Finite Group Databasebeta

← #16858365

Subgroups — #16858365

Order 3968.

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

normal subgroups only

This group has 350 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#14521773C211yesmaximal, characteristic, complemented
2#14521760C211yesmaximal, characteristic, complemented
3#14521405C212yesmaximal, complemented
4#14521358C212yesmaximal, complemented
5#14521336C211yesmaximal, characteristic, complemented
6#14521267C212yesmaximal
7#14521251C211yesmaximal, characteristic, complemented
8C8×Dic62C211yesmaximal, characteristic, complemented
9#14521134C212yesmaximal, complemented
10C4×D248C211yesmaximal, characteristic
11C31×#487C211yesmaximal, characteristic, complemented
12C31×C4⋊Q8C2211yescharacteristic
13C31×C4⋊Q8C2211yescharacteristic
14#11758524C2212yes—
15#11758523—22no—
16Q8×Dic31C2212yes—
17C2×#92481C2212yes—
18C2×D248C2211yescharacteristic
19#11758475—22no—
20#11758474—21no—
21#11758474—21no—
22#11758470C2212yes—
23#11758469—21no—
24C4⋊C4×D31—21no—
25#11758467C2212yes—
26C4×D124C2211yescharacteristic
27C4×D124C2211yescharacteristic
28C4×Dic62C2211yescharacteristic
29C31×#103C2212yes—
30C31×#103C2212yes—
31C4×C8×C31C2211yescharacteristic
32#11758423C2212yes—
33#11758409C2211yescharacteristic
34#11758409C2211yescharacteristic
35#11758406C2211yescharacteristic
36Dic31⋊C8C2212yes—
37C8×Dic31C2212yes—
38#11758397C2212yes—
39#11758396C2212yes—
40C4⋊(C31⋊C8)C2211yescharacteristic
41C2×Q8×C31—21no—
42C2×Q8×C31C2312yes—
43C2×D124C2311yescharacteristic
44C2×D124C2311yescharacteristic
45C2×C4×D31—21no—
46C2×C4×D31—21no—
47C2×C4×D31—22no—
48C2×Dic62D411yescharacteristic
49C2×C8×C31C2311yescharacteristic
50C2×C8×C31C2311yescharacteristic
51C4⋊C4×C31—21no—
52C4⋊C4×C31—21no—
53C4⋊C4×C31—21no—
54C4⋊C4×C31C2312yes—
55C42×C31C2311yescharacteristic
56#92481—24no—
57(C2×D31)⋊C4—21no—
58(C2×D31)⋊C4—21no—
59(C2×D31)⋊C4—22no—
60(C2×D31)⋊C4—22no—
61(C2×D31)⋊C4—22no—
62C4⋊Dic31—22no—
63C4⋊Dic31—22no—
64C4⋊Dic31D411yescharacteristic
65C4⋊Dic31C2311yescharacteristic
66C4⋊Dic31C2311yescharacteristic
67Dic31⋊C4—22no—
68Dic31⋊C4D412yes—
69C4×Dic31—22no—
70C4×Dic31C2312yes—
71C2×C31⋊C8C2312yes—
72D248—22no—
73C22×D31—21no—
74C22×D31—21no—
75Q8×C31—22no—
76Q8×C31—22no—
77Q8×C31—81no—
78C2×C4×C31—22no—
79C2×C4×C31—22no—
80C2×C4×C31C2×D411yescharacteristic
81C2×C4×C31C2×D411yescharacteristic
82C2×C4×C31C2411yescharacteristic
83C2×Dic31—21no—
84C2×Dic31—21no—
85C2×Dic31C2×D412yes—
86C2×Dic31C2×D412yes—
87D124—21no—
88D124—21no—
89D124—21no—
90D124#4112yes—
91C4×D31—42no—
92C4×D31—42no—
93C4×D31—82no—
94Dic62—22no—
95C8×C31—21no—
96C8×C31—21no—
97C31⋊C8—22no—
98#3360—311nomaximal, Sylow
99C22×C31C22×D411yescharacteristic
100C2×D31—22no—
101C2×D31—41no—
102C2×D31—41no—
103C2×D31—41no—
104C2×D31—41no—
105C2×D31—41no—
106C4×C31—21no—
107C4×C31—42no—
108C4×C31—42no—
109C4×C31#13512yes—
110C4×C31C2×#4111yescharacteristic
111C4×C312−1+411yescharacteristic
112Dic31—22no—
113Dic31—22no—
114Dic31—41no—
115Dic31—41no—
