Finite Group Databasebeta

← #16817820

Subgroups — #16817820

Order 3712.

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

normal subgroups only

This group has 312 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×C4⋊C4×D29C211yesmaximal, characteristic
2#14271125C212yesmaximal
3#14270889C211yesmaximal, characteristic, complemented
4#14270888C212yesmaximal, complemented
5C29×#324C211yesmaximal, characteristic, complemented
6C22×C4×D29C411yescharacteristic
7C22×C4×D29C411yescharacteristic
8C22×C4×D29C2211yescharacteristic
9C2×C4⋊C4×C29C2211yescharacteristic
10C2×C4⋊Dic29C411yescharacteristic
11C2×#90779C411yescharacteristic
12C2×#90779C2211yescharacteristic
13C2×#90772—22no—
14C4⋊C4×D29—22no—
15C4⋊C4×D29—22no—
16C29×C22⋊C8C2212yes—
17C22⋊#6597C2212yes—
18#11745168—22no—
19C23×D29C2×C411yescharacteristic
20C22×C4×C29C2×C411yescharacteristic
21C22×C4×C29C2×C411yescharacteristic
22C22×C4×C29C2311yescharacteristic
23C22×Dic29C2×C411yescharacteristic
24C22×Dic29C2×C411yescharacteristic
25C22×Dic29C2×C411yescharacteristic
26C2×C4×D29—21no—
27C2×C4×D29—21no—
28C2×C4×D29—22no—
29C2×C4×D29—22no—
30C2×C4×D29—21no—
31C2×C4×D29—21no—
32C2×C4×D29—42no—
33C2×C4×D29—42no—
34C2×C4×D29D412yes—
35C2×C4×D29D412yes—
36C2×C8×C29—22no—
37C4⋊C4×C29—22no—
38C4⋊Dic29—22no—
39#90779—22no—
40#90779—22no—
41C2×#6597—22no—
42#90772—44no—
43C23×C29C22×C411yescharacteristic
44C22×D29—21no—
45C22×D29—21no—
46C22×D29—22no—
47C22×D29—22no—
48C22×D29C22⋊C411yescharacteristic
49C22×D29C22⋊C411yescharacteristic
50C2×C4×C29—21no—
51C2×C4×C29—21no—
52C2×C4×C29—21no—
53C2×C4×C29—41no—
54C2×C4×C29—41no—
55C2×C4×C29M1612yescomplemented
56C2×C4×C29C2×D412yes—
57C2×Dic29—21no—
58C2×Dic29—21no—
59C2×Dic29—21no—
60C2×Dic29—41no—
61C2×Dic29—41no—
62C2×Dic29C22⋊C412yes—
63C2×Dic29M1612yescomplemented
64C4×D29—24no—
65C4×D29—24no—
66C4×D29—24no—
67C4×D29—42no—
68C4×D29—42no—
69C4×D29—42no—
70C8×C29—42no—
71#6597—42no—
72#1463—291nomaximal, Sylow
73C22×C29—21no—
74C22×C29—21no—
75C22×C29C2×C22⋊C411yescharacteristic
76C22×C29C2×M1611yescharacteristic
77C22×C29C2×M1611yescharacteristic
78C2×D29—24no—
79C2×D29—24no—
80C2×D29—21no—
81C2×D29—21no—
82C2×D29—21no—
83C2×D29—21no—
84C2×D29#9912yes—
85C2×D29#10112yes—
86C4×C29—22no—
87C4×C29—22no—
88C4×C29—41no—
89Dic29—22no—
90Dic29—22no—
91Dic29—41no—
92C22×C4⋊C4—291no—
93#407—292no—
94#324—291no—
95#324—292no—
96#324D2911yescharacteristic, complemented
97C2×C29—21no—
98C2×C29—21no—
99C2×C29#40711yescharacteristic
100C2×C29C2×#9911yescharacteristic
101C2×C29C2×#10111yescharacteristic
102D29—22no—
103D29—22no—
104C23×C4—291no—
105C23×C4—291no—
106C23×C4—291no—
107C2×M16—582no—
108C2×C4⋊C4—291no—
109C2×C4⋊C4—291no—
110C2×C4⋊C4—291no—
111C2×C4⋊C4—582no—
112C2×C4⋊C4—582no—
113C2×C4⋊C4C2×D2911yescharacteristic
114C22⋊C8—292no—
115C22⋊C8—582no—
116C22⋊C8C2×D2912yes—
117C29#146311yescharacteristic, complemented, Sylow
118C24—291no—
119C22×C4—291no—
120C22×C4—291no—
121C22×C4—292no—
122C22×C4—292no—
123C22×C4—291no—
124C22×C4—582no—
125C22×C4—581no—
126C22×C4—581no—
127C22×C4—581no—
128C22×C4—581no—
129C22×C4—582no—
130C22×C4—1162no—
131C22×C4—1162no—
132C22×C4C4×D2911yescharacteristic
133C22×C4C4×D2911yescharacteristic
134C22×C4C22×D2911yescharacteristic
135M16—1164no—
136C2×C8—22no—
137C2×C8—582no—
138C4⋊C4—22no—
139C4⋊C4—582no—
140C4⋊C4—582no—
141C4⋊C4—582no—
142C23—291no—
143C23—291no—
144C23—582no—
145C23—582no—
146C23—581no—
147C23—581no—
148C23C2×C4×D2911yescharacteristic
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—41no—
153C2×C4—41no—
154C2×C4—292no—
155C2×C4—292no—
156C2×C4—584no—
157C2×C4—584no—
158C2×C4—584no—
159C2×C4—581no—
160C2×C4—581no—
161C2×C4—581no—
162C2×C4—1162no—
163C2×C4—1162no—
164C2×C4—1162no—
165C2×C4—1161no—
166C2×C4—1161no—
167C2×C4#9077212yescomplemented
168C2×C4D4×D2912yes—
169C8—42no—
170C8—1162no—
171C22—21no—
172C22—21no—
173C22—292no—
174C22—292no—
175C22—584no—
176C22—584no—
177C22—581no—
178C22—581no—
179C22—581no—
180C22—581no—
181C22C22⋊C4×D2911yescharacteristic
182C22C2×#9077211yescharacteristic
183C22M16×D2911yescharacteristic
184C4—22no—
185C4—22no—
186C4—41no—
187C4—582no—
188C4—582no—
189C4—1161no—
190C2—21no—
191C2—21no—
192C2—582no—
193C2—582no—
194C2#1427112511yescharacteristic
195C2#99×D2911yescharacteristic
196C2#101×D2911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D29
commutatorC23×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#324C2
socleC22×C29C2×C22⋊C4
prime radicalC23×D29C2×C4
cosocleC22×C4×C29C23
hypercenter#324D29
hypocenterC29#1463
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
3. #14270889C2semidirect
4. #14270888C2semidirect
5. C29×#324C2semidirect
55. C2×C4×C29M16semidirect
63. C2×Dic29M16semidirect
96. #324D29semidirect
117. C29#1463semidirect
167. C2×C4#90772semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D292
#142711252
#142708892
#142708882
C29×#3242
#146329