Finite Group Databasebeta

← #16818800

Subgroups — #16818800

Order 3712.

228 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 45 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#14271905C211yesmaximal, characteristic
2#14271557C211yesmaximal, characteristic, complemented
3#14271523C211yesmaximal, characteristic, complemented
4#14271522C211yesmaximal, characteristic, complemented
5#14270902C211yesmaximal, characteristic, complemented
6#14270902C211yesmaximal, characteristic, complemented
7C29×#329C211yesmaximal, characteristic, complemented
8C29×#124C2211yescharacteristic
9#11745309—21no—
10#11745299—21no—
11C2×Dic116—21no—
12C2×#90773—21no—
13#11745247—21no—
14#11745247—21no—
15#11745244—21no—
16#11745244—21no—
17#11745237C2211yescharacteristic
18#11745237C2211yescharacteristic
19#11745231C2211yescharacteristic, complemented
20C29×#97C2211yescharacteristic, complemented
21C29×#97C2211yescharacteristic, complemented
22#11745183—21no—
23#11745180—21no—
24#11745169—21no—
25#11745164—21no—
26#11745151C2211yescharacteristic, complemented
27C23×D29—21no—
28C2×Q8×C29D411yescharacteristic
29C2×D4×C29D411yescharacteristic
30C2×C22⋊D29—21no—
31C2×C22⋊D29—21no—
32C2×D116—21no—
33C2×D116D411yescharacteristic
34C2×D116D411yescharacteristic
35C2×Dic58—21no—
36C2×Dic58D411yescharacteristic
37C2×Dic58D411yescharacteristic
38C2×C8×C29—21no—
39C2×C8×C29—21no—
40C22⋊C4×C29—21no—
41C22⋊C4×C29—21no—
42C42×C29C2311yescharacteristic
43C22⋊Dic29—21no—
44#90781—21no—
45#90781—21no—
46#90781—21no—
47#90781—21no—
48#90781—21no—
49#90781—21no—
50C4⋊Dic29—21no—
51C4⋊Dic29—21no—
52C4×Dic29—21no—
53C2×#6597—21no—
54Dic116—42no—
55#90773—42no—
56C23×C29—21no—
57C22×D29—21no—
58C22×D29—21no—
59C22×D29—81no—
60C22×D29—81no—
61C22×D29—81no—
62Q8×C29—41no—
63D4×C29—41no—
64C2×C4×C29—21no—
65C2×C4×C29C2×D411yescharacteristic
66C2×C4×C29C2×D411yescharacteristic
67C2×C4×C29C2×D411yescharacteristic
68C22⋊D29—81no—
69C22⋊D29—81no—
70C2×Dic29—21no—
71C2×Dic29—21no—
72C2×Dic29—41no—
73D116—41no—
74D116—41no—
75D116—81no—
76Dic58—41no—
77Dic58—41no—
78Dic58—41no—
79Dic58—41no—
80C8×C29—22no—
81C8×C29—41no—
82#6597—41no—
83#1659—291nomaximal, Sylow
84C22×C29—41no—
85C22×C29—41no—
86C22×C29—41no—
87C22×C29#12011yescharacteristic
88C2×D29—41no—
89C2×D29—41no—
90C2×D29—41no—
91C2×D29—41no—
92C2×D29—41no—
93C2×D29—41no—
94C2×D29—84no—
95C4×C29—21no—
96C4×C29—21no—
97C4×C29—21no—
98C4×C29—41no—
99Dic29—41no—
100Dic29—41no—
101Dic29—81no—
102H(3,𝔽4)—291no—
103#497—291no—
104#489—291no—
105#489—291no—
106#329—291no—
107#329—291no—
108#329D2911yescharacteristic, complemented
109C2×C29—81no—
110C2×C29#45311yescharacteristic
111C2×C29#45511yescharacteristic
112C2×C29#45511yescharacteristic
113D29—81no—
114D29—81no—
115C2×Q16—581no—
116C2×SD16—581no—
117C4⋊Q8—291no—
118#124—291no—
119#124—291no—
120#124—581no—
121#124—581no—
122#124—581no—
123#124C2×D2911yescharacteristic
124#120—581no—
125#120—581no—
126#120—581no—
127#103—581no—
128#103—581no—
129#102—581no—
130#102—581no—
131#97—291no—
132#97C2×D2911yescharacteristic, complemented
133#97C2×D2911yescharacteristic, complemented
134C29#165911yescharacteristic, complemented, Sylow
135C24—581no—
136C2×Q8—291no—
137C2×Q8—291no—
138C2×Q8—581no—
139C2×Q8D11611yescharacteristic
140C2×D4—291no—
141C2×D4—291no—
142C2×D4—581no—
143C2×D4—581no—
144C2×D4—581no—
145C2×D4D11611yescharacteristic
146Q16—1162no—
147SD16—1162no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—581no—
151C4⋊C4—581no—
152C4⋊C4—581no—
153C22⋊C4—21no—
154C22⋊C4—21no—
155C22⋊C4—581no—
156C22⋊C4—581no—
157C22⋊C4—581no—
158C22⋊C4—581no—
159C22⋊C4—581no—
160C22⋊C4—581no—
161C22⋊C4—581no—
162C42—581no—
163C42C22×D2911yescharacteristic
164C23—21no—
165C23—581no—
166C23—581no—
167C23—2321no—
168C23—2321no—
169C23—2321no—
170Q8—41no—
171Q8—1161no—
172Q8—1161no—
173Q8—1161no—
174Q8—1161no—
175D4—41no—
176D4—1161no—
177D4—1161no—
178D4—2321no—
179D4—2321no—
180D4—2321no—
181C2×C4—21no—
182C2×C4—581no—
183C2×C4—581no—
184C2×C4—1161no—
185C2×C4C2×D11611yescharacteristic
186C2×C4D4×D2911yescharacteristic
187C2×C4D4×D2911yescharacteristic
188C8—22no—
189C8—41no—
190C8—1161no—
191C22—41no—
192C22—41no—
193C22—41no—
194C22—1161no—
195C22—1161no—
196C22—1161no—
197C22—1161no—
198C22—1161no—
199C22—1161no—
200C22—2324no—
201C22#1174524411yescharacteristic
202C4—21no—
203C4—21no—
204C4—21no—
205C4—41no—
206C4—1161no—
207C4—1161no—
208C4—2321no—
209C2—81no—
210C2—2321no—
211C2—2321no—
212C2#1427133211yescharacteristic
213C2#1427134211yescharacteristic
214C2#1427134311yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC42×C29C23
FrattiniC42C22×D29
FittingC29×#329C2
socleC22×C29#120
prime radical#14271905C2
hypercenter#329D29
hypocenterC29#1659
LCSG ▷ C42×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #14271557C2semidirect
3. #14271523C2semidirect
4. #14271522C2semidirect
5. #14270902C2semidirect
6. #14270902C2semidirect
7. C29×#329C2semidirect
19. #11745231C22semidirect
20. C29×#97C22semidirect
21. C29×#97C22semidirect
26. #11745151C22semidirect
108. #329D29semidirect
132. #97C2×D29semidirect
133. #97C2×D29semidirect
134. C29#1659semidirect

Maximal subgroups

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

subgroupindex
#142719052
#142715572
#142715232
#142715222
#142709022
C29×#3292
#165929