Finite Group Databasebeta

← #16820618

Subgroups — #16820618

Order 3712.

638 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 638 conjugacy classes of subgroups — too many to draw. Only its 73 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, complemented
2C2×#11745315C212yesmaximal, complemented
3C2×#11745154C212yesmaximal, complemented
4#14270930C211yesmaximal, characteristic, complemented
5C29×#379C211yesmaximal, characteristic, complemented
6C25×C29C2211yescharacteristic
7C22×C22⋊D29—22no—
8C22×C22⋊D29C2212yes—
9C2×C22⋊C4×C29—22no—
10C2×C22⋊C4×C29C2211yescharacteristic
11C2×C22⋊C4×C29C2211yescharacteristic
12#11745315—24no—
13#11745315—24no—
14C2×C22⋊Dic29—22no—
15C2×C22⋊Dic29C2212yes—
16#11745292—22no—
17#11745248—22no—
18#11745244—22no—
19#11745154—24no—
20C24×C29—22no—
21C24×C29—21no—
22C24×C29—22no—
23C24×C29—21no—
24C24×C29—44no—
25C24×C29D412yescomplemented
26C24×C29C2311yescharacteristic
27C23×D29D412yescomplemented
28C22×C4×C29—21no—
29C22×C4×C29D412yescomplemented
30C2×C22⋊D29—28no—
31C2×C22⋊D29—22no—
32C2×C22⋊D29—22no—
33C2×C22⋊D29—22no—
34C2×C22⋊D29—22no—
35C2×C22⋊D29—22no—
36C2×C22⋊D29—22no—
37C2×C22⋊D29—48no—
38C22×Dic29—22no—
39C22×Dic29D412yescomplemented
40C2×D116—22no—
41C22⋊C4×C29—22no—
42C22⋊C4×C29—22no—
43C22⋊C4×C29—44no—
44C22⋊Dic29—28no—
45C22⋊Dic29—22no—
46C22⋊Dic29D414yescomplemented
47#90781—24no—
48C4⋊Dic29—22no—
49C23×C29—24no—
50C23×C29—28no—
51C23×C29—24no—
52C23×C29—22no—
53C23×C29—44no—
54C23×C29—42no—
55C23×C29—44no—
56C23×C29—42no—
57C23×C29—48no—
58C23×C29—44no—
59C23×C29—41no—
60C23×C29—42no—
61C23×C29—41no—
62C23×C29C2×D411yescharacteristic
63C23×C29C2×D412yes—
64C23×C29C2×D412yes—
65C23×C29C2×D411yescharacteristic
66C23×C29#4111yescharacteristic
67C22×D29—22no—
68C22×D29—22no—
69C22×D29—22no—
70C22×D29—44no—
71C2×C4×C29—22no—
72C2×C4×C29—42no—
73C2×C4×C29—42no—
74C2×C4×C29—41no—
75C22⋊D29—416no—
76C22⋊D29—42no—
77C22⋊D29—42no—
78C22⋊D29—42no—
79C22⋊D29—42no—
80C2×Dic29—22no—
81C2×Dic29—22no—
82C2×Dic29—24no—
83C2×Dic29—22no—
84C2×Dic29—44no—
85D116—82no—
86#2021—291nomaximal, Sylow
87C22×C29—24no—
88C22×C29—22no—
89C22×C29—28no—
90C22×C29—24no—
91C22×C29—41no—
92C22×C29—42no—
93C22×C29—41no—
94C22×C29—44no—
95C22×C29—44no—
96C22×C29—48no—
97C22×C29—42no—
98C22×C29—42no—
99C22×C29—44no—
100C22×C29#12011yescharacteristic
101C22×C29#12012yes—
102C22×C29#12111yescharacteristic
103C22×C29#12112yes—
104C22×C29#12711yescharacteristic
105C2×D29—44no—
106C2×D29—42no—
107C2×D29—44no—
108C2×D29—82no—
109C4×C29—42no—
110C4×C29—81no—
111Dic29—44no—
112Dic29—42no—
113#534—291no—
114C2×#120—292no—
115C2×#99—292no—
116#379D2911yescharacteristic, complemented
117#342—291no—
118C2×C29—22no—
119C2×C29—21no—
120C2×C29—22no—
121C2×C29—21no—
122C2×C29—44no—
123C2×C29#39211yescharacteristic
124C2×C29B(4,𝔽2)12yes—
125D29—82no—
