Finite Group Databasebeta

← #16818016

Subgroups — #16818016

Order 3712.

242 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 63 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#14271699C211yesmaximal, characteristic
2#14271217C211yesmaximal, characteristic, complemented
3#14271014C211yesmaximal, characteristic, complemented
4#14270900C211yesmaximal, characteristic, complemented
5#14270898C211yesmaximal, characteristic
6#14270896C211yesmaximal, characteristic
7C29×#328C211yesmaximal, characteristic, complemented
8C29×C22⋊Q8C2211yescharacteristic
9#11745309C411yescharacteristic, complemented
10Q8×Dic29C411yescharacteristic, complemented
11#11745292C2211yescharacteristic
12C2×#90779—21no—
13C2×C4×Dic29—21no—
14C2×C4×Dic29C2211yescharacteristic
15#11745260—21no—
16#11745255C411yescharacteristic, complemented
17#11745254—21no—
18#11745252C411yescharacteristic, complemented
19#11745248—21no—
20#11745243—21no—
21C29×C22⋊C8C2211yescharacteristic
22C29×#95C2211yescharacteristic
23#11745179C2211yescharacteristic
24C22⋊#6597C2211yescharacteristic
25#11745163—21no—
26#11745162—21no—
27C2×Q8×C29C2×C411yescharacteristic
28C22×C4×C29—21no—
29C22×C4×C29C2311yescharacteristic
30C2×C22⋊D29—21no—
31C22×Dic29—21no—
32C22×Dic29D411yescharacteristic
33C22×Dic29D411yescharacteristic
34C2×D116C2×C411yescharacteristic
35C2×C4×D29—21no—
36C2×C8×C29—21no—
37C4⋊C4×C29—21no—
38C4⋊C4×C29C2×C411yescharacteristic
39C22⋊C4×C29—21no—
40#90781—21no—
41#90781—21no—
42#90781—21no—
43#90781—21no—
44C4⋊Dic29—21no—
45C4⋊Dic29—21no—
46C4⋊Dic29C2×C411yescharacteristic
47#90779—24no—
48#90779—21no—
49C4×Dic29—21no—
50C4×Dic29—42no—
51C4×Dic29C2×C411yescharacteristic
52C4×Dic29C2×C411yescharacteristic
53C4×Dic29D411yescharacteristic
54C4×Dic29D411yescharacteristic
55C2×#6597—21no—
56C23×C29C2×D411yescharacteristic
57C22×D29—21no—
58Q8×C29—41no—
59C2×C4×C29—22no—
60C2×C4×C29—21no—
61C2×C4×C29—21no—
62C2×C4×C29—41no—
63C2×C4×C29—41no—
64C2×C4×C29—41no—
65C2×C4×C29C22×C411yescharacteristic
66C2×C4×C29C2×D411yescharacteristic
67C22⋊D29—41no—
68C22⋊D29—41no—
69C2×Dic29—21no—
70C2×Dic29—21no—
71C2×Dic29—22no—
72C2×Dic29—22no—
73C2×Dic29—21no—
74C2×Dic29—41no—
75C2×Dic29—41no—
76C2×Dic29C22⋊C411yescharacteristic
77C2×Dic29C22⋊C411yescharacteristic
78C2×Dic29C22⋊C411yescharacteristic
79C2×Dic29C22⋊C411yescharacteristic
80D116—41no—
81C4×D29—42no—
82C8×C29—41no—
83#6597—41no—
84#1509—291nomaximal, Sylow
85C22×C29—21no—
86C22×C29—21no—
87C22×C29C2×C22⋊C411yescharacteristic
88C22×C29AGL(1,ℤ/8)11yescharacteristic
89C22×C29#13711yescharacteristic
90C2×D29—41no—
91C2×D29—41no—
92C2×D29—41no—
93C4×C29—21no—
94C4×C29—21no—
95C4×C29—42no—
96C4×C29—41no—
97C4×C29—41no—
98Dic29—21no—
99Dic29—21no—
100Dic29—21no—
101Dic29—42no—
102Dic29—41no—
103Dic29#10412yes—
104#529—291no—
