Finite Group Databasebeta

← #16820716

Subgroups — #16820716

Order 3712.

306 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 69 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#14271744C211yesmaximal, characteristic
2C2×#11745153C212yesmaximal, complemented
3#14271162C212yesmaximal, complemented
4#14270932C211yesmaximal, characteristic, complemented
5C29×#384C211yesmaximal, characteristic, complemented
6C2×#90805C2212yes—
7C2×C4⋊C4×C29—22no—
8C2×C4⋊C4×C29C2211yescharacteristic
9C2×C4⋊C4×C29C2211yescharacteristic
10C2×C42×C29C2211yescharacteristic
11#11745292—22no—
12C2×#90777C2212yes—
13#11745259—22no—
14#11745257—22no—
15#11745158—22no—
16#11745157—22no—
17#11745153—24no—
18C22×C4×C29—21no—
19C22×C4×C29—21no—
20C22×C4×C29D412yes—
21C22×C4×C29C2311yescharacteristic
22C2×C22⋊D29—22no—
23#90805—22no—
24#90805—22no—
25#90805—22no—
26#90805—22no—
27C2×D116—22no—
28C2×D116D412yes—
29C2×C4×D29—22no—
30C2×Dic58D412yes—
31C4⋊C4×C29—22no—
32C4⋊C4×C29—22no—
33C4⋊C4×C29—44no—
34C42×C29—21no—
35C42×C29D412yescomplemented
36#90781—24no—
37C4⋊Dic29—22no—
38#90777—22no—
39#90777—22no—
40C2×#6597—22no—
41C23×C29C2×D411yescharacteristic
42C22×D29—22no—
43C2×C4×C29—22no—
44C2×C4×C29—22no—
45C2×C4×C29—22no—
46C2×C4×C29—22no—
47C2×C4×C29—42no—
48C2×C4×C29—42no—
49C2×C4×C29—41no—
50C2×C4×C29C2×D411yescharacteristic
51C2×C4×C29C2×D412yes—
52C2×C4×C29#4111yescharacteristic
53C2×C4×C29#4112yes—
54C22⋊D29—42no—
55C22⋊D29—42no—
56C2×Dic29—22no—
57D116—22no—
58D116—22no—
59D116—82no—
60C4×D29—42no—
61C4×D29—42no—
62Dic58—22no—
63Dic58—22no—
64#6597—42no—
65#2039—291nomaximal, Sylow
66C22×C29—21no—
67C22×C29—21no—
68C22×C29#12011yescharacteristic
69C22×C29#12111yescharacteristic
70C22×C29#12411yescharacteristic
71C2×D29—42no—
72C2×D29—42no—
73C2×D29—42no—
74C4×C29—24no—
75C4×C29—42no—
76C4×C29—81no—
77C4×C29#12112yes—
78C4×C29#12312yes—
79Dic29—42no—
80#537—291no—
81C2×#104—292no—
82#417—292no—
83#384D2911yescharacteristic, complemented
84#343—291no—
85C2×C29—21no—
86C2×C29—21no—
87C2×C29#39411yescharacteristic
88C2×C29#45311yescharacteristic
89C2×C29#45611yescharacteristic
90D29—82no—
91C2×#41—292no—
92C2×M16—292no—
93C22⋊Q8—582no—
94#121—582no—
95#121—582no—
96C2×C4⋊C4—22no—
97C2×C4⋊C4C2×D2911yescharacteristic
98C2×C4⋊C4C2×D2911yescharacteristic
99C2×C42C2×D2911yescharacteristic
100#104—584no—
101#103—582no—
102#102—582no—
103C29#203911yescharacteristic, complemented, Sylow
104#41—582no—
105#41—582no—
106#41—582no—
107#41—582no—
108C2×Q8—292no—
109C2×D4—292no—
110C2×D4—582no—
111C2×D4—582no—
112C22×C4—21no—
113C22×C4—21no—
114C22×C4—582no—
115C22×C4C22⋊D2912yes—
116C22×C4C22×D2911yescharacteristic
117M16—582no—
118M16—582no—
119C2×C8—582no—
120C4⋊C4—22no—
121C4⋊C4—22no—
122C4⋊C4—44no—
123C4⋊C4—582no—
124C22⋊C4—584no—
125C42—21no—
126C42D11612yescomplemented
127C23—582no—
128C23C2×C22⋊D2911yescharacteristic
129Q8—582no—
130Q8—582no—
131D4—582no—
132D4—582no—
133D4—1162no—
134D4—1162no—
135D4—2322no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—582no—
144C2×C4—1162no—
145C2×C4—1162no—
146C2×C4C2×D11611yescharacteristic
147C2×C4#9080511yescharacteristic
148C2×C4D4×D2912yes—
149C2×C4#9080912yes—
150C8—1162no—
151C22—21no—
152C22—21no—
153C22—1162no—
154C22—1162no—
155C22—1162no—
156C22#1174529211yescharacteristic
157C22#1174529911yescharacteristic
158C22#1174530911yescharacteristic
159C4—24no—
160C4—42no—
161C4—81no—
162C4—1162no—
163C4#1174525612yes—
164C4#1174525712yes—
165C2—21no—
166C2—21no—
167C2—2322no—
168C2#1427108011yescharacteristic
169C2#1427133011yescharacteristic
170C2#1427134511yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#384C2
socleC22×C29#120
prime radical#14271744C2
hypercenter#384D29
hypocenterC29#2039
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. C2×#11745153C2semidirect
3. #14271162C2semidirect
4. #14270932C2semidirect
5. C29×#384C2semidirect
35. C42×C29D4semidirect
83. #384D29semidirect
103. C29#2039semidirect
126. C42D116semidirect

Maximal subgroups

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

subgroupindex
#142717442
C2×#117451532
#142711622
#142709322
C29×#3842
#203929