Finite Group Databasebeta

← #13070093

Subgroups — #13070093

Order 1408.

230 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 91 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×#384C211yesmaximal, characteristic
2C2×#66872C212yesmaximal
3#10622541C211yesmaximal, characteristic
4#10622167C212yesmaximal
5#10622162C211yesmaximal, characteristic
6C2×C11×C4⋊C4—21no—
7C2×C11×C4⋊C4—21no—
8C2×C11×C4⋊C4C2212yes—
9C2×C42×C11C2211yescharacteristic
10C2×C4⋊Dic11C2211yescharacteristic
11C2×C4⋊Dic11C2211yescharacteristic
12C2×Dic11⋊C4—21no—
13C22×C11⋊C8C2212yes—
14C11⋊#95—21no—
15#66872—24no—
16C22×C4×C11—22no—
17C22×C4×C11D411yescharacteristic
18C22×C4×C11D411yescharacteristic
19C22×C4×C11C2311yescharacteristic
20C22×Dic11—21no—
21C22×Dic11—21no—
22C11×C4⋊C4—22no—
23C11×C4⋊C4—22no—
24C11×C4⋊C4—42no—
25C11×C4⋊C4—42no—
26C42×C11—22no—
27C4⋊Dic11—21no—
28C4⋊Dic11—22no—
29C4⋊Dic11D412yes—
30Dic11⋊C4—42no—
31C2×C11⋊C8—22no—
32C2×C11⋊C8—22no—
33C2×C11⋊C8Q814yes—
34#2084—111nomaximal, Sylow
35C23×C11C2×D411yescharacteristic
36C2×C4×C11—21no—
37C2×C4×C11—21no—
38C2×C4×C11—21no—
39C2×C4×C11—21no—
40C2×C4×C11—42no—
41C2×C4×C11—42no—
42C2×C4×C11—42no—
43C2×C4×C11SD1612yes—
44C2×C4×C11SD1612yes—
45C2×C4×C11C2×D411yescharacteristic
46C2×C4×C11C2×Q812yes—
47C2×C4×C11#4112yes—
48C2×C4×C11#4111yescharacteristic
49C2×Dic11—22no—
50C2×Dic11—41no—
51C2×Dic11—41no—
52C2×Dic11—41no—
53C2×Dic11—41no—
54C2×Dic11—41no—
55C11⋊C8—24no—
56C2×#106—112no—
57#389—111no—
58#384D1111yescharacteristic
59#340—112no—
60#336—111no—
61C22×C11#12111yescharacteristic
62C22×C11#12311yescharacteristic
63C22×C11C4⋊Q811yescharacteristic
64C22×C11C2×SD1611yescharacteristic
65C22×C11C2×SD1611yescharacteristic
66C22×C11AGL(1,ℤ/8)11yescharacteristic
67C22×C11#13711yescharacteristic
68C4×C11—22no—
69C4×C11—22no—
70C4×C11—82no—
71C4×C11C22⋊Q812yes—
72C4×C11#12512yes—
73Dic11—42no—
74Dic11—81no—
75C22×C8—112no—
76C2×C4⋊C4—21no—
77C2×C4⋊C4—21no—
78C2×C4⋊C4—111no—
79C2×C4⋊C4—111no—
80C2×C4⋊C4—221no—
81C2×C4⋊C4C2×D1112yes—
82C2×C42C2×D1111yescharacteristic
83#106—224no—
84#95—221no—
85C2×C11#39811yescharacteristic
86C2×C11#46011yescharacteristic
87C2×C11#46111yescharacteristic
88C2×C11#48111yescharacteristic
89C2×C11#48311yescharacteristic
90C2×C11#49811yescharacteristic
91C2×C11#50111yescharacteristic
92C22×C4—22no—
93C22×C4—221no—
94C22×C4—221no—
95C22×C4C22⋊D1111yescharacteristic
96C22×C4C22⋊D1111yescharacteristic
97C22×C4C22×D1111yescharacteristic
98C2×C8—114no—
99C2×C8—222no—
100C2×C8—222no—
101C4⋊C4—22no—
102C4⋊C4—22no—
103C4⋊C4—42no—
104C4⋊C4—42no—
105C4⋊C4—112no—
106C4⋊C4—221no—
107C4⋊C4—222no—
108C4⋊C4—442no—
109C42—22no—
110C11#208411yescharacteristic, complemented, Sylow
111C23C2×C22⋊D1111yescharacteristic
112C2×C4—21no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—42no—
117C2×C4—42no—
118C2×C4—42no—
119C2×C4—222no—
120C2×C4—441no—
121C2×C4—441no—
122C2×C4—441no—
123C2×C4—441no—
124C2×C4—441no—
125C2×C4#432412yes—
126C2×C4#432512yes—
127C2×C4#433912yes—
128C2×C4D4×D1111yescharacteristic
129C2×C4#434111yescharacteristic
130C2×C4Q8×D1112yes—
131C8—224no—
132C22#6698211yescharacteristic
133C22#6698511yescharacteristic
134C22C2×#432411yescharacteristic
135C22#6699111yescharacteristic
136C22C2×#432511yescharacteristic
137C22#6699511yescharacteristic
138C22#6699711yescharacteristic
139C4—22no—
140C4—22no—
141C4—82no—
142C4—442no—
143C4—881no—
144C4#6694212yes—
145C4#6694912yes—
146C2#1062258111yescharacteristic
147C2#1062258411yescharacteristic
148C2#1062259311yescharacteristic
149C2#1062268811yescharacteristic
150C2#1062269211yescharacteristic
151C2#1062269311yescharacteristic
152C2#1062269611yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#384C2
socle, prime radicalC23×C11C2×D4
hypercenter#384D11
hypocenterC11#2084
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
110. C11#2084semidirect

Maximal subgroups

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

subgroupindex
C11×#3842
C2×#668722
#106225412
#106221672
#106221622
#208411