Finite Group Databasebeta

← #16857664

Subgroups — #16857664

Order 3968.

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

normal subgroups only

This group has 408 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#14521764C211yesmaximal, characteristic, complemented
2#14521719C211yesmaximal, characteristic, complemented
3#14521395C211yesmaximal, characteristic, complemented
4#14521371C212yesmaximal, complemented
5#14521345C211yesmaximal, characteristic, complemented
6#14521282C212yesmaximal, complemented
7#14521191C212yesmaximal, complemented
8C4×#92480C211yesmaximal, characteristic, complemented
9#14521114C211yesmaximal, characteristic, complemented
10#14521042C212yesmaximal, complemented
11C31×#459C211yesmaximal, characteristic, complemented
12C2×#92497C2212yes—
13C2×D8×C31C2212yes—
14C31×#127C2211yescharacteristic
15C4×D4×C31C2211yescharacteristic
16#11758517—21no—
17#11758516—22no—
18#11758515C2212yes—
19#11758515C2212yes—
20D4×Dic31—21no—
21C2×#92480C2211yescharacteristic
22#11758507—21no—
23#11758503—21no—
24C2×C8×D31C2212yes—
25#11758469C2212yes—
26#11758462—22no—
27C4×D124C2211yescharacteristic
28#11758446C2211yescharacteristic
29C4×Dic62C2211yescharacteristic
30C31×C4⋊C8C2211yescharacteristic
31C31×#102C2212yes—
32#11758420C2212yes—
33#11758420C2211yescharacteristic
34#11758420C2212yes—
35(C2×D31)⋊C8C2212yes—
36#11758406C2212yes—
37#11758404C2212yes—
38#11758398C2211yescharacteristic
39#11758396C2211yescharacteristic
40C4×C31⋊C8C2211yescharacteristic
41C2×D4×C31—21no—
42C2×D4×C31—21no—
43C2×D4×C31C2312yes—
44C2×D4×C31C2311yescharacteristic
45C22×C4×C31—21no—
46C2×C22⋊D31—22no—
47C2×C22⋊D31—22no—
48C2×C22⋊D31—22no—
49C22×Dic31—22no—
50#92497—24no—
51#92497—42no—
52C2×D124D411yescharacteristic
53C2×C4×D31C2312yes—
54C2×Dic62—21no—
55C2×Dic62C2311yescharacteristic
56D8×C31—42no—
57C2×C8×C31C2312yes—
58C4⋊C4×C31C2311yescharacteristic
59C22⋊C4×C31—21no—
60C42×C31C2311yescharacteristic
61C22⋊Dic31—22no—
62C22⋊Dic31—22no—
63#92480—22no—
64(C2×D31)⋊C4—22no—
65(C2×D31)⋊C4D412yes—
66C4⋊Dic31—21no—
67C4⋊Dic31D411yescharacteristic
68C4⋊Dic31C2311yescharacteristic
69C4⋊Dic31C2312yes—
70Dic31⋊C4—21no—
71C4×Dic31—21no—
72C4×Dic31—22no—
73C2×C31⋊C8C2311yescharacteristic
74C2×C31⋊C8C2311yescharacteristic
75C8×D31—42no—
76C23×C31—21no—
77C23×C31—22no—
78C22×D31C2×D412yes—
79D4×C31—21no—
80D4×C31—22no—
81D4×C31—21no—
82D4×C31—22no—
83D4×C31—42no—
84D4×C31—81no—
85C2×C4×C31—21no—
86C2×C4×C31—42no—
87C2×C4×C31C2×D411yescharacteristic
88C2×C4×C31C2×D411yescharacteristic
89C2×C4×C31C2411yescharacteristic
90C22⋊D31—44no—
91C22⋊D31—82no—
92C22⋊D31—82no—
93C2×Dic31—21no—
94C2×Dic31—21no—
95C2×Dic31—22no—
96C2×Dic31—44no—
97C2×Dic31C2×D412yes—
98D124—22no—
99C4×D31—22no—
100C4×D31—22no—
101Dic62—21no—
102Dic62—81no—
103Dic62#4112yes—
104C8×C31—22no—
105C31⋊C8—21no—
106C31⋊C8—21no—
107#3305—311nomaximal, Sylow
108C22×C31—42no—
109C22×C31—41no—
110C22×C31—41no—
111C22×C31—42no—
112C22×C31—41no—
113C22×C31—42no—
114C22×C31C22×D411yescharacteristic
115C2×D31—22no—
116C2×D31—22no—
117C2×D31—22no—
118C4×C31—21no—
119C4×C31—41no—
120C4×C31#13512yes—
121C4×C31C2×#4111yescharacteristic
122C4×C31H(5,𝔽2)11yescharacteristic
123Dic31—22no—
124Dic31—22no—
