Finite Group Databasebeta

← #16817989

Subgroups — #16817989

Order 3712.

240 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 71 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#14271715C211yesmaximal, characteristic
2#14271213C211yesmaximal, characteristic
3#14271014C211yesmaximal, characteristic
4#14270901C211yesmaximal, characteristic
5#14270900C211yesmaximal, characteristic
6#14270899C211yesmaximal, characteristic
7C29×#328C211yesmaximal, characteristic
8C29×C22⋊Q8C2211yescharacteristic
9Q8×Dic29C411yescharacteristic, complemented
10#11745306C411yescharacteristic, complemented
11#11745286C2211yescharacteristic
12C2×#90779—21no—
13C2×C4×Dic29—21no—
14C2×C4×Dic29C2211yescharacteristic
15#11745251—21no—
16#11745250C411yescharacteristic, complemented
17#11745249—21no—
18#11745249C411yescharacteristic, complemented
19#11745240—21no—
20#11745239—21no—
21C29×C22⋊C8C2211yescharacteristic
22C29×#95C2211yescharacteristic
23#11745179C2211yescharacteristic
24C22⋊#6597C2211yescharacteristic
25#11745162—21no—
26C8×Dic29—21no—
27C2×Q8×C29C2×C411yescharacteristic
28C22×C4×C29—21no—
29C22×C4×C29C2311yescharacteristic
30C22×Dic29—21no—
31C22×Dic29D411yescharacteristic
32C22×Dic29D411yescharacteristic
33C2×Dic58—21no—
34C2×Dic58C2×C411yescharacteristic
35C2×C8×C29—21no—
36C4⋊C4×C29—21no—
37C4⋊C4×C29C2×C411yescharacteristic
38C22⋊C4×C29—21no—
39C22⋊Dic29—21no—
40C4⋊Dic29—21no—
41C4⋊Dic29C2×C411yescharacteristic
42#90779—24no—
43#90779—21no—
44#90779—21no—
45#90779—21no—
46#90779—21no—
47#90779—21no—
48C4×Dic29—21no—
49C4×Dic29—21no—
50C4×Dic29—42no—
51C4×Dic29C2×C411yescharacteristic
52C4×Dic29C2×C411yescharacteristic
53C4×Dic29D411yescharacteristic
54C4×Dic29D411yescharacteristic
55C2×#6597—21no—
56C23×C29C2×D411yescharacteristic
57Q8×C29—41no—
58C2×C4×C29—22no—
59C2×C4×C29—21no—
60C2×C4×C29—21no—
61C2×C4×C29—41no—
62C2×C4×C29—41no—
63C2×C4×C29—41no—
64C2×C4×C29C22×C411yescharacteristic
65C2×C4×C29C2×D411yescharacteristic
66C2×Dic29—22no—
67C2×Dic29—22no—
68C2×Dic29—21no—
69C2×Dic29—21no—
70C2×Dic29—41no—
71C2×Dic29—41no—
72C2×Dic29C22⋊C411yescharacteristic
73C2×Dic29C22⋊C411yescharacteristic
74C2×Dic29C22⋊C411yescharacteristic
75C2×Dic29C22⋊C411yescharacteristic
76C2×Dic29SD1612yes—
77C2×Dic29Q1612yes—
78Dic58—42no—
79Dic58—41no—
80C8×C29—41no—
81#6597—41no—
82#1503—291nomaximal, Sylow
83C22×C29—21no—
84C22×C29—21no—
85C22×C29C2×C22⋊C411yescharacteristic
86C22×C29C2×SD1611yescharacteristic
87C22×C29C2×Q1611yescharacteristic
88C4×C29—21no—
89C4×C29—21no—
90C4×C29—42no—
91C4×C29—41no—
92C4×C29—41no—
93Dic29—21no—
94Dic29—42no—
95Dic29—41no—
96Dic29—41no—
97Dic29#10312yes—
98Dic29#10312yes—
99Dic29#10412yes—
100#533—291no—
101#431—291no—
102C4×C4⋊C4—291no—
103#328—291no—
104#328—291no—
105#328—291no—
106#328D2911yescharacteristic
107C2×C29—21no—
108C2×C29—21no—
109C2×C29#41011yescharacteristic
110C2×C29C2×#10311yescharacteristic
111C2×C29C2×#10411yescharacteristic
112C4⋊Q8—291no—
113C4⋊Q8—291no—
114#125—581no—
115C22⋊Q8—291no—
116C22⋊Q8—581no—
117C22⋊Q8C2×D2911yescharacteristic
118C4×Q8—291no—
119C4×Q8—291no—
120C4×Q8—581no—
121#117—581no—
122C2×C4⋊C4—581no—
123C2×C42—291no—
124C2×C42—581no—
125C4⋊C8—581no—
126C22⋊C8—291no—
127C22⋊C8C2×D2911yescharacteristic
128C4×C8—581no—
129#95—291no—
130#95C2×D2911yescharacteristic
131C29#150311yescharacteristic, complemented, Sylow
132C2×Q8—291no—
133C2×Q8—581no—
134C2×Q8C4×D2911yescharacteristic
135C22×C4—21no—
136C22×C4—291no—
137C22×C4—291no—
138C22×C4—581no—
139C22×C4C22×D2911yescharacteristic
140C2×C8—21no—
141C2×C8—581no—
142C4⋊C4—21no—
143C4⋊C4—291no—
144C4⋊C4—581no—
145C4⋊C4—581no—
146C4⋊C4—581no—
147C4⋊C4—581no—
148C4⋊C4—581no—
149C4⋊C4—584no—
150C4⋊C4—581no—
151C4⋊C4C4×D2911yescharacteristic
152C22⋊C4—21no—
153C22⋊C4—581no—
154C42—291no—
155C42—291no—
156C42—291no—
157C42—291no—
158C42—581no—
159C42—581no—
160C42—1162no—
161C23D4×D2911yescharacteristic
162Q8—41no—
163Q8—1161no—
164Q8—1162no—
165C2×C4—22no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—41no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—291no—
172C2×C4—291no—
173C2×C4—291no—
174C2×C4—292no—
175C2×C4—292no—
176C2×C4—291no—
177C2×C4—582no—
178C2×C4—582no—
179C2×C4—581no—
180C2×C4—581no—
181C2×C4—1161no—
182C2×C4—1161no—
183C2×C4C2×C4×D2911yescharacteristic
184C2×C4D4×D2911yescharacteristic
185C8—41no—
186C8—1161no—
187C22—21no—
188C22—21no—
189C22C22⋊C4×D2911yescharacteristic
190C22SD16×D2911yescharacteristic
191C22Q16×D2911yescharacteristic
192C4—21no—
193C4—21no—
194C4—42no—
195C4—41no—
196C4—41no—
197C4—292no—
198C4—292no—
199C4—292no—
200C4—581no—
201C4—1162no—
202C4—1161no—
203C4—1161no—
204C2—21no—
205C2—21no—
206C2#1427113511yescharacteristic
207C2#103×D2911yescharacteristic
208C2#104×D2911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D29
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#328C2
socleC22×C29C2×C22⋊C4
prime radicalC23×C29C2×D4
cosocleC22×C4×C29C23
hypercenter#328D29
hypocenterC29#1503
LCSG ▷ C2×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
9. Q8×Dic29C4semidirect
10. #11745306C4semidirect
16. #11745250C4semidirect
18. #11745249C4semidirect
131. C29#1503semidirect

Maximal subgroups

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

subgroupindex
#142717152
#142712132
#142710142
#142709012
#142709002
#142708992
C29×#3282
#150329