Finite Group Databasebeta

← #16829024

Subgroups — #16829024

Order 3712.

458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#90785C211yesmaximal, characteristic, complemented
2#14271734C211yesmaximal, characteristic
3#14271641C211yesmaximal, characteristic, complemented
4#14271383C214yesmaximal, complemented
5#14271371C214yesmaximal, complemented
6#14271191C211yesmaximal, characteristic, complemented
7#14271173C211yesmaximal, characteristic, complemented
8#14271159C211yesmaximal, characteristic
9C2×C29×#137C211yesmaximal, characteristic
10C2×#41×C29C2211yescharacteristic
11C22×Q8×C29C2211yescharacteristic
12C22×Dic58C2211yescharacteristic
13C29×#137—24no—
14C2×Q16×C29C2212yes—
15C2×SD16×C29C2212yes—
16C2×M16×C29C2211yescharacteristic
17Q8×Dic29—22no—
18Q8×Dic29C2214yes—
19#11745306C2212yes—
20C2×#90785—24no—
21C2×#90785C2214yes—
22#11745298C2212yes—
23#11745297—22no—
24#11745288—22no—
25#11745288C2211yescharacteristic
26#11745288C2211yescharacteristic
27#11745286—22no—
28C22×#6597C2211yescharacteristic
29#11745183C2212yes—
30#11745180C2212yes—
31#11745164C2214yes—
32#11745162C2214yes—
33#41×C29—22no—
34#41×C29—22no—
35C2×Q8×C29—21no—
36C2×Q8×C29—22no—
37C2×Q8×C29D414yes—
38C2×Q8×C29C2311yescharacteristic
39C2×Q8×C29C2312yes—
40C2×D4×C29—21no—
41C2×D4×C29C2311yescharacteristic
42C22×C4×C29—21no—
43C22×C4×C29—21no—
44C22×C4×C29C2311yescharacteristic
45C22×Dic29—21no—
46C2×Dic58—22no—
47C2×Dic58—22no—
48C2×Dic58—21no—
49C2×Dic58C2312yes—
50Q16×C29—24no—
51SD16×C29—24no—
52M16×C29—22no—
53C2×C8×C29C2312yes—
54C22⋊Dic29—21no—
55C22⋊Dic29—24no—
56C22⋊Dic29D412yes—
57#90785—28no—
58C4⋊Dic29—24no—
59C4⋊Dic29D412yes—
60C4⋊Dic29C2312yes—
61#90779—24no—
62C4×Dic29—21no—
63C4×Dic29—24no—
64C4×Dic29C2312yes—
65C2×#6597—22no—
66C2×#6597C2312yes—
67C23×C29—21no—
68C23×C29C2×D411yescharacteristic
69Q8×C29—24no—
70Q8×C29—22no—
71Q8×C29—21no—
72Q8×C29—21no—
73Q8×C29C2×D414yes—
74D4×C29—21no—
75D4×C29—21no—
76D4×C29—42no—
77C2×C4×C29—24no—
78C2×C4×C29—22no—
79C2×C4×C29—21no—
80C2×C4×C29—42no—
81C2×C4×C29C2×D411yescharacteristic
82C2×C4×C29C2×D412yes—
83C2×C4×C29#4112yes—
84C2×C4×C29C2411yescharacteristic
85C2×Dic29—22no—
86C2×Dic29—22no—
87C2×Dic29—42no—
88C2×Dic29C2×D414yes—
89Dic58—22no—
90Dic58—22no—
91Dic58—42no—
92C8×C29—22no—
93#6597—22no—
94#3044—291nomaximal, Sylow
95C22×C29—22no—
96C22×C29—41no—
97C22×C29—42no—
98C22×C29#12112yes—
99C22×C29C22×D411yescharacteristic
100C4×C29—24no—
101C4×C29—41no—
102C4×C29#12112yes—
103C4×C29C22×D411yescharacteristic
104C4×C29C2×#4111yescharacteristic
105Dic29—24no—
106Dic29—42no—
107Dic29—42no—
108C2×#137D2911yescharacteristic
109C22×Q16—291no—
110#536—291no—
111#519—291no—