125Dic31—42no—
126Dic31—41no—
127#555—311no—
128#550—311no—
129#486—311no—
130#482—312no—
131#477—311no—
132#466—312no—
133#459D3111yescharacteristic, complemented
134#449—312no—
135C4×SD16—311no—
136C8×D4—311no—
137#416—312no—
138C2×C31—82no—
139C2×C31—81no—
140C2×C31#54611yescharacteristic
141C2×C31C2×#13511yescharacteristic
142C2×C31#57611yescharacteristic
143D31—42no—
144C2×#41—312no—
145C2×SD16—311no—
146C2×D8C2×D3112yes—
147C22×C8—312no—
148C4⋊Q8—311no—
149#127—621no—
150#127C2×D3111yescharacteristic
151#124—622no—
152#121—312no—
153#121—312no—
154#121—622no—
155#121—621no—
156C4×Q8—311no—
157C4×D4—311no—
158C4×D4—621no—
159C4×D4C2×D3111yescharacteristic
160#117—312no—
161#117—621no—
162#107—312no—
163#106—311no—
164C4⋊C8C2×D3111yescharacteristic
165#103—312no—
166#103—311no—
167#102—312no—
168#102—311no—
169#102—312no—
170#102C2×D3112yes—
171C22⋊C8—312no—
172C4×C8—311no—
173C31#330511yescharacteristic, complemented, Sylow
174#41—624no—
175#41—1242no—
176C2×Q8—311no—
177C2×Q8—621no—
178C2×D4—21no—
179C2×D4—21no—
180C2×D4—311no—
181C2×D4—622no—
182C2×D4—622no—
183C2×D4—622no—
184C2×D4C22×D3112yes—
185C2×D4C22×D3111yescharacteristic
186C22×C4—21no—
187C22×C4—312no—
188C22×C4—622no—
189SD16—622no—
190D8—42no—
191C2×C8—311no—
192C2×C8—311no—
193C2×C8—1242no—
194C2×C8C22×D3112yes—
195C4⋊C4—311no—
196C4⋊C4—312no—
197C4⋊C4—311no—
198C4⋊C4—621no—
199C4⋊C4—621no—
200C4⋊C4C22×D3111yescharacteristic
201C22⋊C4—21no—
202C22⋊C4—312no—
203C22⋊C4—622no—
204C22⋊C4—622no—
205C22⋊C4—622no—
206C42—622no—
207C42—621no—
208C42C22×D3111yescharacteristic
209C23—21no—
210C23—22no—
211C23—312no—
212Q8—312no—
213Q8—621no—
214Q8—2481no—
215D4—21no—
216D4—22no—
217D4—21no—
218D4—22no—
219D4—42no—
220D4—81no—
221D4—622no—
222D4—1244no—
223D4—2482no—
224D4—2482no—
225C2×C4—21no—
226C2×C4—42no—
227C2×C4—312no—
228C2×C4—621no—
229C2×C4—622no—
230C2×C4—622no—
231C2×C4—621no—
232C2×C4—622no—
233C2×C4—1244no—
234C2×C4D4×D3111yescharacteristic
235C2×C4D4×D3111yescharacteristic
236C2×C4C23×D3111yescharacteristic
237C8—22no—
238C8—621no—
239C8—621no—
240C22—42no—
241C22—41no—
242C22—41no—
243C22—42no—
244C22—42no—
245C22—41no—
246C22—622no—
247C22—622no—
248C22—622no—
249C22C2×D4×D3111yescharacteristic
250C4—21no—
251C4—41no—
252C4—622no—
253C4—622no—
254C4—1241no—
255C4—1242no—
256C4#1175848912yes—
257C4#1175856111yescharacteristic
258C4#41×D3111yescharacteristic
259C2—82no—
260C2—81no—
261C2—1242no—
262C2#1452169611yescharacteristic
263C2C2×#1175848911yescharacteristic
264C2#1452185311yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#459C2
socleC22×C31C22×D4
hypercenter#459D31
hypocenterC31#3305
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #14521764C2semidirect
2. #14521719C2semidirect
3. #14521395C2semidirect
4. #14521371C2semidirect
5. #14521345C2semidirect
6. #14521282C2semidirect
7. #14521191C2semidirect
8. C4×#92480C2semidirect
9. #14521114C2semidirect
10. #14521042C2semidirect
11. C31×#459C2semidirect
133. #459D31semidirect
173. C31#3305semidirect

Maximal subgroups

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

subgroupindex
#145217642
#145217192
#145213952
#145213712
#145213452
#145212822
#145211912
C4×#924802
#145211142
#145210422
C31×#4592
#330531