Finite Group Databasebeta

← #16818698

Subgroups — #16818698

Order 3712.

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

normal subgroups only

This group has 208 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#14271873C211yesmaximal, characteristic
2#14271515C211yesmaximal, characteristic, complemented
3#14271365C211yesmaximal, characteristic
4#14270911C211yesmaximal, characteristic, complemented
5Q8⋊#6597C211yesmaximal, characteristic, complemented
6#14270890C211yesmaximal, characteristic
7C29×#475C211yesmaximal, characteristic, complemented
8C29×C4⋊Q8C2211yescharacteristic
9C4×Q8×C29C2211yescharacteristic
10#11745308—21no—
11C2×#90784—21no—
12#11745258—22no—
13C4⋊C4×D29—21no—
14C4×D116—21no—
15C4×D116C2211yescharacteristic
16#11745232—21no—
17#11745231C2211yescharacteristic
18C29×#106—21no—
19C29×C4⋊C8C2211yescharacteristic
20C29×#103—21no—
21#11745183—21no—
22#11745158—22no—
23C4⋊#6597C2211yescharacteristic
24C4×#6597C2211yescharacteristic
25C2×Q8×C29—21no—
26C2×Q8×C29D411yescharacteristic
27C2×D116D411yescharacteristic
28C2×C4×D29—21no—
29C2×C4×D29—22no—
30C2×Dic58D412yes—
31C2×C8×C29—21no—
32C4⋊C4×C29—21no—
33C4⋊C4×C29—21no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29D411yescharacteristic
36C42×C29—21no—
37C42×C29C2311yescharacteristic
38#90784—42no—
39#90781—22no—
40#90781—21no—
41C4⋊Dic29—21no—
42C4⋊Dic29—21no—
43C4⋊Dic29D411yescharacteristic
44#90779—22no—
45#90779—22no—
46C2×#6597—21no—
47C2×#6597—21no—
48C22×D29—21no—
49Q8×C29—21no—
50Q8×C29—21no—
51Q8×C29—41no—
52Q8×C29—41no—
53C2×C4×C29—21no—
54C2×C4×C29—21no—
55C2×C4×C29—41no—
56C2×C4×C29C2×D411yescharacteristic
57C2×C4×C29C2×D411yescharacteristic
58C2×C4×C29C2×D411yescharacteristic
59C2×Dic29—21no—
60C2×Dic29—22no—
61D116—21no—
62D116SD1612yes—
63C4×D29—41no—
64C4×D29—41no—
65C4×D29—82no—
66Dic58—42no—
67C8×C29—41no—
68#6597—41no—
69#6597—41no—
70#1643—291nomaximal, Sylow
71C22×C29#12011yescharacteristic
72C2×D29—22no—
73C2×D29—41no—
74C2×D29—41no—
75C4×C29—21no—
76C4×C29—41no—
77C4×C29—41no—
78C4×C29—81no—
79C4×C29C2×SD1611yescharacteristic
80C4×C29#13511yescharacteristic
81C4×C29#13711yescharacteristic
82C4×C29#13711yescharacteristic
83Dic29—41no—
84Dic29—42no—
85#554—291no—
86#487—291no—
87#475D2911yescharacteristic, complemented
88#461—291no—
89#333—291no—
90Q8⋊C8—291no—
91D4⋊C8—291no—
92C2×C29#44811yescharacteristic
93C2×C29#45211yescharacteristic
94C2×C29#45511yescharacteristic
95D29—42no—
96C2×SD16—581no—
97C4⋊Q8—291no—
98C4⋊Q8C2×D2911yescharacteristic
99#125—581no—
100C22⋊Q8—582no—
101C22⋊Q8—581no—
102C4×Q8C2×D2911yescharacteristic
103C4×D4—291no—
104C4×D4—581no—
105C2×C4⋊C4—581no—
106#106—21no—
107C4⋊C8—291no—
108C4⋊C8C2×D2911yescharacteristic
109#103—21no—
110#103—582no—
111#103—581no—
112C4×C8—291no—
113C29#164311yescharacteristic, complemented, Sylow
114C2×Q8—21no—
115C2×Q8—292no—
116C2×Q8C22⋊D2911yescharacteristic
117C2×D4—291no—
118C22×C4—582no—
119C22×C4—581no—
120SD16—1162no—
121C2×C8—21no—
122C2×C8—581no—
123C2×C8—581no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—291no—
128C4⋊C4—582no—
129C4⋊C4—582no—
130C4⋊C4—581no—
131C4⋊C4—581no—
132C4⋊C4C22⋊D2911yescharacteristic
133C22⋊C4—582no—
134C22⋊C4—581no—
135C42—21no—
136C42C22×D2911yescharacteristic
137C23—581no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—1162no—
143D4—292no—
144D4—581no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—581no—
149C2×C4—582no—
150C2×C4—1161no—
151C2×C4—1161no—
152C2×C4—2322no—
153C2×C4D4×D2911yescharacteristic
154C2×C4D4×D2911yescharacteristic
155C2×C4C2×C22⋊D2911yescharacteristic
156C8—41no—
157C8—1161no—
158C8—1161no—
159C22—582no—
160C22—1161no—
161C22—1161no—
162C22#1174529911yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—1161no—
168C4—1162no—
169C4SD16×D2911yescharacteristic
170C4#1174527711yescharacteristic
171C4#1174530411yescharacteristic
172C4#1174531211yescharacteristic
173C2—1162no—
174C2#1427130011yescharacteristic
175C2#1427132311yescharacteristic
176C2#1427133911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#475C2
socleC22×C29#120
prime radicalC2×D116D4
hypercenter#475D29
hypocenterC29#1643
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #14271515C2semidirect
4. #14270911C2semidirect
5. Q8⋊#6597C2semidirect
7. C29×#475C2semidirect
87. #475D29semidirect
113. C29#1643semidirect

Maximal subgroups

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

subgroupindex
#142718732
#142715152
#142713652
#142709112
Q8⋊#65972
#142708902
C29×#4752
#164329