Finite Group Databasebeta

← #16818459

Subgroups — #16818459

Order 3712.

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

normal subgroups only

This group has 282 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#14271740C211yesmaximal, characteristic
2#14271302C211yesmaximal, characteristic, complemented
3#14271082C211yesmaximal, characteristic, complemented
4#14270898C211yesmaximal, characteristic, complemented
5#14270897C211yesmaximal, characteristic, complemented
6#14270888C211yesmaximal, characteristic, complemented
7C29×#448C211yesmaximal, characteristic, complemented
8C22×Q8×C29C2211yescharacteristic
9C2×#90807—21no—
10C2×SD16×C29—21no—
11C29×#121C2211yescharacteristic
12C2×#90784—21no—
13#11745301—21no—
14#11745301—21no—
15#11745292C2211yescharacteristic
16C2×#90779—21no—
17C2×#90779C2211yescharacteristic
18#11745258—21no—
19#11745246—21no—
20#11745240—21no—
21C29×#103—21no—
22C29×C22⋊C8C2211yescharacteristic
23#11745183—21no—
24#11745179—21no—
25#11745179C2211yescharacteristic
26C22⋊#6597C2211yescharacteristic
27C2×Q8×C29—21no—
28C2×Q8×C29—21no—
29C2×Q8×C29—42no—
30C2×D4×C29—21no—
31C2×D4×C29D411yescharacteristic
32C22×C4×C29—21no—
33C22×C4×C29C2311yescharacteristic
34C2×C22⋊D29—21no—
35C2×C22⋊D29—21no—
36C2×C22⋊D29—21no—
37C22×Dic29—21no—
38C22×Dic29—21no—
39C22×Dic29D411yescharacteristic
40C22×Dic29D411yescharacteristic
41#90807—42no—
42#90807—42no—
43C2×D116D411yescharacteristic
44C2×C4×D29—21no—
45C2×Dic58—21no—
46SD16×C29—42no—
47C2×C8×C29—21no—
48C4⋊C4×C29D411yescharacteristic
49C22⋊C4×C29—21no—
50C22⋊Dic29—21no—
51#90784—42no—
52#90781—21no—
53#90781—21no—
54C4⋊Dic29D411yescharacteristic
55#90779—21no—
56#90779—21no—
57#90779—21no—
58#90779—42no—
59C2×#6597—21no—
60C23×C29—21no—
61C23×C29C2×D411yescharacteristic
62C22×D29—21no—
63Q8×C29—22no—
64Q8×C29—22no—
65Q8×C29—41no—
66Q8×C29—41no—
67D4×C29—41no—
68D4×C29—41no—
69D4×C29—41no—
70C2×C4×C29—22no—
71C2×C4×C29—21no—
72C2×C4×C29—41no—
73C2×C4×C29—41no—
74C2×C4×C29—41no—
75C2×C4×C29C2×D411yescharacteristic
76C2×C4×C29C2×D411yescharacteristic
77C22⋊D29—42no—
78C22⋊D29—41no—
79C22⋊D29—41no—
80C22⋊D29—81no—
81C2×Dic29—21no—
82C2×Dic29—21no—
83C2×Dic29—22no—
84C2×Dic29—21no—
85C2×Dic29—21no—
86C2×Dic29—42no—
87C2×Dic29—41no—
88C2×Dic29—41no—
89C2×Dic29—41no—
90C2×Dic29SD1612yescomplemented
91D116—41no—
92C4×D29—42no—
93Dic58—42no—
94C8×C29—41no—
95#6597—41no—
96#1604—291nomaximal, Sylow
97C22×C29—21no—
98C22×C29—21no—
99C22×C29—41no—
100C22×C29—41no—
101C22×C29—41no—
102C22×C29#12011yescharacteristic
103C22×C29C2×SD1611yescharacteristic
104C22×C29AGL(1,ℤ/8)11yescharacteristic
105C2×D29—41no—
106C2×D29—41no—
107C2×D29—41no—
108C4×C29—21no—
109C4×C29—21no—
110C4×C29—41no—
111C4×C29—42no—
112Dic29—22no—
113Dic29—42no—
114Dic29—41no—
115Dic29—41no—
116#537—291no—
117#448—291no—
118#448D2911yescharacteristic, complemented
119#395—291no—
120#327—291no—
