Finite Group Databasebeta

← #16858359

Subgroups — #16858359

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#14521769C211yesmaximal, characteristic, complemented
2#14521760C211yesmaximal, characteristic, complemented
3#14521402C212yesmaximal, complemented
4#14521401C211yesmaximal, characteristic, complemented
5#14521359C212yesmaximal, complemented
6#14521263C212yesmaximal
7#14521255C211yesmaximal, characteristic, complemented
8#14521173C211yesmaximal, characteristic, complemented
9#14521136C212yesmaximal, complemented
10C4×#92479C211yesmaximal, characteristic
11C31×#476C211yesmaximal, characteristic, complemented
12C31×C4⋊Q8C2211yescharacteristic
13C4×D4×C31C2211yescharacteristic
14#11758523—22no—
15#11758513C2212yes—
16C2×#92479C2211yescharacteristic
17#11758503—21no—
18#11758501—21no—
19C2×#92470C2212yes—
20#11758474—21no—
21#11758470C2212yes—
22C4⋊C4×D31—21no—
23#11758467C2212yes—
24#11758464C2212yes—
25#11758456—22no—
26C4×D124C2211yescharacteristic
27#11758446C2211yescharacteristic
28C4×Dic62C2211yescharacteristic
29C31×#106C2212yes—
30C31×C4⋊C8C2211yescharacteristic
31C31×#102C2212yes—
32#11758420C2211yescharacteristic
33#11758404C2212yes—
34Dic31⋊C8C2212yes—
35C8×Dic31C2212yes—
36#11758398C2212yes—
37#11758398C2212yes—
38#11758397C2211yescharacteristic
39#11758395C2211yescharacteristic
40C4×C31⋊C8C2211yescharacteristic
41C2×Q8×C31—21no—
42C2×D4×C31C2311yescharacteristic
43C22×C4×C31—21no—
44C2×D124C2311yescharacteristic
45C2×C4×D31—21no—
46C2×C4×D31—22no—
47C2×Dic62D411yescharacteristic
48C2×Dic62C2312yes—
49C2×C8×C31C2312yes—
50C4⋊C4×C31—21no—
51C4⋊C4×C31C2311yescharacteristic
52C4⋊C4×C31C2312yes—
53C22⋊C4×C31—21no—
54C42×C31C2311yescharacteristic
55C22⋊Dic31—22no—
56C22⋊Dic31—22no—
57#92479—22no—
58(C2×D31)⋊C4—21no—
59(C2×D31)⋊C4—22no—
60C4⋊Dic31—21no—
61C4⋊Dic31—21no—
62C4⋊Dic31—22no—
63C4⋊Dic31D411yescharacteristic
64C4⋊Dic31C2311yescharacteristic
65Dic31⋊C4—22no—
66Dic31⋊C4—22no—
67Dic31⋊C4D412yes—
68C4×Dic31—22no—
69C4×Dic31C2312yes—
70C2×C31⋊C8C2311yescharacteristic
71C2×C31⋊C8C2311yescharacteristic
72#92470—24no—
73C23×C31—21no—
74C22×D31—21no—
75Q8×C31—81no—
76D4×C31—21no—
77D4×C31—21no—
78C2×C4×C31—21no—
79C2×C4×C31—22no—
80C2×C4×C31—42no—
81C2×C4×C31C2×D411yescharacteristic
82C2×C4×C31C2×D411yescharacteristic
83C2×C4×C31C2411yescharacteristic
84C2×Dic31—22no—
85C2×Dic31—21no—
86C2×Dic31C2×D412yes—
87C2×Dic31C2×D412yes—
88D124—21no—
89D124#4112yes—
90C4×D31—42no—
91C4×D31—82no—
92Dic62—22no—
93Dic62—22no—
94Dic62—22no—
95C8×C31—22no—
96C31⋊C8—21no—
97C31⋊C8—21no—
98#3360—311nomaximal, Sylow
99C22×C31—41no—
100C22×C31—41no—
101C22×C31—41no—
102C22×C31C22×D411yescharacteristic
103C2×D31—22no—
104C2×D31—41no—
105C2×D31—41no—
106C4×C31—21no—
107C4×C31—41no—
108C4×C31—42no—
109C4×C31#13512yes—
110C4×C31C2×#4111yescharacteristic
111C4×C312−1+411yescharacteristic
112Dic31—22no—
113Dic31—22no—
