Finite Group Databasebeta

← #16818433

Subgroups — #16818433

Order 3712.

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

normal subgroups only

This group has 266 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#14271792C211yesmaximal, characteristic, complemented
2#14271316C211yesmaximal, characteristic
3#14271313C211yesmaximal, characteristic
4#14271081C211yesmaximal, characteristic
5#14270899C211yesmaximal, characteristic, complemented
6#14270888C211yesmaximal, characteristic, complemented
7C29×#328C211yesmaximal, characteristic, complemented
8C22×D116C2211yescharacteristic
9C29×C22⋊Q8C2211yescharacteristic
10#11745306—21no—
11C2×#90784—21no—
12C2×#90781—21no—
13C2×#90781—21no—
14#11745286C2211yescharacteristic
15C2×#90779C2211yescharacteristic
16C2×#90773—21no—
17#11745251—21no—
18#11745251—21no—
19#11745250—21no—
20#11745240—21no—
21#11745239—21no—
22C29×C22⋊C8C2211yescharacteristic
23C29×#95C2211yescharacteristic
24C22⋊#6597C2211yescharacteristic
25#11745169—21no—
26#11745157—21no—
27C23×D29—21no—
28C2×Q8×C29D411yescharacteristic
29C22×C4×C29—21no—
30C22×C4×C29C2311yescharacteristic
31C22×Dic29D411yescharacteristic
32C22×Dic29D411yescharacteristic
33C2×D116—21no—
34C2×D116—21no—
35C2×D116—42no—
36C2×Dic58—21no—
37C2×Dic58D411yescharacteristic
38C2×C8×C29—21no—
39C4⋊C4×C29—21no—
40C4⋊C4×C29D411yescharacteristic
41C22⋊C4×C29—21no—
42C22⋊Dic29—21no—
43#90784—42no—
44#90781—42no—
45#90781—42no—
46C4⋊Dic29—21no—
47C4⋊Dic29D411yescharacteristic
48#90779—21no—
49#90779—21no—
50#90779—21no—
51#90779—21no—
52#90779—21no—
53#90779—21no—
54#90779—21no—
55C4×Dic29—21no—
56C4×Dic29—21no—
57C2×#6597—21no—
58#90773—42no—
59C23×C29C2×D411yescharacteristic
60C22×D29—22no—
61C22×D29—41no—
62C22×D29—41no—
63C22×D29—41no—
64C22×D29—41no—
65C22×D29—41no—
66C22×D29—41no—
67Q8×C29—41no—
68C2×C4×C29—21no—
69C2×C4×C29—21no—
70C2×C4×C29—41no—
71C2×C4×C29—41no—
72C2×C4×C29—41no—
73C2×C4×C29—41no—
74C2×C4×C29C2×D411yescharacteristic
75C2×C4×C29C2×D411yescharacteristic
76C2×Dic29—21no—
77C2×Dic29—21no—
78C2×Dic29—21no—
79C2×Dic29—21no—
80C2×Dic29—21no—
81C2×Dic29—41no—
82C2×Dic29SD1612yescomplemented
83D116—22no—
84D116—22no—
85D116—41no—
86D116—41no—
87Dic58—41no—
88Dic58—81no—
89C8×C29—41no—
90#6597—41no—
91#1599—291nomaximal, Sylow
92C22×C29—21no—
93C22×C29—21no—
94C22×C29#12011yescharacteristic
95C22×C29C2×SD1611yescharacteristic
96C22×C29#13711yescharacteristic
97C2×D29—42no—
98C2×D29—42no—
99C2×D29—42no—
100C2×D29—81no—
101C2×D29—81no—
102C2×D29—81no—
103C2×D29—81no—
104C4×C29—21no—
105C4×C29—21no—
106C4×C29—41no—
107C4×C29—41no—
108C4×C29—81no—
109Dic29—22no—
110Dic29—41no—
111Dic29—41no—
112Dic29—41no—
113#544—291no—
114#450—291no—
115#450—291no—
116#394—291no—
117#328—291no—
118#328D2911yescharacteristic, complemented
