Finite Group Databasebeta

← #16836091

Subgroups — #16836091

Order 3712.

800 conjugacy classes of subgroups; only the 198 normal subgroups are shown.

normal subgroups only

This group has 800 conjugacy classes of subgroups — too many to draw. Only its 198 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#14272230C212yesmaximal, complemented
2#14272143C212yesmaximal, complemented
3#14272142C212yesmaximal, complemented
4D29⋊#99C214yesmaximal, complemented
5C2×#11745227C214yesmaximal, complemented
6C2×#11745359C211yesmaximal, characteristic
7C22×D4×C29C411yescharacteristic, complemented
8C22×C22⋊D29C412yescomplemented
9C22×C22⋊D29C2212yes—
10#11745359—28no—
11C2×#90807C412yescomplemented
12C2×#90807C411yescharacteristic, complemented
13C2×#90807C2211yescharacteristic
14C2×D4×D29C411yescharacteristic, complemented
15C2×D4×D29C2212yes—
16C2×D4×D29C2211yescharacteristic
17C2×#90805C411yescharacteristic, complemented
18C2×#90805C2211yescharacteristic
19C2×C22⋊#1181C2218yescomplemented
20D4×#1181—28no—
21#11745345C2214yescomplemented
22#11745227C2214yescomplemented
23#11745227C2218yescomplemented
24#11745215C2214yescomplemented
25C24×C29C2×C412yescomplemented
26C23×D29C2×C412yescomplemented
27C23×D29C2312yes—
28C22×#1181—28no—
29C2×D4×C29—24no—
30C2×D4×C29C2×C411yescharacteristic
31C2×D4×C29C2×C411yescharacteristic, complemented
32C2×D4×C29C2×C412yescomplemented
33C22×C4×C29C2×C411yescharacteristic, complemented
34C2×C22⋊D29—28no—
35C2×C22⋊D29—28no—
36C2×C22⋊D29C2×C412yes—
37C2×C22⋊D29C2×C412yescomplemented
38C2×C22⋊D29C2×C411yescharacteristic, complemented
39C2×C22⋊D29C2×C412yescomplemented
40C2×C22⋊D29C2×C412yescomplemented
41C2×C22⋊D29C2311yescharacteristic
42C2×C22⋊D29C2312yes—
43C22×Dic29C2×C412yescomplemented
44C22×Dic29C2×C412yescomplemented
45#90807—24no—
46#90807—28no—
47#90807—24no—
48D4×D29—28no—
49D4×D29—24no—
50D4×D29D418yes—
51#90805—24no—
52#90805—24no—
53C2×D116C2×C411yescharacteristic
54C2×D116C2311yescharacteristic
55C2×C4×D29C2×C412yescomplemented
56C2×C4×D29C2×C411yescharacteristic, complemented
57C2×C4×D29C2311yescharacteristic
58C2×Dic58C2×C411yescharacteristic, complemented
59C2×Dic58C2×C411yescharacteristic, complemented
60C22⋊#1181—28no—
61C22⋊#1181C2318yes—
62C4⋊#1181—24no—
63C4×#1181—24no—
64C23×C29—24no—
65C23×C29—82no—
66C23×C29C22×C412yes—
67C23×C29C22×C411yescharacteristic
68C23×C29C22×C412yes—
69C22×D29—24no—
70C22×D29—82no—
71C22×D29—82no—
72C22×D29C22×C411yescharacteristic
73C22×D29C22×C412yes—
74C22×D29C2×D418yes—
75C22×D29C2411yescharacteristic
76C2×#1181—28no—
77C2×#1181—88no—
78D4×C29—24no—
79D4×C29—22no—
80D4×C29C22⋊C414yes—
81C2×C4×C29—22no—
82C2×C4×C29C22×C411yescharacteristic
83C2×C4×C29C22×C411yescharacteristic
84C22⋊D29—24no—
85C22⋊D29—24no—
86C22⋊D29—24no—
87C22⋊D29—22no—
88C22⋊D29—24no—
89C22⋊D29—22no—
90C22⋊D29C22⋊C418yes—
91C2×Dic29—24no—
92C2×Dic29—24no—
93C2×Dic29C22×C412yes—
94C2×Dic29C22×C411yescharacteristic
95C2×Dic29C22×C411yescharacteristic
96D116—22no—
97D116C22⋊C414yes—
98C4×D29—24no—
99C4×D29—22no—
100C4×D29C2×D414yes—
101Dic58—22no—
102Dic58—22no—
103#2883—291nomaximal, Sylow
104C22×C29—22no—
105C22×C29—21no—
106C22×C29—42no—
107C22×C29—42no—
108C22×C29—41no—
109C22×C29—84no—
110C22×C29C2×C22⋊C414yes—
111C22×C29C23×C411yescharacteristic
112C2×D29—21no—
113C2×D29—48no—
114C2×D29—42no—
115C2×D29—41no—
116C2×D29—41no—
117C2×D29—84no—
118C2×D29C2×C22⋊C414yes—
119C2×D29C22×D412yes—
120#1181—48no—
121C4×C29—21no—
122C4×C29C2×C22⋊C412yes—
123Dic29—22no—
124Dic29—21no—
125Dic29C2×C22⋊C412yes—
126C2×H(5,𝔽2)—291no—
127#518—292no—
128#410—292no—
129#410—292no—
130C2×#99—294no—
131C2×#99—294no—
132C2×C29—21no—
133C2×C29—24no—
134C2×C29—42no—
135C2×C29—41no—
136C2×C29C22×C22⋊C411yescharacteristic
137D29—22no—
138D29—24no—
139D29—41no—
