Finite Group Databasebeta

← #16820032

Subgroups — #16820032

Order 3712.

380 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 85 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#14271722C211yesmaximal, characteristic
2#14271638C211yesmaximal, characteristic, complemented
3C2×#11745154C212yesmaximal, complemented
4#14270930C212yesmaximal, complemented
5C2×C29×#99C211yesmaximal, characteristic, complemented
6C22×D4×C29C2211yescharacteristic
7C22×C22⋊D29C2211yescharacteristic
8C2×C22⋊C4×C29C2212yes—
9#11745315—21no—
10C2×C22⋊Dic29—21no—
11C2×C22⋊Dic29C2211yescharacteristic
12C2×C22⋊Dic29C2212yes—
13#11745301—22no—
14#11745299C412yescomplemented
15#11745297C412yescomplemented
16D4×Dic29—24no—
17#11745291—21no—
18#11745288—21no—
19C29×#99—22no—
20#11745154—24no—
21C24×C29D411yescharacteristic
22C24×C29C2311yescharacteristic
23C23×D29C2×C411yescharacteristic, complemented
24C2×D4×C29—22no—
25C2×D4×C29—22no—
26C2×D4×C29C2×C412yes—
27C2×D4×C29D412yes—
28C22×C4×C29—22no—
29C22×C4×C29D411yescharacteristic
30C2×C22⋊D29—21no—
31C2×C22⋊D29—21no—
32C2×C22⋊D29—22no—
33C2×C22⋊D29—22no—
34C2×C22⋊D29—22no—
35C22×Dic29—22no—
36C22×Dic29—22no—
37C22×Dic29—21no—
38C22×Dic29C2×C411yescharacteristic, complemented
39C22⋊C4×C29—22no—
40C22⋊C4×C29—22no—
41C22⋊Dic29—22no—
42C22⋊Dic29—22no—
43C22⋊Dic29—22no—
44C22⋊Dic29—21no—
45C22⋊Dic29C2×C412yescomplemented
46C22⋊Dic29D414yescomplemented
47#90781—22no—
48C4⋊Dic29—22no—
49#90779—22no—
50C4×Dic29—22no—
51C23×C29—21no—
52C23×C29—21no—
53C23×C29—81no—
54C23×C29—81no—
55C23×C29C22⋊C412yes—
56C23×C29C22×C411yescharacteristic
57C23×C29C2×D411yescharacteristic
58C23×C29C2×D412yes—
59C23×C29C2×D411yescharacteristic
60C23×C29#4112yes—
61C22×D29—21no—
62C22×D29—22no—
63C22×D29—81no—
64D4×C29—24no—
65D4×C29—24no—
66C2×C4×C29—21no—
67C2×C4×C29—21no—
68C2×C4×C29—42no—
69C2×C4×C29—82no—
70C2×C4×C29C22⋊C412yes—
71C22⋊D29—41no—
72C22⋊D29—42no—
73C22⋊D29—41no—
74C22⋊D29—82no—
75C2×Dic29—21no—
76C2×Dic29—22no—
77C2×Dic29—22no—
78C2×Dic29—24no—
79C2×Dic29—82no—
80C2×Dic29—82no—
81C2×Dic29—81no—
82#1913—291nomaximal, Sylow
83C22×C29—22no—
84C22×C29—42no—
85C22×C29—41no—
86C22×C29—42no—
87C22×C29—41no—
88C22×C29—41no—
89C22×C29—42no—
90C22×C29—42no—
91C22×C29—81no—
92C22×C29C2×C22⋊C411yescharacteristic
93C22×C29C4×D412yes—
94C22×C29#12011yescharacteristic
95C22×C29#12112yes—
96C22×C29#12311yescharacteristic
97C2×D29—42no—
98C2×D29—41no—
99C2×D29—82no—
100C4×C29—22no—
101C4×C29—82no—
102Dic29—44no—
103Dic29—42no—
104Dic29—41no—
105#534—291no—
106#518—291no—
107C2×#99—292no—
108C2×#99D2911yescharacteristic, complemented
109#342—292no—
110C2×C29—21no—
111C2×C29—21no—
112C2×C29—22no—
113C2×C29—22no—
114C2×C29—21no—
115C2×C29—42no—
