Finite Group Databasebeta

← #13074273

Subgroups — #13074273

Order 1408.

380 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 145 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
1C11×#376C211yesmaximal, characteristic
2#10622550C211yesmaximal, characteristic
3C4×C4⋊Dic11C211yesmaximal, characteristic
4#10622546C212yesmaximal
5#10622541C212yesmaximal
6#10622274C212yesmaximal
7#10622270C212yesmaximal
8#10622267C212yesmaximal
9#10622260C212yesmaximal
10C2×C42×C11C2212yes—
11C2×C42×C11C2211yescharacteristic
12C2×C4⋊Dic11C2212yes—
13C2×C4⋊Dic11C2212yes—
14C2×C4⋊Dic11C2212yes—
15C2×Dic11⋊C4C2212yes—
16C2×Dic11⋊C4C2212yes—
17C2×Dic11⋊C4C2212yes—
18C2×Dic11⋊C4C2212yes—
19C2×C4×Dic11C2211yescharacteristic
20C2×C4×Dic11C2211yescharacteristic
21C11×#95C2212yes—
22C11×#95C2211yescharacteristic
23C11×#95C2211yescharacteristic
24C11⋊#95C2212yes—
25C11⋊#95C2212yes—
26C11⋊#95C2212yes—
27C11⋊#95C2212yes—
28C11⋊#95C2211yescharacteristic
29C11⋊#95C2212yes—
30C11⋊#95C2211yescharacteristic
31C22×C4×C11C2312yes—
32C22×C4×C11C2311yescharacteristic
33C22×C4×C11C2311yescharacteristic
34C22×C4×C11C2311yescharacteristic
35C22×C4×C11C2312yes—
36C22×Dic11C2312yes—
37C22×Dic11C2312yes—
38C22×Dic11C2312yes—
39C22×Dic11C2312yes—
40C42×C11—24no—
41C42×C11Q814yes—
42C4⋊Dic11—24no—
43C4⋊Dic11—24no—
44C4⋊Dic11—24no—
45Dic11⋊C4—24no—
46Dic11⋊C4—24no—
47Dic11⋊C4—42no—
48Dic11⋊C4—42no—
49C4×Dic11—41no—
50C4×Dic11—41no—
51#2606—111nomaximal, Sylow
52C23×C11C2411yescharacteristic
53C2×C4×C11—22no—
54C2×C4×C11—22no—
55C2×C4×C11—22no—
56C2×C4×C11—21no—
57C2×C4×C11—21no—
58C2×C4×C11—22no—
59C2×C4×C11—22no—
60C2×C4×C11—22no—
61C2×C4×C11—22no—
62C2×C4×C11C2×Q812yes—
63C2×C4×C11C2×Q812yes—
64C2×C4×C11C2×Q812yes—
65C2×C4×C11#4114yes—
66C2×Dic11—22no—
67C2×Dic11—22no—
68C2×Dic11—22no—
69C2×Dic11—22no—
70C2×Dic11—22no—
71C2×Dic11—22no—
72C2×Dic11—22no—
73C2×Dic11—22no—
74C2×Dic11—22no—
75C2×Dic11—22no—
76C2×Dic11—22no—
77C2×Dic11#4114yes—
78#398—112no—
79#398—112no—
80#389—112no—
81#389—112no—
82#387—112no—
83#387—112no—
84#383—111no—
85C4×C4⋊C4—111no—
86#376D1111yescharacteristic
87C22×C11C22×Q811yescharacteristic
88C22×C11C2×#4112yes—
89C22×C11C2×#4112yes—
90C22×C11H(5,𝔽2)11yescharacteristic
91C22×C112−1+411yescharacteristic
92C4×C11—22no—
93C4×C11—22no—
94C4×C11—22no—
95C4×C11—24no—
96C4×C11—42no—
97Dic11—24no—
98Dic11—42no—
99Dic11—42no—
100Dic11—42no—
101C2×C4⋊C4—112no—
102C2×C4⋊C4—112no—
103C2×C4⋊C4—112no—
104C2×C4⋊C4—112no—
105C2×C4⋊C4—112no—
106C2×C4⋊C4—112no—
107C2×C4⋊C4—112no—
108C2×C42—111no—
109C2×C42—111no—
110C2×C42C2×D1112yes—
111C2×C42C2×D1111yescharacteristic
112#95—112no—
113#95—111no—
114#95—112no—
115#95—111no—
116#95—112no—
117#95—112no—
118#95—112no—
119#95C2×D1112yes—
120#95C2×D1111yescharacteristic
121#95C2×D1111yescharacteristic
122C2×C11#53311yescharacteristic
123C2×C11#53311yescharacteristic
124C2×C11#54411yescharacteristic
125C2×C11#55212yes—
126C2×C11#55312yes—
127C22×C4—112no—
128C22×C4—112no—
129C22×C4—112no—
130C22×C4—112no—
131C22×C4C22×D1112yes—
132C22×C4C22×D1111yescharacteristic
133C22×C4C22×D1111yescharacteristic
134C22×C4C22×D1111yescharacteristic
135C22×C4C22×D1112yes—
136C4⋊C4—224no—
137C4⋊C4—224no—
138C4⋊C4—224no—
139C4⋊C4—224no—
140C4⋊C4—224no—
141C4⋊C4—442no—
142C4⋊C4—442no—
143C42—24no—
144C42—441no—
145C42—441no—
146C42Dic2214yes—
147C11#260611yescharacteristic, complemented, Sylow
148C23C23×D1111yescharacteristic
149C2×C4—22no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—22no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—114no—
159C2×C4—222no—
160C2×C4—222no—
161C2×C4—222no—
162C2×C4—222no—
163C2×C4—222no—
164C2×C4—222no—
165C2×C4—222no—
166C2×C4—222no—
167C2×C4—222no—
168C2×C4—222no—
169C2×C4—222no—
170C2×C4C2×Dic2212yes—
171C2×C4C2×Dic2212yes—
172C2×C4C2×Dic2212yes—
173C2×C4#433914yes—
174C22C22×Dic2211yescharacteristic
175C22C2×#433912yes—
176C22#41×D1112yes—
177C22#6704211yescharacteristic
178C22#6704311yescharacteristic
179C4—22no—
180C4—22no—
181C4—22no—
182C4—24no—
183C4—42no—
184C4—224no—
185C4—442no—
186C4—442no—
187C4—442no—
188C2#1062300111yescharacteristic
189C2#1062304811yescharacteristic
190C2#1062305011yescharacteristic
191C2#1062306112yes—
192C2#1062306212yes—
subgroupG/H
center, FrattiniC23C23×D11
commutator, socle, prime radical, cosocleC23×C11C24
FittingC11×#376C2
hypercenter#376D11
hypocenterC11#2606
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #376

Complements

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

NH ≅ G/Ntype
147. C11#2606semidirect

Maximal subgroups

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

subgroupindex
C11×#3762
#106225502
C4×C4⋊Dic112
#106225462
#106225412
#106222742
#106222702
#106222672
#106222602
#260611