Finite Group Databasebeta

← #16817811

Subgroups — #16817811

Order 3712.

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

normal subgroups only

This group has 312 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×#11745243C211yesmaximal, characteristic
2#14271213C212yesmaximal, complemented
3#14270887C211yesmaximal, characteristic, complemented
4#14270886C212yesmaximal, complemented
5C29×#323C211yesmaximal, characteristic, complemented
6C22×C22⋊D29C411yescharacteristic
7C23×Dic29C411yescharacteristic
8C22×C4×D29C411yescharacteristic
9C2×C22⋊C4×C29C2211yescharacteristic
10C2×#90781C2211yescharacteristic
11C2×#90779C411yescharacteristic
12C2×C4×Dic29C2211yescharacteristic
13#11745243—22no—
14#11745243—22no—
15C29×C22⋊C8C2212yes—
16C22⋊#6597C2212yes—
17#11745162—22no—
18C8×Dic29—22no—
19C24×C29C2×C411yescharacteristic
20C23×D29C2×C411yescharacteristic
21C22×C4×C29C2×C411yescharacteristic
22C22×C4×C29C2311yescharacteristic
23C2×C22⋊D29—22no—
24C2×C22⋊D29—22no—
25C2×C22⋊D29C814yescomplemented
26C22×Dic29—21no—
27C22×Dic29—21no—
28C22×Dic29—42no—
29C22×Dic29C2×C411yescharacteristic
30C22×Dic29C2×C411yescharacteristic
31C22×Dic29C2×C411yescharacteristic
32C2×C4×D29—21no—
33C2×C4×D29—21no—
34C2×C4×D29—42no—
35C2×C8×C29—22no—
36C22⋊C4×C29—22no—
37#90781—22no—
38#90779—22no—
39C4×Dic29D412yes—
40C4×Dic29D412yes—
41C2×#6597—22no—
42C23×C29—21no—
43C23×C29—21no—
44C23×C29—41no—
45C23×C29—41no—
46C23×C29C2×C812yes—
47C23×C29C22×C411yescharacteristic
48C22×D29—21no—
49C22×D29—21no—
50C22×D29—41no—
51C22×D29—41no—
52C22×D29C2×C812yes—
53C2×C4×C29—21no—
54C2×C4×C29—41no—
55C2×C4×C29—41no—
56C2×C4×C29C2×D412yes—
57C22⋊D29—28no—
58C2×Dic29—22no—
59C2×Dic29—21no—
60C2×Dic29—42no—
61C2×Dic29—42no—
62C2×Dic29—41no—
63C2×Dic29C22⋊C411yescharacteristic
64C2×Dic29C22⋊C412yes—
65C2×Dic29C22⋊C411yescharacteristic
66C2×Dic29C2×C812yes—
67C2×Dic29M1612yes—
68C4×D29—42no—
69C4×D29—42no—
70C8×C29—42no—
71#6597—42no—
72#1460—291nomaximal, Sylow
73C22×C29—21no—
74C22×C29—21no—
75C22×C29—22no—
76C22×C29—42no—
77C22×C29—42no—
78C22×C29—41no—
79C22×C29—41no—
80C22×C29C2×C22⋊C411yescharacteristic
81C22×C29C22×C811yescharacteristic
82C22×C29C2×M1611yescharacteristic
83C2×D29—22no—
84C2×D29—42no—
85C2×D29—41no—
86C2×D29—41no—
87C2×D29—42no—
88C4×C29—22no—
89C4×C29—41no—
90Dic29—21no—
91Dic29—41no—
92Dic29C22⋊C814yes—
93Dic29#10012yes—
94C2×C4×D4—291no—
95#431—292no—
96#323—291no—
97#323—292no—
98#323D2911yescharacteristic, complemented
99C2×C29—21no—
100C2×C29—21no—
101C2×C29—42no—
102C2×C29C2×C22⋊C811yescharacteristic
103C2×C29#41011yescharacteristic
104C2×C29C2×#10011yescharacteristic
105D29—42no—
106C22×D4—291no—
107C23×C4—291no—
108C23×C4—291no—
109C4×D4—582no—
110C4×D4—582no—
111C2×C4⋊C4—291no—
112C2×C22⋊C4—291no—
113C2×C22⋊C4C2×D2911yescharacteristic
114C2×C42—291no—
115C4⋊C8—582no—
116C22⋊C8—292no—
117C22⋊C8C2×D2912yes—
118C4×C8—582no—
119C29#146011yescharacteristic, complemented, Sylow
120C24—291no—
121C24C4×D2911yescharacteristic
122C2×D4—294no—
123C2×D4—582no—
124C2×D4—582no—
125C22×C4—291no—
126C22×C4—291no—
127C22×C4—291no—
128C22×C4—581no—
129C22×C4—581no—
130C22×C4—581no—
131C22×C4—581no—
132C22×C4—1162no—
133C22×C4—1162no—
134C22×C4C4×D2911yescharacteristic
135C22×C4C22×D2911yescharacteristic
136C2×C8—22no—
137C2×C8—582no—
138C4⋊C4—582no—
139C22⋊C4—22no—
140C22⋊C4—582no—
141C42—292no—
142C42—292no—
143C23—21no—
144C23—21no—
145C23—41no—
146C23—41no—
147C23—292no—
148C23—581no—
149C23—581no—
150C23—1161no—
151C23—1161no—
152C23C8×D2912yes—
153C23C2×C4×D2911yescharacteristic
154D4—588no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—292no—
159C2×C4—291no—
160C2×C4—292no—
161C2×C4—292no—
162C2×C4—291no—
163C2×C4—582no—
164C2×C4—581no—
165C2×C4—1162no—
166C2×C4—1162no—
167C2×C4—1162no—
168C2×C4—1162no—
169C2×C4—1161no—
170C2×C4D4×D2912yes—
171C8—42no—
172C8—1162no—
173C22—21no—
174C22—21no—
175C22—22no—
176C22—42no—
177C22—42no—
178C22—41no—
179C22—41no—
180C22—582no—
181C22—1162no—
182C22—1162no—
183C22—1161no—
184C22—1161no—
185C22C22⋊C4×D2911yescharacteristic
186C22C2×C8×D2911yescharacteristic
187C22M16×D2911yescharacteristic
188C4—22no—
189C4—41no—
190C4—294no—
191C4—292no—
192C4—581no—
193C4—1161no—
194C2—21no—
195C2—21no—
196C2—42no—
197C2—1162no—
198C2C22⋊C8×D2911yescharacteristic
199C2#1427113511yescharacteristic
200C2#100×D2911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D29
commutatorC22×C29C22×C8
FrattiniC22×C4C22×D29
FittingC29×#323C2
socleC22×C29C2×C22⋊C4
prime radicalC22×C22⋊D29C4
cosocleC22×C4×C29C23
hypercenter#323D29
hypocenterC29#1460
LCSG ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #14271213C2semidirect
3. #14270887C2semidirect
4. #14270886C2semidirect
5. C29×#323C2semidirect
25. C2×C22⋊D29C8semidirect
98. #323D29semidirect
119. C29#1460semidirect

Maximal subgroups

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

subgroupindex
C2×#117452432
#142712132
#142708872
#142708862
C29×#3232
#146029