Finite Group Databasebeta

← #16818427

Subgroups — #16818427

Order 3712.

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

normal subgroups only

This group has 310 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#14271296C212yesmaximal, complemented
2#14271080C211yesmaximal, characteristic, complemented
3#14270897C212yesmaximal, complemented
4#14270889C211yesmaximal, characteristic, complemented
5C29×#537C211yesmaximal, characteristic, complemented
6C2×#41×C29—21no—
7C22×D116C2211yescharacteristic
8C29×C22⋊Q8—22no—
9C29×#121—22no—
10C29×#121—21no—
11C29×#121C2212yes—
12C2×C4⋊C4×C29C2211yescharacteristic
13C2×#90782—22no—
14C2×#90781—21no—
15C2×#90781—21no—
16#11745179C2211yescharacteristic
17C22⋊#6597C2212yes—
18#11745157—22no—
19C23×D29—21no—
20#41×C29—42no—
21#41×C29—42no—
22C2×Q8×C29—21no—
23C2×D4×C29—21no—
24C2×D4×C29—22no—
25C2×D4×C29—21no—
26C2×D4×C29D412yes—
27C22×C4×C29—22no—
28C22×C4×C29D411yescharacteristic
29C22×C4×C29D411yescharacteristic
30C22×C4×C29C2311yescharacteristic
31C22×Dic29—21no—
32C2×D116—22no—
33C2×D116—42no—
34C4⋊C4×C29—21no—
35C4⋊C4×C29—22no—
36C4⋊C4×C29D412yes—
37C22⋊C4×C29—22no—
38C22⋊C4×C29—22no—
39#90782—44no—
40#90781—42no—
41#90781—42no—
42C2×#6597—22no—
43C23×C29—22no—
44C23×C29C2×D411yescharacteristic
45C22×D29—22no—
46C22×D29—41no—
47C22×D29—41no—
48C22×D29—41no—
49C22×D29—41no—
50C22×D29—41no—
51C22×D29—41no—
52Q8×C29—42no—
53D4×C29—42no—
54D4×C29—42no—
55D4×C29—42no—
56D4×C29—42no—
57D4×C29—81no—
58C2×C4×C29—21no—
59C2×C4×C29—21no—
60C2×C4×C29—21no—
61C2×C4×C29—22no—
62C2×C4×C29—41no—
63C2×C4×C29—44no—
64C2×C4×C29—41no—
65C2×C4×C29D812yescomplemented
66C2×C4×C29C2×D412yes—
67C2×Dic29—41no—
68C2×Dic29—41no—
69C2×Dic29—41no—
70D116—24no—
71D116—42no—
72#6597—42no—
73#1598—291nomaximal, Sylow
74C22×C29—21no—
75C22×C29—21no—
76C22×C29—42no—
77C22×C29—42no—
78C22×C29—42no—
79C22×C29#12011yescharacteristic
80C22×C29C2×D811yescharacteristic
81C22×C29AGL(1,ℤ/8)11yescharacteristic
82C2×D29—42no—
83C2×D29—42no—
84C2×D29—42no—
85C2×D29—81no—
86C2×D29—81no—
87C2×D29—81no—
88C2×D29—81no—
89C4×C29—22no—
90C4×C29—22no—
91C4×C29—42no—
92C4×C29—41no—
93Dic29—81no—
94#537D2911yescharacteristic, complemented
95#447—292no—
96#394—291no—
97#327—292no—
98#324—291no—
99C2×C29—21no—
100C2×C29—21no—
101C2×C29—82no—
102C2×C29#44711yescharacteristic
103C2×C29#45411yescharacteristic
104C2×C29B(4,𝔽2)11yescharacteristic
105D29—82no—
106C2×#41—21no—
107C22×D4—291no—
108C2×D8—582no—
109C22⋊Q8—22no—
110#121—22no—
111#121—21no—
112#121C2×D2912yes—
113C2×C4⋊C4C2×D2911yescharacteristic
114C2×C22⋊C4—581no—
115C2×C22⋊C4—581no—
116#102—582no—
117C22⋊C8—292no—
118#95—291no—
119C29#159811yescharacteristic, complemented, Sylow
120C24—581no—
121#41—42no—
122#41—42no—
123C2×Q8—21no—
124C2×D4—21no—
125C2×D4—22no—
126C2×D4—21no—
127C2×D4—582no—
128C2×D4—1162no—
129C2×D4C22⋊D2912yes—
130C22×C4—22no—
131C22×C4—581no—
132C22×C4C22⋊D2911yescharacteristic
133C22×C4C22⋊D2911yescharacteristic
134C22×C4C22×D2911yescharacteristic
135D8—1164no—
136C2×C8—582no—
137C4⋊C4—21no—
138C4⋊C4—22no—
139C4⋊C4C22⋊D2912yes—
140C22⋊C4—22no—
141C22⋊C4—22no—
142C22⋊C4—1162no—
143C22⋊C4—1162no—
144C23—22no—
145C23—582no—
146C23—1161no—
147C23—1161no—
148C23—1161no—
149C23—1161no—
150C23—1161no—
151C23—1161no—
152C23C2×C22⋊D2911yescharacteristic
153Q8—42no—
154D4—42no—
155D4—42no—
156D4—42no—
157D4—42no—
158D4—81no—
159D4—584no—
160D4—1162no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—22no—
165C2×C4—41no—
166C2×C4—44no—
167C2×C4—41no—
168C2×C4—1161no—
169C2×C4—1161no—
170C2×C4—1161no—
171C2×C4#9078212yescomplemented
172C2×C4C2×C22⋊D2912yes—
173C8—1162no—
174C22—21no—
175C22—21no—
176C22—42no—
177C22—42no—
178C22—42no—
179C22—1162no—
180C22—1162no—
181C22—1162no—
182C22—2321no—
183C22—2321no—
184C22—2321no—
185C22—2321no—
186C22C2×#9078211yescharacteristic
187C22#1174529411yescharacteristic
188C22#1174531511yescharacteristic
189C4—22no—
190C4—22no—
191C4—42no—
192C4—41no—
193C4—2321no—
194C2—21no—
195C2—21no—
196C2—82no—
197C2—2322no—
198C2#1427129711yescharacteristic
199C2#1427133611yescharacteristic
200C2#1427135011yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#537C2
socleC22×C29#120
hypercenter#537D29
hypocenterC29#1598
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. #14271296C2semidirect
2. #14271080C2semidirect
3. #14270897C2semidirect
4. #14270889C2semidirect
5. C29×#537C2semidirect
65. C2×C4×C29D8semidirect
94. #537D29semidirect
119. C29#1598semidirect
171. C2×C4#90782semidirect

Maximal subgroups

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

subgroupindex
#142712962
#142710802
#142708972
#142708892
C29×#5372
#159829