Finite Group Databasebeta

← #16858376

Subgroups — #16858376

Order 3968.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#14521785C211yesmaximal, characteristic, complemented
2#14521760C211yesmaximal, characteristic, complemented
3#14521402C212yesmaximal, complemented
4#14521351C212yesmaximal, complemented
5#14521341C211yesmaximal, characteristic, complemented
6#14521263C212yesmaximal, complemented
7#14521241C211yesmaximal, characteristic
8C8×Dic62C211yesmaximal, characteristic, complemented
9C4×#92470C211yesmaximal, characteristic, complemented
10#14521129C212yesmaximal, complemented
11C31×#486C211yesmaximal, characteristic, complemented
12C31×C4⋊Q8C2211yescharacteristic
13C31×#127C2211yescharacteristic
14#11758523—22no—
15#11758513—21no—
16#11758513C2212yes—
17#11758512—22no—
18D4×Dic31—21no—
19D4×Dic31C2212yes—
20C2×#92479C2212yes—
21C2×#92470C2211yescharacteristic
22#11758474—21no—
23#11758470C2212yes—
24C4⋊C4×D31—21no—
25#11758467C2212yes—
26C4×D124C2211yescharacteristic
27C4×Dic62C2211yescharacteristic
28C4×Dic62C2211yescharacteristic
29C31×#102C2212yes—
30C31×#102C2212yes—
31C4×C8×C31C2211yescharacteristic
32#11758420C2212yes—
33#11758409C2211yescharacteristic
34#11758405C2211yescharacteristic
35#11758404C2211yescharacteristic
36Dic31⋊C8C2212yes—
37C8×Dic31C2212yes—
38#11758398C2212yes—
39#11758395C2212yes—
40C4⋊(C31⋊C8)C2211yescharacteristic
41C2×Q8×C31—21no—
42C2×D4×C31—21no—
43C2×D4×C31—21no—
44C2×D4×C31C2312yes—
45C22×Dic31—22no—
46C2×D124C2311yescharacteristic
47C2×C4×D31—21no—
48C2×C4×D31—22no—
49C2×Dic62D411yescharacteristic
50C2×Dic62C2311yescharacteristic
51C2×C8×C31C2311yescharacteristic
52C2×C8×C31C2311yescharacteristic
53C4⋊C4×C31—21no—
54C4⋊C4×C31C2312yes—
55C42×C31C2311yescharacteristic
56C22⋊Dic31—22no—
57C22⋊Dic31—22no—
58C22⋊Dic31—22no—
59#92479—24no—
60(C2×D31)⋊C4—21no—
61(C2×D31)⋊C4—22no—
62C4⋊Dic31—22no—
63C4⋊Dic31D411yescharacteristic
64C4⋊Dic31C2311yescharacteristic
65C4⋊Dic31C2311yescharacteristic
66Dic31⋊C4—21no—
67Dic31⋊C4—22no—
68Dic31⋊C4D412yes—
69C4×Dic31—21no—
70C4×Dic31C2312yes—
71C2×C31⋊C8C2312yes—
72#92470—22no—
73C23×C31—22no—
74C22×D31—21no—
75Q8×C31—81no—
76D4×C31—22no—
77D4×C31—22no—
78D4×C31—42no—
79D4×C31—81no—
80C2×C4×C31—22no—
81C2×C4×C31C2×D411yescharacteristic
82C2×C4×C31C2×D411yescharacteristic
83C2×C4×C31C2411yescharacteristic
84C2×Dic31—21no—
85C2×Dic31—21no—
86C2×Dic31—21no—
87C2×Dic31—82no—
88C2×Dic31C2×D412yes—
89C2×Dic31C2×D412yes—
90D124—21no—
91D124#4112yes—
92C4×D31—42no—
93C4×D31—82no—
94Dic62—22no—
95Dic62—21no—
96Dic62—21no—
97C8×C31—21no—
98C8×C31—21no—
99C31⋊C8—22no—
100#3361—311nomaximal, Sylow
101C22×C31—42no—
102C22×C31—42no—
103C22×C31—42no—
104C22×C31C22×D411yescharacteristic
105C2×D31—22no—
106C2×D31—41no—
107C2×D31—41no—
108C4×C31—21no—
109C4×C31—42no—
110C4×C31#13512yes—
111C4×C31C2×#4111yescharacteristic
112C4×C312−1+411yescharacteristic
113Dic31—22no—
114Dic31—22no—
115Dic31—41no—
116Dic31—41no—
117Dic31—41no—
118#559—311no—
119#554—311no—
120#488—312no—
