Finite Group Databasebeta

← #16818420

Subgroups — #16818420

Order 3712.

272 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 49 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#14271762C211yesmaximal, characteristic, complemented
2#14271297C211yesmaximal, characteristic
3#14271077C211yesmaximal, characteristic, complemented
4#14270900C211yesmaximal, characteristic, complemented
5#14270898C211yesmaximal, characteristic, complemented
6#14270888C211yesmaximal, characteristic, complemented
7C29×#450C211yesmaximal, characteristic, complemented
8C22×D4×C29C2211yescharacteristic
9C2×SD16×C29—21no—
10C29×C22⋊Q8C2211yescharacteristic
11C2×C22⋊Dic29—21no—
12C2×C22⋊Dic29—21no—
13#11745308—21no—
14C2×#90782—21no—
15#11745292C2211yescharacteristic
16C2×#90779C2211yescharacteristic
17#11745260—21no—
18#11745256—21no—
19#11745252—21no—
20#11745248—21no—
21#11745243—21no—
22C29×#102—21no—
23C29×C22⋊C8C2211yescharacteristic
24#11745180—21no—
25#11745179C2211yescharacteristic
26C22⋊#6597C2211yescharacteristic
27C24×C29—21no—
28C2×Q8×C29D411yescharacteristic
29C2×D4×C29—21no—
30C2×D4×C29—21no—
31C2×D4×C29—42no—
32C22×C4×C29C2311yescharacteristic
33C2×C22⋊D29—21no—
34C22×Dic29—21no—
35C22×Dic29D411yescharacteristic
36C22×Dic29D411yescharacteristic
37C2×D116D411yescharacteristic
38C2×C4×D29—21no—
39SD16×C29—42no—
40C2×C8×C29—21no—
41C4⋊C4×C29—21no—
42C4⋊C4×C29D411yescharacteristic
43C22⋊C4×C29—21no—
44C22⋊Dic29—42no—
45C22⋊Dic29—42no—
46#90782—42no—
47#90781—21no—
48#90781—21no—
49#90781—21no—
50#90781—21no—
51C4⋊Dic29—21no—
52C4⋊Dic29—21no—
53C4⋊Dic29D411yescharacteristic
54#90779—21no—
55#90779—21no—
56#90779—21no—
57C4×Dic29—21no—
58C2×#6597—21no—
59C23×C29—22no—
60C23×C29—41no—
61C23×C29—41no—
62C23×C29—41no—
63C23×C29—41no—
64C23×C29—41no—
65C23×C29—41no—
66C23×C29C2×D411yescharacteristic
67C22×D29—21no—
68Q8×C29—41no—
69D4×C29—22no—
70D4×C29—22no—
71D4×C29—41no—
72D4×C29—41no—
73C2×C4×C29—21no—
74C2×C4×C29—21no—
75C2×C4×C29—41no—
76C2×C4×C29C2×D411yescharacteristic
77C2×C4×C29C2×D411yescharacteristic
78C22⋊D29—41no—
79C22⋊D29—41no—
80C2×Dic29—21no—
81C2×Dic29—21no—
82C2×Dic29—21no—
83C2×Dic29—21no—
84C2×Dic29—21no—
85C2×Dic29—41no—
86C2×Dic29—41no—
87C2×Dic29—41no—
88C2×Dic29—41no—
89D116—41no—
90C4×D29—81no—
91C8×C29—41no—
92#6597—41no—
93#1597—291nomaximal, Sylow
94C22×C29—21no—
95C22×C29—21no—
96C22×C29—42no—
97C22×C29—42no—
98C22×C29—42no—
99C22×C29—81no—
100C22×C29—81no—
101C22×C29—81no—
102C22×C29—81no—
103C22×C29#12011yescharacteristic
104C22×C29#13511yescharacteristic
105C22×C29AGL(1,ℤ/8)11yescharacteristic
106C2×D29—41no—
107C2×D29—41no—
108C2×D29—41no—
109C4×C29—21no—
110C4×C29—21no—
111C4×C29—41no—
112C4×C29—41no—
113Dic29—41no—
114Dic29—41no—
115Dic29—41no—
116Dic29—81no—
117#539—291no—
118#450D2911yescharacteristic, complemented
119#447—291no—
120#394—291no—
121#328—291no—
122#327—291no—
