Finite Group Databasebeta

← #16818114

Subgroups — #16818114

Order 3712.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D29C211yesmaximal, characteristic
2#14271218C212yesmaximal, complemented
3#14270903C211yesmaximal, characteristic, complemented
4#14270902C212yesmaximal, complemented
5C29×#329C211yesmaximal, characteristic, complemented
6C2×Q8×D29C411yescharacteristic
7C2×D4×D29C411yescharacteristic
8C29×#124C2211yescharacteristic
9#11745309C411yescharacteristic
10#11745298C411yescharacteristic
11#11745247—22no—
12C22⋊C4×D29—22no—
13#11745237C2211yescharacteristic
14C42×D29C2211yescharacteristic
15C29×#97C2212yescomplemented
16#11745168—22no—
17#11745162—22no—
18#11745151C2212yescomplemented
19C23×D29—21no—
20C2×Q8×C29C2×C411yescharacteristic
21C2×D4×C29C2×C411yescharacteristic
22C2×C22⋊D29—21no—
23Q8×D29—42no—
24D4×D29—42no—
25C2×D116C2×C411yescharacteristic
26C2×C4×D29—21no—
27C2×C4×D29C2×C411yescharacteristic
28C2×C4×D29D412yes—
29C2×Dic58—21no—
30C2×Dic58C2×C411yescharacteristic
31C2×C8×C29—22no—
32C22⋊C4×C29—22no—
33C42×C29C2311yescharacteristic
34C22⋊Dic29—22no—
35#90781—22no—
36#90781—22no—
37C4×Dic29C2×C411yescharacteristic
38C4×Dic29D412yes—
39C2×#6597—22no—
40C23×C29—21no—
41C22×D29—21no—
42C22×D29—44no—
43C22×D29—42no—
44C22×D29C22⋊C411yescharacteristic
45Q8×C29—41no—
46D4×C29—41no—
47C2×C4×C29—21no—
48C2×C4×C29C22×C411yescharacteristic
49C2×C4×C29C2×D412yes—
50C22⋊D29—42no—
51C2×Dic29—21no—
52C2×Dic29C22⋊C412yes—
53C2×Dic29C22⋊C411yescharacteristic
54D116—41no—
55C4×D29—22no—
56C4×D29—42no—
57C4×D29—42no—
58Dic58—42no—
59Dic58—41no—
60C8×C29—42no—
61#6597—42no—
62#1533—291nomaximal, Sylow
63C22×C29—41no—
64C22×C29—42no—
65C22×C29C2×C22⋊C411yescharacteristic
66C2×D29—22no—
67C2×D29—41no—
68C2×D29—42no—
69C2×D29—84no—
70C2×D29#10012yes—
71C4×C29—21no—
72C4×C29—22no—
73C4×C29—41no—
74Dic29—21no—
75Dic29—22no—
76Dic29—41no—
77C2×#124—291no—
78#432—292no—
79#329—291no—
80#329—292no—
81#329D2911yescharacteristic, complemented
82C2×C29—81no—
83C2×C29C2×#10011yescharacteristic
84C2×C29#42112yes—
85D29—22no—
86D29—81no—
87C22×Q8—291no—
88C22×D4—291no—
89#124—291no—
90#124—291no—
91#124—291no—
92#124—582no—
93#124C2×D2911yescharacteristic
94C2×C22⋊C4—582no—
95C2×C42—291no—
96C4⋊C8—582no—
97C22⋊C8—582no—
98#97—292no—
99#97C2×D2912yescomplemented
100C29#153311yescharacteristic, complemented, Sylow
101C24—581no—
102C2×Q8—291no—
103C2×Q8—581no—
104C2×Q8—1162no—
105C2×Q8C4×D2911yescharacteristic
106C2×D4—291no—
107C2×D4—581no—
108C2×D4—1162no—
109C2×D4C4×D2911yescharacteristic
110C22×C4—291no—
111C22×C4—292no—
112C22×C4—581no—
113C2×C8—22no—
114C2×C8—582no—
115C22⋊C4—22no—
116C22⋊C4—582no—
117C22⋊C4—582no—
118C22⋊C4—582no—
119C42—291no—
120C42—292no—
121C42C22×D2911yescharacteristic
122C23—21no—
123C23—291no—
124C23—581no—
125C23—1162no—
126C23—1164no—
127Q8—41no—
128Q8—1161no—
129Q8—1162no—
130D4—41no—
131D4—1161no—
132D4—1162no—
133C2×C4—21no—
134C2×C4—292no—
135C2×C4—291no—
136C2×C4—582no—
137C2×C4—581no—
138C2×C4—1162no—
139C2×C4—1162no—
140C2×C4C2×C4×D2911yescharacteristic
141C2×C4D4×D2912yes—
142C8—42no—
143C8—1162no—
144C22—41no—
145C22—42no—
146C22—292no—
147C22—582no—
148C22—1161no—
149C22—1162no—
150C22—2324no—
151C22C22⋊C4×D2911yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—581no—
156C4—582no—
157C4—1161no—
158C2—81no—
159C2—582no—
160C2—2321no—
161C2#100×D2911yescharacteristic
162C2#1427117812yes—
subgroupG/H
centerC22C22⋊C4×D29
commutatorC2×C4×C29C22×C4
FrattiniC42C22×D29
FittingC29×#329C2
socleC22×C29C2×C22⋊C4
prime radicalC2×D4×D29C4
cosocleC42×C29C23
hypercenter#329D29
hypocenterC29#1533
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #14271218C2semidirect
3. #14270903C2semidirect
4. #14270902C2semidirect
5. C29×#329C2semidirect
15. C29×#97C22semidirect
18. #11745151C22semidirect
81. #329D29semidirect
99. #97C2×D29semidirect
100. C29#1533semidirect

Maximal subgroups

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

subgroupindex
#124×D292
#142712182
#142709032
#142709022
C29×#3292
#153329