Finite Group Databasebeta

← #16829138

Subgroups — #16829138

Order 3712.

524 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 524 conjugacy classes of subgroups — too many to draw. Only its 127 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×D8×D29C211yesmaximal, characteristic, complemented
2C2×#11745269C211yesmaximal, characteristic, complemented
3#14271729C212yesmaximal, complemented
4#14271417C211yesmaximal, characteristic, complemented
5#14271416C211yesmaximal, characteristic, complemented
6#14271413C211yesmaximal, characteristic, complemented
7#14271398C212yesmaximal, complemented
8#14271397C212yesmaximal, complemented
9#14271198C211yesmaximal, characteristic, complemented
10#14271166C212yesmaximal, complemented
11C29×#469C211yesmaximal, characteristic, complemented
12C2×D4×D29C2212yes—
13C2×#90805C2211yescharacteristic
14C2×D8×C29C2211yescharacteristic
15C2×M16×C29C2211yescharacteristic, complemented
16C29×#121C2212yescomplemented
17#11745302—22no—
18#11745300C2212yescomplemented
19#11745299—22no—
20C2×#90782C2212yes—
21#11745292C2212yescomplemented
22C22×#6597C2211yescharacteristic, complemented
23D8×D29—24no—
24#11745269—24no—
25C2×D232C2211yescharacteristic
26C2×#90772C2211yescharacteristic
27C2×#90772C2211yescharacteristic, complemented
28C2×C8×D29C2211yescharacteristic
29C2×C8×D29C2211yescharacteristic, complemented
30#11745257C2212yescomplemented
31#11745254C2212yes—
32#11745247—22no—
33#11745244—22no—
34C29×#106C2211yescharacteristic, complemented
35C29×#102C2212yescomplemented
36#11745180C2212yescomplemented
37#11745169C2212yescomplemented
38#11745165C2211yescharacteristic, complemented
39#11745157C2212yescomplemented
40#11745155C2212yescomplemented
41C23×D29—22no—
42C2×D4×C29—22no—
43C2×D4×C29C2312yes—
44C22×C4×C29C2311yescharacteristic
45C2×C22⋊D29—22no—
46C2×C22⋊D29—22no—
47C2×C22⋊D29—22no—
48C2×C22⋊D29D411yescharacteristic
49C2×C22⋊D29D411yescharacteristic
50D4×D29—24no—
51D4×D29—24no—
52#90805—22no—
53#90805—22no—
54C2×D116—22no—
55C2×D116D411yescharacteristic
56C2×D116C2312yes—
57C2×C4×D29C2311yescharacteristic
58C2×C4×D29C2311yescharacteristic
59C2×Dic58D411yescharacteristic
60D8×C29—22no—
61M16×C29—22no—
62C2×C8×C29C2311yescharacteristic
63C2×C8×C29C2311yescharacteristic
64C4⋊C4×C29C2312yes—
65C22⋊C4×C29—22no—
66C22⋊Dic29—22no—
67#90782—24no—
68#90781—22no—
69#90781—22no—
70#90781—22no—
71C4⋊Dic29C2312yes—
72C4×Dic29—22no—
73C2×#6597—22no—
74C2×#6597C2311yescharacteristic
75C2×#6597C2311yescharacteristic
76D232—22no—
77#90772—22no—
78#90772—22no—
79C8×D29—22no—
80C8×D29D414yescomplemented
81C23×C29—22no—
82C23×C29C2×D411yescharacteristic
83C22×D29—22no—
84C22×D29—44no—
85C22×D29—82no—
86C22×D29—82no—
87C22×D29C2×D411yescharacteristic
88C22×D29C2×D411yescharacteristic
89D4×C29—22no—
90D4×C29—22no—
91D4×C29—82no—
92C2×C4×C29—21no—
93C2×C4×C29—21no—
94C2×C4×C29—22no—
95C2×C4×C29C2×D411yescharacteristic
96C2×C4×C29C2411yescharacteristic
97C22⋊D29—22no—
98C22⋊D29—22no—
99C22⋊D29—44no—
100C22⋊D29—82no—
101C22⋊D29—82no—
102C2×Dic29—22no—
103C2×Dic29C2×D411yescharacteristic
104C2×Dic29C2×D411yescharacteristic
105D116—22no—
106D116—22no—
107D116—22no—
108D116—82no—
109C4×D29—21no—
110C4×D29—21no—
111C4×D29C2×D412yes—
112C4×D29#4112yes—
113Dic58—22no—
114C8×C29—21no—
115C8×C29C2×D412yes—
116#6597—21no—
117#6597C2×D412yes—
118#3058—291nomaximal, Sylow
119C22×C29—21no—
120C22×C29—22no—
121C22×C29—42no—
122C22×C29—42no—
123C22×C29—42no—
124C22×C29C22×D411yescharacteristic
125C2×D29—22no—
126C2×D29—21no—
127C2×D29—22no—
128C2×D29—42no—
129C2×D29—42no—
130C2×D29—42no—
131C2×D29—88no—
132C2×D29#12112yes—
133C4×C29—21no—
134C4×C29—42no—
135C4×C29C22×D411yescharacteristic
136C4×C29C2×#4111yescharacteristic
137Dic29—21no—
138Dic29—42no—
139Dic29#12112yes—
140C22×D8—291no—
141C2×#131—291no—
142#535—292no—
143#469—291no—
144#469—291no—
145#469—291no—
146#469D2911yescharacteristic, complemented
