Finite Group Databasebeta

← #13069949

Subgroups — #13069949

Order 1408.

282 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 97 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×#66922C211yesmaximal, characteristic
2C11×#389C211yesmaximal, characteristic
3C2×#66872C212yesmaximal
4#10622167C212yesmaximal
5#10622162C211yesmaximal, characteristic
6C22×Dic22—21no—
7C2×C11×C4⋊C4—21no—
8C2×C11×C4⋊C4C2211yescharacteristic
9C2×C11×C4⋊C4C2211yescharacteristic
10C2×C42×C11C2211yescharacteristic
11C2×C4⋊Dic11—21no—
12C2×C4⋊Dic11C2212yes—
13C22×C11⋊C8C2212yes—
14#66922—24no—
15C11×#95—21no—
16#66872—24no—
17C22×C4×C11—21no—
18C22×C4×C11—21no—
19C22×C4×C11D411yescharacteristic
20C22×C4×C11D411yescharacteristic
21C22×C4×C11C2311yescharacteristic
22C22×Dic11—22no—
23C2×Dic22—24no—
24C2×Dic22—42no—
25C2×Dic22—42no—
26C11×C4⋊C4—21no—
27C11×C4⋊C4—22no—
28C11×C4⋊C4—42no—
29C11×C4⋊C4Q812yescomplemented
30C42×C11—22no—
31C4⋊Dic11—24no—
32C4⋊Dic11—22no—
33C4⋊Dic11D414yes—
34C2×C11⋊C8—22no—
35C2×C11⋊C8—22no—
36C2×C11⋊C8Q814yescomplemented
37#2058—111nomaximal, Sylow
38C23×C11C2×D411yescharacteristic
39C2×C4×C11—21no—
40C2×C4×C11—21no—
41C2×C4×C11—21no—
42C2×C4×C11—21no—
43C2×C4×C11—22no—
44C2×C4×C11—41no—
45C2×C4×C11—41no—
46C2×C4×C11—41no—
47C2×C4×C11—41no—
48C2×C4×C11—41no—
49C2×C4×C11SD1612yes—
50C2×C4×C11SD1612yes—
51C2×C4×C11C2×D412yes—
52C2×C4×C11C2×Q811yescharacteristic
53C2×C4×C11C2×Q812yes—
54C2×C4×C11#4111yescharacteristic
55C2×Dic11—24no—
56C2×Dic11—42no—
57C2×Dic11—42no—
58Dic22—48no—
59C11⋊C8—24no—
60C2×C4⋊Q8—111no—
61C2×#106—112no—
62#389D1111yescharacteristic
63#340—112no—
64#336—111no—
65C22×C11#12011yescharacteristic
66C22×C11C22⋊Q811yescharacteristic
67C22×C11C4⋊Q811yescharacteristic
68C22×C11C2×SD1611yescharacteristic
69C22×C11C2×SD1611yescharacteristic
70C22×C11AGL(1,ℤ/8)11yescharacteristic
71C22×C11#13711yescharacteristic
72C4×C11—22no—
73C4×C11—22no—
74C4×C11—42no—
75C4×C11—81no—
76C4×C11C22⋊Q812yes—
77C4×C11C4⋊Q812yes—
78Dic11—44no—
79C22×Q8—221no—
80C22×C8—112no—
81C4⋊Q8—224no—
82C2×C4⋊C4—21no—
83C2×C4⋊C4—112no—
84C2×C4⋊C4—221no—
85C2×C4⋊C4C2×D1111yescharacteristic
86C2×C4⋊C4C2×D1111yescharacteristic
87C2×C42C2×D1111yescharacteristic
88#106—224no—
89#95—21no—
90C2×C11#39511yescharacteristic
91C2×C11#44811yescharacteristic
92C2×C11#45011yescharacteristic
93C2×C11#47511yescharacteristic
94C2×C11#47611yescharacteristic
95C2×C11#49811yescharacteristic
96C2×C11#50111yescharacteristic
97C2×Q8—224no—
98C2×Q8—442no—
99C2×Q8—442no—
100C22×C4—21no—
101C22×C4—21no—
102C22×C4—222no—
103C22×C4C22⋊D1111yescharacteristic
104C22×C4C22⋊D1111yescharacteristic
105C22×C4C22×D1111yescharacteristic
106C2×C8—114no—
107C2×C8—222no—
108C2×C8—222no—
109C4⋊C4—21no—
110C4⋊C4—22no—
111C4⋊C4—42no—
112C4⋊C4—114no—
113C4⋊C4—224no—
114C4⋊C4—222no—
115C4⋊C4Dic2212yescomplemented
116C42—22no—
117C11#205811yescharacteristic, complemented, Sylow
118C23C2×C22⋊D1111yescharacteristic
119Q8—448no—
120C2×C4—21no—
121C2×C4—21no—
122C2×C4—21no—
123C2×C4—21no—
124C2×C4—22no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—41no—
128C2×C4—41no—
129C2×C4—41no—
130C2×C4—224no—
131C2×C4—442no—
132C2×C4—442no—
133C2×C4#432412yes—
134C2×C4#432512yes—
135C2×C4C2×Dic2211yescharacteristic
136C2×C4#433911yescharacteristic
137C2×C4D4×D1112yes—
138C2×C4Q8×D1112yes—
139C8—224no—
140C22#6697711yescharacteristic
141C22C2×#432411yescharacteristic
142C22#6699011yescharacteristic
143C22C2×#432511yescharacteristic
144C22#6699711yescharacteristic
145C22#6700211yescharacteristic
146C22#6700411yescharacteristic
147C4—22no—
148C4—22no—
149C4—42no—
150C4—81no—
151C4—444no—
152C4#6694112yes—
153C4#6694912yes—
154C2#1062259211yescharacteristic
155C2#1062262111yescharacteristic
156C2#1062263311yescharacteristic
157C2#1062265311yescharacteristic
158C2#1062265911yescharacteristic
159C2#1062267811yescharacteristic
160C2#1062269211yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#389C2
socle, prime radicalC23×C11C2×D4
hypercenter#389D11
hypocenterC11#2058
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #389

Complements

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

NH ≅ G/Ntype
29. C11×C4⋊C4Q8semidirect
36. C2×C11⋊C8Q8semidirect
115. C4⋊C4Dic22semidirect
117. C11#2058semidirect

Maximal subgroups

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

subgroupindex
C2×#669222
C11×#3892
C2×#668722
#106221672
#106221622
#205811