Finite Group Databasebeta

← #16818422

Subgroups — #16818422

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#14271758C211yesmaximal, characteristic, complemented
2#14271316C211yesmaximal, characteristic, complemented
3#14271296C211yesmaximal, characteristic
4#14271081C211yesmaximal, characteristic, complemented
5#14270899C211yesmaximal, characteristic, complemented
6#14270888C211yesmaximal, characteristic, complemented
7C29×#327C211yesmaximal, characteristic, complemented
8C22×D116C2211yescharacteristic
9C29×#121C2211yescharacteristic
10#11745297—21no—
11#11745297—21no—
12D4×Dic29—21no—
13C2×#90782—21no—
14C2×#90781—21no—
15C2×#90781—21no—
16#11745286C2211yescharacteristic
17C2×#90779C2211yescharacteristic
18C2×#90773—21no—
19#11745251—21no—
20#11745241—21no—
21#11745240—21no—
22C29×C22⋊C8C2211yescharacteristic
23C29×#95C2211yescharacteristic
24C22⋊#6597C2211yescharacteristic
25#11745169—21no—
26#11745157—21no—
27C23×D29—21no—
28C2×D4×C29—21no—
29C2×D4×C29D411yescharacteristic
30C22×C4×C29—21no—
31C22×C4×C29C2311yescharacteristic
32C22×Dic29—21no—
33C22×Dic29D411yescharacteristic
34C22×Dic29D411yescharacteristic
35C2×D116—21no—
36C2×D116—21no—
37C2×D116—42no—
38C2×Dic58D411yescharacteristic
39C2×C8×C29—21no—
40C4⋊C4×C29D411yescharacteristic
41C22⋊C4×C29—21no—
42C22⋊Dic29—21no—
43C22⋊Dic29—21no—
44C22⋊Dic29—21no—
45C22⋊Dic29—21no—
46#90782—42no—
47#90781—42no—
48#90781—42no—
49C4⋊Dic29—21no—
50C4⋊Dic29D411yescharacteristic
51#90779—21no—
52#90779—21no—
53#90779—21no—
54#90779—21no—
55#90779—21no—
56C4×Dic29—21no—
57C2×#6597—21no—
58#90773—42no—
59C23×C29—21no—
60C23×C29C2×D411yescharacteristic
61C22×D29—22no—
62C22×D29—41no—
63C22×D29—41no—
64C22×D29—41no—
65C22×D29—41no—
66C22×D29—41no—
67C22×D29—41no—
68D4×C29—41no—
69D4×C29—41no—
70D4×C29—41no—
71C2×C4×C29—21no—
72C2×C4×C29—41no—
73C2×C4×C29—41no—
74C2×C4×C29—41no—
75C2×C4×C29—41no—
76C2×C4×C29C2×D411yescharacteristic
77C2×C4×C29C2×D411yescharacteristic
78C2×Dic29—21no—
79C2×Dic29—21no—
80C2×Dic29—21no—
81C2×Dic29—21no—
82C2×Dic29—21no—
83C2×Dic29—21no—
84C2×Dic29—41no—
85C2×Dic29—81no—
86D116—22no—
87D116—22no—
88D116—41no—
89D116—41no—
90Dic58—41no—
91C8×C29—41no—
92#6597—41no—
93#1597—291nomaximal, Sylow
94C22×C29—21no—
95C22×C29—21no—
96C22×C29—41no—
97C22×C29—41no—
98C22×C29—41no—
99C22×C29#12011yescharacteristic
100C22×C29#13511yescharacteristic
101C22×C29AGL(1,ℤ/8)11yescharacteristic
102C2×D29—42no—
103C2×D29—42no—
104C2×D29—42no—
105C2×D29—81no—
106C2×D29—81no—
107C2×D29—81no—
108C2×D29—81no—
109C4×C29—21no—
110C4×C29—21no—
111C4×C29—41no—
112C4×C29—81no—
113Dic29—41no—
114Dic29—41no—
115Dic29—41no—
116Dic29—41no—
117#539—291no—
118#450—291no—
119#447—291no—
120#394—291no—
121#328—291no—
122#327D2911yescharacteristic, complemented
123#324—291no—
124C2×C29—21no—
125C2×C29—21no—
126C2×C29—81no—
