Finite Group Databasebeta

← #16835517

Subgroups — #16835517

Order 3712.

390 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 74 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
1C22×#90800C211yesmaximal, characteristic, complemented
2C2×#11745229C212yesmaximal, complemented
3#14272133C211yesmaximal, characteristic, complemented
4#14272043C212yesmaximal, complemented
5C2×#11745301C211yesmaximal, characteristic
6C22×D4×C29C411yescharacteristic
7C22×C22⋊D29C411yescharacteristic
8C22×C22⋊D29C2211yescharacteristic
9C23×Dic29C2211yescharacteristic
10C2×#90800—21no—
11C2×#90800—24no—
12C2×#90800C2212yes—
13C2×#90800C2212yes—
14C22×#6599—21no—
15C2×C22⋊Dic29C411yescharacteristic
16#11745301—21no—
17#11745301—21no—
18#11745301—21no—
19#11745301—21no—
20C2×#90781C411yescharacteristic
21C2×#90779C2211yescharacteristic
22#11745229—24no—
23C22⋊#6599—21no—
24C22⋊#6599—21no—
25C24×C29C2×C411yescharacteristic
26C24×C29C2×C411yescharacteristic
27C23×D29C2×C411yescharacteristic
28C2×D4×C29—21no—
29C2×D4×C29—21no—
30C2×D4×C29—42no—
31C22×C4×C29C2×C411yescharacteristic
32C2×C22⋊D29—21no—
33C2×C22⋊D29—21no—
34C2×C22⋊D29—21no—
35C2×C22⋊D29—21no—
36C2×C22⋊D29—22no—
37C2×C22⋊D29—22no—
38C2×C22⋊D29—42no—
39C22×Dic29—22no—
40C22×Dic29—22no—
41C22×Dic29C2×C411yescharacteristic
42C22×Dic29C2×C411yescharacteristic
43C22×Dic29D411yescharacteristic
44C22×Dic29D411yescharacteristic
45C22×Dic29D411yescharacteristic
46C22×Dic29D411yescharacteristic
47C22×Dic29C2311yescharacteristic
48#90800—24no—
49#90800—22no—
50#90800—22no—
51#90800—22no—
52#90800D414yescomplemented
53C2×#6599—24no—
54C2×#6599—22no—
55C2×#6599—22no—
56C22⋊Dic29—21no—
57C22⋊Dic29—21no—
58#90781—21no—
59#90781—21no—
60#90779—21no—
61#90779—21no—
62C23×C29—22no—
63C23×C29—22no—
64C23×C29—21no—
65C23×C29—22no—
66C23×C29—41no—
67C23×C29—41no—
68C23×C29—41no—
69C23×C29C22⋊C411yescharacteristic
70C23×C29C22⋊C411yescharacteristic
71C23×C29C22×C411yescharacteristic
72C22×D29—21no—
73C22×D29—22no—
74C22×D29—41no—
75C22×D29—41no—
76D4×C29—42no—
77D4×C29—42no—
78C2×C4×C29—21no—
79C2×C4×C29—41no—
80C22⋊D29—42no—
81C22⋊D29—42no—
82C22⋊D29—41no—
83C22⋊D29—42no—
84C22⋊D29—41no—
85C2×Dic29—22no—
86C2×Dic29—21no—
87C2×Dic29—21no—
88C2×Dic29—22no—
89C2×Dic29—22no—
90C2×Dic29—21no—
91C2×Dic29—21no—
92C2×Dic29—21no—
93C2×Dic29—41no—
94C2×Dic29C22⋊C411yescharacteristic
95C2×Dic29C22⋊C411yescharacteristic
96C2×Dic29C2×D412yes—
97C2×Dic29C2×D411yescharacteristic
98C2×Dic29C2×D411yescharacteristic
99C2×Dic29#4112yes—
100#6599—24no—
101#6599—42no—
102#1900—291nomaximal, Sylow
103C22×C29—21no—
104C22×C29—21no—
105C22×C29—21no—
106C22×C29—21no—
107C22×C29—21no—
108C22×C29—21no—
109C22×C29—21no—
110C22×C29—44no—
111C22×C29—41no—
112C22×C29—41no—
113C22×C29—41no—
114C22×C29—82no—
115C22×C29#10012yescomplemented
116C22×C29C2×C22⋊C411yescharacteristic
117C22×C29C4×D412yes—
118C2×D29—41no—
119C2×D29—41no—
120C2×D29—41no—
121C2×D29—82no—
122C4×C29—41no—
123Dic29—21no—
124Dic29—21no—
125Dic29—41no—
126Dic29#12011yescharacteristic
127Dic29#12112yes—
128Dic29#12311yescharacteristic
129C22×M16—291no—
130C2×#121—291no—
131C2×#100—292no—
