Finite Group Databasebeta

← #16818565

Subgroups — #16818565

Order 3712.

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

normal subgroups only

This group has 236 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, complemented
2#14271537C211yesmaximal, characteristic, complemented
3#14271364C211yesmaximal, characteristic, complemented
4#14271359C211yesmaximal, characteristic
5#14270893C211yesmaximal, characteristic, complemented
6#14270890C211yesmaximal, characteristic, complemented
7C29×#333C211yesmaximal, characteristic, complemented
8C29×C4⋊Q8C2211yescharacteristic
9#11745308—22no—
10C2×#90784—22no—
11C2×D232—21no—
12C2×#90773—21no—
13#11745259—21no—
14#11745255—21no—
15C4⋊C4×D29—21no—
16#11745252—21no—
17#11745236C2211yescharacteristic
18C4×D116C2211yescharacteristic
19C4×Dic58C2211yescharacteristic
20C29×C4⋊C8C2211yescharacteristic
21C29×C4⋊C8C2211yescharacteristic
22#11745169—21no—
23#11745169—21no—
24C4×#6597C2211yescharacteristic
25C2×Q8×C29D412yes—
26C2×D116—21no—
27C2×D116—21no—
28C2×D116—21no—
29C2×D116D411yescharacteristic
30C2×C4×D29—21no—
31C2×C4×D29—22no—
32C2×Dic58D411yescharacteristic
33C2×C8×C29—21no—
34C2×C8×C29—21no—
35C4⋊C4×C29—21no—
36C4⋊C4×C29—21no—
37C42×C29C2311yescharacteristic
38#90784—44no—
39#90781—22no—
40#90781—21no—
41C4⋊Dic29—22no—
42C4⋊Dic29D411yescharacteristic
43C4⋊Dic29D411yescharacteristic
44#90779—22no—
45#90779—21no—
46C4×Dic29—21no—
47C2×#6597—21no—
48D232—42no—
49#90773—42no—
50C22×D29—21no—
51C22×D29—41no—
52Q8×C29—42no—
53C2×C4×C29—22no—
54C2×C4×C29C2×D411yescharacteristic
55C2×C4×C29C2×D411yescharacteristic
56C2×C4×C29C2×D411yescharacteristic
57C2×Dic29—21no—
58C2×Dic29—21no—
59C2×Dic29—21no—
60D116—21no—
61D116—42no—
62D116—41no—
63D116—41no—
64D116—41no—
65D116—41no—
66D116SD1612yescomplemented
67C4×D29—41no—
68C4×D29—41no—
69C4×D29—82no—
70Dic58—21no—
71Dic58—21no—
72C8×C29—41no—
73C8×C29—41no—
74#6597—22no—
75#1622—291nomaximal, Sylow
76C22×C29#12011yescharacteristic
77C2×D29—22no—
78C2×D29—41no—
79C2×D29—41no—
80C2×D29—81no—
81C2×D29—81no—
82C2×D29—81no—
83C4×C29—21no—
84C4×C29—42no—
85C4×C29C2×SD1611yescharacteristic
86C4×C29#13511yescharacteristic
87C4×C29AGL(1,ℤ/8)11yescharacteristic
88C4×C29#13711yescharacteristic
89Dic29—41no—
90Dic29—41no—
91Dic29—41no—
92#554—291no—
93#492—291no—
94#460—291no—
95#459—291no—
96#333D2911yescharacteristic, complemented
97Q8⋊C8—291no—
98D4⋊C8—291no—
99C2×C29#44811yescharacteristic
100C2×C29#44911yescharacteristic
101C2×C29#45311yescharacteristic
102D29—42no—
103D29—161no—
104C2×SD16—581no—
105C2×SD16—582no—
106C2×D8—581no—
107C4⋊Q8C2×D2911yescharacteristic
108#127—291no—
109#125—581no—
110C22⋊Q8—581no—
111C22⋊Q8—582no—
112C4×Q8—291no—
113C4×D4—291no—
114C4×D4—581no—
115C2×C4⋊C4—581no—
116C4⋊C8C2×D2911yescharacteristic
117C4⋊C8C2×D2911yescharacteristic
118#102—581no—
119#102—581no—
120C4×C8—291no—
121C29#162211yescharacteristic, complemented, Sylow
122C2×Q8—291no—
123C2×Q8D11612yes—
124C2×D4—291no—
125C2×D4—581no—
126C2×D4—581no—
127C2×D4—581no—
128C22×C4—582no—
129C22×C4—581no—
130SD16—1162no—
131SD16—1164no—
132D8—1162no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—581no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—291no—
139C4⋊C4—291no—
140C4⋊C4—582no—
141C4⋊C4—582no—
142C4⋊C4—581no—
143C22⋊C4—582no—
144C22⋊C4—581no—
145C42—581no—
146C42C22×D2911yescharacteristic
147C23—581no—
148C23—1161no—
149Q8—42no—
150Q8—581no—
151Q8—581no—
152D4—292no—
153D4—581no—
154D4—1162no—
155D4—1161no—
156D4—1161no—
157D4—1161no—
158D4—1161no—
159C2×C4—22no—
160C2×C4—581no—
161C2×C4—581no—
162C2×C4—581no—
163C2×C4—1161no—
164C2×C4—1161no—
165C2×C4—2322no—
166C2×C4C2×D11611yescharacteristic
167C2×C4D4×D2911yescharacteristic
168C2×C4D4×D2911yescharacteristic
169C8—41no—
170C8—41no—
171C8—582no—
172C22—582no—
173C22—1161no—
174C22—1161no—
175C22—2321no—
176C22—2321no—
177C22—2321no—
178C22#1174524411yescharacteristic
179C4—21no—
180C4—42no—
181C4—1161no—
182C4—1161no—
183C4—1161no—
184C4SD16×D2911yescharacteristic
185C4#1174527611yescharacteristic
186C4#1174528011yescharacteristic
187C4#1174528111yescharacteristic
188C2—1162no—
189C2—4641no—
190C2#1427130311yescharacteristic
191C2#1427131111yescharacteristic
192C2#1427133311yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#333C2
socleC22×C29#120
prime radical#14271359C2
hypercenter#333D29
hypocenterC29#1622
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #14271874C2semidirect
2. #14271537C2semidirect
3. #14271364C2semidirect
5. #14270893C2semidirect
6. #14270890C2semidirect
7. C29×#333C2semidirect
66. D116SD16semidirect
96. #333D29semidirect
121. C29#1622semidirect

Maximal subgroups

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

subgroupindex
#142718742
#142715372
#142713642
#142713592
#142708932
#142708902
C29×#3332
#162229