Finite Group Databasebeta

← #16818623

Subgroups — #16818623

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#14271455C211yesmaximal, characteristic, complemented
3#14271450C211yesmaximal, characteristic
4#14270912C211yesmaximal, characteristic, complemented
5#14270895C211yesmaximal, characteristic, complemented
6#14270892C211yesmaximal, characteristic
7C29×#494C211yesmaximal, characteristic, complemented
8C2×Q16×C29—22no—
9C29×C4⋊Q8C2211yescharacteristic
10C29×C4⋊Q8C2211yescharacteristic
11#11745308—22no—
12#11745259—21no—
13#11745255—21no—
14C4⋊C4×D29—21no—
15#11745252—21no—
16C4×D116C2211yescharacteristic
17C4×Dic58C2211yescharacteristic
18C4×C8×C29C2211yescharacteristic
19#11745158—21no—
20#11745157—21no—
21#11745156—21no—
22#11745155—21no—
23C4⋊#6597C2211yescharacteristic
24C4⋊#6597C2211yescharacteristic
25C2×Q8×C29—21no—
26C2×Q8×C29D412yes—
27C2×D116D411yescharacteristic
28C2×C4×D29—21no—
29C2×C4×D29—22no—
30C2×Dic58D411yescharacteristic
31Q16×C29—44no—
32C2×C8×C29—21no—
33C4⋊C4×C29—21no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29—21no—
36C4⋊C4×C29—21no—
37C42×C29C2311yescharacteristic
38#90781—22no—
39#90781—21no—
40C4⋊Dic29—22no—
41C4⋊Dic29D411yescharacteristic
42C4⋊Dic29D411yescharacteristic
43#90779—22no—
44#90779—21no—
45C4×Dic29—21no—
46C2×#6597—21no—
47C2×#6597—21no—
48C22×D29—21no—
49Q8×C29—42no—
50Q8×C29—42no—
51C2×C4×C29—22no—
52C2×C4×C29—41no—
53C2×C4×C29C2×D411yescharacteristic
54C2×C4×C29C2×D411yescharacteristic
55C2×C4×C29C2×D411yescharacteristic
56C2×Dic29—21no—
57C2×Dic29—21no—
58C2×Dic29—21no—
59D116—21no—
60D116Q1612yescomplemented
61C4×D29—41no—
62C4×D29—41no—
63C4×D29—82no—
64Dic58—21no—
65Dic58—21no—
66C8×C29—22no—
67#6597—41no—
68#6597—41no—
69#1632—291nomaximal, Sylow
70C22×C29#12011yescharacteristic
71C2×D29—22no—
72C2×D29—41no—
73C2×D29—41no—
74C4×C29—21no—
75C4×C29—42no—
76C4×C29—81no—
77C4×C29C2×Q1611yescharacteristic
78C4×C29#13511yescharacteristic
79C4×C29#13711yescharacteristic
80C4×C29#13711yescharacteristic
81Dic29—41no—
82Dic29—41no—
83Dic29—41no—
84#554—291no—
85#494D2911yescharacteristic, complemented
86#477—291no—
87#476—291no—
88#333—291no—
89Q8⋊C8—291no—
90D4⋊C8—291no—
91C2×C29#45111yescharacteristic
92C2×C29#45211yescharacteristic
93C2×C29#45311yescharacteristic
94D29—42no—
95C2×Q16—22no—
96C4⋊Q8C2×D2911yescharacteristic
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⋊C8—291no—
108C4⋊C8—291no—
109#103—581no—
110#102—581no—
111C4×C8C2×D2911yescharacteristic
112C29#163211yescharacteristic, complemented, Sylow
113C2×Q8—21no—
114C2×Q8—291no—
115C2×Q8C22⋊D2912yes—
116C2×D4—291no—
117C22×C4—582no—
118C22×C4—581no—
119Q16—44no—
120C2×C8—21no—
121C2×C8—581no—
122C2×C8—581no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—291no—
128C4⋊C4—291no—
129C4⋊C4—582no—
130C4⋊C4—582no—
131C4⋊C4—581no—
132C22⋊C4—582no—
133C22⋊C4—581no—
134C42—581no—
135C42C22×D2911yescharacteristic
136C23—581no—
137Q8—42no—
138Q8—42no—
139Q8—581no—
140Q8—581no—
141D4—292no—
142D4—581no—
143C2×C4—22no—
144C2×C4—41no—
145C2×C4—581no—
146C2×C4—581no—
147C2×C4—581no—
148C2×C4—1161no—
149C2×C4—1161no—
150C2×C4—2322no—
151C2×C4D4×D2911yescharacteristic
152C2×C4D4×D2911yescharacteristic
153C2×C4C2×C22⋊D2911yescharacteristic
154C8—22no—
155C8—1161no—
156C8—1161no—
157C22—582no—
158C22—1161no—
159C22—1161no—
160C22#1174529911yescharacteristic
161C4—21no—
162C4—42no—
163C4—81no—
164C4—1161no—
165C4—1161no—
166C4—1161no—
167C4Q16×D2911yescharacteristic
168C4#1174528011yescharacteristic
169C4#1174528011yescharacteristic
170C4#1174528111yescharacteristic
171C2—1162no—
172C2#1427131711yescharacteristic
173C2#1427132411yescharacteristic
174C2#1427133011yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#494C2
socleC22×C29#120
prime radicalC2×D116D4
hypercenter#494D29
hypocenterC29#1632
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
2. #14271455C2semidirect
4. #14270912C2semidirect
5. #14270895C2semidirect
7. C29×#494C2semidirect
60. D116Q16semidirect
85. #494D29semidirect
112. C29#1632semidirect

Maximal subgroups

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

subgroupindex
#142718742
#142714552
#142714502
#142709122
#142708952
#142708922
C29×#4942
#163229