Finite Group Databasebeta

← #13069778

Subgroups — #13069778

Order 1408.

246 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 246 conjugacy classes of subgroups — too many to draw. Only its 67 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
1#10623031C211yesmaximal, characteristic
2#10622733C212yesmaximal
3#10622587C211yesmaximal, characteristic
4C11×#343C211yesmaximal, characteristic
5#10622193C212yesmaximal
6C22×Dic22C2211yescharacteristic
7C2×C11×M16C2212yes—
8C2×C11×C4⋊C4C2211yescharacteristic
9#66979C2212yes—
10#66977—22no—
11C2×C4×Dic11C2211yescharacteristic
12#66943—22no—
13#66941—22no—
14C11⋊#95—22no—
15#66880—22no—
16#66880—22no—
17C22×C4×C11D412yes—
18C22×C4×C11C2311yescharacteristic
19C22×Dic11—21no—
20C22×Dic11—21no—
21C2×Dic22—22no—
22C2×Dic22—22no—
23C2×Dic22—22no—
24C2×Dic22—21no—
25C2×Dic22Q812yescomplemented
26C11×M16—22no—
27C11×M16—22no—
28C2×C8×C11—22no—
29C11×C4⋊C4—22no—
30C22⋊Dic11—22no—
31C4⋊Dic11—22no—
32C4⋊Dic11D412yes—
33C4⋊Dic11D412yes—
34Dic11⋊C4—24no—
35C4×Dic11—22no—
36C4×Dic11—22no—
37#2028—111nomaximal, Sylow
38C23×C11C2×D411yescharacteristic
39C2×C4×C11—22no—
40C2×C4×C11—42no—
41C2×C4×C11C2×D412yes—
42C2×C4×C11C2×Q811yescharacteristic
43C2×C4×C11#4112yes—
44C2×C4×C11#4111yescharacteristic
45C2×Dic11—22no—
46C2×Dic11—22no—
47C2×Dic11—22no—
48C2×Dic11—22no—
49C2×Dic11—41no—
50C2×Dic11—41no—
51C2×Dic11—41no—
52C2×Dic11—41no—
53Dic22—24no—
54Dic22—42no—
55Dic22—82no—
56C8×C11—42no—
57#544—111no—
58#419—112no—
59#391—111no—
60#343D1111yescharacteristic
61#339—112no—
62C22×C11—21no—
63C22×C11—21no—
64C22×C11#12011yescharacteristic
65C22×C11C22⋊Q811yescharacteristic
66C22×C11#12411yescharacteristic
67C4×C11—42no—
68C4×C11C22⋊Q812yes—
69C4×C11#12412yes—
70Dic11—42no—
71Dic11—42no—
72Dic11—42no—
73Dic11—42no—
74C22×Q8—111no—
75C2×M16C2×D1112yes—
76C4⋊Q8—222no—
77#125—222no—
78C22⋊Q8—222no—
79#117—112no—
80C2×C4⋊C4C2×D1111yescharacteristic
81C2×C42—111no—
82#103—222no—
83#103—222no—
84#95—222no—
85C2×C11—21no—
86C2×C11—21no—
87C2×C11#39311yescharacteristic
88C2×C11#45511yescharacteristic
89C2×C11#45611yescharacteristic
90C2×Q8—112no—
91C2×Q8—222no—
92C2×Q8—221no—
93C2×Q8—222no—
94C2×Q8—222no—
95C22×C4—221no—
96C22×C4—221no—
97C22×C4D4412yes—
98C22×C4C22×D1111yescharacteristic
99M16—22no—
100M16—22no—
101C2×C8—22no—
102C4⋊C4—22no—
103C4⋊C4—112no—
104C4⋊C4—112no—
105C4⋊C4—222no—
106C4⋊C4—224no—
107C22⋊C4—222no—
108C42—222no—
109C42—222no—
110C11#202811yescharacteristic, complemented, Sylow
111C23C2×D4411yescharacteristic
112Q8—224no—
113Q8—442no—
114Q8—882no—
115C2×C4—22no—
116C2×C4—42no—
117C2×C4—222no—
118C2×C4—222no—
119C2×C4—222no—
120C2×C4—222no—
121C2×C4—441no—
122C2×C4—441no—
123C2×C4—441no—
124C2×C4—441no—
125C2×C4#433912yes—
126C2×C4D4×D1112yes—
127C2×C4#434111yescharacteristic
128C2×C4Q8×D1111yescharacteristic
129C8—42no—
130C22—21no—
131C22—21no—
132C22#6692811yescharacteristic
133C22#6693511yescharacteristic
134C22#6695011yescharacteristic
135C4—42no—
136C4—442no—
137C4—442no—
138C4—442no—
139C4—442no—
140C4#6693812yes—
141C4#6694912yes—
142C2—21no—
143C2—21no—
144C2#1062228611yescharacteristic
145C2#1062235911yescharacteristic
146C2#1062236511yescharacteristic
subgroupG/H
centerC22#66935
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
FittingC11×#343C2
socleC22×C11#120
prime radicalC23×C11C2×D4
hypercenter#343D11
hypocenterC11#2028
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
25. C2×Dic22Q8semidirect
110. C11#2028semidirect

Maximal subgroups

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

subgroupindex
#106230312
#106227332
#106225872
C11×#3432
#106221932
#202811