Finite Group Databasebeta

← #16835749

Subgroups — #16835749

Order 3712.

280 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 54 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×#11745229C211yesmaximal, characteristic, complemented
2C2×#11745227C211yesmaximal, characteristic, complemented
3#14272066C212yesmaximal, complemented
4#14272064C212yesmaximal, complemented
5#14271725C211yesmaximal, characteristic
6C22×C22⋊D29C411yescharacteristic, complemented
7C22×C22⋊D29C2211yescharacteristic
8C2×C22⋊#1181—21no—
9C2×#90800—21no—
10C2×C22⋊C4×C29C411yescharacteristic, complemented
11#11745292—21no—
12#11745292—21no—
13#11745248—21no—
14#11745248C411yescharacteristic, complemented
15#11745248C2211yescharacteristic
16#11745244—21no—
17#11745244C411yescharacteristic, complemented
18#11745244C2211yescharacteristic
19#11745229—21no—
20#11745229C2212yes—
21#11745227—21no—
22#11745227C2212yes—
23C24×C29C2×C411yescharacteristic
24C23×D29C2×C411yescharacteristic, complemented
25C23×D29D411yescharacteristic
26C22×#1181—41no—
27C22×C4×C29—21no—
28C2×C22⋊D29—21no—
29C2×C22⋊D29—21no—
30C2×C22⋊D29—41no—
31C2×C22⋊D29—41no—
32C2×C22⋊D29—41no—
33C2×C22⋊D29—41no—
34C2×C22⋊D29C2×C411yescharacteristic
35C2×C22⋊D29D411yescharacteristic
36C2×C22⋊D29D411yescharacteristic
37C2×C22⋊D29C2311yescharacteristic
38C22×Dic29C2×C411yescharacteristic, complemented
39C22×Dic29D411yescharacteristic
40C2×D116—21no—
41C2×D116—21no—
42C22⋊#1181—22no—
43C22⋊#1181—41no—
44#90800—22no—
45#90800—41no—
46C2×#6599—41no—
47C22⋊C4×C29—21no—
48C22⋊C4×C29C2×C411yescharacteristic, complemented
49C22⋊C4×C29C2×C411yescharacteristic, complemented
50#90781—21no—
51#90781—21no—
52#90781—21no—
53#90781—21no—
54C4⋊Dic29—21no—
55C4⋊Dic29—21no—
56C23×C29—21no—
57C23×C29—21no—
58C23×C29—81no—
59C23×C29C22⋊C411yescharacteristic
60C23×C29C22⋊C411yescharacteristic
61C23×C29C22×C411yescharacteristic
62C22×D29—21no—
63C22×D29—21no—
64C22×D29—21no—
65C22×D29—41no—
66C22×D29—81no—
67C22×D29—81no—
68C22×D29C22⋊C411yescharacteristic
69C22×D29C2×D411yescharacteristic
70C2×#1181—42no—
71C2×#1181—82no—
72C2×C4×C29—21no—
73C2×C4×C29—21no—
74C2×C4×C29—81no—
75C22⋊D29—41no—
76C22⋊D29—41no—
77C22⋊D29—41no—
78C22⋊D29—41no—
79C22⋊D29—42no—
80C22⋊D29—41no—
81C22⋊D29—41no—
82C2×Dic29—21no—
83C2×Dic29—21no—
84C2×Dic29—21no—
85C2×Dic29—41no—
86C2×Dic29C22⋊C411yescharacteristic
87C2×Dic29C2×D411yescharacteristic
88D116—81no—
89D116—81no—
90#6599—42no—
91#2121—291nomaximal, Sylow
92C22×C29—21no—
93C22×C29—21no—
94C22×C29—41no—
95C22×C29—41no—
96C22×C29—41no—
97C22×C29—81no—
98C22×C29—81no—
99C22×C29#9911yescharacteristic
100C22×C29#9911yescharacteristic
101C22×C29C2×C22⋊C411yescharacteristic
102C2×D29—21no—
103C2×D29—21no—
104C2×D29—42no—
105C2×D29—41no—
106C2×D29—41no—
107C2×D29—41no—
108C2×D29—41no—
109C2×D29—41no—
110C2×D29—81no—
111C2×D29—82no—
112#1181—82no—
113C4×C29—41no—
114C4×C29—41no—
115Dic29—21no—
116Dic29—21no—
117Dic29—41no—
118#534—291no—
119C2×#100—291no—
120C2×#99—291no—
121#352—292no—
122AΣL(1,𝔽16)—292no—
123C2×C29—21no—
124C2×C29—21no—
125C2×C29—21no—
126C2×C29—41no—
127C2×C29—41no—
