4—24no—
63C4×Dic11—21no—
64C4×Dic11—21no—
65C4×Dic11D412yes—
66#4318—21no—
67#4318—21no—
68C2×C11⋊C8—21no—
69#2003—111nomaximal, Sylow
70C23×C11—21no—
71C23×C11—22no—
72C23×C11—44no—
73C23×C11—41no—
74C23×C11—41no—
75C23×C11C2×D411yescharacteristic
76Q8×C11—21no—
77Q8×C11—21no—
78D4×C11—21no—
79D4×C11—22no—
80D4×C11—22no—
81D4×C11—21no—
82D4×C11—41no—
83D4×C11—41no—
84D4×C11—41no—
85D4×C11—41no—
86C2×C4×C11—21no—
87C2×C4×C11—41no—
88C2×C4×C11—41no—
89C2×C4×C11C2×D411yescharacteristic
90C2×C4×C11C2×D411yescharacteristic
91C2×C4×C11C2×D411yescharacteristic
92C2×C4×C11C2×D411yescharacteristic
93C2×C4×C11C2×D411yescharacteristic
94C2×C4×C11#4111yescharacteristic
95C2×Dic11—22no—
96C2×Dic11—22no—
97C2×Dic11—22no—
98C2×Dic11—22no—
99C2×Dic11—22no—
100C2×Dic11—42no—
101Dic22—41no—
102Dic22—41no—
103Dic22—41no—
104Dic22—41no—
105C8×C11—22no—
106C11⋊C8—41no—
107C2×AGL(1,ℤ/8)D1111yescharacteristic
108#536—111no—
109C2×#124—111no—
110C2×#104—111no—
111#418—111no—
112C2×#101—111no—
113#339—111no—
114C22×C11—22no—
115C22×C11—44no—
116C22×C11—41no—
117C22×C11—42no—
118C22×C11—42no—
119C22×C11—82no—
120C22×C11—82no—
121C22×C11#12011yescharacteristic
122C22×C11#12011yescharacteristic
123C22×C11#12111yescharacteristic
124C4×C11—41no—
125C4×C11#12011yescharacteristic
126C4×C11#12111yescharacteristic
127C4×C11#12111yescharacteristic
128C4×C11#12711yescharacteristic
129Dic11—42no—
130Dic11—42no—
131Dic11—42no—
132C2×#41C2×D1111yescharacteristic
133C22×Q8—111no—
134C22×D4C2×D1111yescharacteristic
135AGL(1,ℤ/8)—22no—
136AGL(1,ℤ/8)—22no—
137C2×SD16—21no—
138C2×D8—21no—
139C2×M16—111no—
140C2×M16C2×D1111yescharacteristic
141C4⋊Q8—221no—
142#124—222no—
143#124—222no—
144#124—221no—
145#123—222no—
146C22⋊Q8—222no—
147#117—111no—
148C2×C22⋊C4—222no—
149C2×C42—111no—
150#104—222no—
151#102—222no—
152#101—222no—
153C2×C11—21no—
154C2×C11—21no—
155C2×C11—81no—
156C2×C11—82no—
157C2×C11#39211yescharacteristic
158C2×C11#45412yes—
159C24—21no—
160#41—21no—
161#41—21no—
162#41—21no—
163#41—21no—
164C2×Q8—221no—
165C2×Q8—221no—
166C2×Q8—221no—
167C2×Q8—221no—
168C2×Q8—221no—
169C2×Q8—221no—
170C2×Q8C22⋊D1111yescharacteristic
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—21no—
175C2×D4—21no—
176C2×D4—21no—
177C2×D4C22⋊D1111yescharacteristic
178C2×D4C22⋊D1112yes—
179C22×C4—21no—
180C22×C4—112no—
181C22×C4—221no—
182C22×C4C22×D1111yescharacteristic
183SD16—24no—
184D8—24no—
185M16—21no—
186M16—221no—
187M16—221no—
188M16C22⋊D1112yes—
189C2×C8—21no—
190C2×C8—221no—
191C4⋊C4—112no—
192C4⋊C4—224no—
193C22⋊C4—228no—
194C22⋊C4—224no—
195C22⋊C4—221no—
196C42—112no—
197C42—221no—
198C42—221no—
199C11#200311yescharacteristic, complemented, Sylow
200C23—22no—
201C23—21no—
202C23—44no—
203C23—41no—
204C23—41no—
205C23D4×D1111yescharacteristic
206Q8—21no—
207Q8—21no—
208Q8—441no—
209Q8—441no—
210Q8—441no—
211Q8—441no—
212D4—22no—
213D4—21no—
214D4—21no—
215D4—22no—
216D4—41no—
217D4—41no—
218D4—41no—
219D4—41no—
220C2×C4—21no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—222no—
224C2×C4—222no—
225C2×C4—222no—
226C2×C4—222no—
227C2×C4—222no—
228C2×C4—442no—
229C2×C4D4×D1111yescharacteristic
230C2×C4D4×D1111yescharacteristic
231C2×C4#434111yescharacteristic
232C2×C4C2×C22⋊D1111yescharacteristic
233C2×C4C2×C22⋊D1111yescharacteristic
234C2×C4C2×C22⋊D1111yescharacteristic
235C8—22no—
236C8—441no—
237C22—22no—
238C22—44no—
239C22—42no—
240C22—41no—
241C22—42no—
242C22—82no—
243C22—82no—
244C22#6699011yescharacteristic
245C22#6699011yescharacteristic
246C22#6699111yescharacteristic
247C4—41no—
248C4—442no—
249C4—442no—
250C4—442no—
251C4#6699211yescharacteristic
252C4#6699211yescharacteristic
253C4#6699311yescharacteristic
254C4#6700611yescharacteristic
255C2—21no—
256C2—21no—
257C2—82no—
258C2—81no—
259C2#1062281412yes—
260C2#1062283611yescharacteristic
subgroupG/H
centerC22#66990
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
Fitting, prime radicalC2×C11×AGL(1,ℤ/8)C2
socleC22×C11#120
hypercenterC2×AGL(1,ℤ/8)D11
hypocenterC11#2003
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
2. #10623356C2semidirect
3. C2×#66989C2semidirect
4. C2×#66901C2semidirect
5. #10622828C2semidirect
6. C2×#66888C2semidirect
7. #10622193C2semidirect
199. C11#2003semidirect

Maximal subgroups

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

subgroupindex
C2×C11×AGL(1,ℤ/8)2
#106233562
C2×#669892
C2×#669012
#106228282
C2×#668882
#106221932
#200311