Finite Group Databasebeta

← #28391715

Subgroups — #28391715

Order 14464.

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×#16813622C211yesmaximal, characteristic
2C2×#16813546C212yesmaximal
3#20298360C212yesmaximal
4#20298353C211yesmaximal, characteristic
5#391×C113C211yesmaximal, characteristic
6C22×Dic226—21no—
7C22×#11744751C2212yes—
8#16813622—24no—
9C2×C4⋊Dic113—21no—
10C2×C4⋊Dic113C2212yes—
11#16813546—24no—
12C22×Q8×C113C2211yescharacteristic
13C2×C4⋊C4×C113C2211yescharacteristic
14C2×C42×C113C2211yescharacteristic
15#95×C113—21no—
16#95×C113—21no—
17C2×Dic226—24no—
18C2×Dic226—42no—
19C2×Dic226—42no—
20C22×Dic113—22no—
21C2×#11744751—22no—
22C2×#11744751—22no—
23C2×#11744751—22no—
24C4⋊Dic113—24no—
25C4⋊Dic113—22no—
26C4⋊Dic113D414yes—
27C2×Q8×C113—21no—
28C2×Q8×C113—22no—
29C2×Q8×C113—22no—
30C2×Q8×C113Q812yescomplemented
31C22×C4×C113—21no—
32C22×C4×C113—21no—
33C22×C4×C113D411yescharacteristic
34C22×C4×C113D411yescharacteristic
35C22×C4×C113C2311yescharacteristic
36C4⋊C4×C113—22no—
37C42×C113—22no—
38C23×C113C2×D411yescharacteristic
39Q8×C113—24no—
40Q8×C113—42no—
41C2×C4×C113—21no—
42C2×C4×C113—21no—
43C2×C4×C113—21no—
44C2×C4×C113—21no—
45C2×C4×C113—22no—
46C2×C4×C113—41no—
47C2×C4×C113—41no—
48C2×C4×C113—41no—
49C2×C4×C113—41no—
50C2×C4×C113—41no—
51C2×C4×C113SD1612yes—
52C2×C4×C113Q1612yes—
53C2×C4×C113C2×D412yes—
54C2×C4×C113C2×Q811yescharacteristic
55C2×C4×C113#4112yes—
56C2×C4×C113#4111yescharacteristic
57C2×Dic113—24no—
58C2×Dic113—42no—
59C2×Dic113—42no—
60Dic226—48no—
61#11744751—42no—
62C22×C113#12011yescharacteristic
63C22×C113C22⋊Q811yescharacteristic
64C22×C113#12411yescharacteristic
65C22×C113C2×SD1611yescharacteristic
66C22×C113C2×Q1611yescharacteristic
67C22×C113AGL(1,ℤ/8)11yescharacteristic
68C22×C113#13711yescharacteristic
69C4×C113—22no—
70C4×C113—22no—
71C4×C113—42no—
72C4×C113—81no—
73C4×C113C22⋊Q812yes—
74C4×C113#12412yes—
75Dic113—44no—
76C2×C113#39311yescharacteristic
77C2×C113#45011yescharacteristic
78C2×C113#45111yescharacteristic
79C2×C113#47511yescharacteristic
80C2×C113#47711yescharacteristic
81C2×C113#48711yescharacteristic
82C2×C113#48911yescharacteristic
83#2024—1131nomaximal, Sylow
84C113#202411yescharacteristic, complemented, Sylow
85C2×C4⋊Q8—1131no—
86C2×#103—1132no—
87#391D11311yescharacteristic
88#340—1132no—
89#336—1131no—
90C22×Q8—2261no—
91C22×Q8C2×D11311yescharacteristic
92C22×C8—1132no—
93C4⋊Q8—2264no—
94C2×C4⋊C4—1132no—
95C2×C4⋊C4—2261no—
96C2×C4⋊C4C2×D11311yescharacteristic
97C2×C42C2×D11311yescharacteristic
98#103—2264no—
99#95—21no—
100#95—21no—
101C2×Q8—21no—
102C2×Q8—22no—
103C2×Q8—22no—
104C2×Q8—4522no—
105C2×Q8—4522no—
106C2×Q8—2264no—
107C2×Q8Dic22612yescomplemented
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—2262no—
111C22×C4C22⋊D11311yescharacteristic
112C22×C4C22⋊D11311yescharacteristic
113C22×C4C22×D11311yescharacteristic
114C2×C8—2262no—
115C2×C8—2262no—
116C2×C8—2262no—
117C4⋊C4—22no—
118C4⋊C4—1134no—
119C4⋊C4—2264no—
120C4⋊C4—2262no—
121C42—22no—
122C23C2×C22⋊D11311yescharacteristic
123Q8—24no—
124Q8—42no—
125Q8—4528no—
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—4522no—
137C2×C4—4522no—
138C2×C4—2264no—
139C2×C4#1426863412yes—
140C2×C4#1426863712yes—
141C2×C4D4×D11312yes—
142C2×C4C2×Dic22611yescharacteristic
143C2×C4#1426864612yes—
144C2×C4#1426864711yescharacteristic
145C8—4522no—
146C22#1681359011yescharacteristic
147C22#1681360111yescharacteristic
148C22#1681360911yescharacteristic
149C22C2×#1426863411yescharacteristic
150C22C2×#1426863711yescharacteristic
151C22#1681364711yescharacteristic
152C22#1681365211yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—81no—
157C4—4524no—
158C4#1681359912yes—
159C4#1681360812yes—
160C2#2029851011yescharacteristic
161C2#2029874811yescharacteristic
162C2#2029875311yescharacteristic
163C2#2029888311yescharacteristic
164C2#2029889311yescharacteristic
165C2#2029894811yescharacteristic
166C2#2029895711yescharacteristic
subgroupG/H
centerC23C2×C22⋊D113
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
Fitting#391×C113C2
socle, prime radicalC23×C113C2×D4
hypercenter#391D113
hypocenterC113#2024
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C113Q8semidirect
84. C113#2024semidirect
107. C2×Q8Dic226semidirect

Maximal subgroups

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

subgroupindex
C2×#168136222
C2×#168135462
#202983602
#202983532
#391×C1132
#2024113