Finite Group Databasebeta

← #16855879

Subgroups — #16855879

Order 3968.

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

normal subgroups only

This group has 386 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#14521580C211yesmaximal, characteristic
2C2×#11758464C211yesmaximal, characteristic, complemented
3#14521384C211yesmaximal, characteristic, complemented
4#14521359C212yesmaximal, complemented
5#14521270C212yesmaximal, complemented
6#14521207C211yesmaximal, characteristic, complemented
7#14521187C211yesmaximal, characteristic
8#14521155C212yesmaximal, complemented
9#14521146C212yesmaximal, complemented
10#14521103C211yesmaximal, characteristic, complemented
11C31×#481C211yesmaximal, characteristic
12C22×Dic62C2211yescharacteristic
13C31×#121C2211yescharacteristic
14C2×C4⋊C4×C31C2211yescharacteristic
15#11758513C2211yescharacteristic
16#11758512—21no—
17D4×Dic31—21no—
18D4×Dic31C2211yescharacteristic
19C2×#92480C2212yes—
20#11758501C2211yescharacteristic
21C2×Dic31⋊C4—21no—
22C2×C4×Dic31—21no—
23C2×C4×Dic31C2211yescharacteristic
24C2×Dic124C2212yes—
25#11758467C2211yescharacteristic
26#11758464—21no—
27#11758464—21no—
28#11758464C2212yes—
29#11758464C2212yes—
30#11758464C2211yescharacteristic
31#11758456—21no—
32#11758454—21no—
33C31×#106C2212yes—
34C31×#102C2212yes—
35C31×C22⋊C8C2211yescharacteristic
36C22⋊(C31⋊C8)C2211yescharacteristic
37#11758404C2212yes—
38#11758403C2212yes—
39Dic31⋊C8C2212yes—
40#11758398C2212yes—
41#11758398C2212yes—
42#11758395C2212yes—
43C2×D4×C31—21no—
44C2×D4×C31C2311yescharacteristic
45C22×C4×C31—21no—
46C22×C4×C31C2311yescharacteristic
47C22×Dic31—21no—
48C22×Dic31—21no—
49C22×Dic31D411yescharacteristic
50C22×Dic31D411yescharacteristic
51C2×Dic62—21no—
52C2×Dic62—24no—
53C2×Dic62C2311yescharacteristic
54C2×Dic62C2312yes—
55C2×C8×C31C2312yes—
56C4⋊C4×C31—21no—
57C4⋊C4×C31C2312yes—
58C4⋊C4×C31C2311yescharacteristic
59C22⋊C4×C31—21no—
60C22⋊Dic31—21no—
61C22⋊Dic31—21no—
62C22⋊Dic31—21no—
63C22⋊Dic31—21no—
64#92480—24no—
65C4⋊Dic31—21no—
66C4⋊Dic31C2311yescharacteristic
67Dic31⋊C4—21no—
68Dic31⋊C4—21no—
69Dic31⋊C4—21no—
70Dic31⋊C4—22no—
71Dic31⋊C4—22no—
72C4×Dic31—21no—
73C4×Dic31—22no—
74C4×Dic31—22no—
75C4×Dic31D411yescharacteristic
76C4×Dic31D411yescharacteristic
77C4×Dic31C2311yescharacteristic
78C4×Dic31C2311yescharacteristic
79C2×C31⋊C8C2312yes—
80Dic124—24no—
81C23×C31—21no—
82C23×C31C2×D411yescharacteristic
83D4×C31—22no—
84D4×C31—42no—
85C2×C4×C31—22no—
86C2×C4×C31—22no—
87C2×C4×C31—21no—
88C2×C4×C31—42no—
89C2×C4×C31C2×D411yescharacteristic
90C2×C4×C31C2411yescharacteristic
91C2×Dic31—24no—
92C2×Dic31—22no—
93C2×Dic31—22no—
94C2×Dic31—21no—
95C2×Dic31—21no—
96C2×Dic31—41no—
97C2×Dic31—42no—
98C2×Dic31C2×D411yescharacteristic
99C2×Dic31C2×D411yescharacteristic
100C2×Dic31C2×D411yescharacteristic
101C2×Dic31C2×D411yescharacteristic
102Dic62—24no—
103Dic62—22no—
104Dic62—22no—
105Dic62#4114yes—
106C8×C31—22no—
107C31⋊C8—22no—
108#3117—311nomaximal, Sylow
109C22×C31—21no—
110C22×C31—21no—
111C22×C31—41no—
112C22×C31—41no—
113C22×C31—41no—
114C22×C31#13712yes—
115C22×C31C22×D411yescharacteristic
116C4×C31—21no—
117C4×C31—41no—
118C4×C31—42no—
119C4×C31C2×#4112yes—
120Dic31—24no—
121Dic31—21no—
122Dic31—21no—
123Dic31—21no—
124Dic31—21no—