116#556—311no—
117#554—311no—
118#488—312no—
119#487D3111yescharacteristic, complemented
120#479—312no—
121#476—311no—
122#463—312no—
123#461—311no—
124C8×Q8—311no—
125C4×SD16—312no—
126C4×D8—311no—
127C2×C31#54811yescharacteristic
128C2×C31C2×#13511yescharacteristic
129C2×C31#57711yescharacteristic
130D31—42no—
131D31—81no—
132C2×SD16—312no—
133C2×D8—311no—
134C4⋊Q8C2×D3111yescharacteristic
135C4⋊Q8C2×D3111yescharacteristic
136#126—622no—
137#125—312no—
138#124—312no—
139C22⋊Q8—621no—
140C22⋊Q8—621no—
141C22⋊Q8—622no—
142C4×Q8—311no—
143C4×Q8—312no—
144C4×D4—312no—
145C4×D4—311no—
146C4×D4—311no—
147#117—621no—
148C2×C4⋊C4—621no—
149#107—311no—
150#106—312no—
151C4⋊C8—312no—
152C4⋊C8—311no—
153#103—312no—
154#103C2×D3112yes—
155#103C2×D3112yes—
156#102—311no—
157#102—311no—
158#102—312no—
159C4×C8—312no—
160C4×C8C2×D3111yescharacteristic
161C31#336011yescharacteristic, complemented, Sylow
162C2×Q8—21no—
163C2×Q8—311no—
164C2×Q8C22×D3112yes—
165C2×D4—311no—
166C2×D4—311no—
167C22×C4—622no—
168C22×C4—621no—
169C22×C4—621no—
170SD16—624no—
171D8—622no—
172C2×C8—312no—
173C2×C8C22×D3111yescharacteristic
174C2×C8C22×D3111yescharacteristic
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—21no—
178C4⋊C4—312no—
179C4⋊C4—311no—
180C4⋊C4—311no—
181C4⋊C4—311no—
182C4⋊C4—622no—
183C4⋊C4—622no—
184C4⋊C4—622no—
185C4⋊C4C22×D3112yes—
186C22⋊C4—622no—
187C22⋊C4—622no—
188C22⋊C4—622no—
189C22⋊C4—621no—
190C22⋊C4—621no—
191C42—312no—
192C42—622no—
193C42C22×D3111yescharacteristic
194C23—621no—
195C23—621no—
196Q8—22no—
197Q8—22no—
198Q8—81no—
199Q8—622no—
200D4—312no—
201D4—621no—
202D4—621no—
203D4—621no—
204C2×C4—22no—
205C2×C4—22no—
206C2×C4—312no—
207C2×C4—312no—
208C2×C4—621no—
209C2×C4—621no—
210C2×C4—1242no—
211C2×C4—1242no—
212C2×C4—2482no—
213C2×C4D4×D3111yescharacteristic
214C2×C4D4×D3111yescharacteristic
215C2×C4C23×D3111yescharacteristic
216C8—21no—
217C8—21no—
218C8—622no—
219C22—622no—
220C22—1241no—
221C22—1241no—
222C22—1241no—
223C22—1241no—
224C22—1241no—
225C22C2×D4×D3111yescharacteristic
226C4—21no—
227C4—42no—
228C4—42no—
229C4—622no—
230C4—622no—
231C4—1241no—
232C4—1241no—
233C4#1175849612yes—
234C4#41×D3111yescharacteristic
235C4#1175856711yescharacteristic
236C2—1242no—
237C2—2481no—
238C2#1452170711yescharacteristic
239C2C2×#1175849611yescharacteristic
240C2#1452185511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#487C2
socleC22×C31C22×D4
prime radicalC2×D248C22
hypercenter#487D31
hypocenterC31#3360
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
1. #14521773C2semidirect
2. #14521760C2semidirect
3. #14521405C2semidirect
4. #14521358C2semidirect
5. #14521336C2semidirect
7. #14521251C2semidirect
8. C8×Dic62C2semidirect
9. #14521134C2semidirect
11. C31×#487C2semidirect
119. #487D31semidirect
161. C31#3360semidirect

Maximal subgroups

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

subgroupindex
#145217732
#145217602
#145214052
#145213582
#145213362
#145212672
#145212512
C8×Dic622
#145211342
C4×D2482
C31×#4872
#336031