Finite Group Databasebeta

← #16820541

Subgroups — #16820541

Order 3712.

370 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 75 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×#11745271C212yesmaximal, complemented
2#14271744C211yesmaximal, characteristic
3C2×#11745173C212yesmaximal, complemented
4#14271068C211yesmaximal, characteristic, complemented
5C29×#343C211yesmaximal, characteristic, complemented
6C2×#90805C2212yes—
7C22×Dic58C2211yescharacteristic
8C2×M16×C29C2212yes—
9C2×C4⋊C4×C29C2211yescharacteristic
10#11745292—22no—
11C2×C4×Dic29C2211yescharacteristic
12#11745271—24no—
13#11745271—24no—
14C2×Dic116—22no—
15C2×#90773—22no—
16#11745259—22no—
17#11745257—22no—
18#11745179—22no—
19#11745173—24no—
20C22×C4×C29D412yes—
21C22×C4×C29C2311yescharacteristic
22C2×C22⋊D29—22no—
23C22×Dic29—21no—
24C22×Dic29—21no—
25#90805—22no—
26#90805—22no—
27#90805—22no—
28#90805—22no—
29C2×D116—22no—
30C2×D116D412yes—
31C2×C4×D29—22no—
32C2×Dic58—22no—
33C2×Dic58—22no—
34C2×Dic58—21no—
35C2×Dic58D412yes—
36C2×Dic58D412yescomplemented
37M16×C29—22no—
38M16×C29D414yescomplemented
39C2×C8×C29—22no—
40C4⋊C4×C29—22no—
41#90781—24no—
42C4⋊Dic29—22no—
43C4×Dic29—22no—
44Dic116—28no—
45#90773—28no—
46C23×C29C2×D411yescharacteristic
47C22×D29—22no—
48C2×C4×C29—22no—
49C2×C4×C29—42no—
50C2×C4×C29C2×D412yes—
51C2×C4×C29C2×D411yescharacteristic
52C2×C4×C29C2×D412yes—
53C2×C4×C29#4111yescharacteristic
54C22⋊D29—42no—
55C22⋊D29—42no—
56C2×Dic29—22no—
57C2×Dic29—22no—
58C2×Dic29—22no—
59C2×Dic29—41no—
60C2×Dic29—41no—
61C2×Dic29—41no—
62C2×Dic29—41no—
63D116—22no—
64D116—22no—
65D116—82no—
66C4×D29—42no—
67C4×D29—42no—
68Dic58—24no—
69Dic58—22no—
70Dic58—22no—
71Dic58—42no—
72C8×C29—24no—
73#2007—291nomaximal, Sylow
74C22×C29—21no—
75C22×C29—21no—
76C22×C29#12011yescharacteristic
77C22×C29#12111yescharacteristic
78C22×C29#12711yescharacteristic
79C2×D29—42no—
80C2×D29—42no—
81C2×D29—42no—
82C4×C29—42no—
83C4×C29#12012yes—
84C4×C29#12112yes—
85Dic29—42no—
86Dic29—42no—
87Dic29—42no—
88C2×#137—292no—
89#537—291no—
90C2×#104—292no—
91#391—291no—
92#343D2911yescharacteristic, complemented
93C2×C29—21no—
94C2×C29—21no—
95C2×C29#39211yescharacteristic
96C2×C29#45511yescharacteristic
97C2×C29#45611yescharacteristic
98D29—82no—
99C2×#41—292no—
100C22×Q8—291no—
101#137—584no—
102#137—584no—
103C2×Q16—582no—
104C2×SD16—582no—
105C2×M16C2×D2912yes—
106C22⋊Q8—582no—
107#121—582no—
108#121—582no—
109C2×C4⋊C4C2×D2911yescharacteristic
110C2×C42—291no—
111#104—584no—
112#95—582no—
113C29#200711yescharacteristic, complemented, Sylow
114#41—582no—
115#41—582no—
116#41—582no—
117#41—582no—
118C2×Q8—292no—
119C2×Q8—292no—
120C2×Q8—581no—
121C2×Q8—582no—
122C2×Q8—582no—
123C2×D4—292no—
124C2×D4—582no—
125C2×D4—582no—
126C22×C4—581no—
127C22×C4—581no—
128C22×C4—582no—
129C22×C4D11612yes—
130C22×C4C22×D2911yescharacteristic
131Q16—588no—
132SD16—588no—
133M16—22no—
134M16D11614yescomplemented
135C2×C8—22no—
136C4⋊C4—22no—
137C4⋊C4—582no—
138C22⋊C4—584no—
139C42—582no—
140C23—582no—
141C23C2×D11611yescharacteristic
142Q8—584no—
143Q8—582no—
144Q8—582no—
145Q8—1162no—
146D4—582no—
147D4—582no—
148D4—1162no—
149D4—1162no—
150D4—2322no—
151C2×C4—22no—
152C2×C4—42no—
153C2×C4—582no—
154C2×C4—582no—
155C2×C4—582no—
156C2×C4—1161no—
157C2×C4—1161no—
158C2×C4—1161no—
159C2×C4—1161no—
160C2×C4—1162no—
161C2×C4—1162no—
162C2×C4C2×D11612yes—
163C2×C4D4×D2911yescharacteristic
164C2×C4D4×D2912yes—
165C2×C4#9080911yescharacteristic
166C8—24no—
167C22—21no—
168C22—21no—
169C22—1162no—
170C22—1162no—
171C22—1162no—
172C22#1174523611yescharacteristic
173C22#1174524411yescharacteristic
174C22#1174525711yescharacteristic
175C4—42no—
176C4—1162no—
177C4—1162no—
178C4—1162no—
179C4#1174524412yes—
180C4#1174525712yes—
181C2—21no—
182C2—21no—
183C2—2322no—
184C2#1427107311yescharacteristic
185C2#1427134311yescharacteristic
186C2#1427134811yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#343C2
socleC22×C29#120
prime radical#14271744C2
hypercenter#343D29
hypocenterC29#2007
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
1. C2×#11745271C2semidirect
3. C2×#11745173C2semidirect
4. #14271068C2semidirect
5. C29×#343C2semidirect
36. C2×Dic58D4semidirect
38. M16×C29D4semidirect
92. #343D29semidirect
113. C29#2007semidirect
134. M16D116semidirect

Maximal subgroups

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

subgroupindex
C2×#117452712
#142717442
C2×#117451732
#142710682
C29×#3432
#200729