Finite Group Databasebeta

← #16835518

Subgroups — #16835518

Order 3712.

390 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 72 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×D29⋊M16C211yesmaximal, characteristic, complemented
2C2×#11745229C212yesmaximal, complemented
3#14272135C211yesmaximal, characteristic, complemented
4#14272043C212yesmaximal, complemented
5C2×#11745246C211yesmaximal, characteristic
6C22×C22⋊D29C411yescharacteristic
7C22×C22⋊D29C2211yescharacteristic
8C22×D116C411yescharacteristic
9C22×C4×D29C2211yescharacteristic
10C2×#90800C2212yes—
11C2×#90800C2212yes—
12D29⋊M16—24no—
13C2×#90796—21no—
14C2×D29⋊C8—21no—
15C2×C22⋊C4×C29C411yescharacteristic
16C2×#90781C411yescharacteristic
17C2×#90779C2211yescharacteristic
18#11745246—21no—
19#11745246—21no—
20#11745246—21no—
21#11745246—21no—
22#11745229—24no—
23#11745219—21no—
24#11745219—21no—
25C24×C29C2×C411yescharacteristic
26C23×D29C2×C411yescharacteristic
27C23×D29C2×C411yescharacteristic
28C22×C4×C29C2×C411yescharacteristic
29C22×C4×C29C2×C411yescharacteristic
30C2×C22⋊D29—21no—
31C2×C22⋊D29—21no—
32C2×C22⋊D29—22no—
33C2×C22⋊D29—21no—
34C2×C22⋊D29—21no—
35C2×C22⋊D29—22no—
36C2×C22⋊D29—42no—
37C22×Dic29C2×C411yescharacteristic
38C22×Dic29C2311yescharacteristic
39C2×D116—21no—
40C2×D116—21no—
41C2×D116—42no—
42C2×C4×D29—22no—
43C2×C4×D29—22no—
44C2×C4×D29D411yescharacteristic
45C2×C4×D29D411yescharacteristic
46C2×C4×D29D411yescharacteristic
47C2×C4×D29D411yescharacteristic
48#90800—22no—
49#90800—22no—
50#90800—22no—
51#90800D414yescomplemented
52C2×#6599—22no—
53C2×#6599—22no—
54#90796—24no—
55D29⋊C8—24no—
56C22⋊C4×C29—21no—
57C22⋊C4×C29—21no—
58#90781—21no—
59#90781—21no—
60#90779—21no—
61#90779—21no—
62C23×C29—21no—
63C23×C29—22no—
64C23×C29—41no—
65C23×C29—41no—
66C23×C29C22×C411yescharacteristic
67C22×D29—22no—
68C22×D29—22no—
69C22×D29—21no—
70C22×D29—22no—
71C22×D29—41no—
72C22×D29—41no—
73C22×D29—41no—
74C22×D29C22⋊C411yescharacteristic
75C22×D29C22⋊C411yescharacteristic
76C2×C4×C29—22no—
77C2×C4×C29—21no—
78C2×C4×C29—41no—
79C2×C4×C29C22⋊C411yescharacteristic
80C2×C4×C29C22⋊C411yescharacteristic
81C22⋊D29—42no—
82C22⋊D29—42no—
83C22⋊D29—41no—
84C22⋊D29—42no—
85C22⋊D29—41no—
86C2×Dic29—21no—
87C2×Dic29—41no—
88C2×Dic29C2×D412yes—
89C2×Dic29C2×D411yescharacteristic
90C2×Dic29C2×D411yescharacteristic
91C2×Dic29#4112yes—
92D116—42no—
93D116—42no—
94C4×D29—21no—
95C4×D29—21no—
96C4×D29—22no—
97C4×D29—22no—
98C4×D29—21no—
99C4×D29—21no—
100#6599—24no—
101#6599—42no—
102#1900—291nomaximal, Sylow
103C22×C29—21no—
104C22×C29—21no—
105C22×C29—41no—
106C22×C29—41no—
107C22×C29—41no—
108C22×C29—82no—
109C22×C29C2×C22⋊C411yescharacteristic
110C22×C29C4×D412yes—
111C2×D29—21no—
112C2×D29—21no—
113C2×D29—21no—
114C2×D29—21no—
115C2×D29—21no—
116C2×D29—44no—
117C2×D29—41no—
118C2×D29—41no—
119C2×D29—41no—
120C2×D29—82no—
