Finite Group Databasebeta

← #16817817

Subgroups — #16817817

Order 3712.

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

normal subgroups only

This group has 440 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×C22⋊C4×D29C211yesmaximal, characteristic
2#14271125C212yesmaximal, complemented
3#14270887C211yesmaximal, characteristic, complemented
4#14270886C212yesmaximal, complemented
5C29×#323C211yesmaximal, characteristic, complemented
6C24×D29C411yescharacteristic
7C22×C4×D29C411yescharacteristic
8C22×C4×D29C2211yescharacteristic
9C2×C22⋊C4×C29C2211yescharacteristic
10C2×C22⋊Dic29C411yescharacteristic
11C2×#90781C411yescharacteristic
12C2×#90781C2211yescharacteristic
13C2×#90772—22no—
14C22⋊C4×D29—22no—
15C22⋊C4×D29—22no—
16C29×C22⋊C8C2212yescomplemented
17C22⋊#6597C2212yescomplemented
18#11745168—22no—
19C24×C29C2×C411yescharacteristic
20C23×D29—22no—
21C23×D29—21no—
22C23×D29—21no—
23C23×D29—22no—
24C23×D29—42no—
25C23×D29—42no—
26C23×D29C2×C411yescharacteristic
27C23×D29C2×C411yescharacteristic
28C22×C4×C29C2×C411yescharacteristic
29C22×C4×C29C2311yescharacteristic
30C22×Dic29C2×C411yescharacteristic
31C22×Dic29C2×C411yescharacteristic
32C2×C4×D29—21no—
33C2×C4×D29—21no—
34C2×C4×D29—42no—
35C2×C4×D29—42no—
36C2×C4×D29D412yes—
37C2×C4×D29D412yes—
38C2×C8×C29—22no—
39C22⋊C4×C29—22no—
40C22⋊Dic29—22no—
41#90781—22no—
42#90781—22no—
43C2×#6597—22no—
44#90772—44no—
45C23×C29—21no—
46C23×C29—21no—
47C23×C29—41no—
48C23×C29—41no—
49C23×C29M1612yescomplemented
50C23×C29C22×C411yescharacteristic
51C22×D29—21no—
52C22×D29—21no—
53C22×D29—22no—
54C22×D29—22no—
55C22×D29—24no—
56C22×D29—24no—
57C22×D29—21no—
58C22×D29—21no—
59C22×D29—48no—
60C22×D29—48no—
61C22×D29—42no—
62C22×D29—42no—
63C22×D29—42no—
64C22×D29—42no—
65C22×D29—41no—
66C22×D29—41no—
67C22×D29C22⋊C411yescharacteristic
68C22×D29C22⋊C411yescharacteristic
69C22×D29M1612yescomplemented
70C2×C4×C29—21no—
71C2×C4×C29—41no—
72C2×C4×C29—41no—
73C2×C4×C29C2×D412yes—
74C2×Dic29—21no—
75C2×Dic29—41no—
76C2×Dic29—41no—
77C2×Dic29C22⋊C412yes—
78C4×D29—24no—
79C4×D29—42no—
80C4×D29—42no—
81C4×D29—42no—
82C8×C29—42no—
83#6597—42no—
84#1462—291nomaximal, Sylow
85C22×C29—21no—
86C22×C29—21no—
87C22×C29—22no—
88C22×C29—42no—
89C22×C29—42no—
90C22×C29—41no—
91C22×C29—41no—
92C22×C29C2×C22⋊C411yescharacteristic
93C22×C29C2×M1611yescharacteristic
94C22×C29C2×M1611yescharacteristic
95C2×D29—24no—
96C2×D29—24no—
97C2×D29—21no—
98C2×D29—21no—
99C2×D29—21no—
100C2×D29—21no—
101C2×D29—22no—
102C2×D29—48no—
103C2×D29—48no—
104C2×D29—42no—
105C2×D29—41no—
106C2×D29—41no—
107C2×D29—42no—
108C2×D29#9912yes—
109C2×D29#10012yes—
110C4×C29—22no—
111C4×C29—41no—
112Dic29—22no—
113Dic29—41no—
114C22×C22⋊C4—291no—
115#407—292no—
116#323—291no—
117#323—292no—
118#323D2911yescharacteristic, complemented
119C2×C29—21no—
120C2×C29—21no—
121C2×C29—42no—
