Finite Group Databasebeta

← #16821134

Subgroups — #16821134

Order 3712.

264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 65 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
1#14271670C211yesmaximal, characteristic
2#14271137C211yesmaximal, characteristic, complemented
3#14270954C212yesmaximal, complemented
4#14270951C212yesmaximal, complemented
5C29×#413C211yesmaximal, characteristic, complemented
6C2×#41×C29C2211yescharacteristic
7C22×C4×D29C411yescharacteristic, complemented
8C2×M16×C29—21no—
9#11745308—21no—
10#11745300—21no—
11#11745299C411yescharacteristic, complemented
12#11745299C2211yescharacteristic
13#11745297C411yescharacteristic, complemented
14#11745297C2211yescharacteristic
15C4×C22⋊D29—21no—
16C4×C22⋊D29—21no—
17#11745288—21no—
18#11745288C411yescharacteristic, complemented
19C29×#101—21no—
20C29×#100C2212yes—
21#11745182—21no—
22#11745182C2212yes—
23C23×D29C2×C411yescharacteristic
24#41×C29—41no—
25#41×C29—41no—
26C2×Q8×C29D411yescharacteristic
27C2×D4×C29C2×C411yescharacteristic
28C2×D4×C29D411yescharacteristic
29C2×D4×C29C2311yescharacteristic
30C22×C4×C29C2×C411yescharacteristic
31C22×C4×C29D411yescharacteristic
32C22×C4×C29D411yescharacteristic
33C2×C22⋊D29—21no—
34C2×C22⋊D29—21no—
35C22×Dic29C2×C411yescharacteristic
36C2×C4×D29—21no—
37C2×C4×D29—21no—
38C2×C4×D29—41no—
39C2×C4×D29—41no—
40M16×C29—22no—
41M16×C29—41no—
42C2×C8×C29—41no—
43C22⋊Dic29—21no—
44C22⋊Dic29—21no—
45C22⋊Dic29—22no—
46C22⋊Dic29C2×C411yescharacteristic
47C22⋊Dic29C2×C411yescharacteristic
48#90781—21no—
49#90781—21no—
50C4⋊Dic29—21no—
51C4⋊Dic29—41no—
52#90779—21no—
53#90779—21no—
54C4×Dic29—21no—
55C4×Dic29—41no—
56C23×C29C22⋊C411yescharacteristic
57C23×C29C22×C411yescharacteristic
58C23×C29C2×D411yescharacteristic
59C22×D29—21no—
60C22×D29—42no—
61C22×D29—41no—
62Q8×C29—41no—
63D4×C29—41no—
64D4×C29—41no—
65D4×C29—41no—
66C2×C4×C29—21no—
67C2×C4×C29—21no—
68C2×C4×C29—21no—
69C2×C4×C29—21no—
70C2×C4×C29—21no—
71C2×C4×C29—21no—
72C2×C4×C29C22⋊C411yescharacteristic
73C2×C4×C29C22⋊C411yescharacteristic
74C2×C4×C29C22⋊C411yescharacteristic
75C2×C4×C29C2×D411yescharacteristic
76C22⋊D29—42no—
77C22⋊D29—42no—
78C2×Dic29—21no—
79C2×Dic29—21no—
80C2×Dic29—21no—
81C2×Dic29—41no—
82C2×Dic29—42no—
83C4×D29—42no—
84C4×D29—41no—
85C4×D29—41no—
86C8×C29—42no—
87#2120—291nomaximal, Sylow
88C22×C29—21no—
89C22×C29—21no—
90C22×C29—21no—
91C22×C29—41no—
92C22×C29—41no—
93C22×C29—41no—
94C22×C29C2×C22⋊C411yescharacteristic
95C2×D29—22no—
96C2×D29—41no—
97C2×D29—42no—
98C2×D29—41no—
99C2×D29—42no—
100C4×C29—21no—
101C4×C29—21no—
102C4×C29—21no—
103C4×C29#9911yescharacteristic
104C4×C29#9911yescharacteristic
105Dic29—41no—
106Dic29—41no—
107Dic29—41no—
108Dic29—82no—
109#525—291no—
110#413D2911yescharacteristic, complemented
