Finite Group Databasebeta

← #16858364

Subgroups — #16858364

Order 3968.

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

normal subgroups only

This group has 350 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
2#14521756C211yesmaximal, characteristic, complemented
3#14521405C212yesmaximal, complemented
4#14521399C211yesmaximal, characteristic, complemented
5#14521354C212yesmaximal, complemented
6#14521340C211yesmaximal, characteristic, complemented
7#14521266C212yesmaximal
8#14521173C211yesmaximal, characteristic, complemented
9SD16×Dic31C212yesmaximal, complemented
10C4×#92479C211yesmaximal, characteristic
11C31×#461C211yesmaximal, characteristic, complemented
12C2×SD16×C31C2212yes—
13C31×C4⋊Q8C2211yescharacteristic
14C4×D4×C31C2211yescharacteristic
15#11758524C2212yes—
16Q8×Dic31C2212yes—
17D4×Dic31C2212yes—
18C2×#92479C2211yescharacteristic
19C2×C4⋊Dic31—21no—
20#11758501—21no—
21#11758475—22no—
22#11758474—21no—
23#11758469—21no—
24#11758467C2212yes—
25#11758455—22no—
26C4×D124C2211yescharacteristic
27#11758446C2211yescharacteristic
28C4×Dic62C2211yescharacteristic
29C31×C4⋊C8C2211yescharacteristic
30C31×#103C2212yes—
31#11758423C2212yes—
32#11758423C2212yes—
33#11758420C2211yescharacteristic
34#11758409C2212yes—
35#11758405C2212yes—
36Dic31⋊C8C2212yes—
37C8×Dic31C2212yes—
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×Dic62D411yescharacteristic
49SD16×C31—24no—
50C2×C8×C31C2312yes—
51C4⋊C4×C31—21no—
52C4⋊C4×C31—21no—
53C4⋊C4×C31C2311yescharacteristic
54C22⋊C4×C31—21no—
55C42×C31C2311yescharacteristic
56C22⋊Dic31—22no—
57#92479—22no—
58(C2×D31)⋊C4—21no—
59(C2×D31)⋊C4—22no—
60(C2×D31)⋊C4—22no—
61C4⋊Dic31—21no—
62C4⋊Dic31—22no—
63C4⋊Dic31—22no—
64C4⋊Dic31D411yescharacteristic
65C4⋊Dic31C2311yescharacteristic
66C4⋊Dic31C2312yes—
67Dic31⋊C4—22no—
68Dic31⋊C4D412yes—
69C4×Dic31—22no—
70C4×Dic31C2312yes—
71C2×C31⋊C8C2311yescharacteristic
72C2×C31⋊C8C2311yescharacteristic
73C23×C31—21no—
74C22×D31—21no—
75Q8×C31—22no—
76Q8×C31—22no—
77D4×C31—21no—
78D4×C31#4112yes—
79C2×C4×C31—22no—
80C2×C4×C31—21no—
81C2×C4×C31—42no—
82C2×C4×C31C2×D411yescharacteristic
83C2×C4×C31C2×D411yescharacteristic
84C2×C4×C31C2411yescharacteristic
85C2×Dic31—21no—
86C2×Dic31—22no—
87C2×Dic31—82no—
88C2×Dic31C2×D412yes—
89C2×Dic31C2×D412yes—
90D124—21no—
91D124—21no—
92C4×D31—42no—
93Dic62—22no—
94Dic62—81no—
95C8×C31—22no—
96C31⋊C8—21no—
97C31⋊C8—21no—
98#3360—311nomaximal, Sylow
99C22×C31—22no—
100C22×C31—41no—
101C22×C31—41no—
102C22×C31C22×D411yescharacteristic
103C2×D31—41no—
104C2×D31—41no—
105C2×D31—41no—
106C4×C31—21no—
107C4×C31—42no—
108C4×C31—41no—
109C4×C31#13512yes—
110C4×C31C2×#4111yescharacteristic
111C4×C312−1+411yescharacteristic
112Dic31—22no—
113Dic31—22no—
114Dic31—41no—
115Dic31—42no—
116#556—311no—
117#554—311no—
118#488—312no—
119#487—311no—
120#479—312no—
121#476—311no—
122#463—312no—