121#327—291no—
122#324—291no—
123C2×C29—21no—
124C2×C29—21no—
125C2×C29—81no—
126C2×C29#45011yescharacteristic
127C2×C29#45611yescharacteristic
128C2×C29B(4,𝔽2)11yescharacteristic
129D29—81no—
130C2×#41—581no—
131C22×Q8C2×D2911yescharacteristic
132C2×SD16—21no—
133C2×SD16—581no—
134C22⋊Q8—581no—
135C22⋊Q8—581no—
136#121—291no—
137#121—581no—
138#121—581no—
139#121—581no—
140#121C2×D2911yescharacteristic
141C2×C4⋊C4—291no—
142C2×C4⋊C4—581no—
143#103—21no—
144#103—581no—
145C22⋊C8—291no—
146C22⋊C8C2×D2911yescharacteristic
147#95—291no—
148#95—581no—
149C29#160411yescharacteristic, complemented, Sylow
150#41—1162no—
151#41—1162no—
152C2×Q8—21no—
153C2×Q8—21no—
154C2×Q8—42no—
155C2×Q8—581no—
156C2×D4—21no—
157C2×D4—291no—
158C2×D4—581no—
159C2×D4—581no—
160C2×D4—581no—
161C2×D4C22⋊D2911yescharacteristic
162C22×C4—21no—
163C22×C4—291no—
164C22×C4—291no—
165C22×C4—581no—
166C22×C4—581no—
167C22×C4—581no—
168C22×C4C22×D2911yescharacteristic
169SD16—42no—
170SD16—1162no—
171C2×C8—21no—
172C2×C8—581no—
173C4⋊C4—291no—
174C4⋊C4—581no—
175C4⋊C4—581no—
176C4⋊C4—581no—
177C4⋊C4—1162no—
178C4⋊C4C22⋊D2911yescharacteristic
179C22⋊C4—21no—
180C22⋊C4—581no—
181C22⋊C4—581no—
182C22⋊C4—581no—
183C23—21no—
184C23—581no—
185C23D4×D2911yescharacteristic
186Q8—22no—
187Q8—22no—
188Q8—41no—
189Q8—41no—
190Q8—1162no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—1161no—
195D4—1162no—
196D4—1161no—
197D4—1161no—
198D4—2321no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—292no—
205C2×C4—581no—
206C2×C4—581no—
207C2×C4—582no—
208C2×C4—581no—
209C2×C4—581no—
210C2×C4—1162no—
211C2×C4—1162no—
212C2×C4—1161no—
213C2×C4—1161no—
214C2×C4—1161no—
215C2×C4D4×D2911yescharacteristic
216C2×C4C2×C22⋊D2911yescharacteristic
217C8—41no—
218C8—1161no—
219C22—21no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—1161no—
225C22—1161no—
226C22—1161no—
227C22SD16×D2911yescharacteristic
228C22#1174527611yescharacteristic
229C22#1174529911yescharacteristic
230C4—21no—
231C4—21no—
232C4—41no—
233C4—42no—
234C4—582no—
235C4—1162no—
236C4—1161no—
237C4—1161no—
238C2—21no—
239C2—21no—
240C2—81no—
241C2—2321no—
242C2#1427131211yescharacteristic
243C2#1427134411yescharacteristic
244C2#1427134911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#448C2
socleC22×C29#120
prime radical#14271740C2
hypercenter#448D29
hypocenterC29#1604
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #448

Complements

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

NH ≅ G/Ntype
2. #14271302C2semidirect
3. #14271082C2semidirect
4. #14270898C2semidirect
5. #14270897C2semidirect
6. #14270888C2semidirect
7. C29×#448C2semidirect
90. C2×Dic29SD16semidirect
118. #448D29semidirect
149. C29#1604semidirect

Maximal subgroups

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

subgroupindex
#142717402
#142713022
#142710822
#142708982
#142708972
#142708882
C29×#4482
#160429