Finite Group Databasebeta

← #16820596

Subgroups — #16820596

Order 3712.

350 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 69 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#14271963C211yesmaximal, characteristic, complemented
2#14271961C212yesmaximal, complemented
3#14271129C212yesmaximal, complemented
4#14270921C211yesmaximal, characteristic, complemented
5C29×#408C211yesmaximal, characteristic, complemented
6C2×#41×C29C2211yescharacteristic
7C2×#90805C2212yes—
8C2×M16×C29C2211yescharacteristic
9C22×C8×C29C2211yescharacteristic
10#11745313—22no—
11#11745312—24no—
12#11745311—22no—
13#11745304—22no—
14#11745294—22no—
15C2×#90777C2212yes—
16#11745271—22no—
17#11745270—22no—
18#11745266—22no—
19C29×C22⋊C8—22no—
20#11745168—24no—
21#41×C29—22no—
22#41×C29—22no—
23C2×Q8×C29D411yescharacteristic
24C2×D4×C29—21no—
25C2×D4×C29D411yescharacteristic
26C22×C4×C29—21no—
27C22×C4×C29C2311yescharacteristic
28C2×C22⋊D29—22no—
29#90805—22no—
30#90805—22no—
31#90805—22no—
32#90805—22no—
33C2×D116D412yes—
34C2×C4×D29—22no—
35C2×Dic58D412yes—
36M16×C29—22no—
37C2×C8×C29—22no—
38C2×C8×C29—21no—
39C2×C8×C29D412yes—
40#90785—24no—
41#90784—24no—
42#90783—24no—
43#90782—24no—
44#90777—22no—
45#90777—22no—
46C2×#6597D414yes—
47Dic116—22no—
48D232—22no—
49#90773—24no—
50C23×C29—21no—
51C23×C29#4111yescharacteristic
52C22×D29—22no—
53Q8×C29—22no—
54D4×C29—22no—
55D4×C29—42no—
56C2×C4×C29—21no—
57C2×C4×C29—41no—
58C2×C4×C29—41no—
59C2×C4×C29C2×D411yescharacteristic
60C2×C4×C29C2×D412yes—
61C2×C4×C29C2×D412yes—
62C2×C4×C29C2×D411yescharacteristic
63C22⋊D29—42no—
64C22⋊D29—42no—
65C2×Dic29—22no—
66D116—22no—
67D116—22no—
68C4×D29—42no—
69C4×D29—42no—
70Dic58—22no—
71Dic58—22no—
72C8×C29—22no—
73C8×C29—41no—
74#6597—24no—
75#2017—291nomaximal, Sylow
76C22×C29—41no—
77C22×C29—42no—
78C22×C29—41no—
79C22×C29#12111yescharacteristic
80C22×C29#12112yes—
81C2×D29—44no—
82C2×D29—42no—
83C4×C29—41no—
84C4×C29#12011yescharacteristic
85C4×C29#12012yes—
86C4×C29#12711yescharacteristic
87Dic29—42no—
88#575—292no—
89#575—291no—
90#408—292no—
91#408D2911yescharacteristic, complemented
92#338—291no—
93C2×C29—22no—
94C2×C29—21no—
95C2×C29—81no—
96C2×C29#39211yescharacteristic
97D29—82no—
98C2×#41—292no—
99C2×#41C2×D2911yescharacteristic
100#137—582no—
101#137—582no—
102#137—582no—
103AGL(1,ℤ/8)—582no—
104AGL(1,ℤ/8)—582no—
105AGL(1,ℤ/8)—582no—
106#135—584no—
107#135—582no—
108C2×M16—292no—
109C2×M16C2×D2911yescharacteristic
110C22×C8C2×D2911yescharacteristic
111C22⋊C8—22no—
112C22⋊C8—584no—
113C29#201711yescharacteristic, complemented, Sylow
114#41—22no—
115#41—22no—
116#41—582no—
117#41—582no—
118#41—582no—
119#41—582no—
120C2×Q8—292no—
121C2×Q8D11611yescharacteristic
122C2×D4—21no—
123C2×D4—292no—
124C2×D4—582no—
125C2×D4D11611yescharacteristic
126C22×C4—21no—
127C22×C4—582no—
128C22×C4C22×D2911yescharacteristic
129Q16—582no—
130Q16—584no—
131SD16—584no—
132SD16—584no—
133SD16—584no—
134D8—582no—
135D8—584no—
136M16—22no—
137M16—582no—
138M16—582no—
139C2×C8—22no—
140C2×C8—21no—
141C2×C8—294no—
142C2×C8C22⋊D2912yes—
143C23—21no—
144C23—582no—
145C23#9080511yescharacteristic
146Q8—22no—
147Q8—582no—
148Q8—582no—
149D4—22no—
150D4—42no—
151D4—582no—
152D4—582no—
153D4—1162no—
154D4—1162no—
155C2×C4—21no—
156C2×C4—41no—
157C2×C4—41no—
158C2×C4—582no—
159C2×C4—1162no—
160C2×C4—1162no—
161C2×C4C2×D11611yescharacteristic
162C2×C4D4×D2912yes—
163C2×C4D4×D2912yes—
164C2×C4C2×C22⋊D2911yescharacteristic
165C8—22no—
166C8—41no—
167C8—584no—
168C22—41no—
169C22—42no—
170C22—41no—
171C22—1164no—
172C22—1162no—
173C22#1174524612yes—
174C22#1174529211yescharacteristic
175C4—41no—
176C4—1162no—
177C4#1174524412yes—
178C4#1174529911yescharacteristic
179C4#1174530211yescharacteristic
180C2—21no—
181C2—22no—
182C2—81no—
183C2—2322no—
184C2#1427107211yescharacteristic
subgroupG/H
centerC4#11745302
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#408C2
socleC2×C29#392
hypercenter#408D29
hypocenterC29#2017
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C4 ◁ C22×C4 ◁ #408

Complements

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

NH ≅ G/Ntype
1. #14271963C2semidirect
2. #14271961C2semidirect
3. #14271129C2semidirect
4. #14270921C2semidirect
5. C29×#408C2semidirect
91. #408D29semidirect
113. C29#2017semidirect

Maximal subgroups

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

subgroupindex
#142719632
#142719612
#142711292
#142709212
C29×#4082
#201729