Finite Group Databasebeta

← #16857538

Subgroups — #16857538

Order 3968.

462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 123 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#14521759C211yesmaximal, characteristic, complemented
2#14521684C211yesmaximal, characteristic
3#14521395C211yesmaximal, characteristic, complemented
4#14521366C212yesmaximal, complemented
5#14521340C211yesmaximal, characteristic, complemented
6#14521275C212yesmaximal, complemented
7#14521198C212yesmaximal, complemented
8C4×#92481C211yesmaximal, characteristic, complemented
9#14521114C211yesmaximal, characteristic, complemented
10#102×D31C212yesmaximal, complemented
11C31×#460C211yesmaximal, characteristic, complemented
12C2×D4×D31—21no—
13C2×D4×D31C2212yes—
14C2×SD16×C31C2212yescomplemented
15C31×#127C2211yescharacteristic
16C4×Q8×C31C2211yescharacteristic, complemented
17#11758523C2212yescomplemented
18C2×#92481C2211yescharacteristic
19#11758515—21no—
20#11758515C2212yes—
21#11758514—22no—
22C2×C8×D31C2212yescomplemented
23#11758473—22no—
24C4⋊C4×D31C2212yescomplemented
25C4×D124—21no—
26C4×D124C2211yescharacteristic
27C4×D124C2211yescharacteristic
28#11758447—21no—
29#11758446C2211yescharacteristic, complemented
30C31×C4⋊C8C2211yescharacteristic, complemented
31C31×#102C2212yescomplemented
32#11758423C2211yescharacteristic, complemented
33#11758420C2212yescomplemented
34#11758420C2212yescomplemented
35#11758409C2212yes—
36(C2×D31)⋊C8C2212yescomplemented
37#11758405C2212yescomplemented
38#11758397C2211yescharacteristic
39#11758396C2211yescharacteristic, complemented
40C4×C31⋊C8C2211yescharacteristic, complemented
41C23×D31—22no—
42C2×Q8×C31C2311yescharacteristic
43C2×D4×C31—21no—
44C2×D4×C31—21no—
45C2×D4×C31C2312yes—
46C2×C22⋊D31—22no—
47C2×C22⋊D31—22no—
48D4×D31—24no—
49D4×D31—42no—
50D4×D31—44no—
51C2×D124D411yescharacteristic
52C2×D124C2311yescharacteristic
53C2×C4×D31—21no—
54C2×C4×D31—22no—
55C2×C4×D31C2312yes—
56C2×Dic62—21no—
57SD16×C31—42no—
58C2×C8×C31C2312yes—
59C4⋊C4×C31—21no—
60C4⋊C4×C31C2311yescharacteristic
61C42×C31—21no—
62C42×C31C2311yescharacteristic
63C22⋊Dic31—22no—
64#92481—22no—
65(C2×D31)⋊C4—22no—
66(C2×D31)⋊C4—21no—
67(C2×D31)⋊C4D412yes—
68C4⋊Dic31—21no—
69C4⋊Dic31D411yescharacteristic
70C4⋊Dic31C2311yescharacteristic
71C4⋊Dic31C2312yes—
72Dic31⋊C4—22no—
73Dic31⋊C4—22no—
74C2×C31⋊C8C2311yescharacteristic
75C2×C31⋊C8C2311yescharacteristic
76C8×D31—42no—
77C23×C31—22no—
78C22×D31—21no—
79C22×D31—44no—
80C22×D31—44no—
81C22×D31—82no—
82C22×D31C2×D412yes—
83Q8×C31—21no—
84Q8×C31—21no—
85D4×C31—22no—
86D4×C31—22no—
87D4×C31—42no—
88D4×C31—81no—
89C2×C4×C31—21no—
90C2×C4×C31—21no—
91C2×C4×C31C2×D411yescharacteristic
92C2×C4×C31C2×D411yescharacteristic
93C2×C4×C31C2411yescharacteristic
94C22⋊D31—44no—
95C22⋊D31—44no—
96C2×Dic31—22no—
97C2×Dic31—21no—
98C2×Dic31C2×D412yes—
99D124—21no—
100D124SD1614yescomplemented
101D124#4112yes—
102C4×D31—22no—
103C4×D31—22no—
104C4×D31—42no—
105C4×D31—82no—
106Dic62—81no—
107C8×C31—22no—
108C31⋊C8—21no—
109C31⋊C8—21no—
110#3295—311nomaximal, Sylow
111C22×C31—42no—
112C22×C31—42no—
113C22×C31—42no—
114C22×C31C22×D411yescharacteristic
115C2×D31—22no—
116C2×D31—22no—
117C2×D31—22no—
118C2×D31—41no—
119C2×D31—41no—
120C2×D31—88no—
121C2×D31C2×SD1614yes—
122C4×C31—21no—
123C4×C31—41no—
124C4×C31—41no—
125C4×C31C2×SD1612yes—
126C4×C31C2×#4111yescharacteristic
127C4×C31H(5,𝔽2)11yescharacteristic
128Dic31—22no—
129Dic31—41no—
130Dic31—42no—
131#554—311no—
132D42—311no—
133#486—311no—
134#481—312no—
135#476—311no—
136#465—312no—
137#460D3111yescharacteristic, complemented
138#450—312no—
139C4×SD16—311no—
140C8×D4—311no—
141C2×#102—312no—
142C2×C31—82no—
