Finite Group Databasebeta

← #16858433

Subgroups — #16858433

Order 3968.

372 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 372 conjugacy classes of subgroups — too many to draw. Only its 117 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#14521773C211yesmaximal, characteristic, complemented
2D4×Dic62C211yesmaximal, characteristic, complemented
3#14521410C212yesmaximal, complemented
4#14521399C211yesmaximal, characteristic, complemented
5#14521342C212yesmaximal, complemented
6#14521330C211yesmaximal, characteristic, complemented
7#14521266C212yesmaximal
8#14521176C211yesmaximal, characteristic, complemented
9#14521150C212yesmaximal, complemented
10C4×#92479C211yesmaximal, characteristic
11C31×#461C211yesmaximal, characteristic, complemented
12C22×Dic62—21no—
13C2×SD16×C31C2212yes—
14C31×C4⋊Q8C2211yescharacteristic
15C4×D4×C31C2211yescharacteristic
16#11758524C2212yes—
17Q8×Dic31C2212yes—
18D4×Dic31C2212yes—
19C2×#92479C2211yescharacteristic
20#11758501—21no—
21#11758475—22no—
22#11758474—21no—
23#11758469—21no—
24#11758465C2212yes—
25#11758455—22no—
26C4×D124C2211yescharacteristic
27#11758446C2211yescharacteristic
28C4×Dic62C2211yescharacteristic
29C31×C4⋊C8C2211yescharacteristic
30C31×#103C2212yes—
31#11758423C2212yes—
32#11758423C2212yes—
33#11758420C2211yescharacteristic
34#11758409C2212yes—
35#11758406C2212yes—
36#11758403C2212yes—
37Dic31⋊C8C2212yes—
38#11758397C2211yescharacteristic
39#11758395C2211yescharacteristic
40C4×C31⋊C8C2211yescharacteristic
41C2×Q8×C31C2312yes—
42C2×D4×C31C2311yescharacteristic
43C22×C4×C31—21no—
44C22×Dic31—22no—
45C2×D124C2311yescharacteristic
46C2×C4×D31—21no—
47C2×Dic62—21no—
48C2×Dic62—22no—
49C2×Dic62—44no—
50C2×Dic62D411yescharacteristic
51SD16×C31—24no—
52C2×C8×C31C2312yes—
53C4⋊C4×C31—21no—
54C4⋊C4×C31—21no—
55C4⋊C4×C31C2311yescharacteristic
56C22⋊C4×C31—21no—
57C42×C31C2311yescharacteristic
58C22⋊Dic31—22no—
59#92479—22no—
60(C2×D31)⋊C4—21no—
61(C2×D31)⋊C4—22no—
62(C2×D31)⋊C4—22no—
63C4⋊Dic31—21no—
64C4⋊Dic31—22no—
65C4⋊Dic31D411yescharacteristic
66C4⋊Dic31C2311yescharacteristic
67C4⋊Dic31C2312yes—
68Dic31⋊C4—22no—
69Dic31⋊C4D412yes—
70C4×Dic31—22no—
71C4×Dic31C2312yes—
72C2×C31⋊C8C2311yescharacteristic
73C2×C31⋊C8C2311yescharacteristic
74C23×C31—21no—
75C22×D31—21no—
76Q8×C31—22no—
77Q8×C31—22no—
78D4×C31—21no—
79D4×C31#4112yes—
80C2×C4×C31—22no—
81C2×C4×C31—21no—
82C2×C4×C31—42no—
83C2×C4×C31C2×D411yescharacteristic
84C2×C4×C31C2×D411yescharacteristic
85C2×C4×C31C2411yescharacteristic
86C2×Dic31—21no—
87C2×Dic31—22no—
88C2×Dic31—44no—
89C2×Dic31C2×D412yes—
90C2×Dic31C2×D412yes—
91D124—21no—
92D124—21no—
93C4×D31—42no—
94Dic62—22no—
95Dic62—44no—
96Dic62—42no—
97C8×C31—22no—
98C31⋊C8—21no—
99C31⋊C8—21no—
100#3367—311nomaximal, Sylow
101C22×C31—22no—
102C22×C31—41no—
103C22×C31—41no—
104C22×C31C22×D411yescharacteristic
105C2×D31—41no—
106C2×D31—41no—
107C2×D31—41no—
108C4×C31—21no—
109C4×C31—42no—
110C4×C31—41no—
111C4×C31AGL(1,ℤ/8)12yes—
112C4×C31C2×#4111yescharacteristic
113C4×C312−1+411yescharacteristic
114Dic31—22no—
115Dic31—22no—
116Dic31—42no—