126C25C2×D2911yescharacteristic
127C22×D4—292no—
128C22×D4—582no—
129#123—582no—
130#121—582no—
131#120—582no—
132#120—584no—
133#120—584no—
134C2×C22⋊C4—22no—
135C2×C22⋊C4—292no—
136C2×C22⋊C4—582no—
137C2×C22⋊C4C2×D2911yescharacteristic
138C2×C22⋊C4C2×D2911yescharacteristic
139#99—584no—
140C29#202111yescharacteristic, complemented, Sylow
141C24—22no—
142C24—21no—
143C24—21no—
144C24—22no—
145C24—44no—
146C24—292no—
147C24D11612yescomplemented
148C24C22×D2911yescharacteristic
149C2×D4—582no—
150C2×D4—588no—
151C2×D4—582no—
152C2×D4—582no—
153C2×D4—582no—
154C2×D4—582no—
155C2×D4—582no—
156C2×D4—582no—
157C2×D4—1168no—
158C22×C4—21no—
159C22×C4—292no—
160C22×C4—582no—
161C22×C4C22⋊D2912yescomplemented
162C4⋊C4—582no—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—44no—
166C22⋊C4—294no—
167C22⋊C4—584no—
168C22⋊C4—588no—
169C22⋊C4—582no—
170C23—24no—
171C23—28no—
172C23—22no—
173C23—24no—
174C23—44no—
175C23—42no—
176C23—42no—
177C23—44no—
178C23—48no—
179C23—44no—
180C23—41no—
181C23—41no—
182C23—42no—
183C23—582no—
184C23—582no—
185C23—582no—
186C23—1164no—
187C23C2×D11611yescharacteristic
188C23#9080511yescharacteristic
189C23D4×D2912yes—
190C23D4×D2912yes—
191C23C2×C22⋊D2911yescharacteristic
192D4—11616no—
193D4—1162no—
194D4—1162no—
195D4—1162no—
196D4—1162no—
197D4—2322no—
198C2×C4—22no—
199C2×C4—42no—
200C2×C4—42no—
201C2×C4—41no—
202C2×C4—582no—
203C2×C4—584no—
204C2×C4—582no—
205C2×C4—582no—
206C2×C4—1164no—
207C22—22no—
208C22—24no—
209C22—28no—
210C22—24no—
211C22—41no—
212C22—41no—
213C22—42no—
214C22—44no—
215C22—44no—
216C22—42no—
217C22—48no—
218C22—42no—
219C22—44no—
220C22—1164no—
221C22—1162no—
222C22—1164no—
223C22—2322no—
224C22#1174524412yes—
225C22#1174524612yes—
226C22#1174529211yescharacteristic
227C22#1174529911yescharacteristic
228C22#1174530211yescharacteristic
229C4—42no—
230C4—81no—
231C4—1164no—
232C4—1162no—
233C2—21no—
234C2—22no—
235C2—21no—
236C2—22no—
237C2—44no—
238C2—2322no—
239C2#1427107211yescharacteristic
240C2#1427134912yes—
subgroupG/H
centerC22#11745299
commutator, cosocleC24×C29C23
FrattiniC24C22×D29
FittingC29×#379C2
socleC22×C29#120
hypercenter#379D29
hypocenterC29#2021
LCSG ▷ C24×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C24 ◁ #379

Complements

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

NH ≅ G/Ntype
1. #14271725C2semidirect
2. C2×#11745315C2semidirect
3. C2×#11745154C2semidirect
4. #14270930C2semidirect
5. C29×#379C2semidirect
25. C24×C29D4semidirect
27. C23×D29D4semidirect
29. C22×C4×C29D4semidirect
39. C22×Dic29D4semidirect
46. C22⋊Dic29D4semidirect
116. #379D29semidirect
140. C29#2021semidirect
147. C24D116semidirect
161. C22×C4C22⋊D29semidirect

Maximal subgroups

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

subgroupindex
#142717252
C2×#117453152
C2×#117451542
#142709302
C29×#3792
#202129