Finite Group Databasebeta

← #13078130

Subgroups — #13078130

Order 1408.

494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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
3#10623329C211yesmaximal, characteristic, complemented
4C22×#4324C211yesmaximal, characteristic, complemented
5#10622846C211yesmaximal, characteristic, complemented
6#10622775C214yesmaximal, complemented
7#10622766C214yesmaximal, complemented
8#10622733C211yesmaximal, characteristic, complemented
9#10622732C211yesmaximal, characteristic, complemented
10C2×C11×#41C2211yescharacteristic
11C22×D4×C11C2211yescharacteristic
12C22×Dic22C2211yescharacteristic
13C11×AGL(1,ℤ/8)—24no—
14C2×C11×SD16C2212yes—
15C2×C11×D8C2212yes—
16C2×C11×M16C2211yescharacteristic
17C2×C22⋊Dic11—22no—
18#66997C2212yescomplemented
19#66989C2212yescomplemented
20#66988—22no—
21D4×Dic11—22no—
22D4×Dic11C2214yes—
23C2×#4324—24no—
24C2×#4324C2214yes—
25#66979C2211yescharacteristic
26#66979C2211yescharacteristic
27#66977—22no—
28C22×C11⋊C8C2211yescharacteristic
29#66899C2212yescomplemented
30#66896C2212yescomplemented
31#66880C2214yescomplemented
32Dic11⋊C8C2214yescomplemented
33C24×C11—21no—
34C11×#41—22no—
35C11×#41—22no—
36C2×Q8×C11C2311yescharacteristic
37C2×D4×C11—21no—
38C2×D4×C11—21no—
39C2×D4×C11—22no—
40C2×D4×C11D414yes—
41C2×D4×C11C2311yescharacteristic
42C2×D4×C11C2312yes—
43C22×C4×C11—21no—
44C22×C4×C11C2311yescharacteristic
45C22×Dic11—24no—
46C22×Dic11—21no—
47C2×Dic22—22no—
48C2×Dic22—21no—
49C2×Dic22—22no—
50C2×Dic22C2312yes—
51C11×SD16—24no—
52C11×D8—24no—
53C11×M16—22no—
54C2×C8×C11C2312yes—
55C22⋊Dic11—24no—
56C22⋊Dic11—24no—
57C22⋊Dic11—21no—
58C22⋊Dic11D412yes—
59#4324—28no—
60C4⋊Dic11D412yes—
61C4⋊Dic11C2312yes—
62Dic11⋊C4—24no—
63C4×Dic11—21no—
64C4×Dic11C2312yes—
65C2×C11⋊C8—22no—
66C2×C11⋊C8C2312yes—
67#3042—111nomaximal, Sylow
68C23×C11—22no—
69C23×C11—24no—
70C23×C11—21no—
71C23×C11—82no—
72C23×C11C2×D411yescharacteristic
73Q8×C11—21no—
74Q8×C11—21no—
75D4×C11—24no—
76D4×C11—21no—
77D4×C11—22no—
78D4×C11—21no—
79D4×C11—42no—
80D4×C11C2×D414yes—
81C2×C4×C11—21no—
82C2×C4×C11—42no—
83C2×C4×C11C2×D411yescharacteristic
84C2×C4×C11C2×D412yes—
85C2×C4×C11#4112yes—
86C2×C4×C11C2411yescharacteristic
87C2×Dic11—22no—
88C2×Dic11—22no—
89C2×Dic11—42no—
90C2×Dic11—84no—
91C2×Dic11C2×D414yes—
92Dic22—22no—
93Dic22—22no—
94Dic22—42no—
95C8×C11—22no—
96C11⋊C8—22no—
97C2×AGL(1,ℤ/8)D1111yescharacteristic
98C22×SD16—111no—
99#536—111no—
100#518—111no—
101#463—114no—
102#461—114no—
103#424—111no—
104#419—111no—
105#416—111no—
106C22×C11—22no—
107C22×C11—24no—
108C22×C11—44no—
109C22×C11—41no—
110C22×C11—42no—
111C22×C11—84no—
112C22×C11#12112yes—
113C22×C11C22×D411yescharacteristic
114C4×C11—41no—
115C4×C11#12112yes—
116C4×C11C22×D411yescharacteristic
117C4×C11C2×#4111yescharacteristic
118Dic11—24no—
