Finite Group Databasebeta

← #16820536

Subgroups — #16820536

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×#11745270C212yesmaximal, complemented
2#14271744C211yesmaximal, characteristic, complemented
3C2×#11745173C212yesmaximal, complemented
4#14271064C211yesmaximal, characteristic, complemented
5C29×#343C211yesmaximal, characteristic, complemented
6C2×#90805C2212yes—
7C22×D116C2211yescharacteristic
8C2×M16×C29C2212yes—
9C2×C4⋊C4×C29C2211yescharacteristic
10#11745292—22no—
11C2×#90781—22no—
12C2×C4×Dic29C2211yescharacteristic
13#11745270—24no—
14#11745270—24no—
15C2×D232—22no—
16C2×#90773—22no—
17#11745259—22no—
18#11745257—22no—
19#11745173—24no—
20C23×D29—21no—
21C22×C4×C29D412yes—
22C22×C4×C29C2311yescharacteristic
23C2×C22⋊D29—22no—
24C22×Dic29—21no—
25#90805—22no—
26#90805—22no—
27#90805—22no—
28#90805—22no—
29C2×D116—22no—
30C2×D116—22no—
31C2×D116—21no—
32C2×D116—22no—
33C2×D116D412yes—
34C2×D116D412yescomplemented
35C2×C4×D29—22no—
36C2×Dic58D412yes—
37M16×C29—22no—
38M16×C29D414yescomplemented
39C2×C8×C29—22no—
40C4⋊C4×C29—22no—
41#90781—24no—
42#90781—44no—
43C4⋊Dic29—22no—
44C4×Dic29—22no—
45D232—28no—
46#90773—28no—
47C23×C29C2×D411yescharacteristic
48C22×D29—22no—
49C22×D29—22no—
50C22×D29—42no—
51C22×D29—42no—
52C22×D29—41no—
53C22×D29—41no—
54C2×C4×C29—22no—
55C2×C4×C29—42no—
56C2×C4×C29C2×D412yes—
57C2×C4×C29C2×D411yescharacteristic
58C2×C4×C29C2×D412yes—
59C2×C4×C29#4111yescharacteristic
60C22⋊D29—42no—
61C22⋊D29—42no—
62C2×Dic29—22no—
63C2×Dic29—22no—
64C2×Dic29—41no—
65C2×Dic29—41no—
66D116—24no—
67D116—22no—
68D116—22no—
69D116—42no—
70D116—82no—
71C4×D29—42no—
72C4×D29—42no—
73Dic58—22no—
74Dic58—22no—
75C8×C29—24no—
76#2006—291nomaximal, Sylow
77C22×C29—21no—
78C22×C29—21no—
79C22×C29#12011yescharacteristic
80C22×C29#12111yescharacteristic
81C22×C29#12711yescharacteristic
82C2×D29—44no—
83C2×D29—42no—
84C2×D29—42no—
85C2×D29—42no—
86C2×D29—42no—
87C2×D29—82no—
88C2×D29—81no—
89C2×D29—81no—
90C4×C29—42no—
91C4×C29#12012yes—
92C4×C29#12112yes—
93Dic29—42no—
94Dic29—42no—
95C2×AGL(1,ℤ/8)—292no—
96#537—291no—
97C2×#104—292no—
98#390—291no—
99#343D2911yescharacteristic, complemented
100C2×C29—21no—
101C2×C29—21no—
102C2×C29#39211yescharacteristic
103C2×C29#45311yescharacteristic
104C2×C29#45411yescharacteristic
105D29—82no—
106D29—82no—
107C2×#41—292no—
108C22×D4—291no—
109AGL(1,ℤ/8)—584no—
110AGL(1,ℤ/8)—584no—
111C2×SD16—582no—
112C2×D8—582no—
113C2×M16C2×D2912yes—
114C22⋊Q8—582no—
115#121—582no—
116#121—582no—
117C2×C4⋊C4C2×D2911yescharacteristic
118C2×C22⋊C4—582no—
119C2×C42—291no—
120#104—584no—
121C29#200611yescharacteristic, complemented, Sylow
122C24—581no—
123#41—582no—
124#41—582no—
125#41—582no—
126#41—582no—
127C2×Q8—292no—
128C2×D4—292no—
129C2×D4—292no—
130C2×D4—582no—
131C2×D4—582no—
132C2×D4—582no—
133C2×D4—582no—
134C2×D4—581no—
135C22×C4—581no—
136C22×C4—582no—
137C22×C4D11612yes—
138C22×C4C22×D2911yescharacteristic
139SD16—588no—
140D8—588no—
141M16—22no—
142M16D11614yescomplemented
143C2×C8—22no—
144C4⋊C4—22no—
145C4⋊C4—582no—
146C22⋊C4—584no—
147C22⋊C4—1164no—
148C42—582no—
149C23—582no—
150C23—582no—
151C23—1162no—
152C23—1162no—
153C23—1161no—
154C23—1161no—
155C23C2×D11611yescharacteristic
156Q8—582no—
157Q8—582no—
158D4—582no—
159D4—584no—
160D4—582no—
161D4—1162no—
162D4—1162no—
163D4—1162no—
164D4—2322no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—582no—
168C2×C4—582no—
169C2×C4—1161no—
170C2×C4—1161no—
171C2×C4—1162no—
172C2×C4—1162no—
173C2×C4C2×D11612yes—
174C2×C4D4×D2911yescharacteristic
175C2×C4D4×D2912yes—
176C2×C4#9080911yescharacteristic
177C8—24no—
178C22—21no—
179C22—21no—
180C22—1164no—
181C22—1162no—
182C22—1162no—
183C22—1162no—
184C22—1162no—
185C22—2322no—
186C22—2321no—
187C22—2321no—
188C22#1174523611yescharacteristic
189C22#1174524411yescharacteristic
190C22#1174525711yescharacteristic
191C4—42no—
192C4—1162no—
193C4—1162no—
194C4#1174524412yes—
195C4#1174525712yes—
196C2—21no—
197C2—21no—
198C2—2322no—
199C2—2322no—
200C2#1427107311yescharacteristic
201C2#1427133311yescharacteristic
202C2#1427133811yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#343C2
socleC22×C29#120
hypercenter#343D29
hypocenterC29#2006
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×#11745270C2semidirect
2. #14271744C2semidirect
3. C2×#11745173C2semidirect
4. #14271064C2semidirect
5. C29×#343C2semidirect
34. C2×D116D4semidirect
38. M16×C29D4semidirect
99. #343D29semidirect
121. C29#2006semidirect
142. M16D116semidirect

Maximal subgroups

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

subgroupindex
C2×#117452702
#142717442
C2×#117451732
#142710642
C29×#3432
#200629