Finite Group Databasebeta

← #16829615

Subgroups — #16829615

Order 3712.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 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#14271713C211yesmaximal, characteristic
2C2×C4×Dic58C211yesmaximal, characteristic, complemented
3#14271477C212yesmaximal, complemented
4#14271459C212yesmaximal, complemented
5#14271364C212yesmaximal, complemented
6#14271304C212yesmaximal, complemented
7#14271265C214yesmaximal, complemented
8C29×#432C211yesmaximal, characteristic, complemented
9C2×#90805—21no—
10C22×Dic58C2211yescharacteristic
11C2×C42×C29C2211yescharacteristic
12#11745292—21no—
13#11745292C2212yes—
14C2×C4⋊Dic29C2211yescharacteristic
15C2×#90779—21no—
16C2×C4×Dic29—21no—
17C2×#90773C2214yes—
18#11745237—21no—
19#11745236C2211yescharacteristic
20C4×D116—21no—
21C4×D116C2212yes—
22#11745231C2211yescharacteristic
23C4×Dic58—21no—
24C4×Dic58—21no—
25C4×Dic58C2212yes—
26C4×Dic58C2212yes—
27C29×C4⋊C8C2212yes—
28C29×C22⋊C8C2212yes—
29C29×#97C2212yes—
30#11745169C2214yes—
31#11745166C2214yes—
32#11745164C2214yes—
33C22×C4×C29D411yescharacteristic
34C22×C4×C29D411yescharacteristic
35C22×C4×C29C2311yescharacteristic
36C2×C22⋊D29—22no—
37C22×Dic29—21no—
38C22×Dic29—21no—
39#90805—44no—
40C2×D116—21no—
41C2×D116—21no—
42C2×D116C2312yes—
43C2×C4×D29—22no—
44C2×Dic58—21no—
45C2×Dic58—24no—
46C2×Dic58—21no—
47C2×Dic58C2312yes—
48C2×C8×C29C2314yes—
49C42×C29D411yescharacteristic
50C42×C29D411yescharacteristic
51C42×C29C2311yescharacteristic
52C42×C29C2311yescharacteristic
53#90781—22no—
54#90781—22no—
55C4⋊Dic29—21no—
56C4⋊Dic29—21no—
57C4⋊Dic29C2312yes—
58C4⋊Dic29C2312yes—
59#90779—22no—
60#90779—22no—
61C4×Dic29—22no—
62C4×Dic29—22no—
63#90773—28no—
64C23×C29C2×D411yescharacteristic
65C22×D29—22no—
66C2×C4×C29—22no—
67C2×C4×C29—22no—
68C2×C4×C29—22no—
69C2×C4×C29C2×D411yescharacteristic
70C2×C4×C29C2×D411yescharacteristic
71C2×C4×C29C2×D411yescharacteristic
72C2×C4×C29C2×D411yescharacteristic
73C2×C4×C29C2×D411yescharacteristic
74C2×C4×C29C2411yescharacteristic
75C22⋊D29—44no—
76C2×Dic29—24no—
77C2×Dic29—22no—
78C2×Dic29—22no—
79C2×Dic29—22no—
80C2×Dic29—42no—
81D116—24no—
82D116—42no—
83D116—42no—
84C4×D29—44no—
85Dic58—24no—
86Dic58—22no—
87Dic58—42no—
88Dic58#4114yescomplemented
89C8×C29—24no—
90#3112—291nomaximal, Sylow
91C22×C29—21no—
92C22×C29—21no—
93C22×C29AGL(1,ℤ/8)12yes—
94C22×C29C22×D411yescharacteristic
95C2×D29—42no—
96C2×D29—42no—
97C2×D29—42no—
98C4×C29—21no—
99C4×C29—21no—
100C4×C29—21no—
101C4×C29—21no—
102C4×C29#13712yes—
103C4×C29C2×#4112yes—
104Dic29—24no—
105Dic29—42no—
106Dic29—42no—
107#532—291no—
108C2×C4×Q8—291no—
109#480—292no—
110#477—292no—
111#460—292no—
112#448—292no—
113#440—294no—
114#432D2911yescharacteristic, complemented