128C2×C29C2×#9911yescharacteristic
129D29—41no—
130D29—41no—
131D29—81no—
132C22×D4—291no—
133C22×D4—291no—
134C2×M16—581no—
135#123—291no—
136#123—291no—
137#123—581no—
138#121—581no—
139#121—581no—
140#120—291no—
141#120—291no—
142#120—581no—
143C2×C22⋊C4—581no—
144C2×C22⋊C4#118111yescharacteristic, complemented
145#100—292no—
146#100—581no—
147#99—292no—
148#99—581no—
149C29#212111yescharacteristic, complemented, Sylow
150C24—291no—
151C24—291no—
152C24C2×#118111yescharacteristic
153C2×D4—291no—
154C2×D4—291no—
155C2×D4—291no—
156C2×D4—291no—
157C2×D4—581no—
158C2×D4—581no—
159C2×D4—581no—
160C2×D4—581no—
161C2×D4—1161no—
162C2×D4—1161no—
163C2×D4—1161no—
164C2×D4—1161no—
165C22×C4—21no—
166C22×C4—291no—
167C22×C4—291no—
168C22×C4—1161no—
169M16—582no—
170M16—1161no—
171C2×C8—1161no—
172C4⋊C4—581no—
173C4⋊C4—581no—
174C22⋊C4—21no—
175C22⋊C4—581no—
176C22⋊C4—581no—
177C22⋊C4—581no—
178C22⋊C4—581no—
179C22⋊C4—582no—
180C22⋊C4—1161no—
181C22⋊C4C2×#118111yescharacteristic, complemented
182C22⋊C4C2×#118111yescharacteristic, complemented
183C23—21no—
184C23—21no—
185C23—81no—
186C23—291no—
187C23—291no—
188C23—581no—
189C23—581no—
190C23—581no—
191C23—1161no—
192C23—2321no—
193C23—2321no—
194C23C22⋊#118111yescharacteristic
195C23C22⋊#118111yescharacteristic
196C23C22×#118111yescharacteristic
197D4—1161no—
198D4—1161no—
199D4—1161no—
200D4—1161no—
201D4—1162no—
202D4—1161no—
203D4—1161no—
204D4—2321no—
205D4—2321no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—81no—
209C2×C4—291no—
210C2×C4—291no—
211C2×C4—581no—
212C2×C4—581no—
213C2×C4—581no—
214C2×C4—1161no—
215C2×C4—1162no—
216C2×C4—2322no—
217C8—1162no—
218C22—21no—
219C22—21no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22—81no—
224C22—81no—
225C22—581no—
226C22—581no—
227C22—1161no—
228C22—1161no—
229C22—1162no—
230C22—1161no—
231C22—1161no—
232C22—1161no—
233C22—2321no—
234C22—2322no—
235C22#1174521511yescharacteristic
236C22#1174521511yescharacteristic
237C22C2×C22⋊#118111yescharacteristic
238C4—41no—
239C4—41no—
240C4—581no—
241C4—581no—
242C4—1161no—
243C4—2322no—
244C2—21no—
245C2—21no—
246C2—21no—
247C2—41no—
248C2—41no—
249C2—1161no—
250C2—1161no—
251C2—2321no—
252C2C2×#1174521511yescharacteristic
subgroupG/H
centerC2C2×#11745215
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC2×C22⋊C4×C29C4
socleC2×C29C2×#99
prime radical#14271725C2
cosocleC2×C22⋊D29C23
hypercenterC2×C22⋊C4#1181
hypocenterC29#2121
LCSG ▷ C23×C29 ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#11745229C2semidirect
2. C2×#11745227C2semidirect
3. #14272066C2semidirect
4. #14272064C2semidirect
6. C22×C22⋊D29C4semidirect
10. C2×C22⋊C4×C29C4semidirect
14. #11745248C4semidirect
17. #11745244C4semidirect
24. C23×D29C2×C4semidirect
38. C22×Dic29C2×C4semidirect
48. C22⋊C4×C29C2×C4semidirect
49. C22⋊C4×C29C2×C4semidirect
144. C2×C22⋊C4#1181semidirect
149. C29#2121semidirect
181. C22⋊C4C2×#1181semidirect
182. C22⋊C4C2×#1181semidirect

Maximal subgroups

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

subgroupindex
C2×#117452292
C2×#117452272
#142720662
#142720642
#142717252
#212129