Finite Group Databasebeta

← #16830053

Subgroups — #16830053

Order 3712.

412 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 133 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#14271718C211yesmaximal, characteristic, complemented
2#14271714C211yesmaximal, characteristic
3#14271536C211yesmaximal, characteristic, complemented
4#14271515C211yesmaximal, characteristic, complemented
5#14271511C211yesmaximal, characteristic, complemented
6#14271393C214yesmaximal, complemented
7#14271250C214yesmaximal, complemented
8C4×C8×D29C211yesmaximal, characteristic, complemented
9C29×#498C211yesmaximal, characteristic, complemented
10C2×#90809—21no—
11C29×C4⋊Q8C2211yescharacteristic
12C29×C4⋊Q8C2211yescharacteristic
13#11745309—21no—
14#11745308—21no—
15Q8×Dic29—21no—
16C2×#90773C2214yes—
17C2×C8×D29C2212yes—
18#11745259C2212yes—
19#11745257—21no—
20#11745257C2212yes—
21#11745255—21no—
22#11745255C2212yes—
23#11745254—21no—
24#11745252—21no—
25#11745249C2212yes—
26#11745236C2211yescharacteristic
27C42×D29C2211yescharacteristic
28#11745231C2211yescharacteristic
29C29×#106C2214yes—
30C4×C8×C29C2211yescharacteristic
31C8×Dic29C2212yes—
32#11745158C2214yes—
33#11745157C2214yes—
34C4×#6597C2211yescharacteristic
35C2×Q8×C29—21no—
36C2×Q8×C29—21no—
37#90809—44no—
38C2×D116—22no—
39C2×D116—21no—
40C2×D116—21no—
41C2×D116C2312yes—
42C2×C4×D29—22no—
43C2×C4×D29D411yescharacteristic
44C2×C4×D29D411yescharacteristic
45C2×C4×D29C2311yescharacteristic
46C2×Dic58C2312yes—
47C2×C8×C29C2312yes—
48C4⋊C4×C29—21no—
49C4⋊C4×C29—21no—
50C4⋊C4×C29C2312yes—
51C4⋊C4×C29C2312yes—
52C42×C29C2311yescharacteristic
53#90781—22no—
54#90781—22no—
55#90781—22no—
56C4⋊Dic29—21no—
57C4⋊Dic29—21no—
58C4⋊Dic29—22no—
59#90779—22no—
60C4×Dic29—22no—
61C4×Dic29D411yescharacteristic
62C4×Dic29D411yescharacteristic
63C4×Dic29C2311yescharacteristic
64C2×#6597C2312yes—
65#90773—28no—
66C8×D29—24no—
67C22×D29—22no—
68C22×D29C2×D411yescharacteristic
69Q8×C29—42no—
70Q8×C29—42no—
71C2×C4×C29—22no—
72C2×C4×C29—22no—
73C2×C4×C29C2×D411yescharacteristic
74C2×C4×C29C2×D411yescharacteristic
75C2×C4×C29C2411yescharacteristic
76C2×Dic29—22no—
77C2×Dic29C2×D411yescharacteristic
78C2×Dic29C2×D411yescharacteristic
79C2×Dic29C2×D411yescharacteristic
80D116—24no—
81D116—44no—
82D116—42no—
83D116—42no—
84C4×D29—22no—
85C4×D29—22no—
86C4×D29—44no—
87C4×D29SD1614yescomplemented
88Dic58—24no—
89C8×C29#4114yescomplemented
90#6597—22no—
91#3167—291nomaximal, Sylow
92C22×C29C22×D411yescharacteristic
93C2×D29—21no—
94C2×D29—21no—
95C2×D29—42no—
96C2×D29—42no—
97C2×D29—42no—
98C2×D29C2×SD1612yes—
99C4×C29—42no—
100C4×C29—42no—
101C4×C29C2×SD1612yes—
102C4×C29#13512yes—
103C4×C29C2×#4112yes—
104Dic29—21no—
105Dic29—21no—
106Dic29—42no—
107Dic29C2×SD1612yes—
108#533—291no—
109#532—291no—
110#498D2911yescharacteristic, complemented
111#492—291no—
112#487—291no—
113#486—291no—
114#465—294no—