122C2×C29#40711yescharacteristic
123C2×C29C2×#9911yescharacteristic
124C2×C29C2×#10011yescharacteristic
125D29—22no—
126D29—22no—
127D29—42no—
128C25—291no—
129C23×C4—291no—
130C23×C4—291no—
131C2×M16—582no—
132C2×C22⋊C4—291no—
133C2×C22⋊C4—291no—
134C2×C22⋊C4—291no—
135C2×C22⋊C4—582no—
136C2×C22⋊C4—582no—
137C2×C22⋊C4C2×D2911yescharacteristic
138C22⋊C8—292no—
139C22⋊C8—582no—
140C22⋊C8C2×D2912yescomplemented
141C29#146211yescharacteristic, complemented, Sylow
142C24—291no—
143C24—291no—
144C24—581no—
145C24—581no—
146C24—582no—
147C24—582no—
148C24—1162no—
149C24—1162no—
150C24C4×D2911yescharacteristic
151C22×C4—291no—
152C22×C4—292no—
153C22×C4—292no—
154C22×C4—291no—
155C22×C4—581no—
156C22×C4—581no—
157C22×C4—1162no—
158C22×C4—1162no—
159C22×C4C4×D2911yescharacteristic
160C22×C4C22×D2911yescharacteristic
161M16—1164no—
162C2×C8—22no—
163C2×C8—582no—
164C22⋊C4—22no—
165C22⋊C4—582no—
166C22⋊C4—582no—
167C22⋊C4—582no—
168C23—21no—
169C23—21no—
170C23—41no—
171C23—41no—
172C23—291no—
173C23—291no—
174C23—292no—
175C23—582no—
176C23—582no—
177C23—584no—
178C23—584no—
179C23—581no—
180C23—581no—
181C23—581no—
182C23—581no—
183C23—1161no—
184C23—1161no—
185C23—1162no—
186C23—1162no—
187C23—1168no—
188C23—1168no—
189C23—1162no—
190C23—1162no—
191C23#9077212yescomplemented
192C23C2×C4×D2911yescharacteristic
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—292no—
197C2×C4—584no—
198C2×C4—581no—
199C2×C4—1162no—
200C2×C4—1162no—
201C2×C4—1162no—
202C2×C4—1161no—
203C2×C4—1161no—
204C2×C4D4×D2912yes—
205C8—42no—
206C8—1162no—
207C22—21no—
208C22—21no—
209C22—22no—
210C22—42no—
211C22—42no—
212C22—41no—
213C22—41no—
214C22—292no—
215C22—292no—
216C22—584no—
217C22—584no—
218C22—581no—
219C22—581no—
220C22—581no—
221C22—581no—
222C22—582no—
223C22—1162no—
224C22—1162no—
225C22—1168no—
226C22—1168no—
227C22—1161no—
228C22—1161no—
229C22C22⋊C4×D2911yescharacteristic
230C22C2×#9077211yescharacteristic
231C22M16×D2911yescharacteristic
232C4—22no—
233C4—41no—
234C4—582no—
235C4—1161no—
236C2—21no—
237C2—21no—
238C2—42no—
239C2—582no—
240C2—582no—
241C2—1162no—
242C2#1427112511yescharacteristic
243C2#99×D2911yescharacteristic
244C2#100×D2911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D29
commutatorC23×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#323C2
socleC22×C29C2×C22⋊C4
prime radicalC24×D29C4
cosocleC22×C4×C29C23
hypercenter#323D29
hypocenterC29#1462
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #14271125C2semidirect
3. #14270887C2semidirect
4. #14270886C2semidirect
5. C29×#323C2semidirect
16. C29×C22⋊C8C22semidirect
17. C22⋊#6597C22semidirect
49. C23×C29M16semidirect
69. C22×D29M16semidirect
118. #323D29semidirect
140. C22⋊C8C2×D29semidirect
141. C29#1462semidirect
191. C23#90772semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D292
#142711252
#142708872
#142708862
C29×#3232
#146229