112#464—294no—
113#462—294no—
114#424—291no—
115#419—291no—
116#416—291no—
117C2×C29—22no—
118C2×C29—81no—
119C2×C29C2×#12111yescharacteristic
120C2×C29#57812yes—
121C2×#41C2×D2911yescharacteristic
122C22×Q8—291no—
123C22×Q8C2×D2911yescharacteristic
124#137—24no—
125C2×Q16—294no—
126C2×Q16—584no—
127C2×Q16C2×D2912yes—
128C2×SD16C2×D2912yes—
129C2×M16C2×D2911yescharacteristic
130C22×C8—291no—
131C4⋊Q8—292no—
132#124—292no—
133#123—582no—
134C22⋊Q8—582no—
135C4×Q8—294no—
136C4×Q8—582no—
137#117—291no—
138#117—291no—
139#117—582no—
140C4⋊C8—294no—
141#103—292no—
142#103—294no—
143#102—292no—
144C29#304411yescharacteristic, complemented, Sylow
145#41—22no—
146#41—22no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—292no—
150C2×Q8—581no—
151C2×Q8—582no—
152C2×Q8—582no—
153C2×Q8C22⋊D2914yes—
154C2×Q8C22×D2911yescharacteristic
155C2×Q8C22×D2912yes—
156C2×D4—21no—
157C2×D4C22×D2911yescharacteristic
158C22×C4—21no—
159C22×C4—21no—
160C22×C4—581no—
161C22×C4C22×D2911yescharacteristic
162Q16—24no—
163Q16—588no—
164SD16—24no—
165M16—22no—
166C2×C8—292no—
167C2×C8—582no—
168C2×C8C22×D2912yes—
169C4⋊C4—292no—
170C4⋊C4—292no—
171C4⋊C4—584no—
172C4⋊C4—584no—
173C22⋊C4—292no—
174C22⋊C4—584no—
175C22⋊C4—581no—
176C42—292no—
177C42—584no—
178C42—581no—
179C23—21no—
180C23D4×D2911yescharacteristic
181Q8—24no—
182Q8—22no—
183Q8—21no—
184Q8—21no—
185Q8—582no—
186Q8—582no—
187Q8—1162no—
188Q8C2×C22⋊D2914yes—
189D4—21no—
190D4—21no—
191D4—42no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—21no—
195C2×C4—42no—
196C2×C4—294no—
197C2×C4—582no—
198C2×C4—582no—
199C2×C4—1162no—
200C2×C4D4×D2911yescharacteristic
201C2×C4#9080712yes—
202C2×C4C2×C22⋊D2912yes—
203C2×C4C23×D2911yescharacteristic
204C8—22no—
205C8—582no—
206C22—22no—
207C22—41no—
208C22—42no—
209C22#1174530112yes—
210C22C2×D4×D2911yescharacteristic
211C4—24no—
212C4—41no—
213C4—584no—
214C4—1162no—
215C4—1162no—
216C4#1174530112yes—
217C4C2×#9080711yescharacteristic
218C4C22×C22⋊D2911yescharacteristic
219C2—22no—
220C2—81no—
221C2C2×#1174530111yescharacteristic
222C2#1427197912yes—
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC2×C29×#137C2
socleC22×C29C22×D4
prime radicalC2×#41×C29C22
hypercenterC2×#137D29
hypocenterC29#3044
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
1. C22×#90785C2semidirect
3. #14271641C2semidirect
4. #14271383C2semidirect
5. #14271371C2semidirect
6. #14271191C2semidirect
7. #14271173C2semidirect
144. C29#3044semidirect

Maximal subgroups

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

subgroupindex
C22×#907852
#142717342
#142716412
#142713832
#142713712
#142711912
#142711732
#142711592
C2×C29×#1372
#304429