Finite Group Databasebeta

← #16819940

Subgroups — #16819940

Order 3712.

358 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 93 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#14271674C211yesmaximal, characteristic
2C2×#11745153C212yesmaximal, complemented
3#14271127C211yesmaximal, characteristic, complemented
4#14270923C212yesmaximal, complemented
5C2×C29×#117C211yesmaximal, characteristic, complemented
6C23×C4×C29C2211yescharacteristic
7C2×#90805C2211yescharacteristic
8C29×#117—24no—
9C2×C4⋊C4×C29—21no—
10C2×C22⋊C4×C29—21no—
11C2×C42×C29C2212yes—
12#11745315—21no—
13#11745292C412yescomplemented
14#11745291—21no—
15C4×C22⋊D29—22no—
16#11745288C2211yescharacteristic
17#11745286C412yescomplemented
18C2×#90777C2212yes—
19C22⋊#6597—22no—
20#11745153—24no—
21C24×C29D411yescharacteristic
22C22×C4×C29—22no—
23C22×C4×C29—22no—
24C22×C4×C29—22no—
25C22×C4×C29C2×C412yes—
26C22×C4×C29D412yes—
27C22×C4×C29D411yescharacteristic
28C22×C4×C29C2311yescharacteristic
29C2×C22⋊D29—22no—
30C2×C22⋊D29—21no—
31#90805—22no—
32#90805—22no—
33C2×D116C2×C411yescharacteristic
34C2×C4×D29—21no—
35C2×Dic58C2×C411yescharacteristic
36C4⋊C4×C29—24no—
37C22⋊C4×C29—24no—
38C42×C29—22no—
39C42×C29D414yescomplemented
40C22⋊Dic29—22no—
41C22⋊Dic29—21no—
42#90781—22no—
43C4⋊Dic29C2×C412yes—
44#90779—22no—
45C4×Dic29—21no—
46#90777—22no—
47#90777—22no—
48C2×#6597—22no—
49C23×C29—21no—
50C23×C29—21no—
51C23×C29—42no—
52C23×C29C22⋊C412yes—
53C23×C29C2×D411yescharacteristic
54C22×D29—21no—
55C2×C4×C29—21no—
56C2×C4×C29—21no—
57C2×C4×C29—24no—
58C2×C4×C29—24no—
59C2×C4×C29—24no—
60C2×C4×C29—44no—
61C2×C4×C29C22⋊C412yes—
62C2×C4×C29C22×C411yescharacteristic
63C2×C4×C29C2×D411yescharacteristic
64C2×C4×C29C2×D412yes—
65C2×C4×C29#4112yes—
66C22⋊D29—44no—
67C22⋊D29—41no—
68C22⋊D29—41no—
69C2×Dic29—22no—
70C2×Dic29—21no—
71D116—22no—
72C4×D29—42no—
73Dic58—22no—
74#6597—42no—
75#1897—291nomaximal, Sylow
76C22×C29—22no—
77C22×C29—22no—
78C22×C29—22no—
79C22×C29—22no—
80C22×C29—42no—
81C22×C29—42no—
82C22×C29C2×C22⋊C411yescharacteristic
83C22×C29#12011yescharacteristic
84C22×C29#12311yescharacteristic
85C2×D29—41no—
86C2×D29—42no—
87C4×C29—22no—
88C4×C29—44no—
89C4×C29C4×D412yes—
90C4×C29#12112yes—
91Dic29—41no—
92Dic29—42no—
93#525—291no—
94C2×#117D2911yescharacteristic, complemented
95C2×#104—292no—
96#407—291no—
97#339—292no—
98C2×C29—21no—
99C2×C29—21no—
100C2×C29—42no—
101C2×C29#38611yescharacteristic
102C2×C29#42112yes—
103D29—81no—
104C2×#41—291no—
105C23×C4C2×D2911yescharacteristic
106C2×M16—292no—
107#123—581no—
108C22⋊Q8—292no—
109#121—292no—
110#120—581no—
111C4×D4—582no—
112#117—24no—
113#117—291no—
114C2×C4⋊C4—21no—
115C2×C22⋊C4—21no—
116C2×C42C2×D2912yes—
117#104—584no—
118C22⋊C8—582no—
119C29#189711yescharacteristic, complemented, Sylow
120C24C22⋊D2911yescharacteristic
121#41—582no—
122#41—582no—
123C2×Q8—291no—
124C2×D4—291no—
125C2×D4—582no—
126C2×D4—581no—
127C22×C4—22no—
128C22×C4—22no—
129C22×C4—22no—
130C22×C4—581no—
131C22×C4C4×D2912yes—
132C22×C4D11612yes—
133C22×C4C22⋊D2911yescharacteristic
134C22×C4C22×D2911yescharacteristic
135M16—582no—
136M16—582no—
137C2×C8—582no—
138C4⋊C4—24no—
139C4⋊C4—292no—
140C4⋊C4—582no—
141C22⋊C4—24no—
142C22⋊C4—582no—
143C22⋊C4—581no—
144C22⋊C4—582no—
145C42—22no—
146C42—581no—
147C42C22⋊D2914yescomplemented
148C23—21no—
149C23—21no—
150C23—42no—
151C23—581no—
152C23#9078112yes—
153C23C2×C22⋊D2911yescharacteristic
154Q8—582no—
155D4—582no—
156D4—1164no—
157D4—1161no—
158D4—1161no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—24no—
162C2×C4—24no—
163C2×C4—24no—
164C2×C4—44no—
165C2×C4—582no—
166C2×C4—581no—
167C2×C4—1162no—
168C2×C4#9078112yes—
169C2×C4C2×C4×D2911yescharacteristic
170C2×C4C2×D11611yescharacteristic
171C2×C4#9080512yes—
172C2×C4C2×C22⋊D2912yes—
173C8—1162no—
174C22—22no—
175C22—22no—
176C22—22no—
177C22—22no—
178C22—42no—
179C22—42no—
180C22—1161no—
181C22—1162no—
182C22C2×#9078111yescharacteristic
183C22#1174529111yescharacteristic
184C22#1174531511yescharacteristic
185C4—22no—
186C4—44no—
187C4—1161no—
188C4—1162no—
189C4C4×C22⋊D2912yes—
190C4#1174529212yes—
191C2—21no—
192C2—21no—
193C2—42no—
194C2—2321no—
195C2#1427104211yescharacteristic
196C2#1427118112yes—
subgroupG/H
centerC2×C4C2×D116
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC2×C29×#117C2
socleC22×C29C2×C22⋊C4
prime radical#14271674C2
cosocleC22×C4×C29C23
hypercenterC2×#117D29
hypocenterC29#1897
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. C2×#11745153C2semidirect
3. #14271127C2semidirect
4. #14270923C2semidirect
5. C2×C29×#117C2semidirect
13. #11745292C4semidirect
17. #11745286C4semidirect
39. C42×C29D4semidirect
94. C2×#117D29semidirect
119. C29#1897semidirect
147. C42C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
#142716742
C2×#117451532
#142711272
#142709232
C2×C29×#1172
#189729