Finite Group Databasebeta

← #16820713

Subgroups — #16820713

Order 3712.

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

normal subgroups only

This group has 306 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
1C2×#11745185C212yesmaximal, complemented
2#14271164C212yesmaximal, complemented
3#14271032C211yesmaximal, characteristic, complemented
4#14270932C211yesmaximal, characteristic, complemented
5C29×#537C211yesmaximal, characteristic
6C2×#41×C29C2212yes—
7C29×C22⋊Q8—22no—
8C29×#121—22no—
9C29×#121—22no—
10C2×C4⋊C4×C29C2211yescharacteristic
11C2×C4⋊Dic29C2211yescharacteristic
12C2×#90779—22no—
13C2×C4×Dic29C2211yescharacteristic
14C2×#90777C2212yes—
15#11745185—24no—
16#11745183—22no—
17#11745180—22no—
18#41×C29—22no—
19#41×C29—22no—
20#41×C29—22no—
21#41×C29—22no—
22C2×Q8×C29D412yes—
23C2×D4×C29—22no—
24C2×D4×C29—22no—
25C2×D4×C29D412yes—
26C22×C4×C29—22no—
27C22×C4×C29D412yes—
28C22×C4×C29C2311yescharacteristic
29C22×Dic29—21no—
30C22×Dic29—21no—
31C4⋊C4×C29—22no—
32C4⋊C4×C29—22no—
33C22⋊C4×C29—24no—
34C4⋊Dic29—22no—
35#90779—44no—
36C4×Dic29—21no—
37C4×Dic29D412yescomplemented
38#90777—22no—
39#90777—22no—
40C2×#6597—22no—
41C23×C29—22no—
42C23×C29C2×D411yescharacteristic
43Q8×C29—22no—
44Q8×C29—22no—
45D4×C29—22no—
46D4×C29—22no—
47D4×C29—42no—
48D4×C29—42no—
49D4×C29—82no—
50C2×C4×C29—22no—
51C2×C4×C29—22no—
52C2×C4×C29—42no—
53C2×C4×C29—42no—
54C2×C4×C29—42no—
55C2×C4×C29C2×D411yescharacteristic
56C2×C4×C29C2×D412yes—
57C2×C4×C29#4112yes—
58C2×C4×C29#4111yescharacteristic
59C2×Dic29—22no—
60C2×Dic29—22no—
61C2×Dic29—22no—
62C2×Dic29—42no—
63C2×Dic29—41no—
64#6597—42no—
65#2039—291nomaximal, Sylow
66C22×C29—21no—
67C22×C29—21no—
68C22×C29—42no—
69C22×C29—42no—
70C22×C29—42no—
71C22×C29#12011yescharacteristic
72C22×C29#12111yescharacteristic
73C22×C29#12411yescharacteristic
74C4×C29—42no—
75C4×C29—42no—
76C4×C29#12112yes—
77C4×C29#12312yes—
78Dic29—24no—
79Dic29—81no—
80#537D2911yescharacteristic
81C2×#104—292no—
82#417—292no—
83#384—291no—
84#343—291no—
85C2×C29—21no—
86C2×C29—21no—
87C2×C29—82no—
88C2×C29#39411yescharacteristic
89C2×C29#45311yescharacteristic
90C2×C29#45611yescharacteristic
91C2×#41C2×D2912yes—
92C2×M16—292no—
93C22⋊Q8—22no—
94#121—22no—
95#121—22no—
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—22no—
105#41—22no—
106#41—22no—
107#41—22no—
108C2×Q8C22⋊D2912yes—
109C2×D4—22no—
110C2×D4—22no—
111C2×D4C22⋊D2912yes—
112C22×C4—22no—
113C22×C4—581no—
114C22×C4—581no—
115C22×C4C22⋊D2912yes—
116C22×C4C22×D2911yescharacteristic
117M16—582no—
118M16—582no—
119C2×C8—582no—
120C4⋊C4—22no—
121C4⋊C4—22no—
122C4⋊C4—582no—
123C4⋊C4—1164no—
124C22⋊C4—24no—
125C42—292no—
126C42—581no—
127C23—22no—
128C23C2×C22⋊D2911yescharacteristic
129Q8—22no—
130Q8—22no—
131D4—22no—
132D4—22no—
133D4—42no—
134D4—42no—
135D4—82no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—582no—
142C2×C4—582no—
143C2×C4—582no—
144C2×C4—1162no—
145C2×C4—1161no—
146C2×C4D4×D2911yescharacteristic
147C2×C4#9080711yescharacteristic
148C2×C4#9080712yes—
149C2×C4C2×C22⋊D2912yes—
150C8—1162no—
151C22—21no—
152C22—21no—
153C22—42no—
154C22—42no—
155C22—42no—
156C22#1174529811yescharacteristic
157C22#1174530011yescharacteristic
158C22#1174531511yescharacteristic
159C4—42no—
160C4—42no—
161C4—584no—
162C4—2321no—
163C4#1174529712yes—
164C4#1174530112yes—
165C2—21no—
166C2—21no—
167C2—82no—
168C2#1427107711yescharacteristic
169C2#1427133111yescharacteristic
170C2#1427134611yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
Fitting, prime radicalC29×#537C2
socleC22×C29#120
hypercenter#537D29
hypocenterC29#2039
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#11745185C2semidirect
2. #14271164C2semidirect
3. #14271032C2semidirect
4. #14270932C2semidirect
37. C4×Dic29D4semidirect
103. C29#2039semidirect

Maximal subgroups

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

subgroupindex
C2×#117451852
#142711642
#142710322
#142709322
C29×#5372
#203929