Finite Group Databasebeta

← #16819906

Subgroups — #16819906

Order 3712.

386 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 97 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#14271638C211yesmaximal, characteristic
2C2×#11745182C211yesmaximal, characteristic
3#14271026C212yesmaximal, complemented
4#14270929C212yesmaximal, complemented
5C2×C29×#123C211yesmaximal, characteristic
6C22×D4×C29C2211yescharacteristic
7C23×C4×C29C2211yescharacteristic
8C29×#123—22no—
9C29×#123C414yescomplemented
10C2×C4⋊C4×C29—21no—
11C2×C22⋊C4×C29—21no—
12C2×C22⋊C4×C29C2211yescharacteristic
13C2×C22⋊Dic29—21no—
14C2×C22⋊Dic29C2212yes—
15C2×C22⋊Dic29C2212yes—
16D4×Dic29—24no—
17#11745288—21no—
18#11745182—22no—
19#11745179—24no—
20C24×C29D411yescharacteristic
21C24×C29C2311yescharacteristic
22C2×D4×C29—22no—
23C2×D4×C29—22no—
24C2×D4×C29C2×C412yes—
25C2×D4×C29D412yes—
26C22×C4×C29—21no—
27C22×C4×C29—21no—
28C22×C4×C29—21no—
29C22×C4×C29—22no—
30C22×C4×C29—22no—
31C22×C4×C29C2×C412yescomplemented
32C22×C4×C29D411yescharacteristic
33C22×Dic29—22no—
34C22×Dic29—22no—
35C22×Dic29D414yes—
36C4⋊C4×C29—24no—
37C22⋊C4×C29—24no—
38C22⋊C4×C29—21no—
39C22⋊C4×C29C2×C412yescomplemented
40C22⋊Dic29—22no—
41C22⋊Dic29—22no—
42C22⋊Dic29—22no—
43C22⋊Dic29—22no—
44C22⋊Dic29—22no—
45C4⋊Dic29—22no—
46C4×Dic29—22no—
47C23×C29—21no—
48C23×C29—21no—
49C23×C29—42no—
50C23×C29—42no—
51C23×C29C22⋊C412yes—
52C23×C29C22×C411yescharacteristic
53C23×C29C2×D412yes—
54C23×C29C2×D411yescharacteristic
55C23×C29C2×D411yescharacteristic
56C23×C29#4112yes—
57D4×C29—24no—
58D4×C29—24no—
59C2×C4×C29—21no—
60C2×C4×C29—21no—
61C2×C4×C29—22no—
62C2×C4×C29—22no—
63C2×C4×C29—24no—
64C2×C4×C29—42no—
65C2×C4×C29—41no—
66C2×C4×C29—42no—
67C2×C4×C29—41no—
68C2×C4×C29C22⋊C412yes—
69C2×Dic29—24no—
70C2×Dic29—44no—
71C2×Dic29—44no—
72C2×Dic29—42no—
73C2×Dic29—82no—
74#1890—291nomaximal, Sylow
75C22×C29—24no—
76C22×C29—22no—
77C22×C29—22no—
78C22×C29—41no—
79C22×C29—41no—
80C22×C29—42no—
81C22×C29—42no—
82C22×C29—42no—
83C22×C29—81no—
84C22×C29C2×C22⋊C411yescharacteristic
85C22×C29C4×D412yes—
86C22×C29#12011yescharacteristic
87C22×C29#12112yes—
88C22×C29#12311yescharacteristic
89C4×C29—22no—
90C4×C29—42no—
91C4×C29—42no—
92Dic29—44no—
93Dic29—82no—
94C2×#123D2911yescharacteristic
95#518—291no—
96C2×#99—291no—
97#381—292no—
98#342—292no—
99C2×C29—22no—
100C2×C29—21no—
101C2×C29—21no—
102C2×C29—22no—
103C2×C29—42no—
104C2×C29#38611yescharacteristic
105C2×C29#45812yes—
106C22×D4C2×D2911yescharacteristic
107C23×C4C2×D2911yescharacteristic
108#123—22no—
109#123Dic2914yescomplemented
110C4×D4—584no—
111#117—581no—
112C2×C4⋊C4—21no—
113C2×C22⋊C4—21no—
114C2×C22⋊C4—292no—
115C2×C22⋊C4—292no—
116C2×C22⋊C4—581no—
117C2×C22⋊C4C2×D2911yescharacteristic
118#99—582no—
119#95—584no—
120C29#189011yescharacteristic, complemented, Sylow
121C24C22⋊D2911yescharacteristic
122C24C22×D2911yescharacteristic
123C2×D4—22no—
124C2×D4—22no—
125C2×D4C2×Dic2912yes—
126C2×D4C22⋊D2912yes—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—21no—
132C22×C4—294no—
133C22×C4—582no—
134C22×C4—582no—
135C22×C4C2×Dic2912yescomplemented
136C22×C4C22⋊D2911yescharacteristic
137C4⋊C4—24no—
138C4⋊C4—582no—
139C22⋊C4—24no—
140C22⋊C4—21no—
141C22⋊C4—582no—
142C22⋊C4—582no—
143C22⋊C4—582no—
144C22⋊C4—582no—
145C22⋊C4—582no—
146C22⋊C4C2×Dic2912yescomplemented
147C42—582no—
148C23—21no—
149C23—21no—
150C23—42no—
151C23—42no—
152C23C22⋊Dic2912yes—
153C23D4×D2912yes—
154C23#9080712yes—
155C23C22×Dic2911yescharacteristic
156C23C2×C22⋊D2911yescharacteristic
157C23C2×C22⋊D2911yescharacteristic
158D4—24no—
159D4—24no—
160C2×C4—21no—
161C2×C4—21no—
162C2×C4—24no—
163C2×C4—22no—
164C2×C4—22no—
165C2×C4—42no—
166C2×C4—41no—
167C2×C4—41no—
168C2×C4—42no—
169C2×C4—584no—
170C2×C4—1164no—
171C2×C4—1164no—
172C2×C4—1162no—
173C2×C4—2322no—
174C2×C4C22⋊Dic2912yes—
175C22—22no—
176C22—24no—
177C22—22no—
178C22—42no—
179C22—41no—
180C22—41no—
181C22—42no—
182C22—42no—
183C22—81no—
184C22D4×Dic2912yes—
185C22#1174529711yescharacteristic
186C22#1174529911yescharacteristic
187C22#1174530112yes—
188C22C2×C22⋊Dic2911yescharacteristic
189C4—22no—
190C4—42no—
191C4—42no—
192C4—1164no—
193C4—2322no—
194C2—21no—
195C2—22no—
196C2—21no—
197C2—22no—
198C2—42no—
199C2#1427104311yescharacteristic
200C2#1427135212yes—
subgroupG/H
centerC22#11745299
commutatorC23×C29C22×C4
FrattiniC24C22×D29
FittingC2×C29×#123C2
socleC22×C29#120
prime radicalC22×D4×C29C22
cosocleC24×C29C23
hypercenterC2×#123D29
hypocenterC29#1890
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C24 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
3. #14271026C2semidirect
4. #14270929C2semidirect
9. C29×#123C4semidirect
31. C22×C4×C29C2×C4semidirect
39. C22⋊C4×C29C2×C4semidirect
109. #123Dic29semidirect
120. C29#1890semidirect
135. C22×C4C2×Dic29semidirect
146. C22⋊C4C2×Dic29semidirect

Maximal subgroups

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

subgroupindex
#142716382
C2×#117451822
#142710262
#142709292
C2×C29×#1232
#189029