121#486D3111yescharacteristic, complemented
122#478—312no—
123#477—311no—
124#463—312no—
125#459—311no—
126C8×Q8—311no—
127C4×SD16—311no—
128C4×D8—312no—
129C2×C31—82no—
130C2×C31#54811yescharacteristic
131C2×C31C2×#13511yescharacteristic
132C2×C31#57611yescharacteristic
133D31—42no—
134C2×SD16—311no—
135C2×D8—312no—
136C4⋊Q8C2×D3111yescharacteristic
137#127C2×D3111yescharacteristic
138#125—312no—
139#124—312no—
140#124—621no—
141#123—622no—
142C22⋊Q8—621no—
143C22⋊Q8—622no—
144C4×Q8—311no—
145C4×Q8—311no—
146C4×D4—312no—
147C4×D4—312no—
148C4×D4—311no—
149C4×D4—621no—
150C2×C4⋊C4—621no—
151#107—312no—
152#106—311no—
153C4⋊C8—312no—
154C4⋊C8—311no—
155#103—311no—
156#103—312no—
157#102—312no—
158#102—311no—
159#102C2×D3112yes—
160#102C2×D3112yes—
161C4×C8—312no—
162C4×C8C2×D3111yescharacteristic
163C31#336111yescharacteristic, complemented, Sylow
164C2×Q8—21no—
165C2×Q8—311no—
166C2×Q8—311no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—311no—
170C2×D4C22×D3112yes—
171C22×C4—622no—
172C22×C4—622no—
173C22×C4—621no—
174SD16—622no—
175D8—624no—
176C2×C8—312no—
177C2×C8C22×D3111yescharacteristic
178C2×C8C22×D3111yescharacteristic
179C4⋊C4—21no—
180C4⋊C4—312no—
181C4⋊C4—311no—
182C4⋊C4—311no—
183C4⋊C4—311no—
184C4⋊C4—622no—
185C4⋊C4—622no—
186C4⋊C4—621no—
187C4⋊C4C22×D3112yes—
188C22⋊C4—622no—
189C22⋊C4—622no—
190C22⋊C4—622no—
191C22⋊C4—622no—
192C22⋊C4—621no—
193C42—312no—
194C42—621no—
195C42C22×D3111yescharacteristic
196C23—22no—
197C23—621no—
198Q8—81no—
199Q8—622no—
200Q8—621no—
201Q8—621no—
202D4—22no—
203D4—22no—
204D4—42no—
205D4—81no—
206D4—312no—
207D4—621no—
208C2×C4—22no—
209C2×C4—312no—
210C2×C4—312no—
211C2×C4—621no—
212C2×C4—621no—
213C2×C4—621no—
214C2×C4—1242no—
215C2×C4—2482no—
216C2×C4—2482no—
217C2×C4D4×D3111yescharacteristic
218C2×C4D4×D3111yescharacteristic
219C2×C4C23×D3111yescharacteristic
220C8—21no—
221C8—21no—
222C8—622no—
223C22—42no—
224C22—42no—
225C22—42no—
226C22—622no—
227C22—1241no—
228C22—1241no—
229C22C2×D4×D3111yescharacteristic
230C4—21no—
231C4—42no—
232C4—622no—
233C4—622no—
234C4—1241no—
235C4—1241no—
236C4—1241no—
237C4#1175849312yes—
238C4#41×D3111yescharacteristic
239C4#1175856711yescharacteristic
240C2—82no—
241C2—1242no—
242C2#1452170711yescharacteristic
243C2C2×#1175849311yescharacteristic
244C2#1452185011yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#486C2
socleC22×C31C22×D4
prime radical#14521241C2
hypercenter#486D31
hypocenterC31#3361
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #14521785C2semidirect
2. #14521760C2semidirect
3. #14521402C2semidirect
4. #14521351C2semidirect
5. #14521341C2semidirect
6. #14521263C2semidirect
8. C8×Dic62C2semidirect
9. C4×#92470C2semidirect
10. #14521129C2semidirect
11. C31×#486C2semidirect
121. #486D31semidirect
163. C31#3361semidirect

Maximal subgroups

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

subgroupindex
#145217852
#145217602
#145214022
#145213512
#145213412
#145212632
#145212412
C8×Dic622
C4×#924702
#145211292
C31×#4862
#336131