Finite Group Databasebeta

← #16818679

Subgroups — #16818679

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#14271899C211yesmaximal, characteristic
2#14271509C211yesmaximal, characteristic
3#14271449C211yesmaximal, characteristic, complemented
4#14271374C211yesmaximal, characteristic, complemented
5#14270893C211yesmaximal, characteristic, complemented
6#14270893C211yesmaximal, characteristic, complemented
7C29×#331C211yesmaximal, characteristic
8C29×#127C2211yescharacteristic
9#11745298—21no—
10#11745298—21no—
11#11745297—22no—
12D4×Dic29—21no—
13D4×Dic29—21no—
14C2×Dic116—21no—
15#11745231C2211yescharacteristic
16C4×Dic58C2211yescharacteristic
17C4×Dic58C2211yescharacteristic
18C29×C4⋊C8C2211yescharacteristic
19C29×C4⋊C8C2211yescharacteristic
20#11745180—22no—
21#11745165—21no—
22#11745164—21no—
23#11745164—21no—
24C4×#6597C2211yescharacteristic
25C2×D4×C29—21no—
26C2×D4×C29—21no—
27C2×D4×C29D412yes—
28C22×Dic29—22no—
29C2×Dic58—21no—
30C2×Dic58D411yescharacteristic
31C2×Dic58D411yescharacteristic
32C2×C8×C29—21no—
33C2×C8×C29—21no—
34C42×C29C2311yescharacteristic
35C22⋊Dic29—22no—
36C22⋊Dic29—22no—
37C22⋊Dic29—22no—
38C4⋊Dic29—21no—
39C4⋊Dic29—21no—
40C4⋊Dic29D411yescharacteristic
41C4⋊Dic29D411yescharacteristic
42#90779—21no—
43#90779—21no—
44C4×Dic29—21no—
45C4×Dic29—21no—
46C2×#6597—21no—
47Dic116—42no—
48C23×C29—22no—
49D4×C29—42no—
50D4×C29—41no—
51D4×C29—41no—
52D4×C29—41no—
53D4×C29—41no—
54C2×C4×C29C2×D411yescharacteristic
55C2×C4×C29C2×D411yescharacteristic
56C2×C4×C29C2×D411yescharacteristic
57C2×Dic29—21no—
58C2×Dic29—21no—
59C2×Dic29—21no—
60C2×Dic29—21no—
61C2×Dic29—41no—
62C2×Dic29—82no—
63Dic58—21no—
64Dic58—21no—
65Dic58—21no—
66Dic58—21no—
67Dic58—41no—
68Dic58—41no—
69C8×C29—41no—
70C8×C29—41no—
71#6597—41no—
72#1640—291nomaximal, Sylow
73C22×C29—42no—
74C22×C29—42no—
75C22×C29—42no—
76C22×C29#12011yescharacteristic
77C4×C29—21no—
78C4×C29#13511yescharacteristic
79C4×C29#13511yescharacteristic
80C4×C29AGL(1,ℤ/8)11yescharacteristic
81C4×C29#13711yescharacteristic
82Dic29—41no—
83Dic29—41no—
84Dic29—41no—
85Dic29—41no—
86Dic29—81no—
87#559—291no—
88#486—291no—
89#475—291no—
90#462—291no—
91#331D2911yescharacteristic
92Q8⋊C8—291no—
93Q8⋊C8—291no—
94C2×C29—82no—
95C2×C29#44911yescharacteristic
96C2×C29#45211yescharacteristic
97C2×C29#45511yescharacteristic
98C2×Q16—581no—
99C4⋊Q8—291no—
100#127C2×D2911yescharacteristic
101#124—581no—
102#124—581no—
103#123—582no—
104C4×Q8—291no—
105C4×Q8—291no—
106C4×D4—581no—
107C4×D4—581no—
108#106—581no—
109C4⋊C8C2×D2911yescharacteristic
110C4⋊C8C2×D2911yescharacteristic
111#103—581no—
112#103—581no—
113#102—582no—
114C4×C8—291no—
115C29#164011yescharacteristic, complemented, Sylow
116C2×Q8—291no—
117C2×Q8—291no—
118C2×Q8—581no—
119C2×D4—21no—
120C2×D4—21no—
121C2×D4D11612yes—
122C22×C4—582no—
123Q16—1162no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—581no—
127C4⋊C4—291no—
128C4⋊C4—291no—
129C4⋊C4—581no—
130C4⋊C4—581no—
131C4⋊C4—581no—
132C4⋊C4—581no—
133C22⋊C4—582no—
134C22⋊C4—582no—
135C22⋊C4—582no—
136C42—581no—
137C42—581no—
138C42C22×D2911yescharacteristic
139C23—22no—
140Q8—581no—
141Q8—581no—
142Q8—581no—
143Q8—581no—
144Q8—1161no—
145Q8—1161no—
146D4—42no—
147D4—41no—
148D4—41no—
149D4—41no—
150D4—41no—
151C2×C4—581no—
152C2×C4—581no—
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—42no—
164C22—42no—
165C22—42no—
166C22#1174524411yescharacteristic
167C4—21no—
168C4—1161no—
169C4—1161no—
170C4—1161no—
171C4—1161no—
172C4—2321no—
173C4#1174527311yescharacteristic
174C4#1174527411yescharacteristic
175C4#1174527711yescharacteristic
176C4#1174527811yescharacteristic
177C2—82no—
178C2#1427130911yescharacteristic
179C2#1427132611yescharacteristic
180C2#1427134311yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#331C2
socleC22×C29#120
prime radicalC29×#127C22
hypercenter#331D29
hypocenterC29#1640
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
3. #14271449C2semidirect
4. #14271374C2semidirect
5. #14270893C2semidirect
6. #14270893C2semidirect
115. C29#1640semidirect

Maximal subgroups

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

subgroupindex
#142718992
#142715092
#142714492
#142713742
#142708932
C29×#3312
#164029