Finite Group Databasebeta

← #16835628

Subgroups — #16835628

Order 3712.

320 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 70 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#14272168C211yesmaximal, characteristic, complemented
2C2×#11745226C214yesmaximal, complemented
3#14272099C211yesmaximal, characteristic, complemented
4#14271714C211yesmaximal, characteristic
5C2×#90809C2212yes—
6C2×C4×#1181C2212yes—
7C2×#90796C2212yes—
8C29×C4⋊Q8C411yescharacteristic, complemented
9#11745309C412yescomplemented
10#11745257—22no—
11#11745255—22no—
12#11745236C411yescharacteristic, complemented
13C42×D29C2211yescharacteristic
14#11745226—28no—
15(C2×#1181)⋊C4—22no—
16#11745220—22no—
17C22×#1181—22no—
18C2×Q8×C29C2×C412yes—
19#90809—24no—
20#90809—24no—
21C2×D116—22no—
22C2×D116—22no—
23C2×D116C2×C412yes—
24C2×C4×D29—22no—
25C2×C4×D29D412yes—
26C2×C4×D29C2311yescharacteristic
27C2×#6599—22no—
28C4×#1181—22no—
29C4×#1181D414yescomplemented
30#90796—24no—
31C4⋊C4×C29—22no—
32C42×C29C2×C411yescharacteristic
33#90781—24no—
34C4×Dic29C2×C411yescharacteristic
35C4×Dic29D412yes—
36C22×D29—22no—
37C22×D29C2×D411yescharacteristic
38C2×#1181—24no—
39C2×#1181—44no—
40Q8×C29—24no—
41C2×C4×C29—22no—
42C2×C4×C29C22⋊C412yes—
43C2×C4×C29C22×C411yescharacteristic
44C2×Dic29C22⋊C412yes—
45C2×Dic29C2×D411yescharacteristic
46D116—24no—
47D116—44no—
48D116—44no—
49C4×D29—42no—
50C4×D29—42no—
51C4×D29—42no—
52C4×D29C2×D412yes—
53C4×D29#4112yes—
54#6599—42no—
55#1963—291nomaximal, Sylow
56C22×C29C2×C22⋊C411yescharacteristic
57C2×D29—22no—
58C2×D29—42no—
59C2×D29—44no—
60C2×D29#12112yes—
61#1181—44no—
62C4×C29—22no—
63C4×C29—42no—
64C4×C29C4×D412yes—
65Dic29—22no—
66Dic29#12411yescharacteristic
67Dic29#12711yescharacteristic
68#532—291no—
69#423—291no—
70C2×#104—294no—
71#376—291no—
72C2×C29#39011yescharacteristic
73C2×C29#42112yes—
74D29—22no—
75D29—82no—
76C2×#41—292no—
77C2×M16—292no—
78C4⋊Q8#118111yescharacteristic, complemented
79#127—291no—
80#124—292no—
81#121—582no—
82C4×D4—582no—
83C2×C42—291no—
84C2×C42—292no—
85C4⋊C8—582no—
86#104—588no—
87#95—582no—
88C29#196311yescharacteristic, complemented, Sylow
89#41—584no—
90#41—584no—
91C2×Q8C2×#118112yes—
92C2×D4—292no—
93C2×D4—582no—
94C2×D4—582no—
95C22×C4—291no—
96C22×C4—292no—
97C22×C4—582no—
98C22×C4—582no—
99M16—584no—
100C2×C8—582no—
101C4⋊C4—22no—
102C22⋊C4—584no—
103C42—292no—
104C42—291no—
105C42—294no—
106C42—582no—
107C42C2×#118111yescharacteristic
108C23—291no—
109C23—582no—
110Q8—24no—
111D4—584no—
112D4—1164no—
113D4—1164no—
114C2×C4—22no—
115C2×C4—291no—
116C2×C4—292no—
117C2×C4—292no—
118C2×C4—292no—
119C2×C4—584no—
120C2×C4—1162no—
121C2×C4—1162no—
122C2×C4—1162no—
123C2×C4—1164no—
124C2×C4C22⋊#118112yes—
125C2×C4C22×#118111yescharacteristic
126C8—1162no—
127C22—292no—
128C22—582no—
129C22—1162no—
130C22—1164no—
131C22C2×C22⋊#118111yescharacteristic
132C4—22no—
133C4—42no—
134C4—291no—
135C4—291no—
136C4—582no—
137C4—1164no—
138C4D4×#118112yes—
139C2—582no—
140C2—2322no—
141C2#1427211511yescharacteristic
142C2#1427216212yes—
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×C4⋊Q8C4
socleC22×C29C2×C22⋊C4
prime radical#14271714C2
cosocleC2×C4×D29C23
hypercenterC4⋊Q8#1181
hypocenterC29#1963
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #14272168C2semidirect
2. C2×#11745226C2semidirect
3. #14272099C2semidirect
8. C29×C4⋊Q8C4semidirect
9. #11745309C4semidirect
12. #11745236C4semidirect
29. C4×#1181D4semidirect
78. C4⋊Q8#1181semidirect
88. C29#1963semidirect

Maximal subgroups

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

subgroupindex
#142721682
C2×#117452262
#142720992
#142717142
#196329