Finite Group Databasebeta

← #16829021

Subgroups — #16829021

Order 3712.

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

normal subgroups only

This group has 458 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
1C2×#11745271C211yesmaximal, characteristic
2C22×#90785C211yesmaximal, characteristic, complemented
3#14271737C211yesmaximal, characteristic
4#14271640C211yesmaximal, characteristic, complemented
5#14271388C214yesmaximal, complemented
6#14271372C214yesmaximal, complemented
7#14271191C211yesmaximal, characteristic, complemented
8#14271157C211yesmaximal, characteristic
9C29×#419C211yesmaximal, characteristic, complemented
10C22×Q8×C29C2211yescharacteristic
11C2×#90805C2211yescharacteristic
12C22×Dic58C2211yescharacteristic
13C2×M16×C29C2211yescharacteristic
14C29×#117C2211yescharacteristic
15#11745309C2212yes—
16#11745308—22no—
17#11745306C2212yes—
18C2×#90785—24no—
19C2×#90785C2214yes—
20#11745291—22no—
21#11745288C2211yescharacteristic
22C22×#6597C2211yescharacteristic
23#11745271—24no—
24C2×Dic116C2212yes—
25C2×#90773C2212yes—
26#11745249C2214yes—
27#11745239—22no—
28C4×Dic58—22no—
29C29×#103C2214yes—
30#11745162C2214yes—
31#11745158C2212yes—
32#11745157C2212yes—
33C2×Q8×C29—21no—
34C2×Q8×C29—22no—
35C2×Q8×C29—22no—
36C2×Q8×C29C2312yes—
37C22×C4×C29—21no—
38C22×C4×C29C2311yescharacteristic
39C2×C22⋊D29—21no—
40C22×Dic29—21no—
41#90805—22no—
42#90805—22no—
43C2×D116C2311yescharacteristic
44C2×C4×D29—21no—
45C2×Dic58—21no—
46C2×Dic58—22no—
47C2×Dic58D414yes—
48C2×Dic58C2311yescharacteristic
49C2×Dic58C2312yes—
50M16×C29—22no—
51C2×C8×C29C2312yes—
52C4⋊C4×C29C2312yes—
53C22⋊C4×C29—21no—
54C42×C29—21no—
55C22⋊Dic29D412yes—
56#90785—28no—
57#90781—24no—
58C4⋊Dic29D412yes—
59#90779—24no—
60#90779—24no—
61C4×Dic29—24no—
62C4×Dic29C2312yes—
63C2×#6597—22no—
64C2×#6597C2312yes—
65Dic116—24no—
66#90773—24no—
67C23×C29C2×D411yescharacteristic
68C22×D29—21no—
69Q8×C29—22no—
70Q8×C29—22no—
71Q8×C29—42no—
72C2×C4×C29—22no—
73C2×C4×C29—22no—
74C2×C4×C29—42no—
75C2×C4×C29C2×D411yescharacteristic
76C2×C4×C29C2×D412yes—
77C2×C4×C29#4112yes—
78C2×C4×C29C2411yescharacteristic
79C22⋊D29—42no—
80C2×Dic29—24no—
81C2×Dic29—22no—
82C2×Dic29—21no—
83C2×Dic29C2×D414yes—
84D116—21no—
85D116—21no—
86C4×D29—42no—
87Dic58—24no—
88Dic58—22no—
89Dic58—21no—
90Dic58—21no—
91Dic58C2×D414yes—
92C8×C29—22no—
93#6597—22no—
94#3044—291nomaximal, Sylow
95C22×C29—22no—
96C22×C29#12112yes—
97C22×C29C22×D411yescharacteristic
98C2×D29—41no—
99C2×D29—42no—
100C4×C29—42no—
101C4×C29—42no—
102C4×C29#12112yes—
103C4×C29C22×D411yescharacteristic
104C4×C29C2×#4111yescharacteristic
105Dic29—24no—
106Dic29—24no—
107Dic29—41no—
108C2×#137—291no—
109C22×Q16—291no—
110#536—291no—
111#519—291no—
112#464—294no—
113#462—294no—
114#424—291no—
115#419D2911yescharacteristic, complemented
116#416—291no—
117C2×C29—22no—
118C2×C29C2×#12111yescharacteristic
119C2×C29#57812yes—
120D29—81no—
121C2×#41—291no—
122C22×Q8—291no—
123C22×Q8C2×D2911yescharacteristic
124#137—584no—
125C2×Q16—294no—
126C2×Q16—292no—
127C2×Q16—584no—
128C2×SD16—292no—
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—582no—
139#117C2×D2911yescharacteristic
140C4⋊C8—294no—
141#103—292no—
142#103C2×D2914yes—
143#102—292no—
144C29#304411yescharacteristic, complemented, Sylow
145#41—582no—
146#41—582no—
147C2×Q8—21no—
148C2×Q8—22no—
149C2×Q8—22no—
150C2×Q8—294no—
151C2×Q8—292no—
152C2×Q8—291no—
153C2×Q8—582no—
154C2×Q8—581no—
155C2×Q8C22×D2912yes—
156C2×D4—291no—
157C2×D4—581no—
158C22×C4—21no—
159C22×C4—581no—
160C22×C4—581no—
161C22×C4C22×D2911yescharacteristic
162Q16—584no—
163Q16—588no—
164SD16—584no—
165M16—22no—
166C2×C8—292no—
167C2×C8—582no—
168C2×C8C22×D2912yes—
169C4⋊C4—292no—
170C4⋊C4—584no—
171C4⋊C4—584no—
172C4⋊C4C22×D2912yes—
173C22⋊C4—21no—
174C22⋊C4—292no—
175C22⋊C4—584no—
176C42—21no—
177C42—292no—
178C42—584no—
179C23—581no—
180C23D4×D2911yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—42no—
184Q8—294no—
185Q8—582no—
186Q8—584no—
187Q8—581no—
188Q8—581no—
189D4—581no—
190D4—581no—
191D4—1162no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—294no—
196C2×C4—582no—
197C2×C4—584no—
198C2×C4—581no—
199C2×C4—1162no—
200C2×C4#9080512yes—
201C2×C4D4×D2912yes—
202C2×C4D4×D2911yescharacteristic
203C2×C4C23×D2911yescharacteristic
204C8—22no—
205C8—582no—
206C22—22no—
207C22—1161no—
208C22—1162no—
209C22#1174524612yes—
210C22C2×D4×D2911yescharacteristic
211C4—42no—
212C4—42no—
213C4—584no—
214C4—584no—
215C4—1161no—
216C4#1174524612yes—
217C4C2×#9080511yescharacteristic
218C4C2×D4×D2911yescharacteristic
219C2—22no—
220C2—2321no—
221C2C2×#1174524611yescharacteristic
222C2#1427197912yes—
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#419C2
socleC22×C29C22×D4
prime radicalC2×#90805C22
hypercenter#419D29
hypocenterC29#3044
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
2. C22×#90785C2semidirect
4. #14271640C2semidirect
5. #14271388C2semidirect
6. #14271372C2semidirect
7. #14271191C2semidirect
9. C29×#419C2semidirect
115. #419D29semidirect
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×#907852
#142717372
#142716402
#142713882
#142713722
#142711912
#142711572
C29×#4192
#304429