Finite Group Databasebeta

← #16818506

Subgroups — #16818506

Order 3712.

232 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 53 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#14271491C211yesmaximal, characteristic, complemented
2#14271474C211yesmaximal, characteristic, complemented
3#14271088C211yesmaximal, characteristic, complemented
4#14270900C211yesmaximal, characteristic, complemented
5#14270897C211yesmaximal, characteristic, complemented
6#14270887C211yesmaximal, characteristic, complemented
7C29×#538C211yesmaximal, characteristic
8C29×#126—21no—
9C29×#124—21no—
10C29×#123—21no—
11C29×C22⋊Q8C2211yescharacteristic
12C29×#121—21no—
13C29×#121C2211yescharacteristic
14C29×#120—21no—
15C4×D4×C29—21no—
16C2×C22⋊C4×C29C2211yescharacteristic
17C2×C22⋊Dic29—21no—
18C2×C4⋊Dic29C2211yescharacteristic
19#11745183—21no—
20#11745180—21no—
21#11745179—21no—
22#11745179C2211yescharacteristic
23C22⋊#6597C2211yescharacteristic
24C22⋊#6597C2211yescharacteristic
25#11745156—21no—
26#11745155—21no—
27C24×C29D411yescharacteristic
28C2×Q8×C29D411yescharacteristic
29C2×D4×C29—21no—
30C2×D4×C29—21no—
31C2×D4×C29—21no—
32C2×D4×C29D411yescharacteristic
33C22×C4×C29—21no—
34C22×C4×C29D411yescharacteristic
35C22×C4×C29C2311yescharacteristic
36C22×Dic29—21no—
37C22×Dic29—21no—
38C4⋊C4×C29—21no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29D411yescharacteristic
41C4⋊C4×C29D411yescharacteristic
42C22⋊C4×C29—21no—
43C22⋊C4×C29—21no—
44C22⋊C4×C29—21no—
45C22⋊C4×C29—21no—
46C22⋊C4×C29—21no—
47C22⋊C4×C29—21no—
48C22⋊C4×C29—21no—
49C42×C29—21no—
50C22⋊Dic29—42no—
51C4⋊Dic29—21no—
52C4⋊Dic29—21no—
53C2×#6597—21no—
54C2×#6597—21no—
55C23×C29—21no—
56C23×C29—21no—
57C23×C29—21no—
58C23×C29—21no—
59C23×C29—41no—
60C23×C29—41no—
61C23×C29C2×D411yescharacteristic
62Q8×C29—41no—
63D4×C29—41no—
64D4×C29—41no—
65D4×C29—41no—
66D4×C29—81no—
67D4×C29—81no—
68C2×C4×C29—21no—
69C2×C4×C29—21no—
70C2×C4×C29—21no—
71C2×C4×C29—21no—
72C2×C4×C29—41no—
73C2×C4×C29—41no—
74C2×C4×C29—81no—
75C2×C4×C29C2×D411yescharacteristic
76C2×C4×C29C2×D411yescharacteristic
77C2×Dic29—41no—
78C2×Dic29—41no—
79C2×Dic29—41no—
80C2×Dic29—41no—
81C2×Dic29—41no—
82C2×Dic29—41no—
83#6597—41no—
84#6597—41no—
85#1612—291nomaximal, Sylow
86C22×C29—21no—
87C22×C29—21no—
88C22×C29—42no—
89C22×C29—41no—
90C22×C29—41no—
91C22×C29—41no—
92C22×C29—41no—
93C22×C29—41no—
94C22×C29—41no—
95C22×C29—81no—
96C22×C29#12011yescharacteristic
97C22×C29#13511yescharacteristic
98C22×C29AGL(1,ℤ/8)11yescharacteristic
99C4×C29—21no—
100C4×C29—21no—
101C4×C29—41no—
102C4×C29—41no—
103C4×C29—41no—
104C4×C29—41no—
105Dic29—81no—
106Dic29—81no—
107#538D2911yescharacteristic
108#483—291no—
109#480—291no—
110#397—291no—
111#328—291no—
112#327—291no—
113#323—291no—
114C2×C29—21no—
115C2×C29—21no—
116C2×C29—81no—
117C2×C29—81no—
118C2×C29#44911yescharacteristic
119C2×C29#45511yescharacteristic
120C2×C29#45811yescharacteristic
121#126—21no—
122#124—21no—
123#123—21no—
124C22⋊Q8C2×D2911yescharacteristic
125#121—21no—
126#121C2×D2911yescharacteristic
127#120—21no—
128C4×D4—21no—
129C2×C4⋊C4—291no—
130C2×C22⋊C4—581no—
131C2×C22⋊C4C2×D2911yescharacteristic
132#107—581no—
133#106—581no—
134#103—581no—
135#102—581no—
136C22⋊C8—291no—
137C22⋊C8—291no—
138#95—291no—
139#95—581no—
140C29#161211yescharacteristic, complemented, Sylow
141C24C22⋊D2911yescharacteristic
142C2×Q8C22⋊D2911yescharacteristic
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4C22⋊D2911yescharacteristic
147C22×C4—21no—
148C22×C4—581no—
149C22×C4—581no—
150C22×C4C22⋊D2911yescharacteristic
151C22×C4C22×D2911yescharacteristic
152C2×C8—581no—
153C2×C8—581no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—581no—
157C4⋊C4—581no—
158C4⋊C4C22⋊D2911yescharacteristic
159C4⋊C4C22⋊D2911yescharacteristic
160C22⋊C4—21no—
161C22⋊C4—21no—
162C22⋊C4—21no—
163C22⋊C4—21no—
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—21no—
167C22⋊C4—1162no—
168C42—21no—
169C23—21no—
170C23—21no—
171C23—21no—
172C23—21no—
173C23—41no—
174C23—41no—
175C23C2×C22⋊D2911yescharacteristic
176Q8—41no—
177D4—41no—
178D4—41no—
179D4—41no—
180D4—81no—
181D4—81no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—81no—
189C2×C4—1161no—
190C2×C4—1161no—
191C2×C4—1161no—
192C2×C4—1161no—
193C2×C4—1161no—
194C2×C4—1161no—
195C2×C4C2×C22⋊D2911yescharacteristic
196C2×C4C2×C22⋊D2911yescharacteristic
197C8—1161no—
198C8—1161no—
199C22—21no—
200C22—21no—
201C22—42no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—81no—
209C22#1174531111yescharacteristic
210C22#1174531211yescharacteristic
211C22#1174531511yescharacteristic
212C4—21no—
213C4—21no—
214C4—41no—
215C4—41no—
216C4—41no—
217C4—41no—
218C4—2321no—
219C4—2321no—
220C2—21no—
221C2—21no—
222C2—81no—
223C2—81no—
224C2#1427130811yescharacteristic
225C2#1427134111yescharacteristic
226C2#1427135311yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
Fitting, prime radicalC29×#538C2
socleC22×C29#120
hypercenter#538D29
hypocenterC29#1612
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #14271491C2semidirect
2. #14271474C2semidirect
3. #14271088C2semidirect
4. #14270900C2semidirect
5. #14270897C2semidirect
6. #14270887C2semidirect
140. C29#1612semidirect

Maximal subgroups

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

subgroupindex
#142714912
#142714742
#142710882
#142709002
#142708972
#142708872
C29×#5382
#161229