Finite Group Databasebeta

← #16834974

Subgroups — #16834974

Order 3712.

196 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 58 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#14272183C211yesmaximal, characteristic
2#14272183C211yesmaximal, characteristic
3#14272020C214yesmaximal, complemented
4C2×#11745252C211yesmaximal, characteristic
5C2×C4⋊C4×C29C411yescharacteristic
6C2×C4⋊Dic29—21no—
7C2×C4⋊Dic29C411yescharacteristic
8C2×#90779—21no—
9C2×C4×Dic29C2211yescharacteristic
10#11745252—21no—
11#11745252—21no—
12#11745252C412yes—
13#11745252C2212yes—
14C22⋊#6599—21no—
15C22⋊#6599—21no—
16#11745220—21no—
17#11745220—21no—
18#11745218C2212yes—
19#11745218C2212yes—
20C22×C4×C29—21no—
21C22×C4×C29C2×C411yescharacteristic
22C22×Dic29—21no—
23C22×Dic29D411yescharacteristic
24C22×Dic29D411yescharacteristic
25C2×#6599—22no—
26C2×#6599—22no—
27C4⋊C4×C29—21no—
28C4⋊C4×C29C2×C412yes—
29C4⋊Dic29—21no—
30C4⋊Dic29—22no—
31C4⋊Dic29—22no—
32C4⋊Dic29C2×C412yes—
33#90779—22no—
34#90779—22no—
35C4×Dic29C2×C411yescharacteristic
36C4×Dic29D411yescharacteristic
37C4×Dic29D411yescharacteristic
38C4×Dic29C2311yescharacteristic
39C23×C29C22⋊C411yescharacteristic
40C2×C4×C29—22no—
41C2×C4×C29—22no—
42C2×C4×C29—42no—
43C2×C4×C29C22⋊C411yescharacteristic
44C2×C4×C29C22×C411yescharacteristic
45C2×Dic29—22no—
46C2×Dic29—41no—
47C2×Dic29—41no—
48C2×Dic29—42no—
49C2×Dic29C22⋊C411yescharacteristic
50C2×Dic29C22⋊C411yescharacteristic
51C2×Dic29C2×D411yescharacteristic
52C2×Dic29C2×D411yescharacteristic
53#6599—42no—
54#6599—42no—
55#1534—291nomaximal, Sylow
56C22×C29—21no—
57C22×C29—21no—
58C22×C29#10112yes—
59C22×C29C2×C22⋊C411yescharacteristic
60C4×C29—21no—
61C4×C29—21no—
62C4×C29—42no—
63Dic29—21no—
64Dic29—21no—
65Dic29—21no—
66Dic29—21no—
67Dic29—42no—
68C2×#125—291no—
69#432—291no—
70#432—291no—
71#330—294no—
72C2×C29—22no—
73C2×C29C2×#10111yescharacteristic
74C2×C29#42111yescharacteristic
75C2×C29#42111yescharacteristic
76#125—292no—
77#125—292no—
78#125—581no—
79#125—581no—
80C2×C4⋊C4—291no—
81C2×C4⋊C4—581no—
82C2×C4⋊C4—581no—
83C2×C4⋊C4#118111yescharacteristic
84C2×C42—291no—
85C4⋊C8—581no—
86C4⋊C8—581no—
87C22⋊C8—581no—
88C22⋊C8—581no—
89#97—292no—
90#97—292no—
91C29#153411yescharacteristic, complemented, Sylow
92C22×C4—21no—
93C22×C4—291no—
94C22×C4—291no—
95C22×C4—581no—
96C22×C4C2×#118111yescharacteristic
97C2×C8—582no—
98C2×C8—582no—
99C4⋊C4—21no—
100C4⋊C4—292no—
101C4⋊C4—582no—
102C4⋊C4—582no—
103C4⋊C4—582no—
104C4⋊C4—582no—
105C4⋊C4—581no—
106C4⋊C4C2×#118112yes—
107C42—291no—
108C42—291no—
109C42—291no—
110C42—291no—
111C23C22⋊#118111yescharacteristic
112C2×C4—22no—
113C2×C4—22no—
114C2×C4—42no—
115C2×C4—291no—
116C2×C4—291no—
117C2×C4—291no—
118C2×C4—291no—
119C2×C4—582no—
120C2×C4—1161no—
121C2×C4—1161no—
122C2×C4—1162no—
123C2×C4C22⋊#118111yescharacteristic
124C2×C4C22×#118111yescharacteristic
125C8—1162no—
126C8—1162no—
127C22—21no—
128C22—21no—
129C22#1174522112yes—
130C22C2×C22⋊#118111yescharacteristic
131C4—21no—
132C4—21no—
133C4—42no—
134C4—581no—
135C4—581no—
136C4—581no—
137C4—581no—
138C4—1162no—
139C2—22no—
140C2C2×#1174522111yescharacteristic
141C2#1427216111yescharacteristic
142C2#1427216211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC2×C4⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC23×C29C22⋊C4
cosocleC4×Dic29C23
hypercenterC2×C4⋊C4#1181
hypocenterC29#1534
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. #14272020C2semidirect
91. C29#1534semidirect

Maximal subgroups

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

subgroupindex
#142721832
#142720202
C2×#117452522
#153429