Finite Group Databasebeta

← #16818510

Subgroups — #16818510

Order 3712.

288 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 51 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#14271721C211yesmaximal, characteristic
2#14271481C211yesmaximal, characteristic, complemented
3#14271098C211yesmaximal, characteristic, complemented
4#14270898C211yesmaximal, characteristic, complemented
5#14270897C211yesmaximal, characteristic, complemented
6#14270886C211yesmaximal, characteristic, complemented
7C29×#481C211yesmaximal, characteristic, complemented
8C2×D4×D29—21no—
9C29×#121C2211yescharacteristic
10C2×C4⋊C4×C29C2211yescharacteristic, complemented
11#11745301—21no—
12#11745299—21no—
13#11745292C2211yescharacteristic
14C2×#90781—21no—
15C2×#90781C2211yescharacteristic
16C2×#90779—21no—
17#11745256—21no—
18#11745245—21no—
19#11745244—21no—
20C29×#106—21no—
21C29×#102—21no—
22C29×C22⋊C8C2211yescharacteristic, complemented
23#11745179C2211yescharacteristic, complemented
24C22⋊#6597C2211yescharacteristic, complemented
25#11745157—21no—
26#11745156—21no—
27C23×D29—21no—
28C23×D29D411yescharacteristic
29C2×D4×C29—21no—
30C2×D4×C29D411yescharacteristic
31C22×C4×C29—21no—
32C22×C4×C29C2311yescharacteristic
33C2×C22⋊D29—21no—
34C2×C22⋊D29—21no—
35C2×C22⋊D29—21no—
36C22×Dic29—21no—
37C22×Dic29D411yescharacteristic
38D4×D29—42no—
39D4×D29—42no—
40C2×D116—21no—
41C2×D116D411yescharacteristic
42C2×C4×D29—21no—
43C2×C8×C29—21no—
44C4⋊C4×C29—21no—
45C4⋊C4×C29—21no—
46C4⋊C4×C29D411yescharacteristic
47C22⋊C4×C29—21no—
48C22⋊Dic29—21no—
49#90781—21no—
50#90781—21no—
51#90781—21no—
52#90781—21no—
53#90781—42no—
54C4⋊Dic29D411yescharacteristic
55#90779—21no—
56#90779—42no—
57C2×#6597—21no—
58C23×C29—21no—
59C23×C29C2×D411yescharacteristic
60C22×D29—21no—
61C22×D29—21no—
62C22×D29—21no—
63C22×D29—42no—
64C22×D29—41no—
65C22×D29—41no—
66C22×D29—81no—
67C22×D29—81no—
68C22×D29SD1612yes—
69D4×C29—41no—
70D4×C29—41no—
71D4×C29—41no—
72C2×C4×C29—21no—
73C2×C4×C29—41no—
74C2×C4×C29—41no—
75C2×C4×C29—41no—
76C2×C4×C29—41no—
77C2×C4×C29C2×D411yescharacteristic
78C2×C4×C29C2×D411yescharacteristic
79C22⋊D29—42no—
80C22⋊D29—41no—
81C22⋊D29—41no—
82C22⋊D29—81no—
83C2×Dic29—22no—
84C2×Dic29—21no—
85C2×Dic29—21no—
86C2×Dic29—41no—
87C2×Dic29—41no—
88C2×Dic29—41no—
89D116—41no—
90D116—42no—
91C4×D29—42no—
92C8×C29—41no—
93#6597—41no—
94#1613—291nomaximal, Sylow
95C22×C29—21no—
96C22×C29—21no—
97C22×C29—41no—
98C22×C29—41no—
99C22×C29—41no—
100C22×C29#12011yescharacteristic
101C22×C29C2×SD1611yescharacteristic
102C22×C29AGL(1,ℤ/8)11yescharacteristic
103C2×D29—22no—
104C2×D29—41no—
105C2×D29—41no—
106C2×D29—42no—
107C2×D29—41no—
108C2×D29—41no—
109C2×D29—41no—
110C2×D29—81no—
111C2×D29—84no—
112C4×C29—21no—
113C4×C29—21no—
114C4×C29—41no—
115C4×C29—81no—
116Dic29—42no—
117Dic29—41no—
118Dic29—41no—
119#534—291no—
120#481—291no—
121#481D2911yescharacteristic, complemented
122#399—291no—
123#327—291no—
124#327—291no—
125#323—291no—
126C2×C29—21no—
127C2×C29—21no—
