Finite Group Databasebeta

← #16818530

Subgroups — #16818530

Order 3712.

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

normal subgroups only

This group has 246 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#14271740C211yesmaximal, characteristic
2#14271482C211yesmaximal, characteristic, complemented
3#14271479C211yesmaximal, characteristic, complemented
4#14271103C211yesmaximal, characteristic, complemented
5#14270896C211yesmaximal, characteristic, complemented
6#14270888C211yesmaximal, characteristic, complemented
7C29×#327C211yesmaximal, characteristic, complemented
8C2×#90807—21no—
9C29×#121C2211yescharacteristic
10#11745301—21no—
11#11745301—21no—
12#11745292C2211yescharacteristic
13C2×C4⋊Dic29C2211yescharacteristic
14C2×#90779C2211yescharacteristic
15#11745258—21no—
16#11745246—21no—
17#11745240—21no—
18C29×C22⋊C8C2211yescharacteristic
19C29×#95C2211yescharacteristic
20#11745180—21no—
21#11745179—21no—
22#11745179—21no—
23C22⋊#6597C2211yescharacteristic
24#11745169—21no—
25#11745165—21no—
26#11745156—21no—
27C2×D4×C29—21no—
28C2×D4×C29D411yescharacteristic
29C22×C4×C29—21no—
30C22×C4×C29C2311yescharacteristic
31C2×C22⋊D29—21no—
32C2×C22⋊D29—21no—
33C2×C22⋊D29—21no—
34C22×Dic29—21no—
35C22×Dic29—21no—
36C22×Dic29D411yescharacteristic
37C22×Dic29D411yescharacteristic
38#90807—42no—
39#90807—42no—
40C2×D116D411yescharacteristic
41C2×C4×D29—21no—
42C2×Dic58—21no—
43C2×C8×C29—21no—
44C4⋊C4×C29D411yescharacteristic
45C22⋊C4×C29—21no—
46C22⋊Dic29—21no—
47#90781—21no—
48#90781—21no—
49C4⋊Dic29—21no—
50C4⋊Dic29—21no—
51C4⋊Dic29D411yescharacteristic
52#90779—21no—
53#90779—21no—
54#90779—21no—
55C2×#6597—21no—
56C23×C29—21no—
57C23×C29C2×D411yescharacteristic
58C22×D29—21no—
59D4×C29—41no—
60D4×C29—41no—
61D4×C29—41no—
62C2×C4×C29—21no—
63C2×C4×C29—41no—
64C2×C4×C29—41no—
65C2×C4×C29—41no—
66C2×C4×C29—41no—
67C2×C4×C29C2×D411yescharacteristic
68C2×C4×C29C2×D411yescharacteristic
69C22⋊D29—42no—
70C22⋊D29—41no—
71C22⋊D29—41no—
72C22⋊D29—81no—
73C2×Dic29—21no—
74C2×Dic29—21no—
75C2×Dic29—21no—
76C2×Dic29—21no—
77C2×Dic29—42no—
78C2×Dic29—41no—
79C2×Dic29—42no—
80C2×Dic29—41no—
81C2×Dic29SD1612yes—
82D116—41no—
83C4×D29—42no—
84Dic58—42no—
85C8×C29—41no—
86#6597—41no—
87#1616—291nomaximal, Sylow
88C22×C29—21no—
89C22×C29—21no—
90C22×C29—41no—
91C22×C29—41no—
92C22×C29—41no—
93C22×C29#12011yescharacteristic
94C22×C29C2×SD1611yescharacteristic
95C22×C29AGL(1,ℤ/8)11yescharacteristic
96C2×D29—41no—
97C2×D29—41no—
98C2×D29—41no—
99C4×C29—21no—
100C4×C29—21no—
101C4×C29—41no—
102C4×C29—81no—
103Dic29—22no—
104Dic29—41no—
105Dic29—41no—
106Dic29—81no—
107#537—291no—
108#481—291no—
109#481—291no—
110#400—291no—
111#327—291no—
112#327D2911yescharacteristic, complemented
113#324—291no—
114C2×C29—21no—
115C2×C29—21no—
116C2×C29—81no—
117C2×C29#45011yescharacteristic
118C2×C29#45411yescharacteristic
119C2×C29#45811yescharacteristic
120D29—81no—
121C2×#41—581no—
122C22⋊Q8—581no—
123C22⋊Q8—581no—
124#121—291no—
125#121—581no—
126#121—581no—
127#121—581no—
128#121C2×D2911yescharacteristic
129C2×C4⋊C4—291no—
130C2×C4⋊C4—291no—
131#106—581no—
132#106—581no—
133#102—581no—
134#102—581no—
135C22⋊C8—291no—
136C22⋊C8C2×D2911yescharacteristic
137#95—581no—
138#95—581no—
139#95C2×D2911yescharacteristic
140C29#161611yescharacteristic, complemented, Sylow
141#41—1162no—
142#41—1162no—
143C2×Q8—581no—
144C2×D4—21no—
145C2×D4—291no—
146C2×D4—581no—
147C2×D4—581no—
148C2×D4—581no—
149C2×D4D11611yescharacteristic
150C22×C4—21no—
151C22×C4—291no—
152C22×C4—291no—
153C22×C4—581no—
154C22×C4—581no—
155C22×C4—581no—
156C22×C4C22×D2911yescharacteristic
157C2×C8—21no—
158C2×C8—581no—
159C4⋊C4—291no—
160C4⋊C4—581no—
161C4⋊C4—581no—
162C4⋊C4—581no—
163C4⋊C4—581no—
164C4⋊C4—581no—
165C4⋊C4D11611yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—581no—
168C22⋊C4—581no—
169C22⋊C4—581no—
170C23—21no—
171C23—581no—
172C23D4×D2911yescharacteristic
173Q8—1162no—
174D4—41no—
175D4—41no—
176D4—41no—
177D4—1161no—
178D4—1162no—
179D4—1161no—
180D4—1161no—
181D4—2321no—
182C2×C4—21no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—292no—
188C2×C4—581no—
189C2×C4—581no—
190C2×C4—581no—
191C2×C4—581no—
192C2×C4—1162no—
193C2×C4—1162no—
194C2×C4—1161no—
195C2×C4—1162no—
196C2×C4—1161no—
197C2×C4C2×D11611yescharacteristic
198C2×C4D4×D2911yescharacteristic
199C8—41no—
200C8—1161no—
201C22—21no—
202C22—21no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—1161no—
207C22—1161no—
208C22—1161no—
209C22#1174524411yescharacteristic
210C22#1174527311yescharacteristic
211C22SD16×D2911yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—81no—
216C4—582no—
217C4—1161no—
218C4—1161no—
219C4—2321no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—2321no—
224C2#1427131511yescharacteristic
225C2#1427133711yescharacteristic
226C2#1427135411yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#327C2
socleC22×C29#120
prime radical#14271740C2
hypercenter#327D29
hypocenterC29#1616
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
2. #14271482C2semidirect
3. #14271479C2semidirect
4. #14271103C2semidirect
5. #14270896C2semidirect
6. #14270888C2semidirect
7. C29×#327C2semidirect
112. #327D29semidirect
140. C29#1616semidirect

Maximal subgroups

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

subgroupindex
#142717402
#142714822
#142714792
#142711032
#142708962
#142708882
C29×#3272
#161629