Finite Group Databasebeta

← #16818457

Subgroups — #16818457

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#14271760C211yesmaximal, characteristic
2#14271321C211yesmaximal, characteristic, complemented
3#14271304C211yesmaximal, characteristic
4#14271083C211yesmaximal, characteristic, complemented
5#14270901C211yesmaximal, characteristic, complemented
6#14270898C211yesmaximal, characteristic
7C29×#324C211yesmaximal, characteristic, complemented
8C22×Dic58C2211yescharacteristic
9C2×C4⋊C4×C29C2211yescharacteristic
10#11745292C2211yescharacteristic
11#11745291—21no—
12C4×C22⋊D29—21no—
13#11745286C2211yescharacteristic
14C2×#90779—21no—
15C2×Dic116—21no—
16C2×#90773—21no—
17#11745260—21no—
18#11745258—21no—
19#11745256—21no—
20#11745251—21no—
21C29×C22⋊C8C2211yescharacteristic
22C29×C22⋊C8C2211yescharacteristic
23#11745179—21no—
24#11745179C2211yescharacteristic
25#11745164—21no—
26#11745164—21no—
27C22×C4×C29D411yescharacteristic
28C22×C4×C29D411yescharacteristic
29C22×C4×C29C2311yescharacteristic
30C2×C22⋊D29—21no—
31C22×Dic29—21no—
32C22×Dic29—21no—
33C2×D116D411yescharacteristic
34C2×C4×D29—21no—
35C2×Dic58—21no—
36C2×Dic58—21no—
37C2×Dic58—42no—
38C2×Dic58D411yescharacteristic
39C2×C8×C29—21no—
40C2×C8×C29—21no—
41C4⋊C4×C29—21no—
42C4⋊C4×C29—21no—
43C22⋊Dic29—21no—
44#90781—21no—
45#90781—21no—
46#90781—21no—
47#90781—21no—
48C4⋊Dic29D411yescharacteristic
49C4⋊Dic29D411yescharacteristic
50#90779—21no—
51#90779—21no—
52#90779—21no—
53#90779—21no—
54#90779—42no—
55C4×Dic29—21no—
56Dic116—42no—
57#90773—42no—
58C23×C29C2×D411yescharacteristic
59C22×D29—21no—
60C2×C4×C29—21no—
61C2×C4×C29—21no—
62C2×C4×C29—21no—
63C2×C4×C29—21no—
64C2×C4×C29—41no—
65C2×C4×C29—41no—
66C2×C4×C29C2×D411yescharacteristic
67C2×C4×C29C2×D411yescharacteristic
68C22⋊D29—41no—
69C22⋊D29—41no—
70C2×Dic29—22no—
71C2×Dic29—22no—
72C2×Dic29—21no—
73C2×Dic29—21no—
74C2×Dic29—21no—
75C2×Dic29—41no—
76C2×Dic29—41no—
77C2×Dic29—41no—
78C2×Dic29—41no—
79D116—41no—
80C4×D29—81no—
81Dic58—22no—
82Dic58—22no—
83Dic58—41no—
84Dic58—41no—
85Dic58—41no—
86C8×C29—41no—
87C8×C29—41no—
88#1603—291nomaximal, Sylow
89C22×C29—21no—
90C22×C29—21no—
91C22×C29#12011yescharacteristic
92C22×C29#13511yescharacteristic
93C22×C29#13711yescharacteristic
94C2×D29—41no—
95C2×D29—41no—
96C2×D29—41no—
97C4×C29—21no—
98C4×C29—21no—
99C4×C29—41no—
100C4×C29—41no—
101Dic29—42no—
102Dic29—41no—
103Dic29—41no—
104Dic29—42no—
105Dic29—41no—
106#539—291no—
107#451—291no—
108#448—291no—
109#395—291no—
110#328—291no—
111#327—291no—
112#324D2911yescharacteristic, complemented
113C2×C29—21no—
114C2×C29—21no—
115C2×C29#45211yescharacteristic
116C2×C29#45611yescharacteristic
117C2×C29B(4,𝔽2)11yescharacteristic
118D29—81no—
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#121—291no—
129C4×D4—581no—
130C2×C4⋊C4—581no—
131C2×C4⋊C4C2×D2911yescharacteristic
132#103—581no—
133#103—581no—
134C22⋊C8C2×D2911yescharacteristic
135C22⋊C8C2×D2911yescharacteristic
136#95—291no—
137#95—581no—
138C29#160311yescharacteristic, complemented, Sylow
139C2×Q8—291no—
140C2×Q8—581no—
141C2×Q8—581no—
142C2×Q8—1162no—
143C2×D4—291no—
144C2×D4—581no—
145C22×C4—581no—
146C22×C4—581no—
147C22×C4—581no—
148C22×C4D11611yescharacteristic
149C22×C4D11611yescharacteristic
150C22×C4C22×D2911yescharacteristic
151Q16—1162no—
152SD16—1162no—
153C2×C8—21no—
154C2×C8—21no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—291no—
158C4⋊C4—291no—
159C4⋊C4—581no—
160C4⋊C4—581no—
161C4⋊C4—581no—
162C4⋊C4—581no—
163C4⋊C4—1162no—
164C22⋊C4—581no—
165C22⋊C4—581no—
166C22⋊C4—581no—
167C22⋊C4—581no—
168C22⋊C4—581no—
169C42—581no—
170C23—581no—
171C23C2×D11611yescharacteristic
172Q8—582no—
173Q8—582no—
174Q8—1161no—
175Q8—1161no—
176Q8—1161no—
177D4—1161no—
178D4—1161no—
179D4—1161no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—582no—
187C2×C4—582no—
188C2×C4—581no—
189C2×C4—581no—
190C2×C4—581no—
191C2×C4—1161no—
192C2×C4—1161no—
193C2×C4—1161no—
194C2×C4—1161no—
195C2×C4—2321no—
196C2×C4D4×D2911yescharacteristic
197C2×C4D4×D2911yescharacteristic
198C8—41no—
199C8—41no—
200C22—21no—
201C22—21no—
202C22—1161no—
203C22—1161no—
204C22—1161no—
205C22#1174524411yescharacteristic
206C22#1174526611yescharacteristic
207C22#1174527111yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—41no—
212C4—1162no—
213C4—1161no—
214C4—1161no—
215C4—1162no—
216C4—1161no—
217C2—21no—
218C2—21no—
219C2—2321no—
220C2#1427132711yescharacteristic
221C2#1427134811yescharacteristic
222C2#1427135111yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#324C2
socleC22×C29#120
prime radical#11745292C22
hypercenter#324D29
hypocenterC29#1603
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #14271321C2semidirect
4. #14271083C2semidirect
5. #14270901C2semidirect
7. C29×#324C2semidirect
112. #324D29semidirect
138. C29#1603semidirect

Maximal subgroups

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

subgroupindex
#142717602
#142713212
#142713042
#142710832
#142709012
#142708982
C29×#3242
#160329