Finite Group Databasebeta

← #16820556

Subgroups — #16820556

Order 3712.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#14271670C212yesmaximal, complemented
2#14271180C212yesmaximal, complemented
3#14271126C211yesmaximal, characteristic, complemented
4#14270920C211yesmaximal, characteristic, complemented
5C29×#575C211yesmaximal, characteristic, complemented
6C2×#41×C29C2212yes—
7C22×C4×D29C2211yescharacteristic
8C29×#137—22no—
9C29×AGL(1,ℤ/8)—22no—
10C29×#135—22no—
11C2×M16×C29C2211yescharacteristic
12#11745308—22no—
13#11745300—22no—
14#11745299—22no—
15#11745297—22no—
16C4×C22⋊D29—24no—
17#11745288C2212yes—
18C2×#90777C2211yescharacteristic
19#11745185—24no—
20#11745168—22no—
21C23×D29D411yescharacteristic
22#41×C29—22no—
23#41×C29—22no—
24#41×C29—22no—
25#41×C29—22no—
26C2×Q8×C29D412yescomplemented
27C2×D4×C29—22no—
28C2×D4×C29D412yescomplemented
29C22×C4×C29—22no—
30C22×C4×C29C2311yescharacteristic
31C2×C22⋊D29—24no—
32C22×Dic29D411yescharacteristic
33C2×C4×D29—22no—
34C2×C4×D29—22no—
35C2×C4×D29—21no—
36C2×C4×D29—21no—
37Q16×C29—22no—
38SD16×C29—24no—
39D8×C29—22no—
40M16×C29—22no—
41C2×C8×C29D412yescomplemented
42C22⋊Dic29—24no—
43C22⋊Dic29—22no—
44#90781—24no—
45C4⋊Dic29—22no—
46#90779—24no—
47C4×Dic29D414yescomplemented
48#90777—22no—
49C2×#6597—21no—
50C23×C29—22no—
51C23×C29C2×D411yescharacteristic
52C22×D29—22no—
53C22×D29—21no—
54C22×D29—42no—
55Q8×C29—22no—
56Q8×C29—22no—
57D4×C29—22no—
58D4×C29—22no—
59D4×C29—42no—
60D4×C29—42no—
61C2×C4×C29—22no—
62C2×C4×C29—42no—
63C2×C4×C29—42no—
64C2×C4×C29C2×D412yes—
65C2×C4×C29C2×D412yes—
66C2×C4×C29C2×D411yescharacteristic
67C2×C4×C29#4111yescharacteristic
68C22⋊D29—48no—
69C2×Dic29—24no—
70C2×Dic29—22no—
71C2×Dic29—21no—
72C4×D29—41no—
73C4×D29—42no—
74C4×D29—41no—
75C8×C29—22no—
76#6597—41no—
77#2010—291nomaximal, Sylow
78C22×C29—41no—
79C22×C29—44no—
80C22×C29—42no—
81C22×C29#12012yes—
82C22×C29#12111yescharacteristic
83C2×D29—24no—
84C2×D29—22no—
85C2×D29—42no—
86C2×D29—41no—
87C2×D29—41no—
88C4×C29—42no—
89C4×C29#12011yescharacteristic
90C4×C29#12112yes—
91C4×C29#12711yescharacteristic
92Dic29—44no—
93Dic29—41no—
94#575D2911yescharacteristic, complemented
95#525—292no—
96#421—292no—
97#407—291no—
98H(3,ℤ/4)—291no—
99C2×C29—22no—
100C2×C29—21no—
101C2×C29—82no—
102C2×C29#39211yescharacteristic
103D29—42no—
104C2×#41C2×D2912yes—
105C23×C4—291no—
106#137—22no—
107AGL(1,ℤ/8)—22no—
108#135—22no—
109C2×M16—291no—
110C2×M16C2×D2911yescharacteristic
111#123—582no—
112C22⋊Q8—582no—
113#121—582no—
114#120—582no—
115C4×D4—584no—
116#117—292no—
117#104—584no—
118C22⋊C8—582no—
119C29#201011yescharacteristic, complemented, Sylow
120C24—291no—
121#41—22no—
122#41—22no—
123#41—22no—
124#41—22no—
125C2×Q8C22⋊D2912yescomplemented
126C2×D4—22no—
127C2×D4—584no—
128C2×D4C22⋊D2912yescomplemented
129C22×C4—22no—
130C22×C4—291no—
131C22×C4—582no—
132C22×C4—581no—
133C22×C4—581no—
134C22×C4—582no—
135C22×C4C22×D2911yescharacteristic
136Q16—22no—
137SD16—24no—
138D8—22no—
139M16—22no—
140M16—582no—
141C2×C8—581no—
142C2×C8C22⋊D2912yescomplemented
143C4⋊C4—584no—
144C4⋊C4—582no—
145C22⋊C4—584no—
146C22⋊C4—584no—
147C22⋊C4—582no—
148C42—294no—
149C23—22no—
150C23—582no—
151C23—581no—
152C23—1162no—
153C23D4×D2911yescharacteristic
154Q8—22no—
155Q8—22no—
156D4—22no—
157D4—22no—
158D4—42no—
159D4—42no—
160D4—1168no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—584no—
165C2×C4—582no—
166C2×C4—581no—
167C2×C4—1162no—
168C2×C4—1161no—
169C2×C4—1161no—
170C2×C4D4×D2912yes—
171C2×C4#9080711yescharacteristic
172C2×C4C2×C22⋊D2912yes—
173C2×C4C2×C22⋊D2911yescharacteristic
174C8—22no—
175C8—1161no—
176C22—41no—
177C22—44no—
178C22—42no—
179C22—584no—
180C22—582no—
181C22—1162no—
182C22—1161no—
183C22—1161no—
184C22#1174529912yes—
185C22#1174530011yescharacteristic
186C4—42no—
187C4—1164no—
188C4—1161no—
189C4#1174530112yes—
190C4#1174530211yescharacteristic
191C4#1174531511yescharacteristic
192C2—22no—
193C2—21no—
194C2—82no—
195C2—1162no—
196C2#1427107111yescharacteristic
subgroupG/H
centerC4#11745302
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#575C2
socleC2×C29#392
hypercenter#575D29
hypocenterC29#2010
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #14271670C2semidirect
2. #14271180C2semidirect
3. #14271126C2semidirect
4. #14270920C2semidirect
5. C29×#575C2semidirect
26. C2×Q8×C29D4semidirect
28. C2×D4×C29D4semidirect
41. C2×C8×C29D4semidirect
47. C4×Dic29D4semidirect
94. #575D29semidirect
119. C29#2010semidirect
125. C2×Q8C22⋊D29semidirect
128. C2×D4C22⋊D29semidirect
142. C2×C8C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
#142716702
#142711802
#142711262
#142709202
C29×#5752
#201029