127C2×C29#44911yescharacteristic
128C2×C29#45411yescharacteristic
129C2×C29B(4,𝔽2)11yescharacteristic
130D29—82no—
131C22×D4—291no—
132C2×SD16—581no—
133C2×D8—581no—
134#126—581no—
135#125—581no—
136#123—581no—
137#123—581no—
138C22⋊Q8—291no—
139C22⋊Q8—581no—
140#121C2×D2911yescharacteristic
141C4×D4—581no—
142C2×C4⋊C4—291no—
143C2×C22⋊C4—581no—
144C2×C22⋊C4—581no—
145#102—581no—
146#102—581no—
147C22⋊C8—291no—
148C22⋊C8C2×D2911yescharacteristic
149#95C2×D2911yescharacteristic
150C29#159711yescharacteristic, complemented, Sylow
151C24—581no—
152C2×Q8—291no—
153C2×D4—21no—
154C2×D4—581no—
155C2×D4—581no—
156C2×D4—1162no—
157C2×D4D11611yescharacteristic
158C22×C4—21no—
159C22×C4—291no—
160C22×C4—291no—
161C22×C4—581no—
162C22×C4C22×D2911yescharacteristic
163SD16—1162no—
164D8—1162no—
165C2×C8—21no—
166C2×C8—581no—
167C4⋊C4—291no—
168C4⋊C4—581no—
169C4⋊C4—581no—
170C4⋊C4—581no—
171C4⋊C4—581no—
172C4⋊C4—581no—
173C4⋊C4—581no—
174C4⋊C4D11611yescharacteristic
175C22⋊C4—21no—
176C22⋊C4—581no—
177C22⋊C4—581no—
178C22⋊C4—581no—
179C22⋊C4—581no—
180C22⋊C4—1162no—
181C22⋊C4—1162no—
182C42—581no—
183C23—21no—
184C23—582no—
185C23—1161no—
186C23—1161no—
187C23—1161no—
188C23—1161no—
189C23—1161no—
190C23—1161no—
191C23D4×D2911yescharacteristic
192Q8—1161no—
193D4—41no—
194D4—41no—
195D4—41no—
196D4—582no—
197D4—582no—
198D4—1161no—
199D4—1161no—
200C2×C4—21no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—41no—
205C2×C4—581no—
206C2×C4—581no—
207C2×C4—581no—
208C2×C4—581no—
209C2×C4—581no—
210C2×C4—581no—
211C2×C4—1161no—
212C2×C4—2321no—
213C2×C4C2×D11611yescharacteristic
214C2×C4D4×D2911yescharacteristic
215C8—41no—
216C8—1161no—
217C22—21no—
218C22—21no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—1162no—
223C22—1162no—
224C22—1162no—
225C22—2321no—
226C22—2321no—
227C22—2321no—
228C22—2321no—
229C22#1174524411yescharacteristic
230C22#1174527311yescharacteristic
231C22#1174527811yescharacteristic
232C4—21no—
233C4—21no—
234C4—41no—
235C4—81no—
236C4—1161no—
237C4—1161no—
238C4—1161no—
239C4—1161no—
240C2—21no—
241C2—21no—
242C2—81no—
243C2—2322no—
244C2#1427130911yescharacteristic
245C2#1427133711yescharacteristic
246C2#1427135111yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#327C2
socleC22×C29#120
prime radical#14271296C2
hypercenter#327D29
hypocenterC29#1597
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #327

Complements

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

NH ≅ G/Ntype
1. #14271758C2semidirect
2. #14271316C2semidirect
4. #14271081C2semidirect
5. #14270899C2semidirect
6. #14270888C2semidirect
7. C29×#327C2semidirect
122. #327D29semidirect
150. C29#1597semidirect

Maximal subgroups

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

subgroupindex
#142717582
#142713162
#142712962
#142710812
#142708992
#142708882
C29×#3272
#159729