Finite Group Databasebeta

← #16820022

Subgroups — #16820022

Order 3712.

362 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 85 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#14271730C211yesmaximal, characteristic
2#14271638C211yesmaximal, characteristic, complemented
3#14271179C212yesmaximal, complemented
4#14270920C212yesmaximal, complemented
5C2×C29×#100C211yesmaximal, characteristic, complemented
6C22×D4×C29C2211yescharacteristic
7C2×#90805C2211yescharacteristic
8C2×M16×C29C2212yes—
9#11745315—22no—
10C2×C22⋊Dic29—22no—
11#11745302C412yescomplemented
12#11745300—22no—
13#11745298C412yescomplemented
14D4×Dic29—24no—
15#11745288C2211yescharacteristic
16#11745288C2212yes—
17C29×#100—22no—
18#11745173—24no—
19C24×C29D412yes—
20C2×D4×C29—22no—
21C2×D4×C29—22no—
22C2×D4×C29C2×C412yes—
23C2×D4×C29D412yes—
24C22×C4×C29C2311yescharacteristic
25C2×C22⋊D29—21no—
26C2×C22⋊D29—24no—
27C22×Dic29—24no—
28#90805—22no—
29#90805—22no—
30C2×D116C2×C411yescharacteristic, complemented
31C2×C4×D29—21no—
32C2×Dic58C2×C411yescharacteristic, complemented
33M16×C29—22no—
34M16×C29—22no—
35C2×C8×C29—22no—
36C22⋊Dic29—24no—
37C22⋊Dic29—24no—
38C22⋊Dic29—22no—
39C22⋊Dic29—21no—
40C4⋊Dic29—22no—
41C4⋊Dic29—21no—
42C4×Dic29C2×C412yescomplemented
43C4×Dic29D414yescomplemented
44C23×C29—22no—
45C23×C29—22no—
46C23×C29—82no—
47C23×C29C22⋊C414yes—
48C23×C29C2×D411yescharacteristic
49C22×D29—21no—
50D4×C29—24no—
51D4×C29—24no—
52C2×C4×C29C22×C411yescharacteristic
53C2×C4×C29C2×D412yes—
54C2×C4×C29C2×D411yescharacteristic
55C2×C4×C29#4112yes—
56C22⋊D29—41no—
57C22⋊D29—41no—
58C22⋊D29—84no—
59C2×Dic29—22no—
60C2×Dic29—21no—
61C2×Dic29—24no—
62C2×Dic29—84no—
63D116—22no—
64C4×D29—42no—
65Dic58—22no—
66C8×C29—42no—
67#1911—291nomaximal, Sylow
68C22×C29—24no—
69C22×C29—41no—
70C22×C29—44no—
71C22×C29—44no—
72C22×C29—82no—
73C22×C29C2×C22⋊C411yescharacteristic
74C22×C29#12011yescharacteristic
75C22×C29#12311yescharacteristic
76C2×D29—42no—
77C2×D29—41no—
78C4×C29C4×D412yes—
79C4×C29#12112yes—
80Dic29—44no—
81Dic29—42no—
82Dic29—41no—
83#535—291no—
84#518—291no—
85#421—292no—
86C2×#100D2911yescharacteristic, complemented
87H(3,ℤ/4)—292no—
88C2×C29—21no—
89C2×C29—21no—
90C2×C29—21no—
91C2×C29—44no—
92C2×C29#38611yescharacteristic
93D29—81no—
94C2×#41—291no—
95C22×D4C2×D2911yescharacteristic
96C2×M16C2×D2912yes—
97#127—292no—
98#124—292no—
99#121—582no—
100#120—582no—
101C4×D4—584no—
102#117—292no—
103#117—291no—
104C2×C22⋊C4—582no—
105#104—584no—
106#100—22no—
107C29#191111yescharacteristic, complemented, Sylow
108C24D11612yes—
109#41—582no—
110#41—582no—
111C2×Q8—291no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—291no—
115C2×D4—581no—
116C2×D4—584no—
117C2×D4C4×D2912yes—
118C2×D4C22⋊D2912yes—
119C22×C4—584no—
120C22×C4—581no—
121C22×C4C22×D2911yescharacteristic
122M16—22no—
123M16—22no—
124C2×C8—22no—
125C4⋊C4—582no—
126C4⋊C4—581no—
127C22⋊C4—584no—
128C22⋊C4—584no—
129C22⋊C4—582no—
130C22⋊C4—581no—
131C42—292no—
132C42—294no—
133C23—22no—
134C23—22no—
135C23—82no—
136C23—581no—
137C23#9078114yes—
138C23C2×D11611yescharacteristic
139Q8—582no—
140D4—24no—
141D4—24no—
142D4—582no—
143D4—1161no—
144D4—1161no—
145D4—2324no—
146C2×C4—582no—
147C2×C4—581no—
148C2×C4—584no—
149C2×C4—1162no—
150C2×C4—2324no—
151C2×C4C2×C4×D2911yescharacteristic
152C2×C4D4×D2912yes—
153C2×C4#9080712yes—
154C2×C4C2×C22⋊D2911yescharacteristic
155C8—42no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—82no—
161C22—1162no—
162C22—1161no—
163C22#1174524411yescharacteristic
164C22#1174524811yescharacteristic
165C22C2×#9078111yescharacteristic
166C4—1164no—
167C4—1162no—
168C4—1161no—
169C4#1174524312yes—
170C4#1174530112yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—2321no—
176C2#1427104011yescharacteristic
subgroupG/H
centerC2#14271040
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC2×C29×#100C2
socleC2×C29#386
prime radical#14271730C2
cosocleC22×C4×C29C23
hypercenterC2×#100D29
hypocenterC29#1911
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#100

Complements

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

NH ≅ G/Ntype
2. #14271638C2semidirect
3. #14271179C2semidirect
4. #14270920C2semidirect
5. C2×C29×#100C2semidirect
11. #11745302C4semidirect
13. #11745298C4semidirect
30. C2×D116C2×C4semidirect
32. C2×Dic58C2×C4semidirect
42. C4×Dic29C2×C4semidirect
43. C4×Dic29D4semidirect
86. C2×#100D29semidirect
107. C29#1911semidirect

Maximal subgroups

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

subgroupindex
#142717302
#142716382
#142711792
#142709202
C2×C29×#1002
#191129