Finite Group Databasebeta

← #13069757

Subgroups — #13069757

Order 1408.

290 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 93 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×#391C211yesmaximal, characteristic
3C2×#66899C212yesmaximal
4#10622167C212yesmaximal
5#10622162C211yesmaximal, characteristic
6C22×Q8×C11C2211yescharacteristic
7C22×Dic22—21no—
8C2×C11×C4⋊C4C2211yescharacteristic
9C2×C42×C11C2211yescharacteristic
10C2×C4⋊Dic11—21no—
11C2×C4⋊Dic11C2212yes—
12C22×C11⋊C8C2212yes—
13#66922—24no—
14C11×#95—21no—
15C11×#95—21no—
16#66899—24no—
17C2×Q8×C11—21no—
18C2×Q8×C11—22no—
19C2×Q8×C11—22no—
20C2×Q8×C11Q812yescomplemented
21C22×C4×C11—21no—
22C22×C4×C11—21no—
23C22×C4×C11D411yescharacteristic
24C22×C4×C11D411yescharacteristic
25C22×C4×C11C2311yescharacteristic
26C22×Dic11—22no—
27C2×Dic22—24no—
28C2×Dic22—42no—
29C2×Dic22—42no—
30C11×C4⋊C4—22no—
31C42×C11—22no—
32C4⋊Dic11—24no—
33C4⋊Dic11—22no—
34C4⋊Dic11D414yes—
35C2×C11⋊C8—22no—
36C2×C11⋊C8—22no—
37C2×C11⋊C8—22no—
38#2024—111nomaximal, Sylow
39C23×C11C2×D411yescharacteristic
40Q8×C11—24no—
41Q8×C11—42no—
42C2×C4×C11—21no—
43C2×C4×C11—21no—
44C2×C4×C11—21no—
45C2×C4×C11—21no—
46C2×C4×C11—22no—
47C2×C4×C11—41no—
48C2×C4×C11—41no—
49C2×C4×C11—41no—
50C2×C4×C11—41no—
51C2×C4×C11—41no—
52C2×C4×C11SD1612yes—
53C2×C4×C11Q1612yes—
54C2×C4×C11C2×D412yes—
55C2×C4×C11C2×Q811yescharacteristic
56C2×C4×C11#4111yescharacteristic
57C2×C4×C11#4112yes—
58C2×Dic11—24no—
59C2×Dic11—42no—
60C2×Dic11—42no—
61Dic22—48no—
62C11⋊C8—42no—
63C2×C4⋊Q8—111no—
64C2×#103—112no—
65#391D1111yescharacteristic
66#340—112no—
67#336—111no—
68C22×C11#12011yescharacteristic
69C22×C11C22⋊Q811yescharacteristic
70C22×C11#12411yescharacteristic
71C22×C11C2×SD1611yescharacteristic
72C22×C11C2×Q1611yescharacteristic
73C22×C11AGL(1,ℤ/8)11yescharacteristic
74C22×C11#13711yescharacteristic
75C4×C11—22no—
76C4×C11—22no—
77C4×C11—42no—
78C4×C11—81no—
79C4×C11C22⋊Q812yes—
80C4×C11#12412yes—
81Dic11—44no—
82C22×Q8—221no—
83C22×Q8C2×D1111yescharacteristic
84C22×C8—112no—
85C4⋊Q8—224no—
86C2×C4⋊C4—112no—
87C2×C4⋊C4—221no—
88C2×C4⋊C4C2×D1111yescharacteristic
89C2×C42C2×D1111yescharacteristic
90#103—224no—
91#95—21no—
92#95—21no—
93C2×C11#39311yescharacteristic
94C2×C11#45011yescharacteristic
95C2×C11#45111yescharacteristic
96C2×C11#47511yescharacteristic
97C2×C11#47711yescharacteristic
98C2×C11#48711yescharacteristic
99C2×C11#48911yescharacteristic
100C2×Q8—21no—
101C2×Q8—22no—
102C2×Q8—22no—
103C2×Q8—224no—
104C2×Q8—442no—
105C2×Q8—442no—
106C2×Q8Dic2212yescomplemented
107C22×C4—21no—
108C22×C4—21no—
109C22×C4—222no—
110C22×C4C22⋊D1111yescharacteristic
111C22×C4C22⋊D1111yescharacteristic
112C22×C4C22×D1111yescharacteristic
113C2×C8—222no—
114C2×C8—222no—
115C2×C8—222no—
116C4⋊C4—22no—
117C4⋊C4—114no—
118C4⋊C4—224no—
119C4⋊C4—222no—
120C42—22no—
121C11#202411yescharacteristic, complemented, Sylow
122C23C2×C22⋊D1111yescharacteristic
123Q8—24no—
124Q8—42no—
125Q8—448no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—224no—
137C2×C4—442no—
138C2×C4—442no—
139C2×C4#432512yes—
140C2×C4#432612yes—
141C2×C4C2×Dic2211yescharacteristic
142C2×C4#433911yescharacteristic
143C2×C4D4×D1112yes—
144C2×C4#434112yes—
145C8—442no—
146C22#6697711yescharacteristic
147C22#6698911yescharacteristic
148C22#6699011yescharacteristic
149C22C2×#432511yescharacteristic
150C22C2×#432611yescharacteristic
151C22#6700211yescharacteristic
152C22#6700411yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—81no—
157C4—444no—
158C4#6693112yes—
159C4#6693812yes—
160C2#1062256011yescharacteristic
161C2#1062263311yescharacteristic
162C2#1062263411yescharacteristic
163C2#1062265911yescharacteristic
164C2#1062266311yescharacteristic
165C2#1062266811yescharacteristic
166C2#1062269411yescharacteristic
subgroupG/H
centerC23C2×C22⋊D11
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#391C2
socle, prime radicalC23×C11C2×D4
hypercenter#391D11
hypocenterC11#2024
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
20. C2×Q8×C11Q8semidirect
106. C2×Q8Dic22semidirect
121. C11#2024semidirect

Maximal subgroups

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

subgroupindex
C2×#669222
C11×#3912
C2×#668992
#106221672
#106221622
#202411