132#407—291no—
133#343—292no—
134C2×C29—22no—
135C2×C29—22no—
136C2×C29—41no—
137C2×C29—81no—
138C2×C29#38611yescharacteristic
139C2×C29C2×#10011yescharacteristic
140C2×C29#41311yescharacteristic
141D29—81no—
142C22×D4—291no—
143C22×D4—291no—
144C22×D4#118111yescharacteristic
145C23×C4—291no—
146C2×M16—292no—
147C2×M16—292no—
148C2×M16—584no—
149C2×M16—581no—
150C22×C8—581no—
151#121—581no—
152#121—581no—
153#121—581no—
154#121—581no—
155C2×C4⋊C4—291no—
156C2×C22⋊C4—291no—
157C2×C22⋊C4—291no—
158#100—584no—
159C22⋊C8—581no—
160C22⋊C8—581no—
161C29#190011yescharacteristic, complemented, Sylow
162C24—291no—
163C24C2×#118111yescharacteristic
164C24C2×#118111yescharacteristic
165C2×D4—21no—
166C2×D4—21no—
167C2×D4—42no—
168C2×D4—582no—
169C2×D4—581no—
170C2×D4—581no—
171C2×D4—582no—
172C2×D4—581no—
173C2×D4—581no—
174C2×D4—1162no—
175C22×C4—291no—
176C22×C4—291no—
177C22×C4—291no—
178C22×C4—291no—
179C22×C4—291no—
180C22×C4—291no—
181C22×C4—291no—
182C22×C4—582no—
183C22×C4—582no—
184C22×C4C2×#118111yescharacteristic
185M16—294no—
186M16—582no—
187M16—584no—
188M16—582no—
189M16—582no—
190C2×C8—582no—
191C2×C8—584no—
192C2×C8—582no—
193C4⋊C4—581no—
194C4⋊C4—581no—
195C22⋊C4—581no—
196C22⋊C4—581no—
197C22⋊C4—581no—
198C22⋊C4—581no—
199C23—22no—
200C23—22no—
201C23—21no—
202C23—22no—
203C23—41no—
204C23—41no—
205C23—41no—
206C23—581no—
207C23—582no—
208C23—1161no—
209C23—1161no—
210C23C22⋊#118111yescharacteristic
211C23C22⋊#118111yescharacteristic
212C23C22×#118111yescharacteristic
213D4—42no—
214D4—42no—
215D4—1161no—
216D4—1162no—
217D4—1161no—
218D4—1162no—
219D4—1162no—
220C2×C4—21no—
221C2×C4—41no—
222C2×C4—292no—
223C2×C4—292no—
224C2×C4—291no—
225C2×C4—291no—
226C2×C4—291no—
227C2×C4—291no—
228C2×C4—581no—
229C2×C4—581no—
230C2×C4—582no—
231C2×C4—582no—
232C2×C4—581no—
233C2×C4—581no—
234C2×C4—582no—
235C2×C4—581no—
236C2×C4—1161no—
237C8—584no—
238C8—1162no—
239C22—21no—
240C22—21no—
241C22—21no—
242C22—21no—
243C22—21no—
244C22—21no—
245C22—21no—
246C22—44no—
247C22—41no—
248C22—41no—
249C22—41no—
250C22—82no—
251C22—1161no—
252C22—1161no—
253C22—1161no—
254C22—2322no—
255C22#1174522912yescomplemented
256C22D4×#118112yes—
257C22C2×C22⋊#118111yescharacteristic
258C4—41no—
259C4—291no—
260C4—292no—
261C4—291no—
262C4—581no—
263C4—581no—
264C4—1161no—
265C2—22no—
266C2—22no—
267C2—41no—
268C2—81no—
269C2—2321no—
270C2#1427211111yescharacteristic
271C2C2×#1174522911yescharacteristic
272C2#1427215011yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC22×D4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC2×#11745301C2
cosocleC22×Dic29C23
hypercenterC22×D4#1181
hypocenterC29#1900
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C24 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#90800C2semidirect
2. C2×#11745229C2semidirect
3. #14272133C2semidirect
4. #14272043C2semidirect
52. #90800D4semidirect
115. C22×C29#100semidirect
161. C29#1900semidirect
255. C22#11745229semidirect

Maximal subgroups

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

subgroupindex
C22×#908002
C2×#117452292
#142721332
#142720432
C2×#117453012
#190029