Finite Group Databasebeta

← #16855538

Subgroups — #16855538

Order 3968.

398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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#14521680C211yesmaximal, characteristic, complemented
2#14521524C211yesmaximal, characteristic
3#14521351C212yesmaximal, complemented
4#14521347C212yesmaximal, complemented
5#14521337C212yesmaximal, complemented
6#14521327C212yesmaximal, complemented
7#14521089C211yesmaximal, characteristic, complemented
8#14521087C211yesmaximal, characteristic, complemented
9#14521075C211yesmaximal, characteristic, complemented
10#14521054C211yesmaximal, characteristic
11C2×C31×#102C211yesmaximal, characteristic
12C22×D4×C31C2211yescharacteristic
13C22×C8×C31C2211yescharacteristic
14C2×C4⋊C4×C31C2211yescharacteristic
15C2×C22⋊Dic31—22no—
16D4×Dic31—21no—
17D4×Dic31—21no—
18D4×Dic31C2212yes—
19D4×Dic31C2212yes—
20#11758503C2211yescharacteristic
21#11758503C2211yescharacteristic
22#11758503C2211yescharacteristic
23#11758501—22no—
24C2×#92474C2211yescharacteristic
25#11758467—21no—
26#11758467C2212yescomplemented
27#11758465—21no—
28#11758465C2212yescomplemented
29C31×#102C2212yes—
30C31×#102C2212yes—
31#11758420C2212yes—
32#11758420C2212yes—
33#11758406C2211yescharacteristic, complemented
34#11758406C2211yescharacteristic, complemented
35#11758405C2211yescharacteristic, complemented
36#11758405C2211yescharacteristic, complemented
37Dic31⋊C8C2212yescomplemented
38Dic31⋊C8C2212yescomplemented
39#11758396C2212yescomplemented
40#11758395C2212yescomplemented
41C24×C31—21no—
42C2×D4×C31—21no—
43C2×D4×C31—22no—
44C2×D4×C31Q814yescomplemented
45C2×D4×C31C2312yes—
46C22×C4×C31—21no—
47C22×C4×C31C2311yescharacteristic
48C22×Dic31—22no—
49C22×Dic31—22no—
50C2×Dic62—22no—
51C2×C8×C31—22no—
52C2×C8×C31C2311yescharacteristic
53C2×C8×C31C2311yescharacteristic
54C4⋊C4×C31—21no—
55C4⋊C4×C31C2312yes—
56C22⋊Dic31—21no—
57C22⋊Dic31—21no—
58C22⋊Dic31—22no—
59C22⋊Dic31—22no—
60C22⋊Dic31D412yes—
61C4⋊Dic31—22no—
62C4⋊Dic31D411yescharacteristic
63C4⋊Dic31D411yescharacteristic
64C4⋊Dic31C2311yescharacteristic
65C4⋊Dic31C2311yescharacteristic
66C4⋊Dic31C2311yescharacteristic
67C4⋊Dic31C2311yescharacteristic
68Dic31⋊C4—22no—
69Dic31⋊C4—22no—
70C4×Dic31—21no—
71C4×Dic31—21no—
72C4×Dic31C2312yes—
73#92474—22no—
74C2×C31⋊C8C2312yes—
75C23×C31—22no—
76C23×C31—24no—
77C23×C31—81no—
78C23×C31—81no—
79C23×C31C2×D411yescharacteristic
80D4×C31—24no—
81D4×C31—22no—
82D4×C31C2×Q814yes—
83C2×C4×C31—22no—
84C2×C4×C31—81no—
85C2×C4×C31C2×D411yescharacteristic
86C2×C4×C31C2×Q812yes—
87C2×C4×C31#4112yes—
88C2×C4×C31C2411yescharacteristic
89C2×Dic31—21no—
90C2×Dic31—21no—
91C2×Dic31—21no—
92C2×Dic31—21no—
93C2×Dic31—82no—
94C2×Dic31—82no—
95C2×Dic31C2×D412yes—
96C2×Dic31C2×D412yes—
97Dic62—82no—
98C8×C31—21no—
99C8×C31—21no—
100C31⋊C8—22no—
101#3081—311nomaximal, Sylow
102C22×C31—21no—
103C22×C31—21no—
104C22×C31—24no—
105C22×C31—42no—
106C22×C31—42no—
107C22×C31—84no—
108C22×C31C22⋊Q812yes—
109C22×C31C22×D411yescharacteristic
110C4×C31—42no—
111C4×C31C22⋊Q812yes—
112C4×C31C22×Q811yescharacteristic
113C4×C31C2×#4111yescharacteristic
114Dic31—22no—
115Dic31—22no—
116Dic31—41no—
117Dic31—41no—
118Dic31—41no—
119Dic31—41no—
120#544—311no—
121#518—311no—
122#478—312no—
123#478—312no—
124#476—312no—
125#474—312no—
126#428—311no—
127#427—311no—