119Dic11—42no—
120Dic11—42no—
121C2×#41C2×D1111yescharacteristic
122C22×Q8—111no—
123C22×D4C2×D1111yescharacteristic
124AGL(1,ℤ/8)—24no—
125C2×SD16—114no—
126C2×SD16—224no—
127C2×SD16C2×D1112yes—
128C2×D8C2×D1112yes—
129C2×M16C2×D1111yescharacteristic
130C22×C8—111no—
131C4⋊Q8—112no—
132#124—112no—
133#123—222no—
134C22⋊Q8—222no—
135C4×D4—114no—
136C4×D4—222no—
137#117—111no—
138#117—111no—
139C2×C22⋊C4—222no—
140C4⋊C8—114no—
141#103—112no—
142#103—114no—
143#102—112no—
144C2×C11—22no—
145C2×C11—44no—
146C2×C11—81no—
147C2×C11C2×#12111yescharacteristic
148C2×C11#57712yes—
149C24—21no—
150#41—22no—
151#41—22no—
152C2×Q8—112no—
153C2×Q8—221no—
154C2×Q8—222no—
155C2×Q8—222no—
156C2×Q8C22×D1111yescharacteristic
157C2×D4—21no—
158C2×D4—21no—
159C2×D4—22no—
160C2×D4C22⋊D1114yes—
161C2×D4C22×D1111yescharacteristic
162C2×D4C22×D1112yes—
163C22×C4—21no—
164C22×C4—224no—
165C22×C4—221no—
166C22×C4C22×D1111yescharacteristic
167SD16—24no—
168SD16—228no—
169D8—24no—
170M16—22no—
171C2×C8—112no—
172C2×C8—222no—
173C2×C8C22×D1112yes—
174C4⋊C4—112no—
175C4⋊C4—112no—
176C4⋊C4—224no—
177C22⋊C4—112no—
178C22⋊C4—224no—
179C22⋊C4—224no—
180C22⋊C4—221no—
181C42—112no—
182C42—221no—
183C11#304211yescharacteristic, complemented, Sylow
184C23—22no—
185C23—24no—
186C23—21no—
187C23—82no—
188C23D4×D1111yescharacteristic
189Q8—21no—
190Q8—21no—
191Q8—222no—
192Q8—222no—
193Q8—442no—
194D4—24no—
195D4—22no—
196D4—21no—
197D4—21no—
198D4—42no—
199D4C2×C22⋊D1114yes—
200C2×C4—21no—
201C2×C4—42no—
202C2×C4—114no—
203C2×C4—222no—
204C2×C4—222no—
205C2×C4—442no—
206C2×C4—884no—
207C2×C4D4×D1111yescharacteristic
208C2×C4#434112yes—
209C2×C4C2×C22⋊D1112yes—
210C2×C4C23×D1111yescharacteristic
211C8—22no—
212C8—222no—
213C22—22no—
214C22—24no—
215C22—44no—
216C22—42no—
217C22—41no—
218C22—84no—
219C22#6699212yes—
220C22C2×D4×D1111yescharacteristic
221C4—41no—
222C4—224no—
223C4—442no—
224C4—442no—
225C4#6699212yes—
226C4C2×#434111yescharacteristic
227C4C22×C22⋊D1111yescharacteristic
228C2—22no—
229C2—44no—
230C2—81no—
231C2#1062330612yes—
232C2C2×#6699211yescharacteristic
subgroupG/H
centerC22C2×D4×D11
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
Fitting, prime radicalC2×C11×AGL(1,ℤ/8)C2
socleC22×C11C22×D4
hypercenterC2×AGL(1,ℤ/8)D11
hypocenterC11#3042
LCSG ▷ C2×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. #10623329C2semidirect
4. C22×#4324C2semidirect
5. #10622846C2semidirect
6. #10622775C2semidirect
7. #10622766C2semidirect
8. #10622733C2semidirect
9. #10622732C2semidirect
18. #66997C22semidirect
19. #66989C22semidirect
29. #66899C22semidirect
30. #66896C22semidirect
31. #66880C22semidirect
32. Dic11⋊C8C22semidirect
183. C11#3042semidirect

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
#106233292
C22×#43242
#106228462
#106227752
#106227662
#106227332
#106227322
#304211