Finite Group Databasebeta

← #16818509

Subgroups — #16818509

Order 3712.

232 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 49 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#14271753C211yesmaximal, characteristic
2#14271491C211yesmaximal, characteristic, complemented
3#14271477C211yesmaximal, characteristic, complemented
4#14271090C211yesmaximal, characteristic, complemented
5#14270896C211yesmaximal, characteristic, complemented
6#14270886C211yesmaximal, characteristic, complemented
7C29×#328C211yesmaximal, characteristic, complemented
8C29×C22⋊Q8C2211yescharacteristic
9#11745309—21no—
10#11745292C2211yescharacteristic
11C2×#90781—21no—
12C2×#90781C2211yescharacteristic
13C2×C4⋊Dic29C2211yescharacteristic
14#11745260—21no—
15#11745257—21no—
16#11745256—21no—
17#11745244—21no—
18#11745243—21no—
19C29×C22⋊C8C2211yescharacteristic
20C29×#95C2211yescharacteristic
21#11745183—21no—
22#11745179—21no—
23C22⋊#6597C2211yescharacteristic
24#11745169—21no—
25#11745166—21no—
26#11745156—21no—
27C23×D29D411yescharacteristic
28C2×Q8×C29D411yescharacteristic
29C22×C4×C29—21no—
30C22×C4×C29C2311yescharacteristic
31C2×C22⋊D29—21no—
32C22×Dic29—21no—
33C22×Dic29D411yescharacteristic
34C2×D116—21no—
35C2×D116—21no—
36C2×D116D411yescharacteristic
37C2×C4×D29—21no—
38C2×C8×C29—21no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29D411yescharacteristic
41C22⋊C4×C29—21no—
42#90781—21no—
43#90781—21no—
44#90781—21no—
45#90781—21no—
46#90781—21no—
47#90781—21no—
48#90781—42no—
49C4⋊Dic29—21no—
50C4⋊Dic29—21no—
51C4⋊Dic29D411yescharacteristic
52#90779—21no—
53C4×Dic29—21no—
54C2×#6597—21no—
55C23×C29C2×D411yescharacteristic
56C22×D29—21no—
57C22×D29—21no—
58C22×D29—21no—
59C22×D29—21no—
60C22×D29—41no—
61C22×D29—41no—
62Q8×C29—41no—
63C2×C4×C29—21no—
64C2×C4×C29—21no—
65C2×C4×C29—41no—
66C2×C4×C29—41no—
67C2×C4×C29—41no—
68C2×C4×C29—41no—
69C2×C4×C29C2×D411yescharacteristic
70C2×C4×C29C2×D411yescharacteristic
71C22⋊D29—41no—
72C22⋊D29—41no—
73C2×Dic29—21no—
74C2×Dic29—21no—
75C2×Dic29—41no—
76C2×Dic29—41no—
77C2×Dic29—41no—
78C2×Dic29—41no—
79D116—41no—
80D116—81no—
81D116—81no—
82C4×D29—81no—
83C8×C29—41no—
84#6597—41no—
85#1612—291nomaximal, Sylow
86C22×C29—21no—
87C22×C29—21no—
88C22×C29#12011yescharacteristic
89C22×C29#13511yescharacteristic
90C22×C29AGL(1,ℤ/8)11yescharacteristic
91C2×D29—42no—
92C2×D29—41no—
93C2×D29—41no—
94C2×D29—41no—
95C2×D29—41no—
96C2×D29—41no—
97C2×D29—41no—
98C2×D29—81no—
99C4×C29—21no—
100C4×C29—21no—
101C4×C29—41no—
102C4×C29—41no—
103C4×C29—81no—
104Dic29—41no—
105Dic29—41no—
106Dic29—81no—
107#538—291no—
108#483—291no—
109#480—291no—
110#397—291no—
111#328D2911yescharacteristic, complemented
112#327—291no—
113#323—291no—
114C2×C29—21no—
115C2×C29—21no—
116C2×C29#44911yescharacteristic
117C2×C29#45511yescharacteristic
118C2×C29#45811yescharacteristic
119D29—81no—
120D29—81no—
121#126—581no—
122#124—581no—
123#123—581no—
124C22⋊Q8C2×D2911yescharacteristic
125#121—291no—
126#121—581no—
127#120—581no—
128C4×D4—581no—
129C2×C4⋊C4—291no—
130C2×C22⋊C4—291no—
131C2×C22⋊C4—581no—
132#107—581no—
133#106—581no—
134#103—581no—
135#102—581no—
136C22⋊C8—291no—
137C22⋊C8C2×D2911yescharacteristic
138#95—581no—
139#95C2×D2911yescharacteristic
140C29#161211yescharacteristic, complemented, Sylow
141C24—291no—
142C2×Q8D11611yescharacteristic
143C2×D4—291no—
144C2×D4—581no—
145C2×D4—581no—
146C2×D4—581no—
147C22×C4—21no—
148C22×C4—291no—
149C22×C4—581no—
150C22×C4—581no—
151C22×C4C22×D2911yescharacteristic
152C2×C8—21no—
153C2×C8—581no—
154C4⋊C4—21no—
155C4⋊C4—291no—
156C4⋊C4—581no—
157C4⋊C4—581no—
158C4⋊C4—581no—
159C4⋊C4D11611yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—581no—
162C22⋊C4—581no—
163C22⋊C4—581no—
164C22⋊C4—581no—
165C22⋊C4—581no—
166C22⋊C4—581no—
167C22⋊C4—1162no—
168C42—581no—
169C23—581no—
170C23—581no—
171C23—581no—
172C23—581no—
173C23—1161no—
174C23—1161no—
175C23D4×D2911yescharacteristic
176Q8—41no—
177D4—1161no—
178D4—1161no—
179D4—1161no—
180D4—2321no—
181D4—2321no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—581no—
189C2×C4—581no—
190C2×C4—1161no—
191C2×C4—1161no—
192C2×C4—1161no—
193C2×C4—1161no—
194C2×C4—2321no—
195C2×C4C2×D11611yescharacteristic
196C2×C4D4×D2911yescharacteristic
197C8—41no—
198C8—1161no—
199C22—21no—
200C22—21no—
201C22—1162no—
202C22—1161no—
203C22—1161no—
204C22—1161no—
205C22—1161no—
206C22—1161no—
207C22—1161no—
208C22—2321no—
209C22#1174524411yescharacteristic
210C22#1174527611yescharacteristic
211C22#1174528111yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—81no—
217C4—1161no—
218C4—1161no—
219C4—2321no—
220C2—21no—
221C2—21no—
222C2—2321no—
223C2—2321no—
224C2#1427131111yescharacteristic
225C2#1427134211yescharacteristic
226C2#1427135411yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#328C2
socleC22×C29#120
prime radical#14271753C2
hypercenter#328D29
hypocenterC29#1612
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
2. #14271491C2semidirect
3. #14271477C2semidirect
4. #14271090C2semidirect
5. #14270896C2semidirect
6. #14270886C2semidirect
7. C29×#328C2semidirect
111. #328D29semidirect
140. C29#1612semidirect

Maximal subgroups

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

subgroupindex
#142717532
#142714912
#142714772
#142710902
#142708962
#142708862
C29×#3282
#161229