125Dic31—41no—
126Dic31—41no—
127#529—311no—
128C2×C4×Q8—311no—
129#484—311no—
130#481D3111yescharacteristic
131#479—312no—
132#464—312no—
133#451—311no—
134#448—311no—
135#441—312no—
136#440—312no—
137#432—311no—
138C2×C31—22no—
139C2×C31—81no—
140C2×C31#52511yescharacteristic
141C2×C31C2×#13711yescharacteristic
142C2×C31#57511yescharacteristic
143C22×Q8—311no—
144C2×Q16—312no—
145C2×SD16—312no—
146#126—621no—
147#125—311no—
148#124—311no—
149#123—621no—
150C22⋊Q8—311no—
151#121C2×D3111yescharacteristic
152C4×Q8—312no—
153C4×Q8—312no—
154C4×Q8—311no—
155C4×Q8—621no—
156C4×Q8—621no—
157C4×D4—311no—
158C4×D4—621no—
159#117—621no—
160C2×C4⋊C4—621no—
161C2×C4⋊C4C2×D3111yescharacteristic
162C2×C42—311no—
163C2×C42—621no—
164#107—312no—
165#106C2×D3112yes—
166C4⋊C8—312no—
167#103—312no—
168#103—312no—
169#103—312no—
170#102C2×D3112yes—
171C22⋊C8—311no—
172C22⋊C8C2×D3111yescharacteristic
173#97—312no—
174C31#311711yescharacteristic, complemented, Sylow
175C2×Q8—312no—
176C2×Q8—311no—
177C2×Q8—624no—
178C2×Q8—621no—
179C2×D4—21no—
180C2×D4C22×D3111yescharacteristic
181C22×C4—21no—
182C22×C4—311no—
183C22×C4—311no—
184C22×C4—621no—
185C22×C4—621no—
186C22×C4C22×D3111yescharacteristic
187Q16—624no—
188SD16—624no—
189C2×C8—312no—
190C2×C8C22×D3112yes—
191C4⋊C4—21no—
192C4⋊C4—311no—
193C4⋊C4—622no—
194C4⋊C4—622no—
195C4⋊C4—621no—
196C4⋊C4—621no—
197C4⋊C4—621no—
198C4⋊C4—621no—
199C4⋊C4C22×D3112yes—
200C4⋊C4C22×D3111yescharacteristic
201C22⋊C4—21no—
202C22⋊C4—621no—
203C22⋊C4—621no—
204C22⋊C4—621no—
205C22⋊C4—621no—
206C42—311no—
207C42—311no—
208C42—311no—
209C42—311no—
210C42—622no—
211C42—622no—
212C42—621no—
213C23—21no—
214C23D4×D3111yescharacteristic
215Q8—314no—
216Q8—624no—
217Q8—622no—
218Q8—622no—
219D4—22no—
220D4—42no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—42no—
225C2×C4—311no—
226C2×C4—311no—
227C2×C4—311no—
228C2×C4—311no—
229C2×C4—624no—
230C2×C4—622no—
231C2×C4—622no—
232C2×C4—621no—
233C2×C4—621no—
234C2×C4—1241no—
235C2×C4—1242no—
236C2×C4D4×D3111yescharacteristic
237C2×C4C23×D3111yescharacteristic
238C8—22no—
239C8—622no—
240C22—21no—
241C22—21no—
242C22—41no—
243C22—41no—
244C22—41no—
245C22#1175849212yes—
246C22C2×D4×D3111yescharacteristic
247C4—21no—
248C4—41no—
249C4—42no—
250C4—624no—
251C4—621no—
252C4—621no—
253C4—621no—
254C4—621no—
255C4—1241no—
256C4—1241no—
257C4#41×D3112yes—
258C2—22no—
259C2—81no—
260C2#1452155711yescharacteristic
261C2C2×#1175849211yescharacteristic
262C2#1452184511yescharacteristic
subgroupG/H
centerC22C2×D4×D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#481C2
socleC22×C31C22×D4
prime radicalC31×#121C22
hypercenter#481D31
hypocenterC31#3117
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #481

Complements

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

NH ≅ G/Ntype
2. C2×#11758464C2semidirect
3. #14521384C2semidirect
4. #14521359C2semidirect
5. #14521270C2semidirect
6. #14521207C2semidirect
8. #14521155C2semidirect
9. #14521146C2semidirect
10. #14521103C2semidirect
174. C31#3117semidirect

Maximal subgroups

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

subgroupindex
#145215802
C2×#117584642
#145213842
#145213592
#145212702
#145212072
#145211872
#145211552
#145211462
#145211032
C31×#4812
#311731