Finite Group Databasebeta

← #16817809

Subgroups — #16817809

Order 3712.

332 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 81 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×#11745255C211yesmaximal, characteristic
2C22⋊C8×D29C212yesmaximal, complemented
3#14270889C211yesmaximal, characteristic, complemented
4#14270886C212yesmaximal, complemented
5C29×#324C211yesmaximal, characteristic, complemented
6C22×D116C411yescharacteristic
7C22×C4×D29C411yescharacteristic
8C22×C4×D29C2211yescharacteristic
9C2×C4⋊C4×C29C2211yescharacteristic
10C2×#90781C411yescharacteristic
11C2×#90781C2211yescharacteristic
12C2×C4×Dic29C411yescharacteristic
13C2×C8×D29—22no—
14#11745255—22no—
15#11745255—22no—
16C29×C22⋊C8C2212yes—
17C22⋊#6597C2212yes—
18#11745168—22no—
19C23×D29C2×C411yescharacteristic
20C23×D29C2×C411yescharacteristic
21C22×C4×C29C2×C411yescharacteristic
22C22×C4×C29C2×C411yescharacteristic
23C22×C4×C29C2311yescharacteristic
24C22×Dic29C2×C411yescharacteristic
25C22×Dic29C2×C411yescharacteristic
26C2×D116—22no—
27C2×D116—22no—
28C2×D116C814yescomplemented
29C2×C4×D29—21no—
30C2×C4×D29—21no—
31C2×C4×D29—42no—
32C2×C4×D29—42no—
33C2×C4×D29D412yes—
34C2×C4×D29D412yes—
35C2×C8×C29—22no—
36C4⋊C4×C29—22no—
37#90781—22no—
38#90781—22no—
39C4×Dic29—21no—
40C4×Dic29—21no—
41C2×#6597—22no—
42C8×D29—44no—
43C23×C29C22×C411yescharacteristic
44C22×D29—21no—
45C22×D29—21no—
46C22×D29—41no—
47C22×D29—41no—
48C22×D29—41no—
49C22×D29—41no—
50C22×D29C22⋊C412yes—
51C22×D29C2×C812yes—
52C22×D29C2×C812yescomplemented
53C22×D29M1612yes—
54C2×C4×C29—21no—
55C2×C4×C29—21no—
56C2×C4×C29—21no—
57C2×C4×C29—41no—
58C2×C4×C29—41no—
59C2×C4×C29C2×C812yescomplemented
60C2×C4×C29C2×D412yes—
61C2×Dic29—22no—
62C2×Dic29—21no—
63C2×Dic29—41no—
64C2×Dic29C22⋊C411yescharacteristic
65C2×Dic29C22⋊C411yescharacteristic
66D116—28no—
67C4×D29—24no—
68C4×D29—42no—
69C4×D29—42no—
70C4×D29—42no—
71C8×C29—42no—
72#6597—42no—
73#1459—291nomaximal, Sylow
74C22×C29—21no—
75C22×C29—21no—
76C22×C29C2×C22⋊C411yescharacteristic
77C22×C29C22×C811yescharacteristic
78C22×C29C2×M1611yescharacteristic
79C2×D29—22no—
80C2×D29—22no—
81C2×D29—22no—
82C2×D29—42no—
83C2×D29—42no—
84C2×D29—42no—
85C2×D29—41no—
86C2×D29—41no—
87C2×D29—42no—
88C2×D29C22⋊C814yes—
89C4×C29—22no—
90C4×C29—22no—
91C4×C29—41no—
92Dic29—21no—
93Dic29—41no—
94Dic29#9912yes—
95C2×C4×D4—291no—
96C2×C22⋊C8—292no—
97#324—291no—
98#324D2911yescharacteristic, complemented
99#323—292no—
100C2×C29—21no—
101C2×C29—21no—
102C2×C29C2×C22⋊C811yescharacteristic
103C2×C29C2×#9911yescharacteristic
104C2×C29#41311yescharacteristic
105D29—24no—
106D29—42no—
107C22×D4—291no—
108C23×C4—291no—
109C23×C4—291no—
110C22×C8—582no—
111C4×D4—582no—
112C4×D4—582no—
113C2×C4⋊C4C2×D2911yescharacteristic
114C2×C22⋊C4—291no—
115C2×C22⋊C4—291no—
116C2×C42—291no—
117C22⋊C8—292no—
118C22⋊C8—582no—
119C22⋊C8C2×D2912yes—
120C29#145911yescharacteristic, complemented, Sylow
121C24—291no—
122C24—291no—
123C2×D4—294no—
124C2×D4—582no—
125C2×D4—582no—
126C22×C4—291no—
127C22×C4—292no—
128C22×C4—292no—
129C22×C4—291no—
130C22×C4—581no—
131C22×C4—581no—
132C22×C4—1162no—
133C22×C4—1162no—
134C22×C4C4×D2911yescharacteristic
135C22×C4C4×D2911yescharacteristic
136C22×C4C22×D2911yescharacteristic
137C2×C8—22no—
138C2×C8—582no—
139C2×C8—1164no—
140C4⋊C4—22no—
141C22⋊C4—582no—
142C22⋊C4—582no—
143C42—581no—
144C42—581no—
145C23—292no—
146C23—292no—
147C23—292no—
148C23—292no—
149C23—581no—
150C23—581no—
151C23—1161no—
152C23—1161no—
153C23—1161no—
154C23—1161no—
155C23C2×C4×D2911yescharacteristic
156D4—588no—
157C2×C4—21no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—291no—
163C2×C4—291no—
164C2×C4—584no—
165C2×C4—582no—
166C2×C4—581no—
167C2×C4—1162no—
168C2×C4—1162no—
169C2×C4—1162no—
170C2×C4—1161no—
171C2×C4C8×D2912yescomplemented
172C2×C4D4×D2912yes—
173C8—42no—
174C8—1162no—
175C22—21no—
176C22—21no—
177C22—294no—
178C22—582no—
179C22—582no—
180C22—582no—
181C22—1162no—
182C22—1162no—
183C22—1162no—
184C22—1162no—
185C22—1161no—
186C22—1161no—
187C22C22⋊C4×D2911yescharacteristic
188C22C2×C8×D2911yescharacteristic
189C22M16×D2911yescharacteristic
190C4—22no—
191C4—22no—
192C4—41no—
193C4—292no—
194C4—581no—
195C4—1161no—
196C2—21no—
197C2—21no—
198C2—584no—
199C2—1162no—
200C2C22⋊C8×D2911yescharacteristic
201C2#99×D2911yescharacteristic
202C2#1427114611yescharacteristic
subgroupG/H
centerC22C22⋊C4×D29
commutatorC22×C29C22×C8
FrattiniC22×C4C22×D29
FittingC29×#324C2
socleC22×C29C2×C22⋊C4
prime radicalC22×D116C4
cosocleC22×C4×C29C23
hypercenter#324D29
hypocenterC29#1459
LCSG ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. C22⋊C8×D29C2semidirect
3. #14270889C2semidirect
4. #14270886C2semidirect
5. C29×#324C2semidirect
28. C2×D116C8semidirect
52. C22×D29C2×C8semidirect
59. C2×C4×C29C2×C8semidirect
98. #324D29semidirect
120. C29#1459semidirect
171. C2×C4C8×D29semidirect

Maximal subgroups

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

subgroupindex
C2×#117452552
C22⋊C8×D292
#142708892
#142708862
C29×#3242
#145929