Finite Group Databasebeta

← #16818429

Subgroups — #16818429

Order 3712.

310 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 310 conjugacy classes of subgroups — too many to draw. Only its 53 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#14271744C211yesmaximal, characteristic, complemented
2#14271299C212yesmaximal, complemented
3#14271080C211yesmaximal, characteristic, complemented
4#14270898C212yesmaximal, complemented
5C29×#324C211yesmaximal, characteristic, complemented
6C2×#90805—21no—
7C22×D116C2211yescharacteristic
8C2×C4⋊C4×C29C2211yescharacteristic
9#11745292—21no—
10#11745292C2212yes—
11C2×#90781—21no—
12C2×#90781—21no—
13C2×D232—22no—
14#11745259—22no—
15#11745257—22no—
16C29×C22⋊C8C2212yes—
17#11745179C2211yescharacteristic
18#11745169—22no—
19C23×D29—21no—
20C22×C4×C29D411yescharacteristic
21C22×C4×C29D411yescharacteristic
22C22×C4×C29C2311yescharacteristic
23C2×C22⋊D29—22no—
24C22×Dic29—21no—
25#90805—42no—
26#90805—42no—
27C2×D116—22no—
28C2×D116—21no—
29C2×D116—21no—
30C2×D116—42no—
31C2×D116D412yes—
32C2×C4×D29—22no—
33C2×Dic58—21no—
34C2×C8×C29—22no—
35C4⋊C4×C29—22no—
36#90781—22no—
37#90781—22no—
38#90781—42no—
39#90781—42no—
40C4⋊Dic29—21no—
41C4⋊Dic29D412yes—
42D232—44no—
43C23×C29C2×D411yescharacteristic
44C22×D29—22no—
45C22×D29—22no—
46C22×D29—41no—
47C22×D29—41no—
48C22×D29—41no—
49C22×D29—41no—
50C22×D29—41no—
51C22×D29—41no—
52C2×C4×C29—21no—
53C2×C4×C29—21no—
54C2×C4×C29—21no—
55C2×C4×C29—41no—
56C2×C4×C29—41no—
57C2×C4×C29D812yescomplemented
58C2×C4×C29C2×D412yes—
59C22⋊D29—42no—
60C22⋊D29—42no—
61C2×Dic29—22no—
62C2×Dic29—41no—
63C2×Dic29—41no—
64C2×Dic29—41no—
65D116—24no—
66D116—42no—
67D116—42no—
68D116—42no—
69D116—81no—
70C4×D29—44no—
71Dic58—42no—
72C8×C29—42no—
73#1598—291nomaximal, Sylow
74C22×C29—21no—
75C22×C29—21no—
76C22×C29#12011yescharacteristic
77C22×C29C2×D811yescharacteristic
78C22×C29AGL(1,ℤ/8)11yescharacteristic
79C2×D29—42no—
80C2×D29—42no—
81C2×D29—42no—
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—41no—
92Dic29—42no—
93Dic29—81no—
94#537—291no—
95#447—292no—
96#394—291no—
97#327—292no—
98#324D2911yescharacteristic, complemented
99C2×C29—21no—
100C2×C29—21no—
101C2×C29#44711yescharacteristic
102C2×C29#45411yescharacteristic
103C2×C29B(4,𝔽2)11yescharacteristic
104D29—82no—
105D29—82no—
106C2×#41—581no—
107C22×D4—291no—
108C2×D8—582no—
109C22⋊Q8—582no—
110#121—292no—
111#121—582no—
112#121—581no—
113C2×C4⋊C4C2×D2911yescharacteristic
114C2×C22⋊C4—581no—
115C2×C22⋊C4—581no—
116#102—582no—
117C22⋊C8C2×D2912yes—
118#95—291no—
119C29#159811yescharacteristic, complemented, Sylow
120C24—581no—
121#41—1162no—
122#41—1162no—
123C2×Q8—581no—
124C2×D4—292no—
125C2×D4—581no—
126C2×D4—581no—
127C2×D4—582no—
128C2×D4—582no—
129C2×D4—1162no—
130C22×C4—582no—
131C22×C4—581no—
132C22×C4D11611yescharacteristic
133C22×C4D11611yescharacteristic
134C22×C4C22×D2911yescharacteristic
135D8—1164no—
136C2×C8—22no—
137C4⋊C4—22no—
138C4⋊C4—292no—
139C4⋊C4—581no—
140C22⋊C4—582no—
141C22⋊C4—582no—
142C22⋊C4—1162no—
143C22⋊C4—1162no—
144C23—582no—
145C23—582no—
146C23—1161no—
147C23—1161no—
148C23—1161no—
149C23—1161no—
150C23—1161no—
151C23—1161no—
152C23C2×D11611yescharacteristic
153Q8—1162no—
154D4—584no—
155D4—1162no—
156D4—1162no—
157D4—1162no—
158D4—1162no—
159D4—1162no—
160D4—2321no—
161C2×C4—21no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—582no—
167C2×C4—1164no—
168C2×C4—1161no—
169C2×C4—1161no—
170C2×C4—1161no—
171C2×C4D23212yescomplemented
172C2×C4D4×D2912yes—
173C8—42no—
174C22—21no—
175C22—21no—
176C22—1162no—
177C22—1162no—
178C22—1162no—
179C22—1162no—
180C22—1162no—
181C22—1162no—
182C22—2321no—
183C22—2321no—
184C22—2321no—
185C22—2321no—
186C22#1174524411yescharacteristic
187C22C2×D23211yescharacteristic
188C22#1174527011yescharacteristic
189C4—22no—
190C4—22no—
191C4—41no—
192C4—1162no—
193C4—2321no—
194C2—21no—
195C2—21no—
196C2—2322no—
197C2—2322no—
198C2#1427129911yescharacteristic
199C2#1427133811yescharacteristic
200C2#1427135111yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#324C2
socleC22×C29#120
hypercenter#324D29
hypocenterC29#1598
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
1. #14271744C2semidirect
2. #14271299C2semidirect
3. #14271080C2semidirect
4. #14270898C2semidirect
5. C29×#324C2semidirect
57. C2×C4×C29D8semidirect
98. #324D29semidirect
119. C29#1598semidirect
171. C2×C4D232semidirect

Maximal subgroups

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

subgroupindex
#142717442
#142712992
#142710802
#142708982
C29×#3242
#159829