Finite Group Databasebeta

← #16836092

Subgroups — #16836092

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#14272144C212yesmaximal, complemented
3#14272142C212yesmaximal, complemented
4C2×#11745215C214yesmaximal, complemented
5D29⋊#99C214yesmaximal, complemented
6C2×#11745364C211yesmaximal, characteristic
7C2×#41×C29C411yescharacteristic, complemented
8#11745364—28no—
9C2×#90809C411yescharacteristic, complemented
10C2×#90809C2211yescharacteristic
11C2×D4×D29C412yescomplemented
12C2×D4×D29C411yescharacteristic, complemented
13C2×D4×D29C2212yes—
14C2×D4×D29C2211yescharacteristic
15C2×#90805C412yescomplemented
16C2×#90805C2211yescharacteristic
17C22×D116C411yescharacteristic, complemented
18C22×D116C2212yes—
19C2×C22⋊#1181C2218yescomplemented
20D4×#1181—28no—
21#11745345C2214yescomplemented
22#11745227C2214yescomplemented
23#11745215C2218yescomplemented
24#11745215C2214yescomplemented
25C23×D29C2×C412yescomplemented
26C23×D29C2×C412yescomplemented
27C23×D29C2312yes—
28C22×#1181—28no—
29#41×C29—24no—
30C2×Q8×C29C2×C411yescharacteristic, complemented
31C2×D4×C29C2×C411yescharacteristic
32C2×D4×C29C2×C412yescomplemented
33C22×C4×C29C2×C411yescharacteristic, complemented
34C22×C4×C29C2×C412yescomplemented
35C2×C22⋊D29C2×C412yes—
36C2×C22⋊D29C2×C412yescomplemented
37C2×C22⋊D29C2×C411yescharacteristic, complemented
38C2×C22⋊D29C2311yescharacteristic
39#90809—24no—
40#90809—24no—
41D4×D29—28no—
42D4×D29—24no—
43D4×D29—28no—
44D4×D29D418yes—
45#90805—28no—
46#90805—24no—
47C2×D116—28no—
48C2×D116—24no—
49C2×D116C2×C411yescharacteristic
50C2×D116C2×C412yescomplemented
51C2×D116C2×C411yescharacteristic, complemented
52C2×D116C2×C412yescomplemented
53C2×D116C2311yescharacteristic
54C2×D116C2312yes—
55C2×C4×D29C2×C412yescomplemented
56C2×C4×D29C2×C412yescomplemented
57C2×C4×D29C2×C411yescharacteristic, complemented
58C2×C4×D29C2311yescharacteristic
59C2×Dic58C2×C411yescharacteristic, complemented
60C22⋊#1181—28no—
61C22⋊#1181C2318yes—
62C4⋊#1181—24no—
63C4×#1181—24no—
64C23×C29C22×C411yescharacteristic
65C23×C29C22×C412yes—
66C22×D29—24no—
67C22×D29—24no—
68C22×D29—82no—
69C22×D29—82no—
70C22×D29—82no—
71C22×D29C22×C412yes—
72C22×D29C22×C411yescharacteristic
73C22×D29C22×C412yes—
74C22×D29C2×D418yes—
75C22×D29C2411yescharacteristic
76C2×#1181—28no—
77C2×#1181—88no—
78Q8×C29—22no—
79D4×C29—24no—
80D4×C29C22⋊C414yes—
81C2×C4×C29—24no—
82C2×C4×C29—22no—
83C2×C4×C29C22×C411yescharacteristic
84C2×C4×C29C22×C412yes—
85C2×C4×C29C22×C411yescharacteristic
86C22⋊D29—24no—
87C22⋊D29—22no—
88C22⋊D29—22no—
89C22⋊D29C22⋊C418yes—
90C2×Dic29C22×C411yescharacteristic
91C2×Dic29C22×C411yescharacteristic
92D116—24no—
93D116—24no—
94D116—22no—
95D116—24no—
96D116—22no—
97D116C22⋊C414yes—
98C4×D29—24no—
99C4×D29—22no—
100C4×D29—24no—
101C4×D29C2×D414yes—
102Dic58—22no—
103#2883—291nomaximal, Sylow
104C22×C29—21no—
105C22×C29—42no—
106C22×C29—41no—
107C22×C29C2×C22⋊C414yes—
108C22×C29C23×C411yescharacteristic
109C2×D29—21no—
110C2×D29—22no—
111C2×D29—48no—
112C2×D29—42no—
113C2×D29—41no—
114C2×D29—42no—
115C2×D29—41no—
116C2×D29—84no—
117C2×D29—84no—
118C2×D29C2×C22⋊C414yes—
119C2×D29C22×D412yes—
120#1181—48no—
121C4×C29—21no—
122C4×C29—22no—
123C4×C29C2×C22⋊C412yes—
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—41no—
135C2×C29C22×C22⋊C411yescharacteristic
136D29—22no—
137D29—24no—
138D29—42no—
139D29—41no—
140H(5,𝔽2)—588no—
141C2×#41—291no—
142C2×#41—291no—
143C2×#41—292no—
144C2×#41—291no—
145C2×#41#118111yescharacteristic, complemented
146C22×D4—291no—