116C2×C29#38611yescharacteristic
117D29—81no—
118C22×D4—291no—
119C22×D4C2×D2911yescharacteristic
120#123—292no—
121#123—581no—
122#121—582no—
123#120—292no—
124#120—581no—
125C4×D4—584no—
126#117—581no—
127C2×C22⋊C4—292no—
128C2×C22⋊C4—291no—
129C2×C22⋊C4—581no—
130C2×C22⋊C4C2×D2912yes—
131#99—22no—
132#99—584no—
133C29#191311yescharacteristic, complemented, Sylow
134C24—291no—
135C24D11611yescharacteristic
136C24C22×D2911yescharacteristic
137C2×D4—22no—
138C2×D4—22no—
139C2×D4—581no—
140C2×D4—582no—
141C2×D4—582no—
142C2×D4—581no—
143C2×D4—582no—
144C2×D4C4×D2912yes—
145C2×D4C22⋊D2912yes—
146C22×C4—22no—
147C22×C4—291no—
148C22×C4—582no—
149C22×C4—582no—
150C22×C4—581no—
151C22×C4D11611yescharacteristic
152C4⋊C4—582no—
153C4⋊C4—582no—
154C22⋊C4—22no—
155C22⋊C4—22no—
156C22⋊C4—292no—
157C22⋊C4—294no—
158C22⋊C4—582no—
159C22⋊C4—582no—
160C22⋊C4—582no—
161C22⋊C4—581no—
162C22⋊C4—582no—
163C42—582no—
164C23—21no—
165C23—21no—
166C23—81no—
167C23—81no—
168C23—581no—
169C23—582no—
170C23—2321no—
171C23#9078112yes—
172C23C2×C4×D2911yescharacteristic
173C23C2×D11611yescharacteristic
174C23D4×D2912yes—
175C23#9080712yes—
176C23C2×C22⋊D2911yescharacteristic
177D4—24no—
178D4—24no—
179D4—1162no—
180D4—1161no—
181D4—1161no—
182D4—2322no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—42no—
186C2×C4—82no—
187C2×C4—582no—
188C2×C4—581no—
189C2×C4—582no—
190C2×C4—584no—
191C2×C4—2322no—
192C2×C4—2322no—
193C2×C4—2321no—
194C2×C4#9078112yes—
195C22—22no—
196C22—42no—
197C22—42no—
198C22—41no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22—42no—
203C22—81no—
204C22—1162no—
205C22—1161no—
206C22—2322no—
207C22#1174524312yes—
208C22#1174524411yescharacteristic
209C22#1174524811yescharacteristic
210C22C2×#9078111yescharacteristic
211C22#1174530112yes—
212C4—22no—
213C4—82no—
214C4—1164no—
215C4—1162no—
216C4—1161no—
217C2—22no—
218C2—21no—
219C2—21no—
220C2—21no—
221C2—22no—
222C2—42no—
223C2—2321no—
224C2#1427104011yescharacteristic
subgroupG/H
centerC2#14271040
commutatorC23×C29C22×C4
FrattiniC24C22×D29
FittingC2×C29×#99C2
socleC2×C29#386
prime radical#14271722C2
cosocleC24×C29C23
hypercenterC2×#99D29
hypocenterC29#1913
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. #14271638C2semidirect
3. C2×#11745154C2semidirect
4. #14270930C2semidirect
5. C2×C29×#99C2semidirect
14. #11745299C4semidirect
15. #11745297C4semidirect
23. C23×D29C2×C4semidirect
38. C22×Dic29C2×C4semidirect
45. C22⋊Dic29C2×C4semidirect
46. C22⋊Dic29D4semidirect
108. C2×#99D29semidirect
133. C29#1913semidirect

Maximal subgroups

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

subgroupindex
#142717222
#142716382
C2×#117451542
#142709302
C2×C29×#992
#191329