105#432—291no—
106C4×C4⋊C4—291no—
107#328—291no—
108#328D2911yescharacteristic, complemented
109#327—291no—
110#327—291no—
111C2×C29—21no—
112C2×C29—21no—
113C2×C29#41011yescharacteristic
114C2×C29#41711yescharacteristic
115C2×C29C2×#10411yescharacteristic
116D29—81no—
117#126—581no—
118#125—291no—
119#124—291no—
120#123—581no—
121C22⋊Q8C2×D2911yescharacteristic
122#121—291no—
123C4×Q8—291no—
124C4×D4—291no—
125C4×D4—581no—
126#117—581no—
127C2×C4⋊C4—581no—
128C2×C42—291no—
129C2×C42—581no—
130C4⋊C8—581no—
131C22⋊C8—291no—
132C22⋊C8C2×D2911yescharacteristic
133#97—581no—
134#95—291no—
135#95C2×D2911yescharacteristic
136C29#150911yescharacteristic, complemented, Sylow
137C2×Q8C4×D2911yescharacteristic
138C2×D4—291no—
139C2×D4—581no—
140C22×C4—21no—
141C22×C4—291no—
142C22×C4—291no—
143C22×C4—581no—
144C22×C4—581no—
145C22×C4C22×D2911yescharacteristic
146C2×C8—21no—
147C2×C8—581no—
148C4⋊C4—21no—
149C4⋊C4—291no—
150C4⋊C4—581no—
151C4⋊C4—581no—
152C4⋊C4—581no—
153C4⋊C4—584no—
154C4⋊C4C4×D2911yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—581no—
157C22⋊C4—581no—
158C22⋊C4—581no—
159C22⋊C4—581no—
160C42—291no—
161C42—291no—
162C42—291no—
163C42—291no—
164C42—581no—
165C42—1162no—
166C23—581no—
167C23D4×D2911yescharacteristic
168Q8—41no—
169D4—1161no—
170D4—1161no—
171D4—1161no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—291no—
179C2×C4—291no—
180C2×C4—291no—
181C2×C4—291no—
182C2×C4—582no—
183C2×C4—581no—
184C2×C4—581no—
185C2×C4—582no—
186C2×C4—581no—
187C2×C4—1162no—
188C2×C4—1161no—
189C2×C4—1161no—
190C2×C4C2×C4×D2911yescharacteristic
191C2×C4D4×D2911yescharacteristic
192C8—41no—
193C8—1161no—
194C22—21no—
195C22—21no—
196C22—1161no—
197C22—1161no—
198C22—1161no—
199C22C22⋊C4×D2911yescharacteristic
200C22#1174527611yescharacteristic
201C22#1174528011yescharacteristic
202C4—21no—
203C4—21no—
204C4—42no—
205C4—41no—
206C4—41no—
207C4—292no—
208C4—581no—
209C4—581no—
210C4—581no—
211C4—1162no—
212C4—1161no—
213C2—21no—
214C2—21no—
215C2—2321no—
216C2#1427113511yescharacteristic
217C2#1427116311yescharacteristic
218C2#104×D2911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D29
commutatorC2×C4×C29C22×C4
FrattiniC22×C4C22×D29
FittingC29×#328C2
socleC22×C29C2×C22⋊C4
prime radical#11745292C22
cosocleC22×C4×C29C23
hypercenter#328D29
hypocenterC29#1509
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
2. #14271217C2semidirect
3. #14271014C2semidirect
4. #14270900C2semidirect
7. C29×#328C2semidirect
9. #11745309C4semidirect
10. Q8×Dic29C4semidirect
16. #11745255C4semidirect
18. #11745252C4semidirect
108. #328D29semidirect
136. C29#1509semidirect

Maximal subgroups

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

subgroupindex
#142716992
#142712172
#142710142
#142709002
#142708982
#142708962
C29×#3282
#150929