Finite Group Databasebeta

← #16818444

Subgroups — #16818444

Order 3712.

308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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#14271301C212yesmaximal, complemented
2#14271075C211yesmaximal, characteristic, complemented
3#14270897C212yesmaximal, complemented
4#14270887C211yesmaximal, characteristic, complemented
5C29×#534C211yesmaximal, characteristic
6C22×D4×C29—21no—
7C22×Dic58C2211yescharacteristic, complemented
8C29×#123—22no—
9C29×#121—21no—
10C29×#121C2212yes—
11C29×#120—22no—
12C2×C22⋊C4×C29C2211yescharacteristic
13C2×C22⋊Dic29—21no—
14C2×#90783—22no—
15#11745179—21no—
16#11745179C2211yescharacteristic, complemented
17C22⋊#6597C2212yescomplemented
18#11745158—22no—
19C24×C29—21no—
20C24×C29D411yescharacteristic
21C2×D4×C29—22no—
22C2×D4×C29—22no—
23C2×D4×C29—21no—
24C2×D4×C29—42no—
25C2×D4×C29—42no—
26C2×D4×C29D412yes—
27C22×C4×C29—21no—
28C22×C4×C29D411yescharacteristic
29C22×C4×C29C2311yescharacteristic
30C22×Dic29—21no—
31C22×Dic29—21no—
32C2×Dic58—22no—
33C2×Dic58—42no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29D412yes—
36C22⋊C4×C29—22no—
37C22⋊C4×C29—22no—
38C22⋊C4×C29—22no—
39C22⋊Dic29—42no—
40#90783—44no—
41C2×#6597—22no—
42C23×C29—21no—
43C23×C29—21no—
44C23×C29—22no—
45C23×C29—41no—
46C23×C29—41no—
47C23×C29—42no—
48C23×C29—81no—
49C23×C29—81no—
50C23×C29SD1612yescomplemented
51C23×C29C2×D411yescharacteristic
52D4×C29—42no—
53D4×C29—44no—
54D4×C29—42no—
55D4×C29—42no—
56D4×C29—81no—
57C2×C4×C29—21no—
58C2×C4×C29—22no—
59C2×C4×C29—41no—
60C2×C4×C29—42no—
61C2×C4×C29—41no—
62C2×C4×C29C2×D412yes—
63C2×Dic29—22no—
64C2×Dic29—41no—
65C2×Dic29—41no—
66C2×Dic29—41no—
67C2×Dic29—41no—
68C2×Dic29—41no—
69Dic58—24no—
70Dic58—42no—
71#6597—42no—
72#1601—291nomaximal, Sylow
73C22×C29—21no—
74C22×C29—21no—
75C22×C29—22no—
76C22×C29—42no—
77C22×C29—41no—
78C22×C29—41no—
79C22×C29—42no—
80C22×C29—42no—
81C22×C29—42no—
82C22×C29—81no—
83C22×C29—84no—
84C22×C29#12011yescharacteristic
85C22×C29C2×SD1611yescharacteristic
86C22×C29AGL(1,ℤ/8)11yescharacteristic
87C4×C29—22no—
88C4×C29—42no—
89C4×C29—41no—
90Dic29—42no—
91Dic29—81no—
92#534D2911yescharacteristic
93#448—292no—
94#393—291no—
95#327—292no—
96#323—291no—
97C2×C29—21no—
98C2×C29—21no—
99C2×C29—42no—
100C2×C29—82no—
101C2×C29#45011yescharacteristic
102C2×C29#45511yescharacteristic
103C2×C29B(4,𝔽2)11yescharacteristic
104C22×Q8—291no—
105C22×D4—21no—
106C2×SD16—582no—
107#123—22no—
108#121—21no—
109#121C2×D2912yes—
110#120—22no—
111C2×C22⋊C4—581no—
112C2×C22⋊C4C2×D2911yescharacteristic
113#103—582no—
114C22⋊C8—292no—
115#95—291no—
116#95—581no—
117C29#160111yescharacteristic, complemented, Sylow
118C24—21no—
119C24C22⋊D2911yescharacteristic
120C2×Q8—582no—
121C2×Q8—1162no—
122C2×D4—22no—
123C2×D4—22no—
124C2×D4—21no—
125C2×D4—42no—
126C2×D4—42no—
127C2×D4C22⋊D2912yes—
128C22×C4—21no—
129C22×C4—581no—
130C22×C4—581no—
131C22×C4C22⋊D2911yescharacteristic
132C22×C4C22×D2911yescharacteristic
133SD16—1164no—
134C2×C8—582no—
135C4⋊C4—21no—
136C4⋊C4C22⋊D2912yes—
137C22⋊C4—22no—
138C22⋊C4—22no—
139C22⋊C4—22no—
140C22⋊C4—1162no—
141C23—21no—
142C23—21no—
143C23—22no—
144C23—41no—
145C23—41no—
146C23—42no—
147C23—81no—
148C23—81no—
149C23#9078312yescomplemented
150C23C2×C22⋊D2911yescharacteristic
151Q8—584no—
152Q8—1162no—
153D4—42no—
154D4—44no—
155D4—42no—
156D4—42no—
157D4—81no—
158C2×C4—21no—
159C2×C4—22no—
160C2×C4—41no—
161C2×C4—42no—
162C2×C4—41no—
163C2×C4—582no—
164C2×C4—1161no—
165C2×C4—1161no—
166C2×C4—1161no—
167C2×C4—1161no—
168C2×C4—1161no—
169C2×C4C2×C22⋊D2912yes—
170C8—1162no—
171C22—21no—
172C22—21no—
173C22—22no—
174C22—42no—
175C22—41no—
176C22—41no—
177C22—42no—
178C22—42no—
179C22—42no—
180C22—81no—
181C22—84no—
182C22#1174529411yescharacteristic
183C22C2×#9078311yescharacteristic
184C22#1174531511yescharacteristic
185C4—22no—
186C4—42no—
187C4—41no—
188C4—1162no—
189C4—2321no—
190C2—21no—
191C2—21no—
192C2—42no—
193C2—82no—
194C2#1427131411yescharacteristic
195C2#1427134111yescharacteristic
196C2#1427135011yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
Fitting, prime radicalC29×#534C2
socleC22×C29#120
hypercenter#534D29
hypocenterC29#1601
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #534

Complements

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

NH ≅ G/Ntype
1. #14271301C2semidirect
2. #14271075C2semidirect
3. #14270897C2semidirect
4. #14270887C2semidirect
7. C22×Dic58C22semidirect
16. #11745179C22semidirect
17. C22⋊#6597C22semidirect
50. C23×C29SD16semidirect
117. C29#1601semidirect
149. C23#90783semidirect

Maximal subgroups

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

subgroupindex
#142713012
#142710752
#142708972
#142708872
C29×#5342
#160129