Finite Group Databasebeta

← #13078739

Subgroups — #13078739

Order 1408.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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
1#10623008C211yesmaximal, characteristic
2C2×C4×Dic22C211yesmaximal, characteristic, complemented
3C11×#432C211yesmaximal, characteristic, complemented
4#10622463C212yesmaximal, complemented
5#10622461C212yesmaximal, complemented
6#10622351C212yesmaximal, complemented
7#10622349C212yesmaximal, complemented
8#10622323C214yesmaximal, complemented
9C2×#4339—21no—
10C22×Dic22C2211yescharacteristic
11C2×C42×C11C2211yescharacteristic
12#66983—21no—
13#66983C2212yes—
14C2×C4⋊Dic11C2211yescharacteristic
15C2×Dic11⋊C4—21no—
16C2×C4×Dic11—21no—
17C2×#4314C2214yes—
18#66928—21no—
19#66927C2211yescharacteristic
20C4×D44—21no—
21C4×D44C2212yes—
22#66922C2211yescharacteristic
23C4×Dic22—21no—
24C4×Dic22—21no—
25C4×Dic22C2212yes—
26C4×Dic22C2212yes—
27C11×C4⋊C8C2212yes—
28C11×C22⋊C8C2212yes—
29C11×#97C2212yes—
30#66885C2214yes—
31#66882C2214yes—
32#66880C2214yes—
33C22×C4×C11D411yescharacteristic
34C22×C4×C11D411yescharacteristic
35C22×C4×C11C2311yescharacteristic
36C2×C22⋊D11—22no—
37C22×Dic11—21no—
38C22×Dic11—21no—
39#4339—44no—
40C2×D44—21no—
41C2×D44—21no—
42C2×D44C2312yes—
43C2×C4×D11—22no—
44C2×Dic22—24no—
45C2×Dic22—21no—
46C2×Dic22—21no—
47C2×Dic22C2312yes—
48C2×C8×C11C2314yes—
49C42×C11D411yescharacteristic
50C42×C11D411yescharacteristic
51C42×C11C2311yescharacteristic
52C42×C11C2311yescharacteristic
53(C2×D11)⋊C4—22no—
54(C2×D11)⋊C4—22no—
55C4⋊Dic11—21no—
56C4⋊Dic11—21no—
57C4⋊Dic11C2312yes—
58C4⋊Dic11C2312yes—
59Dic11⋊C4—22no—
60Dic11⋊C4—22no—
61C4×Dic11—22no—
62C4×Dic11—22no—
63#4314—28no—
64#3112—111nomaximal, Sylow
65C23×C11C2×D411yescharacteristic
66C22×D11—22no—
67C2×C4×C11—22no—
68C2×C4×C11—22no—
69C2×C4×C11—22no—
70C2×C4×C11C2×D411yescharacteristic
71C2×C4×C11C2×D411yescharacteristic
72C2×C4×C11C2×D411yescharacteristic
73C2×C4×C11C2×D411yescharacteristic
74C2×C4×C11C2×D411yescharacteristic
75C2×C4×C11C2411yescharacteristic
76C22⋊D11—44no—
77C2×Dic11—24no—
78C2×Dic11—22no—
79C2×Dic11—22no—
80C2×Dic11—22no—
81C2×Dic11—42no—
82D44—24no—
83D44—42no—
84D44—42no—
85C4×D11—44no—
86Dic22—24no—
87Dic22—22no—
88Dic22—42no—
89Dic22#4114yescomplemented
90C8×C11—24no—
91#532—111no—
92C2×C4×Q8—111no—
93#480—112no—
94#477—112no—
95#460—112no—
96#448—112no—
97#440—114no—
98#432D1111yescharacteristic, complemented
99C22×C11—21no—
100C22×C11—21no—
101C22×C11AGL(1,ℤ/8)12yes—
102C22×C11C22×D411yescharacteristic
103C2×D11—42no—
104C2×D11—42no—
105C2×D11—42no—
106C4×C11—21no—
107C4×C11—21no—
108C4×C11—21no—
109C4×C11—21no—
110C4×C11#13712yes—
111C4×C11C2×#4112yes—
112Dic11—24no—
113Dic11—42no—
114Dic11—42no—
115C2×#41—221no—
