Finite Group Databasebeta

← #16820717

Subgroups — #16820717

Order 3712.

306 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 67 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×#11745173C212yesmaximal, complemented
3#14271165C212yesmaximal, complemented
4#14271032C211yesmaximal, characteristic, complemented
5C29×#343C211yesmaximal, characteristic, complemented
6C2×#90805C2212yes—
7C2×M16×C29C2212yes—
8C2×C4⋊C4×C29C2211yescharacteristic
9#11745292—22no—
10C2×C4⋊Dic29C2211yescharacteristic
11C2×#90779—22no—
12C2×C4×Dic29C2211yescharacteristic
13#11745259—22no—
14#11745257—22no—
15#11745173—24no—
16#11745169—22no—
17#11745164—22no—
18C22×C4×C29D412yes—
19C22×C4×C29C2311yescharacteristic
20C2×C22⋊D29—22no—
21C22×Dic29—21no—
22C22×Dic29—21no—
23#90805—22no—
24#90805—22no—
25#90805—22no—
26#90805—22no—
27C2×D116—22no—
28C2×D116D412yes—
29C2×C4×D29—22no—
30C2×Dic58D412yes—
31M16×C29—22no—
32M16×C29—22no—
33C2×C8×C29—22no—
34C4⋊C4×C29—22no—
35#90781—24no—
36C4⋊Dic29—22no—
37C4⋊Dic29—22no—
38#90779—44no—
39C4×Dic29—21no—
40C4×Dic29D412yescomplemented
41C23×C29C2×D411yescharacteristic
42C22×D29—22no—
43C2×C4×C29—22no—
44C2×C4×C29—42no—
45C2×C4×C29C2×D411yescharacteristic
46C2×C4×C29C2×D412yes—
47C2×C4×C29#4112yes—
48C2×C4×C29#4111yescharacteristic
49C22⋊D29—42no—
50C22⋊D29—42no—
51C2×Dic29—22no—
52C2×Dic29—22no—
53C2×Dic29—22no—
54C2×Dic29—22no—
55C2×Dic29—42no—
56C2×Dic29—41no—
57D116—22no—
58D116—22no—
59D116—82no—
60C4×D29—42no—
61C4×D29—42no—
62Dic58—22no—
63Dic58—22no—
64C8×C29—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—42no—
75C4×C29#12112yes—
76C4×C29#12312yes—
77Dic29—24no—
78Dic29—42no—
79Dic29—81no—
80#537—291no—
81C2×#104—292no—
82#417—292no—
83#384—291no—
84#343D2911yescharacteristic, complemented
85C2×C29—21no—
86C2×C29—21no—
87C2×C29#39411yescharacteristic
88C2×C29#45311yescharacteristic
89C2×C29#45611yescharacteristic
90D29—82no—
91C2×#41—292no—
92C2×M16C2×D2912yes—
93C22⋊Q8—582no—
94#121—582no—
95#121—582no—
96C2×C4⋊C4—291no—
97C2×C4⋊C4—582no—
98C2×C4⋊C4C2×D2911yescharacteristic
99C2×C42—291no—
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—581no—
113C22×C4—582no—
114C22×C4—581no—
115C22×C4D11612yes—
116C22×C4C22×D2911yescharacteristic
117M16—22no—
118M16—22no—
119C2×C8—22no—
120C4⋊C4—22no—
121C4⋊C4—582no—
122C4⋊C4—582no—
123C4⋊C4—1164no—
124C22⋊C4—584no—
125C42—292no—
126C42—581no—
127C23—582no—
128C23C2×D11611yescharacteristic
129Q8—582no—
130Q8—582no—
131D4—582no—
132D4—582no—
133D4—1162no—
134D4—1162no—
135D4—2322no—
136C2×C4—22no—
137C2×C4—42no—
138C2×C4—582no—
139C2×C4—582no—
140C2×C4—582no—
141C2×C4—582no—
142C2×C4—1162no—
143C2×C4—1162no—
144C2×C4—1162no—
145C2×C4—1161no—
146C2×C4#9080512yes—
147C2×C4D4×D2911yescharacteristic
148C2×C4D4×D2912yes—
149C2×C4#9080911yescharacteristic
150C8—42no—
151C22—21no—
152C22—21no—
153C22—1162no—
154C22—1162no—
155C22—1162no—
156C22#1174523711yescharacteristic
157C22#1174524411yescharacteristic
158C22#1174525711yescharacteristic
159C4—42no—
160C4—584no—
161C4—1162no—
162C4—2321no—
163C4#1174524612yes—
164C4#1174525612yes—
165C2—21no—
166C2—21no—
167C2—2322no—
168C2#1427108111yescharacteristic
169C2#1427133311yescharacteristic
170C2#1427134811yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#343C2
socleC22×C29#120
prime radical#14271744C2
hypercenter#343D29
hypocenterC29#2039
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. C2×#11745173C2semidirect
3. #14271165C2semidirect
4. #14271032C2semidirect
5. C29×#343C2semidirect
40. C4×Dic29D4semidirect
84. #343D29semidirect
103. C29#2039semidirect

Maximal subgroups

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

subgroupindex
#142717442
C2×#117451732
#142711652
#142710322
C29×#3432
#203929