121C2×D29#10012yescomplemented
122C4×C29—21no—
123C4×C29—21no—
124C4×C29—41no—
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—81no—
136C2×C29#38611yescharacteristic
137C2×C29C2×#10011yescharacteristic
138C2×C29#41311yescharacteristic
139D29—22no—
140D29—41no—
141D29—81no—
142C22×D4—291no—
143C22×D4—291no—
144C22×D4—291no—
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#118111yescharacteristic
158#100—584no—
159C22⋊C8—581no—
160C22⋊C8—581no—
161C29#190011yescharacteristic, complemented, Sylow
162C24—291no—
163C24—291no—
164C24C2×#118111yescharacteristic
165C2×D4—581no—
166C2×D4—581no—
167C2×D4—582no—
168C2×D4—581no—
169C2×D4—581no—
170C2×D4—582no—
171C2×D4—581no—
172C2×D4—581no—
173C2×D4—1162no—
174C2×D4—1162no—
175C22×C4—291no—
176C22×C4—291no—
177C22×C4—291no—
178C22×C4—291no—
179C22×C4—291no—
180C22×C4—291no—
181C22×C4—582no—
182C22×C4—582no—
183C22×C4C2×#118111yescharacteristic
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—21no—
196C22⋊C4—21no—
197C22⋊C4—581no—
198C22⋊C4—581no—
199C23—21no—
200C23—22no—
201C23—41no—
202C23—41no—
203C23—291no—
204C23—291no—
205C23—582no—
206C23—582no—
207C23—581no—
208C23—582no—
209C23—1161no—
210C23—1161no—
211C23—1161no—
212C23C22×#118111yescharacteristic
213D4—1162no—
214D4—1162no—
215D4—1161no—
216D4—1162no—
217D4—1161no—
218D4—1162no—
219D4—1162no—
220C2×C4—22no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—292no—
224C2×C4—292no—
225C2×C4—291no—
226C2×C4—291no—
227C2×C4—581no—
228C2×C4—581no—
229C2×C4—582no—
230C2×C4—582no—
231C2×C4—581no—
232C2×C4—581no—
233C2×C4—581no—
234C2×C4—1161no—
235C2×C4C22⋊#118111yescharacteristic
236C2×C4C22⋊#118111yescharacteristic
237C8—584no—
238C8—1162no—
239C22—21no—
240C22—21no—
241C22—41no—
242C22—41no—
243C22—41no—
244C22—82no—
245C22—292no—
246C22—581no—
247C22—581no—
248C22—581no—
249C22—581no—
250C22—581no—
251C22—1164no—
252C22—1161no—
253C22—1161no—
254C22—1161no—
255C22—2322no—
256C22D4×#118112yes—
257C22C2×C22⋊#118111yescharacteristic
258C4—21no—
259C4—21no—
260C4—41no—
261C4—291no—
262C4—292no—
263C4—291no—
264C4—1161no—
265C2—22no—
266C2—81no—
267C2—582no—
268C2—1161no—
269C2—2321no—
270C2#1427211111yescharacteristic
271C2D29⋊#10011yescharacteristic
272C2#1427214911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#1181
commutatorC23×C29C22×C4
FrattiniC23C22×#1181
FittingC2×C22⋊C4×C29C4
socleC22×C29C2×C22⋊C4
prime radicalC2×#11745246C2
cosocleC22×Dic29C23
hypercenterC2×C22⋊C4#1181
hypocenterC29#1900
LCSG ▷ C23×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×D29⋊M16C2semidirect
2. C2×#11745229C2semidirect
3. #14272135C2semidirect
4. #14272043C2semidirect
51. #90800D4semidirect
121. C2×D29#100semidirect
161. C29#1900semidirect

Maximal subgroups

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

subgroupindex
C2×D29⋊M162
C2×#117452292
#142721352
#142720432
C2×#117452462
#190029