Finite Group Databasebeta

← #16820533

Subgroups — #16820533

Order 3712.

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

normal subgroups only

This group has 406 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×#11745294C212yesmaximal, complemented
2#14271744C211yesmaximal, characteristic, complemented
3C2×#11745153C212yesmaximal, complemented
4#14270932C211yesmaximal, characteristic, complemented
5C29×#390C211yesmaximal, characteristic, complemented
6C22×D4×C29C2211yescharacteristic
7C2×#90805C2212yes—
8C2×C4⋊C4×C29C2211yescharacteristic
9C2×C22⋊C4×C29—22no—
10C2×C42×C29C2211yescharacteristic
11C2×#90783—22no—
12#11745294—24no—
13#11745294—24no—
14C2×#90782—22no—
15#11745292—22no—
16C2×#90777C2212yes—
17#11745259—22no—
18#11745257—22no—
19#11745153—24no—
20C24×C29—21no—
21C2×D4×C29—22no—
22C2×D4×C29—22no—
23C2×D4×C29—21no—
24C2×D4×C29D412yescomplemented
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—
38C22⋊C4×C29—44no—
39C42×C29—22no—
40#90783—28no—
41#90782—28no—
42#90781—24no—
43C4⋊Dic29—22no—
44#90777—22no—
45#90777D414yescomplemented
46C2×#6597—22no—
47C23×C29—22no—
48C23×C29—42no—
49C23×C29—42no—
50C23×C29—41no—
51C23×C29—41no—
52C23×C29C2×D411yescharacteristic
53C22×D29—22no—
54D4×C29—24no—
55D4×C29—42no—
56C2×C4×C29—22no—
57C2×C4×C29—22no—
58C2×C4×C29—41no—
59C2×C4×C29—41no—
60C2×C4×C29—42no—
61C2×C4×C29C2×D411yescharacteristic
62C2×C4×C29C2×D412yes—
63C2×C4×C29C2×D412yes—
64C2×C4×C29#4111yescharacteristic
65C22⋊D29—42no—
66C22⋊D29—42no—
67C2×Dic29—22no—
68D116—22no—
69D116—22no—
70D116—82no—
71C4×D29—42no—
72C4×D29—42no—
73Dic58—22no—
74Dic58—22no—
75#6597—24no—
76#2006—291nomaximal, Sylow
77C22×C29—21no—
78C22×C29—21no—
79C22×C29—44no—
80C22×C29—42no—
81C22×C29—82no—
82C22×C29—81no—
83C22×C29—81no—
84C22×C29#12011yescharacteristic
85C22×C29#12111yescharacteristic
86C22×C29#12711yescharacteristic
87C2×D29—42no—
88C2×D29—42no—
89C2×D29—42no—
90C4×C29—42no—
91C4×C29—42no—
92C4×C29#12012yes—
93C4×C29#12112yes—
94Dic29—42no—
95C2×AGL(1,ℤ/8)—292no—
96#537—291no—
97C2×#104—292no—
98#390D2911yescharacteristic, complemented
99#343—291no—
100C2×C29—21no—
101C2×C29—21no—
102C2×C29—82no—
103C2×C29#39211yescharacteristic
104C2×C29#45311yescharacteristic
105C2×C29#45411yescharacteristic
106D29—82no—
107C2×#41—292no—
108C22×D4C2×D2911yescharacteristic
109AGL(1,ℤ/8)—584no—
110AGL(1,ℤ/8)—584no—
111C2×SD16—582no—
112C2×D8—582no—
113C2×M16—292no—
114C22⋊Q8—582no—
115#121—582no—
116#121—582no—
117C2×C4⋊C4C2×D2911yescharacteristic
118C2×C22⋊C4—22no—
119C2×C42C2×D2911yescharacteristic
120#104—584no—
121C29#200611yescharacteristic, complemented, Sylow
122C24—21no—
123#41—582no—
124#41—582no—
125#41—582no—
126#41—582no—
127C2×Q8—292no—
128C2×D4—21no—
129C2×D4—22no—
130C2×D4—22no—
131C2×D4—292no—
132C2×D4—582no—
133C2×D4—582no—
134C2×D4D11612yescomplemented
135C22×C4—21no—
136C22×C4—582no—
137C22×C4C22⋊D2912yes—
138C22×C4C22×D2911yescharacteristic
139SD16—588no—
140D8—588no—
141M16—294no—
142M16—582no—
143C2×C8—582no—
144C4⋊C4—22no—
145C4⋊C4—582no—
146C22⋊C4—44no—
147C22⋊C4—584no—
148C42—22no—
149C23—22no—
150C23—42no—
151C23—42no—
152C23—41no—
153C23—41no—
154C23—582no—
155C23C2×C22⋊D2911yescharacteristic
156Q8—582no—
157Q8—582no—
158D4—24no—
159D4—42no—
160D4—582no—
161D4—582no—
162D4—1162no—
163D4—1162no—
164D4—2322no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—582no—
171C2×C4—1162no—
172C2×C4—1162no—
173C2×C4C2×D11611yescharacteristic
174C2×C4#9080511yescharacteristic
175C2×C4D4×D2912yes—
176C2×C4D4×D2912yes—
177C8—584no—
178C22—21no—
179C22—21no—
180C22—44no—
181C22—42no—
182C22—82no—
183C22—81no—
184C22—81no—
185C22—1162no—
186C22—1162no—
187C22—1162no—
188C22#1174529211yescharacteristic
189C22#1174529911yescharacteristic
190C22#1174530211yescharacteristic
191C4—42no—
192C4—42no—
193C4—1162no—
194C4#1174524412yes—
195C4#1174524612yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—2322no—
200C2#1427107211yescharacteristic
201C2#1427133011yescharacteristic
202C2#1427133511yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#390C2
socleC22×C29#120
hypercenter#390D29
hypocenterC29#2006
LCSG ▷ C22×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#11745294C2semidirect
2. #14271744C2semidirect
3. C2×#11745153C2semidirect
4. #14270932C2semidirect
5. C29×#390C2semidirect
24. C2×D4×C29D4semidirect
45. #90777D4semidirect
98. #390D29semidirect
121. C29#2006semidirect
134. C2×D4D116semidirect

Maximal subgroups

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

subgroupindex
C2×#117452942
#142717442
C2×#117451532
#142709322
C29×#3902
#200629