Finite Group Databasebeta

← #13069719

Subgroups — #13069719

Order 1408.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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×#575C211yesmaximal, characteristic, complemented
2#10623353C212yesmaximal, complemented
3#10622847C212yesmaximal, complemented
4#10622742C211yesmaximal, characteristic, complemented
5C11⋊#338C211yesmaximal, characteristic, complemented
6C2×C11×#41C2212yes—
7C2×#4339C2211yescharacteristic
8C11×#137—22no—
9C11×AGL(1,ℤ/8)—22no—
10C11×#135—22no—
11C2×C11×M16C2211yescharacteristic
12#67004—22no—
13#67003—24no—
14#67002—22no—
15#66995—22no—
16#66985—22no—
17C2×#4318C2212yes—
18C22×C11⋊C8C2211yescharacteristic
19C22⋊(C11⋊C8)—24no—
20(C2×D11)⋊C8—22no—
21C11×#41—22no—
22C11×#41—22no—
23C11×#41—22no—
24C11×#41—22no—
25C2×Q8×C11D412yes—
26C2×D4×C11—22no—
27C2×D4×C11D412yes—
28C22×C4×C11—22no—
29C22×C4×C11C2311yescharacteristic
30C2×C22⋊D11—21no—
31#4339—22no—
32#4339—22no—
33C2×D44D411yescharacteristic
34C2×C4×D11—21no—
35C2×Dic22D411yescharacteristic
36C11×Q16—22no—
37C11×SD16—24no—
38C11×D8—22no—
39C11×M16—22no—
40C2×C8×C11D412yes—
41#4326—24no—
42#4325—24no—
43#4324—24no—
44#4323—24no—
45#4318—22no—
46#4318—22no—
47C2×C11⋊C8—21no—
48C2×C11⋊C8—22no—
49C2×C11⋊C8D414yes—
50#2017—111nomaximal, Sylow
51C23×C11—22no—
52C23×C11#4111yescharacteristic
53C22×D11—21no—
54Q8×C11—22no—
55Q8×C11—22no—
56D4×C11—22no—
57D4×C11—22no—
58D4×C11—42no—
59D4×C11—42no—
60C2×C4×C11—22no—
61C2×C4×C11—42no—
62C2×C4×C11—42no—
63C2×C4×C11C2×D411yescharacteristic
64C2×C4×C11C2×D412yes—
65C2×C4×C11C2×D412yes—
66C2×C4×C11C2×D411yescharacteristic
67C22⋊D11—42no—
68C2×Dic11—21no—
69D44—22no—
70C4×D11—41no—
71C4×D11—41no—
72Dic22—22no—
73C8×C11—22no—
74C11⋊C8—24no—
75C11⋊C8—41no—
76#575—112no—
77#575D1111yescharacteristic, complemented
78#408—112no—
79#408—111no—
80#338—111no—
81C22×C11—41no—
82C22×C11—44no—
83C22×C11—42no—
84C22×C11#12111yescharacteristic
85C22×C11#12112yes—
86C2×D11—42no—
87C2×D11—41no—
88C4×C11—42no—
89C4×C11#12012yes—
90C4×C11#12011yescharacteristic
91C4×C11#12711yescharacteristic
92Dic11—41no—
93C2×#41—111no—
94C2×#41C2×D1112yes—
95#137—22no—
96#137—222no—
97#137—222no—
98AGL(1,ℤ/8)—22no—
99AGL(1,ℤ/8)—222no—
100AGL(1,ℤ/8)—222no—
101#135—22no—
102#135—224no—
103C2×M16—112no—
104C2×M16C2×D1111yescharacteristic
105C22×C8—111no—
106C22⋊C8—224no—
107C22⋊C8—222no—
108C2×C11—21no—
109C2×C11—22no—
110C2×C11—82no—
111C2×C11#39211yescharacteristic
112D11—81no—
113#41—22no—
114#41—22no—
115#41—22no—
116#41—22no—
117#41—222no—
118#41—222no—
119C2×Q8—111no—
120C2×Q8C22⋊D1112yes—
121C2×D4—22no—
122C2×D4—111no—
123C2×D4—221no—
124C2×D4C22⋊D1112yes—
125C22×C4—22no—
126C22×C4—221no—
127C22×C4C22×D1111yescharacteristic
128Q16—22no—
129Q16—224no—
130SD16—24no—
131SD16—224no—
132SD16—224no—
133D8—22no—
134D8—224no—
135M16—22no—
136M16—222no—
137M16—222no—
138C2×C8—114no—
139C2×C8—222no—
140C2×C8—221no—
141C2×C8C22⋊D1112yes—
142C11#201711yescharacteristic, complemented, Sylow
143C23—22no—
144C23—221no—
145C23#434111yescharacteristic
146Q8—22no—
147Q8—22no—
148Q8—222no—
149D4—22no—
150D4—22no—
151D4—42no—
152D4—42no—
153D4—222no—
154D4—442no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—221no—
159C2×C4—441no—
160C2×C4—441no—
161C2×C4D4×D1111yescharacteristic
162C2×C4D4×D1112yes—
163C2×C4C2×C22⋊D1112yes—
164C2×C4C2×C22⋊D1111yescharacteristic
165C8—22no—
166C8—224no—
167C8—441no—
168C22—41no—
169C22—44no—
170C22—42no—
171C22—442no—
172C22—441no—
173C22#6699111yescharacteristic
174C22#6699212yes—
175C4—42no—
176C4—441no—
177C4#6699012yes—
178C4#6699311yescharacteristic
179C4#6700611yescharacteristic
180C2—22no—
181C2—21no—
182C2—82no—
183C2—881no—
184C2#1062283611yescharacteristic
subgroupG/H
centerC4#66993
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#575C2
socleC2×C11#392
hypercenter#575D11
hypocenterC11#2017
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C11×#575C2semidirect
2. #10623353C2semidirect
3. #10622847C2semidirect
4. #10622742C2semidirect
5. C11⋊#338C2semidirect
77. #575D11semidirect
142. C11#2017semidirect

Maximal subgroups

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

subgroupindex
C11×#5752
#106233532
#106228472
#106227422
C11⋊#3382
#201711