111#410—291no—
112#352—292no—
113AΣL(1,𝔽16)—292no—
114C2×C29—21no—
115C2×C29—41no—
116C2×C29—41no—
117C2×C29—41no—
118C2×C29C2×#9911yescharacteristic
119D29—42no—
120C2×#41C2×D2911yescharacteristic
121C23×C4—291no—
122C2×M16—21no—
123#123—291no—
124#123—291no—
125C22⋊Q8—581no—
126#121—581no—
127#120—291no—
128#120—291no—
129C4×D4—581no—
130C4×D4—581no—
131#117—291no—
132#117—581no—
133#101—21no—
134#100C2×D2912yes—
135#99—292no—
136#99—581no—
137C29#212011yescharacteristic, complemented, Sylow
138C24—291no—
139#41—41no—
140#41—41no—
141C2×Q8C22⋊D2911yescharacteristic
142C2×D4—581no—
143C2×D4—581no—
144C2×D4C4×D2911yescharacteristic
145C2×D4D11611yescharacteristic
146C2×D4C22×D2911yescharacteristic
147C22×C4—291no—
148C22×C4—581no—
149C22×C4—581no—
150C22×C4—1161no—
151C22×C4—1161no—
152C22×C4C4×D2911yescharacteristic
153C22×C4D11611yescharacteristic
154C22×C4C22⋊D2911yescharacteristic
155M16—22no—
156M16—41no—
157C2×C8—41no—
158C4⋊C4—581no—
159C4⋊C4—581no—
160C4⋊C4—581no—
161C4⋊C4—1161no—
162C22⋊C4—291no—
163C22⋊C4—291no—
164C22⋊C4—581no—
165C22⋊C4—581no—
166C22⋊C4—581no—
167C22⋊C4—581no—
168C22⋊C4—582no—
169C42—581no—
170C42—1161no—
171C23—581no—
172C23—1161no—
173C23—1162no—
174C23#9078111yescharacteristic
175C23C2×C4×D2911yescharacteristic
176C23C2×D11611yescharacteristic
177Q8—41no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—1162no—
182D4—1162no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—581no—
190C2×C4—581no—
191C2×C4—581no—
192C2×C4—1162no—
193C2×C4—1161no—
194C2×C4—1161no—
195C2×C4—1161no—
196C2×C4—1162no—
197C2×C4#9078111yescharacteristic
198C2×C4#9078111yescharacteristic
199C2×C4#9078111yescharacteristic
200C2×C4C2×C22⋊D2911yescharacteristic
201C8—42no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—582no—
209C22—1161no—
210C22—1162no—
211C22—1162no—
212C22—1161no—
213C22C2×#9078111yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—1161no—
218C4—1161no—
219C4—1161no—
220C4—2322no—
221C4#1174515411yescharacteristic
222C4#1174515411yescharacteristic
223C2—21no—
224C2—41no—
225C2—41no—
226C2—41no—
227C2—1162no—
228C2C2×#1174515411yescharacteristic
subgroupG/H
centerC4#11745154
commutatorC23×C29C22×C4
FrattiniC2×D4C22×D29
FittingC29×#413C2
socleC2×C29C2×#99
prime radical#14271670C2
cosocleC2×D4×C29C23
hypercenter#413D29
hypocenterC29#2120
LCSG ▷ C23×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #14271137C2semidirect
3. #14270954C2semidirect
4. #14270951C2semidirect
5. C29×#413C2semidirect
7. C22×C4×D29C4semidirect
11. #11745299C4semidirect
13. #11745297C4semidirect
18. #11745288C4semidirect
110. #413D29semidirect
137. C29#2120semidirect

Maximal subgroups

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

subgroupindex
#142716702
#142711372
#142709542
#142709512
C29×#4132
#212029