115C2×C29—22no—
116C2×C29#52511yescharacteristic
117C2×C29C2×AGL(1,ℤ/8)11yescharacteristic
118C2×C29C2×#13711yescharacteristic
119D29—82no—
120C2×#41—581no—
121C22×Q8—291no—
122C2×SD16—294no—
123C4⋊Q8—291no—
124#127—291no—
125#124—581no—
126#121—292no—
127#121—581no—
128C4×Q8—292no—
129C4×Q8—292no—
130C4×Q8—581no—
131C4×Q8—581no—
132C4×D4—292no—
133C4×D4—581no—
134C2×C4⋊C4—291no—
135C2×C4⋊C4—581no—
136C2×C42—581no—
137C2×C42C2×D2911yescharacteristic
138#107—294no—
139C4⋊C8C2×D2912yes—
140#103—294no—
141#102—294no—
142C22⋊C8C2×D2912yes—
143#97C2×D2912yes—
144C29#311211yescharacteristic, complemented, Sylow
145#41—1164no—
146C2×Q8—292no—
147C2×Q8—584no—
148C2×Q8—581no—
149C2×Q8—581no—
150C2×D4—292no—
151C2×D4—582no—
152C2×D4—581no—
153C2×D4—581no—
154C22×C4—581no—
155C22×C4—581no—
156C22×C4—582no—
157C22×C4D11611yescharacteristic
158C22×C4D11611yescharacteristic
159C22×C4C22×D2911yescharacteristic
160SD16—588no—
161C2×C8C22×D2914yes—
162C4⋊C4—292no—
163C4⋊C4—292no—
164C4⋊C4—581no—
165C4⋊C4—582no—
166C4⋊C4—582no—
167C4⋊C4—581no—
168C22⋊C4—582no—
169C22⋊C4—582no—
170C42—582no—
171C42—582no—
172C42D11611yescharacteristic
173C42D11611yescharacteristic
174C42C22×D2911yescharacteristic
175C42C22×D2911yescharacteristic
176C23—582no—
177C23C2×D11611yescharacteristic
178Q8—294no—
179Q8—584no—
180Q8—582no—
181Q8—1162no—
182D4—584no—
183D4—1162no—
184D4—1164no—
185D4—1162no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—584no—
190C2×C4—582no—
191C2×C4—582no—
192C2×C4—582no—
193C2×C4—1164no—
194C2×C4—1162no—
195C2×C4C2×D11611yescharacteristic
196C2×C4C2×D11611yescharacteristic
197C2×C4C2×D11611yescharacteristic
198C2×C4C2×D11611yescharacteristic
199C2×C4C2×D11611yescharacteristic
200C2×C4C23×D2911yescharacteristic
201C8—24no—
202C22—21no—
203C22—21no—
204C22—1162no—
205C22—1162no—
206C22—1162no—
207C22#1174527012yes—
208C22C22×D11611yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—584no—
214C4—1162no—
215C4—1162no—
216C4#1174527112yes—
217C4#41×D2912yes—
218C2—22no—
219C2—2322no—
220C2#1427167511yescharacteristic
221C2C2×#1174527011yescharacteristic
222C2C2×#1174527111yescharacteristic
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#432C2
socleC22×C29C22×D4
prime radical#14271713C2
hypercenter#432D29
hypocenterC29#3112
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic58C2semidirect
3. #14271477C2semidirect
4. #14271459C2semidirect
5. #14271364C2semidirect
6. #14271304C2semidirect
7. #14271265C2semidirect
8. C29×#432C2semidirect
88. Dic58#41semidirect
114. #432D29semidirect
144. C29#3112semidirect

Maximal subgroups

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

subgroupindex
#142717132
C2×C4×Dic582
#142714772
#142714592
#142713642
#142713042
#142712652
C29×#4322
#311229