Finite Group Databasebeta

← #16817838

Subgroups — #16817838

Order 3712.

280 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#11745291C211yesmaximal, characteristic
2#14271127C211yesmaximal, characteristic, complemented
3#14270888C212yesmaximal, complemented
4#14270886C212yesmaximal, complemented
5C2×C29×C22⋊C8C211yesmaximal, characteristic, complemented
6C23×C4×C29C2211yescharacteristic
7C22×C22⋊D29C411yescharacteristic
8C22×C8×C29—21no—
9C2×C22⋊Dic29C411yescharacteristic
10#11745291—21no—
11#11745291—21no—
12#11745291—21no—
13#11745291—21no—
14C2×#90781C411yescharacteristic
15C2×#90781C2211yescharacteristic
16C2×#90779C411yescharacteristic
17C2×#90779C2211yescharacteristic
18C2×#90777—21no—
19C29×C22⋊C8—21no—
20C29×C22⋊C8C2212yes—
21C22⋊#6597—21no—
22C22⋊#6597C2212yes—
23C24×C29C2×C411yescharacteristic
24C23×D29C2×C411yescharacteristic
25C22×C4×C29—42no—
26C22×C4×C29C2×C411yescharacteristic
27C22×C4×C29D411yescharacteristic
28C22×C4×C29D411yescharacteristic
29C22×C4×C29D411yescharacteristic
30C22×C4×C29D411yescharacteristic
31C22×C4×C29C2311yescharacteristic
32C2×C22⋊D29—21no—
33C2×C22⋊D29—21no—
34C2×C22⋊D29—42no—
35C22×Dic29C2×C411yescharacteristic
36C22×Dic29C2×C411yescharacteristic
37C22×Dic29C2×C411yescharacteristic
38C2×C8×C29—22no—
39C2×C8×C29—42no—
40C22⋊Dic29—21no—
41C22⋊Dic29—21no—
42#90781—21no—
43#90781—21no—
44#90781—21no—
45#90781—21no—
46#90779—21no—
47#90779—21no—
48#90779—21no—
49#90779—21no—
50#90777—42no—
51C2×#6597—22no—
52C23×C29—22no—
53C23×C29—22no—
54C23×C29—41no—
55C23×C29C22⋊C411yescharacteristic
56C23×C29C22⋊C411yescharacteristic
57C23×C29C22×C411yescharacteristic
58C22×D29—21no—
59C22×D29—22no—
60C22×D29—41no—
61C22×D29—41no—
62C2×C4×C29—22no—
63C2×C4×C29—22no—
64C2×C4×C29—41no—
65C2×C4×C29—41no—
66C2×C4×C29—41no—
67C2×C4×C29—41no—
68C2×C4×C29C22⋊C411yescharacteristic
69C2×C4×C29C22⋊C411yescharacteristic
70C2×C4×C29C2×D411yescharacteristic
71C2×C4×C29C2×D411yescharacteristic
72C22⋊D29—42no—
73C22⋊D29—42no—
74C2×Dic29—21no—
75C2×Dic29—21no—
76C2×Dic29—21no—
77C2×Dic29—22no—
78C2×Dic29—41no—
79C2×Dic29—41no—
80C8×C29—42no—
81#6597—42no—
82#1468—291nomaximal, Sylow
83C22×C29—21no—
84C22×C29—21no—
85C22×C29—21no—
86C22×C29—21no—
87C22×C29—21no—
88C22×C29—21no—
89C22×C29—21no—
90C22×C29—44no—
91C22×C29#9912yes—
92C22×C29C2×C22⋊C411yescharacteristic
93C22×C29#13112yes—
94C2×D29—41no—
95C2×D29—41no—
96C2×D29—41no—
97C2×D29—82no—
98C4×C29—21no—
99C4×C29—21no—
100C4×C29—21no—
101C4×C29—21no—
102Dic29—41no—
103Dic29—41no—
104Dic29—41no—
105C2×#123—291no—
106#407—291no—
107C2×C22⋊C8D2911yescharacteristic, complemented
108#324—292no—
109#323—292no—
110C2×C29—22no—
111C2×C29—22no—
112C2×C29—41no—
113C2×C29#40811yescharacteristic
