Finite Group Databasebeta

← #16818680

Subgroups — #16818680

Order 3712.

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

normal subgroups only

This group has 212 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#14271898C211yesmaximal, characteristic
2#14271510C211yesmaximal, characteristic
3#14271449C211yesmaximal, characteristic, complemented
4#14271373C211yesmaximal, characteristic, complemented
5#14270906C211yesmaximal, characteristic
6#14270895C211yesmaximal, characteristic, complemented
7C29×Q8⋊C8C211yesmaximal, characteristic, complemented
8C4×Q8×C29C2211yescharacteristic
9#11745309—21no—
10C2×#90785—21no—
11#11745256—22no—
12#11745255—21no—
13#11745237—21no—
14#11745236C2211yescharacteristic
15C4×D116—21no—
16#11745231C2211yescharacteristic
17C4×Dic58C2211yescharacteristic
18C29×C4⋊C8C2211yescharacteristic
19C4×C8×C29C2211yescharacteristic
20#11745169—22no—
21#11745165—21no—
22#11745164—21no—
23#11745158—21no—
24C4⋊#6597C2211yescharacteristic
25C2×Q8×C29D411yescharacteristic
26C2×D116—21no—
27C2×D116—21no—
28C2×D116D412yes—
29C2×C4×D29—22no—
30C2×Dic58—21no—
31C2×Dic58D411yescharacteristic
32C2×C8×C29—21no—
33C2×C8×C29—21no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29D411yescharacteristic
36C42×C29—21no—
37C42×C29C2311yescharacteristic
38#90785—42no—
39#90781—22no—
40#90781—22no—
41#90781—22no—
42C4⋊Dic29—21no—
43C4⋊Dic29—21no—
44C4⋊Dic29D411yescharacteristic
45#90779—21no—
46C4×Dic29—21no—
47C2×#6597—21no—
48C22×D29—22no—
49Q8×C29—21no—
50Q8×C29—21no—
51C2×C4×C29—21no—
52C2×C4×C29—21no—
53C2×C4×C29C2×D411yescharacteristic
54C2×C4×C29C2×D411yescharacteristic
55C2×C4×C29C2×D411yescharacteristic
56C2×Dic29—21no—
57C2×Dic29—21no—
58C2×Dic29—41no—
59D116—42no—
60D116—41no—
61D116—41no—
62D116—41no—
63D116—41no—
64C4×D29—82no—
65Dic58—21no—
66Dic58—21no—
67Dic58—41no—
68Dic58—41no—
69C8×C29—41no—
70C8×C29—41no—
71#6597—41no—
72#1640—291nomaximal, Sylow
73C22×C29#12011yescharacteristic
74C2×D29—42no—
75C2×D29—42no—
76C2×D29—42no—
77C4×C29—21no—
78C4×C29—41no—
79C4×C29—41no—
80C4×C29#13511yescharacteristic
81C4×C29#13511yescharacteristic
82C4×C29AGL(1,ℤ/8)11yescharacteristic
83C4×C29#13711yescharacteristic
84Dic29—41no—
85Dic29—41no—
86Dic29—81no—
87#559—291no—
88#486—291no—
89#475—291no—
90#462—291no—
91#331—291no—
92Q8⋊C8—291no—
93Q8⋊C8D2911yescharacteristic, complemented
94C2×C29#44911yescharacteristic
95C2×C29#45211yescharacteristic
96C2×C29#45511yescharacteristic
97D29—82no—
98C2×Q16—581no—
99C4⋊Q8—291no—
100#127—291no—
101#124—581no—
102#124—581no—
103#123—582no—
104C4×Q8—291no—
105C4×Q8C2×D2911yescharacteristic
106C4×D4—581no—
107C4×D4—581no—
108#106—581no—
109C4⋊C8—291no—
110C4⋊C8C2×D2911yescharacteristic
111#103—581no—
112#103—581no—
113#102—582no—
114C4×C8C2×D2911yescharacteristic
115C29#164011yescharacteristic, complemented, Sylow
116C2×Q8—291no—
117C2×Q8—581no—
118C2×Q8D11611yescharacteristic
119C2×D4—292no—
120C2×D4—581no—
121C2×D4—581no—
122C22×C4—582no—
123Q16—1162no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—581no—
127C4⋊C4—21no—
128C4⋊C4—291no—
129C4⋊C4—581no—
130C4⋊C4—581no—
131C4⋊C4—581no—
132C4⋊C4D11611yescharacteristic
133C22⋊C4—582no—
134C22⋊C4—582no—
135C22⋊C4—582no—
136C42—21no—
137C42—581no—
138C42C22×D2911yescharacteristic
139C23—582no—
140Q8—21no—
141Q8—21no—
142Q8—581no—
143Q8—581no—
144Q8—1161no—
145Q8—1161no—
146D4—1162no—
147D4—1161no—
148D4—1161no—
149D4—1161no—
150D4—1161no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—581no—
154C2×C4—581no—
155C2×C4—1161no—
156C2×C4—2322no—
157C2×C4C2×D11611yescharacteristic
158C2×C4D4×D2911yescharacteristic
159C2×C4D4×D2911yescharacteristic
160C8—41no—
161C8—41no—
162C8—1161no—
163C22—1162no—
164C22—1162no—
165C22—1162no—
166C22#1174524411yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—1161no—
171C4—1161no—
172C4—2321no—
173C4#1174526611yescharacteristic
174C4#1174527011yescharacteristic
175C4#1174527811yescharacteristic
176C4#1174528011yescharacteristic
177C2—2322no—
178C2#1427131011yescharacteristic
179C2#1427132811yescharacteristic
180C2#1427134211yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×Q8⋊C8C2
socleC22×C29#120
prime radical#11745236C22
hypercenterQ8⋊C8D29
hypocenterC29#1640
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
3. #14271449C2semidirect
4. #14271373C2semidirect
6. #14270895C2semidirect
7. C29×Q8⋊C8C2semidirect
93. Q8⋊C8D29semidirect
115. C29#1640semidirect

Maximal subgroups

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

subgroupindex
#142718982
#142715102
#142714492
#142713732
#142709062
#142708952
C29×Q8⋊C82
#164029