Finite Group Databasebeta

← #16818455

Subgroups — #16818455

Order 3712.

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

normal subgroups only

This group has 244 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#14271318C211yesmaximal, characteristic, complemented
2#14271301C211yesmaximal, characteristic
3#14271083C211yesmaximal, characteristic, complemented
4#14270900C211yesmaximal, characteristic, complemented
5#14270897C211yesmaximal, characteristic
6#14270889C211yesmaximal, characteristic, complemented
7C29×#539C211yesmaximal, characteristic
8C22×Dic58C2211yescharacteristic
9C29×#126—21no—
10C29×#125—21no—
11C29×#123—21no—
12C29×#123—21no—
13C29×C22⋊Q8—21no—
14C29×C22⋊Q8C2211yescharacteristic
15C29×#121C2211yescharacteristic
16C4×D4×C29—21no—
17C2×C4⋊C4×C29C2211yescharacteristic
18C2×#90785—21no—
19C2×#90783—21no—
20C2×#90779—21no—
21#11745179—21no—
22#11745179C2211yescharacteristic
23C22⋊#6597C2211yescharacteristic
24C22⋊#6597C2211yescharacteristic
25#11745158—21no—
26#11745158—21no—
27C2×Q8×C29D411yescharacteristic
28C2×D4×C29—21no—
29C2×D4×C29D411yescharacteristic
30C22×C4×C29—21no—
31C22×C4×C29D411yescharacteristic
32C22×C4×C29D411yescharacteristic
33C22×C4×C29C2311yescharacteristic
34C22×Dic29—21no—
35C22×Dic29—21no—
36C2×Dic58—21no—
37C2×Dic58—21no—
38C2×Dic58—42no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29—21no—
41C4⋊C4×C29—21no—
42C4⋊C4×C29—21no—
43C4⋊C4×C29—21no—
44C4⋊C4×C29—21no—
45C4⋊C4×C29D411yescharacteristic
46C4⋊C4×C29D411yescharacteristic
47C22⋊C4×C29—21no—
48C22⋊C4×C29—21no—
49C22⋊C4×C29—21no—
50C22⋊C4×C29—21no—
51C22⋊C4×C29—21no—
52C42×C29—21no—
53#90785—42no—
54#90783—42no—
55#90779—42no—
56C2×#6597—21no—
57C2×#6597—21no—
58C23×C29—21no—
59C23×C29C2×D411yescharacteristic
60Q8×C29—41no—
61D4×C29—41no—
62D4×C29—41no—
63D4×C29—41no—
64C2×C4×C29—21no—
65C2×C4×C29—21no—
66C2×C4×C29—21no—
67C2×C4×C29—21no—
68C2×C4×C29—21no—
69C2×C4×C29—21no—
70C2×C4×C29—21no—
71C2×C4×C29—41no—
72C2×C4×C29—41no—
73C2×C4×C29—81no—
74C2×C4×C29C2×D411yescharacteristic
75C2×C4×C29C2×D411yescharacteristic
76C2×Dic29—22no—
77C2×Dic29—22no—
78C2×Dic29—41no—
79C2×Dic29—41no—
80C2×Dic29—41no—
81C2×Dic29—41no—
82Dic58—22no—
83Dic58—22no—
84Dic58—41no—
85Dic58—41no—
86#6597—41no—
87#6597—41no—
88#1603—291nomaximal, Sylow
89C22×C29—21no—
90C22×C29—21no—
91C22×C29—41no—
92C22×C29—41no—
93C22×C29—41no—
94C22×C29#12011yescharacteristic
95C22×C29#13511yescharacteristic
96C22×C29#13711yescharacteristic
97C4×C29—21no—
98C4×C29—21no—
99C4×C29—41no—
100C4×C29—41no—
101C4×C29—41no—
102C4×C29—41no—
103C4×C29—41no—
104Dic29—42no—
105Dic29—42no—
106#539D2911yescharacteristic
107#451—291no—
108#448—291no—
109#395—291no—
110#328—291no—
111#327—291no—
112#324—291no—
113C2×C29—21no—
114C2×C29—21no—
115C2×C29—81no—
116C2×C29#45211yescharacteristic
117C2×C29#45611yescharacteristic
118C2×C29B(4,𝔽2)11yescharacteristic
119C22×Q8—291no—
120C2×Q16—581no—
121C2×SD16—581no—
122#126—21no—
123#125—21no—
124#123—21no—
125#123—21no—
126C22⋊Q8—21no—
127C22⋊Q8C2×D2911yescharacteristic
128#121C2×D2911yescharacteristic
129C4×D4—21no—
130C2×C4⋊C4—581no—
131C2×C4⋊C4C2×D2911yescharacteristic
132#103—581no—
133#103—581no—
134C22⋊C8—291no—
135C22⋊C8—291no—
136#95—291no—
137#95—581no—
138C29#160311yescharacteristic, complemented, Sylow
139C2×Q8—581no—
140C2×Q8—581no—
141C2×Q8—1162no—
142C2×Q8C22⋊D2911yescharacteristic
143C2×D4—21no—
144C2×D4C22⋊D2911yescharacteristic
145C22×C4—21no—
146C22×C4—581no—
147C22×C4—581no—
148C22×C4C22⋊D2911yescharacteristic
149C22×C4C22⋊D2911yescharacteristic
150C22×C4C22×D2911yescharacteristic
151Q16—1162no—
152SD16—1162no—
153C2×C8—581no—
154C2×C8—581no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—1162no—
162C4⋊C4C22⋊D2911yescharacteristic
163C4⋊C4C22⋊D2911yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—21no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C42—21no—
170C23—21no—
171C23C2×C22⋊D2911yescharacteristic
172Q8—41no—
173Q8—582no—
174Q8—582no—
175Q8—1161no—
176Q8—1161no—
177D4—41no—
178D4—41no—
179D4—41no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—81no—
190C2×C4—582no—
191C2×C4—582no—
192C2×C4—1161no—
193C2×C4—1161no—
194C2×C4—1161no—
195C2×C4—1161no—
196C2×C4C2×C22⋊D2911yescharacteristic
197C2×C4C2×C22⋊D2911yescharacteristic
198C8—1161no—
199C8—1161no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22#1174531211yescharacteristic
206C22#1174531311yescharacteristic
207C22#1174531511yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—41no—
212C4—41no—
213C4—41no—
214C4—41no—
215C4—1162no—
216C4—1162no—
217C2—21no—
218C2—21no—
219C2—81no—
220C2#1427132511yescharacteristic
221C2#1427134611yescharacteristic
222C2#1427135011yescharacteristic
subgroupG/H
centerC22#11745315
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#539C2
socleC22×C29#120
prime radicalC29×#121C22
hypercenter#539D29
hypocenterC29#1603
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #14271318C2semidirect
3. #14271083C2semidirect
4. #14270900C2semidirect
6. #14270889C2semidirect
138. C29#1603semidirect

Maximal subgroups

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

subgroupindex
#142713182
#142713012
#142710832
#142709002
#142708972
#142708892
C29×#5392
#160329