117Dic31—41no—
118#556—311no—
119D4×Q8—311no—
120#489—312no—
121#487—311no—
122#477—312no—
123#474—311no—
124#463—312no—
125#461D3111yescharacteristic, complemented
126#446—311no—
127#440—312no—
128C4×D8—311no—
129C2×C31—42no—
130C2×C31#54811yescharacteristic
131C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
132C2×C31#57811yescharacteristic
133D31—81no—
134C22×Q8—621no—
135C2×SD16C2×D3112yes—
136C2×D8—311no—
137C4⋊Q8—312no—
138C4⋊Q8—311no—
139C4⋊Q8C2×D3111yescharacteristic
140#126—622no—
141#124—312no—
142C22⋊Q8—622no—
143C22⋊Q8—621no—
144C22⋊Q8—621no—
145C4×Q8—311no—
146C4×Q8—312no—
147C4×D4—312no—
148C4×D4—311no—
149C4×D4C2×D3111yescharacteristic
150#117—621no—
151#107—312no—
152#107—311no—
153C4⋊C8—312no—
154C4⋊C8C2×D3111yescharacteristic
155#103—312no—
156#103—312no—
157#103C2×D3112yes—
158#102—311no—
159#102—312no—
160#102—311no—
161#97—312no—
162C4×C8—311no—
163C31#336711yescharacteristic, complemented, Sylow
164C2×Q8—311no—
165C2×Q8—622no—
166C2×Q8—621no—
167C2×Q8—1244no—
168C2×Q8C22×D3112yes—
169C2×D4—311no—
170C2×D4C22×D3111yescharacteristic
171C22×C4—21no—
172C22×C4—622no—
173C22×C4—621no—
174SD16—24no—
175D8—622no—
176C2×C8—311no—
177C2×C8—311no—
178C2×C8C22×D3112yes—
179C4⋊C4—21no—
180C4⋊C4—21no—
181C4⋊C4—312no—
182C4⋊C4—311no—
183C4⋊C4—312no—
184C4⋊C4—311no—
185C4⋊C4—622no—
186C4⋊C4—622no—
187C4⋊C4—621no—
188C4⋊C4C22×D3111yescharacteristic
189C22⋊C4—21no—
190C22⋊C4—622no—
191C22⋊C4—622no—
192C22⋊C4—622no—
193C22⋊C4—621no—
194C42—312no—
195C42—622no—
196C42C22×D3111yescharacteristic
197C23—21no—
198C23—621no—
199Q8—22no—
200Q8—22no—
201Q8—622no—
202Q8—1244no—
203Q8—1242no—
204D4—21no—
205D4—621no—
206D4—621no—
207D4#9249712yes—
208C2×C4—22no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—312no—
212C2×C4—312no—
213C2×C4—621no—
214C2×C4—622no—
215C2×C4—1244no—
216C2×C4—1242no—
217C2×C4D4×D3111yescharacteristic
218C2×C4D4×D3111yescharacteristic
219C2×C4C23×D3111yescharacteristic
220C8—22no—
221C8—621no—
222C8—621no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—1241no—
227C22—1241no—
228C22—1241no—
229C22C2×D4×D3111yescharacteristic
230C4—21no—
231C4—42no—
232C4—41no—
233C4—622no—
234C4—622no—
235C4—1242no—
236C4—1241no—
237C4#1175849112yes—
238C4C2×#9249711yescharacteristic
239C4#1175856711yescharacteristic
240C2—42no—
241C2—2481no—
242C2#1452170511yescharacteristic
243C2C2×#1175849111yescharacteristic
244C2#1452186511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#461C2
socleC22×C31C22×D4
prime radicalC2×#92479C22
hypercenter#461D31
hypocenterC31#3367
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #14521773C2semidirect
2. D4×Dic62C2semidirect
3. #14521410C2semidirect
4. #14521399C2semidirect
5. #14521342C2semidirect
6. #14521330C2semidirect
8. #14521176C2semidirect
9. #14521150C2semidirect
11. C31×#461C2semidirect
125. #461D31semidirect
163. C31#3367semidirect

Maximal subgroups

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

subgroupindex
#145217732
D4×Dic622
#145214102
#145213992
#145213422
#145213302
#145212662
#145211762
#145211502
C4×#924792
C31×#4612
#336731