Finite Group Databasebeta

← #16818467

Subgroups — #16818467

Order 3712.

238 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 51 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#14271792C211yesmaximal, characteristic
2#14271321C211yesmaximal, characteristic
3#14271318C211yesmaximal, characteristic
4#14271084C211yesmaximal, characteristic
5#14270899C211yesmaximal, characteristic
6#14270888C211yesmaximal, characteristic
7C29×#328C211yesmaximal, characteristic
8C22×Dic58C2211yescharacteristic
9C29×C22⋊Q8C2211yescharacteristic
10#11745306—21no—
11C2×#90785—21no—
12C2×C4⋊Dic29—21no—
13#11745286C2211yescharacteristic
14C2×#90779C2211yescharacteristic
15C2×Dic116—21no—
16#11745251—21no—
17#11745251—21no—
18#11745250—21no—
19#11745240—21no—
20#11745239—21no—
21C29×C22⋊C8C2211yescharacteristic
22C29×#95C2211yescharacteristic
23#11745179—21no—
24C22⋊#6597C2211yescharacteristic
25#11745164—21no—
26#11745158—21no—
27C2×Q8×C29D411yescharacteristic
28C22×C4×C29—21no—
29C22×C4×C29C2311yescharacteristic
30C22×Dic29—21no—
31C22×Dic29D411yescharacteristic
32C22×Dic29D411yescharacteristic
33C2×Dic58—21no—
34C2×Dic58—21no—
35C2×Dic58—21no—
36C2×Dic58—42no—
37C2×Dic58D411yescharacteristic
38C2×C8×C29—21no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29D411yescharacteristic
41C22⋊C4×C29—21no—
42C22⋊Dic29—21no—
43#90785—42no—
44C4⋊Dic29—21no—
45C4⋊Dic29—42no—
46C4⋊Dic29D411yescharacteristic
47#90779—21no—
48#90779—21no—
49#90779—21no—
50#90779—21no—
51#90779—21no—
52#90779—21no—
53#90779—21no—
54C4×Dic29—21no—
55C4×Dic29—21no—
56C2×#6597—21no—
57Dic116—42no—
58C23×C29C2×D411yescharacteristic
59Q8×C29—41no—
60C2×C4×C29—22no—
61C2×C4×C29—21no—
62C2×C4×C29—21no—
63C2×C4×C29—41no—
64C2×C4×C29—41no—
65C2×C4×C29—41no—
66C2×C4×C29C2×D411yescharacteristic
67C2×C4×C29C2×D411yescharacteristic
68C2×Dic29—21no—
69C2×Dic29—21no—
70C2×Dic29—22no—
71C2×Dic29—21no—
72C2×Dic29—21no—
73C2×Dic29—21no—
74C2×Dic29—41no—
75C2×Dic29—41no—
76C2×Dic29—41no—
77C2×Dic29Q1612yescomplemented
78Dic58—22no—
79Dic58—22no—
80Dic58—41no—
81Dic58—41no—
82Dic58—41no—
83Dic58—81no—
84C8×C29—41no—
85#6597—41no—
86#1605—291nomaximal, Sylow
87C22×C29—21no—
88C22×C29—21no—
89C22×C29#12011yescharacteristic
90C22×C29C2×Q1611yescharacteristic
91C22×C29#13711yescharacteristic
92C4×C29—21no—
93C4×C29—21no—
94C4×C29—42no—
95C4×C29—41no—
96C4×C29—41no—
97Dic29—22no—
98Dic29—41no—
99Dic29—42no—
100Dic29—41no—
101Dic29—41no—
102#544—291no—
103#451—291no—
104#451—291no—
105#395—291no—
106#328—291no—
107#328D2911yescharacteristic
108#324—291no—
109C2×C29—21no—
110C2×C29—21no—
111C2×C29#45111yescharacteristic
112C2×C29#45611yescharacteristic
113C2×C29B(4,𝔽2)11yescharacteristic
114C22×Q8—291no—
115C2×Q16—581no—
116C2×Q16—581no—
117C4⋊Q8—581no—
118C4⋊Q8—581no—
119#125—581no—
120#125—581no—
121C22⋊Q8—291no—
122C22⋊Q8—581no—
123C22⋊Q8C2×D2911yescharacteristic
124#117—581no—
125C2×C4⋊C4—291no—
126C2×C4⋊C4—581no—
127#103—581no—
128#103—581no—
129C22⋊C8—291no—
130C22⋊C8C2×D2911yescharacteristic
131#95—581no—
132#95C2×D2911yescharacteristic
133C29#160511yescharacteristic, complemented, Sylow
134C2×Q8—291no—
135C2×Q8—581no—
136C2×Q8—581no—
137C2×Q8—581no—
138C2×Q8—1162no—
139C2×Q8D11611yescharacteristic
140C22×C4—21no—
141C22×C4—291no—
142C22×C4—291no—
143C22×C4—581no—
144C22×C4C22×D2911yescharacteristic
145Q16—1162no—
146Q16—1162no—
147C2×C8—21no—
148C2×C8—581no—
149C4⋊C4—21no—
150C4⋊C4—291no—
151C4⋊C4—581no—
152C4⋊C4—581no—
153C4⋊C4—581no—
154C4⋊C4—581no—
155C4⋊C4—581no—
156C4⋊C4—581no—
157C4⋊C4—581no—
158C4⋊C4—581no—
159C4⋊C4—1162no—
160C4⋊C4D11611yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—581no—
163C42—581no—
164C42—581no—
165C23D4×D2911yescharacteristic
166Q8—41no—
167Q8—582no—
168Q8—582no—
169Q8—1161no—
170Q8—1161no—
171Q8—1161no—
172Q8—2321no—
173C2×C4—22no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—41no—
179C2×C4—292no—
180C2×C4—581no—
181C2×C4—581no—
182C2×C4—582no—
183C2×C4—581no—
184C2×C4—581no—
185C2×C4—581no—
186C2×C4—1161no—
187C2×C4—1161no—
188C2×C4—1161no—
189C2×C4C2×D11611yescharacteristic
190C2×C4D4×D2911yescharacteristic
191C8—41no—
192C8—1161no—
193C22—21no—
194C22—21no—
195C22#1174524411yescharacteristic
196C22#1174527711yescharacteristic
197C22Q16×D2911yescharacteristic
198C4—21no—
199C4—21no—
200C4—42no—
201C4—41no—
202C4—41no—
203C4—582no—
204C4—1161no—
205C4—1162no—
206C4—1161no—
207C4—1161no—
208C2—21no—
209C2—21no—
210C2#1427132011yescharacteristic
211C2#1427134711yescharacteristic
212C2#1427135111yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#328C2
socleC22×C29#120
prime radicalC23×C29C2×D4
hypercenter#328D29
hypocenterC29#1605
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
77. C2×Dic29Q16semidirect
133. C29#1605semidirect

Maximal subgroups

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

subgroupindex
#142717922
#142713212
#142713182
#142710842
#142708992
#142708882
C29×#3282
#160529