147#466—292no—
148#466—292no—
149#427—291no—
150#418—292no—
151C2×C29—41no—
152C2×C29—82no—
153C2×C29C2×#12111yescharacteristic
154C2×C29#57612yes—
155D29—22no—
156D29—41no—
157D29—82no—
158C2×#41—291no—
159C22×D4—292no—
160C2×D8—292no—
161C2×D8—291no—
162C2×D8—584no—
163C2×D8C2×D2911yescharacteristic
164#131—584no—
165C2×M16—291no—
166C2×M16—291no—
167C2×M16C2×D2911yescharacteristic, complemented
168C22×C8—291no—
169C22×C8—291no—
170C22×C8—291no—
171#127—582no—
172#124—582no—
173#121—292no—
174#121—292no—
175#121—292no—
176#121C2×D2912yescomplemented
177#120—582no—
178#120—582no—
179#117—292no—
180#107—292no—
181#106—291no—
182#106C2×D2911yescharacteristic, complemented
183#102—292no—
184#102—292no—
185#102—292no—
186#102C2×D2912yescomplemented
187C29#305811yescharacteristic, complemented, Sylow
188C24—582no—
189#41—582no—
190#41—582no—
191C2×Q8—291no—
192C2×D4—22no—
193C2×D4—291no—
194C2×D4—291no—
195C2×D4—291no—
196C2×D4—292no—
197C2×D4—582no—
198C2×D4—584no—
199C2×D4—584no—
200C2×D4—582no—
201C2×D4—582no—
202C2×D4—582no—
203C2×D4C22×D2912yes—
204C22×C4—291no—
205C22×C4—291no—
206C22×C4C22×D2911yescharacteristic
207D8—22no—
208D8—584no—
209D8—582no—
210M16—22no—
211M16—582no—
212M16—582no—
213C2×C8—291no—
214C2×C8—294no—
215C2×C8—291no—
216C2×C8—582no—
217C2×C8—582no—
218C2×C8C22×D2911yescharacteristic
219C2×C8C22×D2911yescharacteristic
220C4⋊C4—292no—
221C4⋊C4C22×D2912yes—
222C22⋊C4—22no—
223C22⋊C4—582no—
224C22⋊C4—582no—
225C22⋊C4—582no—
226C22⋊C4—582no—
227C42—582no—
228C23—22no—
229C23—291no—
230C23—291no—
231C23—582no—
232C23—1164no—
233C23—2322no—
234C23—2322no—
235C23D4×D2911yescharacteristic
236Q8—582no—
237D4—22no—
238D4—22no—
239D4—82no—
240D4—582no—
241D4—582no—
242D4—582no—
243D4—582no—
244D4—582no—
245D4—1164no—
246D4—2322no—
247D4—2322no—
248D4—2322no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—22no—
252C2×C4—291no—
253C2×C4—292no—
254C2×C4—292no—
255C2×C4—291no—
256C2×C4—581no—
257C2×C4—581no—
258C2×C4—582no—
259C2×C4D4×D2911yescharacteristic
260C2×C4C23×D2911yescharacteristic
261C8—21no—
262C8—292no—
263C8—581no—
264C8D4×D2912yes—
265C22—21no—
266C22—22no—
267C22—42no—
268C22—42no—
269C22—42no—
270C22—292no—
271C22—582no—
272C22—581no—
273C22—582no—
274C22—1162no—
275C22—1162no—
276C22—1162no—
277C22—2328no—
278C22C2×D4×D2911yescharacteristic
279C4—21no—
280C4—42no—
281C4—292no—
282C4—581no—
283C4—1162no—
284C4C2×D4×D2911yescharacteristic
285C4#41×D2911yescharacteristic
286C2—41no—
287C2—82no—
288C2—582no—
289C2—1161no—
290C2—2322no—
291C2#121×D2911yescharacteristic
292C2#1427196712yes—
subgroupG/H
centerC22C2×D4×D29
commutator, cosocleC2×C4×C29C24
FrattiniC2×C4C23×D29
FittingC29×#469C2
socleC22×C29C22×D4
hypercenter#469D29
hypocenterC29#3058
LCSG ▷ C2×C4×C29 ▷ C2×C29 ▷ C29
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. C2×D8×D29C2semidirect
2. C2×#11745269C2semidirect
3. #14271729C2semidirect
4. #14271417C2semidirect
5. #14271416C2semidirect
6. #14271413C2semidirect
7. #14271398C2semidirect
8. #14271397C2semidirect
9. #14271198C2semidirect
10. #14271166C2semidirect
11. C29×#469C2semidirect
15. C2×M16×C29C22semidirect
16. C29×#121C22semidirect
18. #11745300C22semidirect
21. #11745292C22semidirect
22. C22×#6597C22semidirect
27. C2×#90772C22semidirect
29. C2×C8×D29C22semidirect
30. #11745257C22semidirect
34. C29×#106C22semidirect
35. C29×#102C22semidirect
36. #11745180C22semidirect
37. #11745169C22semidirect
38. #11745165C22semidirect
39. #11745157C22semidirect
40. #11745155C22semidirect
80. C8×D29D4semidirect
146. #469D29semidirect
167. C2×M16C2×D29semidirect
176. #121C2×D29semidirect
182. #106C2×D29semidirect
186. #102C2×D29semidirect
187. C29#3058semidirect

Maximal subgroups

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

subgroupindex
C2×D8×D292
C2×#117452692
#142717292
#142714172
#142714162
#142714132
#142713982
#142713972
#142711982
#142711662
C29×#4692
#305829