128#424—311no—
129#418—311no—
130C2×#102D3111yescharacteristic
131C2×C31—22no—
132C2×C31—44no—
133C2×C31C2×C22⋊Q811yescharacteristic
134C2×C31#57611yescharacteristic
135C2×C31#57711yescharacteristic
136C22×D4C2×D3111yescharacteristic
137C2×M16—311no—
138C22×C8C2×D3111yescharacteristic
139C4⋊Q8—312no—
140C4⋊Q8—621no—
141#125—312no—
142#125—621no—
143C22⋊Q8—622no—
144C4×D4—312no—
145C4×D4—312no—
146C4×D4—621no—
147C4×D4—621no—
148#117—311no—
149#117—311no—
150#117—311no—
151C2×C4⋊C4C2×D3111yescharacteristic
152C2×C22⋊C4—622no—
153#107—311no—
154#107—311no—
155#107—312no—
156#106—311no—
157#106—311no—
158#106—312no—
159C4⋊C8—312no—
160C4⋊C8—312no—
161#102—312no—
162#102—312no—
163#102C2×D3112yes—
164#102C2×D3112yes—
165C31#308111yescharacteristic, complemented, Sylow
166C24—21no—
167C2×Q8—622no—
168C2×D4—21no—
169C2×D4—22no—
170C2×D4Dic6214yescomplemented
171C2×D4C22×D3112yes—
172C22×C4—21no—
173C22×C4—622no—
174C22×C4—622no—
175C22×C4C22×D3111yescharacteristic
176M16—622no—
177C2×C8—22no—
178C2×C8—312no—
179C2×C8C22×D3111yescharacteristic
180C2×C8C22×D3111yescharacteristic
181C4⋊C4—21no—
182C4⋊C4—311no—
183C4⋊C4—311no—
184C4⋊C4—311no—
185C4⋊C4—311no—
186C4⋊C4—311no—
187C4⋊C4—311no—
188C4⋊C4—622no—
189C4⋊C4—622no—
190C4⋊C4—622no—
191C4⋊C4C22×D3112yes—
192C22⋊C4—312no—
193C22⋊C4—622no—
194C22⋊C4—622no—
195C22⋊C4—621no—
196C22⋊C4—621no—
197C42—312no—
198C42—621no—
199C42—621no—
200C23—22no—
201C23—24no—
202C23—81no—
203C23—81no—
204C23D4×D3111yescharacteristic
205Q8—2482no—
206D4—24no—
207D4—22no—
208D4C2×Dic6214yes—
209C2×C4—22no—
210C2×C4—81no—
211C2×C4—312no—
212C2×C4—312no—
213C2×C4—621no—
214C2×C4—621no—
215C2×C4—621no—
216C2×C4—621no—
217C2×C4—2482no—
218C2×C4—2482no—
219C2×C4C2×Dic6212yes—
220C2×C4D4×D3111yescharacteristic
221C2×C4#9249712yes—
222C2×C4C23×D3111yescharacteristic
223C8—21no—
224C8—21no—
225C8—622no—
226C22—21no—
227C22—21no—
228C22—24no—
229C22—42no—
230C22—42no—
231C22—84no—
232C22#1175845512yes—
233C22C2×D4×D3111yescharacteristic
234C4—42no—
235C4—622no—
236C4—622no—
237C4—1241no—
238C4—1241no—
239C4—1241no—
240C4—1241no—
241C4#1175845512yes—
242C4C22×Dic6211yescharacteristic
243C4C2×#9249711yescharacteristic
244C2—22no—
245C2—44no—
246C2C2×#1175845511yescharacteristic
247C2#1452185011yescharacteristic
248C2#1452185511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C31×#102C2
socleC22×C31C22×D4
prime radicalC22×D4×C31C22
hypercenterC2×#102D31
hypocenterC31#3081
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#102

Complements

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

NH ≅ G/Ntype
1. #14521680C2semidirect
3. #14521351C2semidirect
4. #14521347C2semidirect
5. #14521337C2semidirect
6. #14521327C2semidirect
7. #14521089C2semidirect
8. #14521087C2semidirect
9. #14521075C2semidirect
26. #11758467C22semidirect
28. #11758465C22semidirect
33. #11758406C22semidirect
34. #11758406C22semidirect
35. #11758405C22semidirect
36. #11758405C22semidirect
37. Dic31⋊C8C22semidirect
38. Dic31⋊C8C22semidirect
39. #11758396C22semidirect
40. #11758395C22semidirect
44. C2×D4×C31Q8semidirect
165. C31#3081semidirect
170. C2×D4Dic62semidirect

Maximal subgroups

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

subgroupindex
#145216802
#145215242
#145213512
#145213472
#145213372
#145213272
#145210892
#145210872
#145210752
#145210542
C2×C31×#1022
#308131