Finite Group Databasebeta

← #16818627

Subgroups — #16818627

Order 3712.

214 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 55 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#14271874C211yesmaximal, characteristic
2#14271542C211yesmaximal, characteristic, complemented
3#14271459C211yesmaximal, characteristic, complemented
4#14271454C211yesmaximal, characteristic
5#14270893C211yesmaximal, characteristic, complemented
6#14270890C211yesmaximal, characteristic
7C29×#333C211yesmaximal, characteristic, complemented
8C29×C4⋊Q8C2211yescharacteristic
9#11745308—22no—
10C2×#90785—22no—
11#11745259—21no—
12#11745255—21no—
13C4⋊C4×D29—21no—
14#11745252—21no—
15C4×D116C2211yescharacteristic
16#11745231C2211yescharacteristic
17C4×Dic58C2211yescharacteristic
18C29×C4⋊C8C2211yescharacteristic
19C29×C4⋊C8C2211yescharacteristic
20#11745169—21no—
21#11745166—21no—
22#11745165—21no—
23#11745164—21no—
24C4×#6597C2211yescharacteristic
25C2×Q8×C29D412yes—
26C2×D116D411yescharacteristic
27C2×C4×D29—21no—
28C2×C4×D29—22no—
29C2×Dic58—21no—
30C2×Dic58D411yescharacteristic
31C2×C8×C29—21no—
32C2×C8×C29—21no—
33C4⋊C4×C29—21no—
34C4⋊C4×C29—21no—
35C42×C29C2311yescharacteristic
36#90785—44no—
37#90781—22no—
38#90781—21no—
39C4⋊Dic29—22no—
40C4⋊Dic29—21no—
41C4⋊Dic29—21no—
42C4⋊Dic29D411yescharacteristic
43C4⋊Dic29D411yescharacteristic
44#90779—22no—
45#90779—21no—
46C4×Dic29—21no—
47C2×#6597—21no—
48C22×D29—21no—
49Q8×C29—42no—
50C2×C4×C29—22no—
51C2×C4×C29C2×D411yescharacteristic
52C2×C4×C29C2×D411yescharacteristic
53C2×C4×C29C2×D411yescharacteristic
54C2×Dic29—21no—
55C2×Dic29—21no—
56C2×Dic29—21no—
57C2×Dic29—41no—
58D116—21no—
59D116Q1612yescomplemented
60C4×D29—41no—
61C4×D29—41no—
62C4×D29—82no—
63Dic58—21no—
64Dic58—21no—
65Dic58—42no—
66C8×C29—41no—
67C8×C29—41no—
68#6597—22no—
69#1632—291nomaximal, Sylow
70C22×C29#12011yescharacteristic
71C2×D29—22no—
72C2×D29—41no—
73C2×D29—41no—
74C4×C29—21no—
75C4×C29—42no—
76C4×C29C2×Q1611yescharacteristic
77C4×C29#13511yescharacteristic
78C4×C29#13711yescharacteristic
79C4×C29#13711yescharacteristic
80Dic29—41no—
81Dic29—41no—
82Dic29—41no—
83Dic29—81no—
84#554—291no—
85#494—291no—
86#477—291no—
87#476—291no—
88#333D2911yescharacteristic, complemented
89Q8⋊C8—291no—
90D4⋊C8—291no—
91C2×C29#45111yescharacteristic
92C2×C29#45211yescharacteristic
93C2×C29#45311yescharacteristic
94D29—42no—
95C2×Q16—582no—
96C4⋊Q8—291no—
97C4⋊Q8C2×D2911yescharacteristic
98#125—581no—
99C22⋊Q8—581no—
100C22⋊Q8—582no—
101C4×Q8—291no—
102C4×D4—291no—
103C4×D4—581no—
104C2×C4⋊C4—581no—
105#107—581no—
106#106—581no—
107C4⋊C8C2×D2911yescharacteristic
108C4⋊C8C2×D2911yescharacteristic
109#103—581no—
110#102—581no—
111C4×C8—291no—
112C29#163211yescharacteristic, complemented, Sylow
113C2×Q8—291no—
114C2×Q8—581no—
115C2×Q8D11612yes—
116C2×D4—291no—
117C22×C4—582no—
118C22×C4—581no—
119Q16—1164no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—581no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—291no—
126C4⋊C4—291no—
127C4⋊C4—582no—
128C4⋊C4—582no—
129C4⋊C4—581no—
130C4⋊C4—581no—
131C4⋊C4—581no—
132C22⋊C4—582no—
133C22⋊C4—581no—
134C42—581no—
135C42C22×D2911yescharacteristic
136C23—581no—
137Q8—42no—
138Q8—581no—
139Q8—581no—
140Q8—1162no—
141D4—292no—
142D4—581no—
143C2×C4—22no—
144C2×C4—581no—
145C2×C4—581no—
146C2×C4—581no—
147C2×C4—1161no—
148C2×C4—1161no—
149C2×C4—1161no—
150C2×C4—2322no—
151C2×C4C2×D11611yescharacteristic
152C2×C4D4×D2911yescharacteristic
153C2×C4D4×D2911yescharacteristic
154C8—41no—
155C8—41no—
156C8—582no—
157C22—582no—
158C22—1161no—
159C22—1161no—
160C22#1174524411yescharacteristic
161C4—21no—
162C4—42no—
163C4—1161no—
164C4—1161no—
165C4—1161no—
166C4—2321no—
167C4#1174527711yescharacteristic
168C4#1174527811yescharacteristic
169C4Q16×D2911yescharacteristic
170C4#1174528011yescharacteristic
171C2—1162no—
172C2#1427132011yescharacteristic
173C2#1427132811yescharacteristic
174C2#1427133311yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#333C2
socleC22×C29#120
prime radicalC2×D116D4
hypercenter#333D29
hypocenterC29#1632
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #14271542C2semidirect
3. #14271459C2semidirect
5. #14270893C2semidirect
7. C29×#333C2semidirect
59. D116Q16semidirect
88. #333D29semidirect
112. C29#1632semidirect

Maximal subgroups

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

subgroupindex
#142718742
#142715422
#142714592
#142714542
#142708932
#142708902
C29×#3332
#163229