Finite Group Databasebeta

← #16820595

Subgroups — #16820595

Order 3712.

350 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 71 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#14271961C212yesmaximal, complemented
2#14271131C211yesmaximal, characteristic, complemented
3#14271130C212yesmaximal, complemented
4#14270921C211yesmaximal, characteristic, complemented
5C29×#575C211yesmaximal, characteristic, complemented
6C2×#41×C29C2212yes—
7C2×#90805C2211yescharacteristic
8C29×#137—22no—
9C29×AGL(1,ℤ/8)—22no—
10C29×#135—22no—
11C2×M16×C29C2211yescharacteristic
12#11745313—22no—
13#11745312—24no—
14#11745311—22no—
15#11745304—22no—
16#11745294—22no—
17C2×#90777C2212yes—
18C22×#6597C2211yescharacteristic
19C22⋊#6597—24no—
20#11745168—22no—
21#41×C29—22no—
22#41×C29—22no—
23#41×C29—22no—
24#41×C29—22no—
25C2×Q8×C29D412yes—
26C2×D4×C29—22no—
27C2×D4×C29D412yes—
28C22×C4×C29—22no—
29C22×C4×C29C2311yescharacteristic
30C2×C22⋊D29—21no—
31#90805—22no—
32#90805—22no—
33C2×D116D411yescharacteristic
34C2×C4×D29—21no—
35C2×Dic58D411yescharacteristic
36Q16×C29—22no—
37SD16×C29—24no—
38D8×C29—22no—
39M16×C29—22no—
40C2×C8×C29D412yes—
41#90785—24no—
42#90784—24no—
43#90783—24no—
44#90782—24no—
45#90777—22no—
46#90777—22no—
47C2×#6597—21no—
48C2×#6597—22no—
49C2×#6597D414yes—
50C23×C29—22no—
51C23×C29#4111yescharacteristic
52C22×D29—21no—
53Q8×C29—22no—
54Q8×C29—22no—
55D4×C29—22no—
56D4×C29—22no—
57D4×C29—42no—
58D4×C29—42no—
59C2×C4×C29—22no—
60C2×C4×C29—42no—
61C2×C4×C29—42no—
62C2×C4×C29C2×D411yescharacteristic
63C2×C4×C29C2×D412yes—
64C2×C4×C29C2×D412yes—
65C2×C4×C29C2×D411yescharacteristic
66C22⋊D29—42no—
67C2×Dic29—21no—
68D116—22no—
69C4×D29—41no—
70C4×D29—41no—
71Dic58—22no—
72C8×C29—22no—
73#6597—24no—
74#6597—41no—
75#2017—291nomaximal, Sylow
76C22×C29—41no—
77C22×C29—44no—
78C22×C29—42no—
79C22×C29#12111yescharacteristic
80C22×C29#12112yes—
81C2×D29—42no—
82C2×D29—41no—
83C4×C29—42no—
84C4×C29#12012yes—
85C4×C29#12011yescharacteristic
86C4×C29#12711yescharacteristic
87Dic29—41no—
88#575—292no—
89#575D2911yescharacteristic, complemented
90#408—292no—
91#408—291no—
92#338—291no—
93C2×C29—21no—
94C2×C29—22no—
95C2×C29—82no—
96C2×C29#39211yescharacteristic
97D29—81no—
98C2×#41—291no—
99C2×#41C2×D2912yes—
100#137—22no—
101#137—582no—
102#137—582no—
103AGL(1,ℤ/8)—22no—
104AGL(1,ℤ/8)—582no—
105AGL(1,ℤ/8)—582no—
106#135—22no—
107#135—584no—
108C2×M16—292no—
109C2×M16C2×D2911yescharacteristic
110C22×C8—291no—
111C22⋊C8—584no—
112C22⋊C8—582no—
113C29#201711yescharacteristic, complemented, Sylow
114#41—22no—
115#41—22no—
116#41—22no—
117#41—22no—
118#41—582no—
119#41—582no—
120C2×Q8—291no—
121C2×Q8C22⋊D2912yes—
122C2×D4—22no—
123C2×D4—291no—
124C2×D4—581no—
125C2×D4C22⋊D2912yes—
126C22×C4—22no—
127C22×C4—581no—
128C22×C4C22×D2911yescharacteristic
129Q16—22no—
130Q16—584no—
131SD16—24no—
132SD16—584no—
133SD16—584no—
134D8—22no—
135D8—584no—
136M16—22no—
137M16—582no—
138M16—582no—
139C2×C8—294no—
140C2×C8—582no—
141C2×C8—581no—
142C2×C8C22⋊D2912yes—
143C23—22no—
144C23—581no—
145C23#9080711yescharacteristic
146Q8—22no—
147Q8—22no—
148Q8—582no—
149D4—22no—
150D4—22no—
151D4—42no—
152D4—42no—
153D4—582no—
154D4—1162no—
155C2×C4—22no—
156C2×C4—42no—
157C2×C4—42no—
158C2×C4—581no—
159C2×C4—1161no—
160C2×C4—1161no—
161C2×C4D4×D2911yescharacteristic
162C2×C4D4×D2912yes—
163C2×C4C2×C22⋊D2912yes—
164C2×C4C2×C22⋊D2911yescharacteristic
165C8—22no—
166C8—584no—
167C8—1161no—
168C22—41no—
169C22—44no—
170C22—42no—
171C22—1162no—
172C22—1161no—
173C22#1174530011yescharacteristic
174C22#1174530112yes—
175C4—42no—
176C4—1161no—
177C4#1174529912yes—
178C4#1174530211yescharacteristic
179C4#1174531511yescharacteristic
180C2—22no—
181C2—21no—
182C2—82no—
183C2—2321no—
184C2#1427107111yescharacteristic
subgroupG/H
centerC4#11745302
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#575C2
socleC2×C29#392
hypercenter#575D29
hypocenterC29#2017
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #14271961C2semidirect
2. #14271131C2semidirect
3. #14271130C2semidirect
4. #14270921C2semidirect
5. C29×#575C2semidirect
89. #575D29semidirect
113. C29#2017semidirect

Maximal subgroups

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

subgroupindex
#142719612
#142711312
#142711302
#142709212
C29×#5752
#201729