Finite Group Databasebeta

← #16829023

Subgroups — #16829023

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
1C2×#11745271C211yesmaximal, characteristic
2C22×Dic116C211yesmaximal, characteristic, complemented
3#14271739C211yesmaximal, characteristic
4#14271640C211yesmaximal, characteristic, complemented
5#14271386C214yesmaximal, complemented
6#14271374C214yesmaximal, complemented
7#14271173C211yesmaximal, characteristic, complemented
8#14271160C211yesmaximal, characteristic
9C29×#424C211yesmaximal, characteristic, complemented
10C2×#90805C2211yescharacteristic
11C22×Dic58C2211yescharacteristic
12C22×Dic58C2211yescharacteristic
13C2×M16×C29C2211yescharacteristic
14C22×C8×C29C2211yescharacteristic
15C29×#117C2211yescharacteristic
16#11745288C2211yescharacteristic
17#11745271—24no—
18C2×Dic116—24no—
19C2×Dic116C2212yes—
20C2×Dic116C2214yes—
21C2×#90773C2212yes—
22#11745259—22no—
23#11745249—22no—
24#11745248—22no—
25#11745239—22no—
26#11745237C2212yes—
27#11745231C2212yes—
28C4×Dic58C2214yes—
29C29×C4⋊C8C2214yes—
30#11745169C2212yes—
31#11745164C2212yes—
32#11745164C2214yes—
33C22×C4×C29C2311yescharacteristic
34C2×C22⋊D29—21no—
35C22×Dic29—21no—
36C22×Dic29—21no—
37#90805—22no—
38#90805—22no—
39C2×D116C2311yescharacteristic
40C2×C4×D29—21no—
41C2×Dic58—21no—
42C2×Dic58—22no—
43C2×Dic58—22no—
44C2×Dic58—22no—
45C2×Dic58—21no—
46C2×Dic58D414yes—
47C2×Dic58C2312yes—
48C2×Dic58C2311yescharacteristic
49C2×Dic58C2312yes—
50M16×C29—22no—
51C2×C8×C29—22no—
52C2×C8×C29C2312yes—
53C2×C8×C29C2312yes—
54C4⋊C4×C29D412yes—
55C22⋊C4×C29D412yes—
56C42×C29C2312yes—
57C22⋊Dic29—21no—
58#90781—24no—
59C4⋊Dic29—24no—
60C4⋊Dic29C2312yes—
61#90779—24no—
62C4×Dic29—21no—
63C4×Dic29—24no—
64Dic116—28no—
65Dic116—24no—
66#90773—24no—
67C23×C29C2×D411yescharacteristic
68C22×D29—21no—
69C2×C4×C29C2×D414yes—
70C2×C4×C29C2×D411yescharacteristic
71C2×C4×C29C2×D412yes—
72C2×C4×C29#4112yes—
73C2×C4×C29C2411yescharacteristic
74C22⋊D29—42no—
75C2×Dic29—24no—
76C2×Dic29—22no—
77C2×Dic29—22no—
78C2×Dic29—21no—
79C2×Dic29—22no—
80C2×Dic29—42no—
81D116—21no—
82D116—21no—
83C4×D29—42no—
84Dic58—24no—
85Dic58—22no—
86Dic58—22no—
87Dic58—21no—
88Dic58—22no—
89Dic58—21no—
90Dic58—42no—
91Dic58C2×D414yes—
92C8×C29—22no—
93C8×C29—22no—
94#3044—291nomaximal, Sylow
95C22×C29—22no—
96C22×C29#12112yes—
97C22×C29C22×D411yescharacteristic
98C2×D29—41no—
99C2×D29—42no—
100C4×C29—24no—
101C4×C29#12112yes—
102C4×C29C22×D411yescharacteristic
103C4×C29C2×#4111yescharacteristic
104Dic29—24no—
105Dic29—42no—
106Dic29—41no—
107Dic29—42no—
108C2×#137—291no—
109C22×Q16—291no—
110#536—291no—
111#519—291no—
112#464—294no—
113#462—294no—
114#424D2911yescharacteristic, complemented
115#419—291no—