128C2×C29—81no—
129C2×C29#45011yescharacteristic
130C2×C29#45311yescharacteristic
131C2×C29#45811yescharacteristic
132D29—42no—
133D29—81no—
134C22×D4—581no—
135#123—581no—
136#123—581no—
137#121—291no—
138#121—581no—
139#121C2×D2911yescharacteristic
140#120—581no—
141#120—581no—
142C2×C4⋊C4—581no—
143C2×C4⋊C4C2×D2911yescharacteristic, complemented
144C2×C22⋊C4—291no—
145C2×C22⋊C4—581no—
146#106—21no—
147#106—581no—
148#102—21no—
149#102—581no—
150C22⋊C8—291no—
151C22⋊C8C2×D2911yescharacteristic, complemented
152#95—291no—
153C29#161311yescharacteristic, complemented, Sylow
154C24—291no—
155C24—581no—
156C2×D4—21no—
157C2×D4—291no—
158C2×D4—581no—
159C2×D4—581no—
160C2×D4—581no—
161C2×D4—581no—
162C2×D4—1162no—
163C2×D4—1162no—
164C2×D4C22⋊D2911yescharacteristic
165C22×C4—21no—
166C22×C4—291no—
167C22×C4—581no—
168C22×C4—581no—
169C22×C4C22×D2911yescharacteristic
170C2×C8—21no—
171C2×C8—581no—
172C4⋊C4—21no—
173C4⋊C4—21no—
174C4⋊C4—291no—
175C4⋊C4—581no—
176C4⋊C4—1162no—
177C4⋊C4C22⋊D2911yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—581no—
180C22⋊C4—581no—
181C22⋊C4—581no—
182C22⋊C4—581no—
183C22⋊C4—581no—
184C22⋊C4—1162no—
185C23—21no—
186C23—292no—
187C23—581no—
188C23—581no—
189C23—581no—
190C23—1161no—
191C23—1161no—
192C23—1162no—
193C23—2321no—
194C23—2321no—
195C23D4×D2911yescharacteristic
196D4—41no—
197D4—41no—
198D4—41no—
199D4—1161no—
200D4—1162no—
201D4—1162no—
202D4—1161no—
203D4—1161no—
204D4—2321no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—582no—
211C2×C4—581no—
212C2×C4—581no—
213C2×C4—1162no—
214C2×C4—1161no—
215C2×C4—1161no—
216C2×C4—1161no—
217C2×C4D4×D2911yescharacteristic
218C2×C4C2×C22⋊D2911yescharacteristic
219C8—41no—
220C8—1161no—
221C22—21no—
222C22—21no—
223C22—41no—
224C22—41no—
225C22—41no—
226C22—582no—
227C22—1162no—
228C22—1161no—
229C22—1161no—
230C22—1161no—
231C22—1161no—
232C22—1161no—
233C22—2321no—
234C22—2324no—
235C22SD16×D2911yescharacteristic
236C22#1174527611yescharacteristic
237C22#1174529911yescharacteristic
238C4—21no—
239C4—21no—
240C4—41no—
241C4—81no—
242C4—1162no—
243C4—1161no—
244C4—1161no—
245C2—21no—
246C2—21no—
247C2—81no—
248C2—1162no—
249C2—2321no—
250C2#1427131211yescharacteristic
251C2#1427132911yescharacteristic
252C2#1427135211yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#481C2
socleC22×C29#120
prime radical#14271721C2
hypercenter#481D29
hypocenterC29#1613
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. #14271481C2semidirect
3. #14271098C2semidirect
4. #14270898C2semidirect
5. #14270897C2semidirect
6. #14270886C2semidirect
7. C29×#481C2semidirect
10. C2×C4⋊C4×C29C22semidirect
22. C29×C22⋊C8C22semidirect
23. #11745179C22semidirect
24. C22⋊#6597C22semidirect
121. #481D29semidirect
143. C2×C4⋊C4C2×D29semidirect
151. C22⋊C8C2×D29semidirect
153. C29#1613semidirect

Maximal subgroups

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

subgroupindex
#142717212
#142714812
#142710982
#142708982
#142708972
#142708862
C29×#4812
#161329