Finite Group Databasebeta

← #16820538

Subgroups — #16820538

Order 3712.

370 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 73 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×#11745304C212yesmaximal, complemented
2#14271744C211yesmaximal, characteristic
3C2×#11745153C212yesmaximal, complemented
4#14270932C211yesmaximal, characteristic, complemented
5C29×#391C211yesmaximal, characteristic, complemented
6C22×Q8×C29C2211yescharacteristic
7C2×#90805C2212yes—
8C2×C4⋊C4×C29C2211yescharacteristic
9C2×C42×C29C2211yescharacteristic
10C2×#90785—22no—
11#11745304—24no—
12#11745304—24no—
13C2×#90784—22no—
14#11745292—22no—
15C2×#90777C2212yes—
16#11745259—22no—
17#11745257—22no—
18C29×#95—22no—
19#11745153—24no—
20C2×Q8×C29—21no—
21C2×Q8×C29—22no—
22C2×Q8×C29—22no—
23C2×Q8×C29D412yescomplemented
24C22×C4×C29—21no—
25C22×C4×C29—21no—
26C22×C4×C29D412yes—
27C22×C4×C29C2311yescharacteristic
28C2×C22⋊D29—22no—
29#90805—22no—
30#90805—22no—
31#90805—22no—
32#90805—22no—
33C2×D116—22no—
34C2×D116D412yes—
35C2×C4×D29—22no—
36C2×Dic58D412yes—
37C4⋊C4×C29—22no—
38C42×C29—22no—
39#90785—28no—
40#90784—28no—
41#90781—24no—
42C4⋊Dic29—22no—
43#90777—22no—
44#90777D414yescomplemented
45C2×#6597—22no—
46C23×C29C2×D411yescharacteristic
47C22×D29—22no—
48Q8×C29—24no—
49Q8×C29—42no—
50C2×C4×C29—22no—
51C2×C4×C29—22no—
52C2×C4×C29—22no—
53C2×C4×C29—41no—
54C2×C4×C29—41no—
55C2×C4×C29—41no—
56C2×C4×C29—41no—
57C2×C4×C29—42no—
58C2×C4×C29C2×D411yescharacteristic
59C2×C4×C29C2×D412yes—
60C2×C4×C29C2×D412yes—
61C2×C4×C29#4111yescharacteristic
62C22⋊D29—42no—
63C22⋊D29—42no—
64C2×Dic29—22no—
65D116—22no—
66D116—22no—
67D116—82no—
68C4×D29—42no—
69C4×D29—42no—
70Dic58—22no—
71Dic58—22no—
72#6597—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—42no—
84C4×C29—42no—
85C4×C29#12012yes—
86C4×C29#12112yes—
87Dic29—42no—
88C2×#137—292no—
89#537—291no—
90C2×#104—292no—
91#391D2911yescharacteristic, complemented
92#343—291no—
93C2×C29—21no—
94C2×C29—21no—
95C2×C29#39211yescharacteristic
96C2×C29#45511yescharacteristic
97C2×C29#45611yescharacteristic
98D29—82no—
99C2×#41—292no—
100C22×Q8C2×D2911yescharacteristic
101#137—584no—
102#137—584no—
103C2×Q16—582no—
104C2×SD16—582no—
105C2×M16—292no—
106C22⋊Q8—582no—
107#121—582no—
108#121—582no—
109C2×C4⋊C4C2×D2911yescharacteristic
110C2×C42C2×D2911yescharacteristic
111#104—584no—
112#95—22no—
113C29#200711yescharacteristic, complemented, Sylow
114#41—582no—
115#41—582no—
116#41—582no—
117#41—582no—
118C2×Q8—21no—
119C2×Q8—22no—
120C2×Q8—22no—
121C2×Q8—292no—
122C2×Q8D11612yescomplemented
123C2×D4—292no—
124C2×D4—582no—
125C2×D4—582no—
126C22×C4—21no—
127C22×C4—21no—
128C22×C4—582no—
129C22×C4C22⋊D2912yes—
130C22×C4C22×D2911yescharacteristic
131Q16—588no—
132SD16—588no—
133M16—294no—
134M16—582no—
135C2×C8—582no—
136C4⋊C4—22no—
137C4⋊C4—582no—
138C22⋊C4—584no—
139C42—22no—
140C23—582no—
141C23C2×C22⋊D2911yescharacteristic
142Q8—24no—
143Q8—42no—
144Q8—582no—
145Q8—582no—
146D4—582no—
147D4—582no—
148D4—1162no—
149D4—1162no—
150D4—2322no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—22no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—42no—
159C2×C4—582no—
160C2×C4—1162no—
161C2×C4—1162no—
162C2×C4C2×D11611yescharacteristic
163C2×C4#9080511yescharacteristic
164C2×C4D4×D2912yes—
165C2×C4D4×D2912yes—
166C8—584no—
167C22—21no—
168C22—21no—
169C22—1162no—
170C22—1162no—
171C22—1162no—
172C22#1174529211yescharacteristic
173C22#1174529911yescharacteristic
174C22#1174530211yescharacteristic
175C4—42no—
176C4—42no—
177C4—42no—
178C4—1162no—
179C4#1174524412yes—
180C4#1174524612yes—
181C2—21no—
182C2—21no—
183C2—2322no—
184C2#1427107211yescharacteristic
185C2#1427134011yescharacteristic
186C2#1427134511yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#391C2
socleC22×C29#120
prime radical#14271744C2
hypercenter#391D29
hypocenterC29#2007
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
1. C2×#11745304C2semidirect
3. C2×#11745153C2semidirect
4. #14270932C2semidirect
5. C29×#391C2semidirect
23. C2×Q8×C29D4semidirect
44. #90777D4semidirect
91. #391D29semidirect
113. C29#2007semidirect
122. C2×Q8D116semidirect

Maximal subgroups

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

subgroupindex
C2×#117453042
#142717442
C2×#117451532
#142709322
C29×#3912
#200729