Finite Group Databasebeta

← #16820744

Subgroups — #16820744

Order 3712.

382 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 67 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#14271725C211yesmaximal, characteristic
2C2×#11745154C212yesmaximal, complemented
3#14271040C212yesmaximal, complemented
4#14271035C211yesmaximal, characteristic, complemented
5C29×#342C211yesmaximal, characteristic, complemented
6C22×C22⋊D29C2212yes—
7C23×Dic29C2211yescharacteristic
8C2×C22⋊C4×C29C2212yes—
9C2×C22⋊C4×C29C2211yescharacteristic
10C2×C22⋊Dic29C2211yescharacteristic
11#11745292—21no—
12#11745292—21no—
13C2×#90781—22no—
14C2×#90779—21no—
15#11745248—22no—
16#11745244—22no—
17#11745179—21no—
18#11745179—22no—
19#11745154—24no—
20C24×C29C2311yescharacteristic
21C23×D29D412yes—
22C22×C4×C29—22no—
23C22×C4×C29D411yescharacteristic
24C22×C4×C29D411yescharacteristic
25C2×C22⋊D29—22no—
26C2×C22⋊D29—22no—
27C2×C22⋊D29—22no—
28C2×C22⋊D29—22no—
29C2×C22⋊D29—22no—
30C2×C22⋊D29—22no—
31C22×Dic29—21no—
32C22×Dic29—21no—
33C22×Dic29—22no—
34C22×Dic29—42no—
35C22×Dic29D412yes—
36C2×D116—21no—
37C2×D116—21no—
38C22⋊C4×C29—22no—
39C22⋊C4×C29—22no—
40C22⋊C4×C29—22no—
41C22⋊Dic29—21no—
42C22⋊Dic29D412yescomplemented
43#90781—22no—
44#90781—22no—
45#90781—44no—
46C4⋊Dic29—21no—
47C4⋊Dic29—21no—
48#90779—42no—
49C23×C29—41no—
50C23×C29—41no—
51C23×C29C2×D411yescharacteristic
52C23×C29C2×D412yes—
53C23×C29C2×D411yescharacteristic
54C23×C29#4112yes—
55C23×C29#4111yescharacteristic
56C22×D29—22no—
57C22×D29—22no—
58C22×D29—22no—
59C22×D29—42no—
60C22×D29—42no—
61C2×C4×C29—21no—
62C2×C4×C29—21no—
63C2×C4×C29—41no—
64C2×C4×C29—41no—
65C2×C4×C29—42no—
66C2×C4×C29—42no—
67C2×C4×C29—42no—
68C22⋊D29—42no—
69C22⋊D29—42no—
70C22⋊D29—42no—
71C22⋊D29—42no—
72C2×Dic29—22no—
73C2×Dic29—24no—
74C2×Dic29—22no—
75C2×Dic29—22no—
76C2×Dic29—22no—
77C2×Dic29—22no—
78C2×Dic29—41no—
79C2×Dic29—41no—
80C2×Dic29—41no—
81C2×Dic29—42no—
82C2×Dic29—41no—
83D116—81no—
84D116—81no—
85#2044—291nomaximal, Sylow
86C22×C29—21no—
87C22×C29—22no—
88C22×C29—21no—
89C22×C29—22no—
90C22×C29—41no—
91C22×C29—42no—
92C22×C29—41no—
93C22×C29#12011yescharacteristic
94C22×C29#12112yes—
95C22×C29#12111yescharacteristic
96C22×C29#12312yes—
97C22×C29#12411yescharacteristic
98C2×D29—44no—
99C2×D29—42no—
100C2×D29—42no—
101C2×D29—42no—
102C2×D29—82no—
103C4×C29—41no—
104C4×C29—41no—
105C4×C29—82no—
106Dic29—42no—
107Dic29—42no—
108Dic29—42no—
109#534—291no—
110C2×#99—292no—
111#386—292no—
112#385—291no—
113#342D2911yescharacteristic, complemented
114C2×C29—21no—
115C2×C29—22no—
116C2×C29—22no—
117C2×C29—21no—