115C4×SD16—294no—
116C2×C4×C8—291no—
117C2×C29#53211yescharacteristic
118C2×C29C22×SD1611yescharacteristic
119C2×C29C2×#13511yescharacteristic
120D29—22no—
121D29—82no—
122C2×#41—581no—
123C2×SD16—294no—
124C22×C8—292no—
125C4⋊Q8—291no—
126C4⋊Q8C2×D2911yescharacteristic
127C4⋊Q8C2×D2911yescharacteristic
128#127—291no—
129#125—581no—
130#124—581no—
131C22⋊Q8—292no—
132C22⋊Q8—581no—
133#121—292no—
134#121—581no—
135C4×Q8—292no—
136C4×Q8—581no—
137C4×D4—292no—
138C4×D4—581no—
139#117—581no—
140C2×C42—291no—
141#106C2×D2914yes—
142#103—294no—
143#102—294no—
144C4×C8—292no—
145C4×C8—291no—
146C4×C8C2×D2911yescharacteristic
147C29#316711yescharacteristic, complemented, Sylow
148#41—1164no—
149C2×Q8—21no—
150C2×Q8—21no—
151C2×Q8—292no—
152C2×D4—292no—
153C2×D4—582no—
154C2×D4—581no—
155C2×D4—581no—
156C22×C4—291no—
157C22×C4—291no—
158C22×C4—291no—
159C22×C4—582no—
160SD16—588no—
161C2×C8—292no—
162C2×C8—584no—
163C2×C8C22×D2912yes—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—582no—
167C4⋊C4—582no—
168C4⋊C4—581no—
169C4⋊C4—581no—
170C4⋊C4C22×D2912yes—
171C4⋊C4C22×D2912yes—
172C22⋊C4—582no—
173C22⋊C4—582no—
174C22⋊C4—582no—
175C42—291no—
176C42—291no—
177C42—291no—
178C42—582no—
179C42C22×D2911yescharacteristic
180C23—291no—
181C23—582no—
182Q8—42no—
183Q8—42no—
184Q8—584no—
185D4—584no—
186D4—1164no—
187D4—1162no—
188D4—1162no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—291no—
192C2×C4—294no—
193C2×C4—291no—
194C2×C4—291no—
195C2×C4—582no—
196C2×C4—582no—
197C2×C4—582no—
198C2×C4—1164no—
199C2×C4D4×D2911yescharacteristic
200C2×C4D4×D2911yescharacteristic
201C2×C4C23×D2911yescharacteristic
202C8—582no—
203C8#9080914yescomplemented
204C22—292no—
205C22—581no—
206C22—581no—
207C22—1162no—
208C22—1162no—
209C22—1162no—
210C22C2×D4×D2911yescharacteristic
211C4—42no—
212C4—42no—
213C4—292no—
214C4—581no—
215C4—581no—
216C4—1162no—
217C4SD16×D2912yes—
218C4#1174527812yes—
219C4C2×#9080912yes—
220C2—582no—
221C2—2322no—
222C2#1427171411yescharacteristic
223C2C2×SD16×D2911yescharacteristic
224C2C2×#1174527811yescharacteristic
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#498C2
socleC22×C29C22×D4
prime radical#14271714C2
hypercenter#498D29
hypocenterC29#3167
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #498

Complements

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

NH ≅ G/Ntype
1. #14271718C2semidirect
3. #14271536C2semidirect
4. #14271515C2semidirect
5. #14271511C2semidirect
6. #14271393C2semidirect
7. #14271250C2semidirect
8. C4×C8×D29C2semidirect
9. C29×#498C2semidirect
87. C4×D29SD16semidirect
89. C8×C29#41semidirect
110. #498D29semidirect
147. C29#3167semidirect
203. C8#90809semidirect

Maximal subgroups

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

subgroupindex
#142717182
#142717142
#142715362
#142715152
#142715112
#142713932
#142712502
C4×C8×D292
C29×#4982
#316729