Finite Group Databasebeta

← #13076677

Subgroups — #13076677

Order 1408.

430 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 133 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×#66929C211yesmaximal, characteristic
2C2×#66922C211yesmaximal, characteristic, complemented
3C11×#383C211yesmaximal, characteristic, complemented
4#10622290C212yesmaximal
5#10622287C212yesmaximal
6#10622286C212yesmaximal
7#10622274C212yesmaximal, complemented
8#10622272C212yesmaximal, complemented
9#10622269C212yesmaximal, complemented
10C22×Dic22C2212yes—
11C2×C42×C11C2211yescharacteristic
12C2×(C2×D11)⋊C4C2211yescharacteristic
13C2×(C2×D11)⋊C4C2211yescharacteristic
14C2×(C2×D11)⋊C4C2211yescharacteristic
15C2×(C2×D11)⋊C4C2214yes—
16C2×C4⋊Dic11C2212yes—
17C2×C4⋊Dic11C2212yes—
18C2×C4⋊Dic11C2214yes—
19C2×Dic11⋊C4C2211yescharacteristic
20C2×Dic11⋊C4C2211yescharacteristic
21C2×Dic11⋊C4C2211yescharacteristic
22#66929—24no—
23#66922—24no—
24C11×#95C2212yes—
25C11×#95C2212yes—
26C11×#95C2212yes—
27C11⋊#95C2214yes—
28C11⋊#95C2214yes—
29C23×D11C2311yescharacteristic
30C22×C4×C11C2314yes—
31C22×C4×C11C2311yescharacteristic
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2311yescharacteristic
34C22×Dic11C2311yescharacteristic
35C22×Dic11C2311yescharacteristic
36C22×Dic11C2314yes—
37C22×Dic11C2311yescharacteristic
38C2×Dic22—24no—
39C2×Dic22—44no—
40C42×C11D414yes—
41(C2×D11)⋊C4—22no—
42(C2×D11)⋊C4—22no—
43(C2×D11)⋊C4—22no—
44(C2×D11)⋊C4—44no—
45C4⋊Dic11—24no—
46C4⋊Dic11—24no—
47C4⋊Dic11—44no—
48Dic11⋊C4—22no—
49Dic11⋊C4—22no—
50Dic11⋊C4—22no—
51#2821—111nomaximal, Sylow
52C23×C11C2411yescharacteristic
53C22×D11—21no—
54C22×D11—22no—
55C22×D11—22no—
56C22×D11—22no—
57C2×C4×C11—22no—
58C2×C4×C11—22no—
59C2×C4×C11—22no—
60C2×C4×C11—24no—
61C2×C4×C11—24no—
62C2×C4×C11—24no—
63C2×C4×C11C2×D412yes—
64C2×C4×C11C2×D412yes—
65C2×C4×C11C2×D412yes—
66C2×Dic11—21no—
67C2×Dic11—21no—
68C2×Dic11—21no—
69C2×Dic11—24no—
70C2×Dic11—22no—
71C2×Dic11—24no—
72C2×Dic11—24no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75Dic22—48no—
76C2×C4⋊Q8—111no—
77C2×#126—111no—
78#400—112no—
79#399—112no—
80#398—112no—
81#397—112no—
82#395—112no—
83#393—112no—
84#383D1111yescharacteristic, complemented
85C22×C11C22×D411yescharacteristic
86C22×C11H(5,𝔽2)12yes—
87C22×C112−1+412yes—
88C22×C112−1+412yes—
89C2×D11—41no—
90C2×D11—41no—
91C2×D11—41no—
92C2×D11—44no—
93C4×C11—22no—
94C4×C11—22no—
95C4×C11—22no—
96C4×C11—44no—
97Dic11—44no—
98Dic11—41no—
99Dic11—41no—
100Dic11—41no—
101C22×Q8—112no—
102C4⋊Q8—224no—
103#126—224no—
104C2×C4⋊C4—111no—
105C2×C4⋊C4—111no—
106C2×C4⋊C4—111no—
107C2×C4⋊C4—112no—
108C2×C4⋊C4—112no—
109C2×C4⋊C4—114no—
110C2×C22⋊C4—111no—
111C2×C22⋊C4—111no—
112C2×C22⋊C4—111no—
113C2×C22⋊C4—114no—
114C2×C42C2×D1111yescharacteristic
115#95—114no—
116#95—114no—
117#95C2×D1112yes—
118#95C2×D1112yes—
119#95C2×D1112yes—
120C2×C11#53511yescharacteristic
121C2×C11#53611yescharacteristic
122C2×C11#53611yescharacteristic
123C2×C11#56314yes—
124D11—81no—
125C24—111no—
126C2×Q8—224no—
127C2×Q8—444no—
128C22×C4—111no—
129C22×C4—111no—
130C22×C4—114no—
131C22×C4—111no—
132C22×C4C22×D1114yes—
133C22×C4C22×D1111yescharacteristic
134C22×C4C22×D1111yescharacteristic
135C22×C4C22×D1111yescharacteristic
136C4⋊C4—222no—
137C4⋊C4—222no—
138C4⋊C4—222no—
139C4⋊C4—224no—
140C4⋊C4—224no—
141C4⋊C4—444no—
142C22⋊C4—222no—
143C22⋊C4—222no—
144C22⋊C4—222no—
145C22⋊C4—444no—
146C42D4414yes—
147C11#282111yescharacteristic, complemented, Sylow
148C23—221no—
149C23—222no—
150C23—222no—
151C23—222no—
152C23C23×D1111yescharacteristic
153Q8—448no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—24no—
158C2×C4—24no—
159C2×C4—24no—
160C2×C4—221no—
161C2×C4—221no—
162C2×C4—221no—
163C2×C4—224no—
164C2×C4—224no—
165C2×C4—222no—
166C2×C4—224no—
167C2×C4—222no—
168C2×C4—222no—
169C2×C4C2×D4412yes—
170C2×C4C2×D4412yes—
171C2×C4C2×D4412yes—
172C22—444no—
173C22—441no—
174C22—441no—
175C22—441no—
176C22C22×D4411yescharacteristic
177C22#6704212yes—
178C22#6704312yes—
179C22#6704312yes—
180C4—22no—
181C4—22no—
182C4—22no—
183C4—44no—
184C4—444no—
185C4—441no—
186C4—441no—
187C4—441no—
188C2—881no—
189C2#1062305611yescharacteristic
190C2#1062305711yescharacteristic
191C2#1062305711yescharacteristic
192C2#1062324314yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, cosocleC23×C11C24
FittingC11×#383C2
prime radicalC23×D11C23
hypercenter#383D11
hypocenterC11#2821
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #383

Complements

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

NH ≅ G/Ntype
2. C2×#66922C2semidirect
3. C11×#383C2semidirect
7. #10622274C2semidirect
8. #10622272C2semidirect
9. #10622269C2semidirect
84. #383D11semidirect
147. C11#2821semidirect

Maximal subgroups

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

subgroupindex
C2×#669292
C2×#669222
C11×#3832
#106222902
#106222872
#106222862
#106222742
#106222722
#106222692
#282111