123#461D3111yescharacteristic, complemented
124C8×Q8—311no—
125C4×SD16—312no—
126C4×D8—311no—
127C2×C31—42no—
128C2×C31#54811yescharacteristic
129C2×C31C2×#13511yescharacteristic
130C2×C31#57711yescharacteristic
131D31—81no—
132C2×SD16C2×D3112yes—
133C2×D8—311no—
134C4⋊Q8—311no—
135C4⋊Q8C2×D3111yescharacteristic
136#126—622no—
137#125—312no—
138#124—312no—
139C22⋊Q8—622no—
140C22⋊Q8—621no—
141C22⋊Q8—621no—
142C4×Q8—311no—
143C4×Q8—312no—
144C4×D4—312no—
145C4×D4—311no—
146C4×D4C2×D3111yescharacteristic
147#117—621no—
148C2×C4⋊C4—621no—
149#107—311no—
150#106—312no—
151C4⋊C8—312no—
152C4⋊C8C2×D3111yescharacteristic
153#103—312no—
154#103—312no—
155#103C2×D3112yes—
156#102—311no—
157#102—312no—
158#102—311no—
159C4×C8—312no—
160C4×C8—311no—
161C31#336011yescharacteristic, complemented, Sylow
162C2×Q8—311no—
163C2×Q8—621no—
164C2×Q8C22×D3112yes—
165C2×D4—311no—
166C2×D4C22×D3111yescharacteristic
167C22×C4—21no—
168C22×C4—622no—
169C22×C4—621no—
170SD16—24no—
171D8—622no—
172C2×C8—311no—
173C2×C8—311no—
174C2×C8C22×D3112yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—312no—
178C4⋊C4—311no—
179C4⋊C4—312no—
180C4⋊C4—311no—
181C4⋊C4—622no—
182C4⋊C4—622no—
183C4⋊C4—622no—
184C4⋊C4—621no—
185C4⋊C4C22×D3111yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—622no—
188C22⋊C4—622no—
189C22⋊C4—622no—
190C22⋊C4—621no—
191C42—312no—
192C42—622no—
193C42C22×D3111yescharacteristic
194C23—21no—
195C23—621no—
196Q8—22no—
197Q8—22no—
198Q8—622no—
199Q8—2481no—
200D4—21no—
201D4—621no—
202D4—621no—
203D4#9249712yes—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—312no—
208C2×C4—312no—
209C2×C4—621no—
210C2×C4—622no—
211C2×C4—1242no—
212C2×C4—2482no—
213C2×C4D4×D3111yescharacteristic
214C2×C4D4×D3111yescharacteristic
215C2×C4C23×D3111yescharacteristic
216C8—22no—
217C8—621no—
218C8—621no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—1241no—
223C22—1241no—
224C22—1241no—
225C22C2×D4×D3111yescharacteristic
226C4—21no—
227C4—42no—
228C4—41no—
229C4—622no—
230C4—622no—
231C4—1242no—
232C4—1241no—
233C4#1175849312yes—
234C4C2×#9249711yescharacteristic
235C4#1175856711yescharacteristic
236C2—42no—
237C2—2481no—
238C2#1452170511yescharacteristic
239C2C2×#1175849311yescharacteristic
240C2#1452185811yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#461C2
socleC22×C31C22×D4
prime radicalC2×#92479C22
hypercenter#461D31
hypocenterC31#3360
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. #14521756C2semidirect
3. #14521405C2semidirect
4. #14521399C2semidirect
5. #14521354C2semidirect
6. #14521340C2semidirect
8. #14521173C2semidirect
9. SD16×Dic31C2semidirect
11. C31×#461C2semidirect
123. #461D31semidirect
161. C31#3360semidirect

Maximal subgroups

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

subgroupindex
#145217732
#145217562
#145214052
#145213992
#145213542
#145213402
#145212662
#145211732
SD16×Dic312
C4×#924792
C31×#4612
#336031