114C2×C29C2×#9911yescharacteristic
115C2×C29#41311yescharacteristic
116D29—81no—
117C22×D4—291no—
118C23×C4C2×D2911yescharacteristic
119C2×M16—581no—
120C22×C8—21no—
121#123—581no—
122#123—581no—
123#123—581no—
124#123—581no—
125C2×C4⋊C4—291no—
126C2×C4⋊C4—291no—
127C2×C22⋊C4—291no—
128C2×C22⋊C4—291no—
129C2×C22⋊C4—291no—
130C22⋊C8—21no—
131C22⋊C8—292no—
132C22⋊C8—581no—
133C22⋊C8C2×D2912yes—
134C29#146811yescharacteristic, complemented, Sylow
135C24—291no—
136C24C4×D2911yescharacteristic
137C2×D4—581no—
138C2×D4—581no—
139C2×D4—1162no—
140C22×C4—42no—
141C22×C4—291no—
142C22×C4—291no—
143C22×C4—291no—
144C22×C4C4×D2911yescharacteristic
145C22×C4D11611yescharacteristic
146C22×C4D11611yescharacteristic
147C22×C4C22⋊D2911yescharacteristic
148C22×C4C22⋊D2911yescharacteristic
149C22×C4C22×D2911yescharacteristic
150M16—1162no—
151C2×C8—22no—
152C2×C8—42no—
153C2×C8—582no—
154C4⋊C4—581no—
155C4⋊C4—581no—
156C4⋊C4—581no—
157C4⋊C4—581no—
158C22⋊C4—581no—
159C22⋊C4—581no—
160C22⋊C4—581no—
161C22⋊C4—581no—
162C22⋊C4—581no—
163C22⋊C4—581no—
164C23—22no—
165C23—22no—
166C23—41no—
167C23—581no—
168C23—582no—
169C23—1161no—
170C23—1161no—
171C23#9078111yescharacteristic
172C23#9078111yescharacteristic
173C23C2×C4×D2911yescharacteristic
174D4—1162no—
175D4—1162no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—41no—
179C2×C4—41no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—581no—
183C2×C4—581no—
184C2×C4—581no—
185C2×C4—582no—
186C2×C4—1161no—
187C2×C4—1161no—
188C2×C4#9078111yescharacteristic
189C2×C4#9078111yescharacteristic
190C2×C4C2×D11611yescharacteristic
191C2×C4C2×C22⋊D2911yescharacteristic
192C8—42no—
193C8—1162no—
194C22—21no—
195C22—21no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—1161no—
203C22—1161no—
204C22—1161no—
205C22—2322no—
206C22#1174515412yes—
207C22#1174526312yes—
208C22C2×#9078111yescharacteristic
209C4—21no—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—1161no—
214C4—1161no—
215C4—1161no—
216C2—22no—
217C2—22no—
218C2—41no—
219C2—2321no—
220C2#1427112911yescharacteristic
221C2C2×#1174515411yescharacteristic
222C2#1427114511yescharacteristic
subgroupG/H
centerC22C2×#90781
commutatorC23×C29C22×C4
FrattiniC22×C4C22×D29
FittingC2×C29×C22⋊C8C2
socleC22×C29C2×C22⋊C4
prime radicalC22×C22⋊D29C4
cosocleC22×C4×C29C23
hypercenterC2×C22⋊C8D29
hypocenterC29#1468
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. #14271127C2semidirect
3. #14270888C2semidirect
4. #14270886C2semidirect
5. C2×C29×C22⋊C8C2semidirect
107. C2×C22⋊C8D29semidirect
134. C29#1468semidirect

Maximal subgroups

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

subgroupindex
C2×#117452912
#142711272
#142708882
#142708862
C2×C29×C22⋊C82
#146829