Finite Group Databasebeta

← #16820534

Subgroups — #16820534

Order 3712.

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

normal subgroups only

This group has 406 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×#11745311C212yesmaximal, complemented
2C2×#11745185C212yesmaximal, complemented
3#14271064C211yesmaximal, characteristic, complemented
4#14270932C211yesmaximal, characteristic, complemented
5C29×#537C211yesmaximal, characteristic, complemented
6C2×#41×C29C2212yes—
7C22×D116C2211yescharacteristic
8C29×C22⋊Q8—22no—
9C29×#121—22no—
10C29×#121—22no—
11C2×C4⋊C4×C29C2211yescharacteristic
12#11745311—24no—
13#11745311—24no—
14C2×#90784—22no—
15C2×#90782—22no—
16C2×#90781—22no—
17C2×C4×Dic29C2211yescharacteristic
18C2×#90777C2212yes—
19#11745185—24no—
20C23×D29—21no—
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×C29—22no—
28C2×D4×C29D412yes—
29C22×C4×C29—22no—
30C22×C4×C29D412yes—
31C22×C4×C29C2311yescharacteristic
32C22×Dic29—21no—
33C2×D116—22no—
34C2×D116—22no—
35C2×D116—21no—
36C2×D116D412yescomplemented
37C4⋊C4×C29—22no—
38C4⋊C4×C29—22no—
39C22⋊C4×C29—24no—
40#90784—28no—
41#90782—28no—
42#90781—44no—
43C4×Dic29—22no—
44#90777—22no—
45#90777D414yescomplemented
46C2×#6597—22no—
47C23×C29—22no—
48C23×C29C2×D411yescharacteristic
49C22×D29—22no—
50C22×D29—42no—
51C22×D29—42no—
52C22×D29—41no—
53C22×D29—41no—
54Q8×C29—22no—
55Q8×C29—22no—
56D4×C29—22no—
57D4×C29—22no—
58D4×C29—42no—
59D4×C29—42no—
60D4×C29—82no—
61C2×C4×C29—22no—
62C2×C4×C29—22no—
63C2×C4×C29—42no—
64C2×C4×C29—42no—
65C2×C4×C29—42no—
66C2×C4×C29C2×D411yescharacteristic
67C2×C4×C29C2×D412yes—
68C2×C4×C29C2×D412yes—
69C2×C4×C29#4111yescharacteristic
70C2×Dic29—22no—
71C2×Dic29—41no—
72C2×Dic29—41no—
73D116—24no—
74D116—42no—
75#6597—24no—
76#2006—291nomaximal, Sylow
77C22×C29—21no—
78C22×C29—21no—
79C22×C29—42no—
80C22×C29—42no—
81C22×C29—42no—
82C22×C29#12011yescharacteristic
83C22×C29#12111yescharacteristic
84C22×C29#12711yescharacteristic
85C2×D29—44no—
86C2×D29—42no—
87C2×D29—82no—
88C2×D29—81no—
89C2×D29—81no—
90C4×C29—42no—
91C4×C29—42no—
92C4×C29#12012yes—
93C4×C29#12112yes—
94Dic29—42no—
95C2×AGL(1,ℤ/8)—292no—
96#537D2911yescharacteristic, complemented
97C2×#104—292no—
98#390—291no—
99#343—291no—
100C2×C29—21no—
101C2×C29—21no—
102C2×C29—82no—
103C2×C29#39211yescharacteristic
104C2×C29#45311yescharacteristic
105C2×C29#45411yescharacteristic
106D29—82no—
107C2×#41C2×D2912yes—
108C22×D4—291no—
109AGL(1,ℤ/8)—584no—
110AGL(1,ℤ/8)—584no—
111C2×SD16—582no—
112C2×D8—582no—
113C2×M16—292no—
114C22⋊Q8—22no—
115#121—22no—
116#121—22no—
117C2×C4⋊C4C2×D2911yescharacteristic
118C2×C22⋊C4—582no—
119C2×C42—291no—
120#104—584no—
121C29#200611yescharacteristic, complemented, Sylow
122C24—581no—
123#41—22no—
124#41—22no—
125#41—22no—
126#41—22no—
127C2×Q8C22⋊D2912yes—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—292no—
131C2×D4—582no—
132C2×D4—581no—
133C2×D4—582no—
134C2×D4C22⋊D2912yes—
135C22×C4—22no—
136C22×C4—581no—
137C22×C4C22⋊D2912yes—
138C22×C4C22×D2911yescharacteristic
139SD16—588no—
140D8—588no—
141M16—294no—
142M16—582no—
143C2×C8—582no—
144C4⋊C4—22no—
145C4⋊C4—22no—
146C22⋊C4—24no—
147C22⋊C4—1164no—
148C42—582no—
149C23—22no—
150C23—582no—
151C23—1162no—
152C23—1162no—
153C23—1161no—
154C23—1161no—
155C23C2×C22⋊D2911yescharacteristic
156Q8—22no—
157Q8—22no—
158D4—22no—
159D4—22no—
160D4—42no—
161D4—42no—
162D4—82no—
163D4—584no—
164D4—1162no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—582no—
171C2×C4—1161no—
172C2×C4—1161no—
173C2×C4D4×D2911yescharacteristic
174C2×C4D4×D2912yes—
175C2×C4#9080711yescharacteristic
176C2×C4C2×C22⋊D2912yes—
177C8—584no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—1164no—
184C22—1162no—
185C22—2322no—
186C22—2321no—
187C22—2321no—
188C22#1174530011yescharacteristic
189C22#1174530211yescharacteristic
190C22#1174531511yescharacteristic
191C4—42no—
192C4—42no—
193C4—1162no—
194C4#1174529912yes—
195C4#1174530112yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—2322no—
200C2#1427107111yescharacteristic
201C2#1427133111yescharacteristic
202C2#1427133611yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#537C2
socleC22×C29#120
hypercenter#537D29
hypocenterC29#2006
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#11745311C2semidirect
2. C2×#11745185C2semidirect
3. #14271064C2semidirect
4. #14270932C2semidirect
5. C29×#537C2semidirect
36. C2×D116D4semidirect
45. #90777D4semidirect
96. #537D29semidirect
121. C29#2006semidirect

Maximal subgroups

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

subgroupindex
C2×#117453112
C2×#117451852
#142710642
#142709322
C29×#5372
#200629