118C2×C29#39411yescharacteristic
119C2×C29B(4,𝔽2)11yescharacteristic
120C2×C29#45811yescharacteristic
121D29—82no—
122C22×D4—292no—
123C23×C4—291no—
124#123—582no—
125#121—581no—
126#121—581no—
127#120—582no—
128C2×C4⋊C4—581no—
129C2×C22⋊C4—291no—
130C2×C22⋊C4—582no—
131C2×C22⋊C4C2×D2912yes—
132C2×C22⋊C4C2×D2911yescharacteristic
133#99—584no—
134#95—582no—
135#95—581no—
136C29#204411yescharacteristic, complemented, Sylow
137C24—292no—
138C24C22×D2911yescharacteristic
139C2×D4—581no—
140C2×D4—581no—
141C2×D4—582no—
142C2×D4—582no—
143C2×D4—582no—
144C2×D4—582no—
145C2×D4—582no—
146C2×D4—582no—
147C22×C4—22no—
148C22×C4—292no—
149C22×C4—581no—
150C22×C4—581no—
151C22×C4—582no—
152C22×C4—1162no—
153C22×C4D11611yescharacteristic
154C22×C4D11611yescharacteristic
155C4⋊C4—581no—
156C4⋊C4—581no—
157C4⋊C4—1162no—
158C22⋊C4—22no—
159C22⋊C4—22no—
160C22⋊C4—22no—
161C22⋊C4—292no—
162C22⋊C4—582no—
163C22⋊C4—582no—
164C22⋊C4—581no—
165C22⋊C4—1164no—
166C23—41no—
167C23—41no—
168C23—582no—
169C23—582no—
170C23—582no—
171C23—1162no—
172C23—1162no—
173C23C2×D11611yescharacteristic
174C23#9080512yes—
175C23D4×D2912yes—
176C23D4×D2911yescharacteristic
177C23#9080911yescharacteristic
178D4—1162no—
179D4—1162no—
180D4—1162no—
181D4—1162no—
182D4—2321no—
183D4—2321no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—584no—
192C2×C4—582no—
193C2×C4—582no—
194C2×C4—582no—
195C2×C4—582no—
196C2×C4—582no—
197C2×C4—1161no—
198C2×C4—1161no—
199C2×C4—1162no—
200C2×C4—1161no—
201C2×C4—1161no—
202C22—21no—
203C22—22no—
204C22—21no—
205C22—22no—
206C22—42no—
207C22—41no—
208C22—41no—
209C22—1164no—
210C22—1162no—
211C22—1162no—
212C22—1162no—
213C22—2322no—
214C22#1174523711yescharacteristic
215C22#1174524411yescharacteristic
216C22#1174524612yes—
217C22#1174525612yes—
218C22#1174525711yescharacteristic
219C4—41no—
220C4—41no—
221C4—82no—
222C4—1162no—
223C4—1162no—
224C4—1162no—
225C2—22no—
226C2—21no—
227C2—22no—
228C2—21no—
229C2—2322no—
230C2#1427108111yescharacteristic
231C2#1427135111yescharacteristic
232C2#1427135411yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC24×C29C23
FrattiniC24C22×D29
FittingC29×#342C2
socleC22×C29#120
prime radical#14271725C2
hypercenter#342D29
hypocenterC29#2044
LCSG ▷ C24×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
2. C2×#11745154C2semidirect
3. #14271040C2semidirect
4. #14271035C2semidirect
5. C29×#342C2semidirect
42. C22⋊Dic29D4semidirect
113. #342D29semidirect
136. C29#2044semidirect

Maximal subgroups

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

subgroupindex
#142717252
C2×#117451542
#142710402
#142710352
C29×#3422
#204429