123#324—291no—
124C2×C29—21no—
125C2×C29—21no—
126C2×C29—82no—
127C2×C29#44911yescharacteristic
128C2×C29#45411yescharacteristic
129C2×C29B(4,𝔽2)11yescharacteristic
130D29—81no—
131C22×D4C2×D2911yescharacteristic
132C2×SD16—21no—
133C2×D8—581no—
134#126—581no—
135#125—581no—
136#123—581no—
137#123—581no—
138C22⋊Q8—581no—
139C22⋊Q8C2×D2911yescharacteristic
140#121—291no—
141C4×D4—581no—
142C2×C4⋊C4—291no—
143C2×C22⋊C4—581no—
144C2×C22⋊C4—581no—
145#102—21no—
146#102—581no—
147C22⋊C8—291no—
148C22⋊C8C2×D2911yescharacteristic
149#95—291no—
150C29#159711yescharacteristic, complemented, Sylow
151C24—21no—
152C2×Q8C22⋊D2911yescharacteristic
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—42no—
156C2×D4—291no—
157C2×D4—581no—
158C22×C4—291no—
159C22×C4—291no—
160C22×C4—581no—
161C22×C4—581no—
162C22×C4C22×D2911yescharacteristic
163SD16—42no—
164D8—1162no—
165C2×C8—21no—
166C2×C8—581no—
167C4⋊C4—21no—
168C4⋊C4—291no—
169C4⋊C4—581no—
170C4⋊C4—581no—
171C4⋊C4—581no—
172C4⋊C4—581no—
173C4⋊C4—581no—
174C4⋊C4C22⋊D2911yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—581no—
177C22⋊C4—581no—
178C22⋊C4—581no—
179C22⋊C4—581no—
180C22⋊C4—1162no—
181C22⋊C4—1162no—
182C42—581no—
183C23—22no—
184C23—41no—
185C23—41no—
186C23—41no—
187C23—41no—
188C23—41no—
189C23—41no—
190C23—581no—
191C23D4×D2911yescharacteristic
192Q8—41no—
193D4—22no—
194D4—22no—
195D4—41no—
196D4—41no—
197D4—1161no—
198D4—1161no—
199D4—1161no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—581no—
204C2×C4—581no—
205C2×C4—581no—
206C2×C4—581no—
207C2×C4—581no—
208C2×C4—1161no—
209C2×C4—1161no—
210C2×C4—1161no—
211C2×C4—1161no—
212C2×C4—2321no—
213C2×C4D4×D2911yescharacteristic
214C2×C4C2×C22⋊D2911yescharacteristic
215C8—41no—
216C8—1161no—
217C22—21no—
218C22—21no—
219C22—42no—
220C22—42no—
221C22—42no—
222C22—81no—
223C22—81no—
224C22—81no—
225C22—81no—
226C22—1161no—
227C22—1161no—
228C22—1161no—
229C22#1174527611yescharacteristic
230C22#1174527811yescharacteristic
231C22#1174529911yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—41no—
236C4—1161no—
237C4—1161no—
238C4—1161no—
239C4—2321no—
240C2—21no—
241C2—21no—
242C2—82no—
243C2—2321no—
244C2#1427130711yescharacteristic
245C2#1427133411yescharacteristic
246C2#1427134911yescharacteristic
subgroupG/H
centerC22#11745299
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#450C2
socleC22×C29#120
prime radical#14271297C2
hypercenter#450D29
hypocenterC29#1597
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #14271762C2semidirect
3. #14271077C2semidirect
4. #14270900C2semidirect
5. #14270898C2semidirect
6. #14270888C2semidirect
7. C29×#450C2semidirect
118. #450D29semidirect
150. C29#1597semidirect

Maximal subgroups

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

subgroupindex
#142717622
#142712972
#142710772
#142709002
#142708982
#142708882
C29×#4502
#159729