116C22×Q8—111no—
117C2×SD16—114no—
118C4⋊Q8—111no—
119#127—111no—
120#124—221no—
121#121—112no—
122#121—221no—
123C4×Q8—112no—
124C4×Q8—112no—
125C4×Q8—221no—
126C4×Q8—221no—
127C4×D4—112no—
128C4×D4—221no—
129C2×C4⋊C4—111no—
130C2×C4⋊C4—221no—
131C2×C42—221no—
132C2×C42C2×D1111yescharacteristic
133#107—114no—
134C4⋊C8C2×D1112yes—
135#103—114no—
136#102—114no—
137C22⋊C8C2×D1112yes—
138#97C2×D1112yes—
139C2×C11—22no—
140C2×C11#52511yescharacteristic
141C2×C11C2×AGL(1,ℤ/8)11yescharacteristic
142C2×C11C2×#13711yescharacteristic
143D11—82no—
144#41—444no—
145C2×Q8—112no—
146C2×Q8—224no—
147C2×Q8—221no—
148C2×Q8—221no—
149C2×D4—112no—
150C2×D4—222no—
151C2×D4—221no—
152C2×D4—221no—
153C22×C4—221no—
154C22×C4—221no—
155C22×C4—222no—
156C22×C4D4411yescharacteristic
157C22×C4D4411yescharacteristic
158C22×C4C22×D1111yescharacteristic
159SD16—228no—
160C2×C8C22×D1114yes—
161C4⋊C4—112no—
162C4⋊C4—112no—
163C4⋊C4—221no—
164C4⋊C4—222no—
165C4⋊C4—222no—
166C4⋊C4—221no—
167C22⋊C4—222no—
168C22⋊C4—222no—
169C42—222no—
170C42—222no—
171C42D4411yescharacteristic
172C42D4411yescharacteristic
173C42C22×D1111yescharacteristic
174C42C22×D1111yescharacteristic
175C11#311211yescharacteristic, complemented, Sylow
176C23—222no—
177C23C2×D4411yescharacteristic
178Q8—114no—
179Q8—224no—
180Q8—222no—
181Q8—442no—
182D4—224no—
183D4—442no—
184D4—444no—
185D4—442no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—224no—
190C2×C4—222no—
191C2×C4—222no—
192C2×C4—222no—
193C2×C4—444no—
194C2×C4—442no—
195C2×C4C2×D4411yescharacteristic
196C2×C4C2×D4411yescharacteristic
197C2×C4C2×D4411yescharacteristic
198C2×C4C2×D4411yescharacteristic
199C2×C4C2×D4411yescharacteristic
200C2×C4C23×D1111yescharacteristic
201C8—24no—
202C22—21no—
203C22—21no—
204C22—442no—
205C22—442no—
206C22—442no—
207C22#6696112yes—
208C22C22×D4411yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—224no—
214C4—442no—
215C4—442no—
216C4#6696212yes—
217C4#41×D1112yes—
218C2—22no—
219C2—882no—
220C2#1062305511yescharacteristic
221C2C2×#6696111yescharacteristic
222C2C2×#6696211yescharacteristic
subgroupG/H
centerC22C22×D44
commutator, cosocleC2×C4×C11C24
FrattiniC2×C4C23×D11
FittingC11×#432C2
socleC22×C11C22×D4
prime radical#10623008C2
hypercenter#432D11
hypocenterC11#3112
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic22C2semidirect
3. C11×#432C2semidirect
4. #10622463C2semidirect
5. #10622461C2semidirect
6. #10622351C2semidirect
7. #10622349C2semidirect
8. #10622323C2semidirect
89. Dic22#41semidirect
98. #432D11semidirect
175. C11#3112semidirect

Maximal subgroups

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

subgroupindex
#106230082
C2×C4×Dic222
C11×#4322
#106224632
#106224612
#106223512
#106223492
#106223232
#311211