Finite Group Databasebeta

← #16835669

Subgroups — #16835669

Order 3712.

260 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 72 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
1C4×#90796C211yesmaximal, characteristic
2C4×C4⋊#1181C211yesmaximal, characteristic
3#14272033C212yesmaximal
4#14272033C212yesmaximal
5#14271719C211yesmaximal, characteristic
6C2×C4⋊#1181—21no—
7C2×C4×#1181C2212yes—
8C2×#90796C2212yes—
9C29×#125C411yescharacteristic, complemented
10#11745258—21no—
11#11745258—21no—
12#11745254C2211yescharacteristic
13#11745254C2211yescharacteristic
14#11745250C411yescharacteristic, complemented
15#11745250C411yescharacteristic, complemented
16#11745249—21no—
17#11745249—21no—
18C42×D29C2211yescharacteristic
19#11745232C411yescharacteristic, complemented
20(C2×#1181)⋊C4—21no—
21#11745218—21no—
22C4×#6599—21no—
23C22×#1181—22no—
24C2×C4×D29D411yescharacteristic
25C2×C4×D29D411yescharacteristic
26C2×C4×D29C2311yescharacteristic
27C2×Dic58—21no—
28C2×Dic58—21no—
29C2×#6599—22no—
30C4⋊#1181—24no—
31C4×#1181—24no—
32#90796—22no—
33#90796Q814yescomplemented
34C4⋊C4×C29—21no—
35C4⋊C4×C29—21no—
36C4⋊C4×C29C2×C411yescharacteristic
37C4⋊C4×C29C2×C411yescharacteristic
38C42×C29C2×C411yescharacteristic
39#90781—21no—
40#90781—21no—
41C4⋊Dic29C2×C411yescharacteristic
42C4⋊Dic29C2×C411yescharacteristic
43#90779—21no—
44#90779—21no—
45#90779—21no—
46#90779—21no—
47C4×Dic29—21no—
48C4×Dic29—21no—
49C4×Dic29C2×C411yescharacteristic
50C4×Dic29D411yescharacteristic
51C4×Dic29D411yescharacteristic
52C22×D29C2×D411yescharacteristic
53C2×#1181—24no—
54C2×#1181—42no—
55C2×#1181—42no—
56C2×C4×C29—21no—
57C2×C4×C29—21no—
58C2×C4×C29C22⋊C411yescharacteristic
59C2×C4×C29C22⋊C411yescharacteristic
60C2×C4×C29C22×C411yescharacteristic
61C2×Dic29—21no—
62C2×Dic29—21no—
63C2×Dic29C22⋊C411yescharacteristic
64C2×Dic29C22⋊C411yescharacteristic
65C2×Dic29C2×D411yescharacteristic
66C4×D29—22no—
67C4×D29—41no—
68C4×D29C2×Q812yes—
69C4×D29#4112yes—
70Dic58—42no—
71Dic58—42no—
72#6599—24no—
73#1986—291nomaximal, Sylow
74C22×C29C2×C22⋊C411yescharacteristic
75C2×D29—21no—
76C2×D29—21no—
77C2×D29#12411yescharacteristic
78C2×D29C4⋊Q811yescharacteristic
79#1181—44no—
80C4×C29—21no—
81C4×C29—21no—
82C4×C29—41no—
83C4×C29—41no—
84C4×C29C4×Q812yes—
85Dic29—21no—
86Dic29—41no—
87Dic29—41no—
88Dic29#10412yes—
89Dic29C22⋊Q812yes—
90#533—291no—
91C4×M16—291no—
92C4×C4⋊C4—291no—
93#339—292no—
94#339—292no—
95C2×C29#39111yescharacteristic
96C2×C29C2×#10411yescharacteristic
97C2×C29#42111yescharacteristic
98D29—21no—
99D29—21no—
100C2×M16—292no—
101C4⋊Q8—291no—
102C4⋊Q8—291no—
103#125—291no—
104#125#118111yescharacteristic, complemented
105C22⋊Q8—581no—
106C22⋊Q8—581no—
107C4×Q8—581no—
108C4×Q8—581no—
109#117—291no—
110#117—291no—
111C2×C4⋊C4—581no—
112C2×C42—291no—
113C2×C42—292no—
114#97—581no—
115C4×C8—581no—
116#95—581no—
117C29#198611yescharacteristic, complemented, Sylow
118C2×Q8—581no—
119C2×Q8—581no—
120C22×C4—291no—
121C22×C4—291no—
122C22×C4—291no—
123C22×C4—582no—
124M16—294no—
125M16—582no—
126C2×C8—582no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—291no—
130C4⋊C4—291no—
131C4⋊C4—581no—
132C4⋊C4—581no—
133C4⋊C4—584no—
134C4⋊C4—581no—
135C4⋊C4—581no—
136C4⋊C4C2×#118111yescharacteristic
137C4⋊C4C2×#118111yescharacteristic
138C22⋊C4—581no—
139C22⋊C4—581no—
140C42—291no—
141C42—291no—
142C42—291no—
143C42—581no—
144C42—581no—
145C42—584no—
146C42C2×#118111yescharacteristic
147C23—291no—
148Q8—1162no—
149Q8—1162no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—291no—
153C2×C4—291no—
154C2×C4—292no—
155C2×C4—292no—
156C2×C4—291no—
157C2×C4—582no—
158C2×C4—584no—
159C2×C4—581no—
160C2×C4—581no—
161C2×C4—1161no—
162C2×C4—1162no—
163C2×C4—1162no—
164C2×C4C22⋊#118111yescharacteristic
165C2×C4C22⋊#118111yescharacteristic
166C2×C4C22×#118111yescharacteristic
167C8—584no—
168C22—291no—
169C22—291no—
170C22—581no—
171C22—581no—
172C22C2×C22⋊#118111yescharacteristic
173C4—21no—
174C4—21no—
175C4—41no—
176C4—41no—
177C4—292no—
178C4—292no—
179C4—581no—
180C4—1164no—
181C4—1161no—
182C4—1161no—
183C4Q8×#118112yes—
184C2—581no—
185C2—581no—
186C2(C2×#1181)⋊Q811yescharacteristic
187C2D29⋊#10411yescharacteristic
188C2#1427216011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC2×C4×C29C22×C4
FrattiniC2×C4C22×#1181
FittingC29×#125C4
socleC22×C29C2×C22⋊C4
prime radicalC22×D29C2×D4
cosocleC2×C4×D29C23
hypercenter#125#1181
hypocenterC29#1986
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #125

Complements

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

NH ≅ G/Ntype
9. C29×#125C4semidirect
14. #11745250C4semidirect
15. #11745250C4semidirect
19. #11745232C4semidirect
33. #90796Q8semidirect
104. #125#1181semidirect
117. C29#1986semidirect

Maximal subgroups

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

subgroupindex
C4×#907962
C4×C4⋊#11812
#142720332
#142717192
#198629