143C2×C31#54611yescharacteristic
144C2×C31C22×SD1611yescharacteristic
145C2×C31#57611yescharacteristic
146D31—24no—
147D31—42no—
148C22×D4—312no—
149C22×D4—621no—
150C2×SD16—311no—
151C2×SD16C2×D3112yescomplemented
152C22×C8—312no—
153C4⋊Q8—311no—
154#127C2×D3111yescharacteristic
155#125—621no—
156C22⋊Q8—312no—
157C22⋊Q8—622no—
158#121—312no—
159#121—621no—
160#120—622no—
161C4×Q8C2×D3111yescharacteristic, complemented
162C4×D4—311no—
163C4×D4—311no—
164C4×D4—621no—
165C2×C4⋊C4—312no—
166#106—312no—
167#106—311no—
168C4⋊C8C2×D3111yescharacteristic, complemented
169#103—311no—
170#102—312no—
171#102—312no—
172#102—312no—
173#102—311no—
174#102C2×D3112yescomplemented
175C22⋊C8—312no—
176C4×C8—311no—
177C31#329511yescharacteristic, complemented, Sylow
178C24—622no—
179C2×Q8—621no—
180C2×Q8C22×D3111yescharacteristic
181C2×D4—21no—
182C2×D4—21no—
183C2×D4—311no—
184C2×D4—311no—
185C2×D4—622no—
186C2×D4—624no—
187C2×D4—622no—
188C2×D4—1242no—
189C2×D4—1244no—
190C2×D4C22×D3112yes—
191C22×C4—312no—
192C22×C4—622no—
193C22×C4—621no—
194SD16—42no—
195SD16—622no—
196C2×C8—311no—
197C2×C8—311no—
198C2×C8—1242no—
199C2×C8C22×D3112yes—
200C4⋊C4—21no—
201C4⋊C4—311no—
202C4⋊C4—312no—
203C4⋊C4—311no—
204C4⋊C4—622no—
205C4⋊C4—622no—
206C4⋊C4—621no—
207C4⋊C4C22×D3111yescharacteristic
208C22⋊C4—312no—
209C22⋊C4—622no—
210C22⋊C4—622no—
211C22⋊C4—621no—
212C42—21no—
213C42C22×D3111yescharacteristic
214C23—22no—
215C23—312no—
216C23—621no—
217C23—1244no—
218C23—1244no—
219C23—2482no—
220Q8—21no—
221Q8—21no—
222Q8—2481no—
223D4—22no—
224D4—22no—
225D4—42no—
226D4—81no—
227D4—314no—
228D4—312no—
229D4—621no—
230D4—1244no—
231D4—1244no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—312no—
235C2×C4—622no—
236C2×C4—622no—
237C2×C4—621no—
238C2×C4—622no—
239C2×C4—1242no—
240C2×C4—2482no—
241C2×C4D4×D3111yescharacteristic
242C2×C4D4×D3111yescharacteristic
243C2×C4C23×D3111yescharacteristic
244C8—22no—
245C8—621no—
246C8—621no—
247C22—42no—
248C22—42no—
249C22—42no—
250C22—314no—
251C22—622no—
252C22—622no—
253C22—622no—
254C22—1241no—
255C22—1241no—
256C22—2488no—
257C22C2×D4×D3111yescharacteristic
258C4—21no—
259C4—41no—
260C4—41no—
261C4—622no—
262C4—1241no—
263C4—1242no—
264C4SD16×D3112yes—
265C4#1175856111yescharacteristic
266C4#41×D3111yescharacteristic
267C2—82no—
268C2—624no—
269C2—1242no—
270C2#1452169611yescharacteristic
271C2C2×SD16×D3111yescharacteristic
272C2#1452185311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#460C2
socleC22×C31C22×D4
prime radical#14521684C2
hypercenter#460D31
hypocenterC31#3295
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #14521759C2semidirect
3. #14521395C2semidirect
4. #14521366C2semidirect
5. #14521340C2semidirect
6. #14521275C2semidirect
7. #14521198C2semidirect
8. C4×#92481C2semidirect
9. #14521114C2semidirect
10. #102×D31C2semidirect
11. C31×#460C2semidirect
14. C2×SD16×C31C22semidirect
16. C4×Q8×C31C22semidirect
17. #11758523C22semidirect
22. C2×C8×D31C22semidirect
24. C4⋊C4×D31C22semidirect
29. #11758446C22semidirect
30. C31×C4⋊C8C22semidirect
31. C31×#102C22semidirect
32. #11758423C22semidirect
33. #11758420C22semidirect
34. #11758420C22semidirect
36. (C2×D31)⋊C8C22semidirect
37. #11758405C22semidirect
39. #11758396C22semidirect
40. C4×C31⋊C8C22semidirect
100. D124SD16semidirect
137. #460D31semidirect
151. C2×SD16C2×D31semidirect
161. C4×Q8C2×D31semidirect
168. C4⋊C8C2×D31semidirect
174. #102C2×D31semidirect
177. C31#3295semidirect

Maximal subgroups

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

subgroupindex
#145217592
#145216842
#145213952
#145213662
#145213402
#145212752
#145211982
C4×#924812
#145211142
#102×D312
C31×#4602
#329531