Finite Group Databasebeta

← #16818464

Subgroups — #16818464

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#14271319C211yesmaximal, characteristic
3#14271082C211yesmaximal, characteristic
4#14270901C211yesmaximal, characteristic
5#14270900C211yesmaximal, characteristic
6#14270888C211yesmaximal, characteristic
7C29×#451C211yesmaximal, characteristic
8C22×Q8×C29C2211yescharacteristic
9C2×Q16×C29—21no—
10C29×C22⋊Q8C2211yescharacteristic
11#11745306—21no—
12C2×#90785—21no—
13#11745286C2211yescharacteristic
14C2×#90779—21no—
15C2×#90779C2211yescharacteristic
16#11745251—21no—
17#11745251—21no—
18#11745250—21no—
19#11745240—21no—
20#11745239—21no—
21C29×#103—21no—
22C29×C22⋊C8C2211yescharacteristic
23#11745183—21no—
24#11745179—21no—
25#11745179C2211yescharacteristic
26C22⋊#6597C2211yescharacteristic
27C2×Q8×C29—21no—
28C2×Q8×C29—21no—
29C2×Q8×C29—42no—
30C2×Q8×C29D411yescharacteristic
31C22×C4×C29—21no—
32C22×C4×C29C2311yescharacteristic
33C22×Dic29—21no—
34C22×Dic29D411yescharacteristic
35C22×Dic29D411yescharacteristic
36C2×Dic58—21no—
37C2×Dic58D411yescharacteristic
38Q16×C29—42no—
39C2×C8×C29—21no—
40C4⋊C4×C29—21no—
41C4⋊C4×C29D411yescharacteristic
42C22⋊C4×C29—21no—
43C22⋊Dic29—21no—
44#90785—42no—
45C4⋊Dic29—21no—
46C4⋊Dic29D411yescharacteristic
47#90779—21no—
48#90779—21no—
49#90779—21no—
50#90779—21no—
51#90779—21no—
52#90779—21no—
53#90779—21no—
54#90779—42no—
55C4×Dic29—21no—
56C4×Dic29—21no—
57C2×#6597—21no—
58C23×C29C2×D411yescharacteristic
59Q8×C29—22no—
60Q8×C29—22no—
61Q8×C29—41no—
62Q8×C29—41no—
63Q8×C29—41no—
64C2×C4×C29—22no—
65C2×C4×C29—21no—
66C2×C4×C29—21no—
67C2×C4×C29—41no—
68C2×C4×C29—41no—
69C2×C4×C29—41no—
70C2×C4×C29C2×D411yescharacteristic
71C2×C4×C29C2×D411yescharacteristic
72C2×Dic29—21no—
73C2×Dic29—21no—
74C2×Dic29—22no—
75C2×Dic29—21no—
76C2×Dic29—21no—
77C2×Dic29—21no—
78C2×Dic29—41no—
79C2×Dic29—41no—
80C2×Dic29—41no—
81C2×Dic29Q1612yescomplemented
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—41no—
95C4×C29—41no—
96C4×C29—42no—
97Dic29—22no—
98Dic29—42no—
99Dic29—41no—
100Dic29—41no—
101Dic29—41no—
102#544—291no—
103#451—291no—
104#451D2911yescharacteristic
105#395—291no—
106#328—291no—
107#328—291no—
108#324—291no—
109C2×C29—21no—
110C2×C29—21no—
111C2×C29#45111yescharacteristic
112C2×C29#45611yescharacteristic
113C2×C29B(4,𝔽2)11yescharacteristic
114C22×Q8C2×D2911yescharacteristic
115C2×Q16—21no—
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—21no—
128#103—581no—
129C22⋊C8—291no—
130C22⋊C8C2×D2911yescharacteristic
131#95—291no—
132#95—581no—
133C29#160511yescharacteristic, complemented, Sylow
134C2×Q8—21no—
135C2×Q8—21no—
136C2×Q8—42no—
137C2×Q8—291no—
138C2×Q8—581no—
139C2×Q8C22⋊D2911yescharacteristic
140C22×C4—21no—
141C22×C4—291no—
142C22×C4—291no—
143C22×C4—581no—
144C22×C4C22×D2911yescharacteristic
145Q16—42no—
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⋊C4C22⋊D2911yescharacteristic
161C22⋊C4—21no—
162C22⋊C4—581no—
163C42—581no—
164C42—581no—
165C23D4×D2911yescharacteristic
166Q8—22no—
167Q8—22no—
168Q8—41no—
169Q8—41no—
170Q8—41no—
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×C4D4×D2911yescharacteristic
190C2×C4C2×C22⋊D2911yescharacteristic
191C8—41no—
192C8—1161no—
193C22—21no—
194C22—21no—
195C22Q16×D2911yescharacteristic
196C22#1174528011yescharacteristic
197C22#1174529911yescharacteristic
198C4—21no—
199C4—21no—
200C4—41no—
201C4—42no—
202C4—41no—
203C4—582no—
204C4—1162no—
205C4—1161no—
206C4—1161no—
207C4—1161no—
208C2—21no—
209C2—21no—
210C2#1427131711yescharacteristic
211C2#1427134411yescharacteristic
212C2#1427134911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#451C2
socleC22×C29#120
prime radicalC23×C29C2×D4
hypercenter#451D29
hypocenterC29#1605
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
81. 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
#142713192
#142710822
#142709012
#142709002
#142708882
C29×#4512
#160529