Finite Group Databasebeta

← #16818456

Subgroups — #16818456

Order 3712.

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

normal subgroups only

This group has 244 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#14271758C211yesmaximal, characteristic
2#14271321C211yesmaximal, characteristic, complemented
3#14271301C211yesmaximal, characteristic
4#14271084C211yesmaximal, characteristic, complemented
5#14270899C211yesmaximal, characteristic, complemented
6#14270888C211yesmaximal, characteristic, complemented
7C29×#327C211yesmaximal, characteristic
8C22×Dic58C2211yescharacteristic
9C29×#121C2211yescharacteristic
10#11745297—21no—
11#11745297—21no—
12D4×Dic29—21no—
13C2×#90783—21no—
14C2×C4⋊Dic29—21no—
15#11745286C2211yescharacteristic
16C2×#90779C2211yescharacteristic
17C2×Dic116—21no—
18#11745251—21no—
19#11745241—21no—
20#11745240—21no—
21C29×C22⋊C8C2211yescharacteristic
22C29×#95C2211yescharacteristic
23#11745179—21no—
24C22⋊#6597C2211yescharacteristic
25#11745164—21no—
26#11745158—21no—
27C2×D4×C29—21no—
28C2×D4×C29D411yescharacteristic
29C22×C4×C29—21no—
30C22×C4×C29C2311yescharacteristic
31C22×Dic29—21no—
32C22×Dic29—21no—
33C22×Dic29D411yescharacteristic
34C22×Dic29D411yescharacteristic
35C2×Dic58—21no—
36C2×Dic58—21no—
37C2×Dic58—42no—
38C2×Dic58D411yescharacteristic
39C2×C8×C29—21no—
40C4⋊C4×C29D411yescharacteristic
41C22⋊C4×C29—21no—
42C22⋊Dic29—21no—
43C22⋊Dic29—21no—
44C22⋊Dic29—21no—
45C22⋊Dic29—21no—
46#90783—42no—
47C4⋊Dic29—21no—
48C4⋊Dic29—42no—
49C4⋊Dic29D411yescharacteristic
50#90779—21no—
51#90779—21no—
52#90779—21no—
53#90779—21no—
54#90779—21no—
55C4×Dic29—21no—
56C2×#6597—21no—
57Dic116—42no—
58C23×C29—21no—
59C23×C29C2×D411yescharacteristic
60D4×C29—41no—
61D4×C29—41no—
62D4×C29—41no—
63C2×C4×C29—22no—
64C2×C4×C29—21no—
65C2×C4×C29—41no—
66C2×C4×C29—41no—
67C2×C4×C29—41no—
68C2×C4×C29C2×D411yescharacteristic
69C2×C4×C29C2×D411yescharacteristic
70C2×Dic29—22no—
71C2×Dic29—21no—
72C2×Dic29—21no—
73C2×Dic29—21no—
74C2×Dic29—21no—
75C2×Dic29—21no—
76C2×Dic29—21no—
77C2×Dic29—41no—
78C2×Dic29—41no—
79C2×Dic29—41no—
80C2×Dic29—81no—
81Dic58—22no—
82Dic58—22no—
83Dic58—41no—
84Dic58—41no—
85Dic58—41no—
86C8×C29—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—42no—
100C4×C29—41no—
101Dic29—41no—
102Dic29—41no—
103Dic29—42no—
104Dic29—41no—
105Dic29—41no—
106#539—291no—
107#451—291no—
108#448—291no—
109#395—291no—
110#328—291no—
111#327D2911yescharacteristic
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—581no—
123#125—581no—
124#123—581no—
125#123—581no—
126C22⋊Q8—291no—
127C22⋊Q8—581no—
128#121C2×D2911yescharacteristic
129C4×D4—581no—
130C2×C4⋊C4—291no—
131C2×C4⋊C4—581no—
132#103—581no—
133#103—581no—
134C22⋊C8—291no—
135C22⋊C8C2×D2911yescharacteristic
136#95—581no—
137#95C2×D2911yescharacteristic
138C29#160311yescharacteristic, complemented, Sylow
139C2×Q8—291no—
140C2×Q8—581no—
141C2×Q8—581no—
142C2×Q8—1162no—
143C2×D4—21no—
144C2×D4D11611yescharacteristic
145C22×C4—21no—
146C22×C4—291no—
147C22×C4—291no—
148C22×C4—581no—
149C22×C4—581no—
150C22×C4C22×D2911yescharacteristic
151Q16—1162no—
152SD16—1162no—
153C2×C8—21no—
154C2×C8—581no—
155C4⋊C4—291no—
156C4⋊C4—581no—
157C4⋊C4—581no—
158C4⋊C4—581no—
159C4⋊C4—581no—
160C4⋊C4—581no—
161C4⋊C4—581no—
162C4⋊C4—1162no—
163C4⋊C4D11611yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—581no—
166C22⋊C4—581no—
167C22⋊C4—581no—
168C22⋊C4—581no—
169C42—581no—
170C23—21no—
171C23D4×D2911yescharacteristic
172Q8—582no—
173Q8—582no—
174Q8—1161no—
175Q8—1161no—
176Q8—1161no—
177D4—41no—
178D4—41no—
179D4—41no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—582no—
186C2×C4—581no—
187C2×C4—581no—
188C2×C4—581no—
189C2×C4—581no—
190C2×C4—581no—
191C2×C4—581no—
192C2×C4—1161no—
193C2×C4—1161no—
194C2×C4—1161no—
195C2×C4—2321no—
196C2×C4C2×D11611yescharacteristic
197C2×C4D4×D2911yescharacteristic
198C8—41no—
199C8—1161no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22#1174524411yescharacteristic
206C22#1174527411yescharacteristic
207C22#1174527711yescharacteristic
208C4—21no—
209C4—21no—
210C4—42no—
211C4—41no—
212C4—1161no—
213C4—1161no—
214C4—1162no—
215C4—1161no—
216C4—1161no—
217C2—21no—
218C2—21no—
219C2—81no—
220C2#1427132611yescharacteristic
221C2#1427134711yescharacteristic
222C2#1427135111yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#327C2
socleC22×C29#120
prime radicalC29×#121C22
hypercenter#327D29
hypocenterC29#1603
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. #14271321C2semidirect
4. #14271084C2semidirect
5. #14270899C2semidirect
6. #14270888C2semidirect
138. C29#1603semidirect

Maximal subgroups

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

subgroupindex
#142717582
#142713212
#142713012
#142710842
#142708992
#142708882
C29×#3272
#160329