Finite Group Databasebeta

← #16818749

Subgroups — #16818749

Order 3712.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#14271887C211yesmaximal, characteristic
2#14271566C211yesmaximal, characteristic, complemented
3#14271449C211yesmaximal, characteristic, complemented
4#14271369C211yesmaximal, characteristic
5#14270893C211yesmaximal, characteristic, complemented
6#14270890C211yesmaximal, characteristic
7C29×#332C211yesmaximal, characteristic, complemented
8C29×C4⋊Q8C2211yescharacteristic
9#11745309—21no—
10Q8×Dic29—21no—
11C2×#90773—21no—
12#11745260—22no—
13#11745259—21no—
14#11745254—21no—
15C4×D116C2211yescharacteristic
16#11745231C2211yescharacteristic
17C4×Dic58C2211yescharacteristic
18C29×C4⋊C8C2211yescharacteristic
19C29×C4⋊C8C2211yescharacteristic
20#11745165—21no—
21#11745164—21no—
22#11745164—21no—
23#11745155—22no—
24C4×#6597C2211yescharacteristic
25C2×Q8×C29—21no—
26C2×D116D411yescharacteristic
27C2×C4×D29—21no—
28C2×Dic58—21no—
29C2×Dic58D411yescharacteristic
30C2×C8×C29—21no—
31C2×C8×C29—21no—
32C4⋊C4×C29—21no—
33C4⋊C4×C29D412yes—
34C42×C29C2311yescharacteristic
35#90781—22no—
36#90781—22no—
37#90781—21no—
38C4⋊Dic29—22no—
39C4⋊Dic29—21no—
40C4⋊Dic29—21no—
41C4⋊Dic29D411yescharacteristic
42C4⋊Dic29D411yescharacteristic
43#90779—21no—
44C4×Dic29—22no—
45C4×Dic29—21no—
46C2×#6597—21no—
47#90773—42no—
48C22×D29—21no—
49Q8×C29—41no—
50Q8×C29—41no—
51C2×C4×C29—22no—
52C2×C4×C29C2×D411yescharacteristic
53C2×C4×C29C2×D411yescharacteristic
54C2×C4×C29C2×D411yescharacteristic
55C2×Dic29—21no—
56C2×Dic29—21no—
57C2×Dic29—21no—
58C2×Dic29—41no—
59D116—21no—
60D116—21no—
61C4×D29—41no—
62C4×D29—41no—
63Dic58—21no—
64Dic58—21no—
65Dic58—41no—
66Dic58—41no—
67C8×C29—41no—
68C8×C29—41no—
69#6597—22no—
70#1650—291nomaximal, Sylow
71C22×C29#12011yescharacteristic
72C2×D29—41no—
73C2×D29—41no—
74C2×D29—41no—
75C4×C29—21no—
76C4×C29—42no—
77C4×C29#13511yescharacteristic
78C4×C29#13511yescharacteristic
79C4×C29AGL(1,ℤ/8)11yescharacteristic
80C4×C29#13711yescharacteristic
81Dic29—41no—
82Dic29—41no—
83Dic29—41no—
84Dic29—81no—
85#556—291no—
86#500—291no—
87#475—291no—
88#461—291no—
89#332D2911yescharacteristic, complemented
90Q8⋊C8—291no—
91D4⋊C8—291no—
92C2×C29#44911yescharacteristic
93C2×C29#45211yescharacteristic
94C2×C29#45611yescharacteristic
95D29—81no—
96C2×SD16—581no—
97C4⋊Q8—291no—
98C4⋊Q8C2×D2911yescharacteristic
99#126—582no—
100#124—581no—
101C22⋊Q8—581no—
102C4×Q8—291no—
103C4×Q8—581no—
104C4×D4—291no—
105#117—581no—
106#107—582no—
107#106—581no—
108C4⋊C8C2×D2911yescharacteristic
109C4⋊C8C2×D2911yescharacteristic
110#103—581no—
111#103—581no—
112C4×C8—291no—
113C29#165011yescharacteristic, complemented, Sylow
114C2×Q8—21no—
115C2×Q8—291no—
116C2×Q8—581no—
117C2×D4—291no—
118C22×C4—581no—
119SD16—1162no—
120C2×C8—21no—
121C2×C8—21no—
122C2×C8—581no—
123C4⋊C4—21no—
124C4⋊C4—291no—
125C4⋊C4—291no—
126C4⋊C4—582no—
127C4⋊C4—581no—
128C4⋊C4—581no—
129C4⋊C4—581no—
130C4⋊C4D11612yes—
131C22⋊C4—582no—
132C22⋊C4—582no—
133C22⋊C4—581no—
134C42—582no—
135C42—581no—
136C42C22×D2911yescharacteristic
137C23—581no—
138Q8—41no—
139Q8—41no—
140Q8—581no—
141Q8—581no—
142Q8—1161no—
143Q8—1161no—
144D4—581no—
145D4—581no—
146C2×C4—22no—
147C2×C4—581no—
148C2×C4—581no—
149C2×C4—581no—
150C2×C4—1161no—
151C2×C4—1161no—
152C2×C4—1161no—
153C2×C4C2×D11611yescharacteristic
154C2×C4D4×D2911yescharacteristic
155C2×C4D4×D2911yescharacteristic
156C8—41no—
157C8—41no—
158C8—582no—
159C22—1161no—
160C22—1161no—
161C22—1161no—
162C22#1174524411yescharacteristic
163C4—21no—
164C4—42no—
165C4—1161no—
166C4—1161no—
167C4—1161no—
168C4—2321no—
169C4#1174527311yescharacteristic
170C4#1174527811yescharacteristic
171C4#1174527811yescharacteristic
172C4#1174528011yescharacteristic
173C2—2321no—
174C2#1427130911yescharacteristic
175C2#1427132811yescharacteristic
176C2#1427134811yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#332C2
socleC22×C29#120
prime radicalC2×D116D4
hypercenter#332D29
hypocenterC29#1650
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #14271566C2semidirect
3. #14271449C2semidirect
5. #14270893C2semidirect
7. C29×#332C2semidirect
89. #332D29semidirect
113. C29#1650semidirect

Maximal subgroups

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

subgroupindex
#142718872
#142715662
#142714492
#142713692
#142708932
#142708902
C29×#3322
#165029