119#324—291no—
120C2×C29—21no—
121C2×C29—21no—
122C2×C29#44811yescharacteristic
123C2×C29#45411yescharacteristic
124C2×C29B(4,𝔽2)11yescharacteristic
125D29—82no—
126C22×D4—291no—
127C2×SD16—581no—
128C2×SD16—581no—
129C4⋊Q8—581no—
130C4⋊Q8—581no—
131#125—581no—
132#125—581no—
133C22⋊Q8—291no—
134C22⋊Q8—581no—
135C22⋊Q8C2×D2911yescharacteristic
136#117—581no—
137C2×C4⋊C4—291no—
138C2×C22⋊C4—581no—
139C2×C22⋊C4—581no—
140#102—581no—
141#102—581no—
142C22⋊C8—291no—
143C22⋊C8C2×D2911yescharacteristic
144#95C2×D2911yescharacteristic
145C29#159911yescharacteristic, complemented, Sylow
146C24—581no—
147C2×Q8—291no—
148C2×Q8—581no—
149C2×Q8D11611yescharacteristic
150C2×D4—581no—
151C2×D4—581no—
152C2×D4—1162no—
153C22×C4—21no—
154C22×C4—291no—
155C22×C4—291no—
156C22×C4C22×D2911yescharacteristic
157SD16—1162no—
158SD16—1162no—
159C2×C8—21no—
160C2×C8—581no—
161C4⋊C4—21no—
162C4⋊C4—291no—
163C4⋊C4—581no—
164C4⋊C4—581no—
165C4⋊C4—581no—
166C4⋊C4—581no—
167C4⋊C4—581no—
168C4⋊C4—581no—
169C4⋊C4—581no—
170C4⋊C4—581no—
171C4⋊C4D11611yescharacteristic
172C22⋊C4—21no—
173C22⋊C4—581no—
174C22⋊C4—1162no—
175C22⋊C4—1162no—
176C42—581no—
177C42—581no—
178C23—582no—
179C23—1161no—
180C23—1161no—
181C23—1161no—
182C23—1161no—
183C23—1161no—
184C23—1161no—
185C23D4×D2911yescharacteristic
186Q8—41no—
187Q8—1161no—
188Q8—2321no—
189D4—582no—
190D4—582no—
191D4—1161no—
192D4—1161no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—292no—
200C2×C4—581no—
201C2×C4—581no—
202C2×C4—581no—
203C2×C4—581no—
204C2×C4—581no—
205C2×C4—1161no—
206C2×C4C2×D11611yescharacteristic
207C2×C4D4×D2911yescharacteristic
208C8—41no—
209C8—1161no—
210C22—21no—
211C22—21no—
212C22—1162no—
213C22—1162no—
214C22—1162no—
215C22—2321no—
216C22—2321no—
217C22—2321no—
218C22—2321no—
219C22#1174524411yescharacteristic
220C22SD16×D2911yescharacteristic
221C22#1174528011yescharacteristic
222C4—21no—
223C4—21no—
224C4—41no—
225C4—41no—
226C4—81no—
227C4—582no—
228C4—1161no—
229C4—1161no—
230C4—1161no—
231C2—21no—
232C2—21no—
233C2—2322no—
234C2#1427130311yescharacteristic
235C2#1427133711yescharacteristic
236C2#1427135111yescharacteristic
subgroupG/H
centerC22#11745244
commutator, cosocleC22×C4×C29C23
FrattiniC22×C4C22×D29
FittingC29×#328C2
socleC22×C29#120
prime radicalC22×D116C22
hypercenter#328D29
hypocenterC29#1599
LCSG ▷ C22×C4×C29 ▷ C22×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
1. #14271792C2semidirect
5. #14270899C2semidirect
6. #14270888C2semidirect
7. C29×#328C2semidirect
82. C2×Dic29SD16semidirect
118. #328D29semidirect
145. C29#1599semidirect

Maximal subgroups

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

subgroupindex
#142717922
#142713162
#142713132
#142710812
#142708992
#142708882
C29×#3282
#159929