147C22×D4—291no—
148C22×D4—292no—
149C22×D4—292no—
150C22×D4—291no—
151C22×D4—292no—
152C4×D4—588no—
153#117—294no—
154C2×C22⋊C4—298no—
155#99—298no—
156#99—294no—
157#99—294no—
158C29#288311yescharacteristic, complemented, Sylow
159C24—292no—
160C24—292no—
161C24—292no—
162#41—24no—
163#41—584no—
164#41—588no—
165#41—584no—
166#41—584no—
167C2×Q8—291no—
168C2×Q8C2×#118111yescharacteristic, complemented
169C2×D4—292no—
170C2×D4—298no—
171C2×D4—291no—
172C2×D4—291no—
173C2×D4—292no—
174C2×D4—291no—
175C2×D4—292no—
176C2×D4—291no—
177C2×D4—292no—
178C2×D4—292no—
179C2×D4—291no—
180C2×D4—584no—
181C2×D4—588no—
182C2×D4—588no—
183C2×D4—588no—
184C2×D4—584no—
185C2×D4C2×#118111yescharacteristic
186C2×D4C2×#118112yescomplemented
187C22×C4—291no—
188C22×C4—292no—
189C22×C4—292no—
190C22×C4—291no—
191C22×C4—588no—
192C22×C4C2×#118112yescomplemented
193C22×C4C2×#118111yescharacteristic, complemented
194C4⋊C4—584no—
195C22⋊C4—298no—
196C22⋊C4—588no—
197C42—584no—
198C23—298no—
199C23—291no—
200C23—292no—
201C23—292no—
202C23—291no—
203C23—584no—
204C23—584no—
205C23—2322no—
206C23—2322no—
207C23—2322no—
208C23C22×#118111yescharacteristic
209C23C22×#118112yes—
210Q8—22no—
211Q8—582no—
212D4—24no—
213D4—298no—
214D4—294no—
215D4—582no—
216D4—584no—
217D4—584no—
218D4—584no—
219D4—582no—
220D4—582no—
221D4—584no—
222D4—582no—
223D4C22⋊#118114yes—
224C2×C4—24no—
225C2×C4—22no—
226C2×C4—291no—
227C2×C4—294no—
228C2×C4—291no—
229C2×C4—584no—
230C2×C4—584no—
231C2×C4—582no—
232C2×C4—588no—
233C2×C4—2328no—
234C2×C4C22×#118112yes—
235C2×C4C22×#118111yescharacteristic
236C2×C4C22×#118111yescharacteristic
237C22—21no—
238C22—42no—
239C22—41no—
240C22—292no—
241C22—294no—
242C22—582no—
243C22—581no—
244C22—1168no—
245C22—1161no—
246C22—1162no—
247C22—1161no—
248C22—1162no—
249C22—2324no—
250C22—2324no—
251C22C2×C22⋊#118114yes—
252C22C23×#118111yescharacteristic
253C4—21no—
254C4—22no—
255C4—292no—
256C4—581no—
257C4—1168no—
258C4C2×C22⋊#118112yes—
259C2—21no—
260C2—24no—
261C2—41no—
262C2—582no—
263C2—584no—
264C2—1161no—
265C2—1162no—
266C2C22×C22⋊#118111yescharacteristic
subgroupG/H
centerC2C22×C22⋊#1181
commutatorC22×C29C23×C4
FrattiniC22C23×#1181
FittingC2×#41×C29C4
socleC2×C29C22×C22⋊C4
prime radicalC2×#11745364C2
cosocleC22×D29C24
hypercenterC2×#41#1181
hypocenterC29#2883
LCSG ▷ C22×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C2 ◁ C2×D4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #14272230C2semidirect
2. #14272144C2semidirect
3. #14272142C2semidirect
4. C2×#11745215C2semidirect
5. D29⋊#99C2semidirect
7. C2×#41×C29C4semidirect
9. C2×#90809C4semidirect
11. C2×D4×D29C4semidirect
12. C2×D4×D29C4semidirect
15. C2×#90805C4semidirect
17. C22×D116C4semidirect
19. C2×C22⋊#1181C22semidirect
21. #11745345C22semidirect
22. #11745227C22semidirect
23. #11745215C22semidirect
24. #11745215C22semidirect
25. C23×D29C2×C4semidirect
26. C23×D29C2×C4semidirect
30. C2×Q8×C29C2×C4semidirect
32. C2×D4×C29C2×C4semidirect
33. C22×C4×C29C2×C4semidirect
34. C22×C4×C29C2×C4semidirect
36. C2×C22⋊D29C2×C4semidirect
37. C2×C22⋊D29C2×C4semidirect
50. C2×D116C2×C4semidirect
51. C2×D116C2×C4semidirect
52. C2×D116C2×C4semidirect
55. C2×C4×D29C2×C4semidirect
56. C2×C4×D29C2×C4semidirect
57. C2×C4×D29C2×C4semidirect
59. C2×Dic58C2×C4semidirect
145. C2×#41#1181semidirect
158. C29#2883semidirect
168. C2×Q8C2×#1181semidirect
186. C2×D4C2×#1181semidirect
192. C22×C4C2×#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
#142721442
#142721422
C2×#117452152
D29⋊#992
C2×#117453642
#288329