140H(5,𝔽2)—588no—
141C2×#41—291no—
142C2×#41—292no—
143C2×#41—291no—
144C2×#41—291no—
145C2×#41—291no—
146C22×D4—291no—
147C22×D4—292no—
148C22×D4—292no—
149C22×D4—291no—
150C22×D4—292no—
151C22×D4#118111yescharacteristic, complemented
152C4×D4—588no—
153#117—294no—
154C2×C22⋊C4—298no—
155#99—294no—
156#99—294no—
157#99—298no—
158C29#288311yescharacteristic, complemented, Sylow
159C24—292no—
160C24—292no—
161C24C2×#118112yescomplemented
162#41—584no—
163#41—584no—
164#41—584no—
165#41—588no—
166#41—584no—
167C2×Q8—291no—
168C2×Q8—291no—
169C2×D4—24no—
170C2×D4—292no—
171C2×D4—298no—
172C2×D4—292no—
173C2×D4—291no—
174C2×D4—291no—
175C2×D4—292no—
176C2×D4—292no—
177C2×D4—292no—
178C2×D4—291no—
179C2×D4—291no—
180C2×D4—584no—
181C2×D4—588no—
182C2×D4—588no—
183C2×D4—588no—
184C2×D4C2×#118111yescharacteristic
185C2×D4C2×#118112yescomplemented
186C2×D4C2×#118111yescharacteristic, complemented
187C22×C4—291no—
188C22×C4—292no—
189C22×C4—292no—
190C22×C4—292no—
191C22×C4—291no—
192C22×C4—588no—
193C22×C4C2×#118111yescharacteristic, complemented
194C4⋊C4—584no—
195C22⋊C4—298no—
196C22⋊C4—588no—
197C42—584no—
198C23—24no—
199C23—82no—
200C23—298no—
201C23—291no—
202C23—292no—
203C23—291no—
204C23—584no—
205C23—2322no—
206C23—2322no—
207C23C22×#118112yes—
208C23C22×#118111yescharacteristic
209C23C22×#118112yes—
210Q8—582no—
211Q8—582no—
212D4—24no—
213D4—22no—
214D4—298no—
215D4—294no—
216D4—582no—
217D4—582no—
218D4—582no—
219D4—584no—
220D4—584no—
221D4—584no—
222D4—584no—
223D4C22⋊#118114yes—
224C2×C4—22no—
225C2×C4—291no—
226C2×C4—294no—
227C2×C4—292no—
228C2×C4—291no—
229C2×C4—584no—
230C2×C4—584no—
231C2×C4—584no—
232C2×C4—582no—
233C2×C4—588no—
234C2×C4—2328no—
235C2×C4C22×#118111yescharacteristic
236C2×C4C22×#118111yescharacteristic
237C22—21no—
238C22—22no—
239C22—42no—
240C22—41no—
241C22—42no—
242C22—84no—
243C22—292no—
244C22—294no—
245C22—581no—
246C22—1168no—
247C22—1161no—
248C22—1162no—
249C22—1161no—
250C22—2324no—
251C22C2×C22⋊#118114yes—
252C22C23×#118111yescharacteristic
253C4—21no—
254C4—292no—
255C4—582no—
256C4—581no—
257C4—1168no—
258C4C2×C22⋊#118112yes—
259C2—21no—
260C2—24no—
261C2—41no—
262C2—42no—
263C2—582no—
264C2—584no—
265C2—1161no—
266C2C22×C22⋊#118111yescharacteristic
subgroupG/H
centerC2C22×C22⋊#1181
commutatorC22×C29C23×C4
FrattiniC22C23×#1181
FittingC22×D4×C29C4
socleC2×C29C22×C22⋊C4
prime radicalC2×#11745359C2
cosocleC22×D29C24
hypercenterC22×D4#1181
hypocenterC29#2883
LCSG ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×D4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. #14272230C2semidirect
2. #14272143C2semidirect
3. #14272142C2semidirect
4. D29⋊#99C2semidirect
5. C2×#11745227C2semidirect
7. C22×D4×C29C4semidirect
8. C22×C22⋊D29C4semidirect
11. C2×#90807C4semidirect
12. C2×#90807C4semidirect
14. C2×D4×D29C4semidirect
17. C2×#90805C4semidirect
19. C2×C22⋊#1181C22semidirect
21. #11745345C22semidirect
22. #11745227C22semidirect
23. #11745227C22semidirect
24. #11745215C22semidirect
25. C24×C29C2×C4semidirect
26. C23×D29C2×C4semidirect
31. C2×D4×C29C2×C4semidirect
32. C2×D4×C29C2×C4semidirect
33. C22×C4×C29C2×C4semidirect
37. C2×C22⋊D29C2×C4semidirect
38. C2×C22⋊D29C2×C4semidirect
39. C2×C22⋊D29C2×C4semidirect
40. C2×C22⋊D29C2×C4semidirect
43. C22×Dic29C2×C4semidirect
44. C22×Dic29C2×C4semidirect
55. C2×C4×D29C2×C4semidirect
56. C2×C4×D29C2×C4semidirect
58. C2×Dic58C2×C4semidirect
59. C2×Dic58C2×C4semidirect
151. C22×D4#1181semidirect
158. C29#2883semidirect
161. C24C2×#1181semidirect
185. C2×D4C2×#1181semidirect
186. C2×D4C2×#1181semidirect
193. C22×C4C2×#1181semidirect

Maximal subgroups

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

subgroupindex
#142722302
#142721432
#142721422
D29⋊#992
C2×#117452272
C2×#117453592
#288329