Finite Group Databasebeta

← #16818823

Subgroups — #16818823

Order 3712.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#14271917C211yesmaximal, characteristic
2#14271569C211yesmaximal, characteristic, complemented
3#14271525C211yesmaximal, characteristic
4#14270905C211yesmaximal, characteristic, complemented
5#14270904C211yesmaximal, characteristic, complemented
6#14270902C211yesmaximal, characteristic
7C29×#491C211yesmaximal, characteristic, complemented
8C29×C4⋊Q8C2211yescharacteristic
9C29×#125C2211yescharacteristic
10#11745260—21no—
11#11745260—21no—
12#11745259—21no—
13#11745258—21no—
14#11745256—21no—
15#11745250—21no—
16#11745237C2211yescharacteristic
17#11745232C2211yescharacteristic
18C29×#103—21no—
19C29×#103—21no—
20C29×#97C2211yescharacteristic
21#11745158—21no—
22#11745157—21no—
23#11745156—21no—
24#11745155—21no—
25#11745151C2211yescharacteristic
26#11745151C2211yescharacteristic
27C2×Q8×C29—21no—
28C2×D116D411yescharacteristic
29C2×C4×D29—21no—
30C2×Dic58—21no—
31C2×Dic58D411yescharacteristic
32C2×C8×C29—21no—
33C4⋊C4×C29—21no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29—21no—
36C4⋊C4×C29—21no—
37C4⋊C4×C29D411yescharacteristic
38C4⋊C4×C29D411yescharacteristic
39C42×C29C2311yescharacteristic
40#90781—21no—
41#90781—21no—
42#90781—21no—
43#90781—21no—
44#90781—21no—
45C4⋊Dic29—21no—
46C4⋊Dic29D411yescharacteristic
47C4⋊Dic29D411yescharacteristic
48#90779—21no—
49#90779—21no—
50#90779—21no—
51C4×Dic29—21no—
52C2×#6597—21no—
53C2×#6597—21no—
54C22×D29—21no—
55Q8×C29—42no—
56C2×C4×C29—21no—
57C2×C4×C29—21no—
58C2×C4×C29—41no—
59C2×C4×C29C2×D411yescharacteristic
60C2×C4×C29C2×D411yescharacteristic
61C2×C4×C29C2×D411yescharacteristic
62C2×Dic29—21no—
63C2×Dic29—21no—
64C2×Dic29—21no—
65D116—41no—
66C4×D29—81no—
67Dic58—41no—
68Dic58—81no—
69C8×C29—41no—
70#6597—22no—
71#6597—41no—
72#1664—291nomaximal, Sylow
73C22×C29#12011yescharacteristic
74C2×D29—41no—
75C2×D29—41no—
76C2×D29—41no—
77C4×C29—21no—
78C4×C29—21no—
79C4×C29—21no—
80C4×C29—41no—
81C4×C29—41no—
82C4×C29—81no—
83Dic29—41no—
84Dic29—41no—
85Dic29—41no—
86#563—291no—
87#501—291no—
88#491D2911yescharacteristic, complemented
89#489—291no—
90#330—291no—
91#330—291no—
92#329—291no—
93C2×C29#45411yescharacteristic
94C2×C29#45511yescharacteristic
95C2×C29#45611yescharacteristic
96D29—81no—
97C4⋊Q8—581no—
98C4⋊Q8C2×D2911yescharacteristic
99#126—581no—
100#126—581no—
101#125—291no—
102#125C2×D2911yescharacteristic
103#124—291no—
104#123—581no—
105C22⋊Q8—581no—
106C22⋊Q8—581no—
107#107—581no—
108#106—581no—
109#103—21no—
110#103—21no—
111#103—581no—
112#102—581no—
113#97—291no—
114#97—291no—
115#97C2×D2911yescharacteristic
116C29#166411yescharacteristic, complemented, Sylow
117C2×Q8—21no—
118C2×Q8—291no—
119C2×Q8—581no—
120C2×D4—291no—
121C22×C4—581no—
122C2×C8—21no—
123C2×C8—581no—
124C2×C8—581no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—291no—
130C4⋊C4—291no—
131C4⋊C4—581no—
132C4⋊C4—581no—
133C4⋊C4—581no—
134C4⋊C4—581no—
135C4⋊C4C22⋊D2911yescharacteristic
136C4⋊C4C22⋊D2911yescharacteristic
137C22⋊C4—581no—
138C22⋊C4—581no—
139C22⋊C4—581no—
140C22⋊C4—581no—
141C22⋊C4—581no—
142C42—581no—
143C42C22×D2911yescharacteristic
144C23—581no—
145Q8—42no—
146Q8—1161no—
147Q8—2321no—
148D4—1161no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—581no—
153C2×C4—581no—
154C2×C4—581no—
155C2×C4—2321no—
156C2×C4D4×D2911yescharacteristic
157C2×C4D4×D2911yescharacteristic
158C2×C4C2×C22⋊D2911yescharacteristic
159C8—41no—
160C8—582no—
161C8—1161no—
162C22—1161no—
163C22—1161no—
164C22—1161no—
165C22#1174529911yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—1161no—
173C4—1161no—
174C4—1161no—
175C2—2321no—
176C2#1427133511yescharacteristic
177C2#1427133911yescharacteristic
178C2#1427134411yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#491C2
socleC22×C29#120
prime radicalC2×D116D4
hypercenter#491D29
hypocenterC29#1664
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #14271569C2semidirect
4. #14270905C2semidirect
5. #14270904C2semidirect
7. C29×#491C2semidirect
88. #491D29semidirect
116. C29#1664semidirect

Maximal subgroups

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

subgroupindex
#142719172
#142715692
#142715252
#142709052
#142709042
#142709022
C29×#4912
#166429