116#416—291no—
117C2×C29—22no—
118C2×C29C2×#12111yescharacteristic
119C2×C29#57812yes—
120D29—81no—
121C2×#41—291no—
122C22×Q8—291no—
123C22×Q8—291no—
124#137—584no—
125C2×Q16—294no—
126C2×Q16—292no—
127C2×Q16—584no—
128C2×SD16—292no—
129C2×M16C2×D2911yescharacteristic
130C22×C8C2×D2911yescharacteristic
131C4⋊Q8—292no—
132#124—292no—
133#123—582no—
134C22⋊Q8—582no—
135C4×Q8—294no—
136C4×Q8—582no—
137#117—291no—
138#117—582no—
139#117C2×D2911yescharacteristic
140C4⋊C8C2×D2914yes—
141#103—292no—
142#103—294no—
143#102—292no—
144C29#304411yescharacteristic, complemented, Sylow
145#41—582no—
146#41—582no—
147C2×Q8—294no—
148C2×Q8—292no—
149C2×Q8—292no—
150C2×Q8—291no—
151C2×Q8—581no—
152C2×Q8—581no—
153C2×Q8—582no—
154C2×Q8—582no—
155C2×Q8—582no—
156C2×D4—291no—
157C2×D4—581no—
158C22×C4—581no—
159C22×C4—581no—
160C22×C4—581no—
161C22×C4C22×D2911yescharacteristic
162Q16—588no—
163Q16—584no—
164SD16—584no—
165M16—22no—
166C2×C8—22no—
167C2×C8C22×D2912yes—
168C2×C8C22×D2912yes—
169C4⋊C4—292no—
170C4⋊C4—584no—
171C4⋊C4—584no—
172C4⋊C4D11612yes—
173C22⋊C4—581no—
174C22⋊C4—584no—
175C22⋊C4D11612yes—
176C42—581no—
177C42—584no—
178C42C22×D2912yes—
179C23—581no—
180C23C2×D11611yescharacteristic
181Q8—294no—
182Q8—582no—
183Q8—584no—
184Q8—582no—
185Q8—581no—
186Q8—582no—
187Q8—581no—
188Q8—1162no—
189D4—581no—
190D4—581no—
191D4—1162no—
192C2×C4—582no—
193C2×C4—584no—
194C2×C4—582no—
195C2×C4—582no—
196C2×C4—581no—
197C2×C4—1162no—
198C2×C4—1162no—
199C2×C4C2×D11614yes—
200C2×C4C2×D11611yescharacteristic
201C2×C4D4×D2912yes—
202C2×C4#9080912yes—
203C2×C4C23×D2911yescharacteristic
204C8—22no—
205C8—22no—
206C22—22no—
207C22—1161no—
208C22—1162no—
209C22#1174525712yes—
210C22C22×D11611yescharacteristic
211C4—24no—
212C4—584no—
213C4—1161no—
214C4—1162no—
215C4—1162no—
216C4#1174525712yes—
217C4C2×D4×D2911yescharacteristic
218C4C2×#9080911yescharacteristic
219C2—22no—
220C2—2321no—
221C2C2×#1174525711yescharacteristic
222C2#1427198012yes—
subgroupG/H
centerC22C22×D116
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#424C2
socleC22×C29C22×D4
prime radicalC2×#90805C22
hypercenter#424D29
hypocenterC29#3044
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ #117 ◁ #424

Complements

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

NH ≅ G/Ntype
2. C22×Dic116C2semidirect
4. #14271640C2semidirect
5. #14271386C2semidirect
6. #14271374C2semidirect
7. #14271173C2semidirect
9. C29×#424C2semidirect
114. #424D29semidirect
144. C29#3044semidirect

Maximal subgroups

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

subgroupindex
C2×#117452712
C22×Dic1162
#142717392
#142716402
#142713862
#142713742
#142711732
#142711602
C29×#4242
#304429