114Dic31—42no—
115Dic31—41no—
116#556—311no—
117#554—311no—
118#488—312no—
119#487—311no—
120#479—312no—
121#476D3111yescharacteristic, complemented
122#463—312no—
123#461—311no—
124C8×Q8—311no—
125C4×SD16—312no—
126C4×D8—311no—
127C2×C31—81no—
128C2×C31#54811yescharacteristic
129C2×C31C2×#13511yescharacteristic
130C2×C31#57711yescharacteristic
131D31—42no—
132C2×SD16—312no—
133C2×D8—311no—
134C4⋊Q8—311no—
135C4⋊Q8C2×D3111yescharacteristic
136#126—622no—
137#125—312no—
138#124—312no—
139C22⋊Q8—621no—
140C22⋊Q8—622no—
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#106C2×D3112yes—
151C4⋊C8—312no—
152C4⋊C8C2×D3111yescharacteristic
153#103—312no—
154#103—312no—
155#103—312no—
156#102—311no—
157#102—311no—
158#102C2×D3112yes—
159C4×C8—312no—
160C4×C8—311no—
161C31#336011yescharacteristic, complemented, Sylow
162C2×Q8—21no—
163C2×Q8—311no—
164C2×Q8—312no—
165C2×D4—311no—
166C2×D4C22×D3111yescharacteristic
167C22×C4—21no—
168C22×C4—622no—
169C22×C4—621no—
170SD16—624no—
171D8—622no—
172C2×C8—311no—
173C2×C8—311no—
174C2×C8C22×D3112yes—
175C4⋊C4—21no—
176C4⋊C4—312no—
177C4⋊C4—311no—
178C4⋊C4—311no—
179C4⋊C4—622no—
180C4⋊C4—622no—
181C4⋊C4—622no—
182C4⋊C4—621no—
183C4⋊C4—621no—
184C4⋊C4C22×D3111yescharacteristic
185C4⋊C4C22×D3112yes—
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—81no—
197Q8—622no—
198Q8—622no—
199Q8—622no—
200D4—21no—
201D4—21no—
202D4—312no—
203D4—621no—
204C2×C4—21no—
205C2×C4—22no—
206C2×C4—42no—
207C2×C4—312no—
208C2×C4—312no—
209C2×C4—622no—
210C2×C4—621no—
211C2×C4—1242no—
212C2×C4—2482no—
213C2×C4D4×D3111yescharacteristic
214C2×C4D4×D3111yescharacteristic
215C2×C4C23×D3111yescharacteristic
216C8—22no—
217C8—621no—
218C8—621no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—622no—
223C22—1241no—
224C22—1241no—
225C22C2×D4×D3111yescharacteristic
226C4—21no—
227C4—42no—
228C4—41no—
229C4—622no—
230C4—622no—
231C4—1242no—
232C4—1241no—
233C4#1175849312yes—
234C4#1175856411yescharacteristic
235C4#41×D3111yescharacteristic
236C2—81no—
237C2—1242no—
238C2#1452170911yescharacteristic
239C2C2×#1175849311yescharacteristic
240C2#1452185911yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#476C2
socleC22×C31C22×D4
prime radicalC2×#92479C22
hypercenter#476D31
hypocenterC31#3360
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #476

Complements

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

NH ≅ G/Ntype
1. #14521769C2semidirect
2. #14521760C2semidirect
3. #14521402C2semidirect
4. #14521401C2semidirect
5. #14521359C2semidirect
7. #14521255C2semidirect
8. #14521173C2semidirect
9. #14521136C2semidirect
11. C31×#476C2semidirect
121. #476D31semidirect
161. C31#3360semidirect

Maximal subgroups

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

subgroupindex
#145217692
#145217602
#145214022
#145214012
#145213592
#145212632
#145212552
#145211732
#145211362
C4×#924792
C31×#4762
#336031