Finite Group Databasebeta

← #16818553

Subgroups — #16818553

Order 3712.

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

normal subgroups only

This group has 240 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, complemented
2#14271540C211yesmaximal, characteristic
3#14271364C211yesmaximal, characteristic, complemented
4#14271363C211yesmaximal, characteristic, complemented
5#14270906C211yesmaximal, characteristic, complemented
6#14270895C211yesmaximal, characteristic, complemented
7C29×Q8⋊C8C211yesmaximal, characteristic, complemented
8C4×Q8×C29C2211yescharacteristic
9#11745309—21no—
10C2×#90784—21no—
11C2×D232—22no—
12C2×#90773—21no—
13#11745256—22no—
14#11745255—21no—
15#11745237—21no—
16#11745236C2211yescharacteristic
17#11745236C2211yescharacteristic
18C4×D116—21no—
19C4×Dic58C2211yescharacteristic
20C29×C4⋊C8C2211yescharacteristic
21C4×C8×C29C2211yescharacteristic
22#11745169—21no—
23#11745157—21no—
24C4⋊#6597C2211yescharacteristic
25C2×Q8×C29D411yescharacteristic
26C2×D116—21no—
27C2×D116—21no—
28C2×D116—21no—
29C2×D116—21no—
30C2×D116—21no—
31C2×D116D412yes—
32C2×C4×D29—22no—
33C2×Dic58D411yescharacteristic
34C2×C8×C29—21no—
35C2×C8×C29—21no—
36C4⋊C4×C29—21no—
37C4⋊C4×C29D411yescharacteristic
38C42×C29—21no—
39C42×C29C2311yescharacteristic
40#90784—42no—
41#90781—22no—
42#90781—22no—
43#90781—22no—
44C4⋊Dic29D411yescharacteristic
45#90779—21no—
46C4×Dic29—21no—
47C2×#6597—21no—
48D232—44no—
49#90773—42no—
50C22×D29—22no—
51C22×D29—41no—
52Q8×C29—21no—
53Q8×C29—21no—
54C2×C4×C29—21no—
55C2×C4×C29—21no—
56C2×C4×C29C2×D411yescharacteristic
57C2×C4×C29C2×D411yescharacteristic
58C2×C4×C29C2×D411yescharacteristic
59C2×Dic29—21no—
60C2×Dic29—21no—
61D116—42no—
62D116—42no—
63D116—41no—
64D116—41no—
65D116—41no—
66D116—41no—
67D116—41no—
68D116—41no—
69D116—41no—
70D116—41no—
71C4×D29—82no—
72Dic58—21no—
73Dic58—21no—
74C8×C29—22no—
75C8×C29—41no—
76#6597—41no—
77#1620—291nomaximal, Sylow
78C22×C29#12011yescharacteristic
79C2×D29—42no—
80C2×D29—42no—
81C2×D29—42no—
82C2×D29—81no—
83C2×D29—81no—
84C2×D29—81no—
85C4×C29—21no—
86C4×C29—41no—
87C4×C29—41no—
88C4×C29#13511yescharacteristic
89C4×C29#13511yescharacteristic
90C4×C29AGL(1,ℤ/8)11yescharacteristic
91C4×C29AGL(1,ℤ/8)11yescharacteristic
92Dic29—41no—
93Dic29—41no—
94#559—291no—
95#493—291no—
96#460—291no—
97#460—291no—
98#331—291no—
99Q8⋊C8—291no—
100Q8⋊C8D2911yescharacteristic, complemented
101C2×C29#44911yescharacteristic
102C2×C29#44911yescharacteristic
103C2×C29#45311yescharacteristic
104D29—82no—
105D29—161no—
106C2×SD16—581no—
107C2×SD16—581no—
108C2×D8—582no—
109#127—291no—
110#127—291no—
111#124—581no—
112#124—581no—
113#123—582no—
114C4×Q8—291no—
115C4×Q8C2×D2911yescharacteristic
116C4×D4—581no—
117C4×D4—581no—
118C4⋊C8—291no—
119C4⋊C8C2×D2911yescharacteristic
120#102—581no—
121#102—581no—
122C4×C8C2×D2911yescharacteristic
123C29#162011yescharacteristic, complemented, Sylow
124C2×Q8—291no—
125C2×Q8D11611yescharacteristic
126C2×D4—292no—
127C2×D4—581no—
128C2×D4—581no—
129C2×D4—581no—
130C2×D4—581no—
131C2×D4—581no—
132C22×C4—582no—
133SD16—1162no—
134SD16—1162no—
135D8—1164no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—581no—
139C4⋊C4—21no—
140C4⋊C4—291no—
141C4⋊C4—581no—
142C4⋊C4D11611yescharacteristic
143C22⋊C4—582no—
144C22⋊C4—582no—
145C22⋊C4—582no—
146C42—21no—
147C42—581no—
148C42C22×D2911yescharacteristic
149C23—582no—
150C23—1161no—
151Q8—21no—
152Q8—21no—
153Q8—581no—
154Q8—581no—
155D4—1162no—
156D4—1162no—
157D4—1161no—
158D4—1161no—
159D4—1161no—
160D4—1161no—
161D4—1161no—
162D4—1161no—
163D4—1161no—
164D4—1161no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—581no—
168C2×C4—581no—
169C2×C4—2322no—
170C2×C4C2×D11611yescharacteristic
171C2×C4D4×D2911yescharacteristic
172C2×C4D4×D2911yescharacteristic
173C8—22no—
174C8—41no—
175C8—1161no—
176C22—1162no—
177C22—1162no—
178C22—1162no—
179C22—2321no—
180C22—2321no—
181C22—2321no—
182C22#1174524411yescharacteristic
183C4—21no—
184C4—41no—
185C4—41no—
186C4—1161no—
187C4—1161no—
188C4#1174526611yescharacteristic
189C4#1174527011yescharacteristic
190C4#1174527611yescharacteristic
191C4#1174528111yescharacteristic
192C2—4641no—
193C2—2322no—
194C2#1427131011yescharacteristic
195C2#1427131111yescharacteristic
196C2#1427133211yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×Q8⋊C8C2
socleC22×C29#120
prime radical#14271540C2
hypercenterQ8⋊C8D29
hypocenterC29#1620
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
1. #14271898C2semidirect
3. #14271364C2semidirect
4. #14271363C2semidirect
5. #14270906C2semidirect
6. #14270895C2semidirect
7. C29×Q8⋊C8C2semidirect
100. Q8⋊C8D29semidirect
123. C29#1620semidirect

Maximal subgroups

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

subgroupindex
#142718982
#142715402
#142713642
#142713632
#142709062
#142708952
C29×Q8⋊C82
#162029