Finite Group Databasebeta

← #28392597

Subgroups — #28392597

Order 14464.

216 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 41 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#20299348C211yesmaximal, characteristic, complemented
2#20298783C212yesmaximal, complemented
3#20298770C211yesmaximal, characteristic
4#20298396C212yesmaximal, complemented
5#355×C113C211yesmaximal, characteristic, complemented
6#16813670C2211yescharacteristic
7#16813655—22no—
8#16813648—21no—
9#16813620C2212yes—
10#16813615—22no—
11#16813614—21no—
12#16813603—21no—
13#16813599—22no—
14#16813550—21no—
15#16813548—22no—
16#16813541C2211yescharacteristic
17#124×C113C2211yescharacteristic
18#101×C113C2212yes—
19#14268648—41no—
20#14268647—21no—
21#14268647—22no—
22C2×Dic226D412yes—
23Q8×D113—41no—
24C22×Dic113—21no—
25Dic452—42no—
26#14268636—42no—
27#14268635—41no—
28#14268632—41no—
29#14268631—21no—
30C4⋊Dic113—21no—
31C4⋊Dic113—21no—
32#14268626—22no—
33#14268626—22no—
34#14268626—22no—
35C22⋊Dic113—22no—
36C22⋊Dic113—21no—
37C4×Dic113D412yes—
38C2×Q8×C113C2311yescharacteristic
39C2×D4×C113D411yescharacteristic
40M16×C113—22no—
41C22⋊C4×C113—22no—
42C42×C113D411yescharacteristic
43C23×C113—21no—
44Q8×C113—41no—
45D4×C113—41no—
46C2×C4×C113—21no—
47C2×C4×C113C2×D412yes—
48C2×C4×C113C2×D411yescharacteristic
49C22⋊D113—41no—
50C2×Dic113—22no—
51C2×Dic113—22no—
52C2×Dic113—81no—
53D452—21no—
54D452—22no—
55C4×D113—41no—
56C4×D113—42no—
57Dic226—21no—
58Dic226—22no—
59Dic226—42no—
60C8×C113—42no—
61#11744751—41no—
62C22×C113—42no—
63C22×C113—41no—
64C22×C113#12011yescharacteristic
65C2×D113—41no—
66C4×C113—21no—
67C4×C113—22no—
68C4×C113—41no—
69Dic113—42no—
70Dic113—41no—
71Dic113—42no—
72C2×C113—21no—
73C2×C113—81no—
74C2×C113B(4,𝔽2)11yescharacteristic
75D113—81no—
76#2203—1131nomaximal, Sylow
77C113#220311yescharacteristic, complemented, Sylow
78#563—1131no—
79#456—1132no—
80#454—1131no—
81#356—1132no—
82#355D11311yescharacteristic, complemented
832−1+4—1131no—
84#137—2262no—
85AGL(1,ℤ/8)—2261no—
86C4⋊Q8—1132no—
87#126—2262no—
88#125—2261no—
89#124C2×D11311yescharacteristic
90#123—2261no—
91C22⋊Q8—2262no—
92#104—2262no—
93#104—2261no—
94#101—1131no—
95#101C2×D11312yes—
96#41—4521no—
97#41—2262no—
98#41—2261no—
99C2×Q8—1132no—
100C2×Q8—4521no—
101C2×Q8C22×D11311yescharacteristic
102C2×D4D45211yescharacteristic
103C22×C4—2261no—
104Q16—4522no—
105SD16—4522no—
106SD16—4521no—
107D8—4521no—
108M16—22no—
109M16—2261no—
110C4⋊C4—2261no—
111C4⋊C4—2262no—
112C4⋊C4—2261no—
113C4⋊C4—2262no—
114C4⋊C4—2262no—
115C22⋊C4—22no—
116C22⋊C4—2262no—
117C22⋊C4—2261no—
118C42—1132no—
119C42D45211yescharacteristic
120C23—21no—
121Q8—41no—
122Q8—4522no—
123Q8—2261no—
124Q8—2262no—
125D4—41no—
126D4—4521no—
127D4—2261no—
128D4—2262no—
129C2×C4—21no—
130C2×C4—9041no—
131C2×C4—4522no—
132C2×C4—4521no—
133C2×C4—2262no—
134C2×C4—2262no—
135C2×C4D4×D11312yes—
136C2×C4C2×D45211yescharacteristic
137C8—42no—
138C8—4521no—
139C22—42no—
140C22—41no—
141C22—4521no—
142C22#1681359211yescharacteristic
143C4—22no—
144C4—21no—
145C4—41no—
146C4—4522no—
147C4—4522no—
148C4—4521no—
149C2—21no—
150C2—81no—
151C2—9041no—
152C2#2029878611yescharacteristic
subgroupG/H
centerC2#20298786
commutator, cosocleC2×Q8×C113C23
FrattiniC2×Q8C22×D113
Fitting#355×C113C2
socleC2×C113B(4,𝔽2)
prime radical#20298770C2
hypercenter#355D113
hypocenterC113#2203
LCSG ▷ C2×Q8×C113 ▷ C22×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
1. #20299348C2semidirect
2. #20298783C2semidirect
4. #20298396C2semidirect
5. #355×C113C2semidirect
77. C113#2203semidirect
82. #355D113semidirect

Maximal subgroups

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

subgroupindex
#202993482
#202987832
#202987702
#202983962
#355×C1132
#2203113